Baffle Drop Structure 설계, 정말 안전할까요? 경사수로에서 발생하는 난류와 침식은 예측하기 어렵고, 설계 오류는 곧 재앙적인 결과를 초래할 수 있습니다. FLOW-3D HYDRO와 함께라면 이러한 위험을 사전에 방지할 수 있습니다. 저희가 직접 Baffle Drop Structure의 유동을 분석한 영상을 확인해보세요! 이 영상은 단순히 아름다운 시각화를 넘어, 다음과 같은 실제 문제를 해결하는 데 도움을 줍니다: 최적의 에너지 소산 능력 예측: 다양한 배플의 형태와 간격이 유동에 미치는 영향을 분석하여 가장 효과적인 에너지 소산 설계안을 찾을 수 있습니다. 침식 가능성 평가: 고유속 구간을 시각적으로 확인하여 침식이 발생할 수 있는 지점을 파악하고, 보강 설계를 검토할 수 있습니다. 물 튀김(Splashing) 현상 제어: 구조물 외부로 물이 튀는 현상을 최소화하여 주변 환경에 미치는 영향을 줄일 수 있습니다. FLOW-3D HYDRO의 강력한 유체 해석 기술로 더 안전하고 지속 가능한 수리 구조물을 설계하세요.
3D 수치 시뮬레이션과 실험을 통해 초음파 처리를 병행한 경우와 병행하지 않은 경우의 전기화학 반응기에서의 스트론튬 제거 효율을 분석하였다. 초음파는 작동 주파수 25kHz의 초음파 트랜스듀서 4개를 사용하여 발생시켰다. 반응기에는 두 개의 블록으로 배열된 8개의 알루미늄 전극이 사용되었다. 수중의 스트론튬 이온은 전하량 3.2•10⁻¹⁹ C, 직경 1.2•10⁻⁸ m의 입자로 모델링되었다. 수치 모델은 Flow-3D 소프트웨어를 사용하여 기본 유체역학 모듈, 정전기 모듈, 일반 이동 물체 모듈을 통해 생성되었다. 수치 시뮬레이션을 통한 반응기 성능 평가는 시뮬레이션 종료 시점에 전극에 영구적으로 붙잡힌 모델 스트론튬 입자의 수와 초기 물속 입자 수의 비율로 정의된다. 실험 반응기의 경우, 스트론튬 제거 효과는 실험 시작 및 종료 시점의 물속 스트론튬 균일 농도의 비율로 정의된다. 결과에 따르면, 초음파를 사용하면 180초의 처리 후 스트론튬 제거 효과가 10.3%에서 11.2%로 증가한다. 수치 시뮬레이션 결과는 동일한 기하학적 특성을 가진 반응기에 대한 실험 측정 결과와 일치한다.
스트론튬(Sr)은 자연적으로 존재하는 원소로, 많은 퇴적암과 일부 방해석 광물에서 발견된다. 주요 인위적 발생원으로는 산업 활동, 비료, 핵 낙진 등이 있다(Scott et al., 2020). 수중 Sr 농도가 1.5 mg L⁻¹를 초과할 경우, 특히 어린이에게 스트론튬 구루병 및 기타 건강 문제를 유발할 수 있다(Epa et al., n.d.; Peng et al., 2021; Scott et al., 2020). 전 세계적으로 식수에서 높은 Sr 농도가 보고되었으며, 미국 북부의 지하수에서는 최대 52 mg L⁻¹의 농도가 관측된 바 있다(Luczaj and Masarik, 2015; Peng et al., 2021; Scott et al., 2020). Sr 제거를 위한 가능한 정화 기술 중 하나는 전기화학적 공정이다(Kamaraj and Vasudevan, 2015). 이 공정은 금속 전극에 전류를 가해 반응기 내부에서 응집제를 형성하는 방식으로 작동한다. 공정은 희생 양극의 용해, 음극에서의 수산화이온 및 수소 생성, 전극 표면에서의 전해질 반응, 콜로이드 불순물과 전극에 대한 응집제의 흡착, 그리고 생성된 플록의 침전 또는 부상 제거로 구성된다(Mollah et al., 2001). 이 공정의 주요 단점 중 하나는 전극의 분극과 피막 형성이며, 이는 초음파 처리를 병행함으로써 줄일 수 있다(Dong et al., 2016; Ince, 2018; Moradi et al., 2021). 초음파 캐비테이션은 용질의 열분해 및 수산기 라디칼, 과산화수소 등 반응성 종의 형성을 유도할 수 있다(Mohapatra and Kirpalani, 2019). 또한 이는 용질의 물질 전달 속도를 증가시키고, 고체 입자의 표면 특성을 향상시킨다(Fu et al., 2016; Ziylan et al., 2013). 본 연구의 목적은 주로 Sr 농도가 높은 오염수를 정화하기 위한 전기화학적(EC) 일괄 반응기의 초음파(US) 병행 여부에 따른 처리 효율을 평가하는 것이다. 3D 수치 시뮬레이션 결과는 실험실 EC 반응기에서의 측정 결과를 통해 검증된다.
References
Dong, B., Fishgold, A., Lee, P., Runge, K., Deymier, P. and Keswani, M. (2016), Sono-electrochemical recovery of metal ions from their aqueous solutions, Journal of Hazardous Materials, 318, 379–387.
Kamaraj, R. and Vasudevan, S. (2015), Evaluation of electrocoagulation processfor the removal of strontium and cesium from aqueous solution, Chemical Engineering Research and Design, 93, 522–530.
Luczaj, J. and Masarik, K. (2015), Groundwater Quantity and Quality Issues in a Water-Rich Region: Examples from Wisconsin, USA, Resources, 4(2), 323–357.
Mohapatra, D.P. and Kirpalani, D.M. (2019), Selenium in wastewater: fast analysis method development and advanced oxidation treatment applications, Water Science and Technology: A Journal of the International Association on Water Pollution Research, 79(5), 842–849. https://doi.org/10.2166/wst.2019.010
Mollah, M.Y.A., Schennach, R., Parga, J.R. and Cocke, D.L. (2001), Electrocoagulation (EC)- Science and
applications, Journal of Hazardous Materials, 84(1), 29–41. https://doi.org/10.1016/S0304-3894(01)00176-5 Moradi, M., Vasseghian, Y., Arabzade, H. and Khaneghah, A.M. (2021), Various wastewaters treatment by sono-electrocoagulation process: A comprehensive review of operational parameters and future outlook, Chemosphere, 263, 128314.https://doi.org/10.1016/J.CHEMOSPHERE.2020.128314
Peng, H., Yao, F., Xiong, S., Wu, Z., Niu, G. and Lu, T. (2021), Strontium in public drinking water and associated public health risks in Chinese cities, Environmental Science and Pollution Research International, 28(18), 23048.
Scott, V., Juran, L., Ling, E.J., Benham, B. and Spiller, A. (2020), Assessing strontium and vulnerability to
strontium in private drinking water systems in Virginia, Water, 12(4). https://doi.org/10.3390/w12041053
Ziylan, A., Koltypin, Y., Gedanken, A. and Ince, N.H. (2013), More on sonolytic and sonocatalytic decomposition of Diclofenac using zero-valent iron, Ultrasonics Sonochemistry, 20(1), 580–586.
Tailings dams are structures that store both tailings and water, so almost all tailings dam accidents are water related. This paper investigates a tailings dam’s failure pattern and damage development under flood conditions by conducting a 1:100 large-scale tailings dam failure model test. It also simulates the tailings dam breach discharge process based on the breach mode using FLOW-3D software, and the extent of the impact of the dam failure debris flow downstream was derived. Dam failure tests show that the form of dam failure under flood conditions is seepage failure. The damage manifests itself in the form of flowing soil, which is broadly divided into two processes: the seepage stabilization phase and the flowing soil development damage phase. The dam failure test shows that the rate of rise in the height of the dam saturation line is faster and then slower. The order of the saturation line at the dam face is second-level sub-dam, third-level sub-dam, first-level sub-dam, and fourth-level sub-dam. The final failure of the tailings dam is the production of a breach at the top of the dam due to the development of the dam’s fluid damage zone to the dam top. The simulated dam breach release results show that by the time the dam breach fluid is released at 300 s, the area of over mud has reached 95,250 square meters. Local farmland and roads were submerged, and other facilities and buildings would be damaged to varying degrees. Based on the data from these studies, targeted measures for rectifying hidden dangers and preventing dam breaks from both technical and management aspects can be proposed for tailings dams.
1. Introduction
1.1. Research Status
The mud wastewater containing tailings will be discharged after metal and non-metal mine beneficiation. Tailings slurry contains mercury, arsenic, and other heavy metal ions, both resources and pollution sources [1]. The tailings dam is a dam body formed by the accumulation and rolling of the tailings after the mine selects the useful components [2]. It is of great significance to research the dynamic stability of tailings reservoirs for mine safety production, protection of downstream life and property safety, and the surrounding environment [3]. Tailings dams, an important source of danger if an accident, are bound to people’s lives and property [4]. In 2008, a dam break accident occurred in the 980 ditch tailings pond of Shanxi Xinta Mining Co., Ltd., Yuncheng, China, resulting in 281 deaths and 33 injuries. The direct economic loss was as high as CNY 96,192,000 [5]. On the afternoon of 30 April 2006, the tailings dam of Zhen’an Gold Mine in Shaanxi Province was constructed. The accident caused 17 people to disappear, five people were injured, and 76 houses were destroyed [6,7].
In many tailings reservoir accidents, due to the lack of flood discharge capacity of flood discharge structures in the reservoir area, flood overtopping, tailings dam break, and other phenomena occur occasionally [8,9]. In this regard, scholars in related fields have performed much research and achieved certain results. Chen Zhang et al. [10] established three-dimensional and two-dimensional finite element models. The seepage field of the project under different operating conditions was simulated, and the safety factor under different operating conditions was obtained by combining the seepage field with the stable surface. The influence of the length of the dry beach and the upstream slope ratio on the seepage and stability of the tailings dam was determined. Sánchez-Peralta et al. [11] took a dry tailings pond in Colombia as the research object, studied the movement characteristics of dam break debris flow with different water contents, and obtained the relationship between the length and width of dam break debris flow movement. Changbo Du et al. [12] studied and analyzed the influence of reinforcement on tailings dam and the change law of pore water pressure and internal pressure of the dam body after mud discharge. The pore water pressure and internal earth pressure of the accumulation dam after grouting gradually increased with time. Reinforcement can greatly reduce the pore water pressure and internal pressure of reinforced dams. Gregor Petkovšek et al. [13] proposed a dam break model EMBREA-MUD to calculate the water and tailings outflow of the tailings reservoir and the corresponding break growth. Weile Geng et al. [14] conducted experimental research on the settlement deformation and mesostructure evolution of unsaturated tailings under continuous load. The results showed that the mesostructure deformation of unsaturated tailings with different moisture contents under load was the same and could be divided into four stages: pore compression, elastic deformation, structure change, and further compaction. Alan Lolaev et al. [15] developed a method to determine the tailings filtration and secondary consolidation coefficient in the process of alluvial according to the physical conditions, density, and water phreatic, and a mathematical model to calculate the consolidation time. Kun Wang et al. [16] proposed a multidisciplinary program to simulate the dam break runoff of hypothetical tailings reservoirs on the downstream complex terrain using UAV photogrammetry and smooth particle hydrodynamics (SPH) numerical method. Rawya M. Kansoh [17] studied the influence of the earth-rock dam’s structural parameters on the dam failure process. Kehui Liu et al. [18] studied the microscopic characteristics of hydraulic erosion of reinforced tailings dams and revealed the influence of different reinforcement spacing on the critical start-up speed of tailings particles. It shows that the smaller the reinforcement spacing, the greater the critical start-up speed of the reinforced tailings samples. Luca Piciullo et al. [19] proposed a regression analysis that considers the functional relationship between the release amount and the characteristics of the tailings dam, such as height and water storage (i.e., dam factor). The effects of construction type, filling material, and failure mode on the release amount were also evaluated, as well as the failure frequency of the tailings dam as a function of the construction method. Tailing dams built using upstream construction methods are more prone to failure and are more susceptible to static and dynamic liquefaction. Chunhui Ma et al. [20] pointed out that a reasonable construction schedule and flexible waterproof material are key features of impervious bodies for dams with significant deformation. When the dam deformation becomes stable, consideration should be given to secondary treatment of the impervious body to enhance dam safety. Fukumoto et al. [21] used finite element software to simulate the seepage failure process caused by seepage. Alibek Issakhov et al. [22] combined the k-ω turbulence model to study this process numerically. The VOF (volume of fluid) method was used to simulate the fluid movement behind the tailings dam during the break-up of the fluid and the riverbed landscape. Yonas B. Dibike et al. [23] A two-dimensional hydrodynamic and component transport model was used to study the effect of OS tailings release on the water quality and sediment quality of LAR by simulating sediments and related chemicals. It was concluded that the tailings release location was different; 40% to 70% of the sediments and related chemicals were deposited on the riverbed of the 160 km study section, while the remaining sediments and related chemicals left the study area in the first three days after the release event. Research conducted by Xiaofei Jing et al. [24] investigated the overflow characteristics of tailings dams reinforced with steel bars. During the overflow process, they measured dam displacements, saturation lines, and internal stresses. The study demonstrated that the erosion resistance of tailings dams significantly improves with an increase in the number of reinforcement layers. Abdellah Mahdi et al. [25] studied the potential consequences of a hypothetical oil sand tailings dam failure. For this reason, a non-Newtonian dam–dam model with a viscoplastic rheological relationship is used. The model can reproduce the flood and water level changes in downstream lakes (due to destructive waves). The simulation study of oil sand tailings overflow proves the importance of considering the non-Newtonian characteristics of tailings. Naeini et al. [26] used SIGMA/W and QUAKE/W software to analyze the high-middle line tailings dam’s dynamic response and permanent deformation and evaluated the dam’s performance. Mohammad Reza Boroomand [27] used the numerical analysis method to analyze the earth dam’s seepage under the uncertainty of geotechnical parameters and analyzed the seepage of the earth dam under the condition of uncertainty of geotechnical parameters. Sumin Li et al. [28] simulated and analyzed the hazard range, degree, and spatial state of sediment flow after the dam break and obtained the influence of sand flow velocity, flow depth, and impact on the downstream villages in the disaster area. The feasibility of the expansion and heightening of the tailings dam project was demonstrated, and the disaster risk levels of different spatial locations in the downstream villages were obtained through simulation. Through experiments, Kong et al. [29] studied the influence parameters of tailings dams under seepage. They concluded that the particle size gradation, non-uniformity coefficient, and water content of tailings sand were the main factors affecting the critical hydraulic gradient. It is concluded that the seepage failure gradient with suitable gradation, uniform particles, and suitable water content is significantly higher than that with poor gradation, uneven particles, and poor water content.
Flood overtopping and seepage failure account for 80% of the total accidents, and these two failure forms mainly occur in flood season and are closely related to water. Therefore, it is necessary to explore the tailings dam failure mode, development process, and the impact on the downstream after dam failure under flood conditions to ensure its safe operation. Based on the engineering background of a tungsten mine tailings dam in Ganzhou City, Jiangxi Province, a 1:100 physical model test was carried out to explore the dam break form and failure development process of the tailings dam under flood conditions. The FLOW-3D fluid simulation software was used to solve the influence of the tailings dam on the downstream after the dam break, and the change law of the flow area, velocity development, and submerged depth of the dam break fluid during the flood discharge process was analyzed. Finally, reasonable prevention and remediation suggestions are proposed for the hidden dangers of tailings dams.
The innovation of this paper is to determine the dam break mode and dam break position of the tailings dam under flood conditions by constructing a physical model, which provides a basis for simulating the influence of dam break on the downstream of the dam body.
1.2. Research Flowchart
Figure 1. Research flowchart.
2. Design and Construction of Large Physical Models
2.1. Overview of the Prototype Tailings Dam
The prototype tailings dam is a tungsten tailings dam located in a narrow valley running north–south in Ganzhou City, Jiangxi Province, China. The downstream of the tailings accumulation dam is farmland, dormitory buildings, mountain roads, etc., and the valleys in the downstream are relatively open. Figure 2 shows an overhead view of the prototype tailings dam. The tailings dam is built using the upstream damming method. The initial dam is a clay core wall weathering material dam located at the mouth of the northern valley. The bottom elevation is 262.0 m, the top elevation is 284.0 m, the dam height is 22 m, the upstream and downstream slope ratio is 1:2.5. The design average external slope ratio of the tailings accumulation dam is 1:5, the average slope of the tailings deposition beach is 5%, the design final tailings accumulation dam elevation is 368.00 m, the total dam height 106.00 m, with a complete storage capacity of 1550 × 104 m3 and a service life of 65 years. The present top elevation of the stacked dam is about 315 m, the height of the dam is 53 m, the accumulated storage capacity is about 559 × 104 m3, and the average external slope ratio of the stacked dam is 1:4.9. The reservoir is currently a fourth-class reservoir, with a flood protection standard of one in 200 years. At a later stage, it will be a second-class reservoir with a flood protection standard of 1000 years.
Figure 2. Top view of a tailings dam.
2.2. Selection of Model Sand
To ensure the relative reliability of the test results, the selected dam materials are properly relaxed to meet the primary conditions of similar main influencing factors. The model test focuses on the agglomeration effect of particle movement during the deformation of the dam body. For the selection of model sand, the initial dam is built with silty clay, and the accumulation dam adopts the mine prototype tailings. Figure 3 is the particle size distribution curve of the model sand. According to the particle size distribution curve, two quantitative indexes of soil particles can be determined: non-uniformity coefficient Cu and curvature coefficient Cc. Cu and Cc can jointly determine the gradation of soil. The expressions of the two are:
Figure 3. Cumulative distribution curve of particle size.
The calculated Cu and Cc of the model sand are 2.29 and 0.84, respectively. It is generally believed that the sand soil with Cu < 5 or Cc outside 1~3 belongs to the poorly graded soil, so the model sand is determined to be the poorly graded soil. If the seepage failure occurs in the dam, the development mode of seepage failure can be predicted by some parameters of the soil, that is, whether the soil is piping or flowing soil. According to the non-uniform coefficient discrimination method proposed by the former Soviet Union scholar Istomina, it is preliminarily judged that the model sand is a flowing soil-type soil.
2.3. Construction of the Dam Failure Model
The dam break process of a tailings reservoir involves many aspects, such as hydraulics, mud and sand dynamics, and soil mechanics. It involves many disciplines and is highly complex, which leads to the similarity relationship of model tests.
Therefore, we must put aside the generality of similarity and focus on the similarity of critical elements. This experiment uses the engineering background of a tungsten mine tailings dam in Jiangxi Province, China. The similarity criterion is appropriately relaxed, and the accumulation effect of particle movement during the deformation of the dam body is emphasized to construct the physical model.
Under the condition of geometric similarity, the physical model test of the 1:100 large-scale tailings dam is carried out according to the level of the second-class reservoir of the prototype tailings dam. The prototype range of the tailings dam is 1200 m × 700 m, and the model size is 12 m × 7 m. The model mainly comprises bedrock, a dam body, an observation system, and a water supply circulation system. The specific steps are as follows: According to the topographic map data provided by the mine, the three-dimensional model of the prototype tailings dam is established using Civil-3D modeling software (ver.2018) according to the size of the actual tailings dam (Figure 4). Then, several vertical sections are cut out in the model with the east–west direction as the standard line, and the points on each vertical section are taken equidistantly to extract the elevation value of each point on each vertical section. The model is intended to build a model with an elevation of 230 m in the actual terrain. The steel frame structure of the bedrock is made based on the elevation of each point on the vertical section. The square steel pipe is used as the bedrock support. Each steel pipe corresponds to the elevation of its relative point in proportion. Finally, the waterproof cloth is covered on the steel frame group and fixed to obtain a complete view of the bedrock terrain. Figure 5 is the completed mountain steel frame group, and Figure 6 is the complete bedrock after laying waterproof cloth.
Figure 4. Three-dimensional model of the tailings dam.
Figure 5. Mountain support structures.
Figure 6. A complete view of bedrock.
The initial dam is piled up with silty clay. In the process of stacking the initial dam, two PVC pipes with holes in the wall body and tightly wrapped with permeable geotextiles are symmetrically buried at the bottom of the initial dam to simulate the drainage pipe. A valve is installed at the outlet end of the two drainage pipes to control the drainage speed. The sub-dam uses the pipeline method commonly used in the mine to simulate the ore drawing. An ore drawing main pipe is introduced from the slurry pool to start the ore drawing from the model’s right side, and a valve is set in the main pipe to control the flow rate of the square ore. When the pulp flows into the tailings pond, the tailings will be layered and precipitated under hydraulic screening. After precipitation, the ore is suspended when the tailings reach the target dam height. Start to build the next sub-dam, use the layered filling method to build the dam body to the design elevation, and use the vertical line method to control the elevation when building the dam. (Figure 7) is the construction of the second sub-dam. Four pore water pressure gauges are buried in the dam construction process to monitor the position of the saturation line of the dam body. The four pore water pressure gauges’ positions are arranged along the dam body’s central axis. They are located directly below the dam crest of the first-, second-, third-, and fourth-level accumulation dams. They are named as site 1, site 2, site 3, and site 4 (Figure 8).
Figure 7. Second-stage sub-dam stacking.
Figure 8. Buried pore water pressure gauges.
Due to the need to supply a large amount of water for the test, a water tower was placed on the site (Figure 9), and a return water collection system was designed to achieve a water supply cycle (Figure 10). The observation equipment of the test (Figure 11) uses a trinocular camera and a high-definition camera to record the dam break process of the tailings dam.
Figure 9. Water tower.
Figure 10. Water supply circulation system.
Figure 11. Experimental observation system.
3. Tailings Dam Break Model Experiment
The dam failure mode under specific flood conditions is characterized by permeation damage, manifested as soil erosion. Through analysis of experimental phenomena and data, the development process of dam failure is elucidated, revealing the variation patterns of pore water pressure at different locations and the saturation line of the dam body.
3.1. Dam Failure Experiment
The test was carried out by intermittently injecting water into the reservoir to simulate flood conditions, keeping the flow rate stable during the injection, and keeping the drainage pipe open during the whole test. The beginning of the water injection was taken as the beginning of the test, and the entire dam break test lasted 448 min. It can be roughly divided into two stages, each accounting for one-half of the total length. Figure 12 shows a typical picture of the damage to the dam during the test. Figure 13 shows a timeline of the test damage development. The specific tailings dam damage development process is as follows:
Figure 12. Dam failure model tests.
Figure 13. Timeline of the development of the flowing soil destruction.
The first stage is seepage stabilization: the overflow water is clear, the dam’s surface is stable, and there is no movement of particles. At 138 min of the test, the contact zone between the right end of the second sub-dam and the bedrock began to seep first (Figure 12a). The seepage water flows along the contact zone between the dam body and the bedrock and overflows down the dam face. There are two reasons for the seepage here. The first is fine cracks in the contact area between the soil and the bedrock, which provides a breakthrough for the seepage water. The second is based on calculating the data collected by the pore water pressure gauge. It can be seen that the saturation line at this time escapes on the slope of the second sub-dam, where the dam surface overflows. Subsequently, the second-stage sub-dam continued to seep, and the overflow area gradually expanded and merged with the second-stage sub-dam dam surface. At 174 min, the third-stage sub-dam began to overflow on the left side (Figure 12b). At this time, according to the collected data, it can be calculated that the buried depth of the saturation line has been exposed to the third-level sub-dam. At 190 min, the first sub-dam also overflowed (Figure 12c). Then, the sand boiling point appears at the right end of the first-stage sub-dam, and the soil particles fluctuate obviously with the overflow water. The sand boiling causes the soil particles to be continuously taken out of the soil body. At 203 min, the dam surfaces of the first, second, and third sub-dams have all become swampy. The second stage is the development and failure stage of the flowing soil: seepage deformation occurs continuously, and more earthwork is lost. At 236 min, the first flow soil damage happened at the right end of the second sub-dam (Figure 12d). The failure form is flow slip. At 239 min, a second flow soil damage occurred on the left side of the first sub-dam (Figure 12e). The flow-slipping soil will form a pit that evolves into a breach, making the seepage velocity and seepage flow faster and larger. Then, the pit part of the soil slides, and the seepage water erodes the downstream dam surface. At 248 min, two erosion ditches have been formed in the flow soil failure area on both sides of the dam (Figure 12f,g). The erosion gully on the left side is located at the junction of the right side of the first-order sub-dam and the bedrock. The critical hydraulic gradient is lower, the dominant flow develops more rapidly, the sand is wrapped violently, and the subsequent seepage damage is more likely to occur. The erosion gully produces more water flow to scour multiple branches on the dam’s surface. The right erosion ditch is located at the junction of the secondary dam and the bedrock. At this time, the erosion ditch has developed to a certain depth, and the sand boiling point has reached 6. The flowing soil migrates downward under the action of overflow water. The flowing water will bring the fine particles to the downstream area. The coarse particles will be accumulated to form a ‘filter layer‘ to block the overflow water channel. The seepage pressure on both sides of the filter layer gradually increases. A new seepage channel will be formed when the seepage pressure on one side reaches the critical value. At 292 min, the flow soil damage eroded to the third sub-dam and further developed upstream along the boundary. Part of the erosion gully’s inner wall soil is washed away underwater, and the internal wall forms holes and expands upward until the upper part forms a suspended surface. When the shear strength of the upper soil is greater than the shear strength of the soil, it will collapse and continue to repeat the next round of erosion. At this time, the left-flowing soil does not develop to the upstream failure but to the proper lateral erosion, and the right side flushes out a new channel due to the obstruction of the ‘filter layer‘. At 303 min, the third flow soil failure occurred on the left side of the third sub-dam (Figure 12h). Because of the increase in overflow water and the acceleration of water flow, the right scouring area opens the downstream channel at the particle deposition, and fine particles are continuously taken out of the dam by seepage water. The overflow water also washes away the ‘filter layer‘ on the left side. After that, the first sub-dam eroded to the deep, and the dam surface failure area did not expand. There is a hydraulic–gravity erosion cycle in the flow soil damage area of the second-stage sub-dam, which extends to the upstream and the middle of the dam body. With the increase in the erosion damage area of the water flow, the more the sand boiling point, the faster the seepage damage, and the erosion area of the lower section continues to expand, and the water flow in the erosion gully is large and fast. The flowing soil failure zone of the third-stage sub-dam has not yet formed a penetrating failure path and is in the initial stage of erosion. At 348 min, the fourth-stage sub-dam overflowed (Figure 12i). At 448 min, the flow soil was eroded to the fourth sub-dam (Figure 12j). The flow soil damage area is eroded to the fourth sub-dam, which is regarded as the whole dam damage. It is measured that the depth of the collapse area is about 12 cm, and the width is about 80 cm. It should be noted that although the dam body has undergone a large area of seepage failure, the dam body has not yet experienced an unstable landslide. The tailings dam finally broke because the dam body soil damage zone developed to the top of the dam to produce a breach.
3.2. The Change Rule of the Saturation Line
Figure 14 is about the change curve of the saturation line. At the beginning of the test, as the upstream water level rose, the saturation line rose rapidly despite the drain being in a normal discharge condition. After the lifting of the head has ceased, the rate of the upward lifting of the saturation line becomes significantly slower due to the hysteresis effect. Then, a certain depth of burial is maintained. In the middle and late stages of the test, most of the dam had become saturated, and the soil matrix suction had weakened. When water is again stored in the reservoir, the saturation line will again lift, but at a reduced rate compared to the initial period. If the reservoir level is no longer raised, the saturation line tends to fall after a period of time. By approximately 270 min into the test, the dam face had already developed a certain size of the flow damage zone, and it was no longer meaningful to discuss the depth of the saturation line.
Figure 14. Variation curve of saturation line.
In the previous study [30], a two-dimensional finite element model of the tailings dam, chosen from the central axis of the three-dimensional tailings dam model, was used to analyze the distribution of saturation line in the tailings dam under flood conditions. The numerical simulation results show that when the upstream water head rose to 125 m (Figure 15), the saturation line intersected with the first and fourth-level accumulation dams and was exposed throughout the dam surface. The variation law of the saturation line obtained by the numerical simulation is consistent with the experimental phenomenon; that is, the saturation line increases with the rise of the reservoir water level, and the order of the dam surface exposure is the second-stage sub-dam, the third-stage sub-dam, the first-stage sub-dam, and the fourth-stage sub-dam. According to the simulation results, the displacement of the dam body does not change greatly, and the plastic strain zone does not appear on the slope and crest of the dam body, and there is no penetration. It can be judged that the tailings dam model does not have deep slip when the water level is about to overflow; that is, the skeleton structure of the dam body is stable. Combined with the physical model test, before the saturation line of the dam body reaches the dam surface of the fourth-level sub-dam, the tailings dam has undergone seepage failure, but the dam body has not undergone structural instability. The results of numerical simulation are consistent with the phenomenon of physical model test. After that, with the development of flowing soil, the damaged area of the dam body continues to extend to the top of the dam, which will eventually cause the breach of the dam top and cause the flood discharge of the dam.
Figure 15. Saturation line distribution of the tailings dam under 125 m water level.
4. Impact Analysis after Dam Break and Prevention Suggestions
Based on the results of the physical model experiment, it can be inferred that the tailings dam failure was triggered by seepage failure. This means the area of flowing soil gradually eroded upstream until a breach was created at the top of the dam, and the reservoir fluid poured downstream. Therefore, an erosion damage trench was set up on the model for the dam breach calculation in FLOW-3D (ver. 9.3), extending from the top of the initial dam to the top of the dam, and the shape was simplified to a semi-cylinder. Figure 16 shows a model of the tailings dam after completion of the pre-treatment.
Figure 16. FLOW-3D 3D calculation model.
4.1. Dam Failure Test Results
An overview of the area downstream of the tailings dam is shown in Figure 17. The downstream area is dominated by the production facilities (red and yellow line areas in the figure), staff accommodation buildings (pink line area), the road around the mountain (blue curve), villages (green line area), and scattered agricultural land.
Figure 17. Aerial view downstream of tailings dam.
4.1.1. Overflow Area
Figure 18 shows the change in the extent of fluid inundation at 60 s, 120 s, 180 s, 240 s, and 300 s as calculated by the software, with the fluid in blue in the figure. As can be seen from the diagram, the breached fluid was rapidly released downstream in a short period and, by 300 s, covered the entire flat area downstream, with an overflow area of approximately 95,250,000 square meters. Farmland and roads in the area will be flooded, and production facilities and residential buildings will also be affected. In addition, emergency escape plans can be challenging to implement successfully at short notice. It is thus clear that in the event of a breach of this tailings dam, it would be a major accidental disaster.
Figure 18. Time-course diagram of mud area.
4.1.2. Flooding Depth
Figure 19 shows a cloud of the distribution of flooding depth at 60 s, 120 s, 180 s, 240 s, and 300 s. Due to the lower topography in the eastern part of the downstream area, the fluids that wash down first collect in the east and then spread westwards. As can be seen from the graph, the maximum inundation depth is always located in the eastern part of the lower reaches near the initial dam. The mudslide did not affect the northern area due to the terrain’s advantage; when the situation was urgent, people could be evacuated along the northwest-facing road to the north.
Figure 19. Cloud map of flooding depth.
4.1.3. Flow Rate Analysis
The flow velocity during the release process reflects the magnitude of the fluid impact. Figure 20 shows the flow velocity clouds during the dam breach release process at 60 s, 120 s, 180 s, 240 s, and 300 s. Due to inertia, the fluid emerges from the breach. It rapidly completes the transformation from potential energy to kinetic energy in the trench eroded by the flowing soil, with the flow velocity reaching a maximum. In addition, there is some leakage around the dam at the junction of the tailings dam and the mountain. After the fluid is flushed off the tailings dam, the average flow velocity decreases due to the diffusion principle and frictional forces. In general, the flow of emissions increases and then falls.
Figure 20. Cloud map of flow rate.
Three points, A, B, and C, are selected in the flow direction of the release to analyze the fluid’s flow velocity characteristics, specifically during the dam failure process. The three points are located at the top of the initial dam, the foot of the initial dam, and the downstream area adjacent to the tailings dam (Figure 21). Figure 22 shows the variation in flow rate over time at three points. Overall, the flow velocities at points A, B, and C are successively reduced as the flow path develops. From the point of view of the flow velocity at a single point, it does not increase to a peak all at once but has an undulating, phased variation. At about 30 s, the overflow velocity starts to appear at the three points, after which the trend is a cyclic process of “increase-smooth or decrease” because the increase in flow velocity does not coincide with the expansion of the breach, which, in turn, determines the flow velocity of the discharge. The flow rate increases accordingly when the breach expands and becomes deeper again. After several cycles of this until the breach is no longer extended, the flow rate at points A, B, and C all fall during the last 30 s of the figures and will return to zero as the flooding stops.
Figure 21. Flow rate reference points.
Figure 22. Flow rate time history diagram.
The analysis of the variation in the flow rate of the release shows that the debris flow impacts downstream in a segmented manner. Therefore, the decrease in flow velocity should not be regarded as the end of the entire dam break, nor should blindly carry out the aftermath of the accident at this stage, but should wait for a longer period to observe and confirm so as not to cause more damage.
4.2. Recommendations for Prevention and Management
4.2.1. Technical Measures
Dam surface treatment: According to the seepage characteristics of the tailings dam, to prevent overflow water and rainwater from scouring the shoulder and face of the dam and to collect the seepage water, a shoulder drainage ditch should be installed along the junction of the dam with the slopes of the two banks, and a face drainage ditch should be installed on the face of the dam. Moreover, the downstream slope of the dam can be mulched, turfed, and, if necessary, reinforced by stone pitching at the foot of the dam.
Additional seepage facilities: Combined with the model test results, it is clear that control of the saturation line of the tailings dam should be a top priority for safety management. To effectively control the depth of the saturation line, additional drainage facilities can be provided in the form of a combined horizontal drainage pipe and a vertical shaft connected to the end of the horizontal drainage pipe. In addition, the vertical drainage pipe should be raised with the height of the stockpile dam and pumped out periodically.
4.2.2. Management Measures
Routine inspection and maintenance: Besides monitoring various safety indicators such as the tailings dam saturation line and dry beach length, the person responsible for safety should regularly inspect the dam body for cracks, collapses, and surface erosion. They should also ensure that the slope protection is intact and that the drainage facilities are clear of blockages, siltation, or waterlogging. Check for seepage, pipe surges, or flowing soil, focusing on the junction between the dam and the hills on either side, and be vigilant for changes in seepage flow and turbidity. If a potential problem is identified, the cause must be immediately determined, and remedial action must be taken to prevent it.
Ensure excellence in flood management, including pre-flood preparation, response during flooding, and post-flood rescue work.
5. Conclusions
The reservoir’s water level had not yet crested before the dam was damaged. In other words, the cause of dam failure under flood conditions is seepage failure, which manifests itself in the form of flowing soil. Before the flow soil is destroyed, the dam surface will produce overflow, water accumulation, sand boiling, and other phenomena. The phenomenon of the dam failure test shows that the flow soil damage starts at the weak point of the dam at the junction with the bedrock. These areas have a high saturation gradient and are more prone to local damage. In the early stage of soil flow failure, multiple sand boiling points were generated on the dam surface. With the development of seepage, collapsible cracks appeared on the dam surface one after another, forming erosion ditches. In the middle stage of soil failure, the failure area is widened. The soil cycle undergoes the process of erosion–gravity erosion, and the ‘filter layer’ will slow down the failure rate to a certain extent. In the later stage of flow soil damage, the flow water damage area began to penetrate, and the erosion intensified until the whole dam body was damaged. Therefore, when the sand boiling point is generated, and the collapsible cracks appear on the dam surface, these can be used as a warning sign of seepage failure.
The buried depth of the saturation line becomes shallow with the increase in the upstream water head. And, the rate of increase is first fast and then slow. After the lifting head is stopped, the saturation line will still rise slightly for a period of time due to the lag effect. If the reservoir water level is not replenished for a long time, the saturation line will be reduced under normal drainage. The order of the saturation line escaping from the dam surface is the second sub-dam, the third sub-dam, the first sub-dam, and the fourth sub-dam. It can be seen that before the flood, it is necessary to check and repair the drainage facilities to ensure their suitable operation. During the flood season, all measures should be taken to enhance the flood discharge, reduce the saturation line, and avoid the seepage damage of the tailings dam.
The results of the FLOW-3D hydrodynamic simulation software show that the breach fluid was rapidly discharged within a short period, covering the entire flat area downstream by 300 s. The local farmland and roads were submerged, and the rest of the construction facilities were also damaged to a certain extent. Therefore, it will be a major disaster once the tailings dam breaks. The rapid development of the dam breach mudslide and the short release time make it impractical to organize the evacuation of people when the release occurs. Therefore, in combination with the mechanism of tailings dam failure, targeted measures for potential remediation and dam failure prevention can be proposed from both technical and management aspects.
The innovation point is to use a large-scale physical model test to study the dam break mode of tailings dam under flood conditions. By monitoring the internal changes of the tailings reservoir under flood conditions, the stage of seepage failure of the dam body can be judged, which can serve as an early warning for the subsequent break of the tailings dam. The experimental process and experimental results of the model can provide a reference for the changes in tailings reservoir under flood conditions under real working conditions so as to correspond to the changes of tailings reservoir fluid under flood conditions under real working conditions. Provide guidance for staff to monitor changes in tailings ponds. The determination of dam break position and dam break mode by model test provides a basis for simulating the influence of tailings dam break on the downstream. The use of a steel frame structure to build a tailings dam model can cover the entire tailings dam terrain more comprehensively and economically and can more comprehensively analyze the entire dam break process of the tailings dam. Compared with the local tailings dam similarity simulation and on-site exploration, it is more profound and comprehensive, which has practical significance for the safety of the tailings reservoir. The defect is that there is a prototype of the model, and it cannot be used for all tailings mines. The actual situation needs to be analyzed in detail. In addition, according to the tailings pond model test, it can be expected that the tailings pond model can be used to study the useful mineral components in the recovery reservoir, which has practical significance for environmental protection and resource recovery.
References
Yue, T.; Wu, X. Effect of magnetic starch on the clarification of hematite tailings wastewater. IOP Conf. Ser. Earth Environ. Sci. 2018, 121, 032051.
Jin, W.; Wei, Z. Research progress on land reclamation and environmental management benefit estimation of non-ferrous metal tailings reservoir. Environ. Sci. Res. 2019, 8, 1304–1313. (In Chinese)
Kang, Z.; Han, Q.; Wang, S. umerical model of dynamic stability of a proposed tailings dam To be studied. Min. Res. Dev. 2015, 35, 59–62.
Zhou, K.; Liu, F.; Hu, J.; Gao, F. Research on dam-break disaster chain and chain-breaking disaster reduction control technology of tailings reservoir. Disasterology 2013, 28, 24–29. (In Chinese)
Chen, C.; Zhao, Y.; Jiang, L. Review on the current research of dam break of tailings pond. Min. Res. Dev. 2019, 39, 103–108. (In Chinese)
Zhou, Z.; Li, X. Causes and ecological environment impact assessment of tailings dam break accident in China. Met. Mine 2012, 11, 121–124. (In Chinese)
Zhou, L.; Huang, Y. Discussion on the causes and countermeasures of tailings reservoir accident. China Manganese Ind. 2016, 34, 37–39. (In Chinese)
Yang, M.; Song, Z. A tailings reservoir based on flood calculation and flood routing analysis. China Met. Bull. 2020, 5, 263–264. (In Chinese)
Zhang, X.; Song, Z.; Zhang, Z. Example analysis of a tailings pond flooded with a dam failure. Eng. Constr. 2020, 52, 44–48. (In Chinese)
Zhang, C.; Chai, J.; Cao, J.; Xu, Z.; Qin, Y.; Lv, Z. Numerical simulation of seepage and stability of tailings dams: A case study in Lixi, China. Water 2020, 12, 742.
Sánchez-Peralta, J.A.; Beltrán-Rodríguez, L.N.; Trujillo-Vela, M.G.; Larrahondo, J.M. Flows of liquefied filtered tailings: Laboratory-scale physical and numerical modeling. Int. J. Civ. Eng. 2020, 18, 393–404.
Du, C.; Liang, L.; Yi, F.; Niu, B. Effects of geosynthetic reinforcement on tailings accumulation dams. Water 2021, 13, 2986.
Petkovšek, G.; Hassan, M.A.A.M.; Lumbroso, D.; Roca, M. A two-fluid simulation of tailings dam breaching. Mine Water Environ. 2021, 40, 151–165.
Geng, W.; Wang, W.; Wei, Z.; Huang, G.; Jing, X.; Jiang, C.; Tian, S. Experimental study of mesostructure deformation characteristics of unsaturated tailings with different moisture content. Water 2021, 13, 15.
Lolaev, A.; Oganesyan, A.; Badoev, A.; Oganesyan, E. Tailing dams formation algorithm. Arab. J. Geosci. 2020, 13, 974.
Wang, K.; Yang, P.; Yu, G.; Yang, C.; Zhu, L. 3D numerical modelling of tailings dam breach run out flow over complex terrain: A multidisciplinary procedure. Water 2020, 12, 2538.
Kansoh, R.M.; Elkholy, M.; Abo-Zaid, G. Effect of shape parameters on failure of earthen embankment due to overtopping. KSCE J. Civ. Eng. 2020, 24, 1476–1485.
Liu, K.; Cai, H.; Jing, X.; Chen, Y.; Li, L.; Wu, S.; Wang, W. Study on hydraulic incipient motion model of reinforced tailings. Water 2021, 13, 2033.
Piciullo, L.; Storrøsten, E.B.; Liu, Z.; Nadim, F.; Lacasse, S. A new look at the statistics of tailings dam failures. Eng. Geol. 2022, 303, 106–657.
Ma, C.; Gao, Z.; Yang, J.; Cheng, L.; Chen, L. Operation performance and seepage flow of impervious body in blast-fill dams using discrete element method and measured data. Water 2022, 14, 1443.
Fukumoto, Y.; Ohtsuka, S. 3-D direct numerical model for failure of non-cohesive granular soils with upward seepage flow. Comput. Part. Mech. 2018, 5, 443–454.
Issakhov, A.; Borsikbayeva, A. The impact of a multilevel protection column on the propagation of a water wave and pressure distribution during a dam break: Numerical simulation. J. Hydrol. 2021, 598, 126–212.
Dibike, Y.B.; Shakibaeinia, A.; Droppo, I.G.; Caron, E. Modeling the potential effects of Oil-Sands tailings pond breach on the water and sediment quality of the Lower Athabasca River. Sci. Total Environ. 2018, 642, 1263–1281.
Jing, X.; Chen, Y.; Williams, D.J.; Serna, M.L.; Zheng, H. Overtopping failure of a reinforced tailings dam: Laboratory investigation and forecasting model of dam failure. Water 2019, 11, 315.
Mahdi, A.; Shakibaeinia, A.; Dibike, B.Y. Numerical modelling of oil-sands tailings dam breach runout and overland flow. Sci. Total Environ. 2020, 703, 134–568.
Naeini, M.; Akhtarpour, A. Numerical analysis of seismic stability of a high centerline tailings dam. Soil Dyn. Earthq. Eng. 2018, 107, 179–194.
Boroomand, M.R.; Mohammadi, A. Evaluation of earth dam leakage considering the uncertainty in soil hydraulic parameters. Civ. Eng. J. 2019, 5, 1543–1556.
Li, S.; Yuan, L.; Yang, H.; An, H.; Wang, G. Tailings dam safety monitoring and early warning based on spatial evolution process of mud-sand flow. Saf. Sci. 2020, 124, 104–579.
Kong, X.; Liu, Y.; Li, X.; Li, R.; He, Y. Analysis and experimental study of mechanical factors of permeation damage of a uranium tailings pond dam. Eng. Saf. Environ. Prot. 2019, 45, 30–36. (In Chinese)
He, W.; Chen, H.; Zheng, C. Experimental study on dam break of a tailings dam under flood conditions. J. Saf. Environ. 2022, 22, 3126–3134. (In Chinese)
중간 수심에서 고정된 박스형 자유 수면 방파제의 유체역학적 성능 공식을 결정하기 위한 연구
Guoxu Niu, Yaoyong Chen, Jiao Lu, Jing Zhang, Ning Fan
Abstract
two-dimensional viscous numerical wave tank coded mass source function in a computational fluid dynamics (CFD) software Flow-3D 11.2 is built and validated. The effect of the core influencing factors (draft, breakwater width, wave period, and wave height) on the hydrodynamic performance of a fixed box-type free surface breakwater (abbreviated to F-BW in the following texts) are highlighted in the intermediate waters. The results show that four influence factors, except wave period, impede wave transmission; the draft and breakwater width boost wave reflection, and the wave period and wave height are opposite; the draft impedes wave energy dissipation, and the wave height is opposite; the draft and wave height boost the horizontal extreme wave force; four influence factors, except the draft, boost the vertical extreme wave force. Finally, new formulas are provided to determine the transmission, reflection, and dissipation coefficients and extreme wave forces of the F-BW by applying multiple linear regression. The new formulas are verified by comparing with existing literature observation datasets. The results show that it is in good agreement with previous datasets.
1. Introduction
A breakwater dissipates wave energy and reflects waves from the open sea, representing a crucial protective structure for the exploitation and utilization of marine resources. It is also an essential auxiliary marine structure that improves offshore engineering construction conditions and shortens ship berthing times [1,2,3]. With the development and utilization of ocean space and resources, the demand for breakwaters has also varied. The construction of breakwaters has shifted from onshore to offshore. Because most wave energy is concentrated near the water surface, a fixed box-type free surface breakwater (F-BW, Figure 1) was created [4,5]. The F-BW is a type of reflective breakwater with simple structure and high efficiency, which reduces the transmitted wave height by reflecting the incident wave energy [6,7]. Compared with the traditional bottom-founded breakwater, F-BW does not influence water exchange inside and outside the breakwater while maintaining a high wave attenuation efficiency, and has a high application prospect.
Figure 1. Two-dimensional schematic sketch of the F-BW models.
The hydrodynamic performance of the breakwater is important for the research and development of the F-BW, which mainly comprises two aspects. One aspect is the wave attenuation performance, including wave transmission coefficient Ct, reflection coefficient Cr, and dissipation coefficient Cd (hereinafter referred to as RTD coefficients). The other is the wave force, which concerns the safety and stability of the breakwater, including the horizontal wave force and vertical wave force. In terms of research on the RTD coefficients of an F-BW, some scholars have studied the influence of the breakwater width and draft on the reflection and transmission coefficients when energy dissipation was ignored. [8,9,10,11]. In order to provide some judgement for the needy practitioners, a closed-form formula has been created to predict the transmission coefficient in deep water [8,9,10]. A study by Kolahdoozan et al. [12] showed the poor prediction performance of the formula proposed by Macagno [8] for intermediate water. Therefore, it is necessary to explore a proposed formula for the transmission coefficient under intermediate-water conditions. Different from the analytical solution of potential flow theory, other scholars studied the influence of the draft, breakwater width, and wave height on the performance of wave reflection, transmission, and dissipation of the F-BW via experimental tests conducted in intermediate waters [13,14,15,16]. The computational fluid dynamics (CFD) technique provides us an alternative way to interpret the interaction between wave and F-BW. Koftis and Prinos [16] applied the two-dimensional unsteady Reynolds Averaged Navier–Stokes model to study the influence of the dimensionless draft on the transmission and reflection coefficients of an F-BW. Elsharnouby et al. [17] studied the influence of the draft on the wave transmission of the F-BW by using Flow-3D 11.2 software. Their results showed that the increasing draft impedes wave transmission. Some researchers carried out earlier work on wave force of F-BW due to concerns regarding safety and stability of the F-BW. Guo et al. [11] confirmed that draft, breakwater width and wave period also influenced the horizontal and vertical wave forces by adopting mathematical analysis based on linear potential flow theory. Chen et al. [18] investigated the effects of wave height and wave period on the horizontal and vertical wave forces of F-BW through a series of experiments. The results showed that the horizontal and vertical wave forces increase with increasing wave height. Limited by the fact that the mathematical analysis tends to ignore flow viscosity [19,20,21] and the physical model test is complicated and costly, considerable effort has been devoted to studying the hydrodynamic performance of an F-BW through numerical simulation in recent years. Zheng et al. [22] and Ren et al. [23] used the smoothed particle hydrodynamics (SPH) method to numerically simulate the horizontal and vertical wave forces of F-BWs under regular waves. Unlike previous studies which overlooked the nonlinearity of wave forces, the positive and negative maximum wave force could be observed in the studies of Zheng et al. [22] and Ren et al. [23]. Human activities are less involved in deep water, and the cost-effectiveness of F-BW construction is poorer in deep water than intermediate water. Reflection coefficient Ct, and dissipation coefficient Cd are also an indispensable part of the wave attenuation performance of F-BW. The horizontal and vertical wave forces are related to the security of the F-BW. However, the prediction formulas based on tests or numerical simulations for horizontal and vertical wave forces of the F-BW in the above studies were rare. Therefore, an attempt is necessary to present a proposed formula for the prediction of RTD coefficients and wave forces, which will provide design judgments for the relevant practitioners in intermediate waters. The objective of this paper is to provide the prediction formulas for RTD coefficients and wave forces in the intermediate waters under the condition that waves do not overtop the breakwater. With the rapid development of the CFD technique, Kurdistani et al. [24] proposed a formula for submerged homogeneous rubble mound breakwaters based on a large dataset from the CFD model, and the proposed formula was verified by using the literature observation datasets. Inspired by their research method, a numerical wave flume is built through a grid convergence test and validated with the existing experimental results. The prediction equations of RTD coefficients and wave forces are provided by applying multiple linear regression and verified by comparing with existing literature observation datasets. The major conclusions are finally summarized, and some prospects are proposed.
2. Theoretical Introduction
2.1. Governing Equations
Flow-3D 11.2 is widely used in coastal engineering as a powerful CFD software program [25]. The interaction of waves and breakwaters is simulated in a numerical wave tank by using Flow-3D 11.2 software in this paper. The numerical wave tank adopts an incompressible viscous fluid in the wave and F-BW interaction. The Reynolds averaged Navier–Stokes (RANS) equation was applied as the governing equation for turbulent flow. Assuming that the Cartesian coordinate system o-xyz originates from the still water surface, the continuity equation is shown in Equation (1), and the momentum equation is expressed in Equation (2).
where i,j = 1,2 for two-dimensional flows, xi represents the Cartesian coordinate, and ui is the fluid velocity along the x- and z-axes. Ax and Az are the area fractions open to flow in the x and z directions, respectively, ρ is the fluid density, p is the pressure, v is the dynamic viscosity, and g is the gravity force. The Reynolds stresses term, 𝜌𝑢𝑖′𝑢𝑗, is modeled by the renormalized-group (RNG) turbulence model.
2.2. RNG Turbulence Model
The interaction of waves and an F-BW induces turbulence. The RNG turbulence model is adopted to close the governing equations [26], and the discrete governing equations are solved by the finite difference method. The transport equations of turbulent kinetic energy kT and dissipation rate εT in this model are as follows:
The volume of fluid (VOF) method was developed to track the evolution of the free surface [27]. The governing equation is shown as follows:
where F represents the fractional volume of water fluid, F = 1 indicates that the numerical cell is full of water, and F = 0 corresponds to the cell fully occupied by air. Numerical cells with a value of 0 < F < 1 represent a water surface.
Furthermore, the generalized minimal residual (GMRES) method was used to solve the velocity-pressure term [28], and the first-order upwind scheme and Split Lagrangian method were used to solve the volume of fluid advection. The structure of the F-BW is directly imported into Flow-3D 11.2 by the software built-in drawing function. The appearance of an F-BW depicted by the mesh could be viewed with the fractional area volume obstacle representation (FAVOR) method. All numerical simulations were run in parallel using an Intel Core (TM) i5-4460 processor (3.20 GHz). Furthermore, to ensure the accuracy of the numerical solution, the maximum iteration time step was set to 0.001 s, and the results were output at 0.01-s intervals.
2.3. Principle of Mass Source Wavemaker
The present study emerged from the interest shown in the use of F-BW in a specific zone at an actual project in East China Sea. The detailed structural design dimensions of F-BW and wave characteristics are shown in Table 1. All the incident waves are considered to be regular waves. The regular waves used in the study contain a large range of wave periods and wave heights, which represent the majority of wave parameters in real-world problems, making this study of great practical importance. The interaction between the second-order Stokes wave and the current is not considered in the twelve major wave parameters, due to the differing time and spatial scales between the wave and the current [29]. The twelve waves in this research are all in the range of either linear or nonlinear second-order Stokes waves. Figure 2 shows the suitability range of different wave theories. According to Figure 2, the F-BW at this project is located in intermediate waters. Equation (5) presents the wave elevation equation η of the second-order Stokes wave and the wave elevation equation of the linear wave is the first term on the right side of this equation.
where Hi is the incident wave height, k is the wavenumber, σ is the wave frequency, and h is the still water depth.
Figure 2. Wave parameter conditions analyzed in this study and their relations in the Le Méhauté diagram.
Table 1. Summary of the simulated scenarios.
The boundary wavemaker method produces re-reflection waves. Lin and Liu [30] proposed a popular mass source wave generation method [31,32,33,34,35,36]. In the present method, numerical wave generation is achieved by importing a given volume flow rate Vfr into the mass source model. The expression of the volume flow rate Vfr is as follows:
where C is the phase velocity, W is the tank width, η(t) is the wave surface elevation by solving Equation (5).
To effectively reduce the calculation divergence caused by excessive waves in the NWT at the initial stage, the volume flow rate Vfr is multiplied by an increasing envelope function to make the wave increase gradually in the first three wave periods. The equation of the increasing function is as follows:
where t is time and T is the wave period.
2.4. Principle of Numerical Solution
In this paper, the time series of wave elevations were recorded at five different locations (i.e., WG1–WG5) on the onshore and offshore sides of the F-BW (Figure 3a). Furthermore, the current WG spacings are selected according to the water depth and wave period. The distances between the wave source and WG1, WG1 and WG2, WG2 and F-BW, and F-BW and WG5 are set at 1.5 m, 0.2 m, 1.8 m, and 1.435 m, respectively. Note that the distance between wave gauges WG1 and WG2 is more than 0.05 L and less than 0.45 L, and the distances between wave gauges WG2 and F-BW and between WG5 and F-BW are less than 0.25 L and more than 0.2 L (wavelength), as recommended by the two-point method [37]. Two wave gauges (WG1 and WG2) are mounted in a line on the offshore side of the F-BW to separate the incident wave heights Hi and the reflected wave heights Hr by using this method. To prove that the horizontal wave force of the F-BW is related to the free surface onshore and offshore of the breakwater, probe WG3 is placed 0.02 m in front of the F-BW, while probe WG4 is placed 0.02 m behind the F-BW to measure the wave profile at the front (η3) and back (η4) of the F-BW. The wave gauge (WG5) is mounted on the onshore side of the F-BW to obtain the surface elevation of the transmitted wave heights Ht. The wave transmission, reflection, and wave energy dissipation coefficients are defined by solving Equation (8a)–(8c).
where Ct is the transmission coefficient; Cr is the reflection coefficient; and Cd is the wave energy dissipation coefficient.
Figure 3. Schematic layout and mesh sketch of the numerical wave tank for the F-BW.
Furthermore, the horizontal and vertical wave forces are simulated by the integration of the water pressure p at the wet surface of the F-BW. The two kinds of wave forces include the hydrostatic force and hydrodynamic force according to the FLOW-3D theory manual [25]. Because the F-BW is always fixed at the free surface, the vertical wave force needs to remove part of the hydrostatic force (the value up to ρVg, where ρ is the density of water and V is the volume of the F-BW). The shear stress is small enough to be ignored in this paper relative to the wave force. The horizontal wave force and the vertical wave force are denoted by Fx and Fz, respectively. The horizontal wave force is consistent with the direction of wave propagation, and the vertical wave force is vertically upward. To facilitate the research, obtaining the extreme value of the steady part of the wave force time series, we define the average value of the horizontal wave force positive and negative peak as the horizontal positive maximum wave force Fx+max and horizontal negative maximum wave force Fx−max, the vertical wave force positive and negative peak as the vertical positive maximum wave force Fz+max and vertical negative maximum wave force Fz−max. The representative time series of the dimensionless wave elevation, horizontal, and vertical wave forces are shown in Figure 4. The numerical results of Hi, Hr, Ht, Fx±max, Fz±max were acquired based on the stable elevations in this figure. To facilitate discussion, we define Fx±max/0.005 ρgh2 and Fz±max/0.005 ρgh2 as the dimensionless horizontal and vertical maximum wave forces on the F-BW, respectively. The crest and trough values of the time series of the wave forces are studied because the extreme values of the horizontal and vertical wave forces on the F-BW under the Stokes second-order wave have a slightly sharper crest and flatter trough.
Figure 4. Time histories of wave elevation η measured by WG1, WG2, and WG5 and horizontal and vertical wave forces of F-BW at Hi = 0.07 m, T = 1.4 s, B = 0.5 m, dr = 0.14 m, and h = 0.75 m.
The integral formula of the horizontal and vertical wave force is shown in Equation (9).
where 𝑛⃗ is the unit normal vector of the object surface s and the water pressure p is determined by the Bernoulli equation.
3. Model Setup and Validation
3.1. Numerical Wave Tank Setup
The detailed numerical wave tank (NWT) setup is shown in Figure 3b,c. The total length of the NWT was twenty-four wavelengths L long in the x-axis direction, 0.1 m wide in the y-axis direction, and 1 m deep in the z-axis direction. A scale ratio of 1:40 and a constant water depth h of 0.75 m are adopted based on the Froude similarity law. The mesh consisted of two distinct regions. The first region was the computation domain, four wavelengths length, with a width of 0.1 m and a depth of 1 m. The unit grid size of the total NWT was L/100~L/200 in the x and z directions, and ten grids were partitioned in the y directions in this domain. The second region was two identical damping domains with ten wavelength lengths. The Sommerfeld radiation method was employed to bate the secondary reflection of waves at both ends of the NWT. The grid size along the x-axis direction was gradually extended with an identical ratio of 1.01, and one grid was set for the lateral width of the NWT [38].
To describe the F-BW more accurately, nested grids were applied in the domain around the F-BW. The uniform nested grid was equal to half of the compute domain grid in the x, y and z-axis directions. Furthermore, the finer mesh resolution of 0.0035 cm in z direction was nested near the still water level (SWL), The region extends ±0.07 m from the SWL to ensure that the expected wave heights (0.03 m, 0.05 m, 0.07 m, 0.09 m) are encompassed within the region.
The boundary conditions of this NWT were set as follows: both ends of the NWT were defined as outflow boundaries, two sides of the domain were defined as symmetry boundaries, the atmospheric pressure was utilized at the upper boundary, and the lower surface of the computational domain was a no-slip wall boundary without surface roughness.
A mass source model with wide WS and high HS was added to the numerical flume. The symmetry boundaries were used overspreading with the mass source form, and the y-direction width of the mass source block was consistent with the width of the NWT. Pledging each edge of the mass block to coincide with the grid line of the NWT is shown in Figure 3b,c.
3.2. Numerical Model Validation
The present research is mainly implemented under the framework of CFD technology. To demonstrate the accuracy of the simulation results, it is essential to compare them with the extant results. The model is verified by the following three aspects in this section.
3.2.1. Grid Independent Verification
The mesh partition is a crucial procedure in CFD numerical simulation and needs much attention. The number and size of grids are essential criteria for evaluating the convergence of numerical results. Poor grid quality will directly affect the accuracy of numerical results and computation time. Consider that the proposed calculation cases Hi = 0.06 m, T = 1.2 s, and h = 1.2 m by Ren et al. are close to the target cases in this paper [23]. This wave condition is applied to complete the grid independence verification. Different grid arrangements can be seen in Table 2, and the time series of the wave profiles under the three grid sizes are compared with the theoretical results by solving Equation (5), as shown in Figure 5. The error of the numerical simulation results was calculated according to Equation (10). The wave profile deviations among the coarse mesh, medium mesh, and fine mesh are compared. The wave profiles under the medium mesh and the fine mesh are closer, and the deviation from the theoretical value is less than 5%, which meets the requirements of Det Norske Veritas (DNV) [39]. It can be judged that only medium meshes and refined meshes meet the requirements of numerical simulation. Considering the balance between calculation accuracy and calculation efficiency, the following numerical simulations always chose a medium mesh.
where Htheoretical is the wave height of the theoretical result and Hnumerical is the wave height of the numerical result.
Figure 5. Grid independent verification: influence of mesh size on wave profile.
Mesh Type
Computation Domain Grid Size (cm)
Nested Domain Grid Size (cm)
Cell Number
Elapsed Time (×104 s)
Wave Height (cm)
Error %
Coarse
2
1
701460
0.6496
5.642
5.96
Middle
1
0.5
3411180
7.6832
5.768
3.87
Fine
0.5
0.25
13350960
48.1437
5.769
3.85
Theoretical
–
–
–
–
6.000
–
Table 2. Mesh independence check results.
3.2.2. Validation of Wave Forces
In this section, to further inspect the accuracy of the numerical results of wave forces in this paper, according to the wave conditions of Hi = 0.06 m, T = 1.2 s, h = 1.2 m, and draft dr = 0.2 m, a rectangular box of width B = 0.8 m and wave height Hi = 0.4 m is fixed and semi-immersed, as proposed by Ren et al. [23]. The horizontal and vertical wave forces of the F-BW were verified by comparison with the theoretical results of Mei and Black [40] and the numerical simulation results of Ren et al. [23]. The time series of the wave forces are compared in Figure 6. The total simulation time of this case is 16 wave cycles. Since it takes some time for the progressive wave to arrive at the F-BW from the source, the horizontal and vertical wave forces begin to reach the stable state at t = 7 T seconds in Figure 6. By comparison, the simulated time series of horizontal and vertical wave forces are almost consistent with those presented by Ren et al. [23] and Mei and Black [40]. This result indicated that the present NWT could meet the calculation accuracy.
Figure 6. Comparison of the normalized wave force on an F-BW with previous studies (Mei and Black [40]; Ren et al. [23]). (a) Normalized horizontal wave force; (b) Normalized vertical wave force.
4. Results and Discussion
4.1. Influence Analysis of Four Factors on the Hydrodynamic Performance of F-BW
Among all the influencing factors (refer to Appendix A), the hydrodynamic performance of the F-BW is significantly affected by the following four factors: draft (dr/h), breakwater width (B/h), wave period (T*sqrt(g/h)), and wave height (Hi/h). For the mechanism analysis of the interaction between waves and breakwater, the mechanism study of the horizontal wave force is rather complicated. Since the breakwater is in a semisubmerged state, the Morison formula is no longer applicable to the guidance of the calculation of the horizontal wave force. The horizontal wave force is studied separately from the water particle velocity; see the free surface difference (η3–η4) in the front and back sides of the F-BW and the water particle streamline in Figure 7 and Figure 8 for details. Among them, five representative cases are selected from all cases in this article for comparative analysis corresponding to Figure 7a–e. Note that case (a) T1.2dr0.14B0.5Hi0.07 represents a wave period of 1.2 s, draft of 0.14 m, breakwater width of 0.5 m and incident wave height of 0.07 m. Due to the effect of water blockage, flow separation is generated at the bottom corner of the offshore side of the breakwater, and the generated clockwise vortex destroys the original motion path of the wave water particles without structure in Figure 8a and allows the free surface difference in the front and back of the F-BW to gradually reach a maximum. At time instant t0 in Figure 7, the horizontal wave force also reaches a maximum. It can be seen in Figure 8b that the vertical wave force is easier to analyze. When the vertical wave force is at its maximum, the streamline realizes complete diffraction, and no vortex is generated. Furthermore, to understand the mechanism and contribution of each influencing factor on the hydrodynamic performance of the F-BW in detail, the statistical results are shown in Figure 9, Figure 10, Figure 11 and Figure 12.
Figure 7. Comparative analysis of five different cases under the interaction between waves and breakwater: First column: numerically obtained snapshots of free surface profile and velocity field; Second column: time history of free surface and horizontal wave force.
Figure 8. Snapshots of the velocity streamline field: (a) Time instant of the horizontal positive maximum wave force; (b) Time instant of the vertical positive maximum wave force.
Figure 9. Effect of the draft dr on the hydrodynamic performance of the F-BW at wave heights Hi = 0.05 m and Hi = 0.07 m. (a) Horizontal positive and negative maximum wave forces Fx+max and Fx−max; (b) Vertical positive and negative maximum wave forces Fz+max and Fz−max; (c) Transmission coefficient Ct, reflection coefficient Cr, and dissipation coefficient Cd.
Figure 10. Influence of the breakwater width B on the hydrodynamic performance of the F-BW at wave heights Hi = 0.05 m and Hi = 0.07 m. (a) Horizontal positive and negative maximum wave forces Fx+max and Fx−max; (b) Vertical positive and negative maximum wave forces Fz+max and Fz−max; (c) Transmission coefficient Ct, reflection coefficient Cr, and dissipation coefficient Cd.
Figure 11. Influence of the wave period T on the hydrodynamic performance of the F-BW at wave heights Hi = 0.05 m and Hi = 0.07 m. (a) Horizontal positive and negative maximum wave forces Fx+max and Fx−max; (b) Vertical positive and negative maximum wave forces Fz+max and Fz−max; (c) Transmission coefficient Ct, reflection coefficient Cr, and dissipation coefficient Cd.
Figure 12. Influence of the wave height Hi on the hydrodynamic performance of the F-BW at draft dr = 0.14 m and dr = 0.28 m. (a) Horizontal positive and negative maximum wave forces Fx+max and Fx−max; (b) Vertical positive and negative maximum wave forces Fz+max and Fz−max; (c) Transmission coefficient Ct, reflection coefficient Cr, and dissipation coefficient Cd.
4.1.1. Effect of Draft
Figure 7 lists the distribution diagram of the free surface difference and water particle velocity under cases (a) and (b) at the time instant of the horizontal wave force maximum. Except for the draft being different, the two cases are consistent. Among them, case (a) has a wave period of 1.2 s, draft of 0.14 m, wave height of 0.07 m and breakwater width of 0.5 m. Case (b) has a period of 1.2 s, draft of 0.35 m, wave height of 0.07 m and breakwater width of 0.5 m.
In the second column of Figure 7a, when time t0 = 11.48 s, the maximum free surface difference is 0.068 m, and the maximum horizontal wave force is 7.98 N. In the second column of Figure 7b, when time t0 = 11.52 s, the maximum free surface difference is 0.083 m, and the maximum horizontal wave force is 15.91 N. Obviously, the increase in the draft enhances the water blockage action in front of the F-BW, weakens the diffraction effect of the wave, and delays the time for the horizontal wave force to reach its maximum. Figure 9a shows that Fx+max increases with increasing draft under wave heights of Hi = 0.05 m and Hi = 0.07 m. Similarly, the absolute values of Fx−max exhibit a similar law. The absolute values of Fz−max and Fz+max decrease with increasing draft under wave heights of Hi = 0.05 m and Hi = 0.07 m in Figure 9b, which is related to the exponential decay of the wave kinetic energy along the water depth. It is not difficult to see in Figure 7a,b that the wave hydrodynamic pressure on the lower surface of the F-BW decreases with decreasing wave kinetic energy as the water depth increases. The effective action area increases as the draft reduces the penetration of waves. Figure 9c shows that the transmission coefficient decreases with increasing draft under wave heights of Hi = 0.05 m and Hi = 0.07 m. Due to the increase in the interaction area between waves and F-BW, the reflected wave energy increases in Figure 7, and Figure 7b is more obvious than Figure 7a. The wave energy dissipation coefficient increases with decreasing draft in Figure 9c. Since the wave energy is mainly concentrated on the still water level, the fluid particle velocity maximum at the lower corner of F-BW is 0.30 m/s in Figure 7a is more than the 0.17 m/s in Figure 7b, more wave energy is dissipated when the fluid particle with higher velocity collides with F-BW due to decreasing draft.
Overall, the increasing draft impedes incident waves cross F-BW and promotes the increase in horizontal wave force and wave reflection, which threatens the stability of the structure.
4.1.2. Effect of Breakwater Width
To clarify the mechanism of the breakwater width effect on the hydrodynamic performance of the F-BW, except that the breakwater width is different, cases (a) and (c) in Figure 7 are consistent. In case (c), the period is 1.2 s, the draft is 014 m, the wave height is 0.07 m, and the breakwater width is 0.2 m.
The free surface difference and vortex in Figure 7a,c are similar. Figure 10a shows that the breakwater width effect on Fx−max and Fx+max is not obvious. When the vertical wave force is at its maximum, the streamline realizes complete diffraction, and no vortex is generated in Figure 8b. Therefore, the vertical wave force is related to the acting area of the F-BW lower surface. Figure 10b shows that the absolute values of Fz−max and Fz+max increase with increasing breakwater width. In the second column of Figure 7c, when time t0 = 11.42 s, the free surface difference and the horizontal wave force reach a maximum faster than in case (a). Obviously, the increase in the breakwater width increases the wave diffraction difficulty. Figure 10c shows that the transmission coefficient decreases with increasing breakwater width, and the reflection coefficient increases with increasing breakwater width. Due to fluid particle velocity maximum is similar between Figure 7a,c. The increase in breakwater width has little influence on wave energy dissipation.
In short, the increasing breakwater width is not conducive to incident wave cross F-BW, and promotes the increase of wave reflection and vertical wave force. Obviously, more weights need to be added to ensure the safety of the breakwater when breakwater width increases.
4.1.3. Effect of Wave Period
To clarify the mechanism of the wave period effects on the hydrodynamic performance of the breakwater, except that the wave period is different, cases (a) and (d) are consistent. Figure 7d shows that the wave period is 1.8 s, the draft is 0.14 m, the wave height is 0.07 m and the breakwater width is 0.5 m.
In the second column of Figure 7d, when time t0 = 11.13 s, the maximum free surface difference is 0.051 m, and the maximum horizontal wave force is 6.90 N. According to Equation (9), because the wave energy is more abundant on the two sides of the breakwater in case (4), the horizontal wave force is comparable even if the free surface difference is smaller than that in case (1). Figure 11a shows that Fx−max and Fx+max are weakly related to the wave period under wave heights of Hi = 0.05 m and Hi = 0.07 m. Because the long-period waves possess a large wave energy in Figure 7d, they increase the wave pressure on the lower surface of the F-BW. Therefore, the absolute values of Fz−max and Fz+max increase linearly with the wave period in Figure 11b. Figure 11c shows that the transmission coefficient increases with increasing wave period under wave heights of Hi = 0.05 m and Hi = 0.07 m. Long-period waves have a better diffraction ability at the same depth, and more wave energy passes through the F-BW. The decreasing ratio of the breakwater width to wavelength weakens the ability to block progressive waves, and the reflection coefficient decreases accordingly. The wave energy dissipation coefficient shows an alphabetic symbol “M” distribution with the wave period. This indicates that the wave energy dissipation is more complex and requires further study. When the dimensionless wave period is 5.06, both the transmission and reflection coefficients are close to 0.71, the dissipation coefficient is at the minimum by applying Equation (8c).
In brief, the increasing wave period plays a significant role in increasing the wave transmission and the reducing wave reflection. Although it has little effect on the horizontal wave force, it promotes an increase in the vertical wave force, which is unfavorable to the security of the breakwater.
4.1.4. Effect of Wave Height
To clarify the mechanism of the wave height effects on the hydrodynamic performance of the breakwater, except that the wave height is different, cases (a) and (e) are consistent. Figure 7e shows that the wave period is 1.2 s, the draft is 014 m, the wave height is 0.03 m and the breakwater width is 0.5 m.
In the second column of Figure 7e, when time t0 = 11.44 s, the maximum free surface difference is 0.031 m, and the maximum horizontal wave force is 3.43 N. Obviously, the increase in wave height increases the diffraction difficulty of the wave and delays the time when the horizontal wave force reaches its maximum. The higher the wave height, the more abundant the wave energy in Figure 7a,e. The water particle velocity maximum is 0.11 m/s in Figure 7e, which is much less than the water particle velocity maximum in Figure 7a. The larger wave height causes a larger wave elevation difference, and the larger horizontal wave force under other variable conditions is consistent by comparing Figure 7a,e. Therefore, Fx−max and Fx+max increase linearly with increasing wave height under drafts dr = 0.14 m and dr = 0.28 m in Figure 12a. The increase in wave height leads to increasing dynamic wave pressure, which in turn leads to increasing wave pressure on the F-BW lower surface and an increase in vertical wave force. Therefore, Fz−max and Fz+max increase linearly with increasing wave height under drafts dr = 0.14 m and dr = 0.28 m in Figure 12b. Figure 12c shows that the increasing wave height results in more wave reflection and less transmission due to the increasing blockage effect. The reflection ability weakens with decreasing interaction area (the ratio of the wetted surface height of the front wall of the F-BW to the wave height). The water particle velocity maximum of 0.11 m/s in Figure 7e is less than the water particle velocity maximum of 0.3 m/s in Figure 7a. The increasing water particle velocity with increasing wave height results in better vortex dissipation near the F-BW. Hence, the wave energy dissipation coefficient increases.
In conclusion, the increasing wave height reduces the wave reflection but increases horizontal and vertical wave forces, which is disadvantageous to the security of the breakwater.
4.2. Prediction Equations of F-BW Hydrodynamic Performance Parameters
To understand the contribution of each influencing factor to the hydrodynamic performance of the F-BW in detail, the factors affecting the RTD coefficients and wave force mainly include the wave period T, wave height Hi, draft dr, breakwater width B, and still water depth h. In Equation (11), the RTD coefficients Ct,r,d and wave force extremum Fx,z±max are expressed as follows:
Using the dimensionless analysis method and the numerical simulation results of 30 groups of simulated conditions in Table 1 based on the Origin 2019b software platform, multiple linear regression was performed by the least squares method, and the prediction equations of the RTD coefficients and wave force are given in Equation (12a–g). The detailed formulas are shown in Table 3.
Table 3. Statistics of prediction equation. Note that 0.0933 ≤ dr/h ≤ 0.4667, 0.26667 ≤ B/h ≤ 0.8, 3.6166 ≤ T*sqrt(g/h) ≤ 6.5099, and 0.04 ≤ Hi/h ≤ 0.12.
4.3. Deviation Analysis of the Prediction Equations
Inspired by Kurdistani et al.’s [24] research method, the current study uses their method to assess the reliability of each predictive formula. The literature observation datasets include the measured RTD coefficients from Koutandos [13] (three cases (R1, R2 and R3) in Figure 16 of his literature) and Liang et al. [14] (six cases in Figures 14a, 19a and 22a of their literature), the wave forces from Mei and Black [40] and Ren et al. [23] (a case in Figure 10 of their literature). The numerical results obtained by Flow-3D are plotted on the x-axis in Figure 13, and predicted values of the predictive equations are plotted on the y-axis in Figure 13. Figure 13a shows a 20% error for the application of Liang et al. [14] transmission coefficient datasets that are mostly lower-estimated values of transmission coefficient with respect to Equation (12a), an almost 10% error for the application of Liang et al.’s [14] reflection coefficient and dissipation coefficient datasets, and Koutandos’s [13] RTD coefficients datasets. Figure 13b shows an almost 10% error for the application of Mei and Black [40] and Ren et al. [23] maximum wave force, which indicates that the present prediction equations are valid.
Figure 13. Comparison of the results between previous studies and the numerical results of this study. (a) Transmission coefficient Ct, reflection coefficient Cr, and dissipation coefficient Cd (Koutandos [13], Liang et al. [14]) and (b) Maximum wave force (Mei and Black [40]; Ren et al. [23]).
It is clearly found that the distribution points of the reflection coefficient and wave energy dissipation coefficient of the F-BW are relatively concentrated in a particular region in Figure 13a, indicating that the F-BW is dominant in reflecting waves and has stable wave dissipation ability. In addition, the horizontal negative maximum wave force of the F-BW is similar to the vertical negative maximum wave force, and the horizontal positive maximum wave force of the F-BW is slightly larger than the vertical positive maximum wave force in Figure 13b.
5. Conclusions
The present study investigated a high-accuracy numerical wave tank (NWT) based on the Flow-3D platform. A series of numerical simulations in the intermediate waters were carried out at a constant water depth (h) of 0.75 m under regular wave conditions, with a wave height range between 0.03–0.09 m, a wave period range between 1–1.8 s, and a breakwater width range between 0.2–0.6 m. The effects of four influencing factors (dr, B, T, Hi) on the hydrodynamic performance (RTD coefficients and wave forces) are highlighted. The vital conclusions are as follows:
The performance of two-dimensional viscous numerical wave tanks (NWTs) with a mass source wave maker and small length scale (1:40) are analyzed. By comparison, the wave model employed in this paper is competent for the numerical simulation of the F-BW.
The results show that the increase in the four influence factors, except the wave period, benefits the decrease in the wave transmission. The increase in draft and breakwater width is beneficial to the increase in the wave reflection, and the wave period and wave height are opposite. The increase in draft benefits the decrease in wave energy dissipation, and the wave height is opposite.
The increase in the draft and wave height benefits the increase in the horizontal positive and negative maximum wave forces. In addition to the draft, the increase in the other three influence factors benefits the increase in the vertical positive and negative maximum wave forces.
Applying multiple linear regression presents the prediction equations of RTD coefficients and the extreme wave force. The prediction equations are verified by comparing them with literature observation datasets.
This study provides insight into the relation of RTD coefficients and wave forces with parameters such as draft, breakwater width, wave period and wave height. The simulated results of the given predicted equations can be generalized to the prototype scale by using Froude’s scaling law and can be used to guide the design of F-BWs in intermediate waters.
Appendix A
The wave period T, wave height Hi, draft dr, breakwater width B, and water depth h are the main factors that affect the wave dissipation performance and wave force of an F-BW in the intermediate waters. Therefore, the wave force of an F-BW can be expressed as a function of the above factors as follows:
Taking water depth h, gravity acceleration g, and water density ρ as the repetitive parameters, the three dimensionless parameters are expressed as follows:
[h] = [M0L1T0], [g] = [M0L1T−2], [ρ] = [M1L−3T0], where wave force per breakwater length in the vertical wave direction 𝐹F, expressed as [F = ρgh2], Equation (A1) can be written as follows:
According to wave theory, there is a nonlinear relationship between the wave force and the four dimensionless parameters in Equation (A2). The relationship between the dependent variable and independent variable in nature is exponential. It can be expressed as follows:
where α, x1, x2, x3, and x4 are the unknown coefficients.
Taking the natural logarithm of both sides of Equation (A3) to obtain the double logarithm function model, the equation can be written in linear form as follows:
Using multiple function linear regression analysis, each unknown coefficient in the equations can be obtained and then substituted into Equation (A3) to obtain the wave force equations. Similarly,
Reference
He, F.; Huang, Z.H.; Law, A.W.K. Hydrodynamic performance of a rectangular floating breakwater with and without pneumatic chambers: An experimental study. Ocean Eng. 2012, 51, 16–27.
Zhan, J.; Chen, X.; Gong, Y.; Hu, W. Numerical investigation of the interaction between an inverse T-type fixed/floating breakwater and regular/irregular waves. Ocean Eng. 2017, 137, 110–119.
Fu, D.; Zhao, X.Z.; Wang, S.; Yan, D.M. Numerical study on the wave dissipating performance of a submerged heaving plate breakwater. Ocean Eng. 2021, 219, 108310.
Hales, L.Z. Floating Breakwaters: State-of-the-Art Literature Review; Coastal Engineering Research Center: London, UK, 1981.
Teh, H.M. Hydraulic performance of free surface breakwaters: A review. Sains Malays. 2013, 42, 1301–1310.
Liang, J.M.; Chen, Y.K.; Liu, Y.; Li, A.J. Hydrodynamic performance of a new box-type breakwater with superstructure: Experimental study and SPH simulation. Ocean Eng. 2022, 266, 112819.
Zhao, X.L.; Ning, D.Z. Experimental investigation of breakwater-type WEC composed of both stationary and floating pontoons. Energy 2018, 155, 226–233.
Macagno, A. Wave action in a flume containing a submerged culvert. In La Houille Blanche; Taylor and Francis: London, UK, 1954.
Wiegel, R.L. Transmission of waves past a rigid vertical thin barrier. J. Waterw. Harb. Div. 1960, 86, 1–12.
Ursell, F. The effect of a fixed vertical barrier on surface waves in deep water. Math. Proc. Camb. Philos. Soc. 1947, 43, 374–382.
Guo, Y.; Mohapatra, S.C.; Guedes Soares, C. Wave interaction with a rectangular long floating structure over flat bottom. In Progress in Maritime Technology and Engineering; CRC Press: Boca Raton, FL, USA, 2018; pp. 647–654.
Kolahdoozan, M.; Bali, M.; Rezaee, M.; Moeini, M.H. Wave-transmission prediction of π-type floating breakwaters in intermediate waters. J. Coast. Res. 2017, 33, 1460–1466.
Koutandos, E. Regular-irregular wave pressures on a semi-immersed breakwater. J. Mar. Environ. Eng. 2018, 10, 109–145.
Liang, J.M.; Liu, Y.; Chen, Y.K.; Li, A.J. Experimental study on hydrodynamic characteristics of the box-type floating breakwater with different mooring configurations. Ocean Eng. 2022, 254, 111296.
Fugazza, M.; Natale, L. Energy losses and floating breakwater response. J. Waterw. Port Coast. Ocean Eng. 1988, 114, 191–205.
Koftis, T.; Prinos, P. 2 DV Hydrodynamics of a Catamaran-Shaped Floating Structure. Iasme Trans. 2005, 2, 1180–1189.
Elsharnouby, B.; Soliman, A.; Elnaggar, M.; Elshahat, M. Study of environment friendly porous suspended breakwater for the Egyptian Northwestern Coast. Ocean Eng. 2012, 48, 47–58.
Chen, Y.; Niu, G.; Ma, Y. Study on hydrodynamics of a new comb-type floating breakwater fixed on the water surface. In Proceedings of the E3S Web of Conferences, Wuhan, China, 14–16 December 2018; EDP Sciences: Les Ulis, France, 2018; Volume 79, p. 02003.
Fan, N.; Nian, T.K.; Jiao, H.B.; Guo, X.S.; Zheng, D.F. Evaluation of the mass transfer flux at interfaces between submarine sliding soils and ambient water. Ocean Eng. 2020, 216, 108069.
Fan, N.; Jiang, J.X.; Dong, Y.K.; Guo, L.; Song, L.F. Approach for evaluating instantaneous impact forces during submarine slide-pipeline interaction considering the inertial action. Ocean Eng. 2022, 245, 110466.
Ghafari, A.; Tavakoli, M.R.; Nili-Ahmadabadi, M.; Teimouri, K.; Kim, K.C. Investigation of interaction between solitary wave and two submerged rectangular obstacles. Ocean Eng. 2021, 237, 109659.
Zheng, X.; Lv, X.P.; Ma, Q.W.; Duan, W.Y.; Khayyer, A.; Shao, S.D. An improved solid boundary treatment for wave–float interactions using ISPH method. Int. J. Nav. Archit. Ocean Eng. 2018, 10, 329–347.
Ren, B.; He, M.; Dong, P.; Wen, H.J. Nonlinear simulations of wave-induced motions of a freely floating body using WCSPH method. Appl. Ocean Res. 2015, 50, 1–12.
Kurdistani, S.M.; Tomasicchio, G.R.; D’Alessandro, F.; Francone, A. Formula for Wave Transmission at Submerged Homogeneous Porous Breakwaters. Ocean Eng. 2022, 266, 113053.
Hirt, C.W.; Nichols, B.D. Flow-3D User’s Manuals; Flow science Inc.: Santa Fe, NM, USA, 2012.
Yakhot, V.; Orszag, S.A. Renormalization group analysis of turbulence. I. Basic theory. J. Sci. Comput. 1986, 1, 3–51.
Hirt, C.W.; Nichols, B.D. Volume of fluid (VOF) method for the dynamics of free boundaries. J. Comput. Phys. 1981, 39, 201–225.
Saad, Y.; Schultz, M.H. GMRES: A generalized minimal residual algorithm for solving nonsymmetric linear systems. SIAM J. Sci. Stat. Comput. 1986, 7, 856–869.
Lin, P.Z.; Liu, P.L.-F. Internal wave-maker for Navier-Stokes equations models. J. Waterw. Port Coast. Ocean Eng. 1999, 125, 207–215.
Lara, J.L.; Garcia, N.; Losada, I.J. RANS modelling applied to random wave interaction with submerged permeable structures. Coast. Eng. 2006, 53, 395–417.
Ha, T.; Lin, P.Z.; Cho, Y.S. Generation of 3D regular and irregular waves using Navier-Stokes equations model with an internal wave maker. Coast. Eng. 2013, 76, 55–67.
Chen, Y.L.; Hsiao, S.C. Generation of 3D water waves using mass source wavemaker applied to Navier-Stokes model. Coast. Eng. 2016, 109, 76–95.
Windt, C.; Davidson, J.; Schmitt, P.; Ringwood, J.V. On the assessment of numericalwave makers in CFD simulations. J. Mar. Sci. Eng. 2019, 7, 47.
Wang, D.X.; Dong, S. Generating shallow-and intermediate-water waves using a line-shaped mass source wavemaker. Ocean Eng. 2021, 220, 108493.
Wang, D.X.; Sun, D.; Dong, S. Numerical investigation into effect of the rubble mound inside perforated caisson breakwaters under random sea states. Proc. Inst. Mech. Eng. Part M J. Eng. Marit. Environ. 2022, 236, 48–61.
Goda, Y.; Suzuki, Y. Estimation of incident and reflected waves in random wave experiments. In Proceedings of the 15th International Conference on Coastal Engineering, Honolulu, HI, USA, 11–17 July 1976; pp. 828–845.
Orlanski, I. A simple boundary condition for unbounded hyperbolic flows. J. Comput. Phys. 1976, 21, 251–269.
Veritas, D.N. Environmental Conditions and Environmental Loads: Recommended Practice; DNV-RP-C205; Det Norske Veritas (DNV): Oslo, Norway, 2010.
Mei, C.C.; Black, J.L. Scattering of surface waves by rectangular obstacles in waters of finite depth. J. Fluid Mech. 1969, 38, 499–511.
지표 산사태로 발생한 파랑의 3차원 시뮬레이션: OpenFOAM과 FLOW-3D HYDRO 모델 비교
Ramtin Sabeti, Mohammad Heidarzadeh, Alessandro Romano, Gabriel Barajas Ojeda & Javier L. Lara
Abstract
The recent destructive landslide tsunamis, such as the 2018 Anak Krakatau event, were fresh reminders for developing validated three-dimensional numerical tools to accurately model landslide tsunamis and to predict their hazards. In this study, we perform Three-dimensional physical modelling of waves generated by subaerial solid-block landslides, and use the data to validate two numerical models: the commercial software FLOW-3D HYDRO and the open-source OpenFOAM package. These models are key representatives of the primary types of modelling tools—commercial and open-source—utilized by scientists and engineers in the field. This research is among a few studies on 3D physical and numerical models for landslide-generated waves, and it is the first time that the aforementioned two models are systematically compared. We show that the two models accurately reproduce the physical experiments and give similar performances in modelling landslide-generated waves. However, they apply different approaches, mechanisms and calibrations to deliver the tasks. It is found that the results of the two models are deviated by approximately 10% from one another. This guide helps engineers and scientists implement, calibrate, and validate these models for landslide-generated waves. The validity of this research is confined to solid-block subaerial landslides and their impact in the near-field zone.
1 Introduction and Literature Review
Subaerial landslide-generated waves represent major threats to coastal areas and have resulted in destruction and casualties in several locations worldwide (Heller et al., 2016; Paris et al., 2021). Interest in landslide-generated tsunamis has risen in the last decade due to a number of devastating events, especially after the December 2018 Anak Krakatau tsunami which left a death toll of more than 450 people (Grilli et al., 2021; Heidarzadeh et al., 2020a). Another significant subaerial landslide tsunami occurred on 16 October 1963 in Vajont dam reservoir (Northern Italy), when an impulsive landslide-generated wave overtopped the dam, killing more than 2000 people (Heller & Spinneken, 2013; Panizzo et al., 2005). The largest tsunami run-up (524 m) was recorded in Lituya Bay landslide tsunami event in 1958 where it killed five people (Fritz et al., 2009).
To achieve a better understanding of subaerial landslide tsunamis, laboratory experiments have been performed using two- and three-dimensional (2D, 3D) set-ups (Bellotti & Romano, 2017; Di Risio et al., 2009; Fritz et al., 2004; Romano et al., 2013; Sabeti & Heidarzadeh, 2022a). Results of physical models are essential to shed light on the nonlinear physical phenomena involved. Furthermore, they can be used to validate numerical models (Fritz et al., 2009; Grilli & Watts, 2005; Liu et al., 2005; Takabatake et al., 2022). However, the complementary development of numerical tools for modelling of landslide-generated waves is inevitable, as these models could be employed to accelerate understanding the nature of the processes involved and predict the detailed outcomes in specific areas (Cremonesi et al. 2011). Due to the high flexibility of numerical models and their low costs in comparison to physical models, validated numerical models can be used to replicate actual events at a fair cost and time (e.g., Cecioni et al., 2011; Grilli et al., 2017; Heidarzadeh et al., 2020b, 2022; Horrillo et al., 2013; Liu et al., 2005; Løvholt et al., 2005; Lynett & Liu, 2005).
Table 1 lists some of the existing numerical models for landslide tsunamis although the list is not exhaustive. Traditionally, Boussinesq-type models, and Shallow water equations have been used to simulate landslide tsunamis, among which are TWO-LAYER (Imamura and Imteaz,1995), LS3D (Ataie-Ashtiani & Najafi Jilani, 2007), GLOBOUSS (Løvholt et al., 2017), and BOUSSCLAW (Kim et al., 2017). Numerical models that solve Navier–Stokes equations showed good capability and reliability to simulate subaerial landslide-generated waves (Biscarini, 2010). Considering the high computational cost of solving the full version of Navier–Stokes equations, a set of methods such as RANS (Reynolds-averaged Navier–Stokes equations) are employed by some existing numerical models (Table 1), which provide an approximate averaged solution to the Navier–Stokes equations in combination with turbulent models (e.g., k–ε, k–ω). Multiphase flow models were used to simulate the complex dynamics of landslide-generated waves, including scenarios where the landslide mass is treated as granular material, as in the work by Lee and Huang (2021), or as a solid block (Abadie et al., 2010). Among the models listed in Table 1, FLOW-3D HYDRO and OpenFOAM solve Navier–Stokes equations with different approaches (e.g., solving the RANS by IHFOAM) (Paris et al., 2021; Rauter et al., 2022). They both offer a wide range of turbulent models (e.g., Large Eddy Simulation—LES, k–ε, k–ω model with Renormalization Group—RNG), and they both use the VOF (Volume of Fluid) method to track the water surface elevation. These similarities are one of the motivations of this study to compare the performance of these two models. Details of governing equations and numerical schemes are discussed in the following.
Numerical models
Approach
Developer
FLOW-3D HYDRO
This CFD package solves Navier–Stokes equations using finite-difference and finite volume approximations, along with Volume of Fluid (VOF) method for tracking the free surface
Flow Science, Inc. (https://www.flow3d.com/)
MIKE 21
This model is based on the numerical solution of 2D and 3D incompressible RANS equations subject to the assumptions of Boussinesq and hydrostatic pressure
Danish Hydraulic Institute (DHI) (https://www.mikepoweredbydhi.com/products/mike-21-3)
OpenFOAM (IHFOAM solver)
IHFOAM is a newly developed 3D numerical two-phase flow solver. Its core is based on OpenFOAM®. IHFOAM can also solve two-phase flow within porous media using RANS/VARANS equations
IHCantabria research institute (https://ihfoam.ihcantabria.com/)
NHWAVE
NHWAVE is a 3D shock-capturing non-Hydrostatic model which solves the incompressible Navier–Stokes equations in terrain and surface-following sigma coordinates
Kirby et al. (2022) (https://sites.google.com/site/gangfma/nhwave, https://github.com/JimKirby/NHWAVE)
GLOBOUSS
GloBouss is a depth-averaged model based on the standard Boussinesq equations including higher order dispersion terms, Coriolis terms, and numerical hydrostatic correction terms
Løvholt et al. (2022) (https://www.duo.uio.no/handle/10852/10184)
BOUSSCLAW
BoussClaw is a new hybrid Boussinesq type model which is an extension of the GeoClaw model. It employs a hybrid of finite volume and finite difference methods to solve Boussinesq equations
Clawpack Development Team (http://www.clawpack.org/)Kim et al. (2017)
THETIS-MUI
THETIS is a multi-fluid Navier–Stokes solver which can be considered a one-fluid model as only one velocity is defined at each point of the mesh and there is no mixing between the three considered fluids (water, air, and slide). It applies VOF method
TREFLE department of the I2M Laboratory at Bordeaux, France (https://www.i2m.u-bordeaux.fr/en)
LS3D
A 2D depth-integrated numerical model which applies a fourth-order Boussinesq approximation for an arbitrary time-variable bottom boundary
Ataie-Ashtiani and Najafi Jilani (2007)
LYNETT- Mild-Slope Equation (MSE)
MSE is a depth-integrated version of the Laplace equation operating under the assumption of inviscid flow and mildly varying bottom slopes
A simplified 3D Navier–Stokes model for two fluids (water and landslide material) using VOF for tracking of water surface
Horrillo et al. (2013)Kim et al. (2020)
(Cornell Multi-grid Coupled Tsunami Mode (COMCOT)
COMCOT adopts explicit staggered leap-frog finite difference schemes to solve Shallow Water Equations in both Spherical and Cartesian Coordinates
Liu et al. (1998); Wang and Liu (2006)
TWO-LAYER
A mathematical model for a two-layer flow along a non-horizontal bottom. Conservation of mass and momentum equations are depth integrated in each layer, and nonlinear kinematic and dynamic conditions are specified at the free surface and at the interface between fluids
Imamura and Imteaz (1995)
Table 1 Some of the existing numerical models for simulating landslide-generated waves
In this work, we apply two Computational Fluid Dynamic (CFD) frameworks, FLOW-3D HYDRO, and OpenFOAM to simulate waves generated by solid-block subaerial landslides in a 3D set-up. We calibrate and validate both numerical models using our physical experiments in a 3D wave tank and compare the performances of these models systematically. These two numerical models are selected among the existing CFD solvers because they have been reported to provide valuable insights into landslide-generated waves (Kim et al., 2020; Romano et al., 2020a, b ; Sabeti & Heidarzadeh, 2022a). As there is no study to compare the performances of these two models (FLOW-3D HYDRO and OpenFOAM) with each other in reproducing landslide-generated waves, this study is conducted to offer such a comparison, which can be helpful for model selection in future research studies or industrial projects. In the realm of tsunami generation by subaerial landslides, the solid-block approach serves as an effective representative for scenarios where the landslide mass is more cohesive and rigid, rather than granular. This methodology is particularly relevant in cases such as the 2018 Anak Krakatau or 1963 Vajont landslides, where the landslide’s nature aligns closely with the characteristics simulated by a solid-block model (Zaniboni & Tinti, 2014; Heidarzadeh et al., 2020a, 2020b).
The objectives of this research are: (i) To provide a detailed implementation and calibration for simulating solid-block subaerial landslide-generated waves using FLOW-3D HYDRO and OpenFOAM, and (ii) To compare the performance of these two numerical models based on three criteria: free surface elevation of the landslide-generated waves, capabilities of the models in simulating 3D features of the waves in the near-field, velocity fields, and velocity variations at different locations. The innovations of this study are twofold: firstly, it is a 3D study involving physical and numerical modelling and thus the data can be useful for other studies, and secondly, it compares the performance of two popular CFD models in modelling landslide-generated waves for the first time. The validated models such as those reported in this study and comparison of their performances can be useful for engineers and scientists addressing landslide tsunami hazards worldwide.
2 Data and Methods
2.1 Physical Modelling
To validate our numerical models, a series of three-dimensional physical experiments were carried out at the Hydraulic Laboratory of the Brunel University London (UK) in a 3D wave tank 2.40 m long, 2.60 m wide, and 0.60 m high (Figs. 1 and 2). To mitigate experimental errors and enhance the reliability of our results, each physical experiment was conducted three times. The reported data in the manuscript reflects the average of these three trials, assuming no anomalous outliers, thus ensuring an accurate reflection of the experimental tests. One experiment was used for validation of our numerical models. The slope angle (α) and water depth (h) were 45° and 0.246 m, respectively for this experiment. The movement of the sliding mass was recorded by a digital camera with a sampling frequency of 120 frames per second, which was used to calculate the slide impact velocity (vs). The travel distance (D), defined as the distance from the toe of the sliding mass to the water surface, was D=0.045 m. The material of the solid block used in our study was concrete with a density of 2600 kg/m3. Table 2 provides detailed information on the dimensions and kinematics of this solid block used in our physical experiments.
Figure 1. The geometrical and kinematic parameters of a subaerial landslide tsunami. Parameters are: h, water depth; aM, maximum wave amplitude; α, slope angle;vs, slide velocity; ls, length of landslide; bs, width of landslide; s, thickness of landslide; SWL, still water level; D, travel distance (the distance from the toe of the sliding mass to the water surface); L, length of the wave tank; and W, width of the wave tank and H, is the hight of the wave tank
Figure 2. a Wave tank setup of the physical experiments of this study. b Numerical simulation setup for the FLOW-3D HYDRO Model. c The numerical set-up for the OpenFOAM model. The location of the physical wave gauge (represented by numerical gauge WG-3 in the numerical simulations) is at X = 1.03 m, Y = 1.21 m, and Z = 0.046 m. d Top view showing the locations of numerical wave gauges (WG-1, WG-2, WG-3, WG-4, WG-5)
Parameter, unit
Value/type
Slide width (bs), m
0.26
Slide length (ls), m
0.20
Slide thickness (s), m
0.10
Slide volume (V), m3
2.60 × 10–3
Specific gravity, (γs)
2.60
Slide weight (ms), kg
6.86
Slide impact velocity (vs), m/s
1.84
Slide Froude number (Fr)
1.18
Material
Concrete
Table 2 Geometrical and kinematic information of the sliding mass used for physical experiments in this study
We took scale effects into account during physical experiments by considering the study by Heller et al. (2008) who proposed a criterion for avoiding scale effects. Heller et al. (2008) stated that the scale effects can be negligible as long as the Weber number (W=ρgh2/σ; where σ is surface tension coefficient) is greater than 5.0 × 103 and the Reynolds number (R=g0.5h1.5/ν; where ν is kinematic viscosity) is greater than 3.0 × 105 or water depth (h) is approximately above 0.20 m. Considering the water temperature of approximately 20 °C during our experiments, the kinematic viscosity (ν) and surface tension coefficient (σ) of water become 1.01 × 10–6 m2/s and 0.073 N/m, respectively. Therefore, the Reynolds and Weber numbers were as R= 3.8 × 105 and W= 8.1 × 105, indicating that the scale effect can be insignificant in our experiments. To record the waves, we used a twin wire wave gauge provided by HR Wallingford (https://equipit.hrwallingford.com). This wave gauge was placed at X = 1.03 m, Y = 1.21 m based on the coordinate system shown in Fig. 2a.
2.2 Numerical Simulations
The numerical simulations in this work were performed employing two CFD packages FLOW-3D HYDRO, and OpenFOAM which have been widely used in industry and academia (e.g., Bayon et al., 2016; Jasak, 2009; Rauter et al., 2021; Romano et al., 2020a, b; Yin et al., 2015).
2.2.1 Governing Equations and Turbulent Models
2.2.1.1 FLOW-3D HYDRO
The FLOW-3D HYDRO solver is based on the fundamental law of mass, momentum and energy conservation. To estimate the influence of turbulent fluctuations on the flow quantities, it is expressed by adding the diffusion terms in the following mass continuity and momentum transport equations:
quation (1) is the general mass continuity equation, where u is fluid velocity in the Cartesian coordinate directions (x), Ax is the fractional area open to flow in the x direction, VF is the fractional volume open to flow, ρ is the fluid density, R and ξ are coefficients that depend on the choice of the coordinate system. When Cartesian coordinates are used, R is set to unity and ξ is set to zero. RDIF and RSOR are the turbulent diffusion and density source terms, respectively. Uρ=Scμ∗/ρ, in which Sc is the turbulent Schmidt number, μ∗ is the dynamic viscosity, and ρ is fluid density. RSOR is applied to model mass injection through porous obstacle surfaces.
The 3D equations of motion are solved with the following Navier–Stokes equations with some additional terms:
where t is time, Gx is accelerations due to gravity, fx is viscous accelerations, and bx is the flow losses in porous media.
According to Flow Science (2022), FLOW-3D HYDRO’s turbulence models differ slightly from other formulations by generalizing the turbulence production with buoyancy forces at non-inertial accelerations and by including the influence of fractional areas/volumes of the FAVOR method (Fractional Area-Volume Obstacle Representation) method. Here we use k–ω model for turbulence modelling. The k–ω model demonstrates enhanced performance over the k-ε and Renormalization-Group (RNG) methods in simulating flows near wall boundaries. Also, for scenarios involving pressure changes that align with the flow direction, the k–ω model provides more accurate simulations, effectively capturing the effects of these pressure variations on the flow (Flow Science, 2022). The equations for turbulence kinetic energy are formulated as below based on Wilcox’s k–ω model (Flow Science, 2022):
where kT is turbulent kinetic energy, PT is the turbulent kinetic energy production, DiffKT is diffusion of turbulent kinetic energy, GT is buoyancy production, β∗=0.09 is closure coefficient, and ω is turbulent frequency.
2.2.1.2 OpenFOAM
For the simulations conducted in this study, OpenFOAM utilizes the Volume-Averaged RANS equations (VARANS) to enable the representation of flow within porous material, treated as a continuous medium. The momentum equation incorporates supplementary terms to accommodate frictional forces from the porous media. The mass and momentum conservation equations are linked to the VOF equation (Jesus et al., 2012) and are expressed as follows:
where the gravitational acceleration components are denoted bygj. The term u¯i=1Vf∫Vf0ujdV represents the volume averaged ensemble averaged velocity (or Darcy velocity) component, Vf is the fluid volume contained in the average volumeV,τ is the surface tension constant (assumed to be 1 for the water phase and 0 for the air phase), and fσi is surface tension, defined as fσi=σκ∂α∂xi, where σ (N/m) is the surface tension constant and κ (1/m) is the curvature (Brackbill et al., 1992). μeff is the effective dynamic viscosity that is defined as μeff=μ+ρνt and takes into account the dynamic molecular (μ) and the turbulent viscosity effects (ρνt). νt is eddy viscosity, which is provided by the turbulence closure model. n is the porosity, defined as the volume of voids over total volume, and P∗=1Vf∫∂Vf0P∗dS is the ensemble averaged pressure in excess of hydrostatic pressure. The coefficient A accounts for the frictional force induced by laminar Darcy-type flow, B considers the frictional force under turbulent flow conditions, and c accounts for the added mass. These coefficients (A,B, and c) are defined based on the work of Engelund (1953) and later modified by Van Gent (1995) as given below:
where D50 is the mean nominal diameter of the porous material, KC is the Keulegan–Carpenter number, a and b are empirical nondimensional coefficients (see Lara et al., 2011; Losada et al., 2016) and γ = 0.34 is a nondimensional parameter as proposed by Van Gent (1995). The k-ω Shear Stress Transport (SST) turbulence is employed to capture the effect of turbulent flow conditions (Zhang & Zhang, 2023) with the enhancement proposed by Larsen and Fuhrman (2018) for the over-production of turbulence beneath surface waves. Boundary layers are modelled with wall functions. The reader is referred to Larsen and Fuhrman (2018) for descriptions, validations, and discussions of the stabilized turbulence models.
2.2.2 FLOW-3D HYDRO Simulation Procedure
In our specific case in this study, FLOW-3D HYDRO utilizes the finite-volume method to numerically solve the equations described in the previous Sect. 2.2.1.1, ensuring a high level of accuracy in the computational modelling. The use of structured rectangular grids in FLOW-3D HYDRO offers the advantages of easier development of numerical methods, greater transparency in their relation to physical problems, and enhanced accuracy and stability of numerical solutions. (Flow Science, 2022). Curved obstacles, wall boundaries, or other geometric features are embedded in the mesh by defining the fractional face areas and fractional volumes of the cells that are open to flow (the FAVOR method). The VOF method is employed in FLOW-3D HYDRO for accurate capturing of the free-surface dynamics (Hirt and Nichols 1981). This approach then is upgraded to method of the TruVOF which is a split Lagrangian method that typically produces lower cumulative volume error than the alternative methods (Flow Science, 2022).
For numerical simulation using FLOW-3D HYDRO, the entire flow domain was 2.60 m wide, 0.60 m deep and 2.50 m long (Fig. 2b). The specific gravity (γs) for solid blocks was set to 2.60 in our model, aligning closely with the density of the actual sliding mass, which was approximately determined in our physical experiments. The fluid medium was modelled as water with a density of 1000 kg/m3 at 20 °C. A uniform grid comprising of one single mesh plane was applied with a grid size of 0.005 m. The top, front and back of the mesh areas were defined as symmetry, and the other surfaces were of wall type with no-slip conditions around the walls.
To simulate turbulent flows, k-ω model was used because of its accuracy in modelling turbulent flows (Menter 1992). Landslide movement was replicated in simulations using coupled motion objects, which implies that the movement of landslides is based on gravity and the friction between surfaces rather than a specified motion in which the model should be provided by force and torques. The time intervals of the numerical model outputs were set to 0.02 s to be consistent with the actual sampling rates of our wave gauges in the laboratory. In order to calibrate the FLOW-3D HYDRO model, the friction coefficient is set to 0.45, which is consistent with the Coulombic friction measurements in the laboratory. The Courant Number (C=UΔtΔx) is considered as the criterion for the stability of numerical simulations which gives the maximum time step (Δt) for a prespecified mesh size (Δx) and flow speed (U). The Courant number was always kept below one.
2.2.3 OpenFOAM Simulation Procedure
OpenFOAM is an open-source platform containing several C++ libraries which solves both 3D Reynolds-Averaged Navier–Stokes equations (RANS) and Volume-Averaged RANS equations (VARANS) for two-phase flows (https://www.openfoam.com/documentation/user-guide). Its implementation is based on a tensorial approach using object-oriented programming techniques and the Finite Volume Method (McDonald 1971). In order to simulate the subaerial landslide-generated waves, the IHFOAM solver based on interFoam (Higuera et al., 2013a, 2013b), and the overset mesh framework method are employed. The implementation of the overset mesh method for porous mediums in OpenFOAM is described in Romano et al. (2020a, b) for submerged rigid and impermeable landslides.
The overset mesh technique, as outlined by Romano et al. (2020a, b), uses two distinct domains: a moving domain that captures the dynamics of the rigid landslide and a static background domain to characterize the numerical wave tank. The overlapping of these domains results in a composite mesh that accurately depicts complex geometrical transformations while preserving mesh quality. A porous media with a very low permeability (n = 0.001) was used to simulate the impermeable sliding surfaces. RANS equations were solved within the porous media. The Multidimensional Universal Limiter with Explicit Solution (MULES) algorithm is employed for solving the (VOF) equation, ensuring precision in tracking fluid interfaces. Simultaneously, the PIMPLE algorithm is employed for the effective resolution of velocity–pressure coupling in the Eqs. 7 and 8. A background domain was created to reproduce the subaerial landslide waves with dimensions 2.50 m (x-direction) × 2.60 m (y-direction) × 0.6 m (z-direction) (Fig. 2c). The grid size is set to 0.005 m for the background mesh. A moving domain was applied in an area of 0.35 m (x-direction) × 0.46 m (y-direction) × 0.32 m (z-direction) with a grid spacing of 0.005 m and applying a body-fitted mesh approach, which contains the rigid and impermeable wedges. Wall condition with No-slip is defined as the boundary for the four side walls (left, right, front and back, in Fig. 1). Also, a non-slip boundary condition is specified to the bottom, whereas the top boundary is defined as open. The experimental slide movement time series is used to model the landslide motion in OpenFOAM. The applied equation is based on the analytical solution by Pelinovsky and Poplavsky (1996) which was later elaborated by Watts (1998). The motion of a sliding rigid body is governed by the following equation:
where, m represents the mass of the landslide, s is the displacement of the landslide down the slope, t is time elapsed, g stands for the acceleration due to gravity, θ is the slope angle, Cf is the Coulomb friction coefficient, Cm is the added mass coefficient, m0 denotes the mass of the water displaced by the moving landslide, A is the cross-sectional area of the landslide perpendicular to the direction of motion, ρ is the water density, and Cd is the drag coefficient.
2.2.4 Mesh Sensitivity Analysis
In order to find the most efficient mesh size, mesh sensitivity analyses were conducted for both numerical models (Fig. 3). We considered the influence of mesh density on simulated waveforms by considering three mesh sizes (Δx) of 0.0025 m, 0.005 m and 0.010 m. The results of FLOW-3D HYDRO revealed that the largest mesh deviates 9% (Fig. 3a, Δx = 0.0100 m) from two other finer meshes. Since the simulations by FLOW-3D HYDRO for the finest mesh (Δx = 0.0025 m) do not show any improvements in comparison with the 0.005 m mesh, therefore the mesh with the size of Δx = 0.0050 m is used for simulations (Fig. 3a). A similar approach was followed for mesh sensitivity of OpenFOAM mesh grids. The mesh with the grid spacing of Δx = 0.0050 m was selected for further simulations since a satisfactory independence was observed in comparison with the half size mesh (Δx = 0.0025 m). However, results showed that the mesh size with the double size of the selected mesh (Δx = 0.0100 m) was not sufficiently fine to minimize the errors (Fig. 3b).
Figure 3. a, b Sensitivity of numerical simulations to the sizes of the mesh (Δx) for FLOW-3D HYDRO, and OpenFOAM, respectively. The location of the wave gauge 3 (WG-3) is at X = 1.03 m, Y = 1.21 m, and Z = -0.55 m (see Fig. 2d)
In terms of computational cost, the time required for 2 s simulations by FLOW-3D HYDRO is approximately 4.0 h on a PC Intel® Core™ i7-8700 CPU with a frequency of 3.20 GHz equipped with a 32 GB RAM. OpenFOAM requires 20 h to run 2 s of numerical simulation on 2 processors on a PC Intel® Core™ i9-9900KF CPU with a frequency of 3.60 GHz equipped with a 364 GB RAM. Differences in computational time for simulations run with FLOW-3D HYDRO and OpenFOAM reflect the distinct characteristics of each numerical methods, and the specific hardware setups.
2.2.5 Validation
We validated both numerical models based on our laboratory experimental data (Fig. 4). The following criterion was used to assess the level of agreement between numerical simulations and laboratory observations:
where ε is the mismatch error, Obsi is the laboratory observation values, Simi is the simulation values, and the mathematical expression |X| represents the absolute value of X. The slope angle (α), water depth (h) and travel distance (D) were: α = 45°, h = 0.246 m and D = 0.045 m in both numerical models, consistent with the physical model. We find the percentage error between each simulated data point and its corresponding observed value, and subsequently average these errors to assess the overall accuracy of the simulation against the observed time series. Our results revealed that the mismatch errors between physical experiments and numerical models for the FLOW-3D HYDRO and OpenFOAM are 8% and 18%, respectively, indicating that our models reproduce the measured waveforms satisfactorily (Fig. 4). The simulated waveform by OpenFOAM shows a minor mismatch at t = 0.76 s which resulted from a droplet immediately after the slide hits the water surface in the splash zone. In term of the maximum negative amplitude, the simulated waves by OpenFOAM indicates a relatively better performance than FLOW-3D HYDRO, whereas the maximum positive amplitude (aM) simulated by FLOW-3D HYDRO is closer to the experimental value. The recorded maximum positive amplitude in physical experiment is 0.022 m, whereas it is 0.020 m for FLOW-3D HYDRO and 0.017 m for OpenFOAM simulations. In acknowledging the deviations observed, it is pertinent to highlight that while numerical models offer robust insights, the difference in meshing techniques and the distinct computational methods to resolve the governing equations in FLOW-3D HYDRO and OpenFOAM have contributed to the variance. Moreover, the intrinsic uncertainties associated with the physical experimentation process, including the precision of wave gauges and laboratory conditions, are non-negligible factors influencing the results.
Figure 4. Validation of the simulated waves (brown line for FLOW-3D HYDRO and green line for OpenFOAM) using the laboratory-measured waves (black solid diamonds). This physical experiment was conducted for wave gauge 3 (WG-3) located at X = 1.03 m, Y = 1.21 m, and Z = -0.55 m (see Fig. 2d). Here, ε shows the errors between simulations and actual physical measurements using Eq. (13)
3 Results
Following the validations of the two numerical models (FLOW-3D HYDRO and OpenFOAM), a series of simulations were performed to compare the performances of these two CFD solvers. The generation process of landslide waves, waveforms, and velocity fields are considered as the basis for comparing the performance of the two models (Figs. 5, 6, 7 and 8).
Figure 5.Comparison between the simulated waveforms by FLOW-3D HYDRO (black) and OpenFOAM (red) at four different locations in the near-field zone (WG-1,2,4 and 5). WG is the abbreviation for wave gauge. The mismatch (Δ) between the two models at each wave gauge is calculated using Eq. (14)
Figure 6. Comparison of water surface elevations produced by solid-block subaerial landslides for the two numerical models FLOW-3D-HYDRO (a–c) and OpenFOAM (e–g) at different times
Figure 7. Snapshots of the simulations at different times for FLOW-3D HYDRO (a–c) and OpenFOAM (e–g) showing velocity fields (colour maps and arrows). The colormaps indicate water particle velocity in m/s, and the lines indicate the velocities of water particles
Figure 8. Comparison of velocity variations at (WG-3) for FLOW-3D HYDRO (light blue) and OpenFOAM (brown)
3.1 Comparison of Waveforms
Five numerical wave gauges were placed in our numerical models to measure water surface oscillations in the near-field zone (Fig. 5). These gauges offer an azimuthal coverage of 60° (Fig. 2d). Figure 5 reveals that the simulated waveforms from two models (FLOW-3D HYDRO and OpenFOAM) are similar. The highest wave amplitude (aM) is recorded at WG-3 for both models, whereas the lowest amplitude is recorded at WG-5 and WG-1 which can be attributed to the longer distances of these gauges from the source region as well as their lateral offsets, resulting in higher wave energy dissipation at these gauges. The sharp peaks observed in the simulated waveforms, such as the red peak between 0.8–1.0 s in Fig. 5a from OpenFOAM, the red peak between 0.6–0.8 s in Fig. 5b also from OpenFOAM, and the black peak between 1.4–1.6 s in Fig. 5d from FLOW-3D HYDRO, are due to the models’ spatial and temporal discretization. They reflect the sensitivity of the models to capturing transient phenomena, where the chosen mesh and time-stepping intervals are key factors in the models’ ability to track rapid changes in the flow field. To quantify the deviations of the two models from one another, we apply the following equation for mismatch calculation:
where Δ is the mismatch error, Sim1 is the simulation values from FLOW-3D HYDRO, Sim2 is the simulation values from OpenFOAM, and the mathematical expression |X| implies the absolute value of X. We calculate the percentage difference for each corresponding pair of simulation results, then take the mean of these percentage differences to determine the average deviation between the two simulation time series. Using Eq. (14), we found a deviation range from 9 to 11% between the two models at various numerical gauges (Fig. 5), further confirming that the two models give similar simulation results.
3.2 Three-Dimensional Vision of Landslide Generation Process by Numerical Models
A sequence of four water surface elevation snapshots at different times is shown in Fig. 6 for both numerical modes. In both simulations, the sliding mass travels a constant distance of 0.045 m before hitting the water surface at t = 0.270 s which induces an initial change in water surface elevation (Figs. 6a and e). At t = 0.420 s, the mass is fully immersed for both simulations and an initial dipole wave is generated (Figs. 6b and f). Based on both numerical models, the maximum positive amplitude (0.020 m for FLOW-3D HYDRO, and 0.017 m for OpenFOAM) is observed at this stage (Fig. 6). The maximum propagation of landslide-simulated waves along with more droplets in the splash zone could be seen at t = 0.670 s for both models (Fig. 6c and g). The observed distinctions in water surface elevation simulations as illustrated in Fig. 6 are rooted in the unique computational methodologies intrinsic to each model. In the OpenFOAM simulations, a more diffused water surface elevation profile is evident. Such diffusion is an outcome of the simulation’s intrinsic treatment of turbulent kinetic energy dissipation, aligning with the solver’s numerical dissipation characteristics. These traits are influenced by the selected turbulence models and the numerical advection schemes, which prioritize computational stability, possibly at the expense of interface sharpness. The diffusion in the wave pattern as rendered by OpenFOAM reflects the application of a turbulence model with higher dissipative qualities, which serves to moderate the energy retained during wave propagation. This approach can provide insights into the potential overestimation of energy loss under specific simulation conditions. In contrast, the simulations from FLOW-3D HYDRO depict a more localized wave pattern, indicative of a different approach to turbulent dissipation. This coherence in wave fronts is a function of the model’s specific handling of the air–water interface and its targeted representation of the energy dynamics resulting from the landslide’s interaction with the water body. They each have specific attributes that cater to different aspects of wave simulation fidelity, thereby contributing to a more comprehensive understanding of the phenomena under study.
3.3 Wave Velocity Analysis
We show four velocity fields at different times during landslide motion in Fig. 7 and one time series of velocity (Fig. 8) for both numerical models. The velocity varies in the range of 0–1.9 m/s for both models, and the spatial distribution of water particle velocity appears to be similar in both. The models successfully reproduce the complex wavefield around the landslide generation area, which is responsible for splashing water and mixing with air around the source zone (Fig. 7). The first snapshot at t = 0.270 s (Fig. 7a and e) shows the initial contact of the sliding mass with water surface for both numerical models which generates a small elevation wave in front of the mass exhibiting a water velocity of approximately 1.2 m/s. The slide fully immerses for the first time at t = 0.420 s producing a water velocity of approximately 1.5 m/s at this time (Fig. 7b and f). The last snapshot (t = 0.670 s) shows 1.20 s after the slide hits the bottom of the wave tank. Both models show similar patterns for the propagation of the waves towards the right side of the wave tank. The differences in water surface profiles close to the slope and solid block at t = 0.67 s, observed in the FLOW-3D HYDRO and OpenFOAM simulations (Figs. 6 and 7), are due to the distinct turbulence models employed by each (RNG and k-ω SST, respectively) which handle the complex interactions of the landslide-induced waves with the structures differently. Additionally, the methods of simulating landslide movement further contribute to this discrepancy, with FLOW-3D HYDRO’s coupled motion objects possibly affecting the waves’ initiation and propagation unlike OpenFOAM’s prescribed motion from experimental data. In addition to the turbulence models, the variations in VOF methodologies between the two models also contribute to the observed discrepancies.
For the simulated time series of velocity, both models give similar patterns and close maximum velocities (Fig. 8). For both models the WG-3 located at X = 1.03 m, Y = 1.21 m, and Z = − 0.55 m (Fig. 2d) were used to record the time series. WG-3 is positioned 5 mm above the wave tank bottom, ensuring that the measurements taken reflect velocities very close to the bottom of the wave tank. The maximum velocity calculated by FLOW-3D HYDRO is 0.162 m/s while it is 0.132 m/s for OpenFOAM, implying a deviation of approximately 19% from one another. Some oscillations in velocity records are observed for both models, but these oscillations are clearer and sharper for OpenFOAM. Although it is hard to see velocity oscillations in the FLOW-3D HYDRO record, a close look may reveal some small oscillations (around t = 0.55 s and 0.9 s in Fig. 8). In fact, velocity oscillations are expected due to the variations in velocity of the sliding mass during the travel as well as due to the interferences of the initial waves with the reflected wave from the beach. In general, it appears that the velocity time series of the two models show similar patterns and similar maximum values although they have some differences in the amplitudes of the velocity oscillations. The differences between the two curves are attributed to factors such as difference in meshing between the two models, turbulence models, as well as the way that two models record the outputs.
4 Discussions
An important step for CFD modelling in academic or industrial projects is the selection of an appropriate numerical model that can deliver the task with satisfactory performance and at a reasonable computational cost. Obviously, the major drivers when choosing a CFD model are cost, capability, flexibility, and accessibility. In this sense, the existing options are of two types as follows:
Commercial models, such as FLOW-3D HYDRO, which are optimised to solve free-surface flow problems, with customer support and an intuitive Graphical User Interface (GUI) that significantly facilitates meshing, setup, simulation monitoring, visualization, and post-processing. They usually offer high-quality customer support. Although these models show high capabilities and flexibilities for numerical modelling, they are costly, and thus less accessible.
Open-source models, such as OpenFOAM, which come without a GUI but with coded tools for meshing, setup, parallel running, monitoring, post-processing, and visualization. Although these models offer no customer support, they have a big community support and online resources. Open-source models are free and widely accessible, but they may not be necessarily always flexible and capable.
OpenFOAM provides freedom for experimenting and diving through the code and formulating the problem for a user whereas FLOW-3D HYDRO comes with high-level customer supports, tutorial videos and access to an extensive set of example simulations (https://www.flow3d.com/). While FLOW-3D-HYDRO applies a semi-automatic meshing process where users only need to input the 3D model of the structure, OpenFOAM provides meshing options for simple cases, and in many advanced cases, users need to create the mesh in other software (e.g., ANSYS) (Ariza et al., 2018) and then convert it to OpenFOAM format. Auspiciously, there are numerous online resources (https://www.openfoam.com/trainings/about-trainings), and published examples for OpenFOAM (Rauter et al., 2021; Romano et al., 2020a, b; Zhang & Zhang, 2023).
The capabilities of both FLOW-3D HYDRO and OpenFOAM to simulate actual, complex landslide-generated wave events have been showcased in significant case studies. The study by Ersoy et al. (2022) applied FLOW-3D HYDRO to simulate impulse waves originating from landslides near an active fault at the Çetin Dam Reservoir, highlighting the model’s capacity for detailed, site-specific modelling. Concurrently, the work by Alexandre Paris (2021) applied OpenFOAM to model the 2017 Karrat Fjord landslide tsunami events, providing a robust validation of OpenFOAM’s utility in capturing the dynamics of real-world geophysical phenomena. Both instances exemplify the sophisticated computational approaches of these models in aiding the prediction and analysis of natural hazards from landslides.
As for limitations of this study, we acknowledge that our numerical models are validated by one real-world measured wave time series. However, it is believed that this one actual measurement was sufficient for validation of this study because it was out of the scope of this research to fully validate the FLOW-3D HYDRO and OpenFOAM models. These two models have been fully validated by more actual measurements by other researchers in the past (e.g., Sabeti & Heidarzadeh, 2022b). It is also noted that some of the comparisons made in this research were qualitative, such as the 3D wave propagation snapshots, as it was challenging to develop quantitative comparisons for snapshots. Another limitation of this study concerns the number of tests conducted here. We fixed properties such as water depth, slope angle, and travel distance throughout this study because it was out of the scope of this research to perform sensitivity analyses.
5 Conclusions
We configured, calibrated, validated and compared two numerical models, FLOW-3D HYDRO, and OpenFOAM, using physical experiments in a 3D wave tank. These validated models were used to simulate subaerial solid-block landslides in the near-field zone. Our results showed that both models are fully compatible with investigating waves generated by subaerial landslides, although they use different approaches to simulate the phenomenon. The properties of solid-block, water depth, slope angle, and travel distance were kept constant in this study as we focused on comparing the performance of the two models rather than conducting a full sensitivity analysis. The findings are as follows:
Different settings were used in the two models for modelling landslide-generated waves. In terms of turbulent flow modelling, we used the Renormalization Group (RNG) turbulence model in FLOW-3D HYDRO, and k-ω (SST) turbulence model in OpenFOAM. Regarding meshing techniques, the overset mesh method was used in OpenFOAM, whereas the structured cartesian mesh was applied in FLOW-3D HYDRO. As for simulation of landslide movement, the coupled motion objects method was used in FLOW-3D HYDRO, and the experimental slide movement time series were prescribed in OpenFOAM.
Our modelling revealed that both models successfully reproduced the physical experiments. The two models deviated 8% (FLOW-3D HYDRO) and 18% (OpenFOAM) from the physical experiments, indicating satisfactory performances. The maximum water particle velocity was approximately 1.9 m/s for both numerical models. When the simulated waveforms from the two numerical models are compared with each other, a deviation of 10% was achieved indicating that the two models perform approximately equally. Comparing the 3D snapshots of the two models showed that there are some minor differences in reproducing the details of the water splash in the near field.
Regarding computational costs, FLOW-3D HYDRO was able to complete the same simulations in 4 h as compared to nearly 20 h by OpenFOAM. However, the hardware that were used for modelling were not the same; the computer used for the OpenFOAM model was stronger than the one used for running FLOW-3D HYDRO. Therefore, it is challenging to provide a fair comparison for computational time costs.
Overall, we conclude that the two models give approximately similar performances, and they are both capable of accurately modelling landslide-generated waves. The choice of a model for research or industrial projects may depend on several factors such as availability of local knowledge of the models, computational costs, accessibility and flexibilities of the model, and the affordability of the cost of a license (either a commercial or an open-source model).
Reference
Abadie, S., Morichon, D., Grilli, S., & Glockner, S. (2010). Numerical simulation of waves generated by landslides using a multiple-fluid Navier–Stokes model. Coastal Engineering, 57(9), 779–794. https://doi.org/10.1016/j.coastaleng.2010.04.002
Ariza, C., Casado, C., Wang, R.-Q., Adams, E., & Marugán, J. (2018). Comparative evaluation of OpenFOAM® and ANSYS® Fluent for the modeling of annular reactors. Chemical Engineering & Technology, 41(7), 1473–1483. https://doi.org/10.1002/ceat.201700455
Ataie-Ashtiani, B., & Najafi Jilani, A. (2007). A higher-order Boussinesq-type model with moving bottom boundary: Applications to submarine landslide tsunami waves. Pure and Applied Geophysics, 164(6), 1019–1048. https://doi.org/10.1002/fld.1354
Bayon, A., Valero, D., García-Bartual, R., & López-Jiménez, P. A. (2016). Performance assessment of OpenFOAM and FLOW-3D in the numerical modeling of a low Reynolds number hydraulic jump. Environmental Modelling & Software, 80, 322–335. https://doi.org/10.1016/j.envsoft.2016.02.018
Bellotti, G., & Romano, A. (2017). Wavenumber-frequency analysis of landslide-generated tsunamis at a conical island. Part II: EOF and modal analysis. Coastal Engineering, 128, 84–91. https://doi.org/10.1016/j.coastaleng.2017.07.008
Biscarini, C. (2010). Computational fluid dynamics modelling of landslide generated water waves. Landslides, 7(2), 117–124. https://doi.org/10.1007/s10346-009-0194-z
Brackbill, J. U., Kothe, D. B., & Zemach, C. (1992). A continuum method for modeling surface tension. Journal of computational physics, 100(2), 335–354.
Cecioni, C., Romano, A., Bellotti, G., Di Risio, M., & De Girolamo, P. (2011). Real-time inversion of tsunamis generated by landslides. Natural Hazards & Earth System Sciences, 11(9), 2511–2520. https://doi.org/10.5194/nhess-11-2511-2011
Cremonesi, M., Frangi, A., & Perego, U. (2011). A Lagrangian finite element approaches the simulation of water-waves induced by landslides. Computers & Structures, 89(11–12), 1086–1093.
Del Jesus, M., Lara, J. L., & Losada, I. J. (2012). Three-dimensional interaction of waves and porous coastal structures: Part I: Numerical model formulation. Coastal Engineering, 64, 57–72. https://doi.org/10.1016/J.COASTALENG.2012.01.008
Di Risio, M., De Girolamo, P., Bellotti, G., Panizzo, A., Aristodemo, F., Molfetta, M. G., & Petrillo, A. F. (2009). Landslide-generated tsunamis runup at the coast of a conical island: New physical model experiments. Journal of Geophysical Research: Oceans. https://doi.org/10.1029/2008JC004858
Engelund, F., & Munch-Petersen, J. (1953). Steady flow in contracted and expanded rectangular channels. La Houille Blanche, (4), 464–481.
Ersoy, H., Oğuz Sünnetci, M., Karahan, M., & Perinçek, D. (2022). Three-dimensional simulations of impulse waves originating from concurrent landslides near an active fault using FLOW-3D software: A case study of Çetin Dam Reservoir (Southeast Turkey). Bulletin of Engineering Geology and the Environment, 81(7), 267. https://doi.org/10.1007/s10064-022-02675-8
Flow Science. (2022). FLOW-3D HYDRO version 12.0 user’s manual. Santa Fe, NM, USA. Retrieved from https://www.flow3d.com/. 6 Aug 2023.
Fritz, H. M., Hager, W. H., & Minor, H. E. (2004). Near field characteristics of landslide generated impulse waves. Journal of waterway, port, coastal, and ocean engineering, 130(6), 287–302.
Fritz, H. M., Mohammed, F., & Yoo, J. (2009). Lituya bay landslide impact generated mega-tsunami 50th anniversary. In: Tsunami science four years after the 2004 Indian Ocean Tsunami (pp. 153–175). Birkhäuser Basel, Switzerland.
Grilli, S. T., Shelby, M., Kimmoun, O., Dupont, G., Nicolsky, D., Ma, G., Kirby, J. T., & Shi, F. (2017). Modelling coastal tsunami hazard from submarine mass failures: Effect of slide rheology, experimental validation, and case studies off the US East Coast. Natural Hazards, 86(1), 353–391. https://doi.org/10.1007/s11069-016-2692-3
Grilli, S. T., & Watts, P. (2005). Tsunami generation by submarine mass failure. I: Modelling, experimental validation, and sensitivity analyses. Journal of Waterway, Port, Coastal, and Ocean Engineering, 131(6), 283–297. https://doi.org/10.1061/(ASCE)0733-950X
Grilli, S. T., Zhang, C., Kirby, J. T., Grilli, A. R., Tappin, D. R., Watt, S. F. L., et al. (2021). Modeling of the Dec. 22nd, 2018, Anak Krakatau volcano lateral collapse and tsunami based on recent field surveys: Comparison with observed tsunami impact. Marine Geology. https://doi.org/10.1016/j.margeo.2021.106566
Heidarzadeh, M., Gusman, A., Ishibe, T., Sabeti, R., & Šepić, J. (2022). Estimating the eruption-induced water displacement source of the 15 January 2022 Tonga volcanic tsunami from tsunami spectra and numerical modelling. Ocean Engineering, 261, 112165. https://doi.org/10.1016/j.oceaneng.2022.112165
Heidarzadeh, M., Ishibe, T., Sandanbata, O., Muhari, A., & Wijanarto, A. B. (2020a). Numerical modeling of the subaerial landslide source of the 22 December 2018 Anak Krakatoa volcanic tsunami, Indonesia. Ocean Engineering, 195, 106733. https://doi.org/10.1016/j.oceaneng.2019.106733
Heidarzadeh, M., Putra, P. S., Nugroho, H. S., & Rashid, D. B. Z. (2020b). Field survey of tsunami heights and runups following the 22 December 2018 Anak Krakatau volcano tsunami, Indonesia. Pure and Applied Geophysics, 177, 4577–4595. https://doi.org/10.1007/s00024-020-02587-w
Heller, V., Bruggemann, M., Spinneken, J., & Rogers, B. D. (2016). Composite modelling of subaerial landslide–tsunamis in different water body geometries and novel insight into slide and wave kinematics. Coastal Engineering, 109, 20–41. https://doi.org/10.1016/j.coastaleng.2015.12.004
Heller, V., Hager, W. H., & Minor, H. E. (2008). Scale effects in subaerial landslide generated impulse waves. Experiments in Fluids, 44(5), 691–703. https://doi.org/10.1007/s00348-007-0427-7
Heller, V., & Spinneken, J. (2013). Improved landslide-tsunami prediction: Effects of block model parameters and slide model. Journal of Geophysical Research: Oceans, 118(3), 1489–1507. https://doi.org/10.1002/jgrc.20099
Higuera, P., Lara, J. L., & Losada, I. J. (2013a). Realistic wave generation and active wave absorption for Navier–Stokes models: Application to OpenFOAM®. Coastal Engineering, 71, 102–118. https://doi.org/10.1016/j.coastaleng.2012.07.002
Higuera, P., Lara, J. L., & Losada, I. J. (2013b). Simulating coastal engineering processes with OpenFOAM®. Coastal Engineering, 71, 119–134. https://doi.org/10.1016/j.coastaleng.2012.06.002
Hirt, C.W. and Nichols, B.D., 1981. Volume of fluid (VOF) method for the dynamics of free boundaries. Journal of computational physics, 39(1), 201–225.
Horrillo, J., Wood, A., Kim, G.-B., & Parambath, A. (2013). A simplified 3-D Navier–Stokes numerical model for landslide-tsunami: Application to the Gulf of Mexico. Journal of Geophysical Research, 118(12), 6934–6950. https://doi.org/10.1002/2012JC008689
Imamura, F., & Imteaz, M. A. (1995). Long waves in two-layers: Governing equations and numerical model. Science of Tsunami Hazards, 13(1), 3–24.
Jasak, H. (2009). OpenFOAM: Open source CFD in research and industry. International Journal of Naval Architecture and Ocean Engineering, 1(2), 89–94. https://doi.org/10.2478/IJNAOE-2013-0011
Kim, G. B., Cheng, W., Sunny, R. C., Horrillo, J. J., McFall, B. C., Mohammed, F., Fritz, H. M., Beget, J., & Kowalik, Z. (2020). Three-dimensional landslide generated tsunamis: Numerical and physical model comparisons. Landslides, 17(5), 1145–1161. https://doi.org/10.1007/s10346-019-01308-2
Kim, J., Pedersen, G. K., Løvholt, F., & LeVeque, R. J. (2017). A Boussinesq type extension of the GeoClaw model-a study of wave breaking phenomena applying dispersive long wave models. Coastal Engineering, 122, 75–86. https://doi.org/10.1016/j.coastaleng.2017.01.005
Kirby, J. T., Grilli, S. T., Horrillo, J., Liu, P. L. F., Nicolsky, D., Abadie, S., Ataie-Ashtiani, B., Castro, M. J., Clous, L., Escalante, C., Fine, I., et al. (2022). Validation and inter-comparison of models for landslide tsunami generation. Ocean Modelling, 170, 101943. https://doi.org/10.1016/j.ocemod.2021.101943
Lara, J. L., Ruju, A., & Losada, I. J. (2011). Reynolds averaged Navier–Stokes modelling of long waves induced by a transient wave group on a beach. Proceedings of the Royal Society A: Mathematical, Physical and Engineering Sciences, 467(2129), 1215–1242.
Larsen, B. E., & Fuhrman, D. R. (2018). On the over-production of turbulence beneath surface waves in Reynolds-averaged Navier–Stokes models. Journal of Fluid Mechanics, 853, 419–460.
Lee, C. H., & Huang, Z. (2021). Multi-phase flow simulation of impulsive waves generated by a sub-aerial granular landslide on an erodible slope. Landslides, 18(3), 881–895. https://doi.org/10.1007/s10346-020-01560-z
Liu, P. L. F., Woo, S. B., & Cho, Y. S. (1998). Computer programs for tsunami propagation and inundation. Technical Report. Cornell University, Ithaca, New York.
Liu, F., Wu, T.-R., Raichlen, F., Synolakis, C. E., & Borrero, J. C. (2005). Runup and rundown generated by three-dimensional sliding masses. Journal of Fluid Mechanics, 536(1), 107–144. https://doi.org/10.1017/S0022112005004799
Losada, I. J., Lara, J. L., & del Jesus, M. (2016). Modeling the interaction of water waves with porous coastal structures. Journal of Waterway, Port, Coastal, and Ocean Engineering, 142(6), 03116003
Løvholt, F., Harbitz, C. B., & Haugen, K. (2005). A parametric study of tsunamis generated by submarine slides in the Ormen Lange/Storegga area off western Norway. In: Ormen Lange—An integrated study for safe field development in the Storegga submarine area (pp. 219–231). Elsevier. https://doi.org/10.1016/B978-0-08-044694-3.50023-8
Løvholt, F., Bondevik, S., Laberg, J. S., Kim, J., & Boylan, N. (2017). Some giant submarine landslides do not produce large tsunamis. Geophysical Research Letters, 44(16), 8463–8472
Løvholt, F. J. M. R., Griffin, J., & Salgado-Gálvez, M. A. (2022). Tsunami hazard and risk assessment on the global scale. Complexity in Tsunamis, Volcanoes, and their Hazards, 213–246
Lynett, P., & Liu, P. L. F. (2005). A numerical study of the run-up generated by three-dimensional landslides. Journal of Geophysical Research: Oceans. https://doi.org/10.1029/2004JC002443
Lynett, P. J., & Martinez, A. J. (2012). A probabilistic approach for the waves generated by a submarine landslide. Coastal Engineering Proceedings, 33, 15–15. https://doi.org/10.9753/icce.v33.currents.15
McDonald, P. W. (1971). The computation of transonic flow through two-dimensional gas turbine cascades (Vol. 79825, p. V001T01A089). American Society of Mechanical Engineers
Menter, F. R. (1992). Improved two-equation k-omega turbulence models for aerodynamic flows (No. A-92183). https://ntrs.nasa.gov/citations/19930013620
Panizzo, A., De Girolamo, P., Di Risio, M., Maistri, A., & Petaccia, A. (2005). Great landslide events in Italian artificial reservoirs. Natural Hazards and Earth System Sciences, 5(5), 733–740. https://doi.org/10.5194/nhess-5-733-2005
Paris, A. (2021). Comparison of landslide tsunami models and exploration of fields of application. Doctoral dissertation, Université de Pau et des Pays de l’Adour.
Paris, A., Heinrich, P., & Abadie, S. (2021). Landslide tsunamis: Comparison between depth-averaged and Navier–Stokes models. Coastal Engineering, 170, 104022. https://doi.org/10.1016/j.coastaleng.2021.104022
Pelinovsky, E., & Poplavsky, A. (1996). Simplified model of tsunami generation by submarine landslides. Physics and Chemistry of the Earth, 21(1–2), 13–17. https://doi.org/10.1016/S0079-1946(97)00003-7
Rauter, M., Hoße, L., Mulligan, R. P., Take, W. A., & Løvholt, F. (2021). Numerical simulation of impulse wave generation by idealized landslides with OpenFOAM. Coastal Engineering, 165, 103815. https://doi.org/10.1016/j.coastaleng.2020.103815
Rauter, M., Viroulet, S., Gylfadóttir, S. S., Fellin, W., & Løvholt, F. (2022). Granular porous landslide tsunami modelling–the 2014 Lake Askja flank collapse. Nature Communications, 13(1), 678. https://doi.org/10.1038/s41467-022-28356-2
Romano, A., Bellotti, G., & Di Risio, M. (2013). Wavenumber–frequency analysis of the landslide-generated tsunamis at a conical island. Coastal Engineering, 81, 32–43. https://doi.org/10.1016/j.coastaleng.2013.06.007
Romano, A., Lara, J., Barajas, G., Di Paolo, B., Bellotti, G., Di Risio, M., Losada, I., & De Girolamo, P. (2020a). Tsunamis generated by submerged landslides: Numerical analysis of the near-field wave characteristics. Journal of Geophysical Research: Oceans, 125(7), e2020JC016157. https://doi.org/10.1029/2020JC016157
Romano, M., Ruggiero, A., Squeglia, F., Maga, G., & Berisio, R. (2020b). A structural view of SARS-CoV-2 RNA replication machinery: RNA synthesis, proofreading and final capping. Cells, 9(5), 1267.
Sabeti, R., & Heidarzadeh, M. (2022a). Numerical simulations of water waves generated by subaerial granular and solid-block landslides: Validation, comparison, and predictive equations. Ocean Engineering, 266, 112853. https://doi.org/10.1016/j.oceaneng.2022.112853
Sabeti, R., & Heidarzadeh, M. (2022b). Numerical simulations of tsunami wave generation by submarine landslides: Validation and sensitivity analysis to landslide parameters. Journal of Waterway, Port, Coastal, and Ocean Engineering, 148(2), 05021016. https://doi.org/10.1061/(ASCE)WW.1943-5460.0000694
Takabatake, T., Han, D. C., Valdez, J. J., Inagaki, N., Mäll, M., Esteban, M., & Shibayama, T. (2022). Three-dimensional physical modeling of tsunamis generated by partially submerged landslides. Journal of Geophysical Research: Oceans, 127(1), e2021JC017826. https://doi.org/10.1029/2021JC017826
Van Gent, M. R. A. (1995). Porous flows through rubble-mound material. Journal of waterway, port, coastal, and ocean engineering, 121(3), 176–181.
Wang, X., & Liu, P. L. F. (2006). An analysis of 2004 Sumatra earthquake fault plane mechanisms and Indian Ocean tsunami. Journal of Hydraulic Research, 44, 147–154. https://doi.org/10.1080/00221686.2006.9521671
Watts, P. (1998). Wavemaker curves for tsunamis generated by underwater landslides. Journal of Waterway, Port, Coastal, and Ocean Engineering, 124(3), 127–137. https://doi.org/10.1061/(ASCE)0733-950X(1998)124:3(127)
Yin, Y., Zhang, C., Imamura, F., Harris, J. C., & Li, Z. (2015). Numerical analysis on wave generated by the Qianjiangping landslide in Three Gorges Reservoir. China. Landslides, 12(2), 355–364. https://doi.org/10.1007/s10346-015-0564-7
Zaniboni, F., & Tinti, S. (2014). Numerical simulations of the 1963 Vajont landslide, Italy: application of 1D Lagrangian modelling. Natural hazards, 70, 567–592.
Zhang, C., & Zhang, M. (2023). Numerical investigation of solitary wave attenuation and mitigation caused by vegetation using OpenFOAM. Coastal Engineering Journal, 65(2), 198–216. https://doi.org/10.1080/21664250.2022.2163844
In this study, experimental investigations were conducted on rectangular side weirs with different widths and heights. Corresponding simulations were also performed to analyze hydraulic characteristics including the water surface profile, flow velocity, and pressure. The relationship between the discharge coefficient and the Froude number, as well as the ratios of the side weir height and width to upstream water depth, was determined. A discharge formula was derived based on a dimensional analysis. The results demonstrated good agreement between simulated and experimental data, indicating the reliability of numerical simulations using FLOW-3D software (version 11.1). Notably, significant fluctuations in water surface profiles near the side weir were observed compared to those along the center line or away from the side weir in the main channel, suggesting that the entrance effect of the side weir did not propagate towards the center line of the main channel. The proposed discharge formula exhibited relative errors within 10%, thereby satisfying the flow measurement requirements for small channels and field inlets.
1. Introduction
Sharp crested weirs are used to obtain discharge in open channels by solely measuring the water head upstream of the water. Side weirs, as a kind of sharp-crested weir, are extensively used for flow measurement, flow diversion, and flow regulation in open channels. Side weirs can be placed directly in the channel direction or field inlet, without changing the original structure of the channel. Thus, side weirs have certain advantages in the promotion and application of flow measurement facilities in small channels and field inlets. The rectangular sharp-crested weir is the most commonly available, and many scholars have conducted research on it. Research on side weirs started in 1934. De Marchi studied the side weir in the rectangular channel and derived the theoretical formula based on the assumption that the specific energy of the main flow section of the rectangular channel in the side weir section was constant [1]. Ackers discussed the existing formulas for the prediction of the side weir discharge coefficient [2]. Chen concluded that the momentum theorem was more suitable for the analytical calculation of the side weir based on the experimental data [3]. Based on previous theoretical research, more and more scholars began to carry out experimental research on side weirs. Uyumaz and Muslu conducted experiments under subcritical and supercritical flow regimes and derived expressions for the side weir discharge and water surface profiles for these regimes by comparing them with experimental results [4]. Borghei et al. developed a discharge coefficient equation for rectangular side weirs in subcritical flow [5]. Ghodsian [6] and Durga and Pillai [7] developed a discharge coefficient equation of rectangular side weirs in supercritical flow. Mohamed proposed a new approach based on the video monitoring concept to measure the free surface of flow over rectangular side weirs [8]. Durga conducted experiments on rectangular side weirs of different lengths and sill heights and discussed the application of momentum and energy principles to the analysis of spatially varied flow under supercritical conditions. The results showed that the momentum principle was fitting better [7]. Omer et al. obtained sharp-crested rectangular side weirs discharge coefficients in the straight channel by using an artificial neural network model for a total of 843 experiments [9]. Emiroglu et al. studied water surface profile and surface velocity streamlines, and developed a discharge coefficient formula of the upstream Froude number, the ratios of weir length to channel width, weir length to flow depth, and weir height to flow depth [10]. Other investigators [11,12,13,14] have conducted experiments to study flow over rectangular side weirs in different flow conditions. Numerous studies have been conducted in laboratories to this day. Compared to experimental methods, the numerical simulation method has many attractive advantages. We can easily obtain a wide range of hydraulic parameters of side weirs using numerical simulation methods, without investing a lot of manpower and resources. In addition, we can conduct small changes in inlet condition, outlet condition, and geometric parameters, and study their impact on the flow characteristics of side weirs. Therefore, with the development and improvement of computational fluid dynamics, the numerical simulation method has begun to be widely applied on side weirs. Salimi et al. studied the free surface changes and the velocity field along a side weir located on a circular channel in the supercritical regime by numerical simulation [15]. Samadi et al. conducted a three-dimensional simulation on rectangular sharp-crested weirs with side contraction and without side contraction and verified the accuracy of numerical simulation compared with the experimental results [16]. Aydin investigated the effect of the sill on rectangular side weir flow by using a three-dimensional computational fluid dynamics model [17]. Azimi et al. studied the discharge coefficient of rectangular side weirs on circular channels in a supercritical flow regime using numerical simulation and experiments [18]. The discharge coefficient over the two compound side weirs (Rectangular and Semi-Circle) was modeled by using the FLOW-3D software to describe the flow characteristics in subcritical flow conditions [19]. Safarzadeh and Noroozi compared the hydraulics and 3D flow features of the ordinary rectangular and trapezoidal plan view piano key weirs (PKWs) using two-phase RANS numerical simulations [20]. Tarek et al. investigated the discharge performance, flow characteristics, and energy dissipation over PK and TL weirs under free-flow conditions using the FLOW-3D software [21]. As evident from the aforementioned, the majority of studies have primarily focused on determining the discharge coefficient, while comparatively less attention has been devoted to investigating the hydraulic characteristics of rectangular side weirs. Numerical simulations were conducted on different types of side weirs, including compound side weirs and piano key weirs, in different cross-section channels under different flow regimes. It is imperative to derive the discharge formula and investigate other crucial flow parameters such as depth, velocity, and pressure near side weirs for their effective implementation in water measurement. In this study, a combination of experimental and numerical simulation methods was employed to examine the relationship between the discharge coefficient and its influencing factors; furthermore, a dimensionless analysis was utilized to derive the discharge formula. Additionally, water surface profiles near side weirs and pressure distribution at the bottom of the side channel were analyzed to assess safety operation issues associated with installing side weirs.
2. Principle of Flow Measurement
Flow discharge over side weirs is a function of different dominant physical and geometrical quantities, which is defined as
where Q is flow discharge over the side weir, b is the side weir width, B is the channel width, P is the side weir height, v is the mean velocity, h1 is water depth upstream the side weir in the main channel, g is the gravitational acceleration, μ is the dynamic viscosity of fluid, ρ is fluid density, and i is the channel slope (Figure 1).
Figure 1. Definition sketch of parameters of rectangular side weir under subcritical flow. Note: h1 and h2 represent water depth upstream and downstream of the side weir in the main channel, respectively; y1 and y2 represent weir head upstream and downstream of the side weir in the main channel, respectively.
In experiments when the upstream weir head was over 30 mm, the effects of surface tension on discharge were found to be minor [22]. The viscosity effect was far less than the gravity effect in a turbulent flow. Hence μ and σ were excluded from the analysis [23,24]. In addition, the channel width, the channel slope, and the fluid density were all constant, so the discharge formula can be simplified as:
According to the Buckingham π theorem, the following relationship among the dimensionless parameters is established:
Selected h1 and g as basic fundamental quantities, and the remaining physical quantities were represented in terms of these fundamental quantities as follows:
In which
Based on dimensional analysis, the following equations were derived.
Namely
So the discharge formula can be simplified as:
In a sharp-crested weir, discharge over the weir is proportional to 𝐻1.51H11.5 (H1 is the upstream total head above the crest, namely H1 = y1 + v2/2 g), so Equation (6) can be transformed as follows:
Consequently, the discharge formula over rectangular side weirs is defined as follows, in which 𝑚=𝑓(𝑏ℎ1m=f(bh1,𝑃ℎ1,𝐹𝑟1)Ph1,Fr1). Parameter m represents the dimensionless discharge coefficient. Parameter Fr1 represents the Froude number at the upstream end of the side weir in the main channel.
3. Experiment Setup
The experimental setup contained a storage reservoir, a pumping station, an electromagnetic flow meter, a control valve, a stabilization pond, rectangular channels, a side weir, and a sluice gate. The layout of the experimental setup is shown in Figure 2. Water was supplied from the storage reservoir using a pump. The flow discharge was measured with an electromagnetic flow meter with precision of ±3‰. Water depth was measured with a point gauge with an accuracy of ±0.1 mm. The flow velocity was measured with a 3D Acoustic Doppler Velocimeter (Nortek Vectrino, manufactured by Nortek AS in Rud, Norway). In order to eliminate accidental and human error, multiple measurements of the water depth and flow velocity at the same point were performed and the average values were used as the actual water depth and flow velocity of the point. The main and side channels were both rectangular open channels measuring 47 cm in width and 60 cm in height. The geometrical parameters of rectangular side weirs are shown in Table 1.
Figure 2. Layout of the test system.
Table 1. The geometrical parameters of rectangular side weirs.
When water passes through a side weir, its quality point is affected not only by gravity but also by centrifugal inertia force, leading to an inclined water surface within that particular cross-section before reaching the weir. In order to examine water profiles adjacent to side weirs, cross-sectional measurements were conducted at regular intervals of 12 cm both upstream and downstream of each side weir, denoted as sections ① to ⑩, respectively. Measuring points were positioned near the side weir (referred to as “Side I”), along the center line of the main channel (referred to as “Side II”), and far away from the side weir (referred to as “Side III”) for each cross-section. The schematic diagram illustrating these measuring points is presented in Figure 3.
Figure 3. Schematic diagram of measurement points.
4. Numerical Simulation Settings
4.1. Mathematical Model
4.1.1. Governing Equations
Establishing the controlling equations is a prerequisite for solving any problem. For the flow analysis problem of water flowing over a side weir in a rectangular channel, assuming that no heat exchange occurs, the continuity equation (Equation (9)) and momentum equation (Equation (10)) can be used as the controlling equations as follows:
The continuity equation:
Momentum equation:
where: ρ is the fluid density, kg/m3; t is time, s; ui, uj are average flow velocities, u1, u2, u3 represent average flow velocity components in Cartesian coordinates x, y, and z, respectively, m/s; μ is dynamic viscosity of fluid, N·s/m2; p is the pressure, pa; Si is the body force, S1 = 0, S2 = 0, S3 = −ρg, N [24].
4.1.2. RNG k-ε Model
The water flow in the main channel is subcritical flow. When the water flows through the side weir, the flow line deviates sharply, the cross section suddenly decreases, and due to the blocking effect of the side weir, the water reflects and diffracts, resulting in strong changes in the water surface and obvious three-dimensional characteristics of the water flow [25]. Therefore the RNG k–ε model is selected. The model can better handle flows with greater streamline curvature, and its corresponding k and ε equation is, respectively, as follows:
where: k is the turbulent kinetic energy, m2/s2; μeff is the effective hydrodynamic viscous coefficient; Gk is the generation item of turbulent kinetic energy k due to gradient of the average flow velocity; C∗1εC1ε*, C2ε are empirical constants of 1.42 and 1.68, respectively; ε is turbulence dissipation rate, kg·m2/s2.
4.1.3. TruVOF Model
Because the shape of the free surface is very complex and the overall position is constantly changing, the fluid flow phenomenon with a free surface is a typical flow phenomenon that is difficult to simulate. The current methods used to simulate free surfaces mainly include elevation function method, the MAC method [26] and the VOF (Volume of Fluid) method [27]. The VOF method is a method proposed by Hirt and Nichols to deal with the complex motion of the free surface of a fluid, which can describe all the complexities of the free surface with only one function. The basic idea of the method is to define functions αw and αa, which represent the volume percentage of the calculation area occupied by water and air, respectively. In each unit cell, the sum of the volume fractions of water and air is equal to 1, i.e.,
The TruVOF calculation method can accurately track the change of free liquid level and accurately simulate the flow problems with free interface. Its equation is:
where: u_¯m is the average velocity of the mixture; t is the time; F is the volume fraction of the required fluid.
4.2. Parameter Setting and Boundary Conditions
To streamline the iterative calculation and minimize simulation time, we selected a main channel measuring 7.5 m in length and a side channel measuring 2.5 m in length for simulation. Three-dimensional geometrical models were developed using the software AutoCAD (version 2016-Simplified Chinese). The spatial domain was meshed using a constructed rectangular hexahedral mesh and each cell size was 2 cm. A volume flow rate was set in the channel inlet with an auto-adjusted fluid height. An outflow–outlet condition was positioned at the end of the side channel. A symmetry boundary condition was set in the air inlet at the top of the model, which represented that no fluid flows through the boundary. The lower Z (Zmin) and both of the side boundaries were treated as a rigid wall (W). No-slip conditions were applied at the wall boundaries. Figure 4 illustrates these boundary conditions.
Figure 4. Diagram of boundary conditions.
5. Results
5.1. Water Surface Profiles
Water surface profiles were crucial parameters for selecting water-measuring devices. Upon analyzing the consistent patterns observed in different conditions, one specific condition was chosen for further analysis. To validate the reliability of numerical simulation, measured and simulated water depths of rectangular side weirs with different widths and heights at a discharge rate of 25 L/s were extracted for comparison (Table 2 and Figure 5). The results in Table 2 and Figure 5 indicate a maximum absolute relative error value of 9.97% and all absolute relative error values within 10%, demonstrating satisfactory agreement between experimental and simulated results.
Figure 5. Comparison between measured and simulated flow depth.
P/cm
Section Position
b = 20 cm
b = 30 cm
b = 40 cm
b = 47 cm
hm/cm
hs/cm
R/%
hm/cm
hs/cm
R/%
hm/cm
hs/cm
R/%
hm/cm
hs/cm
R/%
7
④
21.49
19.4
9.73
17.74
16.9
4.74
16.07
14.51
9.71
13.79
12.50
9.35
④′
20.48
19.05
6.98
17.78
16.14
9.22
15.69
14.31
8.80
⑥
20.71
19.02
8.16
17.82
16.31
8.47
15.92
14.53
8.73
15.23
13.80
9.39
⑧′
22.00
20.22
8.09
18.27
16.74
8.37
16.59
14.96
9.83
⑧
22.37
20.17
9.83
17.73
16.80
5.25
16.27
15.08
7.31
15.36
14.36
6.51
10
④
24.15
22.6
6.42
19.96
18.84
5.61
19.03
18.58
2.36
16.83
15.85
5.82
④′
24.21
22.05
8.92
19.49
18.19
6.67
18.75
18.35
2.13
⑥
24.01
21.78
9.29
19.65
18.34
6.67
18.95
18.63
1.69
17.52
16.09
8.16
⑧′
24.88
22.4
9.97
20.65
19.21
6.97
20.12
19.29
4.13
⑧
24.03
22.96
4.45
21.16
19.34
8.60
19.71
19.43
1.42
18.39
17.36
5.60
15
④
28.85
27.56
4.47
25.86
24.09
6.84
24.05
21.89
8.98
22.73
20.80
8.49
④′
28.49
26.97
5.34
25.19
23.84
5.36
23.42
21.46
8.37
⑥
28.85
26.98
6.48
25.72
23.99
6.73
23.23
21.82
6.07
23.10
21.05
8.87
⑧′
28.96
27.30
5.73
26.38
24.19
8.30
24.18
22.27
7.90
⑧
29.18
27.96
4.18
26.57
24.54
7.64
24.57
22.33
9.12
23.20
21.10
9.05
20
④
33.29
32.34
2.85
30.63
29.02
5.26
28.49
26.87
5.69
26.99
25.81
4.37
④′
33.14
31.95
3.59
29.75
28.62
3.80
28.11
26.79
4.70
⑥
33.32
31.79
4.59
30.04
28.45
5.29
28.99
26.86
7.35
27.42
26.72
2.55
⑧′
34.02
32.39
4.79
30.69
28.95
5.67
29.59
27.25
7.91
⑧
34.62
32.84
5.14
31.44
29.29
6.84
29.51
27.31
7.46
28.21
27.00
4.29
Table 2. Comparison of measured and simulated water depths on Side I of each side weir at a discharge of 25 L/s
Due to the diversion caused by the side weir, there was a rapid variation in flow near the side weir in the main channel. In order to investigate the impact of the side weir on water flow in the main channel, water surface profiles on Side I, Side II, and Side III were plotted with a side weir width and height both set at 20 cm at a discharge rate of 25 L/s (Figure 6). As depicted in Figure 6, within a certain range of the upstream end of the main channel, water depths on Side I, Side II, and Side III were nearly equal with almost horizontal profiles. As the distance between the location of water flow and the upstream end of the weir crest decreased gradually, there was a gradual decrease in water depth on Side I along with an inclined trend in its corresponding profile; however, both Side II and Side III still maintained almost horizontal profiles. When approaching closer to the side weir area with flowing water, there was an evident reduction in water depth on Side I accompanied by a significant downward trend visible across an expanded decline range. The minimum point occurred near the upstream end of the weir crest before gradually increasing again towards downstream sections. At the crest section of the side weir, there is an upward trend observed in the water surface. The water surface tended to stabilize downstream of the main channel within a certain range from the downstream end of the weir crest. There was no significant change in the water surface profiles of Side Ⅱ and Side Ⅲ in the crest section. It can be inferred that the side weir entrance effect occurred only between Side Ⅰ and Side Ⅱ. M. Emin reported the same pattern [10].
Figure 6. Water surface profiles on Side I, Side II, and Side III with a side weir width of 20 cm and height of 15 cm at a discharge of 25 L/s.
For a more accurate study on the entrance effect of the side weir on the Water Surface Profile (WSP) for Side I; a comparative analysis conducted using different widths but the same height (15 cm) at a discharge rate of 25 L/s is presented through Figure 7, Figure 8, Figure 9 and Figure 10.
Figure 7. Water surface profile on Side Ⅰ with a side weir width of 20 cm and height of 15 cm at a discharge of 25 L/s.
Figure 8. Water surface profile on Side Ⅰ with a side weir width of 30 cm and height of 15 cm at a discharge of 25 L/s.
Figure 9. Water surface profile on Side Ⅰ with a side weir width of 40 cm and height of 15 cm at a discharge of 25 L/s.
Figure 10. Water surface profile on Side Ⅰ with a side weir width of 47 cm and height of 15 cm at a discharge of 25 L/s.
According to Figure 7, Figure 8, Figure 9 and Figure 10, the water depth upstream of the main channel started to decrease as it approached the upstream end of the weir crest and then gradually increased at the weir crest section. In other words, the water surface profile exhibited a backwater curve along the length of the weir crest. The water depth remained relatively stable downstream of the main channel within a certain range from the downstream end of the weir crest. Additionally, there was a higher water depth downstream of the main channel compared to that upstream of the main channel. Furthermore, an increase in the width of the side weir led to a gradual reduction in fluctuations on its water surface.
5.2. Velocity Distribution
The law of flow velocity distribution near the side weir is the focus of research and analysis, so the simulated and measured values of flow velocity near the side weir were compared and analyzed. Take the discharge of 25 L/s, the height of 15 cm, and the width of 30 cm of the side weir as an example to illustrate. Figure 11 shows the measured and simulated velocity distribution in the x-direction of cross-section ④. As can be seen from Figure 11, the diagrams of the measured and simulated velocity distribution were relatively consistent, and the maximum absolute relative error between the measured and simulated values at the same measurement point was 9.37%, and the average absolute relative error was 3.97%, which indicated a satisfactory agreement between the experimental and simulated results.
Figure 11. Velocity distribution in the x-direction of section ④: when the discharge is 25 L/s, the height of the side weir is 15 cm and the width of the side weir is 30 cm. (a) Measured velocity distribution; (b) Simulated velocity distribution.
From Figure 11, it can be seen that the flow velocity gradually increased from the bottom of the channel towards the water surface in the Z-direction, and the flow velocity gradually increased from Side Ⅲ to Side Ⅰ in the Y-direction. The maximum flow velocity occurred near the weir crest.
Figure 12 shows the distribution of flow velocity at different depths (z/P = 0.3, z/P = 0.8, z/P = 1.6) with a side weir width of 30 cm and height of 15 cm at a discharge of 25 L/s. The water flow line began to bend at a certain point upstream of the main channel, and the closer it was to the upstream end of the weir crest, the greater the curvature. The maximum curvature occurred at the downstream end of the weir crest. The flow patterns at the bottom, near the side weir crest, and above the side weir crest were significantly different. There was a reverse flow at the bottom of the main channel, where the forward and reverse flows intersect, resulting in a detention zone. The maximum flow velocity at the bottom layer occurred at the upstream end of the side weir crest. When the location of water flow approached the weir crest, the maximum flow velocity occurred at the upstream end of the weir crest. The maximum flow velocity on the water surface occurred at the downstream end of the weir crest. As the water depth decreased, the position of the maximum flow velocity gradually moved from the upstream end of the side weir to the downstream end of the side weir.
Figure 12. Distribution of flow velocity at different depths with a side weir width of 30 cm and height of 15 cm at a discharge of 25 L/s. (a) z/P = 0.3; (b) z/P = 0.8; (c) z/P = 1.6.
5.3. Side Channel Pressure Distribution
When water flowed through the side weir, an upstream water level was formed, resulting in a pressure zone at the junction with the side channel. This pressure zone led to increased water pressure on the floor of the side channel, which affected its stability and durability. In small channels or fields where erosion resistance is weak, excessive pressure can cause scour holes. Therefore, analyzing the pressure distribution in the side channel is necessary to select an appropriate height and width for the side weir that effectively reduces its impact on the bottom plate.
To investigate the impact of side weir width on hydraulic characteristics, pressure data was collected at a discharge rate of 25 L/s for side weirs with heights of 20 cm and widths ranging from 20 cm to 47 cm. The pressure distribution map was drawn, as shown in Figure 13.
Figure 13. Comparison of pressure distribution on the bottom plate of the side channel with different widths of side weirs when the discharge is 25 L/s and the height of side weirs is 20 cm. (a) P = 20 cm, b = 20 cm; (b) P = 20 cm, b = 30 cm; (c) P = 20 cm, b = 40 cm; (d) P = 20 cm, b = 47 cm.
As can be seen from Figure 13, the pressure at the bottom of the side channel decreased as the width of the side weir increased. This uneven distribution of water flow on the weir was caused by the sharp bending of water flow lines and the influence of centrifugal inertia force over a short period. After passing through the side weir, the water flow became symmetrically distributed with respect to the axis of the side channel, leaning towards the right bank at a certain distance. As we increased the width of the side weir, we noticed that its position gradually approached the side weir and maximum pressure decreased at this location where the water tongue formed due to flowing through it (Figure 13). For a constant height (20 cm) but varying widths (20 cm, 30 cm, 40 cm, and 47 cm), we measured maximum pressures at these positions as follows: 103,713 Pa, 103,558 Pa, 103,324 Pa, and 103,280 Pa, respectively. Consequently, increasing width reduced the impact on the side channel from water flowing through it while changing pressure distribution from concentration to dispersion in a vertical direction. In the practical application of side weirs, appropriate height should be selected based on the bottom plate’s capacity to withstand the pressure exerted by flowing water within channels.
To investigate how height affects the hydraulic characteristics of rectangular side weirs further (Figure 14), we extracted pressures on bottom plates when discharge was fixed at 25 L/s while varying heights were set as follows: 7 cm, 10 cm, 15 cm, and 20 cm, respectively.
Figure 14. Comparison of pressure distribution on the bottom plate of the side channel with different heights of side weirs when discharge is 25 L/s and the width of side weirs is 20 cm. (a) P = 7 cm, b = 20 cm; (b) P = 10 cm, b = 20 cm; (c) P = 15 cm, b = 20 cm; (d) P = 20 cm, b = 20 cm.
As shown in Figure 14, when the width of the side weir was constant, the pressure at the bottom of the side channel increased with the height of the side weir. As the height of the side weir increased, the water tongue formed by flow through the side weir gradually moved away from it in a downstream direction. In terms of vertical water flow, as the height of the side weir increased, the position of maximum pressure at which the water tongue falls shifted closer to the axis of the side channel from its right bank. Moreover, an increase in height resulted in higher maximum pressure at this falling point. For a constant width (20 cm) and varying heights (7 cm, 10 cm, 15 cm, and 20 cm), corresponding maximum pressures at this landing point were measured as 102,422 Pa, 102,700 Pa, 103,375 Pa, and 103,766 Pa, respectively. Consequently, increasing width led to a greater impact on both flow through and pressure distribution within the side channel; transforming it from scattered to concentrated along its lengthwise direction. Therefore, when applying such weirs practically one should select an appropriate width based on what pressure can be sustained by their respective channel bottom plates.
5.4. Discharge Coefficient
Based on dimensionless analysis, the influencing parameters of the discharge coefficient were obtained. To study the effect of parameters Fr1, b/h1, and P/h1, discharge coefficient values were plotted against Fr1, b/h1, and P/h1, shown in Figure 15, Figure 16 and Figure 17. The discharge coefficient decreased as parameters Fr1 and b/h1 increased. The discharge coefficient increased as parameter P/h1 increased. As Uyumaz and Muslu reported in a previous study, the variation of the discharge coefficient with respect to the Froude number showed a second-degree curve for a subcritical regime [4].
Figure 15. Variation of discharge coefficient values against Froude number.
Figure 16. Variation of discharge coefficient values against the percentage of the side weir width to the upstream flow depth over the side weir.
Figure 17. Variation of discharge coefficient values against the percentage of the side weir height to the upstream flow depth over the side weir.
Quantitative analysis between discharge coefficient values and parameters Fr1, b/h1, and P/h1 was conducted using data analysis software (IBM SPSS Statistics 19). The various coefficients obtained are shown in Table 3.
Model
Unstandardized Coefficients
Standardized Coefficients
t
Sig
B
Std. Error
Beta (β)
Constant
−1.294
0.155
−8.369
0.000
Fr1
3.430
0.286
3.401
12.013
0.000
b/h1
−0.004
0.004
−0.045
−0.944
0.348
P/h1
2.401
0.167
4.064
14.394
0.000
Table 3. Coefficient.
The value of t and Sig are the significance results of the independent variable, and the value of Sig corresponding to the value of t is less than 0.05, indicating that the independent variable has a significant impact on the dependent variable. Therefore, the values of Sig corresponding to the parameters Fr1 and P/h1 were less than 0.05, indicating that the parameters Fr1 and P/h1 have a significant impact on the discharge coefficient. On the contrary, the parameter b/h1 has less impact on the discharge coefficient. Therefore, quantitative analysis between discharge coefficient values and parameters Fr1, and P/h1 was conducted using data analysis software by removing factor b/h1. The model summary, ANOVA, and coefficient obtained are shown respectively in Table 4, Table 5 and Table 6. R and adjusted R square in Table 4 were approaching 1, which indicated the goodness of fit of the regression model was high. The value of Sig corresponding to the value of F in Table 5 was less than 0.05, which indicated that the regression equation was useful. The values of Sig corresponding to the parameters Fr1 and P/h1 in Table 6 were less than 0.05, indicating that the parameters Fr1 and P/h1 have a significant impact on the discharge coefficient.
Model
R
R Square
Adjusted R Square
Std. Error of the Estimate
1
0.913 a
0.833
0.829
0.03232
Table 4. Model Summary b. Note: a. Predictors:(Constant), Fr1, P/h1; b. Discharge coefficient.
Model
Sum of Squares
df
Mean Square
F
Sig
1
Regression
0.402
2
0.201
192.545
0.000 a
Residual
0.080
77
0.001
Total
0.483
79
Table 5. ANOVA b. Note: a. Predictors:(Constant), Fr1, P/h1; b. Discharge coefficient.
Model
Unstandardized Coefficients
Standardized Coefficients
t
Sig
B
Std. Error
Beta (β)
Constant
−1.326
0.151
−8.796
0.000
Fr1
3.479
0.281
3.449
12.396
0.000
P/h1
2.427
0.164
4.108
14.765
0.000
Table 6. Coefficient a. Note: a. Predictors:(Constant), Fr1, P/h1.
Based on the above analysis, the flow coefficient formula has been obtained, shown as follows:
Discharge formula were obtained by substituting Equation (15) into Equation (12), as shown in Equation (16).
where Q ∈ [0.006, 0.030], m3/s; b ∈ [0.20, 0.47], m; P ∈ [0.07, 0.20], m.
Figure 18 showed the measured discharge coefficient values with those calculated from discharge formulas in Table 3. The scatter of the data with respect to perfect line was limited to ±10%.
Figure 18. Comparison of the measured discharge coefficient values with those calculated from discharge formulas in Table 3.
6. Discussions
Determining water surface profile near the side weir in the main channel is one of the tasks of hydraulic calculation for side weirs. As the water flows through the side weir, discharge in the main channel is gradually decreasing, namely dQ/ds<0. According to the Equation (17) derived from Qimo Chen [3], it can be inferred that the value of 𝑑ℎ/𝑑𝑠 is greater than zero in subcritical flow (Fr < 1), that is, the water surface profile near the side weir in the main channel is a backwater curve. Due to the side weir entrance effect at the upstream end, water surface profiles drop slightly at the upstream end of the side weir crest, as EI-Khashab [28] and Emiroglu et al. [29] reported in previous experimental studies.
In this study, the water surface profile exhibited a backwater curve along the length of the weir crest. Therefore, during side weir application, it is crucial to ensure that downstream water levels do not exceed the highest water level of the channel.
The head on the weir is one of the important factors that flow over side weirs depends on. At the same time, the head depends on the water surface profile near the side weir in the main channel. Therefore, further research on the quantitative analysis of water surface profile needs to be conducted. Mohamed Khorchani proposed a new approach based on the video monitoring concept to measure the free surface of flow over side weirs. It points out a new direction for future research [8].
The maximum flow velocity, a key parameter in assessing the efficiency of a weir, occurs at the upstream end of the weir crest, typically near the crest. This is attributed to the convergence of the flow as it approaches the crest, resulting in a significant increase in velocity. It was found that in this study the minimum flow velocity occurred at the bottom of the main channel away from the side weir. Under such conditions, the accumulation of sediments could lead to siltation, which in turn can affect the accuracy of flow measurement through side weirs. This is because the presence of sediments can alter the flow patterns and cause errors in the measurement. Therefore, it becomes crucial to explore methods to optimize the selection of side weirs in order to minimize or eliminate the effects of sedimentation on flow measurement.
Pressure distribution plays a crucial role in ensuring structural safety for side weirs since small channels and field inlets have relatively limited pressure-bearing capacities. Therefore, it is important to select an appropriate geometrical parameter of rectangular side weirs based on their ability to withstand the pressure exerted on their bottom combined with pressure distribution data at the bottom of the side channel we have obtained in this study.
The discharge coefficient formula (Equation (15)), which incorporates Fr1 and P/h1, was derived based on dimensional analysis. However, it is worth noting that previous research has contradicted this formula by suggesting that the discharge coefficient solely depends on the Froude number. This conclusion can be observed in this study such as in Equations (18)–(23) in Table 7 of the manuscript [30,31,32,33,34,35], which clearly demonstrate the dependency of the discharge coefficient on the Froude number. In contrast, our derived discharge coefficient formula (Equation (15)) offers a more streamlined and simplified approach compared to Equation (25) [36] and Equation (29) [10]—making it easier to comprehend and apply—an advantageous feature particularly valuable in fluid dynamics where intricate calculations can be time-consuming. Furthermore, our derived discharge coefficient formula (Equation (15)) exhibits a broader application scope than that of Equation (24) [37] as shown in Table 8. Equation (26) [38] and Equation (27) [5] are specifically applicable under high flow discharge conditions. Conversely, our derived discharge coefficient formula (Equation (15)) is better suited for low-flow discharge conditions.
Table 7. Discharge coefficient formulas of rectangular side weirs presented in previous studies.
Discharge/(L·s−1)
Width of Side Weir/cm
Height of Side Weir/cm
Number of Formula
10~14
10~20
6~12
(24)
35–100
20~75
1~19
(26), (27)
6~30
20~47
7~20
(15)
Table 8. Application scope of discharge coefficient formulas.
In addition to the factors studied in the paper, factors such as the sediment content in the flow, the bottom slope, and the cross-section shape of the channel also have a certain impact on the hydraulic characteristics of the side weir. Further numerical simulation methods can be used to study the hydraulic characteristics and the influencing factors of the side weir. Water measurement facilities generally require high accuracy of water measurement, the flow of sharp-crested side weirs is complex, and the water surface fluctuates greatly. While conducting numerical simulations, experimental research on prototype channels is necessary to ensure the reliability of the results and provide reference for the body design and optimization of side weirs in small channels and field inlets.
7. Conclusions
This paper presents a comprehensive study that encompasses both experimental and numerical simulation research on rectangular side weirs of varying heights and widths within rectangular channels. A thorough analysis of the experimental and numerical simulation results has been conducted, leading to the derivation of several notable conclusions:
A comparative analysis was conducted on the measured and simulated values of water depth and flow velocity. Both of the maximum absolute relative errors were within 10%, which indicated that the numerical simulation of the side weir was feasible and effective.
The water surface profile exhibited a backwater curve along the length of the weir crest. The side weir entrance effect occurred only between Side Ⅰ and Side Ⅱ. This indicates that flow patterns and associated hydraulic forces at the weir entrance play a crucial role in determining water level distribution along the weir crest.
The maximum flow velocity of the cross-section at the upstream end of the weir crest occurred near the weir crest, while the minimum flow velocity occurred at the bottom of the main channel away from the side weir. As the water depth decreased, the position of the maximum flow velocity gradually moved from the upstream end of the side weir to the downstream end of the side weir.
When the height of the side weir remains constant, an increase in the width of the side weir leads to a decrease in pressure at the bottom of the side channel. Conversely, when the width of the side weir is kept constant, an increase in its height results in an increase in pressure at the bottom of the side channel. Therefore, during practical applications involving side weirs, it is crucial to select an appropriate weir width based on the maximum pressure that can be sustained by the channel’s bottom plate.
The discharge coefficient was found to depend on the upstream Froude number Fr1 and the percentage of the side weir height to the upstream flow depth over the side weir P/h1. The relationship between the discharge coefficient and parameters Fr1 and P/h1 was obtained using multiple regression analysis, which was of linear form and provided an easy means to estimate the discharge coefficient. The discharge formula is of high accuracy with relative errors within 10%, which met the water measurement accuracy requirements of small channels in irrigation areas.
Reference
De Marchi, G. Essay on the performance of lateral weirs. L’Energ Electr. 1934, 11, 849.
Ackers, P. A theoretical consideration of side weirs as storm water overflows. Proc. Inst. Civ. Eng. 1957, 6, 250–269.
Chen, Q.M.; Xie, P.Z.; Chen, Q.R. Experiment on hydraulic characteristics of side weir. J. Fuzhou Univ. 1979, 19, 26–29.
Uyumaz, A.; Muslu, Y. Flow over side weir in circular channels. ASCE J. Hydraul. Eng. 1985, 111, 144–160.
Borghei, M.; Jalili, M.R.; Ghodsian, M. Discharge coefficient for sharp-crested side weir in subcritical flow. ASCE J. Hydraul. Eng. 1999, 125, 1051–1056.
Ghodsian, M. Supercritical flow over rectangular side weir. Can. J. Civ. Eng. 2003, 30, 596–600.
Durga Rao, K.H.V.; Pillai, C.R.S. Study of Flow Over Side Weirs Under Supercritical Conditions. Water Resour Manag. 2008, 22, 131–143.
Khorchani, M.; Blanpain, O. Free surface measurement of flow over side weirs using the video monitoring concept. Flow Meas. Instrum. 2004, 15, 111–117.
Bilhan, O.; Emiroglu, M.E.; Kisi, O. Application of two different neural network techniques to lateral outflow over rectangular side weirs located on a straight channel. Adv. Eng. Softw. 2010, 41, 831–837.
Emiroglu, M.E.; Agaccioglu, H.; Kaya, N. Discharging capacity of rectangular side weirs in straight open channels. Flow Meas. Instrum. 2011, 22, 319–330.
Azza, N.; Al-Talib, A.N. Flow over oblique side weir. J. Damascus Univ. 2012, 28, 15–22.
Bagheri, S.; Kabiri-Samani, A.R.; Heidarpour, M. Discharge coefficient of rectangular sharp-crested side weirs part i: Traditional weir equation, Flow Measure. Instrumentation 2014, 35, 109–115.
Shariq, A.; Hussain, A.; Ansari, M.A. Lateral flow through the sharp crested side rectangular weirs in open channels. Flow Measure. Instrumentation 2018, 59, 8–17.
Li, G.D.; Shen, G.Y.; Li, S.S.; Lu, Q.N. Prediction Model of Side Weir Discharge Capacity Based on LS-SVM. J. Basic Sci. Eng. 2023, 4, 843–851.
Shabanlou, S.; Salimi, M.S. Free surface and velocity field in a circular channel along the side weir in supercritical flow conditions. Flow Meas. Instrum. 2014, 38, 108–115.
Samadi, A.; Arvanaghi, H.; Abbaspour, A. Three-Dimensional Simulation of Free Surface Flow over Rectangular Sharp crested Weirs. Int. J. Agric. Biosci. 2015, 4, 83–86.
Aydin, M.C. Investigation of a Sill Effect on Rectangular Side-Weir Flow by Using CFD. J. Irrig. Drain. Eng. 2016, 142.
Azimi, H.; Shabanlou, S.; Ebtehaj, I.; Bonakdari, H. Discharge Coefficient of Rectangular Side Weirs on Circular Channels. Int. J. Nonlinear Sci. Numer. Simul. 2016, 17, 391–399.
Khassaf, S.I.; Attiyah, A.N.; Al-Yousify, H.A. Experimental investigation of compound side weir with modeling using computational fluid dynamic. Energy Environ. 2018, 7, 169–178.
Safarzadeh, A.; Noroozi, B. 3D Hydrodynamics of Trapezoidal Piano Key Spillways. Int. J. Civ. Eng. 2017, 15, 89–101.
Selim, T.; Hamed, A.K.; Elkiki, M.; Eltarabily, M.G. Numerical investigation of flow characteristics and energy dissipation over piano key and trapezoidal labyrinth weirs under free-flow conditions. Model. Earth Syst. Environ. 2023, 10, 1253–1272.
Novak, P.; Cabelka, J. Models in Hydraulic Engineering; Pitman: London, UK, 1981.
Henderson, F.M. Open Channel Flow; Prentice-Hall: Englewood Cliffs, NJ, USA, 1966.
Wang, F.J. Computational Fluid Dynamics Analysis-Theory and Application of CFD; Tsinghua University Press: Beijing, China, 2004.
Zhu, Y.L.; Ma, X.Y.; Zhan, G.L.; Lv, J.W. Numerical simulation of flow in flat V-weir. Yellow River 2010, 32, 99–100.
Harlow, F.H.; Welch, J.E. Numberical calculation of time-dependent viscous incompressible flow of fluid with free surface. Phys. Fluids 1965, 8, 2182–2189.
Hirt, C.W.; Nichols, B.D. Volume of fluid (VOF) method for dynamics of free boundaries. Phys. Fluids 1981, 39, 201–221.
El-Khashab, A.M.M. Hydraulics of Flow over Side Weirs. Ph.D. Thesis, University of Southampton, Southampton, UK, 1975.
Emiroglu, M.E.; Kaya, N.; Agaccioglu, H. Discharge capacity of labyrinth side-weir located on a straight channel. ASCE J. Irrig. Drain. Eng. 2010, 136, 37–46.
Subramanya, K.; Awasthy, S.C. Spatially varied flow over side weirs. ASCE J. Hydraul. Div. 1972, 98, 1–10.
Nandesamoorthy, T.; Thomson, A. Discussion of spatially varied flow over side weir. ASCE J. Hydraul. Eng. 1972, 98, 2234–2235.
Yu-Tech, L. Discussion of spatially varied flow over side weir. ASCE J. Hydraul. Div. 1972, 98, 2046–2048.
Ranga Raju, K.G.; Prasad, B.; Grupta, S.K. Side weir in rectangular channel. ASCE J. Hydraul. Div. 1979, 105, 547–554.
Hager, W.H. Lateral outflow over side weirs. ASCE J. Hydraul. Eng. 1987, 113, 491–504.
Cheong, H.F. Discharge coefficient oflateral diversion from trapezoidal channel. ASCE J. Irrig. Drain. Eng. 1991, 117, 321–333.
Swamee, P.K.; Santosh, K.P.; Masoud, S.A. Side weir analysis using elementary discharge coefficient. ASCE J. Irrig. Drain. Eng. 1994, 120, 742–755.
Singh, R.; Manivannan, D.; Satyanarayana, T. Discharge coefficient of rectangular side weirs. ASCE J. Irrig. Drain. Eng. 1994, 120, 814–819.
Jalili, M.R.; Borghei, S.M. Discussion of Discharge coefficient of rectangular side weir. ASCE J. Irrig. Drain. Eng. 1996, 122, 132.
Enhanced understanding of flow structure in braided rivers is essential for river regulation, flood control, and infrastructure safety across the river. It has been revealed that the basic morphological element of braided rivers is confluence-bifurcation units. However, flow structure in these units has so far remained poorly understood with previous studies having focused mainly on single confluences/bifurcations. Here, the flow structure in a laboratory-scale confluence-bifurcation unit is numerically investigated based on the FLOW–3D® software platform. Two discharges are considered, with the central bars submerged or exposed respectively when the discharge is high or low. The results show that flow convergence and divergence in the confluence-bifurcation unit are relatively weak when the central bars are submerged. Based on comparisons with a single confluence/bifurcation, it is found that the effects of the upstream central bar on the flow structure in the confluence-bifurcation unit reign over those of the downstream central bar. Concurrently, the high-velocity zone in the confluence-bifurcation unit is less concentrated than that in a single confluence while being more concentrated than that observed in a single bifurcation. The present work unravels the flow structure in a confluence-bifurcation unit and provides a unique basis for further investigating morphodynamics in braided rivers.
1 Introduction
Confluences and bifurcations commonly exist in alluvial rivers and usually are important nodes of riverbed planform (Szupiany et al., 2012; Hackney et al., 2018). Flow convergence and divergence in these junctions result in highly three-dimensional (3D) flow characteristics, which greatly influence sediment transport, and hence riverbed evolution and channel formation (Le et al., 2019; Xie et al., 2020). Braided rivers, characterized by unstable networks of channels separated by central bars (Ashmore, 2013), have confluence-bifurcation units as their basic morphological elements (Ashmore, 1982; 1991; 2013; Federici & Paola, 2003; Jang & Shimizu, 2005). In particular, confluence-bifurcation units exhibit a distinct morphology from single confluences/bifurcations and bifurcation-confluence regions because two adjacent central bars are included. Within a confluence-bifurcation unit, two tributaries converge at the upstream bar tail and soon diverge to two anabranches again at the downstream bar head. Therefore, the flow structure in the unit may be significantly influenced by both the two central bars, and thus considerably different from that in single confluences, single bifurcations, and bifurcation-confluence regions, where the flow is affected by only one central bar. Enhanced understanding of flow structure in confluence-bifurcation units is urgently needed, which is essential for water resources management, river regulation, flood control, protection of river ecosystems and the safety of infrastructures across the rivers such as bridges, oil pipelines and communication cables (Redolfi et al., 2019; Ragno et al., 2021).
The flow dynamics, turbulent coherent structures, and turbulent characteristics in single confluences have been widely studied since the 1980s (Yuan et al., 2022). Flow dynamics at river channel confluences have been systematically and completely analyzed, which can be characterized by six major regions of flow stagnation, flow deflection, flow separation, maximum velocity, flow recovery and distinct shear layers (Best, 1987). For example, the field observation of Roy et al. (1988) and Roy and Bergeron (1990) highlighted the flow separation zones and recirculation at downstream natural confluence corners. Ashmore et al. (1992) measured the flow field in a natural confluence and found flow accelerates suddenly at the confluence junction with two separated high-velocity cores merging into one single core at the channel centre. De Serres et al. (1999) investigated the three-dimensional flow structure at a river confluence and identified the existence of the mixing layer, stagnation zones, separation zones and recovery zones. Sharifipour et al. (2015) numerically studied the flow structure in a 90° single confluence and found that the size of the separation zone decreases with the width ratio between the tributary and the main channel. Recently, three main classes of large-scale turbulent coherent structures (Duguay et al., 2022) have been presented, i.e. vertical-orientated vortices or Kelvin-Helmholtz instabilities (Rhoads & Sukhodolov, 2001; Constantinescu et al., 2011; 2016; Biron et al., 2019), channel-scale ‘back-to-back’ helical cells, (Mosley, 1976; Ashmore, 1982; Ashmore et al., 1992; Ashworth, 1996; Best, 1987; Rhoads & Kenworthy, 1995; Bradbrook et al., 1998; Lane et al., 2000), and smaller, strongly coherent streamwise-orientated vortices (Constantinescu et al., 2011; Sukhodolov & Sukhodolova, 2019; Duguay et al., 2022). However, no consensus on a universal turbulent coherent structure mode has been reached so far (Duguay et al., 2022). In addition, some studies (Ashworth, 1996; Constantinescu et al., 2011; Sukhodolov et al., 2017; Le et al., 2019; Yuan et al., 2023) have focused on turbulent characteristics, e.g. turbulent kinetic energy, turbulent dissipation rate and Reynolds stress, which can be critical parameters to further explaining the diversity of these turbulent coherent structure modes.
Investigations on the flow structure in single bifurcations have mainly focused on hydrodynamics in anabranches (Hua et al., 2009; van der Mark & Mosselman, 2013; Iwantoro et al., 2022) and around bifurcation bars (McLelland et al., 1999; Bertoldi & Tubino, 2005; 2007; Marra et al., 2014), whereas few studies have considered the effects of bifurcations on the upstream flow structure. Thomas et al. (2011) found that the velocity core upstream of the bifurcation is located near the water surface and towards the channel center in experimental investigations of a Y-shaped bifurcation. Miori et al. (2012) simulated flow in a Y-shaped bifurcation and found two circulation cells upstream of the bifurcation with flow converging at the water surface and diverging near the bed. Szupiany et al. (2012) reported velocity decreasing and back-to-back circulation cells upstream of the bifurcation junction in the field observation of a bifurcation of the Rio Parana River. These investigations provide insight into how bifurcations affect the flow patterns upstream, yet there is a need for further research on the dynamics of flow occurring immediately before the bifurcation junction.
Generally, the findings of studies on bifurcation-confluence regions are similar to those concerning single confluences and bifurcations. Hackney et al. (2018) measured the hydrodynamic characteristics in a bifurcation-confluence of the Mekong River and found the velocity cores located at the channel centre and strong secondary current occurring under low discharges. Le et al. (2019) reported a high-turbulent-kinetic-energy (high-TKE) zone located near the bed in their numerical simulation of flow in a natural bifurcation-confluence region. Moreover, a stagnation zone was found upstream of the confluence and back-to-back secondary current cells were detected at the confluence according to Xie et al. (2020) and Xu et al. (2022). Overall, these studies have further unraveled the flow patterns in river confluences and bifurcations.
Unfortunately, limited attention has been paid to the flow structure in confluence-bifurcation units. Parsons et al. (2007) investigated a large confluence-bifurcation unit in Rio Parana, Argentina, and no classical back-to-back secondary current cells were observed under a discharge of 12000 m3·s−1. To date, the differences in flow structure between confluence-bifurcation units and single confluences/bifurcations have remained far from clear. In addition, although the effects of discharge on flow structure have been investigated in several studies on single confluences/bifurcations, (Hua et al., 2009; Le et al., 2019; Luz et al., 2020; Xie et al., 2020; Xu et al., 2022), cases with fully submerged central bars were not considered, which is typical in braided rivers during floods. In-depth studies concerning these issues are urgently needed to gain better insight into the flow structure in confluence-bifurcation units of braided rivers.
This paper aims to (1) reveal the 3D flow structure in a confluence-bifurcation unit under different discharges and (2) elucidate the differences in the flow structure between confluence-bifurcation units and single confluence/bifurcation cases. Using the commercial computational fluid dynamics software FLOW-3D® (Version 11.2; https://www.flow3d.com; Flow Science, Inc.), fixed-bed simulations of a laboratory-scale confluence-bifurcation unit are conducted, and cases of a single confluence/bifurcation are also included for comparison. Two discharges are considered, with the central bars fully submerged or exposed respectively when the discharge is high or low. Based on the computational results, the 3D flow structure in the confluence-bifurcation unit conditions is analyzed from various aspects including free surface elevation, time-averaged flow velocity distribution, recirculation vortex structure, secondary current, and turbulent kinetic energy and dissipation rate. In particular, the flow structure in the confluence-bifurcation unit is compared with that in the single confluence/bifurcation cases to unravel the differences.h
2. Conceptual flume and computational cases
2.1. Conceptual flume
In this paper, a laboratory-scale conceptual flume is designed and used in numerical simulations. Figure 1(a–d) shows the morphological characteristics of the flume. To ensure that the conceptual flume reflects morphology features of natural braided channels, key parameters governing the flume morphology, e.g. unit length, width, and channel width-depth ratio, are determined according to studies on morphological characteristics of natural confluence-bifurcation units (Hundey & Ashmore, 2009; Ashworth, 1996; Orfeo et al., 2006; Parsons et al., 2007; Sambrook Smith et al., 2005; Kelly, 2006; Ashmore, 2013; Egozi & Ashmore, 2009; Redolfi et al., 2016; Ettema & Armstrong, 2019).
Figure 1. The sketch of the conceptual flume: (a) the original flume, (b) the central bar: (c) the sketch of cross-section C-C, (d) the sketch of cross-section D-D, (e) the modified part for the single confluence, (f) the modified part for the single bifurcation, (g) the position of different cross-sections. The red dashed boxes denote the regions of primary concern.
Figure 1. The sketch of the conceptual flume: (a) the original flume, (b) the central bar: (c) the sketch of cross-section C-C, (d) the sketch of cross-section D-D, (e) the modified part for the single confluence, (f) the modified part for the single bifurcation, (g) the position of different cross-sections. The red dashed boxes denote the regions of primary concern.
2.1.1. Length and width scales of the confluence-bifurcation unit
The length and width scales of the flume are first determined. The inner relation among the length LCB and average width B of a confluence-bifurcation unit and the average width Bi of a single branch was statistically studied by Hundey and Ashmore (2009), which indicates the following relations: 𝐿CB =(4∼5)𝐵 (1) 𝐵 =1.41𝐵𝑖 (2) In addition, Ashworth (1996) gave B = 2Bi in his experimental research on mid-bar formation downstream of a confluence, while the confluence-bifurcation unit of Rio Parana, Argentina has a relation of B≈1.71Bi (Orfeo et al., 2006; Parsons et al., 2007). Accordingly, the following relations are used in the present paper: 𝐿CB =4𝐵 (3) 𝐵 =1.88𝐵𝑖 (4) where LCB = 6 m, B = 1.5 m and Bi = 0.8 m.
2.1.2. Central bar morphology
The idealized plane pattern of central bars in braided rivers is a slightly fusiform leaf shape with a short upstream side and a long downstream side (Ashworth, 1996; Sambrook Smith et al., 2005; Kelly, 2006; Ashmore, 2013). To simplify the design, the bar is approximated as a combination of two different semi-ellipses (Figure 1(b)). The major axis Lb is two to ten times longer than the minor axis Bb according to the statistical data in Kelly’s study, and the regression equation is given as (Kelly, 2006): 𝐿𝑏=4.62𝐵0.96𝑏 (5) In this study, the bar width Bb is set as 0.8 m, whilst the lengths of downstream (LT1) and upstream sides (LT2) are 2 and 1.5 m, respectively (Figure 1(b)). Thus, the relation of Lb and Bb is given as: 𝐿𝑏=(𝐿𝑇1+𝐿𝑇2)=4.375𝐵𝑏 (6) The lengths of the inlet and outlet parts are determined as Lin = Lout = 8 m, which ensures negligible effects of boundary conditions without exceptional computational cost.
2.1.3. Width-depth ratio
Channel flow capacity can be significantly affected by cross-section shapes. For natural rivers, cross-section shapes can be generalized into three sorts based on the following width-depth curve (Redolfi et al., 2016): 𝐵=𝜓𝐻𝜑(7) Braided rivers usually have ψ = 5∼50 and φ>1, which indicates a rather wide and shallow cross-section. The central bar form should also be taken into account, so a parabolic cross-section shape is used here with ψ = 8 and φ>1 (Figure 1(c,d)).
2.1.4. Bed slope
In addition, natural braided rivers are usually located in mountainous areas and thus have a relatively large bed slope. According to flume experiments and field observations, the bed slope Sb is mostly in the range of 0.01∼0.02, and a few are below 0.01 (Ashworth, 1996; Egozi & Ashmore, 2009; Ashmore, 2013; Redolfi et al., 2016; Ettema & Armstrong, 2019). In this study, Sb takes 0.005.
2.1.5. Complete sketch of the conceptual flume
In summary, the flume is 29 m long, 2.4 m wide, and 0.6 m high. The plane coordinates (x-direction and y-direction) used in the calculation process are shown in Figure 1 (a). Note that the inlet corresponds to x = 0 m, and the centreline of the flume is located at y = 1.3 m. Besides, the thalweg elevation of the outlet is set as z = 0 m.
2.2. Computational cases
As stated before, the first aim of this paper is to reveal the flow structure in the confluence-bifurcation unit under different discharges. Therefore, two basic cases are set first: (1) case 1a under a low discharge (0.05 m3·s−1) with exposed central bars and (2) case 2a under a high discharge (0.30 m3·s−1) with fully submerged central bars. A total of 22 cross-sections are identified to examine the results (Figure 1(g)).
Further, cases of a single confluence/bifurcation are generated by splitting the original confluence-bifurcation unit into two parts. Part 1 only includes the upstream central bar and focuses on the flow convergence downstream of CS04 (Figure 1(e)), while Part 2 only includes the downstream central bar and focuses on the flow divergence upstream of CS19 (Figure 1(f)). Notably, the numbers of corresponding cross-sections in the original flume are reserved to facilitate comparison. The outlet section of the single confluence as well as the inlet section of the single bifurcation is extended to make the total length equivalent to the original flume (29 m). Also, two discharge conditions (0.05 and 0.30 m3·s−1), which correspond to exposed and fully submerged central bars, are considered for the single confluence/bifurcation. In total, six computational cases are conducted, as listed in Table 1. As the conceptual flume is designed to be symmetrical about the centreline, the momentum flux ratio (Mr) of the two branches should be 1 in all six cases. This is confirmed by further examining the computational results.
Case
Configuration
Qin (m3·s−1)
Zout (m)
Mr
Condition of bars
1a
CBU
0.05
0.15
1
Exposed
1b
SC
0.05
0.15
1
Exposed
1c
SB
0.05
0.15
1
Exposed
2a
CBU
0.30
0.34
1
Submerged
2b
SC
0.30
0.34
1
Submerged
2c
SB
0.30
0.34
1
Submerged
Table 1. Computational cases with inlet and outlet boundary conditions.
3. Numerical method
In this section, the 3D Large Eddy Simulation (LES) model integrated in the FLOW-3D® (Version 11.2; https://www.flow3d.com; Flow Science, Inc.) software platform is introduced, including governing equations and boundary conditions. Information on computational meshes with mesh independence test can be found in the Supplementary material.
3.1. Governing equations
The LES model was applied in the present paper to simulate flow in the laboratory-scale confluence-bifurcation unit. The LES model has been proven to be effective in simulating turbulent flow in river confluences and bifurcations (Constantinescu et al., 2011; Le et al., 2019). The basic idea of the LES model is that one should directly compute all turbulent flow structures that can be resolved by the computational meshes and only approximate those features that are too small to be resolved (Smagorinsky, 1963). Therefore, a filtering operation is applied to the original Navier-Stokes (NS) equations for incompressible fluids to distinguish the large-scale eddies and small-scale eddies (Liu et al., 2018). The filtered NS equations are then generated, which can be expressed in the form of a Cartesian tensor as (Liu, 2012):
(10) where ¯𝑢𝑖 is the resolved velocity component in the i – direction (i goes from 1 to 3, denoting the x-, y – and z-directions, respectively); t is the flow time; ρ is the density of the fluid; ¯𝑝 is the pressure; ν is the kinematic viscosity; τij is the sub-grid scale (SGS) stress; ¯𝐺𝑖 is the body acceleration. In FLOW–3D®, the full NS equations are discretized and solved using the finite-volume/finite-difference method (Bombardelli et al., 2011; Lu et al., 2023).
Due to the filtering process, the velocity can be divided into a resolved part (¯𝑢(𝑥,𝑡)) and an approximate part (𝑢′(𝑥,𝑡)) which is also known as the SGS part (Liu, 2012). To achieve model closure, the standard Smagorinsky SGS stress model is introduced here (Smagorinsky, 1963): 𝜏ij−13𝜏kk𝛿ij=−2𝜈SGS¯𝑆ij(11) where νSGS is the SGS turbulent viscosity, and ¯𝑆ij is the resolved rate-of-strain tensor for the resolved scale defined by (Smagorinsky, 1963): ¯𝑆ij=12(∂¯𝑢𝑖∂𝑥𝑗+∂¯𝑢𝑗∂𝑥𝑖)(12) In the standard Smagorinsky SGS stress model, the eddy viscosity is modelled by (Smagorinsky, 1963): 𝜈SGS=(𝐶𝑠¯𝛥)2∣¯𝑆∣,∣¯𝑆∣=√2¯𝑆ij¯𝑆ij(13) ¯𝛥=(ΔxΔyΔz)1/3(14) where Cs is the Smagorinsky constant, Δx, Δy, and Δz are mesh scales. In FLOW–3D®, Cs is between 0.1 to 0.2 (Smagorinsky, 1963). One of the key problems in simulating 3D open channel flow is the calculation of free surface. FLOW–3D® uses the Volume of Fluid (VOF) method (Hirt & Nichols, 1981) to track the change of free surface. The VOF method introduces a fluid phase fraction function f to characterize the proportion of a certain fluid in each mesh cell. In that case, the surface position can be precisely located if the mesh cell is fine enough. To monitor the change of f with time and space, the following convection equation is added:
For open channel flow, only two kinds of fluids are involved: water and air. If f is the fraction of water, the state of the fluid in each mesh cell can be defined as:
In FLOW–3D®, the interface between water and air is assumed to be shear-free, which means that the drag force on the water from the air is negligible. Moreover, in most cases, the details of the gas motion are not crucial for the heavier water motion so the computational processes will be more efficient.
3.2. Boundary conditions
Six boundary conditions need to be preset in the 3D numerical simulation process. Discharge boundary conditions are used for the inlet of the flume, where the free surface elevation is automatically calculated based on the free surface elevation boundary conditions set for the outlet. The specific information on the inlet and outlet boundary conditions for all computational cases is shown in Table 1. Moreover, because the free surface moves temporally, the free surface boundary conditions are just set as no shear stress and having a normal pressure, and the position of the free surface will be automatically adjusted over time by the VOF method in FLOW–3D®. Furthermore, the bed and two side walls are all set to be no-slip for fixed bed conditions, and a standard wall function is employed at the wall boundaries for wall treatment.
The inlet turbulent boundary conditions also need to be considered. They are set by default here. The turbulent velocity fluctuations V’ are assumed to be 10% of the mean flow velocity with the turbulent kinetic energy (TKE) (per unit mass) equaling 0.5V’2. The maximum turbulent mixing length is assumed to be 7% of the minimum computational domain scale, and the turbulent dissipation rate is evaluated automatically from the TKE.
4. Results and discussion
4.1. Flow structure in the confluence-bifurcation unit
4.1.1. Free surface elevation
Figure 2 shows the free surface elevation at five different longitudinal profiles (i.e. α = 0.2, 0.4, 0.5, 0.6, 0.8) for cases 1a and 2a. The parameter α was defined as follows:𝛼=𝑠𝐵(17) where s is the transverse distance between a certain profile and the left boundary of the flume. In general, the longitudinal change of free surface in the two cases is very similar despite different discharge levels. The free surface elevation decreases as the channel narrows from the upstream bifurcation to the front of the confluence-bifurcation unit. On the contrary, when the flow diverges again at the end of the confluence-bifurcation unit, the free surface elevation increases with channel widening. However, whether the fall or rise of free surface elevation in case 1a is much sharper than that in case 2a, especially at profiles with α = 0.2 and 0.8 (Figure 2(a)), which indicates there may be distinct flow states between the two cases. To further illustrate this finding, the Froude number Fr at different cross-sections (CS08∼CS15) is examined. In case 2a, the flow remains subcritical within the confluence-bifurcation unit. By contrast, in case 1a, a local supercritical flow is observed near the side banks of CS09 (i.e. α = 0.2 and 0.8), with Fr being about 1.2. This local supercritical flow can lead to a hydraulic drop followed by a hydraulic jump, which accounts for the sharp change of the free surface. The foregoing reveals that when central bars are exposed under relatively low discharge, supercritical flow is more likely to occur near the side banks of the confluence junction due to flow convergence.
Figure 2. Five time-averaged free surface elevation profiles in the confluence-bifurcation unit, in which α denotes the lateral position of the certain profile. Note that the black dashed line denotes the position of CS09, where Fr is about 1.2 near the side banks (α = 0.2 and 0.8) in case 1a. Z’ = z/h2, X’ = x/B, h2 is the maximum flow depth at the outlet boundary of cases 2a, 2b and 2c, h2 = 0.34 m.
Moreover, in both cases 1a and 2a, the free surface is higher at the channel centre than near the side banks, whether at the front or the end of the confluence-bifurcation unit. Thus, lateral free surface slopes from the centre to the side banks are generated. For example, the lateral free surface slopes at CS09 are 0.022 and 0.016 respectively for cases 1a and 2a. These lateral slopes can lead to lateral pressure gradient force whose direction is from the channel centreline to the side banks. Notably, the lateral surface slope in case 1a is steeper than that in case 2a, which may also result from the effect of the supercritical flow.
4.1.2. Time-averaged streamwise flow velocity
Figure 3. Time-averaged flow velocity distribution at three different slices over z-direction in the confluence-bifurcation unit: (a)∼(c) case 1a, (d)∼(f) case 2a. The flow direction is from the left to the right. StZ = Stagnation Zones, MiL = Mixing Layer. X’ = x/B, Y’ = y/B, Ui’ = Ui/Uti, Ui denotes the time-averaged streamwise flow velocity in case series i (i = 1,2), Uti denotes the cross-section-averaged streamwise flow velocity in case series i, Ut1 = 0.385 m/s, for case 2a Ut2 = 0.714 m/s.Figure 4. Time-averaged flow velocity contours at eight different cross-sections in the confluence-bifurcation unit: (a) case 1a, (b) case 2a.
Besides the shared features described above, some differences between the two cases are also identified. First, flow stagnation zones at the upstream bar tail are found exclusively in case 1a as the central bars are exposed (Figure 3 (a–c)). Second, in case 1a the mixing layer is obvious in both the lower or upper flows (Figure 3 (a–c)), while in case 2a the mixing layer can be inconspicuous in the upper flow (Figure 3 (f)). Third, in case 1a, two high-velocity cores gradually transform into one single core downstream of the confluence [Figure 4 (a), CS08∼CS11] and are divided into two cores again at the downstream bar head [Figure 4 (a), CS15]. By contrast, in case 2a, the two cores merge much more rapidly [Figure 4 (a), CS08∼CS09], and no obvious reseparation of the merged core is found at the downstream bar head (Figure 3 (d–f)). The latter two differences between cases 1a and 2a indicate that the flow convergence and divergence are relatively weak when the central bars are fully submerged. It is noticed that when the central bars are exposed, the flow in branches needs to steer around the central bar, which can cause a large angle between the two flow directions at the confluence, and thus relatively strong flow convergence and divergence may occur. By contrast, when the central bars are fully submerged, the flow behavior resembles that of a straight channel, with flow predominantly moving straight along the main axis of the central bars. Therefore, a small angle between two tributary flow forms, and thus flow convergence and divergence are relatively mild.
4.1.3. Recirculation vortex
A recirculation vortex with a vertical axis is a typical structure usually found where flow steers sharply, and is generated from flow separation (Lu et al., 2023). This vortex structure is found in the confluence-bifurcation unit in the present study, marking several significant flow separation zones. Figure 5 shows the recirculation vortex structure at the bifurcation junction of the confluence-bifurcation unit. In both cases 1a and 2a, two recirculation vortices BV1 and BV2 are found at the bifurcation junction corner. Moreover, BV1 and BV2 seem well-established near the bed but tend to transform into premature ones in the upper flow, and there is also a tendency for the cores of BV1 and BV2 to shift downstream as they transition from the lower to the upper flow (Figure 5(a–c,d–f)). This finding indicates that flow separation zones exist at the bifurcation junction corner, and the vortex structure is similar in the separation zones under low and high discharges. These flow separation zones are generated due to the inertia effect as flow suddenly diverges and steers towards the curved side banks of the channel (Xie et al., 2020). Notably, two additional vortices BV3 and BV4 are found at both sides of the downstream bar in case 1a (Figure 5(a–c)), but no such vortices exist in case 2a. This difference shows that flow separation zones at both sides of the downstream bar are hard to form when the bars are completely submerged under the high discharge.
Figure 5. Recirculation vortices at the bifurcation junction (streamline view at three different slices over z-direction): (a)∼(c) case 1a, (d)∼(f) case 2a. The red solid line marked out the position of these vortices (BV1∼BV4).
Similarly, Figure 6 shows the recirculation vortex structure at the confluence junction of the confluence-bifurcation unit. No noteworthy similarities but a key difference between the two cases are observed at this site. Two vortices CV1 and CV2 are found downstream of the confluence junction corner in case 1a (Figure 6(c)), which mark two separation zones. Conversely, no such separation zones are found in case 2a. In fact, separation zones were reported at similar sites under relatively low discharges in some previous studies (Ashmore et al., 1992, Luz et al., 2020, Sukhodolov & Sukhodolova, 2019; Xie et al., 2020). Nevertheless, the flow separation zones at the confluence corner are very restricted in the present study (Figure 6(c)). Ashmore et al. (1992) also reported that no, or very restricted flow separation zones occur downstream of natural river confluence corners, primarily because of the relatively slow change in bank orientation compared with the sharp corners of laboratory confluences where separation is pronounced (Best & Reid, 1984; Best, 1988). In the present study, the bank orientation also changes slowly, which may explain why flow separation zones are inconspicuous at the confluence corner.
Figure 6. Recirculation vortices at the confluence junction (streamline view at three different slices over z-direction): (a)∼(c) case 1a, (d)∼(f) case 2a. The red solid line marked out the position of these vortices (CV1 & CV2).
The differences in the distribution of recirculation vortices discussed above may be mainly attributed to the difference in the angle between the tributary flows under different discharges. Some previous studies have reported that the confluence/bifurcation angle can significantly influence the flow structure at confluences/bifurcations (Best & Roy, 1991; Ashmore et al., 1992; Miori et al., 2012). Although the confluence/bifurcation angle is fixed due to the determined central bar shape in the present study, the angle between two tributary flows is affected by the varying discharge. When the central bars are exposed under the low discharge, the flow is characterized by a more pronounced curvature of the streamlines, and a large angle between the two tributary flows is noted (Figure 6(b)), causing strong flow convergence and divergence. By contrast, a small angle forms as the central bars are submerged, thereby leading to relatively weak flow convergence/divergence (Figure 6(e)). Overall, the differences mentioned above can be attributed to the differences in the intensity of flow convergence and divergence under different discharges.
It should be noted that some previous studies (Constantinescu et al., 2011; Sukhodolov & Sukhodolova, 2019) presented that there is a wake mode in the mixing layer of two streams at the confluence junction. The wake mode means that in the mixing layer, multiple streamwise coherent vortices moving downstream will form, which is similar to the flow structure around a bluffing body (Constantinescu et al., 2011). However, no such structure has been found within the confluence-bifurcation unit in this study. According to the numerical simulations of Constantinescu et al. (2011), a wake mode was found at a river confluence with a concordant bed and a momentum flux ratio of about 1. The confluence has a much larger angle (∼60°) between the two streams when compared to the confluence junction of the confluence-bifurcation unit in the present study where the angle is about 25°. As flow mechanics at river confluences may include several dominant mechanisms depending on confluence morphology, momentum ratio, the angle between the tributaries and the main channel, and other factors (Constantinescu et al., 2011), the relatively small confluence angle in the present study may explain why the wake mode is absent. The possible effects of the confluence/bifurcation angle are reserved for future study. Additionally, flow separation can lead to reduced local sediment transport capacity, thus causing considerable sediment deposition under natural conditions. Hence, the bank may migrate towards the inner side of the channel at the positions of CV1, CV2, BV1, and BV2, while the bar may expand laterally at the positions of BV3 and BV4.
4.1.4. Secondary current
Secondary current is the flow perpendicular to the mainstream axis (Thorne et al., 1985) and can be categorized into two primary types based on its origin: (1) Secondary current generated by the interaction between centrifugal force and pressure gradient force; (2) Secondary current resulting from turbulence heterogeneity and anisotropy (Lane et al., 2000). There are some widely recognized definitions of secondary current strength (SCS) (Lane et al., 2000). In this paper, the secondary current cells are identified by visible vortex with a streamwise axis, and the definition of SCS proposed by Shukry (1950) is used:
where ux, uy, and uz are flow velocities in x, y, and z directions and ux represents the mainstream flow velocity.
Figure 7 presents contour plots of SCS and the secondary current structure at key cross-sections of the study area. When the central bars are exposed, at the upstream bar tail (CS08), intense transverse flow occurs with flow converging to the centreline, but no secondary current cell is formed (Figure 7(a)). This is consistent with the findings of Hackney et al. (2018). At the confluence junction (CS09), transverse flow still plays a major role in the secondary current structure, with flow converging to the centreline at the surface and diverging to side banks near the bed (Figure 7(b)). Moreover, ‘back-to-back’ helical cells, which are two vortices rotating reversely, tend to generate at CS09 with their cores located near the side banks (Figure 7(b)) (Mosley, 1976; Ashmore, 1982; Ashmore et al., 1992), yet their forms are rather premature. As the flow goes downstream, the cores of the helical cells gradually rise to the upper flow and approach towards the centreline, and the helical cells become well-established (Figure 7(c–e)). When the flow diverges again at the downstream bar head (CS15), the helical cells attenuate rapidly, and the secondary current structure is once again characterized predominantly by transverse flow (Figure 7(f)).
Figure 7. Distribution of secondary current strength and secondary current cells at six different cross-sections: (a)∼(f) case 1a, (g)∼(l) case 2a. The secondary current cells are identified by visible lateral vortices (streamline view). The zero distance of each cross-section is located on the right bank.
When the central bars are fully submerged under the high discharge, the secondary current structure at the upstream bar tail and the confluence junction exhibits a resemblance to that under the low discharge (Figure 7(g,h)). However, at CS09, two pairs of cells with different scales tend to form under the high discharge (Figure 7(h)). The large and premature helical cells are similar to those under the low discharge, whereas the small helical cells are located near side banks possibly due to wall effects. As the flow moves downstream, the large helical cells tend to diminish rapidly and merge with the small ones near both side walls (Figure 7(i–k)). Moreover, the secondary current structure is once again characterized predominantly by transverse flow at CS14 under the high discharge, which occurs earlier than that under the low discharge (Figure 7(k)). At the downstream bar head, transverse flow still takes a dominant place, while the helical cells seem to become premature with increased scale (Figure 7(l)).
In general, in both cases 1a and 2a, the lateral distribution of SCS at all cross-sections is symmetrical about the channel centreline, where SCS is relatively small. A relatively high SCS is detected at both the upstream bar tail and the downstream bar head due to the effects of centrifugal force caused by flow steering. SCS decreases rapidly from the upstream bar tail (CS08) to the entrance of the downstream bifurcation junction (CS14), followed by a sudden increase at the downstream bar head (CS15) (Figure 7 (a–e, g–k)). However, the distribution of high-SCS zones is different between the two discharges. Under the low discharge, high-SCS zones appear along the bottom near the centerline and at the free surface on both sides of the centreline. Although similar high-SCS zones are found along the bottom near the centerline under the high discharge, the high-SCS zones are not found at the free surface. Furthermore, it is noticed that more obvious high-SCS zones appear under the low discharge compared with the high discharge, especially at CS09. This may be attributed to the differences in the intensity of flow convergence and divergence under different submerging conditions of the central bars. When the central bars are exposed, flow convergence and divergence are strong and sharp flow steering occurs, thereby causing large SCS. By contrast, when the central bars are fully submerged, flow convergence and divergence are relatively weak, and thus small SCS is observed.
4.1.5. Turbulent characteristics
Turbulent characteristics reflect the performance of energy and momentum transfer activities in flow (Sukhodolov et al., 2017). Comprehensive analysis of turbulent characteristics is crucial as they greatly impact the incipient motion, settling behavior, diffusion pattern, and transport process of sediment. Here, the TKE and turbulent dissipation rate (TDR) of flow in the confluence-bifurcation unit are analyzed.
Figure 8 shows the distribution of TKE on various cross-sections in cases 1a and 2a. In the same way, Figure 10 shows the distribution of TDR. The values of TKE and TDR are nondimensionalized with mid-values of TKE = 0.005 m2·s−2 and TDR = 0.007 m3·s−2. In both cases 1a and 2a, the distributions of TKE and TDR show symmetrical patterns concerning the channel centreline. High-TKE and high-TDR zones exhibit a belt distribution near the channel bottom (McLelland et al., 1999; Ashworth, 1996; Constantinescu et al., 2011), indicating that turbulence primarily originates at the channel bottom due to the influence of bed shear stress. A sudden increase of TKE (Weber et al., 2001) and TDR occurs near the channel bottom at the confluence junction [Figure 8 and 9, CS08∼CS09] and from the entrance of the bifurcation junction (CS14) to the downstream bar head (CS15) (Figures 8 and 9).
Figure 8. Turbulent kinetic energy contours at eight different cross-sections in the confluence-bifurcation unit: (a) case 1a, (b) case 2a. TKE = turbulent kinetic energy. TKE’ = dimensionless value of TKE, with regard to a mid-value of TKE = 0.005 m2·s−2.Figure 9. Turbulent dissipation rate contours at eight different cross-sections in the confluence-bifurcation unit: (a) case 1a, (b) case 2a. TDR = turbulent dissipation rate. TDR’ = dimensionless value of TDR, with regard to a mid-value of TDR = 0.007 m3·s−2.Figure 10. Comparison of the distribution of time-averaged streamwise flow velocity along the flow depth at different cross-sections between the confluence-bifurcation unit and the single confluence. (a)∼(f) 1a vs. 1b, (g)∼(l) 2a vs. 2b.
Despite the common turbulent characteristics between cases 1a and 2a, additional high-TKE zones are found in the upper flow at the upstream bar tail (CS08), the confluence junction (CS09) and the downstream bar head (CS15) (Figure 8) when the central bars are fully submerged. The formation mechanism of these high-TKE zones near the water surface is more complicated, which may result from interactions of velocity gradient, secondary current structure and wall shear stress (Engel & Rhoads, 2017; Lu et al., 2023).
4.2. Comparison with single confluence/bifurcation cases
In this section, the results of a single confluence (cases 1b and 2b) and a single bifurcation (cases 1c and 2c) are compared with those of the confluence-bifurcation unit (cases 1a and 2a) under two discharges. Flow structure at CS08∼CS15 is mainly concerned below.
4.2.1. Comparison with single confluence cases
First, the patterns of time-averaged streamwise velocity, TKE and TDR within the single confluence (presented by contour plots in the supplementary materials) are assessed and then compared with those within the confluence-bifurcation unit (Figures 4, 8, and 9). It is found that distributions of these parameters are similar in the confluence-bifurcation unit and the single confluence from the upstream bar tail (CS08) to the entrance of the bifurcation junction (CS14), despite varying discharges. As the existence of the downstream central bar is the main difference between the single confluence and the confluence-bifurcation unit, this finding indicates that the downstream bar may have limited influence on the flow structure in the confluence-bifurcation unit. In other words, the flow structure in the confluence-bifurcation unit appears to be mainly shaped by the presence of the upstream bar, with its impact potentially reaching as far as the entrance of the bifurcation (CS14). Moreover, under the low discharge, the two high-velocity cores seem to merge later (at CS11) in the single confluence than in the confluence-bifurcation unit (at CS10), which indicates the convergence of two tributary flows may achieve a steady state faster in the confluence-bifurcation unit. To further elucidate the differences, results on the distribution of time-averaged streamwise velocity and TKE along the flow depth are discussed below.
4.2.1.1. Time-averaged streamwise velocity
Figure 10 shows the distribution of time-averaged streamwise flow velocity along the flow depth at different cross-sections. Note that α = 0.5 denotes the channel centreline and α = 0.7 denotes a position near the side banks. As only marginal differences are found at α = 0.3 and 0.7, only profiles at α = 0.7 are displayed for clarity.
Under the low discharge, no obvious difference in the distribution of time-averaged streamwise flow velocity is observed at the upstream bar tail (Figure 10(a)). At the confluence junction (Figure 10(b)), the velocities near the side banks (α = 0.7) are larger than those at the centre (α = 0.5) in both the confluence-bifurcation unit and the single confluence, which suggests that the two tributary flows have not sufficiently merged. The two tributary flows achieve convergence at CS11 in both the confluence-bifurcation unit and the single confluence (Figure 10(c)), with the velocity at the centre (α = 0.5) is larger than that near the side banks. Nevertheless, the velocities at the centre (α = 0.5) and near the side banks (α = 0.7) are closer to each other in the confluence-bifurcation unit than those in the single confluence, which represents less sufficient flow convergence in the confluence-bifurcation unit than in the single confluence. Therefore, it can be inferred that the convergence of two tributary flows may achieve a steady state faster in the confluence-bifurcation unit. After reaching the steady state, the velocity near the side banks (α = 0.7) is smaller in the single confluence than in the confluence-bifurcation unit despite close values at the centre (α = 0.5) (Figure 10(d,e)). This leads to a more pronounced disparity between velocities at the centre and near the side banks in the single confluence than that observed in the confluence-bifurcation unit. In other words, the high-velocity zone is more concentrated on the channel centreline in the single confluence, while the lateral distribution of flow velocity tends to be more uniform in the confluence-bifurcation unit. This may be attributed to the influence of the downstream central bar, which is further proved by comparing the velocity profiles at CS15 (Figure 10(e)).
As for the high discharge condition, from CS08 to CS14, the quantitative differences in velocity distribution between the confluence-bifurcation unit and the single confluence seem small. This indicates that the effect of morphology appears to be subdued when the central bars are fully submerged under the high discharge. It should be also noted that under both the low and high discharge, velocity profiles at the corresponding location exhibit the same shapes in the confluence-bifurcation unit and the single confluence, which indicates that the upstream confluence may dominate the flow structure in the confluence-bifurcation unit.
4.2.1.2. Secondary current
Figure 11 shows contour plots of SCS and the secondary current structure for single confluence cases. Compared with Figure 7, under both low and high discharge conditions, the distribution of SCS and the structure of helical cells in the confluence-bifurcation unit and the single confluence are very similar from CS08 to CS12 (Figure 7(a–d, g–j) and Figure 11(a–d, g–j)]. This indicates that the secondary current structure in the confluence-bifurcation unit exhibits certain consistent features when compared to those in the single confluence, thus proving that the effects of the upstream central bar may dominate the flow structure in the confluence-bifurcation unit. However, the secondary current structure at CS14 and CS15 is different between the confluence-bifurcation unit and the single confluence (Figure 7 and 11(e, f, k,l)). Under the low discharge, transverse flow is from the side banks to the centre and relatively high SCS is found near the side banks at CS14 in the single confluence, while the transverse flow is always from the centre to the side banks and SCS is relatively low at the corresponding sites in the confluence-bifurcation unit (Figure 11(e)). Under the high discharge, the helical cells near the side walls almost diminish in the single confluence, while they still exist in the confluence-bifurcation unit at CS14 (Figure 11(k)). Under both low and high discharges, the secondary current pattern at CS15 is similar to that at CS14 in the single confluence, while they are different in the confluence-bifurcation unit due to the existence of the downstream central bar. This comparison indicates that the existence of the downstream central bar can influence the upstream secondary current structure, nevertheless, the effects are fairly limited.
Figure 11. Secondary current at different cross-sections in the single confluence condition: (a)∼(f) case 1b, (g)∼(l) case 2b. The zero distance of each cross-section is located on the right bank.
4.2.1.3. Turbulent kinetic energy
Figure 12 shows TKE distribution along the flow depth at different cross-sections. Under the low discharge, in general, the maximum TKE tends to appear near the channel bottom in both the confluence-bifurcation unit and the single confluence. No obvious difference is observed at the upstream bar tail (CS08) (Figure 12(a)). Downstream this site (at CS09), the maximum TKE near the side banks (α = 0.7) is larger than that at the channel centre in the single confluence, while they are close to each other in the confluence-bifurcation unit (Figure 12(b)). This can also be attributed to the insufficient convergence of the two tributary flows. At CS11, flow convergence achieves a steady state in the confluence-bifurcation unit, while it remains insufficient in the single confluence. As flow convergence reaches a steady state at CS12, the maximum TKE in the single confluence exhibits a more concentrated distribution on the channel centre than that in the confluence-bifurcation unit (Figure 12(d)). This effect becomes more obvious downstream at CS14 (Figure 12(e)). The less-concentrated distribution of the maximum TKE in the confluence-bifurcation unit can be owing to the effects of the downstream central bar as well, which appears analogous to that mentioned in 4.2.1.1.
Figure 12. Comparison of the distribution of TKE along the flow depth at different cross-sections between the confluence-bifurcation unit and the single confluence. (a)∼(f) 1a vs. 1b, (g)∼(l) 2a vs. 2b.
Under the high discharge condition, two peaks of TKE appear in both the confluence-bifurcation unit and the single confluence (Figure 12(g–l)). Moreover, in both the confluence-bifurcation unit and the single confluence, from the upstream bar tail to the downstream bar head, the peak of TKE in the upper flow is larger at the channel centre (α = 0.5), while the peak of TKE in the lower flow is larger near the side banks (α = 0.7). However, the disparity between the TKE near the side banks and at the channel centre seems to be larger in the single confluence, while the TKE in the confluence-bifurcation unit takes a more uniform distribution. Even though, TKE profiles at the corresponding location exhibit highly similar shapes in the confluence-bifurcation unit and the single confluence, suggesting that the effects of channel morphology seem to be inhibited when the central bars are submerged under the high discharge.
4.2.2. Comparison with single bifurcation cases
Distributions of time-averaged streamwise velocity, TKE and TDR at corresponding cross-sections are also compared between the single bifurcation (see the Supplementary material) and the confluence-bifurcation unit (Figures 4, 8 and 9). Unlike the high similarity in flow characteristics exhibited between the confluence-bifurcation unit and the single confluence, significant differences are found between the confluence-bifurcation unit and the single bifurcation, especially at CS08∼CS14. On the one hand, the high-velocity zones are broader and asymmetrical concerning the channel centreline in the single bifurcation, with a belt-like and an approximately elliptic-like distribution respectively under the low and high discharges. By contrast, the high-velocity zone is a core that concentrates on the channel centre in the confluence-bifurcation unit. Moreover, the maximum velocity seems smaller in the single bifurcation than that in the confluence-bifurcation unit. On the other hand, the high-TKE belt near the channel bottom appears to be narrower in the single bifurcation than in the confluence-bifurcation unit, especially at CS08∼CS14 under the low discharge. Furthermore, additional high-TKE zones are found near the side walls at CS08∼CS11 in the single bifurcation, of which the scale is obviously smaller than those in the confluence-bifurcation unit. In addition, TKE at the channel centre is smaller near the free surface in the single bifurcation than that in the confluence-bifurcation unit. Nevertheless, the distributions of velocity, TKE and TDR seem to be similar in the confluence-bifurcation unit and the single bifurcation at CS15. As the existence of the upstream central bar is the main difference between the single confluence and the confluence-bifurcation unit, all the above findings indicate that the upstream central bar greatly influences the flow structure in the confluence-bifurcation unit. On the other hand, the downstream central bar may have a restricted influence on the flow structure in the confluence-bifurcation unit, whose impact may be limited to a range between the entrance of the bifurcation (CS14) and the downstream bar head (CS15). To further elucidate the differences, results on the distribution of time-averaged streamwise velocity and TKE along the flow depth are discussed below.
4.2.2.1. Time-averaged streamwise velocity
Figure 13 shows the distribution of time-averaged streamwise velocity along the flow depth at different cross-sections. Under the low discharge, distinct distribution patterns of flow velocity between the confluence-bifurcation unit and the single bifurcation are found at CS08, CS09 and CS11, which can be attributed to the effects of upstream flow convergence (Figure 13(a–c)). However, when the flow convergence reaches a steady state in the confluence-bifurcation unit (Figure 13(d–f)), the high-velocity zone is more concentrated in the confluence-bifurcation unit than in the single bifurcation due to to the significant influence of the upstream central bar on the flow structure. The velocity profiles at the downstream bar head can be a shred of evidence as well, with the maximum velocity larger at the channel centre but smaller near the side banks in the confluence-bifurcation unit than in the single bifurcation.
Figure 13. Comparison of the distribution of time-averaged streamwise flow velocity along the flow depth at different cross-sections between the confluence-bifurcation unit and the single bifurcation. (a)∼(f) 1a vs. 1c, (g)∼(l) 2a vs. 2c.
Under the high discharge, the distribution of velocity seems to exhibit limited differences between the two kinds of morphology, which indicates that the effects of channel morphology may be less noticeable when the central bars are fully submerged under the high discharge. Nevertheless, the velocity in the lower flow (below a relative depth of 0.45) shows a uniform lateral distribution in the single bifurcation, as the velocity profile at the channel centreline (α = 0.5) is in line with that near the side banks (α = 0.7) (Figure 13(g–l)). However, in the confluence-bifurcation unit, different velocity distributions in the lower flow can be observed at the channel centreline (α = 0.5) and near the side banks (α = 0.7). The foregoing results indicate that when the central bars are fully submerged, the high-velocity zones are more concentrated on the channel centreline in the confluence-bifurcation unit, while the lateral distribution of flow velocity within the single bifurcation tends to be more uniform, especially near the bifurcation junction (Figure 13(j,k)). This can also be attributed to the dominant influence of the upstream central bar over the downstream central bar.
It is also noted that the flow velocity distribution along the flow depth in the confluence-bifurcation unit is of a similar pattern despite varying discharges. As a critical point, the maximum velocity appears in the upper flow. The distribution above the critical point is approximately linear whereas it appears logarithmic below. By contrast, despite the similarity observed under the low discharge, the flow velocity distribution along the flow depth within the single bifurcation exhibits a distinct pattern under the high discharge, especially near the side banks (Figure 13(e–h)). On the one hand, the critical point in the upper flow no longer corresponds to the maximum velocity. On the other hand, the velocity distribution deviates from logarithmic below the critical point, with the maximum velocity appearing at a relative depth of 0.45. Succinctly, the distribution of streamwise velocity along the flow depth may retain the same pattern regardless of discharge levels in the confluence-bifurcation unit, while it may exhibit distinct patterns under different discharge levels in the single bifurcation.
4.2.2.2. Secondary current
Figure 14 shows contour plots of SCS and the distribution of secondary current for single bifurcation cases. In general, the value of SCS near the side banks at CS08∼CS14 (Figure 14(a–d, g–j)) in the single bifurcation seems smaller than that in the confluence-bifurcation unit (Figure 7(a–d, g–j)), especially under the low discharge. SCS distribution at CS14 is similar in the confluence-bifurcation unit and the single bifurcation under both low and high discharges. This difference in SCS distribution between the confluence-bifurcation unit and the single bifurcation indicates that the downstream bifurcation may have a restricted influence on the flow structure in the confluence-bifurcation unit. This influence is limited to a range between the entrance of the bifurcation (CS14) and the downstream bar head (CS15).
Figure 14. Secondary current at different cross-sections in the single bifurcation condition: (a)∼(f) case 1c, (g)∼(l) case 2c. The zero distance of each cross-section is located on the right bank.
In addition, the secondary current structure may also present different patterns in response to varying channel morphologies and discharge conditions. Under the low discharge condition, multiple unstable helical cells with asymmetrical distribution are formed from CS08 to CS12 in the single bifurcation (Figure 14(a–d)), while no obvious helical cells are found at CS14 and CS15 (Figure 14(d,e)). These findings are quite different from the stable and symmetrical helical cells at all cross-sections shown in the confluence-bifurcation unit (Figure 7). This difference may be attributed to the significant influence of the upstream central bar and the limited influence of the downstream central bar. Under the high discharge condition, only one pair of premature helical cells are found from CS08 to CS12 in the single bifurcation with their cores located near the side banks (Figure 14(e,f)). As the flow moves downstream, the helical cells gradually develop and become well-established (Figure 14(g,h)). These helical cells in the single bifurcation show symmetric cross-sectional distribution and a similar longitudinal development as in the confluence-bifurcation unit. However, in the confluence-bifurcation unit, two pairs of helical cells appear upstream of CS12 and CS14 and gradually fuse to one pair under the high discharge. As the ‘two-pairs’ structure in the confluence-bifurcation unit origins from the upstream confluence, the differences in the secondary current structure between the single bifurcation and the confluence-bifurcation unit under the high discharge can also be owing to the effects of the upstream central bar in excess of those of the downstream central bar.
4.2.2.3. Turbulent kinetic energy
Figure 15 shows the TKE distribution along the flow depth at different cross-sections. Under the low discharge, when the two tributary flows have not achieved sufficient convergence in the confluence-bifurcation unit, the maximum TKE is more concentrated in the single bifurcation (Figure 15(a–c)). As flow convergence achieves a steady state, more concentrated high-TKE zones appear at the channel centre within the confluence-bifurcation unit, confirming the finding that the effects of the upstream central bar reign over those of the downstream central bar in the confluence-bifurcation unit. However, things can be very complicated under the high discharge. For TKE distribution at the channel centreline, two peaks appear in the confluence-bifurcation unit with one close to the free surface and the other near the bed (Figure 15(g–l)). By contrast, only one peak near the bed is present in the single bifurcation. Therefore, a larger TKE can be found in the upper flow of the channel centreline in the confluence-bifurcation unit. For TKE distribution near the side banks, two peaks appear in both the confluence-bifurcation unit and the single bifurcation at CS09∼CS14 (Figure 15(h–l)). The upper peak is larger but the lower peak is smaller within the single bifurcation than those within the confluence-bifurcation unit. These significant discordances in TKE distribution under the high discharge further prove that the effects of the upstream bar on the flow structure in the confluence-bifurcation unit are more prominent than those of the downstream central bar.
Figure 15. Comparison of the distribution of TKE along the flow depth at different cross-sections between the confluence-bifurcation unit and the single bifurcation. (a)∼(f) 1a vs. 1c, (g)∼(l) 2a vs. 2c.
4.2.3. Further discussion of the comparisons
The above subsections have revealed significant differences in flow structure within the confluence-bifurcation unit and the single confluence and bifurcation, which directly result from the distinct channel morphologies and vary with the discharge conditions as well. These differences are summarized and further discussed below.
The distinctive morphology of a confluence-bifurcation unit plays a pivotal role in governing streamwise flow velocity distribution, secondary current structure, and turbulent kinetic energy distribution within the channel. Generally, from the upstream bar tail (CS08) to the entrance of the bifurcation (CS14), the flow structure in the confluence-bifurcation unit is highly similar to that in the single confluence, while it exhibits great differences (as shown in 4.2.2) between the confluence-bifurcation unit and the single bifurcation. This indicates that the upstream central bar greatly influences the flow structure in the confluence-bifurcation unit, with the effects spreading to the entrance of the bifurcation. At the downstream bar head (CS15), the flow structure (e.g. the transverse flow patterns) in the confluence-bifurcation unit exhibits high similarity to that in the single bifurcation. However, these similarities do not spread to upstream cross-sections, suggesting that the influence of the downstream central bar is limited at the bifurcation junction. In a word, the effects of the upstream central bar on the flow structure in the confluence-bifurcation unit are in excess of those of the downstream central bar.
However, despite the influence of channel morphology, discharge may also have some important effects on the streamwise flow velocity distribution. On the one hand, when the central bars are exposed under the low discharge, the high-velocity zone is less concentrated in the confluence-bifurcation unit than in the single confluence, while it is more concentrated in the confluence-bifurcation unit than in the single bifurcation. On the other hand, it is noticed that when the central bars are fully submerged under the high discharge, reduced differences in flow structure between the confluence-bifurcation unit and the single confluence/bifurcation are witnessed, and thus the morphology effect seems to be subdued.
4.3. Implications
The present work unravels the flow structure in a laboratory-scale confluence-bifurcation unit and takes the first step to further investigating morphodynamics in such channel morphology. Based on the comparison with a single confluence/bifurcation, the findings provide insight into the complex 3D interactions between water flow and channel morphology. The distinct flow structure in the laboratory-scale confluence-bifurcation unit may appreciably alter sediment transport and morphological evolution, of which research is underway. As the basic morphological element of braided river planform is confluence-bifurcation units, the present work should have direct implications for flow structure in natural braided rivers. This is pivotal for the sustainable management of braided rivers which deals with water and land resources planning, eco-hydrological well-being, and infrastructure safety such as cross-river bridges and oil pipelines (Redolfi et al., 2019; Ragno et al., 2021).
Notably, braided rivers worldwide (e.g. in the Himalayas, North America, and New Zealand) have undergone increased pressures and will continue to evolve due to forces of global climate change and intensified anthropogenic activities (Caruso et al., 2017; Hicks et al., 2021; Lu et al., 2022). In particular, channel aggradation caused by increased sediment supply as well as exploitation of braidplain compromise space for flood conveyance, making the rivers prone to flooding. In this sense, an enhanced understanding of the flow structure under high discharge when central bars are fully submerged is essential for mitigating flooding hazards.
5. Conclusions
This study has numerically investigated the 3D flow structure in a laboratory-scale confluence-bifurcation unit based on the LES model integrated in the FLOW–3D® software platform. Two different discharges are considered with the central bars fully submerged or exposed respectively when the discharge is high or low. Cases of a single confluence/bifurcation are included for comparison. The key findings of this paper are as follows:
Several differences are highlighted in the comparison of the flow structure in the confluence-bifurcation unit between the two discharges. When the central bars are fully submerged under the high discharge, the mixing layer of two tributary flows is less obvious, and two high-velocity cores merge more rapidly as compared with those under the low discharge. Besides, flow separation zones are found neither at the confluence corner nor on both sides of the downstream bar when the central bars are fully submerged. Moreover, SCS seems to be smaller near the side banks under the high discharge than under the low discharge. Therefore, it is suggested that flow convergence/divergence is relatively weak in the confluence-bifurcation unit when central bars are fully submerged under the high discharge.
From the upstream bar tail to the entrance of the bifurcation, the flow structure in the confluence-bifurcation unit is highly similar to that in the single confluence, while it exhibits great differences from that in the single bifurcation. Only at the downstream bar head does the flow structure in the confluence-bifurcation unit exhibit high similarity to that in the single bifurcation. Consequently, the effects of the upstream central bar on the flow structure in the confluence-bifurcation unit reign over those of the downstream central bar.
Despite the influence of channel morphology, discharge may also have significant effects on the distribution of streamwise flow velocity. On the one hand, when the central bars are exposed under the low discharge, the high-velocity zone is less concentrated in the confluence-bifurcation unit than in the single confluence, while it is more concentrated in the confluence-bifurcation unit than in the single bifurcation. On the other hand, when the central bars are fully submerged under the high discharge, reduced differences in flow structure between the confluence-bifurcation unit and the single confluence/bifurcation are witnessed, and thus the morphology effect seems to be subdued.
It is noticed that the effects of other factors (e.g. confluence and bifurcation angles, bed discordance) on the flow structure in the confluence-bifurcation unit are not discussed here. Studies on these issues are warranted and reserved for future work.
Reference
Ashmore, P. E. (1982). Laboratory modelling of gravel braided stream morphology. Earth Surface Processes and Landforms, 7(3), 201–225. https://doi.org/10.1002/esp.3290070301
Ashmore, P. E. (1991). How do gravel-bed rivers braid? Canadian Journal of Earth Sciences, 28(3), 326–341. https://doi.org/10.1139/e91-030
Ashmore, P. E. (2013). Morphology and dynamics of braided rivers. In J. Shroder, & (Editor in Chief) E. Wohl (Eds.), Treatise on geomorphology (Vol. 9, pp. 289–312). https://doi.org/10.1016/B978-0-12-374739-6.00242-6
Ashmore, P. E., Ferguson, R. I., Prestegaard, K. L., Ashworth, P. J., & Paola, C. (1992). Secondary flow in anabranch confluences of a braided, gravel-bed stream. Earth Surface Processes and Landforms, 17(3), 299–311. https://doi.org/10.1002/esp.3290170308
Ashworth, P. J. (1996). Mid channel bar growth and its relationship to local flow strength and direction. Earth Surface Processes and Landforms, 21(2), 103–123.
Bertoldi, W., & Tubino, M. (2005). Bed and bank evolution of bifurcating channels. Water Resources Research, 41(7), W07001. https://doi.org/10.1029/2004WR003333
Bertoldi, W., & Tubino, M. (2007). River bifurcations: Experimental observations on equilibrium configurations. Water Resources Research, 43(10), W10437. https://doi.org/10.1029/2007WR005907
Best, J. L. (1987). Flow dynamics at river channel confluences: Implications for sediment transport and bed morphology. In F. G. Ethridge, R. M. Flores, & M. D. Harvey (Eds.), Recent developments in fluvial sedimentology (pp. 27–35).
Best, J. L. (1988). Sediment transport and bed morphology at river channel confluences. Sedimentology, 35(3), 481–498. https://doi.org/10.1111/j.1365-3091.1988.tb00999.x
Best, J. L., & Reid, I. (1984). Separation zone at open-channel junctions. Journal of Hydraulic Engineering, 110(11), 1588–1594. https://doi.org/10.1061/(ASCE)0733-9429(1984)110:11(1588)
Best, J. L., & Roy, A. G. (1991). Mixing-layer distortion at the confluence of channels of different depth. Nature, 350(6317), 411–413. https://doi.org/10.1038/350411a0
Biron, P. M., Buffin-Bélanger, T., & Martel, N. (2019). Three-dimensional turbulent structures at a medium-sized confluence with and without an ice cover. Earth Surface Processes and Landforms, 44(15), 3042–3056. https://doi.org/10.1002/esp.4718
Bombardelli, F. A., Meireles, I., & Matos, J. (2011). Laboratory measurements and multi-block numerical simulations of the mean flow and turbulence in the nonaerated skimming flow region of steep stepped spillways. Environmental Fluid Mechanics, 11(3), 263–288. https://doi.org/10.1007/s10652-010-9188-6
Bradbrook, K. F., Biron, P. M., Lane, S. N., Richards, K. S., & Roy, A. G. (1998). Investigation of controls on secondary circulation in a simple confluence geometry using a three-dimensional numerical model. Hydrological Processes, 12(8), 1371–1396. https://doi.org/10.1002/(SICI)1099-1085(19980630)12:8<1371::AID-HYP620>3.0.CO;2-C
Caruso, B., Newton, S., King, R., & Zammit, C. (2017). Modelling climate change impacts on hydropower lake inflows and braided rivers in a mountain basin. Hydrological Sciences Journal, 62(6), 928–946. https://doi.org/10.1080/02626667.2016.1267860
Constantinescu, G., Miyawaki, S., Rhoads, B., & Sukhodolov, A. (2016). Influence of planform geometry and momentum ratio on thermal mixing at a stream confluence with a concordant bed. Environmental Fluid Mechanics, 16(4), 845–873. https://doi.org/10.1007/s10652-016-9457-0
Constantinescu, G., Miyawaki, S., Rhoads, B., Sukhodolov, A., & Kirkil, G. (2011). Structure of turbulent flow at a river confluence with momentum and velocity ratios close to 1: Insight provided by an eddy-resolving numerical simulation. Water Resources Research, 47(5), W05507. https://doi.org/10.1029/2010WR010018
De Serres, B., Roy, A. G., Biron, M. P., & Best, J. L. (1999). Three-dimensional structure of flow at a confluence of river channels with discordant beds. Geomorphology, 26(4), 313–335. https://doi.org/10.1016/S0169-555X(98)00064-6
Duguay, J., Biron, P., & Buffin-Bélanger, T. (2022). Large-scale turbulent mixing at a mesoscale confluence assessed through drone imagery and eddy-resolved modelling. Earth Surface Processes and Landforms, 47(1), 345–363. https://doi.org/10.1002/esp.5251
Egozi, R., & Ashmore, P. E. (2009). Experimental analysis of braided channel pattern response to increased discharge. Journal of Geophysical Research: Earth Surface, 114, F02012. https://doi.org/10.1029/2008JF001099
Engel, F. L., & Rhoads, B. L. (2017). Velocity profiles and the structure of turbulence at the outer bank of a compound meander bend. Geomorphology, 295, 191–201. https://doi.org/10.1016/j.geomorph.2017.06.018
Ettema, R., & Armstrong, D. L. (2019). Bedload and channel morphology along a braided, sand-bed channel: Insights from a large flume. Journal of Hydraulic Research, 57(6), 822–835. https://doi.org/10.1080/00221686.2018.1555557
Federici, B., & Paola, C. (2003). Dynamics of channel bifurcations in noncohesive sediments. Water Resources Research, 39(6), 1162. https://doi.org/10.1029/2002WR001434
Hackney, C. R., Darby, S. E., Parsons, D. R., Leyland, J., Aalto, R., Nicholas, A. P., & Best, J. L. (2018). The influence of flow discharge variations on the morphodynamics of a diffluence-confluence unit on a large river. Earth Surface Processes and Landforms, 43(2), 349–362. https://doi.org/10.1002/esp.4204
Hicks, D. M., Baynes, E. R. C., Measures, R., Stecca, G., Tunnicliffe, J., & Fredrich, H. (2021). Morphodynamic research challenges for braided river environments: Lessons from the iconic case of New Zealand. Earth Surface Processes and Landforms, 46(1), 188–204. https://doi.org/10.1002/esp.5014
Hirt, C. W., & Nichols, B. D. (1981). Volume of fluid (VOF) method for the dynamics of free boundaries. Journal of Computational Physics, 39(1), 201–225. https://doi.org/10.1016/0021-9991(81)90145-5
Hua, Z. L., Gu, L., & Chu, K. J. (2009). Experiments of three-dimensional flow structure in braided rivers. Journal of Hydrodynamics, 21(2), 228–237. https://doi.org/10.1016/S1001-6058(08)60140-7
Hundey, E. J., & Ashmore, P. E. (2009). Length scale of braided river morphology. Water Resources Research, 45(8), W08409. https://doi.org/10.1029/2008WR007521
Iwantoro, A. P., van der Vegt, M., & Kleinhans, M. G. (2022). Stability and asymmetry of tide-influenced river bifurcations. Journal of Geophysical Research: Earth Surface, 127(6), e2021JF006282. https://doi.org/10.1029/2021JF006282
Jang, C. L., & Shimizu, Y. (2005). Numerical simulation of relatively wide, shallow channels with erodible banks. Journal of Hydraulic Engineering, 131, 565–575.
Kelly, S. (2006). Scaling and hierarchy in braided rivers and their deposits: Examples and implications for reservoir modelling. In G. H. Smith, J. L. Best, C. S. Bristow, & G. E. Petts (Eds.), Braided rivers: Process, deposits, ecology and management (pp. 75–106).
Lane, S. N., Bradbrook, K. F., Richards, K. S., Biron, P. M., & Roy, A. G. (2000). Secondary circulation cells in river channel confluences: Measurement artefacts or coherent flow structures? Hydrological Processes, 14(11-12), 2047–2071. https://doi.org/10.1002/1099-1085(20000815/30)14:11/12<2047::AID-HYP54>3.0.CO;2-4
Le, T. B., Khosronejad, A., Sotiropoulos, F., Bartelt, N., Woldeamlak, S., & Dewall, P. (2019). Large-eddy simulation of the Mississippi River under base-flow condition: Hydrodynamics of a natural diffluence-confluence region. Journal of Hydraulic Research, 57(6), 836–851. https://doi.org/10.1080/00221686.2018.1534282
Liu, C. B., Li, J., Bu, W. Y., Ma, W. X., Shen, G., & Yuan, Z. (2018). Large eddy simulation for improvement of performance estimation and turbulent flow analysis in a hydrodynamic torque converter. Engineering Applications of Computational Fluid Mechanics, 12(1), 635–651. https://doi.org/10.1080/19942060.2018.1489896
Liu, Z. (2012). Investigation of flow characteristics around square cylinder with inflow turbulence. Engineering Applications of Computational Fluid Mechanics, 6(3), 426–446. https://doi.org/10.1080/19942060.2012.11015433
Lu, G. W., Liu, J. X., Cao, Z. X., Li, Y. W., Lei, X. T., & Li, Y. (2023). A computational study of 3D flow structure in two consecutive bends subject to the influence of tributary inflow in the middle Yangtze River. Engineering Applications of Computational Fluid Mechanics, 17(1), 2183901. https://doi.org/10.1080/19942060.2023.2183901
Lu, H. Y., Li, Z. W., Hu, X. Y., Chen, B., & You, Y. C. (2022). Morphodynamic processes in a large gravel–bed braided channel in response to runof change: A case study in the Source Region of Yangtze River. Arabian Journal of Geosciences, 15(5), 377. https://doi.org/10.1007/s12517-022-09641-y
Luz, L. D., Szupiany, R. N., Parolin, M., Silva, A., & Stevaux, J. C. (2020). Obtuse-angle vs. confluent sharp meander bends: Insights from the Paraguay-Cuiabá confluence in the tropical Pantanal wetlands, Brazil. Geomorphology, 348, 106907. https://doi.org/10.1016/j.geomorph.2019.106907
Marra, W. A., Parsons, D. R., Kleinhans, M. G., Keevil, G. M., & Thomas, R. E. (2014). Near-bed and surface flow division patterns in experimental river bifurcations. Water Resources Research, 50(2), 1506–1530. https://doi.org/10.1002/2013WR014215
McLelland, S. J., Ashworth, P. J., Best, J. L., Roden, J., & Klaassen, G. J. (1999). Flow structure and transport of sand-grade suspended sediment around an evolving braid bar, Jamuna River, Bangladesh. Fluvial Sedimentology VI, 28, 43–57. https://doi.org/10.1002/9781444304213.ch4
Miori, S., Hardy, R. J., & Lane, S. N. (2012). Topographic forcing of flow partition and flow structures at river bifurcations. Earth Surface Processes and Landforms, 37(6), 666–679. https://doi.org/10.1002/esp.3204
Mosley, M. P. (1976). An experimental study of channel confluences. The Journal of Geology, 84(5), 535–562. https://doi.org/10.1086/628230
Orfeo, O., Parsons, D. R., Best, J. L., Lane, S. N., Hardy, R. J., Kostaschuk, R., Szupiany, R. N., & Amsler, M. L. (2006). Morphology and flow structures in a large confluence-diffluence: Rio Parana, Argentina. In R. M. L. Ferreira, C. T. L. Alves, G. A. B. Leal, & A. H. Cardoso (Eds.), River Flow 2006 (pp. 1277–1282).
Parsons, D. R., Best, J. L., Lane, S. N., Orfeo, O., Hardy, R. J., & Kostaschuk, R. (2007). Form roughness and the absence of secondary flow in a large confluence–diffluence, Rio Paraná, Argentina. Earth Surface Processes and Landforms, 32(1), 155–162. https://doi.org/10.1002/esp.1457
Ragno, N., Redolfi, M., & Tubino, M. (2021). Coupled morphodynamics of river bifurcations and confluences. Water Resources Research, 57(1), e2020WR028515. https://doi.org/10.1029/2020WR028515
Redolfi, M., Tubino, M., Bertoldi, W., & Brasington, J. (2016). Analysis of reach-scale elevation distribution in braided rivers: Definition of a new morphologic indicator and estimation of mean quantities. Water Resources Research, 52(8), 5951–5970. https://doi.org/10.1002/2015WR017918
Redolfi, M., Zolezzi, G., & Tubino, M. (2019). Free and forced morphodynamics of river bifurcations. Earth Surface Processes and Landforms, 44(4), 973–987. https://doi.org/10.1002/esp.4561
Rhoads, B. L., & Kenworthy, S. T. (1995). Flow structure at an asymmetrical stream confluence. Geomorphology, 11(4), 273–293. https://doi.org/10.1016/0169-555X(94)00069-4
Rhoads, B. L., & Sukhodolov, A. N. (2001). Field investigation of three-dimensional flow structure at stream confluences: 1. Thermal mixing and time-averaged velocities. Water Resources Research, 37(9), 2393–2410. https://doi.org/10.1029/2001WR000316
Roy, A. G., & Bergeron, N. (1990). Flow and particle paths at a natural river confluence with coarse bed material. Geomorphology, 3(2), 99–112. https://doi.org/10.1016/0169-555X(90)90039-S
Roy, A. G., Roy, R., & Bergeron, N. (1988). Hydraulic geometry and changes in flow velocity at a river confluence with coarse bed material. Earth Surface Processes and Landforms, 13(7), 583–598. https://doi.org/10.1002/esp.3290130704
Sambrook Smith, G. H., Ashworth, P. J., Best, J. L., Woodward, J., & Simpson, C. J. (2005). The morphology and facies of sandy braided rivers: Some considerations of scale invariance. In M. D. Blum, S. B. Marriott, & S. F. Leclair (Eds.), Fluvial sedimentology VII. International association of sedimentologists. Special Publication No. 35 (pp. 145–158). Blackwell.
Sharifipour, M., Bonakdari, H., Zaji, A. H., & Shamshirband, S. (2015). Numerical investigation of flow field and flowmeter accuracy in open-channel junctions. Engineering Applications of Computational Fluid Mechanics, 9(1), 280–290. https://doi.org/10.1080/19942060.2015.1008963
Shukry, A. (1950). Flow around bends in an open flume. Transactions of the American Society of Civil Engineers, 115(1), 751–778. https://doi.org/10.1061/TACEAT.0006426
Smagorinsky, J. (1963). General circulation experiments with the primitive equations. Monthly Weather Review, 91(3), 99–164. https://doi.org/10.1175/1520-0493(1963)091<0099:GCEWTP>2.3.CO;2
Sukhodolov, A. N., Krick, J., Sukhodolova, T. A., Cheng, Z. Y., Rhoads, B. L., & Constantinescu, G. S. (2017). Turbulent flow structure at a discordant river confluence: Asymmetric jet dynamics with implications for channel morphology. Journal of Geophysical Research: Earth Surface, 122(6), 1278–1293. https://doi.org/10.1002/2016JF004126
Sukhodolov, A. N., & Sukhodolova, T. A. (2019). Dynamics of flow at concordant gravel bed river confluences: Effects of junction angle and momentum flux ratio. Journal of Geophysical Research: Earth Surface, 124(2), 588–615. https://doi.org/10.1029/2018JF004648
Szupiany, R. N., Amsler, M. L., Hernandez, J., Parsons, D. R., Best, J. L., Fornari, E., & Trento, A. (2012). Flow fields, bed shear stresses, and suspended bed sediment dynamics in bifurcations of a large river. Water Resources Research, 48(11), W11515. https://doi.org/10.1029/2011WR011677.
Thomas, R. E., Parsons, D. R., Sandbach, S. D., Keevil, G. M., Marra, W. A., Hardy, R. J., Best, J. L., Lane, S. N., & Ross, J. A. (2011). An experimental study of discharge partitioning and flow structure at symmetrical bifurcations. Earth Surface Processes and Landforms, 36(15), 2069–2082. https://doi.org/10.1002/esp.2231
Thorne, C. R., Zevenbergen, L. W., Pitlick, J. C., Rais, S., Bradley, J. B., & Julien, P. Y. (1985). Direct measurements of secondary currents in a meandering sand-bed river. Nature, 315, 746–747. https://doi.org/10.1038/315746a0.
van der Mark, C. F., & Mosselman, E. (2013). Effects of helical flow in one-dimensional modelling of sediment distribution at river bifurcations. Earth Surface Processes and Landforms, 38(5), 502–511. https://doi.org/10.1002/esp.3335
Wang, X. G., Yan, Z. M., & Guo, W. D. (2007). Three-dimensional simulation for effects of bed discordance on flow dynamics at Y-shaped open channel confluences. Journal of Hydrodynamics, 19(5), 587–593. https://doi.org/10.1016/S1001-6058(07)60157-7
Weber, L. J., Schumate, E. D., & Mawer, N. (2001). Experiments on flow at a 90° open-channel junction. Journal of Hydraulic Engineering, 127(5), 340–350. https://doi.org/10.1061/(ASCE)0733-9429(2001)127:5(340)
Xie, Q. C., Yang, J., & Lundström, T. S. (2020). Flow and sediment behaviours and morpho-dynamics of a diffluence−Confluence unit. River Research and Applications, 36(8), 1515–1528. https://doi.org/10.1002/rra.3697
Xu, L., Yuan, S. Y., Tang, H. W., Qiu, J. J., Whittaker, C., & Gualtieri, C. (2022). Mixing dynamics at the large confluence between the Yangtze River and Poyang Lake. Water Resources Research, 58(11), e2022WR032195. https://doi.org/10.1029/2022WR032195
Yuan, S. Y., Xu, L., Tang, H. W., Xiao, Y., & Gualtieri, C. (2022). The dynamics of river confluences and their effects on the ecology of aquatic environment: A review. Journal of Hydrodynamics, 34(1), 1–14. https://doi.org/10.1007/s42241-022-0001-z
Yuan, S. Y., Yan, G. H., Tang, H. W., Xiao, Y., Rahimi, H., Aye, M. N., & Gualtieri, C. (2023). Effects of tributary floodplain on confluence hydrodynamics. Journal of Hydraulic Research, 61(4), 552–572. https://doi.org/10.1080/00221686.2023.2231413
인텔 : 모델명이 ‘2’로 시작하고 ‘V’로 끝나는 코어 울트라 시리즈 2(Core Ultra Series 2). 예를 들면 인텔 코어 울트라 5 226V(시리즈2)가 있다.
AMD : 라이젠 AI 300 시리즈. 예시로 AMD 라이젠 AI 7 프로 360.
퀄컴 : 스냅드래곤 X 시리즈의 플러스(Plus) 또는 엘리트(Elite) 제품
이 세 가지 프로세서는 성능과 배터리 수명 면에서 애플 맥북의 M 시리즈와 경쟁하도록 설계됐다. 그러나 노트북을 선택할 때는 프로세서뿐 아니라 다양한 요소를 함께 고려해야 한다.
인텔 프로세서
인텔의 최신 프로세서는 다음 세 가지 범주로 나뉜다.
인텔 코어 울트라(Intel Core Ultra) : 프리미엄 칩으로, AI 전용 프로세서를 탑재했다(예 : 인텔 코어 울트라 7 155U).
인텔 코어(Intel Core) : 주류 노트북에 사용되는 칩으로, 코어 울트라보다 한 단계 아래다(예 : 인텔 코어 7 150U).
인텔 프로세서(Intel Processor) : 과거 펜티엄과 셀러론 브랜드를 대체하는 저가형 PC 칩이다(예 : 인텔 프로세서 N200).
인텔은 프로세서를 성능 등급에 따라 ‘3’, ‘5’, ‘7’, ‘9’로 세분화했다. 숫자가 높을수록 더 많은 코어를 가지고 있다는 의미이며, 이미지 처리 및 비디오 작업 속도가 향상된다. 코어 5와 코어 울트라 5 칩은 웹 브라우징 및 오피스 작업에 적합하다.
Intel
모델명 뒤에 붙는 접미사도 중요하다. 이 글자는 프로세서가 어떻게 최적화되었는지를 나타낸다. 긴 접미사 목록 중에 알아두어야 할 주요 단어는 ‘U’와 ‘H’다. U는 배터리 수명을, H는 성능을 강조한다. 코어 울트라 5 226V의 ‘V’는 코어 울트라 제품 라인에만 적용되는 접미사다.
구형 모델은 12세대 코어 i5 1235U처럼 이름에 ‘i’와 세대 번호가 포함되어 있다. 14세대에 이르러 인텔은 모든 것을 재설정하고 이제 ‘시리즈 1’부터 세기 시작했다(예 : 코어 울트라 155U). 즉, 최신 인텔 칩의 모델명은 구형 모델보다 짧다. 가격이 적당한 경우라면 구형 모델도 여전히 고려해 볼만하다.
AMD 프로세서
AMD는 인텔만큼 브랜딩 개편에 적극적이지는 않다. 애플 및 퀄컴과 경쟁하는 AI 300 시리즈 칩 외에 나머지 프로세서는 2023년 도입된 더 길고 혼란스러운 명명 체계를 따르고 있다.
AMD
예시로 AMD 라이젠 5 8640HS를 살펴본다.
첫 번째 숫자 ‘8’은 세대를 의미하며, 2024년에 출시된 칩을 나타낸다(7735HS는 2023년 제품).
‘5’는 성능 등급을 나타내며, 인텔과 마찬가지로 숫자가 높을수록 성능이 좋다는 의미다. 인텔 코어 5와 코어 7 체계와 유사하게 홀수로 계산된다.
마지막 글자는 프로세서의 최적화 방식이다. ‘U’는 배터리 수명, ‘H’는 성능을 우선시한다.
이 명명 체계를 따르는 칩은 AMD의 구형 젠 4(Zen 4) 아키텍처를 기반으로 하지만, 최신 AI 300 시리즈는 젠 5 아키텍처를 사용한다. AMD가 프로세서 라인 대부분을 최신 아키텍처로 전환함에 따라 이에 맞는 새로운 브랜드가 등장할 것으로 예상된다.
퀄컴 프로세서
퀄컴은 올해 초 전력 효율성에 중점을 두고 PC CPU 경쟁에 합류했다. 퀄컴의 스냅드래곤 X 칩은 휴대폰, 태블릿, 애플의 M 시리즈 프로세서에서 볼 수 있는 것과 동일한 Arm 기반 아키텍처를 사용하며, 우수한 PC 성능과 긴 배터리 수명을 제공한다. 무엇보다 퀄컴의 직관적인 브랜드 전략이 신선하게 다가온다.
스냅드래곤 X 엘리트(Snapdragon X Elite) : 최고급 모델
스냅드래곤 X 플러스(Snapdragon X Plus) : 그보다 한 단계 낮은 모델
마이크로소프트 서피스 노트북에 탑재된 스냅드래곤 X 플러스를 사용해 본 경험에 따르면, 충분한 성능과 하루 종일 지속되는 배터리 수명을 제공했다.
다만, Arm 기반 프로세서가 모든 윈도우 소프트웨어와 호환되는 것은 아니다. 스냅드래곤 PC에서 Arm이 아닌 앱을 실행하는 마이크로소프트의 에뮬레이션 엔진에서도 호환성 문제가 발생할 수 있다. 에뮬레이션 개선과 Arm 버전의 소프트웨어를 출시하는 개발자가 늘어나면서 상황이 점점 개선되고 있지만, 인텔과 AMD 노트북에서는 겪지 않아도 될 골칫거리가 여전히 남아 있다.
CPU 시장의 긍정적인 변화
복잡한 이름을 살펴보는 것이 혼란스러울 수 있고 AI에 대한 강조가 다소 과장된 면이 있지만, PC 프로세서 분야에서 3가지 업체가 경쟁하는 덕분에 상황은 개선되고 있다. 지난 4년간 애플은 전력 효율성 측면에서 독보적인 성과를 보여줬다. 그러나 인텔, AMD, 퀄컴이 새로운 프로세서를 내놓으며 애플의 수준에 도달하고 있다.
물론 복잡한 브랜드와 명명 체계는 단점이지만, 이런 경쟁 덕분에 더 나은 성능과 배터리 수명을 갖춘 제품이 등장하고 있다. 사용자에게 긍정적인 변화다. dl-itworldkorea@foundryco.com
아래 과거 자료도 선택에 큰 도움이 됩니다.
2023년 01월 11일
본 자료는 IT WORLD에서 인용한 자료입니다.
일반적으로 수치해석을 주 업무로 사용하는 경우 노트북을 사용하는 경우는 그리 많지 않습니다. 그 이유는 CPU 성능을 100%로 사용하는 해석 프로그램의 특성상 발열과 부품의 성능 측면에서 데스크탑이나 HPC의 성능을 따라 가기는 어렵기 때문입니다.
그럼에도 불구하고, 이동 편의성이나 발표, Demo 등의 업무 필요성이 자주 있는 경우, 또는 계산 시간이 짧은 경량 해석을 주로 하는 경우, 노트북이 주는 이점이 크기 때문에 수치해석용 노트북을 고려하기도 합니다.
보통 수치해석용 컴퓨터를 검토하는 경우 CPU의 Core수나 클럭, 메모리, 그래픽카드 등을 신중하게 검토하게 되는데 모든 것이 예산과 직결되어 있기 때문입니다. 따라서 해석용 컴퓨터 구매 시 어떤 것을 선정 우선순위에 두는지에 따라 사양이 달라지게 됩니다.
해석용으로 노트북을 고려하는 경우, 보통 CPU의 클럭은 비교적 선택 기준이 명확합니다. 메모리 또한 용량에 따라 가격이 정해지기 때문에 이것도 비교적 명확합니다. 나머지 가격에 가장 큰 영향을 주는 것이 그래픽카드인데, 이는 그래픽 카드의 경우 일반적인 게임용이나 포토샵으로 일반적인 이미지 처리 작업을 수행하는 그래픽카드와 3차원 CAD/CAE에 사용되는 업무용 그래픽 카드는 명확하게 분리되어 있고, 이는 가격 측면에서 매우 차이가 많이 납니다.
통상 게임용 그래픽카드는 수치해석의 경우 POST 작업시 문제가 발생하는 경우가 종종 발생하기 때문에 일반적으로 선택 우선 순위에서 충분한 확인을 한 후 구입하는 것이 좋습니다.
FLOW-3D는 OpenGL 드라이버가 만족스럽게 수행되는 최신 그래픽 카드가 적합합니다. 최소한 OpenGL 3.0을 지원하는 것이 좋습니다. FlowSight는 DirectX 11 이상을 지원하는 그래픽 카드에서 가장 잘 작동합니다. 권장 옵션은 NVIDIA의 Quadro K 시리즈와 AMD의 Fire Pro W 시리즈입니다.
특히 엔비디아 쿼드로(NVIDIA Quadro)는 엔비디아가 개발한 전문가 용도(워크스테이션)의 그래픽 카드입니다. 일반적으로 지포스 그래픽 카드가 게이밍에 초점이 맞춰져 있지만, 쿼드로는 다양한 산업 분야의 전문가가 필요로 하는 영역에 광범위한 용도로 사용되고 있습니다. 주로 산업계의 그래픽 디자인 분야, 영상 콘텐츠 제작 분야, 엔지니어링 설계 분야, 과학 분야, 의료 분석 분야 등의 전문가 작업용으로 사용되고 있습니다. 따라서 일반적인 소비자를 대상으로 하는 지포스 그래픽 카드와는 다르계 산업계에 포커스 되어 있으며 가격이 매우 비싸서 도입시 예산을 고려해야 합니다.
MSI가 새로운 노트북 CPU 벤치마크, 그리고 그 CPU가 내장돼 있는 신제품 노트북 제품군을 모두 CES 2023에서 공개했다. CES에서 인텔은 노트북용 13세대 코어 칩, 코드명 랩터 레이크와 핵심 제품인 코어 i9-13980HX를 발표했다.
새로운 노트북용 13세대 코어 칩이 게임 플레이에서 12% 더 빠르다는 정도의 약간의 정보는 이미 알려져 있다. 사용자가 기다리는 것은 실제 CPU가 탑재된 노트북에서의 성능이지만 보통 벤치마크는 제품 출시가 임박해서야 공개되는 것이 보통이다. 올해는 다르다.
CES 2023에서 MSI는 인텔 최고급 제품군인 코어 i9-13980HX 프로세서가 탑재된 타이탄 GT77 HX과 레이더 GE78 HX를 공개했다. 이례적으로 여기에 더해 PCI 익스프레서 5 SSD의 실제 성능을 측정하는 크리스털디스크마크, 모바일 프로세서 실행 속도를 측정하는 시네벤치 벤치마크 점수도 함께 제공했다. 다음 영상의 결과부터 말하자면 인텔 최신 프로세서를 큰 폭으로 따돌릴 만한 수치다.
MSI는 레이더 GE78 HX 외에도 레이더 GE68 HX 그리고 게이밍 노트북 같지 않은 외관의 스텔스 16 스튜디오, 스텔스 14, 사이보그 14 등 2023년에 출시될 다른 노트북도 전시했다. 오래된 PC 애호가라면 MSI 노트북 전면을 장식한 화려한 복고풍의 라이트 브라이트(Lite Brite) LED를 반가워할지도 모른다. 바닥면 섀시가 투명한 플라스틱 소재로 MSI 로고가 새겨져 있는 제품도 있다. 상세한 가격, 출시일, 사양 등은 추후 공개 예정이다. editor@itworld.co.kr
고성능 노트북을 구매할 때는 코어 i7과 코어 i9 사이에서 선택의 갈림길에 서게 된다. 코어 i7 CPU도 강력하지만 코어 i9는 최고의 성능을 위해 만들어진 CPU이며 보통 그에 상응하는 높은 가격대로 판매된다.
CPU에 초점을 둔다면 관건은 성능이다. 성능을 좌우하는 두 가지 주요소는 CPU의 동작 클록 속도(MHz), 그리고 탑재된 연산 코어의 수다. 그러나 노트북에서 한 가지 중요한 제약 요소는 냉각이다. 냉각이 제대로 되지 않으면 고성능도 쓸모가 없다. 가장 적합한 노트북 CPU를 결정하는 데 도움이 되도록 인텔의 지난 3개 세대 CPU의 코어 i7과 i9에 대한 정보를 모았다. 최신 세대부터 시작해 역순으로 살펴보자.
11세대: 코어 i9 vs. 코어 i7
인텔의 11세대 타이거 레이크(Tiger Lake) H는 한 가지 큰 이정표를 달성했다. 인텔이 2015년부터 H급 CPU에 사용해 온 14nm 공정을 마침내 최신 10nm 슈퍼핀(SuperFin) 공정으로 바꾼 것이다. 오랫동안 기다려온 변화다.
인텔이 자랑할 만한 10nm 고성능 칩을 내놓자 타이거 레이크 H를 장착한 노트북도 속속 발표됐다. 얇고 가볍고 예상외로 가격도 저렴한 에이서 프레데터 트라이톤(Acer Predator Triton) 300 SE를 포함해 일부는 벌써 매장에 출시됐다. 모든 타이거 레이크 H 칩이 8코어 CPU라는 점도 달라진 부분이다. 이전 세대의 경우 같은 제품군 내에서 코어 수에 차이를 둬 성능 기대치를 구분했다.
클록 차이도 크지 않다. 코어 i7-11800H의 최대 클록은 4.6GHz, 코어 i9-11980HK는 5GHz로, 클록 속도 증가폭은 약 8.6% 차이다. 나쁘지 않은 수치지만 둘 다 8코어 CPU임을 고려하면 대부분의 사용자에게 코어 i9는 큰 매력은 없다.
다만 코어 i9에 유리한 부분을 하나 더 꼽자면 코어 i9-11980HK가 65W의 열설계전력(TDP)을 옵션으로 제공한다는 점이다. 높은 TDP는 최상위 코어 i9에만 제공되는데, 이는 전력 및 냉각 요구사항을 충족하는 노트북에서는 코어 i7 버전보다 더 높은 지속 클록 속도를 제공할 수 있음을 의미한다.
대신 이런 노트북은 두껍고 크기도 클 가능성이 높다. 따라서 두 개의 얇은 랩톱 중에서(하나는 코어 i9, 하나는 코어 i7) 고민하는 사람에겐 열 및 전력 측면의 여유분은 두께와 크기를 희생할 만큼의 가치는 없을 것이다.
*11세대의 승자: 대부분의 사용자에게 코어 i7
10세대: 코어 i9 vs. 코어 i7
인텔은 10세대 코멧 레이크(Comet Lake) H 제품군에서 14nm를 고수했다. 그 대신 코어 i9 CPU 외에 코어 i7에도 8코어 CPU를 도입, 사용자가 비싼 최상위 CPU를 사지 않고도 더 뛰어난 성능을 누릴 수 있게 했다.
11세대 노트북이 나오기 시작했지만 10세대 CPU 제품 중에서도 아직 괜찮은 제품이 많다. 예를 들어 MSI GE76 게이밍 노트북은 빠른 CPU와 고성능 155W GPU를 탑재했고, 전면 모서리에는 RGB 라이트가 달려 있다.
11세대 칩과 마찬가지로 코어와 클록 속도의 차이가 크지 않으므로 대부분의 사용자에게 코어 i7과 코어 i9 간의 차이는 미미하다. 코어 i9-10980HK의 최대 부스트 클록은 5.3GHz, 코어 i7-10870H는 5GHz로, 두 칩의 차이는 약 6%다. PC를 최대 한계까지 사용해야 하는 경우가 아니라면 더 비싼 비용을 들여 10세대 코어 i9를 구매할 이유가 없다.
*10세대 승자: 대부분의 사용자에게 코어 i7
9세대: 코어 i9 대 코어 i7
인텔은 9세대 커피 레이크 리프레시(Coffee Lake Refresh) 노트북 H급 CPU에서 14nm 공정을 계속 유지했다. 코어 i9는 더 높은 클록 속도(최대 5GHz)를 제공하며 8개의 CPU 코어를 탑재했다. 물론 이 칩은 2년 전에 출시됐지만 인텔이 설계를 도운 XPG 제니아(Xenia) 15 등 아직 괜찮은 게이밍 노트북이 있다. 얇고 가볍고 빠르며 엔비디아 RTX GPU를 내장했다.
8코어 4.8GHz 코어 i9-9880HK와 4.6GHz 6코어 코어 i7-9850의 클록 속도 차이는 약 4%로, 실제 사용 시 유의미한 차이로 이어지는 경우는 극소수다. 두 CPU 모두 기업용 노트북에 많이 사용됐다. 대부분의 소비자용 노트북에는 8코어 5GHz 코어 i9-9880HK와 6코어 4.5GHz 코어 i7-9750H가 탑재됐다. 이 두 CPU의 클록 차이는 약 11%로, 이 정도면 유의미한 차이지만 마찬가지로 대부분의 경우 실제로 체감하기는 어렵다.
그러나 코어 수의 차이는 멀티 스레드 애플리케이션에서 큰 체감 효과로 이어지는 경우가 많다. 3D 모델링 테스트인 씨네벤치(Cinebench) R20에서 코어 i9-9980HK를 탑재한 구형 XPS 15의 점수는 코어 i7-9750H를 탑재한 게이밍 노트북보다 42% 더 높았다. 8코어 코어 i9의 발열을 심화하는 무거운 부하에서는 성능 차이가 약 7%로 줄어들었다. 여기에는 노트북의 설계가 큰 영향을 미칠 것이다. 어쨌든 일부 상황에서는 8코어가 6코어보다 유리하다.
또한 수치해석의 경우 결과를 분석하는 작업중의 많은 부분이 POST 작업으로 그래픽처리가 필요하다. 따라서 아래 영상편집을 위한 노트북에 대한 자료도 선택에 도움이 될것으로 보인다.
영상 편집을 위한 최고의 노트북 9선
Brad Chacos, Ashley Biancuzzo, Sam Singleton | PCWorld
영상을 편집하다 보면 컴퓨터의 여러 리소스를 집약적으로 사용하기 마련이다. 그래서 영상 편집은 대부분 데스크톱 PC에서 하는 경우가 많지만, 노트북에서 영상을 편집하려 한다면 PC만큼 강력한 사양이 뒷받침되어야 한다.
영상 편집용 노트북을 구매할 때 가장 비싼 제품을 선택할 필요는 없다. 사용 환경에 맞게 프로세서, 디스플레이의 품질, 포트 종류 등을 다양하게 고려해야 한다. 다음은 영상 편집에 최적화된 노트북 제품이다. 추천 제품을 확인한 후 영상 편집용 노트북을 테스트하는 팁도 참고하자.
1. 영상 편집용 최고의 노트북, 델 XPS 17(2022)
장점 • 가격 대비 강력한 기능 • 밝고 풍부한 색채의 대형 디스플레이 • 썬더볼트 4 포트 4개 제공 • 긴 배터리 수명 • 시중에서 가장 빠른 GPU인 RTX 3060
단점 • 무겁고 두꺼움 • 평범한 키보드 • USB-A, HDMI, 이더넷 미지원
델 XPS 17(2022)이야말로 콘텐츠 제작에 최적화된 노트북이다. 인텔 12세대 코어 i7-12700H 프로세서 및 엔비디아 지포스 RTX 3060는 편집을 위한 뛰어난 성능을 제공한다. 1TB SSD도 함께 지원되기에 데이터를 옮길 때도 편하다.
XPS 17은 SD카드 리더, 여러 썬더볼트 4 포트, 3840×2400 해상도의 17인치 터치스크린 패널, 16:10 화면 비율과 같은 영상 편집자에게 필요한 기능을 포함한다. 무게도 2.5kg 대로 비교적 가볍다. 배터리 지속 시간은 한번 충전 시 11시간인데, 이전 XPS 17 버전보다 1시간 이상 늘어난 수치다.
2. 영상 편집에 최적화된 스크린, 델 XPS 15 9520
장점 • 뛰어난 OLED 디스플레이 • 견고하고 멋진 섀시(Chassis) • 강력한 오디오 • 넓은 키보드 및 터치패드
단점 • 다소 부족한 화면 크기 • 실망스러운 배터리 수명 • 시대에 뒤떨어진 웹캠 • 제한된 포트
델 XPS 15 9520은 놀라운 OLED 디스플레이를 갖추고 있으며, 최신 인텔 코어 i7-12700H CPU 및 지포스 RTX 3050 Ti 그래픽이 탑재되어 있다. 컨텐츠 제작 및 영상 편집용으로 가장 선호하는 제품이다. 시스템도 좋지만 투박하면서 금속 소재로 이루어진 외관이 특히 매력적이다.
15인치 노트북이지만 매일 갖고 다니기에 다소 무거운 것은 단점이다. XPS 17 모델에서 제공되는 포트도 일부 없다. 그러나 멋진 OLED 디스플레이가 단연 돋보이며, 3456X2160 해상도, 16:10 화면 비율, 그리고 매우 선명하고 정확한 색상을 갖추고 있어 좋다.
3. 최고의 듀얼 모니터 지원, 에이수스 젠북 프로 14 듀오 올레드
장점 • 놀라운 기본 디스플레이와 보기 쉬운 보조 디스플레이 • 탁월한 I/O 옵션 및 무선 연결 • 콘텐츠 제작에 알맞은 CPU 및 GPU 성능
단점 • 생산성 노트북 치고는 부족한 배터리 수명 • 작고 어색하게 배치된 트랙패드 • 닿기 어려운 포트 위치
에이수스 젠북 프로 14 듀오(Asus Zenbook Pro 14 Duo OLED)는 일반적이지 않은 노트북이다. 일단 사양은 코어 i7 프로세서, 지포스 RTX 3050 그래픽, 16GB DDR5 메모리, 빠른 1TB NVMe SSD를 포함해 상당한 성능을 자랑한다. 또한 초광도의 547니트로 빛을 발하는 한편 DCI-P3 색영역의 100%를 커버하는 14.5인치 4K 터치 OLED 패널을 갖추고 있다. 사실상 콘텐츠 제작자를 위해 만들어진 제품이라 볼 수 있다.
가장 흥미로운 부분은 키보드 바로 위에 위치한 12.7인치 2880×864 스크린이다. 윈도우에서는 해당 모니터를 보조 모니터로 간주하며, 사용자는 번들로 제공된 에이수스 소프트웨어를 사용해 트랙패드로 사용하거나 어도비 앱을 위한 터치 제어 패널을 표시할 수 있다. 어떤 작업이든 유용하게 써먹을 수 있다.
젠북 프로 14 듀오 올레드는 기본적으로 휴대용이자 중간급 워크스테이션이다. 단, 배터리 수명은 평균 수준이기 때문에 중요한 작업 수행이 필요한 경우, 반드시 충전 케이블을 가지고 다녀야 한다. 그럼에도 불구하고 젠북 프로 14 듀오 올레드는 3D 렌더링 및 인코딩과 같은 작업에서 탁월한 성능을 보여 콘텐츠 제작자들에게 맞춤화 된 컴퓨터이다. 듀얼 스크린은 역대 최고의 기능이다.
4. 영상 편집하기 좋은 포터블 노트북, 레이저 블레이드 14(2021)
장점 • AAA 게임에서 뛰어난 성능 • 훌륭한 QHD 패널 • 유난히 적은 소음
단점 • 700g으로 무거운 AC 어댑터 • 비싼 가격 • 썬더볼트 4 미지원
휴대성이 핵심 고려 사항이라면, 레이저 블레이드 14(Razer Blade 14) (2021)를 선택해 보자. 노트북 두께는 1.5cm, 무게는 1.7kg에 불과해 비슷한 수준의 노트북보다 훨씬 가볍다. 사양은 AMD의 8-코어 라이젠 9 5900HX CPU, 엔비디아의 8GB 지포스 RTX 3080, 1TB NVMe SSD, 16GB 메모리를 탑재하고 있어 사양도 매우 좋다.
그러나 휴대성을 대가로 몇 가지 이점을 포기해야 할 수 있다. 일단 14인치 IPS 등급 스크린은 공장에서 보정된 상태로 제공되지만, 최대 해상도는 2560×1440다. 또 풀 DCI-P3 색영역을 지원하지만 4K 영상 편집은 불가능하다. 거기에 레이저 블레이드 14는 SD 카드 슬롯도 없다. 다만 편집 및 렌더링을 위한 강력한 성능을 갖추고 있고 가방에 쉽게 넣을 수 있는 제품인 것은 분명하다.
5. 배터리 수명이 긴 노트북, 델 인스피론 16
장점 • 넉넉한 16인치 16:10 디스플레이 • 긴 배터리 수명 • 경쟁력 있는 애플리케이션 성능 • 편안한 키보드 및 거대한 터치패드 • 쿼드 스피커(Quad speakers)
단점 • GPU 업그레이드 어려움 • 512GB SSD 초과 불가 • 태블릿 모드에서는 어색하게 느껴질 수 있는 큰 스크린
긴 배터리 수명을 가장 최우선으로 고려한다면, 델 인스피론 16(Dell Inspiron 16)을 살펴보자. 콘텐츠 제작 작업을 하며테스트해보니, 인스피론 16은 한 번 충전으로 16.5시간 동안 이용할 수 있다. 외부에서 작업을 마음껏 편집할 수 있는 시간이다. 그러나 무거운 배터리로 인해 무게가 2.1 kg에 달하므로 갖고 다니기에 적합한 제품은 아니다.
가격은 저렴한 편이나 몇 가지 단점이 있다. 일단 인텔 코어 i7-1260P CPU, 인텔 아이리스 Xe 그래픽, 16GB 램, 512GB SSD 스토리지를 탑재하고 있다. 이 정도 사양으로 영상 편집 프로젝트 대부분을 작업할 수 있으나, 스토리지 용량이 부족하기 때문에 영상 파일을 저장할 경우 외장 드라이브가 필요하다. 그러나 델 인스피론 16이 진정으로 빛을 발하는 부분은 단연 배터리 수명이다. 또한 강력한 쿼드 스피커 시스템도 사용해 보면 만족할 것이다. 포트의 경우, USB 타입-C 2개, USB-A 3.2 Gen 1 1개, HDMI 1개, SD 카드 리더 1개, 3.5mm 오디오 잭 1개가 제공된다.
6. 게이밍과 영상 편집 모두에 적합한 노트북, MSI GE76 레이더
장점 • 뛰어난 성능을 발휘하는 12세대 코어 i9-12900HK • 팬 소음을 크게 줄이는 AI 성능 모드 • 1080p 웹캠과 훌륭한 마이크 및 오디오로 우수한 화상 회의 경험 제공
단점 • 동일한 유형의 세 번째 버전 • 어수선한 UI • 비싼 가격
사양이 제일 좋은 제품을 찾고 있을 경우, 크고 무거운 게이밍 노트북을 선택해 보자. MSI GE76 레이더(Raider)는 강력한 14-코어 인텔 코어 i9-12900HK 칩, 175와트의 엔비디아 RTX 3080 Ti가 탑재됐고, 충분한 내부 냉각 성능 덕분에 UL의 프로시온(Procyon) 벤치마크의 어도비 프리미어 테스트에서 다른 노트북보다 훨씬 뛰어난 성능을 보였다. MSI GE76 레이더는 심지어 고속 카드 전송을 위해 PCle 버스에 연결된 SD 익스프레스(SD Express) 카드 리더도 갖추고 있다.
동일한 제품의 작년 모델은 게이머 중심의 360Hz 1080p 디스플레이를 지원한다. 영상 편집 과정에서는 그닥 이상적이지 않은 사양이다. 그러나 2022년의 12UHS 고급 버전은 4K, 120Hz 패널을 추가했는데, 이 패널은 콘텐츠 생성에 맞춰 튜닝 되지는 않았으나 17.3인치의 넓은 스크린 크기이기에 영상 편집자에게 꽤 유용하다.
7. 가성비 좋은 노트북, HP 엔비 14t-eb000(2021)
장점 • 높은 가격 대비 우수한 성능 • 환상적인 배터리 수명 • 성능 조절이 감지되지 않을 정도의 저소음 팬 • 썬더볼트 4 지원
단점 • 약간 특이한 키보드 레이아웃 • 비효율적인 웹캠의 시그니처 기능
가장 빠른 영상 편집 및 렌더링을 원할 경우 하드웨어에 더 많은 비용을 들여야 하지만, 예산이 넉넉하지 않을 때가 있다. 이때 HP 엔비(Envy) 14 14t-eb000) (2021)를 이용해보면 좋다. 가격은 상대적으로 저렴한 편이고 견고한 기본 컨텐츠 제작에 유용하다.
엔트리 레벨의 지포스 GTX 1650 Ti GPU 및 코어 i5-1135G7 프로세서는 그 자체로 업계 최고 제품은 아니다. 하지만 일반적인 편집 작업을 충분히 수행할 수 있는 사양이다. 분명 가성비 좋은 제품이다. 14인치 1900×1200 디스플레이는 16:10 화면 비율로 생산성을 향상하고, 공장 색 보정과 DCI-P3는 지원하지 않지만 100% sRGB 지원을 제공한다. 그뿐만 아니라, HP 엔비 14의 경우 중요한 SD 카드 및 썬더볼트 포트가 포함되며, 놀라울 정도로 조용하게 실행된다.
8. 컨텐츠 제작에 알맞은 또다른 게이밍 노트북, 에이수스 ROG 제피러스 S17
장점 • 뛰어난 CPU 및 GPU 성능 • 강력하고 혁신적인 디자인 • 편안한 맞춤형 키보드
단점 • 약간의 압력이 필요한 트랙패드 • 상당히 높은 가격
에이수스 ROG 제피러스(Zephyrus) S17은 영상 편집자의 궁극적인 꿈이다. 이 노트북은 초고속 GPU 및 CPU 성능과 함께 120Hz 화면 재생률을 갖춘 놀라운 17.3인치 4K 디스플레이를 탑재하고 있다. 견고한 전면 금속 섀시, 6개의 스피커 사운드 시스템 및 맞춤형 키보드는 프리미엄급 경험을 더욱 향상한다. 거기다 SD 카드 슬롯 및 풍부한 썬더볼트 포트가 포함되어 있어 더욱 좋다. 그러나 이를 위해 상당한 비용을 지불해야 한다. 예산이 넉넉하고 최상의 제품을 원한다면 제피루스 S17을 선택하면 된다.
9. 강력한 휴대성을 가진 노트북, XPG 제니아 15 KC
장점 • 가벼운 무게 • 조용함 • 상대적으로 빠른 속도
단점 • 중간 수준 이하의 RGB • 평범한 오디오 성능 • 느린 SD 카드 리더
사양이 좋은 노트북의 경우, 대부분 부피가 크고 무거워서 종종 2.2kg 또는 2.7kg를 넘기도 한다. XPG 제니아 15 KC(XPG Xenia 15 KC)만은 예외다. XPG 제니아 15 KC의 무게는 1.8kg가 조금 넘는 수준으로, 타제품에 비해 상당히 가볍다. 또한 소음도 별로 없다. 원래 게이밍 노트북 자체가 소음이 크기에 비교해보면 큰 장점이 될 수 있다. 1440p 디스플레이와 상대적으로 느린 SD 카드 리더 성능으로 인해 일부 콘텐츠 제작자들이 구매를 주저할 수 있으나, 조용하고 휴대하기 좋은 제품을 찾고 있다면 제니아 15 KC가 좋은 선택지다.
영상 편집 노트북 구매 시 고려 사항
영상 편집 노트북 구매 시 고려해야 할 가장 중요한 사항은 CPU 및 GPU다. 하드웨어가 빨라질수록 편집 속도도 빨라진다. 필자는 UL 프로시온 영상 편집 테스트(UL Procyon Video Editing Test)를 통해 속도를 테스트해보았다. 이 벤치마크는 2개의 서로 다른 영상 프로젝트를 가져와 색상 그레이딩 및 전환과 같은 시각적 효과를 적용한 다음, 1080p와 4K 모두에서 H.264, H.265를 사용해 내보내는 작업을 어도비 프리미어가 수행하도록 한다.
성능은 인텔의 11세대 프로세서를 실행하는 크고 무거운 노트북에서 가장 높았고, AMD의 비피 라이젠 9(beefy Ryzen 9) 프로세서를 탑재한 노트북이 바로 뒤를 이었다. 10세대 인텔 칩은 여전히 상당한 점수를 기록하고 있다. 위의 차트에는 없으나 새로운 인텔 12세대 노트북은 더 빨리 실행된다. 최고 성능의 노트북은 모두 최신 인텔 CPU 및 엔비디아의 RTX 30 시리즈 GPU를 결합했는데, 두 기업 모두 어도비 성능 최적화에 많은 시간 및 리소스를 투자했기 때문에 놀라운 일은 아니다.
GPU는 어도비 프리미어 프로에서 CPU보다 더 중요하지만, 매우 빠르게 수확체감 지점에 다다른다. 최고급 RTX 3080 그래픽을 사용하는 노트북은 RTX 3060 그래픽을 사용하는 노트북보다 영상 편집 속도가 더 빠르나, 속도 차이가 크지는 않다. 델 XPS 17 9710의 점수를 살펴보면, 지포스 RTX 3060 노트북 GPU는 MSI GE76 레이더의 가장 빠른 RTX 3080보다 14% 더 느릴 수 있다. 특히 GE76 레이더가 델 노트북에 비해 얼마나 더 크고 두꺼운지를 고려할 때 수치가 크지는 않다.
일반적으로 그래픽과 영상 편집을 위해 적어도 RTX 3060을 갖추는 것을 권장한다. 그러나 영상 편집은 워크플로에 크게 의존한다. 특정 작업 및 도구는 CPU 집약적이거나 프리미어보다 GPU에 더 의존할 수 있다. 이 경우 원하는 요소의 우선순위를 조정하길 바란다. 앞서 언급한 목록은 기본적으로 여러 요소를 종합적으로 고려해서 만든 내용이다.
인텔 및 엔비디아는 각각 퀵 싱크(Quick Sync) 및 쿠다(CUDA)와 같은 도구를 구축하는 데 수년을 보냈고, 이로 인해 많은 영상 편집 앱의 속도는 크게 향상될 수 있다. AMD 하드웨어는 영상 편집에 적합하나 특히 워크플로가 공급업체별 소프트웨어 최적화에 의존하는 경우, 특별한 이유가 없는 한 인텔 및 엔비디아를 사용하는 것을 추천한다.
그러나 내부 기능만 신경 써서는 안된다. PC월드의 영상 디렉터인 아담 패트릭 머레이는 “영상 편집에 이상적인 노트북에는 카메라로 촬영 중 영상 파일을 저장하는 SD 카드 리더가 포함되어 있다”라고 강조한다. 또한 머레이는 영상 편집에 이상적인 게임용 노트북에서 흔히 볼 수 있는 초고속 1080p 패널보다 4k, 60Hz 패널을 갖춘 노트북을 선택할 것을 추천한다.
4K 영상을 잘 편집하려면 4K 패널이 필요하며, 초고속 화면 재생률은 게임에서처럼 영상 편집에는 아무런 의미가 없다. 예를 들어, 개인 유튜브 채널용으로 일상적인 영상만 만드는 경우 색상 정확도가 중요하지 않을 수 있다. 그러나 색상 정확도가 중요할 경우, 델타 E < 2 색상 정확도와 더불어 DCI-P3 색 영역 지원은 필수적이다.
게임용 노트북은 사양이 좋지만 콘텐츠 제작용으로는 조금 부족해 보일 수 있다. 게임용과 콘텐츠 제작용으로 함께 쓰는 노트북을 원한다면, 게임용으로 노트북 한 대를 구매하고, 색상을 정확히 파악하기 위한 모니터를 추가로 구매하는 것도 방법이다. editor@itworld.co.kr
코어가 많은 그래픽카드의 경우 가격이 상상 이상으로 높습니다. 빠르면 빠를수록 좋겠지만 어디까지나 예산에 맞춰 구매를 해야 하는 현실을 감안할 수 밖에 없는 것 같습니다.
한가지 유의할 점은 엔비디아의 GTX 게이밍 하드웨어는 모델에 따라 다르기는 하지만, 볼륨 렌더링의 속도가 느리거나 오동작 등 몇 가지 제한 사항이 있습니다. 일반적으로 노트북에 내장된 통합 그래픽 카드보다는 개별 그래픽 카드를 강력하게 추천합니다. 최소한 그래픽 메모리는 512MB 이상이어야 하고 1GB이상을 권장합니다.
2021-12-15 현재 그래픽카드의 성능 순위는 위와 다음과 같습니다. 출처: https://www.videocardbenchmark.net/high_end_gpus.html
주요 Notebook
출시된 모든 그래픽 카드가 노트북용으로 장착되어 출시되지는 않기 때문에, 현재 오픈마켓 검색서비스를 제공하는 네이버에서 Lenovo Quadro 그래픽카드를 사용하는 노트북을 검색하면 아래와 같습니다. 검색 시점에 따라 상위 그래픽카드를 장착한 노트북의 대략적인 가격을 볼 수 있을 것입니다.
<검색 방법> 네이버 쇼핑 검색 키워드 : 컴퓨터 제조사 + 그래픽카드 모델 + NoteBook 형태로 검색 Lenovo quadro notebook or HP quadro notebook 또는 Lenovo firepro notebookorHP firepronotebook
( 2021-12-15기준)
대부분 검색 시점에 따라 최신 CPU와 최신 그래픽카드를 선택하여 검색을 하면 예산에 적당한 노트북을 자신에게 맞는 최상의 노트북을 어렵지 않게 선택할 수 있습니다.
Turbidity currents are important carriers for transporting terrestrial sediment into the deep sea, facilitating the transfer of matter and energy between land and the deep sea. Previous studies have suggested that turbidity currents can exhibit high velocities during their movement in submarine canyons. However, the maximum vertical descent velocity of high-concentration turbid water simulating turbidity currents does not exceed 1 m/s, which does not support the understanding that turbidity currents can reach speeds of over twenty meters per second in submarine canyons. During their movement, turbidity currents can compress and push the water ahead, generating propagating waves. These waves, known as excitation waves, exert a force on the seafloor, resuspending bottom sediments and potentially leading to the generation of secondary turbidity currents downstream. Therefore, the propagation distance of excitation waves is not the same as the initial journey of the turbidity currents, and the velocity of excitation waves within this journey has been mistakenly regarded as the velocity of the turbidity currents. Research on the propagation velocity of excitation waves is of great significance for understanding the sediment supply patterns of turbidity currents and the transport patterns of deep-sea sediments. In this study, numerical simulations were conducted to investigate the velocity of excitation waves induced by turbidity currents and to explore the factors that can affect their propagation velocity and amplitude. The relationship between the velocity and amplitude of excitation waves and different influencing factors was determined. The results indicate that the propagation velocity of excitation waves induced by turbidity currents is primarily determined by the water depth, and an expression (v2 = 0.63gh) for the propagation velocity of excitation waves is provided.
Submarine turbidity currents, often referred to as underwater rivers, are important carriers that transport terrestrial sediments to the deep sea [1,2,3,4,5,6,7]. These turbidity currents, carrying a large amount of silt and sand, not only have strong erosive capabilities on the seabed [8,9,10], but also pose a threat to underwater communication cables, resulting in significant economic losses [11,12,13]. For example, the 2006 Pingdong earthquake in Taiwan caused the rupture of 11 submarine cables within the Kaoping Canyon, resulting in a slowdown in network speed in Southeast Asia for 49 days and requiring the deployment of 11 cable ships for repairs [13,14,15]. Investigating the velocity and patterns of turbidity currents in submarine canyons is of great significance for the protection of infrastructure such as pipelines and cables in these canyons. One of the main methods for quantitatively studying the velocity of turbidity currents in submarine canyons is to infer their speed through cable ruptures. The first confirmed occurrence of cable rupture caused by a turbidity current was in 1929, when the Grand Banks earthquake triggered the continuous rupture of 12 submarine cables. Inferred maximum turbidity current velocities reached 28 m/s [16,17,18]. Subsequently, multiple cable rupture incidents caused by turbidity currents have occurred worldwide. Table 1 summarizes the inferred maximum turbidity current velocities from these cable rupture incidents.
Event
Maximum Turbidity Velocity
References
18 November 1929 Grand Banks earthquake
28 m/s
[16,19,20,21]
1953 Suva earthquake in the Fiji Islands
5.1 m/s
[22]
The Orleansville earthquake of 9 September 1954, Algeria
20.6 m/s
[23]
Earthquake, Solomon Islands, Western Pacific, 23 December 1966
10.3 m/s
[24]
Incident at Nice airport, France, 16 October 1979
7 m/s
[25]
Taitung earthquake, 22 August 2002
9.8 m/s
[26]
21 May 2003 earthquake in Algeria
15.8 m/s
[27]
The Taitung earthquake of 10 December 2003
16.5 m/s
[26]
The Taitung earthquake of 18 December 2003
18.6 m/s
[26]
Pingtung earthquake on 26 December 2006
20 m/s
[28]
Typhoon Morakot on 7–9 August 2009
16.6 m/s
[29]
The 15 January 2022 eruption of Hunga volcano
33.9 m/s
[30]
Table 1. Cable breakage events caused by turbidity currents worldwide.
Previous studies have shown that the maximum vertical velocity of high-concentration turbidity currents in water does not exceed 1 m/s, and the maximum downward velocity of spherical particles in water does not exceed 10 m/s [31]. The maximum velocity of professional athlete Usain Bolt in the 100 m sprint on land is 9.58 m/s, while dolphins in the ocean can reach speeds of up to 20 m/s. Deep-sea turbidity currents, characterized by a small density difference compared to water, are primarily driven by the gravitational component along the direction of flow. However, factors such as bed friction also need to be considered. The driving force behind turbidity currents is primarily the density difference between the turbulent flow and the surrounding water, as well as the gravitational downslope component. Previous studies have detected a maximum sediment concentration of 12% in the basal layer of turbidity currents [32]. However, even high concentrations of suspended sediment, such as 1720 g/L, in seawater with a density of 1020 g/L, do not exceed a maximum vertical velocity of 1 m/s [33]. Similarly, spherical particles also have a maximum settling velocity in water of less than 10 m/s [33]. Turbidity currents, being density-driven flows, have relatively low density differences compared to water, and the gentle slope of submarine canyons also contributes to a smaller gravitational downslope force. Additionally, the influence of bed friction and other factors related to sediment deposition needs to be considered. It is incredible to think that turbidity currents can achieve flow velocities as high as 28 m/s [16,18,28,34,35]. When submarine landslides occur on continental slopes, the sliding mass entering the bottom of submarine canyons can cause the destruction of soft sediment beds. The mixing of sliding or flowing sediment with water forms turbidity currents. Turbidity currents exert pressure and propel the water ahead, forming an excitation wave. This aligns with Paull’s hypothesis that in the course of turbidity currents, a high-pressure zone is formed ahead, capable of causing an increase in pore water pressure in the sediment ahead [36]. Similar to surging waves, the excitation waves generated can propagate downstream along the submarine canyon, with a propagation velocity much greater than the velocity of turbidity currents [31]. The rapid propagation of excitation waves can exert a force on the seafloor of the submarine canyon, causing the resuspension of sediment in front of the head of the turbidity currents, which may lead to the formation of secondary turbidity currents at some downstream locations. The distance between the secondary and initial turbidity currents is actually the propagation distance of the excitation waves, rather than the journey of the initial turbidity currents. Therefore, the speed of the excitation waves within this distance is mistakenly considered as the velocity of the turbidity currents (see Figure 1). This may explain why the velocity of the turbidity currents as deduced from cable breakages is so high.
Figure 1. Diagram of excitation wave propagation due to turbidity current (v1 is the velocity of turbidity current. This refers to the ratio of distance to time experienced by a turbidity current mass moving underwater. v2 is the velocity of secondary turbidity current: the rapidly propagating excitation wave applies a force on the submarine canyon floor, leading to the destruction of the soft sediment floor and the secondary turbidity current. v is the propagation velocity of the excitation wave; this refers to the propagation velocity of the turbidity current excitation wave. This speed is not the velocity of the motion of the water mass. At time t0, the initial turbidity current moves underwater, pushing the stationary water in front to generate an excitation wave. At time t1, the excitation wave is propagating. At time t2, the rapidly propagating excitation wave exerts pressure on the soft bottom bed, resulting in the destruction of the bottom bed and secondary turbidity current).
Turbidity currents are mass movements composed of sediment particles, with a high concentration of the dense basal layer near the seabed. Depending on their density and granulometric composition, turbidity currents can move along submarine canyons through mechanisms such as diffusion, collapse, and flow [37], which differ from the downward movement as a single entity of landslide bodies after slope failure (this distinguishes them from surges). Additionally, during the long-distance movement of turbidity currents in canyons, the completion of subsequent water replenishment may generate multiple excitation waves. Furthermore, secondary excitation waves may also occur during the movement of secondary turbidity currents triggered by the initial turbidity current, which differs significantly from the surges caused by submarine landslides. Furthermore, previous studies [38,39,40,41] on sediment supply during turbidity current movements have mostly focused on the scouring action on the seabed, whereas the resuspension of sedimentary deposits in front of the initial turbidity current caused by excitation waves may serve as an effective mode of sediment supply during the long-distance transport of turbidity currents. In 2023, Ren et al. proposed that the cause of the long-distance high-speed motion of turbidity currents is due to the excitation waves caused by the primary turbidity currents. However, only preliminary research has been conducted on the comparison of excitation wave velocity and solitary wave velocity, and there has been no specific discussion on the reasons for the excitation wave velocity being much greater than that of the turbidity current. In an experiment conducted using an indoor flume, it was observed that the wavelength of the excitation waves was much larger than the water depth, similar to shallow water waves [33]. The amplitude of excitation waves in proportion to their wavelength was small, consistent with the theory of small-amplitude waves. Similar to the velocity model of shallow water waves, it is expected that the propagation speed of excitation waves is also influenced by the water depth. However, since excitation waves are triggered by sediment-laden turbidity currents, the velocity model may differ from that of surface waves induced by gravitational flows. The purpose of this study is to simulate and investigate the effects of different factors on the propagation velocity and amplitude of excitation waves through a validated numerical model based on laboratory experiments. The study aims to determine the maximum propagation velocity of excitation waves at a field scale and whether there is attenuation in the long-distance propagation after their formation. In recent studies, seafloor sediment flows have been collectively referred to as turbidity currents [42]. Therefore, we simulated the movement of turbidity currents by sediment flow. This study uses the CFD-based fluid computation software FLOW-3D to simulate the underwater movement process of turbidity currents. The numerical model is validated against indoor experimental results. During the simulation process, a velocity model for surging wave generation triggered by submarine landslides is used as a reference, and multiple factors that may affect the propagation velocity of the excitation wave are considered. By controlling a single variable, the main factors influencing the excitation wave propagation velocity are determined, and the corresponding expression for excitation wave propagation velocity is provided. The results indicate that the propagation velocity of the excitation wave induced by turbidity currents is primarily determined by the water depth. This research provides a new perspective for understanding the high-speed movement of turbidity currents in submarine canyons and enriches the understanding of the movement patterns of turbidity currents in submarine canyons. In addition, studying the propagation speed of excitation waves is highly significant for the resuspension of underwater sediments, as well as the re-circulation of carbon sequestration, nutrients, heavy metals, and microplastics.
2. Experimental Study on Excitation Waves Induced by Turbidity Currents
2.1. Experimental Design and Apparatus
The experimental apparatus used for the turbidity current-induced excitation wave tests is a straight water tank [33]. The water tank is 12.5 m long, 0.5 m wide, and 0.7 m high. A turbidity source area is located on the right side of the tank to generate turbidity currents. The tank is equipped with a terrain with a certain slope. Turbidity currents are generated underwater using a weir. The mass ratio of silt and clay used in the experimental turbid water solution was 8:2, with a density of 1600 kg/m3. Previous experiments have shown that this turbid mixture can reach a maximum flow velocity of 18.7 cm/s [31]. Three pressure sensors are placed along the straight section of the tank at intervals of 0.4 m. These sensors continuously monitor the bottom shear stress caused by the turbidity current-induced excitation wave, as well as the force exerted by the turbidity current itself on the bed. The monitoring frequency is set at 100 Hz.
2.2. Experimental Phenomenon and Results
In the laboratory water tank experiments, it was observed that as the turbidity current propagates, a wave is generated ahead of the turbidity front, moving in the same direction as the current and with a velocity greater than the turbidity current velocity [33]. By monitoring the pressure changes on the bed during the turbidity current motion [33], the propagation velocity of the excitation wave, the head movement velocity of the turbidity current, and the amplitude of the excitation wave (obtained from the measured surface elevation changes caused by the wave) can be estimated based on the distances between the sensors and the time when the pressure change peaks occur. The results of indoor experiments on turbidity currents indicate that they can compress and propel the water ahead of them, generating excitation waves similar to pulses. The propagation speed of these excitation waves caused by turbidity currents is found to be much greater than the velocity of the turbidity current movement at its head, as determined by pressure sensors installed on the seabed.
3. Numerical Simulation of Excitation Waves Induced by Turbidity Currents
FLOW-3D is a powerful computational fluid dynamics (CFD) software that excels in making accurate calculations of free surface and six-degrees-of-freedom motions of objects. Similar to other CFD software, FLOW-3D consists of three modules: pre-processing, solver, and post-processing. In recent years, there have been many simulations of turbidity currents using FLOW-3D due to its superior capabilities. For example, Heimsund (2007) simulated turbidity currents in the Monterey Canyon system using FLOW-3D based on high-resolution bathymetry and flow data [43]. Zhou et al. (2017) used FLOW-3D software to simulate turbidity currents in a flume with obstacles, analyzing the impact of the proportion between obstacle height and flume height on the movement of turbidity currents, including their velocity, flow state, and morphological evolution [44]. In this study, using the CFD software FLOW-3D, the underwater motion process of turbidity currents is simulated. The model is validated by comparing it with experimental results, and the motion of the waves induced by turbidity currents is simulated based on this validation.
3.1. Control Equations
FLOW-3D, a mature three-dimensional fluid simulation software, is used in this study. It employs the RNG turbulence model, which is capable of handling high strain rate flows and is suitable for simulating excitation waves. The research focus of this paper is on sediment gravity flows (turbulent flows), and the control equations used in the calculations include the basic continuity equation, the momentum equation, the turbulent kinetic energy k equation, and the turbulent kinetic energy dissipation rate ε equation.
The continuity equation:
The momentum equation:
The turbulence model:
k equation:
ε equation:
where u, v and w is the flow velocity component in x, y and z directions; Ax, Ay and Az represent the area fraction that can flow in x, y and z directions; Gx, Gy and Gz are the gravitational acceleration in x, y and z directions; fx, fy and fz are the viscous forces in the three directions; VF is the fraction of the volume that can flow; ρ is the fluid density; p is the pressure acting on the fluid element; k is the turbulence energy; ε is the turbulence kinetic energy dissipation rate; μ is turbulence viscosity coefficient
where u, v and w is the flow velocity component in x, y and z directions; Ax, Ay and Az represent the area fraction that can flow in x, y and z directions; Gx, Gy and Gz are the gravitational acceleration in x, y and z directions; fx, fy and fz are the viscous forces in the three directions; VF is the fraction of the volume that can flow; ρ is the fluid density; p is the pressure acting on the fluid element; k is the turbulence energy; ε is the turbulence kinetic energy dissipation rate;
μ is turbulence viscosity coefficient where Cμ = 0.0845;
Gk is the turbulent kinetic energy generation term, expressed as
and σk and σε are the Prandtl numbers corresponding to the turbulent kinetic energy and dissipation rate, respectively, both of which are 1.39.
In addition,where Cε1 and Cε2 are the empirical constants, 1.42 and 1.68, respectively.
Furthermore,
where , η0 = 4.377, β = 0.012.
The general mass continuity equation is as follows:
where VF is the fractional volume open to flow, ρ is the fluid density, RDIF is a turbulent diffusion term, and RSOR is the mass source.
3.2. Model Validation
To determine the factors affecting the velocity of the turbidity-induced excitation wave and its velocity expression, first, the indoor flume test was taken as the prototype. Then, a 1:1 geometric solid model was established, and the simulation parameters were set to be consistent with the flume test parameters [33]. Finally, the simulation results were compared with the laboratory test results.
The computational domain employs the method of unstructured grid and is entirely divided into structured orthogonal grids. Nested grids are used for local refinement at the interfaces of straight sections, resulting in a total of 800,000 grid cells after refinement.
The simulation results were compared with the indoor experimental results, with the velocity of the excitation wave and the turbidity current head being represented by changes in surface elevation and water density. The experimental and simulation results are shown in Table 2, and the calculation formula for the error is |Calculated value−Test value|Test value×100%Calculated value-Test valueTest value×100%.
Result
Propagation Velocity of Excitation Wave (m/s)
Velocity of Turbidity Current (m/s)
Excitation Wave Amplitude (m)
Sensor 1 to 2
Sensor 2 to 3
Sensor 1 to 2
Sensor 2 to 3
Sensor 1 to 2
Sensor 2 to 3
Test results
1.54
1.48
0.24
0.23
0.029
0.03
Computed results
1.55
1.52
0.25
0.23
0.03
0.03
Error range
0.6%
2.7%
4.2%
0%
3.4%
0%
Table 2. The test results of the propagation velocity of the excitation wave, the turbidity current velocity, and the excitation wave amplitude are compared with the simulation results.
From the above comparison, it can be observed that the simulated velocities of the excitation wave and the head of the turbidity current align well with the experimental results, indicating the rationality of using the numerical model established in this study for simulating the propagation velocity of the excitation wave induced by turbidity currents.
3.3. Analysis of Factors Affecting the Propagation Velocity of Excitation Waves
An analysis of the factors influencing the propagation velocity of excitation waves was conducted using numerical simulation. The reference model for wave velocity was based on the surge velocity model. The main factors affecting the propagation velocity of excitation waves were summarized, including the turbidity current density ρ, the thickness of the turbidity current source area d, the length of the turbidity current source area L, the depth at the initial flow of turbidity currents h, the canyon width l, and the initial velocity of the turbidity current v0 (as shown in Figure 2). The simulations were performed using a controlled variable approach for different parameters, and the velocity changes of the excitation wave were obtained, as shown in Table 3. The slope angle was fixed at 3°, and sensors were placed at intervals of 100 m starting from a distance of 500 m from the turbidity current source area (named Sensors 1, 2, 3). These sensors were used to extract surface elevation, density, and other relevant parameters at their respective locations. We can obtain the propagating velocity of excitation waves by measuring the time difference in surface elevation changes at the monitoring points. Similarly, we can determine the propagation velocity of turbidity currents by measuring the time difference in density changes.
Figure 2. Excitation wave velocity simulation model and parameters.
Group Order
Turbidity Current Density (kg/m3)
Length of Turbidity Source Area (m)
Canyon Width (m)
Thickness of Turbidity Source Area (m)
Depth (m)
Initial Velocity of Turbidity Current (m/s)
Propagation Velocity of Excitation Wave (m/s)
Excitation Wave Amplitude (m)
Velocity of Turbidity Current (m/s)
1
1600
1000
200
20
200
0
33.43
0.345
5.88
2
1500
1000
200
20
200
0
33.09
0.304
5.41
3
1400
1000
200
20
200
0
33.35
0.223
4.99
4
1300
1000
200
20
200
0
33.33
0.177
4.35
5
1200
1000
200
20
200
0
33.86
0.092
3.74
6
1600
1000
200
40
200
0
33.05
1.109
9.09
7
1600
1000
200
60
200
0
33.39
2.689
10.79
8
1600
1000
200
80
200
0
33.21
4.828
12.91
9
1600
1000
200
100
200
0
36.43
7.744
13.79
10
1600
200
200
20
200
0
32.93
0.181
5.58
11
1600
400
200
20
200
0
33.49
0.25
5.71
12
1600
600
200
20
200
0
33.06
0.278
5.79
13
1600
800
200
20
200
0
33.17
0.31
5.72
14
1600
1000
200
20
100
0
26.67
0.56
5.72
15
1600
1000
200
20
300
0
39.65
0.169
5.80
16
1600
1000
200
20
400
0
45.98
0.12
5.80
17
1600
1000
200
20
500
0
49.97
0.08
5.96
18
1600
1000
100
20
200
0
33.60
0.354
5.72
19
1600
1000
300
20
200
0
32.98
0.338
5.97
20
1600
1000
400
20
200
0
33.27
0.356
5.87
21
1600
1000
500
20
200
0
33.31
0.365
5.86
22
1600
1000
200
20
200
2
33.50
0.532
4.35
23
1600
1000
200
20
200
5
33.12
1.389
6.56
24
1600
1000
200
20
200
8
33.52
2.271
8.10
25
1600
1000
200
20
200
10
33.33
2.878
8.99
Table 3. Simulation results under different variables conditions.
The variations in surface elevation at three sensor locations in the simulated results of five different turbidity current density groups are presented in Figure 3.
Figure 3. Simulation of propagating velocity of excitation wave under the sole variable condition of turbulent current density. (Length of turbidity source area: 1000 m; canyon width: 200 m; thickness of turbidity source area: 20 m; depth: 200 m; initial velocity of turbidity current: 0 m/s).
Based on the simulation results described above, while keeping all other conditions constant, the impact of a single variable, namely, the turbidity current density, on the propagation velocity and amplitude of the excitation wave was analyzed. By fitting the data, the relationship between turbidity current density and the propagation velocity of turbidity currents as well as the amplitude of the excitation wave was obtained, as shown in Figure 4.
Figure 4. Relationship between turbidity current density and turbidity current velocity, as well as excitation wave amplitude.
The simulation results indicate that changes in turbidity current density, while keeping the other conditions constant, do not result in a change in the propagation velocity of the excitation waves. However, they do affect the amplitude of the excitation waves and the velocity of the turbidity current itself. The simulation reveals that within the selected density range, both the amplitude of the excitation waves and the velocity of the turbidity current increase with increasing turbidity current density. When the turbidity current density is equal to that of water (ρTurbidity current = ρWater), there is no turbidity current or excitation wave generation. Thus, the relationship between the turbidity current velocity (v) and density (ρ) is expressed as v = −34.80643 + 0.05082•ρ − 1.59286 × 10−5ρ2 (ρ > 1000, R2 = 0.994). Additionally, the relationship between the amplitude of the excitation waves (A) caused by turbidity currents and density (ρ) is expressed as A = −0.6021 + 5.9729 × 10−4ρ (ρ > 1000, R2 = 0.991).
3.3.2. The Influence of the Thickness of the Turbidity Source Area on the Propagation Velocity and Amplitude of Excitation Waves
The variations in surface elevation at three sensor locations in the simulated results of five different thickness of turbidity source area groups are presented in Figure 5.
Figure 5. Simulation of propagating velocity of excitation wave under the sole variable condition of thickness of turbidity source area. (Turbidity current density: 1600 kg/m3; length of turbidity source area: 1000 m; canyon width: 200 m; depth: 200 m; initial velocity of turbidity current: 0 m/s).
Based on the simulation results described above, while keeping all other conditions constant, the impact of a single variable, namely, the thickness of the turbidity source area, on the propagation velocity and amplitude of the excitation wave was analyzed. By fitting the data, the relationship between the thickness of the turbidity source area and the propagation velocity of the turbidity current as well as the amplitude of the excitation wave was obtained, as shown in Figure 6.
Figure 6. Relationship between thickness of turbidity source area and turbidity current velocity, as well as excitation wave amplitude.
Based on the simulated results mentioned above, it can be concluded that, while keeping the other conditions constant, changing only the thickness of the turbidity current source area does not affect the propagation velocity of the excitation waves. However, it does impact both the amplitude of the excitation waves and the velocity of the turbidity current itself. The simulation reveals that within the selected range of thickness values for the turbidity current source area, both the amplitude of the excitation waves and the velocity of the turbidity current increase with an increase in the thickness of the source area. Additionally, it is observed that when the length of the turbidity current source area is zero, neither the turbidity current nor the excitation waves are generated (i.e., no turbidity current is produced when hTurbidity current = 0). Therefore, the relationship between the velocity (v) of the turbidity current and its thickness (h) is expressed as v = 0.27983•h − 0.00146•h2 (h ≥ 0, R2 = 0.999). Similarly, the relationship between the amplitude (A) of the excitation waves caused by the turbidity current and its thickness (h) is A = −0.00375•h − 0.0008•h2 (h ≥ 0, R2 = 0.999).
3.3.3. The Influence of the Length of the Turbidity Source Area on the Propagation Velocity and Amplitude of Excitation Waves
The variations in surface elevation at three sensor locations in the simulated results of five different length of turbidity source area groups are presented in Figure 7.
Figure 7. Simulation of propagating velocity of excitation wave under the sole variable condition of length of turbidity source area. (Turbidity current density: 1600 kg/m3; canyon width: 200 m; thickness of turbidity source area: 20 m; depth: 200 m; initial velocity of turbidity current: 0 m/s).
Based on the simulation results described above, while keeping all other conditions constant, the impact of a single variable, namely, the length of the turbidity source area, on the propagation velocity and amplitude of the excitation wave was analyzed. By fitting the data, the relationship between the length of the turbidity source area and the amplitude of the excitation wave was obtained, as shown in Figure 8.
Figure 8. Relationship between length of turbidity source area and excitation wave amplitude.(Amplitude refers to the surface elevation change caused by the excitation wave).
Through simulations, it has been determined that within the chosen range of the length of the turbidity source area, the amplitude of the excitation waves increases with an increase in the length of the turbidity source area. When the length of the turbidity source area is zero, there is no turbidity current and no generation of excitation waves (i.e., when LTurbidity current = 0). Additionally, for large lengths of the turbidity source area, under the condition of sufficient sediment supply, the variations in surface elevation caused by the waves generated by turbidity currents are negligible. Therefore, the relationship between the amplitude of the excitation waves (A) generated by turbidity currents and the length of the turbidity source area (L) is expressed as follows: A = −0.3624 + 0.10305•ln(L − 6.15619) (L ≥ 0, R2 = 0.997).
3.3.4. The Influence of Depth on the Propagation Velocity and Amplitude of Excitation Waves
The variations in surface elevation at three sensor locations in the simulated results of five different depth groups are presented in Figure 9.
Figure 9. Simulation of propagation velocity of excitation wave under the sole variable condition of depth. (Turbidity current density: 1600 kg/m3; length of turbidity source area: 1000 m; canyon width: 200 m; thickness of turbidity source area: 20 m; initial velocity of turbidity current: 0 m/s).
Based on the simulation results described above, while keeping all other conditions constant, the impact of a single variable, namely, depth, on the propagation velocity and amplitude of the excitation wave was analyzed. By fitting the data, the relationship between depth and the propagation velocity of the excitation wave as well as the amplitude of the excitation wave was obtained, as shown in Figure 10.
Figure 10. Relationship between depth and propagating velocity of excitation wave, as well as excitation wave amplitude.
As the water depth approaches infinity, the excitation wave amplitude can only approach zero but cannot reach zero. Therefore, the characteristics of the excitation wave amplitude change with the water depth are similar to those of the velocity propagation of the excitation wave. The relationship between the velocity of the excitation wave induced by turbidity currents (vExcitation wave) and the water depth (H) can be described as vExcitation wave = −287.05446 + 48.59211•ln(H + 535.14863) (R2 = 0.998). The relationship between the excitation wave amplitude (A) and the water depth (H) can be expressed as A = 1.46573 − 0.22816•ln(H − 47.67563) (R2 = 0.985).
3.3.5. The Influence of the Canyon Width on the Propagation Velocity and Amplitude of Excitation Waves
The variations in surface elevation at three sensor locations in the simulated results of five different canyon width groups are presented in Figure 11.
Figure 11. Simulation of propagating velocity of excitation wave under the sole variable condition of canyon width. (Turbidity current density: 1600 kg/m3; length of turbidity source area: 1000 m; thickness of turbidity source area: 20 m; depth: 200 m; initial velocity of turbidity current: 0 m/s).
When the canyon width is taken as the single variable condition, changing the canyon width does not significantly affect the propagation velocity of excitation waves, the amplitude of excitation waves, and the velocity of turbidity currents. Therefore, it can be concluded that, without considering the impact of the differences in the terrain and sediment on the canyon width, the canyon width has no impact on the propagation of excitation waves and the movement of turbidity currents.
3.3.6. The Influence of the Initial Velocity of the Turbidity Current on the Propagation Velocity and Amplitude of Excitation Waves
The variations in surface elevation at three sensor locations in the simulated results of five different initial velocity of turbidity current groups are presented in Figure 12.
Figure 12. Simulation of propagating velocity of excitation wave under the sole variable condition of initial velocity of turbidity current. (Turbidity current density: 1600 kg/m3; length of turbidity source area: 1000 m; canyon width: 200 m; thickness of turbidity source area: 20 m; depth: 200 m).
Based on the simulation results described above, while keeping all other conditions constant, the impact of a single variable, namely, the initial velocity of the turbidity current, on the propagation velocity and amplitude of the excitation wave was analyzed. By fitting the data, the relationship between the initial velocity of the turbidity current and the amplitude of the excitation wave was obtained, as shown in Figure 13.
Figure 13. Relationship between initial velocity of turbidity current and excitation wave amplitude.
Based on the simulation, it is observed that within the selected range of the initial velocity of the turbidity current, the amplitude of the excitation wave increases linearly with the increase in the initial velocity of the turbidity current. Therefore, the relationship between the amplitude (A) of the excitation wave caused by the turbidity current and the initial velocity of the turbidity current (v0) can be expressed as A = 0.34 + 0.24084•v0 (A ≥ 0, R2 = 0.992).
Through controlling the simulation calculation of a single variable, it was found that there are several factors that can affect the amplitude of the excitation wave. These factors include the turbidity current density ρ, the thickness of the turbidity current source area d, the length of the turbidity current source area L, the water depth h, and the initial velocity of the turbidity current v0. In contrast, there are relatively few factors that influence the propagation velocity of the excitation wave. Within the selected parameter range, only the water depth can affect the propagation velocity of the excitation wave. The physical parameters of the turbidity current, including the turbidity current density ρ, the thickness of the turbidity current source area d, the length of the turbidity current source area L, the canyon width l, and the initial velocity of the turbidity current v0, have no direct influence on the propagation velocity of the excitation wave. Therefore, the turbidity current only serves as a triggering factor for the excitation wave and is not directly related to the propagation velocity of the excitation wave.
3.4. Analyze the Changes in Propagation Velocity of Excitation Waves along a Path
In order to further investigate the underlying truth behind the variation in the propagation velocity of the excitation wave, a discussion on whether there is velocity attenuation along the propagation path of the excitation wave is conducted. Since the seventh group of the excitation wave causes significant changes in surface elevation, the seventh group of the excitation wave is selected as the research object in order to study the variations in surface elevation along the propagation path of the excitation wave. The changes in surface elevation are extracted every 200 m along the sediment slope (with the first extraction point located 400 m away from the source area of the turbidity current). A total of six sets of surface elevation data are extracted (ranging from 400 m to 1400 m distance from the source area of the turbidity current), as shown in Figure 14.
Figure 14. Surface elevation changes during excitation wave propagation along sediment slopes.
The amplitudes and propagation velocities of the excitation wave at each point are shown in Table 4.
Distance from Turbidity Current Source Area (m)
Propagation Velocity of Excitation Wave (m/s)
Excitation Wave Amplitude (m)
400
33.34
2.524
600
36.79
2.596
800
37.13
2.589
1000
39.99
2.566
1200
40.04
2.542
1400
40.13
2.523
Table 4. Excitation wave velocity during the excitation wave propagation along the sediment slope.
From the table above, it can be observed that the amplitude of the excitation wave does not change while traveling along the slope. This indicates that the change in surface elevation caused by the propagation of the excitation wave does not attenuate. Furthermore, the propagation velocity of the excitation wave gradually increases, although the change is not very pronounced. This variation may be attributed to the change in the water depth caused by the sloping bed. To investigate this, a simulation was conducted in a straight channel with a length of 3000 m. Six sampling points were established from 400 m to 1400 m away from the turbidity current source area to extract the amplitude of the excitation wave. The results of the simulation are presented in Figure 15.
Figure 15. Surface elevation changes during wave propagation along a straight channel.
The amplitudes and propagation velocities of the excitation wave at each point are shown in Table 5.
Distance from Turbidity Current Source Area (m)
Propagation Velocity of Excitation Wave (m/s)
Excitation Wave Amplitude (m)
400
33.89
2.559
600
37.66
2.692
800
37.12
2.712
1000
36.92
2.717
1200
37.09
2.715
1400
37.48
2.718
Table 5. Excitation wave velocity during the propagation along the straight channel.
The data from the table above indicate that during the propagation of the excitation wave along a straight water channel, its velocity remains constant, except for a slight decrease at the initial point. This phenomenon may be attributed to the fact that in the starting phase, the excitation wave is not fully developed, and hence its velocity is relatively smaller. However, once it is fully developed, the propagation velocity of the excitation wave does not decrease in subsequent processes. Therefore, the propagation velocity of the excitation wave is only dependent on the real-time water depth of the wave. In future studies, we aim to explore the relationships between these influencing factors and other physical parameters, such as the speed of wave propagation, using the effective and accurate method of machine learning algorithms [45].
3.5. Expression of the Propagation Velocity of the Excitation Wave
The propagation of the excitation wave along a long distance does not experience an attenuation in velocity, as is the case with the propagation velocity of solitary waves. Referring to the estimated wave propagation velocity (the square of the propagation velocity is directly proportional to the water depth amplitude) [46], the wavelengths under different water depth conditions were extracted, as shown in Table 6.
Depth (m)
Propagation Velocity of Excitation Wave (m/s)
Excitation Wave Amplitude (m)
Excitation Wave Length (m)
100
26.67
0.56
2580
200
33.43
0.35
2850
300
39.65
0.17
3250
400
45.98
0.12
3600
500
49.97
0.08
4150
1000
66.67
0.04
6000
2000
90.91
0.02
9500
4000
165.84
0.3
17600
Table 6. Physical parameters of excitation wave under different water depth conditions.
From the simulation results of a single variable, the water depth, it could be seen that the wavelengths of the excitation waves were much larger than the water depth. Therefore, further simulations were conducted under water depth conditions ranging from 1000 m to 4000 m. Due to the minimal change in wave amplitude when the water depth reached 4000 m, it was not possible to observe a distinct waveform. However, through simulations with the thickness of the turbidity current source area as the single variable, it was found that an increase in the thickness of the source region led to a larger amplitude of the excitation waves, but it did not affect the wavelength of the excitation waves. Therefore, in order to better extract the wavelength of the excitation waves, the thickness of the source region in the simulation with a water depth of 4000 m was set to 200 m.
Through simulations at water depths of 1000 m and 4000 m, it is observed that the wavelengths of the excitation waves are much larger than the water depth, indicating that these waves belong to the category of shallow water waves. The amplitude of the excitation waves is relatively small compared to their wavelength, aligning with the small amplitude wave theory [47]. According to this theory, the wave velocity of shallow water waves is only dependent on the water depth (h) and gravity acceleration (g), regardless of the wave period. In the case of excitation waves induced by turbidity currents in deep water, the amplitudes of these waves are relatively small compared to the water depth. Referring to the expression for shallow water waves (when the relative water depth, which is the ratio of water depth to wavelength, is much smaller than 1/2), the wave velocity is denoted as 𝐶𝑠=√𝑔ℎ. This implies that the propagation velocity of the excitation waves is also solely related to the water depth. Therefore, a fitting of the square of the propagation velocity of the excitation waves (v2) and the water depth (h) was conducted (Figure 16).
Figure 16. The relationship between the propagation velocity of excitation wave and the depth.
Through fitting, the following can be obtained:
Through fitting, it can be discovered that the propagation model of the velocity of excitation waves is different from the shallow water wave theory. This is because turbidity currents, as granular materials, generate excitation waves by pushing the water in front of them with sediment particles underwater, which is different from the surges formed by solid blocks entering the ocean. Additionally, excitation waves formed by turbidity currents occur in an underwater environment, which may be the reason why the propagation velocity equation for the excitation waves behaves as if the velocity squared is equal to half the Earth’s gravity. This equation reveals the variation in the propagation velocity of the excitation wave with depth, explaining why the average velocity between the monitoring points in the field is greater than the instantaneous velocity measured at these points [41]. Further theoretical research on the propagation velocity of excitation waves requires subsequent field monitoring and the deployment of monitoring systems to more thoroughly investigate the fundamental causes.
4. Conclusions
This study aimed to investigate the velocity of turbidity current-induced excitation waves through numerical simulation. By fixing a single variable, different factors that could affect the propagation velocity and amplitude of the excitation waves were analyzed and discussed, leading to the following three conclusions:
Within the selected parameter range, there are several factors that can influence the amplitude of the excitation waves, including the turbidity current density ρ, the thickness of the turbidity current source area d, the length of the turbidity current source area L, the water depth h, and the initial velocity of the turbidity current v0.The amplitude of the excitation waves is positively correlated with the turbidity density, the thickness of the source area, the length of the source area, and the initial velocity, while it is negatively correlated with the water depth.
Within the selected parameter range, only the water depth can affect the propagation velocity of the excitation waves. As the water depth increases, the propagation velocity of the excitation waves also increases, and a relationship of v2 = 0.63gh (R2 = 0.967) is established between the square of the propagation velocity v2 and the water depth h.
During the propagation of the excitation waves, both the propagation velocity and the changes in surface elevation caused by the waves do not attenuate. Considering the relatively calm deep-sea environment, the high-speed propagation of the excitation waves and the resuspension of bottom sediments they cause not only complement the understanding of turbidity current motion patterns in canyons, but also provide new research directions for deep-sea sediment transport.
References
Azpiroz-Zabala, M.; Cartigny, M.J.B.; Talling, P.J.; Parsons, D.R.; Sumner, E.J.; Clare, M.A.; Simmons, S.M.; Cooper, C.; Pope, E.L. Newly recognized turbidity current structure can explain prolonged flushing of submarine canyons. Sci. Adv.2017, 3, e1700200.
Daly, R.A. Origin of submarine canyons. Am. J. Sci.1936, 5, 401–420.
Winterwerp, J. Stratification effects by fine suspended sediment at low, medium, and very high concentrations. J. Geophys. Res. Oceans.2006, 111, C5.
Nilsen, T.H.; Shew, R.D.; Steffens, G.S.; Studlick, J.R.J. Atlas of Deep-Water Outcrops; American Association of Petroleum Geologists: Tulsa, OK, USA, 2008.
Xu, J. Turbidity Current Research in the Past Century: An Overview. J. Ocean Univ. China2014, 44, 98–105.
Talling, P.J.; Allin, J.; Armitage, D.A.; Arnott, R.W.C.; Cartigny, M.J.B.; Clare, M.A.; Felletti, F.; Covault, J.A.; Girardclos, S.; Hansen, E.; et al. Key future directions for research on turbidity currents and their deposits. J. Sediment. Res.2015, 85, 153–169.
Maier, K.L.; Gales, J.A.; Paull, C.K.; Rosenberger, K.; Talling, P.J.; Simmons, S.M.; Gwiazda, R.; McGann, M.; Cartigny, M.J.; Lundsten, E. Linking direct measurements of turbidity currents to submarine canyon-floor deposits. Front. Earth Sci.2019, 7, 144.
Hughes Clarke, J.E. First wide-angle view of channelized turbidity currents links migrating cyclic steps to flow characteristics. Nat. Commun.2016, 7, 11896.
Normandeau, A.; Bourgault, D.; Neumeier, U.; Lajeunesse, P.; St-Onge, G.; Gostiaux, L.; Chavanne, C. Storm-induced turbidity currents on a sediment-starved shelf: Insight from direct monitoring and repeat seabed mapping of upslope migrating bedforms. Sedimentology2020, 67, 1045–1068.
Hill, P.R.; Lintern, D.G. Turbidity currents on the open slope of the Fraser Delta. Mar. Geol.2022, 445, 106738.
Summers, M. Review of deep-water submarine cable design. In Proceedings of the SubOptic 2001, Kyoto, Japan, 20–24 May 2001; p. 4.
Carter, L.; Gavey, R.; Talling, P.J.; Liu, J.T. Insights into Submarine Geohazards from Breaks in Subsea Telecommunication Cables. Oceanography2014, 27, 58–67.
Gavey, R.; Carter, L.; Liu, J.T.; Talling, P.J.; Hsu, R.; Pope, E.; Evans, G. Frequent sediment density flows during 2006 to 2015, triggered by competing seismic and weather events: Observations from subsea cable breaks off southern Taiwan. Mar. Geol.2017, 384, 147–158.
Carter, L.; Burnett, D.; Drew, S.; Hagadorn, L.; Marle, G.; Bartlett-Mcneil, D.; Irvine, N. Submarine Cables and the Oceans: Connecting the World; UNEP-WCMC Biodiversity Series 31; UNEP World Conservation Monitoring Centre: Cambridge, UK, 2010.
Qiu, W. Submarine cables cut after Taiwan earthquake in Dec 2006. Submar. Cable Netw.2011, 19.
Heezen, B.C.; Ewing, W.M. Turbidity currents and submarine slumps, and the 1929 Grand Banks [Newfoundland] earthquake. Am. J. Sci.1952, 250, 849–873.
Kuenen, P.H. Estimated size of the Grand Banks [Newfoundland] turbidity current. Am. J. Sci.1952, 250, 874–884.
Heezen, B.C.; Ericson, D.; Ewing, M. Further evidence for a turbidity current following the 1929 Grand Banks earthquake. Deep-Sea Res.1954, 1, 193–202.
Heezen, B.C. Whales entangled in deep sea cables. Deep-Sea Res.1957, 4, 105–115.
Piper, D.J.; Shor, A.N.; Farre, J.A.; O’Connell, S.; Jacobi, R. Sediment slides and turbidity currents on the Laurentian Fan: Sidescan sonar investigations near the epicenter of the 1929 Grand Banks earthquake. Geology1985, 13, 538–541.
Piper, D.J.; Cochonat, P.; Morrison, M.L. The sequence of events around the epicentre of the 1929 Grand Banks earthquake: Initiation of debris flows and turbidity current inferred from sidescan sonar. Sedimentology1999, 46, 79–97.
Houtz, R.; Wellman, H. Turbidity current at Kadavu Passage, Fiji. Geol. Mag.1962, 99, 57–62.
Heezen, B.C.; Ewing, M. Orleansville earthquake and turbidity currents. AAPG Bull.1955, 39, 2505–2514.
Krause, D.C.; White, W.C.; PIPER, D.J.W.; Heezen, B.C. Turbidity currents and cable breaks in the western New Britain Trench. Geol. Soc. Am. Bull.1970, 81, 2153–2160.
Piper, D.J.; Savoye, B. Processes of late Quaternary turbidity current flow and deposition on the Var deep-sea fan, north-west Mediterranean Sea. Sedimentology1993, 40, 557–582.
Soh, W.; Machiyama, H.; Shirasaki, Y.; Kasahara, J. Deep-sea floor instability as a cause of deepwater cable fault, off eastern part of Taiwan. AGU Fall Meet. Abstr.2004, 2, 1–8.
Cattaneo, A.; Babonneau, N.; Ratzov, G.; Dan-Unterseh, G.; Yelles, K.; Bracène, R.; De Lepinay, B.M.; Boudiaf, A.; Déverchère, J. Searching for the seafloor signature of the 21 May 2003 Boumerdès earthquake offshore central Algeria. Nat. Hazards Earth Syst. Sci.2012, 12, 2159–2172.
Hsu, S.-K.; Kuo, J.; Chung-Liang, L.; Ching-Hui, T.; Doo, W.-B.; Ku, C.-Y.; Sibuet, J.-C. Turbidity currents, submarine landslides and the 2006 Pingtung earthquake off SW Taiwan. Terr. Atmos. Ocean. Sci.2008, 19, 7.
Carter, L.; Milliman, J.D.; Talling, P.J.; Gavey, R.; Wynn, R.B. Near-synchronous and delayed initiation of long run-out submarine sediment flows from a record-breaking river flood, offshore Taiwan. Geophys. Res. Lett.2012, 39, L12603.
Clare, M.A.; Yeo, I.A.; Watson, S.; Wysoczanski, R.; Seabrook, S.; Mackay, K.; Hunt, J.E.; Lane, E.; Talling, P.J.; Pope, E.; et al. Fast and destructive density currents created by ocean-entering volcanic eruptions. Science2023, 381, 1085–1092.
Ren, Y.; Zhang, Y.; Xu, G.; Xu, X.; Wang, H.; Chen, Z. The failure propagation of weakly stable sediment: A reason for the formation of high-velocity turbidity currents in submarine canyons. J. Ocean. Limnol.2023, 41, 100–117.
Wang, Z.; Xu, J.; Talling, P.J.; Cartigny, M.J.B.; Simmons, S.M.; Gwiazda, R.; Paull, C.K.; Maier, K.L.; Parsons, D.R. Direct evidence of a high-concentration basal layer in a submarine turbidity current. Deep-Sea Res. Part I Oceanogr. Res. Pap.2020, 161, 103300.
Ren, Y.; Tian, H.; Chen, Z.; Xu, G.; Liu, L.; Li, Y. Two Kinds of Waves Causing the Resuspension of Deep-Sea Sediments: Excitation and Internal Solitary Waves. J. Ocean Univ. China2023, 22, 429–440.
Lambert, A.M.; Kelts, K.R.; Marshall, N.F. Measurements of density underflows from Walensee, Switzerland. Sedimentology1976, 23, 87–105.
Piper, D.J.W.; Shor, A.N.; Hughes Clarke, J.E. The 1929 “Grand Banks” earthquake, slump, and turbidity current. In Sedimentologic Consequences of Convulsive Geologic Events; Geological Society of America: Boulder, CO, USA, 1988; pp. 77–92.
Ren, Y.; Zhou, H.; Wang, H.; Wu, X.; Xu, G.; Meng, Q. Study on the critical sediment concentration determining the optimal transport capability of submarine sediment flows with different particle size composition. Mar. Geol.2023, 464, 107142.
Bagnold, R.A. Auto-suspension of transported sediment; turbidity currents. Proc. R. Soc. Lond. Ser. A Math. Phys. Sci.1962, 265, 315–319.
Parker, G. Conditions for the ignition of catastrophically erosive turbidity currents. Mar. Geol.2003, 46, 307–327.
Pantin, H.M. Interaction between velocity and effective density in turbidity flow: Phase-plane analysis, with criteria for autosuspension. Mar. Geol.1979, 31, 59–99.
Heerema, C.J.; Talling, P.J.; Cartigny, M.J.; Paull, C.K.; Bailey, L.; Simmons, S.M.; Parsons, D.R.; Clare, M.A.; Gwiazda, R.; Lundsten, E.; et al. What determines the downstream evolution of turbidity currents? Earth Planet. Sci. Lett.2020, 532, 116023.
Talling, P.J.; Cartigny, M.J.B.; Pope, E.; Baker, M.; Clare, M.A.; Heijnen, M.; Hage, S.; Parsons, D.R.; Simmons, S.M.; Paull, C.K.; et al. Detailed monitoring reveals the nature of submarine turbidity currents. Nat. Rev. Earth Environ.2023, 4, 642–658.
Heimsund, S. Numerical Simulation of Turbidity Currents: A New Perspective for Small-and Large-Scale Sedimentological Experiments; Sedimentology/Petroleum Geology; University of Bergen: Bergen, Norway, 2007.
Zhou, J.; Cenedese, C.; Williams, T.; Ball, M.; Venayagamoorthy, S.K.; Nokes, R.I. On the Propagation of Gravity Currents Over and through a Submerged Array of Circular Cylinders. J. Fluid Mech.2017, 831, 394–417.
Saha, S.; De, S.; Changdar, S. An Application of Machine Learning Algorithms on the Prediction of the Damage Level of Rubble-Mound Breakwaters. J. Offshore Mech. Arct. Eng.2024, 146, 011202.
Russell, J.S. Report on Waves: Made to the Meetings of the British Association; Richard and John E Taylor: London, UK, 1845.
Airy, G.B. Tides and Waves; B. Fellowes: London, UK, 1845.
Hongliang Wang, Xuanwen Jia,Chuan Wang, Bo Hu, Weidong Cao, Shanshan Li, Hui Wang
Abstract
Water-jet-scouring technology finds extensive applications in various fields, including marine engineering. In this study, the pulse characteristics are introduced on the basis of jet-scouring research, and the sand-scouring characteristics of a pulsed jet under different Reynolds numbers and the impact distances are deeply investigated using Flow-3D v11.2. The primary emphasis is on the comprehensive analysis of the unsteady flow structure within the scouring process, the impulse characteristics, and the geometric properties of the resulting scouring pit. The results show that both the radius and depth of the scour pit show a good linear correlation with the jet-flow rate. The concentration of suspended sediment showed an increasing and then decreasing trend with impinging distance. The study not only helps to enrich the traditional theory of jet scouring, but also provides useful guidance for engineering applications, which have certain theoretical and practical significance.
Water-jet-scouring technology is widely used in marine engineering and its related ancillary fields, such as in the maintenance and repair of marine structures, extraction of deep-sea resources, dredging works, seabed geological research, and cleaning and maintenance of ships. The jet flow establishes a velocity shear layer at its boundary, leading to the destabilization and subsequent generation of vortices. These vortices undergo continuous deformation, rupture, merging, and evolution into turbulence during their movement. Consequently, they entrain surrounding fluid into the jet region, facilitating the transfer of momentum, heat, and mass between the jet and its ambient environment [1,2,3]. Therefore, numerous scholars have carried out detailed studies on the scouring characteristics associated with jets. Chatterjee et al. [4] investigated the local scouring and sediment-transport phenomena due to the formation of horizontal jets during the opening of sluice gates based on experiments, and successfully established empirical expressions for the correlation between the time of reaching the equilibrium stage, the maximum depth of scouring, and the peak of the dune. The important role of jet-diffusion properties in the scouring process was also emphasized. Hoffmans [5] calculated the equilibrium scour process induced using a horizontal jet in the absence of a streambed and used experiments to verify the accuracy of the equations for jet-scour depths in the relevant literature. Luo et al. [6] investigated the induction mechanism of scour in planar jets through particle-image velocimetry (PIV). It was found that the initial stage of scour was dominated by wall shear, while the later stages of the scour process were mainly influenced by the turbulent vortex. Canepa et al. [7] investigated the scour characteristics of gas-doped water jets and found that gas-doped jets significantly reduce the scour depth if the velocity of the mixture is used as a reference. Pulsed jets introduce pulsation, resulting in a water-hammer effect, as well as increased diffusion and coil suction rates. These factors contribute to a more intricate interaction between the pulsed jet and the adjacent wall. The process of generation, development and evolution of its internal vortex structure as well as the interaction between the vortex structure and the surrounding ambient fluid and solid wall have changed significantly [8,9]. At this juncture, researchers in this domain have undertaken investigations centered on the utilization of pulsed jets. Coussement et al. [10] investigated the flow characteristics of a pulsed jet in a cross-flow environment based on Large Eddy Simulation (LES). A new approach to characterize mixing was introduced, which successfully explains and quantifies the complex mixing process between the pulsating jet and the ambient fluid. Bi et al. [11] investigated the thrust of a deformable body generated through a pulsed jet based on an axisymmetric immersed-boundary model. The numerical results show that in addition to the momentum flux of the jet, the jet acceleration is also an important source of thrust generation. Zhang et al. [12] studied the complex unsteady flow characteristics of a pulsed jet impinging on a rotating wall using numerical methods, and it was found that the impact pressure of the pulsed jet on the wall is greater than that of the continuous jet on the wall for a certain period of time when the water-hammer effect occurs. Rakhsha et al. [13] used experiments and numerical simulations to study the effect of pulsed jets on the flow and heat-transfer characteristics over a heated plane. It was found that the Nussell number increases with increasing pulse frequency and Reynolds number and decreases with increasing impinging distance. It is evident that existing studies predominantly center on the unsteady flow characteristics of pulsed jets and their properties related to heat and mass transfer. Conversely, there is a noticeable dearth of research concerning the scouring attributes of pulsed jets in the available literature. The pulsed submerged impinging jet represents a complex jet flow with a significant engineering application background and substantial theoretical research value. Exploring the unsteady hydraulic characteristics of pulsed jets can enhance classical impinging jet theory, deepen our comprehension of the jet–wall interaction mechanism, and establish a scientific foundation for addressing engineering-application challenges. Therefore, this paper introduces the pulse characteristics into the impinging jet, and, based on the Flow-3D software, the sand-scouring characteristics of the impinging jet under different Reynolds numbers and impinging distances are deeply investigated. The surface geometry of the scour pit is characterized while obtaining the pulsation characteristics of the unsteady flow structure during sand scouring. This study not only offers a foundation for implementing flow control and enhancing the understanding of unsteady flow characteristics but also furnishes theoretical backing for predicting impact pressure and impact pit formation.
2. Modeling and Numerical Methods
2.1. Model Building
The geometric model consists of a jet pipe, a body of water, a baffle, and a sand bed, as shown in Figure 1. The inner diameter D of the jet pipe is 20 mm, and the length L is set to 50D to ensure that the turbulence inside the pipe is fully developed. H represents the impinging height, and the initial water height (Hw) is 1600 mm. Baffles positioned on both sides serve to maintain a constant water level. The length Ls and thickness Hs of the sand bed are 5000 mm and 160 mm, respectively. It is worth stating that the sand bed is composed of non-cohesive sand. The median grain size dm of the sand is 0.77 mm, the specific gravity Δ is 1.65, and the particle gradation σg is 1.21.
Figure 1. Geometric modeling for sand scouring.
2.2. Numerical Models
In fluid mechanics, the continuity and momentum equations are the basic governing equations [14]:
where u, v, w denote the velocity of the fluid in the x, y, z direction, respectively; Ax, Ay, Az denote the area fraction of the fluid in the x, y, z direction, respectively; VF denotes the volume fraction; P is the pressure exerted on the fluid micrometric elements; Gx, Gy, Gz are the gravitational acceleration in the x, y, z direction, respectively; and fx, fy, fz are the viscous forces in the x, y, z direction, respectively.
In numerical simulations, the selection of a turbulence model significantly influences the accuracy of the calculations. Hence, it is imperative to choose an appropriate turbulence model. Given that this paper primarily deals with fully developed circular tube turbulence, which entails velocity and momentum coupling among fluids and features substantial time and spatial scales in the non-constant flow, the RNG k–ε turbulence model [15,16,17] has been chosen for the conclusive numerical simulation work. The RNG model takes into account the effect of eddies on turbulence and improves the accuracy of vortex-flow prediction [18]. Its equations are as follows:
where vt is the eddy viscosity coefficient; μ is the kinetic viscosity coefficient; the empirical constants cε1 and cε2 have values of 1.42 and 1.68; c3 = 0.012; η0 = 4.38; cμ = 0.085; and the values of Prandtl numbers αk and αε corresponding to the turbulent kinetic energy k and the dissipation rate ε are both 0.7194.
The Flow-3D software realizes an accurate description of the sediment movement with the help of an empirical equation model proposed by Mastbergen and Van den Berg [19]. The critical Shields number first needs to be calculated from the Soulsby–Whitehouse equation [20], which is given below:
where ρi is the sediment density, ρf is the fluid density, di is the sediment diameter, μf is the hydrodynamic viscosity, and ‖g‖ is the magnitude of gravitational acceleration.
Under the action of the jet, part of the deposited sediment will be disturbed to show a suspended state and it will continue to move under the carrying of the fluid. The uplifting velocities of entrained sediment ulift,i and usetting,i are calculated as follows:
where αi is the sediment carryover coefficient with a recommended value of 0.018 [19]; ns is the normal direction of the bed; and vf is the kinematic viscosity of the liquid.
2.3. Grid-Independent Analysis
It is well known that the number of the grid is closely related to the accuracy and cost of the numerical calculation. In order to investigate the optimal number of grids suitable for this numerical simulation, the scour depth Ht of the sand bed at H/D = 2 and inlet flow velocity Vb = 1.485 m/s is chosen as the monitoring parameter for the grid-independent analysis. Five sets of grid schemes with increasing numbers are set, and the results of the independence analysis are shown in Figure 2. From the figure, it can be seen that the depth of the scour pit Ht increases gradually with the encryption of the grid. When the grid is encrypted to Scheme 4, Ht almost no longer increases. It is considered that the number of meshes at this time can already meet the accuracy requirements of numerical calculations. Therefore, the grid number scheme in Scheme 4 is selected for the subsequent numerical simulation study, and the grid number is 43,825.
Figure 2. Grid-independent analysis.
2.4. Grid Delineation and Boundary Conditions
Within the Flow-3D software, a grid block is used that covers the entire 2D computational area as shown in Figure 1. Given the large aspect ratio of the jet pipe and the significant turbulent coupling between the fluid and sediment near the pipe outlet, grid refinement is implemented in the vicinity of the pipe outlet. The grid-encrypted area is mainly the area between the jet outlet and the sand bed, as shown in Figure 3. In addition, a mesh node is provided at the baffle on each side of the computational domain to ensure proper identification of the fluid boundary during numerical simulations. The upper boundary of the computational domain is defined as a velocity inlet, where the velocity magnitude is denoted as Vb, and the direction is oriented vertically downward. The lower boundary is the wall and no fluid or sediment flux is allowed. The two side boundaries are specified as pressure boundaries and the pressure is set to be 0 Pa. Based on the requirement of 2D numerical simulation, the boundaries of the front and rear sides are set as symmetric boundaries, both with one grid node. At the same time, the boundary-layer mesh near the pipe and the sand bed is encrypted accordingly. y+ is set at around 30 to ensure that the first grid nodes are in the turbulence core region, so as to ensure that the RNG k–ε turbulence model is perfectly adapted to the boundary conditions. Considering that the velocity strength and pressure gradient of the fluid around the baffle are small and it is not an observation area, the encryption of the boundary-layer grid is not performed for the time being.
Figure 3. Computational grid.
Numerical simulations are performed using the discrete control equations of the control volume method, with the diffusion term of the equations in the central difference format and the convection term in the second-order upwind format, and the equations are solved using a coupled algorithm. The standard wall equations are used, and the no-slip option in the wall shear boundary conditions is checked. In the non-stationary numerical simulation, the time step is set to 0.05 s. In order to ensure the accuracy of the numerical calculations, each time step is iterated 100 times, and the convergence accuracy is set to 10−5.
In this paper, the continuous jet is periodically truncated to form a blocking pulsed jet. The pulse period of its pulse velocity can be expressed as T = tj + t0 (tj and t0 are the jet time and truncation time, respectively, taking the value of 0.5 s), and the inlet flow rate of the jet pipe is Vb during the jet time period, while the inlet flow rate of the jet pipe is 0 during the truncation time period, as shown in Figure 4.
Figure 4. Velocity characteristics of the blocking pulsed jet.
3. Experimental Validation
To validate the accuracy of the numerical simulations, an experimental investigation of jet impingement on sediment is conducted. The experimental setup is shown in Figure 5. The parameters characterizing the sediment in the experiments are guaranteed to be the same as the settings in the numerical simulations. Specifically, non-cohesive sand is used with a median particle size dm of 0.77 mm, a specific gravity Δ of 1.65, and a particle gradation σg of 1.21. An angle plate is employed to control the impinging angle of the jet pipe, a COMS camera captures images of the pit, and a laser range finder is utilized for precise measurements of pit depth and dune height. In order to quantitatively describe the effect of jet impingement, the depth of the sand pit and the height of the dune are defined as d and h, respectively.
Figure 5. Schematic diagram of the experimental setup.
Figure 6 compares the stabilized morphology of the sand bed formed under the scouring of the jet for an impinging distance H/D of two in the numerical simulation and the experiment. The inlet flow velocities Vb of the jet pipe are 0.424 m/s, 0.955 m/s, and 1.485 m/s, respectively. As depicted in the figure, the ultimate scouring morphology of the sand bed, as obtained through numerical simulation, closely aligns with the experimental results. This alignment underscores the strong agreement between the numerical simulation and the experimental data. Nevertheless, it must be recognized that the final scour depths of the numerical simulations are all slightly smaller than the experimental values under the same conditions. The possible reason for this is the wall effect, i.e., the porosity of the actual sand bed is not homogeneous, with the upper sand layer being slightly more porous [21], whereas the porosity of the sand bed in the numerical simulation strictly follows the set value. Given that the accuracy of numerical calculations is subject to various influencing factors, and considering that the numerical solution inherently involves an approximation process, the numerical methods employed in this study can be deemed both accurate and dependable.
There are many factors that affect the performance of jet scouring, such as the shape of the nozzle, the size of the nozzle, the inlet flow rate of the jet pipe, the impinging distance, and the sediment parameters. Changes in any one of these factors can have a large effect on the parameters that measure the scouring performance of the jet, such as the depth of the scouring pit |ymin|, the height of the dune ymax, the radius of the scouring pit R. In this paper, the effects of the inlet velocity Vb and impinging distance H/D on the scouring performance of the jet pipe are investigated. Seven working conditions with inlet velocity Vb of 0.424 m/s, 0.690 m/s, 0.955 m/s, 1.220 m/s, 1.485 m/s, 1.751 m/s and 2.016 m/s are calculated for different impinging distances H/D (H/D = 2, 4, 6 and 8). The corresponding Reynolds numbers Re are 8404, 13,657, 18,910, 24,162, 29,415, 34,667, and 39,920, respectively.
4.1. Characterization of Pit at Different Impinging Distances
After the jet impinges on the sand bed for a sustained period of time, the shape of the sand bed will no longer change and remain stable. Figure 7 shows the stable bed morphology formed by the jet impinging on the sand bed with different velocities Vb, and at different impinging distances H/D. The x-axis is at the axial position of the jet pipe, and the y-axis is the initial horizontal plane of the sand bed. As can be seen from the figure, under the condition of Vb = 0.424 m/s, the pit depths |ymin| corresponding to impinging distances H/D of two and four are basically equal. However, when H/D is increased to six, |ymin| becomes significantly smaller, and when H/D is eight, |ymin| increases again. Under the Vb = 0.690 m/s condition, the effect of H/D on the scour pit depth |ymin| is small, and its size basically stays around 3.5 cm. Under the Vb = 0.955 m/s condition, the pit depth corresponding to H/D = eight is slightly smaller than the pit depths at other impinging distances, and the magnitude of |ymin| is basically maintained near 4.6 cm. Under the Vb = 1.220 m/s condition, the change of the scouring pit depth |ymin| with the impinging distance H/D starts to be gradually significant, especially the scouring pit depth |ymin| which decreases by about 1.7 cm when the size of H/D increases from two to six. Under the condition of Vb = 1.220 m/s, the larger the H/D, the smaller the pit depth |ymin|, especially when the H/D is eight, the pit depth is obviously larger than the pit depth at other impinging distances. The corresponding pit depths |ymin| for Vb of 1.751 m/s and 2.016 m/s remain basically unchanged. From the above analysis, it can be seen that under the same Reynolds number conditions to some extent the impinging distance has a very limited effect on the depth of the pit |ymin|. When the impinging distance increases, the depth of the pit begins to decrease. This can be attributed to the fact that the increased distance results in the jet encountering the initial static water resistance over a longer duration, leading to a greater dissipation of kinetic energy and a subsequent reduction in the impinging force of the jet.
The depth of the scouring pit serves as a critical parameter for assessing the impact of jet impingement on sand beds, just as the height of the dune represents a key indicator for evaluating the effectiveness of this process. In Figure 7a, it can be seen that the dune height ymax increases synchronously with the increase of the impinging distance H/D at Vb = 0.424 m/s. When Vb ≥ 0.955 m/s, the dune height ymax no longer grows significantly with the increase of impinging distance H/D. To further explore the relationship between dune height and impinging distance, Figure 8 is plotted with the impinging distance as the horizontal coordinate and the dune heights on either side as the vertical coordinate. From the figure, it can be seen that when 0.424 m/s ≤ Vb ≤ 1.485 m/s, the dune height ymax increases with the increase of the impinging distance H/D, and the dune height ymax starts to decrease with the increase of the impinging distance H/D when Vb > 1.485 m/s. The reason behind the aforementioned phenomenon is that when the inlet velocity Vb of the jet pipe is low, suspended sediment tends to displace towards the sides of the dune, causing some of the sediment to accumulate on the dune and thereby increase its height. When Vb ≥ 1.485 m/s, due to the enhanced impact force, most of the suspended sediment no longer moves and accumulates near the dunes and sand pits, and it starts to move on the outside of the dunes, causing the dune height to decrease.
Figure 8. Variation in the height of dunes on either side of the scour pit with Vb: (a) left; (b) right.
In order to clarify the relationship between the pit radius R and the impinging distance H/D, the relationship is given in Figure 9. From the figure, it can be seen that when 0.424 ≤ Vb ≤ 0.690, the increase of impinging distance H/D has basically no effect on the radius R of the pit, and its magnitude always stays near 13 cm. As the inlet velocity Vb of the jet pipe increases (1.220 ≤ Vb ≤ 1.485), the impact of the pulsed jet intensifies. Consequently, the suspended sediment is propelled towards the sides of the sand pit; although, it has not reached the dune and the area beyond it. Instead, a substantial amount of suspended sediment settles within the sand pit on both sides. Simultaneously, as the impact distance increases, the reach of jet impact and the turbulence induced by the jet expand, leading to enhanced sediment transport on both sides of the sand pit. This ultimately results in a reduction in the radius of the scouring pit as the impinging distance increases.
Figure 9. Relationship between pit size and impinging distance.
4.2. Characterization of Piting at Different Reynolds Numbers
Figure 10 depicts the stabilized morphology of the sand pit resulting from the influence of jets with varying Reynolds numbers. Under the conditions of H/D = two and four, the inlet velocity Vb of the jet pipe is 0.424 m/s and 0.690 m/s, and the depth of the pit |ymin| is basically equal, which indicates that the impact of the jet on the sand bed at this time is small, and the sediment is only transported and circulated in the sand pit. When Vb ≥ 0.955, the depth of the pit |ymin| increases significantly with the increase of Vb. Under the condition of H/D = 6, the depth of the pit, denoted as |ymin|, ceases to remain constant when Vb is less than or equal to 0.690 m/s. However, the disparity between the two measurements remains relatively small, suggesting that the impact force and turbulence of the jet are already capable of transporting sediment from the bottom of the pit to its flanks when Vb ≤ 0.690 m/s. In the H/D = 8 condition, due to the impinging distance H/D is larger, and when the velocity of the jet pipe is small (Vb ≤ 0.690 m/s), the kinetic energy of the jet is continuously exchanged with the static water body and then reduced, making its impact force reduce, and the sediment can only be transported and circulated at the bottom of the sand pit. To further investigate the effect of the Reynolds number of the jet on the depth of the pit |ymin|, Figure 11 is plotted with the jet velocity Vb as the horizontal coordinate and the depth of the pit |ymin| as the vertical coordinate. From the figure, it is evident that there exists a strong linear relationship between the depth of the scouring pit and the jet velocity. The data points in the figure can be fitted to establish the following relationship between the depth of the scouring pit and the jet velocity:
Figure 11. Linear relationship between scouring-pit depth and jet velocity.
4.3. Characterization of Pits with Different Impinging Times
Figure 12 illustrates the deformation of the sand bed caused by the impact of the pulsed jet over a time range from 0.75 s to 3.5 s (with intervals of 0.25 s). When the jet velocity Vb is 0.424 m/s, within the initial 0.75 s of jet initiation, the impact of the pulsed jet leads to noticeable deformation of the sand pit and dune, with their fundamental shapes taking form. The depth of the pit, denoted as |ymin|, continuously increases from 0.75 s to 2 s, eventually stabilizing around 2.75 s. By the onset of the pulsed jet, the dune has already assumed a fundamental profile, and its maximum height, represented as ymax, exhibits minimal variation over time, remaining relatively constant.
In this paper, a numerical computational study is conducted to examine the characteristics of sand-bed impingement using obstructing pulsed jets. A comprehensive analysis is undertaken, encompassing impingement-pit depth, dune height, and impingement-pit radius. The following conclusions are drawn:
Under consistent jet-velocity conditions, the impingement distance (H/D) has minimal impact on the depth of the scouring pit within the range of 2 ≤ H/D ≤ 6. However, beyond this range (H/D > 6), increased impingement distance leads to heightened jet-energy dissipation, resulting in a weakened impact force and a subsequent reduction in pit depth. Additionally, for lower jet velocities, impinging-distance variations have negligible effects on pit radius, while higher jet velocities induce a decrease in pit radius with an increase in impinging distance.
The study establishes strong linear relationships between both the radius and depth of the scouring pit and the jet velocity. However, the relationship between dune height and pulsed-jet velocity is characterized by randomness and uncertainty. The dynamics of sediment transport contribute to the lack of symmetry in the stable configuration of the sand pit concerning the jet-pipe axis. Furthermore, the relationship between dune height and pulsed-jet velocity exhibits transient characteristics, highlighting the complex nature of these interactions.
The numerical computational analysis emphasizes the transient characteristics of the sand-pit configuration due to sediment-transport dynamics. The stable state of the pit does not assume symmetry with the jet pipe as the axis, introducing a level of asymmetry in the system. This asymmetry is crucial in understanding the complex behavior of the sand-bed impingement. The findings underscore the need to consider dynamic and transient factors when studying the impact of obstructing pulsed jets on sand-bed characteristics.
References
Wang, C.; Wang, X.; Shi, W.; Lu, W.; Tan, S.K.; Zhou, L. Experimental investigation on impingement of a submerged circular water jet at varying impinging angles and Reynolds numbers. Exp. Therm. Fluid Sci.2017, 89, 189–198.
Hu, B.; Yao, Y.; Wang, M.; Wang, C.; Liu, Y. Flow and Performance of the Disk Cavity of a Marine Gas Turbine at Varying Nozzle Pressure and Low Rotation Speeds: A Numerical Investigation. Machines2023, 11, 68.
Yu, H.; Wang, C.; Li, G.; Wang, H.; Yang, Y.; Wu, S.; Cao, W.; Li, S. Steady and Unsteady Flow Characteristics inside Short Jet Self-Priming Pump. Sustainability2023, 15, 13643.
Chatterjee, S.S.; Ghosh, S.N.; Chatterjee, M. Local scour due to submerged horizontal jet. J. Hydraul. Eng.1994, 120, 973–992.
Hoffmans, G.J. Jet scour in equilibrium phase. J. Hydraul. Eng.1998, 124, 430–437.
Luo, A.; Cheng, N.-S.; Lu, Y.; Wei, M. Characteristics of Initial Development of Plane Jet Scour. J. Hydraul. Eng.2023, 149, 06023004.
Canepa, S.; Hager, W.H. Effect of jet air content on plunge pool scour. J. Hydraul. Eng.2003, 129, 358–365.
Krueger, P.S. Vortex ring velocity and minimum separation in an infinite train of vortex rings generated by a fully pulsed jet. Theor. Comput. Fluid Dyn.2010, 24, 291–297.
Zhou, Z.; Ge, Z.; Lu, Y.; Zhang, X. Experimental study on characteristics of self-excited oscillation pulsed water jet. J. Vibroeng.2017, 19, 1345–1357.
Coussement, A.; Gicquel, O.; Degrez, G. Large eddy simulation of a pulsed jet in cross-flow. J. Fluid Mech.2012, 695, 1–34.
Bi, X.; Zhu, Q. Pulsed-jet propulsion via shape deformation of an axisymmetric swimmer. Phys. Fluids2020, 32, 081902.
Zhang, L.; Wang, C.; Zhang, Y.; Xiang, W.; He, Z.; Shi, W. Numerical study of coupled flow in blocking pulsed jet impinging on a rotating wall. J. Braz. Soc. Mech. Sci. Eng.2021, 43, 508.
Rakhsha, S.; Zargarabadi, M.R.; Saedodin, S. Experimental and numerical study of flow and heat transfer from a pulsed jet impinging on a pinned surface. Exp. Heat Transf.2021, 34, 376–391.
Idowu, I.A.; Adewuyi, J.B. Relationship between continuity and momentum equation in two dimensional flow. Afr. J. Math. Comput. Sci. Res.2010, 3, 031–035.
Kim, B.J.; Hwang, J.H.; Kim, B. FLOW-3D Model Development for the Analysis of the Flow Characteristics of Downstream Hydraulic Structures. Sustainability2022, 14, 10493.
Jalal, H.K.; Hassan, W.H. Three-Dimensional Numerical Simulation of Local Scour around Circular Bridge Pier Using Flow-3D Software. In Proceedings of the Fourth Scientific Conference for Engineering and Postgraduate Research, Baghdad, Iraq, 16–17 December 2019; IOP Publishing: Bristol, UK, 2020; Volume 745, p. 012150.
Nazari-Sharabian, M.; Nazari-Sharabian, A.; Karakouzian, M.; Karami, M. Sacrificial piles as scour countermeasures in river bridges a numerical study using flow-3D. Civ. Eng. J.2020, 6, 1091–1103.
Abraham, J.; Magi, V. Computations of transient jets: RNG ke model versus standard ke model. SAE Trans.1997, 106, 1442–1452.
Mastbergen, D.R.; Van Den Berg, J.H. Breaching in fine sands and the generation of sustained turbidity currents in submarine canyons. Sedimentology2003, 50, 625–637.
Soulsby, R. Dynamics of Marine Sands; Thomas Telford Ltd.: London, UK, 1997; ISBN 9780727725844.
Atkins, J.E.; Mcbride, E.F. Porosity and packing of holocene river, dune, and beach sands (1). AAPG Bull.1992, 76, 339–355.
In practical use, there is shrinkage in the width direction in existing overflow water film. This study introduces the ” flow deflectors ” to solve the problem of discontinuous water film. According to the principle of the experimental devices, the model was established by FLOW-3D software and the corresponding boundary conditions were set up, the minimum size of the grid was 0.25mm × 0.25mm × 0.25mm. The film model was investigated under ten working conditions with three factors. Through the analysis of the distribution curves of velocities and thickness, impacts of unit width flux, tank width and the distance between the flow deflectors on the velocity and thickness of the liquid film were obtained. The results indicated that the water film was able to keep continuous and airtight with flow deflectors. The variation law of water film with unit width flux was obtained and a correlation formula was proposed according to Nusselt correlation. And, it was found that the tank width has little influence on the water film itself. The “dry zones” were also founded on the film when the distance between flow deflectors increased.
References
Gong H, Jiang J, Qiu J, Jiang R and Zhang W 2016 Theoretical and Experimental Study on the Water Curtain Shape and Mechanical Relationship of the Smoke Control System Advances in Engineering Research 500-7 Gong H, Jiang J, Zhang W and Guan Y 2017 Theory and Simulation of the Relationship between Smoke-proof Water Curtain’s Tank Structure and Flow Non-uniformity DEStech Transactions on Environment, Energy and Earth Science iceepe 257-63 ZHENG Li, QIAN Zhongdong, CAO Zhixian and TAN Guangming 2009 Comparison of computed result for dam over-topping flow with two 3D models Engineering Journal of Wuhan University 06 758-63 Hartley DE and Murgatroyd W 1964 Criteria for the break-up of thin liquid layers flowing isothermally over solid surfaces International Journal of Heat and Mass Transfer 9 1003-15 QIN Wei, LIU Jianhua, WENG Zemin and JIANG Zhangyan 1997 Characteristics of Interfacial Surface Wave of Free-Falling Liquid Film JOURNAL OF JIMEI NAVIGATION INSTITUTE 02 3-8 Ye X, Yan W, Jiang Z and Li C 2002 Hydrodynamics of Free-Falling Turbulent Wavy Films and Implications for Enhanced Heat Transfer Heat Transfer Engineering 1 48-60
Omega-Luitex법을 이용한 수력점프 발생시 러프 베드의 와류 진화 예측 및 영향 분석
Cong Trieu Tran, Cong Ty Trinh
Abstract
The dissipation of energy downstream of hydropower projects is a significant issue. The hydraulic jump is exciting and widely applied in practice to dissipate energy. Many hydraulic jump characteristics have been studied, such as length of jump Lj and sequent flow depth y2. However, understanding the evolution of the vortex structure in the hydraulic jump shows a significant challenge. This study uses the RNG k-e turbulence model to simulate hydraulic jumps on the rough bed. The Omega-Liutex method is compared with Q-criterion for capturing vortex structure in the hydraulic jump. The formation, development, and shedding of the vortex structure at the rough bed in the hydraulic jumper are analyzed. The vortex forms and rapidly reduces strength on the rough bed, resulting in fast dissipation of energy. At the rough block rows 2nd and 3rd, the vortex forms a vortex rope that moves downstream and then breaks. The vortex-shedding region represents a significant energy attenuation of the flow. Therefore, the rough bed dissipates kinetic energy well. Adding reliability to the vortex determined by the Liutex method, the vorticity transport equation is used to compare the vorticity distribution with the Liutex distribution. The results show a further comprehension of the hydraulic jump phenomenon and its energy dissipation.
[1] Viti, N., Valero, D., & Gualtieri, C. (2019). Numerical Simulation of Hydraulic Jumps. Part 2: Recent Results and Future Outlook. Water, 11(1), 28. https://doi.org/10.3390/w11010028
[2] Peterka, A. J. (1978.) Hydraulic Design of Stilling Basins and Energy Dissipators. Department of the Interior, Bureau of Reclamation.
[3] Bejestan, M. S. & Neisi, K. (2009). A new roughened bed hydraulic jump stilling basin. Asian journal of applied sciences, 2(5), 436-445. https://doi.org/10.3923/ajaps.2009.436.445
[4] Tokyay, N. D. (2005). Effect of channel bed corrugations on hydraulic jumps. Impacts of Global Climate Change, 1-9. https://doi.org/10.1061/40792(173)408
[5] Nikmehr, S. & Aminpour, Y. (2020). Numerical Simulation of Hydraulic Jump over Rough Beds. Periodica Polytechnica Civil Engineering, 64(2), 396-407. https://doi.org/10.3311/PPci.15292
[6] Hunt, J. C., Wray, A. A., & Moin, P. (1988). Eddies, streams, and convergence zones in turbulent flows. Studying turbulence using numerical simulation databases. 2. Proceedings of the 1988 summer program.
[7] Gao, Y. & Liu, C. (2018). Rortex and comparison with eigenvalue-based vortex identification criteria. Physics of Fluids, 30(8), 085107. https://doi.org/10.1063/1.5040112
[8] Liu, C., Gao, Y., Tian, S., & Dong, X. (2018). Rortex – A new vortex vector definition and vorticity tensor and vector decompositions. Physics of Fluids, 30(3), 035103. https://doi.org/10.1063/1.5023001
[9] Liu, C. et al. (2019). Third generation of vortex identification methods: Omega and Liutex/Rortex based systems. Journal of Hydrodynamics, 31(2), 205-223. https://doi.org/10.1007/s42241-019-0022-4
[10] Liu, C., Wang, Y., Yang, Y. et al (2016). New omega vortex identification method. Science China Physics, Mechanics & Astronomy, (8), 56-64. https://doi.org/10.1007/s11433-016-0022-6
[11] Tran, C. T. & Pham, D. C. (2022). Application of Liutex and Entropy Production to Analyze the Influence of Vortex Rope in the Francis-99 Turbine Draft Tube. Tehnički vjesnik, 29(4), 1177-1183. https://doi.org/10.17559/TV-20210821070801
[12] Dong, X., Gao, Y., & Liu, C. (2019). New normalized Rortex/vortex identification method. Physics of Fluids, 31(1), 011701. https://doi.org/10.1063/1.5066016
[13] Wang, L., Zheng, Z., Cai, W. et al. (2019). Extension Omega and Omega-Liutex methods applied to identify vortex structures in viscoelastic turbulent flow. Journal of Hydrodynamics, 31(5), 911-921. https://doi.org/10.1007/s42241-019-0045-x
[14] Xu, H., Cai, X., & Liu, C. (2019). Liutex (vortex) core definition and automatic identification for turbulence vortex structures. Journal of Hydrodynamics, 31(5), 857-863. https://doi.org/10.1007/s42241-019-0066-5
[15] Tran, C. T. et al. (2020). Prediction of the precessing vortex core in the Francis-99 draft tube under off-design conditions by using Liutex/Rortex method. Journal of Hydrodynamics, 32, 623-628. https://doi.org/10.1007/s42241-020-0031-3
[16] Liu, C. et al. (2019). A Liutex based definition of vortex axis line. arXiv preprint arXiv:1904.10094. https://doi.org/10.48550/arXiv.1904.10094
[17] Samadi-Boroujeni, H. et al. (2013). Effect of triangular corrugated beds on the hydraulic jump characteristics. Canadian Journal of Civil Engineering, 40(9), 841-847. https://doi.org/10.1139/cjce-2012-0019
[18] Ghaderi, A. et al. (2020). Characteristics of free and submerged hydraulic jumps over different macroroughnesses. Journal of Hydroinformatics, 22(6), 1554-1572. https://doi.org/10.2166/hydro.2020.298
[19] Wu, Z. et al. (2021). Analysis of the influence of transverse groove structure on the flow of a flat-plate surface based on Liutex parameters. Engineering Applications of Computational Fluid Mechanics, 15(1), 1282-1297. https://doi.org/10.1080/19942060.2021.1968955
[20] Ji, B., et al. (2014). Numerical simulation of threedimensional cavitation shedding dynamics with special emphasis on cavitation – vortex interaction. Ocean Engineering, 87, 64-77. https://doi.org/10.1016/j.oceaneng.2014.05.005
[21] Tran, C., Bin, J., & Long, X. (2019). Simulation and Analysis of Cavitating Flow in the Draft Tube of the Francis Turbine with Splitter Blades at Off-Design Condition. Tehnicki vjesnik – Technical Gazette, 26(6). https://doi.org/10.17559/TV-20190316042929
Mohammad Nazari-Sharabian, Aliasghar Nazari-Sharabian, Moses Karakouzian, Mehrdad Karami
Abstract
Scour is defined as the erosive action of flowing water, as well as the excavating and carrying away materials from beds and banks of streams, and from the vicinity of bridge foundations, which is one of the main causes of river bridge failures. In the present study, implementing a numerical approach, and using the FLOW-3D model that works based on the finite volume method (FVM), the applicability of using sacrificial piles in different configurations in front of a bridge pier as countermeasures against scouring is investigated. In this regard, the numerical model was calibrated based on an experimental study on scouring around an unprotected circular river bridge pier. In simulations, the bridge pier and sacrificial piles were circular, and the riverbed was sandy. In all scenarios, the flow rate was constant and equal to 45 L/s. Furthermore, one to five sacrificial piles were placed in front of the pier in different locations for each scenario. Implementation of the sacrificial piles proved to be effective in substantially reducing the scour depths. The results showed that although scouring occurred in the entire area around the pier, the maximum and minimum scour depths were observed on the sides (using three sacrificial piles located upstream, at three and five times the pier diameter) and in the back (using five sacrificial piles located upstream, at four, six, and eight times the pier diameter) of the pier. Moreover, among scenarios where single piles were installed in front of the pier, installing them at a distance of five times the pier diameter was more effective in reducing scour depths. For other scenarios, in which three piles and five piles were installed, distances of six and four times the pier diameter for the three piles scenario, and four, six, and eight times the pier diameter for the five piles scenario were most effective.
Keywords
Scouring; River Bridges; Sacrificial Piles; Finite Volume Method (FVM); FLOW-3D.
References
Karakouzian, Chavez, Hayes, and Nazari-Sharabian. “Bulbous Pier: An Alternative to Bridge Pier Extensions as a Countermeasure Against Bridge Deck Splashing.” Fluids 4, no. 3 (July 24, 2019): 140. doi:10.3390/fluids4030140.
Karami, Mehrdad, Abdorreza Kabiri-Samani, Mohammad Nazari-Sharabian, and Moses Karakouzian. “Investigating the Effects of Transient Flow in Concrete-Lined Pressure Tunnels, and Developing a New Analytical Formula for Pressure Wave Velocity.” Tunnelling and Underground Space Technology 91 (September 2019): 102992. doi:10.1016/j.tust.2019.102992.
Karakouzian, Moses, Mohammad Nazari-Sharabian, and Mehrdad Karami. “Effect of Overburden Height on Hydraulic Fracturing of Concrete-Lined Pressure Tunnels Excavated in Intact Rock: A Numerical Study.” Fluids 4, no. 2 (June 19, 2019): 112. doi:10.3390/fluids4020112.
Chiew, Yee-Meng. “Scour protection at bridge piers.” Journal of Hydraulic Engineering 118, no. 9 (1992): 1260-1269. doi:10.1061/(ASCE)0733-9429(1992)118:9(1260).
Shen, Hsieh Wen, Verne R. Schneider, and Susumu Karaki. “Local scour around bridge piers.” Journal of the Hydraulics Division (1969): 1919-1940.
Richardson, E.V., and Davis, S.R. “Evaluating Scour at Bridges”. Hydraulic Engineering Circular. (2001), 18 (HEC-18), Report no. FHWA NHI 01–001, U.S. Department of Transportation, Federal Highway Administration, Washington, DC, USA.
Elsaeed, Gamal, Hossam Elsersawy, and Mohammad Ibrahim. “Scour Evaluation for the Nile River Bends on Rosetta Branch.” Advances in Research 5, no. 2 (January 10, 2015): 1–15. doi:10.9734/air/2015/17380.
Chang, Wen-Yi, Jihn-Sung Lai, and Chin-Lien Yen. “Evolution of scour depth at circular bridge piers.” Journal of Hydraulic Engineering 130, no. 9 (2004): 905-913. doi:10.1061/(ASCE)0733-9429(2004)130:9(905).
Unger, Jens, and Willi H. Hager. “Riprap failure at circular bridge piers.” Journal of Hydraulic Engineering 132, no. 4 (2006): 354-362. doi:10.1061/(ASCE)0733-9429(2006)132:4(354).
Abdeldayem, Ahmed W., Gamal H. Elsaeed, and Ahmed A. Ghareeb. “The effect of pile group arrangements on local scour using numerical models.” Advances in Natural and Applied Sciences 5, no. 2 (2011): 141-146.
Sheppard, D. M., B. Melville, and H. Demir. “Evaluation of Existing Equations for Local Scour at Bridge Piers.” Journal of Hydraulic Engineering 140, no. 1 (January 2014): 14–23. doi:10.1061/(asce)hy.1943-7900.0000800.
Melville, Bruce W., and Anna C. Hadfield. “Use of sacrificial piles as pier scour countermeasures.” Journal of Hydraulic Engineering 125, no. 11 (1999): 1221-1224. doi:10.1061/(ASCE)0733-9429(1999)125:11(1221).
Yao, Weidong, Hongwei An, Scott Draper, Liang Cheng, and John M. Harris. “Experimental Investigation of Local Scour Around Submerged Piles in Steady Current.” Coastal Engineering 142 (December 2018): 27–41. doi:10.1016/j.coastaleng.2018.08.015.
Link, Oscar, Marcelo García, Alonso Pizarro, Hernán Alcayaga, and Sebastián Palma. “Local Scour and Sediment Deposition at Bridge Piers During Floods.” Journal of Hydraulic Engineering 146, no. 3 (March 2020): 04020003. doi:10.1061/(asce)hy.1943-7900.0001696.
Khan, Mujahid, Mohammad Tufail, Muhammad Fahad, Hazi Muhammad Azmathullah, Muhammad Sagheer Aslam, Fayaz Ahmad Khan, and Asif Khan. “Experimental analysis of bridge pier scour pattern.” Journal of Engineering and Applied Sciences 36, no. 1 (2017): 1-12.
Yang, Yifan, Bruce W. Melville, D. M. Sheppard, and Asaad Y. Shamseldin. “Clear-Water Local Scour at Skewed Complex Bridge Piers.” Journal of Hydraulic Engineering 144, no. 6 (June 2018): 04018019. doi:10.1061/(asce)hy.1943-7900.0001458.
Moussa, Yasser Abdallah Mohamed, Tarek Hemdan Nasr-Allah, and Amera Abd-Elhasseb. “Studying the Effect of Partial Blockage on Multi-Vents Bridge Pier Scour Experimentally and Numerically.” Ain Shams Engineering Journal 9, no. 4 (December 2018): 1439–1450. doi:10.1016/j.asej.2016.09.010.
Guan, Dawei, Yee-Meng Chiew, Maoxing Wei, and Shih-Chun Hsieh. “Characterization of Horseshoe Vortex in a Developing Scour Hole at a Cylindrical Bridge Pier.” International Journal of Sediment Research 34, no. 2 (April 2019): 118–124. doi:10.1016/j.ijsrc.2018.07.001.
Dougherty, E.M. “CFD Analysis of Bridge Pier Geometry on Local Scour Potential” (2019). LSU Master’s Theses. 5031.
Vijayasree, B. A., T. I. Eldho, B. S. Mazumder, and N. Ahmad. “Influence of Bridge Pier Shape on Flow Field and Scour Geometry.” International Journal of River Basin Management 17, no. 1 (November 10, 2017): 109–129. doi:10.1080/15715124.2017.1394315.
Farooq, Rashid, and Abdul Razzaq Ghumman. “Impact Assessment of Pier Shape and Modifications on Scouring Around Bridge Pier.” Water 11, no. 9 (August 23, 2019): 1761. doi:10.3390/w11091761.
Link, Oscar, Cristian Castillo, Alonso Pizarro, Alejandro Rojas, Bernd Ettmer, Cristián Escauriaza, and Salvatore Manfreda. “A Model of Bridge Pier Scour During Flood Waves.” Journal of Hydraulic Research 55, no. 3 (November 18, 2016): 310–323. doi:10.1080/00221686.2016.1252802.
Karakouzian, Moses, Mehrdad Karami, Mohammad Nazari-Sharabian, and Sajjad Ahmad. “Flow-Induced Stresses and Displacements in Jointed Concrete Pipes Installed by Pipe Jacking Method.” Fluids 4, no. 1 (February 21, 2019): 34. doi:10.3390/fluids4010034.
Flow Science, Inc. FLOW-3D User’s Manual, Flow Science (2018).
Brethour, J. Modeling Sediment Scour. Flow Science, Santa Fe, NM. (2003).
Brethour, James, and Jeff Burnham. “Modeling sediment erosion and deposition with the FLOW-3D sedimentation & scour model.” Flow Science Technical Note, FSI-10-TN85 (2010): 1-22.
Balouchi, M., and Chamani, M.R. “Investigating the Effect of using a Collar around a Bridge Pier, on the Shape of the Scour Hole”. Proceedings of the First International Conference on Dams and Hydropower (2012) (In Persian).
Bayon, Arnau, Daniel Valero, Rafael García-Bartual, Francisco José Vallés-Morán, and P. Amparo López-Jiménez. “Performance Assessment of OpenFOAM and FLOW-3D in the Numerical Modeling of a Low Reynolds Number Hydraulic Jump.” Environmental Modelling & Software 80 (June 2016): 322–335. doi:10.1016/j.envsoft.2016.02.018.
Aminoroayaie Yamini, O., S. Hooman Mousavi, M. R. Kavianpour, and Azin Movahedi. “Numerical Modeling of Sediment Scouring Phenomenon Around the Offshore Wind Turbine Pile in Marine Environment.” Environmental Earth Sciences 77, no. 23 (November 24, 2018). doi:10.1007/s12665-018-7967-4.
Nazari-Sharabian, Mohammad, Masoud Taheriyoun, Sajjad Ahmad, Moses Karakouzian, and Azadeh Ahmadi. “Water Quality Modeling of Mahabad Dam Watershed–Reservoir System under Climate Change Conditions, Using SWAT and System Dynamics.” Water 11, no. 2 (February 24, 2019): 394. doi:10.3390/w11020394.
Waqed H. Hassan| Zahraa Mohammad Fadhe*| Rifqa F. Thiab| Karrar Mahdi Civil Engineering Department, Faculty of Engineering, University of Warith Al-Anbiyaa, Kerbala 56001, Iraq Civil Engineering Department, Faculty of Engineering, University of Kerbala, Kerbala 56001, Iraq Corresponding Author Email: Waqed.hammed@uowa.edu.iq
OPEN ACCESS
Abstract:
This work investigates numerically a local scour moves in irregular waves around tripods. It is constructed and proven to use the numerical model of the seabed-tripod-fluid with an RNG k turbulence model. The present numerical model then examines the flow velocity distribution and scour characteristics. After that, the suggested computational model Flow-3D is a useful tool for analyzing and forecasting the maximum scour development and the flow field in random waves around tripods. The scour values affecting the foundations of the tripod must be studied and calculated, as this phenomenon directly and negatively affects the structure of the structure and its design life. The lower diagonal braces and the main column act as blockages, increasing the flow accelerations underneath them. This increases the number of particles that are moved, which in turn creates strong scouring in the area. The numerical model has a good agreement with the experimental model, with a maximum percentage of error of 10% between the experimental and numerical models. In addition, Based on dimensional analysis parameters, an empirical equation has been devised to forecast scour depth with flow depth, median size ratio, Keulegan-Carpenter (Kc), Froud number flow, and wave velocity that the results obtained in this research at various flow velocities and flow depths demonstrated that the maximum scour depth rate depended on wave height with rising velocities and decreasing particle sizes (d50) and the scour depth attains its steady-current value for Vw < 0.75. As the Froude number rises, the maximum scour depth will be large.
Keywords:
local scour, tripod foundation, Flow-3D, waves
1. Introduction
New energy sources have been used by mankind since they become industrialized. The main energy sources have traditionally been timber, coal, oil, and gas, but advances in the science of new energies, such as nuclear energy, have emerged [1, 2]. Clean and renewable energy such as offshore wind has grown significantly during the past few decades. There are numerous different types of foundations regarding offshore wind turbines (OWTs), comprising the tripod, jacket, gravity foundation, suction anchor (or bucket), and monopile [3, 4]. When the water depth is less than 30 meters, Offshore wind farms usually employ the monopile type [4]. Engineers must deal with the wind’s scouring phenomenon turbine foundations when planning and designing wind turbines for an offshore environment [5]. Waves and currents generate scour, this is the erosion of soil near a submerged foundation and at its location [6]. To predict the regional scour depth at a bridge pier, Jalal et al. [7-10] developed an original gene expression algorithm using artificial neural networks. Three monopiles, one main column, and several diagonal braces connecting the monopiles to the main column make up the tripod foundation, which has more complicated shapes than a single pile. The design of the foundation may have an impact on scour depth and scour development since the foundation’s form affects the flow field [11, 12]. Stahlmann [4] conducted several field investigations. He discovered that the main column is where the greatest scour depth occurred. Under the main column is where the maximum scour depth occurs in all experiments. The estimated findings show that higher wave heights correspond to higher flow velocities, indicating that a deeper scour depth is correlated with finer silt granularity [13] recommends as the design value for a single pile. These findings support the assertion that a tripod may cause the seabed to scour more severely than a single pile. The geography of the scour is significantly more influenced by the KC value (Keulegan–Carpenter number)
The capability of computer hardware and software has made computational fluid dynamics (CFD) quite popular to predict the behavior of fluid flow in industrial and environmental applications has increased significantly in recent years [14].
Finding an acceptable piece of land for the turbine’s construction and designing the turbine pile precisely for the local conditions are the biggest challenges. Another concern related to working in a marine environment is the effect of sea waves and currents on turbine piles and foundations. The earth surrounding the turbine’s pile is scoured by the waves, which also render the pile unstable.
In this research, the main objective is to investigate numerically a local scour around tripods in random waves. It is constructed and proven to use the tripod numerical model. The present numerical model is then used to examine the flow velocity distribution and scour characteristics.
2. Numerical Model
To simulate the scouring process around the tripod foundation, the CFD code Flow-3D was employed. By using the fractional area/volume method, it may highlight the intricate boundaries of the solution domain (FAVOR).
This model was tested and validated utilizing data derived experimentally from Schendel et al. [15] and Sumer and Fredsøe [6]. 200 runs were performed at different values of parameters.
2.1 Momentum equations
The incompressible viscous fluid motion is described by the three RANS equations listed below [16]:
where, respectively, u, v, and w represent the x, y, and z flow velocity components; volume fraction (VF), area fraction (Ai; I=x, y, z), water density (f), viscous force (fi), and body force (Gi) are all used in the formula.
2.2 Model of turbulence
Several turbulence models would be combined to solve the momentum equations. A two-equation model of turbulence is the RNG k-model, which has a high efficiency and accuracy in computing the near-wall flow field. Therefore, the flow field surrounding tripods was captured using the RNG k-model.
2.3 Model of sediment scour
2.3.1 Induction and deposition
Eq. (4) can be used to determine the particle entrainment lift velocity [17].
α𝛼i is the Induction parameter, ns the normal vector is parallel to the seafloor, and for the present numerical model, ns=(0,0,1), θ𝜃cr is the essential Shields variable, g is the accelerated by gravity, di is the size of the particles, ρi is species density in beds, and d∗ The diameter of particles without dimensions; these values can be obtained in Eq. (5).
fbis the essential particle packing percentage, qb, i is the bed load transportation rate, and cb, I the percentage of sand by volume i. These variables can be found in Eq. (9), Eq. (10), fb, δ𝛿i the bed load thickness.
In this paper, after the calibration of numerous trials, the selection of parameters for sediment scour is crucial. Maximum packing fraction is 0.64 with a shields number of 0.05, entrainment coefficient of 0.018, the mass density of 2650, bed load coefficient of 12, and entrainment coefficient of 0.01.
3. Model Setup
To investigate the scour characteristics near tripods in random waves, the seabed-tripod-fluid numerical model was created as shown in Figure 1. The tripod basis, a seabed, and fluid and porous medium were all components of the model. The seabed was 240 meters long, 40 meters wide, and three meters high. It had a median diameter of d50 and was composed of uniformly fine sand. The 2.5-meter main column diameter D. The base of the main column was three dimensions above the original seabed. The center of the seafloor was where the tripod was, 130 meters from the offshore and 110 meters from the onshore. To prevent wave reflection, the porous media were positioned above the seabed on the onshore side.
Figure 1. An illustration of the numerical model for the seabed-tripod-fluid
3.1 Generation of meshes
Figure 2 displays the model’s mesh for the Flow-3D software grid. The current model made use of two different mesh types: global mesh grid and nested mesh grid. A mesh grid with the following measurements was created by the global hexahedra mesh grid: 240m length, 40m width, and 32m height. Around the tripod, a finer nested mesh grid was made, with dimensions of 0 to 32m on the z-axis, 10 to 30 m on the x-axis, and 25 to 15 m on the y-axis. This improved the calculation’s precision and mesh quality.
To increase calculation efficiency, the top side, The model’s two x-z plane sides, as well as the symmetry boundaries, were all specified. For u, v, w=0, the bottom boundary wall was picked. The offshore end of the wave boundary was put upstream. For the wave border, random waves were generated using the wave spectrum from the Joint North Sea Wave Project (JONSWAP). Boundary conditions are shown in Figure 3.
Figure 3. Boundary conditions of the typical problem
The wave spectrum peak enhancement factor (=3.3 for this work) and can be used to express the unidirectional JONSWAP frequency spectrum.
3.3 Mesh sensitivity
Before doing additional research into scour traits and scour depth forecasting, mesh sensitivity analysis is essential. Three different mesh grid sizes were selected for this section: Mesh 1 has a 0.45 by 0.45 nested fine mesh and a 0.6 by 0.6 global mesh size. Mesh 2 has a 0.4 global mesh size and a 0.35 nested fine mesh size, while Mesh 3 has a 0.25 global mesh size and a nested fine mesh size of 0.15. Comparing the relative fine mesh size (such as Mesh 2 or Mesh 3) to the relatively coarse mesh size (such as Mesh 1), a larger scour depth was seen; this shows that a finer mesh size can more precisely represent the scouring and flow field action around a tripod. Significantly, a lower mesh size necessitates a time commitment and a more difficult computer configuration. Depending on the sensitivity of the mesh guideline utilized by Pang et al., when Mesh 2 is applied, the findings converge and the mesh size is independent [20]. In the next sections, scouring the area surrounding the tripod was calculated using Mesh 2 to ensure accuracy and reduce computation time. The working segment generates a total of 14, 800,324 cells.
3.4 Model validation
Comparisons between the predicted outcomes from the current model and to confirm that the current numerical model is accurate and suitably modified, experimental data from Sumer and Fredsøe [6] and Schendel et al. [15] were used. For the experimental results of Run 05, Run 15, and Run 22 from Sumer and Fredsøe [6], the experimental A9, A13, A17, A25, A26, and A27 results from Schendel et al. [15], and the numerical results from the current model are shown in Figure 4. The present model had d50=0.051cm, the height of the water wave(h)=10m, and wave velocity=0.854 m.s-1.
Figure 5. Comparison of the present study’s maximum scour depth with that authored by Sumer and Fredsøe [6] and Schendel et al. [15]
According to Figure 5, the highest discrepancy between the numerical results and experimental data is about 10%, showing that overall, there is good agreement between them. The ability of the current numerical model to accurately depict the scour process and forecast the maximum scour depth (S) near foundations is demonstrated by this. Errors in the simulation were reduced by using the calibrated values of the parameter. Considering these results, a suggested simulated scouring utilizing a Flow-3D numerical model is confirmed as a superior way for precisely forecasting the maximum scour depth near a tripod foundation in random waves.
3.5 Dimensional analysis
The variables found in this study as having the greatest impacts, variables related to flow, fluid, bed sediment, flume shape, and duration all had an impact on local scouring depth (t). Hence, scour depth (S) can be seen as a function of these factors, shown as:
With the aid of dimensional analysis, the 14-dimensional parameters in Eq. (11) were reduced to 6 dimensionless variables using Buckingham’s -theorem. D, V, and were therefore set as repetition parameters and others as constants, allowing for the ignoring of their influence. Eq. (12) thus illustrates the relationship between the effect of the non-dimensional components on the depth of scour surrounding a tripod base.
(12)
\frac{S}{D}=f\left(\frac{h}{D}, \frac{d 50}{D}, \frac{V}{V W}, F r, K c\right)
where, SD𝑆𝐷 are scoured depth ratio, VVw𝑉𝑉𝑤 is flow wave velocity, d50D𝑑50𝐷 median size ratio, $Fr representstheFroudnumber,and𝑟𝑒𝑝𝑟𝑒𝑠𝑒𝑛𝑡𝑠𝑡ℎ𝑒𝐹𝑟𝑜𝑢𝑑𝑛𝑢𝑚𝑏𝑒𝑟,𝑎𝑛𝑑Kc$is the Keulegan-Carpenter.
4. Result and Discussion
4.1 Development of scour
Similar to how the physical model was used, this numerical model was also used. The numerical model’s boundary conditions and other crucial variables that directly influence the outcomes were applied (flow depth, median particle size (d50), and wave velocity). After the initial 0-300 s, the scour rate reduced as the scour holes grew quickly. The scour depths steadied for about 1800 seconds before reaching an asymptotic value. The findings of scour depth with time are displayed in Figure 6.
4.2 Features of scour
Early on (t=400s), the scour hole began to appear beneath the main column and then began to extend along the diagonal bracing connecting to the wall-facing pile. Gradually, the geography of the scour; of these results is similar to the experimental observations of Stahlmann [4] and Aminoroayaie Yamini et al. [1]. As the waves reached the tripod, there was an enhanced flow acceleration underneath the main column and the lower diagonal braces as a result of the obstructing effects of the structural elements. More particles are mobilized and transported due to the enhanced near-bed flow velocity, it also increases bed shear stress, turbulence, and scour at the site. In comparison to a single pile, the main column and structural components of the tripod have a significant impact on the flow velocity distribution and, consequently, the scour process and morphology. The main column and seabed are separated by a gap, therefore the flow across the gap may aid in scouring. The scour hole first emerged beneath the main column and subsequently expanded along the lower structural components, both Aminoroayaie Yamini et al. [1] and Stahlmann [4] made this claim. Around the tripod, there are several different scour morphologies and the flow velocity distribution as shown in Figures 7 and 8.
Figure 8. Random waves of flow velocity distribution around a tripod
4.3 Wave velocity’s (Vw) impact on scour depth
In this study’s section, we looked at how variations in wave current velocity affected the scouring depth. Bed scour pattern modification could result from an increase or decrease in waves. As a result, the backflow area produced within the pile would become stronger, which would increase the depth of the sediment scour. The quantity of current turbulence is the primary cause of the relationship between wave height and bed scour value. The current velocity has increased the extent to which the turbulence energy has changed and increased in strength now present. It should be mentioned that in this instance, the Jon swap spectrum random waves are chosen. The scour depth attains its steady-current value for Vw<0.75, Figure 9 (a) shows that effect. When (V) represents the mean velocity=0.5 m.s-1.
Figure 9. Main effects on maximum scour depth (Smax) as a function of column diameter (D)
4.4 Impact of a median particle (d50) on scour depth
In this section of the study, we looked into how variations in particle size affected how the bed profile changed. The values of various particle diameters are defined in the numerical model for each run numerical modeling, and the conditions under which changes in particle diameter have an impact on the bed scour profile are derived. Based on Figure 9 (b), the findings of the numerical modeling show that as particle diameter increases the maximum scour depth caused by wave contact decreases. When (d50) is the diameter of Sediment (d50). The Shatt Al-Arab soil near Basra, Iraq, was used to produce a variety of varied diameters.
4.5 Impact of wave height and flow depth (h) on scour depth
One of the main elements affecting the scour profile brought on by the interaction of the wave and current with the piles of the wind turbines is the height of the wave surrounding the turbine pile causing more turbulence to develop there. The velocity towards the bottom and the bed both vary as the turbulence around the pile is increased, modifying the scour profile close to the pile. According to the results of the numerical modeling, the depth of scour will increase as water depth and wave height in random waves increase as shown in Figure 9 (c).
4.6 Froude number’s (Fr) impact on scour depth
No matter what the spacing ratio, the Figure 9 shows that the Froude number rises, and the maximum scour depth often rises as well increases in Figure 9 (d). Additionally, it is crucial to keep in mind that only a small portion of the findings regarding the spacing ratios with the smallest values. Due to the velocity acceleration in the presence of a larger Froude number, the range of edge scour downstream is greater than that of upstream. Moreover, the scouring phenomena occur in the region farthest from the tripod, perhaps as a result of the turbulence brought on by the collision of the tripod’s pile. Generally, as the Froude number rises, so does the deposition height and scour depth.
4.7 Keulegan-Carpenter (KC) number
The geography of the scour is significantly more influenced by the KC value. Greater KC causes a deeper equilibrium scour because an increase in KC lengthens the horseshoe vortex’s duration and intensifies it as shown in Figure 10.
The result can be attributed to the fact that wave superposition reduced the crucial KC for the initiation of the scour, particularly under small KC conditions. The primary variable in the equation used to calculate This is the depth of the scouring hole at the bed. The following expression is used to calculate the Keulegan-Carpenter number:
Kc=Vw∗TpD𝐾𝑐=𝑉𝑤∗𝑇𝑝𝐷 (13)
where, the wave period is Tp and the wave velocity is shown by Vw.
Figure 10. Relationship between the relative maximum scour depth and KC
5. Conclusion
(1) The existing seabed-tripod-fluid numerical model is capable of faithfully reproducing the scour process and the flow field around tripods, suggesting that it may be used to predict the scour around tripods in random waves.
(2) Their results obtained in this research at various flow velocities and flow depths demonstrated that the maximum scour depth rate depended on wave height with rising velocities and decreasing particle sizes (d50).
(3) A diagonal brace and the main column act as blockages, increasing the flow accelerations underneath them. This raises the magnitude of the disturbance and the shear stress on the seafloor, which in turn causes a greater number of particles to be mobilized and conveyed, as a result, causes more severe scour at the location.
(4) The Froude number and the scouring process are closely related. In general, as the Froude number rises, so does the maximum scour depth and scour range. The highest maximum scour depth always coincides with the bigger Froude number with the shortest spacing ratio.
Since the issue is that there aren’t many experiments or studies that are relevant to this subject, therefore we had to rely on the monopile criteria. Therefore, to gain a deeper knowledge of the scouring effect surrounding the tripod in random waves, further numerical research exploring numerous soil, foundation, and construction elements as well as upcoming physical model tests will be beneficial.
Nomenclature
CFD
Computational fluid dynamics
FAVOR
Fractional Area/Volume Obstacle Representation
VOF
Volume of Fluid
RNG
Renormalized Group
OWTs
Offshore wind turbines
Greek Symbols
ε, ω
Dissipation rate of the turbulent kinetic energy, m2s-3
Subscripts
d50
Median particle size
Vf
Volume fraction
GT
Turbulent energy of buoyancy
KT
Turbulent velocity
PT
Kinetic energy of the turbulence
Αi
Induction parameter
ns
Induction parameter
ΘΘcr
The essential Shields variable
Di
Diameter of sediment
d∗
The diameter of particles without dimensions
µf
Dynamic viscosity of the fluid
qb,i
The bed load transportation rate
Cs,i
Sand particle’s concentration of mass
D
Diameter of pile
Df
Diffusivity
D
Diameter of main column
Fr
Froud number
Kc
Keulegan–Carpenter number
G
Acceleration of gravity g
H
Flow depth
Vw
Wave Velocity
V
Mean Velocity
Tp
Wave Period
S
Scour depth
References
[1] Aminoroayaie Yamini, O., Mousavi, S.H., Kavianpour, M.R., Movahedi, A. (2018). Numerical modeling of sediment scouring phenomenon around the offshore wind turbine pile in marine environment. Environmental Earth Sciences, 77: 1-15. https://doi.org/10.1007/s12665-018-7967-4
[2] Hassan, W.H., Hashim, F.S. (2020). The effect of climate change on the maximum temperature in Southwest Iraq using HadCM3 and CanESM2 modelling. SN Applied Sciences, 2(9): 1494. https://doi.org/10.1007/s42452-020-03302-z
[3] Fazeres-Ferradosa, T., Rosa-Santos, P., Taveira-Pinto, F., Pavlou, D., Gao, F.P., Carvalho, H., Oliveira-Pinto, S. (2020). Preface: Advanced research on offshore structures and foundation design part 2. In Proceedings of the Institution of Civil Engineers-Maritime Engineering. Thomas Telford Ltd, 173(4): 96-99. https://doi.org/10.1680/jmaen.2020.173.4.96
[4] Stahlmann, A. (2013). Numerical and experimental modeling of scour at foundation structures for offshore wind turbines. In ISOPE International Ocean and Polar Engineering Conference. ISOPE, pp. ISOPE-I.
[5] Petersen, T.U., Sumer, B.M., Fredsøe, J. (2014). Edge scour at scour protections around offshore wind turbine foundations. In 7th International Conference on Scour and Erosion. CRC Press, pp. 587-592.
[6] Sumer, B.M., Fredsøe, J. (2001). Scour around pile in combined waves and current. Journal of Hydraulic Engineering, 127(5): 403-411. https://doi.org/10.1061/(ASCE)0733-9429(2001)127:5(403)
[7] Jalal, H.K., Hassan, W.H. (2020). Effect of bridge pier shape on depth of scour. In IOP Conference Series: Materials Science and Engineering. IOP Publishing, 671(1): 012001. https://doi.org/10.1088/1757-899X/671/1/012001
[8] Hassan, W.H., Jalal, H.K. (2021). Prediction of the depth of local scouring at a bridge pier using a gene expression programming method. SN Applied Sciences, 3(2): 159. https://doi.org/10.1007/s42452-020-04124-9
[9] Jalal, H.K., Hassan, W.H. (2020). Three-dimensional numerical simulation of local scour around circular bridge pier using Flow-3D software. In IOP Conference Series: Materials Science and Engineering. IOP Publishing, 745(1): 012150. https://doi.org/10.1088/1757-899X/745/1/012150
[10] Hassan, W.H., Attea, Z.H., Mohammed, S.S. (2020). Optimum layout design of sewer networks by hybrid genetic algorithm. Journal of Applied Water Engineering and Research, 8(2): 108-124. https://doi.org/10.1080/23249676.2020.1761897
[11] Hassan, W.H., Hussein, H.H., Alshammari, M.H., Jalal, H.K., Rasheed, S.E. (2022). Evaluation of gene expression programming and artificial neural networks in PyTorch for the prediction of local scour depth around a bridge pier. Results in Engineering, 13: 100353. https://doi.org/10.1016/j.rineng.2022.100353
[12] Hassan, W.H., Hh, H., Mohammed, S.S., Jalal, H.K., Nile, B.K. (2021). Evaluation of gene expression programming to predict the local scour depth around a bridge pier. Journal of Engineering Science and Technology, 16(2): 1232-1243. https://doi.org/10.1016/j.rineng.2022.100353
[13] Nerland, C. (2010). Offshore wind energy: Balancing risk and reward. In Proceedings of the Canadian Wind Energy Association’s 2010 Annual Conference and Exhibition, Canada, p. 2000.
[14] Hassan, W.H., Nile, B.K., Mahdi, K., Wesseling, J., Ritsema, C. (2021). A feasibility assessment of potential artificial recharge for increasing agricultural areas in the kerbala desert in Iraq using numerical groundwater modeling. Water, 13(22): 3167. https://doi.org/10.3390/w13223167
[15] Schendel, A., Welzel, M., Schlurmann, T., Hsu, T.W. (2020). Scour around a monopile induced by directionally spread irregular waves in combination with oblique currents. Coastal Engineering, 161: 103751. https://doi.org/10.1016/j.coastaleng.2020.103751
[16] Yakhot, V., Orszag, S.A. (1986). Renormalization group analysis of turbulence. I. Basic theory. Journal of Scientific Computing, 1(1): 3-51. https://doi.org/10.1007/BF01061452
[17] Mastbergen, D.R., Van Den Berg, J.H. (2003). Breaching in fine sands and the generation of sustained turbidity currents in submarine canyons. Sedimentology, 50(4): 625-637. https://doi.org/10.1046/j.1365-3091.2003.00554.x
[18] Soulsby, R. (1997). Dynamics of marine sands. https://doi.org/10.1680/doms.25844
[19] Van Rijn, L.C. (1984). Sediment transport, part I: Bed load transport. Journal of Hydraulic Engineering, 110(10): 1431-1456. https://doi.org/10.1061/(ASCE)0733-9429(1984)110:10(1431)
[20] Pang, A.L.J., Skote, M., Lim, S.Y., Gullman-Strand, J., Morgan, N. (2016). A numerical approach for determining equilibrium scour depth around a mono-pile due to steady currents. Applied Ocean Research, 57: 114-124. https://doi.org/10.1016/j.apor.2016.02.010
Mohammad Raze Raeisi Dehkordi1*, Amir Hossein Yeganeh Mazhar1 , Farzaneh Kheradzare2 1– PhD. Student in the Department of Construction and Water Management, Science and Research Unit, Islamic Azad University, Tehran, Iran 2– M.Sc. Graduate Water resource management, Department of Civil Engineering and Mechanics, Ghiaseddin Jamshid Kashani University, Qazvin, Iran
One of the key issues in river engineering is analyzing the flow properties at the intersection of natural rivers and canals. The flow of the side channel moves away from the intersection of the two channels as a result of the exchange of input force from the side channel with the main flow after coming into contact with it. One of the most evident properties of the flow in these sections is the development of a revolving region with low pressure and even negative pressure close to the inner wall of the side channel. One advantage of the whirling flow in this low-pressure region is that it gives the flow enough space to sediment, but it also increases flow speed near the channel’s bottom and outside wall by lowering the intersectional area of the flow. One of the most crucial considerations in the design of these intersections is minimizing sedimentation in the rotating region and scouring in the area above the shear plane.
Materials and methods:
The channel (flume) created in the laboratory based on Weber et al., (2001) model, was employed in the current investigation to confirm the validity and examine other study objectives. The main channel is 21. 95 meters long, while the side channel, which is at a 90-degree angle to the main channel, is 3. 66 meters long. The total downstream discharge is approximately 0. 17 m3/s, with the upstream velocities of the main channel being 0. 166 m/s and the side channel being 0. 5 m/s. In both channels, the flow depth and width are 0. 91 meters and 0. 296 meters, respectively. In this study, 6 various models’ angles of intersection between the main and side channels, inlet flow velocity, intersectional area, and side channel length have been examined. Models 2 and 3 have intersection angles of 60 and 30 degrees, respectively, and share the rest of their attributes with the fundamental model, or model number 1. Model 1 is the same as Weber’s experimental model. The length of the side channel in model 4 is different from model 1. The only difference between model 6 and the basic model is the side channel intake speed.
Results and Discussion
Analyzing the intersection angle The angle between the main channel and the side channel is investigated in this section of the findings. Models 1, 2, and 3 are assessed using the intersection angles of 90, 60, and 30 degrees, respectively. In some studies, the impact of the intersection angle has been examined, but in this study, three-dimensional investigation in transverse and longitudinal sections as well as the plan of the intersection is discussed, as can be observed from the literature review. Considering three models with intersection angles of 90, 60, and 30 degrees, the kinetic energy contours at the channel’s middle height can be obtained for each model. The channel with a 30-degree intersection angle (model 3) has the maximum kinetic energy in the flow. The channel with a 60-degree intersection has the minimum kinetic energy. As a result of the maximum deviation of the flow in the main channel caused by the flow of the side channel, the channel with a 90-degree intersection also has the maximum kinetic energy near the wall in front of the side channel.
Examining the side channel length In model 1, the side channel is 3. 66 meters long, whereas in model 4, it is 5. 52 meters long. This study aims to determine how changing the side channel’s length affects the flow pattern where two channels intersect. The kinetic energy contours were obtained for two states of the channel length, which are known to extend the lateral channel, increase the energy of the flow after the intersection, and shorten the length of the high-kinetic energy zone. When compared to model 1 with a shorter length of the side channel, the width of the flow separation zone is reduced by approximately 20%, which results in less flow sedimentation. Figure 12 illustrates the rotating zones in the flow separation area. The flow separation region’s length is essentially unchanged. Studying the intersection of the lateral channel After determining the lateral channel’s length, its width and, consequently, its intersectional area should be evaluated.
This section compares model 1 width of 0. 91 meters to model 5 width of 1. 40 meters. One of the most recent topics related to the intersection of the main and side channels is examining the intersection of the side channel. In model 5, the side channel’s flow rate has also increased due to an increase in the width or intersection of the channel. The flow rate through the intersection and the momentum of the flow from the side channel and the main channel increase when the side channel flow rate rises. The findings indicate that when flow width and side channel flow rise, energy increases after the inlet.
Investigating the value of inlet speed in the side channel Unlike the preceding sections, which were all concerned with the channel geometry, the inlet velocity in the side channel is one of the hydraulic parameters of the flow. In this section, models 1 and 6 with inlet velocities of the side channel of 0. 5 and 0. 75 m/s are evaluated. According to the modeling, the flow is somewhat horst before and immediately on the intersection of the flow level, but it undergoes a substantial prolapse just after the intersection. Model 6 has a larger volume and height of flow, but a smaller and softer prolapse after the intersection.
Conclusion
Some hydraulic and geometric properties of the intersection of channels have been examined using Flow-3D software. The RNG turbulence model was used for three-dimensional modeling. Some of the results are listed below. The flow is uniform upstream of the main and minor channels and only slightly becomes horst at the intersection. The analysis of the lengthening of the side channel revealed a 20% reduction in the separation zone’s width and a considerable reduction in the kinetic energy at the intersection. The input flow rate of this channel to the intersection increases with the speed and width of the side channel, which accounts for the local drop in the width of the main channel flow.
References
Azhdari, K., Talebi, Z. & Hosseini, S. H. (2020). Simulation of Subcritical Flow Distribution and Water Surface Fluctuations in Fourbranch Open Channel Junction with FLOW 3D. Irrigation and Drainage, 14(3), 1018- 1031. (In persian).
Behdarvandi, M., Hajipour, M., Parsi, E. & Ansari ghojghar, M. (2022). Investigation of Velocity Changes in a Straight Asymmetric pattern at river bend. Water and Soil Conservation, 22(6), 81-89. (In Persian).
Ghobadian, R. & Seyedi tabar, Z. (2016). Numerical investigating of the effect of lateral channel junction position on flow Rectangular Composite Channel Using Flow3D Software. Irrigation and Water Engineering, 13(1), 1-16. Doi: 10.22125/iwe.2022.158503 (In Persian).
Burqaʻi, S. M. & Nazari, A. (2003). Laboratory investigation of sediment pattern at the intersection of channels. 6th International Civil Engineering Conference, Amirkabir University of Technology, Tehran, Iran (In Persian).
Hemmati, M. & Aghazade-Soureh, T. (2018). Simulation of the Effect of Bed Discordance on Flow Pattern at the River Confluence by Flow-3D Model. Irrigation and Drainage, 11(5), 785-797.
Hosseini, S, M. & Abrishami, J. (2018). OpenChannel Hydraulics. 35th Edition: Imam Reza International University, 613 pages (In Persian).
Karami moghadam, M., Keshavarz, A. & Sabzevar, T. (2019). The Effect of Diversion Flow, Intake Inlet Shape, Topography and Bed Roughness on the Flow Separation Dimensions and Shear Stress at the Lateral Intake. Irrigation and Drainage Structures Engineering Research, 73(19), 113-126. (In Persian).
Khosravinia, P., Hosseini, S.H. & Hosseinzadeh Dalir, A. (2018). Numerical analyzing of flow in open channel junction with effect of side slope of channel. Irrigation and Water Engineering, 10(1), 1-16. Doi: 10.22125/iwe.2019.95871 (In Persian).
Kwanza, J.K., Kinyanjui, M. & Nkoroi, J.M. (2007). Modelling fluid flow in rectangular and trapezoidal open channels. Advances and Applications in Fluid Mechanics, 2(2), 149- 158.
Masjedi, A. & Taeedi, A. (2011). Experimental Investigations of Effect Intake Angle on Discharge in Lateral Intakes in 180 Degree Bend. World Applied Sciences Journal, 15(10), 1442-1444
Musavi Jahromi, S.M., & Goudarzizadeh, R. (2011). Numerical Simulation of 3D Flow Pattern at Open-Channel Junctions. Irrigation Sciences and Engineering, 34(2), 61-70 (In Persian).
Nikpour, M. & Khosravinia, P. (2018). Numerical Simulation of Side Slope Effect of Main Channel Wall on Flow Behavior in Open Channels Junction. Irrigation and Drainage, 11(6), 1024-1037. (In persian).
Raeisi Dehkordi, M. (2022). Description of types of pollution in water resources and protection of water resources, New Approaches in Civil Engineering, 6(1), 42- 52. Doi: 10.30469/jnace.2022.154373 (In Persian).
Ramamurthy, A.S., Carballada, L.B. & Tran, D.M. (1988). Combining Open Channel Flow at Right Angled Junctions. Journal of hydraulic engineering, 114(12), 1449-1460.
Tabesh, M. (2018). Advanced Modeling of Water Distribution Networks. 4th Edition: University of Tehran Press, 585 pages.
Taylor, E. (1944). Flow Characteristics at Rectangular Open-Channel Junctions. Journal of hydraulic engineering, 10(6), 893- 902.
Thiong’o, J.W. (2011). Investigations of fluid flows in open rectangular and triangular channels. Master’s thesis, Jomo Kenyatta University of Agriculture and Technology, Juja, Kenya.
Weber, L.J., Schumate, E.D. & Mawer, N. (2001). Experiments on Flow at a 90° Open-Channel Junction. Journal of hydraulic engineering, 127(5), 340-350.
This paper conducts a three-dimensional numerical analysis on the surges generated by landslides of different water entry scales, and analyzes the characteristics of surge disasters induced by landslides of different water entry scales, such as surge height, surge speed, and bank climbing height. Meanwhile, the impact of surges caused by landslides of different water entry scales on the dam is explored.
The FLOW-3D numerical simulation method is employed to simulate and analyze the entire process of landslide instability, surge formation and propagation, surge climbing, and surge backflow. The results show that the maximum climbing height of the surge generated by the 3. 1 million m~3 landslide of water entry is 54. 5 m on the opposite bank, and the surge height in front of the dam is 6. 69 m.
The surge has a small area of overflow at the right bank dam shoulder. The surge generated by the 0. 8 million m~3 landslide of water entry has a maximum climbing height of 26. 00 m on the opposite bank, and the surge height in front of the dam is 5. 38 m, without influence exerted by the surge on the dam safety. The results indicate that the induced surge caused by 3. 1×10~6 m~3 landslide of water entry is more catastrophic than that brought by 0. 8×10~6 m~3 landslide of water entry.
Difference Analysis of Wave Disaster Characteristics Induced by Landslides of Different Water Entry Scales
Artificial Intelligence (AI) techniques, such as Artificial Neural Networks (ANN) and Adaptive Neuro-Fuzzy Inference Systems (ANFIS), and dimensional analysis-based empirical equations (DAEEs), can estimate scour depth around bridge piers. AI’s accuracy depends on various architectures, while DAEEs’ performance depends on experimental data. This study evaluated the performance of AI and DAEEs for scour depth estimation using flow velocity, depth, size of bed sediment, critical approach velocity, and pier width. The data from a smooth rectangular (20 m × 1 m) flume and a high-precision particle image velocimetry to study the flow structure around the pier – width: 1.5 – 91.5 cm evaluated DAEEs. Various ANNs (5, 10, and 15 neurons), double layer (DL) and triple layers (TL), and different ANFIS settings were trained, tested, and verified. The Generalized Reduced Gradient optimization identified the parameters of DAEEs, and Nash–Sutcliffe efficiency (NSE) and Mean Square Error (MSE) evaluated the performance of different models. The study revealed that DL ANN-3 with 10 neurons (NSE = 0.986) outperformed ANFIS, other ANN (ANN1, ANN2, ANN4 & ANN5) models, and empirical equations with NSE values between 0.76 and 0.983. The study found pier dimensions to be the most influential parameter for pier scour.
Abadie J (1969) Generalization of the Wolfe reduced gradient method to the case of non-linear constraints. Optimization, 37–47
Abd El-Hady Rady R (2020) Prediction of local scour around bridge piers: Artificial-intelligence-based modeling versus conventional regression methods. Applied Water Science 10(2):57, DOI: https://doi.org/10.1007/s13201-020-1140-4ArticleGoogle Scholar
Akhlaghi E, Babarsad MS, Derikvand EM, Abedini M (2020) Assessment the effects of different parameters to rate scour around single piers and pile groups: A review. Archives of Computational Methods in Engineering 27(1):183–197, DOI: https://doi.org/10.1007/s11831-018-09304-wArticleGoogle Scholar
Alharbi S, Mills G (2022) Assessment of exposure to flash flooding in an arid environment: A case study of the jeddah city neighborhood abruq ar rughamah, saudi arabia. In: Wadi Flash Floods: Challenges and Advanced Approaches for Disaster Risk Reduction. Springer Nature Singapore, 383–397ChapterGoogle Scholar
Annad M, Lefkir A (2022) Analytic network process for local scour formula ranking with parametric sensitivity analysis and soil class clustering. Water Supply 22(11):8287–8304, DOI: https://doi.org/10.2166/ws.2022.357ArticleGoogle Scholar
Annad M, Lefkir A, Mammar-kouadri M, Bettahar I (2021) Development of a local scour prediction model clustered by soil class. Water Practice & Technology 16(4):1159–1172, DOI: https://doi.org/10.2166/wpt.2021.065ArticleGoogle Scholar
Arifin F, Robbani H, Annisa T, Ma’Arof N (2019) Variations in the number of layers and the number of neurons in artificial neural networks: Case study of pattern recognition. Journal of Physics: Conference Series 1413(1):12016, DOI: https://doi.org/10.1088/1742-6596/1413/1/012016Google Scholar
Arneson LA, Zevenbergen LW, Lagasse PF, Clopper PE (2012) Evaluating scour at bridges. Report No. FHWA-HIF-12-003 HEC-18, National Highway Institute, Arlington, VA, USAGoogle Scholar
Benedict ST, Caldwell AW (2014) A pier-scour database: 2427 Field and Laboratory Measurements of Pier Scour, Data Series No. 845, US Department of the Interior, US Geol. Surv. Reston, VA, USAGoogle Scholar
Cao J, Chen J, Zhu D, Wei S (2021) Evaluation of local scour calculation equations for bridge piers in sandy riverbed. IOP Conference Series: Earth and Environmental Science 692(4):042022, DOI: https://doi.org/10.1088/1755-1315/692/4/042022Google Scholar
Chabert J (1956) Etude des affouillements autour des piles de ponts. Laboratoire National d’Hydraulique, ChatouGoogle Scholar
Chavan R, Gualtieri P, Kumar B (2019) Turbulent flow structures and scour hole characteristics around circular bridge piers over nonuniform sand bed channels with downward seepage. Water 11(8):1580, DOI: https://doi.org/10.3390/w11081580ArticleGoogle Scholar
Chavan R, Kumar B (2020) Downward seepage effects on dynamics of scour depth and migrating dune-like bedforms at tandem piers. Canadian Journal of Civil Engineering 47(1):13–24, DOI: https://doi.org/10.1139/cjce-2017-0640ArticleGoogle Scholar
Cikojević A, Gilja G, Kuspilić N (2019) Sensitivity analysis of empirical equations applicable on bridge piers in sand-bed rivers, Proceedings of the 16th International Symposium on Water Management and Hydraulic Engineering, September 5–7, Skopje, Republic of Macedonia
Dimitriadis P, Koutsoyiannis D, Iliopoulou T, Papanicolaou P (2021) A global-scale investigation of stochastic similarities in marginal distribution and dependence structure of key hydrological-cycle processes. Hydrology 8(2):59, DOI: https://doi.org/10.3390/hydrology8020059ArticleGoogle Scholar
Ettema R (1980) Scour at bridge piers: A report submitted to the National Roads Board. PhD Thesis, The University of Auckland, Auckland, New ZealandGoogle Scholar
Farooq R, Ghumman AR, Ahmed A, Latif A, Masood A (2021) Performance evaluation of scour protection around a bridge pier through experimental approach. Tehnički Vjesnik 28(6):1975–1982, DOI: https://doi.org/10.17559/TV-20200213211932Google Scholar
Fattah MY, Hassan WH, Rasheed SE (2018) Behavior of flexible buried pipes under geocell reinforced subbase subjected to repeated loading. International Journal of Geotechnical Earthquake Engineering 9(1):22–41, DOI: https://doi.org/10.4018/IJGEE.2018010102ArticleGoogle Scholar
FHWA (1998) Recording and coding guide for the structural inventory and appraisal of the nations’ bridges. Report No. FHWA-PD-96-001, US Department of Transportation, Federal Highway Administration. Office of Engineering, Washigton DC, USAGoogle Scholar
Hassan WH, Hussein HH, Alshammari MH, Jalal HK, Rasheed SE (2022) Evaluation of gene expression programming and artificial neural networks in PyTorch for the prediction of local scour depth around a bridge pier. Results in Engineering 13:100353, DOI: https://doi.org/10.1016/j.rineng.2022.100353ArticleGoogle Scholar
Imhof D (2004) Risk assessment of existing bridge structures. PhD Thesis, University of Cambridge, Cambridge, UKGoogle Scholar
Jalal HK, Hassan WH (2020) Three-dimensional numerical simulation of local scour around circular bridge pier using Flow-3D software. IOP Conference Series: Materials Science and Engineering 745(1): 12150, DOI: https://doi.org/10.1088/1757-899X/745/1/012150ArticleGoogle Scholar
Khassaf SI, Ahmed SI (2021) Development an empirical formula to calculate the scour depth at different shapes of non-uniform piers. Journal of Physics: Conference Series 1973(1):012179, DOI: https://doi.org/10.1088/1742-6596/1973/1/012179Google Scholar
Lasdon LS, Waren AD, Jain A, Ratner M (1978) Design and testing of a generalized reduced gradient code for non-linear programming. ACM Transactions on Mathematical Software 4(1):34–50, DOI: https://doi.org/10.1145/355769.355773ArticleGoogle Scholar
Moriasi DN, Arnold JG, Van Liew MW, Bingner RL, Harmel RD, Veith TL (2007) Model evaluation guidelines for systematic quantification of accuracy in watershed simulations. Transactions of ASABE 50(3): 885–900, DOI: https://doi.org/10.13031/2013.23153ArticleGoogle Scholar
Namaee MR, Li Y, Sui J, Whitcombe T (2018) Comparison of three commonly used equations for calculating local scour depth around bridge pier under ice covered flow condition. World Journal of Engineering and Technology 6(2):50–62ArticleGoogle Scholar
Oğuz K, Bor A (2022) Prediction of local scour around bridge piers using hierarchical clustering and adaptive genetic programming. Applied Artificial Intelligence 36(1), DOI: https://doi.org/10.1080/08839514.2021.2001734
Parola AC, Hagerty DJ, Mueller DS, Melville BW, Parker G, Usher JS (1997) The need for research on scour at bridge crossings, 1997. Proceedings of the 27th IAHR World Congress. San Fransisco, CA, USA
Pizarro A, Samela C, Fiorentino M, Link O, Manfreda S (2017) BRISENT: An entropy-based model for bridge-pier scour estimation under complex hydraulic scenarios. Water 9(11):889, DOI: https://doi.org/10.3390/w9110889ArticleGoogle Scholar
Pregnolato M, Winter AO, Mascarenas D, Sen AD, Bates P, Motley MR (2022) Assessing flooding impact to riverine bridges: An integrated analysis. Natural Hazards and Earth System Sciences 22(5):1559–1576, DOI: https://doi.org/10.5194/nhess-22-1559-2022ArticleGoogle Scholar
Sarshari E, Mullhaupt P (2015) Application of artificial neural networks in assessing the equilibrium depth of local scour around bridge piers. ASME 2015 34th International Conference on Ocean, Offshore and Arctic Engineering, May 31–June 5, St. John’s, NL, Canada
Sharafati A, Tafarojnoruz A, Yaseen ZM (2020) New stochastic modeling strategy on the prediction enhancement of pier scour depth in cohesive bed materials. Journal of Hydroinformatics 22(3):457–472, DOI: https://doi.org/10.2166/hydro.2020.047ArticleGoogle Scholar
Sreedhara BM, Patil AP, Pushparaj J, Kuntoji G, Naganna SR (2021) Application of gradient tree boosting regressor for the prediction of scour depth around bridge piers. Journal of Hydroinformatics 23(4): 849–863, DOI: https://doi.org/10.2166/hydro.2021.011ArticleGoogle Scholar
Wang C, Yu X, Liang F (2017) Comparison and estimation of the local scour depth around pile groups and wide piers. In Geotechnical Frontiers, American Scciety of Civil Engineers, Reston, VA, USA, 11–19Google Scholar
Youssef AM, Abu-Abdullah MM, AlFadail EA, Skilodimou HD, Bathrellos GD (2018) The devastating flood in the arid region a consequence of rainfall and dam failure: Case study. Al-Lith flood on 23th November 2018, Kingdom of Saudi Arabia, Zeitschrift für Geomorphol 63(1):115–136, DOI: https://doi.org/10.1127/zfg/2021/0672Google Scholar
Zhang B, Zhao H, Tan C, OBrien EJ, Fitzgerald PC, Kim CW (2022) Laboratory investigation on detecting bridge scour using the indirect measurement from a passing vehicle. Remote Sensing 14(13):3106, DOI: https://doi.org/10.3390/rs14133106ArticleGoogle Scholar
Authors also thank “The US Department of the Interior,” US Geol. Surv. Reston, VA, USA” for providing access to scour data. The Researchers would like to thank the Deanship of Graduate Studies and Scientific Research at Qassim University for financial support (QU-APC-2024-9/1).
Author information
Authors and Affiliations
Dept. of Civil Engineering, College of Engineering, Qassim University, Buraydah, 51452, Saudi ArabiaAbdul Razzaq Ghumman, Husnain Haider, Ibrahim Saleh Al Salamah, Md. Shafiquzzaman, Abdullah Alodah & Mohammad Alresheedi
Dept. of Civil Engineering, International Islamic University, Islamabad, 44000, PakistanRashid Farooq
Dept. of Civil Engineering, University of Engineering and Technology, Taxila, 47050, PakistanAfzal Ahmed & Ghufran Ahmed Pasha
•Landslide travel distance is considered for the first time in a predictive equation.
•Predictive equation derived from databases using 3D physical and numerical modeling.
•The equation was successfully tested on the 2018 Anak Krakatau tsunami event.
•The developed equation using three-dimensional data exhibits a 91 % fitting quality.
Abstract
Landslide tsunamis, responsible for thousands of deaths and significant damage in recent years, necessitate the allocation of sufficient time and resources for studying these extreme natural hazards. This study offers a step change in the field by conducting a large number of three-dimensional numerical experiments, validated by physical tests, to develop a predictive equation for the maximum initial amplitude of tsunamis generated by subaerial landslides. We first conducted a few 3D physical experiments in a wave basin which were then applied for the validation of a 3D numerical model based on the Flow3D-HYDRO package. Consequently, we delivered 100 simulations using the validated model by varying parameters such as landslide volume, water depth, slope angle and travel distance. This large database was subsequently employed to develop a predictive equation for the maximum initial tsunami amplitude. For the first time, we considered travel distance as an independent parameter for developing the predictive equation, which can significantly improve the predication accuracy. The predictive equation was tested for the case of the 2018 Anak Krakatau subaerial landslide tsunami and produced satisfactory results.
The Anak Krakatau landslide tsunami on 22nd December 2018 was a stark reminder of the dangers posed by subaerial landslide tsunamis (Ren et al., 2020; Mulia et al. 2020a; Borrero et al., 2020; Heidarzadeh et al., 2020; Grilli et al., 2021). The collapse of the volcano’s southwest side into the ocean triggered a tsunami that struck the Sunda Strait, leading to approximately 450 fatalities (Syamsidik et al., 2020; Mulia et al., 2020b) (Fig. 1). As shown in Fig. 1, landslide tsunamis (both submarine and subaerial) have been responsible for thousands of deaths and significant damage to coastal communities worldwide. These incidents underscored the critical need for advanced research into landslide-generated waves to aid in hazard prediction and mitigation. This is further emphasized by recent events such as the 28th of November 2020 landslide tsunami in the southern coast mountains of British Columbia (Canada), where an 18 million m3 rockslide generated a massive tsunami, with over 100 m wave run-up, causing significant environmental and infrastructural damage (Geertsema et al., 2022).
Physical modelling and numerical simulation are crucial tools in the study of landslide-induced waves due to their ability to replicate and analyse the complex dynamics of landslide events (Kim et al., 2020). In two-dimensional (2D) modelling, the discrepancy between dimensions can lead to an artificial overestimation of wave amplification (e.g., Heller and Spinneken, 2015). This limitation is overcome with 3D modelling, which enables the scaled-down representation of landslide-generated waves while avoiding the simplifications inherent in 2D approaches (Erosi et al., 2019). Another advantage of 3D modelling in studying landslide-generated waves is its ability to accurately depict the complex dynamics of wave propagation, including lateral and radial spreading from the slide impact zone, a feature unattainable with 2D models (Heller and Spinneken, 2015).
Physical experiments in tsunami research, as presented by authors such as Romano et al. (2020), McFall and Fritz (2016), and Heller and Spinneken (2015), have supported 3D modelling works through validation and calibration of the numerical models to capture the complexities of wave generation and propagation. Numerical modelling has increasingly complemented experimental approach in tsunami research due to the latter’s time and resource-intensive nature, particularly for 3D models (Li et al., 2019; Kim et al., 2021). Various numerical approaches have been employed, from Eulerian and Lagrangian frameworks to depth-averaged and Navier–Stokes models, enhancing our understanding of tsunami dynamics (Si et al., 2018; Grilli et al., 2019; Heidarzadeh et al., 2017, 2020; Iorio et al., 2021; Zhang et al., 2021; Kirby et al., 2022; Wang et al., 2021, 2022; Hu et al., 2022). The sophisticated numerical techniques, including the Particle Finite Element Method and the Immersed Boundary Method, have also shown promising results in modelling highly dynamic landslide scenarios (Mulligan et al., 2020; Chen et al., 2020). Among these methods and techniques, FLOW-3D HYDRO stands out in simulating landslide-generated tsunami waves due to its sophisticated technical features such as offering Tru Volume of Fluid (VOF) method for precise free surface tracking (e.g., Sabeti and Heidarzadeh 2022a). TruVOF distinguishes itself through a split Lagrangian approach, adeptly reducing cumulative volume errors in wave simulations by dynamically updating cell volume fractions and areas with each time step. Its intelligent adaptation of time step size ensures precise capture of evolving free surfaces, offering unparalleled accuracy in modelling complex fluid interfaces and behaviour (Flow Science, 2023).
Predictive equations play a crucial role in assessing the potential hazards associated with landslide-generated tsunami waves due to their ability to provide risk assessment and warnings. These equations can offer swift and reasonable evaluations of potential tsunami impacts in the absence of detailed numerical simulations, which can be time-consuming and expensive to produce. Among multiple factors and parameters within a landslide tsunami generation, the initial maximum wave amplitude (Fig. 1) stands out due to its critical role. While it is most likely that the initial wave generated by a landslide will have the highest amplitude, it is crucial to clarify that the term “initial maximum wave amplitude” refers to the highest amplitude within the first set of impulse waves. This parameter is essential in determining the tsunami’s impact severity, with higher amplitudes signalling a greater destructive potential (Sabeti and Heidarzadeh 2022a). Additionally, it plays a significant role in tsunami modelling, aiding in the prediction of wave propagation and the assessment of potential impacts.
In this study, we initially validate the FLOW-3D HYDRO model through a series of physical experiments conducted in a 3D wave tank at University of Bath (UK). Upon confirmation of the model’s accuracy, we use it to systematically vary parameters namely landslide volume, water depth, slope angle, and travel distance, creating an extensive database. Alongside this, we perform a sensitivity analysis on these variables to discern their impacts on the initial maximum wave amplitude. The generated database was consequently applied to derive a non-dimensional predictive equation aimed at estimating the initial maximum wave amplitude in real-world landslide tsunami events.
Two innovations of this study are: (i) The predictive equation of this study is based on a large number of 3D experiments whereas most of the previous equations were based on 2D results, and (ii) For the first time, the travel distance is included in the predictive equation as an independent parameter. To evaluate the performance of our predictive equation, we applied it to a previous real-world subaerial landslide tsunami, i.e., the Anak Krakatau 2018 event. Furthermore, we compare the performance of our predictive equation with other existing equations.
2. Data and methods
The methodology applied in this research is a combination of physical and numerical modelling. Limited physical modelling was performed in a 3D wave basin at the University of Bath (UK) to provide data for calibration and validation of the numerical model. After calibration and validation, the numerical model was employed to model a large number of landslide tsunami scenarios which allowed us to develop a database for deriving a predictive equation.
2.1. Physical experiments
To validate our numerical model, we conducted a series of physical experiments including two sets in a 3D wave basin at University of Bath, measuring 2.50 m in length (WL), 2.60 m in width (WW), and 0.60 m in height (WH) (Fig. 2a). Conducting two distinct sets of experiments (Table 1), each with different setups (travel distance, location, and water depth), provided a robust framework for validation of the numerical model. For wave measurement, we employed a twin wire wave gauge from HR Wallingford (https://equipit.hrwallingford.com). In these experiments, we used a concrete prism solid block, the dimensions of which are outlined in Table 2. In our experiments, we employed a concrete prism solid block with a density of 2600 kg/m3, chosen for its similarity to the natural density of landslides, akin to those observed with the 2018 Anak Krakatau tsunami, where the landslide composition is predominantly solid rather than granular. The block’s form has also been endorsed in prior studies (Watts, 1998; Najafi-Jilani and Ataie-Ashtiani, 2008) as a suitable surrogate for modelling landslide-induced waves. A key aspect of our methodology was addressing scale effects, following the guidelines proposed by Heller et al. (2008) as it is described in Table 1. To enhance the reliability and accuracy of our experimental data, we conducted each physical experiment three times which revealed all three experimental waveforms were identical. This repetition was aimed at minimizing potential errors and inconsistencies in laboratory measurements.
Table 1. The locations and other information of the laboratory setups for making landslide-generated waves in the physical wave basin. This table details the specific parameters for each setup, including slope range (α), slide volume (V), kinematic viscosity (ν), water depth (h), travel distance (D), surface tension coefficient of water (σ), Reynolds number (R), Weber number (W), and the precise coordinates of the wave gauges (WG).
The acceptable ranges for avoiding scale effects are based on the study by Heller et al. (2008).⁎⁎
The Reynolds number (R) is given by g0.5h1.5/ν, with ν denoting the kinematic viscosity. The Weber number (W) is W = ρgh2/σ, where σ represents surface tension coefficient and ρ = 1000kg/m3 is the density of water. In our experiments, conducted at a water temperature of approximately 20 °C, the kinematic viscosity (ν) and the surface tension coefficient of water (σ) are 1.01 × 10−6 m²/s and 0.073 N/m, respectively (Kestin et al., 1978).
Table 2. Specifications of the solid block used in physical experiments for generating subaerial landslides in the laboratory.
Solid-block attributes
Property metrics
Geometric shape
Slide width (bs)
0.26 m
Slide length (ls)
0.20 m
Slide thickness (s)
0.10 m
Slide volume (V)
2.60 × 10−3 m3
Specific gravity, (γs)
2.60
Slide weight (ms)
6.86 kg
2.2. Numerical simulations applying FLOW-3D hydro
The detailed theoretical framework encompassing the governing equations, the computational methodologies employed, and the specific techniques used for tracking the water surface in these simulations are thoroughly detailed in the study by Sabeti et al. (2024). Here, we briefly explain some of the numerical details. We defined a uniform mesh for our flow domain, carefully crafted with a fine spatial resolution of 0.005 m (i.e., grid size). The dimensions of the numerical model directly matched those of our wave basin used in the physical experiment, being 2.60 m wide, 0.60 m deep, and 2.50 m long (Fig. 2). This design ensures comprehensive coverage of the study area. The output intervals of the numerical model are set at 0.02 s. This timing is consistent with the sampling rates of wave gauges used in laboratory settings. The friction coefficient in the FLOW-3D HYDRO is designated as 0.45. This value corresponds to the Coulombic friction measurements obtained in the laboratory, ensuring that the simulation accurately reflects real-world physical interactions.
In order to simulate the landslide motion, we applied coupled motion objects in FLOW-3D-HYDRO where the dynamics are predominantly driven by gravity and surface friction. This methodology stands in contrast to other models that necessitate explicit inputs of force and torque. This approach ensures that the simulation more accurately reflects the natural movement of landslides, which is heavily reliant on gravitational force and the interaction between sliding surfaces. The stability of the numerical simulations is governed by the Courant Number criterion (Courant et al., 1928), which dictates the maximum time step (Δt) for a given mesh size (Δx) and flow speed (U). According to Courant et al. (1928), this number is required to stay below one to ensure stability of numerical simulations. In our simulations, the Courant number is always maintained below one.
In alignment with the parameters of physical experiments, we set the fluid within the mesh to water, characterized by a density of 1000 kg/m³ at a temperature of 20 °C. Furthermore, we defined the top, front, and back surfaces of the mesh as symmetry planes. The remaining surfaces are designated as wall types, incorporating no-slip conditions to accurately simulate the interaction between the fluid and the boundaries. In terms of selection of an appropriate turbulence model, we selected the k–ω model that showed a better performance than other turbulence methods (e.g., Renormalization-Group) in a previous study (Sabeti et al., 2024). The simulations are conducted using a PC Intel® Core™ i7-10510U CPU with a frequency of 1.80 GHz, and a 16 GB RAM. On this PC, completion of a 3-s simulation required approximately 12.5 h.
2.3. Validation
The FLOW-3D HYDRO numerical model was validated using the two physical experiments (Fig. 3) outlined in Table 1. The level of agreement between observations (Oi) and simulations (Si) is examined using the following equation:(1)�=|��−����|×100where ε represents the mismatch error, Oi denotes the observed laboratory values, and Si represents the simulated values from the FLOW-3D HYDRO model. The results of this validation process revealed that our model could replicate the waves generated in the physical experiments with a reasonable degree of mismatch (ε): 14 % for Lab 1 and 8 % for Lab 2 experiments, respectively (Fig. 3). These values indicate that while the model is not perfect, it provides a sufficiently close approximation of the real-world phenomena.
In terms of mesh efficiency, we varied the mesh size to study sensitivity of the numerical results to mesh size. First, by halving the mesh size and then by doubling it, we repeated the modelling by keeping other parameters unchanged. This analysis guided that a mesh size of ∆x = 0.005 m is the most effective for the setup of this study. The total number of computational cells applying mesh size of 0.005 m is 9.269 × 106.
2.4. The dataset
The validated numerical model was employed to conduct 100 simulations, incorporating variations in four key landslide parameters namely water depth, slope angle, slide volume, and travel distance. This methodical approach was essential for a thorough sensitivity analysis of these variables, and for the creation of a detailed database to develop a predictive equation for maximum initial tsunami amplitude. Within the model, 15 distinct slide volumes were established, ranging from 0.10 × 10−3 m3 to 6.25 × 10−3 m3 (Table 3). The slope angle varied between 35° and 55°, and water depth ranged from 0.24 m to 0.27 m. The travel distance of the landslides was varied, spanning from 0.04 m to 0.07 m. Detailed configurations of each simulation, along with the maximum initial wave amplitudes and dominant wave periods are provided in Table 4.
Table 3. Geometrical information of the 15 solid blocks used in numerical modelling for generating landslide tsunamis. Parameters are: ls, slide length; bs, slide width; s, slide thickness; γs, specific gravity; and V, slide volume.
Solid block
ls (m)
bs (m)
s (m)
V (m3)
γs
Block-1
0.310
0.260
0.155
6.25 × 10−3
2.60
Block-2
0.300
0.260
0.150
5.85 × 10−3
2.60
Block-3
0.280
0.260
0.140
5.10 × 10−3
2.60
Block-4
0.260
0.260
0.130
4.39 × 10−3
2.60
Block-5
0.240
0.260
0.120
3.74 × 10−3
2.60
Block-6
0.220
0.260
0.110
3.15 × 10−3
2.60
Block-7
0.200
0.260
0.100
2.60 × 10−3
2.60
Block-8
0.180
0.260
0.090
2.11 × 10−3
2.60
Block-9
0.160
0.260
0.080
1.66 × 10−3
2.60
Block-10
0.140
0.260
0.070
1.27 × 10−3
2.60
Block-11
0.120
0.260
0.060
0.93 × 10−3
2.60
Block-12
0.100
0.260
0.050
0.65 × 10−3
2.60
Block-13
0.080
0.260
0.040
0.41 × 10−3
2.60
Block-14
0.060
0.260
0.030
0.23 × 10−3
2.60
Block-15
0.040
0.260
0.020
0.10 × 10−3
2.60
Table 4. The numerical simulation for the 100 tests performed in this study for subaerial solid-block landslide-generated waves. Parameters are aM, maximum wave amplitude; α, slope angle; h, water depth; D, travel distance; and T, dominant wave period. The location of the wave gauge is X=1.030 m, Y=1.210 m, and Z=0.050 m. The properties of various solid blocks are presented in Table 3.
Test-
Block No
α (°)
h (m)
D (m)
T(s)
aM (m)
1
Block-7
45
0.246
0.029
0.510
0.0153
2
Block-7
45
0.246
0.030
0.505
0.0154
3
Block-7
45
0.246
0.031
0.505
0.0156
4
Block-7
45
0.246
0.032
0.505
0.0158
5
Block-7
45
0.246
0.033
0.505
0.0159
6
Block-7
45
0.246
0.034
0.505
0.0160
7
Block-7
45
0.246
0.035
0.505
0.0162
8
Block-7
45
0.246
0.036
0.505
0.0166
9
Block-7
45
0.246
0.037
0.505
0.0167
10
Block-7
45
0.246
0.038
0.505
0.0172
11
Block-7
45
0.246
0.039
0.505
0.0178
12
Block-7
45
0.246
0.040
0.505
0.0179
13
Block-7
45
0.246
0.041
0.505
0.0181
14
Block-7
45
0.246
0.042
0.505
0.0183
15
Block-7
45
0.246
0.043
0.505
0.0190
16
Block-7
45
0.246
0.044
0.505
0.0197
17
Block-7
45
0.246
0.045
0.505
0.0199
18
Block-7
45
0.246
0.046
0.505
0.0201
19
Block-7
45
0.246
0.047
0.505
0.0191
20
Block-7
45
0.246
0.048
0.505
0.0217
21
Block-7
45
0.246
0.049
0.505
0.0220
22
Block-7
45
0.246
0.050
0.505
0.0226
23
Block-7
45
0.246
0.051
0.505
0.0236
24
Block-7
45
0.246
0.052
0.505
0.0239
25
Block-7
45
0.246
0.053
0.510
0.0240
26
Block-7
45
0.246
0.054
0.505
0.0241
27
Block-7
45
0.246
0.055
0.505
0.0246
28
Block-7
45
0.246
0.056
0.505
0.0247
29
Block-7
45
0.246
0.057
0.505
0.0248
30
Block-7
45
0.246
0.058
0.505
0.0249
31
Block-7
45
0.246
0.059
0.505
0.0251
32
Block-7
45
0.246
0.060
0.505
0.0257
33
Block-1
45
0.246
0.045
0.505
0.0319
34
Block-2
45
0.246
0.045
0.505
0.0294
35
Block-3
45
0.246
0.045
0.505
0.0282
36
Block-4
45
0.246
0.045
0.505
0.0262
37
Block-5
45
0.246
0.045
0.505
0.0243
38
Block-6
45
0.246
0.045
0.505
0.0223
39
Block-7
45
0.246
0.045
0.505
0.0196
40
Block-8
45
0.246
0.045
0.505
0.0197
41
Block-9
45
0.246
0.045
0.505
0.0198
42
Block-10
45
0.246
0.045
0.505
0.0184
43
Block-11
45
0.246
0.045
0.505
0.0173
44
Block-12
45
0.246
0.045
0.505
0.0165
45
Block-13
45
0.246
0.045
0.404
0.0153
46
Block-14
45
0.246
0.045
0.404
0.0124
47
Block-15
45
0.246
0.045
0.505
0.0066
48
Block-7
45
0.202
0.045
0.404
0.0220
49
Block-7
45
0.204
0.045
0.404
0.0219
50
Block-7
45
0.206
0.045
0.404
0.0218
51
Block-7
45
0.208
0.045
0.404
0.0217
52
Block-7
45
0.210
0.045
0.404
0.0216
53
Block-7
45
0.212
0.045
0.404
0.0215
54
Block-7
45
0.214
0.045
0.505
0.0214
55
Block-7
45
0.216
0.045
0.505
0.0214
56
Block-7
45
0.218
0.045
0.505
0.0213
57
Block-7
45
0.220
0.045
0.505
0.0212
58
Block-7
45
0.222
0.045
0.505
0.0211
59
Block-7
45
0.224
0.045
0.505
0.0208
60
Block-7
45
0.226
0.045
0.505
0.0203
61
Block-7
45
0.228
0.045
0.505
0.0202
62
Block-7
45
0.230
0.045
0.505
0.0201
63
Block-7
45
0.232
0.045
0.505
0.0201
64
Block-7
45
0.234
0.045
0.505
0.0200
65
Block-7
45
0.236
0.045
0.505
0.0199
66
Block-7
45
0.238
0.045
0.404
0.0196
67
Block-7
45
0.240
0.045
0.404
0.0194
68
Block-7
45
0.242
0.045
0.404
0.0193
69
Block-7
45
0.244
0.045
0.404
0.0192
70
Block-7
45
0.246
0.045
0.505
0.0190
71
Block-7
45
0.248
0.045
0.505
0.0189
72
Block-7
45
0.250
0.045
0.505
0.0187
73
Block-7
45
0.252
0.045
0.505
0.0187
74
Block-7
45
0.254
0.045
0.505
0.0186
75
Block-7
45
0.256
0.045
0.505
0.0184
76
Block-7
45
0.258
0.045
0.505
0.0182
77
Block-7
45
0.259
0.045
0.505
0.0183
78
Block-7
45
0.260
0.045
0.505
0.0191
79
Block-7
45
0.261
0.045
0.505
0.0192
80
Block-7
45
0.262
0.045
0.505
0.0194
81
Block-7
45
0.263
0.045
0.505
0.0195
82
Block-7
45
0.264
0.045
0.505
0.0195
83
Block-7
45
0.265
0.045
0.505
0.0197
84
Block-7
45
0.266
0.045
0.505
0.0197
85
Block-7
45
0.267
0.045
0.505
0.0198
86
Block-7
45
0.270
0.045
0.505
0.0199
87
Block-7
30
0.246
0.045
0.505
0.0101
88
Block-7
35
0.246
0.045
0.505
0.0107
89
Block-7
36
0.246
0.045
0.505
0.0111
90
Block-7
37
0.246
0.045
0.505
0.0116
91
Block-7
38
0.246
0.045
0.505
0.0117
92
Block-7
39
0.246
0.045
0.505
0.0119
93
Block-7
40
0.246
0.045
0.505
0.0121
94
Block-7
41
0.246
0.045
0.505
0.0127
95
Block-7
42
0.246
0.045
0.404
0.0154
96
Block-7
43
0.246
0.045
0.404
0.0157
97
Block-7
44
0.246
0.045
0.404
0.0162
98
Block-7
45
0.246
0.045
0.505
0.0197
99
Block-7
50
0.246
0.045
0.505
0.0221
100
Block-7
55
0.246
0.045
0.505
0.0233
In all these 100 simulations, the wave gauge was consistently positioned at coordinates X=1.09 m, Y=1.21 m, and Z=0.05 m. The dominant wave period for each simulation was determined using the Fast Fourier Transform (FFT) function in MATLAB (MathWorks, 2023). Furthermore, the classification of wave types was carried out using a wave categorization graph according to Sorensen (2010), as shown in Fig. 4a. The results indicate that the majority of the simulated waves are on the border between intermediate and deep-water waves, and they are categorized as Stokes waves (Fig. 4a). Four sample waveforms from our 100 numerical experiments are provided in Fig. 4b.
The dataset in Table 4 was used to derive a new predictive equation that incorporates travel distance for the first time to estimate the initial maximum tsunami amplitude. In developing this equation, a genetic algorithm optimization technique was implemented using MATLAB (MathWorks 2023). This advanced approach entailed the use of genetic algorithms (GAs), an evolutionary algorithm type inspired by natural selection processes (MathWorks, 2023). This technique is iterative, involving selection, crossover, and mutation processes to evolve solutions over several generations. The goal was to identify the optimal coefficients and powers for each landslide parameter in the predictive equation, ensuring a robust and reliable model for estimating maximum wave amplitudes. Genetic Algorithms excel at optimizing complex models by navigating through extensive combinations of coefficients and exponents. GAs effectively identify highly suitable solutions for the non-linear and complex relationships between inputs (e.g., slide volume, slope angle, travel distance, water depth) and the output (i.e., maximum initial wave amplitude, aM). MATLAB’s computational environment enhances this process, providing robust tools for GA to adapt and evolve solutions iteratively, ensuring the precision of the predictive model (Onnen et al., 1997). This approach leverages MATLAB’s capabilities to fine-tune parameters dynamically, achieving an optimal equation that accurately estimates aM. It is important to highlight that the nondimensionalized version of this dataset is employed to develop a predictive equation which enables the equation to reproduce the maximum initial wave amplitude (aM) for various subaerial landslide cases, independent of their dimensional differences (e.g., Heler and Hager 2014; Heller and Spinneken 2015; Sabeti and Heidarzadeh 2022b). For this nondimensionalization, we employed the water depth (h) to nondimensionalize the slide volume (V/h3) and travel distance (D/h). The slide thickness (s) was applied to nondimensionalize the water depth (h/s).
2.5. Landslide velocity
In discussing the critical role of landslide velocity for simulating landslide-generated waves, we focus on the mechanisms of landslide motion and the techniques used to record landslide velocity in our simulations (Fig. 5). Also, we examine how these methods were applied in two distinct scenarios: Lab 1 and Lab 2 (see Table 1 for their details). Regarding the process of landslide movement, a slide starts from a stationary state, gaining momentum under the influence of gravity and this acceleration continues until the landslide collides with water, leading to a significant reduction in its speed before eventually coming to a stop (Fig. 5) (e.g., Panizzo et al. 2005).
To measure the landslide’s velocity in our simulations, we attached a probe at the centre of the slide, which supplied a time series of the velocity data. The slide’s velocity (vs) peaks at the moment it enters the water (Fig. 5), a point referred to as the impact time (tImp). Following this initial impact, the slides continue their underwater movement, eventually coming to a complete halt (tStop). Given the results in Fig. 5, it can be seen that Lab 1, with its longer travel distance (0.070 m), exhibits a higher peak velocity of 1.89 m/s. This increase in velocity is attributed to the extended travel distance allowing more time for the slide to accelerate under gravity. Whereas Lab 2, featuring a shorter travel distance (0.045 m), records a lower peak velocity of 1.78 m/s. This difference underscores how travel distance significantly influences the dynamics of landslide motion. After reaching the peak, both profiles show a sharp decrease in velocity, marking the transition to submarine motion until the slides come to a complete stop (tStop). There are noticeable differences observable in Fig. 5 between the Lab-1 and Lab-2 simulations, including the peaks at 0.3 s . These variations might stem from the placement of the wave gauge, which differs slightly in each scenario, as well as the water depth’s minor discrepancies and, the travel distance.
2.6. Effect of air entrainment
In this section we examine whether it is required to consider air entrainment for our modelling or not as the FLOW-3D HYDRO package is capable of modelling air entrainment. The process of air entrainment in water during a landslide tsunami and its subsequent transport involve two key components: the quantification of air entrainment at the water surface, and the simulation of the air’s transport within the fluid (Hirt, 2003). FLOW-3D HYDRO employs the air entrainment model to compute the volume of air entrained at the water’s surface utilizing three approaches: a constant density model, a variable density model accounting for bulking, and a buoyancy model that adds the Drift-FLUX mechanism to variable density conditions (Flow Science, 2023). The calculation of the entrainment rate is based on the following equation:(2)�������=������[2(��−�����−2�/���)]1/2where parameters are: Vair, volume of air; Cair, entrainment rate coefficient; As, surface area of fluid; ρ, fluid density; k, turbulent kinetic energy; gn, gravity normal to surface; Lt, turbulent length scale; and σ, surface tension coefficient. The value of k is directly computed from the Reynolds-averaged Navier-Stokes (RANS) (k–w) calculations in our model.
In this study, we selected the variable density + Drift-FLUX model, which effectively captures the dynamics of phase separation and automatically activates the constant density and variable density models. This method simplifies the air-water mixture, treating it as a single, homogeneous fluid within each computational cell. For the phase volume fractions f1and f2, the velocities are expressed in terms of the mixture and relative velocities, denoted as u and ur, respectively, as follows:(3)��1��+�.(�1�)=��1��+�.(�1�)−�.(�1�2��)=0(4)��2��+�.(�2�)=��2��+�.(�2�)−�.(�1�2��)=0
The outcomes from this simulation are displayed in Fig. 6, which indicates that the influence of air entrainment on the generated wave amplitude is approximately 2 %. A value of 0.02 for the entrained air volume fraction means that, in the simulated fluid, approximately 2 % of the volume is composed of entrained air. In other words, for every unit volume of the fluid-air mixture at that location, 2 % is air and the remaining 98 % is water. The configuration of Test-17 (Table 4) was employed for this simulation. While the effect of air entrainment is anticipated to be more significant in models of granular landslide-generated waves (Fritz, 2002), in our simulations we opted not to incorporate this module due to its negligible impact on the results.
3. Results
In this section, we begin by presenting a sequence of our 3D simulations capturing different time steps to illustrate the generation process of landslide-generated waves. Subsequently, we derive a new predictive equation to estimate the maximum initial wave amplitude of landslide-generated waves and assess its performance.
3.1. Wave generation and propagation
To demonstrate the wave generation process in our simulation, we reference Test-17 from Table 4, where we employed Block-7 (Tables 3, 4). In this configuration, the slope angle was set to 45°, with a water depth of 0.246 m and a travel distance at 0.045 m (Fig. 7). At 0.220 s, the initial impact of the moving slide on the water is depicted, marking the onset of the wave generation process (Fig. 7a). Disturbances are localized to the immediate area of impact, with the rest of the water surface remaining undisturbed. At this time, a maximum water particle velocity of 1.0 m/s – 1.2 m/s is seen around the impact zone (Fig. 7d). Moving to 0.320 s, the development of the wave becomes apparent as energy transfer from the landslide to the water creates outwardly radiating waves with maximum water particle velocity of up to around 1.6 m/s – 1.8 m/s (Fig. 7b, e). By the time 0.670 s, the wave has fully developed and is propagating away from the impact point exhibiting maximum water particle velocity of up to 2.0 m/s – 2.1 m/s. Concentric wave fronts are visible, moving outwards in all directions, with a colour gradient signifying the highest wave amplitude near the point of landslide entry, diminishing with distance (Fig. 7c, f).
3.2. Influence of landslide parameters on tsunami amplitude
In this section, we investigate the effects of various landslide parameters namely slide volume (V), water depth (h), slipe angle (α) and travel distance (D) on the maximum initial wave amplitude (aM). Fig. 8 presents the outcome of these analyses. According to Fig. 8, the slide volume, slope angle, and travel distance exhibit a direct relationship with the wave amplitude, meaning that as these parameters increase, so does the amplitude. Conversely, water depth is inversely related to the maximum initial wave amplitude, suggesting that the deeper the water depth, the smaller the maximum wave amplitude will be (Fig. 8b).
Fig. 8a highlights the pronounced impact of slide volume on the aM, demonstrating a direct correlation between the two variables. For instance, in the range of slide volumes we modelled (Fig. 8a), The smallest slide volume tested, measuring 0.10 × 10−3 m3, generated a low initial wave amplitude (aM= 0.0066 m) (Table 4). In contrast, the largest volume tested, 6.25 × 10−3 m3, resulted in a significantly higher initial wave amplitude (aM= 0.0319 m) (Table 4). The extremities of these results emphasize the slide volume’s paramount impact on wave amplitude, further elucidated by their positions as the smallest and largest aM values across all conducted tests (Table 4). This is corroborated by findings from the literature (e.g., Murty, 2003), which align with the observed trend in our simulations.
The slope angle’s influence on aM was smooth. A steady increase of wave amplitude was observed as the slope angle increased (Fig. 8c). In examining travel distance, an anomaly was identified. At a travel distance of 0.047 m, there was an unexpected dip in aM, which deviates from the general increasing trend associated with longer travel distances. This singular instance could potentially be attributed to a numerical error. Beyond this point, the expected pattern of increasing aM with longer travel distances resumes, suggesting that the anomaly at 0.047 m is an outlier in an otherwise consistent trend, and thus this single data point was overlooked while deriving the predictive equation. Regarding the inverse relationship between water depth and wave amplitude, our result (Fig. 8b) is consistent with previous reports by Fritz et al. (2003), (2004), and Watts et al. (2005).
The insights from Fig. 8 informed the architecture of the predictive equation in the next Section, with slide volume, travel distance, and slope angle being multiplicatively linked to wave amplitude underscoring their direct correlations with wave amplitude. Conversely, water depth is incorporated as a divisor, representing its inverse relationship with wave amplitude. This structure encapsulates the dynamics between the landslide parameters and their influence on the maximum initial wave amplitude as discussed in more detail in the next Section.
3.3. Predictive equation
Building on our sensitivity analysis of landslide parameters, as detailed in Section 3.2, and utilizing our nondimensional dataset, we have derived a new predictive equation as follows:(5)��/ℎ=0.015(tan�)0.10(�ℎ3)0.90(�ℎ)0.10(ℎ�)−0.11where, V is sliding volume, h is water depth, α is slope angle, and s is landslide thickness. It is important to note that this equation is valid only for subaerial solid-block landslide tsunamis as all our experiments were for this type of waves. The performance of this equation in predicting simulation data is demonstrated by the satisfactory alignment of data points around a 45° line, indicating its accuracy and reliability with regard to the experimental dataset (Fig. 9). The quality of fit between the dataset and Eq. (5) is 91 % indicating that Eq. (5) represents the dataset very well. Table 5 presents Eq. (5) alongside four other similar equations previously published. Two significant distinctions between our Eq. (5) and these others are: (i) Eq. (5) is derived from 3D experiments, whereas the other four equations are based on 2D experiments. (ii) Unlike the other equations, our Eq. (5) incorporates travel distance as an independent parameter.
Table 5. Performance comparison among our newly-developed equation and existing equations for estimating the maximum initial amplitude (aM) of the 2018 Anak Krakatau subaerial landslide tsunami. Parameters: aM, initial maximum wave amplitude; h, water depth; vs, landslide velocity; V, slide volume; bs, slide width; ls, slide length; s, slide thickness; α, slope angle; and ����, volume of the final immersed landslide. We considered ����= V as the slide volume.
Geometrical and kinematic parameters of the 2018 Anak Krakatau subaerial landslide based on Heidarzadeh et al. (2020), Grilli et al. (2019) and Grilli et al. (2021): V=2.11 × 107 m3, h= 50 m; s= 114 m; α= 45°; ls=1250 m; bs= 2700 m; vs=44.9 m/s; D= 2500 m; aM= 100 m −150 m.⁎⁎
aM= An average value of aM = 134 m is considered in this study.⁎⁎⁎
The equation of Bolin et al. (2014) is based on the reformatted one reported by Lindstrøm (2016).⁎⁎⁎⁎
Error is calculated using Eq. (1), where the calculated aM is assumed as the simulated value.
Additionally, we evaluated the performance of this equation using the real-world data from the 2018 Anak Krakatau subaerial landslide tsunami. Based on previous studies (Heidarzadeh et al., 2020; Grilli et al., 2019, 2021), we were able to provide a list of parameters for the subaerial landslide and associated tsunami for the 2018 Anak Krakatau event (see footnote of Table 5). We note that the data of the 2018 Anak Krakatau event was not used while deriving Eq. (5). The results indicate that Eq. (5) predicts the initial amplitude of the 2018 Anak Krakatau tsunami as being 130 m indicating an error of 2.9 % compared to the reported average amplitude of 134 m for this event. This performance indicates an improvement compared to the previous equation reported by Sabeti and Heidarzadeh (2022a) (Table 5). In contrast, the equations from Robbe-Saule et al. (2021) and Bolin et al. (2014) demonstrate higher discrepancies of 4200 % and 77 %, respectively (Table 5). Although Noda’s (1970) equation reproduces the tsunami amplitude of 134 m accurately (Table 5), it is crucial to consider its limitations, notably not accounting for parameters such as slope angle and travel distance.
It is essential to recognize that both travel distance and slope angle significantly affect wave amplitude. In our model, captured in Eq. (5), we integrate the slope angle (α) through the tangent function, i.e., tan α. This choice diverges from traditional physical interpretations that often employ the cosine or sine function (e.g., Heller and Hager, 2014; Watts et al., 2003). We opted for the tangent function because it more effectively reflects the direct impact of slope steepness on wave generation, yielding superior estimations compared to conventional methods.
The significance of this study lies in its application of both physical and numerical 3D experiments and the derivation of a predictive equation based on 3D results. Prior research, e.g. Heller et al. (2016), has reported notable discrepancies between 2D and 3D wave amplitudes, highlighting the important role of 3D experiments. It is worth noting that the suitability of applying an equation derived from either 2D or 3D data depends on the specific geometry and characteristics inherent in the problem being addressed. For instance, in the case of a long, narrow dam reservoir, an equation derived from 2D data would likely be more suitable. In such contexts, the primary dynamics of interest such as flow patterns and potential wave propagation are predominantly two-dimensional, occurring along the length and depth of the reservoir. This simplification to 2D for narrow dam reservoirs allows for more accurate modelling of these dynamics.
This study specifically investigates waves initiated by landslides, focusing on those characterized as solid blocks instead of granular flows, with slope angles confined to a range of 25° to 60°. We acknowledge the additional complexities encountered in real-world scenarios, such as dynamic density and velocity of landslides, which could affect the estimations. The developed equation in this study is specifically designed to predict the maximum initial amplitude of tsunamis for the aforementioned specified ranges and types of landslides.
4. Conclusions
Both physical and numerical experiments were undertaken in a 3D wave basin to study solid-block landslide-generated waves and to formulate a predictive equation for their maximum initial wave amplitude. At the beginning, two physical experiments were performed to validate and calibrate a 3D numerical model, which was subsequently utilized to generate 100 experiments by varying different landslide parameters. The generated database was then used to derive a predictive equation for the maximum initial wave amplitude of landslide tsunamis. The main features and outcomes are:
•The predictive equation of this study is exclusively derived from 3D data and exhibits a fitting quality of 91 % when applied to the database.
•For the first time, landslide travel distance was considered in the predictive equation. This inclusion provides more accuracy and flexibility for applying the equation.
•To further evaluate the performance of the predictive equation, it was applied to a real-world subaerial landslide tsunami (i.e., the 2018 Anak Krakatau event) and delivered satisfactory performance.
The authors declare that they have no known competing financial interests or personal relationships that could have appeared to influence the work reported in this paper.
Funding
RS is supported by the Leverhulme Trust Grant No. RPG-2022-306. MH is funded by open funding of State Key Lab of Hydraulics and Mountain River Engineering, Sichuan University, grant number SKHL2101. We acknowledge University of Bath Institutional Open Access Fund. MH is also funded by the Great Britain Sasakawa Foundation grant no. 6217 (awarded in 2023).
Acknowledgements
Authors are sincerely grateful to the laboratory technician team, particularly Mr William Bazeley, at the Faculty of Engineering, University of Bath for their support during the laboratory physical modelling of this research. We appreciate the valuable insights provided by Mr. Brian Fox (Senior CFD Engineer at Flow Science, Inc.) regarding air entrainment modelling in FLOW-3D HYDRO. We acknowledge University of Bath Institutional Open Access Fund.
Data availability
All data used in this study are given in the body of the article.
References
Baptista et al., 2020M.A. Baptista, J.M. Miranda, R. Omira, I. El-HussainStudy of the 24 September 2013 Oman Sea tsunami using linear shallow water inversionArab. J. Geosci., 13 (14) (2020), p. 606View in ScopusGoogle Scholar
Bolin et al., 2014H. Bolin, Y. Yueping, C. Xiaoting, L. Guangning, W. Sichang, J. ZhibingExperimental modeling of tsunamis generated by subaerial landslides: two case studies of the Three Gorges Reservoir, ChinaEnviron. Earth Sci., 71 (2014), pp. 3813-3825View at publisher CrossRefView in ScopusGoogle Scholar
Borrero et al., 2020J.C. Borrero, T. Solihuddin, H.M. Fritz, P.J. Lynett, G.S. Prasetya, V. Skanavis, S. Husrin, Kushendratno, W. Kongko, D.C. Istiyanto, A. DaulatField survey and numerical modelling of the December 22, 2018, Anak Krakatau TsunamiPure Appl. Geophys, 177 (2020), pp. 2457-2475View at publisher CrossRefView in ScopusGoogle Scholar
Ersoy et al., 2019H. Ersoy, M. Karahan, K. Gelişli, A. Akgün, T. Anılan, M.O. Sünnetci, B.K. YahşiModelling of the landslide-induced impulse waves in the Artvin Dam reservoir by empirical approach and 3D numerical simulationEng. Geol., 249 (2019), pp. 112-128View PDFView articleView in ScopusGoogle Scholar
Fritz et al., 2004H.M. Fritz, W.H. Hager, H.E. MinorNear field characteristics of landslide generated impulse wavesJ. Waterw. Port Coastal Ocean Eng., 130 (6) (2004), pp. 287-302View in ScopusGoogle Scholar
Geertsema et al., 2022M. Geertsema, B. Menounos, G. Bullard, J.L. Carrivick, J.J. Clague, C. Dai, D. Donati, G. Ekstrom, J.M. Jackson, P. Lynett, M. PichierriThe 28 Nov 2020 landslide, tsunami, and outburst flood – a hazard cascade associated with rapid deglaciation at Elliot Creek, BC, CanadaGeophys. Res. Lett., 49 (6) (2022)Google Scholar
Grilli et al., 2021S.T. Grilli, C. Zhang, J.T. Kirby, A.R. Grilli, D.R. Tappin, S.F.L. Watt, J.E. Hunt, A. Novellino, S. Engwell, M.E.M. Nurshal, M. AbdurrachmanModeling of the Dec. 22nd, 2018, Anak Krakatau volcano lateral collapse and tsunami based on recent field surveys: comparison with observed tsunami impactMar. Geol., 440 (2021), Article 106566View PDFView articleView in ScopusGoogle Scholar
Grilli et al., 2019S.T. Grilli, D.R. Tappin, S. Carey, S.F. Watt, S.N. Ward, A.R. Grilli, S.L. Engwell, C. Zhang, J.T. Kirby, L. Schambach, M. MuinModelling of the tsunami from the Dec. 22, 2018, lateral collapse of Anak Krakatau volcano in the Sunda Straits, IndonesiaSci. Rep., 9 (1) (2019), p. 11946 View at publisher This article is free to access.View in ScopusGoogle Scholar
Heidarzadeh et al., 2023M. Heidarzadeh, A.R. Gusman, I.E. MuliaThe landslide source of the eastern Mediterranean tsunami on 6 Feb 2023 following the Mw 7.8 Kahramanmaraş (Türkiye) inland earthquakeGeosci. Lett., 10 (1) (2023), p. 50 View at publisher This article is free to access.View in ScopusGoogle Scholar
Heidarzadeh et al., 2020M. Heidarzadeh, T. Ishibe, O. Sandanbata, A. Muhari, A.B. WijanartoNumerical modeling of the subaerial landslide source of the 22 Dec 2018 Anak Krakatoa volcanic tsunami, IndonesiaOcean. Eng., 195 (2020), Article 106733View PDFView articleView in ScopusGoogle Scholar
Heidarzadeh et al., 2017M. Heidarzadeh, T. Harada, K. Satake, T. Ishibe, T. TakagawaTsunamis from strike-slip earthquakes in the Wharton Basin, northeast Indian Ocean: March 2016 M w7. 8 event and its relationship with the April 2012 M w 8.6 eventGeophys. J. Int., 211 (3) (2017), pp. 1601-1612, 10.1093/gji/ggx395 View at publisher This article is free to access.View in ScopusGoogle Scholar
Heller et al., 2016V. Heller, M. Bruggemann, J. Spinneken, B.D. RogersComposite modelling of subaerial landslide–tsunamis in different water body geometries and novel insight into slide and wave kinematicsCoastal Eng., 109 (2016), pp. 20-41View PDFView articleView in ScopusGoogle Scholar
Hirt, 2003C.W. HirtModeling Turbulent Entrainment of Air at a Free SurfaceFlow Science, Inc (2003)Google Scholar
Hu et al., 2023G. Hu, K. Satake, L. Li, P. DuOrigins of the tsunami following the 2023 Turkey–Syria earthquakeGeophys. Res. Lett., 50 (18) (2023)Google Scholar
Hu et al., 2022G. Hu, W. Feng, Y. Wang, L. Li, X. He, Ç. Karakaş, Y. TianSource characteristics and exacerbated tsunami hazard of the 2020 Mw 6.9 Samos earthquake in Eastern Aegean SeaJ. Geophys. Res., 127 (5) (2022)e2022JB023961Google Scholar
Kim et al., 2020G.B. Kim, W. Cheng, R.C. Sunny, J.J. Horrillo, B.C. McFall, F. Mohammed, H.M. Fritz, J. Beget, Z. KowalikThree-dimensional landslide generated tsunamis: numerical and physical model comparisonsLandslides, 17 (2020), pp. 1145-1161View at publisher CrossRefView in ScopusGoogle Scholar
Kirby et al., 2022J.T. Kirby, S.T. Grilli, J. Horrillo, P.L.F. Liu, D. Nicolsky, S. Abadie, B. Ataie-Ashtiani, M.J. Castro, L. Clous, C. Escalante, I. Fine, J.M. González-Vida, F. Løvholt, P. Lynett, G. Ma, J. Macías, S. Ortega, F. Shi, S. Yavari-Ramshe, C. ZhangValidation and inter-comparison of models for landslide tsunami generationOcean Model., 170 (2022), Article 101943View PDFView articleView in ScopusGoogle Scholar
McFall and Fritz, 2016B.C. McFall, H.M. FritzPhysical modelling of tsunamis generated by three-dimensional deformable granular landslides on planar and conical island slopesProc. R. Soc. A. Math. Phys. Eng. Sci., 472 (2188) (2016), Article 20160052View at publisher CrossRefGoogle Scholar
Mulia et al., 2020aI.E. Mulia, S. Watada, T.C. Ho, K. Satake, Y. Wang, A. AditiyaSimulation of the 2018 tsunami due to the flank failure of Anak Krakatau volcano and implication for future observing systemsGeophys. Res. Lett., 47 (14) (2020), Article e2020GL087334 View at publisher This article is free to access.View in ScopusGoogle Scholar
Mulia et al., 2020bI.E. Mulia, S. Watada, T.C. Ho, K. Satake, Y. Wang, A. AditiyaSimulation of the 2018 tsunami due to the flank failure of Anak Krakatau volcano and implication for future observing systemsGeophys. Res. Lett., 47 (14) (2020)Google Scholar
Mulligan et al., 2020R.P. Mulligan, A. Franci, M.A. Celigueta, W.A. TakeSimulations of landslide wave generation and propagation using the particle finite element methodJ. Geophys. Res. Oceans, 125 (6) (2020)Google Scholar
Ren et al., 2020Z. Ren, Y. Wang, P. Wang, J. Hou, Y. Gao, L. ZhaoNumerical study of the triggering mechanism of the 2018 Anak Krakatau tsunami: eruption or collapsed landslide?Nat. Hazards, 102 (2020), pp. 1-13View in ScopusGoogle Scholar
Robbe-Saule et al., 2021M. Robbe-Saule, C. Morize, Y. Bertho, A. Sauret, A. Hildenbrand, P. GondretFrom laboratory experiments to geophysical tsunamis generated by subaerial landslidesSci. Rep., 11 (1) (2021), pp. 1-9Google Scholar
Sabeti et al. 2024R. Sabeti, M. Heidarzadeh, A. Romano, G. Barajas Ojeda, J.L. LaraThree-Dimensional Simulations of Subaerial Landslide-Generated Waves: Comparing OpenFOAM and FLOW-3D HYDRO ModelsPure Appl. Geophys. (2024), 10.1007/s00024-024-03443-x View at publisher This article is free to access.Google Scholar
Sorensen, 2010R.M. SorensenBasic Coastal Engineering(3rd edition), Springer Science & Business Media (2010), p. 324Google Scholar
Syamsidik et al., 2020Benazir Syamsidik, M. Luthfi, A. Suppasri, L.K. ComfortThe 22 December 2018 Mount Anak Krakatau volcanogenic tsunami on Sunda Strait coasts, Indonesia: tsunami and damage characteristicsNat. Hazards Earth Syst. Sci., 20 (2) (2020), pp. 549-565View in ScopusGoogle Scholar
Synolakis et al., 2002C.E. Synolakis, J.P. Bardet, J.C. Borrero, H.L. Davies, E.A. Okal, E.A. Silver, D.R. TappinThe slump origin of the 1998 Papua New Guinea tsunamiProc. R. Soc. Lond. A Math. Phys. Eng. Sci., 45 (2002), pp. 763-789View in ScopusGoogle Scholar
Wang et al., 2022Y. Wang, H.Y. Su, Z. Ren, Y. MaSource properties and resonance characteristics of the tsunami generated by the 2021 M 8.2 Alaska earthquakeJ. Geophys. Res. Oceans, 127 (3) (2022), Article e2021JC018308 View at publisher This article is free to access.View in ScopusGoogle Scholar
Watts et al., 2005P. Watts, S.T. Grilli, D.R. Tappin, G.J. FryerTsunami generation by submarine mass failure. II: predictive equations and case studiesJ. Waterw. Port Coast. Ocean Eng., 131 (6) (2005), pp. 298-310View in ScopusGoogle Scholar
Watts, 1998P. WattsWavemaker curves for tsunamis generated by underwater landslidesJ. Waterw. Port. Coast. Ocean. Eng., 124 (3) (1998), pp. 127-137Google Scholar
Zhang et al., 2021C. Zhang, J.T. Kirby, F. Shi, G. Ma, S.T. GrilliA two-layer non-hydrostatic landslide model for tsunami generation on irregular bathymetry. 2. Numerical discretization and model validationOcean Model., 160 (2021), Article 101769View PDFView articleView in ScopusGoogle Scholar
M.T. Mansouri Kia1,2, H.R. Sheibani 3, A. Hoback 4 1 Manager of Dam and Power Plant Construction, Khuzestan Water and Power Authority (KWPA), Ahwaz, Iran. 2 Ph.D., Department of Civil Engineering, Payame Noor University, Tehran, Iran. 3 Associate Professor of PNU University, Tehran, Iran. 4 Professor of Civil, Architectural & Environmental Engineering, University of Detroit Mercy Civil, Rome, Italy.
Abstract
Mared Dam in northern Abadan is under construction on the Karun River and it is the first ship lock in Iran. In this study, the ship’s lock was examined. Every vessel must pass through this lock in order to transport water from Arvand River to Karun and vice versa. The interior dimensions of the Mared Shipping Lock are 160 meters long, 25 meters wide and 8 meters deep. Several important times are calculated for lock operation. 𝑇is the first time the gates open, 𝑇15 the time the initial gates remain open until the height difference between the two sides reaches 150 mm, 𝑇filled is the duration between the start of the opening the gates till the difference between the two ends becomes zero after 𝑇15. Finally, T is the total time required for opening or closing the gates completely. The rotational speeds of the gates range from 5 to 35 radians per minute. Numerical modeling has been used to study fluid behavior and interaction between fluid and gates in flow 3D software. Different lock maintenance scenarios have been analyzed. Important parameters such as inlet and outlet flow rate changes from gates, water depth changes at different times, stress and strain fields, hydrodynamic forces acting on different points of the lock have been calculated. Based on this, the forces acting on hydraulic jacks and gates have been calculated. The minimum time required for the safe passage of the ship through the lock is calculated.
북부 아바단의 마레드 댐은 카룬 강에 건설 중이며 이란 최초의 선박 잠금 장치입니다. 본 연구에서는 선박의 자물쇠를 조사하였습니다. Arvand 강에서 Karun으로 또는 그 반대로 물을 운송하려면 모든 선박이 이 수문을 통과해야 합니다.
Mared Shipping Lock의 내부 치수는 길이 160m, 너비 25m, 깊이 8m입니다. 잠금 작동을 위해 몇 가지 중요한 시간이 계산됩니다. 𝑇은 게이트가 처음 열릴 때, 𝑇15는 양쪽의 높이 차이가 150mm에 도달할 때까지 초기 게이트가 열린 상태로 유지되는 시간, 𝑇filled는 게이트가 열리는 시작부터 이후 두 끝의 차이가 0이 될 때까지의 시간입니다.
𝑇15. 마지막으로 T는 게이트를 완전히 열거나 닫는 데 필요한 총 시간입니다. 게이트의 회전 속도는 분당 5~35라디안입니다. 수치 모델링은 유동 3D 소프트웨어에서 유체 거동과 유체와 게이트 사이의 상호 작용을 연구하는 데 사용되었습니다. 다양한 잠금 유지 관리 시나리오가 분석되었습니다.
게이트의 입구 및 출구 유속 변화, 다양한 시간에 따른 수심 변화, 응력 및 변형 필드, 수문의 다양한 지점에 작용하는 유체역학적 힘과 같은 중요한 매개변수가 계산되었습니다.
이를 바탕으로 유압잭과 게이트에 작용하는 힘을 계산하였습니다. 선박이 자물쇠를 안전하게 통과하는 데 필요한 최소 시간이 계산됩니다.
Fig 1. (a) The Location of the Bahman Shir dam (upstream), (b) Bahman Shir dam (downstream dam) and (c) Mared Dam. Note: The borders of the countries are not exact.
References
Ables, J.H., 1978. Filling and Emptying System, New Ship Lock, Mississippi River-Gulf Outlet, Louisiana: Hydraulic Model Investigation, 78. US Army Engineer Waterways Experiment Station.
Army, U., 1964. Corps of Engineers, 1965. National Inventory of Physical Resources. Agency for International Development, Costa Rica.
Belzner, F., Simons, F., Thorenz, C., 2018. An application-oriented model for lock filling processes, 34th PIANC-World Congress (Proceedings). Online verfügbar unter https://coms.events/piancpanama/data/full_pa pers/full_paper_183.pdf, zuletzt geprüft am, pp. 2018.
Brolsma, J., Roelse, K., 2011. Waterway guidelines 2011. ISBN 9789036900690. Dhanuka, A., Agrawal, S., Mehra, H., 2018. Hydraulic and Structural Design of Navigational Locks. J Civil Environ Eng, 8(297): 2.
Gao, Z., Fang, S.L., Shi, X.T., Gu, Z.H., 2013. Computation of Filling Time of a Ship Lock. Applied Mechanics and Materials, 256: 2509- 2513.
Hu, Q., Li, Y., Zhu, L., 2024. Effect of Parameters of Ditch Geometry on the Uniformity of Water Filling in Ship Lock Chambers. Journal of Marine Science and Engineering, 12(1): 86. Iranian sahel Omid Co., Engineer, L.C., 2015. Numerical Modeling of Flow in Lock Chamber, Abadan ship Lock Dam Project. 0920-4741.
Iuorio, L., 2024. Dams are fragile: the frenzy and legacy of modern infrastructures along the Klamath and Allegheny Rivers. Water History: 1-26.
Li, J., Hu, Y., Wang, X., Diao, M., 2023. Operation safety evaluation system of ship lock based on extension evaluation and combination weighting method. Journal of Hydroinformatics, 25(3): 755-781.
Liu, B., Yang, J., Huang, Y., Wang, L., 2022. Hydraulic Research on Filling and Emptying System of Water-Saving Ship Lock for Navigation-Power Junction in Mountainous River, Smart Rivers. Springer, pp. 1492-1501.
Mäck, A., Lorke, A., 2014. Ship‐lock–induced surges in an impounded river and their impact on subdaily flow velocity variation. River research and applications, 30(4): 494-507. Mahab., S., 1976. Final technical Report of Feasibility study. 25-96.
Mansouri Kia, M.T., 2022. Hydraulic design and optimization of navigation lock performance – A case study of Karun and Bahman Shir river locks. . PNU University. The Ph. D thesis (in Civil Engineering).
Mansouri Kia, M.T., Ansari, Z., 2008. Feasibility of Water Transport in Karun Waterway. 4th National Congress of Civil Engineering, Tehran University Iran: 1-8 (in Persian).
Mansouri Kia, M.T., Rajabi, E., Sheybani, H.R., 2022. Determining the Optimal Dimensions of River Transportation Channel in Iran. . Fourth International Conference of Civil, Architectural and sustainable green city, Hamedan, Iran. (in Persian): 298-309.
Moore, F.G., 1950. Three canal projects, Roman and Byzantine. American Journal of Archaeology, 54(2): 97-111.
Negi, P., Kromanis, R., Dorée, A.G., Wijnberg, K.M., 2024. Structural health monitoring of inland navigation structures and ports: a review on developments and challenges. Structural Health Monitoring, 23(1): 605-645.
Nogueira, H.I., Van Der Hout, A., O’Mahoney, T.S., Kortlever, W.C., 2024. The Impact of Density Differences on the Hydraulic Design of Leveling Systems: The Case of New Large Sea Locks in IJmuiden and Terneuzen. Journal of Waterway, Port, Coastal, and Ocean Engineering, 150(1): 05023002.
O’Mahoney, T., De Loor, A., 2015. Paper 55- Computational Fluid Dynamics simulations of the effects of density differences during the filling process in a sea lock. Scott_Wilson;, Piesold., 2005. Karun River, Interim report NO 6, Transportation component.
Wang, H.-z., Zou, Z.-j., 2014. Numerical prediction of hydrodynamic forces on a ship passing through a lock. China Ocean Engineering, 28(3): 421-432.
Yang, Z., Sun, Y., Lian, F., Feng, H., Li, G., 2024. Optimization of river container port-access transport based on the innovatively designed electric ship in the Yangtze River Delta. Ocean & Coastal Management, 248: 106976.
Gonzalo Duró, Mariano De Dios, Alfredo López, Sergio O. Liscia
ABSTRACT
This study presents comparisons between the results of a commercial CFD code and physical model measurements. The case study is a hydro-combined power station operating in spillway mode for a given scenario. Two turbulence models and two scales are implemented to identify the capabilities and limitations of each approach and to determine the selection criteria for CFD modeling for this kind of structure. The main flow characteristics are considered for analysis, but the focus is on a fluctuating frequency phenomenon for accurate quantitative comparisons. Acceptable representations of the general hydraulic functioning are found in all approaches, according to physical modeling. The k-ε RNG, and LES models give good representation of the discharge flow, mean water depths, and mean pressures for engineering purposes. The k-ε RNG is not able to characterize fluctuating phenomena at a model scale but does at a prototype scale. The LES is capable of identifying the dominant frequency at both prototype and model scales. A prototype-scale approach is recommended for the numerical modeling to obtain a better representation of fluctuating pressures for both turbulence models, with the complement of physical modeling for the ultimate design of the hydraulic structures.
본 연구에서는 상용 CFD 코드 결과와 물리적 모델 측정 결과를 비교합니다. 사례 연구는 주어진 시나리오에 대해 배수로 모드에서 작동하는 수력 복합 발전소입니다.
각 접근 방식의 기능과 한계를 식별하고 이러한 종류의 구조에 대한 CFD 모델링의 선택 기준을 결정하기 위해 두 개의 난류 모델과 두 개의 스케일이 구현되었습니다. 주요 흐름 특성을 고려하여 분석하지만 정확한 정량적 비교를 위해 변동하는 주파수 현상에 중점을 둡니다.
일반적인 수리학적 기능에 대한 허용 가능한 표현은 물리적 모델링에 따라 모든 접근 방식에서 발견됩니다. k-ε RNG 및 LES 모델은 엔지니어링 목적을 위한 배출 유량, 평균 수심 및 평균 압력을 잘 표현합니다.
k-ε RNG는 모델 규모에서는 변동 현상을 특성화할 수 없지만 프로토타입 규모에서는 특성을 파악합니다. LES는 프로토타입과 모델 규모 모두에서 주요 주파수를 식별할 수 있습니다.
수력학적 구조의 궁극적인 설계를 위한 물리적 모델링을 보완하여 두 난류 모델에 대한 변동하는 압력을 더 잘 표현하기 위해 수치 모델링에 프로토타입 규모 접근 방식이 권장됩니다.
Figure 1 – Physical scale model (left). Upstream flume and point gauge (right)
Figure 4 – Water levels: physical model (maximum values) and CFD results (mean values)Figure 5 – Instantaneous pressures [Pa] and velocities [m/s] at model scale (bay center)
ADRIAN R. J. (2007). “Hairpin vortex organization in wall turbulence.” Phys. Fluids 19(4), 041301. DEWALS B., ARCHAMBEAU P., RULOT F., PIROTTON M. and ERPICUM S. (2013). “Physical and Numerical Modelling in Low-Head Structures Design.” Proc. International Workshop on Hydraulic Design of Low-Head Structures, Aachen, Germany, Bundesanstalt für Wasserbau Publ., D.B. BUNG and S. PAGLIARA Editors, pp.11-30. GRENANDER, U. (1959). Probability and Statistics: The Harald Cramér Volume. Wiley. HIRT, C. W. and NICHOLS B. D. (1981). “Volume of fluid (VOF) method for the dynamics of free boundaries.” Journal of Computational Physics 39(1): 201-225. JOHNSON M. C. and SAVAGE B. M. (2006). “Physical and numerical comparison of flow over ogee spillway in the presence of tailwater.” J. Hydraulic Eng. 132(12): 1353–1357. KHAN L.A., WICKLEIN E.A., RASHID M., EBNER L.L. and RICHARDS N.A. (2004). “Computational fluid dynamics modeling of turbine intake hydraulics at a hydropower plant.” Journal of Hydraulic Research, 42:1, 61-69 LAROCQUE L.A., IMRAN J. and CHAUDHRY M. (2013). “3D numerical simulation of partial breach dam-break flow using the LES and k–ϵ turbulence models.” Jl of Hydraulic Research, 51:2, 145-157 LI S., LAI Y., WEBER L., MATOS SILVA J. and PATEL V.C. (2004). “Validation of a threedimensional numerical model for water-pump intakes.” Journal of Hydraulic Research, 42:3, 282-292 NOVAK P., GUINOT V., JEFFREY A. and REEVE D.E. (2010). “Hydraulic modelling – An introduction.” Spon Press, London and New York, ISBN 978-0-419-25010-4, 616 pp.
This work investigates numerically a local scour moves in irregular waves around tripods. It is constructed and proven to use the numerical model of the seabed-tripodfluid with an RNG k turbulence model. The present numerical model then examines the flow velocity distribution and scour characteristics. After that, the suggested computational model Flow-3D is a useful tool for analyzing and forecasting the maximum scour development and the flow field in random waves around tripods. The scour values affecting the foundations of the tripod must be studied and calculated, as this phenomenon directly and negatively affects the structure of the structure and its design life. The lower diagonal braces and the main column act as blockages, increasing the flow accelerations underneath them. This increases the number of particles that are moved, which in turn creates strong scouring in the area. The numerical model has a good agreement with the experimental model, with a maximum percentage of error of 10% between the experimental and numerical models. In addition, Based on dimensional analysis parameters, an empirical equation has been devised to forecast scour depth with flow depth, median size ratio, Keulegan-Carpenter (Kc), Froud number flow, and wave velocity that the results obtained in this research at various flow velocities and flow depths demonstrated that the maximum scour depth rate depended on wave height with rising velocities and decreasing particle sizes (d50) and the scour depth attains its steady-current value for Vw < 0.75. As the Froude number rises, the maximum scour depth will be large.
The overtopping breach is the most probable reason of embankment dam failures. Hence, the investigation of the mentioned phenomenon is one of the vital hydraulic issues. This research paper tries to utilize three numerical models, i.e., BREACH, HEC-RAS, and FLOW-3D for modeling the hydraulic outcomes of overtopping breach phenomenon. Furthermore, the outputs have been compared with experimental model results given by authors. The BREACH model presents a desired prediction for the peak flow. The HEC-RAS model has a more realistic performance in terms of the peak flow prediction, its occurrence time (5-s difference with observed status), and maximum flow depth. The variations diagram in the reservoir water level during the breach process has a descending trend. Whereas it initially ascended; and then, it experienced a descending trend in the observed status. The FLOW-3D model computes the flow depth, flow velocity, and Froude number due to the physical model breach. Moreover, it revealed a peak flow damping equals to 5% and 5-s difference in the peak flow occurrence time at 4-m distance from the physical model downstream. In addition, the current research work demonstrates the mentioned numerical models and provides a possible comprehensive perspective for a dam breach scope. They also help to achieve the various hydraulic parameters computations. Besides, they may calculate unmeasured parameters using the experimental data.
월류 현상은 제방 댐 실패의 가장 유력한 원인입니다. 따라서 언급된 현상에 대한 조사는 중요한 수리학적 문제 중 하나입니다.
본 연구 논문에서는 월류 침해 현상의 수리적 결과를 모델링하기 위해 BREACH, HEC-RAS 및 FLOW-3D의 세 가지 수치 모델을 활용하려고 합니다. 또한 출력은 저자가 제공한 실험 모델 결과와 비교되었습니다. BREACH 모델은 최대 유량에 대해 원하는 예측을 제시합니다.
HEC-RAS 모델은 최고유량 예측, 발생시간(관찰상태와 5초 차이), 최대유량수심 측면에서 보다 현실적인 성능을 가지고 있습니다. 위반 과정 중 저수지 수위의 변동 다이어그램은 감소하는 추세를 보입니다. 처음에는 상승했지만 그런 다음 관찰된 상태가 감소하는 추세를 경험했습니다.
FLOW-3D 모델은 물리적 모델 위반으로 인한 흐름 깊이, 흐름 속도 및 Froude 수를 계산합니다. 또한, 실제 모델 하류로부터 4m 거리에서 최대유량 발생시간이 5%, 5초 차이에 해당하는 최대유량 감쇠를 나타냈습니다.
또한, 현재 연구 작업은 언급된 수치 모델을 보여주고 댐 침해 범위에 대한 가능한 포괄적인 관점을 제공합니다. 또한 다양한 유압 매개변수 계산을 수행하는 데 도움이 됩니다. 게다가 실험 데이터를 사용하여 측정되지 않은 매개변수를 계산할 수도 있습니다.
Association of state dam safety officials (2023) Kentucky, USA. Available from https://damsafety.org
ASTM D1557 (2007) Standard test methods for laboratory compaction characteristics of soil using standard effort. West Conshohocken, PA, USA
ASTM D422–63 (2002) Standard test method for particle size analysis of soils
Azimi H, Shabanlou S (2016) Comparison of subcritical and supercritical flow patterns within triangular channels along the side weir. Int J Nonlinear Sci Numer Simul 17(7–8):361–368ArticleMathSciNetGoogle Scholar
Azimi H, Shabanlou S (2018) Numerical study of bed slope change effect of circular channel with side weir in supercritical flow conditions. Appl Water Sci 8(6):166ArticleADSGoogle Scholar
Azimi H, Shabanlou S, Kardar S (2017) Characteristics of hydraulic jump in U-shaped channels. Arab J Sci Eng 42:3751–3760ArticleGoogle Scholar
Brunner GW (2016) HEC-RAS Reference Manual, version 5.0. Hydrologic Engineering Center, Institute for Water Resources, US Army Corps of Engineers, Davis, California
Brunner GW (2016) HEC-RAS user’s Manual, version 5.0. Hydrologic Engineering Center, Institute for Water Resources, US Army Corps of Engineers, Davis, California
Chanson H, Wang H (2013) Unsteady discharge calibration of a large V-notch weir. Flow Meas Instrum 29:19–24ArticleGoogle Scholar
Committee on Dam Safety (2019) ICOLD incident database bulletin 99 update: statistical analysis of dam failures, technical report, international commission on large dams. Available from: https://www.icoldchile.cl/boletines/188.pdf
Engomoen B, Witter DT, Knight K, Luebke TA (2014) Design Standards No 13: Embankment Dams. United States Bureau of Reclamation
Flow Science Corporation (2017) Flow-3D v11.0 User Manual. Available from: http://flow3d.com
Froehlich DC (2016) Predicting peak discharge from gradually breached embankment dam. J Hydrol Eng 21(11):04016041ArticleGoogle Scholar
Hakimzadeh H, Nourani V, Amini AB (2014) Genetic programming simulation of dam breach hydrograph and peak outflow discharge. J Hydrol Eng 19:757–768ArticleGoogle Scholar
Hooshyaripor F, Tahershamsi A, Golian S (2014) Application of copula method and neural networks for predicting peak outflow from breached embankments. J Hydro-Environ Res 8(3):292–303ArticleGoogle Scholar
Irmakunal CI (2019) Two-dimensional dam break analyses of Berdan dam. MSC thesis, Middle East Technical University, Turkey
kumar Gupta A, Narang I, Goyal P, (2020) Dam break analysis of JAWAI dam PALI, Rajasthan using HEC-RAS. IOSR J Mech Civ Eng 17(2):43–52Google Scholar
Mo C, Cen W, Le X, Ban H, Ruan Y, Lai S, Shen Y (2023) Simulation of dam-break flood and risk assessment: a case study of Chengbi river dam in Baise, China. J Hydroinformatics 25(4):1276–1294ArticleGoogle Scholar
Morris M, Kortenhaus A, Visser P (2009) Modelling breach initiation and growth. FLOODsite report: T06–08–02, FLOODsite Consortium, Wallingford, UK
Pierce MW, Thornton CI, Abt SR (2010) Predicting peak outflow from breached embankment dams. J Hydrol Eng 15(5):338–349ArticleGoogle Scholar
Saberi O (2016) Embankment dam failure outflow hydrograph development. PhD thesis, Graz University of Technology, Austria
Sylvestre J, Sylvestre P (2018) User’s guide for BRCH GUI. 2018. Available from: http://rivermechanics.net
USACE) 2004) General design and construction considerations for Earth and rockfill dams, US Army Corps of Engineers, Washington DC, USA
USBR (1987) Design of small dams, Bureau of Reclamation, Water Resources Technical Publication
Versteeg HK, Malalasekera W (2007) An introduction to computational fluid dynamics: the finite volume method. Pearson education
Wang Z, Bowles DS (2006) Three-dimensional non-cohesive earthen dam breach model. Part 1: theory and methodology. Adv Water Resour 29(10):1528–1545ArticleADSGoogle Scholar
Webby MG (1996) Discussion of peak outflow from breached embankment dam by David C. Froehlich. J Water Resour Plan Manag 122(4):316–317
Wu W, Marsooli R, He Z (2012) Depth-averaged two-dimensional model of unsteady flow and sediment transport due to noncohesive embankment break/breaching. J Hydraul Eng 138(6):503–516ArticleGoogle Scholar
Xu Y, Zhang LM (2009) Breaching parameters for earth and rockfill dams. J Geotech Geoenviron Eng 135(12):1957–1970ArticleGoogle Scholar
Weirs are essential structures used to manage excess water flow from behind dams to downstream areas. Enhancing discharge efficiency often involves extending the effective length of Piano Key Weirs (PKW) in dams or regulating flow within irrigation and drainage networks. This study employed both numerical and laboratory investigations to assess the impact of different base nose shapes installed beneath the outlet keys and varying Input to output key width ratios (Wi/Wo) on discharges ranging from 5 to 80 liters per second. Furthermore, the study aimed to achieve research objectives and compare the performance of Piano Key Weirs with Ogee Weir. For numerical simulation, the optimal number of cells for meshing was determined, and an appropriate turbulence model was selected. The results indicated that the numerical model accurately simulated the laboratory sample with a high degree of precision. Moreover, the numerical model closely approximated PKW for all parameters Q, H, and Cd compared to the laboratory sample. The findings revealed that in laboratory models with a maximum discharge area of 80 liters per second, the weir with Wi/Wo=1.2 and a flow head value of 285 mm exhibited the lowest value, whereas the weir with Wi/Wo=0.71 and a flow head value of 305 mm showed the highest, attributed to the higher discharge in the input-output ratio. Additionally, as the ratio of flow head to weir height H/P increased, the discharge coefficient Cd decreased. Comparing the flow conditions in weirs with different base nose shapes, it was observed that the weir with a spindle nose shape (PKW1.2S) outperformed the PKW with a flat (PKW1.2), semi-cylindrical (PKW1.2CL) and triangular base nose (PKW1.2TR). The results emphasized that models featuring semi-cylindrical and flat noses exhibited notable flow deviation and abrupt disruption upon impact with the nose. However, this effect was significantly reduced in models equipped with triangular and spindle-shaped noses. Also, the coefficient of discharge in PKW1.2S and PKW1.2TR weirs, compared to the PKW1.20 weir, increased by 27% and 20%, respectively.
웨어는 댐 뒤에서 하류 지역으로의 과도한 물 흐름을 관리하는 데 사용되는 필수 구조물입니다. 배출 효율을 높이는 데에는 댐의 피아노 키 위어(PKW) 유효 길이를 연장하거나 관개 및 배수 네트워크 내 흐름을 조절하는 것이 포함됩니다.
이 연구에서는 콘센트 키 아래에 설치된 다양한 베이스 노즈 모양과 초당 5~80리터 범위의 배출에 대한 다양한 입력 대 출력 키 너비 비율(Wi/Wo)의 영향을 평가하기 위해 수치 및 실험실 조사를 모두 사용했습니다. 또한 본 연구에서는 연구 목적을 달성하고 Piano Key Weir와 Ogee Weir의 성능을 비교하는 것을 목표로 했습니다.
수치 시뮬레이션을 위해 메시 생성을 위한 최적의 셀 수를 결정하고 적절한 난류 모델을 선택했습니다. 결과는 수치 모델이 높은 정밀도로 실험실 샘플을 정확하게 시뮬레이션했음을 나타냅니다. 더욱이, 수치 모델은 실험실 샘플과 비교하여 모든 매개변수 Q, H 및 Cd에 대해 PKW에 매우 근접했습니다.
연구 결과, 최대 배출 면적이 초당 80리터인 실험실 모델에서는 Wi/Wo=1.2, 플로우 헤드 값이 285mm인 웨어가 가장 낮은 값을 나타냈고, Wi/Wo=0.71 및 a인 웨어는 가장 낮은 값을 나타냈습니다. 플로우 헤드 값은 305mm로 가장 높은 것으로 나타났는데, 이는 입출력 비율의 높은 토출량에 기인합니다. 또한, 웨어 높이에 대한 유수두 비율 H/P가 증가함에 따라 유출계수 Cd는 감소하였다.
베이스 노즈 모양이 다른 웨어의 흐름 조건을 비교해 보면, 스핀들 노즈 모양(PKW1.2S)의 웨어가 평면(PKW1.2), 반원통형(PKW1.2CL) 및 삼각형 모양의 PKW보다 성능이 우수한 것으로 관찰되었습니다. 베이스 노즈(PKW1.2TR) 결과는 반원통형 및 편평한 노즈를 특징으로 하는 모델이 노즈에 충격을 가할 때 눈에 띄는 흐름 편차와 급격한 중단을 나타냄을 강조했습니다.
그러나 삼각형 및 방추형 노즈를 장착한 모델에서는 이러한 효과가 크게 감소했습니다. 또한 PKW1.20보에 비해 PKW1.2S보와 PKW1.2TR보의 유출계수는 각각 27%, 20% 증가하였다.
Keywords
Piano Key Weir, Base Nose Shape, Flow Hydraulics, Numerical Model, Triangular Nose Shape, Flat Nose Shape, Semi-Cylindrical Nose Shape, Spindle Nose Shape
Figure (17): Stream Lines Indicating Average Flow Speed in the Model with Various Nose shapes, Measured at Mid-Depth and at the Flow Surface Level, at a Flow Rate of 78 Liters per Second.
Reference
Chow, V.T. (1959). “Open channel hydraulics.” McGraw-Hill Book Company, New York, NY.
Ouamane, A., and Lempérière, F. (2006). “Design of a new economic shape of weir.” Proc., Intl. Symp. on Dams in the Societies of the 21st Century, 463-470, Barcelona, Spain.
Crookston, B. M., Anderson, A., Shearin-Feimster, L., and Tullis, B. P. (2014). “Mitigation investigation of flow-induced vibrations at a rehabilitated spillway.” Proc., 5th IAHR Intl. Symp. on Hydraulic Structures, Univ. of Queensland Brisbane, Brisbane, Australia.
Machiels, O. (2012). “Experimental study of the hydraulic behaviour of Piano Key Weirs.” Ph.D. Dissertation, Faculty of Applied Science, University of Liège, Liège, Belgium.
Blanc, P., and Lempérière, F. (2001). “Labyrinth spillways have a promising future.” Intl. J. of Hydropower and Dams, 8(4), 129-131.
Muslu, Y. (2001). “Numerical analysis for lateral weir flow.” J. of Irrigation and Drainage Eng., ASCE, 127, 246.
Erpicum, S., Machiels, O., Dewals, B., Pirotton, M., and Archambeau, P. (2012). “Numerical and physical hydraulic modeling of Piano Key Weirs.” Proc., ASIA 2012 – 4th Intl. Conf. on Water Resources and Renewable Energy Development in Asia, Chiang Mai, Thailand.
Tullis, J.P., Amanian, N., and Waldron, D. (1995). “Design of Labyrinth Spillways.” J. of Hydraulic Eng., ASCE, 121.
Lux, F.L., and Hinchcliff, D. (1985). “Design and construction of labyrinth spillways.” Proc., 15th Intl. Congress on Large Dams, ICOLD, Vol. 4, 249-274, Paris, France.
Erpicum, S., Laugier, F., Ho to Khanh, M., & Pfister, M. (2017). Labyrinth and Piano Key Weirs III–PKW 2017. CRC Press, Boca Raton, FL.
Kabiri-Samani, A., and Javaheri, A. (2012). “Discharge coefficient for free and submerged flow over Piano Key weirs.” Hydraulic Research J., 50(1), 114-120.
Hien, T.C., Son, H.T., and Khanh, M.H.T. (2006). “Results of some piano Key weirs hydraulic model tests in Vietnam.” Proc., 22nd ICOLD Congress, CIGB/ICOLD, Barcelona, Spain.
Laugier, F., Lochu, A., Gille, C., Leite Ribeiro, M., and Boillat, J-L. (2009). “Design and construction of a labyrinth PKW spillway at St-Marc Dam.” Hydropower and Dams J., 15(5), 100-107.
Cicero, G.M., Menon, J.M., Luck, M., and Pinchard, T. (2011). “Experimental study of side and scale effects on hydraulic performances of a Piano Key Weir.” In: Erpicum, S., Laugier, F., Boillat, J-L, Pirotton, M., Reverchon, B., and Schleiss, A-J (Eds.), Labyrinth and Piano Key Weirs, 167-172, CRC Press, London.
Pralong, J., Vermeulen, J., Blancher, B., Laugier, F., Erpicum, S., Machiels, O., Pirotton, M., Boillat, J.L, Leite Ribeiro, M., and Schleiss, A.J. (2011). “A naming convention for the piano key weirs geometrical parameters.” In: Erpicum, S., Laugier, F., Boillat, J-L, Pirotton, M., Reverchon, B., and Schleiss, A-J (Eds.), Labyrinth and Piano Key Weirs, 271-278, CRC Press, London.
Denys, F. J. M., and Basson, G. R. (2018). “Transient hydrodynamics of Piano Key Weirs.” Proc., 7th IAHR Intl. Symp. on Hydraulic Structures, ISHS2018, 518-527, DigitalCommons@USU, Logan, UT.
Anderson, A., and Tullis, B. P. (2018). “Finite crest length weir nappe oscillation.” J. of Hydraulic Eng., ASCE, 144(6), 04018020. https://doi.org/10.1061/(ASCE)HY.1943- 7900.0001461
Erpicum, S., Laugier, F., Boillat, J.-L., Pirotton, M., Reverchon, B., and Schleiss, A. J. (2011). “Labyrinth and Piano Key Weirs–PKW 2011.” CRC Press, Boca Raton, FL.
Aydin, C.M., and Emiroglu, M.E. (2011). “Determination of capacity of labyrinth side weir by CFD.” Flow Measurement and Instrumentation, 29, 1-8.
Cicero, G.M., Delisle, J.R., Lefebvre, V., and Vermeulen, J. (2013). “Experimental and numerical study of the hydraulic performance of a trapezoidal PKW.” Proc., Intl. Workshop on Labyrinths and Piano Key Weirs PKW II 2013, 265-272, CRC Press.
Anderson, R. M. (2011). “Piano Key Weir Head Discharge Relationships.” Master’s Thesis, Utah State University, Logan, Utah.
Crookston, B.M., Anderson, R.M., and Tullis, B.P. (2018). “Free-flow discharge estimation method for Piano Key weir geometries.” J. of Hydro-environment Research, 19, 160-167
Este documento está relacionado con un proyecto en curso para el cual se está desarrollando e implementando un gemelo digital estructural del puente de Kalix en Suecia. 이 문서는 스웨덴 Kalix 교량의 구조적 디지털 트윈이 개발 및 구현되고 있는 진행 중인 프로젝트와 관련이 있습니다.
RESUMEN Las cargas ambientales, como el viento y el caudal de los ríos, juegan un papel esencial en el diseño y evaluación estructural de puentes de grandes luces. El cambio climático y los eventos climáticos extremos son amenazas para la confiabilidad y seguridad de la red de transporte.
Esto ha llevado a una creciente demanda de modelos de gemelos digitales para investigar la resistencia de los puentes en condiciones climáticas extremas. El puente de Kalix, construido sobre el río Kalix en Suecia en 1956, se utiliza como banco de pruebas en este contexto.
La estructura del puente, realizada en hormigón postensado, consta de cinco vanos, siendo el más largo de 94 m. En este estudio, las características aerodinámicas y los valores extremos de la simulación numérica del viento, como la presión en la superficie, se obtienen utilizando la simulación de remolinos desprendidos retardados (DDES) de Spalart-Allmaras como un enfoque de turbulencia RANS-LES híbrido que es práctico y computacionalmente eficiente para cerca de la pared densidad de malla impuesta por el método LES.
La presión del viento en la superficie se obtiene para tres escenarios climáticos extremos, que incluyen un clima con mucho viento, un clima extremadamente frío y el valor de cálculo para un período de retorno de 3000 años. El resultado indica diferencias significativas en la presión del viento en la superficie debido a las capas de tiempo que provienen de la simulación del flujo de viento transitorio. Para evaluar el comportamiento estructural en el escenario de viento crítico, se considera el valor más alto de presión en la superficie para cada escenario.
Además, se realiza un estudio hidrodinámico en los pilares del puente, en el que se simula el flujo del río por el método VOF, y se examina el proceso de movimiento del agua alrededor de los pilares de forma transitoria y en diferentes momentos. En cada una de las superficies del pilar se calcula la presión superficial aplicada por el caudal del río con el caudal volumétrico más alto registrado.
Para simular el flujo del río, se ha utilizado la información y las condiciones meteorológicas registradas en períodos anteriores. Los resultados muestran que la presión en la superficie en el momento en que el flujo del río golpea los pilares es mucho mayor que en los momentos posteriores. Esta cantidad de presión se puede usar como carga crítica en los cálculos de interacción fluido-estructura (FSI).
Finalmente, para ambas secciones, la presión en la superficie del viento, el campo de velocidades con respecto a las líneas de sondas auxiliares, los contornos del movimiento circunferencial del agua alrededor de los pilares y el diagrama de presión en ellos se informan en diferentes intervalos de tiempo.
요약 바람, 강의 흐름과 같은 환경 하중은 장대 교량의 설계 및 구조 평가에 필수적인 역할을 합니다. 기후 변화와 기상 이변은 교통 네트워크의 신뢰성과 보안에 위협이 됩니다.
이로 인해 극한 기상 조건에서 교량의 복원력을 조사하기 위한 디지털 트윈 모델에 대한 수요가 증가했습니다. 1956년 스웨덴 칼릭스 강 위에 건설된 칼릭스 다리는 이러한 맥락에서 테스트베드로 사용됩니다.
포스트텐션 콘크리트로 만들어진 교량 구조는 5개 경간으로 구성되며 가장 긴 길이는 94m입니다. 본 연구에서는 하이브리드 RANS-LES 난류 접근 방식인 Spalart-Allmaras 지연 분리 와류 시뮬레이션(DDES)을 사용하여 수치적 바람 시뮬레이션의 공기역학적 특성과 표면압 등 극한값을 얻습니다. LES 방법으로 부과된 벽 근처 메쉬 밀도.
바람이 많이 부는 기후, 극도로 추운 기후, 그리고 3000년의 반환 기간에 대해 계산된 값을 포함한 세 가지 극한 기후 시나리오에 대해 표면 풍압을 얻습니다. 결과는 과도 풍류 시뮬레이션에서 나오는 시간 레이어로 인해 표면 풍압에 상당한 차이가 있음을 나타냅니다. 임계 바람 시나리오에서 구조적 거동을 평가하기 위해 각 시나리오에 대해 가장 높은 표면 압력 값이 고려됩니다.
또한 교량 기둥에 대한 유체 역학 연구를 수행하여 하천의 흐름을 VOF 방법으로 시뮬레이션하고 기둥 주변의 물 이동 과정을 일시적이고 다른 시간에 조사합니다. 각 기둥 표면에서 기록된 체적 유량이 가장 높은 강의 흐름에 의해 적용되는 표면 압력이 계산됩니다.
강의 흐름을 시뮬레이션하기 위해 이전 기간에 기록된 정보와 기상 조건이 사용되었습니다. 결과는 강의 흐름이 기둥에 닿는 순간의 표면 압력이 나중에 순간보다 훨씬 높다는 것을 보여줍니다. 이 압력의 양은 유체-구조 상호작용(FSI) 계산에서 임계 하중으로 사용될 수 있습니다.
마지막으로 두 섹션 모두 바람 표면의 압력, 보조 프로브 라인에 대한 속도장, 기둥 주위 물의 원주 운동 윤곽 및 압력 다이어그램이 서로 다른 시간 간격으로 보고됩니다.
키워드: 디지털 트윈 , 풍력 공학, 콘크리트 교량, 유체역학, CFD 시뮬레이션, DDES 난류 모델, Kalix 교량
Palabras clave: Gemelo digital , Ingeniería eólica, Puente de hormigón, Hidrodinámica, Simulación CFD, Modelo de turbulencia DDES, Puente Kalix
1. Introducción
Las infraestructuras de transporte son la columna vertebral de nuestra sociedad y los puentes son el cuello de botella de la red de transporte [1]. Además, el cambio climático que da como resultado tasas de deterioro más altas y los eventos climáticos extremos son amenazas importantes para la confiabilidad y seguridad de las redes de transporte. Durante la última década, muchos puentes se han dañado o fallado por condiciones climáticas extremas como tifones e inundaciones.
Wang et al. analizó los impactos del cambio climático y mostró que se espera que el deterioro de los puentes de hormigón sea aún peor que en la actualidad, y se prevé que los eventos climáticos extremos sean más frecuentes y con mayor gravedad [2].
Además, la demanda de capacidad de carga a menudo aumenta con el tiempo, por ejemplo, debido al uso de camiones más pesados para el transporte de madera en el norte de Europa y América del Norte. Por lo tanto, existe una necesidad creciente de métodos confiables para evaluar la resistencia estructural de la red de transporte en condiciones climáticas extremas que tengan en cuenta los escenarios futuros de cambio climático.
Los activos de transporte por carretera se diseñan, construyen y explotan basándose en numerosas fuentes de datos y varios modelos. Por lo tanto, los ingenieros de diseño usan modelos establecidos proporcionados por las normas; ingenieros de construccion documentar los datos en el material real y proporcionar planos según lo construido; los operadores recopilan datos sobre el tráfico, realizan inspecciones y planifican el mantenimiento; los científicos del clima combinan datos y modelos climáticos para predecir eventos climáticos futuros, y los ingenieros de evaluación calculan el impacto de la carga climática extrema en la estructura.
Dadas las fuentes abrumadoras y la complejidad de los datos y modelos, es posible que la información y los cálculos actualizados no estén disponibles para decisiones cruciales, por ejemplo, con respecto a la seguridad estructural y la operabilidad de la infraestructura durante episodios de eventos extremos. La falta de una integración perfecta entre los datos de la infraestructura, los modelos estructurales y la toma de decisiones a nivel del sistema es una limitación importante de las soluciones actuales, lo que conduce a la inadaptación e incertidumbre y crea costos e ineficiencias.
El gemelo digital estructural de la infraestructura es una simulación estructural viva que reúne todos los datos y modelos y se actualiza desde múltiples fuentes para representar su contraparte física. El Digital Twin estructural, mantenido durante todo el ciclo de vida de un activo y fácilmente accesible en cualquier momento, proporciona al propietario/usuarios de la infraestructura una idea temprana de los riesgos potenciales para la movilidad inducidos por eventos climáticos, cargas de vehículos pesados e incluso el envejecimiento de un infraestructura de transporte.
En un proyecto en curso, estamos desarrollando e implementando un gemelo digital estructural para el puente de Kalix en Suecia. El objetivo general del presente artículo es presentar un método y estudiar los resultados de la cuantificación de las cargas estructurales resultantes de eventos climáticos extremos basados en escenarios climáticos futuros para el puente de Kalix. El puente de Kalix, construido sobre el río Kalix en Suecia en 1956, está hecho de una viga cajón de hormigón postensado. El puente se utiliza como banco de pruebas para la demostración de métodos de evaluación y control de la salud estructural (SHM) de última generación.
El objetivo específico de la investigación actual es dar cuenta de parámetros climáticos como el viento y el flujo de agua, que imponen cargas estáticas y dinámicas en las estructuras. Nuestro método, en el primer paso, consiste en simulaciones de flujo de viento y simulaciones de flujo de agua utilizando un modelado CFD transitorio basado en el modelo de turbulencia LES/DES para cuantificar las cargas de viento e hidráulicas; esto constituye el punto focal principal de este artículo.
En el siguiente paso, se estudiará la respuesta estructural del puente mediante la transformación de los perfiles de carga eólica e hidráulica en cargas estructurales en el análisis de EF estructural no lineal. Por último, el modelo estructural se actualizará incorporando sin problemas los datos del SHM y, por lo tanto, creando un gemelo digital estructural que refleje la verdadera respuesta de la estructura. Los dos primeros enfoques de investigación permanecen fuera del alcance inmediato del presente artículo.
2. Descripción del puente de Kalix
El puente de Kalix consta de 5 vanos largos de los cuales el más largo tiene unos 94 metros y el más corto 43,85 m. El puente es de hormigón postensado, el cual se cuela in situ de forma segmentaria y una viga cajón no prismática como se muestra en la Fig. 1. El puente es simétrico en geometría y hay una bisagra en el punto medio. El ancho del tablero del puente en la losa superior e inferior es de aproximadamente 13 my 7,5 m, respectivamente. El espesor del muro es de 45 cm y el espesor de la losa inferior varía de 20 cm a 50 cm.
Las pruebas en túnel de viento solían ser la única forma de examinar la reacción de los puentes a las cargas de viento Consulte [3]; sin embargo, estos experimentos requieren mucho tiempo y son costosos. Se requieren cerca de 6 a 8 semanas para realizar una prueba típica en un túnel de viento Consulte [4]. Los últimos logros en la capacidad computacional de las computadoras brindan oportunidades para la simulación práctica del viento alrededor de puentes utilizando la dinámica de fluidos computacional (CFD).
Es beneficioso investigar la presión del viento en los componentes del puente utilizando una simulación por computadora. Es necesario determinar los parámetros de simulación del puente y el campo de viento a su alrededor; por lo tanto, se pueden evaluar con precisión sus impactos en las fuerzas aplicadas en el puente.
Las demandas de diseño de las estructuras de puentes requieren una investigación rigurosa de la acción del viento, especialmente en condiciones climáticas extremas. Garantizar la estabilidad de los puentes de grandes luces, ya que sus características y formaciones son más propensas a la carga de viento, se encuentra entre las principales consideraciones de diseño [3].
3.1. Parámetros de simulación
La velocidad básica del viento se elige 22 m/s según el mapa de viento de Suecia y la ubicación del puente de Kalix según EN 1991-1-4 [5] y el código sueco BFS 2019: 1 EKS 11; ver figura 1. La superficie libre sobre el agua se considera un área expuesta a la carga de viento. La dirección del ataque del viento dominante se considera perpendicular al tablero del puente.
Las simulaciones actuales se basan en tres escenarios que incluyen: viento extremo, frío extremo y valor de diseño para un período de retorno de 3000 años. Cada condición tiene diferentes valores de temperatura, viento básico velocidad, viscosidad cinemática y densidad del aire, como se muestra en la Tabla 1. Los conjuntos de datos meteorológicos se sintetizaron para dos semanas meteorológicas extremas durante el período de 30 años de 2040-2069, considerando 13 escenarios climáticos futuros diferentes con diferentes modelos climáticos globales (GCM) y rutas de concentración representativas (RCP).
Se seleccionaron una semana de frío extremo y una semana de viento extremo utilizando el enfoque desarrollado de Nik [7]. El planteamiento se adaptó a las necesidades de este trabajo, considerando el horario semanal en lugar de mensual. Se ha verificado la aplicación del enfoque para simulaciones complejas, incluidos los sistemas de energía Consulte [7]Consulte [8], hidrotermal Consulte [ 9] y simulaciones de microclimas Consulte [10].
Para considerar las condiciones climáticas extremas de una infraestructura muy importante, el valor de la velocidad básica del viento debe transferirse del período de retorno de 50 años a 3000 años como se indica en la ecuación 1 [6]. El perfil de velocidad y turbulencia se crea en base a EN 1991-1-4 [5] para la categoría de terreno 0 (Z0 = 0,003 my Zmín = 1 m), donde Z0 y Zmín son la longitud de rugosidad y la altura mínima, respectivamente. La variación de la velocidad del viento con la altura se define en la ecuación 2, donde co (z) es el factor de orografía tomado como 1, vm (z) es la velocidad media del viento a la altura z, kr es el factor del terreno que depende de la longitud de la rugosidad , e Iv (z) es la intensidad de la turbulencia; ver ecuación 3.���50=[0.36+0.1ln12�] 1�����=��·ln��0·��� [2]���=�����=�1�0�·ln�/�0 ��� ����≤�≤���� [3]���=������ ��� �<���� [4]
Se calcula que el valor de la velocidad del viento para T = período de retorno de 3000 años es de 31 m/s; por lo tanto, los diagramas de velocidad del viento e intensidad de turbulencia se obtienen como se muestra en la figura 2.
Para que las investigaciones sean precisas en el flujo alrededor de estructuras importantes como puentes, se aplica un enfoque híbrido que incluye simulaciones de remolinos desprendidos retardados (DDES) y es computacionalmente eficiente [11][12]. Este modelo de turbulencia usa un método RANS cerca de las capas límite y el método LES lejos de las capas límite y en el área del flujo de la región separada ‘.
En el primer paso, el enfoque de simulación de remolinos separados se ha ampliado para adquirir predicciones de fuerza fiables en los modelos con un gran impacto del flujo separado. Hay varios ejemplos en la parte de revisión de Spalart Consulte [11] para varios casos que usan la aplicación del modelo de turbulencia de simulación de remolino separado (DES).
La formulación DES inicial [13] se desarrolla utilizando el enfoque de Spalart-Allmaras. Con respecto a la transición del enfoque RANS al LES, se revisa el término de destrucción en la ecuación de transporte de viscosidad modificada: la distancia entre un punto en el dominio y la superficie sólida más cercana (d) se sustituye por el factor introducido por:�~=���(�.����·∆)
Se ha empleado un enfoque modificado de DES, conocido como simulación de remolinos desprendidos retardados (DDES), para dominar el probable problema de la “separación inducida por la rejilla” (GIS) que está relacionado con la geometría de la rejilla. El objetivo de este nuevo enfoque es confirmar que el modelado de turbulencia se mantiene en modo RANS en todas las capas de contorno [14]. Por lo tanto, la definición del parámetro se modifica como se define:�~=�-�����(0. �-����·�) 6
donde fd es una función de filtro que considera un valor de 0 en las capas límite cercanas al muro (zona RANS) y un valor de 1 en las áreas donde se realizó la separación del flujo (zona LES).
3.3. Rejilla computacional y resultados
RWIND 2.01 Pro se emplea para la simulación de viento CFD, que usa el código CFD externo OpenFOAM® versión 17.10. La simulación CFD tridimensional se realiza como una simulación de viento transitorio para flujo turbulento incompresible utilizando el algoritmo SIMPLE (Método semi-implícito para ecuaciones vinculadas a presión).
En la simulación actual, el solucionador de estado estacionario se considera como la condición inicial, lo que significa que cuando se está calculando el flujo transitorio, el cálculo del estado estacionario de la condición inicial comienza en la primera parte de la simulación y tan pronto como se calcula. completado, el cálculo de transitorios se iniciará automáticamente.
La cuadrícula computacional se realiza mediante 8.057.279 celdas tridimensionales y 8.820.901 nudos, también se consideran las dimensiones del dominio del túnel de viento 2000 m * 1000 m * 100 m (largo, ancho, alto) como se muestra en la figura 3. El volumen mínimo de la celda es de 6,34 * 10-5 m3, el volumen máximo es de 812,30 m3 y la desviación máxima es de 1,80.
La presión residual final se considera 5 * 10-5. El proceso de generación de mallas e independencia de la rejilla se ha realizado utilizando los cuatro tamaños de malla que se muestran en la figura 4 para la malla de referencia, y finalmente se ha conseguido la independencia de la rejilla.
Se han realizado tres simulaciones para obtener el valor de la presión del viento para condiciones climáticas extremas y el valor de cálculo del viento que se muestra en la Fig. 5. Para cada escenario, el resultado de la presión del viento se obtiene utilizando el modelo de turbulencia transitoria DDES con respecto a 30 (s) de duración que incluye 60 capas de tiempo (Δt = 0,5 s).
Se puede observar que el área frontal del puente está expuesta a la presión del viento positiva y la cantidad de presión aumenta en la altura cerca del borde del tablero para todos los escenarios. Además, la Fig. 5. ilustra los valores negativos de la presión del viento en su totalidad en la superficie de la cubierta. El valor de pertenencia para el período de 3000 años es mucho más alto que los otros escenarios.
Es importante tener en cuenta que el intervalo de la velocidad del viento de entrada tiene un gran impacto en el valor de la presión en la superficie más que en los otros parámetros. Además, para cada escenario, el intervalo más alto de presión del viento y succión durante el tiempo total debe considerarse como una carga de viento crítica impuesta a la estructura. El valor más bajo de la presión en la superficie se obtiene en el escenario de condiciones de frío extremo, mientras que en condiciones de mucho viento, el valor de la presión se vuelve un orden de magnitud más alto.
Además, es importante tener en cuenta que el comportamiento del puente sería completamente diferente debido a las diferentes temperaturas del aire, y puede ocurrir un posible caso crítico en el escenario que experimente una presión menor. Con respecto al valor de entrada de cada escenario, el rango más alto de presión del viento pertenece al nivel de diseño debido al período de retorno de 3000 años, que ha recibido la velocidad del viento más alta como velocidad de entrada.
4. Simulación hidráulica
Los pilares de los puentes a través del río pueden bloquear el flujo al reducir la sección transversal del río, crear corrientes parásitas locales y cambiar la velocidad del flujo, lo que puede ejercer presión en las superficies de los pilares. Cuando el río fluye hacia los pilares del puente, el proceso del flujo de agua alrededor de la base se puede dividir en dos partes: aplicando presión en el momento en que el agua golpea el pilar del puente y después de la presión inicial cuando el agua fluye alrededor de los pilares [15].
Cuando el agua alcanza los pilares del puente a una cierta velocidad, el efecto de la presión sobre los pilares es mucho mayor que la presión del fluido que queda a su alrededor. Debido a los desarrollos de la ciencia de la computación, así como al desarrollo cada vez mayor de los códigos dinámicos de fluidos computacionales, se han utilizado ampliamente varias simulaciones numéricas y se ha demostrado que los resultados de muchas simulaciones son consistentes con los resultados experimentales [16].
Por ello, en esta investigación se ha utilizado el método de la dinámica de fluidos computacional para simular los fenómenos que gobiernan el comportamiento del flujo de los ríos. Para este estudio se ha seleccionado una solución tridimensional basada en cálculos numéricos utilizando el modelo de turbulencia LES. La simulación tridimensional del flujo del río en diferentes direcciones y velocidades nos permite calcular y analizar todas las presiones en la superficie de los pilares del puente en diferentes intervalos de tiempo.
4.1. Parámetros de simulación
El flujo del río se puede definir como un flujo de dos fases, que incluye agua y aire, en un canal abierto. El flujo de canal abierto es un flujo de fluido con una superficie libre en la que la presión atmosférica se distribuye uniformemente y se crea por el peso del fluido. Para simular este tipo de flujo se utiliza el método multifase VOF.
El programa Flow3D, disponible en el mercado, utiliza los métodos de fracciones volumétricas VOF y FAVOF. En el método VOF, el dominio de modelado se divide primero en celdas de elementos o volúmenes de controles más pequeños. Para los elementos que contienen fluidos, se mantienen valores numéricos para cada una de las variables de flujo dentro de ellos.
Estos valores representan la media volumétrica de los valores en cada elemento. En las corrientes superficiales libres, no todas las celdas están llenas de líquido; algunas celdas en la superficie de flujo están medio llenas. En este caso, se define una cantidad llamada volumen de fluido, F, que representa la parte de la celda que se llena con el fluido.
Después de determinar la posición y el ángulo de la superficie del flujo, será posible aplicar las condiciones de contorno apropiadas en la superficie del flujo para calcular el movimiento del fluido. A medida que se mueve el fluido, el valor de F también cambia con él. Las superficies libres son monitoreadas automáticamente por el movimiento de fluido dentro de una red fija. El método FAVOR se usa para determinar la geometría.
También se puede usar otra cantidad de fracción volumétrica para determinar el nivel de un cuerpo rígido desocupado ( Vf ). Cuando se conoce el volumen que ocupa el cuerpo rígido en cada celda, el límite del fluido dentro de la red fija se puede determinar como VOF. Este límite se usa para determinar las condiciones de contorno del muro que sigue el arroyo. En general, la ecuación de continuidad de masa es la siguiente:��𝜕�𝜕�+𝜕𝜕�(����)+�𝜕𝜕�(����)+𝜕𝜕�(����)+������=���� 10
Las ecuaciones de movimiento para los componentes de la velocidad de un fluido en coordenadas 3D, o en otras palabras, las ecuaciones de Navier-Stokes, son las siguientes:𝜕�𝜕�+1�����𝜕�𝜕�+���𝜕�𝜕�+���𝜕�𝜕�+��2�����=-1�𝜕�𝜕�+��+��-��-��������-��-��� 11𝜕�𝜕�+1�����𝜕�𝜕�+���𝜕�𝜕�+���𝜕�𝜕�+��������=-�1�𝜕�𝜕�+��+��-��-��������-��-��� 12𝜕�𝜕�+1�����𝜕�𝜕�+���𝜕�𝜕�+���𝜕�𝜕�=-1�𝜕�𝜕�+��+��-��-��������-��-��� 13
Donde VF es la relación del volumen abierto al flujo, ρ es la densidad del fluido, (u, v, w) son las componentes de la velocidad en las direcciones x, y y z, respectivamente, R SOR es la función de la fuente, (Ax, Ay, Az ) son las áreas fraccionales, (Gx, Gy, Gz ) son las fuerzas gravitacionales, (fx, fy, fz ) son las aceleraciones de la viscosidad y (bx, by, bz ) son las pérdidas de flujo en medios porosos en las direcciones x, y, z, respectivamente [17].
La zona de captación del río Kalix es grande y amplia, por lo que tiene un clima subpolar con inviernos fríos y largos y veranos suaves y cortos. Aproximadamente el 50% de las precipitaciones en esta zona es nieve. En mayo, por lo general, el deshielo provoca un aumento significativo en el caudal del río. Las condiciones climáticas del río se resumen en la Tabla 2, [18].
Contrariamente a la tendencia general de este estudio, la previsión de las condiciones meteorológicas mencionadas está utilizando la información meteorológica registrada en los períodos pasados. En función de la información meteorológica disponible, definimos las condiciones de contorno al realizar los cálculos.
Primero, según las dimensiones de los pilares en tres direcciones X, Y, Z, y según la dimensión longitudinal de los pilares (D = 8,5 m; véase la figura 7), el dominio se extiende 10D aguas arriba y 20D aguas abajo. Se ha utilizado el método de mallado estructurado (cartesiano) y el software Flow3D para resolver este problema. Para una cuadrícula correcta, el dominio se debe dividir en diferentes secciones.
Esta división se basa en lugares con fuertes pendientes. Usando la creación de una nueva superficie, el dominio se puede dividir en varias secciones para crear una malla regular con las dimensiones correctas y apropiadas, se puede especificar el número de celdas en cada superficie.
Esto aumenta el volumen final de las células. Por esta razón, hemos dividido este dominio en tres niveles: Grueso, medio y fino. Los resultados de los estudios de independencia de la red se muestran en la figura 6. Para comprobar los resultados calculados, primero debemos asegurarnos de que la corriente de entrada sea la correcta. Para hacer esto, el caudal de entrada se mide en el dominio de la solución y se compara con el valor base. Las dimensiones del dominio de la solución se especifican en la figura 7. Esta figura también contribuye al reconocimiento de los pilares del puente y su denominación de superficies.
Como se muestra en la Fig. 8, el caudal del río se encuentra dentro del intervalo admisible durante el 90% del tiempo de simulación y el caudal de entrada se ha simulado correctamente. Además, en la Fig. 9, la velocidad media del río se calcula en función del caudal y del área de la sección transversal del río.
Para extraer la cantidad de presión aplicada a los diferentes lados de las columnas, hemos seleccionado el intervalo de tiempo de simulación de 10 a 25 segundos (tiempo de estabilización de descarga en la cantidad de 1800 metros cúbicos por segundo). Los resultados calculados para cada lado se muestran en la Fig. 10 y 11. Los contornos de velocidad también se muestran en las Figuras 12 y 13. Estos contornos se ajustan en función de la velocidad del fluido en un momento dado.
Debido a las dimensiones del dominio de la solución y al caudal del río, el flujo de agua llega a los pilares del puente en el décimo segundo y la presión inicial del flujo del río afecta las superficies de los pilares del puente. Esta presión inicial decrece con el tiempo y se estabiliza en un rango determinado para cada lado según el área y el porcentaje de interacción con el flujo. Para los cálculos de interacción fluido-estructura (FSI), se puede usar la presión crítica calculada en el momento en que la corriente golpea los pilares.
Los efectos de las condiciones meteorológicas extremas, incluido el viento dinámico y el flujo de agua, se investigaron numéricamente para el puente de Kalix. Se definieron tres escenarios para las simulaciones dinámicas de viento, incluido el clima con mucho viento, el clima extremadamente frío y el valor de diseño para un período de retorno de 3.000 años. Aprovechando las simulaciones CFD, se determinaron las presiones del viento en pasos de 60 tiempos (30 segundos) utilizando el modelo de turbulencia transitoria DDES.
Los resultados indican diferencias significativas entre los escenarios, lo que implica la importancia de los datos de entrada, especialmente el diagrama de velocidades del viento. Se observó que el valor de diseño para el período de devolución de 3000 años tiene un impacto mucho mayor que los otros escenarios. Además, se mostró la importancia de considerar el rango más alto de presión del viento en la superficie a través de los pasos de tiempo para evaluar el comportamiento estructural del puente en la condición más crítica.
Además, se consideró el caudal máximo del río para una simulación transitoria según las condiciones meteorológicas registradas, y los pilares del puente se sometieron al caudal máximo del río durante 30 segundos. Por lo tanto, además de las condiciones físicas del flujo del río y cómo cambia la dirección del flujo aguas abajo, se cuantificaron las presiones máximas del agua en el momento en que el flujo golpea los pilares.
En el trabajo futuro, el rendimiento estructural del puente de Kalix será evaluado por imposición de la carga del viento, la presión del agua y la carga del tráfico, creando así un gemelo digital estructural que refleja la verdadera respuesta de la estructura.
6. Reconocimiento
Los autores agradecen enormemente el apoyo de Dlubal Software por proporcionar la licencia de RWIND Simulation, así como de Flow Sciences Inc. por proporcionar la licencia de FLOW-3D.
Jančula, M., Jošt, J., & Gocál, J. (2021). Influencia de las acciones ambientales agresivas en las estructuras de los puentes. Transportation Research Procedia, 55 , 1229–1235. https://doi.org/10.1016/j.trpro.2021.07.104
Wang, X., Nguyen, M., Stewart, MG, Syme, M. y Leitch, A. (2010). Análisis de los impactos del cambio climático en el deterioro de la infraestructura de hormigón – Informe de síntesis. CSIRO, Canberra.
Kemayou, BTM (2016). Análisis de secciones de tableros de puentes por el método de la pseudocompresibilidad basado en FDM y LES: Mejora del rendimiento mediante la implementación de la computación en paralelo (tesis). Universidad de Arkansas.
Larsen, A. y Walther, JH (1997). Análisis aeroelástico de secciones de vigas de puentes basado en simulaciones discretas de vórtices. Journal of Wind Engineering and Industrial Aerodynamics, 67–68 , 253–265. https://doi.org/10.1016/s0167-6105(97)00077-9
Eurocódigo 1: Acciones en estructuras. (2006). Instituto Británico de Normas.
ASCE. Cargas mínimas de cálculo para edificios y otras estructuras. (2013). Sociedad Estadounidense de Ingenieros Civiles.
Nik, VM (2016). Facilitación de la simulación energética para el clima futuro: síntesis de conjuntos de datos meteorológicos típicos y extremos a partir de modelos climáticos regionales (RCM). Applied Energy, 177 , 204–226. https://doi.org/10.1016/j.apenergy.2016.05.107
Perera, AT, Nik, VM, Chen, D., Scartezzini, J.‑L. y Hong, T. (2020). Cuantificación de los impactos del cambio climático y los eventos climáticos extremos en los sistemas energéticos. Nature Energy, 5 (2), 150–159. https://doi.org/10.1038/s41560-020-0558-0
Nik, VM (2017). Aplicación de conjuntos de datos meteorológicos típicos y extremos en la simulación higrotérmica de componentes de construcción para el clima futuro: un estudio de caso para un muro de entramado de madera. Energy and Buildings, 154 , 30–45. https://doi.org/10.1016/j.enbuild.2017.08.042
Hosseini, M., Javanroodi, K. y Nik, VM (2022). Evaluación de impacto de alta resolución del cambio climático en el rendimiento energético de los edificios considerando los eventos meteorológicos extremos y el microclima – Investigando las variaciones en el confort térmico interior y los grados-día. Ciudades sostenibles y sociedad, 78 , 103634. https://doi.org/10.1016/j.scs.2021.103634
Spalart, P. R. (2009). Simulación de remolinos separados. Revisión anual de mecánica de fluidos, 41 , 181–202. https://doi.org/10.1146/annurev.fluid.010908.165130
Spalart, PR, et al. (2006) Una nueva versión de simulación de remolinos separados, resistente a densidades de rejilla ambiguas. Dinámica de fluidos teórica y computacional, 2006. 20 (3), 181-195. https://doi.org/10.1007/s00162-006-0015-0
Spalart, PR (1997). Comentarios sobre la viabilidad de LES para alas y sobre una aproximación híbrida RANS/LES. En Actas de la Primera Conferencia Internacional de AFOSR sobre DNS/LES. Prensa de Greyden.
Boudreau, M., Dumas, G. y Veilleux, J.-C. (2017). Evaluación de la capacidad del enfoque de modelado de turbulencia DDES para simular la estela de un cuerpo de farol. Aeroespacial, 4 (3), 41. https://doi.org/10.3390/aerospace4030041
Wang, Y., Zou, Y., Xu, L. y Luo, Z. (2015). Análisis de la presión del flujo de agua en pilas de puentes considerando el efecto del impacto. Problemas matemáticos en ingeniería, 2015 , 1–8. https://doi.org/10.1155/2015/687535
Qi, H., Zheng, J. y Zhang, C. (2020). Simulación numérica del campo de velocidades alrededor de dos pilares de pilas en tándem del puente longitudinal. Fluidos, 5 (1), 32. https://doi.org/10.3390/fluids5010032
Jalal, H. K. y Hassan, W. H (2020). Simulación numérica tridimensional de la socavación local alrededor de la pila de un puente circular utilizando el software flow-3d. Ciclo de conferencias de IOP: Ciencia e ingeniería de materiales, 745 , 012150. https://doi.org/10.1088/1757-899x/745/1/012150
Herzog, S. D., Conrad, S., Ingri, J., Persson, P. y Kritzberg, E. S (2019). Cambios inducidos por crecidas de primavera en la especiación y destino del Fe a mayor salinidad. Geoquímica aplicada, 109 , 104385. https://doi.org/10.1016/j.apgeochem.2019.104385
다양한 수력학적 및 기하학적 조건에서 아래에 반원형 게이트가 결합된 두 개의 직사각형 복합 웨어의 배수 계수
ABSTRACT
Two-component composite hydraulic structures are commonly employed in irrigation systems. The first component, responsible for managing the overflow, is represented by a weir consisting of two rectangles. The second component, responsible for regulating the underflow, is represented by a semicircular gate. Both components are essential for measuring, directing, and controlling the flow. In this study, we experimentally investigated the flow through a combined two-rectangle sharp-crested weir with a semicircular gate placed across the channel as a control structure. The upper rectangle of the weir has a width of 20 cm, while the lower rectangle has varying widths (W2 ) of 5, 7, and 9 cm and depths (z) of 6, 9, and 11 cm. Additionally, three different values were considered for the gate diameter (d), namely 8, 12, and 15 cm. These dimensions were tested interchangeably, including a weir without a gate (d = 0), under different water head conditions. The results indicate that the discharge passing through the combined structure of the two rectangles and the gate is significantly affected by the weir and gate dimensions. After analyzing the data, empirical formulas were developed to predict the discharge coefficient (Cd ) of the combined structure. It is important to note that the analysis and results presented in this study are limited to the range of data that were tested.
2성분 복합 수력 구조물은 일반적으로 관개 시스템에 사용됩니다. 오버플로 관리를 담당하는 첫 번째 구성 요소는 두 개의 직사각형으로 구성된 웨어로 표시됩니다.
언더플로우 조절을 담당하는 두 번째 구성 요소는 반원형 게이트로 표시됩니다. 두 구성 요소 모두 흐름을 측정, 지시 및 제어하는 데 필수적입니다. 본 연구에서 우리는 제어 구조로 수로를 가로질러 배치된 반원형 게이트를 갖춘 결합된 두 개의 직사각형 뾰족한 둑을 통한 흐름을 실험적으로 조사했습니다.
웨어의 위쪽 직사각형은 폭이 20cm인 반면, 아래쪽 직사각형은 5, 7, 9cm의 다양한 폭(W2)과 6, 9, 11cm의 깊이(z)를 갖습니다. 또한 게이트 직경(d)에 대해 8, 12, 15cm의 세 가지 다른 값이 고려되었습니다.
이러한 치수는 게이트가 없는 둑(d = 0)을 포함하여 다양한 수두 조건에서 상호 교환적으로 테스트되었습니다. 결과는 두 개의 직사각형과 게이트가 결합된 구조를 통과하는 방전이 위어와 게이트 크기에 크게 영향을 받는다는 것을 나타냅니다.
데이터를 분석한 후, 결합구조물의 유출계수(Cd)를 예측하기 위한 실험식을 개발하였다. 본 연구에서 제시된 분석 및 결과는 테스트된 데이터 범위에 국한된다는 점에 유의하는 것이 중요합니다.
[1] S. S. Ibrahim, R. A. Jafer, and B. M. A. S. Ali, “An Experimental Study of a Combined Oblique Cylindrical Weir and Gate Structure,” Engineering, Technology & Applied Science Research, vol. 13, no. 2, pp. 10483–10488, Apr. 2023, https://doi.org/10.48084/etasr.5646. [2] F. Rooniyan, “The Effect of Confluence Angle on the Flow Pattern at a Rectangular Open Channel,” Engineering, Technology & Applied Science Research, vol. 4, no. 1, pp. 576–580, Feb. 2014, https://doi.org/10.48084/etasr.395. [3] A. S. Kote and P. B. Nangare, “Hydraulic Model Investigation on Stepped Spillway’s Plain and Slotted Roller Bucket,” Engineering, Technology & Applied Science Research, vol. 9, no. 4, pp. 4419–4422, Aug. 2019, https://doi.org/10.48084/etasr.2837. [4] S. M. Kori, A. A. Mahessar, M. Channa, A. A. Memon, and A. R. Kori, “Study of Flow Characteristics Over a Rounded Edge Drop Structure in Open Channel,” Engineering, Technology & Applied Science Research, vol. 9, no. 3, pp. 4136–4139, Jun. 2019, https://doi.org/ 10.48084/etasr.2584. [5] F. Granata, F. Di Nunno, R. Gargano, G. de Marinis, “Equivalent Discharge Coefficient of Side Weirs in Circular Channel—A Lazy Machine Learning Approach,” Water, vol. 11, no.11, 2019, Art. no. 2406, https://doi.org/10.3390/w11112406. [6] S. Salehi and A. H. Azimi, “Discharge Characteristics of Weir-Orifice and Weir-Gate Structures,” Journal of Irrigation and Drainage Engineering, vol. 145, no. 11, Nov. 2019, Art. no. 04019025, https://doi.org/10.1061/(ASCE)IR.1943-4774.0001421. [7] M. G. Bos, Ed., Discharge Measurement Structures. Wageningen, The Netherlands: International Institute for Land Reclamation and Improvement, 1989. [8] S. Emami, J. Parsa, H. Emami, A. Abbaspour, “An ISaDE algorithm combined with support vector regression for estimating discharge coefficient of W-planform weirs,” Water Supply, vol. 21, no.7, pp. 3459–3476, 2021, https://doi.org/10.2166/ws.2021.112. [9] A. B. Altan-Sakarya, M. A. Kokpinar, and A. Duru, “Numerical modelling of contracted sharp-crested weirs and combined weir and gate systems,” Irrigation and Drainage, vol. 69, no. 4, pp. 854–864, 2020, https://doi.org/10.1002/ird.2468. [10] P. Ackers, W. R. White, J. A. Perkins, A. J. M. Harrison, Weirs and Flumes for Flow Measurement, New York, NY, USA: Wiley, 1978. [11] A. Alhamid, D. Husain, and A. Negm, “Discharge equation for simultaneous flow over rectangular weirs and below inverted triangular weirs,” Arab Gulf Journal of Scientific Research, vol. 14, no. 3, pp. 595– 607, Dec. 1996. [12] N. Rajaratnam and K. Subramanya, “Flow Equation for the Sluice Gate,” Journal of the Irrigation and Drainage Division, vol. 93, no. 3, pp. 167– 186, Sep. 1967, https://doi.org/10.1061/JRCEA4.0000503. [13] A. Zahiri, H. Md. Azamathulla, and S. Bagheri, “Discharge coefficient for compound sharp crested side weirs in subcritical flow conditions,” Journal of Hydrology, vol. 480, pp. 162–166, Feb. 2013, https://doi.org/10.1016/j.jhydrol.2012.12.022. [14] S. A. Sarhan and S. A. Jalil, “Analysis of Simulation Outputs for the Mutual Effect of Flow in Weir and Gate System,” Journal of University of Babylon for Engineering Sciences, vol. 26, no. 6, pp. 48–59, Apr. 2018, https://doi.org/10.29196/jubes.v26i6.1050. [15] M. Muhammad and S. Abdullahi, “Experimental Study of Flow over Sharp Crested Rectangular-Triangular Weir Models,” in Nigeria Engineering Conference Proceedings, Zaria – Nigeria, Jan. 2014, pp. 34–45. [16] M. Piratheepan, N. E. F. Winston, and K. P. P. Pathirana, “Discharge Measurements in Open Channels using Compound Sharp-Crested Weirs,” vol. 40, no. 3, pp. 31-38, Jul. 2007, https://doi.org/10.4038/engineer.v40i3.7144. [17] H. A. Hayawi, A. A. Yahia, G. A. Hayawi, “Free combined flow over a triangular weir and under rectangular gate,” Damascus University Journal, vol. 24, no. 1, pp. 9–22, 2008. [18] A.-A. M. Negm, A. M. Al-Brahim, and A. A. Alhamid, “Combined-free flow over weirs and below gates,” Journal of Hydraulic Research, vol. 40, no. 3, pp. 359–365, May 2002, https://doi.org/10.1080/ 00221680209499950. [19] A. A. Alhamid, A.-A. M. Negm, and A. M. Al-Brahim, “Discharge Equation for Proposed Self-cleaning Device,” Journal of King Saud University – Engineering Sciences, vol. 9, no. 1, pp. 13–23, Jan. 1997, https://doi.org/10.1016/S1018-3639(18)30664-0. [20] S. I. Khassaf and M. Habeeb, “Experimental Investigation for Flow Through Combined Trapezoidal Weir and Rectangular Gate,” International Journal of Scientific & Engineering Research, vol. 5, no. 4, pp. 809–814, 2014. [21] A. A. G. Alniami, D. G. A. M. Hayawi, and H. A. M. Hayawi, “Coefficient Of Discharge For A Combined Hydraulic Measuring Device,” Al-Rafidain Engineering Journal, vol. 17, no. 6, pp. 92–100, Dec. 2009, https://doi.org/10.33899/rengj.2009.43616. [22] J. M. Samani and M. Mazaheri, “Combined Flow over Weir and under Gate,” Journal of Hydraulic Engineering, vol. 135, no. 3, pp. 224–227, Mar. 2009, https://doi.org/10.1061/(ASCE)0733-9429(2009)135:3(224). [23] B. Balouchi and G. Rakhshandehroo, “Using Physical and Soft Computing Models to Evaluate Discharge Coefficient for Combined Weir–Gate Structures Under Free Flow Conditions,” Iranian Journal of Science and Technology, Transactions of Civil Engineering, vol. 42, no. 4, pp. 427–438, Dec. 2018, https://doi.org/10.1007/s40996-018-0117-0. [24] M. A. R. Eltoukhy, F. S. Abdelhaleem, T. H. Nasralla, S. Shaban, “Effect of Compound Weir and below Circular Gate Geometric Characteristics on its Discharge Coefficient,” International Journal of Scientific & Engineering Research, Vol. vol. 11, no. 10, pp. 1115–1130, Oct. 2020. [25] C. E. Kindsvater and R. W. Carter, “Discharge Characteristics of Rectangular Thin-Plate Weirs,” Transactions of the American Society of Civil Engineers, vol. 124, no. 1, pp. 772–801, Jan. 1959, https://doi.org/10.1061/TACEAT.0007696. [26] H. R. Henry, “Discussion of Diffusion of Submerged Jets,” Transactions of ASCE, vol. 115, no. 1, pp. 687–694, Jan. 1950.
프로필 오목부가 탁도 퇴적물에 미치는 영향: 전 세계 대륙 경계에 대한 해저 협곡의 통찰력
Kaiqi Yu a, Elda Miramontes bc, Matthieu J.B. Cartigny d, Yuping Yang a, Jingping Xu a aDepartment of Ocean Science and Engineering, Southern University of Science and Technology, 1088 Xueyuan Rd., Shenzhen 518055, Guangdong, China bMARUM-Center for Marine Environmental Sciences, University of Bremen, Bremen, Germanyc Faculty of Geosciences, University of Bremen, Bremen, Germany dDepartment of Geography, Durham University, South Road, Durham DH1 3LE, UK
Received 10 August 2023, Revised 13 March 2024, Accepted 13 March 2024, Available online 17 March 2024, Version of Record 20 March 2024.
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•The impact of submarine canyon concavity on turbidite deposition was assessed.
•Distribution of turbidite deposits varies with changes in canyon concavity.
•Three distinct deposition patterns were identified.
•The recognized deposition patterns align well with the observed turbidite deposits.
Abstract
Submarine canyons are primary conduits for turbidity currents transporting terrestrial sediments, nutrients, pollutants and organic carbon to the deep sea. The concavity in the longitudinal profile of these canyons (i.e. the downstream flattening rate along the profiles) influences the transport processes and results in variations in turbidite thickness, impacting the transfer and burial of particles. To better understand the controlling mechanisms of canyon concavity on the distribution of turbidite deposits, here we investigate the variation in sediment accumulation as a function of canyon concavity of 20 different modern submarine canyons, distributed on global continental margins. In order to effectively assess the isolated impact of the concavity of 20 different canyons, a series of two-dimensional, depth-resolved numerical simulations are conducted. Simulation results show that the highly concave profile (e.g. Surveyor and Horizon) tends to concentrate the turbidite deposits mainly at the slope break, while nearly straight profiles (e.g. Amazon and Congo) result in deposition focused at the canyon head. Moderately concave profiles with a smoother canyon floor (e.g. Norfolk-Washington and Mukluk) effectively facilitate the downstream transport of suspended sediments in turbidity currents. Furthermore, smooth and steep upper reaches of canyons commonly contribute to sediment bypass (i.e. Mukluk and Chirikof), while low slope angles lead to deposition at upper reaches (i.e. Bounty and Valencia). At lower reaches, the distribution of turbidite deposits is consistent with the occurrence of hydraulic jumps. Under the influence of different canyon concavities, three types of deposition patterns are inferred in this study, and verified by comparison with observed turbidite deposits on the modern or paleo-canyon floor. This study demonstrates a potential difference in sediment transport efficiency of submarine canyons with different concavities, which has potential consequences for sediment and organic carbon transport through submarine canyons.
Introduction
Submarine canyons are pivotal links in source-to-sink systems on continental margins (Sømme et al., 2009; Nyberg et al., 2018; Pope et al., 2022a, Pope et al., 2022b) that provide efficient pathways for moving prodigious volumes of terrestrial materials to the abyssal basin (Spychala et al., 2020; Heijnen et al., 2022). When turbidity currents, the main force that transports the above mentioned sediments (Xu et al., 2004; Xu, 2010; Talling et al., 2013; Stevenson et al., 2015), slow down after entering a flatter and/or wider stretch of the canyon downstream, the laden sediments settle, often rapidly, to form a deposit called turbidite that is known for organic carbon burial, hydrocarbon reserves and the accumulation of microplastics (Galy et al., 2007; Pohl et al., 2020a; Pope et al., 2022b; Pierdomenico et al., 2023). A set of flume experiments by Pohl et al. (2020b) revealed that the variation of bed slope plays a dominant role in controlling the sizes and locations of the deposit: a) a more gently dipping upper slope leads to upstream migration of upslope pinch-out; b) the increase of lower slope results in a decrease of the deposit thickness (Fig. 1a).
From upper continental slopes to deepwater basins, turbidity currents are commonly confined by submarine canyons that facilitate the longer distance transport of sediments (Eggenhuisen et al., 2022; Pope et al., 2022a; Wahab et al., 2022, Li et al., 2023a). The concavity, defined here as the downstream flattening rate of profiles (Covault et al., 2011; Chen et al., 2019; Seybold et al., 2021; Soutter et al., 2021a), of the longitudinal bed profile of the submarine canyons is therefore a key factor that determines hydrodynamic processes of turbidity currents, including the accumulation of sediments along the canyon thalweg (Covault et al., 2014; de Leeuw et al., 2016; Heerema et al., 2022; Heijnen et al., 2022). Due to the comprehensive impacts of sediment supply, grain size, climate change, regional tectonics, associated river and self-incision, the concavity of submarine canyons on global continental margins varies greatly (Parker et al., 1986; Harris and Whiteway, 2011; Casalbore et al., 2018; Nyberg et al., 2018; Soutter et al., 2021a, Li et al., 2023b), which is much more complex than the two constant slope setup of Pohl et al. (2020b)’s flume experiment (Fig. 1a). This raises the question of how the more complex concavity influences the dynamics of turbidity currents and the resultant distribution of turbidite deposits. For instance, the longitudinal profile concavity can also be increased by steepening the upper slope and/or gentling the lower slope of canyons (Fig. 1b). Parameters, known as significant factors influencing flow dynamics, include dip angle (Pohl et al., 2019), bed roughness (Baghalian and Ghodsian, 2020), obstacle presence (Howlett et al., 2019), and confinement conditions (Soutter et al., 2021b). However, the role of channel concavity in determining the downstream evolution of flow dynamics remains poorly understood (Covault et al., 2011; Georgiopoulou and Cartwright, 2013), and it is still unclear whether changes in concavity can result in different locations of pinch-out points and variations in turbidite deposit thicknesses (Pohl et al., 2020b).
In this study, we hypothesize that a more concave profile resulting from a steeper upper slope and a gentler lower slope may lead to a downstream migration of the upslope pinch-out and an increase of deposit thickness (Fig. 1b). This hypothesis is tested in 20 modern submarine canyons (shown in Fig. 2) whose longitudinal profiles are extracted from the GEBCO_2022 grid. Due to the lack of data describing the turbidite thickness trends in these canyons, we used a numerical model (FLOW-3D® software) to simulate the depositional process. The simulation results allow us to address at least two questions: (1) How does the concavity affect the distribution and thickness of turbidite deposits along the canyon thalwegs? (2) What is the impact of canyon concavity on the dynamics of the turbidity currents? Such answers on a global scale are undoubtedly helpful in understanding not only the sediment transport processes but also the efficient transfer and burial of organic carbon along global continental margins.
Section snippets
Submarine canyons used in this study
The longitudinal profiles of 20 modern submarine canyons are obtained using Global Mapper® from a public domain database GEBCO_2022 (doi:https://doi.org/10.5285/e0f0bb80-ab44-2739-e053-6c86abc0289c). The GEBCO_2022 grid provides elevation data, in meters, on a 15 arc-second interval grid. The 20 selected submarine canyons, which span the typical distance covered by turbidity currents, have been chosen from a diverse range of submarine canyon and channel systems that extend at least 250 km
Concavity of longitudinal canyon profiles
The NCI and α values of all 20 canyon profiles utilized in this study are plotted in Fig. 4, indicating the majority of these submarine canyons typically exhibit a concave profile, characterized by a negative NCI, except for the Amazon. In most of the profiles, the NCI is lower than −0.08, with the most concave point (indicated by the minimum ratio α) located closer to the canyon head than to the profile end, and their upper reaches are steeper than lower reaches, typically observed as the
Validation of the hypothesis
As previously mentioned in this paper, one of the primary objectives of this study is to evaluate the hypothesis inferred from the flume tank experiment of Pohl et al. (2020b): whether a more concave canyon profile can exert a comparable influence on turbidite deposits as the steepness of the lower and upper slopes in a slope-break system (Fig. 1). Shown as the modeling results, the deposition pattern of this study is more ‘irregular’ compared with the flume tank experiment (Pohl et al., 2020b
Conclusion
Based on global bathymetry, this study simulates the depositional behavior of turbidity currents flowing through the 20 different submarine canyons on the margins of open ocean and marginal sea. Influenced by the different concavities, the resulted deposition patterns are characterized by a variable distribution of turbidite deposits.
1)The simulation results demonstrate that the accumulation of turbidite deposits is primarily observed in downstream regions near the slope break for highly concave
The authors declare that they have no known competing financial interests or personal relationships that could have appeared to influence the work reported in this paper.
Acknowledgements
This study is supported by the Shenzhen Natural Science Foundation (JCYJ20210324105211031). Matthieu J. B. Cartigny was supported by Royal Society Research Fellowship (DHF/R1/180166). We thank the Chief Editor Zhongyuan Chen, the associate editor and two reviewers for their constructive comments that helped us improve our manuscript.
M. Azpiroz-Zabala et al.Newly recognized turbidity current structure can explain prolonged flushing of submarine canyonsSci. Adv.(2017)
N. Babonneau et al.Sedimentary Architecture in Meanders of a Submarine Channel: Detailed Study of the Present Congo Turbidite Channel (Zaiango Project)J. Sediment. Res.(2010)
R. Basani et al.MassFLOW-3DTM as a simulation tool for turbidity currents: some preliminary results
H.L. Brooks et al.Disconnected submarine lobes as a record of stepped slope evolution over multiple sea-level cyclesGeosphere(2018)
S.A. Chen et al.Aridity is expressed in river topography globallyNature(2019)
J.A. Covault et al.The natural range of submarine canyon-and-channel longitudinal profilesGeosphere(2011)
J.A. Covault et al.Deep-water channel run-out length: insights from seafloor geomorphologyJ. Sediment. Res.(2012)
J.A. Covault et al.Submarine channel initiation, filling and maintenance from sea-floor geomorphology and morphodynamic modelling of cyclic stepsSedimentology(2014)
J. de Leeuw et al.Morphodynamics of submarine channel inception revealed by new experimental approachNat. Commun.(2016)
J. de Leeuw et al.Entrainment and suspension of sand and gravelEarth Surf. Dyn.(2020)
J.T. Eggenhuisen et al.The Sediment Budget Estimator (SBE): a process model for the stochastic estimation of fluxes and budgets of sediment through submarine channel systemsJ. Sediment. Res.(2022)
T.H. Ellison et al.Turbulent entrainment in stratified flowsJ. Fluid Mech.(1959)
R.I. Ferguson et al.A simple universal equation for grain settling velocityJ. Sediment. Res.(2004)
A.M. Fernandes et al.Flow substrate interactions in aggrading and degrading submarine channelsJ. Sediment. Res.(2020)
Flow ScienceFLOW-3D User Manual v11. 2(2018)
V. Galy et al.Efficient organic carbon burial in the Bengal fan sustained by the Himalayan erosional systemNature(2007)
Z. Ge et al.How is a turbidite actually deposited?Sci. Adv.(2022)
B. Gomez et al.An assessment of bed load sediment transport formulae for gravel bed riversWater Resour. Res.(1989)
W.H. Graf et al.Suspension flows in open channels; experimental studyJ. Hydraul. Res.(2010)
C.J. Heerema et al.How distinctive are flood-triggered turbidity currents?J. Sediment. Res.(2022)
D.M. Howlett et al.Response of unconfined turbidity current to deep-water fold and thrust belt topography: orthogonal incidence on solitary and segmented foldsSedimentology(2019)
S. Kim et al.Seismostratigraphic and geomorphic evidence for the glacial history of the Northwestern Chukchi Margin, Arctic OceanJ. Geophys. Res. Earth Surf.(2021)
M. Liu et al.Two distinct types of turbidity currents observed in the Manila Trench, South China SeaCommun. Earth Environ.(2023)
There are more references available in the full text version of this article.
Alireza Khoshkonesh1, Blaise Nsom2, Saeid Okhravi3*, Fariba Ahmadi Dehrashid4, Payam Heidarian5, Silvia DiFrancesco6 1 Department of Geography, School of Social Sciences, History, and Philosophy, Birkbeck University of London, London, UK. 2 Université de Bretagne Occidentale. IRDL/UBO UMR CNRS 6027. Rue de Kergoat, 29285 Brest, France. 3 Institute of Hydrology, Slovak Academy of Sciences, Dúbravská cesta 9, 84104, Bratislava, Slovak Republic. 4Department of Water Science and Engineering, Faculty of Agriculture, Bu-Ali Sina University, 65178-38695, Hamedan, Iran. 5 Department of Civil, Environmental, Architectural Engineering and Mathematics, University of Brescia, 25123 Brescia, Italy. 6Niccol`o Cusano University, via Don C. Gnocchi 3, 00166 Rome, Italy. * Corresponding author. Tel.: +421-944624921. E-mail: saeid.okhravi@savba.sk
Abstract
This study aimed to comprehensively investigate the influence of substrate level difference and material composition on dam break wave evolution over two different erodible beds. Utilizing the Volume of Fluid (VOF) method, we tracked free surface advection and reproduced wave evolution using experimental data from the literature. For model validation, a comprehensive sensitivity analysis encompassed mesh resolution, turbulence simulation methods, and bed load transport equations. The implementation of Large Eddy Simulation (LES), non-equilibrium sediment flux, and van Rijn’s (1984) bed load formula yielded higher accuracy compared to alternative approaches. The findings emphasize the significant effect of substrate level difference and material composition on dam break morphodynamic characteristics. Decreasing substrate level disparity led to reduced flow velocity, wavefront progression, free surface height, substrate erosion, and other pertinent parameters. Initial air entrapment proved substantial at the wavefront, illustrating pronounced air-water interaction along the bottom interface. The Shields parameter experienced a one-third reduction as substrate level difference quadrupled, with the highest near-bed concentration observed at the wavefront. This research provides fresh insights into the complex interplay of factors governing dam break wave propagation and morphological changes, advancing our comprehension of this intricate phenomenon.
이 연구는 두 개의 서로 다른 침식층에 대한 댐 파괴파 진화에 대한 기질 수준 차이와 재료 구성의 영향을 종합적으로 조사하는 것을 목표로 했습니다. VOF(유체량) 방법을 활용하여 자유 표면 이류를 추적하고 문헌의 실험 데이터를 사용하여 파동 진화를 재현했습니다.
모델 검증을 위해 메쉬 해상도, 난류 시뮬레이션 방법 및 침대 하중 전달 방정식을 포함하는 포괄적인 민감도 분석을 수행했습니다. LES(Large Eddy Simulation), 비평형 퇴적물 플럭스 및 van Rijn(1984)의 하상 부하 공식의 구현은 대체 접근 방식에 비해 더 높은 정확도를 산출했습니다.
연구 결과는 댐 붕괴 형태역학적 특성에 대한 기질 수준 차이와 재료 구성의 중요한 영향을 강조합니다. 기판 수준 차이가 감소하면 유속, 파면 진행, 자유 표면 높이, 기판 침식 및 기타 관련 매개변수가 감소했습니다.
초기 공기 포집은 파면에서 상당한 것으로 입증되었으며, 이는 바닥 경계면을 따라 뚜렷한 공기-물 상호 작용을 보여줍니다. 기판 레벨 차이가 4배로 증가함에 따라 Shields 매개변수는 1/3로 감소했으며, 파면에서 가장 높은 베드 근처 농도가 관찰되었습니다.
이 연구는 댐 파괴파 전파와 형태학적 변화를 지배하는 요인들의 복잡한 상호 작용에 대한 새로운 통찰력을 제공하여 이 복잡한 현상에 대한 이해를 향상시킵니다.
Fig. 3. Free surface and substrate profiles in all Sp and Ls cases at t = 1 s, t = 3 s, and t = 5 s, arranged left to right (note: the colour contours
correspond to the horizontal component of the flow velocity (u), expressed in m/s).
Aleixo, R., Soares-Frazão, S., Zech, Y., 2010. Velocity profiles in dam-break flows: water and sediment layers. In: Proc. Int. Conf. on Fluvial Hydraulics “River Flow 2010”, pp. 533–540. An, S., Ku, H., Julien, P.Y., 2015. Numerical modelling of local scour caused by submerged jets. Maejo Int. J. Sci. Technol., 9, 3, 328–343. Bahmanpouri, F., Daliri, M., Khoshkonesh, A., Namin, M.M., Buccino, M., 2021. Bed compaction effect on dam break flow over erodible bed; experimental and numerical modeling. J. Hydrol., 594, 125645. https://doi.org/10.1016/j.jhydrol.2020.125645 Baklanov, A., 2007. Environmental risk and assessment modelling – scientific needs and expected advancements. In: Ebel, A., Davitashvili, T. (Eds.): Air, Water and Soil Quality Modelling for Risk and Impact Assessment Springer, Dordrecht, pp. 29–44. Biscarini, C., Di Francesco, S., Nardi, F., Manciola, P., 2013. Detailed simulation of complex hydraulic problems with macroscopic and mesoscopic mathematical methods. Math. Probl. Eng., 928309. https://doi.org/10.1155/2013/928309 Cao, Z., Pender, G., Wallis, S., Carling, P., 2004. Computational dam-break hydraulics over erodible sediment bed. J. Hydraul. Eng., 130, 7, 689–703. Catucci, D., Briganti, R., Heller, V., 2021. Numerical validation of novel scaling laws for air entrainment in water. Proc. R. Soc. A, 477, 2255,20210339. https://doi.org/10.1098/rspa.2021.0339 Dehrashid, F.A., Heidari, M., Rahimi, H., Khoshkonesh, A., Yuan, S., Tang, X., Lu, C., Wang, X., 2023. CFD modeling the flow dynamics in an open channel with double-layered vegetation. Model. Earth Syst. Environ., 9, 1, 543–555. Desombre, J., Morichon, D., Mory, M., 2013. RANS v2-f simulation of a swash event: Detailed flow structure. Coastal Eng., 71, 1–12. Dodangeh, E., Afzalimehr, H., 2022. Incipient motion of sediment particles in the presence of bed forms under decelerating and accelerating flows. J. Hydrol. Hydromech., 70, 1, 89–102. Dong, Z., Wang, J., Vetsch, D.F., Boes, R.M., Tan, G., 2019. Numerical simulation of air entrainment on stepped spillways. In: E-proceedings of the 38th IAHR World Congress (pp. 1494). September 1–6, 2019, Panama City, Panama. DOI: 10.3850/38WC092019-0755 Flow3D [computer software]. 2023. Santa Fe, NM: Flow Science, Inc. Fraccarollo, L., Capart, H., 2002. Riemann wave description of erosional dam-break flows. J. Fluid Mech., 461, 183–228. Gu, Z., Wang, T., Meng, W., Yu, C.H., An, R., 2023. Numerical investigation of silted-up dam-break flow with different silted-up sediment heights. Water Supply, 23, 2, 599–614. Gualtieri, P., De Felice, S., Pasquino, V., Doria, G.P., 2018. Use of conventional flow resistance equations and a model for the Nikuradse roughness in vegetated flows at high submergence. J. Hydrol. Hydromech., 66, 1, 107–120. Heller, V., 2011. Scale effects in physical hydraulic engineering models. J. Hydraul. Res., 49, 3, 293–306. Hirt, C.W., 2003. Modeling turbulent entrainment of air at a free surface. Flow Science, Inc. Hirt, C.W., Nichols, B.D., 1981. Volume of fluid (VOF) method for the dynamics of free boundaries. J. Comput. Phys., 39, 1, 201– 225. Issakhov, A., Zhandaulet, Y., Nogaeva, A., 2018. Numerical simulation of dam break flow for various forms of the obstacle by VOF method. Int. J. Multiphase Flow, 109, 191–206. Khayyer, A., Gotoh, H., 2010. On particle-based simulation of a dam break over a wet bed. J. Hydraul. Res., 48, 2, 238–249. Khoshkonesh, A., Daliri, M., Riaz, K., Dehrashid, F.A., Bahmanpouri, F., Di Francesco, S., 2022. Dam-break flow dynamics over a stepped channel with vegetation. J. Hydrol., 613,128395. https://doi.org/10.1016/j.jhydrol.2022.128395 Khoshkonesh, A., Nsom, B., Gohari, S., Banejad, H., 2019. A comprehensive study on dam-break flow over dry and wet beds. Ocean Eng., 188, 106279. https://doi.org/10.1016/j.oceaneng.2019.106279 Khoshkonesh, A., Sadeghi, S.H., Gohari, S., Karimpour, S., Oodi, S., Di Francesco, S., 2023. Study of dam-break flow over a vegetated channel with and without a drop. Water Resour. Manage., 37, 5, 2107–2123. Khosravi, K., Chegini, A.H.N., Cooper, J., Mao, L., Habibnejad, M., Shahedi, K., Binns, A., 2021. A laboratory investigation of bedload transport of gravel sediments under dam break flow. Int. J. Sediment Res., 36, 2, 229–234. Kim, Y., Zhou, Z., Hsu, T.J., Puleo, J.A., 2017. Large eddy simulation of dam‐break‐driven swash on a rough‐planar beach. J. Geophys. Res.: Oceans, 122, 2, 1274–1296. Kocaman, S., Ozmen-Cagatay, H., 2012. The effect of lateral channel contraction on dam break flows: Laboratory experiment. J. Hydrol., 432, 145–153. Leal, J.G., Ferreira, R.M., Cardoso, A.H., 2006. Dam-break wavefront celerity. J. Hydraul. Eng., 132, 1, 69–76. Leal, J.G.A.B., Ferreira, R.M., Cardoso, A.H., 2003. Dam-break wave propagation over a cohesionless erodible bed. In: Proc. 30rd IAHR Congress, 100, 261–268. Li, Y. L., Ma, Y., Deng, R., Jiang, D.P., Hu, Z., 2019. Research on dam-break induced tsunami bore acting on the triangular breakwater based on high order 3D CLSVOF-THINC/WLICIBM approaching. Ocean Eng., 182, 645–659. Li, Y.L., Yu, C.H., 2019. Research on dam-break flow induced front wave impacting a vertical wall based on the CLSVOF and level set methods. Ocean Eng., 178, 442–462. Mei, S., Chen, S., Zhong, Q., Shan, Y., 2022. Detailed numerical modeling for breach hydrograph and morphology evolution during landslide dam breaching. Landslides, 19, 12, 2925–2949. Meng, W., Yu, C.H., Li, J., An, R., 2022. Three-dimensional simulation of silted-up dam-break flow striking a rigid structure. Ocean Eng., 261, 112042. https://doi.org/10.1016/j.oceaneng.2022.112042 Meyer-Peter, E., Müller, R., 1948. Formulas for bed-load transport. In: IAHSR 2nd meeting, Stockholm, appendix 2. IAHR. Nielsen, P., 1984. Field measurements of time-averaged suspended sediment concentrations under waves. Coastal Eng., 8, 1, 51–72. Nielsen, P., 2018. Bed shear stress, surface shape and velocity field near the tips of dam-breaks, tsunami and wave runup. Coastal Eng., 138, 126–131. Nsom, B., Latrache, N., Ramifidisoa, L., Khoshkonesh, A., 2019. Analytical solution to the stability of gravity-driven stratified flow of two liquids over an inclined plane. In: 24th French Mechanics Congress in Brest. Brest, p. 244178. Nsom, B., Ravelo, B., Ndong, W., 2008. Flow regimes in horizontal viscous dam-break flow of Cayous mud. Appl. Rheol., 18, 4, 43577-1. https://doi.org/10.1515/arh-2008-0012 Oguzhan, S., Aksoy, A.O., 2020. Experimental investigation of the effect of vegetation on dam break flood waves. J. Hydrol. Hydromech., 68, 3, 231–241. Okhravi, S., Gohari, S., Alemi, M., Maia, R., 2022. Effects of bedmaterial gradation on clear water scour at single and group of piles. J. Hydrol. Hydromech., 70, 1, 114–127. Okhravi, S., Gohari, S., Alemi, M., Maia, R., 2023. Numerical modeling of local scour of non-uniform graded sediment for two arrangements of pile groups. Int. J. Sediment Res., 38, 4, 597–614. Parambath, A., 2010. Impact of tsunamis on near shore wind power units. Master’s Thesis. Texas A&M University. Available electronically from https://hdl.handle.net/1969.1/ETD-TAMU2010-12-8919 Pintado-Patiño, J.C., Puleo, J.A., Krafft, D., Torres-Freyermuth, A.,
Hydrodynamics and sediment transport under a dambreak-driven swash: An experimental study. Coastal Eng., 170,
https://doi.org/10.1016/j.coastaleng.2021.103986 Riaz, K., Aslam, H.M.S., Yaseen, M.W., Ahmad, H.H., Khoshkonesh, A., Noshin, S., 2022. Flood frequency analysis and hydraulic design of bridge at Mashan on river Kunhar. Arch. Hydroengineering Environ. Mech., 69, 1, 1–12. Ritter, A., 1892. Die Fortpflanzung der Wasserwellen. Zeitschrift des Vereines Deutscher Ingenieure, 36, 33, 947–954. (In German.) Smagorinsky, J., 1963. General circulation experiments with the primitive equations: I. The basic experiment. Mon. Weather Rev., 91, 3, 99–164. Soulsby, R.L., 1997. Dynamics of marine sands: a manual for practical applications. Oceanogr. Lit. Rev., 9, 44, 947. Spinewine, B., Capart, H., 2013. Intense bed-load due to a sudden dam-break. J. Fluid Mech., 731, 579–614. Van Rijn, L.C., 1984. Sediment transport, part I: bed load transport. J. Hydraul. Eng., 110, 10, 1431–1456. Vosoughi, F., Rakhshandehroo, G., Nikoo, M.R., Sadegh, M.,
Experimental study and numerical verification of silted-up dam break. J. Hydrol., 590, 125267. https://doi.org/10.1016/j.jhydrol.2020.125267 Wu, W., Wang, S.S., 2008. One-dimensional explicit finite-volume model for sediment transport. J. Hydraul. Res., 46, 1, 87–98. Xu, T., Huai, W., Liu, H., 2023. MPS-based simulation of dam-break wave propagation over wet beds with a sediment layer. Ocean Eng., 281, 115035. https://doi.org/10.1016/j.oceaneng.2023.115035 Yang, S., Yang, W., Qin, S., Li, Q., Yang, B., 2018. Numerical study on characteristics of dam-break wave. Ocean Eng., 159, 358–371. Yao, G.F., 2004. Development of new pressure-velocity solvers in FLOW-3D. Flow Science, Inc., USA.
대규모 홍수 구호 작업에 대한 일반적인 흐름 회로 현상의 영향은 많은 보고서에서 연구되었으며 비교적 자세하게 연구되었습니다. 그러나 유량 변동이 제방 암거 작동에 미치는 악영향에 대해서는 많이 언급되지 않았습니다.
실제 운영에 따르면 에너지 소산 탱크 또는 뒷마당의 국부적 불안정성, 운하 지붕의 부력 또는 붕괴, 하류 또는 제방 본체 일부 등 암거 구조 및 제방 시스템에 영향을 미치는 흐름 회로의 부정적인 영향이 많이 있음을 알 수 있습니다.
홍수기 운영 시 암거 및 제방의 안전성을 확보하기 위해서는 유동현상으로 인한 사업에 미치는 유해영향을 최소화할 필요가 있으며 본 연구에서는 이를 검증하고자 합니다.
제방을 통과하는 암거의 동적 회로 현상은 FLOW-3D 소프트웨어를 사용하여 수학적 모델로 시뮬레이션됩니다. 제방을 통한 암거 작동에 잠재적으로 영향을 미칠 수 있는 동맥 유형이 연구에서 구체적으로 논의됩니다.
동시에 암거와 제방 위치는 이 기사에서 지적한 흐름 회로 현상에 의해 부정적인 영향을 받을 가능성이 더 높습니다. 또한 Phuc Tho 마을의 제방을 가로지르는 암거 게이트 뒤의 회로 현상을 줄이기 위한 구조적, 비구조적 조치도 연구되고 평가됩니다.
이를 토대로 운영하수관로의 구조를 저해하지 않고 회로를 축소할 수 있는 방안을 제안한다.
The flow fluctuation has been studied in quite extensively for large-scale flood control works, however, this issue has been less addressed for culverts through levee. The operational experience has shown that there are many negative impacts of flow dynamics on the culvert structure and levee system such as the uplift instability, the local surface erosion of the stilling basin or the downstream channel, collapsing of part of the levee system, etc. According to the requirement of sluice and levee safety during flood season, the task of reducing fluctuation needs to be performed. The article not only pointed out the types of fluctuation that need to pay attention behind the operation gate, but also specified the locations where the sluice and levee could be destructively affected by the fluctuation. In addition, structural and non-structural countermeasures reducing negative impacts of fluctuation are also mentioned. Research has proposed measures to reduce flow dynamics for operating culverts without interfering with their structure.
Hệ thống giám sát thiên tai Việt Nam (2023). http://vndms.dmc.gov.vn/ (Accessed: 28 February 2023). Viện Thủy Công (2015) Nghiên cứu đánh giá các sự cố đê, cống dưới đê và đề xuất giải pháp xử lý. HyCI. Nguyễn Phương Dung (2017) Thí nghiệm xác định ảnh hưởng của áp lực thủy động tới độ dày bản đáy bể tiêu năng và sân sau ở công trình tháo. TLU. Nguyễn Chiến (2015) Tính toán thủy lực công trình tháo nước. NXB Xây dựng. Nguyễn Ngọc Thắng (2019) Đề cương Đề tài cấp Bộ ‘Nghiên cứu đánh giá nguyên nhân, các biện pháp đã áp dụng và đề xuất giải pháp xử lý sự cố cống dưới đê đảm bảo an toàn chống lũ’. ‘Flow 3D’ (2023). (User’s Manual). Yong Peng (2018) ‘Experimental Optimization of Gate-Opening Modes to Minimize Near-Field Vibrations in Hydropower Stations’, Water, 10(1435). Available at: https://doi.org/doi:10.3390/w10101435. Guibing HUANG (2021) ‘Pressure Fluctuations Characteristics of the Stilling Basin with a Negative Step’, Hydraulic and Civil Engineering Technology VI [Preprint]. Available at: https://doi.org/doi:10.3233/ATDE210196. O. Fecarotta (2016) Experimental results on the physical model of an USBR type II stilling basin. Taylor & Francis Group.
Ali Poorkarimi1 Khaled Mafakheri2 Shahrzad Maleki2
Journal of Hydraulic Structures J. Hydraul. Struct., 2023; 9(4): 76-87 DOI: 10.22055/jhs.2024.44817.1265
Abstract
중력에 의한 침전은 부유 물질을 제거하기 위해 물과 폐수 처리 공정에 널리 적용됩니다. 이 연구에서는 침전조의 제거 효율에 대한 입구 및 배플 위치의 영향을 간략하게 설명합니다. 실험은 CCD(중심복합설계) 방법론을 기반으로 수행되었습니다. 전산유체역학(CFD)은 유압 설계, 미래 발전소에 대한 계획 연구, 토목 유지 관리 및 공급 효율성과 관련된 복잡한 문제를 모델링하고 분석하는 데 광범위하게 사용됩니다. 본 연구에서는 입구 높이, 입구로부터 배플까지의 거리, 배플 높이의 다양한 조건에 따른 영향을 조사하였다. CCD 접근 방식을 사용하여 얻은 데이터를 분석하면 축소된 2차 모델이 R2 = 0.77의 결정 계수로 부유 물질 제거를 예측할 수 있음이 나타났습니다. 연구 결과, 유입구와 배플의 부적절한 위치는 침전조의 효율에 부정적인 영향을 미칠 수 있음을 보여주었습니다. 입구 높이, 배플 거리, 배플 높이의 최적 값은 각각 0.87m, 0.77m, 0.56m였으며 제거 효율은 80.6%였습니다.
Sedimentation due to gravitation is applied widely in water and wastewater treatment processes to remove suspended solids. This study outlines the effect of the inlet and baffle position on the removal efficiency of sedimentation tanks. Experiments were carried out based on the central composite design (CCD) methodology. Computational fluid dynamics (CFD) is used extensively to model and analyze complex issues related to hydraulic design, planning studies for future generating stations, civil maintenance, and supply efficiency. In this study, the effect of different conditions of inlet elevation, baffle’s distance from the inlet, and baffle height were investigated. Analysis of the obtained data with a CCD approach illustrated that the reduced quadratic model can predict the suspended solids removal with a coefficient of determination of R2 = 0.77. The results showed that the inappropriate position of the inlet and the baffle can have a negative effect on the efficiency of the sedimentation tank. The optimal values of inlet elevation, baffle distance, and baffle height were 0.87 m, 0.77 m, and 0.56 m respectively with 80.6% removal efficiency.
Figure 3. Computed contour of velocity magnitude (m/s) for Run 1 to Run 15.
References
Shahrokhi, M., F. Rostami, M.A. Md. Said, S.R.S. Yazdi, and Syafalni, (2013). Experimental investigation of the influence of baffle position on the flow field, sediment concentration, and efficiency of rectangular primary sedimentation tanks. Journal of Hydraulic Engineering,. 139(1): p. 88-94.
Shahrokhi, M., F. Rostami, M.A.M. Said, and S.R.S. Yazdi, (2012). The effect of number of baffles on the improvement efficiency of primary sedimentation tanks. Applied Mathematical Modelling,. 36(8): p. 3725-3735.
Borna, M., A. Janfeshan, E. Merufinia, and A. Asnaashari, (2014). Numerical simulations of distribution and sediment transmission in pre-settled pools using Finite Volume Method and comparison with experimental results. Journal of Civil Engineering and Urbanism,. 4(3): p. 287-292.
Rad, M.J., P.E. Firoozabadi, and F. Rostami, (2022). Numerical Investigation of the Effect Dimensions of Rectangular Sedimentation Tanks on Its Hydraulic Efficiency Using Flow-3D Software. Acta Technica Jaurinensis,. 15(4): p. 207-220.
Hirom, K. and T.T. Devi, (2022). Application of computational fluid dynamics in sedimentation tank design and its recent developments: A review. Water, Air, & Soil Pollution,. 233: p. 1- 26.
Shahrokhi, M., F. Rostami, M.A.M. Said, S.-R. Sabbagh-Yazdi, S. Syafalni, and R. Abdullah, (2012). The effect of baffle angle on primary sedimentation tank efficiency. Canadian Journal of Civil Engineering,. 39(3): p. 293-303.
Tarpagkou, R. and A. Pantokratoras, (2014). The influence of lamellar settler in sedimentation tanks for potable water treatment—A computational fluid dynamic study. Powder Technology,. 268: p. 139-149.
Ekama, G. and P. Marais, (2004). Assessing the applicability of the 1D flux theory to full-scale secondary settling tank design with a 2D hydrodynamic model. Water research,. 38(3): p. 495- 506.
Gharagozian, A., (1998). Circular secondary clarifier investigations using a numerical model., University of California, Los Angeles.
Shahrokhi, M., F. Rostami, and M.A.M. Said, (2013). Numerical modeling of baffle location effects on the flow pattern of primary sedimentation tanks. Applied Mathematical Modelling,. 37(6): p. 4486-4496.
Razmi, A.M., R. Bakhtyar, B. Firoozabadi, and D.A. Barry, (2013). Experiments and numerical modeling of baffle configuration effects on the performance of sedimentation tanks. Canadian Journal of Civil Engineering,. 40(2): p. 140-150.
Liu, Y., P. Zhang, and W. Wei, (2016). Simulation of effect of a baffle on the flow patterns and hydraulic efficiency in a sedimentation tank. Desalination and Water Treatment,. 57(54): p. 25950-25959.
Saeedi, E., E. Behnamtalab, and S. Salehi Neyshabouri, (2020). Numerical simulation of baffle effect on the performance of sedimentation basin. Water and environment journal,. 34(2): p. 212-222.
Miri, J.K., B. Aminnejad, and A. Zahiri, (2023). Numerical Study of Flow Pattern, Sediment Field and Effect of the Arrangement of Guiding Blades (Baffles) on Sedimentation in PreSedimentation Basins by Numerical Models. Water Resources,. 50(1): p. 68-81.
Heydari, M.M., M. Rahbani, and S.M.M. Jamal, (2014). Experimental and numerical investigations of baffle effect on the removal efficiency of sedimentation basin. Advances in Environmental Biology,: p. 1015-1022.
Guo, H., S.J. Ki, S. Oh, Y.M. Kim, S. Wang, and J.H. Kim, (2017). Numerical simulation of separation process for enhancing fine particle removal in tertiary sedimentation tank mounting adjustable baffle. Chemical engineering science,. 158: p. 21-29.
Farhoud Kalateh a,*, Ehsan Aminvash a and Rasoul Daneshfaraz b a Faculty of Civil Engineering, University of Tabriz, Tabriz, Iran b Faculty of Engineering, University of Maragheh, Maragheh, Iran *Corresponding author. E-mail: f.kalateh@gmail.com
ABSTRACT
The main goal of the present study is to investigate the effects of macro-roughnesses downstream of the inclined drop through numerical models. Due to the vital importance of geometrical properties of the macro-roughnesses in the hydraulic performance and efficient energy dissipation downstream of inclined drops, two different geometries of macro-roughnesses, i.e., semi-circular and triangular geometries, have been investigated using the Flow-3D model. Numerical simulation showed that with the flow rate increase and relative critical depth, the flow energy consumption has decreased. Also, relative energy dissipation increases with the increase in height and slope angle, so that this amount of increase in energy loss compared to the smooth bed in semi-circular and triangular elements is 86.39 and 76.80%, respectively, in the inclined drop with a height of 15 cm and 86.99 and 65.78% in the drop with a height of 20 cm. The Froude number downstream on the uneven bed has been dramatically reduced, so this amount of reduction has been approximately 47 and 54% compared to the control condition. The relative depth of the downstream has also increased due to the turbulence of the flow on the uneven bed with the increase in the flow rate.
본 연구의 주요 목표는 수치 모델을 통해 경사 낙하 하류의 거시 거칠기 효과를 조사하는 것입니다. 수력학적 성능과 경사 낙하 하류의 효율적인 에너지 소산에서 거시 거칠기의 기하학적 특성이 매우 중요하기 때문에 두 가지 서로 다른 거시 거칠기 형상, 즉 반원형 및 삼각형 형상이 Flow를 사용하여 조사되었습니다.
3D 모델 수치 시뮬레이션을 통해 유량이 증가하고 상대 임계 깊이가 증가함에 따라 유동 에너지 소비가 감소하는 것으로 나타났습니다. 또한, 높이와 경사각이 증가함에 따라 상대적인 에너지 소산도 증가하는데, 반원형 요소와 삼각형 요소에서 평활층에 비해 에너지 손실의 증가량은 경사낙하에서 각각 86.39%와 76.80%입니다.
높이 15cm, 높이 20cm의 드롭에서 86.99%, 65.78%입니다. 고르지 못한 베드 하류의 프루드 수가 극적으로 감소하여 이 감소량은 대조 조건에 비해 약 47%와 54%였습니다. 유속이 증가함에 따라 고르지 못한 층에서의 흐름의 난류로 인해 하류의 상대적 깊이도 증가했습니다.
Key words
flow energy dissipation, Froude number, inclined drop, numerical simulation
Figure 1 | Schematic of the present research model with dimensions and macro-roughnesses installed.Figure 2 | Meshing, boundary condition, and solution field network
REFERENCES
Abbaspour, A., Taghavianpour, T. & Arvanaghi, H. 2019 Experimental study of the hydraulic jump on the reverse bed with porous screens. Applied Water Science 9, 155. Abbaspour, A., Shiravani, P. & Hosseinzadeh Dalir, A. 2021 Experimental study of the energy dissipation on rough ramps. ISH Journal of Hydraulic Engineering 27, 334–342. Akib, S., Ahmed, A. A., Imran, H. M., Mahidin, M. F., Ahmed, H. S. & Rahman, S. 2015 Properties of a hydraulic jump over apparent corrugated beds. Dam Engineering 25, 65–77. AlTalib, A. N., Mohammed, A. Y. & Hayawi, H. A. 2015 Hydraulic jump and energy dissipation downstream stepped weir. Flow Measurement and Instrumentation 69, 101616. Bayon-Barrachina, A. & Lopez-Jimenez, P. A. 2015 Numerical analysis of hydraulic jumps using OpenFOAM. Journal of Hydroinformatics 17, 662–678. Canovaro, F. & Solari, L. 2007 Dissipative analogies between a schematic macro-roughness arrangement and step–pool morphology. Earth Surface Processes and Landforms: The Journal of the British Geomorphological Research Group 32, 1628–1640. Daneshfaraz, R., Ghaderi, A., Akhtari, A. & Di Francesco, S. 2020 On the effect of block roughness in ogee spill-ways with flip buckets. Fluids 5, 182. Daneshfaraz, R., Aminvash, E., Di Francesco, S., Najibi, A. & Abraham, J. 2021a Three-dimensional study of the effect of block roughness geometry on inclined drop. Numerical Methods in Civil Engineering 6, 1–9. Daneshfaraz, R., Aminvash, E., Ghaderi, A., Abraham, J. & Bagherzadeh, M. 2021b SVM performance for predicting the effect of horizontal screen diameters on the hydraulic parameters of a vertical drop. Applied Science 11, 4238. Daneshfaraz, R., Aminvash, E., Ghaderi, A., Kuriqi, A. & Abraham, J. 2021c Three-dimensional investigation of hydraulic properties of vertical drop in the presence of step and grid dissipators. Symmetry 13, 895. Dey, S. & Sarkar, A. 2008 Characteristics of turbulent flow in submerged jumps on rough beds. Journal of Engineering Mechanics 134, 49–59. Ead, S. A. & Rajaratnam, N. 2002 Hydraulic jumps on corrugated beds. Journal of Hydraulic Engineering 128, 656–663. Fang, H., Han, X., He, G. & Dey, S. 2018 Influence of permeable beds on hydraulically macro-rough flow. Journal of Fluid Mechanics 847, 552–590. Federico, I., Marrone, S., Colagrossi, A., Aristodemo, F. & Antuono, M. 2019 Simulating 2D open-channel flows through an SPH model. European Journal of Mechanics-B/Fluids 34, 35–46. Ghaderi, A., Dasineh, M., Aristodemo, F. & Aricò, C. 2021 Numerical simulations of the flow field of a submerged hydraulic jump over triangular macroroughnesses. Water 13, 674. Ghare, A. D., Ingl, R. N., Porey, P. D. & Gokhale, S. S. 2010 Block ramp design for efficient energy dissipation. Journal of Energy Dissipation 136, 1–5. Habibzadeh, A., Rajaratnam, N. & Loewen, M. 2019 Characteristics of the flow field downstream of free and submerged hydraulic jumps. Proceedings of the Institution of Civil Engineers-Water Management 172, 180–194. Hajiahmadi, A., Ghaeini-Hessaroeyeh, M. & Khanjani, M. J. 2021 Experimental evaluation of vertical shaft efficiency in vortex flow energy dissipation. International Journal of Civil Engineering 19, 1445–1455.
Katourani, S. & Kashefipour, S. M. 2012 Effect of the geometric characteristics of baffle on hydraulic flow condition in baffled apron drop. Irrigation Sciences and Engineering 37, 51–59. Kurdistani, S. M., Varaki, M. E. & Moayedi Moshkaposhti, M. 2024 Apron and macro roughness as scour countermeasures downstream of block ramps. ISH Journal of Hydraulic Engineering 1–9. Lopardo, R. A. 2013 Extreme velocity fluctuations below free hydraulic jumps. Journal of Engineering 1–5. Mahmoudi-Rad, M. & Najafzadeh, M. 2023 Experimental evaluation of the energy dissipation efficiency of the vortex flow section of drop shafts. Scientific Reports 13, 1679. Matin, M. A., Hasan, M. & Islam, M. R. 2018 Experiment on hydraulic jump in sudden expansion in a sloping rectangular channel. Journal of Civil Engineering 36, 65–77. Moghadam, K. F., Banihashemi, M. A., Badiei, P. & Shirkavand, A. 2019 A numerical approach to solve fluid-solid two-phase flows using time splitting projection method with a pressure correction technique. Progress in Computational Fluid Dynamics, an International Journal 19, 357–367. Moghadam, K. F., Banihashemi, M. A., Badiei, P. & Shirkavand, A. 2020 A time-splitting pressure-correction projection method for complete two-fluid modeling of a local scour hole. International Journal of Sediment Research 35, 395–407. Moradi-SabzKoohi, A., Kashefipour, S. M. & Bina, M. 2011 Experimental comparison of energy dissipation on drop structures. JWSS – Isfahan University of Technology 15, 209–223. (in Persian). Mouaze, D., Murzyn, F. & Chaplin, J. R. 2005 Free surface length scale estimation in hydraulic jumps. Journal of Fluids Engineering 127, 1191–1193. Nicosia, A., Carollo, F. G. & Ferro, V. 2023 Effects of boulder arrangement on flow resistance due to macro-scale bed roughness. Water 15, 349. Ohtsu, I. & Yasuda, Y. 1991 Hydraulic jump in sloping channel. Journal of Hydraulic Engineering 117, 905–921. Pagliara, S. & Palermo, M. 2012 Effect of stilling basin geometry on the dissipative process in the presence of block ramps. Journal of Irrigation and Drainage Engineering 138, 1027–1031. Pagliara, S., Das, R. & Palermo, M. 2008 Energy dissipation on submerged block ramps. Journal of Irrigation and Drainage Engineering 134, 527–532. Pagliara, S., Roshni, T. & Palermo, M. 2015 Energy dissipation over large-scale roughness for both transition and uniform flow conditions. International Journal of Civil Engineering 13, 341–346. Parsaie, A., Dehdar-Behbahani, S. & Haghiabi, A. H. 2016 Numerical modeling of cavitation on spillway’s flip bucket. Frontiers of Structural and Civil Engineering 10, 438–444. Pourabdollah, N., Heidarpour, M. & Abedi Koupai, J. 2018 Characteristics of free and submerged hydraulic jumps in different stilling basins. In: Proceedings of the Institution of Civil Engineers-Water Management. Thomas Telford Ltd, pp. 1–11. Roushangar, K. & Ghasempour, R. 2019 Evaluation of the impact of channel geometry and rough elements arrangement in hydraulic jump energy dissipation via SVM. Journal of Hydroinformatics 21, 92–103. Samadi-Boroujeni, H., Ghazali, M., Gorbani, B. & Nafchi, R. F. 2013 Effect of triangular corrugated beds on the hydraulic jump characteristics. Canadian Journal of Civil Engineering 40, 841–847. Shekari, Y., Javan, M. & Eghbalzadeh, A. 2014 Three-dimensional numerical study of submerged hydraulic jumps. Arabian Journal for Science and Engineering 39, 6969–6981. Tokyay, N. D., Evcimen, T. U. & Şimsek, Ç. 2011 Forced hydraulic jump on non-protruding rough beds. Canadian Journal of Civil Engineering 38, 1136–1144. Wagner, W. E. 1956 Hydraulic model studies of the check intake structure-potholes East canal. Bureau of Reclamation Hydraulic Laboratory Report Hyd, 411. Witt, A., Gulliver, J. S. & Shen, L. 2018 Numerical investigation of vorticity and bubble clustering in an air-entraining hydraulic jump. Computers & Fluids 172, 162–180.
험프 웨어는 수위 제어 및 배출 측정을 위한 기존의 수력 구조물 중 하나입니다. 상류 및 하류 경사로의 경사는 자유 및 침수 흐름 조건 모두에서 험프 웨어의 성능에 영향을 미치는 설계 매개변수입니다.
침수된 험프보의 유출 특성 및 수위 변화에 대한 램프 경사 및 유출의 영향을 조사하기 위해 일련의 수치 시뮬레이션이 수행되었습니다. 1V:1H에서 1V:5H까지의 5개 램프 경사를 다양한 업스트림 방전에서 테스트했습니다.
수치모델의 검증을 위해 수치결과를 실험실 데이터와 비교하였다. 수면수위 예측과 유출계수의 시뮬레이션 불일치는 각각 전체 범위의 ±10%와 ±5% 이내였습니다.
모듈 한계 및 방전 감소 계수의 변화에 대한 램프 경사의 영향을 연구했습니다. 험프보의 경사로 경사가 증가함에 따라 상대적으로 높은 침수율에서 모듈러 한계가 발생함을 알 수 있었다.
침수 시작은 방류 수위를 작은 증분으로 조심스럽게 증가시켜 모델링되었으며 그 결과는 모듈 한계의 고전적인 정의와 비교되었습니다. 램프 경사와 방전이 증가함에 따라 모듈러 한계가 증가하는 것으로 밝혀졌지만, 모듈러 한계의 고전적인 정의는 모듈러 한계가 방전과 무관하다는 것을 나타냅니다.
Hump weir 하류의 속도와 와류장은 램프 경사에 의해 제어되는 와류 구조 형성을 나타냅니다. 에너지 손실은 수치 출력으로부터 계산되었으며 정규화된 에너지 손실은 침수에 따라 선형적으로 감소하는 것으로 나타났습니다.
Hump weirs are amongst conventional hydraulic structures for water level control and discharge measurement. The slope in the upstream and downstream ramps is a design parameter that affects the performance of Hump weirs in both free and submerged flow conditions. A series of numerical simulations was performed to investigate the effects of ramp slope and discharge on discharge characteristics and water level variations of submerged Hump weirs. Five ramp slopes ranging from 1V:1H to 1V:5H were tested at different upstream discharges. The numerical results were compared with the laboratory data for verifications of the numerical model. The simulation discrepancies in prediction of water surface level and discharge coefficient were within ±10 % and ±5 % of the full range, respectively. The effects of ramp slope on variations of modular limit and discharge reduction factor were studied. It was found that the modular limit occurred at relatively higher submergence ratios as the ramp slope in Hump weirs increased. The onset of submergence was modeled by carefully increasing tailwater level with small increments and the results were compared with the classic definition of modular limit. It was found that the modular limit increases with increasing the ramp slope and discharge while the classic definition of modular limit indicated that the modular limit is independent of the discharge. The velocity and vortex fields in the downstream of Hump weirs indicated the formation vortex structure, which is controlled by the ramp slope. The energy losses were calculated from the numerical outputs, and it was found that the normalized energy losses decreased linearly with submergence.
Weirs have been utilized predominantly for discharge measurement, flow diversion, and water level control in open channels, irrigation canal, and natural streams due to their simplicity of operation and accuracy. Several research studies have been conducted to determine the head-discharge relationship in weirs as one of the most common hydraulic structures for flow measurement (Rajaratnam and Muralidhar, 1969 [[1], [2], [3]]; Vatankhah, 2010, [[4], [5], [6]]; b [[7], [8], [9]]; Azimi and Seyed Hakim, 2019; Salehi et al., 2019; Salehi and Azimi, 2019, [10]. Weirs in general are classified into two major categories named as sharp-crested weirs and weirs of finite-crest length (Rajaratnam and Muralidhar, 1969; [11]. Sharp-crested weirs are typically used for flow measurement in small irrigation canals and laboratory flumes. In contrast, weirs of finite crest length are more suitable for water level control and flow diversion in rivers and natural streams [7,[12], [13], [14]].
The head-discharge relationship in sharp-crested weirs is developed by employing energy equation between two sections in the upstream and downstream of the weir and integration of the velocity profile at the crest of the weir as:
where Qf is the free flow discharge, B is the channel width, g is the acceleration due to gravity, ho is the water head in free-flow condition, and Cd is the discharge coefficient. Rehbock [15] proposed a linear correlation between discharge coefficient and the ratio of water head, ho, and the weir height, P as Cd = 0.605 + 0.08 (ho/P).
Upstream and/or downstream ramp(s) can be added to sharp-crested weirs to enhance the structural stability of the weir. A sharp-crested weir with upstream and/or downstream ramp(s) are known as triangular weirs in the literature. Triangular weirs with both upstream and downstream ramps are also known as Hump weirs and are first introduced in the experimental study of Bazin [16]. The ramps are constructed upstream and downstream of sharp-crested weirs to enhance the weir’s structural integrity and improve the hydraulic performance of the weir. In free-flow condition, the discharge coefficient of Hump weirs increases with increasing downstream ramp slope but decreases as upstream ramp slope increases (Azimi et al., 2013).
The hydraulic performance of weirs is evaluated in both free and submerged flow conditions. In free flow condition, water freely flows over weirs since the downstream water level is lower than that of the crest level of the weir. Channel blockage or flood in the downstream of weirs can raise the tailwater level, t. As tailwater passes the crest elevation in sharp-crested weirs, the upstream flow decelerates due to the excess pressure force in the downstream and the upstream water level increases. The onset of water level raise due to tailwater raise is called the modular limit. Once the tailwater level passes the modular limit, the weir is submerged. In sharp-crested weirs, the submerged flow regime may occur even before the tailwater reaches the crest elevation [8,14], whereas, in weirs of finite crest length, the upstream water level remains unchanged even if the tailwater raises above the crest elevation and it normally causes submergence once the tailwater level passes the critical depth at the crest of the weir [7,17]. The degree of submergence can be estimated by careful observation of the water surface profile. Observations of water surface at different submergence levels indicated two distinct flow patterns in submerged sharp-crested weirs that was initially classified as impinging jet and surface flow regimes [14]. [8] analyzed the variations of water surface profiles over submerged sharp-crested weirs with different submergence ratios and defined four distinct regimes of impinging jet, surface jump, surface wave, and surface jet.
[18] characterized the onset of submergence by defining the modular limit as a stage when the free flow head increases by +1 mm due to tailwater rise. The definition of modular limit is somewhat arbitrary, and it is difficult to identify for large discharges because the upstream water surface begins to fluctuate. This definition did not consider the effects of channel and weir geometries. The experimental data in triangular weirs and weirs finite-crest length with upstream and downstream ramp(s) revealed that the modular limit varied with the ratio of the free-flow head to the total streamwise length of the weir [17]. Weirs of finite crest length with upstream and downstream ramps are known as embankment weirs in literature [1,19,20] and Azimi et al., 2013) [19]. conducted two series of laboratory experiments to study the hydraulics of submerged embankment weirs with the upstream and downstream ramps of 1V:1H and 1V:2H. Empirical correlations were proposed to directly estimate the flow discharge in submerged embankment weirs for t/h > 0.7 where h is the water head in submerged flow condition. He found that the free flow discharge is a function of upstream water head, but the submerged discharge is a function of submergence level, t/h [21]. studied the hydraulics of four embankment weirs with different weir heights ranging from 0.09 m to 0.36 m. It was found that submerged embankments with a higher ho/P, where P is the height of the weir, have a smaller discharge reduction due to submergence. Effects of crest length in embankment weirs with both upstream and downstream ramps of 1V:2H was studied in both free and submerged flow conditions [1]. It was found that the modular limit in submerged embankment weirs decreased linearly with the relative crest length, Ho/(Ho + L), where Ho is the total head and L is the crest length.
In submerged flow condition, the performance of weirs is quantified by the discharge reduction factor, ψ, which is a ratio of the submerged discharge, Qs, to the corresponding free-flow discharge, Qf, based on the upstream head, h [12]. In submerged-flow conditions, flow discharge can be estimated as:��=���
[1] proposed a formula to predict ψ that could be used for embankment weirs with different crest lengths ranging from 0 to 0.3 m as:�=(1−��)�where n is an exponent varying from 4 to 7 and Yt is the normalized submergence defined as:��=�ℎ−[0.85−(0.5��+�)]1−[0.85−(0.5��+�)]where H is the total upstream head in submerged-flow conditions [7]. proposed a simpler formula to predict ψ for weirs of finite-crest length as:�=[1−(�ℎ)�]�where m and n are exponents varying for different types of weirs. Hakim and Azimi (2017) employed regression analysis to propose values of n = 0.25 and m = 0.28 (ho/L)−2.425 for triangular weirs.
The discharge capacity of weirs decreases in submerged flow condition and the onset of submergence occurs at the modular limit. Therefore, the determination of modular limit in weirs with different geometries is critical to understanding the sensitivity of a particular weir model with tailwater level variations. The available definition of modular limit as when head water raises by +1 mm due to tailwater rise does not consider the effects of channel and weir geometries. Therefore, a new and more accurate definition of modular limit is proposed in this study to consider the effect of other geometry and approaching flow parameters. The second objective of this study is to evaluate the effects of upstream and downstream ramps and ramps slopes on the hydraulic performance of submerged Hump weirs. The flow patterns, velocity distributions, and energy dissipation rates were extracted from validated numerical data to better understand the discharge reduction mechanism in Hump weirs in both free and submerged flow conditions.
Section snippets
Governing equations
Numerical simulation has been employed as an efficient and effective method to analyze free surface flow problems and in particular investigating on the hydraulics of flow over weirs [22]. The weir models were developed in numerical domain and the water pressure and velocity field were simulated by employing the FLOW-3D solver (Flow Science, Inc., Santa Fe, USA). The numerical results were validated with the laboratory measurements and the effects of ramps slopes on the performance of Hump
Verification of numerical model
The experimental observations of Bazin [16,17] were used for model validation in free and submerged flow conditions, respectively. The weir height in the study of Bazin was P = 0.5 m and two ramp slopes of 1V:1H and 1V:2H were tested. The bed and sides of the channel were made of glass, and the roughness distribution of the bed and walls were uniform. The Hump weir models in the study of Seyed Hakim and Azimi (2017) had a weir height of 0.076 m and ramp slopes of 1V:2H in both upstream and
Conclusions
A series of numerical simulations was performed to study the hydraulics and velocity pattern downstream of a Hump weir with symmetrical ramp slopes. Effects of ramp slope and discharge on formation of modular limit and in submerged flow condition were tested by conducting a series of numerical simulations on Hump weirs with ramp slopes varying from 1V:1H to 1V:5H. A comparison between numerical results and experimental data indicated that the proposed numerical model is accurate with a mean
The authors declare that they have no known competing financial interests or personal relationships that could have appeared to influence the work reported in this paper.
References (33)
H.M. Fritz et al.Hydraulics of embankment weirsJ. Hydraul. Eng.(1998)
P.K. Swamee et al.Viscosity and surface tension effects on rectangular weirsThe ISH Journal of Hydraulic Engineering(2001)
R. BaddourHead-discharge equation for the sharp-crested polynomial weirJ. Irrigat. Drain. Eng.(2008)
A.R. VatankhahHead-discharge equation for sharp-crested weir with piecewise-linear sidesJ. Irrigat. Drain. Eng.(2012)
A.H. Azimi et al.A note on sharp-crested weirs and weirs of finite crest lengthCan. J. Civ. Eng.(2012)
A.H. Azimi et al.Discharge characteristics of weirs of finite crest length with upstream and downstream rampsJ. Irrigat. Drain. Eng.(2013)
A.H. Azimi et al.Submerged flows over rectangular weirs of finite crest lengthJ. Irrigat. Drain. Eng.(2014)
A.H. Azimi et al.Water surface characteristics of submerged rectangular sharp-crested weirsJ. Hydraul. Eng.(2016)
M. Bijankhan et al.Experimental study and numerical simulation of inclined rectangular weirsJ. Irrigat. Drain. Eng.(2018)
A.H. AzimiAn Introduction to Hydraulic Structure” in Water Engineering Modeling and Mathematic Tools(2021)
본 연구의 목적은 다양한 위치에서 임계값을 갖는 슬라이딩 밸브의 유량계수를 조사하는 것입니다. 이 목표를 달성하기 위해 슬라이딩 밸브 아래 임계값의 세 위치에서 2.5cm, 22cm 및 22cm의 서로 다른 너비의 반구형, 원통형, 피라미드형 및 직사각형 입방체의 기하학적 모양을 가진 임계값의 효과, 하류에 접하는 임계값 및 임계값 상부에 대한 접선 슬라이딩 밸브의 상류는 실험실에서 조사되었습니다.
문턱의 위치를 조사한 결과 피라미드, 반원통형, 원통형, 직육면체의 기하학적 형태를 갖는 문턱은 폭 22cm의 문턱에 비해 슬라이딩 밸브 하류의 접선 상태에서 유량계수를 갖는 것으로 나타났습니다.
슬라이딩 밸브 아래의 임계값 위치, 22.22, 00/22, 20/22가 0.5% 증가했습니다. 베하트레브 상류의 접선 모드에서 언급된 값은 0.25, 22.22, 20.00 및 22.0%로 증가했습니다. 또한, 결과는 유량계수가 문턱의 위치뿐만 아니라 문턱의 기하학적 구조에 의해 영향을 받는다는 것을 보여주었습니다.
이와 같이 슬라이딩 밸브 아래의 문턱 위치에서는 최대 토출계수를 반구 형상의 문턱으로 지정하고, 슬라이딩 밸브의 하류와 상류의 접선 상태에서는 피라미드 문턱으로 지정하였습니다.
References
Alhamid AA, “Coefficient of discharge for free flow sluice gate”, King Saud University-Engineering Sciences, 1999, 11 (1), 33-47. Daneshfaraz R, Ghahramanzadeh A, Ghaderi A, Joudi AR, Abraham J, “Investigation of the effect of edge shape on characteristics of flow under vertical gates”, American Water Works Association, 2016, 108 (8), E425-E432. Ferro V, “Simultaneous Flow over and under a gate”, Irrigation and Drainage engineering, 2000, 190-193. Heidari M, Karami S, Adibrad M, “Investigation of Free Flow under the Radial Gate with the Sill”, Civil and Environmental Engineering, 2020, 50 (100), 9-19. Rajaratnam N, Subramanya K, “Flow equation for the sluice gate. Irrigation and Drainage Division”, 1967, 93(3), 167-186
웨어의 두 가지 서로 다른 배열(즉, 직선형 웨어와 직사각형 미로 웨어)을 사용하여 웨어 모양, 웨어 간격, 웨어의 오리피스 존재, 흐름 영역에 대한 바닥 경사와 같은 기하학적 매개변수의 영향을 평가했습니다.
유량과 수심의 관계, 수심 평균 속도의 변화와 분포, 난류 특성, 어도에서의 에너지 소산. 흐름 조건에 미치는 영향을 조사하기 위해 FLOW-3D® 소프트웨어를 사용하여 전산 유체 역학 시뮬레이션을 수행했습니다.
수치 모델은 계산된 표면 프로파일과 속도를 문헌의 실험적으로 측정된 값과 비교하여 검증되었습니다. 수치 모델과 실험 데이터의 결과, 급락유동의 표면 프로파일과 표준화된 속도 프로파일에 대한 평균 제곱근 오차와 평균 절대 백분율 오차가 각각 0.014m와 3.11%로 나타나 수치 모델의 능력을 확인했습니다.
수영장과 둑의 흐름 특성을 예측합니다. 각 모델에 대해 L/B = 1.83(L: 웨어 거리, B: 수로 폭) 값에서 급락 흐름이 발생할 수 있고 L/B = 0.61에서 스트리밍 흐름이 발생할 수 있습니다. 직사각형 미로보 모델은 기존 모델보다 무차원 방류량(Q+)이 더 큽니다.
수중 흐름의 기존 보와 직사각형 미로 보의 경우 Q는 각각 1.56과 1.47h에 비례합니다(h: 보 위 수심). 기존 웨어의 풀 내 평균 깊이 속도는 직사각형 미로 웨어의 평균 깊이 속도보다 높습니다.
그러나 주어진 방류량, 바닥 경사 및 웨어 간격에 대해 난류 운동 에너지(TKE) 및 난류 강도(TI) 값은 기존 웨어에 비해 직사각형 미로 웨어에서 더 높습니다. 기존의 웨어는 직사각형 미로 웨어보다 에너지 소산이 더 낮습니다.
더 낮은 TKE 및 TI 값은 미로 웨어 상단, 웨어 하류 벽 모서리, 웨어 측벽과 채널 벽 사이에서 관찰되었습니다. 보와 바닥 경사면 사이의 거리가 증가함에 따라 평균 깊이 속도, 난류 운동 에너지의 평균값 및 난류 강도가 증가하고 수영장의 체적 에너지 소산이 감소했습니다.
둑에 개구부가 있으면 평균 깊이 속도와 TI 값이 증가하고 풀 내에서 가장 높은 TKE 범위가 감소하여 두 모델 모두에서 물고기를 위한 휴식 공간이 더 넓어지고(TKE가 낮아짐) 에너지 소산율이 감소했습니다.
Two different arrangements of the weir (i.e., straight weir and rectangular labyrinth weir) were used to evaluate the effects of geometric parameters such as weir shape, weir spacing, presence of an orifice at the weir, and bed slope on the flow regime and the relationship between discharge and depth, variation and distribution of depth-averaged velocity, turbulence characteristics, and energy dissipation at the fishway. Computational fluid dynamics simulations were performed using FLOW-3D® software to examine the effects on flow conditions. The numerical model was validated by comparing the calculated surface profiles and velocities with experimentally measured values from the literature. The results of the numerical model and experimental data showed that the root-mean-square error and mean absolute percentage error for the surface profiles and normalized velocity profiles of plunging flows were 0.014 m and 3.11%, respectively, confirming the ability of the numerical model to predict the flow characteristics of the pool and weir. A plunging flow can occur at values of L/B = 1.83 (L: distance of the weir, B: width of the channel) and streaming flow at L/B = 0.61 for each model. The rectangular labyrinth weir model has larger dimensionless discharge values (Q+) than the conventional model. For the conventional weir and the rectangular labyrinth weir at submerged flow, Q is proportional to 1.56 and 1.47h, respectively (h: the water depth above the weir). The average depth velocity in the pool of a conventional weir is higher than that of a rectangular labyrinth weir. However, for a given discharge, bed slope, and weir spacing, the turbulent kinetic energy (TKE) and turbulence intensity (TI) values are higher for a rectangular labyrinth weir compared to conventional weir. The conventional weir has lower energy dissipation than the rectangular labyrinth weir. Lower TKE and TI values were observed at the top of the labyrinth weir, at the corner of the wall downstream of the weir, and between the side walls of the weir and the channel wall. As the distance between the weirs and the bottom slope increased, the average depth velocity, the average value of turbulent kinetic energy and the turbulence intensity increased, and the volumetric energy dissipation in the pool decreased. The presence of an opening in the weir increased the average depth velocity and TI values and decreased the range of highest TKE within the pool, resulted in larger resting areas for fish (lower TKE), and decreased the energy dissipation rates in both models.
1 Introduction
Artificial barriers such as detour dams, weirs, and culverts in lakes and rivers prevent fish from migrating and completing the upstream and downstream movement cycle. This chain is related to the life stage of the fish, its location, and the type of migration. Several riverine fish species instinctively migrate upstream for spawning and other needs. Conversely, downstream migration is a characteristic of early life stages [1]. A fish ladder is a waterway that allows one or more fish species to cross a specific obstacle. These structures are constructed near detour dams and other transverse structures that have prevented such migration by allowing fish to overcome obstacles [2]. The flow pattern in fish ladders influences safe and comfortable passage for ascending fish. The flow’s strong turbulence can reduce the fish’s speed, injure them, and delay or prevent them from exiting the fish ladder. In adult fish, spawning migrations are usually complex, and delays are critical to reproductive success [3].
Various fish ladders/fishways include vertical slots, denil, rock ramps, and pool weirs [1]. The choice of fish ladder usually depends on many factors, including water elevation, space available for construction, and fish species. Pool and weir structures are among the most important fish ladders that help fish overcome obstacles in streams or rivers and swim upstream [1]. Because they are easy to construct and maintain, this type of fish ladder has received considerable attention from researchers and practitioners. Such a fish ladder consists of a sloping-floor channel with series of pools directly separated by a series of weirs [4]. These fish ladders, with or without underwater openings, are generally well-suited for slopes of 10% or less [1, 2]. Within these pools, flow velocities are low and provide resting areas for fish after they enter the fish ladder. After resting in the pools, fish overcome these weirs by blasting or jumping over them [2]. There may also be an opening in the flooded portion of the weir through which the fish can swim instead of jumping over the weir. Design parameters such as the length of the pool, the height of the weir, the slope of the bottom, and the water discharge are the most important factors in determining the hydraulic structure of this type of fish ladder [3]. The flow over the weir depends on the flow depth at a given slope S0 and the pool length, either “plunging” or “streaming.” In plunging flow, the water column h over each weir creates a water jet that releases energy through turbulent mixing and diffusion mechanisms [5]. The dimensionless discharges for plunging (Q+) and streaming (Q*) flows are shown in Fig. 1, where Q is the total discharge, B is the width of the channel, w is the weir height, S0 is the slope of the bottom, h is the water depth above the weir, d is the flow depth, and g is the acceleration due to gravity. The maximum velocity occurs near the top of the weir for plunging flow. At the water’s surface, it drops to about half [6].
Fig. 1
Extensive experimental studies have been conducted to investigate flow patterns for various physical geometries (i.e., bed slope, pool length, and weir height) [2]. Guiny et al. [7] modified the standard design by adding vertical slots, orifices, and weirs in fishways. The efficiency of the orifices and vertical slots was related to the velocities at their entrances. In the laboratory experiments of Yagci [8], the three-dimensional (3D) mean flow and turbulence structure of a pool weir fishway combined with an orifice and a slot is investigated. It is shown that the energy dissipation per unit volume and the discharge have a linear relationship.
Considering the beneficial characteristics reported in the limited studies of researchers on the labyrinth weir in the pool-weir-type fishway, and knowing that the characteristics of flow in pool-weir-type fishways are highly dependent on the geometry of the weir, an alternative design of the rectangular labyrinth weir instead of the straight weirs in the pool-weir-type fishway is investigated in this study [7, 9]. Kim [10] conducted experiments to compare the hydraulic characteristics of three different weir types in a pool-weir-type fishway. The results show that a straight, rectangular weir with a notch is preferable to a zigzag or trapezoidal weir. Studies on natural fish passes show that pass ability can be improved by lengthening the weir’s crest [7]. Zhong et al. [11] investigated the semi-rigid weir’s hydraulic performance in the fishway’s flow field with a pool weir. The results showed that this type of fishway performed better with a lower invert slope and a smaller radius ratio but with a larger pool spacing.
Considering that an alternative method to study the flow characteristics in a fishway with a pool weir is based on numerical methods and modeling from computational fluid dynamics (CFD), which can easily change the geometry of the fishway for different flow fields, this study uses the powerful package CFD and the software FLOW-3D to evaluate the proposed weir design and compare it with the conventional one to extend the application of the fishway. The main objective of this study was to evaluate the hydraulic performance of the rectangular labyrinth pool and the weir with submerged openings in different hydraulic configurations. The primary objective of creating a new weir configuration for suitable flow patterns is evaluated based on the swimming capabilities of different fish species. Specifically, the following questions will be answered: (a) How do the various hydraulic and geometric parameters relate to the effects of water velocity and turbulence, expressed as turbulent kinetic energy (TKE) and turbulence intensity (TI) within the fishway, i.e., are conventional weirs more affected by hydraulics than rectangular labyrinth weirs? (b) Which weir configurations have the greatest effect on fish performance in the fishway? (c) In the presence of an orifice plate, does the performance of each weir configuration differ with different weir spacing, bed gradients, and flow regimes from that without an orifice plate?
2 Materials and Methods
2.1 Physical Model Configuration
This paper focuses on Ead et al. [6]’s laboratory experiments as a reference, testing ten pool weirs (Fig. 2). The experimental flume was 6 m long, 0.56 m wide, and 0.6 m high, with a bottom slope of 10%. Field measurements were made at steady flow with a maximum flow rate of 0.165 m3/s. Discharge was measured with magnetic flow meters in the inlets and water level with point meters (see Ead et al. [6]. for more details). Table 1 summarizes the experimental conditions considered for model calibration in this study.
Fig. 2
Table 1 Experimental conditions considered for calibration
Computational fluid dynamics (CFD) simulations were performed using FLOW-3D® v11.2 to validate a series of experimental liner pool weirs by Ead et al. [6] and to investigate the effects of the rectangular labyrinth pool weir with an orifice. The dimensions of the channel and data collection areas in the numerical models are the same as those of the laboratory model. Two types of pool weirs were considered: conventional and labyrinth. The proposed rectangular labyrinth pool weirs have a symmetrical cross section and are sized to fit within the experimental channel. The conventional pool weir model had a pool length of l = 0.685 and 0.342 m, a weir height of w = 0.141 m, a weir width of B = 0.56 m, and a channel slope of S0 = 5 and 10%. The rectangular labyrinth weirs have the same front width as the offset, i.e., a = b = c = 0.186 m. A square underwater opening with a width of 0.05 m and a depth of 0.05 m was created in the middle of the weir. The weir configuration considered in the present study is shown in Fig. 3.
Fig. 3
2.3 Governing Equations
FLOW-3D® software solves the Navier–Stokes–Reynolds equations for three-dimensional analysis of incompressible flows using the fluid-volume method on a gridded domain. FLOW -3D® uses an advanced free surface flow tracking algorithm (TruVOF) developed by Hirt and Nichols [12], where fluid configurations are defined in terms of a VOF function F (x, y, z, t). In this case, F (fluid fraction) represents the volume fraction occupied by the fluid: F = 1 in cells filled with fluid and F = 0 in cells without fluid (empty areas) [4, 13]. The free surface area is at an intermediate value of F. (Typically, F = 0.5, but the user can specify a different intermediate value.) The equations in Cartesian coordinates (x, y, z) applicable to the model are as follows:
�f∂�∂�+∂(���x)∂�+∂(���y)∂�+∂(���z)∂�=�SOR
(1)
∂�∂�+1�f(��x∂�∂�+��y∂�∂�+��z∂�∂�)=−1�∂�∂�+�x+�x
(2)
∂�∂�+1�f(��x∂�∂�+��y∂�∂�+��z∂�∂�)=−1�∂�∂�+�y+�y
(3)
∂�∂�+1�f(��x∂�∂�+��y∂�∂�+��z∂�∂�)=−1�∂�∂�+�z+�z
(4)
where (u, v, w) are the velocity components, (Ax, Ay, Az) are the flow area components, (Gx, Gy, Gz) are the mass accelerations, and (fx, fy, fz) are the viscous accelerations in the directions (x, y, z), ρ is the fluid density, RSOR is the spring term, Vf is the volume fraction associated with the flow, and P is the pressure. The k–ε turbulence model (RNG) was used in this study to solve the turbulence of the flow field. This model is a modified version of the standard k–ε model that improves performance. The model is a two-equation model; the first equation (Eq. 5) expresses the turbulence’s energy, called turbulent kinetic energy (k) [14]. The second equation (Eq. 6) is the turbulent dissipation rate (ε), which determines the rate of dissipation of kinetic energy [15]. These equations are expressed as follows Dasineh et al. [4]:
In these equations, k is the turbulent kinetic energy, ε is the turbulent energy consumption rate, Gk is the generation of turbulent kinetic energy by the average velocity gradient, with empirical constants αε = αk = 1.39, C1ε = 1.42, and C2ε = 1.68, eff is the effective viscosity, μeff = μ + μt [15]. Here, μ is the hydrodynamic density coefficient, and μt is the turbulent density of the fluid.
2.4 Meshing and the Boundary Conditions in the Model Setup
The numerical area is divided into three mesh blocks in the X-direction. The meshes are divided into different sizes, a containing mesh block for the entire spatial domain and a nested block with refined cells for the domain of interest. Three different sizes were selected for each of the grid blocks. By comparing the accuracy of their results based on the experimental data, the reasonable mesh for the solution domain was finally selected. The convergence index method (GCI) evaluated the mesh sensitivity analysis. Based on this method, many researchers, such as Ahmadi et al. [16] and Ahmadi et al. [15], have studied the independence of numerical results from mesh size. Three different mesh sizes with a refinement ratio (r) of 1.33 were used to perform the convergence index method. The refinement ratio is the ratio between the larger and smaller mesh sizes (r = Gcoarse/Gfine). According to the recommendation of Celik et al. [17], the recommended number for the refinement ratio is 1.3, which gives acceptable results. Table 2 shows the characteristics of the three mesh sizes selected for mesh sensitivity analysis.Table 2 Characteristics of the meshes tested in the convergence analysis
The results of u1 = umax (u1 = velocity component along the x1 axis and umax = maximum velocity of u1 in a section perpendicular to the invert of the fishway) at Q = 0.035 m3/s, × 1/l = 0.66, and Y1/b = 0 in the pool of conventional weir No. 4, obtained from the output results of the software, were used to evaluate the accuracy of the calculation range. As shown in Fig. 4, x1 = the distance from a given weir in the x-direction, Y1 = the water depth measured in the y-direction, Y0 = the vertical distance in the Cartesian coordinate system, h = the water column at the crest, b = the distance between the two points of maximum velocity umax and zero velocity, and l = the pool length.
Fig. 4
The apparent index of convergence (p) in the GCI method is calculated as follows:
�=ln(�3−�2)(�2−�1)/ln(�)
(7)
f1, f2, and f3 are the hydraulic parameters obtained from the numerical simulation (f1 corresponds to the small mesh), and r is the refinement ratio. The following equation defines the convergence index of the fine mesh:
GCIfine=1.25|ε|��−1
(8)
Here, ε = (f2 − f1)/f1 is the relative error, and f2 and f3 are the values of hydraulic parameters considered for medium and small grids, respectively. GCI12 and GCI23 dimensionless indices can be calculated as:
GCI12=1.25|�2−�1�1|��−1
(9)
Then, the independence of the network is preserved. The convergence index of the network parameters obtained by Eqs. (7)–(9) for all three network variables is shown in Table 3. Since the GCI values for the smaller grid (GCI12) are lower compared to coarse grid (GCI23), it can be concluded that the independence of the grid is almost achieved. No further change in the grid size of the solution domain is required. The calculated values (GCI23/rpGCI12) are close to 1, which shows that the numerical results obtained are within the convergence range. As a result, the meshing of the solution domain consisting of a block mesh with a mesh size of 0.012 m and a block mesh within a larger block mesh with a mesh size of 0.009 m was selected as the optimal mesh (Fig. 5).Table 3 GCI calculation
The boundary conditions applied to the area are shown in Fig. 6. The boundary condition of specific flow rate (volume flow rate-Q) was used for the inlet of the flow. For the downstream boundary, the flow output (outflow-O) condition did not affect the flow in the solution area. For the Zmax boundary, the specified pressure boundary condition was used along with the fluid fraction = 0 (P). This type of boundary condition considers free surface or atmospheric pressure conditions (Ghaderi et al. [19]). The wall boundary condition is defined for the bottom of the channel, which acts like a virtual wall without friction (W). The boundary between mesh blocks and walls were considered a symmetrical condition (S).
Fig. 6
The convergence of the steady-state solutions was controlled during the simulations by monitoring the changes in discharge at the inlet boundary conditions. Figure 7 shows the time series plots of the discharge obtained from the Model A for the three main discharges from the numerical results. The 8 s to reach the flow equilibrium is suitable for the case of the fish ladder with pool and weir. Almost all discharge fluctuations in the models are insignificant in time, and the flow has reached relative stability. The computation time for the simulations was between 6 and 8 h using a personal computer with eight cores of a CPU (Intel Core i7-7700K @ 4.20 GHz and 16 GB RAM).
Fig. 7
3 Results
3.1 Verification of Numerical Results
Quantitative outcomes, including free surface and normalized velocity profiles obtained using FLOW-3D software, were reviewed and compared with the results of Ead et al. [6]. The fourth pool was selected to present the results and compare the experiment and simulation. For each quantity, the percentage of mean absolute error (MAPE (%)) and root-mean-square error (RMSE) are calculated. Equations (10) and (11) show the method used to calculate the errors.
MAPE(%)100×1�∑1�|�exp−�num�exp|
(10)
RMSE(−)1�∑1�(�exp−�num)2
(11)
Here, Xexp is the value of the laboratory data, Xnum is the numerical data value, and n is the amount of data. As shown in Fig. 8, let x1 = distance from a given weir in the x-direction and Y1 = water depth in the y-direction from the bottom. The trend of the surface profiles for each of the numerical results is the same as that of the laboratory results. The surface profiles of the plunging flows drop after the flow enters and then rises to approach the next weir. The RMSE and MAPE error values for Model A are 0.014 m and 3.11%, respectively, indicating acceptable agreement between numerical and laboratory results. Figure 9 shows the velocity vectors and plunging flow from the numerical results, where x and y are horizontal and vertical to the flow direction, respectively. It can be seen that the jet in the fish ladder pool has a relatively high velocity. The two vortices, i.e., the enclosed vortex rotating clockwise behind the weir and the surface vortex rotating counterclockwise above the jet, are observed for the regime of incident flow. The point where the jet meets the fish passage bed is shown in the figure. The normalized velocity profiles upstream and downstream of the impact points are shown in Fig. 10. The figure shows that the numerical results agree well with the experimental data of Ead et al. [6].
Fig. 8Fig. 9Fig. 10
3.2 Flow Regime and Discharge-Depth Relationship
Depending on the geometric shape of the fishway, including the distance of the weir, the slope of the bottom, the height of the weir, and the flow conditions, the flow regime in the fishway is divided into three categories: dipping, transitional, and flow regimes [4]. In the plunging flow regime, the flow enters the pool through the weir, impacts the bottom of the fishway, and forms a hydraulic jump causing two eddies [2, 20]. In the streamwise flow regime, the surface of the flow passing over the weir is almost parallel to the bottom of the channel. The transitional regime has intermediate flow characteristics between the submerged and flow regimes. To predict the flow regime created in the fishway, Ead et al. [6] proposed two dimensionless parameters, Qt* and L/w, where Qt* is the dimensionless discharge, L is the distance between weirs, and w is the height of the weir:
��∗=���0���
(12)
Q is the total discharge, B is the width of the channel, S0 is the slope of the bed, and g is the gravity acceleration. Figure 11 shows different ranges for each flow regime based on the slope of the bed and the distance between the pools in this study. The results of Baki et al. [21], Ead et al. [6] and Dizabadi et al. [22] were used for this comparison. The distance between the pools affects the changes in the regime of the fish ladder. So, if you decrease the distance between weirs, the flow regime more likely becomes. This study determined all three flow regimes in a fish ladder. When the corresponding range of Qt* is less than 0.6, the flow regime can dip at values of L/B = 1.83. If the corresponding range of Qt* is greater than 0.5, transitional flow may occur at L/B = 1.22. On the other hand, when Qt* is greater than 1, streamwise flow can occur at values of L/B = 0.61. These observations agree well with the results of Baki et al. [21], Ead et al. [6] and Dizabadi et al. [22].
Fig. 11
For plunging flows, another dimensionless discharge (Q+) versus h/w given by Ead et al. [6] was used for further evaluation:
�+=��ℎ�ℎ=23�d�
(13)
where h is the water depth above the weir, and Cd is the discharge coefficient. Figure 12a compares the numerical and experimental results of Ead et al. [6]. In this figure, Rehbock’s empirical equation is used to estimate the discharge coefficient of Ead et al. [6].
�d=0.57+0.075ℎ�
(14)
Fig. 12
The numerical results for the conventional weir (Model A) and the rectangular labyrinth weir (Model B) of this study agree well with the laboratory results of Ead et al. [6]. When comparing models A and B, it is also found that a rectangular labyrinth weir has larger Q + values than the conventional weir as the length of the weir crest increases for a given channel width and fixed headwater elevation. In Fig. 12b, Models A and B’s flow depth plot shows the plunging flow regime. The power trend lines drawn through the data are the best-fit lines. The data shown in Fig. 12b are for different bed slopes and weir geometries. For the conventional weir and the rectangular labyrinth weir at submerged flow, Q can be assumed to be proportional to 1.56 and 1.47h, respectively. In the results of Ead et al. [6], Q is proportional to 1.5h. If we assume that the flow through the orifice is Qo and the total outflow is Q, the change in the ratio of Qo/Q to total outflow for models A and B can be shown in Fig. 13. For both models, the flow through the orifice decreases as the total flow increases. A logarithmic trend line was also found between the total outflow and the dimensionless ratio Qo/Q.
Fig. 13
3.3 Depth-Averaged Velocity Distributions
To ensure that the target fish species can pass the fish ladder with maximum efficiency, the average velocity in the fish ladder should be low enough [4]. Therefore, the average velocity in depth should be as much as possible below the critical swimming velocities of the target fishes at a constant flow depth in the pool [20]. The contour plot of depth-averaged velocity was used instead of another direction, such as longitudinal velocity because fish are more sensitive to depth-averaged flow velocity than to its direction under different hydraulic conditions. Figure 14 shows the distribution of depth-averaged velocity in the pool for Models A and B in two cases with and without orifice plates. Model A’s velocity within the pool differs slightly in the spanwise direction. However, no significant variation in velocity was observed. The flow is gradually directed to the sides as it passes through the rectangular labyrinth weir. This increases the velocity at the sides of the channel. Therefore, the high-velocity zone is located at the sides. The low velocity is in the downstream apex of the weir. This area may be suitable for swimming target fish. The presence of an opening in the weir increases the flow velocity at the opening and in the pool’s center, especially in Model A. The flow velocity increase caused by the models’ opening varied from 7.7 to 12.48%. Figure 15 illustrates the effect of the inverted slope on the averaged depth velocity distribution in the pool at low and high discharge. At constant discharge, flow velocity increases with increasing bed slope. In general, high flow velocity was found in the weir toe sidewall and the weir and channel sidewalls.
Fig. 14Fig. 15
On the other hand, for a constant bed slope, the high-velocity area of the pool increases due to the increase in runoff. For both bed slopes and different discharges, the most appropriate path for fish to travel from upstream to downstream is through the middle of the cross section and along the top of the rectangular labyrinth weirs. The maximum dominant velocities for Model B at S0 = 5% were 0.83 and 1.01 m/s; at S0 = 10%, they were 1.12 and 1.61 m/s at low and high flows, respectively. The low mean velocities for the same distance and S0 = 5 and 10% were 0.17 and 0.26 m/s, respectively.
Figure 16 shows the contour of the averaged depth velocity for various distances from the weir at low and high discharge. The contour plot shows a large variation in velocity within short distances from the weir. At L/B = 0.61, velocities are low upstream and downstream of the top of the weir. The high velocities occur in the side walls of the weir and the channel. At L/B = 1.22, the low-velocity zone displaces the higher velocity in most of the pool. Higher velocities were found only on the sides of the channel. As the discharge increases, the velocity zone in the pool becomes wider. At L/B = 1.83, there is an area of higher velocities only upstream of the crest and on the sides of the weir. At high discharge, the prevailing maximum velocities for L/B = 0.61, 1.22, and 1.83 were 1.46, 1.65, and 1.84 m/s, respectively. As the distance between weirs increases, the range of maximum velocity increases.
Fig. 16
On the other hand, the low mean velocity for these distances was 0.27, 0.44, and 0.72 m/s, respectively. Thus, the low-velocity zone decreases with increasing distance between weirs. Figure 17 shows the pattern distribution of streamlines along with the velocity contour at various distances from the weir for Q = 0.05 m3/s. A stream-like flow is generally formed in the pool at a small distance between weirs (L/B = 0.61). The rotation cell under the jet forms clockwise between the two weirs. At the distances between the spillways (L/B = 1.22), the transition regime of the flow is formed. The transition regime occurs when or shortly after the weir is flooded. The rotation cell under the jet is clockwise smaller than the flow regime and larger than the submergence regime. At a distance L/B = 1.83, a plunging flow is formed so that the plunging jet dips into the pool and extends downstream to the center of the pool. The clockwise rotation of the cell is bounded by the dipping jet of the weir and is located between the bottom and the side walls of the weir and the channel.
Fig. 17
Figure 18 shows the average depth velocity bar graph for each weir at different bed slopes and with and without orifice plates. As the distance between weirs increases, all models’ average depth velocity increases. As the slope of the bottom increases and an orifice plate is present, the average depth velocity in the pool increases. In addition, the average pool depth velocity increases as the discharge increases. Among the models, Model A’s average depth velocity is higher than Model B’s. The variation in velocity ranged from 8.11 to 12.24% for the models without an orifice plate and from 10.26 to 16.87% for the models with an orifice plate.
Fig. 18
3.4 Turbulence Characteristics
The turbulent kinetic energy is one of the important parameters reflecting the turbulent properties of the flow field [23]. When the k value is high, more energy and a longer transit time are required to migrate the target species. The turbulent kinetic energy is defined as follows:
�=12(�x′2+�y′2+�z′2)
(15)
where ux, uy, and uz are fluctuating velocities in the x, y, and z directions, respectively. An illustration of the TKE and the effects of the geometric arrangement of the weir and the presence of an opening in the weir is shown in Fig. 19. For a given bed slope, in Model A, the highest TKE values are uniformly distributed in the weir’s upstream portion in the channel’s cross section. In contrast, for the rectangular labyrinth weir (Model B), the highest TKE values are concentrated on the sides of the pool between the crest of the weir and the channel wall. The highest TKE value in Models A and B is 0.224 and 0.278 J/kg, respectively, at the highest bottom slope (S0 = 10%). In the downstream portion of the conventional weir and within the crest of the weir and the walls of the rectangular labyrinth, there was a much lower TKE value that provided the best conditions for fish to recover in the pool between the weirs. The average of the lowest TKE for bottom slopes of 5 and 10% in Model A is 0.041 and 0.056 J/kg, and for Model B, is 0.047 and 0.064 J/kg. The presence of an opening in the weirs reduces the area of the highest TKE within the pool. It also increases the resting areas for fish (lower TKE). The highest TKE at the highest bottom slope in Models A and B with an orifice is 0.208 and 0.191 J/kg, respectively.
Fig. 19
Figure 20 shows the effect of slope on the longitudinal distribution of TKE in the pools. TKE values significantly increase for a given discharge with an increasing bottom slope. Thus, for a low bed slope (S0 = 5%), a large pool area has expanded with average values of 0.131 and 0.168 J/kg for low and high discharge, respectively. For a bed slope of S0 = 10%, the average TKE values are 0.176 and 0.234 J/kg. Furthermore, as the discharge increases, the area with high TKE values within the pool increases. Lower TKE values are observed at the apex of the labyrinth weir, at the corner of the wall downstream of the weir, and between the side walls of the weir and the channel wall for both bottom slopes. The effect of distance between weirs on TKE is shown in Fig. 21. Low TKE values were observed at low discharge and short distances between weirs. Low TKE values are located at the top of the rectangular labyrinth weir and the downstream corner of the weir wall. There is a maximum value of TKE at the large distances between weirs, L/B = 1.83, along the center line of the pool, where the dip jet meets the bottom of the bed. At high discharge, the maximum TKE value for the distance L/B = 0.61, 1.22, and 1.83 was 0.246, 0.322, and 0.417 J/kg, respectively. In addition, the maximum TKE range increases with the distance between weirs.
Fig. 20Fig. 21
For TKE size, the average value (TKEave) is plotted against q in Fig. 22. For all models, the TKE values increase with increasing q. For example, in models A and B with L/B = 0.61 and a slope of 10%, the TKE value increases by 41.66 and 86.95%, respectively, as q increases from 0.1 to 0.27 m2/s. The TKE values in Model B are higher than Model A for a given discharge, bed slope, and weir distance. The TKEave in Model B is higher compared to Model A, ranging from 31.46 to 57.94%. The presence of an orifice in the weir reduces the TKE values in both weirs. The intensity of the reduction is greater in Model B. For example, in Models A and B with L/B = 0.61 and q = 0.1 m2/s, an orifice reduces TKEave values by 60.35 and 19.04%, respectively. For each model, increasing the bed slope increases the TKEave values in the pool. For example, for Model B with q = 0.18 m2/s, increasing the bed slope from 5 to 10% increases the TKEave value by 14.34%. Increasing the distance between weirs increases the TKEave values in the pool. For example, in Model B with S0 = 10% and q = 0.3 m2/s, the TKEave in the pool increases by 34.22% if you increase the distance between weirs from L/B = 0.61 to L/B = 0.183.
Fig. 22
Cotel et al. [24] suggested that turbulence intensity (TI) is a suitable parameter for studying fish swimming performance. Figure 23 shows the plot of TI and the effects of the geometric arrangement of the weir and the presence of an orifice. In Model A, the highest TI values are found upstream of the weirs and are evenly distributed across the cross section of the channel. The TI values increase as you move upstream to downstream in the pool. For the rectangular labyrinth weir, the highest TI values were concentrated on the sides of the pool, between the top of the weir and the side wall of the channel, and along the top of the weir. Downstream of the conventional weir, within the apex of the weir, and at the corners of the walls of the rectangular labyrinth weir, the percentage of TI was low. At the highest discharge, the average range of TI in Models A and B was 24–45% and 15–62%, respectively. The diversity of TI is greater in the rectangular labyrinth weir than the conventional weir. Fish swimming performance is reduced due to higher turbulence intensity. However, fish species may prefer different disturbance intensities depending on their swimming abilities; for example, Salmo trutta prefers a disturbance intensity of 18–53% [25]. Kupferschmidt and Zhu [26] found a higher range of TI for fishways, such as natural rock weirs, of 40–60%. The presence of an orifice in the weir increases TI values within the pool, especially along the middle portion of the cross section of the fishway. With an orifice in the weir, the average range of TI in Models A and B was 28–59% and 22–73%, respectively.
Fig. 23
The effect of bed slope on TI variation is shown in Fig. 24. TI increases in different pool areas as the bed slope increases for a given discharge. For a low bed slope (S0 = 5%), a large pool area has increased from 38 to 63% and from 56 to 71% for low and high discharge, respectively. For a bed slope of S0 = 10%, the average values of TI are 45–67% and 61–73% for low and high discharge, respectively. Therefore, as runoff increases, the area with high TI values within the pool increases. A lower TI is observed for both bottom slopes in the corner of the wall, downstream of the crest walls, and between the side walls in the weir and channel. Figure 25 compares weir spacing with the distribution of TI values within the pool. The TI values are low at low flows and short distances between weirs. A maximum value of TI occurs at long spacing and where the plunging stream impinges on the bed and the area around the bed. TI ranges from 36 to 57%, 58–72%, and 47–76% for the highest flow in a wide pool area for L/B = 0.61, 1.22, and 1.83, respectively.
Fig. 24Fig. 25
The average value of turbulence intensity (TIave) is plotted against q in Fig. 26. The increase in TI values with the increase in q values is seen in all models. For example, the average values of TI for Models A and B at L/B = 0.61 and slope of 10% increased from 23.9 to 33.5% and from 42 to 51.8%, respectively, with the increase in q from 0.1 to 0.27 m2/s. For a given discharge, a given gradient, and a given spacing of weirs, the TIave is higher in Model B than Model A. The presence of an orifice in the weirs increases the TI values in both types. For example, in Models A and B with L/B = 0.61 and q = 0.1 m2/s, the presence of an orifice increases TIave from 23.9 to 37.1% and from 42 to 48.8%, respectively. For each model, TIave in the pool increases with increasing bed slope. For Model B with q = 0.18 m2/s, TIave increases from 37.5 to 45.8% when you increase the invert slope from 5 to 10%. Increasing the distance between weirs increases the TIave in the pool. In Model B with S0 = 10% and q = 0.3 m2/s, the TIave in the pool increases from 51.8 to 63.7% as the distance between weirs increases from L/B = 0.61 to L/B = 0.183.
Fig. 26
3.5 Energy Dissipation
To facilitate the passage of various target species through the pool of fishways, it is necessary to pay attention to the energy dissipation of the flow and to keep the flow velocity in the pool slow. The average volumetric energy dissipation (k) in the pool is calculated using the following basic formula:
�=����0��
(16)
where ρ is the water density, and H is the average water depth of the pool. The change in k versus Q for all models at two bottom slopes, S0 = 5%, and S0 = 10%, is shown in Fig. 27. Like the results of Yagci [8] and Kupferschmidt and Zhu [26], at a constant bottom slope, the energy dissipation in the pool increases with increasing discharge. The trend of change in k as a function of Q from the present study at a bottom gradient of S0 = 5% is also consistent with the results of Kupferschmidt and Zhu [26] for the fishway with rock weir. The only difference between the results is the geometry of the fishway and the combination of boulders instead of a solid wall. Comparison of the models shows that the conventional model has lower energy dissipation than the rectangular labyrinth for a given discharge. Also, increasing the distance between weirs decreases the volumetric energy dissipation for each model with the same bed slope. Increasing the slope of the bottom leads to an increase in volumetric energy dissipation, and an opening in the weir leads to a decrease in volumetric energy dissipation for both models. Therefore, as a guideline for volumetric energy dissipation, if the value within the pool is too high, the increased distance of the weir, the decreased slope of the bed, or the creation of an opening in the weir would decrease the volumetric dissipation rate.
Fig. 27
To evaluate the energy dissipation inside the pool, the general method of energy difference in two sections can use:
ε=�1−�2�1
(17)
where ε is the energy dissipation rate, and E1 and E2 are the specific energies in Sects. 1 and 2, respectively. The distance between Sects. 1 and 2 is the same. (L is the distance between two upstream and downstream weirs.) Figure 28 shows the changes in ε relative to q (flow per unit width). The rectangular labyrinth weir (Model B) has a higher energy dissipation rate than the conventional weir (Model A) at a constant bottom gradient. For example, at S0 = 5%, L/B = 0.61, and q = 0.08 m3/s.m, the energy dissipation rate in Model A (conventional weir) was 0.261. In Model B (rectangular labyrinth weir), however, it was 0.338 (22.75% increase). For each model, the energy dissipation rate within the pool increases as the slope of the bottom increases. For Model B with L/B = 1.83 and q = 0.178 m3/s.m, the energy dissipation rate at S0 = 5% and 10% is 0.305 and 0.358, respectively (14.8% increase). Figure 29 shows an orifice’s effect on the pools’ energy dissipation rate. With an orifice in the weir, both models’ energy dissipation rates decreased. Thus, the reduction in energy dissipation rate varied from 7.32 to 9.48% for Model A and from 8.46 to 10.57 for Model B.
Fig. 28Fig. 29
4 Discussion
This study consisted of entirely of numerical analysis. Although this study was limited to two weirs, the hydraulic performance and flow characteristics in a pooled fishway are highlighted by the rectangular labyrinth weir and its comparison with the conventional straight weir. The study compared the numerical simulations with laboratory experiments in terms of surface profiles, velocity vectors, and flow characteristics in a fish ladder pool. The results indicate agreement between the numerical and laboratory data, supporting the reliability of the numerical model in capturing the observed phenomena.
When the configuration of the weir changes to a rectangular labyrinth weir, the flow characteristics, the maximum and minimum area, and even the location of each hydraulic parameter change compared to a conventional weir. In the rectangular labyrinth weir, the flow is gradually directed to the sides as it passes the weir. This increases the velocity at the sides of the channel [21]. Therefore, the high-velocity area is located on the sides. In the downstream apex of the weir, the flow velocity is low, and this area may be suitable for swimming target fish. However, no significant change in velocity was observed at the conventional weir within the fish ladder. This resulted in an average increase in TKE of 32% and an average increase in TI of about 17% compared to conventional weirs.
In addition, there is a slight difference in the flow regime for both weir configurations. In addition, the rectangular labyrinth weir has a higher energy dissipation rate for a given discharge and constant bottom slope than the conventional weir. By reducing the distance between the weirs, this becomes even more intense. Finally, the presence of an orifice in both configurations of the weir increased the flow velocity at the orifice and in the middle of the pool, reducing the highest TKE value and increasing the values of TI within the pool of the fish ladder. This resulted in a reduction in volumetric energy dissipation for both weir configurations.
The results of this study will help the reader understand the direct effects of the governing geometric parameters on the hydraulic characteristics of a fishway with a pool and weir. However, due to the limited configurations of the study, further investigation is needed to evaluate the position of the weir’s crest on the flow direction and the difference in flow characteristics when combining boulders instead of a solid wall for this type of labyrinth weir [26]. In addition, hydraulic engineers and biologists must work together to design an effective fishway with rectangular labyrinth configurations. The migration habits of the target species should be considered when designing the most appropriate design [27]. Parametric studies and field observations are recommended to determine the perfect design criteria.
The current study focused on comparing a rectangular labyrinth weir with a conventional straight weir. Further research can explore other weir configurations, such as variations in crest position, different shapes of labyrinth weirs, or the use of boulders instead of solid walls. This would help understand the influence of different geometric parameters on hydraulic characteristics.
5 Conclusions
A new layout of the weir was evaluated, namely a rectangular labyrinth weir compared to a straight weir in a pool and weir system. The differences between the weirs were highlighted, particularly how variations in the geometry of the structures, such as the shape of the weir, the spacing of the weir, the presence of an opening at the weir, and the slope of the bottom, affect the hydraulics within the structures. The main findings of this study are as follows:
The calculated dimensionless discharge (Qt*) confirmed three different flow regimes: when the corresponding range of Qt* is smaller than 0.6, the regime of plunging flow occurs for values of L/B = 1.83. (L: distance of the weir; B: channel width). When the corresponding range of Qt* is greater than 0.5, transitional flow occurs at L/B = 1.22. On the other hand, if Qt* is greater than 1, the streaming flow is at values of L/B = 0.61.
For the conventional weir and the rectangular labyrinth weir with the plunging flow, it can be assumed that the discharge (Q) is proportional to 1.56 and 1.47h, respectively (h: water depth above the weir). This information is useful for estimating the discharge based on water depth in practical applications.
In the rectangular labyrinth weir, the high-velocity zone is located on the side walls between the top of the weir and the channel wall. A high-velocity variation within short distances of the weir. Low velocity occurs within the downstream apex of the weir. This area may be suitable for swimming target fish.
As the distance between weirs increased, the zone of maximum velocity increased. However, the zone of low speed decreased. The prevailing maximum velocity for a rectangular labyrinth weir at L/B = 0.61, 1.22, and 1.83 was 1.46, 1.65, and 1.84 m/s, respectively. The low mean velocities for these distances were 0.27, 0.44, and 0.72 m/s, respectively. This finding highlights the importance of weir spacing in determining the flow characteristics within the fishway.
The presence of an orifice in the weir increased the flow velocity at the orifice and in the middle of the pool, especially in a conventional weir. The increase ranged from 7.7 to 12.48%.
For a given bottom slope, in a conventional weir, the highest values of turbulent kinetic energy (TKE) are uniformly distributed in the upstream part of the weir in the cross section of the channel. In contrast, for the rectangular labyrinth weir, the highest TKE values were concentrated on the sides of the pool between the crest of the weir and the channel wall. The highest TKE value for the conventional and the rectangular labyrinth weir was 0.224 and 0.278 J/kg, respectively, at the highest bottom slope (S0 = 10%).
For a given discharge, bottom slope, and weir spacing, the average values of TI are higher for the rectangular labyrinth weir than for the conventional weir. At the highest discharge, the average range of turbulence intensity (TI) for the conventional and rectangular labyrinth weirs was between 24 and 45% and 15% and 62%, respectively. This reveals that the rectangular labyrinth weir may generate more turbulent flow conditions within the fishway.
For a given discharge and constant bottom slope, the rectangular labyrinth weir has a higher energy dissipation rate than the conventional weir (22.75 and 34.86%).
Increasing the distance between weirs decreased volumetric energy dissipation. However, increasing the gradient increased volumetric energy dissipation. The presence of an opening in the weir resulted in a decrease in volumetric energy dissipation for both model types.
Availability of data and materials
Data is contained within the article.
References
Katopodis C (1992) Introduction to fishway design, working document. Freshwater Institute, Central Arctic Region
Marriner, B.A.; Baki, A.B.M.; Zhu, D.Z.; Thiem, J.D.; Cooke, S.J.; Katopodis, C.: Field and numerical assessment of turning pool hydraulics in a vertical slot fishway. Ecol. Eng. 63, 88–101 (2014). https://doi.org/10.1016/j.ecoleng.2013.12.010ArticleGoogle Scholar
Dasineh, M.; Ghaderi, A.; Bagherzadeh, M.; Ahmadi, M.; Kuriqi, A.: Prediction of hydraulic jumps on a triangular bed roughness using numerical modeling and soft computing methods. Mathematics 9, 3135 (2021)ArticleGoogle Scholar
Silva, A.T.; Bermúdez, M.; Santos, J.M.; Rabuñal, J.R.; Puertas, J.: Pool-type fishway design for a potamodromous cyprinid in the Iberian Peninsula: the Iberian barbel—synthesis and future directions. Sustainability 12, 3387 (2020). https://doi.org/10.3390/su12083387ArticleGoogle Scholar
Santos, J.M.; Branco, P.; Katopodis, C.; Ferreira, T.; Pinheiro, A.: Retrofitting pool-and-weir fishways to improve passage performance of benthic fishes: effect of boulder density and fishway discharge. Ecol. Eng. 73, 335–344 (2014). https://doi.org/10.1016/j.ecoleng.2014.09.065ArticleGoogle Scholar
Ead, S.; Katopodis, C.; Sikora, G.; Rajaratnam, N.J.J.: Flow regimes and structure in pool and weir fishways. J. Environ. Eng. Sci. 3, 379–390 (2004)ArticleGoogle Scholar
Guiny, E.; Ervine, D.A.; Armstrong, J.D.: Hydraulic and biological aspects of fish passes for Atlantic salmon. J. Hydraul. Eng. 131, 542–553 (2005)ArticleGoogle Scholar
Zhong, Z.; Ruan, T.; Hu, Y.; Liu, J.; Liu, B.; Xu, W.: Experimental and numerical assessment of hydraulic characteristic of a new semi-frustum weir in the pool-weir fishway. Ecol. Eng. 170, 106362 (2021). https://doi.org/10.1016/j.ecoleng.2021.106362ArticleGoogle Scholar
Roache, P.J.: Perspective: a method for uniform reporting of grid refinement studies. J. Fluids Eng. 1994(116), 405–413 (1994)ArticleGoogle Scholar
Guo, S.; Chen, S.; Huang, X.; Zhang, Y.; Jin, S.: CFD and experimental investigations of drag force on spherical leak detector in pipe flows at high Reynolds number. Comput. Model. Eng. Sci. 101(1), 59–80 (2014)Google Scholar
Ahmadi, M.; Kuriqi, A.; Nezhad, H.M.; Ghaderi, A.; Mohammadi, M.: Innovative configuration of vertical slot fishway to enhance fish swimming conditions. J. Hydrodyn. 34, 917–933 (2022). https://doi.org/10.1007/s42241-022-0071-yArticleGoogle Scholar
Ahmadi, M.; Ghaderi, A.; MohammadNezhad, H.; Kuriqi, A.; Di Francesco, S.J.W.: Numerical investigation of hydraulics in a vertical slot fishway with upgraded configurations. Water 13, 2711 (2021)ArticleGoogle Scholar
Celik, I.B.; Ghia, U.; Roache, P.J.; Freitas, C.J.J.: Procedure for estimation and reporting of uncertainty due to discretization in CFD applications. J. Fluids Eng. Trans. ASME (2008). https://doi.org/10.1115/1.2960953ArticleGoogle Scholar
Ghaderi, A.; Dasineh, M.; Aristodemo, F.; Aricò, C.: Numerical simulations of the flow field of a submerged hydraulic jump over triangular macroroughnesses. Water 13(5), 674 (2021)ArticleGoogle Scholar
Branco, P.; Santos, J.M.; Katopodis, C.; Pinheiro, A.; Ferreira, M.T.: Pool-type fishways: two different morpho-ecological cyprinid species facing plunging and streaming flows. PLoS ONE 8, e65089 (2013). https://doi.org/10.1371/journal.pone.0065089ArticleGoogle Scholar
Natália Melo da Silva1 1; Jorge Luis Zegarra Tarqui2,Edna Maria de Faria Viana 3
Abstract
저수지 침전은 수력 발전의 지속 가능한 발전을 위한 주요 문제 중 하나이며 브라질에 매우 중요합니다. 브라질의 주요 에너지원은 수력발전소에서 나옵니다. 소규모 수력 발전소(SHP)는 재생 에너지의 보완적 발전을 위한 중요한 대안입니다.
이들의 설계, 건설, 운영 및 재동력을 최적화하기 위해 저수지 내 퇴적물의 유체 역학 및 이동을 연구하는 것이 매우 중요합니다.
3차원 전산유체역학 – CFD 3D 모델링은 복잡한 흐름 문제에 가장 적합한 방법입니다. 제안된 방법은 MG Jeceaba 자치구에 위치한 PCH Salto Paraopeba의 유체 역학 및 퇴적물 이동 현상을 재현하고 평가하는 것을 목표로 하며, 취수구의 완전한 침전으로 인해 작동이 중단되었습니다.
모델의 검증은 미나스제라이스 연방대학교의 수력학 연구 센터(CPH)에 구축된 축소된 물리적 모델의 실험 데이터를 사용하여 수행됩니다.
Abstract: The reservoir silting is one of the main problems for sustainable development in the generation of hydroelectric energy and it is of great significance for Brazil. The main source of energy in Brazil comes from hydroelectric power plant. The Small Hydroelectric Power Plant (SHP) are an important alternative for complementary generation of renewable energy. Seeking to optimize the design, construction, operation, and repowering of these, it is extremely important to study the hydrodynamics and transport of sediments in their reservoirs. Threedimensional Computational Fluid Dynamics – CFD 3D modeling is the most appropriate method for complex flow problems. The proposed method aims to reproduce and evaluate the hydrodynamic and sediment transport phenomena of the PCH Salto Paraopeba, located in the municipality of Jeceaba, MG, which stopped working due to the complete silting up of its water intake. The validation of the model will be done using experimental data from the reduced physical model, built at the Hydraulic Research Center (CPH) at the Federal University of Minas Gerais.
Keywords
퇴적물 수송, 물리적 모델, 소규모 수력 발전소, Sediment transport, physical model, Small Hydroelectric Power Plant.
Figura 1 – Mapa de localização da PCH Salto ParaopebaFigura 2 – PCH Salto Paraopeba e modelo reduzido.
REFERÊNCIAS
ALBARELLO, L. “Guia para implantação de pequenas centrais hidrelétricas- PCHs”. Dissertação de Mestrado. Trabalho de Conclusão de Curso de Especialista. Programa de Pós-Graduação em Eficiência Energética Aplicada aos Processos Produtivos. UFSM, Panambi /RS, 2014.
ANEEL, SIGA – Sistema de Informações de Geração da ANEEL. Disponível em: . Acesso em 10 de maio de 2023.
CAMPELLO, B.S.C. “Estudo Da Velocidade de Queda e do Início do Movimento das Partículas de Borracha e Areia”. Dissertação de Mestrado. Programa de Pós-Graduação em Saneamento, Meio Ambiente e Recursos Hídricos. UFMG, Belo Horizonte /MG, 2017.
CAMPOS, A.S. “A Importância do Coeficiente de Rugosidade de Manning na Avaliação Numérica do Assoreamento de Reservatórios A Fio D’água”. Dissertação de Mestrado. Programa de PósGraduação em Saneamento, Meio Ambiente e Recursos Hídricos. UFMG, Belo Horizonte /MG, 2018.
CARVALHO, N. O. et al. Guia de avaliação de assoreamento de reservatórios, ANEEL, Brasília, 2000.
CARVALHO, N. O. Hidrossedimentologia prática, CPRM, Rio de Janeiro, 1994.
CARVALHO, N. O. Hidrossedimentologia prática, CPRM, Rio de Janeiro, 2008.
EMIG, PCH Salto do Paraopeba. Disponível em: < https://www.cemig.com.br/usina/pch-salto-doparaopeba/>. Acesso em 12 de maio de 2023.
ELETROBRÁS; Instituto de Pesquisas Hidráulicas – IPH. Diagnóstico das Condições sedimentológicas dos Principais Rios Brasileiros. UFRGS, Rio de Janeiro, 1992.
FLOW-3D®. FLOW-3D® 2022R2 – User Manual. Disponível em: < https://users.flow3d.com/flow3d/> FORTUNA, A.O. (2000). Técnicas Computacionais para Dinâmica dos Fluidos – Conceitos Básicos e Aplicações. São Paulo – SP.
GONÇALVES, M.O. “Análise Comparativa Entre Modelo Reduzido e Modelos Computacionais Uni e Bidimensionais”. Dissertação de Mestrado. Programa de Pós-Graduação em Engenharia de Recursos Hídricos e Ambiental. UFRP, Curitiba/PR, 2017.
HILLEBRAND, G.; KLASSEN, I.; OLSEN, N. R. B. (2017). “3D CFD modelling of velocities and sediment transport in the Iffezheim hydropower reservoir”. Hydrology Research 48 (1), pp. 147–159. JULIEN, P. Y. (2010). Erosion and sedimentation, Cambridge University Press, Cambridge, UK, 2nd edn.
MAHMOOD, K. (1987). Reservoir sedimentation – impact, extent and mitigation. World Bank Tech. Paper No. 71. Washington, DC.
MIRANDA, R.B. “A influência do assoreamento na geração de energia hidrelétrica: estudo de caso na Usina de Três Irmãos – SP”. Dissertação de Mestrado. Programa de Pós-Graduação em Ciências da Engenharia Ambiental. USP, São Carlos/SP, 2011.
MOHAMMAD, M.E.; AL-ANSARI, N.; KNUTSSON, S.; LAUE, J. (2020). “A Computational Fluid Dynamics Simulation Model of Sediment Deposition in a Storage Reservoir Subject to Water Withdrawal”. Water, 12, 959.
OLIVEIRA, M. A.“Repotenciação de pequenas centrais hidrelétricas: Avaliação técnica e econômica”. Dissertação de Mestrado. Programa de Pós-Graduação em Engenharia de Energia. UNIFEI, Itajubá/MG, 2012.
SALIBA, A.P.M. Notas de aula, Modelos fundo móvel, Disciplina Introdução a Modelagem Física em Engenharia, Universidade Federal de Minas Gerais. Belo Horizonte, 2020.
SOARES, W.S. “Taxa de Assoreamento no Reservatório da Usina Hidrelétrica do Funil, MG”. Dissertação de Mestrado. Programa de Pós-Graduação em Tecnologias e Inovações Ambientais. UFLA, Lavras/MG, 2015.
2 Researcher of Imam Hossein University, Faculty of Engineering and Passive Defense
3 Ivanki University, Iran.
10.22124/JCR.2023.24324.1618
Abstract
개방 수로의 심한 수력 구배는 침전으로 인한 심각한 침식과 문제를 일으킵니다. 패브릭 콘크리트는 기존의 콘크리트 표면을 대체할 수 있는 높은 실행 속도를 가진 독특한 제품입니다. 이 제품의 기계적 저항 매개변수에 따르면 부식 요인에 대한 우수한 내구성 외에도 직물 콘크리트의 응용 분야 중 하나는 운하 및 수로 암거 표면에 사용하는 것입니다. 이 연구에서는 먼저 사다리꼴 단면의 개방 채널 흐름을 직선 경로 상태의 3가지 공통 채널 형상, 굴곡 및 편차가 있는 경로, 마지막으로 채널 하단의 높이가 변경된 채널 경로를 포함하는 9가지 시나리오에서 시뮬레이션합니다. 각 주에서 flow-3d 소프트웨어를 사용한 흐름 난류 모델링과 함께 3개의 서로 다른 흐름 체제가 조사되었습니다.
FLOW-3D 소프트웨어를 사용한 유동 난류 모델링과 함께 다양한 유동 체제가 조사되었습니다. ABAQUS 소프트웨어를 사용하여 패브릭 콘크리트 구성요소와 연결 영역을 모델링하고, 콘크리트 표면과 취약한 연결 영역에 동일한 힘을 가하여 생성된 응력의 양을 확인했습니다. 결과는 생성된 응력이 직물 콘크리트의 인장 및 압축 응력 용량에 비해 매우 낮다는 것을 보여줍니다. 흐름과 콘크리트의 수력 연구를 검증하기 위해 관련 실험실 결과가 사용되었습니다.
Severe hydraulic gradients in open channels cause severe bed erosion and problems caused by sedimentation. Fabric concrete is a unique product with high execution speed that can replace traditional concrete surfaces. According to the mechanical resistance parameters of this product, in addition to its good durability against corrosive factors, one of the applications of fabric concrete is its use on the surface of canals and water course culverts. In this research, first, the flow of open channels in trapezoidal section is simulated under 9 scenarios, which include 3 common channel geometries in the state of a straight path, a path with bends and deviations, and finally, a channel path with a change in height at the bottom of the channel. In each of the states, 3 different flow regimes have been investigated along with flow turbulence modeling using flow-3d software.
Different flow regimes have been investigated along with flow turbulence modeling using flow-3d software. Using ABAQUS software, fabric concrete components and their connection areas have been modeled, and by applying forces equated to the concrete surface and vulnerable connection areas, the amount of created stresses has been checked. The results show that the created stresses are very low compared to the tensile and compressive stress capacity of fabric concrete. In order to validate the hydraulic studies of flow and concrete, the relevant laboratory results have been used.
In river engineering, the stepped spillway of a dam is an important component that may be used in various ways. It is necessary to conduct research dealing with flood control in order to investigate the method, in which energy is lost along the tiered spillways. In the past, several research projects on stepped spillways without baffles have been carried out utilizing a range of research approaches. In the present study, machine learning techniques such as Support Vector Machine (SVM) and Regression Tree (RT) are used to analyze the energy dissipation on rectangular stepped spillways that make use of baffles in a variety of configurations and at a range of channel slopes. The results of many experiments indicate that the amount of energy that is lost increases with the number of baffles that are present in flat channels with slopes and rises. In order to evaluate the efficiency and usefulness of the suggested model, the statistical indices that were developed for the experimental research are used to validate the models that were created for the study. The findings indicate that the suggested SVM model properly predicted the amount of energy that was dissipated when contrasted with RT and the method that had been developed in the past. This study verifies the use of machine learning techniques in this industry, and it is unique in that it anticipates energy dissipation along stepped spillways utilizing baffle designs. In addition, this work validates the use of machine learning methods in this field.
Keywords
Rectangular Stepped Spillways, Baffle Arrangements, Channel Slope, Support Vector Machine (SVM), Regression Tree (RT)
Introduction
To regulate water flows downstream of a dam, a spillway structure is employed, with stepped spillways preventing water from overflowing and causing damage to the dam. These spillways consist of a channel with built-in steps or drops. Flow patterns observed include nappe flow, transition flow, and skimming flow [1]. Numerous scholars have looked at the energy dissipation in stepped spillways [2-4]. Boes and Hager [5] looked at the benefits of stepped spillways, such as their simplicity of construction, less danger of cavitation, and smaller stilling basins at downstream dam toes owing to considerable energy loss along the chute. Hazzab and Chafic [7] conducted an experimental study on energy dissipation in stepped spillways and reported on flow configurations. Additionally, the Manksvill dam spillway was examined using a 1:25 scale physical wooden model [6]. For moderately inclined stepped channels, Stefan and Chanson [8] explored air-water flow measurements. Daniel [9] discussed how the existence of steps and step heights affect stepped spillways’ ability to dissipate energy. A comparison of the smooth invert chute flow with the self aerated stepped spillway. The energy dissipation in stepped spillways was investigated using various methods. Katourany [10] compared experimental findings to conventional USBR outcomes to examine the effects of different baffle widths, spacing between baffle rows, and step heights of baffled aprons. Salmasi et al. [11] assessed the energy dissipation of through-flow and over-flow in gabion stepped spillways, discovering that gabion spillways with pervious surfaces dissipated energy more efficiently than those with concrete walls. Other forms of stepped spillways, such as inclined steps and steps with end sills, were also quantitatively studied for energy dissipation [12]. Saedi and Asareh [13] examined how the number of drop stairs affected energy dissipation in stepped drops and suggested using stepped drops to increase energy dissipation by providing flow path roughness. Al-Husseini [14] found that decreasing the number of steps and downstream slopes led to an increase in flow energy dissipation, and that the use of cascade spillways reduced energy dissipation compared to the original step spillway. MARS and ANN methods were used to estimate energy dissipation in flow across stepped spillways under skimming flow conditions, with both models proving reliable [15]. Frederic et al. [16] evaluated the energy dissipation effectiveness and stability of the Mekin Dam spillway by confirming that flow did not result in transitional flow and by calculating safety factors at various intervals. A numerical model was developed to validate a physical model examining the impact of geometrical parameters on the dissipation rate in flows through stepped spillways [17]. The regulation of the rates of dissipation is studied using a particular kind of fuzzy inference system (FIS). The findings are compared with a predefined numerical database to determine the predicted energy dissipation under various circumstances. The findings show that the suggested FIS may be a useful tool for the operational management of dissipator structures while taking various geometric characteristics into account. Nasralla [18] studied the four phases of the spillway and conducted eighteen runs to enhance energy dissipation through the contraction-stepped spillway. The study considered alternative baffle placements, heights, and widths. The results showed that downstream baffles on the stepped spillway of the stilling basin improve energy dissipation. Using the Flow 3D software, Ikinciogullari [19] quantitatively analyzed the energy dissipation capabilities of trapezoidal stepped spillways using four distinct models and three different discharges. The findings showed that trapezoidal stepped spillways are up to 30% more efficient in dissipating energy than traditional stepped spillways. In previous works, only a few machine learning algorithms were used to forecast energy dissipation across a rectangular stepped spillway without baffles. Therefore, this study used machine learning approaches such as Support Vector Machine (SVM) and Regression Tree (RT) to predict energy dissipation across a rectangular stepped spillway with varied rectangular-shaped baffle configurations at different channel slopes. The study compared these models using statistical analysis to assess their efficiency in predicting energy dissipation over rectangular stepped spillways with baffles. 2. Materials and Methods 2.1. Experimental Setup The experiments were carried out at the Hydraulics laboratory of Delhi Technological University. The tests were performed in a rectangular tilting flume of 8m long, 0.30m wide and 0.40m deep which has a facility to make it horizontal and sloping as well (shown in Figure 1). The flume consists of an inlet section, an outlet section, and a collecting tank at the downstream end which is used to measure the discharge. Figure 2 depicts the model of a rectangular stepped spillway prepared using an acrylic sheet having a width of 0.30m, a height of 0.20m and a base length of 0.40m. A total of four steps were designed with a step height of 0.05m, the step length is 0.10m and rectangular-shaped baffles of length 0.10m and height of 0.05m were arranged in different manner. Figure 3 represents the different baffle arrangements used in the experimental work. At first, the experiment was conducted for no baffle condition. Thereafter the experiment was conducted for the first arrangement of three baffles, in which two baffles were placed at a distance of 0.10m from the toe of the spillway and a distance of 0.10m was maintained between the first two baffles and the third baffle was placed between the first two baffles at a distance of 0.20m from the toe of the spillway (figure 4a). After that, the experiment was conducted for the third arrangement of baffles which consists of five baffles, two more baffles were introduced at a distance of 0.30m from the toe of the spillway and a distance of 0.10m was maintained between them (figure 4b). The baffles used in the experiment were rectangular shaped which had a height of 0.05m and length of 0.10m. The experiments were conducted for five different discharges 2 l/s, 4 l/s, 6 l/s, 8 l/s and 10 l/s. For the purpose of determining the head values both upstream and downstream of the spillway model, a point gauge with a precision of 0.1mm was used. In order to determine the average velocities of the upstream and downstream portions, respectively, a pitot static tube was used in conjunction with a digital manometer.
Yupeng Ren abc, Huiguang Zhou cd, Houjie Wang ab, Xiao Wu ab, Guohui Xu cd, Qingsheng Meng cd
Abstract
해저 퇴적물 흐름은 퇴적물을 심해로 운반하는 주요 수단 중 하나이며, 종종 장거리를 이동하고 수십 또는 수백 킬로미터에 걸쳐 상당한 양의 퇴적물을 운반합니다. 그것의 강력한 파괴력은 종종 이동 과정에서 잠수함 유틸리티에 심각한 손상을 초래합니다.
퇴적물 흐름의 퇴적물 농도는 주변 해수와의 밀도차를 결정하며, 이 밀도 차이는 퇴적물 흐름의 흐름 능력을 결정하여 이송된 퇴적물의 최종 퇴적 위치에 영향을 미칩니다. 본 논문에서는 다양한 미사 및 점토 중량비(미사/점토 비율이라고 함)를 갖는 다양한 퇴적물 농도의 퇴적물 흐름을 수로 테스트를 통해 연구합니다.
우리의 테스트 결과는 특정 퇴적물 구성에 대해 퇴적물 흐름이 가장 빠르게 이동하는 임계 퇴적물 농도가 있음을 나타냅니다. 4가지 미사/점토 비율 각각에 대한 임계 퇴적물 농도와 이에 상응하는 최대 속도가 구해집니다. 결과는 점토 함량이 임계 퇴적물 농도와 선형적으로 음의 상관 관계가 있음을 나타냅니다.
퇴적물 농도가 증가함에 따라 퇴적물의 흐름 거동은 흐름 상태에서 붕괴된 상태로 변환되고 흐름 거동이 변화하는 두 탁한 현탁액의 유체 특성은 모두 Bingham 유체입니다.
또한 본 논문에서는 퇴적물 흐름 내 입자 배열을 분석하여 위에서 언급한 결과에 대한 미시적 설명도 제공합니다.
Submarine sediment flows is one of the main means for transporting sediment to the deep sea, often traveling long-distance and transporting significant volumes of sediment for tens or even hundreds of kilometers. Its strong destructive force often causes serious damage to submarine utilities on its course of movement. The sediment concentration of the sediment flow determines its density difference with the ambient seawater, and this density difference determines the flow ability of the sediment flow, and thus affects the final deposition locations of the transported sediment. In this paper, sediment flows of different sediment concentration with various silt and clay weight ratios (referred to as silt/clay ratio) are studied using flume tests. Our test results indicate that there is a critical sediment concentration at which sediment flows travel the fastest for a specific sediment composition. The critical sediment concentrations and their corresponding maximum velocities for each of the four silt/clay ratios are obtained. The results further indicate that the clay content is linearly negatively correlated with the critical sediment concentration. As the sediment concentration increases, the flow behaviors of sediment flows transform from the flow state to the collapsed state, and the fluid properties of the two turbid suspensions with changing flow behaviors are both Bingham fluids. Additionally, this paper also provides a microscopic explanation of the above-mentioned results by analyzing the arrangement of particles within the sediment flow.
Introduction
Submarine sediment flows are important carriers for sea floor sediment movement and may carry and transport significant volumes of sediment for tens or even hundreds of kilometers (Prior et al., 1987; Pirmez and Imran, 2003; Zhang et al., 2018). Earthquakes, storms, and floods may all trigger submarine sediment flow events (Hsu et al., 2008; Piper and Normark, 2009; Pope et al., 2017b; Gavey et al., 2017). Sediment flows have strong forces during the movement, which will cause great harm to submarine structures such as cables and pipelines (Pope et al., 2017a). It was first confirmed that the cable breaking event caused by the sediment flow occurred in 1929. The sediment flow triggered by the Grand Banks earthquake damaged 12 cables. According to the time sequence of the cable breaking, the maximum velocity of the sediment flow is as high as 28 m/s (Heezen and Ewing, 1952; Kuenen, 1952; Heezen et al., 1954). Subsequent research shows that the lowest turbidity velocity that can break the cable also needs to reach 19 m/s (Piper et al., 1988). Since then, there have been many damage events of submarine cables and oil and gas pipelines caused by sediment flows in the world (Hsu et al., 2008; Carter et al., 2012; Cattaneo et al., 2012; Carter et al., 2014). During its movement, the sediment flow will gradually deposit a large amount of sediment carried by it along the way, that is, the deposition process of the sediment flow. On the one hand, this process brings a large amount of terrestrial nutrients and other materials to the ocean, while on the other hand, it causes damage and burial to benthic organisms, thus forming the largest sedimentary accumulation on Earth – submarine fans, which are highly likely to become good reservoirs for oil and gas resources (Daly, 1936; Yuan et al., 2010; Wu et al., 2022). The study on sediment flows (such as, the study of flow velocity and the forces acting on seabed structures) can provide important references for the safe design of seabed structures, the protection of submarine ecosystems, and exploration of turbidity sediments related oil and gas deposits. Therefore, it is of great significance to study the movement of sediment flows.
The sediment flow, as a highly sediment-concentrated fluid flowing on the sea floor, has a dense bottom layer and a dilute turbulent cloud. Observations at the Monterey Canyon indicated that the sediment flow can maintain its movement over long distances if its bottom has a relatively high sediment concentration. This dense bottom layer can be very destructive along its movement path to any facilities on the sea floor (Paull et al., 2018; Heerema et al., 2020; Wang et al., 2020). The sediment flow mentioned in this research paper is the general term of sediment density flow.
The sediment flow, which occurs on the seafloor, has the potential to cause erosion along its path. In this process, the suspended sediment is replenished, allowing the sediment flow to maintain its continuous flow capacity (Zhao et al., 2018). The dynamic force of sediment flow movement stem from its own gravity and density difference with surrounding water. In cases that the gravity drive of the slope is absent (on a flat sea floor), the flow velocity and distance of sediment flows are essentially determined by the sediment composition and concentration of the sediment flows as previous studies have demonstrated. Ilstad et al. (2004) conducted underwater flow tests in a sloped tank and employed high speed video camera to perform particle tracking. The results indicated that the premixed sand-rich and clay-rich slurries demonstrated different flow velocity and flow behavior. Using mixed kaolinite(d50 = 6 μm) and silica flour(d50 = 9 μm) in three compositions with total volumetric concentration ranged 22% or 28%, Felix and Peakall (2006) carried out underwater flow tests in a 5° slope Perspex channel and found that the flow ability of sediment flows is different depending on sediment compositions and concentrations. Sumner et al. (2009) used annular flume experiments to investigate the depositional dynamics and deposits of waning sediment-laden flows, finding that decelerating fast flows with fixed sand content and variable mud content resulted in four different deposit types. Chowdhury and Testik (2011) used lock-exchange tank, and experimented the kaolin clay sediment flows in the concentration range of 25–350 g/L, and predicted the fluid mud sediment flows propagation characteristics, but this study focused on giving sediment flows propagate phase transition time parameters, and is limited to clay. Lv et al. (2017) found through experiments that the rheological properties and flow behavior of kaolin clay (d50 = 3.7 μm) sediment flows were correlated to clay concentrations. In the field monitoring conducted by Liu et al. (2023) at the Manila Trench in the South China Sea in 2021, significant differences in the velocity, movement distance, and flow morphology of turbidity currents were observed. These differences may be attributed to variations in the particle composition of the turbidity currents.
On low and gentle slopes, although sediment flow with sand as the main sediment composition moves faster, it is difficult to propagate over long distances because sand has greater settling velocity and subaqueous angle of repose. Whereas the sediment flows with silt and clay as main composition may maintain relatively stable currents. Although its movement speed is slow, it has the ability to propagate over long distances because of the low settling rate of the fine particles (Ilstad et al., 2004; Liu et al., 2023). In a field observation at the Gaoping submarine canyon, the sediments collected from the sediment flows exhibited grain size gradation and the sediment was mostly composed of silt and clay (Liu et al., 2012). At the largest deltas in the world, for instance, the Mississippi River Delta, the sediments are mainly composed of silt and clay, which generally distributed along the coast in a wide range and provided the sediment sources for further distribution. The sediment flows originated and transported sediment from the coast to the deep sea are therefore share the same sediment compositions as delta sediments. To study the sediment flows composed of silt and clay is of great importance.
The sediment concentration of the sediment flows determines the density difference between the sediment flows and the ambient water and plays a key role in its flow ability. For the sediment flow with sediment composed of silt and clay, low sediment concentration means low density and therefore leads to low flow ability; however, although high sediment concentration results in high density, since there is cohesion between fine particles, it changes fluid properties and leads to low flow ability as well. Therefore, there should be a critical sediment concentration with mixed composition of silt and clay, at which the sediment flow maintains its strongest flow capacity and have the highest movement speed. In other words, the two characteristics of particle diameter and concentration of the sediment flow determine its own motion ability, which, if occurs, may become the most destructive force to submarine structures.
The objectives of this work was to study how the sediment composition (measured in relative weight of silt and clay, and referred as silt/clay ratio) and sediment concentration affect flow ability and behavior of the sediment flows, and to quantify the critical sediment concentration at which the sediment flows reached the greatest flow velocity under the experiment setting. We used straight flume without slope and conducted a series of flume tests with varying sediment compositions (silt-rich or clay-rich) and concentrations (96 to 1212 g/L). Each sediment flow sample was tested and analyzed for rheological properties using a rheometer, in order to characterize the relationship between flow behavior and rheological properties. Combined with the particle diameter, density and viscosity characteristics of the sediment flows measured in the experiment, a numerical modeling study is conducted, which are mutually validated with the experimental results.
The sediment concentration determines the arrangements of the sediment particles in the turbid suspension, and the arrangement impacts the fluid properties of the turbid suspension. The microscopic mode of particle arrangement in the turbid suspension can be constructed to further analyze the relationship between the fluid properties of turbid suspension and the flow behaviors of the sediment flow, and then characterize the critical sediment concentration at which the sediment flow runs the fastest. A simplified microscopic model of particle arrangement in turbid suspension was constructed to analyze the microscopic arrangement characteristics of sediment particles in turbid suspension with the fastest velocity.
Section snippets
Equipment and materials
The sediment flows flow experiments were performed in a Perspex channel with smooth transparent walls. The layout and dimensions of the experimental set-up were shown in Fig. 1. The bottom of the channel was flat and straight, and a gate was arranged to separate the two tanks. In order to study the flow capacity of turbidity currents from the perspective of their own composition (particle size distribution and concentration), we used a straight channel instead of an inclined one, to avoid any
Relationship between sediment flow flow velocity and sediment concentration
After the sediment flow is generated, its movement in the first half (50 cm) of the channel is relatively stable, and there is obvious shock diffusion in the second half. The reason is that the excitation wave (similar to the surge) will be formed during the sediment flow movement, and its speed is much faster than the speed of the sediment flow head. When the excitation wave reaches the tail of the channel, it will be reflected, thus affecting the subsequent flow of the sediment flow.
Sediment flows motion simulation based on FLOW-3D
As a relatively mature 3D fluid simulation software, FLOW-3D can accurately predict the free surface flow, and has been used to simulate the movement process of sediment flows for many times (Heimsund, 2007). The model adopted in this paper is RNG turbulence model, which can better deal with the flow with high strain rate and is suitable for the simulation of sediment flows with variable shape during movement. The governing equations of the numerical model involved include continuity equation,
Conclusions
In this study, we conducted a series of sediment flow flume tests with mixed silt and clay sediment samples in four silt/clay ratios on a flat slope. Rheological measurements were carried out on turbid suspension samples and microstructure analysis of the sediment particle arrangements was conducted, we concluded that:
(1)The flow velocity of the sediment flow is controlled by the sediment concentration and its own particle diameter composition, the flow velocity increased with the increase of the
Declaration of Competing Interest
The authors declare that they have no known competing financial interests or personal relationships that could have appeared to influence the work reported in this paper.
Acknowledgements
This work was supported by the National Natural Science Foundation of China [Grant no. 42206055]; the National Natural Science Foundation of China [Grant no. 41976049]; and the National Natural Science Foundation of China [Grant no. 42272327].
R.A. BagnoldAuto-suspension of transported sediment; turbidity currentsProc. R. Soc. Lond.(1962)
L. Carter et al.Near-synchronous and delayed initiation of long run-out submarine sediment flows from a record-breaking river flood, offshore TaiwanGeophys. Res. Lett.(2012)
L. Carter et al.Insights into submarine geohazards from breaks in subsea telecommunication cablesOceanography(2014)
A. Cattaneo et al.Searching for the seafloor signature of the 21 May 2003 Boumerdès earthquake offshore Central AlgeriaNat. Hazard. Earth. Sys.(2012)
S. ChoiLayer-averaged modeling of two-dimensional turbidity currents with a dissipative; galerkin finite element method; part i, formulation and application exampleJ. Hydraul. Res.(1998)
S.U. Choi et al.k-ε Turbulence modeling of density currents developing two dimensionally on a slopeJ. Hydraul. Eng.(2002)
R.A. DalyOrigin of submarine canyonsAm. J. Sci.(1936)
M. Felix et al.Transformation of debris flows into turbidity currents : mechanisms inferred from laboratory experimentsSedimentology(2006)
F.H. Harlow et al.Turbulence transport equationsPhys. Fluids(1967)
G.J. Heerema et al.What determines the downstream evolution of turbidity currents?Earth Planet. Sci. Lett.(2020)
There are more references available in the full text version of this article.
Sous la direction de : Marc Jolin, directeur de recherche Benoit Bissonnette, codirecteur de recherche
Modélisation de l’écoulement du béton frais
Abstract
현재의 기후 비상 사태와 기후 변화에 관한 다양한 과학적 보고서를 고려할 때 인간이 만든 오염을 대폭 줄이는 것은 필수적이며 심지어 중요합니다. 최신 IPCC(기후변화에 관한 정부 간 패널) 보고서(2022)는 2030년까지 배출량을 절반으로 줄여야 함을 나타내며, 지구 보존을 위해 즉각적인 조치를 취해야 한다고 강력히 강조합니다.
이러한 의미에서 콘크리트 생산 산업은 전체 인간 이산화탄소 배출량의 4~8%를 담당하고 있으므로 환경에 미치는 영향을 줄이기 위한 진화가 시급히 필요합니다.
본 연구의 주요 목적은 이미 사용 가능한 기술적 품질 관리 도구를 사용하여 생산을 최적화하고 혼합 시간을 단축하며 콘크리트 폐기물을 줄이기 위한 신뢰할 수 있고 활용 가능한 수치 모델을 개발함으로써 이러한 산업 전환에 참여하는 것입니다.
실제로, 혼합 트럭 내부의 신선한 콘크리트의 거동과 흐름 프로파일을 더 잘 이해할 수 있는 수치 시뮬레이션을 개발하면 혼합 시간과 비용을 더욱 최적화할 수 있으므로 매우 유망합니다. 이러한 복잡한 수치 도구를 활용할 수 있으려면 수치 시뮬레이션을 검증, 특성화 및 보정하기 위해 기본 신 콘크리트 흐름 모델의 구현이 필수적입니다.
이 논문에서는 세 가지 단순 유동 모델의 개발이 논의되고 얻은 결과는 신선한 콘크리트 유동의 수치적 거동을 검증하는 데 사용됩니다. 이러한 각 모델은 강점과 약점을 갖고 있으며, 신선한 콘크리트의 유변학과 유동 거동을 훨씬 더 잘 이해할 수 있는 수치 작업 환경을 만드는 데 기여합니다.
따라서 이 연구 프로젝트는 새로운 콘크리트 생산의 완전한 모델링을 위한 진정한 관문입니다.
In view of the current climate emergency and the various scientific reports on climate change, it is essential and even vital to drastically reduce man-made pollution. The latest IPCC (Intergovernmental Panel on Climate Change) report (2022) indicates that emissions must be halved by 2030 and strongly emphasizes the need to act immediately to preserve the planet. In this sense, the concrete production industry is responsible for 4-8% of total human carbon dioxide emissions and therefore urgently needs to evolve to reduce its environmental impact. The main objective of this study is to participate in this industrial transition by developing a reliable and exploitable numerical model to optimize the production, reduce mixing time and also reduce concrete waste by using technological quality control tools already available. Indeed, developing a numerical simulation allowing to better understand the behavior and flow profiles of fresh concrete inside a mixing-truck is extremely promising as it allows for further optimization of mixing times and costs. In order to be able to exploit such a complex numerical tool, the implementation of elementary fresh concrete flow models is essential to validate, characterize and calibrate the numerical simulations. In this thesis, the development of three simple flow models is discussed and the results obtained are used to validate the numerical behavior of fresh concrete flow. Each of these models has strengths and weaknesses and contributes to the creation of a numerical working environment that provides a much better understanding of the rheology and flow behavior of fresh concrete. This research project is therefore a real gateway to a full modelling of fresh concrete production.
Figure 2-15: Système expérimental du plan inclinéFigure 2-19: Essai d’affaissement au cône d’Abrams
Reference
Amziane, S., Ferraris, C. F., & Koehler, E. (2006). Feasibility of Using a Concrete Mixing Truck as a Rheometer. Anderson, J. D. (1991). Fundamentals of aerodynamics. McGraw-Hill. Balmforth, N. J., Craster, R. V., & Sassi, R. (2002). Shallow viscoplastic flow on an inclined plane. Journal of Fluid Mechanics, 470, 1-29. https://doi.org/10.1017/S0022112002001660 Banfill, P., Beaupré, D., Chapdelaine, F., de Larrard, F., Domone, P., Nachbaur, L., Sedran, T., Wallevik, O., & Wallevik, J. E. (2000). Comparison of concrete rheometers International tests at LCPC (Nantes, France) in October 2000. In NIST. Baracu T. (2012). Computational analysis of the flow around a cylinder and of the drag force. Barreto, D., & Leak, J. (2020). A guide to modeling the geotechnical behavior of soils using the discrete element method. In Modeling in Geotechnical Engineering (p. 79-100). Elsevier. https://doi.org/10.1016/B978-0-12-821205-9.00016-2 Baudez, J. C., Chabot, F., & Coussot, P. (2002). Rheological interpretation of the slump test. Applied Rheology, 12(3), 133-141. https://doi.org/10.1515/arh-2002- 0008 Beaupre, D. (2012). Mixer-mounted probe measures concrete workability. Berger, X. (2023). Proposition de recherche et préparation orale de doctorat (GCI8084). Bergeron, P. (1953). Considérations sur les facteurs influençant l’usure due au transport hydraulique de matériaux solides. Application plus particulière aux machines. https://www.persee.fr/doc/jhydr_0000-0001_1953_act_2_1_3256 Bingham, E. (1922). Fluidity and Plasticity (Digitized by the Internet Archive in 2007). http://www.archive.org/details/fluidityplasticiOObinguoft Bruschi, G., Nishioka, T., Tsang, K., & Wang, R. (2003). A comparison of analytical methods drag coefficient of a cylinder.
Caceres, E. C. (2019). Impact de la rhéologie des matériaux cimentaires sur l’aspect des parements et les procédés de mise en place. https://tel.archivesouvertes.fr/tel-01982159 Chanson, H., Jarny, ; S, & Coussot, P. (2006). Dam Break Wave of Thixotropic Fluid. https://doi.org/10.1061/ASCE0733-94292006132:3280 Chi, Z. P., Yang, H., Li, R., & Sun, Q. C. (2021). Measurements of unconfined fresh concrete flow on a slope using spatial filtering velocimetry. Powder Technology, 393, 349-356. https://doi.org/10.1016/j.powtec.2021.07.088 Cochard, S., & Ancey, C. (2009). Experimental investigation of the spreading of viscoplastic fluids on inclined planes. Journal of Non-Newtonian Fluid Mechanics, 158(1-3), 73-84. https://doi.org/10.1016/j.jnnfm.2008.08.007 Coussot, Philippe., & Ancey, C. (Christophe). (1999). Rhéophysique des pâtes et des suspensions. EDP Sciences. CSA Group. (2019). CSA A23.1:19 / CSA A23.2:19 : Concrete materials and methods of concret construction / Test methods and standard practices for concrete. Daczko, J. A. (2000). A proposal for measuring rheology of production concrete. De Larrard, F. (1999). Structures granulaires et formulation des bétons. http://www.lcpc.fr/betonlabpro De Larrard, F., Ferraris, C. F., & Sedran, T. (1998). Fresh concrete: A HerscheIBulkley material (Vol. 31). Domone P.L.J., J. J. (1999). Properties of mortar for self-compacting concrete. RILEM, 109-120. El-Reedy, M. (2009). Advanced Materials and Techniques for Reinforced Concrete Structures. Emborg M. (1999). Rheology tests for self-compacting concrete – how useful are they for the design of concrete mix for full-scale production. Fall A. (2008). Rhéophysique des fluides complexes : Ecoulement et Blocage de suspensions concentrées. https://www.researchgate.net/publication/30515545 Ferraris, C. F., Brower, L. E., Beaupré, D., Chapdelaine, F., Domone, P., Koehler, E., Shen, L., Sonebi, M., Struble, L., Tepke, D., Wallevik, O., & Wallevik, J. E.
(2003). Comparison of concrete rheometers: International tests at MB. https://doi.org/10.6028/NIST.IR.7154 Ferraris, C. F., & de Larrard, F. (1998a). Rhéologie du béton frais remanié III – L’essai au cône d’Abrams modifié. Ferraris, C. F., & de Larrard, F. (1998b, février). NISTIR 6094 Testing and modelling of fresh concrete rheology. NISTIR 6094. https://ciks.cbt.nist.gov/~garbocz/rheologyNISTIR/FR97html.htm Fischedick, M., Roy, J., Abdel-Aziz, A., Acquaye Ghana, A., Allwood, J., Baiocchi, G., Clift, R., Nenov, V., Yetano Roche Spain, M., Roy, J., Abdel-Aziz, A., Acquaye, A., Allwood, J. M., Ceron, J., Geng, Y., Kheshgi, H., Lanza, A., Perczyk, D., Price, L., … Minx, J. (2014). Climate Change 2014. Fox R., & McDonald A. (2004). Introduction to fluid mechanics. Franco Correa I.-D. (2019). Étude tribologique à hautes températures de matériaux céramiques structurés à différentes échelles. GIEC. (2022). Climate Change 2022 : Mitigation of Climate Change. www.ipcc.ch Gouvernement du Canada. (2021, mai 31). Déclaration commune : L’industrie canadienne du ciment et le gouvernement du Canada annoncent un partenariat. https://www.ic.gc.ca/eic/site/icgc.nsf/fra/07730.html Grenier, M. (1998). Microstructure et résistance à l’usure de revêtements crées par fusion laser avec gaz réactifs sur du titane. Herschel, W. H., & Bulkley, R. (1926). Konsistenzmessungen von GummiBenzollösungen. Kolloid-Zeitschrift, 39(4), 291-300. https://doi.org/10.1007/BF01432034 Hirt, C. W., & Nichols, B. D. (1981). Volume of fluid (VOF) method for the dynamics of free boundaries. Journal of Computational Physics, 39(1), 201-225. https://doi.org/https://doi.org/10.1016/0021-9991(81)90145-5 Hoornahad, H., & Koenders, E. A. B. (2012). Simulation of the slump test based on the discrete element method (DEM). Advanced Materials Research, 446-449, 3766-3773. https://doi.org/10.4028/www.scientific.net/AMR.446-449.3766
Hu, C., de Larrard, F., Sedran, T., Boulay, C., Bosd, F., & Deflorenne, F. (1996). Validation of BTRHEOM, the new rheometer for soft-to-fluid concrete. In Materials and Structures/Mat~riaux et Constructions (Vol. 29). Jeong, S. W., Locat, J., Leroueil, S., & Malet, J. P. (2007). Rheological properties of fine-grained sediments in modeling submarine mass movements: The role of texture. Submarine Mass Movements and Their Consequences, 3rd International Symposium, 191-198. https://doi.org/10.1007/978-1-4020-6512- 5_20 Kabagire, K. D. (2018). Modélisation expérimentale et analytique des propriétés rhéologiques des bétons autoplaçants. Katopodes, N. D. (2019). Volume of Fluid Method. In Free-Surface Flow (p. 766-802). Elsevier. https://doi.org/10.1016/b978-0-12-815485-4.00018-8 Khayat. (2008). Personnal Communication. Kosmatka, S. (2011). Dosage et contrôle des mélanges de béton (8ème édition). Li, H., Wu, A., & Cheng, H. (2022). Generalized models of slump and spread in combination for higher precision in yield stress determination. Cement and Concrete Research, 159. https://doi.org/10.1016/j.cemconres.2022.106863 Massey, B., & Smith, J. (2012). Mechanics of fluids 9ème édition. Mokéddem, S. (2014). Contrôle de la rhéologie d’un béton et de son évolution lors du malaxage par des mesures en ligne à l’aide de la sonde Viscoprobe. https://tel.archives-ouvertes.fr/tel-00993153 Munson, B. R., & Young, D. R. (2006). Fundamental of Fluid Mechanics (5th éd.). Munson, M., Young, M. , & Okiishi, M. (2020). Mécanique des fluides (8ème édition). Murata, J., & Kikukawa, H. (1992). Viscosity Equation for Fresh Concrete. Nakayama, Y., & Boucher, R. F. (2000). Introduction to fluid mechanics. ButterworthHeinemann. Němeček, J. (2021). Numerical simulation of slump flow test of cement paste composites. Acta Polytechnica CTU Proceedings, 30, 58-62. https://doi.org/10.14311/APP.2021.30.0058 Nikitin, K. D., Olshanskii, M. A., Terekhov, K. M., & Vassilevski, Y. V. (2011). A numerical method for the simulation of free surface flows of viscoplastic fluid in
3D. Journal of Computational Mathematics, 29(6), 605-622. https://doi.org/10.4208/jcm.1109-m11si01 Noh, W. F., & Woodward, P. (1976). SLIC (Simple Line Interface Calculation). Odabas, D. (2018). Effects of Load and Speed on Wear Rate of Abrasive Wear for 2014 Al Alloy. IOP Conference Series: Materials Science and Engineering, 295(1). https://doi.org/10.1088/1757-899X/295/1/012008 Pintaude, G. (s. d.). Characteristics of Abrasive Particles and Their Implications on Wear. www.intechopen.com Poullain, P. (2003). Étude comparative de l’écoulement d’un fluide viscoplastique dans une maquette de malaxeur pour béton. R. J. Cattolica. (2003). Experiment F2: Water Tunnel. In MAE171A/175A Mechanical Engineering Laboratory Manual (Winter Quarter). Raper, R. M. (1966). Drag force and pressure distribution on cylindrical protuberances immersed in a turbulent channel flow. RMCAO. (2013). CSA A23.2-5C: Concrete Basics Slump Test. Roques, A., & School, H. (2006). High resolution seismic imaging applied to the geometrical characterization of very high voltage electric pylons. https://www.researchgate.net/publication/281566156 Roussel, N. (2006). Correlation between yield stress and slump: Comparison between numerical simulations and concrete rheometers results. Materials and Structures/Materiaux et Constructions, 39(4), 501-509. https://doi.org/10.1617/s11527-005-9035-2 Roussel, N., & Coussot, P. (2005). “Fifty-cent rheometer” for yield stress measurements: From slump to spreading flow. Journal of Rheology, 49(3), 705-718. https://doi.org/10.1122/1.1879041 Roussel, N., Geiker, M. R., Dufour, F., Thrane, L. N., & Szabo, P. (2007). Computational modeling of concrete flow: General overview. Cement and Concrete Research, 37(9), 1298-1307. https://doi.org/10.1016/j.cemconres.2007.06.007 Schaer, N. (2019). Modélisation des écoulements à surface libre de fluides nonnewtoniens. https://theses.hal.science/tel-02166968
Schowalter, W. R., & Christensen, G. (1998). Toward a rationalization of the slump test for fresh concrete: Comparisons of calculations and experiments. Journal of Rheology, 42(4), 865-870. https://doi.org/10.1122/1.550905 Sofiane Amziane, Chiara F. Ferraris, & Eric P. Koehler. (2005). Measurement of Workability of Fresh Concrete Using a Mixing Truck. Journal of Research of the National Institute of Standards Technology, 55-56. Sooraj, P., Agrawal, A., & Sharma, A. (2018). Measurement of Drag Coefficient for an Elliptical Cylinder. Journal of Energy and Environmental Sustainability, 5, 1-7. https://doi.org/10.47469/jees.2018.v05.100050 Stachowiak G. (2006). Wear – Materials, Mechanisms and Pratice. Stachowiak G.W. (1993). Tribology Series (Vol. 24, p. 557-612). Elsevier. Tattersall, G., & Banfill, P. F. G. (1983). The rheology of fresh concrete. The European Guidelines for Self-Compacting Concrete Specification, Production and Use « The European Guidelines for Self Compacting Concrete ». (2005). www.efnarc.org University College London. (2010). Pressure around a cylinder and cylinder drag. Van Oudheusden, B. W., Scarano, F., Roosenboom, E. W. M., Casimiri, E. W. F., & Souverein, L. J. (2007). Evaluation of integral forces and pressure fields from planar velocimetry data for incompressible and compressible flows. Experiments in Fluids, 43(2-3), 153-162. https://doi.org/10.1007/s00348-007- 0261-y Vasilic, K., Gram, A., & Wallevik, J. E. (2019). Numerical simulation of fresh concrete flow: Insight and challenges. RILEM Technical Letters, 4, 57-66. https://doi.org/10.21809/rilemtechlett.2019.92 Viccione, G., Ferlisi, S., & Marra, E. (2010). A numerical investigation of the interaction between debris flows and defense barriers. http://www.unisa.it/docenti/giacomoviccione/en/index Wallevik J. (2006). Relation between the Bingham parameters and slump. Wallevik, J. E. (2006). Relationship between the Bingham parameters and slump. Cement and Concrete Research, 36(7), 1214-1221. https://doi.org/10.1016/j.cemconres.2006.03.001
Wallevik, J. E., & Wallevik, O. H. (2020). Concrete mixing truck as a rheometer. Cement and Concrete Research, 127. https://doi.org/10.1016/j.cemconres.2019.105930
전기화학 반응기에 대한 3D 수치 시뮬레이션 및 측정을 사용하여 동시 초음파 처리 유무에 관계없이 물에서 스트론튬 제거 효율을 분석했습니다. 초음파는 작동 주파수가 25kHz인 4개의 초음파 변환기를 사용하여 생성되었습니다. 반응기는 2개의 블록으로 배열된 8개의 알루미늄 전극을 사용했습니다.
LICHT K.1*, LONČAR G.1, POSAVČIĆ H.1, HALKIJEVIĆ I.1 1 Department of Hydroscience and Engineering, Faculty of Civil Engineering, University of Zagreb, Andrije Kačića-Miošića 26, 10000 Zagreb, Croatia *corresponding author: e-mail:katarina.licht@grad.unizg.hr
물 속의 스트론튬 이온은 3.2∙10-19C의 전하와 1.2∙10-8m의 직경을 특징으로 하는 입자로 모델링됩니다. 수치 모델은 기본 유체 역학 모듈, 정전기 모듈 및 일반 이동 객체 모듈을 사용하여 Flow-3D 소프트웨어에서 생성되었습니다.
수치 시뮬레이션을 통해 연구된 원자로 변형의 성능은 시뮬레이션 기간이 끝날 때 전극에 영구적으로 유지되는 모델 스트론튬 입자 수와 물 속의 초기 입자 수의 비율로 정의됩니다. 실험실 반응기의 경우 스트론튬 제거 효과는 실험 종료 시와 시작 시 물 내 균일한 스트론튬 농도의 비율로 정의됩니다.
결과는 초음파를 사용하면 수처리 180초 후에 스트론튬 제거 효과가 10.3%에서 11.2%로 증가한다는 것을 보여줍니다. 수치 시뮬레이션 결과는 동일한 기하학적 특성을 갖는 원자로에 대한 측정 결과와 일치합니다.
3D numerical simulations and measurements on an electrochemical reactor were used to analyze the efficiency of strontium removal from water, with and without simultaneous ultrasound treatment. Ultrasound was generated using 4 ultrasonic transducers with an operating frequency of 25 kHz. The reactor used 8 aluminum electrodes arranged in two blocks. Strontium ions in water are modeled as particles characterized by a charge of 3.2∙10-19 C and a diameter of 1.2∙10-8 m. The numerical model was created in Flow-3D software using the basic hydrodynamic module, electrostatic module, and general moving objects module. The performance of the studied reactor variants by numerical simulations is defined by the ratio of the number of model strontium particles permanently retained on the electrodes at the end of the simulation period to the initial number of particles in the water. For the laboratory reactor, the effect of strontium removal is defined by the ratio of the homogeneous strontium concentration in the water at the end and at the beginning of the experiments. The results show that the use of ultrasound increases the effect of strontium removal from 10.3% to 11.2% after 180 seconds of water treatment. The results of numerical simulations agree with the results of measurements on a reactor with the same geometrical characteristics.
Figure 1. US bath modified as an EC reactorFigure 2. Schematic view of the experimental set-up
References
Dong, B., Fishgold, A., Lee, P., Runge, K., Deymier, P. and Keswani, M. (2016), Sono-electrochemical recovery of metal ions from their aqueous solutions, Journal of Hazardous Materials, 318, 379–387. https://doi.org/10.1016/J.JHAZMAT.2016.07.007 EPA. (2014), Announcement of Final Regulatory Determinations for Contaminants on the Third Drinking Water Contaminant Candidate List. Retrieved from http://fdsys.gpo.gov/fdsys/search/home.action Fu, F., Lu, J., Cheng, Z. and Tang, B. (2016), Removal of selenite by zero-valent iron combined with ultrasound: Se(IV) concentration changes, Se(VI) generation, and reaction mechanism, Ultrasonics Sonochemistry, 29, 328–336. https://doi.org/10.1016/j.ultsonch.2015.10.007 Ince, N.H. (2018), Ultrasound-assisted advanced oxidation processes for water decontamination, Ultrasonics Sonochemistry, 40, 97–103. https://doi.org/10.1016/j.ultsonch.2017.04.009 Kamaraj, R. and Vasudevan, S. (2015), Evaluation of electrocoagulation process for the removal of strontium and cesium from aqueous solution, Chemical Engineering Research and Design, 93, 522–530. https://doi.org/10.1016/j.cherd.2014.03.021 Luczaj, J. and Masarik, K. (2015), Groundwater Quantity and Quality Issues in a Water-Rich Region: Examples from Wisconsin, USA, Resources, 4(2), 323–357. https://doi.org/10.3390/resources4020323 Mohapatra, D.P. and Kirpalani, D.M. (2019), Selenium in wastewater: fast analysis method development and advanced oxidation treatment applications, Water Science and Technology: A Journal of the International Association on Water Pollution Research, 79(5), 842–849. https://doi.org/10.2166/wst.2019.010
Mollah, M.Y.A., Schennach, R., Parga, J.R. and Cocke, D.L.(2001), Electrocoagulation (EC)- Science and applications, Journal of Hazardous Materials, 84(1), 29–41. https://doi.org/10.1016/S0304-3894(01)00176-5
Moradi, M., Vasseghian, Y., Arabzade, H. and Khaneghah, A.M. (2021), Various wastewaters treatment by sonoelectrocoagulation process: A comprehensive review of operational parameters and future outlook, Chemosphere, 263, 128314. https://doi.org/10.1016/J.CHEMOSPHERE.2020.12831 4 Peng, H., Yao, F., Xiong, S., Wu, Z., Niu, G. and Lu, T. (2021), Strontium in public drinking water and associated public health risks in Chinese cities, Environmental Science and Pollution Research International, 28(18), 23048. https://doi.org/10.1007/S11356-021-12378-Y Scott, V., Juran, L., Ling, E.J., Benham, B. and Spiller, A. (2020), Assessing strontium and vulnerability to strontium in private drinking water systems in Virginia, Water, 12(4). https://doi.org/10.3390/w12041053 Ziylan, A., Koltypin, Y., Gedanken, A. and Ince, N.H. (2013), More on sonolytic and sonocatalytic decomposition of Diclofenac using zero-valent iron, Ultrasonics Sonochemistry, 20(1), 580–586. https://doi.org/10.1016/j.ultsonch.2012.05.00
액체-증기 상 변화 모델은 밀폐된 용기의 자체 가압 프로세스 시뮬레이션에 매우 큰 영향을 미칩니다. Hertz-Knudsen 관계, 에너지 점프 모델 및 그 파생물과 같은 널리 사용되는 액체-증기 상 변화 모델은 실온 유체를 기반으로 개발되었습니다. 액체-증기 전이를 통한 극저온 시뮬레이션에 널리 적용되었지만 각 모델의 성능은 극저온 조건에서 명시적으로 조사 및 비교되지 않았습니다. 본 연구에서는 171가지 일반적인 액체-증기 상 변화 모델을 통합한 통합 다상 솔버가 제안되었으며, 이를 통해 이러한 모델을 실험 데이터와 직접 비교할 수 있습니다. 증발 및 응축 모델의 예측 정확도와 계산 속도를 평가하기 위해 총 <>개의 자체 가압 시뮬레이션이 수행되었습니다. 압력 예측은 최적화 전략이 서로 다른 모델 계수에 크게 의존하는 것으로 나타났습니다. 에너지 점프 모델은 극저온 자체 가압 시뮬레이션에 적합하지 않은 것으로 나타났습니다. 평균 편차와 CPU 소비량에 따르면 Lee 모델과 Tanasawa 모델은 다른 모델보다 안정적이고 효율적인 것으로 입증되었습니다.
Liquid-vapor phase change models vitally influence the simulation of self-pressurization processes in closed containers. Popular liquid-vapor phase change models, such as the Hertz-Knudsen relation, energy jump model, and their derivations were developed based on room-temperature fluids. Although they had widely been applied in cryogenic simulations with liquid-vapor transitions, the performance of each model was not explicitly investigated and compared yet under cryogenic conditions. A unified multi-phase solver incorporating four typical liquid-vapor phase change models has been proposed in the present study, which enables direct comparison among those models against experimental data. A total number of 171 self-pressurization simulations were conducted to evaluate the evaporation and condensation models’ prediction accuracy and calculation speed. It was found that the pressure prediction highly depended on the model coefficients, whose optimization strategies differed from each other. The energy jump model was found inadequate for cryogenic self-pressurization simulations. According to the average deviation and CPU consumption, the Lee model and the Tanasawa model were proven to be more stable and more efficient than the others.
Introduction
The liquid-vapor phase change of cryogenic fluids is widely involved in industrial applications, such as the hydrogen transport vehicles [1], shipborne liquid natural gas (LNG) containers [2] and on-orbit cryogenic propellant tanks [3]. These applications require cryogenic fluids to be stored for weeks to months. Although high-performance insulation measures are adopted, heat inevitably enters the tank via radiation and conduction. The self-pressurization in the tank induced by the heat leakage eventually causes the venting loss of the cryogenic fluids and threatens the safety of the craft in long-term missions. To reduce the boil-off loss and extend the cryogenic storage duration, a more comprehensive understanding of the self-pressurization mechanism is needed.
Due to the difficulties and limitations in implementing cryogenic experiments, numerical modeling is a convenient and powerful way to study the self-pressurization process of cryogenic fluids. However, how the phase change models influence the mass and heat transfer under cryogenic conditions is still unsettled [4]. As concluded by Persad and Ward [5], a seemingly slight variation in the liquid-vapor phase change models can lead to erroneous predictions.
Among the liquid-vapor phase change models, the kinetic theory gas (KTG) based models and the energy jump model are the most popular ones used in recent self-pressurization simulations [6]. The KTG based models, also known as the Hertz-Knudsen relation models, were developed on the concept of the Maxwell-Boltzmann distribution of the gas molecular [7]. The Hertz-Knudsen relation has evolved to several models, including the Schrage model [8], the Tanasawa model [9], the Lee model [10] and the statistical rate theory (SRT) [11], which will be described in Section 2.2. Since the Schrage model and the Lee model are embedded and configured as the default ones in the commercial CFD solvers Flow-3D® and Ansys Fluent® respectively, they have been widely used in self-pressurization simulations for liquid nitrogen [12], [13] and liquid hydrogen [14], [15]. The major drawback of the KTG models lies in the difficulty of selecting model coefficients, which were reported in a considerably wide range spanning three magnitudes even for the same working fluid [16], [17], [18], [19], [20], [21]. Studies showed that the liquid level, pressure and mass transfer rate are directly influenced by the model coefficients [16], [22], [23], [24], [25]. Wrong coefficients will lead to deviation or even divergence of the results. The energy jump model is also known as the thermal limitation model. It assumes that the evaporation and condensation at the liquid-vapor interface are induced only by heat conduction. The model is widely adopted in lumped node simulations due to its simplicity [6], [26], [27]. To improve the accuracy of mass flux prediction, the energy jump model was modified by including the convection heat transfer [28], [29]. However, the convection correlations are empirical and developed mainly for room-temperature fluids. Whether the correlation itself can be precisely applied in cryogenic simulations still needs further investigation.
Fig. 1 summarizes the cryogenic simulations involving the modeling of evaporation and condensation processes in recent years. The publication has been increasing rapidly. However, the characteristics of each evaporation and condensation model are not explicitly revealed when simulating self-pressurization. A comparative study of the phase change models is highly needed for cryogenic fluids for a better simulation of the self-pressurization processes.
In the present paper, a unified multi-phase solver incorporating four typical liquid-vapor phase change models, namely the Tanasawa model, the Lee model, the energy jump model, and the modified energy jump model has been proposed, which enables direct comparison among different models. The models are used to simulate the pressure and temperature evolutions in an experimental liquid nitrogen tank in normal gravity, which helps to evaluate themselves in the aspects of accuracy, calculation speed and robustness.
Section snippets
Governing equations for the self-pressurization tank
In the present study, both the fluid domain and the solid wall of the tank are modeled and discretized. The heat transportation at the solid boundaries is considered to be irrelevant with the nearby fluid velocity. Consequently, two sets of the solid and the fluid governing equations can be decoupled and solved separately. The pressures in the cryogenic container are usually from 100 kPa to 300 kPa. Under these conditions, the Knudsen number is far smaller than 0.01, and the fluids are
Self-pressurization results and phase change model comparison
This section compares the simulation results by different phase change models. Section 3.1 compares the pressure and temperature outputs from two KTG based models, namely the Lee model and the Tanasawa model. Section 3.2 presents the pressure predictions from the energy transport models, namely the energy jump model and the modified energy jump model, and compares pressure prediction performances between the KTG based models and the energy transport models. Section 3.3 evaluates the four models
Conclusion
A unified vapor-liquid-solid multi-phase numerical solver has been accomplished for the self pressurization simulation in cryogenic containers. Compared to the early fluid-only solver, the temperature prediction in the vicinity of the tank wall improves significantly. Four liquid-vapor phase change models were integrated into the solver, which enables fair and effective comparison for performances between each other. The pressure and temperature prediction accuracies, and the calculation speed
Authors declare that they have no financial and personal relationships with other people or organizations that can inappropriately influence our work, there is no professional or other personal interest of any nature or kind in any product, service and/or company that could be construed as influencing the position presented in, or the review of, the manuscript entitled, “Validity evaluation of popular liquid-vapor phase change models for cryogenic self-pressurization process”.
Acknowledgement
This project is supported by the National Natural Science Foundation of China (No. 51936006).
Progress in physical modelling and numerical simulation of phase transitions in cryogenic pool boiling and cavitation2023, Applied Mathematical ModellingCitation Excerpt :We will not delve into cryogenic evaporation phenomena, that predominantly drive the phase-change in well-insulated storage facilities, and thus are less relevant to spill scenarios. We instead refer the reader to the works of Zuo et al. [31–33]. If the static pressure at any location in a turbomachine drops below a fluid’s saturation pressure, localized evaporation events may occur, followed by rapid collapse of the vapour cavities in a process termed “cavitation” [34].Show abstract
Thermodynamic performance in a liquid oxygen tank during active-pressurization under different gas injection temperatures2023, International Communications in Heat and Mass TransferCitation Excerpt :The volume of fluid method is adopted to predict the tank pressurization performance. The associated governing equations could refer to previous published investigations [33–39,41,45,46]. Subjected to external heat input and gas injection, the phase change occurs at the interface and within the tank.Show abstract
Interfacial mass and energy transport during steady-state evaporation in liquid oxygen storage tanks2022, Applied EnergyCitation Excerpt :However, most of them simply used the Lee model for mass transport as did for regular fluids, and seldom focus on the evaporation itself related to the interfacial temperature distribution or were unable to validate their results against credible experimental data. A recent study proposed an optimized evaporation model for the cryogenic self-pressurization with a thorough comparison between popular phase change models [8], but still lacked of experimental data to validate the results. A series of experiments have been conducted on the heat and mass transport in a thin liquid layer in the vicinity of the liquid–vapor interface of room-temperature fluids [9–14].Show abstract
Thermal destratification of cryogenic liquid storage tanks by continuous bubbling of gases2022, International Journal of Hydrogen EnergyCitation Excerpt :It was concluded that a single injector with a larger diameter configuration showed a higher chance of developing a vertical temperature gradient. Zuo et al. [48] carried out a numerical analysis to investigate the temperature distribution within the LH2 storage tank with a self-pinning spraying bar. They used the SST turbulence model coupled with the 6-DOF model.Show abstract
Fine sediments enter into the river through various sources such as channel bed, bank, and catchment. It has been regarded as a type of pollution in river. Fine sediments present in a river have a significant effect on river health. Benthic micro-organism, plants, and large fishes, all are part of food chain of river biota. Any detrimental effect on any of these components of food chain misbalances the entire riverine ecosystem. Numerous studies have been carried out on the various environmental aspects of rivers considering the presence of fine sediment in river flow. The present paper critically reviews many of these aspects to understand the various environmental impacts of suspended sediment on river health, flora and fauna.
Introduction The existence of fine sediment in a river system is a natural phenomenon. But in many cases it is exacerbated by the manmade activities. The natural cause of fines being in flow generally keeps the whole system in equilibrium except during some calamites whereas anthropogenic activities leading to fines entering into the flow puts several adverse impacts on the entire river system and its ecology. Presence of fines in flow is considered as a type of pollution in water. In United States, the fine sediment in water along with other non point source pollution is considered as a major obstacle in providing quality water for fishes and recreation activities (Diplas and Parker 1985). Sediments in a river are broadly of two types, organic and inorganic, and they both move in two ways either along the bed of the channel called bed load or in suspension called suspended load and their movements depend upon fluid flow and sediment characteristics. Further many investigators have divided the materials in suspension into two different types. One which originates from channel bed and bank is called bed material suspended load and another that migrates from feeding catchment area is called wash load. A general perception is that wash loads are very fine materials like clay, silt but it may not always be true (Woo et al. 1986). In general, suspended materials are of size less than 2 mm. The impact of sand on the various aspects of river is comparatively less than that of silt and clay. The latter are chemically active and good carrier of many contaminants and nutrients such as dioxins, phosphorous, heavy and trace metals, polychlorinated biphenyl (PCBs), radionuclide, etc. (Foster and Charlesworth 1996; Horowitz et al. 1995; Owens et al. 2001; Salomons and Förstner 1984; Stone and Droppo 1994; Thoms 1987). Foy and Bailey-Watt (1998) reported that out of 129 lakes in England and Wales, 69% have phosphorous contamination. Ten percent lakes, rivers, and bays of United States have sediment contaminants with chemicals as reported by USEPA. Several field and experimental studies have been conducted considering, sand, silt, and clay as suspended material. Hence, the subject reported herein is based on considering the fine sediment size smaller than 2 mm. Fine sediments have the ability to alter the hydraulics of the flow. Presence of fines in flow can change the magnitude of turbulence, it can change the friction resistance to flow. Fines can change the mobility and permeability of the bed material. In some extreme cases, fines in flow may even change the morphology of the river (Doeg and Koehn 1994; Nuttall 1972; Wright and Berrie 1987). Fines in the flow adversely affect the producer by increasing the turbidity, hindering the photosynthesis process by limiting the light penetration. This is ultimately reflected in the entire food ecosystem of river (Davis-Colley et al. 1992; Van Niewenhuyre and Laparrieve 1986). In addition, abrasion due to flowing sediment kills the aquatic flora (Edwards 1969; Brookes 1986). Intrusion of fines into the pores of river bed reduces space for several invertebrates, affects the spawning process (Petts 1984; Richards and Bacon 1994; Schalchli 1992). There are several other direct or indirect, short-term or long-term impacts of fines in river. The present paper reports the physical/environmental significance of fines in river. The hydraulic significance of presence of fines in the river has been reviewed in another paper (Effect of fine sediments on river hydraulics – a research review – http://dx.doi.org/10.1080/09715010.2014.982001).
References
Adams, J.N., and Beschta, R.L. (1980). “Gravel bed composition in oregon coastal streams.” Can. J. Fish. Aquat.Sci., 37, 1514–1521.10.1139/f80-196 [Crossref], [Web of Science ®], [Google Scholar]
Alabaster, J.S., and Llyod, R.L. (1980). Water quality criteria for fresh water, Butterworth, London, 297. [Google Scholar]
Aldridge, D.W., Payne, B.S., and Miller, A.C. (1987). “The effects of intermittent exposure to suspended solids and turbulence on three species of freshwater mussels.” Environ. Pollution, 45, 17–28.10.1016/0269-7491(87)90013-3 [Crossref], [PubMed], [Web of Science ®], [Google Scholar]
Barton, B.A. (1977). “Short-term effects of highway construction on the limnology of a small stream in southern Ontario.” Freshwater Biol., 7, 99–108.10.1111/fwb.1977.7.issue-2 [Crossref], [Web of Science ®], [Google Scholar]
Bash, J., Berman, C., and Bolton, S. (2001). Effects of turbidity and suspended solids on salmonids, Center for Streamside Studies, University of Washington, Seattle, WA. [Google Scholar]
Baxter, C.V., and Hauer, F.R. (2000). “Geomorphology, hyporheic exchange, and selection of spawning habitat by bull trout (Salvelinus confuentus).” Can. J. Fish. Aquat.Sci., 57, 1470–1481.10.1139/f00-056 [Crossref], [Web of Science ®], [Google Scholar]
Berkman, H.E., and Rabeni, C.F. (1987). “Effect of siltation on stream fish communities.” Environ. Biol. Fish., 18, 285–294.10.1007/BF00004881 [Crossref], [Web of Science ®], [Google Scholar]
Beschta, R.L., and Jackson, W.L. (1979). “The intrusion of fine sediments into a stable gravel bed.” J. Fish. Res. Board Can., 36, 204–210.10.1139/f79-030 [Crossref], [Google Scholar]
Boon, P.J. (1988). “The impact of river regulation on invertebrate communities in the UK.” Reg. River Res. Manage., 2, 389–409.10.1002/(ISSN)1099-1646 [Crossref], [Google Scholar]
Brookes, A. (1986). “Response of aquatic vegetation to sedimentation downstream from river channelization works in England and Wales.” Biol. Conserv., 38, 352–367. [Crossref], [Web of Science ®], [Google Scholar]
Carling, P.A. (1984). “Deposition of fine and coarse sand in an open-work gravel bed.” Can. J. Fish. Aquat. Sci., 41, 263–270.10.1139/f84-030 [Crossref], [Web of Science ®], [Google Scholar]
Carling, P.A., and McCahon, C.P. (1987). “Natural siltation of brown trout (Salmo trutta L.) spawning gravels during low-flow conditions.” Regulated streams, J.F. Craig and J.B. Kemper, eds., Plenum Press, New York, NY, 229–244.10.1007/978-1-4684-5392-8 [Crossref], [Google Scholar]
Carter, J., Owens, P.N., Walling, D.E., and Leeks, G.J.L. (2003). “Fingerprinting suspended sediment sources in a large urban river system.” Sci. Total Environ., 314–316, 513–534.10.1016/S0048-9697(03)00071-8 [Crossref], [PubMed], [Web of Science ®], [Google Scholar]
Chang, H.H. (1988). Fluvial processes in river engineering, Krieger, Malabar Florida, 432. [Google Scholar]
Chapman, D.W. (1988). “Critical review of variables used to define effects of fines in redds of large salmonids.” Trans. Am. Fish. Soc., 117, 1–21.10.1577/1548-8659(1988)117<0001:CROVUT>2.3.CO;2 [Taylor & Francis Online], [Web of Science ®], [Google Scholar]
Church, M.A., Mclean, D.G., and Wolcott, J.F. (1987). “River bed gravel sampling and analysis.” Sediment transport in gravel-bed rivers, C.R. Thorne, J.C. Bathrust, and R.D. Hey, eds., John Willey, Chichester, 43–79. [Google Scholar]
Cline, L.D., Short, R.A., and Ward, J.V. (1982). “The influence of highway construction on the macroinvertebrates and epilithic algae of a high mountain stream.” Hydrobiologia, 96, 149–159.10.1007/BF02185430 [Crossref], [Web of Science ®], [Google Scholar]
Collins, A.L., Walling, D.E., and Leeks, G.J.L. (1997). “Fingerprinting the origin of fluvial suspended sediment in larger river basins: combining assessment of spatial provenance and source type.” Geografiska Annaler, 79A, 239–254.10.1111/1468-0459.00020 [Crossref], [Google Scholar]
Cordone, A.J., and Kelly, D.W. (1961). “The influence of inorganic sediment on the aquatic life of stream.” Calif. Fish Game, 47, 189–228. [Google Scholar]
Culp, J.M., Wrona, F.J., and Davies, R.W. (1985). “Response of stream benthos and drift to fine sediment depositionversus transport.” Can. J. Zool., 64, 1345–1351. [Crossref], [Web of Science ®], [Google Scholar]
Davies-Colley, R.J., Hickey, C.W., Quinn, J.M., and Ryan, P.A. (1992). “Effects of clay discharges on streams.” Hydrobiologia, 248, 215–234.10.1007/BF00006149 [Crossref], [Web of Science ®], [Google Scholar]
Dhamotharan, S., Wood, A., Parker, G., and Stefan, H. (1980). Bed load transport in a model gravel stream. Project Report No. 190. St. Anthony Falls Hydraulic Laboratory, University of Minnesota. [Google Scholar]
Diplas, P., and Parker, G. (1985). Pollution of gravel spawning grounds due to fine sediment. Project Report, No. 240. St. Anthony Falls Laboratory, University of Minnesota, Minneapolis, MN. [Google Scholar]
Doeg, T.J., and Koehn, J.D. (1994). “Effects of draining and desilting a small weir on downstream fish and macroinvertebrates.” Reg. River Res. Manage., 9, 263–277.10.1002/(ISSN)1099-1646 [Crossref], [Web of Science ®], [Google Scholar]
Droppo, I.G., and Ongley, E.D. (1994). “Flocculation of suspended sediment in rivers of southeastern Canada.” Water Res., 28, 1799–1809.10.1016/0043-1354(94)90253-4 [Crossref], [Web of Science ®], [Google Scholar]
Einstein, H.A. (1968). “Deposition of suspended particles in a gravel bed.” J. Hydraul. Eng., 94, 1197–1205. [Google Scholar]
Erman, D.C., and Ligon, F.K. (1988). “Effects of discharge fluctuation and the addition of fine sediment on stream fish and macroinvertebrates below a water-filtration facility.” Environ. Manage., 12, 85–97.10.1007/BF01867380 [Crossref], [Web of Science ®], [Google Scholar]
Farnsworth, K.L., and Milliman, J.D. (2003). “Effects of climatic and anthropogenic change on small mountainous rivers: the Salinas River example.” Global Planet. Change, 39, 53–64.10.1016/S0921-8181(03)00017-1 [Crossref], [Web of Science ®], [Google Scholar]
Foster, I.D.L., and Charlesworth, S.M. (1996). “Heavy metals in the hydrological cycle: trends and explanation.” Hydrol. Process., 10, 227–261.10.1002/(ISSN)1099-1085 [Crossref], [Web of Science ®], [Google Scholar]
Foy, R.H., and Bailey-Watts, A.E. (1998). “Observations on the spatial and temporal variation in the phosphorus status of lakes in the British Isles.” Soil Use Manage., 14, 131–138.10.1111/sum.1998.14.issue-s4 [Crossref], [Web of Science ®], [Google Scholar]
Frostick, L.E., Lucas, P.M., and Reid, I. (1984). “The infiltration of fine matrices into coarse-grained alluvial sediments and its implications for stratigraphical interpretation.” J. Geol. Soc. London, 141, 955–965.10.1144/gsjgs.141.6.0955 [Crossref], [Web of Science ®], [Google Scholar]
Gagnier, D.L., and Bailey, R.C. (1994). “Balancing loss of information and gains in efficiency in characterizing stream sediment samples.” J. North Am. Benthol. Soc., 13, 170–180.10.2307/1467236 [Crossref], [Web of Science ®], [Google Scholar]
Gammon, J.R. (1970). The effect of inorganic sediment on stream biota. Environmental Protection Agency, Water Pollution Control Research, Series, 18050 DWC 12/70. USGPO, Washington, DC. [Google Scholar]
Graham, A.A. (1990). “Siltation of stone-surface periphyton in rivers by clay-sized particles from low concentrations in suspention.” Hydrobiologia, 199, 107–115.10.1007/BF00005603 [Crossref], [Web of Science ®], [Google Scholar]
Greig, S.M., Sear, D.A., and Carling, P.A. (2005). “The impact of fine sediment accumulation on the survival of incubating salmon progeny: Implications for sediment management.” Sci. Total Environ., 344, 241–258.10.1016/j.scitotenv.2005.02.010 [Crossref], [PubMed], [Web of Science ®], [Google Scholar]
Harrod, T.R., and Theurer, F.D. (2002). “Sediment.” Agriculture, hydrology and water quality, P.M. Haygarth and S.C. Jarvis, eds., CABI, Wallingford, 502. [Crossref], [Google Scholar]
Horowitz, A.J., Elrick, K.A., Robbins, J.A., and Cook, R.B. (1995). “Effect of mining and related activities on the sediment trace element geochemistry of Lake Coeur D’Alene, Idaho, USA part II: Subsurface sediments.” Hydrol. Process., 9, 35–54.10.1002/(ISSN)1099-1085 [Crossref], [Web of Science ®], [Google Scholar]
Hynes, H.B.N. (1970). The ecology of running waters, Liverpool University Press, Liverpool. [Google Scholar]
Khullar, N.K. (2002). “Effect of wash load on transport of uniform and nonuniform sediments.” Ph.D. thesis, Indian Institute of Technology Roorkee. [Google Scholar]
Kondolf, G.M. (1995). “Managing bedload sediment in regulated rivers: Examples from California, USA.” Geophys. Monograph, 89, 165–176. [Google Scholar]
Langer, O.E. (1980). “Effects of sedimentation on salmonid stream life.” Report on the Technical Workshop on Suspended Solids and the Aquatic Environment, K. Weagle, ed., Whitehorse. [Google Scholar]
Lemly, A.D. (1982). “Modification of benthic insect communities in polluted streams: combined effects of sedimentation and nutrient enrichment.” Hydrobiologia, 87, 229–245.10.1007/BF00007232 [Crossref], [Web of Science ®], [Google Scholar]
Levasseur, M., Bergeron, N.E., Lapointe, M.F., and Bérubé, F. (2006). “Effects of silt and very fine sand dynamics in Atlantic salmon (Salmo salar) redds on embryo hatching success.” Can. J. Fish. Aquat. Sci., 63, 1450–1459.10.1139/f06-050 [Crossref], [Web of Science ®], [Google Scholar]
Lewis, K. (1973a). “The effect of suspended coal particles on the life forms of the aquatic moss Eurhynchium riparioides (Hedw.).” Fresh Water Biol., 3, 251–257.10.1111/fwb.1973.3.issue-3 [Crossref], [Google Scholar]
Lewis, K. (1973b). “The effect of suspended coal particles on the life forms of the aquatic moss Eurhynchium riparioides (Hedw.).” Fresh Water Biol., 3, 391–395.10.1111/fwb.1973.3.issue-4 [Crossref], [Google Scholar]
Lisle, T. (1980). “Sedimentation of Spawning Areas during Storm Flows, Jacoby Creek, North Coastal California.” Presented at the fall meeting of the American Geophysical Union, San Francisco, CA. [Google Scholar]
Marchant, R. (1989). “Changes in the benthic invertebrate communities of the thomson river, southeastern Australia, after dam construction.” Reg. River Res. Manage., 4, 71–89.10.1002/(ISSN)1099-1646 [Crossref], [Google Scholar]
McNeil, W.J., and Ahnell, W.H. (1964). Success of pink salmon spawning relative to size of spawning bed material. US Fish and Wildlife Service. Special Scientific Report, Fisheries 469. Washington, DC. [Google Scholar]
Milhous, R.T. (1973). “Sediment transport in a gravel bottomed stream.” Ph.D. thesis, Oregon State University, Corvallis, OR. [Google Scholar]
Milliman, J.D., and Syvitski, J.P.M. (1992). “Geomorphic/tectonic control of sediment discharge to the oceans: the importance of small mountainous rivers.” J. Geol., 100, 525–544.10.1086/jg.1992.100.issue-5 [Crossref], [Web of Science ®], [Google Scholar]
Mohnakrishnan, A. (2001). Reservoir sedimentation, Seminar on Reservoir Sedimentation, Ooty. [Google Scholar]
Mohta, J.A., Wallbrink, P.J., Hairsine, P.B., and Grayson, R.B. (2003). “Determining the sources of suspended sediment in a forested catchment in southeastern Australia.” Water Resour. Res., 39, 1056. [Web of Science ®], [Google Scholar]
Morris, G.L. (1993). “A global perspective of sediment control measures in reservoirs.” Notes on sediment management in reservoirs, S. Fan and G. Morris, eds., Water Resources Publications, Colorado, 13–44. [Google Scholar]
Morris, L.G., and Fan, J. (2010). Reservoir Sedimentation hand book – design and management of dams, reservoirs and watershed for sustainable use. McGraw-Hill, 440 and 499. [Google Scholar]
Newcombe, C.P., and Macdonald, D.D. (1991). “Effects of suspended sediments on aquatic ecosystems.” North Am. J. Fish. Manage., 11, 72–82.10.1577/1548-8675(1991)011<0072:EOSSOA>2.3.CO;2 [Taylor & Francis Online], [Google Scholar]
Nuttal, P.M. (1972). “The effects of sand deposition upon the macroinvertebrate fauna of the River Camel, Cornwall.” Freshwater Biol., 2, 181–186.10.1111/fwb.1972.2.issue-3 [Crossref], [Google Scholar]
Olsson, T.I., and Petersen, B. (1986). “Effects of gravel size and peat material on embryo survival and alevin emergence of brown trout, Salmo trutta L.” Hydrobiologia, 135, 9–14.10.1007/BF00006453 [Crossref], [Web of Science ®], [Google Scholar]
Owens, P.N., Walling, D.E., and Leeks, G.J.L. (2000). “Tracing fluvial suspended sediment sources in the catchment of the River Tweed, Scotland, using composite fingerprints and a numerical mixing model.” Tracers in eomorphology, I.D.L. Foster, ed., Wiley, Chichester, 291–308. [Google Scholar]
Owens, P.N., Walling, D.E., Carton, J., Meharg, A.A., Wright, J., and Leeks, G.J.L. (2001). “Downstream changes in the transport and storage of sediment-associated contaminants (P, Cr and PCBs) in agricultural and industrialized drainage basins.” Sci. Total Environ., 266, 177–186.10.1016/S0048-9697(00)00729-4 [Crossref], [PubMed], [Web of Science ®], [Google Scholar]
Phillips, J.M., and Walling, D.E. (1995). “An assessment of the effects of sample collection, storage and resuspension on the representativeness of measurements of the effective particle size distribution of fluvial suspended sediment.” Water Res., 29, 2498–2508.10.1016/0043-1354(95)00087-2 [Crossref], [Web of Science ®], [Google Scholar]
Quinn, J.M., Davies-Coley, R.J., Hickey, C.W., Vickers, M.L., and Ryan, P.A. (1992). “Effects of clay discharges on streams.” Hydrobiologia, 248, 235–247.10.1007/BF00006150 [Crossref], [Web of Science ®], [Google Scholar]
Reiser, D.W., and White, R.G. (1990). “Effects of stream flow reduction on Chinook salmon egg incubation and fry quality.” Rivers, 1, 110–118. [Google Scholar]
Richards, C., and Bacon, K.L. (1994). “Influence of fine sediment on macroibvertebrates colonization of surface and hyporheic stream substrate.” Great Basin Nat., 54, 106–113. [Google Scholar]
Richards, C., Host, G.H., and Arthur, J.W. (1993). “Identification of predominant environmental factors structuring stream macroinvertebrate communities within a large agricultural catchment.” Freshwater Biol., 29, 285–294.10.1111/fwb.1993.29.issue-2 [Crossref], [Web of Science ®], [Google Scholar]
Rosenberg, D.M., and Wiens, A.P. (1978). “Effects of sediment addition on macrobenthic invertebrates in a Northern Canadian River.” Water Res., 12, 753–763.10.1016/0043-1354(78)90024-6 [Crossref], [Web of Science ®], [Google Scholar]
Salomons, W., and Förstner, U. (1984). Metals in the hydrocycle, Sringer Verglag, New York, NY.10.1007/978-3-642-69325-0 [Crossref], [Google Scholar]
Schalchli, U. (1992). “The clogging of coarse gravel river beds by fine sediment.” Hydrobiologia, 235–236, 189–197.10.1007/BF00026211 [Crossref], [Web of Science ®], [Google Scholar]
Scrivener, J.C., and Brownlee, M.J. (1989). “Effects of forest harvesting on spawning gravel and incubation survival of chum (Oncorhynchus keta) andcoho salmon (O. kisutch) in Carnation Creek, British Columbia.” Can. J. Fish. Aquat. Sci., 46, 681–696.10.1139/f89-087 [Crossref], [Web of Science ®], [Google Scholar]
Sear, D.A. (1993). “Fine sediment infiltration into gravel spawning beds within a regulated river experiencing floods: Ecological implications for salmonids.” Reg Rivers Res. Manage., 8, 373–390.10.1002/(ISSN)1099-1646 [Crossref], [Google Scholar]
Soutar, R.G. (1989). “Afforestation and sediment yields in British fresh waters.” Soil Use Manage., 5, 82–86.10.1111/sum.1989.5.issue-2 [Crossref], [Web of Science ®], [Google Scholar]
Stone, M., and Droppo, I.G. (1994). “In-channel surficial fine-grained sediment laminae: Part II: Chemical characteristics and implications for contaminant transport in fluvial systems.” Hydrol. Process., 8, 113–124.10.1002/(ISSN)1099-1085 [Crossref], [Web of Science ®], [Google Scholar]
Thoms, M.C. (1987). “Channel sedimentation within the urbanized River Tame, UK.” Reg. Rivers Res. Manage., 1, 229–246.10.1002/(ISSN)1099-1646 [Crossref], [Google Scholar]
Trimble, S.W. (1983). “A sediment budget for Coon Creek, Driftless area, Wisconsin, 1853–1977.” Am. J. Sci., 283, 454–474.10.2475/ajs.283.5.454 [Crossref], [Web of Science ®], [Google Scholar]
U.S. Department of Health, Education and Welfare. (1965). Environmental Health Practices in recreational Areas, Public Health Service, Publication No. 1195. [Google Scholar]
Van Nieuwenhuyse, E.E., and LaPerriere, J.D. (1986). “Effects of placer gold mining on primary production in subarctic streams of Alaska.” J. Am. Water Res. Assoc., 22, 91–99. [Crossref], [Google Scholar]
Vörösmarty, C.J., Meybeck, M., Fekete, B., Sharma, K., Green, P., and Syvitski, J.P.M. (2003). “Anthropogenic sediment retention: major global impact from registered river impoundments.” Global Planet. Change, 39, 169–190.10.1016/S0921-8181(03)00023-7 [Crossref], [Web of Science ®], [Google Scholar]
Walling, D.E. (1995). “Suspended sediment yields in a changing environment.” Changing river channels, A. Gurnell and G. Petts, eds., Wiley, Chichester, 149–176. [Google Scholar]
Walling, D.E., and Moorehead, D.W. (1989). “The particle size characteristics of fluvial suspended sediment: an overview.” Hydrobiologia, 176–177, 125–149.10.1007/BF00026549 [Crossref], [Web of Science ®], [Google Scholar]
Walling, D.E., Owens, P.N., and Leeks, G.J.L. (1999). “Fingerprinting suspended sediment sources in the catchment of the River Ouse, Yorkshire, UK.” Hydrol. Process., 13, 955–975.10.1002/(ISSN)1099-1085 [Crossref], [Web of Science ®], [Google Scholar]
Walling, D.E., Owens, P.N., Waterfall, B.D., Leeks, G.J.L., and Wass, P.D. (2000). “The particle size characteristics of fluvial suspended sediment in the Humber and Tweed catchments, UK.” Sci. Total Environ., 251–252, 205–222.10.1016/S0048-9697(00)00384-3 [Crossref], [PubMed], [Web of Science ®], [Google Scholar]
Wilbur, C.G. (1983). Turbidity in the aquatic environment: an environmental factor in fresh and oceanic waters, Charles C. Thomas, Springfield, IL, 133. [Google Scholar]
Woo, H.S., Julien, P.Y., and Richardson, E.V. (1986). “Washload and fine sediment load.” J. Hydraul. Eng., 112, 541–545.10.1061/(ASCE)0733-9429(1986)112:6(541) [Crossref], [Google Scholar]
Wood, P.J., and Armitage, P.D. (1997). “Biological effects of fine sediment in the lotic environment.” Environ. Manage., 21, 203–217.10.1007/s002679900019 [Crossref], [PubMed], [Web of Science ®], [Google Scholar]
Wooster, J.K., Dusterhoff, S.R., Cui, Y., Sklar, L.S., Dietrich, W.E., and Malko, M. (2008). “Sediment supply and relative size distribution effects on fine sediment infiltration into immobile gravels.” Water Res. Res., 44, 1–18. [Crossref], [Web of Science ®], [Google Scholar]
Wren, G.Daniel, Bennett, J.Sean, Barkdoll, D.Brian, and Khunle, A.Roger. (2000). Studies in suspended sediment and turbulence in open channel flows, USDA, Agriculture Research Service, Research Report No. 18. [Google Scholar]
Wright, J.F., and Berrie, A.D. (1987). “Ecological effects of groundwater pumping and a natural drought on the upper reaches of a chalk stream.” Reg. River Res. Manage., 1, 145–160.10.1002/(ISSN)1099-1646 [Crossref], [Google Scholar]
Zhang, H., Xia, M., Chen, S.J., Li, Z., and Xia, H.B. (1976). “Regulation of sediments in some medium and small-sized reservoirs on heavily silt-laden streams in China.” 12th International Commission on Large Dams (ICOLD) Congress, Q. 47, R. 32, Mexico City, 1123–1243. [Google Scholar]
Numerical study of the flow at a vertical pile with net-like scour protection matt Minxi Zhanga,b , Hanyan Zhaoc , Dongliang Zhao d, Shaolin Yuee , Huan Zhoue , Xudong Zhaoa , Carlo Gualtierif , Guoliang Yua,b,∗ a SKLOE, School of Naval Architecture, Ocean & Civil Engineering, Shanghai Jiao Tong University, Shanghai 200240, China b KLMIES, MOE, School of Naval Architecture, Ocean & Civil Engineering, Shanghai Jiao Tong University, Shanghai 200240, China c Guangdong Research Institute of Water Resources and Hydropower, Guangzhou 510610, China d CCCC Second Harbor Engineering Co., Ltd., Wuhan 430040, China e CCCC Road & Bridge Special Engineering Co., Ltd, Wuhan 430071, China f Department of Structures for Engineering and Architecture, University of Naples Federico II, Italy
Abstract
현재 또는 파도 환경에서 말뚝 또는 부두의 국부 세굴은 전 세계적으로 상부 구조물의 안전을 위협합니다. 말뚝이나 부두에서 세굴 방지 덮개로 그물 모양의 매트를 적용하는 것이 제안되었습니다. 매트는 국부 세굴 구덩이의 흐름을 약화 및 확산시켜 국부 세굴을 줄이고 퇴적물 퇴적을 강화합니다. 매트로 덮힌 말뚝의 흐름을 조사하기 위해 수치 시뮬레이션을 수행했습니다. 시뮬레이션 결과는 매트의 두께 dt(2.6d95 ~ 17.9d95)와 개구부 크기 dn(7.7d95 ~ 28.2d95)을 최적화하는 데 사용되었습니다. 매트가 국부 속도를 상당히 감소시키고 말뚝에서 와류를 소멸시켜 국부 세굴 범위를 실질적으로 감소시키는 것으로 밝혀졌습니다. 매트의 개구부 크기가 작을수록 베드에서의 유동확산이 더 효과적이었으며 말뚝에서 더 작은 베드전단응력이 관찰되었다. 본 연구에서 고려한 유동 조건의 경우 상대 두께 T = 7.7 및 상대 개구 크기 S = 7.7인 매트가 세굴 방지에 효과적일 수 있습니다.
Fig. 26. Distribution of the turbulent kinetic energy on the y-z plane (X = 0.5) for various S
References
[1] C. He, Mod. Transp. Technol. 17 (3) (2020) 46–59 in Chinese. [2] X. Wen, D. Zhang, J. Tianjin Univ. 54 (10) (2021) 998–1007 (Science and Technology)in Chinese. [3] M. Zhang, H. Sun, W. Yao, G. Yu, Ocean Eng. 265 (2020) 112652, doi:10.1016/j. oceaneng.2022.112652. [4] K. Wardhana, F.C. Hadipriono, J. Perform. Constr. Fac. 17 (3) (2003) 144–150, doi:10.1061/(ASCE)0887-3828(2003)17:3(144). [5] R. Ettema, G. Constantinescu, B.W. Melville, J. Hydraul. Eng. 143 (9) (2017) 03117006, doi:10.1061/(ASCE)HY.1943-7900.0001330. [6] C. Valela, C.D. Rennie, I. Nistor, Int. J. Sediment Res. 37 (1) (2021) 37–46, doi:10.1016/j.ijsrc.2021.04.004. [7] B.W. Melville, A.J. Sutherland, J. Hydraul. Eng. 114 (10) (1988) 1210–1226, doi:10.1061/(ASCE)0733-9429(1988)114:10(1210). [8] E.V. Richardson, S.R. Davis, Evaluating Scour At Bridges, 4th ed., United States Department of Transportation, Federal Highway Administration, Washington, DC., 2001. [9] D.M. Sheppard, B. Melville, H. Demir, J. Hydraul. Eng. 140 (1) (2014) 14–23, doi:10.1061/(ASCE)HY.1943-7900.0000800. [10] A.O. Aksoy, G. Bombar, T. Arkis, M.S. Guney, J. Hydrol. Hydromech. 65 (1) (2017) 26–34. [11] D.T. Bui, A. Shirzadi, A. Amini, et al., Sustainability 12 (3) (2020) 1063, doi:10. 3390/su12031063. [12] B.M. Sumer, J. Fredsoe, The Mechanics of Scour in Marine Environments. World Advanced Series on Ocean Engineering, 17, World Scientific, Singapore, 2002. [13] J. Unger, W.H. Hager, Exp. Fluids 42 (1) (2007) 1–19. [14] G. Kirkil, S.G. Constantinescu, R. Ettema, J. Hydraul. Eng. 134 (5) (2008) 82–84, doi:10.1061/(ASCE)0733-9429(2008)134:5(572). [15] B. Dargahi, J. Hydraul. Eng. 116 (10) (1990) 1197–1214. [16] A. Bestawy, T. Eltahawy, A. Alsaluli, M. Alqurashi, Water Supply 20 (3) (2020) 1006–1015, doi:10.2166/ws.2020.022. [17] Y.M. Chiew, J. Hydraul. Eng. 118 (9) (1992) 1260–1269. [18] D. Bertoldi, R. Kilgore, in: Hydraulic Engineering ’93, ASCE, San Francisco, California, United States, 1993, pp. 1385–1390. [19] Y.M. Chiew, J. Hydraul. Eng. 121 (9) (1997) 635–642. [20] C.S. Lauchlan, B.W. Melville, J. Hydraul. Eng. 127 (5) (2001) 412–418, doi:10. 1061/(ASCE)0733-9429(2001)127:5(412). [21] P.F. Lagasse, P.E. Clopper, L.W. Zevenbergen, L.G. Girard, National Cooperative Highway Research Program (NCHRPReport 593), Countermeasures to protect bridge piers from scour, Washington, DC, NCHRP, 2007. [22] S. Jiang, Z. Zhou, J. Ou, J. Sediment Res. (4) (2013) 63–67 in Chinese. [23] A. Galan, G. Simarro, G. Sanchez-Serrano, J. Hydraul. Eng. 141 (6) (2015) 06015004, doi:10.1061/(ASCE)HY.1943-7900.0001003. [24] Z. Zhang, H. Ding, J. Liu, Ocean Eng. 33 (2) (2015) 77–83 in Chinese. [25] C. Valela, C.N. Whittaker, C.D. Rennie, I. Nistor, B.W. Melville, J. Hydraul. Eng. 148 (3) (2022) 04022002 10.1061/%28ASCE%29HY.1943-7900.0001967. [26] B.W. Melville, A.C. Hadfield, J. Hydraul. Eng. 6 (2) (1999) 1221–1224, doi:10. 1061/(ASCE)0733-9429(1999)125:11(1221). [27] V. Kumar, K.G. Rangaraju, N. Vittal, J. Hydraul. Eng. 125 (12) (1999) 1302–1305. [28] A.M. Yasser, K.S. Yasser, M.A. Abdel-Azim, Alex. Eng. J. 54 (2) (2015) 197–203, doi:10.1016/j.aej.2015.03.004. [29] S. Khaple, P.R. Hanmaiahgari, R. Gaudio, S. Dey, Acta Geophys. 65 (2017) 957– 975, doi:10.1007/s11600-017-0084-z. [30] C. Valela, I. Nistor, C.D. Rennie, in: Proceedings of the 6th International Disaster Mitigation Specialty Conference, Fredericton, Canada, Canadian Society for Civil Engineering, 2018, pp. 235–244. [31] A. Tafarojnoruz, R. Gaudio, F. Calomino, J. Hydraul. Eng. 138 (3) (2012) 297– 305, doi:10.1061/(ASCE)HY.1943-7900.0000512. [32] H. Tang, S. Fang, Y. Zhou, K. Cai, Y.M. Chiew, S.Y. Lim, N.S. Cheng, in: Proceedings of the 2nd International Conference Scour and Erosion (ICSE-2), Singapore. Singapore, Nanyang Technological University, 2004. [33] W. Zhang, Y. Li, X. Wang, Z. Sun, J. Sichuan Univ. 06 (2005) 34–40 (Engineering Science Edition)in Chinese. [34] S. Yang, B. Shi, Trans. Oceanol. Limnol. 5 (2017) 43–47 in Chinese. [35] H. Wang, F. Si, G. Lou, W. Yang, G. Yu, J. Waterw. Port Coast. Ocean Eng. 141 (1) (2015) 04014030, doi:10.1061/(ASCE)WW.1943-5460.0000270. [36] L.D. Meyer, S.M. Dabney, W.C. Harmon, Trans. ASAE 38 (3) (1995) 809–815. [37] G. Spyreas, B.W. Wilm, A.E. Plocher, D.M. Ketzner, J.W. Matthews, J.L. Ellis, E.J. Heske, Biol. Invasions 12 (5) (2010) 1253–1267, doi:10.1007/ s10530-009-9544-y. [38] T. Lambrechts, S. François, S. Lutts, R. Muñoz-Carpena, C.L. Bielders, J. Hydrol. 511 (2014) 800–810, doi:10.1016/j.jhydrol.2014.02.030. [39] G. Yu, Dynamic Embedded Anchor with High Frequency Micro Amplitude Vibrations. CN patent No: ZL200810038546.0, 2008. [40] X. Chen, M. Zhang, G. Yu, Ocean Eng. 236 (2021) 109315, doi:10.1016/j. oceaneng.2021.109315. [41] F. Gumgum, M.S. Guney, in: Proceedings of the 6th International Conference Engineering and Natural Sciences (ICENS), Serbia, Belgrade, 2020. [42] H. Zhao, S. Yue, H. Zhou, M. Zhang, G. Yu, Ocean Eng. 40 (5) (2022) 111–120 in Chinese. [43] B. Blocken, C. Gualtieri, Environ. Modell. Softw. 33 (2012) 1–22, doi:10.1016/j. envsoft.2012.02.001. [44] N.D. Bennett, B.F. Croke, G. Guariso, et al., Modell. Softw. 40 (2013) 1–20, doi:10.1016/j.envsoft.2012.09.011. [45] X. Zhao, Effectiveness and Mechanism of Lattice On Sedimentation and Anti-Erosion of Local Scour Hole At Piers, Shanghai Jiao Tong University, Shanghai, China, 2023. [46] M. Zhang, G. Yu, Water Resour. Res. 53 (9) (2017) 7798–7815, doi:10.1002/ 2017WR021066.
이 연구에서는 세 가지 다른 말뚝 뚜껑 높이에서 직사각형 말뚝 캡이 있는 복잡한 부두 주변의 지역 세굴 및 관련 흐름 유체 역학을 조사합니다. 말뚝 캡 높이가 초기 모래층에 대해 선택되었으며, 말뚝 캡이 흐름에 노출되지 않고(사례 I), 부분적으로 노출되고(사례 II) 완전히 노출(사례 III)되도록 했습니다. 실험은 맑은 물 세굴 조건 하에서 재순환 수로에서 수행되었으며, 입자 이미지 유속계 (PIV) 기술을 사용하여 다른 수직면에서 순간 유속을 얻었습니다. 부분적으로 노출된 파일 캡 케이스는 최대 수세미 깊이(MSD)를 보여주었습니다. 사례 II에서 MSD가 발생한 이유는 난류 유동장 분석을 통해 밝혀졌는데, 이는 말뚝 캡이 흐름에 노출됨에 따라 더 높은 세굴 깊이를 담당하는 말뚝 가장자리에서 와류 생성에 지배적으로 영향을 미친다는 것을 보여주었습니다. 유동장에 대한 파일 캡의 영향은 평균 속도, 소용돌이, 레이놀즈 전단 응력 및 난류 운동 에너지 윤곽을 통해 사례 III에서 두드러지게 나타났지만 파일 캡이 베드에서 떨어져 있었기 때문에 파일 캡 모서리는 수세미에 직접적인 영향을 미치지 않았습니다.
In this study, the local scour and the associated flow hydrodynamics around a complex pier with rectangular pile-cap at three different pile-cap elevations are investigated. The pile-cap elevations were selected with respect to the initial sand bed, such that the pile-cap was unexposed (case I), partially exposed (case II), and fully exposed (case III) to the flow. The experiments were performed in a recirculating flume under clear-water scour conditions, and the instantaneous flow velocity was obtained at different vertical planes using the particle image velocimetry (PIV) technique. The partially exposed pile-cap case showed the maximum obtained scour-depth (MSD). The reason behind the MSD occurrence in case II was enunciated through the analysis of turbulent flow field which showed that as the pile-cap got exposed to the flow, it dominantly affected the generation of vortices from the pile-cap corners responsible for the higher scour depth. The effect of the pile-cap on the flow field was prominently seen in case III through the mean velocities, vorticity, Reynolds shear stresses and turbulent kinetic energy contours, but since the pile-cap was away from the bed, the pile-cap corners did not show any direct effect on the scour.
Adrian, R. J. (2013). Structure of turbulent boundary layers. In Jeremy G. Venditti, James L. Best, Michael Church, & Richard J. Hardy (Eds.), Coherent flow structures at earth’s surface (pp. 17–24). John Wiley and Sons. [Crossref], [Google Scholar]
Adrian, R. J., & Westerweel, J. (2011). Particle image velocimetry, No. 30. Cambridge University Press. [Google Scholar]
Alemi, M., & Maia, R. (2018). Numerical simulation of the flow and local scour process around single and complex bridge piers. International Journal of Civil Engineering, 16(5), 475–487. https://doi.org/10.1007/s40999-016-0137-8 [Crossref], [Google Scholar]
Alemi, M., Pêgo, J. P., & Maia, R. (2019). Numerical simulation of the turbulent flow around a complex bridge pier on the scoured bed. European Journal of Mechanics – B/Fluids, 76, 316–331. https://doi.org/10.1016/j.euromechflu.2019.03.011 [Crossref], [Web of Science ®], [Google Scholar]
Amini, A., Hamidi, S., Shirzadi, A., Behmanesh, J., & Akib, S. (2021). Efficiency of artificial neural networks in determining scour depth at composite bridge piers. International Journal of River Basin Management, 19(3), 327–333. https://doi.org/10.1080/15715124.2020.1742138 [Taylor & Francis Online], [Web of Science ®], [Google Scholar]
Arneson, L. A., Zevenbergen, L. W., Lagasse, P. F., & Clopper, P. E. (2015). Evaluating scour at bridges, 5th ed. hydraulic engineering circular No. 18 (HEC-18). Federal Highway Administration. [Google Scholar]
Ataie-Ashtiani, B., & Aslani-Kordkandi, A. (2012). Flow field around side-by-side piers with and without a scour hole. European Journal of Mechanics – B/Fluids, 36, 152–166. https://doi.org/10.1016/j.euromechflu.2012.03.007 [Crossref], [Web of Science ®], [Google Scholar]
Ataie-Ashtiani, B., Baratian-Ghorghi, Z., & Beheshti, A. A. (2010). Experimental investigation of clear-water local scour of compound piers. Journal of Hydraulic Engineering, 136(6), 343–351. https://doi.org/10.1061/(ASCE)0733-9429(2010)136:6(343) [Crossref], [Web of Science ®], [Google Scholar]
Avallone, F., Discetti, S., Astarita, T., & Cardone, G. (2015). Convergence enhancement of single-pixel PIV with symmetric double correlation. Experiments in Fluids, 56(4), 71. https://doi.org/10.1007/s00348-015-1938-2 [Crossref], [Web of Science ®], [Google Scholar]
Beheshti, A. A., & Ataie-Ashtiani, B. (2010). Experimental study of three-dimensional flow field around a complex bridge pier. Journal of Engineering Mechanics, 136(2), 143–154. https://doi.org/10.1061/(ASCE)EM.1943-7889.0000073 [Crossref], [Web of Science ®], [Google Scholar]
Beheshti, A. A., & Ataie-Ashtiani, B. (2016). Scour hole influence on turbulent flow field around complex bridge piers. Flow, Turbulence and Combustion, 97(2), 451–474. https://doi.org/10.1007/s10494-016-9707-8 [Crossref], [Web of Science ®], [Google Scholar]
Cameron, S. M., Nikora, V. I., & Marusic, I. (2019). Drag forces on a bed particle in open-channel flow: Effects of pressure spatial fluctuations and very-large-scale motions. Journal of Fluid Mechanics, 863, 494–512. https://doi.org/10.1017/jfm.2018.1003 [Crossref], [Web of Science ®], [Google Scholar]
Cheng, N., & Emadzadeh, A. (2017). Laboratory measurements of vortex-induced sediment pickup rates. International Journal of Sediment Research, 32(1), 98–104. https://doi.org/10.1016/j.ijsrc.2016.04.005 [Crossref], [Web of Science ®], [Google Scholar]
Coleman, S. E. (2005). Clearwater local scour at complex piers. Journal of Hydraulic Engineering, 131(4), 330–334. https://doi.org/10.1061/(ASCE)0733-9429(2005)131:4(330) [Crossref], [Web of Science ®], [Google Scholar]
Das, S., & Mazumdar, A. (2015). Turbulence flow field around two eccentric circular piers in scour hole. International Journal of River Basin Management, 13(3), 343–361. https://doi.org/10.1080/15715124.2015.1012515 [Taylor & Francis Online], [Web of Science ®], [Google Scholar]
Esmaeili Varaki, M., Radice, A., Samira Hossini, S., & Fazl Ola, R. (2019). Local scour at a complex pier with inclined columns footed on capped piles: Effect of the pile arrangement and of the cap thickness and elevation. ISH Journal of Hydraulic Engineering, 1–10. https://doi.org/10.1080/09715010.2019.1702109 [Taylor & Francis Online], [Google Scholar]
Ferraro, D., Tafarojnoruz, A., Gaudio, R., & Cardoso, A. H. (2013). Effects of pile cap thickness on the maximum scour depth at a complex pier. Journal of Hydraulic Engineering, 139(5), 482–491. https://doi.org/10.1061/(ASCE)HY.1943-7900.0000704 [Crossref], [Web of Science ®], [Google Scholar]
Gaudio, R., Tafarojnoruz, A., & Calomino, F. (2012). Combined flow-altering countermeasures against bridge pier scour. Journal of Hydraulic Research, 50(1), 35–43. https://doi.org/10.1080/00221686.2011.649548 [Taylor & Francis Online], [Web of Science ®], [Google Scholar]
Gautam, P., Eldho, T., & Behera, M. (2016). Experimental study of scour around a complex pier with elliptical pile-cap. In J. Harris, R. Whitehouse, & S. Moxon (Eds.), Scour and Erosion: Proceedings of the 8th International Conference on Scour and Erosion (Oxford, UK, 12-15 September 2016) (pp. 759–765). CRC Press. [Crossref], [Google Scholar]
Gautam, P., Eldho, T. I., Mazumder, B. S., & Behera, M. R. (2019). Experimental study of flow and turbulence characteristics around simple and complex piers using PIV. Experimental Thermal and Fluid Science, 100, 193–206. https://doi.org/10.1016/j.expthermflusci.2018.09.010 [Crossref], [Web of Science ®], [Google Scholar]
Graf, W. H., & Istiarto, I. (2002). Flow pattern in the scour hole around a cylinder. Journal of Hydraulic Research, 40(1), 13–20. https://doi.org/10.1080/00221680209499869 [Taylor & Francis Online], [Web of Science ®], [Google Scholar]
Hjulstrom, F. (1935). Study of the morphological activity of Rivers as illustrated by the River fyris bulletin, vol. 25. Geological Institute of Upsala. [Google Scholar]
Kumar, A., & Kothyari, U. C. (2012). Three-dimensional flow characteristics within the scour hole around circular uniform and compound piers. Journal of Hydraulic Engineering, 138(5), 420–429. https://doi.org/10.1061/(ASCE)HY.1943-7900.0000527 [Crossref], [Web of Science ®], [Google Scholar]
Mashahir, M. B., Zarrati, A. R., & Rezayi, M. J. (2004). Time development of scouring around a bridge pier protected by collar. In Proceedings 2nd International Conference on Scour and Erosion (ICSE-2). November 14–17, 2004, Singapore. [Google Scholar]
Melville, B. W. (2008). The physics of local scour at bridge piers. In Proceedings of the 4th International Conference on Scour and Erosion (ICSE-4). November 5-7, 2008, Tokyo, Japan (pp. 28–40). [Google Scholar]
Melville, B. W., & Chiew, Y. M. (1999). Time scale for local scour at bridge piers. Journal of Hydraulic Engineering, 125(1), 59–65. https://doi.org/10.1061/(ASCE)0733-9429(1999)125:1(59) [Crossref], [Web of Science ®], [Google Scholar]
Melville, B. W., & Raudkivi, A. J. (1977). Flow characteristics in local scour at bridge piers. Journal of Hydraulic Research, 15(4), 373–380. https://doi.org/10.1080/00221687709499641 [Taylor & Francis Online], [Web of Science ®], [Google Scholar]
Moreno, M., Maia, R., & Couto, L. (2016a). Effects of relative column width and pile-cap elevation on local scour depth around complex piers. Journal of Hydraulic Engineering, 142(2), 04015051. https://doi.org/10.1061/(ASCE)HY.1943-7900.0001080 [Crossref], [Web of Science ®], [Google Scholar]
Moreno, M., Maia, R., & Couto, L. (2016b). Prediction of equilibrium local scour depth at complex bridge piers. Journal of Hydraulic Engineering, 142(11), 04016045. https://doi.org/10.1061/(ASCE)HY.1943-7900.0001153 [Crossref], [Web of Science ®], [Google Scholar]
Nezu, I., & Rodi, W. (1986). Open-channel flow measurements with a laser Doppler anemometer. Journal of Hydraulic Engineering, 112(5), 335–355. https://doi.org/10.1061/(ASCE)0733-9429(1986)112:5(335) [Crossref], [Web of Science ®], [Google Scholar]
Radice, A., & Tran, C. K. (2012). Study of sediment motion in scour hole of a circular pier. Journal of Hydraulic Research, 50(1), 44–51. https://doi.org/10.1080/00221686.2011.641764 [Taylor & Francis Online], [Web of Science ®], [Google Scholar]
Richardson, J. R., & York, K. (1999). Hydrodynamic countermeasures for local pier scour. Transportation Research Record: Journal of the Transportation Research Board, 1690(1), 186–192. https://doi.org/10.3141/1690-21 [Crossref], [Google Scholar]
Saw, E., Debue, P., Kuzzay, D., Daviaud, F., & Dubrulle, B. (2018). On the universality of anomalous scaling exponents of structure functions in turbulent flows. Journal of Fluid Mechanics, 837, 657–669. https://doi.org/10.1017/jfm.2017.848 [Crossref], [Web of Science ®], [Google Scholar]
Schlichting, H. (1968). Boundary layer theory (Vol. 960). McGraw-Hill. [Google Scholar]
Sheppard, D. M., Demir, H., & Melville, B. W. (2011). Scour at wide piers and long skewed piers (Vol. 682). Transportation Research Board. [Google Scholar]
Tafarojnoruz, A., Gaudio, R., & Calomino, F. (2012). Bridge pier scour mitigation under steady and unsteady flow conditions. Acta Geophysica, 60(4), 1076–1097. https://doi.org/10.2478/s11600-012-0040-x [Crossref], [Web of Science ®], [Google Scholar]
Tafarojnoruz, A., Gaudio, R., & Dey, S. (2010). Flow-altering countermeasures against scour at bridge piers: A review. Journal of Hydraulic Research, 48(4), 441–452. https://doi.org/10.1080/00221686.2010.491645 [Taylor & Francis Online], [Web of Science ®], [Google Scholar]
Tennekes, H., & Lumley, J. L. (1972). A first course in turbulence. MIT press. [Crossref], [Google Scholar]
Veerappadevaru, G., Gangadharaiah, T., & Jagadeesh, T. R. (2011). Vortex scouring process around bridge pier with a caisson. Journal of Hydraulic Research, 49(3), 378–383. https://doi.org/10.1080/00221686.2011.568195 [Taylor & Francis Online], [Web of Science ®], [Google Scholar]
Veerappadevaru, G., Gangadharaiah, T., & Jagadeesh, T. R. (2012). Temporal variation of vortex scour process around caisson piers. Journal of Hydraulic Research, 50(2), 200–207. https://doi.org/10.1080/00221686.2012.666832 [Taylor & Francis Online], [Web of Science ®], [Google Scholar]
Vijayasree, B. A., Eldho, T. I., Mazumder, B. S., & Ahmad, N. (2019). Influence of bridge pier shape on flow field and scour geometry. International Journal of River Basin Management, 17(1), 109–129. https://doi.org/10.1080/15715124.2017.1394315 [Taylor & Francis Online], [Web of Science ®], [Google Scholar]
Yang, Y., Melville, B. W., Sheppard, D. M., & Shamseldin, A. Y. (2018). Clear-water local scour at skewed complex bridge piers. Journal of Hydraulic Engineering, 144(6), 04018019. https://doi.org/10.1061/(ASCE)HY.1943-7900.0001458 [Crossref], [Web of Science ®], [Google Scholar]
Yang, Y., Melville, B. W., Macky, G. H., & Shamseldin, A. Y. (2020). Temporal evolution of clear-water local scour at aligned and skewed complex bridge piers. Journal of Hydraulic Engineering, 146(4), 04020026. https://doi.org/10.1061/(ASCE)HY.1943-7900.0001732 [Crossref], [Web of Science ®], [Google Scholar]
A numerical study was performed on the embankment weir overflows with various surface roughness and tailwater submergence, to better understand the effects of weir roughness on discharge performances under the free and submerged conditions. The variation of flow regime is captured, from the free overflow, submerged hydraulic jump, to surface flow with increasing tailwater depth. A roughness factor is introduced to reflect the reduction in discharge caused by weir roughness. The roughness factor decreases with the roughness height, and it also depends on the tailwater depth, highlighting various relations of the roughness factor with the roughness height between different flow regimes, which is linear for the free overflow and submerged hydraulic jump while exponential for the surface flow. Accordingly, the effects of weir roughness on overflow discharge appear nonnegligible for the significant roughness height and the surface flow regime occurring under considerable tailwater submergence. The established empirical expressions of discharge coefficient and submergence and roughness factors make it possible to predict the discharge over embankment weirs considering both tailwater submergence and surface roughness.
자유 및 침수 조건에서 방류 성능에 대한 둑 거칠기의 영향을 더 잘 이해하기 위해 다양한 표면 거칠기와 테일워터 침수를 갖는 제방 둑 범람에 대한 수치 연구가 수행되었습니다.
자유 범람, 수중 수압 점프, 테일워터 깊이가 증가하는 표면 유동에 이르기까지 유동 체제의 변화가 캡처됩니다. 위어 거칠기로 인한 배출 감소를 반영하기 위해 거칠기 계수가 도입되었습니다.
조도 계수는 조도 높이와 함께 감소하고, 또한 테일워터 깊이에 따라 달라지며, 서로 다른 흐름 영역 사이의 조도 높이와 조도 계수의 다양한 관계를 강조합니다.
이는 자유 범람 및 수중 수압 점프에 대해 선형인 반면 표면에 대해 지수적입니다. 흐름. 따라서 월류 방류에 대한 웨어 조도의 영향은 상당한 조도 높이와 상당한 방수 침수 하에서 발생하는 표면 흐름 체제에 대해 무시할 수 없는 것으로 보입니다.
방류계수와 침수 및 조도계수의 확립된 실증식은 방류수 침수와 지표조도를 모두 고려한 제방보 위의 방류량을 예측할 수 있게 합니다.
References
Kindsvater C. E. Discharge characteristics of embankment -shaped weirs (No. 1617) [R]. Washington DC, USA: US Government Printing Office, 1964.Google Scholar
Fritz H. M., Hager W. H. Hydraulics of embankment weirs [J]. Journal of Hydraulic Engineering, ASCE, 1998, 124(9): 963–971.ArticleGoogle Scholar
Azimi A. H., Rajaratnam N., Zhu D. Z. Water surface characteristics of submerged rectangular sharp-crested weirs [J]. Journal of Hydraulic Engineering, ASCE, 2016, 142(5): 06016001.ArticleGoogle Scholar
Felder S., Islam N. Hydraulic performance of an embankment weir with rough crest [J]. Journal of Hydraulic Engineering, ASCE, 2017, 143(3): 04016086.ArticleGoogle Scholar
Hakim S. S., Azimi A. H. Hydraulics of submerged traingular weirs and weirs of finite-crest length with upstream and downstream ramps [J]. Journal of Irrigation and Drainage Engineering, 2017, 143(8): 06017008.ArticleGoogle Scholar
Safarzadeh A., Mohajeri S. H. Hydrodynamics of rectangular broad-crested porous weirs [J]. Journal of Hydraulic Engineering, ASCE, 2018, 144(10): 04018028.Google Scholar
Sargison J. E., Percy A. Hydraulics of broad-crested weirs with varying side slopes [J]. Journal of Irrigation and Drainage Engineering, 2009, 35(1): 115–118.ArticleGoogle Scholar
Yang Z., Bai F., Huai W. et al. Lattice Boltzmann method for simulating flows in the open-channel with partial emergent rigid vegetation cover [J]. Journal of Hydrodynamics, 2019, 31(4): 717–724.ArticleGoogle Scholar
Fathi-moghaddam M., Sadrabadi M. T., Rahmanshahi M. Numerical simulation of the hydraulic performance of triangular and trapezoidal gabion weirs in free flow condtion [J]. Flow Measurement on Instrumentation, 2018, 62: 93–104.ArticleGoogle Scholar
Zerihun Y. T. A one-dimensional Boussinesq-type momentum model for steady rapidly varied open channel flows [D]. Doctoral Thesis, Melbourne, Australia: The University of Melbourne, 2004.Google Scholar
Pařílková J., Říha J., Zachoval Z. The influence of roughness on the discharge coefficient of a broad-crested weir [J]. Journal of Hydrology and Hydromechanics, 2012, 60(2): 101–114.ArticleGoogle Scholar
Říha J., Duchan D., Zachoval Z. et al. Performance of a shallow-water model for simulating flow over trapezoidal broad-crested weirs [J]. Journal of Hydrology and Hydromechanics, 2019, 67(4): 322–328.ArticleGoogle Scholar
Yan X., Ghodoosipour B., Mohammadian A. Three-dimensional numerical study of multiple vertical buoyant jets in stationary ambient water [J]. Journal of Hydraulic Engineering, ASCE, 2020, 146(7): 04020049.ArticleGoogle Scholar
Qian S., Xu H., Feng J. Flume experiments on baffle-posts for retarding open channel flow: By C. UBING, R. ETTEMA and CI THORNTON, J. Hydraulic Res. 55 (3), 2017, 430–437 [J]. Journal of Hydraulic Research, 2019, 57(2): 280–282.ArticleGoogle Scholar
Sun J., Qian S., Xu H. et al. Three-dimensional numerical simulation of stepped dropshaft with different step shape [J]. Water Science and Technology Water Supply, 2020, 21(1): 581–592.Google Scholar
Qian S., Wu J., Zhou Y. et al. Discussion of “Hydraulic performance of an embankment weir with rough crest” by Stefan Felder and Nushan Islam [J]. Journal of Hydraulic Engineering, ASCE, 2018, 144(4): 07018003.ArticleGoogle Scholar
Mohammadpour R., Ghani A. A., Azamathulla H. M. Numerical modeling of 3-D flow on porous broad crested weirs [J]. Applied Mathematical Modelling, 2013, 37(22): 9324–9337.ArticleGoogle Scholar
Savage B. M., Brian M. C., Greg S. P. Physical and numerical modeling of large headwater ratios for a 15° labyrinth spillway [J]. Journal of Hydraulic Engineering, ASCE, 2016, 142(11): 04016046.ArticleGoogle Scholar
Al-Husseini T. R., Al-Madhhachi A. S. T., Naser Z. A. Laboratory experiments and numerical model of local scour around submerged sharp crested weirs [J]. Journal of King Saud University Science, 2020, 32(3): 167–176.ArticleGoogle Scholar
Zerihun Y. T., Fenton J. D. A Boussinesq-type model for flow over trapezoidal profile weirs [J]. Journal of Hydraulic Research, 2007, 45(4): 519–528.ArticleGoogle Scholar
Flow Science, Inc. FLOW-3D ® Version 12.0 Users Manual (2018) [EB/OL]. Santa Fe, NM, USA: Flow Science, Inc., 2019.Google Scholar
Bazin H. Expériences nouvelles sur l’ecoulement par déversoir [R]. Paris, France: Annales des Ponts et Chaussées, 1898.MATHGoogle Scholar
Hager W. H., Schwalt M. Broad-crested weir [J]. Journal of Irrigation and Drainage Engineering, 1994, 120(1): 13–26.ArticleGoogle Scholar
Citizens’ daily needs such as; transportation, communication, clean water and sewage are supplied with infrastructure systems. Horizontal and vertical expansion in the cities due to the increase in population leads to serious demand for infrastructural improvements. The infrastructure systems in developing cities are required to be designed in a satisfactory capacity to supply the increasing demand for residential and industrial constructions. The districts having insufficient infrastructure systems inevitably confront heavy traffic, flood, air pollution problems, and also having difficulties with the inadequacy of parking area, clear and potable water, communication. The problems may cause social and health problems over time. At this point, it is wished to emphasize that the primary factor of citycivilization development depends on infrastructural systems and it is meaningful to name the engineering field like civil engineering, literally leads civilization. Dropshafts, commonly used in the urban storm and sewage water systems produced generally circular are used for energy dissipation and flow direction control. Aeration is significant for the working principle of the flow in dropshaft and this study is made mainly for this two-phase (air-water) physics of dropshafts. Chanson showed that aeration and energy dissipation is directly linked to each other (2002), but the influencing factors and the action mechanisms of the factors on the phenomena are not discovered entirely. By the comprehension of the factors, more effective dropshafts will be able to design. This study aims to guide the more comprehensive investigation of design factors using Computational Fluid Dynamics-CFD programs. The reasons for the preference of the programs are the cost-effectiveness of material, workmanship and duration relative to hydraulic modelling. The competence of the inputs, outputs and solution system of the CFD code is validated by the comparison of previous hydraulic modelling results.
Keywords
CFD, Dropshaft, Sewer system, Storm Water System, Two-Phase Flow
A series of numerical simulation were conducted to study the local scour around umbrella suction anchor foundation (USAF) under random waves. In this study, the validation was carried out firstly to verify the accuracy of the present model. Furthermore, the scour evolution and scour mechanism were analyzed respectively. In addition, two revised models were proposed to predict the equilibrium scour depth Seq around USAF. At last, a parametric study was carried out to study the effects of the Froude number Fr and Euler number Eu for the Seq. The results indicate that the present numerical model is accurate and reasonable for depicting the scour morphology under random waves. The revised Raaijmakers’s model shows good agreement with the simulating results of the present study when KCs,p < 8. The predicting results of the revised stochastic model are the most favorable for n = 10 when KCrms,a < 4. The higher Fr and Eu both lead to the more intensive horseshoe vortex and larger Seq.
The rapid expansion of cities tends to cause social and economic problems, such as environmental pollution and traffic jam. As a kind of clean energy, offshore wind power has developed rapidly in recent years. The foundation of offshore wind turbine (OWT) supports the upper tower, and suffers the cyclic loading induced by waves, tides and winds, which exerts a vital influence on the OWT system. The types of OWT foundation include the fixed and floating foundation, and the fixed foundation was used usually for nearshore wind turbine. After the construction of fixed foundation, the hydrodynamic field changes in the vicinity of the foundation, leading to the horseshoe vortex formation and streamline compression at the upside and sides of foundation respectively [1,2,3,4]. As a result, the neighboring soil would be carried away by the shear stress induced by vortex, and the scour hole would emerge in the vicinity of foundation. The scour holes increase the cantilever length, and weaken the lateral bearing capacity of foundation [5,6,7,8,9]. Moreover, the natural frequency of OWT system increases with the increase of cantilever length, causing the resonance occurs when the system natural frequency equals the wave or wind frequency [10,11,12]. Given that, an innovative foundation called umbrella suction anchor foundation (USAF) has been designed for nearshore wind power. The previous studies indicated the USAF was characterized by the favorable lateral bearing capacity with the low cost [6,13,14]. The close-up of USAF is shown in Figure 1, and it includes six parts: 1-interal buckets, 2-external skirt, 3-anchor ring, 4-anchor branch, 5-supporting rod, 6-telescopic hook. The detailed description and application method of USAF can be found in reference [13].
Figure 1. The close-up of umbrella suction anchor foundation (USAF).
Numerical and experimental investigations of scour around OWT foundation under steady currents and waves have been extensively studied by many researchers [1,2,15,16,17,18,19,20,21,22,23,24]. The seabed scour can be classified as two types according to Shields parameter θ, i.e., clear bed scour (θ < θcr) or live bed scour (θ > θcr). Due to the set of foundation, the adverse hydraulic pressure gradient exists at upstream foundation edges, resulting in the streamline separation between boundary layer flow and seabed. The separating boundary layer ascended at upstream anchor edges and developed into the horseshoe vortex. Then, the horseshoe vortex moved downstream gradually along the periphery of the anchor, and the vortex shed off continually at the lee-side of the anchor, i.e., wake vortex. The core of wake vortex is a negative pressure center, liking a vacuum cleaner. Hence, the soil particles were swirled into the negative pressure core and carried away by wake vortexes. At the same time, the onset of scour at rear side occurred. Finally, the wake vortex became downflow when the turbulence energy could not support the survival of wake vortex. According to Tavouktsoglou et al. [25], the scale of pile wall boundary layer is proportional to 1/ln(Rd) (Rd is pile Reynolds), which means the turbulence intensity induced by the flow-structure interaction would decrease with Rd increases, but the effects of Rd can be neglected only if the flow around the foundation is fully turbulent [26]. According to previous studies [1,15,27,28,29,30,31,32], the scour development around pile foundation under waves was significantly influenced by Shields parameter θ and KC number simultaneously (calculated by Equation (1)). Sand ripples widely existed around pile under waves in the case of live bed scour, and the scour morphology is related with θ and KC. Compared with θ, KC has a greater influence on the scour morphology [21,27,28]. The influence mechanism of KC on the scour around the pile is reflected in two aspects: the horseshoe vortex at upstream and wake vortex shedding at downstream.
KC=UwmTD��=�wm��(1)
where, Uwm is the maximum velocity of the undisturbed wave-induced oscillatory flow at the sea bottom above the wave boundary layer, T is wave period, and D is pile diameter.
There are two prerequisites to satisfy the formation of horseshoe vortex at upstream pile edges: (1) the incoming flow boundary layer with sufficient thickness and (2) the magnitude of upstream adverse pressure gradient making the boundary layer separating [1,15,16,18,20]. The smaller KC results the lower adverse pressure gradient, and the boundary layer cannot separate, herein, there is almost no horseshoe vortex emerging at upside of pile. Sumer et al. [1,15] carried out several sets of wave flume experiments under regular and irregular waves respectively, and the experiment results show that there is no horseshoe vortex when KC is less than 6. While the scale and lifespan of horseshoe vortex increase evidently with the increase of KC when KC is larger than 6. Moreover, the wake vortex contributes to the scour at lee-side of pile. Similar with the case of horseshoe vortex, there is no wake vortex when KC is less than 6. The wake vortex is mainly responsible for scour around pile when KC is greater than 6 and less than O(100), while horseshoe vortex controls scour nearly when KC is greater than O(100).
Sumer et al. [1] found that the equilibrium scour depth was nil around pile when KC was less than 6 under regular waves for live bed scour, while the equilibrium scour depth increased with the increase of KC. Based on that, Sumer proposed an equilibrium scour depth predicting equation (Equation (2)). Carreiras et al. [33] revised Sumer’s equation with m = 0.06 for nonlinear waves. Different with the findings of Sumer et al. [1] and Carreiras et al. [33], Corvaro et al. [21] found the scour still occurred for KC ≈ 4, and proposed the revised equilibrium scour depth predicting equation (Equation (3)) for KC > 4.
Rudolph and Bos [2] conducted a series of wave flume experiments to investigate the scour depth around monopile under waves only, waves and currents combined respectively, indicting KC was one of key parameters in influencing equilibrium scour depth, and proposed the equilibrium scour depth predicting equation (Equation (4)) for low KC (1 < KC < 10). Through analyzing the extensive data from published literatures, Raaijmakers and Rudolph [34] developed the equilibrium scour depth predicting equation (Equation (5)) for low KC, which was suitable for waves only, waves and currents combined. Khalfin [35] carried out several sets of wave flume experiments to study scour development around monopile, and proposed the equilibrium scour depth predicting equation (Equation (6)) for low KC (0.1 < KC < 3.5). Different with above equations, the Khalfin’s equation considers the Shields parameter θ and KC number simultaneously in predicting equilibrium scour depth. The flow reversal occurred under through in one wave period, so sand particles would be carried away from lee-side of pile to upside, resulting in sand particles backfilled into the upstream scour hole [20,29]. Considering the backfilling effects, Zanke et al. [36] proposed the equilibrium scour depth predicting equation (Equation (7)) around pile by theoretical analysis, and the equation is suitable for the whole range of KC number under regular waves and currents combined.
where, γ is safety factor, depending on design process, typically γ = 1.5, Kwave is correction factor considering wave action, Khw is correction factor considering water depth.
where, n is the 1/n’th highest wave for random waves
For predicting equilibrium scour depth under irregular waves, i.e., random waves, Sumer and Fredsøe [16] found it’s suitable to take Equation (2) to predict equilibrium scour depth around pile under random waves with the root-mean-square (RMS) value of near-bed orbital velocity amplitude Um and peak wave period TP to calculate KC. Khalfin [35] recommended the RMS wave height Hrms and peak wave period TP were used to calculate KC for Equation (6). References [37,38,39,40] developed a series of stochastic theoretical models to predict equilibrium scour depth around pile under random waves, nonlinear random waves plus currents respectively. The stochastic approach thought the 1/n’th highest wave were responsible for scour in vicinity of pile under random waves, and the KC was calculated in Equation (8) with Um and mean zero-crossing wave period Tz. The results calculated by Equation (8) agree well with experimental values of Sumer and Fredsøe [16] if the 1/10′th highest wave was used. To author’s knowledge, the stochastic approach proposed by Myrhaug and Rue [37] is the only theoretical model to predict equilibrium scour depth around pile under random waves for the whole range of KC number in published documents. Other methods of predicting scour depth under random waves are mainly originated from the equation for regular waves-only, waves and currents combined, which are limited to the large KC number, such as KC > 6 for Equation (2) and KC > 4 for Equation (3) respectively. However, situations with relatively low KC number (KC < 4) often occur in reality, for example, monopile or suction anchor for OWT foundations in ocean environment. Moreover, local scour around OWT foundations under random waves has not yet been investigated fully. Therefore, further study are still needed in the aspect of scour around OWT foundations with low KC number under random waves. Given that, this study presents the scour sediment model around umbrella suction anchor foundation (USAF) under random waves. In this study, a comparison of equilibrium scour depth around USAF between this present numerical models and the previous theoretical models and experimental results was presented firstly. Then, this study gave a comprehensive analysis for the scour mechanisms around USAF. After that, two revised models were proposed according to the model of Raaijmakers and Rudolph [34] and the stochastic model developed by Myrhaug and Rue [37] respectively to predict the equilibrium scour depth. Finally, a parametric study was conducted to study the effects of the Froude number (Fr) and Euler number (Eu) to equilibrium scour depth respectively.
2. Numerical Method
2.1. Governing Equations of Flow
The following equations adopted in present model are already available in Flow 3D software. The authors used these theoretical equations to simulate scour in random waves without modification. The incompressible viscous fluid motion satisfies the Reynolds-averaged Navier-Stokes (RANS) equation, so the present numerical model solves RANS equations:
where, VF is the volume fraction; u, v, and w are the velocity components in x, y, z direction respectively with Cartesian coordinates; Ai is the area fraction; ρf is the fluid density, fi is the viscous fluid acceleration, Gi is the fluid body acceleration (i = x, y, z).
2.2. Turbulent Model
The turbulence closure is available by the turbulent model, such as one-equation, the one-equation k-ε model, the standard k-ε model, RNG k-ε turbulent model and large eddy simulation (LES) model. The LES model requires very fine mesh grid, so the computational time is large, which hinders the LES model application in engineering. The RNG k-ε model can reduce computational time greatly with high accuracy in the near-wall region. Furthermore, the RNG k-ε model computes the maximum turbulent mixing length dynamically in simulating sediment scour model. Therefore, the RNG k-ε model was adopted to study the scour around anchor under random waves [41,42].
where, kT is specific kinetic energy involved with turbulent velocity, GT is the turbulent energy generated by buoyancy; εT is the turbulent energy dissipating rate, PT is the turbulent energy, Diffε and DiffkT are diffusion terms associated with VF, Ai; CDIS1, CDIS2 and CDIS3 are dimensionless parameters, and CDIS1, CDIS3 have default values of 1.42, 0.2 respectively. CDIS2 can be obtained from PT and kT.
2.3. Sediment Scour Model
The sand particles may suffer four processes under waves, i.e., entrainment, bed load transport, suspended load transport, and deposition, so the sediment scour model should depict the above processes efficiently. In present numerical simulation, the sediment scour model includes the following aspects:
2.3.1. Entrainment and Deposition
The combination of entrainment and deposition determines the net scour rate of seabed in present sediment scour model. The entrainment lift velocity of sand particles was calculated as [43]:
where, αi is the entrainment parameter, ns is the outward point perpendicular to the seabed, d* is the dimensionless diameter of sand particles, which was calculated by Equation (15), θcr is the critical Shields parameter, g is the gravity acceleration, di is the diameter of sand particles, ρi is the density of seabed species.
In Equation (14), the entrainment parameter αi confirms the rate at which sediment erodes when the given shear stress is larger than the critical shear stress, and the recommended value 0.018 was adopted according to the experimental data of Mastbergen and Von den Berg [43]. ns is the outward pointing normal to the seabed interface, and ns = (0,0,1) according to the Cartesian coordinates used in present numerical model.
The shields parameter was obtained from the following equation:
θ=U2f,m(ρi/ρf−1)gd50�=�f,m2(��/�f−1)��50(16)
where, Uf,m is the maximum value of the near-bed friction velocity; d50 is the median diameter of sand particles. The detailed calculation procedure of θ was available in Soulsby [44].
The critical shields parameter θcr was obtained from the Equation (17) [44]
The sand particles begin to deposit on seabed when the turbulence energy weaken and cann’t support the particles suspending. The setting velocity of the particles was calculated from the following equation [44]:
This is called bed load transport when the sand particles roll or bounce over the seabed and always have contact with seabed. The bed load transport velocity was computed by [45]:
where, qb,i is the bed load transport rate, which was obtained from Equation (20), δi is the bed load thickness, which was calculated by Equation (21), cb,i is the volume fraction of sand i in the multiple species, fb is the critical packing fraction of the seabed.
where, Cs,i is the suspended sand particles mass concentration of sand i in the multiple species, us,i is the sand particles velocity of sand i, Df is the diffusivity.
The velocity of sand i in the multiple species could be obtained from the following equation:
where, u¯�¯ is the velocity of mixed fluid-particles, which can be calculated by the RANS equation with turbulence model, cs,i is the suspended sand particles volume concentration, which was computed from Equation (24).
cs,i=Cs,iρi�s,�=�s,���(24)
3. Model Setup
The seabed-USAF-wave three-dimensional scour numerical model was built using Flow-3D software. As shown in Figure 2, the model includes sandy seabed, USAF model, sea water, two baffles and porous media. The dimensions of USAF are shown in Table 1. The sandy bed (210 m in length, 30 m in width and 11 m in height) is made up of uniform fine sand with median diameter d50 = 0.041 cm. The USAF model includes upper steel tube with the length of 20 m, which was installed in the middle of seabed. The location of USAF is positioned at 140 m from the upstream inflow boundary and 70 m from the downstream outflow boundary. Two baffles were installed at two ends of seabed. In order to eliminate the wave reflection basically, the porous media was set at the outflow side on the seabed.
Figure 2. (a) The sketch of seabed-USAF-wave three-dimensional model; (b) boundary condation:Wv-wave boundary, S-symmetric boundary, O-outflow boundary; (c) USAF model.
Table 1. Numerical simulating cases.
3.1. Mesh Geometric Dimensions
In the simulation of the scour under the random waves, the model includes the umbrella suction anchor foundation, seabed and fluid. As shown in Figure 3, the model mesh includes global mesh grid and nested mesh grid, and the total number of grids is 1,812,000. The basic procedure for building mesh grid consists of two steps. Step 1: Divide the global mesh using regular hexahedron with size of 0.6 × 0.6. The global mesh area is cubic box, embracing the seabed and whole fluid volume, and the dimensions are 210 m in length, 30 m in width and 32 m in height. The details of determining the grid size can see the following mesh sensitivity section. Step 2: Set nested fine mesh grid in vicinity of the USAF with size of 0.3 × 0.3 so as to shorten the computation cost and improve the calculation accuracy. The encryption range is −15 m to 15 m in x direction, −15 m to 15 m in y direction and 0 m to 32 m in z direction, respectively. In order to accurately capture the free-surface dynamics, such as the fluid-air interface, the volume of fluid (VOF) method was adopted for tracking the free water surface. One specific algorithm called FAVORTM (Fractional Area/Volume Obstacle Representation) was used to define the fractional face areas and fractional volumes of the cells which are open to fluid flow.
Figure 3. The sketch of mesh grid.
3.2. Boundary Conditions
As shown in Figure 2, the initial fluid length is 210 m as long as seabed. A wave boundary was specified at the upstream offshore end. The details of determining the random wave spectrum can see the following wave parameters section. The outflow boundary was set at the downstream onshore end. The symmetry boundary was used at the top and two sides of the model. The symmetric boundaries were the better strategy to improve the computation efficiency and save the calculation cost [46]. At the seabed bottom, the wall boundary was adopted, which means the u = v = w= 0. Besides, the upper steel tube of USAF was set as no-slip condition.
3.3. Wave Parameters
The random waves with JONSWAP wave spectrum were used for all simulations as realistic representation of offshore conditions. The unidirectional JONSWAP frequency spectrum was described as [47]:
where, α is wave energy scale parameter, which is calculated by Equation (26), ω is frequency, ωp is wave spectrum peak frequency, which can be obtained from Equation (27). γ is wave spectrum peak enhancement factor, in this study γ = 3.3. σ is spectral width factor, σ equals 0.07 for ω ≤ ωp and 0.09 for ω > ωp respectively.
α=0.0076(gXU2)−0.22�=0.0076(���2)−0.22(26)
ωp=22(gU)(gXU2)−0.33�p=22(��)(���2)−0.33(27)
where, X is fetch length, U is average wind velocity at 10 m height from mean sea level.
In present numerical model, the input key parameters include X and U for wave boundary with JONSWAP wave spectrum. The objective wave height and period are available by different combinations of X and U. In this study, we designed 9 cases with different wave heights, periods and water depths for simulating scour around USAF under random waves (see Table 2). For random waves, the wave steepness ε and Ursell number Ur were acquired form Equations (28) and (29) respectively
ε=2πgHsT2a�=2���s�a2(28)
Ur=Hsk2h3w�r=�s�2ℎw3(29)
where, Hs is significant wave height, Ta is average wave period, k is wave number, hw is water depth. The Shield parameter θ satisfies θ>θcr for all simulations in current study, indicating the live bed scour prevails.
Table 2. Numerical simulating cases.
3.4. Mesh Sensitivity
In this section, a mesh sensitivity analysis was conducted to investigate the influence of mesh grid size to results and make sure the calculation is mesh size independent and converged. Three mesh grid size were chosen: Mesh 1—global mesh grid size of 0.75 × 0.75, nested fine mesh grid size of 0.4 × 0.4, and total number of grids 1,724,000, Mesh 2—global mesh grid size of 0.6 × 0.6, nested fine mesh grid size of 0.3 × 0.3, and total number of grids 1,812,000, Mesh 3—global mesh grid size of 0.4 × 0.4, nested fine mesh grid size of 0.2 × 0.2, and total number of grids 1,932,000. The near-bed shear velocity U* is an important factor for influencing scour process [1,15], so U* at the position of (4,0,11.12) was evaluated under three mesh sizes. As the Figure 4 shown, the maximum error of shear velocity ∆U*1,2 is about 39.8% between the mesh 1 and mesh 2, and 4.8% between the mesh 2 and mesh 3. According to the mesh sensitivity criterion adopted by Pang et al. [48], it’s reasonable to think the results are mesh size independent and converged with mesh 2. Additionally, the present model was built according to prototype size, and the mesh size used in present model is larger than the mesh size adopted by Higueira et al. [49] and Corvaro et al. [50]. If we choose the smallest cell size, it will take too much time. For example, the simulation with Mesh3 required about 260 h by using a computer with Intel Xeon Scalable Gold 4214 CPU @24 Cores, 2.2 GHz and 64.00 GB RAM. Therefore, in this case, considering calculation accuracy and computation efficiency, the mesh 2 was chosen for all the simulation in this study.
Figure 4. Comparison of near-bed shear velocity U* with different mesh grid size.
The nested mesh block was adopted for seabed in vicinity of the USAF, which was overlapped with the global mesh block. When two mesh blocks overlap each other, the governing equations are by default solved on the mesh block with smaller average cell size (i.e., higher grid resolution). It is should be noted that the Flow 3D software used the moving mesh captures the scour evolution and automatically adjusts the time step size to be as large as possible without exceeding any of the stability limits, affecting accuracy, or unduly increasing the effort required to enforce the continuity condition [51].
3.5. Model Validation
In order to verify the reliability of the present model, the results of present study were compared with the experimental data of Khosronejad et al. [52]. The experiment was conducted in an open channel with a slender vertical pile under unidirectional currents. The comparison of scour development between the present results and the experimental results is shown in Figure 5. The Figure 5 reveals that the present results agree well with the experimental data of Khosronejad et al. [52]. In the first stage, the scour depth increases rapidly. After that, the scour depth achieves a maximum value gradually. The equilibrium scour depth calculated by the present model is basically corresponding with the experimental results of Khosronejad et al. [52], although scour depth in the present model is slightly larger than the experimental results at initial stage.
Figure 5. Comparison of time evolution of scour between the present study and Khosronejad et al. [52], Petersen et al. [17].
Secondly, another comparison was further conducted between the results of present study and the experimental data of Petersen et al. [17]. The experiment was carried out in a flume with a circular vertical pile in combined waves and current. Figure 4 shows a comparison of time evolution of scour depth between the simulating and the experimental results. As Figure 5 indicates, the scour depth in this study has good overall agreement with the experimental results proposed in Petersen et al. [17]. The equilibrium scour depth calculated by the present model is 0.399 m, which equals to the experimental value basically. Overall, the above verifications prove the present model is accurate and capable in dealing with sediment scour under waves.
In addition, in order to calibrate and validate the present model for hydrodynamic parameters, the comparison of water surface elevation was carried out with laboratory experiments conducted by Stahlmann [53] for wave gauge No. 3. The Figure 6 depicts the surface wave profiles between experiments and numerical model results. The comparison indicates that there is a good agreement between the model results and experimental values, especially the locations of wave crest and trough. Comparison of the surface elevation instructs the present model has an acceptable relative error, and the model is a calibrated in terms of the hydrodynamic parameters.
Figure 6. Comparison of surface elevation between the present study and Stahlmann [53].
Finally, another comparison was conducted for equilibrium scour depth or maximum scour depth under random waves with the experimental data of Sumer and Fredsøe [16] and Schendel et al. [22]. The Figure 7 shows the comparison between the numerical results and experimental data of Run01, Run05, Run21 and Run22 in Sumer and Fredsøe [16] and test A05 and A09 in Schendel et al. [22]. As shown in Figure 7, the equilibrium scour depth or maximum scour depth distributed within the ±30 error lines basically, meaning the reliability and accuracy of present model for predicting equilibrium scour depth around foundation in random waves. However, compared with the experimental values, the present model overestimated the equilibrium scour depth generally. Given that, a calibration for scour depth was carried out by multiplying the mean reduced coefficient 0.85 in following section.
Figure 7. Comparison of equilibrium (or maximum) scour depth between the present study and Sumer and Fredsøe [16], Schendel et al. [22].
Through the various examination for hydrodynamic and morphology parameters, it can be concluded that the present model is a validated and calibrated model for scour under random waves. Thus, the present numerical model would be utilized for scour simulation around foundation under random waves.
4. Numerical Results and Discussions
4.1. Scour Evolution
Figure 8 displays the scour evolution for case 1–9. As shown in Figure 8a, the scour depth increased rapidly at the initial stage, and then slowed down at the transition stage, which attributes to the backfilling occurred in scour holes under live bed scour condition, resulting in the net scour decreasing. Finally, the scour reached the equilibrium state when the amount of sediment backfilling equaled to that of scouring in the scour holes, i.e., the net scour transport rate was nil. Sumer and Fredsøe [16] proposed the following formula for the scour development under waves
St=Seq(1−exp(−t/Tc))�t=�eq(1−exp(−�/�c))(30)
where Tc is time scale of scour process.
Figure 8. Time evolution of scour for case 1–9: (a) Case 1–5; (b) Case 6–9.
The computing time is 3600 s and the scour development curves in Figure 8 kept fluctuating, meaning it’s still not in equilibrium scour stage in these cases. According to Sumer and Fredsøe [16], the equilibrium scour depth can be acquired by fitting the data with Equation (30). From Figure 8, it can be seen that the scour evolution obtained from Equation (30) is consistent with the present study basically at initial stage, but the scour depth predicted by Equation (30) developed slightly faster than the simulating results and the Equation (30) overestimated the scour depth to some extent. Overall, the whole tendency of the results calculated by Equation (30) agrees well with the simulating results of the present study, which means the Equation (30) is applicable to depict the scour evolution around USAF under random waves.
4.2. Scour Mechanism under Random Waves
The scour morphology and scour evolution around USAF are similar under random waves in case 1~9. Taking case 7 as an example, the scour morphology is shown in Figure 9.
Figure 9. Scour morphology under different times for case 7.
From Figure 9, at the initial stage (t < 1200 s), the scour occurred at upstream foundation edges between neighboring anchor branches. The maximum scour depth appeared at the lee-side of the USAF. Correspondingly, the sediments deposited at the periphery of the USAF, and the location of the maximum accretion depth was positioned at an angle of about 45° symmetrically with respect to the wave propagating direction in the lee-side of the USAF. After that, when t > 2400 s, the location of the maximum scour depth shifted to the upside of the USAF at an angle of about 45° with respect to the wave propagating direction.
According to previous studies [1,15,16,19,30,31], the horseshoe vortex, streamline compression and wake vortex shedding were responsible for scour around foundation. The Figure 10 displays the distribution of flow velocity in vicinity of foundation, which reflects the evolving processes of horseshoe vertex.
Figure 10. Velocity profile around USAF: (a) Flow runup and down stream at upstream anchor edges; (b) Horseshoe vortex at upstream anchor edges; (c) Flow reversal during wave through stage at lee side.
As shown in Figure 10, the inflow tripped to the upstream edges of the USAF and it was blocked by the upper tube of USAF. Then, the downflow formed the horizontal axis clockwise vortex and rolled on the seabed bypassing the tube, that is, the horseshoe vortex (Figure 11). The Figure 12 displays the turbulence intensity around the tube on the seabed. From Figure 12, it can be seen that the turbulence intensity was high-intensity with respect to the region of horseshoe vortex. This phenomenon occurred because of drastic water flow momentum exchanging in the horseshoe vortex. As a result, it created the prominent shear stress on the seabed, causing the local scour at the upstream edges of USAF. Besides, the horseshoe vortex moved downstream gradually along the periphery of the tube and the wake vortex shed off continually at the lee-side of the USAF, i.e., wake vortex.
Figure 11. Sketch of scour mechanism around USAF under random waves.
Figure 12. Turbulence intensity: (a) Turbulence intensity of horseshoe vortex; (b) Turbulence intensity of wake vortex; (c) Turbulence intensity of accretion area.
The core of wake vortex is a negative pressure center, liking a vacuum cleaner [11,42]. Hence, the soil particles were swirled into the negative pressure core and carried away by wake vortex. At the same time, the onset of scour at rear side occurred. Finally, the wake vortex became downflow at the downside of USAF. As is shown in Figure 12, the turbulence intensity was low where the downflow occurred at lee-side, which means the turbulence energy may not be able to support the survival of wake vortex, leading to accretion happening. As mentioned in previous section, the formation of horseshoe vortex was dependent with adverse pressure gradient at upside of foundation. As shown in Figure 13, the evaluated range of pressure distribution is −15 m to 15 m in x direction. The t = 450 s and t = 1800 s indicate that the wave crest and trough arrived at the upside and lee-side of the foundation respectively, and the t = 350 s was neither the wave crest nor trough. The adverse gradient pressure reached the maximum value at t = 450 s corresponding to the wave crest phase. In this case, it’s helpful for the wave boundary separating fully from seabed, which leads to the formation of horseshoe vortex with high turbulence intensity. Therefore, the horseshoe vortex is responsible for the local scour between neighboring anchor branches at upside of USAF. What’s more, due to the combination of the horseshoe vortex and streamline compression, the maximum scour depth occurred at the upside of the USAF with an angle of about 45° corresponding to the wave propagating direction. This is consistent with the findings of Pang et al. [48] and Sumer et al. [1,15] in case of regular waves. At the wave trough phase (t = 1800 s), the pressure gradient became positive at upstream USAF edges, which hindered the separating of wave boundary from seabed. In the meantime, the flow reversal occurred (Figure 10) and the adverse gradient pressure appeared at downstream USAF edges, but the magnitude of adverse gradient pressure at lee-side was lower than the upstream gradient pressure under wave crest. In this way, the intensity of horseshoe vortex behind the USAF under wave trough was low, which explains the difference of scour depth at upstream and downstream, i.e., the scour asymmetry. In other words, the scour asymmetry at upside and downside of USAF was attributed to wave asymmetry for random waves, and the phenomenon became more evident for nonlinear waves [21]. Briefly speaking, the vortex system at wave crest phase was mainly related to the scour process around USAF under random waves.
Figure 13. Pressure distribution around USAF.
4.3. Equilibrium Scour Depth
The KC number is a key parameter for horseshoe vortex emerging and evolving under waves. According to Equation (1), when pile diameter D is fixed, the KC depends on the maximum near-bed velocity Uwm and wave period T. For random waves, the Uwm can be denoted by the root-mean-square (RMS) value of near-bed velocity amplitude Uwm,rms or the significant value of near-bed velocity amplitude Uwm,s. The Uwm,rms and Uwm,s for all simulating cases of the present study are listed in Table 3 and Table 4. The T can be denoted by the mean up zero-crossing wave period Ta, peak wave period Tp, significant wave period Ts, the maximum wave period Tm, 1/10′th highest wave period Tn = 1/10 and 1/5′th highest wave period Tn = 1/5 for random waves, so the different combinations of Uwm and T will acquire different KC. The Table 3 and Table 4 list 12 types of KC, for example, the KCrms,s was calculated by Uwm,rms and Ts. Sumer and Fredsøe [16] conducted a series of wave flume experiments to investigate the scour depth around monopile under random waves, and found the equilibrium scour depth predicting equation (Equation (2)) for regular waves was applicable for random waves with KCrms,p. It should be noted that the Equation (2) is only suitable for KC > 6 under regular waves or KCrms,p > 6 under random waves.
Table 3.Uwm,rms and KC for case 1~9.
Table 4.Uwm,s and KC for case 1~9.
Raaijmakers and Rudolph [34] proposed the equilibrium scour depth predicting model (Equation (5)) around pile under waves, which is suitable for low KC. The format of Equation (5) is similar with the formula proposed by Breusers [54], which can predict the equilibrium scour depth around pile at different scour stages. In order to verify the applicability of Raaijmakers’s model for predicting the equilibrium scour depth around USAF under random waves, a validation of the equilibrium scour depth Seq between the present study and Raaijmakers’s equation was conducted. The position where the scour depth Seq was evaluated is the location of the maximum scour depth, and it was depicted in Figure 14. The Figure 15 displays the comparison of Seq with different KC between the present study and Raaijmakers’s model.
Figure 14. Sketch of the position where the Seq was evaluated.
Figure 15. Comparison of the equilibrium scour depth between the present model and the model of Raaijmakers and Rudolph [34]: (a) KCrms,s, KCrms,a; (b) KCrms,p, KCrms,m; (c) KCrms,n = 1/10, KCrms,n = 1/5; (d) KCs,s, KCs,a; (e) KCs,p, KCs,m; (f) KCs,n = 1/10, KCs,n = 1/5.
As shown in Figure 15, there is an error in predicting Seq between the present study and Raaijmakers’s model, and Raaijmakers’s model underestimates the results generally. Although the error exists, the varying trend of Seq with KC obtained from Raaijmakers’s model is consistent with the present study basically. What’s more, the error is minimum and the Raaijmakers’s model is of relatively high accuracy for predicting scour around USAF under random waves by using KCs,p. Based on this, a further revision was made to eliminate the error as much as possible, i.e., add the deviation value ∆S/D in the Raaijmakers’s model. The revised equilibrium scour depth predicting equation based on Raaijmakers’s model can be written as
As the Figure 16 shown, through trial-calculation, when ∆S/D = 0.05, the results calculated by Equation (31) show good agreement with the simulating results of the present study. The maximum error is about 18.2% and the engineering requirements have been met basically. In order to further verify the accuracy of the revised model for large KC (KCs,p > 4) under random waves, a validation between the revised model and the previous experimental results [21]. The experiment was conducted in a flume (50 m in length, 1.0 m in width and 1.3 m in height) with a slender vertical pile (D = 0.1 m) under random waves. The seabed is composed of 0.13 m deep layer of sand with d50 = 0.6 mm and the water depth is 0.5 m for all tests. The significant wave height is 0.12~0.21 m and the KCs,p is 5.52~11.38. The comparison between the predicting results by Equation (31) and the experimental results of Corvaro et al. [21] is shown in Figure 17. From Figure 17, the experimental data evenly distributes around the predicted results and the prediction accuracy is favorable when KCs,p < 8. However, the gap between the predicting results and experimental data becomes large and the Equation (31) overestimates the equilibrium scour depth to some extent when KCs,p > 8.
Figure 16. Comparison of Seq between the simulating results and the predicting values by Equation (31).
Figure 17. Comparison of Seq/D between the Experimental results of Corvaro et al. [21] and the predicting values by Equation (31).
In ocean environment, the waves are composed of a train of sinusoidal waves with different frequencies and amplitudes. The energy of constituent waves with very large and very small frequencies is relatively low, and the energy of waves is mainly concentrated in a certain range of moderate frequencies. Myrhaug and Rue [37] thought the 1/n’th highest wave was responsible for scour and proposed the stochastic model to predict the equilibrium scour depth around pile under random waves for full range of KC. Noteworthy is that the KC was denoted by KCrms,a in the stochastic model. To verify the application of the stochastic model for predicting scour depth around USAF, a validation between the simulating results of present study and predicting results by the stochastic model with n = 2,3,5,10,20,500 was carried out respectively.
As shown in Figure 18, compared with the simulating results, the stochastic model underestimates the equilibrium scour depth around USAF generally. Although the error exists, the varying trend of Seq with KCrms,a obtained from the stochastic model is consistent with the present study basically. What’s more, the gap between the predicting values by stochastic model and the simulating results decreases with the increase of n, but for large n, for example n = 500, the varying trend diverges between the predicting values and simulating results, meaning it’s not feasible only by increasing n in stochastic model to predict the equilibrium scour depth around USAF.
Figure 18. Comparison of Seq between the simulating results and the predicting values by Equation (8).
The Figure 19 lists the deviation value ∆Seq/D′ between the predicting values and simulating results with different KCrms,a and n. Then, fitted the relationship between the ∆S′and n under different KCrms,a, and the fitting curve can be written by Equation (32). The revised stochastic model (Equation (33)) can be acquired by adding ∆Seq/D′ to Equation (8).
The comparison between the predicting results by Equation (33) and the simulating results of present study is shown in Figure 20. According to the Figure 20, the varying trend of Seq with KCrms,a obtained from the stochastic model is consistent with the present study basically. Compared with predicting results by the stochastic model, the results calculated by Equation (33) is favorable. Moreover, comparison with simulating results indicates that the predicting results are the most favorable for n = 10, which is consistent with the findings of Myrhaug and Rue [37] for equilibrium scour depth predicting around slender pile in case of random waves.
Figure 20. Comparison of Seq between the simulating results and the predicting values by Equation (33).
In order to further verify the accuracy of the Equation (33) for large KC (KCrms,a > 4) under random waves, a validation was conducted between the Equation (33) and the previous experimental results of Sumer and Fredsøe [16] and Corvaro et al. [21]. The details of experiments conducted by Corvaro et al. [21] were described in above section. Sumer and Fredsøe [16] investigated the local scour around pile under random waves. The experiments were conducted in a wave basin with a slender vertical pile (D = 0.032, 0.055 m). The seabed is composed of 0.14 m deep layer of sand with d50 = 0.2 mm and the water depth was maintained at 0.5 m. The JONSWAP wave spectrum was used and the KCrms,a was 5.29~16.95. The comparison between the predicting results by Equation (33) and the experimental results of Sumer and Fredsøe [16] and Corvaro et al. [21] are shown in Figure 21. From Figure 21, contrary to the case of low KCrms,a (KCrms,a < 4), the error between the predicting values and experimental results increases with decreasing of n for KCrms,a > 4. Therefore, the predicting results are the most favorable for n = 2 when KCrms,a > 4.
Figure 21. Comparison of Seq between the experimental results of Sumer and Fredsøe [16] and Corvaro et al. [21] and the predicting values by Equation (33).
Noteworthy is that the present model was built according to prototype size, so the errors between the numerical results and experimental data of References [16,21] may be attribute to the scale effects. In laboratory experiments on scouring process, it is typically impossible to ensure a rigorous similarity of all physical parameters between the model and prototype structure, leading to the scale effects in the laboratory experiments. To avoid a cohesive behaviour, the bed material was not scaled geometrically according to model scale. As a consequence, the relatively large-scaled sediments sizes may result in the overestimation of bed load transport and underestimation of suspended load transport compared with field conditions. What’s more, the disproportional scaled sediment presumably lead to the difference of bed roughness between the model and prototype, and thus large influences for wave boundary layer on the seabed and scour process. Besides, according to Corvaro et al. [21] and Schendel et al. [55], the pile Reynolds numbers and Froude numbers both affect the scour depth for the condition of non fully developed turbulent flow in laboratory experiments.
4.4. Parametric Study
4.4.1. Influence of Froude Number
As described above, the set of foundation leads to the adverse pressure gradient appearing at upstream, leading to the wave boundary layer separating from seabed, then horseshoe vortex formatting and the horseshoe vortex are mainly responsible for scour around foundation (see Figure 22). The Froude number Fr is the key parameter to influence the scale and intensity of horseshoe vortex. The Fr under waves can be calculated by the following formula [42]
Fr=UwgD−−−√�r=�w��(34)
where Uw is the mean water particle velocity during 1/4 cycle of wave oscillation, obtained from the following formula. Noteworthy is that the root-mean-square (RMS) value of near-bed velocity amplitude Uwm,rms is used for calculating Uwm.
Figure 22. Sketch of flow field at upstream USAF edges.
Tavouktsoglou et al. [25] proposed the following formula between Fr and the vertical location of the stagnation y
yh∝Fer�ℎ∝�r�(36)
where e is constant.
The Figure 23 displays the relationship between Seq/D and Fr of the present study. In order to compare with the simulating results, the experimental data of Corvaro et al. [21] was also depicted in Figure 23. As shown in Figure 23, the equilibrium scour depth appears a logarithmic increase as Fr increases and approaches the mathematical asymptotic value, which is also consistent with the experimental results of Corvaro et al. [21]. According to Figure 24, the adverse pressure gradient pressure at upstream USAF edges increases with the increase of Fr, which is benefit for the wave boundary layer separating from seabed, resulting in the high-intensity horseshoe vortex, hence, causing intensive scour around USAF. Based on the previous study of Tavouktsoglou et al. [25] for scour around pile under currents, the high Fr leads to the stagnation point is closer to the mean sea level for shallow water, causing the stronger downflow kinetic energy. As mentioned in previous section, the energy of downflow at upstream makes up the energy of the subsequent horseshoe vortex, so the stronger downflow kinetic energy results in the more intensive horseshoe vortex. Therefore, the higher Fr leads to the more intensive horseshoe vortex by influencing the position of stagnation point y presumably. Qi and Gao [19] carried out a series of flume tests to investigate the scour around pile under regular waves, and proposed the fitting formula between Seq/D and Fr as following
lg(Seq/D)=Aexp(B/Fr)+Clg(�eq/�)=�exp(�/�r)+�(37)
where A, B and C are constant.
Figure 23. The fitting curve between Seq/D and Fr.
Figure 24. Sketch of adverse pressure gradient at upstream USAF edges.
Took the Equation (37) to fit the simulating results with A = −0.002, B = 0.686 and C = −0.808, and the results are shown in Figure 23. From Figure 23, the simulating results evenly distribute around the Equation (37) and the varying trend of Seq/D and Fr in present study is consistent with Equation (37) basically, meaning the Equation (37) is applicable to express the relationship of Seq/D with Fr around USAF under random waves.
4.4.2. Influence of Euler Number
The Euler number Eu is the influencing factor for the hydrodynamic field around foundation. The Eu under waves can be calculated by the following formula. The Eu can be represented by the Equation (38) for uniform cylinders [25]. The root-mean-square (RMS) value of near-bed velocity amplitude Um,rms is used for calculating Um.
Eu=U2mgD�u=�m2��(38)
where Um is depth-averaged flow velocity.
The Figure 25 displays the relationship between Seq/D and Eu of the present study. In order to compare with the simulating results, the experimental data of Sumer and Fredsøe [16] and Corvaro et al. [21] were also plotted in Figure 25. As shown in Figure 25, similar with the varying trend of Seq/D and Fr, the equilibrium scour depth appears a logarithmic increase as Eu increases and approaches the mathematical asymptotic value, which is also consistent with the experimental results of Sumer and Fredsøe [16] and Corvaro et al. [21]. According to Figure 24, the adverse pressure gradient pressure at upstream USAF edges increases with the increasing of Eu, which is benefit for the wave boundary layer separating from seabed, inducing the high-intensity horseshoe vortex, hence, causing intensive scour around USAF.
Figure 25. The fitting curve between Seq/D and Eu.
Therefore, the variation of Fr and Eu reflect the magnitude of adverse pressure gradient pressure at upstream. Given that, the Equation (37) also was used to fit the simulating results with A = 8.875, B = 0.078 and C = −9.601, and the results are shown in Figure 25. From Figure 25, the simulating results evenly distribute around the Equation (37) and the varying trend of Seq/D and Eu in present study is consistent with Equation (37) basically, meaning the Equation (37) is also applicable to express the relationship of Seq/D with Eu around USAF under random waves. Additionally, according to the above description of Fr, it can be inferred that the higher Fr and Eu both lead to the more intensive horseshoe vortex by influencing the position of stagnation point y presumably.
5. Conclusions
A series of numerical models were established to investigate the local scour around umbrella suction anchor foundation (USAF) under random waves. The numerical model was validated for hydrodynamic and morphology parameters by comparing with the experimental data of Khosronejad et al. [52], Petersen et al. [17], Sumer and Fredsøe [16] and Schendel et al. [22]. Based on the simulating results, the scour evolution and scour mechanisms around USAF under random waves were analyzed respectively. Two revised models were proposed according to the model of Raaijmakers and Rudolph [34] and the stochastic model developed by Myrhaug and Rue [37] to predict the equilibrium scour depth around USAF under random waves. Finally, a parametric study was carried out with the present model to study the effects of the Froude number Fr and Euler number Eu to the equilibrium scour depth around USAF under random waves. The main conclusions can be described as follows.(1)
The packed sediment scour model and the RNG k−ε turbulence model were used to simulate the sand particles transport processes and the flow field around UASF respectively. The scour evolution obtained by the present model agrees well with the experimental results of Khosronejad et al. [52], Petersen et al. [17], Sumer and Fredsøe [16] and Schendel et al. [22], which indicates that the present model is accurate and reasonable for depicting the scour morphology around UASF under random waves.(2)
The vortex system at wave crest phase is mainly related to the scour process around USAF under random waves. The maximum scour depth appeared at the lee-side of the USAF at the initial stage (t < 1200 s). Subsequently, when t > 2400 s, the location of the maximum scour depth shifted to the upside of the USAF at an angle of about 45° with respect to the wave propagating direction.(3)
The error is negligible and the Raaijmakers’s model is of relatively high accuracy for predicting scour around USAF under random waves when KC is calculated by KCs,p. Given that, a further revision model (Equation (31)) was proposed according to Raaijmakers’s model to predict the equilibrium scour depth around USAF under random waves and it shows good agreement with the simulating results of the present study when KCs,p < 8.(4)
Another further revision model (Equation (33)) was proposed according to the stochastic model established by Myrhaug and Rue [37] to predict the equilibrium scour depth around USAF under random waves, and the predicting results are the most favorable for n = 10 when KCrms,a < 4. However, contrary to the case of low KCrms,a, the predicting results are the most favorable for n = 2 when KCrms,a > 4 by the comparison with experimental results of Sumer and Fredsøe [16] and Corvaro et al. [21].(5)
The same formula (Equation (37)) is applicable to express the relationship of Seq/D with Eu or Fr, and it can be inferred that the higher Fr and Eu both lead to the more intensive horseshoe vortex and larger Seq.
Author Contributions
Conceptualization, H.L. (Hongjun Liu); Data curation, R.H. and P.Y.; Formal analysis, X.W. and H.L. (Hao Leng); Funding acquisition, X.W.; Writing—original draft, R.H. and P.Y.; Writing—review & editing, X.W. and H.L. (Hao Leng); The final manuscript has been approved by all the authors. All authors have read and agreed to the published version of the manuscript.
Funding
This research was funded by the Fundamental Research Funds for the Central Universities (grant number 202061027) and the National Natural Science Foundation of China (grant number 41572247).
Institutional Review Board Statement
Not applicable.
Informed Consent Statement
Not applicable.
Data Availability Statement
The data presented in this study are available on request from the corresponding author.
Conflicts of Interest
The authors declare no conflict of interest.
References
Sumer, B.M.; Fredsøe, J.; Christiansen, N. Scour Around Vertical Pile in Waves. J. Waterw. Port. Coast. Ocean Eng.1992, 118, 15–31. [Google Scholar] [CrossRef]
Rudolph, D.; Bos, K. Scour around a monopile under combined wave-current conditions and low KC-numbers. In Proceedings of the 6th International Conference on Scour and Erosion, Amsterdam, The Netherlands, 1–3 November 2006; pp. 582–588. [Google Scholar]
Nielsen, A.W.; Liu, X.; Sumer, B.M.; Fredsøe, J. Flow and bed shear stresses in scour protections around a pile in a current. Coast. Eng.2013, 72, 20–38. [Google Scholar] [CrossRef]
Ahmad, N.; Bihs, H.; Myrhaug, D.; Kamath, A.; Arntsen, Ø.A. Three-dimensional numerical modelling of wave-induced scour around piles in a side-by-side arrangement. Coast. Eng.2018, 138, 132–151. [Google Scholar] [CrossRef]
Li, H.; Ong, M.C.; Leira, B.J.; Myrhaug, D. Effects of Soil Profile Variation and Scour on Structural Response of an Offshore Monopile Wind Turbine. J. Offshore Mech. Arct. Eng.2018, 140, 042001. [Google Scholar] [CrossRef]
Li, H.; Liu, H.; Liu, S. Dynamic analysis of umbrella suction anchor foundation embedded in seabed for offshore wind turbines. Géoméch. Energy Environ.2017, 10, 12–20. [Google Scholar] [CrossRef]
Fazeres-Ferradosa, T.; Rosa-Santos, P.; Taveira-Pinto, F.; Vanem, E.; Carvalho, H.; Correia, J.A.F.D.O. Editorial: Advanced research on offshore structures and foundation design: Part 1. Proc. Inst. Civ. Eng. Marit. Eng.2019, 172, 118–123. [Google Scholar] [CrossRef]
Chavez, C.E.A.; Stratigaki, V.; Wu, M.; Troch, P.; Schendel, A.; Welzel, M.; Villanueva, R.; Schlurmann, T.; De Vos, L.; Kisacik, D.; et al. Large-Scale Experiments to Improve Monopile Scour Protection Design Adapted to Climate Change—The PROTEUS Project. Energies2019, 12, 1709. [Google Scholar] [CrossRef][Green Version]
Wu, M.; De Vos, L.; Chavez, C.E.A.; Stratigaki, V.; Fazeres-Ferradosa, T.; Rosa-Santos, P.; Taveira-Pinto, F.; Troch, P. Large Scale Experimental Study of the Scour Protection Damage Around a Monopile Foundation Under Combined Wave and Current Conditions. J. Mar. Sci. Eng.2020, 8, 417. [Google Scholar] [CrossRef]
Sørensen, S.P.H.; Ibsen, L.B. Assessment of foundation design for offshore monopiles unprotected against scour. Ocean Eng.2013, 63, 17–25. [Google Scholar] [CrossRef]
Prendergast, L.; Gavin, K.; Doherty, P. An investigation into the effect of scour on the natural frequency of an offshore wind turbine. Ocean Eng.2015, 101, 1–11. [Google Scholar] [CrossRef][Green Version]
Fazeres-Ferradosa, T.; Chambel, J.; Taveira-Pinto, F.; Rosa-Santos, P.; Taveira-Pinto, F.; Giannini, G.; Haerens, P. Scour Protections for Offshore Foundations of Marine Energy Harvesting Technologies: A Review. J. Mar. Sci. Eng.2021, 9, 297. [Google Scholar] [CrossRef]
Yang, Q.; Yu, P.; Liu, Y.; Liu, H.; Zhang, P.; Wang, Q. Scour characteristics of an offshore umbrella suction anchor foundation under the combined actions of waves and currents. Ocean Eng.2020, 202, 106701. [Google Scholar] [CrossRef]
Yu, P.; Hu, R.; Yang, J.; Liu, H. Numerical investigation of local scour around USAF with different hydraulic conditions under currents and waves. Ocean Eng.2020, 213, 107696. [Google Scholar] [CrossRef]
Sumer, B.M.; Christiansen, N.; Fredsøe, J. The horseshoe vortex and vortex shedding around a vertical wall-mounted cylinder exposed to waves. J. Fluid Mech.1997, 332, 41–70. [Google Scholar] [CrossRef]
Sumer, B.M.; Fredsøe, J. Scour around Pile in Combined Waves and Current. J. Hydraul. Eng.2001, 127, 403–411. [Google Scholar] [CrossRef]
Petersen, T.U.; Sumer, B.M.; Fredsøe, J. Time scale of scour around a pile in combined waves and current. In Proceedings of the 6th International Conference on Scour and Erosion, Paris, France, 27–31 August 2012. [Google Scholar]
Petersen, T.U.; Sumer, B.M.; Fredsøe, J.; Raaijmakers, T.C.; Schouten, J.-J. Edge scour at scour protections around piles in the marine environment—Laboratory and field investigation. Coast. Eng.2015, 106, 42–72. [Google Scholar] [CrossRef]
Qi, W.; Gao, F. Equilibrium scour depth at offshore monopile foundation in combined waves and current. Sci. China Ser. E Technol. Sci.2014, 57, 1030–1039. [Google Scholar] [CrossRef][Green Version]
Corvaro, S.; Marini, F.; Mancinelli, A.; Lorenzoni, C.; Brocchini, M. Hydro- and Morpho-dynamics Induced by a Vertical Slender Pile under Regular and Random Waves. J. Waterw. Port. Coast. Ocean Eng.2018, 144, 04018018. [Google Scholar] [CrossRef]
Schendel, A.; Welzel, M.; Schlurmann, T.; Hsu, T.-W. Scour around a monopile induced by directionally spread irregular waves in combination with oblique currents. Coast. Eng.2020, 161, 103751. [Google Scholar] [CrossRef]
Fazeres-Ferradosa, T.; Taveira-Pinto, F.; Romão, X.; Reis, M.; das Neves, L. Reliability assessment of offshore dynamic scour protections using copulas. Wind. Eng.2018, 43, 506–538. [Google Scholar] [CrossRef]
Fazeres-Ferradosa, T.; Welzel, M.; Schendel, A.; Baelus, L.; Santos, P.R.; Pinto, F.T. Extended characterization of damage in rubble mound scour protections. Coast. Eng.2020, 158, 103671. [Google Scholar] [CrossRef]
Ettema, R.; Melville, B.; Barkdoll, B. Scale Effect in Pier-Scour Experiments. J. Hydraul. Eng.1998, 124, 639–642. [Google Scholar] [CrossRef]
Umeda, S. Scour Regime and Scour Depth around a Pile in Waves. J. Coast. Res. Spec. Issue2011, 64, 845–849. [Google Scholar]
Umeda, S. Scour process around monopiles during various phases of sea storms. J. Coast. Res.2013, 165, 1599–1604. [Google Scholar] [CrossRef]
Baykal, C.; Sumer, B.; Fuhrman, D.R.; Jacobsen, N.; Fredsøe, J. Numerical simulation of scour and backfilling processes around a circular pile in waves. Coast. Eng.2017, 122, 87–107. [Google Scholar] [CrossRef][Green Version]
Miles, J.; Martin, T.; Goddard, L. Current and wave effects around windfarm monopile foundations. Coast. Eng.2017, 121, 167–178. [Google Scholar] [CrossRef][Green Version]
Miozzi, M.; Corvaro, S.; Pereira, F.A.; Brocchini, M. Wave-induced morphodynamics and sediment transport around a slender vertical cylinder. Adv. Water Resour.2019, 129, 263–280. [Google Scholar] [CrossRef]
Yu, T.; Zhang, Y.; Zhang, S.; Shi, Z.; Chen, X.; Xu, Y.; Tang, Y. Experimental study on scour around a composite bucket foundation due to waves and current. Ocean Eng.2019, 189, 106302. [Google Scholar] [CrossRef]
Carreiras, J.; Larroudé, P.; Seabra-Santos, F.; Mory, M. Wave Scour Around Piles. In Proceedings of the Coastal Engineering 2000, American Society of Civil Engineers (ASCE), Sydney, Australia, 16–21 July 2000; pp. 1860–1870. [Google Scholar]
Raaijmakers, T.; Rudolph, D. Time-dependent scour development under combined current and waves conditions—Laboratory experiments with online monitoring technique. In Proceedings of the 4th International Conference on Scour and Erosion, Tokyo, Japan, 5–7 November 2008; pp. 152–161. [Google Scholar]
Khalfin, I.S. Modeling and calculation of bed score around large-diameter vertical cylinder under wave action. Water Resour.2007, 34, 357. [Google Scholar] [CrossRef][Green Version]
Zanke, U.C.; Hsu, T.-W.; Roland, A.; Link, O.; Diab, R. Equilibrium scour depths around piles in noncohesive sediments under currents and waves. Coast. Eng.2011, 58, 986–991. [Google Scholar] [CrossRef]
Myrhaug, D.; Rue, H. Scour below pipelines and around vertical piles in random waves. Coast. Eng.2003, 48, 227–242. [Google Scholar] [CrossRef]
Myrhaug, D.; Ong, M.C.; Føien, H.; Gjengedal, C.; Leira, B.J. Scour below pipelines and around vertical piles due to second-order random waves plus a current. Ocean Eng.2009, 36, 605–616. [Google Scholar] [CrossRef]
Myrhaug, D.; Ong, M.C. Random wave-induced onshore scour characteristics around submerged breakwaters using a stochastic method. Ocean Eng.2010, 37, 1233–1238. [Google Scholar] [CrossRef]
Ong, M.C.; Myrhaug, D.; Hesten, P. Scour around vertical piles due to long-crested and short-crested nonlinear random waves plus a current. Coast. Eng.2013, 73, 106–114. [Google Scholar] [CrossRef]
Yakhot, V.; Orszag, S.A. Renormalization group analysis of turbulence. I. Basic theory. J. Sci. Comput.1986, 1, 3–51. [Google Scholar] [CrossRef]
Yakhot, V.; Smith, L.M. The renormalization group, the e-expansion and derivation of turbulence models. J. Sci. Comput.1992, 7, 35–61. [Google Scholar] [CrossRef]
Mastbergen, D.R.; Berg, J.V.D. Breaching in fine sands and the generation of sustained turbidity currents in submarine canyons. Sedimentology2003, 50, 625–637. [Google Scholar] [CrossRef]
Soulsby, R. Dynamics of Marine Sands; Thomas Telford Ltd.: London, UK, 1998. [Google Scholar] [CrossRef]
Van Rijn, L.C. Sediment Transport, Part I: Bed Load Transport. J. Hydraul. Eng.1984, 110, 1431–1456. [Google Scholar] [CrossRef][Green Version]
Zhang, Q.; Zhou, X.-L.; Wang, J.-H. Numerical investigation of local scour around three adjacent piles with different arrangements under current. Ocean Eng.2017, 142, 625–638. [Google Scholar] [CrossRef]
Yu, Y.X.; Liu, S.X. Random Wave and Its Applications to Engineering, 4th ed.; Dalian University of Technology Press: Dalian, China, 2011. [Google Scholar]
Pang, A.; Skote, M.; Lim, S.; Gullman-Strand, J.; Morgan, N. A numerical approach for determining equilibrium scour depth around a mono-pile due to steady currents. Appl. Ocean Res.2016, 57, 114–124. [Google Scholar] [CrossRef]
Higuera, P.; Lara, J.L.; Losada, I.J. Three-dimensional interaction of waves and porous coastal structures using Open-FOAM®. Part I: Formulation and validation. Coast. Eng.2014, 83, 243–258. [Google Scholar] [CrossRef]
Corvaro, S.; Crivellini, A.; Marini, F.; Cimarelli, A.; Capitanelli, L.; Mancinelli, A. Experimental and Numerical Analysis of the Hydrodynamics around a Vertical Cylinder in Waves. J. Mar. Sci. Eng.2019, 7, 453. [Google Scholar] [CrossRef][Green Version]
Flow3D User Manual, version 11.0.3; Flow Science, Inc.: Santa Fe, NM, USA, 2013.
Khosronejad, A.; Kang, S.; Sotiropoulos, F. Experimental and computational investigation of local scour around bridge piers. Adv. Water Resour.2012, 37, 73–85. [Google Scholar] [CrossRef]
Stahlmann, A. Experimental and Numerical Modeling of Scour at Foundation Structures for Offshore Wind Turbines. Ph.D. Thesis, Franzius-Institute for Hydraulic, Estuarine and Coastal Engineering, Leibniz Universität Hannover, Hannover, Germany, 2013. [Google Scholar]
Breusers, H.N.C.; Nicollet, G.; Shen, H. Local Scour Around Cylindrical Piers. J. Hydraul. Res.1977, 15, 211–252. [Google Scholar] [CrossRef]
Schendel, A.; Hildebrandt, A.; Goseberg, N.; Schlurmann, T. Processes and evolution of scour around a monopile induced by tidal currents. Coast. Eng.2018, 139, 65–84. [Google Scholar] [CrossRef]
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Hu, R.; Liu, H.; Leng, H.; Yu, P.; Wang, X. Scour Characteristics and Equilibrium Scour Depth Prediction around Umbrella Suction Anchor Foundation under Random Waves. J. Mar. Sci. Eng.2021, 9, 886. https://doi.org/10.3390/jmse9080886
AMA Style
Hu R, Liu H, Leng H, Yu P, Wang X. Scour Characteristics and Equilibrium Scour Depth Prediction around Umbrella Suction Anchor Foundation under Random Waves. Journal of Marine Science and Engineering. 2021; 9(8):886. https://doi.org/10.3390/jmse9080886Chicago/Turabian Style
Hu, Ruigeng, Hongjun Liu, Hao Leng, Peng Yu, and Xiuhai Wang. 2021. “Scour Characteristics and Equilibrium Scour Depth Prediction around Umbrella Suction Anchor Foundation under Random Waves” Journal of Marine Science and Engineering 9, no. 8: 886. https://doi.org/10.3390/jmse9080886
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![Figure 5 – Instantaneous pressures [Pa] and velocities [m/s] at model scale (bay center)](https://flow3d.co.kr/wp-content/uploads/s-at-model-scale-bay-center.png)
