Dac DungTruongabBeom-SeonJangaCarl-ErikJansoncJonas W.RingsbergcYasuhiraYamadadKotaTakamotofYasumiKawamuraeHan-BaekJua aResearch Institute of Marine Systems Engineering, Department of Naval Architecture and Ocean Engineering, Seoul National University, Seoul, South Korea bDepartment of Engineering Mechanics, Nha Trang University, Nha Trang, Viet Nam cDivision of Marine Technology, Department of Mechanics and Maritime Sciences, Chalmers University of Technology, Gothenburg, Sweden dNational Maritime Research Institute, National Institute of Maritime, Port and Aviation Technology, Tokyo, Japan eDepartment of Systems Design for Ocean-Space, Yokohama National University, Kanagawa, Japan fDepartment of Mechanical Systems Engineering, Tokyo University of Agriculture and Technology, Tokyo, Japan
이 논문은 해양구조물의 평보강판의 슬래밍 반응에 대한 벤치마크 연구를 제시합니다. 목표는 유체-구조 상호작용(FSI) 시뮬레이션 방법론, 모델링 기술 및 슬래밍 압력 예측에 대한 기존 연구원의 경험을 비교하는 것이었습니다.
수치 FSI 시뮬레이션을 위해 가장 일반적인 상용 소프트웨어 패키지를 사용하는 3개의 연구 그룹(예: LS-Dyna ALE, LS-Dyna ICFD, ANSYS CFX 및 Star-CCM+/ABAQUS)이 이 연구에 참여했습니다.
공개 문헌에서 입수할 수 있는 경량 선박과 같은 바닥 구조의 평평한 강화 알루미늄 판에 대한 습식 낙하 시험 데이터는 FSI 모델링의 검증에 활용되었습니다. 형상 모델 및 재료 속성을 포함한 실험 조건의 요약은 시뮬레이션 전에 참가자에게 배포되었습니다.
충돌 속도와 강판의 강성이 슬래밍 응답에 미치는 영향을 조사하기 위해 해양 설비에 사용되는 실제 치수를 갖는 평판 보강 강판에 대한 매개변수 연구를 수행했습니다. 보강판에 작용하는 전체 수직력에 대한 FE 시뮬레이션 결과와 이러한 힘에 대한 구조적 반응을 참가자로부터 획득하여 분석 및 비교하였다.
앞서 언급한 상용 FSI 소프트웨어 패키지를 사용하여 슬래밍 부하에 대한 신뢰할 수 있고 정확한 예측을 평가했습니다. 또한 FSI 시뮬레이션에서 관찰된 동일한 영구 처짐을 초래하는 등가 정적 슬래밍 압력을 보고하고 분류 표준 DNV에서 제안한 해석 모델 및 슬래밍 압력 계산을 위한 기존 실험 데이터와 비교했습니다.
연구 결과는 등가 하중 모델이 물 충돌 속도와 플레이트 강성에 의존한다는 것을 보여주었습니다. 즉, 등가정압계수는 충돌속도가 증가함에 따라 감소하고 충돌구조가 더 단단해지면 증가한다.
This paper presents a benchmark study on the slamming responses of offshore structures’ flat-stiffened plates. The objective was to compare the fluid-structure interaction (FSI) simulation methodologies, modeling techniques, and established researchers’ experiences in predicting slamming pressure. Three research groups employing the most common commercial software packages for numerical FSI simulations (i.e. LS-Dyna ALE, LS-Dyna ICFD, ANSYS CFX, and Star-CCM+/ABAQUS) participated in this study. Wet drop test data on flat-stiffened aluminum plates of light-ship-like bottom structures available in the open literature was utilized for validation of the FSI modeling. A summary of the experimental conditions including the geometry model and material properties, was distributed to the participants prior to their simulations. A parametric study on flat-stiffened steel plates having actual scantlings used in marine installations was performed to investigate the effect of impact velocity and plate rigidity on slamming response. The FE simulation results for the total vertical forces acting on the stiffened plates and their structural responses to those forces, as obtained from the participants, were analyzed and compared. The reliable and accurate predictions of slamming loads using the aforementioned commercial FSI software packages were evaluated. Additionally, equivalent static slamming pressures resulting in the same permanent deflections, as observed from the FSI simulations, were reported and compared with analytical models proposed by the Classification Standards DNV and existing experimental data for calculation of the slamming pressure. The study results showed that the equivalent load model depends on the water impact velocity and plate rigidity; that is, the equivalent static pressure coefficient decreases with an increase in impact velocity, and increases when impacting structures become stiffer.
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졸업 논문의 목표는 보스코비체 댐의 계획된 방수로의 흐름을 수치적으로 모델링하는 것입니다. 이 졸업 논문은 유형과 프로필에 따라 기본 여수로를 설명하고 나눕니다. 비상용 배수로도 언급되어 있습니다. 그런 다음 논문에서는 범람량 계산에 대한 설명, 수학적 모델링 및 사용된 난류 모델에 대한 설명을 소개합니다. 다음 부분은 Boskovice 댐의 기술적 설명, AutoCAD 2020 소프트웨어에서 방수로 및 방수로 슈트의 가상 3D 모델 생성 및 Blender 소프트웨어에서 모델의 제어 및 수정과 관련되어 있습니다. 논문 말미에는 Flow-3D 소프트웨어를 통해 얻은 유동의 수치적 모델링 결과와 BUT 토목공학부 수구조연구소에서 시행한 수리학적 모델 연구와 비교한 결과를 언급하였다.
The goal of the diploma thesis is the numerical modelling of flow in planned spillway of the Boskovice dam. In the introduction of this diploma thesis are described and divided basic spillways according to their types and profiles. There are also mentioned emergency spillways. Then the thesis introduces the description of calculation of overflow quantity, the description of mathematic modelling and used turbulent models. The next part is concerned with the technical description of the Boskovice dam, the creation of virtual 3D model of spillway and spillway chute in the AutoCAD 2020 software and concerned with the control and revision of model in the Blender software. In the end of the thesis are mentioned results of numeric modelling of flow gained from the Flow-3D software and the comparison of results with the research of hydraulic model implemented at Water structures institute of Faculty of Civil Engineering of BUT.
Numerické modelování proudění v bezpečnostním přelivu: Numerical modeling of flow in spilway
The goal of the diploma thesis is the numerical modelling of flow in planned spillway of the Boskovice dam. In the introduction of this diploma thesis are described and divided basic spillways according to their types and profiles. There are also mentioned emergency spillways. Then the thesis introduces the description of calculation of overflow quantity, the description of mathematic modelling and used turbulent models. The next part is concerned with the technical description of the Boskovice dam, the creation of virtual 3D model of spillway and spillway chute in the AutoCAD 2020 software and concerned with the control and revision of model in the Blender software. In the end of the thesis are mentioned results of numeric modelling of flow gained from the Flow-3D software and the comparison of results with the research of hydraulic model implemented at Water structures institute of Faculty of Civil Engineering of BUT.
Bezpečnostní přeliv; numerický model; 3D model; FLOW-3D; VD Boskovice; sypaná kamenitá hráz.; Spillway; numerical model; 3D model; FLOW-3D; Boskovice dam; rockfill dam.
Jandora, Jan (advisor); Holomek, Petr (referee)
Standardní licenční smlouva – přístup k plnému textu bez omezení
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Investigating the breach outflow hydrograph is an essential task to conduct mitigation plans and flood warnings. In the present study, the spatial dam breach is simulated by using a three-dimensional computational fluid dynamics model, FLOW-3D. The model parameters were adjusted by making a comparison with a previous experimental model. The different parameters (initial breach shape, dimensions, location, and dam slopes) are studied to investigate their effects on dam breaching. The results indicate that these parameters have a significant impact. The maximum erosion rate and peak outflow for the rectangular shape are higher than those for the V-notch by 8.85% and 5%, respectively. Increasing breach width or decreasing depth by 5% leads to increasing maximum erosion rate by 11% and 15%, respectively. Increasing the downstream slope angle by 4° leads to an increase in both peak outflow and maximum erosion rate by 2.0% and 6.0%, respectively.
유출 유출 수문곡선을 조사하는 것은 완화 계획 및 홍수 경보를 수행하는 데 필수적인 작업입니다. 본 연구에서는 3차원 전산유체역학 모델인 FLOW-3D를 사용하여 공간 댐 붕괴를 시뮬레이션합니다. 이전 실험 모델과 비교하여 모델 매개변수를 조정했습니다.
다양한 매개변수(초기 붕괴 형태, 치수, 위치 및 댐 경사)가 댐 붕괴에 미치는 영향을 조사하기 위해 연구됩니다. 결과는 이러한 매개변수가 상당한 영향을 미친다는 것을 나타냅니다. 직사각형 형태의 최대 침식율과 최대 유출량은 V-notch보다 각각 8.85%, 5% 높게 나타났습니다.
위반 폭을 늘리거나 깊이를 5% 줄이면 최대 침식률이 각각 11% 및 15% 증가합니다. 하류 경사각을 4° 증가시키면 최대 유출량과 최대 침식률이 각각 2.0% 및 6.0% 증가합니다.
Spatial dam breach; FLOW-3D; Overtopping erosion; Computational fluid dynamics (CFD)
There are many purposes for dam construction, such as protection from flood disasters, water storage, and power generation. Embankment failures may have a catastrophic impact on lives and infrastructure in the downstream regions. One of the most common causes of embankment dam failure is overtopping. Once the overtopping of the dam begins, the breach formation will start in the dam body then end with the dam failure. This failure occurs within a very short time, which threatens to be very dangerous. Therefore, understanding and modeling the embankment breaching processes is essential for conducting mitigation plans, flood warnings, and forecasting flood damage.
The analysis of the dam breaching process is implemented by different techniques: comparative methods, empirical models with dimensional and dimensionless solutions, physical-based models, and parametric models. These models were described in detail . Parametric modeling is commonly used to simulate breach growth as a time-dependent linear process and calculate outflow discharge from the breach using hydraulics principles . Alhasan et al.  presented a simple one-dimensional mathematical model and a computer code to simulate the dam breaching process. These models were validated by small dams breaching during the floods in 2002 in the Czech Republic. Fread  developed an erosion model (BREACH) based on hydraulics principles, sediment transport, and soil mechanics to estimate breach size, time of formation, and outflow discharge. Říha et al.  investigated the dam break process for a cascade of small dams using a simple parametric model for piping and overtopping erosion, as well as a 2D shallow-water flow model for the flood in downstream areas. Goodarzi et al.  implemented mathematical and statistical methods to assess the effect of inflows and wind speeds on the dam’s overtopping failure.
Dam breaching studies can be divided into two main modes of erosion. The first mode is called “planar dam breach” where the flow overtops the whole dam width. While the second mode is called “spatial dam breach” where the flow overtops through the initial pilot channel (i.e., a channel created in the dam body). Therefore, the erosion will be in both vertical and horizontal directions .
The erosion process through the embankment dams occurs due to the shear stress applied by water flows. The dam breaching evolution can be divided into three stages , , but Y. Yang et al.  divided the breach development into five stages: Stage I, the seepage erosion; Stage II, the initial breach formation; Stage III, the head erosion; Stage IV, the breach expansion; and Stage V, the re-equilibrium of the river channel through the breach. Many experimental tests have been carried out on non-cohesive embankment dams with an initial breach to examine the effect of upstream inflow discharges on the longitudinal profile evolution and the time to inflection point.
Zhang et al.  studied the effect of changing downstream slope angle, sediment grain size, and dam crest length on erosion rates. They noticed that increasing dam crest length and decreasing downstream slope angle lead to decreasing sediment transport rate. While the increase in sediment grain size leads to an increased sediment transport rate at the initial stages. Höeg et al.  presented a series of field tests to investigate the stability of embankment dams made of various materials. Overtopping and piping were among the failure tests carried out for the dams composed of homogeneous rock-fill, clay, or gravel with a height of up to 6.0 m. Hakimzadeh et al.  constructed 40 homogeneous cohesive and non-cohesive embankment dams to study the effect of changing sediment diameter and dam height on the breaching process. They also used genetic programming (GP) to estimate the breach outflow. Refaiy et al.  studied different scenarios for the downstream drain geometry, such as length, height, and angle, to minimize the effect of piping phenomena and therefore increase dam safety.
Zhu et al.  examined the effect of headcut erosion on dam breach growth, especially in the case of cohesive dams. They found that the breach growth in non-cohesive embankments is slower than cohesive embankments due to the little effect of headcut. Schmocker and Hager  proposed a relationship for estimating peak outflow from the dam breach process.(1)QpQin-1=1.7exp-20hc23d5013H0
where: Qp = peak outflow discharge.
Qin = inflow discharge.
hc = critical flow depth.
d50 = mean sediment diameter.
Ho = initial dam height.
Yu et al.  carried out an experimental study for homogeneous non-cohesive embankment dams in a 180° bending rectangular flume to determine the effect of overtopping flows on breaching formation. They found that the main factors influencing breach formation are water level, river discharge, and embankment material diameter.
Wu et al.  carried out a series of experiments to investigate the effect of breaching geometry on both non-cohesive and cohesive embankment dams in a U-bend flume due to overtopping flows. In the case of non-cohesive embankments, the non-symmetrical lateral expansion was noticed during the breach formation. This expansion was described by a coefficient ranging from 2.7 to 3.3.
The numerical models of the dam breach can be categorized according to different parameters, such as flow dimensions (1D, 2D, or 3D), flow governing equations, and solution methods. The 1D models are mainly used to predict the outflow hydrograph from the dam breach. Saberi et al.  applied the 1D Saint-Venant equation, which is solved by the finite difference method to investigate the outflow hydrograph during dam overtopping failure. Because of the ability to study dam profile evolution and breach formation, 2D models are more applicable than 1D models. Guan et al.  and Wu et al.  employed both 2D shallow water equations (SWEs) and sediment erosion equations, which are solved by the finite volume method to study the effect of the dam’s geometry parameters on outflow hydrograph and dam profile evolution. Wang et al.  also proposed a second-order hybrid-type of total variation diminishing (TVD) finite-difference to estimate the breach outflow by solving the 2D (SWEs). The accuracy of (SWEs) for both vertical flow contraction and surface roughness has been assessed . They noted that the accuracy of (SWEs) is acceptable for milder slopes, but in the case of steeper slopes, modelers should be more careful. Generally, the accuracy of 2D models is still low, especially with velocity distribution over the flow depth, lateral momentum exchange, density-driven flows, and bottom friction. Therefore, 3D models are preferred. Larocque et al.  and Yang et al.  started to use three-dimensional (3D) models that depend on the Reynolds-averaged Navier-Stokes (RANS) equations.
Previous experimental studies concluded that there is no clear relationship between the peak outflow from the dam breach and the initial breach characteristics. Some of these studies depend on the sharp-crested weir fixed at the end of the flume to determine the peak outflow from the breach, which leads to a decrease in the accuracy of outflow calculations at the microscale. The main goals of this study are to carry out a numerical simulation for a spatial dam breach due to overtopping flows by using (FLOW-3D) software to find an empirical equation for the peak outflow discharge from the breach and determine the worst-case that leads to accelerating the dam breaching process.
A stereolithographic (STL) file is prepared for each change in the initial breach geometry and dimensions. The CAD program is useful for creating solid objects and converting them to STL format, as shown in Fig. 1.
2.2. Governing equations
The governing equations for water flow are three-dimensional Reynolds Averaged Navier-Stokes equations (RANS).
The momentum equation:(3)∂ui∂t+1VFuj∂ui∂xj=1ρ∂∂xj-pδij+ν∂ui∂xj+∂uj∂xi-ρu`iu`j¯
where u is time-averaged velocity,ν is kinematic viscosity, VF is fractional volume open to flow, p is averaged pressure and -u`iu`j¯ are components of Reynold’s stress. The Volume of Fluid (VOF) technique is used to simulate the free surface profile. Hirt et al.  presented the VOF algorithm, which employs the function (F) to express the occupancy of each grid cell with fluid. The value of (F) varies from zero to unity. Zero value refers to no fluid in the grid cell, while the unity value refers to the grid cell being fully occupied with fluid. The free surface is formed in the grid cells having (F) values between zero and unity.(4)∂F∂t+1VF∂∂xFAxu+∂∂yFAyv+∂∂zFAzw=0
where (u, v, w) are the velocity components in (x, y, z) coordinates, respectively, and (Ax, Ay, Az) are the area fractions.
2.3. Boundary and initial conditions
To improve the accuracy of the results, the boundary conditions should be carefully determined. In this study, two mesh blocks are used to minimize the time consumed in the simulation. The boundary conditions for mesh block 1 are as follows: The inlet and sides boundaries are defined as a wall boundary condition (wall boundary condition is usually used for bound fluid by solid regions. In the case of viscous flows, no-slip means that the tangential velocity is equal to the wall velocity and the normal velocity is zero), the outlet is defined as a symmetry boundary condition (symmetry boundary condition is usually used to reduce computational effort during CFD simulation. This condition allows the flow to be transferred from one mesh block to another. No inputs are required for this boundary condition except that its location should be defined accurately), the bottom boundary is defined as a uniform flow rate boundary condition, and the top boundary is defined as a specific pressure boundary condition with assigned atmospheric pressure. The boundary conditions for mesh block 2 are as follows: The inlet is defined as a symmetry boundary condition, the outlet is defined as a free flow boundary condition, the bottom and sides boundaries are defined as a wall boundary condition, and the top boundary is defined as a specific pressure boundary condition with assigned atmospheric pressure as shown in Fig. 2. The initial conditions required to be set for the fluid (i.e., water) inside of the domain include configuration, temperature, velocities, and pressure distribution. The configuration of water depends on the dimensions and shape of the dam reservoir. While the other conditions have been assigned as follows: temperature is normal water temperature (25 °c) and pressure distribution is hydrostatic with no initial velocity.
2.4. Numerical method
FLOW-3D uses the finite volume method (FVM) to solve the governing equation (Reynolds-averaged Navier-Stokes) over the computational domain. A finite-volume method is an Eulerian approach for representing and evaluating partial differential equations in algebraic equations form . At discrete points on the mesh geometry, values are determined. Finite volume expresses a small volume surrounding each node point on a mesh. In this method, the divergence theorem is used to convert volume integrals with a divergence term to surface integrals. After that, these terms are evaluated as fluxes at each finite volume’s surfaces.
2.5. Turbulent models
Turbulence is the chaotic, unstable motion of fluids that occurs when there are insufficient stabilizing viscous forces. In FLOW-3D, there are six turbulence models available: the Prandtl mixing length model, the one-equation turbulent energy model, the two-equation (k – ε) model, the Renormalization-Group (RNG) model, the two-equation (k – ω) models, and a large eddy simulation (LES) model. For simulating flow motion, the RNG model is adopted to simulate the motion behavior better than the k – ε and k – ω.
models . The RNG model consists of two main equations for the turbulent kinetic energy KT and its dissipation.εT(5)∂kT∂t+1VFuAx∂kT∂x+vAy∂kT∂y+wAz∂kT∂z=PT+GT+DiffKT-εT(6)∂εT∂t+1VFuAx∂εT∂x+vAy∂εT∂y+wAz∂εT∂z=C1.εTKTPT+c3.GT+Diffε-c2εT2kT
where KT is the turbulent kinetic energy, PT is the turbulent kinetic energy production, GT is the buoyancy turbulence energy, εT is the turbulent energy dissipation rate, DiffKT and Diffε are terms of diffusion, c1, c2 and c3 are dimensionless parameters, in which c1 and c3 have a constant value of 1.42 and 0.2, respectively, c2 is computed from the turbulent kinetic energy (KT) and turbulent production (PT) terms.
2.6. Sediment scour model
The sediment scour model available in FLOW-3D can calculate all the sediment transport processes including Entrainment transport, Bedload transport, Suspended transport, and Deposition. The erosion process starts once the water flows remove the grains from the packed bed and carry them into suspension. It happens when the applied shear stress by water flows exceeds critical shear stress. This process is represented by entrainment transport in the numerical model. After entrained, the grains carried by water flow are represented by suspended load transport. After that, some suspended grains resort to settling because of the combined effect of gravity, buoyancy, and friction. This process is described through a deposition. Finally, the grains sliding motions are represented by bedload transport in the model. For the entrainment process, the shear stress applied by the fluid motion on the packed bed surface is calculated using the standard wall function as shown in Eq.7.(7)ks,i=Cs,i∗d50
where ks,i is the Nikuradse roughness and Cs,i is a user-defined coefficient. The critical bed shear stress is defined by a dimensionless parameter called the critical shields number as expressed in Eq.8.(8)θcr,i=τcr,i‖g‖diρi-ρf
where θcr,i is the critical shields number, τcr,i is the critical bed shear stress, g is the absolute value of gravity acceleration, di is the diameter of the sediment grain, ρi is the density of the sediment species (i) and ρf is the density of the fluid. The value of the critical shields number is determined according to the Soulsby-Whitehouse equation.(9)θcr,i=0.31+1.2d∗,i+0.0551-exp-0.02d∗,i
where d∗,i is the dimensionless diameter of the sediment, given by Eq.10.(10)d∗,i=diρfρi-ρf‖g‖μf213
where μf is the fluid dynamic viscosity. For the sloping bed interface, the value of the critical shields number is modified according to Eq.11.(11)θ`cr,i=θcr,icosψsinβ+cos2βtan2φi-sin2ψsin2βtanφi
where θ`cr,i is the modified critical shields number, φi is the angle of repose for the sediment, β is the angle of bed slope and ψ is the angle between the flow and the upslope direction. The effects of the rolling, hopping, and sliding motions of grains along the packed bed surface are taken by the bedload transport process. The volumetric bedload transport rate (qb,i) per width of the bed is expressed in Eq.12.(12)qb,i=Φi‖g‖ρi-ρfρfdi312
where Φi is the dimensionless bedload transport rate is calculated by using Meyer Peter and Müller equation.(13)Φi=βMPM,iθi-θ`cr,i1.5cb,i
where βMPM,i is the Meyer Peter and Müller user-defined coefficient and cb,i is the volume fraction of species i in the bed material. The suspended load transport is calculated as shown in Eq.14.(14)∂Cs,i∂t+∇∙Cs,ius,i=∇∙∇DCs,i
where Cs,i is the suspended sediment mass concentration, D is the diffusivity, and us,i is the grain velocity of species i. Entrainment and deposition are two opposing processes that take place at the same time. The lifting and settling velocities for both entrainment and deposition processes are calculated according to Eq.15 and Eq.16, respectively.(15)ulifting,i=αid∗,i0.3θi-θ`cr,igdiρiρf-1(16)usettling,i=υfdi10.362+1.049d∗,i3-10.36
where αi is the entrainment coefficient of species i and υf is the kinematic viscosity of the fluid.
2.7. Grid type
Using simple rectangular orthogonal elements in planes and hexahedral in volumes in the (FLOW-3D) program makes the mesh generation process easier, decreases the required memory, and improves numerical accuracy. Two mesh blocks were used in a joined form with a size ratio of 2:1. The first mesh block is coarser, which contains the reservoir water, and the second mesh block is finer, which contains the dam. For achieving accuracy and efficiency in results, the mesh size is determined by using a grid convergence test. The optimum uniform cell size for the first mesh block is 0.012 m and for the second mesh block is 0.006 m.
2.8. Time step
The maximum time step size is determined by using a Courant number, which controls the distance that the flow will travel during the simulation time step. In this study, the Courant number was taken equal to 0.25 to prevent the flow from traveling through more than one cell in the time step. Based on the Courant number, a maximum time step value of 0.00075 s was determined.
2.9. Numerical model validation
The numerical model accuracy was achieved by comparing the numerical model results with previous experimental results. The experimental study of Schmocker and Hager  was based on 31 tests with changes in six parameters (d50, Ho, Bo, Lk, XD, and Qin). All experimental tests were conducted in a straight open glass-sided flume. The horizontal flume has a rectangular cross-section with a width of 0.4 m and a height of 0.7 m. The flume was provided with a flow straightener and an intake with a length of 0.66 m. All tested dams were inserted at various distances (XD) from the intake. Test No.1 from this experimental program was chosen to validate the numerical model. The different parameters used in test No.1 are as follows:
(1) uniform sediment with a mean diameter (d50 = 0.31 mm), (2) Ho = 0.2 m, (3) Bo = 0.2 m, (4) Lk = 0.1 m,
(5) XD = 1.0 m, (6) Qin = 6.0 lit/s, (7) Su and Sd = 2:1, (8) mass density (ρs = 2650 kg/m3) (9) Homogenous and non-cohesive embankment dam. As shown in Fig. 2, the simulation is contained within a rectangular grid with dimensions: 3.56 m in the x-direction (where 0.66 m is used as inlet, 0.9 m as dam base width, and 1.0 m as outlet), in y-direction 0.2 m (dam length), and in the z-direction 0.3 m, which represents the dam height (0.2 m) with a free distance (0.1 m) above the dam. There are two main reasons that this experimental program is preferred for the validation process. The first reason is that this program deals with homogenous, non-cohesive soil, which is available in FLOW-3D. The second reason is that this program deals with small-scale models which saves time for numerical simulation. Finally, some important assumptions were considered during the validation process. The flow is assumed to be incompressible, viscous, turbulent, and three-dimensional.
By comparing dam profiles at different time instants for the experimental test with the current numerical model, it appears that the numerical model gives good agreement as shown in Fig. 3 and Fig. 4, with an average error percentage of 9% between the experimental results and the numerical model.
3. Analysis and discussions
The current model is used to study the effects of different parameters such as (initial breach shapes, dimensions, locations, upstream and downstream dam slopes) on the peak outflow discharge, QP, time of peak outflow, tP, and rate of erosion, E.
This study consists of a group of scenarios. The first scenario is changing the shapes of the initial breach according to Singh , the most predicted shapes are rectangular and V-notch as shown in Fig. 5. The second scenario is changing the initial breach dimensions (i.e., width and depth). While the third scenario is changing the location of the initial breach. Eventually, the last scenario is changing the upstream and downstream dam slopes.
All scenarios of this study were carried out under the same conditions such as inflow discharge value (Qin=1.0lit/s), dimensions of the tested dam, where dam height (Ho=0.20m), crest width.
(Lk=0.1m), dam length (Bo=0.20m), and homogenous & non-cohesive soil with a mean diameter (d50=0.31mm).
3.1. Dam breaching process evolution
The dam breaching process is a very complex process due to the quick changes in hydrodynamic conditions during dam failure. The dam breaching process starts once water flows reach the downstream face of the dam. During the initial stage of dam breaching, the erosion process is relatively quiet due to low velocities of flow. As water flows continuously, erosion rates increase, especially in two main zones: the crest and the downstream face. As soon as the dam crest is totally eroded, the water levels in the dam reservoir decrease rapidly, accompanied by excessive erosion in the dam body. The erosion process continues until the water levels in the dam reservoir equal the remaining height of the dam.
According to Zhou et al. , the breaching process consists of three main stages. The first stage starts with beginning overtopping flow, then ends when the erosion point directed upstream and reached the inflection point at the inflection time (ti). The second stage starts from the end of the stage1 until the occurrence of peak outflow discharge at the peak outflow time (tP). The third stage starts from the end of the stage2 until the value of outflow discharge becomes the same as the value of inflow discharge at the final time (tf). The outflow discharge from the dam breach increases rapidly during stage1 and stage2 because of the large dam storage capacity (i.e., the dam reservoir is totally full of water) and excessive erosion. While at stage3, the outflow values start to decrease slowly because most of the dam’s storage capacity was run out. The end of stage3 indicates that the dam storage capacity was totally run out, so the outflow equalized with the inflow discharge as shown in Fig. 6 and Fig. 7.
3.2. The effect of initial breach shape
To identify the effect of the initial breach shape on the evolution of the dam breaching process. Three tests were carried out with different cross-section areas for each shape. The initial breach is created at the center of the dam crest. Each test had an ID to make the process of arranging data easier. The rectangular shape had an ID (Rec5h & 5b), which means that its depth and width are equal to 5% of the dam height, and the V-notch shape had an ID (V-noch5h & 1:1) which means that its depth is equal to 5% of the dam height and its side slope is equal to 1:1. The comparison between rectangular and V-notch shapes is done by calculating the ratio between maximum dam height at different times (ZMax) to the initial dam height (Ho), rate of erosion, and hydrograph of outflow discharge for each test. The rectangular shape achieves maximum erosion rate and minimum inflection time, in addition to a rapid decrease in the dam reservoir levels. Therefore, the dam breaching is faster in the case of a rectangular shape than in a V-notch shape, which has the same cross-section area as shown in Fig. 8.
Also, by comparing the hydrograph for each test, the peak outflow discharge value in the case of a rectangular shape is higher than the V-notch shape by 5% and the time of peak outflow for the rectangular shape is shorter than the V-notch shape by 9% as shown in Fig. 9.
3.3. The effect of initial breach dimensions
The results of the comparison between the different initial breach shapes indicate that the worst initial breach shape is rectangular, so the second scenario from this study concentrated on studying the effect of a change in the initial rectangular breach dimensions. Groups of tests were carried out with different depths and widths for the rectangular initial breach. The first group had a depth of 5% from the dam height and with three different widths of 5,10, and 15% from the dam height, the second group had a depth of 10% with three different widths of 5,10, and 15%, the third group had a depth of 15% with three different widths of 5,10, and 15% and the final group had a width of 15% with three different heights of 5, 10, and 15% for a rectangular breach shape. The comparison was made as in the previous section to determine the worst case that leads to the quick dam failure as shown in Fig. 10.
The results show that the (Rec 5 h&15b) test achieves a maximum erosion rate for a shorter period of time and a minimum ratio for (Zmax / Ho) as shown in Fig. 10, which leads to accelerating the dam failure process. The dam breaching process is faster with the minimum initial breach depth and maximum initial breach width. In the case of a minimum initial breach depth, the retained head of water in the dam reservoir is high and the crest width at the bottom of the initial breach (L`K) is small, so the erosion point reaches the inflection point rapidly. While in the case of the maximum initial breach width, the erosion perimeter is large.
3.4. The effect of initial breach location
The results of the comparison between the different initial rectangular breach dimensions indicate that the worst initial breach dimension is (Rec 5 h&15b), so the third scenario from this study concentrated on studying the effect of a change in the initial breach location. Three locations were checked to determine the worst case for the dam failure process. The first location is at the center of the dam crest, which was named “Center”, the second location is at mid-distance between the dam center and dam edge, which was named “Mid”, and the third location is at the dam edge, which was named “Edge” as shown in Fig. 11. According to this scenario, the results indicate that the time of peak outflow discharge (tP) is the same in the three cases, but the maximum value of the peak outflow discharge occurs at the center location. The difference in the peak outflow values between the three cases is relatively small as shown in Fig. 12.
The rates of erosion were also studied for the three cases. The results show that the maximum erosion rate occurs at the center location as shown in Fig. 13. By making a comparison between the three cases for the dam storage volume. The results show that the center location had the minimum values for the dam storage volume, which means that a large amount of water has passed to the downstream area as shown in Fig. 14. According to these results, the center location leads to increased erosion rate and accelerated dam failure process compared with the two other cases. Because the erosion occurs on both sides, but in the case of edge location, the erosion occurs on one side.
3.5. The effect of upstream and downstream dam slopes
The results of the comparison between the different initial rectangular breach locations indicate that the worst initial breach location is the center location, so the fourth scenario from this study concentrated on studying the effect of a change in the upstream (Su) and downstream (Sd) dam slopes. Three slopes were checked individually for both upstream and downstream slopes to determine the worst case for the dam failure process. The first slope value is (2H:1V), the second slope value is (2.5H:1V), and the third slope value is (3H:1V). According to this scenario, the results show that the decreasing downstream slope angle leads to increasing time of peak outflow discharge (tP) and decreasing value of peak outflow discharge. The difference in the peak outflow values between the three cases for the downstream slope is 2%, as shown in Fig. 15, but changing the upstream slope has a negligible impact on the peak outflow discharge and its time as shown in Fig. 16.
The rates of erosion were also studied in the three cases for both upstream and downstream slopes. The results show that the maximum erosion rate increases by 6.0% with an increasing downstream slope angle by 4°, as shown in Fig. 17. The results also indicate that the erosion rates aren’t affected by increasing or decreasing the upstream slope angle, as shown in Fig. 18. According to these results, increasing the downstream slope angle leads to increased erosion rate and accelerated dam failure process compared with the upstream slope angle. Because of increasing shear stress applied by water flows in case of increasing downstream slope.
According to all previous scenarios, the dimensionless peak outflow discharge QPQin is presented for a fixed dam height (Ho) and inflow discharge (Qin). Fig. 19 illustrates the relationship between QP∗=QPQin and.
Lr=ho2/3∗bo2/3Ho. The deduced relationship achieves R2=0.96.(17)QP∗=2.2807exp-2.804∗Lr
A spatial dam breaching process was simulated by using FLOW-3D Software. The validation process was performed by making a comparison between the simulated results of dam profiles and the dam profiles obtained by Schmocker and Hager  in their experimental study. And also, the peak outflow value recorded an error percentage of 12% between the numerical model and the experimental study. This model was used to study the effect of initial breach shape, dimensions, location, and dam slopes on peak outflow discharge, time of peak outflow, and the erosion process. By using the parameters obtained from the validation process, the results of this study can be summarized in eight points as follows.1.
The rectangular initial breach shape leads to an accelerating dam failure process compared with the V-notch.2.
The value of peak outflow discharge in the case of a rectangular initial breach is higher than the V-notch shape by 5%.3.
The time of peak outflow discharge for a rectangular initial breach is shorter than the V-notch shape by 9%.4.
The minimum depth and maximum width for the initial breach achieve maximum erosion rates (increasing breach width, b0, or decreasing breach depth, h0, by 5% from the dam height leads to an increase in the maximum rate of erosion by 11% and 15%, respectively), so the dam failure is rapid.5.
The center location of the initial breach leads to an accelerating dam failure compared with the edge location.6.
The initial breach location has a negligible effect on the peak outflow discharge value and its time.7.
Increasing the downstream slope angle by 4° leads to an increase in both peak outflow discharge and maximum rate of erosion by 2.0% and 6.0%, respectively.8.
The upstream slope has a negligible effect on the dam breaching process.
측면 분기기(흡입구)의 상류 측에서 흐름 분리는 분기기 입구에서 와류를 일으키는 중요한 문제입니다. 이는 흐름의 유효 폭, 출력 용량 및 효율성을 감소시킵니다. 따라서 분리지대의 크기를 파악하고 크기를 줄이기 위한 방안을 제시하는 것이 필수적이다. 본 연구에서는 분리 구역의 치수를 줄이기 위한 방법으로 7가지 유형의 거칠기 요소를 분기구 입구에 설치하고 4가지 다른 배출(총 84번의 실험을 수행)과 함께 3개의 서로 다른 베드 반전 레벨을 조사했습니다. 또한 3D CFD(Computational Fluid Dynamics) 모델을 사용하여 분리 영역의 흐름 패턴과 치수를 평가했습니다. 결과는 거칠기 계수를 향상시키면 분리 영역 치수를 최대 38%까지 줄일 수 있는 반면, 드롭 구현 효과는 사용된 거칠기 계수를 기반으로 이 영역을 다르게 축소할 수 있음을 보여주었습니다. 두 가지 방법을 결합하면 분리 영역 치수를 최대 63%까지 줄일 수 있습니다.
Flow separation at the upstream side of lateral turnouts (intakes) is a critical issue causing eddy currents at the turnout entrance. It reduces the effective width of flow, turnout capacity and efficiency. Therefore, it is essential to identify the dimensions of the separation zone and propose remedies to reduce its dimensions. Installation of 7 types of roughening elements at the turnout entrance and 3 different bed invert levels, with 4 different discharges (making a total of 84 experiments) were examined in this study as a method to reduce the dimensions of the separation zone. Additionally, a 3-D Computational Fluid Dynamic (CFD) model was utilized to evaluate the flow pattern and dimensions of the separation zone. Results showed that enhancing the roughness coefficient can reduce the separation zone dimensions up to 38% while the drop implementation effect can scale down this area differently based on the roughness coefficient used. Combining both methods can reduce the separation zone dimensions up to 63%.
Turnouts or intakes are amongst the oldest and most widely used hydraulic structures in irrigation networks. Turnouts are also used in water distribution, transmission networks, power generation facilities, and waste water treatment plants etc. The flows that enter a turnout have a strong momentum in the direction of the main waterway and that is why flow separation occurs inside the turnout. The horizontal vortex formed in the separation area is a suitable place for accumulation and deposition of sediments. The separation zone is a vulnerable area for sedimentation and for reduction of effective flow due to a contracted flow region in the lateral channel. Sedimentaion in the entrance of the intake can gradually be transfered into the lateral channel and decrease the capacity of the higher order channels over time (Jalili et al. 2011). On the other hand, the existence of coarse-grained materials causes erosion and destruction of the waterway side walls and bottom. In addition, sedimentation creates conditions for vegetation to take root and damage the waterway cover, which causes water to leak from its perimeter. Therefore, it is important to investigate the pattern of the flow separation area in turnouts and provide solutions to reduce the dimensions of this area.
The three-dimensional flow structure at turnouts is quite complex. In an experimental study by Neary & Odgaard (1993) in a 90-degree water turnout it was found that the secondary currents and separation zone varies from the bed to the water surface. They also found that at a 90-degree water turnout, the bed roughness and discharge ratio play a critical role in flow structure. They asserted that an explanation of sediment behavior at a diversion entrance requires a comprehensive understanding of 3D flow patterns around the lateral-channel entrance. In addition, they suggested that there is a strong similarity between flow in a channel bend and a diversion channel, and that this similarity can rationalize the use of bend flow models for estimation of 3D flow structures in diversion channels.
Some of the distinctive characteristics of dividing flow in a turnout include a zone of separation immediately near the entrance of the lateral turnout (separation zone), a contracted flow region in the branch channel (contracted flow), and a stagnation point near the downstream corner of the junction (stagnation zone). In the region downstream of the junction, along the continuous far wall, separation due to flow expansion may occur (Ramamurthy et al. 2007), that is, a separation zone. This can both reduce the turnout efficiency and the effective width of flow while increasing the sediment deposition in the turnout entrance (Jalili et al. 2011). Installation of submerged vanes in the turnout entrance is a method which is already applied to reduce the size of flow separation zones. The separation zone draws sediments and floating materials into themselves. This reduces effective cross-section area and reduces transmission capacity. These results have also been obtained in past studies, including by Ramamurthy et al. (2007) and in Jalili et al. (2011). Submerged vanes (Iowa vanes) are designed in order to modify the near-bed flow pattern and bed-sediment motion in the transverse direction of the river. The vanes are installed vertically on the channel bed, at an angle of attack which is usually oriented at 10–25 degrees to the local primary flow direction. Vane height is typically 0.2–0.5 times the local water depth during design flow conditions and vane length is 2–3 times its height (Odgaard & Wang 1991). They are vortex-generating devices that generate secondary circulation, thereby redistributing sediment within the channel cross section. Several factors affect the flow separation zone such as the ratio of lateral turnout discharge to main channel discharge, angle of lateral channel with respect to the main channel flow direction and size of applied submerged vanes. Nakato et al. (1990) found that sediment management using submerged vanes in the turnout entrance to Station 3 of the Council Bluffs plant, located on the Missouri River, is applicable and efficient. The results show submerged vanes are an appropriate solution for reduction of sediment deposition in a turnout entrance. The flow was treated as 3D and tests results were obtained for the flow characteristics of dividing flows in a 90-degree sharp-edged, junction. The main and lateral channel were rectangular with the same dimensions (Ramamurthy et al., 2007).
Keshavarzi & Habibi (2005) carried out experiments on intake with angles of 45, 67, 79 and 90 degrees in different discharge ratios and reported the optimum angle for inlet flow with the lowest flow separation area to be about 55 degrees. The predicted flow characteristics were validated using experimental data. The results indicated that the width and length of the separation zone increases with the increase in the discharge ratio Qr (ratio of outflow per unit width in the turnout to inflow per unit width in the main channel).
Abbasi et al. (2004) performed experiments to investigate the dimensions of the flow separation zone at a lateral turnout entrance. They demonstrated that the length and width of the separation zone decreases with the increasing ratio of lateral turn-out discharge. They also found that with a reducing angle of lateral turnout, the length of the separation zone scales up and width of separation zone reduces. Then they compared their observations with results of Kasthuri & Pundarikanthan (1987) who conducted some experiments in an open-channel junction formed by channels of equal width and an angle of lateral 90 degree turnout, which showed the dimensions of the separation zone in their experiments to be smaller than in previous studies. Kasthuri & Pundarikanthan (1987) studied vortex and flow separation dimensions at the entrance of a 90 degree channel. Results showed that increasing the diversion discharge ratio can reduce the length and width of the vortex area. They also showed that the length and width of the vortex area remain constant at diversion ratios greater than 0.7. Karami Moghaddam & Keshavarzi (2007) analyzed the flow characteristics in turnouts with angles of 55 and 90 degrees. They reported that the dimensions of the separation zone decrease by increasing the discharge ratio and reducing the turnout angle with respect to the main channel. Studies about flow separation zone can be found in Jalili et al. (2011), Nikbin & Borghei (2011), Seyedian et al. (2008).
Jamshidi et al. (2016) measured the dimensions of a flow separation zone in the presence of submerged vanes with five arrangements (parallel, stagger, compound, piney and butterflies). Results showed that the ratio of the width to the length of the separation zone (shape index) was between 0.2 and 0.28 for all arrangements.
Karami et al. (2017) developed a 3D computational fluid dynamic (CFD) code which was calibrated by measured data. They used the model to evaluate flow pattern, diversion ratio of discharge, strength of the secondary flow, and dimensions of the vortex inside the channel in various dikes and submerged vane installation scenarios. Results showed that the diversion ratio of discharge in the diversion channel is dependent on the width of the flow separation area in the main channel. A dike, perpendicular to the flow, doubles the ratio of diverted discharge and reduces the suspended sediment load compared with the base-line situation by creating outer arch conditions. In addition, increasing the longitudinal distance between vanes increases the velocity gradient between the vanes and leads to a more severe erosion of the bed near the vanes.Figure 1VIEW LARGEDOWNLOAD SLIDE
Laboratory channel dimensions.
Al-Zubaidy & Hilo (2021) used the Navier–Stokes equation to study the flow of incompressible fluids. Using the CFD software ANSYS Fluent 19.2, 3D flow patterns were simulated at a diversion channel. Their results showed good agreement using the comparison between the experimental and numerical results when the k-omega turbulence viscous model was employed. Simulation of the flow pattern was then done at the lateral channel junction using a variety of geometry designs. These improvements included changing the intake’s inclination angle and chamfering and rounding the inner corner of the intake mouth instead of the sharp edge. Flow parameters at the diversion including velocity streamlines, bed shear stress, and separation zone dimensions were computed in their study. The findings demonstrated that changing the 90° lateral intake geometry can improve the flow pattern and bed shear stress at the intake junction. Consequently, sedimentation and erosion problems are reduced. According to the conclusions of their study, a branching angle of 30° to 45° is the best configuration for increasing branching channel discharge, lowering branching channel sediment concentration.
The review of the literature shows that most of the studies deal with turnout angle, discharge ratio and implementation of vanes as techniques to reduce the area of the separation zone. This study examines the effect of roughness coefficient and drop implementation at the entrance of a 90-degree lateral turnout on the dimensions of the separation zone. As far as the authors are aware, these two variables have never been studied as a remedy to decrease the separation zone dimensions whilst enhancing turnout efficiency. Additionally, a three-dimensional numerical model is applied to simulate the flow pattern around the turnout. The numerical results are verified against experimental data.
The experiments were conducted in a 90 degree dividing flow laboratory channel. The main channel is 15 m long, 0.5 m wide and 0.4 m high and the branch channel is 3 m long, 0.35 m wide and 0.4 m high, as shown in Figure 1. The tests were carried out at 9.65 m from the beginning of the flume and were far enough from the inlet, so we were sure that the flow was fully developed. According to Kirkgöz & Ardiçlioğlu (1997) the length of the developing region would be approximantly 65 and 72 times the flow depth. In this study, the depth is 9 cm, which makes this condition.
Both the main and lateral channel had a slope of 0.0003 with side walls of concrete. A 100 hp pump discharged the water into a stilling basin at the entrance of the main flume. The discharge was measured using an ultrasonic discharge meter around the discharge pipe. Eighty-four experiments in total were carried out at range of 0.1<Fr<0.4 (Froude numbers in main channel and upstream of turnout). The depth of water in the main channel in the experiments was 9 cm, in which case the effect of surface tension can be considered; according to research by Zolghadr & Shafai Bejestan (2020) and Zolghadr et al. (2021), when the water depth is more than 6 cm, the effect of surface tension is reduced and can be ignored given that the separation phenomenon occurs in the boundary layer, the height of the roughness creates disturbances in growth and development of the boundary layer and, as a result, separation growth is also faced with disruption and its dimensions grow less compared to smooth surfaces. Similar conditions occur in case of drop implementation. A disturbance occurs in the growth of the boundary layer and as a result the separation zone dimensions decrease. In order to investigate the effect of roughness coefficient and drop implementation on the separation zone dimensions, four different discharges (16, 18, 21, 23 l/s) in subcritical conditions, seven Manning (Strickler) roughness coefficients (0.009, 0.011, 0.017, 0.023, 0.028, 0.030, 0.032) as shown in Figure 2 and three invert elevation differences between the main channel and lateral turnout invert (0, 5 and 10 cm) at the entrance of the turnout were considered. The Manning roughness coefficient values were selected based on available and feasible values for real conditions, so that 0.009 is equivalent to galvanized sheet roughness and selected for the baseline tests. 0.011 is for concrete with neat surface, 0.017 and 0.023 are for unfinished and gunite concrete respectively. 0.030 and 0.032 values are for concrete on irregular excavated rock (Chow 1959). The roughness coefficients were created by gluing sediment particles on a thin galvanized sheet which was installed at the upstream side of the lateral turnout. The values of roughness coefficients were calculated based on the Manning-Strickler formula. For this purpose, some uniformly graded sediment samples were prepared and the Manning roughness coefficient of each sample was determined with respect to the median size (D50) value pasted into the Manning-Strickler formula. Some KMnO4 was sifted in the main channel upstream to visualize and measure the dimensions of the separation zone. Consequently, when KMnO4 approached the lateral turnout a photo of the separation zone was taken from a top view. All the experiments were recorded and several photos were taken during the experiment after stablishment of steady flow conditions. The photos were then imported to AutoCAD to measure the separation zone dimensions. Because all the shooting was done with a high-definition camera and it was possible to zoom in, the results are very accurate.Figure 2VIEW LARGEDOWNLOAD SLIDE
The velocity values were also recorded by a one-dimensional velocity meter at 15 cm distance from the turnout entrance and in transverse direction (perpendicular to the flow direction).
The water level was also measured by depth gauges with a accuracy of 0.1 mm, and velocity in one direction with a single-dimensional KENEK LP 1100 with an accuracy of ±0.02 m/s (0–1 m/s), ± 0.04 m/s (1–2 m/s), ± 0.08 m/s (2–4 m/s), ±0.10 m/s (4–5 m/s).
ListenA FLOW-3D numerical model was utilized as a solver of the Navier-Stokes equation to simulate the three-dimensional flow field at the entrance of the turnout. The governing equations included continuity momentum equations. The continuity equation, regardless of the density of the fluid in the form of Cartesian coordinates x, y, and z, is as follows:
(1)where u, v, and w represent the velocity components in the x, y, and z directions, respectively; Ax, Ay, and Az are the surface flow fractions in the x, y, and z directions, respectively; VF denotes flow volume fraction; r is the density of the fluid; t is time; and Rsor refers to the source of the mass. Equations (2)–(4) show momentum equations in x, y and z dimensions respectively :
(4)where Gx, Gy, and Gz are the accelerations caused by gravity in the x, y, and z directions, respectively; and fx, fy, and fz are the accelerations caused by viscosity in the x, y, and z directions, respectively.
The turbulence models used in this study were the renormalized group (RNG) models. Evaluation of the concordance of the mentioned models with experimental studies showed that the RNG model provides more accurate results.
Two blocks of mesh were used to simulate the main channels and lateral turnout. The meshes were denser in the vicinity of the entrance of the turnout in order to increase the accuracy of computations. Boundary conditions for the main mesh block included inflow for the channel entrance (volumetric flow rate), outflow for the channel exit, ‘wall’ for the bed and the right boundary and ‘symmetry’ for the top (free surface) and left boundaries (turnout). The side wall roughness coefficient was given to the software as the Manning number in surface roughness of any component. Considering the restrictions in the available processor, a main mesh block with appropriate mesh size was defined to simulate the main flow field in the channel, while the nested mesh-block technique was utilized to create a very dense solution field near the roughness plate in order to provide accurate results around the plates and near the entrance of the lateral turnout. This technique reduced the number of required mesh elements by up to 60% in comparison with the method in which the mesh size of the main solution field was decreased to the required extent.
The numerical outputs are verified against experimental data. The hydraulic characteristics of the experiment are shown in Table 1.Table 1
During the experiments, the dimensions of the separation zone were recorded with an HD camera. Some photos were imported to AutoCad software. Then, the separation zones dimensions were measured and compared in different scenarios.
At the beginning, the flow pattern in the separation zone for four different hydraulic conditions was studied for seven different Manning roughness coefficients from 0.009 to 0.032. To compare the obtained results, roughness of 0.009 was considered as the base line. The percentage of reduction in separation zone area in different roughness coefficients is shown in Figure 3. According to this figure, by increasing the roughness of the turnout side wall, the separation zone area ratio reduces (ratio of separation zone area to turnout area). In other words, in any desired Froud number, the highest dimensions of the separation zone area are related to the lowest roughness coefficients. In Figure 3, ‘A’ is the area of the separation zone and ‘Ai’ represents the total area of the turnout.Figure 3VIEW LARGEDOWNLOAD SLIDE
Effect of roughness on separation zone dimensions.
It should be mentioned that the separation zone dimensions change with depth, so that the area is larger at the surface than near the bed. This study measured the dimensions of this area at the surface. Figure 4 show exactly where the roughness elements were located.Figure 5VIEW LARGEDOWNLOAD SLIDE
Comparison of separation zone for n=0.023 and n=0.032.
Figure 5 shows images of the separation zone at n=0.023 and n=0.032 as examples, and show that the separation area at n=0.032 is smaller than that of n=0.023.
The difference between the effect of the two 0.032 and 0.030 roughnesses is minor. In other words, the dimensions of the separation zone decreased by increasing roughness up to 0.030 and then remained with negligable changes.
In the next step, the effect of intake invert relative to the main stream (drop) on the dimensions of the separation zone was investigated. To do this, three different invert levels were considered: (1) without drop; (2) a 5 cm drop between the main canal and intake canal; and (3) a 10 cm drop between the main canal and intake canal. The without drop mode was considered as the control state. Figure 6 shows the effect of drop implementation on separation zone dimensions. Tables 2 and 3 show the reduced percentage of separation zone areas in 5 and 10 cm drop compared to no drop conditions as the base line. It was found that the best results were obtained when a 10 cm drop was implemented.Table 2
Decrease percentage of separation zone area in 5 cm drop
Decrease percentage of separation zone area in 10 cm drop
Effect of drop implementation on separation zone dimensions.
The combined effect of drop and roughness is shown in Figure 7. According to this figure, by installing a drop structure at the entrance of the intake, the dimensions of the separation zone scales down in any desired roughness coefficient. Results indicated that by increasing the roughness coefficient or drop implementation individually, the separation zone area decreases up to 38 and 25% respectively. However, employing both techniques simultaneously can reduce the separation zone area up to 63% (Table 4). The reason for the reduction of the dimensions of the separation zone area by drop implementation can be attributed to the increase of discharge ratio. This reduces the dimensions of the separation zone area.Table 4
Reduction in percentage of combined effect of roughness and 10 cm drop
Combined effect of roughness and drop on separation zone dimensions.
This method increases the discharge ratio (ratio of turnout to main channel discharge). The results are compatible with the literature. Some other researchers reported that increasing the discharge ratio can scale down the separation zone dimensions (Karami Moghaddam & Keshavarzi 2007; Ramamurthy et al. 2007). However, these researchers employed other methods to enhance the discharge ratio. Drop implementation is simple and applicable in practice, since there is normally an elevation difference between the main and lateral canal in irrigation networks to ensure gravity flow occurance.
Table 4 depicts the decrease in percentage of the separation zone compared to base line conditions in different arrangements of the combined tests.Figure 8VIEW LARGEDOWNLOAD SLIDE
Velocity profiles for various roughness coefficients along turnout width.
A comparison between the proposed methods introduced in this paper and traditional methods such as installation of submerged vanes, and changing the inlet geometry (angle, radius) was performed. Figure 8 shows the comparison of the results. The comparison shows that the new techniques can be highly influential and still practical. In this research, with no change in structural geometry (enhancement of roughness coefficient) or minor changes with respect to drop implementation, the dimensions of the separation zone are decreased noticeably. The velocity values were also recorded by a one-dimensional velocity meter at 15 cm distance from the turnout entrance and in a transverse direction (perpendicular to the flow direction). The results are shown in Figure 9.Figure 9VIEW LARGEDOWNLOAD SLIDE
Effect of roughness on separation zone dimensions in numerical study.
This study examined the flow patterns around the entrance of a diversion channel due to various wall roughnesses in the diversion channel. Results indicated that increasing the discharge ratio in the main channel and diversion channel reduces the area of the separation zone in the diversion channel.Figure 10VIEW LARGEDOWNLOAD SLIDE
Comparision of the vortex area (software output) for three roughnesses (0.009, 0.023 and 0.032).A laboratory and numerical error rate of 0.2605 was calculated from the following formula,
where Uexp is the experimental result, Unum is the numerical result, and N is the number of data.
Figure 9 shows the effect of roughness on separation zone dimensions in numerical study. Figure 10 compares the vortex area (software output) for three roughnesses, 0.009, 0.023 and 0.032 and Figure 11 shows the flow lines (tecplot output) that indicate the effect of roughness on flow in the separation zone. Numerical analysis shows that by increasing the roughness coefficient, the dimensions of the separation zone area decrease, as shown in Figure 10 where the separation zone area at n=0.032 is less than the separation zone area at n=0.009.Figure 11VIEW LARGEDOWNLOAD SLIDE
Comparison of vortex area in 3D mode (tecplot output) with two roughnesses (a) 0.009 and (b) 0.032.Figure 12VIEW LARGEDOWNLOAD SLIDE
Velocity vector for flow condition Q1/422 l/s, near surface.
The velocities intensified moving midway toward the turnout showing that the effective area is scaled down. The velocity values were almost equal to zero near the side walls as expected. As shown in Figure 12 the approach vortex area velocity decreases. Experimental and numerical measured velocity at x=0.15 m of the diversion channel compared in Figure 13 shows that away from the separation zone area, the velocity increases. All longitudinal velocity contours near the vortex area are distinctly different between different roughnesses. The separation zone is larger at less roughness both in length and width.Figure 13VIEW LARGEDOWNLOAD SLIDE
This study introduces practical and feasible methods for enhancing turnout efficiency by reducing the separation zone dimensions. Increasing the roughness coefficient and implementation of inlet drop were considered as remedies for reduction of separation zone dimensions. A data set has been compiled that fully describes the complex, 3D flow conditions present in a 90 degree turnout channel for selected flow conditions. The aim of this numerical model was to compare the results of a laboratory model in the area of the separation zone and velocity. Results showed that enhancing roughness coefficient reduce the separation zone dimensions up to 38% while the drop implementation effect can scale down this area differently based on roughness coefficient used. Combining both methods can reduce the separation zone dimensions up to 63%. Further research is proposed to investigate the effect of roughness and drop implementation on sedimentation pattern at lateral turnouts. The dimensions of the separation zone decreases with the increase of the non-dimensional parameter, due to the reduction ratio of turnout discharge increasing in all the experiments.
This method increases the discharge ratio (ratio of turnout to main channel discharge). The results are compatible with the literature. Other researchers have reported that intensifying the discharge ratio can scale down the separation zone dimensions (Karami Moghaddam & Keshavarzi 2007; Ramamurthy et al. 2007). However, they employed other methods to enhance the discharge ratio. Employing both techniques simultaneously can decrease the separation zone dimensions up to 63%. A comparison between the new methods introduced in this paper and traditional methods such as installation of submerged vanes, and changing the inlet geometry (angle, radius) was performed. The comparison shows that the new techniques can be highly influential and still practical. The numerical and laboratory models are in good agreement and show that the method used in this study has been effective in reducing the separation area. This method is simple, economical and can prevent sediment deposition in the intake canal. Results show that CFD prediction of the fluid through the separation zone at the canal intake can be predicted reasonably well and the RNG model offers the best results in terms of predictability.
Using an improved Carreau constitutive model, a numerical simulation of the casting process of a type of solid propellant slurry vacuum plate casting was carried out using the Flow3D software. Through the flow process in the orifice flow channel and the combustion chamber, the flow velocity of the slurry passing through the plate flow channel was quantitatively analyzed, and the viscosity, shear rate, and leveling characteristics of the slurry in the combustion chamber were qualitatively analyzed and predicted. The pouring time, pouring quality, and flow state predicted by the numerical simulation were verified using a visual tester consisting of a vacuum plate casting system in which a pouring experiment was carried out. Studies have shown that HTPB three-component propellant slurry is a typical yielding pseudoplastic fluid. When the slurry flows through the flower plate and the airfoil, the fluid shear rate reaches its maximum value and the viscosity of the slurry decreases. The visual pouring platform was built and the experiment was controlled according to the numerically-calculated parameters, ensuring the same casting speed. The comparison between the predicted casting quality and the one obtained in the verification test resulted in an error less than 10 %. Moreover, the error between the simulated casting completion time and the process verification test result was also no more than 10 %. Last, the flow state of the slurry during the simulation was consistent with the one during the experimental test. The overall leveling of the slurry in the combustion chamber was adequate and no relatively large holes and flaws developed during the pouring process.
개선된 Carreau 구성 모델을 사용하여 FLOW-3D 소프트웨어를 사용하여 고체 추진제 슬러리 진공판 유형의 Casting Process에 대한 수치 시뮬레이션을 수행했습니다. 오리피스 유로와 연소실에서의 유동과정을 통해 판 유로를 통과하는 슬러리의 유속을 정량적으로 분석하고, 연소실에서 슬러리의 점도, 전단율, 레벨링 특성을 정성적으로 분석하하고, 예측하였습니다.
타설시간, 타설품질, 수치해석으로 예측된 유동상태는 타설실험을 수행한 진공판주조시스템으로 구성된 비주얼 테스터를 이용하여 검증하였습니다.
연구에 따르면 HTPB 3성분 추진제 슬러리는 전형적인 생성 가소성 유체입니다. 슬러리가 플라워 플레이트와 에어포일을 통과할 때 유체 전단율이 최대값에 도달하고 슬러리의 점도가 감소합니다.
시각적 주입 플랫폼이 구축되었고 동일한 주조 속도를 보장하기 위해 수치적으로 계산된 매개변수에 따라 실험이 제어되었습니다. 예측된 casting 품질과 검증 테스트에서 얻은 품질을 비교한 결과 10 % 미만의 오류가 발생했습니다.
또한 모의 casting 완료시간과 공정검증시험 결과의 오차도 10 % 이하로 나타났습니다.
마지막으로 시뮬레이션 중 슬러리의 흐름 상태는 실험 테스트 시와 일치하였다. 연소실에서 슬러리의 전체 레벨링은 적절했으며 주입 과정에서 상대적으로 큰 구멍과 결함이 발생하지 않았습니다.
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Chendi Zhang1 , Yuncheng Xu1,2, Marwan A Hassan3 , Mengzhen Xu1 , Pukang He1 1State Key Laboratory of Hydroscience and Engineering, Tsinghua University, Beijing, 100084, China. 2 College of Water Resources and Civil Engineering, China Agricultural University, Beijing, 100081, China. 5 3Department of Geography, University of British Columbia, 1984 West Mall, Vancouver BC, V6T1Z2, Canada. Correspondence to: Chendi Zhang (firstname.lastname@example.org) and Mengzhen Xu (email@example.com)
스텝 풀 시스템은 계류의 일반적인 기반이며 전 세계의 하천 복원 프로젝트에 활용되었습니다. 스텝 풀 장치는 스텝 풀 기능의 형태학적 진화 및 안정성과 밀접하게 상호 작용하는 것으로 보고된 매우 균일하지 않은 수력 특성을 나타냅니다.
그러나 스텝 풀 형태에 대한 3차원 수리학의 자세한 정보는 측정의 어려움으로 인해 부족했습니다. 이러한 지식 격차를 메우기 위해 SfM(Structure from Motion) 및 CFD(Computational Fluid Dynamics) 기술을 기반으로 하이브리드 모델을 구축했습니다. 이 모델은 CFD 시뮬레이션을 위한 입력으로 6가지 유속의 자연석으로 만든 인공 스텝 풀 장치가 있는 침대 표면의 3D 재구성을 사용했습니다.
하이브리드 모델은 스텝 풀 장치에 대한 3D 흐름 구조의 고해상도 시각화를 제공하는 데 성공했습니다. 결과는 계단 아래의 흐름 영역의 분할, 즉 수면에서의 통합 점프, 침대 근처의 줄무늬 후류 및 그 사이의 고속 제트를 보여줍니다.
수영장에서 난류 에너지의 매우 불균일한 분포가 밝혀졌으며 비슷한 용량을 가진 두 개의 에너지 소산기가 수영장에 공존하는 것으로 나타났습니다. 흐름 증가에 따른 풀 세굴 개발은 점프 및 후류 와류의 확장으로 이어지지만 이러한 증가는 스텝 풀 실패에 대한 임계 조건에 가까운 높은 흐름에서 점프에 대해 멈춥니다.
음의 경사면에서 발달된 곡물 20 클러스터와 같은 미세 지반은 국부 수력학에 상당한 영향을 주지만 이러한 영향은 수영장 바닥에서 억제됩니다. 스텝 스톤의 항력은 가장 높은 흐름이 사용되기 전에 배출과 함께 증가하는 반면 양력은 더 큰 크기와 더 넓은 범위를 갖습니다. 우리의 결과는 계단 풀 형태의 복잡한 흐름 특성을 조사할 때 물리적 및 수치적 모델링을 결합한 하이브리드 모델 접근 방식의 가능성과 큰 잠재력을 강조합니다.
Step-pool systems are common bedforms in mountain streams and have been utilized in river restoration projects around the world. Step-pool units exhibit highly non-uniform hydraulic characteristics which have been reported to closely 10 interact with the morphological evolution and stability of step-pool features. However, detailed information of the threedimensional hydraulics for step-pool morphology has been scarce due to the difficulty of measurement. To fill in this knowledge gap, we established a hybrid model based on the technologies of Structure from Motion (SfM) and computational fluid dynamics (CFD). The model used 3D reconstructions of bed surfaces with an artificial step-pool unit built by natural stones at six flow rates as inputs for CFD simulations. The hybrid model succeeded in providing high-resolution visualization 15 of 3D flow structures for the step-pool unit. The results illustrate the segmentation of flow regimes below the step, i.e., the integral jump at the water surface, streaky wake vortexes near the bed, and high-speed jets in between. The highly non-uniform distribution of turbulence energy in the pool has been revealed and two energy dissipaters with comparable capacity are found to co-exist in the pool. Pool scour development under flow increase leads to the expansion of the jump and wake vortexes but this increase stops for the jump at high flows close to the critical condition for step-pool failure. The micro-bedforms as grain 20 clusters developed on the negative slope affect the local hydraulics significantly but this influence is suppressed at pool bottom. The drag forces on the step stones increase with discharge before the highest flow is used while the lift force has a larger magnitude and wider varying range. Our results highlight the feasibility and great potential of the hybrid model approach combining physical and numerical modeling in investigating the complex flow characteristics of step-pool morphology.
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1 Civil Enigneering Department, Lahijan Branch.Islamic Azad University.Lahijan.Iran
2 Department of Civil Engnieering, University of Qom,Qom,Iran
3 Civil Engineering Department, Lahijan Branch,Islamic Azad Univeristy,Lahijan,Iran
홍수와 그 위험을 통제해야 할 필요성은 누구에게도 숨겨져 있지 않습니다. 또한 이 현상으로 인해 다양한 경제, 사회 및 환경 문제가 영향을 받습니다. 홍수 제어 방법의 설계 및 최적 관리의 첫 번째 단계는 홍수 중 하천 거동을 올바르게 식별하는 것입니다.
홍수 경로 지정, 하상 및 하천 면적 결정 등과 같은 대부분의 하천 엔지니어링 프로젝트에서 하천 단면의 수리학적 매개변수의 평균값을 계산하는 것으로 충분합니다. 오늘날 유체 환경 연구에서 수치 및 분석 방법의 사용이 성장하고 발전했습니다.
신뢰할 수 있는 결과 생성으로 인해 물리적 모델에 대한 좋은 대안이 될 수 있었습니다. 오늘날 수치 모델의 급속한 발전과 컴퓨터 계산 속도의 증가로 인해 3D 수치 모델의 사용이 선호되며 또한 강의 속도 분포 및 전단 응력을 측정하는 데 시간이 많이 걸리고 비용이 많이 들기 때문에 결과 3D 수치 모델의 가치가 있을 것입니다.
한편, 본 연구에서는 복합단면에 대해 FLOW-3D 모델을 이용한 종합적인 수치연구가 이루어지지 않았음을 보여주고 있어 적절한 연구기반을 제공하고 있습니다.
따라서 본 연구의 혁신은 발산 및 수렴 범람원을 동반하는 비 각형 복합 단면에서 흐름의 상태 및 수리 성능에 대한 거칠기와 같은 매개 변수의 영향에 대한 수치 연구입니다.
수치해석 결과를 검증하기 위해 Younesi(2013) 연구를 이용하였습니다. 이 실험에서는 먼저 고정층이 있는 복합 프리즘 및 비 프리즘 단면의 수리 흐름을 조사한 다음 조건을 유지하면서 프리즘 및 비 프리즘 모드에서 퇴적물 이동 실험을 수행했습니다.
실험은 15미터 길이의 연구 채널에서 수행되었습니다. 이 운하는 초당 250리터의 시스템에서 재순환을 위해 제공될 수 있는 유속과 0.0088 000의 종경사를 가진 폭 400mm의 두 개의 대칭 범람원이 있는 합성 운하입니다. 범람원의 가장자리는 0.18미터와 같고 주요 운하의 너비는 0.4미터와 같습니다(그림 1).
본수로의 바닥과 벽을 거칠게 하기 위해 평균직경 0.65mm의 퇴적물을 사용하였으며, 각 단계에서 범람원의 벽과 바닥은 평균직경 0.65, 1.3, 1.78의 퇴적물로 거칠게 하였습다. (mm). 삼각형 오버플로는 운하 상류에서 운하로의 유입량을 측정하는 데 사용됩니다.
상대깊이 0.15와 0.25, 직경 14mm의 마이크로몰리나 실험과 상대깊이 0.35의 실험에서는 유속을 측정하기 위해 3차원 속도계(ADV)를 사용하였습니다. 수위는 0.1mm의 정확도로 깊이 게이지로 측정 되었습니다.
본 연구에서는 수면 프로파일의 수치적 모델을 검증하기 위해 실험 0.25-2에서 발산대의 시작, 중간 및 끝에서 세 단면의 평균 깊이 속도 분포 및 경계 전단 응력) -11.3-NP 및 0.25-2-5.7-NP 및 또한 각형 복합 단면의 0.25-2-2 P 테스트가 평가되었습니다.
각형 합성 단면의 P.20-2-2-P 테스트와 관련된 RMSE 및 NRMSE 지수 값 및 표 (2) 실험 11.3에서 RMSE 및 NRMSE 지수 값 -2-0.25-NP 및 -0.25. 2-5.7-NP가 제공됩니다. 실험 0.25-2-5.7-NP-11.3-2-0.25, NP 및 P.2.0-2-2-P의 평균 깊이 속도의 검증과 관련된 결과가 표시됩니다. 0.25-2-5.7-NP 실험에서 초, 중, 기말 NRMSE의 양은 각각 5.7, 11.8, 10.3%로 계산되었으며, 이는 초급이 우수, 중급이 양호, 최종 성적. 배치. 보시다시피, RMSE 값은 각각 0.026, 0.037 및 0.026으로 계산됩니다.
실험 11.3-2-0.25, NP에서 초급, 중급 및 최종 수준의 NRMSE 값은 각각 7, 11.2 및 15.4%로 계산되었으며, 이는 초급에서 우수 범주 및 우수 범주에서 중간 및 최종 수준. 가져 가다. 보시다시피, RMSE 값은 각각 0.032, 0.038, 0.04로 계산됩니다. 0.25-2-P 실험에서 NRMSE 값은 1.7%로 계산되어 우수 범주에 속한다. 보시다시피 RMSE 값도 0.004로 계산됩니다. 중간 깊이의 속도 분포와 관련하여 수치 모델은 실험실 결과에 적합하며 접합 영역에 작은 오류만 입력되었다고 말할 수 있습니다. 이는 2차 전지의 이동 결과로 간주될 수 있습니다. 모서리를 향해. 결론: 본 연구에서는 3차원 유동 해석이 가능한 Flow 3D 소프트웨어를 사용하여 각형 및 비각형 단면이 복합된 수로의 유동 패턴을 조사했습니다. 3개의 다른 상대 거칠기(1, 2 및 2.74)와 3개의 상대 깊이(0.15, 0.25 및 0.35) 및 5.7 및 11.3도의 발산 각도에 대해 속도의 세로 성분 변화, 평균 깊이 속도 분포, 경계 범람원에 의해 전달되는 유속뿐만 아니라 전단 응력 분포를 조사했습니다.
결과는 수로를 따라 범람원의 폭이 증가함에 따라 유속량이 감소함을 보여주었다. 또한 조도가 유동패턴에 미치는 영향에 대한 연구는 일반적으로 벽의 거칠기에 따라 모든 구간에서 유속량이 감소하는 것으로 나타났으며, 또한 본관과 범람원의 교차점에서의 유동패턴은 벽의 거칠기 영향을 더 많이 받는 것으로 나타났습니다. 결과는 또한 상대 깊이가 증가하거나 상대 거칠기가 감소함에 따라 주 수로와 범람원 사이의 속도 구배가 감소함을 보여주었습니다.
Intrpduction: The need to control floods and their dangers is not hidden from anyone. In addition, a wide range of economic, social and environmental issues are affected by this phenomenon. The first step in the design and optimal management of flood control methods is the correct identification of river behavior during floods. In most river engineering projects such as flood routing, determining the bed and river area, etc., calculating the average values of hydraulic parameters of the river section is sufficient. Today, the use of numerical and analytical methods in the study of fluid environment have grown and developed. Due to the production of reliable results, they have been able to be a good alternative to physical models. Today, with the rapid development of numerical models and increasing the speed of computer calculations, the use of 3D numerical models is preferred and also due to the fact that measuring the velocity distribution and shear stress in rivers is very time consuming and expensive, the results of 3D numerical models It will be valuable. On the other hand, the present studies show that comprehensive numerical research using FLOW-3D model has not been performed on composite sections, so a suitable ground for research is provided. Therefore, the innovation of the present study is the numerical study of the effects of parameters such as roughness on the status and hydraulic performance of the flow in non-prismatic composite sections, which are accompanied by divergent and convergent floodplains, which have received less attention numerically.
Methodology: Younesi (2013) research has been used to validate the results of numerical simulation. In these experiments, first the hydraulic flow in composite prismatic and non-prismatic sections with fixed bed was examined and then, while maintaining the conditions, sediment transfer experiments were performed in prismatic and non-prismatic mode. The experiments were performed in a research channel 15 meters long. This canal is a composite canal with two symmetrical floodplains with a width of 400 mm with a flow rate that can be provided for recirculation in the system of 250 liters per second and a longitudinal slope of 0.0088 000. The depth of the main canal to the edge of the floodplain is equal to 0.18 meters and the width of the main canal is equal to 0.4 meters (Figure 1). In order to roughen the bed and walls of the main canal, sediments with an average diameter of 0.65 mm have been used and at each stage, the walls and bed of floodplains have been roughened by sediments with an average diameter of 0.65, 1.3 and 1.78 (mm). A triangular overflow is used to measure the inflow to the canal, upstream of the canal. In order to measure the flow velocity in experiments with relative depth of 0.15 and 0.25, a micromolina with a diameter of 14 mm and in experiments with relative depth of 0.35, a three-dimensional speedometer (ADV) was used. The water level was also taken by depth gauges with an accuracy of 0.1 mm. Result and Diccussion: In the present study, in order to validate the numerical model of water surface profile, average depth velocity distribution and boundary shear stress in the three sections at the beginning, middle and end of the divergence zone) in experiments 0.25-2-11.3-NP and 0.25-2-5.7-NP and Also, the 0.25-2-2 P test of the prismatic composite section has been evaluated. In Table (1) the values of RMSE and NRMSE indices related to the P.20-2-2-P test of the prismatic composite section, and also in Table (2) the values of the RMSE and NRMSE indices in the experiments 11.3-2-0.25-NP and -0.25. 2-5.7-NP is provided. The results related to the validation of the average depth velocity of the experiments 0.25-2-5.7- NP-11.3-2-0.25, NP and P.2.0-2-2-P are shown. In 0.25-2-5.7-NP experiment, the amount of NRMSE in elementary, middle and final grades was calculated to be 5.7, 11.8 and 10.3%, respectively, which is in the excellent grade in the elementary grade and good in the middle and final grades. Placed. As can be seen, the RMSE values are calculated as 0.026, 0.037 and 0.026, respectively. In the experiment 11.3-2-0.25, NP, the NRMSE values in the primary, middle and final levels were calculated as 7, 11.2 and 15.4%, respectively, which are in the excellent category in the primary level and in the good category in the middle and final levels. Take. As can be seen, the RMSE values are calculated as 0.032, 0.038 and 0.04, respectively. In the 0.25-2-P experiment, the NRMSE value was calculated to be 1.7%, which is in the excellent category. As can be seen, the RMSE value is also calculated to be 0.004. Regarding the medium-depth velocity distribution, it can be said that the numerical model has an acceptable compliance with the laboratory results and only a small error has been entered in the junction area, which can be considered as a result of the movement of secondary cells towards the corners. Conclusion: in this research The flow pattern in waterways with composite prismatic and non-prismatic sections was investigated using Flow 3D software that is capable of three-dimensional flow analysis. For three different relative roughnesses (1, 2 and 2.74) as well as three relative depths (0.15, 0.25 and 0.35) and divergence angles of 5.7 and 11.3 degrees, changes in the longitudinal component of velocity, The average depth velocity distribution, the boundary shear stress distribution as well as the flow rate transmitted by the floodplains were investigated. The results showed that with increasing the width of floodplains along the canal, the amount of velocity decreases. Also, the study of the effect of roughness on the flow pattern showed that in general, with wall roughness, the amount of velocity has decreased in all sections and also the flow pattern at the junction of the main canal and floodplain is more affected by wall roughness. The results also showed that with increasing relative depth or decreasing relative roughness, the velocity gradient between the main channel and floodplains decreases
하천횡단구조물이 하천설계기준(2009)대로 설계되었음에도 불구하고, 하류부에서 물받이공 및 바닥보호공의 피해가 발생하여, 구조물 본체에 대한 안전성이 현저하 게 낮아지고 있는 실정이다. 하천설계기준이 상류부의 수리특성을 반영하였다고 하나 하류부의 수리특성인 유속의 변동 성분 또는 압력의 변동성분까지 고려하고 있지는 않다. 현재 많은 선행연구에서 이러한 난류적 특성이 구조물에 미치는 영 향에 대해 제시하고 있는 실정이며, 국내 하천에서의 피해 또한 이와 관련이 있다 고 판단된다. 이에 본 연구에서는 난류성분 특히 압력의 변동성분이 물받이공과 바닥보호공에 미치는 영향을 정량적으로 분석하여, 하천 횡단구조물의 치수 안전 성 증대에 기여하고자 한다. 물받이공과 바닥보호공에 미치는 압력의 변동성분 (pressure fluctuation) 영향을 분석하기 위해 크게 3가지로 연구내용을 분류하였 다. 첫 번째는 압력의 변동으로 순간적인 음압구배(adversed pressure gradient) 가 발생할 경우 바닥보호공의 사석 및 블록이 이탈하는 것이다. 이를 확인하기 위 해 정밀한 압력 측정장치를 통해 압력변이를 측정하여, 사석의 이탈 가능성을 검 토할 것이며, 최종적으로 이탈에 대한 한계조건을 도출할 것이다. 두 번째는 압력 의 변동이 물받이공의 진동을 유발시켜 이를 지지하고 있는 지반에 다짐효과를 가 져와 물받이공과 지반사이에 공극이 발생하는 경우이다. 이러한 공극으로 물받이 공은 자중 및 물의 압력을 받게 되어, 결국 휨에 의한 파괴가 발생할 가능성이 있 게 된다. 본 연구에서는 실험을 통하여 압력의 변동과 물받이공의 진동을 동시에 측정하여, 진동이 발생하지 않을 최소 두께를 제시할 것이다. 세 번째는 압력변이 로 인한 물받이공의 진동이 피로파괴로 연결되는 경우이다. 이 현상 또한 수리실 험을 통해 압력변이-피로파괴의 관계를 정량적으로 분석하여, 한계 조건을 제시할 것이다. 본 연구는 국내 보 및 낙차공에서 발생하는 다양한 Jet의 특성을 수리실 험으로 재현해야 하며, 이를 위해 평면 Jet 분사기(plane Jet injector)를 고안/ 제작하여, 효율적인 수리실험을 수행할 것이다. 또한 3차원 수치해석을 통해 실제 스케일에 적용함으로써 연구결과의 활용도 및 적용성을 높이고자 한다.
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해저 지반에 설치되는 인공어초는 유속 및 수심이 동일한 경우라도 지반 조건에 따라 세굴 패턴이 크게 차이나는 경우가 있다. 따라서 본 연구에서는 모래, 실트 및 점토 등과 같이 다양한 해저 지반에 설치하는 인공어초의 지반공학적 안정성을 평가하고자 Flow-3D를 이용하여 세굴 해석을 수행하였다. 수치해석 결과 지반 입경이 작을수록 인공어초 주변에서 발생하는 세굴량이 커지며, 평형상태에 도달하는 시간이 더 오래 걸리는 결과를 보였다. 반면 입경이 커질수록 세굴량이 작아지며, 세굴된 지반 입자가 인공어초 후면부에 퇴적되는 결과를 보였다. 또한 최대 세굴심도와 입경은 비선형적인 관계를 나타내었다. 특히 세립토에서 최대 세굴심도가 크게 증가하였다.
Artificial reef-installed seabeds may have significantly different scouring patterns depending on the ground conditions, such as the soil particle size, even though the flow velocity and water depth are similar. In this study, the scour characteristics of the ground were determined using Flow-3D to evaluate the geotechnical stability of artificial reefs installed on various seabeds, such as sand, silt, and clay. The analysis results indicated that the smaller the particle size of the soil, the larger the amount of scour that occurs around the artificial reef and the longer it takes to reach an equilibrium state. However, eroded soil particles were deposited on the rear part of the artificial reef as the soil particle size increased. The maximum scour depth and average particle size showed a non-linear relationship. In particular, the maximum scour depth increased significantly in fine-grained soils.
Maryam Bagheria, Seyed M. Ali Zomorodianb, Masih Zolghadrc, H. MD. Azamathulla d,* and C. Venkata Siva Rama Prasade a Hydraulic Structures, Department of Water Engineering, Shiraz University, Shiraz, Iran b Department of Water Engineering, College of Agriculture, Shiraz University, Shiraz, Iran c Department of Water Sciences Engineering, College of Agriculture, Jahrom University, Jahrom, Iran dCivil & Environmental Engineering, The University of the West Indies, St. Augustine Campus, Port of Spain, Trinidad eDepartment of Civil Engineering, St. Peters Engineering College, Hyderabad, India *Corresponding author. E-mail: firstname.lastname@example.org
Flow separation at the upstream side of the lateral turnouts (intakes) is a critical issue causing eddy currents at the turn-out entrance. It reduces the effective width of flow, turn-out capacity and efficiency.
Therefore, it is essential to identify the dimensions of the separation zone and propose remedies to reduce its dimensions. Installation of 7 types of roughening elements at the turn-out entrance and 3 different bed level inverts, with 4 different discharges (total of 84 experiments) were examined in this study as a method to reduce the dimensions of the separation zone.
Additionally, a 3-D Computational Fluid Dynamic (CFD) model was utilized to evaluate the flow pattern and dimensions of the separation zone. Results showed that enhancing the roughness coefficient can reduce the separation zone dimensions up to 38% while the drop implementation effect can scale down this area differently based on the roughness coefficient used. Combining both methods can reduce the separation zone dimensions up to 63%.
측면 분기기(흡입구)의 상류 측에서 흐름 분리는 분기기 입구에서 와류를 일으키는 중요한 문제입니다. 이는 흐름의 유효 폭, 턴아웃 용량 및 효율성을 감소시킵니다. 따라서 분리지대의 크기를 파악하고 크기를 줄이기 위한 방안을 제시하는 것이 필수적이다.
이 연구에서는 분리 구역의 치수를 줄이기 위한 방법으로 4가지 다른 배출(총 84개 실험)과 함께 7가지 유형의 조면화 요소를 출구 입구에 설치하고 3가지 서로 다른 베드 레벨 반전 장치를 조사했습니다.
또한 3D CFD(Computational Fluid Dynamics) 모델을 사용하여 분리 영역의 흐름 패턴과 치수를 평가했습니다. 결과는 거칠기 계수를 향상시키면 분리 영역 치수를 최대 38%까지 줄일 수 있는 반면 드롭 구현 효과는 사용된 거칠기 계수를 기반으로 이 영역을 다르게 축소할 수 있음을 보여주었습니다.
두 가지 방법을 결합하면 분리 영역 치수를 최대 63%까지 줄일 수 있습니다.
discharge ratio, flow separation zone, intake, three dimensional simulation
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The Palmer-Bowlus flume was developed in 1936, as an adaptation of the Venturi flume for the use in sewer systems, due to the difficulty in modifying the pipe invert. There are commercially available single-body Palmer-Bowlus flume with their respective discharge curves, which increase the cost of sewer projects. Based on the physical model of the Palmer-Bowlus flume (Torres & Vásquez, 2010), the aim of this research was to carry out the three-dimensional numerical modeling of these flow meters, considering four pipe diameters: 160 mm, 200 mm, 250 mm and 400 mm; the selected diameters are the most used ones, according to the information provided by the Empresa Pública Metropolitana de Agua Potable y Saneamiento de Quito (EPMAPS). The discharge curves were calibrated and validated using the FLOW-3D program. Meshing had a great influence on the quality results and duration of the numerical simulation; in contrast, the roughness and turbulence models (RNG y k-e) had little influence. The discharge curves obtained in the numerical modeling have good approximation to those obtained in the physical model.
Palmer-Bowlus 수로는 1936년에 하수도 시스템에 사용하기 위해 Venturi 수로를 개조한 것으로 파이프 인버트를 수정하는 것이 어렵기 때문에 개발되었습니다. 각각의 배출 곡선이 있는 시판되는 단일 몸체 Palmer-Bowlus 수로가 있으며, 이는 하수도 프로젝트 비용을 증가시킵니다.
Palmer-Bowlus 수로의 물리적 모델을 기반으로(Torres & Vásquez, 2010), 이 연구의 목적은 160mm, 200mm, 4개의 파이프 직경을 고려하여 이러한 유량계의 3차원 수치 모델링을 수행하는 것이었습니다. 250mm 및 400mm; Empresa Pública Metropolitana de Agua Potable y Sanaeamiento de Quito(EPMAPS)에서 제공한 정보에 따르면 선택한 지름이 가장 많이 사용되는 지름입니다.
방전 곡선은 FLOW-3D 프로그램을 사용하여 보정 및 검증되었습니다. 메싱은 수치 시뮬레이션의 품질 결과와 기간에 큰 영향을 미쳤습니다. 대조적으로, 거칠기 및 난류 모델(RNG y k-e)은 거의 영향을 미치지 않았습니다. 수치 모델링에서 얻은 방전 곡선은 물리적 모델에서 얻은 것과 유사합니다.
Aulestia, C. (2017). Modelación numérica en tres dimensiones de flujo en las compuertas de la captación del Proyecto Toachi – Pilatón aplicando dinámica de fluidos computacional (CFD). [Tesis Maestría]. Quito, Ecuador: Escuela Politécnica Nacional. Casa, E. (2016). Modelación numérica del flujo rasante en una rápida escalonada aplicando la dinámica de fluidos computacional (CFD) Programa FLOW-3D. [Tesis maestría]. Quito, Ecuador: Escuela Politécnica Nacional. Chow, V. T. (2004). Hidráulica de canales abiertos (Primera ed.). (J. Saldarriaga, Trad.) Santafé de Bogotá, Colombia: McGrawHill. Domínguez, F. (1999). Hidráulica (Sexta Edición ed.). Santiango de Chile, Chile: Editorial Universitaria. Fernández, J. (2012). Introducción a la dinámica de fluidos computacional (CFD) por el método de volúmenes finitos. Barcelona: Editorial Reverté, S.A. Flow Science, Inc. (2016). Flow-3D v11.2 Documentation. Flow Science, Inc. Santa Fe: Flow Science. Ludwig, J., & Ludwig, R. (1951). Design of Palmer-Bowlus Flumes. Sewafe and Insdustrial Wastes, 23(9), 1096-1107. Obtenido de https://www.jstor.org/stable/25031687 Recasens, J. (2014). Modelación tridimensional del glujo de entrada en un sumidero. Barcelona: UPC BARCELONATECH. Sotelo, G. (1997). Hidráulica General Vol. 1. México D.F.: LIMUSA S.A. Torres, C., & Vásquez, E. (2010). Análisis de medidores de caudal para flujo subcrítico en sistemas de alcantarillado. [Tesis ingeniería]. Quito, Ecuador: Escuela Politécnica Nacional. Versteeg, H. K., & Malalasekera, W. (1995). An Introduction to computational fluid dynamics – The finite volume method. New York: John Wiley & Sons.
레이저 분말 베드 퓨전(L-PBF) 적층 제조(AM)는 우수한 기계적 특성으로 그물 모양에 가까운 복잡한 부품을 생산할 수 있습니다. 그러나 빌드 실패 및 다공성과 같은 결함으로 이어지는 원치 않는 잔류 응력 및 왜곡이 L-PBF의 광범위한 적용을 방해하고 있습니다.
L-PBF의 잠재력을 최대한 실현하기 위해 잔류 변형, 용융 풀 및 다공성 형성을 예측하는 다중 규모 모델링 방법론이 개발되었습니다. L-PBF의 잔류 변형 및 응력을 부품 규모에서 예측하기 위해 고유 변형 방법을 기반으로 하는 다중 규모 프로세스 모델링 프레임워크가 제안됩니다.
고유한 변형 벡터는 마이크로 스케일에서 충실도가 높은 상세한 다층 프로세스 시뮬레이션에서 추출됩니다. 균일하지만 이방성인 변형은 잔류 왜곡 및 응력을 예측하기 위해 준 정적 평형 유한 요소 분석(FEA)에서 레이어별로 L-PBF 부품에 적용됩니다.
부품 규모에서의 잔류 변형 및 응력 예측 외에도 분말 규모의 다중물리 모델링을 수행하여 공정 매개변수, 예열 온도 및 스패터링 입자에 의해 유도된 용융 풀 변동 및 결함 형성을 연구합니다. 이러한 요인과 관련된 용융 풀 역학 및 다공성 형성 메커니즘은 시뮬레이션 및 실험을 통해 밝혀졌습니다.
제안된 부품 규모 잔류 응력 및 왜곡 모델을 기반으로 경로 계획 방법은 큰 잔류 변형 및 건물 파손을 방지하기 위해 주어진 형상에 대한 레이저 스캐닝 경로를 조정하기 위해 개발되었습니다.
연속 및 아일랜드 스캐닝 전략을 위한 기울기 기반 경로 계획이 공식화되고 공식화된 컴플라이언스 및 스트레스 최소화 문제에 대한 전체 감도 분석이 수행됩니다. 이 제안된 경로 계획 방법의 타당성과 효율성은 AconityONE L-PBF 시스템을 사용하여 실험적으로 입증되었습니다.
또한 기계 학습을 활용한 데이터 기반 프레임워크를 개발하여 L-PBF에 대한 부품 규모의 열 이력을 예측합니다. 본 연구에서는 실시간 열 이력 예측을 위해 CNN(Convolutional Neural Network)과 RNN(Recurrent Neural Network)을 포함하는 순차적 기계 학습 모델을 제안합니다.
유한 요소 해석과 비교하여 100배의 예측 속도 향상이 달성되어 실제 제작 프로세스보다 빠른 예측이 가능하고 실시간 온도 프로파일을 사용할 수 있습니다.
Laser powder bed fusion (L-PBF) additive manufacturing (AM) is capable of producing complex parts near net shape with good mechanical properties. However, undesired residual stress and distortion that lead to build failure and defects such as porosity are preventing broader applications of L-PBF. To realize the full potential of L-PBF, a multiscale modeling methodology is developed to predict residual deformation, melt pool, and porosity formation. To predict the residual deformation and stress in L-PBF at part-scale, a multiscale process modeling framework based on inherent strain method is proposed.
Inherent strain vectors are extracted from detailed multi-layer process simulation with high fidelity at micro-scale. Uniform but anisotropic strains are then applied to L-PBF part in a layer-by-layer fashion in a quasi-static equilibrium finite element analysis (FEA) to predict residual distortion and stress. Besides residual distortion and stress prediction at part scale, multiphysics modeling at powder scale is performed to study the melt pool variation and defect formation induced by process parameters, preheating temperature and spattering particles. Melt pool dynamics and porosity formation mechanisms associated with these factors are revealed through simulation and experiments.
Based on the proposed part-scale residual stress and distortion model, path planning method is developed to tailor the laser scanning path for a given geometry to prevent large residual deformation and building failures. Gradient based path planning for continuous and island scanning strategy is formulated and full sensitivity analysis for the formulated compliance- and stress-minimization problem is performed.
The feasibility and effectiveness of this proposed path planning method is demonstrated experimentally using the AconityONE L-PBF system. In addition, a data-driven framework utilizing machine learning is developed to predict the thermal history at part-scale for L-PBF.
In this work, a sequential machine learning model including convolutional neural network (CNN) and recurrent neural network (RNN), long shortterm memory unit, is proposed for real-time thermal history prediction. A 100x prediction speed improvement is achieved compared to the finite element analysis which makes the prediction faster than real fabrication process and real-time temperature profile available.
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본 연구에서는 LW(Labyrinth Weir)와 PKW(Piano Key Weir)가 결합된 T자형 웨어(TSW)라는 새로운 비선형 웨어를 도입하여 수압 성능을 비교하였다.
PKW. 입구 키, 출구 키 또는 두 키 모두에서 수직 벽의 존재에 따라 TSW 위어는 각각 A, B 또는 C 유형 웨어로 분류되었습니다. 다른 TSW 사례의 흐름 패턴을 분석하고 배출 계수 곡선을 제공했습니다. 또한 테스트된 둑의 유체역학을 정확하게 연구하기 위해 FLOW-3D 소프트웨어를 사용하여 3D 수치 시뮬레이션을 수행했습니다.
결과는 출구 키(C-TSW 유형)의 상류에 수직 벽을 삽입하는 것이 PKW의 유압 성능에 미미한 영향을 미치는 것으로 나타났습니다. B-TSW의 토출계수는 PKW 대비 최대 16% 증가하였으며, Ht/p 0.45까지 수직벽의 성능향상 효과 증가 B-TSW는 유지되었습니다.
실험적 및 수치적 실험을 통해 가장 높은 방전 용량을 갖는 B-TSW에서 수직벽의 최적 높이비(Pd/P)는 0.4로 결정되었다.
In the present study, a new nonlinear weir called the T-shaped weir (TSW), which is a combination of the labyrinth weir (LW) and the piano key weir (PKW), was introduced, and its hydraulic performance was compared with the PKW. Based on the presence of the vertical walls at the inlet key, outlet key, or both keys, the TSW weirs were classified as type A, B, or C weirs, respectively. The flow pattern of different TSW cases was analyzed, and the discharge coefficient curves were provided. Furthermore, to accurately study the hydrodynamics of the tested weirs, 3D numerical simulations were performed using the FLOW-3D software. The results showed that inserting a vertical wall at the upstream of the outlet keys (C-TSW type) has a negligible effect on the hydraulic performance of the PKW. A maximum increase of 16% occurred in the discharge coefficient of the B-TSW in comparison to the PKW, and up to a head to height ratio (Ht/p) of 0.45, the effect of the vertical wall on increasing the performance of the B-TSW was maintained. Based on the experimental and numerical tests, the optimal height ratio of the vertical wall (Pd/P) in B-TSW with highest discharge capacity was determined to be equal to 0.4.
Bremer F. L. & Oertel M. 2017 Numerical investigation of wall thickness influence on Piano key Weir discharge coefficients: A preliminary study. In Labyrinth and Piano Key Weirs III – PKW 2017. CRC Press, London, UK, pp. 101–108.
Cicero G. M., Delisle J. R., Lefebvre V. & Vermeulen J. 2013 Experimental and Numerical Study of the Hydraulic Performance of A Trapezoidal PKW. In Labyrinths and Piano Key Weirs PKW 2013. CRC Press, Boca Raton, FL, pp. 265–272.
Lefebvre V., Vermeulen J. & Blancher B. 2013 Influence of Geometrical Parameters on PK-Weirs Discharge with 3D Numerical Analysis. In: Labyrinth and Piano key Weirs II – PKW 2013. CRC Press, London, pp. 49–56.
Lempérière F. & Ouamane A. 2003 The piano keys weir: a new cost-effective solution for spillways. International Journal on Hydropower & Dams 10 (5), 144–149.
Machiels O., Erpicum S., Archambeau P., Dewals B. J. & Pirotton M. 2011 Influence of piano key weir height on its discharge capacity. In Proc. Int. Conf. Labyrinth and Piano Key Weirs Liège B, pp. 59–66.
Pralong J., Vermeulen J., Blancher B., Laugier F., Erpicum S., Machiels O., Pirotton M., Boillat J.-L., Leite Ribeiro M. & Schleiss A. 2011a A naming convention for the Piano Key Weirs geometrical parameters. In Labyrinth and Piano key Weirs – PKW 2011. CRC Press, London, pp. 271–278.
Pralong J., Montarros F., Blancher B. & Laugier F. 2011b A sensitivity analysis of Piano Key Weirs geometrical parameters based on 3D numerical modelling. In Labyrinth and Piano key Weirs – PKW 2011. CRC Press, London, pp. 133–139.
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Optimization of Solar CCHP Systems with Collector Enhanced by Porous Media and Nanofluid
Navid Tonekaboni,1Mahdi Feizbahr,2 Nima Tonekaboni,1Guang-Jun Jiang,3,4 and Hong-Xia Chen3,4
태양열 집열기의 낮은 효율은 CCHP(Solar Combined Cooling, Heating, and Power) 사이클의 문제점 중 하나로 언급될 수 있습니다. 태양계를 개선하기 위해 나노유체와 다공성 매체가 태양열 집열기에 사용됩니다.
다공성 매질과 나노입자를 사용하는 장점 중 하나는 동일한 조건에서 더 많은 에너지를 흡수할 수 있다는 것입니다. 이 연구에서는 평균 일사량이 1b인 따뜻하고 건조한 지역의 600 m2 건물의 전기, 냉방 및 난방을 생성하기 위해 다공성 매질과 나노유체를 사용하여 태양열 냉난방 복합 발전(SCCHP) 시스템을 최적화했습니다.
본 논문에서는 침전물이 형성되지 않는 lb = 820 w/m2(이란) 정도까지 다공성 물질에서 나노유체의 최적량을 계산하였다. 이 연구에서 태양열 집열기는 구리 다공성 매체(95% 다공성)와 CuO 및 Al2O3 나노 유체로 향상되었습니다.
나노유체의 0.1%-0.6%가 작동 유체로 물에 추가되었습니다. 나노유체의 0.5%가 태양열 집열기 및 SCCHP 시스템에서 가장 높은 에너지 및 엑서지 효율 향상으로 이어지는 것으로 밝혀졌습니다.
본 연구에서 포물선형 집열기(PTC)의 최대 에너지 및 엑서지 효율은 각각 74.19% 및 32.6%입니다. 그림 1은 태양 CCHP의 주기를 정확하게 설명하기 위한 그래픽 초록으로 언급될 수 있습니다.
The low efficiency of solar collectors can be mentioned as one of the problems in solar combined cooling, heating, and power (CCHP) cycles. For improving solar systems, nanofluid and porous media are used in solar collectors. One of the advantages of using porous media and nanoparticles is to absorb more energy under the same conditions. In this research, a solar combined cooling, heating, and power (SCCHP) system has been optimized by porous media and nanofluid for generating electricity, cooling, and heating of a 600 m2 building in a warm and dry region with average solar radiation of Ib = 820 w/m2 in Iran. In this paper, the optimal amount of nanofluid in porous materials has been calculated to the extent that no sediment is formed. In this study, solar collectors were enhanced with copper porous media (95% porosity) and CuO and Al2O3 nanofluids. 0.1%–0.6% of the nanofluids were added to water as working fluids; it is found that 0.5% of the nanofluids lead to the highest energy and exergy efficiency enhancement in solar collectors and SCCHP systems. Maximum energy and exergy efficiency of parabolic thermal collector (PTC) riches in this study are 74.19% and 32.6%, respectively. Figure 1 can be mentioned as a graphical abstract for accurately describing the cycle of solar CCHP.
Due to the increase in energy consumption, the use of clean energy is one of the important goals of human societies. In the last four decades, the use of cogeneration cycles has increased significantly due to high efficiency. Among clean energy, the use of solar energy has become more popular due to its greater availability . Low efficiency of energy production, transmission, and distribution system makes a new system to generate simultaneously electricity, heating, and cooling as an essential solution to be widely used. The low efficiency of the electricity generation, transmission, and distribution system makes the CCHP system a basic solution to eliminate waste of energy. CCHP system consists of a prime mover (PM), a power generator, a heat recovery system (produce extra heating/cooling/power), and thermal energy storage (TES) . Solar combined cooling, heating, and power (SCCHP) has been started three decades ago. SCCHP is a system that receives its propulsive force from solar energy; in this cycle, solar collectors play the role of propulsive for generating power in this system .
Increasing the rate of energy consumption in the whole world because of the low efficiency of energy production, transmission, and distribution system causes a new cogeneration system to generate electricity, heating, and cooling energy as an essential solution to be widely used. Building energy utilization fundamentally includes power required for lighting, home electrical appliances, warming and cooling of building inside, and boiling water. Domestic usage contributes to an average of 35% of the world’s total energy consumption .
Due to the availability of solar energy in all areas, solar collectors can be used to obtain the propulsive power required for the CCHP cycle. Solar energy is the main source of energy in renewable applications. For selecting a suitable area to use solar collectors, annual sunshine hours, the number of sunny days, minus temperature and frosty days, and the windy status of the region are essentially considered . Iran, with an average of more than 300 sunny days, is one of the suitable countries to use solar energy. Due to the fact that most of the solar radiation is in the southern regions of Iran, also the concentration of cities is low in these areas, and transmission lines are far apart, one of the best options is to use CCHP cycles based on solar collectors . One of the major problems of solar collectors is their low efficiency . Low efficiency increases the area of collectors, which increases the initial cost of solar systems and of course increases the initial payback period. To increase the efficiency of solar collectors and improve their performance, porous materials and nanofluids are used to increase their workability.
There are two ways to increase the efficiency of solar collectors and mechanical and fluid improvement. In the first method, using porous materials or helical filaments inside the collector pipes causes turbulence of the flow and increases heat transfer. In the second method, using nanofluids or salt and other materials increases the heat transfer of water. The use of porous materials has grown up immensely over the past twenty years. Porous materials, especially copper porous foam, are widely used in solar collectors. Due to the high contact surface area, porous media are appropriate candidates for solar collectors . A number of researchers investigated Solar System performance in accordance with energy and exergy analyses. Zhai et al.  reviewed the performance of a small solar-powered system in which the energy efficiency was 44.7% and the electrical efficiency was 16.9%.
Abbasi et al.  proposed an innovative multiobjective optimization to optimize the design of a cogeneration system. Results showed the CCHP system based on an internal diesel combustion engine was the applicable alternative at all regions with different climates. The diesel engine can supply the electrical requirement of 31.0% and heating demand of 3.8% for building.
Jiang et al.  combined the experiment and simulation together to analyze the performance of a cogeneration system. Moreover, some research focused on CCHP systems using solar energy. It integrated sustainable and renewable technologies in the CCHP, like PV, Stirling engine, and parabolic trough collector (PTC) [2, 12–15].
Wang et al.  optimized a cogeneration solar cooling system with a Rankine cycle and ejector to reach the maximum total system efficiency of 55.9%. Jing et al. analyzed a big-scale building with the SCCHP system and auxiliary heaters to produced electrical, cooling, and heating power. The maximum energy efficiency reported in their work is 46.6% . Various optimization methods have been used to improve the cogeneration system, minimum system size, and performance, such as genetic algorithm [18, 19].
Hirasawa et al.  investigated the effect of using porous media to reduce thermal waste in solar systems. They used the high-porosity metal foam on top of the flat plate solar collector and observed that thermal waste decreased by 7% due to natural heat transfer. Many researchers study the efficiency improvement of the solar collector by changing the collector’s shapes or working fluids. However, the most effective method is the use of nanofluids in the solar collector as working fluid . In the experimental study done by Jouybari et al. , the efficiency enhancement up to 8.1% was achieved by adding nanofluid in a flat plate collector. In this research, by adding porous materials to the solar collector, collector efficiency increased up to 92% in a low flow regime. Subramani et al.  analyzed the thermal performance of the parabolic solar collector with Al2O3 nanofluid. They conducted their experiments with Reynolds number range 2401 to 7202 and mass flow rate 0.0083 to 0.05 kg/s. The maximum efficiency improvement in this experiment was 56% at 0.05 kg/s mass flow rate.
Shojaeizadeh et al.  investigated the analysis of the second law of thermodynamic on the flat plate solar collector using Al2O3/water nanofluid. Their research showed that energy efficiency rose up to 1.9% and the exergy efficiency increased by a maximum of 0.72% compared to pure water. Tiwari et al.  researched on the thermal performance of solar ﬂat plate collectors for working fluid water with different nanoﬂuids. The result showed that using 1.5% (optimum) particle volume fraction of Al2O3 nanoﬂuid as an absorbing medium causes the thermal efﬁciency to enhance up to 31.64%.
The effect of porous media and nanofluids on solar collectors has already been investigated in the literature but the SCCHP system with a collector embedded by both porous media and nanofluid for enhancing the ratio of nanoparticle in nanofluid for preventing sedimentation was not discussed. In this research, the amount of energy and exergy of the solar CCHP cycles with parabolic solar collectors in both base and improved modes with a porous material (copper foam with 95% porosity) and nanofluid with different ratios of nanoparticles was calculated. In the first step, it is planned to design a CCHP system based on the required load, and, in the next step, it will analyze the energy and exergy of the system in a basic and optimize mode. In the optimize mode, enhanced solar collectors with porous material and nanofluid in different ratios (0.1%–0.7%) were used to optimize the ratio of nanofluids to prevent sedimentation.
2. Cycle Description
CCHP is one of the methods to enhance energy efficiency and reduce energy loss and costs. The SCCHP system used a solar collector as a prime mover of the cogeneration system and assisted the boiler to generate vapor for the turbine. Hot water flows from the expander to the absorption chiller in summer or to the radiator or fan coil in winter. Finally, before the hot water wants to flow back to the storage tank, it flows inside a heat exchanger for generating domestic hot water .
For designing of solar cogeneration system and its analysis, it is necessary to calculate the electrical, heating (heating load is the load required for the production of warm water and space heating), and cooling load required for the case study considered in a residential building with an area of 600 m2 in the warm region of Iran (Zahedan). In Table 1, the average of the required loads is shown for the different months of a year (average of electrical, heating, and cooling load calculated with CARRIER software).Table 1The average amount of electric charges, heating load, and cooling load used in the different months of the year in the city of Zahedan for a residential building with 600 m2.
According to Table 1, the maximum magnitude of heating, cooling, and electrical loads is used to calculate the cogeneration system. The maximum electric load is 96 kW, the maximum amount of heating load is 62 kW, and the maximum cooling load is 118 kW. Since the calculated loads are average, all loads increased up to 10% for the confidence coefficient. With the obtained values, the solar collector area and other cogeneration system components are calculated. The cogeneration cycle is capable of producing 105 kW electric power, 140 kW cooling capacity, and 100 kW heating power.
2.1. System Analysis Equations
An analysis is done by considering the following assumptions:(1)The system operates under steady-state conditions(2)The system is designed for the warm region of Iran (Zahedan) with average solar radiation Ib = 820 w/m2(3)The pressure drops in heat exchangers, separators, storage tanks, and pipes are ignored(4)The pressure drop is negligible in all processes and no expectable chemical reactions occurred in the processes(5)Potential, kinetic, and chemical exergy are not considered due to their insignificance(6)Pumps have been discontinued due to insignificance throughout the process(7)All components are assumed adiabatic
Schematic shape of the cogeneration cycle is shown in Figure 1 and all data are given in Table 2.
Figure 1Schematic shape of the cogeneration cycle.Table 2Temperature and humidity of different points of system.
Based on the first law of thermodynamic, energy analysis is based on the following steps.
First of all, the estimated solar radiation energy on collector has been calculated:where α is the heat transfer enhancement coefficient based on porous materials added to the collector’s pipes. The coefficient α is increased by the porosity percentage, the type of porous material (in this case, copper with a porosity percentage of 95), and the flow of fluid to the collector equation.
Collector efficiency is going to be calculated by the following equation :
Total energy received by the collector is given by 
In the last step based on thermodynamic second law, exergy efficiency has been calculated from the following equation and the above-mentioned calculated loads :
3. Porous Media
The porous medium that filled the test section is copper foam with a porosity of 95%. The foams are determined in Figure 2 and also detailed thermophysical parameters and dimensions are shown in Table 3.
Figure 2Copper foam with a porosity of 95%.Table 3Thermophysical parameters and dimensions of copper foam.
In solar collectors, copper porous materials are suitable for use at low temperatures and have an easier and faster manufacturing process than ceramic porous materials. Due to the high coefficient conductivity of copper, the use of copper metallic foam to increase heat transfer is certainly more efficient in solar collectors.
Porous media and nanofluid in solar collector’s pipes were simulated in FLOW-3D software using the finite-difference method . Nanoparticles Al2O3 and CUO are mostly used in solar collector enhancement. In this research, different concentrations of nanofluid are added to the parabolic solar collectors with porous materials (copper foam with porosity of 95%) to achieve maximum heat transfer in the porous materials before sedimentation. After analyzing PTC pipes with the nanofluid flow in FLOW-3D software, for energy and exergy efficiency analysis, Carrier software results were used as EES software input. Simulation PTC with porous media inside collector pipe and nanofluids sedimentation is shown in Figure 3.
Figure 3Simulation PTC pipes enhanced with copper foam and nanoparticles in FLOW-3D software.
3.1. Nano Fluid
In this research, copper and silver nanofluids (Al2O3, CuO) have been added with percentages of 0.1%–0.7% as the working fluids. The nanoparticle properties are given in Table 4. Also, system constant parameters are presented in Table 4, which are available as default input in the EES software.Table 4Properties of the nanoparticles .
System constant parameters for input in the software are shown in Table 5.Table 5System constant parameters.
The thermal properties of the nanofluid can be obtained from equations (18)–(21). The basic fluid properties are indicated by the index (bf) and the properties of the nanoparticle silver with the index (np).
The density of the mixture is shown in the following equation :where ρ is density and ϕ is the nanoparticles volume fraction.
The specific heat capacity is calculated from the following equation :
The thermal conductivity of the nanofluid is calculated from the following equation :
The parameter β is the ratio of the nanolayer thickness to the original particle radius and, usually, this parameter is taken equal to 0.1 for the calculated thermal conductivity of the nanofluids.
The mixture viscosity is calculated as follows :
In all equations, instead of water properties, working fluids with nanofluid are used. All of the above equations and parameters are entered in the EES software for calculating the energy and exergy of solar collectors and the SCCHP cycle. All calculation repeats for both nanofluids with different concentrations of nanofluid in the solar collector’s pipe.
4. Results and Discussion
In the present study, relations were written according to Wang et al.  and the system analysis was performed to ensure the correctness of the code. The energy and exergy charts are plotted based on the main values of the paper and are shown in Figures 4 and 5. The error rate in this simulation is 1.07%.
Figure 4Verification charts of energy analysis results.
Figure 5Verification charts of exergy analysis results.
We may also investigate the application of machine learning paradigms [31–41] and various hybrid, advanced optimization approaches that are enhanced in terms of exploration and intensification [42–55], and intelligent model studies [56–61] as well, for example, methods such as particle swarm optimizer (PSO) [60, 62], differential search (DS) , ant colony optimizer (ACO) [61, 64, 65], Harris hawks optimizer (HHO) , grey wolf optimizer (GWO) [53, 67], differential evolution (DE) [68, 69], and other fusion and boosted systems [41, 46, 48, 50, 54, 55, 70, 71].
At the first step, the collector is modified with porous copper foam material. 14 cases have been considered for the analysis of the SCCHP system (Table 6). It should be noted that the adding of porous media causes an additional pressure drop inside the collector [9, 22–26, 30, 72]. All fourteen cases use copper foam with a porosity of 95 percent. To simulate the effect of porous materials and nanofluids, the first solar PTC pipes have been simulated in the FLOW-3D software and then porous media (copper foam with porosity of 95%) and fluid flow with nanoparticles (AL2O3 and CUO) are generated in the software. After analyzing PTC pipes in FLOW-3D software, for analyzing energy and exergy efficiency, software outputs were used as EES software input for optimization ratio of sedimentation and calculating energy and exergy analyses.Table 6Collectors with different percentages of nanofluids and porous media.
In this research, an enhanced solar collector with both porous media and Nanofluid is investigated. In the present study, 0.1–0.5% CuO and Al2O3 concentration were added to the collector fully filled by porous media to achieve maximum energy and exergy efficiencies of solar CCHP systems. All steps of the investigation are shown in Table 6.
Energy and exergy analyses of parabolic solar collectors and SCCHP systems are shown in Figures 6 and 7.
Figure 6Energy and exergy efficiencies of the PTC with porous media and nanofluid.
Figure 7Energy and exergy efficiency of the SCCHP.
Results show that the highest energy and exergy efficiencies are 74.19% and 32.6%, respectively, that is achieved in Step 12 (parabolic collectors with filled porous media and 0.5% Al2O3). In the second step, the maximum energy efficiency of SCCHP systems with fourteen steps of simulation are shown in Figure 7.
In the second step, where 0.1, −0.6% of the nanofluids were added, it is found that 0.5% leads to the highest energy and exergy efficiency enhancement in solar collectors and SCCHP systems. Using concentrations more than 0.5% leads to sediment in the solar collector’s pipe and a decrease of porosity in the pipe . According to Figure 7, maximum energy and exergy efficiencies of SCCHP are achieved in Step 12. In this step energy efficiency is 54.49% and exergy efficiency is 18.29%. In steps 13 and 14, with increasing concentration of CUO and Al2O3 nanofluid solution in porous materials, decreasing of energy and exergy efficiency of PTC and SCCHP system at the same time happened. This decrease in efficiency is due to the formation of sediment in the porous material. Calculations and simulations have shown that porous materials more than 0.5% nanofluids inside the collector pipe cause sediment and disturb the porosity of porous materials and pressure drop and reduce the coefficient of performance of the cogeneration system. Most experience showed that CUO and AL2O3 nanofluids with less than 0.6% percent solution are used in the investigation on the solar collectors at low temperatures and discharges . One of the important points of this research is that the best ratio of nanofluids in the solar collector with a low temperature is 0.5% (AL2O3 and CUO); with this replacement, the cost of solar collectors and SCCHP cycle is reduced.
5. Conclusion and Future Directions
In the present study, ways for increasing the efficiency of solar collectors in order to enhance the efficiency of the SCCHP cycle are examined. The research is aimed at adding both porous materials and nanofluids for estimating the best ratio of nanofluid for enhanced solar collector and protecting sedimentation in porous media. By adding porous materials (copper foam with porosity of 95%) and 0.5% nanofluids together, high efficiency in solar parabolic collectors can be achieved. The novelty in this research is the addition of both nanofluids and porous materials and calculating the best ratio for preventing sedimentation and pressure drop in solar collector’s pipe. In this study, it was observed that, by adding 0.5% of AL2O3 nanofluid in working fluids, the energy efficiency of PTC rises to 74.19% and exergy efficiency is grown up to 32.6%. In SCCHP cycle, energy efficiency is 54.49% and exergy efficiency is 18.29%.
In this research, parabolic solar collectors fully filled by porous media (copper foam with a porosity of 95) are investigated. In the next step, parabolic solar collectors in the SCCHP cycle were simultaneously filled by porous media and different percentages of Al2O3 and CuO nanofluid. At this step, values of 0.1% to 0.6% of each nanofluid were added to the working fluid, and the efficiency of the energy and exergy of the collectors and the SCCHP cycle were determined. In this case, nanofluid and the porous media were used together in the solar collector and maximum efficiency achieved. 0.5% of both nanofluids were used to achieve the biggest efficiency enhancement.
In the present study, as expected, the highest efficiency is for the parabolic solar collector fully filled by porous material (copper foam with a porosity of 95%) and 0.5% Al2O3. Results of the present study are as follows:(1)The average enhancement of collectors’ efficiency using porous media and nanofluids is 28%.(2)Solutions with 0.1 to 0.5% of nanofluids (CuO and Al2O3) are used to prevent collectors from sediment occurrence in porous media.(3)Collector of solar cogeneration cycles that is enhanced by both porous media and nanofluid has higher efficiency, and the stability of output temperature is more as well.(4)By using 0.6% of the nanofluids in the enhanced parabolic solar collectors with copper porous materials, sedimentation occurs and makes a high-pressure drop in the solar collector’s pipe which causes decrease in energy efficiency.(5)Average enhancement of SCCHP cycle efficiency is enhanced by both porous media and nanofluid 13%.
Heat transfer augmentation coefficient
Solar collector area
Specific heat capacity of the nanofluid
Constant of air dilution
Thermal conductivity of the nanofluid
Thermal conductivity of the basic fluid
Viscosity of the nanofluid
Viscosity of the basic fluid
Collector energy receives
Auxiliary boiler heat
Screw expander work
Cooling load, in kilowatts
Heating load, in kilowatts
Solar radiation energy on collector, in Joule
Sanitary hot water load
Heat exchanger efficiency
Natural gas exergy
Steam mass flow rate
Hot water mass flow rate
Specific heat capacity of water
Power output form by the screw expander
Average ambient temperature
Density of the mixture.
Nanoparticles volume fraction
Ratio of the nanolayer thickness.
Combined cooling, heating, and power
Engineering equation solver.
For this study, data were generated by CARRIER software for the average electrical, heating, and cooling load of a residential building with 600 m2 in the city of Zahedan, Iran.
Conflicts of Interest
The authors declare that they have no conflicts of interest.
This work was partially supported by the National Natural Science Foundation of China under Contract no. 71761030 and Natural Science Foundation of Inner Mongolia under Contract no. 2019LH07003.
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A Computer Model to Assess Fire Hazards in Tunnels (FASlT)
David A. Charters, W. Alan Gray, Andrew C. McIntosh Charters is now with NHS Estates in Leeds (previously with AEA Consultancy Services), and Gray and Mclntosh are with the University of Leeds, England.
터널에서 화재 성장 움직임을 시뮬레이션하는 컴퓨터 모델이 설명되고 터널 시스템에 대한 간략한 개요가 표시됩니다. 질량 흐름, 속도, 연기 농도 및 열 전달을 예측하는 방법과 위험 출력 매개 변수 목록이 표시됩니다. 실험에 대한 모델의 유효성 검사와 향후 작업에 대한 가능한 방향도 제시됩니다.
최근 도로 및 철도 터널의 화재 안전에 대해 운송 업계와 여행자들 사이에서 많은 우려가 제기되고 있습니다.
1,2,3 터널에서 연소 생성물은 한 방향 또는 두 방향을 제외한 모든 방향으로 제한되어 매우 빠른 연기 이동과 생명에 대한 빠른 위협을 초래할 수 있습니다.
이 분야의 많은 초기 작업은 Thomas에 의해 수행되었습니다. 4,5 AEA Consultancy Services와 University of Leeds의 연료 및 에너지부는 현재 터널의 구멍으로 인한 위험을 예측하는 컴퓨터 모델을 개발 중입니다.
이 모델은 터널 내 설비의 위험과 화재 위험 수준, 화재 방지 시스템의 이점을 평가하는 데 도움이 됩니다.
유사한 ‘구역’ 화재 모델에서 Considine et al. 7은 유해 물질 운송을 포함하는 피트에 대한 모델을 개발했으며 Miclea 등은 터널 환기에 대한 화재의 영향을 평가하고 비상 환기를 논의하는 터널 환기 모델을 개발했으며 Laage 등은 터널 환기 모델을 개발했습니다.
9는 특히 광산 네트워크의 화재에 대한 모델을 개발했습니다. 다른 터널 화재 모델에서 Kumar et al.10 및 Jones et al.11은 터널 화재의 유체 흐름을 예측하기 위해 전산 유체 역학(CFD) 또는 ‘장’ 모델을 사용합니다.
AEA/Leeds University에서 개발 중인 코드는 터널의 화재 위험을 예측하기 위한 더 큰 모델의 일부가 되도록 의도되었습니다.
이 코드는 FASIT(Fire growth And Smoke movement In Tunnels) 모델이라고 합니다.12 FASIT는 구조가 모듈식이므로 화염, 연기, 부력 흐름, 열 전달 등에 대한 개선된 모델을 많은 수의 재작성 없이 통합할 수 있습니다.
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원추형 중앙 배플 수로는 개방 채널에서 임시 유량 측정을 위한 효과적인 솔루션을 제공합니다.
원추형 중앙 배플 수로는 원뿔 모양의 장애물 또는 열린 수로의 중심에서 수직으로 향하는 중앙 배플로 구성됩니다. 본 연구에서, 원추형 중앙 배플 수로를 사용하여 개방 채널에서 유량 측정을 위해 이전에 개발된 배출 예측 모델은 더 넓은 적용 범위를 커버하기 위해 직사각형 및 사다리꼴 채널에서 사용하기 위해 실험적으로 재 보정되었습니다.
제안된 보정 방정식은 FLOW-3D를 사용한 전산유체역학(CFD) 시뮬레이션 결과를 사용하여 확장된 범위의 흐름 및 기하학적 매개변수에 대해 검증되었습니다.
시뮬레이션 연구는 두 단계로 수행됩니다. 첫 번째 단계는 시뮬레이션의 수면 프로파일과 동일한 배출 및 흐름 조건에 대한 실험 흐름을 비교하여 설정한 정의된 시뮬레이션 문제의 검증입니다.
두 번째 단계는 무차원 방전 및 측면 경사(중1= 0중1=0, 0.50, 1.00 및 1.50). 80% 미만의 수중에서 방전 예측의 오류는 평균값이 거의 3%로 항상 10% 미만인 것으로 나타났습니다.
CFD 분석 결과에 따르면 보정된 배출 예측 모델의 사용은 수중 한계 80%까지 권장되었으며, 그 이상에서는 오차가 10% 이상인 것으로 나타났습니다.
Conical central baffle flumes present an effective solution for temporary flow measurements in open channels. A conical central baffle flume consists of a cone-shaped obstruction, or a central baffle, oriented vertically at the center of an open channel. In the present study, a previously developed discharge prediction model for flow measurements in open channels using the conical central baffle flumes has been experimentally recalibrated for use in rectangular and trapezoidal channels to cover a wider application range. The proposed calibration equation has been validated for an extended range of flow and geometrical parameters using the results of computational fluid dynamics (CFD) simulations using Flow-3D. The simulation studies are carried out in two steps. The first step is the validation of the defined simulation problem set up by comparing the water surface profiles of the simulation and experiment flows for the same discharge and flow conditions. The second step is the validation of the proposed discharge prediction model for the extended range (0–0.50) of the dimensionless discharge and side slopes (m1=0m1=0, 0.50, 1.00, and 1.50). It is found that for submergence less than 80%, the error in discharge prediction is always less than 10% with a mean value of nearly 3%. Based on the results of the CFD analysis, the use of the calibrated discharge prediction model has been recommended up to a submergence limit of 80%, beyond which the errors are found to be greater than 10%.
두 개의 부유체 사이에 간격이 있는 경사진 부유식 방파제(FB)에 대한 새로운 연구가 제안되었습니다. 구조물의 기울기는 파동 에너지 소산을 유발할 수 있습니다. 경사진 구조물의 문제는 파도가 넘친다는 것입니다. 이 문제를 해결하기 위해 두 플로터 사이의 간격을 고려합니다.
오버 토핑이 발생하면 마루를 통과하는 물이 두 플로터 사이의 틈으로 쏟아지며 결과적으로 파도 에너지가 감쇠됩니다. 체인 네트가 모델에 추가되고 전송 계수에 대한 영향이 연구됩니다. 또한, 구조물의 유체역학적 성능에 대한 자유도의 영향을 조사하기 위해 말뚝으로 고정된(1 자유도) 계류 라인으로 고정된(3도의 자유도) 두 가지 고정 시스템에서 자유 모델을 연구했습니다.
게다가, 실험은 5개의 다른 파도 주기와 4개의 다른 파도 높이를 가진 규칙파에서 수행됩니다. 실험 결과, 경사형 부유식 방파제가 직사각형 상자형보다 최대 15% 성능이 우수한 것으로 나타났다. 말뚝에 의해 고정된 FB에 대한 투과계수는 단파에서 케이블에 의해 고정된 FB보다 최대값으로 약 14% 낮고 장파에서 약 4-10% 더 높다. 흘수가 증가함에 따라 전송 계수는 감소하지만 건현은 허용 비율의 초과를 제한하기 위한 최소 요구 사항을 충족해야 합니다.
체인 그물이 있는 모델은 없는 모델에 비해 전달 계수가 최대 14% 감소하여 더 나은 성능을 나타냅니다. 실험 결과, 경사형 부유식 방파제가 직사각형 상자형보다 최대 15% 성능이 우수한 것으로 나타났다. 말뚝에 의해 고정된 FB에 대한 투과계수는 단파에서 케이블에 의해 고정된 FB보다 최대값으로 약 14% 낮고 장파에서 약 4-10% 더 높다. 흘수가 증가함에 따라 전송 계수는 감소하지만 건현은 허용 비율의 초과를 제한하기 위한 최소 요구 사항을 충족해야 합니다.
체인 그물이 있는 모델은 없는 모델에 비해 전달 계수가 최대 14% 감소하여 더 나은 성능을 나타냅니다. 실험 결과, 경사형 부유식 방파제가 직사각형 상자형보다 최대 15% 성능이 우수한 것으로 나타났다. 말뚝에 의해 고정된 FB에 대한 투과계수는 단파에서 케이블에 의해 고정된 FB보다 최대값으로 약 14% 낮고 장파에서 약 4-10% 더 높다. 흘수가 증가함에 따라 전송 계수는 감소하지만 건현은 허용 비율의 초과를 제한하기 위한 최소 요구 사항을 충족해야 합니다.
체인 그물이 있는 모델은 없는 모델에 비해 전달 계수가 최대 14% 감소하여 더 나은 성능을 나타냅니다. 말뚝에 의해 고정된 FB에 대한 투과계수는 단파에서 케이블에 의해 고정된 FB보다 최대값으로 약 14% 낮고 장파에서 약 4-10% 더 높다. 흘수가 증가함에 따라 전송 계수는 감소하지만 건현은 허용 비율의 초과를 제한하기 위한 최소 요구 사항을 충족해야 합니다.
체인 그물이 있는 모델은 없는 모델에 비해 전달 계수가 최대 14% 감소하여 더 나은 성능을 나타냅니다. 말뚝에 의해 고정된 FB에 대한 투과계수는 단파에서 케이블에 의해 고정된 FB보다 최대값으로 약 14% 낮고 장파에서 약 4-10% 더 높다.
흘수가 증가함에 따라 전송 계수는 감소하지만 건현은 허용 비율의 초과를 제한하기 위한 최소 요구 사항을 충족해야 합니다. 체인 그물이 있는 모델은 없는 모델에 비해 전달 계수가 최대 14% 감소하여 더 나은 성능을 나타냅니다.
A novel study of sloping floating breakwater (FB) that has a gap between two floaters is proposed. The slope of a structure can cause wave energy dissipation. A problem with sloping structures is wave overtopping. To solve this problem, a gap is considered between the two floaters. If overtopping occurs, water passing the crest will pour into the gap between the two floaters, as a result wave energy will be attenuated. A chain net is added to the model and its effect on the transmission coefficient is studied. Furthermore, in order to investigate the effects of the degree of freedom on the hydrodynamic performance of the structure, the model is studied in the two anchorage systems which are anchored by pile (1 degree of freedom) and anchored by mooring lines (3 degree of freedom). Moreover, the experiments are performed under regular waves with five different wave periods and four different wave heights. The results of the experiments show a sloping floating breakwater that has a better performance than that of rectangular box type by 15% as maximum value. The transmission coefficients for the FB anchored by pile are lower about 14% as maximum value than that of the FB anchored by cable in shorter waves and are higher about 4–10% in longer waves. With increasing the draft, the transmission coefficient decreases but the freeboard should meet the minimum requirements to restrict overtopping in the allowable rate. The model with a chain net exhibits a better performance as compared with the model without it by a maximum 14% reduction in the transmission coefficients.
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Numerical Modeling of Failure Mechanisms in Articulated Concrete Block Mattress as a Sustainable Coastal Protection Structure
Ramin Safari Ghaleh(Department of Civil Engineering, K. N. Toosi University of Technology, Tehran 19967-15433, Iran)
Omid Aminoroayaie Yamini(Department of Civil Engineering, K. N. Toosi University of Technology, Tehran 19967-15433, Iran)
S. Hooman Mousavi(Department of Civil Engineering, K. N. Toosi University of Technology, Tehran 19967-15433, Iran)
Mohammad Reza Kavianpour(Department of Civil Engineering, K. N. Toosi University of Technology, Tehran 19967-15433, Iran)
해안선 보호는 전 세계적인 우선 순위로 남아 있습니다. 일반적으로 해안 지역은 석회암과 같은 단단하고 비자연적이며 지속 불가능한 재료로 보호됩니다. 시공 속도와 환경 친화성을 높이고 개별 콘크리트 블록 및 보강재의 중량을 줄이기 위해 콘크리트 블록을 ACB 매트(Articulated Concrete Block Mattress)로 설계 및 구현할 수 있습니다. 이 구조물은 필수적인 부분으로 작용하며 방파제 또는 해안선 보호의 둑으로 사용할 수 있습니다. 물리적 모델은 해안 구조물의 현상을 추정하고 조사하는 핵심 도구 중 하나입니다. 그러나 한계와 장애물이 있습니다. 결과적으로, 본 연구에서는 이러한 구조물에 대한 파도의 수치 모델링을 활용하여 방파제에서의 파도 전파를 시뮬레이션하고, VOF가 있는 Flow-3D 소프트웨어를 통해 ACB Mat의 불안정성에 영향을 미치는 요인으로는 파괴파동, 옹벽의 흔들림, 파손으로 인한 인양력으로 인한 장갑의 변위 등이 있다. 본 연구의 가장 중요한 목적은 수치 Flow-3D 모델이 연안 호안의 유체역학적 매개변수를 모사하는 능력을 조사하는 것입니다. 콘크리트 블록 장갑에 대한 파동의 상승 값은 파단 매개변수( 0.5 < ξ m – 1 , 0 < 3.3 )가 증가할 때까지(R u 2 % H m 0 = 1.6) ) 최대값에 도달합니다. 따라서 차단파라미터를 증가시키고 파괴파(ξ m − 1 , 0 > 3.3 ) 유형을 붕괴파/해일파로 변경함으로써 콘크리트 블록 호안의 상대파 상승 변화 경향이 점차 증가합니다. 파동(0.5 < ξ m − 1 , 0 < 3.3 )의 경우 차단기 지수(표면 유사성 매개변수)를 높이면 상대파 런다운의 낮은 값이 크게 감소합니다. 또한, 천이영역에서는 파단파동이 쇄도파에서 붕괴/서징으로의 변화( 3.3 < ξ m – 1 , 0 < 5.0 )에서 상대적 런다운 과정이 더 적은 강도로 발생합니다.
Shoreline protection remains a global priority. Typically, coastal areas are protected by armoring them with hard, non-native, and non-sustainable materials such as limestone. To increase the execution speed and environmental friendliness and reduce the weight of individual concrete blocks and reinforcements, concrete blocks can be designed and implemented as Articulated Concrete Block Mattress (ACB Mat). These structures act as an integral part and can be used as a revetment on the breakwater body or shoreline protection. Physical models are one of the key tools for estimating and investigating the phenomena in coastal structures. However, it does have limitations and obstacles; consequently, in this study, numerical modeling of waves on these structures has been utilized to simulate wave propagation on the breakwater, via Flow-3D software with VOF. Among the factors affecting the instability of ACB Mat are breaking waves as well as the shaking of the revetment and the displacement of the armor due to the uplift force resulting from the failure. The most important purpose of the present study is to investigate the ability of numerical Flow-3D model to simulate hydrodynamic parameters in coastal revetment. The run-up values of the waves on the concrete block armoring will multiply with increasing break parameter ( 0.5 < ξ m − 1 , 0 < 3.3 ) due to the existence of plunging waves until it ( R u 2 % H m 0 = 1.6 ) reaches maximum. Hence, by increasing the breaker parameter and changing breaking waves ( ξ m − 1 , 0 > 3.3 ) type to collapsing waves/surging waves, the trend of relative wave run-up changes on concrete block revetment increases gradually. By increasing the breaker index (surf similarity parameter) in the case of plunging waves ( 0.5 < ξ m − 1 , 0 < 3.3 ), the low values on the relative wave run-down are greatly reduced. Additionally, in the transition region, the change of breaking waves from plunging waves to collapsing/surging ( 3.3 < ξ m − 1 , 0 < 5.0 ), the relative run-down process occurs with less intensity.
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대용량 배출구가 있는 수중 여수로는 일반적으로 홍수 처리 및 침전물 세척의 이중 기능을 수행하기 위해 댐 정상 아래에 제공됩니다. 이 방수로를 통과하는 홍수 물은 난류 거동을 나타냅니다.
게다가 이러한 난류의 수력학적 분석은 어려운 작업입니다.
따라서 본 연구는 파키스탄 Mangla Dam에 건설된 수중 여수로의 수리학적 거동을 수치해석을 통해 조사하는 것을 목적으로 한다. 또한 다양한 작동 조건에서 화기의 유압 성능을 평가했습니다.
Mangla Spillway의 흐름을 수치적으로 모델링하는 데 전산 유체 역학 코드 FLOW 3D가 사용되었습니다. 레이놀즈 평균 Navier-Stokes 방정식은 난류 흐름을 수치적으로 모델링하기 위해 FLOW 3D에서 사용됩니다.
연구 결과에 따르면 개발된 모델은 최대 6%의 허용 오차로 흐름 매개변수를 계산하므로 수중 여수로 흐름을 시뮬레이션할 수 있습니다.
또한, 여수로 슈트 베드 주변 모델에 의해 계산된 공기 농도는 폭기 장치에 램프를 설치한 후 6% 이상으로 상승한 3%로 개발된 모델도 침수형 폭기 장치의 성능을 평가할 수 있음을 보여주었습니다.
Submerged spillways with large capacity outlets are generally provided below the dam crest to perform the dual functions of flood disposal and sediment flushing. Flood water passing through these spillways exhibits turbulent behavior. Moreover; hydraulic analysis of such turbulent flows is a challenging task. Therefore, the present study aims to use numerical simulations to examine the hydraulic behavior of submerged spillways constructed at Mangla Dam, Pakistan. Besides, the hydraulic performance of aerator was also evaluated at different operating conditions. Computational fluid dynamics code FLOW 3D was used to numerically model the flows of Mangla Spillway. Reynolds-averaged Navier–Stokes equations are used in FLOW 3D to numerically model the turbulent flows. The study results indicated that the developed model can simulate the submerged spillway flows as it computed the flow parameters with an acceptable error of up to 6%. Moreover, air concentration computed by model near spillway chute bed was 3% which raised to more than 6% after the installation of ramp on aerator which showed that developed model is also capable of evaluating the performance of submerged spillway aerator.
이 작업의 목적은 FLOW-3D 를 검증하는 것입니다. 밀폐된 좁은 스팬 직사각형 탱크의 출렁거림 문제에 대비하여 탱크의 내부 파동 공명 주기에 가깝거나 같은 주기로 롤 운동을 하여 측면 및 지붕 파동 충격 이벤트가 발생합니다.
탱크는 물이나 해바라기 기름으로 두 가지 다른 수준으로 채워졌고 위의 공간은 공기로 채워졌습니다. 압력 센서는 여러 장소의 벽에 설치되었으며 처음 4개의 출렁이는 기간 동안 기록된 롤 각도와 시간 이력이 있습니다. 오일을 사용하는 경우의 흐름은 레이놀즈 수가 1748인 층류인 반면, 물로 채워진 경우의 흐름은 레이놀즈 수가 97546인 난류입니다.
CFD 시뮬레이션은 탱크의 고조파 롤 운동을 복제하기 위해 본체력 방법을 사용했으며, 난류 및 공기 압축성을 설명하기 위해 다른 모델링 가정과 함께 그리드 의존성 테스트를 수행했습니다.
The objective of this work is to validate FLOW-3D against a sloshing problem in a sealed narrow span rectangular tank, subjected to roll motion at periods close to or equal to the tank’s internal wave resonance period, such that side and roof wave impact events occur. The tank was filled to two different levels with water or sunflower oil, with the space above filled by air. Pressure sensors were installed in the walls at several places and their time histories, along with the roll angle, recorded for the first four sloshing periods. For the cases using oil, the flow is laminar with a Reynolds number of 1748, while for the cases filled with water the flow is turbulent with a Reynolds number of 97546. The CFD simulations used the body force method to replicate the harmonic roll motion of the tank, while grid dependence tests were performed along with different modelling assumptions to account for turbulence and air compressibility.
Experimental Problem Setup
원래 실험은 Souto-Iglesias 및 Botia-Vera에 의해 수행되었으며 모든 실험 데이터 파일은 문제 설명, 비디오 및 불확실성 분석과 함께 사용할 수 있습니다. 그림 1에 표시된 형상은 길이 900mm, 높이 508mm, 스팬 62mm의 직사각형 탱크로 구성되어 있으며 물이나 해바라기 기름으로 93mm 또는 355.3mm로 채워져 있으므로 4가지 경우가 고려됩니다. 탱크 벽과 같은 높이로 설치된 압력 센서의 위치도 표시됩니다. 탱크 회전 중심은 수평에 대한 회전 각도와 함께 그림 1에 나와 있습니다. 각 실험 실행은 반복성을 평가할 수 있도록 100번 수행되었습니다.
The original experiment was performed by Souto-Iglesias and Botia-Vera  and all experimental data files are available along with problem description, videos and an uncertainty analysis. The geometry shown in Fig. 1 consists of a rectangular tank of 900mm length, 508mm height and 62mm span, filled to either 93mm or 355.3 mm with either water or sunflower oil, hence four cases are considered. The locations of the pressure sensors that were installed flush with the tank walls are also shown. The tank rotation center is shown in Fig. 1, along with the rotation angle relative to the horizontal. Each of the experimental runs was performed 100 times to enable their repeatability to be assessed.
문제는 FLOW-3D 내에서 비관성 기준 좌표계 모델을 사용하여 비교적 간단하게 설정할 수 있으며 , 이는 로컬 기준 좌표계의 가속도에 따라 유체에 체력 을 적용합니다. Z축 회전 속도는 탱크의 롤 운동을 시뮬레이션하기 위한 주기 함수로 정의되었으며 음의 수직 방향으로 작용하는 일정한 중력이 가해졌습니다.
메쉬 미세화, 운동량 이류에 대한 수치 근사 순서, 층류 대 난류 모델 및 탱크 내 공기에 대한 세 가지 다른 처리(즉, 일정 압력, 압축성 기체 및 비압축성 기체)와 같은 것을 조사하기 위해 여러 시뮬레이션을 수행했습니다.
93mm 깊이로 채워진 모든 케이스에 대해 압력은 압력 센서 P1에서만 실험 값과 비교되었으며, 355.3mm 깊이로 채워진 모든 케이스에서는 P3 센서의 데이터만 비교되었습니다.
The problem was relatively simple to set up using the non-inertial reference frame model within FLOW-3D, which applies a body force to the fluid depending on the acceleration of the local reference frame. The Z axis rotational velocity was defined as a periodic function to simulate a roll motion of the tank, and a constant gravity force acting in the negative vertical direction was applied.
Multiple simulations were performed to investigate such things as mesh refinement, the numerical approximation order for momentum advection, laminar versus turbulent models and three different treatments for the air in the tank (i.e., constant pressure, compressible gas and incompressible gas).
For all 93mm depth-filled cases, the pressure was compared to the experimental values at pressure sensor P1 only, while for all 355.3mm depth-filled cases, only data at the P3 sensor was compared.
P1에서 측정된 측면 워터 슬로싱에 대한 메쉬 해상도의 영향은 그림 2에서 볼 수 있습니다. 피크 값 예측 측면에서 특별한 편향을 보이지 않습니다. 모든 측면 사례에서 초기 피크 직후의 압력은 시뮬레이션에서 일관되게 과대 평가되었습니다. 모든 메쉬는 피크의 타이밍 측면에서 우수한 일치를 보입니다. 100회 실행에서 보고된 실험 시간 기록은 평균 값에 가장 가까운 최고 압력을 가진 기록입니다.
The effect of mesh resolution on lateral water sloshing measured at P1 is seen in Fig. 2. It shows no particular bias in terms of the prediction of peak values. In all the Lateral cases, the pressures immediately after the initial peaks are consistently over estimated in the simulations. All meshes have excellent agreement in terms of the timing of the peaks. The experimental time histories reported from the 100 runs made are those with peak pressures closest to the average values.
실험 결과의 반복성은 Souto-Iglesias & Elkin Botia-Vera에 의해 각 테스트를 100번 실행하고 처음 4개의 피크 압력의 평균 및 표준 편차를 측정하여 평가했습니다. CFD 실행이 다른 실험 실행으로 간주되는 경우 오류 막대 내에 있을 확률이 95%입니다. 그러나 CFD 결과의 16개 피크 압력 중 9개만 실험 결과의 2 표준 편차 내에 있으므로 CFD 모델이 실험을 대표하지 않거나 피크 압력이 정규 분포를 따르지 않는다는 결론을 내려야 합니다.
어쨌든 표준 편차는 피크 자체에 비해 상당히 크며, 수성 케이스와 측면 오일의 비율이 가장 작은 피크 값에 대한 표준 편차의 비율이 가장 큰 것으로 나타났습니다. 이러한 결과는 그림 1과 2에서 볼 수 있는 벽 충격 역학의 복잡성을 고려할 때 그리 놀라운 일이 아닙니다. 3,4.
The repeatability of the experimental results was assessed by Souto-Iglesias & Elkin Botia-Vera  running each test 100 times and measuring the average and standard deviation of the first four peak pressures. If a CFD run is considered to be another experimental run there is a 95% chance it will lie within the error bars. However, only nine of the 16 peak pressures from the CFD results fall within two standard deviations of the experimental results, so we must conclude that either the CFD model is not representative of the experiment or that the peak pressures are not normally distributed.
In any event, the standard deviations are quite large compared to the peaks themselves, with the largest ratio of standard deviation to peak values occurring for the water-based cases and the lateral oil having the smallest ratio. These results are perhaps not too surprising when one considers the complexity of the wall impact dynamics as seen in Figs. 3,4.
좁은 탱크 슬로싱 문제의 네 가지 구성은 자유 표면 흐름을 위해 설계된 상용 CFD 코드를 사용하여 수치적으로 시뮬레이션되었습니다. 대략 2 X 10 3 및 1 X 10 5 의 Reynolds 수에 해당하는 두 가지 다른 유체 와 두 가지 유체 깊이가 네 가지 경우를 정의하는 데 사용되었습니다. 4가지 경우 모두에 대해 메쉬 셀 크기 독립성 테스트를 수행했지만 메쉬 해상도가 증가함에 따라 실험 결과에 대해 약한 수렴만 발견되었습니다. 조사는 또한 두 가지 다른 운동량 이류 수치 차분 계획을 테스트했으며 두 번째 방법을 사용하여 더 가까운 일치를 발견했습니다 1차 체계를 사용하는 것보다 차수 단조성 보존 체계. 기본 층류 흐름을 포함한 세 가지 난류 모델이 테스트되었지만 더 낮은 계산 비용으로 인해 층류 이외의 모델에 대한 선호도가 발견되지 않았습니다. 실험 데이터와 공기 감소 일치의 압축성을 포함하여 그 이유는 불분명합니다.
실험 압력 프로브 시간 이력 데이터 세트에는 100회 반복 테스트에서 파생된 각 압력 피크에 대해 100개의 값이 포함되어 있으므로 CFD 시뮬레이션과의 일치의 통계적 유의성을 조사할 수 있었습니다. 수치 시뮬레이션과 실험 모두 출렁이는 파동 충격에 해당하는 매우 가파른 압력 펄스를 발생시켰고 실험 결과는 피크 값에서 높은 정도의 자연적 변동성을 갖는 것으로 나타났습니다. CFD 시뮬레이션의 감도 테스트(예: 약간 다른 초기 시작 조건 사용)는 공식적으로 수행되지 않았지만 수치 솔루션은 또한 다른 메쉬, 차분 체계 및 난류 모델,
모든 경우에 압력 피크가 발생하는 수치해의 타이밍은 매우 정확함을 알 수 있었다. 그러나 가장 난이도가 낮은 Lateral Oil의 경우에도 압력 피크와 바로 뒤따르는 압력 값이 과대 평가되어 수치 모델링의 단점이 나타났습니다. 실험적 피크 압력 변동성을 고려할 때 CFD 생성 값은 CFD 솔루션이 통계적 유의성을 나타내기 위해 필요한 15개 이상이 아니라 16개 피크 중 9개에서 2개의 표준편차 한계 내에 떨어졌습니다. 실험을 대표했다. 이것은 피크가 정규 분포를 따르지 않거나 CFD 모델이 피크를 예측하는 데 어떤 식으로든 결함이 있음을 나타냅니다.
Four configurations of a narrow tank sloshing problem were numerically simulated using a commercial CFD code designed for free surface flow. Two different fluids corresponding to Reynolds numbers of approximately 2 X 103 and 1 X 105 and two fluid depths were used to define the four cases. Mesh cell size independence tests were conducted for all four cases, but only a weak convergence towards the experimental results with increasing mesh resolution was found. The investigation also tested two different momentum advection numerical differencing schemes and found closer agreement using the 2nd order monotonicity preserving scheme than by using a first order scheme. Three turbulence models, including the default laminar flow, were tested but no preference was found for any model other than the laminar by virtue of its lower computational cost. Including the compressibility of the air-reduced agreement with the experimental data, the reasons for this are unclear.
The experimental pressure probe time history data sets included 100 values for each of the pressure peaks derived from 100 repeat tests, and thus we were able to examine the statistical significance of the agreement with the CFD simulations. Both the numerical simulations and the experiments gave rise to very steep pressure pulses corresponding to the sloshing wave impacts, and the experimental results were found to have a high degree of natural variability in the peak values. Although sensitivity tests of the CFD simulations (using, for example, slightly different initial starting conditions) were not formally conducted, the numerical solutions also showed a high degree of variability in the pressure peak magnitudes resulting from the use of different meshes, differencing schemes and turbulence models, which could be considered to show that the numerical solution also had a high degree of natural variability.
In all cases, the numerical solutions’ timing of the occurrence of the pressure peaks were found to be very accurate. However, even for the least challenging Lateral Oil case, the pressure peaks and the immediately following pressure values were overestimated, which indicated a shortcoming in the numerical modelling. When the experimental peak pressure variability was taken into account, the CFD-generated values fell inside the two Standard Deviation margin in nine of the 16 peaks rather than the 15 or more that would be required to show statistical significance in the sense that the CFD solution was representative of the experiment. This indicates that either the peaks are not normally distributed and/or the CFD model is in some way deficient at predicting them. Further work is required to establish how the peak pressures are distributed and/or to establish the physical reasons why the CFD model is overestimating the pressure peaks for even the least challenging Lateral Oil configuration.
Spheric Benchmark Test Case, Sloshing Wave Impact Problem, Antonio Souto-Iglesias & Elkin Botia-Vera, https://wiki.manchester.ac.uk/spheric/index.php/Test10
Peregrine DH (1993). Water-wave impact on walls. Annual Review of Fluid Mechanics. Vol 35, pp 23-43.
The complete document from which this note was extracted and the related data and input files are available on our Users Site. Readers are encouraged to read the original validation to get a full appreciation of the detail in this work investigating comparisons between simulation and experimental data. This study is especially noteworthy since it deals with highly non-linear sloshing of fluids interacting with the boundaries of a confining tank.
With regard to the author’s conclusions, it should be mentioned that the over prediction of fluid impact pressures in simulations could be the result of not allowing for sufficient compressibility effects in the liquids. For instance, in Fig. 3, it appears that there has been some air entrained in the liquid near the side wall. Also, negative pressures (i.e., below atmospheric) recorded experimentally might result from liquid drops remaining on the pressure sensors after the main body of liquid has drained away. Such details, which may be hard to quantify, only emphasize the difficulties involved in undertaking detailed validation studies. The author is commended for his excellent work.
Keyword : 3D Hydraulic Modeling,CFD, CFD Model, Computational Fluid Dynamics, Dam Hydraulics, Hydrology structure damage
급격한 변화나 예기치 못한 노후화로 인해 댐에서 복잡한 문제가 발생하는 경우 20세기에 개발된 산업 표준 설계 방정식과 방법론이 많은 경우 올바른 솔루션을 제공할 수는 없습니다. 다행스럽게도 엔지니어들은 적절한 조치나 수리를 적용할 수 있도록 유압 상황을 확인하기 위해 전산유체역학(CFD) 모델을 사용할 수 있게 되었습니다.
About the Expert:
Matthew Hickox, PE, brings civil engineering expertise in stormwater and river design, planning, and construction phase services. His experience is founded on a solid understanding of hydrologic modeling, 1- and 2-dimensional hydraulic modeling, in-stream hydraulic structures, scour protection measures, culvert and bridge hydraulics, and the regulatory environment for stormwater projects.
How Does CFD Work in Practice?
최근의 한 사례에서 하천 수문학 및 지형학은 낮은 수두 전환 댐 주변에서 변경되었습니다. 지난 수십 년 동안 빠르게 발전해 온 도시 지역의 하류에 있는 모래 바닥 하천 시스템에 위치한 댐의 문제는 주변 하천 시스템에서 일어나는 여러 가지 일들로 인해 복잡해졌습니다. 증가하는 도시화는 배출 빈도를 증가시켰을 뿐만 아니라 기본 흐름을 증가시켰습니다. 수리학적으로 가파른 시스템은 일시적인 지류에서 연간 베이스 흐름으로의 변화가 상류가 침식됨에 따라 퇴적물 부하도 증가했음을 의미했습니다.
이 조합은 전환 댐의 하류 수로가 지난 15년 동안 3-4피트 감소했고, 배수가 감소된 정수장 apron에서 속도가 증가했으며 구조물 표면에 마모를 유발하는 퇴적물 하중이 감소했음을 의미합니다. 이러한 문제 중 어느 것도 전환 댐의 원래 설계의 잘못이 아니었지만 변화하는 하천 수문 및 지형학으로 인해 원래 설계자가 예상하지 못한 조건이 발생했습니다.
기존 구조물의 단위 너비 CFD 모델은 기존 현장 조건으로 인해 정수기 계류장에 수압 점프가 형성되지 않았다는 현장 관찰을 확인했습니다. 1).
설계 표고(열화 전)에서 하류 하류 바닥 표고와 함께 개발된 유사한 단위 너비 CFD 모델은 원래 설계가 정수 유역 계류장과 배수로 전면 근처에서 수압 점프를 생성한다는 것을 보여주었습니다. 이 단위 너비 CFD 모델은 구조에 영향을 미치는 수력학의 가치 있는 검증을 제공하지만 구조 손상이 구조 중간에서 매우 뚜렷하고 다른 영역에서는 거의 손대지 않았기 때문에 이것만으로는 충분하지 않습니다. (그림 2)
전체 기존 조건 CFD 모델은 정수조 앞치마 마모의 범위와 그에 따른 손상을 확인했습니다. (그림 3 및 4)
이 구조물에 대한 수리를 위한 예비 설계 동안 간단한 분석에 따르면 구조물의 미수를 높이는 것이 방수로 토우 근처의 구조물에 수력학적 점프를 만드는 데 도움이 될 것이며, 이는 정수 유역 계류장과 계류장을 가로지르는 극한 속도를 감소시킬 것입니다. 따라서 구조의 마모를 크게 줄입니다(그림 5 참조). 이 예비 제안 조건 CFD 모델은 엔드 실 높이만 높였습니다. 구조물 하류의 하천 시스템의 상태와 지형은 나머지 설계 수명 동안 구조물의 안정성을 보장하기 위해 모든 최종 설계 조건에 대해 평가되어야 합니다.
CFD 모델은 설계 상황이 확립된 설계 방정식 및 절차의 한계 내에 깔끔하게 속하지 않을 때 유압을 확인하는 또 다른 도구를 제공합니다. 구조와 유역의 개요에 대해 자세히 설명하는 전체적인 관점은 프로젝트 현장의 현재와 미래의 상태를 평가하는 데 필요합니다. 이 예에서 구조의 설계 및 작동은 원래 설계와 매우 유사하게 유지됩니다. 구조 주변에서 변경된 것은 하천 시스템입니다. CFD는 현장 조건 변경으로 인해 예기치 않은 수리력 및 구조 손상이 발생할 때 복잡한 수리력을 분석할 수 있는 도구 상자의 또 다른 도구를 제공합니다.
CFD 또는 여기 Ayres에서 제공하는 유압 엔지니어링 서비스에 대한 자세한 내용은 Matthew Hickox, PE에게 문의하십시오.
Equation for ship wave crests in the entire range of water depths
Byeong Wook Lee a , Changhoon Lee b, *a Coastal Development and Ocean Energy Research Center, Korea Institute of Ocean Science & Technology, 385 Haeyang-ro, Busan, 49111, Republic of Korea b Department of Civil and Environmental Engineering, Sejong University, 209 Neungdong-ro, Gwangjin-gu, Seoul, 05006, Republic of Korea
An equation for ship wave crests y/x in the entire range of water depths is developed using the linear dispersion relation. In deep water, the developed equation is reduced to the equation of Kelvin (1906). The locations of ship wave crests in the x – and y -directions are obtained using a dimensionless constant C. The wave ray angle θc at the cusp locus is determined using the condition that θc is maximal at the cusp locus and the cusp locus angle is determined as αc=−tan−1(y/x)max. Numerical experiments are conducted using the FLOW-3D to simulate ship wave propagation. The cusp locus angles of the FLOW-3D are similar to both those of the present theory and Havelock (1908) theory in the entire range of the Froude number. Both the present theory and the FLOW-3D yield that, with the increase of ship speed, the Froude number increases and does the wavelength. For the Froude number equal to or greater than unity, the wavelength becomes infinitely large and the transverse waves disappear. The wavelengths of the FLOW-3D are slightly smaller than those of the present theory because the FLOW-3D considers the decrease of wavelength due to energy dissipation which happens because of viscosity of water and turbulence of high-speed particle velocities.
Ship wave crests Cusp locus angle Entire range of water depths Theoretical solution Numerical experiment
kylas, T.R., 1984. On the excitation of long nonlinear water waves by a moving pressure distribution. J. Fluid Mech. 141, 455–466.
Chen, X.N., Sharma, S.D., 1995. A slender ship moving at a near-critical speed in a shallow channel. J. Fluid Mech. 291, 263–285. David, C.G., Roeber, V., Goseberg, N., Schlurmann, T., 2017. Generation and propagation of ship-borne waves – solutions from a Boussinesq-type model. Cost Eng. 127, 170–187. Ersan, D.B., Beji, S., 2013. Numerical simulation of waves generated by a moving pressure field. Ocean Eng. 59, 231–239. Ertekin, R.C., Webster, W.C., Wehausen, J.V., 1986. Waves caused by a moving disturbance in a shallow channel of finite width. J. Fluid Mech. 169, 275–292. Fang, M.-C., Yang, R.-Y., Shugan, I.V., 2011. Kelvin ship wake in the wind waves field and on the finite sea depth. J. Mech. 27 (1), 71–77. Havelock, T.H., 1908. The propagation of groups of waves in dispersive media with application to waves on water produced by a travelling disturbance. Proc. Royal Soc. London Ser. A 398–430. Hennings, I., Romeiser, R., Alpers, W., Viola, A., 1999. Radar imaging of Kelvin arms of ship wakes. Int. J. Remote Sens. 20 (13), 2519–2543. Hur, D.S., Lee, J., Choi, D.S., Lee, H.W., 2011. On run-up characteristics of revetment under interaction among ocean wave, current and ship induced wave in the canal. In: Proceedings of the 37th Conference on the Korean Society of Civil Engineers, pp. 588–591 (in Korean). Johnson, J.W., 1958. Ship waves in navigation channels. In: Proceedings of the 6th Conference on Coastal Engineering, pp. 666–690. Kang, Y.S., Kim, P.J., Hyun, S.K., Sung, H.K., 2008. Numerical simulation of ship-induced wave using FLOW-3D. J. Korean Soc. Coast. Ocean Eng. 20 (3), 255–267 (in Korean). Kelvin, 1887. On ship waves. In: Proceedings of the Institution of Mechanical Engineering, pp. 409–433. Kelvin, 1906. Deep sea ship-waves. Proc. R. Soc. Edinb. 25 (2), 1060–1084. Lamb, H., 1945. Hydrodynamics. Dover Publications. Lee, C., Lee, B.W., Kim, Y.J., Ko, K.O., 2011. Ship wave crests in intermediate-depth water. In: Proceedings of the 6th International Conference on Asian and Pacific Coasts, pp. 1818–1825. Lee, B.W., Lee, C., Kim, Y.J., Ko, K.O., 2013. Prediction of ship wave crests on varying water depths and verification by FLOW-3D. J. Korean Soc. Civil Eng. 33 (4), 1447–1454 (in Korean). Lighthill, M.J., Whitham, G.B., 1955. On kinematic waves: I. Flood movement in long rivers; II. Theory of traffic flow on long crowded roads. Proc. R. Soc. A 229, 281–345. Newman, J.N., 1970. Recent research on ship waves. In: Proceedings of the 8th Symposium on Naval Hydrodynamics, pp. 519–545. Newman, J.N., 1977. Marine Hydrodynamics. The MIT Press. Reed, A.M., Milgram, J.H., 2002. Ship wakes and their radar images. Annu. Rev. Fluid Mech. 34, 469–502. Shemdin, O.H., 1990. Synthetic aperture radar imaging of ship wakes in the Gulf of Alaska. J. Geophys. Res. 95 (C9), 16319–16338. Shi, F., Malej, M., Smith, J.M., Kirby, J.T., 2018. Breaking of ship bores in a Boussinesqtype ship-wake model. Cost Eng. 132, 1–12. Sorensen, R.M., 1967. Investigation of ship-generated waves. J. Waterw. Harb. Div. 85–99. ASCE. Sorensen, R.M., 1969. Waves generated by model ship hull. J. Waterw. Harb. Div. 513–538. ASCE. Sorensen, R.M., Weggel, J.R., 1984. Development of ship wave design information. In: Proceedings of the 19th Conference on Coastal Engineering, pp. 3227–3243. ASCE. Stoker, J.J., 1957. Water Waves: the Mathematical Theory with Applications. Interscience Publishers. Tuck, E.O., 1966. Shallow-water flows past slender bodies. J. Fluid Mech. 26, 81–95. Wu, D.M., Wu, T.Y., 1982. Three-dimensional nonlinear long waves due to moving surface pressure. In: Proceedings of the 14th Symposium on Naval Hydrodynamics, pp. 103–129.
횡단 구조물을 통한 막힘은 안정성을 위협하는 위험한 문제 중 하나입니다. 암거의 막힘 형상 및 하류 세굴 특성에 미치는 영향에 관한 연구는 거의 없습니다.
이 연구의 목적은 수면과 세굴 모두에서 상자 암거를 통한 막힘의 작용을 수치적으로 논의하는 것입니다. 이를 위해 FLOW 3D v11.1.0을 사용하여 퇴적물 수송 모델을 조사했습니다.
상자 암거를 통한 다양한 차단 비율이 연구되었습니다. FLOW 3D 모델은 실험 데이터로 보정되었습니다. 결과는 FLOW 3D 프로그램이 세굴 다운스트림 상자 암거를 정확하게 시뮬레이션할 수 있음을 나타냅니다.
막힌 경우에 대한 속도 분포, 최대 세굴 깊이 및 수심을 플롯하고 비차단된 사례(기본 사례)와 비교했습니다.
그 결과 암거 높이의 70% 차단율은 상류의 수심을 암거 높이의 2.3배 증가시키고 평균 유속은 기본 경우보다 3배 더 증가시키는 것으로 입증되었다. 막힘 비율의 함수로 상대 최대 세굴 깊이를 추정하는 방정식이 만들어졌습니다.
Blockage through crossing structures is one of the dangerous problems that threaten its stability. There are few researches concerned with blockage shape in culverts and its effect on characteristics of scour downstream it.
The study’s purpose is to discuss the action of blockage through box culvert on both water surface and scour numerically. A sediment transport model has been investigated for this purpose using FLOW 3D v11.1.0. Different ratios of blockage through box culvert have been studied. The FLOW 3D model was calibrated with experimental data.
The results present that the FLOW 3D program was capable to simulate accurately the scour downstream box culvert. The velocity distribution, maximum scour depth and water depths for blocked cases have been plotted and compared with the non-blocked case (base case).
The results proved that the blockage ratio 70% of culvert height makes the water depth upstream increases by 2.3 times of culvert height and mean velocity increases by 3 times more than in the base case. An equation has been created to estimate the relative maximum scour depth as a function of blockage ratio.
Local scour is the removal of granular bed material by the action of hydrodynamic forces. As the depth of scour hole increases, the stability of the foundation of the structure may be endangered, with a consequent risk of damage and failure . So the prediction and control of scour is considered to be very important for protecting the water structures from failure. Most previous studies were designed to study the different factors that impact on scour and their relationship with scour hole dimensions like fluid characteristics, flow conditions, bed properties, and culvert geometry. Many previous researches studied the effect of flow rate on scour hole by information Froude number or modified Froude number , , , , . Cesar Mendoza  found a good correlation between the scour depth and the discharge Intensity (Qg−.5D−2.5). Breusers and Raudkiv  used shear velocity in the outlet-scour prediction procedure. Ali and Lim  used the densimetric Froude number in estimation of the scour depth , , , , , , , . “The densimetric Froude number presents the ratio of the tractive force on sediment particle to the submerged specific weight of the sediment” (1)Fd=uρsρ-1gD50
Ali and Lim  pointed to the consequence of tailwater depth on scour behavior , , , . Abida and Townsend  indicated that the maximum depth of local scour downstream culvert was varying with the tailwater depth in three ways: first, for very shallow tailwater depths, local scouring decreases with a decrease in tailwater depth; second, when the ratio of tailwater depth to culvert height ranged between 0.2 and 0.7, the scour depth increases with decreasing tailwater depth; and third for a submerged outlet condition. The tailwater depth has only a marginal effect on the maximum depth of scour . Ruff et al.  observed that for materials having similar mean grain sizes (d50) but different standard deviations (σ). As (σ) increased, the maximum scour hole depth decreased. Abt et al.  mentioned to role of soil type of maximum scour depth. It was noticed that local scour was more dangerous for uniform sands than for well-graded mixtures , , , , , . Abt et al ,  studied the culvert shape effect on scour hole. The results evidenced that the culvert shape has a limited effect on outlet scour. Under equivalent discharge conditions, it was noted that a square culvert with height equal to the diameter of a circular culvert would reduce scour , . The scour hole dimension was also effected by the culvert slope. Abt et al. ,  showed that the culvert slope is a key element in estimating the culvert flow velocity, the discharge capacity, and sediment transport capability. Abt et al. ,  tested experimentally culvert drop height effect on maximum scour depth. It was observed that as the drop height was increasing, the depth of scour was also increasing. From the previous studies, it could have noticed that the most scour prediction formula downstream unblocked culvert was the function of densimetric Froude number, soil properties (d50, σ), tailwater depth and culvert opening size. Blockage is the phenomenon of plugging water structures due to the movement of water flow loaded with sediment and debris. Water structures blockage has a bad effect on water flow where it causes increasing of upstream water level that may cause flooding around the structure and increase of scour rate downstream structures , . The blockage phenomenon through was studied experimentally and numerical , , , , , , , , , . Jaeger and Lucke  studied the debris transport behavior in a natural channel in Australia. Froude number scale model of an existing culvert was used. It was noticed that through rainfall event, the mobility of debris was impressed by stream shape (depth and width). The condition of the vegetation (size and quantities) through the catchment area was the main factor in debris transport. Rigby et al.  reported that steep slope was increasing the ability to mobilize debris that form field data of blocked culverts and bridges during a storm in Wollongong city.
Streftaris et al.  studied the probability of screen blockage by debris at trash screens through a numerical model to relate between the blockage probability and nature of the area around. Recently, many commercial computational fluid programs (CFD) such as SSIIM, Fluent, and FLOW 3D are used in the analysis of the scour process. Scour and sediment transport numerical model need to validate by using experimental data or field data , , , , . Epely-Chauvin et al.  investigated numerically the effect of a series of parallel spur diked. The experimental data were compared by SSIIM and FLOW 3D program. It was found that the accuracy of calibrated FLOW 3D model was better than SSIIM model. Nielsen et al.  used the physical model and FLOW 3D model to analyze the scour process around the pile. The soil around the pile was uniform coarse stones in the physical models that were simulated by regular spheres, porous media, and a mixture of them. The calibrated porous media model can be used to determine the bed shear stress. In partially blocked culverts, there aren’t many studies that explain the blockage impact on scour dimensions. Sorourian et al. ,  studied the effect of inlet partial blockage on scour characteristics downstream box culvert. It resulted that the partial blockage at the culvert inlet could be the main factor in estimating the depth of scour. So, this study is aiming to investigate the effects of blockage through a box culvert on flow and scour characteristics by different blockage ratios and compares the results with a non-blocked case. Create a dimensionless equation relates the blockage ratio of the culvert with scour characteristics downstream culvert.
2. Experimental data
The experimental work of the study was conducted in the Hydraulics and Water Engineering Laboratory, Faculty of Engineering, Zagazig University, Egypt. The flume had a rectangular cross-section of 66 cm width, 65.5 cm depth, and 16.2 m long. A rectangular culvert was built with 0.2 m width, 0.2 m height and 3.00 m long with θ = 25° gradually outlet and 0.8 m fixed apron. The model was located on the mid-point of the channel. The sediment part was extended for a distance 2.20 m with 0.66 m width and 0.20 m depth of coarse sand with specific weight 1.60 kg/cm3, d50 = 2.75 mm and σ (d90/d50) = 1.50. The particle size distribution was as shown in Fig. 1. The experimental model was tested for different inlet flow (Q) of 25, 30, 34, 40 l/s for different submerged ratio (S) of 1.25, 1.50, 1.75.
3. Dimensional analysis
A dimensional analysis has been used to reduce the number of variables which affecting on the scour pattern downstream partial blocked culvert. The main factors affecting the maximum scour depth are:(2)ds=f(b.h.L.hb.lb.Q.ud.hu.hd.D50.ρ.ρs.g.ls.dd.ld)
Fig. 2 shows a definition sketch of the experimental model. The maximum scour depth can be written in a dimensionless form as:(3)dsh=f(B.Fd.S)where the ds/h is the relative maximum scour depth.
4. Numerical work
The FLOW 3D is (CFD) program used by many researchers and appeared high accuracy in solving hydrodynamic and sediment transport models in the three dimensions. Numerical simulation with FLOW 3D was performed to study the impacts of blockage ratio through box culvert on shear stress, velocity distribution and the sediment transport in terms of the hydrodynamic features (water surface, velocity and shear stress) and morphological parameters (scour depth and sizes) conditions in accurately and efficiently. The renormalization group (RNG) turbulence model was selected due to its high ability to predict the velocity profiles and turbulent kinetic energy for the flow through culvert . The one-fluid incompressible mode was used to simulate the water surface. Volume of fluid (VOF) method was employed in FLOW 3D to tracks a liquid interface through arbitrary deformations and apply the correct boundary conditions at the interface .1.
Three-dimensional Reynolds-averaged Navier Stokes (RANS) equation was applied for incompressible viscous fluid motion. The continuity equation is as following:(4)VF∂ρ∂t+∂∂xρuAx+∂∂yρvAy+∂∂zρwAz=RDIF(5)∂u∂t+1VFuAx∂u∂x+vAy∂u∂y+ωAz∂u∂z=-1ρ∂P∂x+Gx+fx(6)∂v∂t+1VFuAx∂v∂x+vAy∂v∂y+ωAz∂v∂z=-1ρ∂P∂y+Gy+fy(7)∂ω∂t+1VFuAx∂ω∂x+vAy∂ω∂y+ωAz∂ω∂z=-1ρ∂P∂z+Gz+fz
ρ is the fluid density,
VF is the volume fraction,
(x,y,z) is the Cartesian coordinates,
(u,v,w) are the velocity components,
(Ax,Ay,Az) are the area fractions and
RDIF is the turbulent diffusion.
P is the average hydrodynamic pressure,
(Gx, Gy, Gz) are the body accelerations and
(fx, fy, fz) are the viscous accelerations.
The motion of sediment transport (suspended, settling, entrainment, bed load) is estimated by predicting the erosion, advection and deposition process as presented in .
The critical shields parameter is (θcr) is defined as the critical shear stress τcr at which sediments begin to move on a flat and horizontal bed :(8)θcr=τcrgd50(ρs-ρ)
The Soulsby–Whitehouse  is used to predict the critical shields parameter as:(9)θcr=0.31+1.2d∗+0.0551-e(-0.02d∗)(10)d∗=d50g(Gs-1ν3where:
d* is the dimensionless grain size
Gs is specific weight (Gs = ρs/ρ)
The entrainment coefficient (0.005) was used to scale the scour rates and fit the experimental data. The settling velocity controls the Soulsby deposition equation. The volumetric sediment transport rate per width of the bed is calculated using Van Rijn .2.
Meshing and geometry of model
After many trials, it was found that the uniform cell size with 0.03 m cell size is the closest to the experimental results and takes less time. As shown in Fig. 3. In x-direction, the total model length in this direction is 700 cm with mesh planes at −100, 0, 300, 380 and 600 cm respectively from the origin point, in y-direction, the total model length in this direction is 66 cm at distances 0, 23, 43 and 66 cm respectively from the origin point. In z-direction, the total model length in this direction is 120 cm. with mesh planes at −20, 0, 20 and 100 cm respectively.3.
As shown in Fig. 4, the boundary conditions of the model have been defined to simulate the experimental flow conditions accurately. The upstream boundary was defined as the volume flow rate with a different flow rate. The downstream boundary was defined as specific pressure with different fluid elevation. Both of the right side, the left side, and the bottom boundary were defined as a wall. The top boundary defined as specified pressure with pressure value equals zero.
5. Validation of experimental results and numerical results
The experimental results investigated the flow and scour characteristics downstream culvert due to different flow conditions. The measured value of maximum scour depth is compared with the simulated depth from FLOW 3D model as shown in Fig. 5. The scour results show that the simulated results from the numerical model is quite close to the experimental results with an average error of 3.6%. The water depths in numerical model results is so close to the experimental results as shown in Fig. 6 where the experiment and numerical results are compared at different submerged ratios and flow rates. The results appear maximum error percentage in water depths upstream and downstream the culvert is about 2.37%. This indicated that the FLOW 3D is efficient for the prediction of maximum scour depth and the flow depths downstream box culvert.
6. Computation time
The run time was chosen according to reaching to the stability limit. Hydraulic stability was achieved after 50 s, where the scour development may still go on. For run 1, the numerical simulation was run for 1000 s as shown in Fig. 7 where it mostly reached to scour stability at 800 s. The simulation time was taken 500 s at about 95% of scour stability.
7. Analysis and discussions
Fig. 8 shows the study sections where sec 1 represents to upstream section, sec2 represents to inside section and sec3 represents to downstream stream section. Table 1 indicates the scour hole dimensions at different blockage case. The symbol (B) represents to blockage and the number points to blockage ratio. B0 case signifies to the non-blocked case, B30 is that blockage height is 30% to the culvert height and so on.
Table 1. The scour results of different blockage ratio.
B = hb/h
7.1. Scour hole geometry
The scour hole geometry mainly depends on the properties of soil of the bed downstream the fixed apron. From Table 1, the results show that the maximum scour depth in B0 case is about 0.58 of culvert height while the maximum deposition in B0 is 0.27 culvert height. There is a symmetric scour hole as shown in Fig. 9 in B0 case. An asymmetric scour hole is created in B50 and B70 due to turbulences that causes the deviation of the jet direction from the center of the flume where appear in Fig. 11 and Fig. 19.
7.2. Flow water surface
Fig. 10 presents the relative free surface water (hw/h) along the x-direction at center of the box culvert. From the mention Figure, it is easy to release the effect of different blockage ratios. The upstream water level rises by increasing the blockage ratio. Increasing upstream water level may cause flooding over the banks of the waterway. In the 70% blockage case, the upstream water level rises to 2.3 times of culvert height more than the non-blocked case at the same discharge and submerged ratio. The water surface profile shows an increase in water level upstream the culvert due to a decrease in transverse velocity. Because of decreasing velocity downstream culvert, there is an increase in water level before it reaches its uniform depth.
7.3. Velocity vectors
Scour downstream hydraulic structures mainly affects by velocities distribution and bed shear stress. Fig. 11 shows the velocity vectors and their magnitude in xz plane at the same flow conditions. The difference in the upstream water level due to the different blockage ratios is so clear. The maximum water level is in B70 and the minimum level is in B0. The inlet mean velocity value is about 0.88 m/s in B0 increases to 2.86 m/s in B70. As the blockage ratio increases, the inlet velocity increases. The outlet velocity in B0 case makes downward jet causes scour hole just after the fixed apron in the middle of the bed while the blockage causes upward water flow that appears clearly in B70. The upward jet decreases the scour depth to 0.13 culvert height less than B0 case. After the scour hole, the velocity decreases and the flow becomes uniform.
7.4. Velocity distribution
Fig. 12 represents flow velocity (Vx) distribution along the vertical depth (z/hu) upstream the inlet for the different blockage ratios at the same flow conditions. From the Figure, the maximum velocity creates closed to bed in B0 while in blocked case, the maximum horizontal velocity creates at 0.30 of relative vertical depth (z/hu). Fig. 13 shows the (Vz) distribution along the vertical depth (z/hu) upstream culvert at sec 1. From the mentioned Figure, it is easy to note that the maximum vertical is in B70 which appears that as the blockage ratio increases the vertical ratio also increases. In the non-blocked case. The vertical velocity (Vz) is maximum at (z/hu) equals 0.64. At the end of the fixed apron (sec 3), the horizontal velocity (Vx) is slowly increasing to reach the maximum value closed to bed in B0 and B30 while the maximum horizontal velocity occurs near to the top surface in B50 and B70 as shown in Fig. 14. The vertical velocity component along the vertical depth (z/hd) is presented in Fig. 15. The vertical velocity (Vz) is maximum in B0 at vertical depth (z/hd) 0.3 with value 0.45 m/s downward. Figs. 16 and 17 observe velocity components (Vx, Vz) along the vertical depth just after the end of blockage length at the centerline of the culvert barrel. It could be noticed the uniform velocity distribution in B0 case with horizontal velocity (Vx) closed to 1.0 m/s and vertical velocity closed to zero. In the blocked case, the maximum horizontal velocity occurs in depth more than the blockage height.
7.5. Bed velocity distribution
Fig. 18 presents the x-velocity vectors at 1.5 cm above the bed for different blockage ratios from the velocity vectors distribution and magnitude, it is easy to realize the position of the scour hole and deposition region. In B0 and B30, the flow is symmetric so that the scour hole is created around the centerline of flow while in B50 and B70 cases, the flow is asymmetric and the scour hole creates in the right of flow direction in B50. The maximum scour depth is found in the left of flow direction in B70 case where the high velocity region is found.
8. Maximum scour depth prediction
Regression analysis is used to estimate maximum scour depth downstream box culvert for different ratios of blockage by correlating the maximum relative scour by other variables that affect on it in one formula. An equation is developed to predict maximum scour depth for blocked and non-blocked. As shown in the equation below, the relative maximum scour depth(ds/hd) is a function of densimetric Froude number (Fd), blockage ratio (B) and submerged ratio (S)(11)dsh=0.56Fd-0.20B+0.45S-1.05
In this equation the coefficient of correlation (R2) is 0.82 with standard error equals 0·08. The developed equation is valid for Fd = [0.9 to 2.10] and submerged ratio (S) ≥ 1.00. Fig. 19 shows the comparison between relative maximum scour depths (ds/h) measured and estimated for different blockage ratios. Fig. 20 clears the comparison between residuals and ds/h estimated for the present study. From these figures, it could be noticed that there is a good agreement between the measured and estimated relative scour depth.
9. Comparison with previous scour equations
Many previous scour formulae have been produced for calculation the maximum scour depth downstream non-blockage culvert. These equations have been included the effect of flow regime, culvert shape, soil properties and the flow rate on maximum scour depth. Two of previous experimental studies data have been chosen to be compared with the present study results in non-blocked study data. Table 2 shows comparison of culvert shape, densmetric Froude number, median particle size and scour equations for these previous studies. By applying the present study data in these studies scour formula as shown in Fig. 21, it could be noticed that there are a good agreement between present formula results and others empirical equations results. Where that Lim  and Abt  are so closed to the present study data.
Table 2. Comparison of some previous scour formula.
The present study has shown that the FLOW 3D model can accurately simulate water surface and the scour hole characteristics downstream the box culvert with error percentage in water depths does not exceed 2.37%. Velocities distribution through and outlets culvert barrel helped on understanding the scour hole shape.
The blockage through culvert had caused of increasing of water surface upstream structure where the upstream water level in B70 was 2.3 of culvert height more than non-blocked case at the same discharge that could be dangerous on the stability of roads above. The depth averaged velocity through culvert barrel increased by 3 times its value in non-blocked case.
On the other hand, blockage through culvert had a limited effect on the maximum scour depth. The little effect of blockage on maximum scour depth could be noticed in Fig. 11. From this Figure, it could be noted that the residual part of culvert barrel after the blockage part had made turbulences. These turbulences caused the deviation of the flow resulting in the formation of asymmetric scour hole on the side of channel. This not only but in B70 the blockage height caused upward jet which made a wide far scour hole as cleared from the results in Table 1.
An empirical equation was developed from the results to estimate the maximum scour depth relative to culvert height function of blockage ratio (B), submerged ratio (S), and densimetric Froude number (Fd). The equation results was compared with some scour formulas at the same densimetric Froude number rang where the present study results was in between the other equations results as shown in Fig. 21.
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.
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Peer review under responsibility of Faculty of Engineering, Alexandria University.
1 Civil Engineering,Enginnering Faculty,,Univeristy of Qom.Qom.Iran 2 Civil Engineering Department,Engineering Faculty,Islamic Azad University of Lahijan,Iran
교각이 물의 흐름 앞에 위치하면 소용돌이가 형성되고 그 활동으로 교각 주변의 하상 재료가 침식되고 세굴 구멍이 생성됩니다. 기초 깊이와 교각 말뚝이 충분하지 않으면 교량은 실패합니다.
말뚝 캡의 다른 레벨링에서 유동층의 총 전단 응력 연구는 말뚝 캡 위치가 동일할 때 가장 높은 전단 응력이 생성됨을 보여줍니다. 강바닥과 같은 수준; 강바닥보다 낮은 위치에 파일 캡을 설치하여 최대 전단 응력을 감소시킵니다.
이 경우에 해당하기 때문일 수 있습니다. 교각 그룹 사이의 거리가 증가하고 두 번째 교각의 존재는 교각 그룹의 유량을 감소시키고 한 교각 그룹의 다른 교각은 흐름 패턴 형성에서 두 개의 독립적인 교각으로 작용합니다.
파일 캡의 다른 레벨링에서 세굴의 최종 길이 방향 단면을 비교함으로써 세굴 깊이의 가장 큰 감소는 에어로포일 모양의 파일 캡에서 발생하며 더 날카로운 노즈와 더 나은 공기 역학적 모양을 가진 파일 캡이 제어하기에 좋은 옵션이라는 결론을 내렸습니다. 말굽 와류를 제거하고 경사 교각 그룹 주변의 세굴 깊이를 줄입니다.
When the bridge piers are located in front of the water flow, vortices are formed against it and due to their activity, the materials of the river bed are eroded around the bridge piers and the scouring hole is created. If the foundation depth and bridge pier piles are insufficient, the bridge will fail.The study of total shear stress in the flow bed at different leveling of the pile caps shows that the highest shear stress is created when the pile cap position is at the same level as the river bed; by installing the pile cap at a lower level than the river bed, the maximum shear stress decreases. This may be due to the fact that in this case, the distance between the pier group increases and the presence of the second pier decreases the flow rate in the pier group and different pier in the one pier group acts as the two independent piers in the formation of the flow pattern. By comparing the final longitudinal sections of the scouring at different leveling of the pile cap, it is concluded that the largest reduction in scouring depth occurs in aerofoil-shaped pile caps and pile caps with the sharper nose and better aerodynamic shapes are good options to control the horseshoe vortices and will reduce the scouring depth around the inclined pier group.
This manual was developed with the purpose of presenting and executing basic numerical models in the software known as Flow 3D within the virtual laboratories of Fluid Mechanics and Applied Hydraulics, to complement and reinforce what was learned in class, the development of the manual covers a theoretical content and an exemplified práctical part for the handling of the software, besides including some feedback for the students, in order to mark the characteristics that the software has. With the handling of the Flow 3D program, the student will be introduced to the concept of Computational Fluid Dynamics or CFD, and a simple procedure to represent numerically and graphically the behavior of hydraulic structures. The hydraulic structures presented in the laboratory manual are: thin and thick wall orifices, gates with free and submerged discharge, thin and thick wall spillways with free and submerged discharge, WES type spillway, submerged intake with pressure conduction and as a complement, hydrostatic pressures on vertical, curved and inclined walls were added. Each of the mentioned hydraulic structures obtained a práctical verification as a verification within the Flow 3D software, presenting a consistency in the results obtained in both ways.
이 매뉴얼은 Fluid Mechanics 및 Applied Hydraulics의 가상 연구실 내에서 Flow 3D로 알려진 소프트웨어에서 기본 수치 모델을 제시하고 실행하기 위해 개발되었으며, 수업에서 배운 내용을 보완하고 강화하기 위해 개발되었으며, 매뉴얼 개발은 이론적인 내용을 다룹니다. 소프트웨어의 특성을 표시하기 위해 학생들을 위한 일부 피드백을 포함하는 것 외에도 소프트웨어 처리에 대한 내용 및 예시된 실제적인 부분. Flow 3D 프로그램을 다루면서 학생은 전산유체역학(Computational Fluid Dynamics) 또는 CFD의 개념과 수력학적 구조의 거동을 수치 및 그래픽으로 표현하는 간단한 절차를 소개합니다. 실험실 매뉴얼에 제시된 유압 구조는 얇고 두꺼운 벽 오리피스, 자유 및 수중 배출이 있는 수문, 자유 및 수중 배출이 있는 얇고 두꺼운 벽 여수로, WES 유형 방수로, 압력 전도 및 보완으로 수중 유입이 있는 수중 흡입구입니다. 수직, 곡선 및 경사 벽에 추가되었습니다. 언급된 각 수력학적 구조는 Flow 3D 소프트웨어 내에서 검증으로 실제 검증을 획득하여 두 가지 방식에서 얻은 결과의 일관성을 나타냅니다.
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CFD Simulations of Tubular Archimedean Screw Turbines Harnessing the Small Hydropotential of Greek Watercourses
Alkistis Stergiopoulou1 , Vassilios Stergiopoulos2 1 Institut für Wasserwirtschaft, Hydrologie und Konstruktiven Wasserbau, B.O.K.U. University, Muthgasse 18, 1190 Vienna, (actually Senior Process Engineer at the VTU Engineering in Vienna, Zieglergasse 53/1/24, 1070 Vienna, Austria). 2 School of Pedagogical and Technological Education, Department of Civil Engineering Educators, ASPETE Campus, Eirini Station, 15122 Amarousio, Athens, Greece.
이 논문은 “그리스 아르키메데스의 부활: 아르키메데스 달팽이관 물레방아의 수리역학 및 유체역학적 거동 연구, 그리스 자연 및 기술 수로의 수력 잠재력 회복에 대한 기여”. 라는 제목의 최근 연구에서 수행한 최초의 아르키메데스 나사 터빈 CFD 모델링 결과에 대한 간략한 견해를 제시합니다.
FLOW-3D 코드를 기반으로 하는 이 CFD 분석은 일반적인 TAST(Tubular Archimedean Screw Turbines)에 관한 것으로, 그리스의 자연 및 기술 수로의 중요한 미개척 수력 잠재력을 활용하는 소규모 수력 발전 시스템에 대한 TWh/년 및 수천 MW 범위의 총 설치 용량등 몇 가지 유망한 성능을 보여줍니다.
This paper presents a short view of the first Archimedean Screw Turbines CFD modelling results, which were carried out within the recent research entitled “Rebirth of Archimedes in Greece: contribution to the study of hydraulic mechanics and hydrodynamic behavior of Archimedean cochlear waterwheels, for recovering the hydraulic potential of Greek natural and technical watercourses”. This CFD analysis, based to the Flow-3D code, concerns typical Tubular Archimedean Screw Turbines (TASTs) and shows some promising performances for such small hydropower systems harnessing the important unexploited hydraulic potential of natural and technical watercourses of Greece, of the order of several TWh / year and of a total installed capacity in the range of thousands MWs.
CFD; Flow-3D; TAST; Small Hydro; Renewable Energy; Greek Watercourses.
 A. Stergiopoulou, Computational and experimental investigation of the hydrodynamic behaviour of screw hydro turbine, Ph.D. Thesis, NTUA, 2017.  B. Pelikan, A. Lashofer, Verbesserung der Strömungseigenschaften sowie Planungs-und Betriebsoptimierung von Wasserkraftschnecken, Research Project, BOKU University, Vienna, 2012.  G. Müller, J. Senior, Simplified theory of Archimedean screws, Journal of Hydraulic Research 47 (5) (2009) 666-669.  C. Rorres, The turn of the screw: Optimal design of an Archimedes screw, Journal of Hydraulic Engineering, 80 (2000) 72-80.  A. Stergiopoulou, V. Stergiopoulos, Return of Archimedes: Harnessing with new Archimedean spirals the hydraulic potential of the Greek watercourses, in: Proceedings of the Conference for Climate Change, Thessaloniki, 2009.  A. Stergiopoulou, V. Stergiopoulos, from the old Archimedean screw pumps to the new Archimedean screw turbines for hydropower production in Greece, in: Proceedings of CEMEPE Conference, Mykonos, June 21-26, 2009.
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Ruigeng Hu 1 , Hongjun Liu 2 , Hao Leng 1 , Peng Yu 3 and Xiuhai Wang 1,2,*
1 College of Environmental Science and Engineering, Ocean University of China, Qingdao 266000, China; email@example.com (R.H.); firstname.lastname@example.org (H.L.) 2 Key Lab of Marine Environment and Ecology (Ocean University of China), Ministry of Education, Qingdao 266000, China; email@example.com 3 Qingdao Geo-Engineering Survering Institute, Qingdao 266100, China; firstname.lastname@example.org
무작위 파동 하에서 우산 흡입 앵커 기초(USAF) 주변의 국부 세굴을 연구하기 위해 일련의 수치 시뮬레이션이 수행되었습니다. 본 연구에서는 먼저 본 모델의 정확성을 검증하기 위해 검증을 수행하였다.
또한, 세굴 진화와 세굴 메커니즘을 각각 분석하였다. 또한 USAF 주변의 평형 세굴 깊이 Seq를 예측하기 위해 두 가지 수정된 모델이 제안되었습니다. 마지막으로 Seq에 대한 Froude 수 Fr과 Euler 수 Eu의 영향을 연구하기 위해 매개변수 연구가 수행되었습니다.
결과는 현재 수치 모델이 무작위 파동에서 세굴 형태를 묘사하는 데 정확하고 합리적임을 나타냅니다.
수정된 Raaijmaker의 모델은 KCs,p < 8일 때 본 연구의 시뮬레이션 결과와 잘 일치함을 보여줍니다. 수정된 확률적 모델의 예측 결과는 KCrms,a < 4일 때 n = 10일 때 가장 유리합니다. Fr과 Eu가 높을수록 둘 다 더 집중적 인 말굽 소용돌이와 더 큰 결과를 초래합니다.
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Mahdi Feizbahr,1 Navid Tonekaboni,2Guang-Jun Jiang,3,4 and Hong-Xia Chen3,4Show moreAcademic Editor: Mohammad YazdiReceived08 Apr 2021Revised18 Jun 2021Accepted17 Jul 2021Published11 Aug 2021
Vegetation along the river increases the roughness and reduces the average flow velocity, reduces flow energy, and changes the flow velocity profile in the cross section of the river. Many canals and rivers in nature are covered with vegetation during the floods. Canal’s roughness is strongly affected by plants and therefore it has a great effect on flow resistance during flood. Roughness resistance against the flow due to the plants depends on the flow conditions and plant, so the model should simulate the current velocity by considering the effects of velocity, depth of flow, and type of vegetation along the canal. Total of 48 models have been simulated to investigate the effect of roughness in the canal. The results indicated that, by enhancing the velocity, the effect of vegetation in decreasing the bed velocity is negligible, while when the current has lower speed, the effect of vegetation on decreasing the bed velocity is obviously considerable.
강의 식생은 거칠기를 증가시키고 평균 유속을 감소시키며, 유속 에너지를 감소시키고 강의 단면에서 유속 프로파일을 변경합니다. 자연의 많은 운하와 강은 홍수 동안 초목으로 덮여 있습니다. 운하의 조도는 식물의 영향을 많이 받으므로 홍수시 유동저항에 큰 영향을 미칩니다. 식물로 인한 흐름에 대한 거칠기 저항은 흐름 조건 및 식물에 따라 다르므로 모델은 유속, 흐름 깊이 및 운하를 따라 식생 유형의 영향을 고려하여 현재 속도를 시뮬레이션해야 합니다. 근관의 거칠기의 영향을 조사하기 위해 총 48개의 모델이 시뮬레이션되었습니다. 결과는 유속을 높임으로써 유속을 감소시키는 식생의 영향은 무시할 수 있는 반면, 해류가 더 낮은 유속일 때 유속을 감소시키는 식생의 영향은 분명히 상당함을 나타냈다.
Considering the impact of each variable is a very popular field within the analytical and statistical methods and intelligent systems [1–14]. This can help research for better modeling considering the relation of variables or interaction of them toward reaching a better condition for the objective function in control and engineering [15–27]. Consequently, it is necessary to study the effects of the passive factors on the active domain [28–36]. Because of the effect of vegetation on reducing the discharge capacity of rivers , pruning plants was necessary to improve the condition of rivers. One of the important effects of vegetation in river protection is the action of roots, which cause soil consolidation and soil structure improvement and, by enhancing the shear strength of soil, increase the resistance of canal walls against the erosive force of water. The outer limbs of the plant increase the roughness of the canal walls and reduce the flow velocity and deplete the flow energy in vicinity of the walls. Vegetation by reducing the shear stress of the canal bed reduces flood discharge and sedimentation in the intervals between vegetation and increases the stability of the walls [38–41].
One of the main factors influencing the speed, depth, and extent of flood in this method is Manning’s roughness coefficient. On the other hand, soil cover , especially vegetation, is one of the most determining factors in Manning’s roughness coefficient. Therefore, it is expected that those seasonal changes in the vegetation of the region will play an important role in the calculated value of Manning’s roughness coefficient and ultimately in predicting the flood wave behavior [43–45]. The roughness caused by plants’ resistance to flood current depends on the flow and plant conditions. Flow conditions include depth and velocity of the plant, and plant conditions include plant type, hardness or flexibility, dimensions, density, and shape of the plant . In general, the issue discussed in this research is the optimization of flood-induced flow in canals by considering the effect of vegetation-induced roughness. Therefore, the effect of plants on the roughness coefficient and canal transmission coefficient and in consequence the flow depth should be evaluated [47, 48].
Current resistance is generally known by its roughness coefficient. The equation that is mainly used in this field is Manning equation. The ratio of shear velocity to average current velocity is another form of current resistance. The reason for using the ratio is that it is dimensionless and has a strong theoretical basis. The reason for using Manning roughness coefficient is its pervasiveness. According to Freeman et al. , the Manning roughness coefficient for plants was calculated according to the Kouwen and Unny  method for incremental resistance. This method involves increasing the roughness for various surface and plant irregularities. Manning’s roughness coefficient has all the factors affecting the resistance of the canal. Therefore, the appropriate way to more accurately estimate this coefficient is to know the factors affecting this coefficient .
To calculate the flow rate, velocity, and depth of flow in canals as well as flood and sediment estimation, it is important to evaluate the flow resistance. To determine the flow resistance in open ducts, Manning, Chézy, and Darcy–Weisbach relations are used . In these relations, there are parameters such as Manning’s roughness coefficient (n), Chézy roughness coefficient (C), and Darcy–Weisbach coefficient (f). All three of these coefficients are a kind of flow resistance coefficient that is widely used in the equations governing flow in rivers .
The three relations that express the relationship between the average flow velocity (V) and the resistance and geometric and hydraulic coefficients of the canal are as follows:where n, f, and c are Manning, Darcy–Weisbach, and Chézy coefficients, respectively. V = average flow velocity, R = hydraulic radius, Sf = slope of energy line, which in uniform flow is equal to the slope of the canal bed, = gravitational acceleration, and Kn is a coefficient whose value is equal to 1 in the SI system and 1.486 in the English system. The coefficients of resistance in equations (1) to (3) are related as follows:
Based on the boundary layer theory, the flow resistance for rough substrates is determined from the following general relation:where f = Darcy–Weisbach coefficient of friction, y = flow depth, Ks = bed roughness size, and A = constant coefficient.
On the other hand, the relationship between the Darcy–Weisbach coefficient of friction and the shear velocity of the flow is as follows:
By using equation (6), equation (5) is converted as follows:
Investigation on the effect of vegetation arrangement on shear velocity of flow in laboratory conditions showed that, with increasing the shear Reynolds number (), the numerical value of the ratio also increases; in other words the amount of roughness coefficient increases with a slight difference in the cases without vegetation, checkered arrangement, and cross arrangement, respectively .
Roughness in river vegetation is simulated in mathematical models with a variable floor slope flume by different densities and discharges. The vegetation considered submerged in the bed of the flume. Results showed that, with increasing vegetation density, canal roughness and flow shear speed increase and with increasing flow rate and depth, Manning’s roughness coefficient decreases. Factors affecting the roughness caused by vegetation include the effect of plant density and arrangement on flow resistance, the effect of flow velocity on flow resistance, and the effect of depth [45, 55].
One of the works that has been done on the effect of vegetation on the roughness coefficient is Darby  study, which investigates a flood wave model that considers all the effects of vegetation on the roughness coefficient. There are currently two methods for estimating vegetation roughness. One method is to add the thrust force effect to Manning’s equation [47, 57, 58] and the other method is to increase the canal bed roughness (Manning-Strickler coefficient) [45, 59–61]. These two methods provide acceptable results in models designed to simulate floodplain flow. Wang et al.  simulate the floodplain with submerged vegetation using these two methods and to increase the accuracy of the results, they suggested using the effective height of the plant under running water instead of using the actual height of the plant. Freeman et al.  provided equations for determining the coefficient of vegetation roughness under different conditions. Lee et al.  proposed a method for calculating the Manning coefficient using the flow velocity ratio at different depths. Much research has been done on the Manning roughness coefficient in rivers, and researchers [49, 63–66] sought to obtain a specific number for n to use in river engineering. However, since the depth and geometric conditions of rivers are completely variable in different places, the values of Manning roughness coefficient have changed subsequently, and it has not been possible to choose a fixed number. In river engineering software, the Manning roughness coefficient is determined only for specific and constant conditions or normal flow. Lee et al.  stated that seasonal conditions, density, and type of vegetation should also be considered. Hydraulic roughness and Manning roughness coefficient n of the plant were obtained by estimating the total Manning roughness coefficient from the matching of the measured water surface curve and water surface height. The following equation is used for the flow surface curve:where is the depth of water change, S0 is the slope of the canal floor, Sf is the slope of the energy line, and Fr is the Froude number which is obtained from the following equation:where D is the characteristic length of the canal. Flood flow velocity is one of the important parameters of flood waves, which is very important in calculating the water level profile and energy consumption. In the cases where there are many limitations for researchers due to the wide range of experimental dimensions and the variety of design parameters, the use of numerical methods that are able to estimate the rest of the unknown results with acceptable accuracy is economically justified.
FLOW-3D software uses Finite Difference Method (FDM) for numerical solution of two-dimensional and three-dimensional flow. This software is dedicated to computational fluid dynamics (CFD) and is provided by Flow Science . The flow is divided into networks with tubular cells. For each cell there are values of dependent variables and all variables are calculated in the center of the cell, except for the velocity, which is calculated at the center of the cell. In this software, two numerical techniques have been used for geometric simulation, FAVOR™ (Fractional-Area-Volume-Obstacle-Representation) and the VOF (Volume-of-Fluid) method. The equations used at this model for this research include the principle of mass survival and the magnitude of motion as follows. The fluid motion equations in three dimensions, including the Navier–Stokes equations with some additional terms, are as follows:where are mass accelerations in the directions x, y, z and are viscosity accelerations in the directions x, y, z and are obtained from the following equations:
Shear stresses in equation (11) are obtained from the following equations:
The standard model is used for high Reynolds currents, but in this model, RNG theory allows the analytical differential formula to be used for the effective viscosity that occurs at low Reynolds numbers. Therefore, the RNG model can be used for low and high Reynolds currents.
Weather changes are high and this affects many factors continuously. The presence of vegetation in any area reduces the velocity of surface flows and prevents soil erosion, so vegetation will have a significant impact on reducing destructive floods. One of the methods of erosion protection in floodplain watersheds is the use of biological methods. The presence of vegetation in watersheds reduces the flow rate during floods and prevents soil erosion. The external organs of plants increase the roughness and decrease the velocity of water flow and thus reduce its shear stress energy. One of the important factors with which the hydraulic resistance of plants is expressed is the roughness coefficient. Measuring the roughness coefficient of plants and investigating their effect on reducing velocity and shear stress of flow is of special importance.
Roughness coefficients in canals are affected by two main factors, namely, flow conditions and vegetation characteristics . So far, much research has been done on the effect of the roughness factor created by vegetation, but the issue of plant density has received less attention. For this purpose, this study was conducted to investigate the effect of vegetation density on flow velocity changes.
In a study conducted using a software model on three density modes in the submerged state effect on flow velocity changes in 48 different modes was investigated (Table 1).Table 1The studied models.
The number of cells used in this simulation is equal to 1955888 cells. The boundary conditions were introduced to the model as a constant speed and depth (Figure 1). At the output boundary, due to the presence of supercritical current, no parameter for the current is considered. Absolute roughness for floors and walls was introduced to the model (Figure 1). In this case, the flow was assumed to be nonviscous and air entry into the flow was not considered. After seconds, this model reached a convergence accuracy of .
Figure 1The simulated model and its boundary conditions.
Due to the fact that it is not possible to model the vegetation in FLOW-3D software, in this research, the vegetation of small soft plants was studied so that Manning’s coefficients can be entered into the canal bed in the form of roughness coefficients obtained from the studies of Chow  in similar conditions. In practice, in such modeling, the effect of plant height is eliminated due to the small height of herbaceous plants, and modeling can provide relatively acceptable results in these conditions.
48 models with input velocities proportional to the height of the regular semihexagonal canal were considered to create supercritical conditions. Manning coefficients were applied based on Chow  studies in order to control the canal bed. Speed profiles were drawn and discussed.
Any control and simulation system has some inputs that we should determine to test any technology [70–77]. Determination and true implementation of such parameters is one of the key steps of any simulation [23, 78–81] and computing procedure [82–86]. The input current is created by applying the flow rate through the VFR (Volume Flow Rate) option and the output flow is considered Output and for other borders the Symmetry option is considered.
Simulation of the models and checking their action and responses and observing how a process behaves is one of the accepted methods in engineering and science [87, 88]. For verification of FLOW-3D software, the results of computer simulations are compared with laboratory measurements and according to the values of computational error, convergence error, and the time required for convergence, the most appropriate option for real-time simulation is selected (Figures 2 and 3 ).
Figure 2Modeling the plant with cylindrical tubes at the bottom of the canal.
Figure 3Velocity profiles in positions 2 and 5.
The canal is 7 meters long, 0.5 meters wide, and 0.8 meters deep. This test was used to validate the application of the software to predict the flow rate parameters. In this experiment, instead of using the plant, cylindrical pipes were used in the bottom of the canal.
The conditions of this modeling are similar to the laboratory conditions and the boundary conditions used in the laboratory were used for numerical modeling. The critical flow enters the simulation model from the upstream boundary, so in the upstream boundary conditions, critical velocity and depth are considered. The flow at the downstream boundary is supercritical, so no parameters are applied to the downstream boundary.
The software well predicts the process of changing the speed profile in the open canal along with the considered obstacles. The error in the calculated speed values can be due to the complexity of the flow and the interaction of the turbulence caused by the roughness of the floor with the turbulence caused by the three-dimensional cycles in the hydraulic jump. As a result, the software is able to predict the speed distribution in open canals.
2. Modeling Results
After analyzing the models, the results were shown in graphs (Figures 4–14 ). The total number of experiments in this study was 48 due to the limitations of modeling. (a) (b) (c) (d) (a) (b) (c) (d)Figure 4Flow velocity profiles for canals with a depth of 1 m and flow velocities of 3–3.3 m/s. Canal with a depth of 1 meter and a flow velocity of (a) 3 meters per second, (b) 3.1 meters per second, (c) 3.2 meters per second, and (d) 3.3 meters per second.
Figure 5Canal diagram with a depth of 1 meter and a flow rate of 3 meters per second.
Figure 6Canal diagram with a depth of 1 meter and a flow rate of 3.1 meters per second.
Figure 7Canal diagram with a depth of 1 meter and a flow rate of 3.2 meters per second.
Figure 8Canal diagram with a depth of 1 meter and a flow rate of 3.3 meters per second. (a) (b) (c) (d) (a) (b) (c) (d)Figure 9Flow velocity profiles for canals with a depth of 2 m and flow velocities of 4–4.3 m/s. Canal with a depth of 2 meters and a flow rate of (a) 4 meters per second, (b) 4.1 meters per second, (c) 4.2 meters per second, and (d) 4.3 meters per second.
Figure 10Canal diagram with a depth of 2 meters and a flow rate of 4 meters per second.
Figure 11Canal diagram with a depth of 2 meters and a flow rate of 4.1 meters per second.
Figure 12Canal diagram with a depth of 2 meters and a flow rate of 4.2 meters per second.
Figure 13Canal diagram with a depth of 2 meters and a flow rate of 4.3 meters per second. (a) (b) (c) (d) (a) (b) (c) (d)Figure 14Flow velocity profiles for canals with a depth of 3 m and flow velocities of 5–5.3 m/s. Canal with a depth of 2 meters and a flow rate of (a) 4 meters per second, (b) 4.1 meters per second, (c) 4.2 meters per second, and (d) 4.3 meters per second.
To investigate the effects of roughness with flow velocity, the trend of flow velocity changes at different depths and with supercritical flow to a Froude number proportional to the depth of the section has been obtained.
According to the velocity profiles of Figure 5, it can be seen that, with the increasing of Manning’s coefficient, the canal bed speed decreases.
According to Figures 5 to 8, it can be found that, with increasing the Manning’s coefficient, the canal bed speed decreases. But this deceleration is more noticeable than the deceleration of the models 1 to 12, which can be justified by increasing the speed and of course increasing the Froude number.
According to Figure 10, we see that, with increasing Manning’s coefficient, the canal bed speed decreases.
According to Figure 11, we see that, with increasing Manning’s coefficient, the canal bed speed decreases. But this deceleration is more noticeable than the deceleration of Figures 5–10, which can be justified by increasing the speed and, of course, increasing the Froude number.
With increasing Manning’s coefficient, the canal bed speed decreases (Figure 12). But this deceleration is more noticeable than the deceleration of the higher models (Figures 5–8 and 10, 11), which can be justified by increasing the speed and, of course, increasing the Froude number.
According to Figure 13, with increasing Manning’s coefficient, the canal bed speed decreases. But this deceleration is more noticeable than the deceleration of Figures 5 to 12, which can be justified by increasing the speed and, of course, increasing the Froude number.
According to Figure 15, with increasing Manning’s coefficient, the canal bed speed decreases.
Figure 15Canal diagram with a depth of 3 meters and a flow rate of 5 meters per second.
According to Figure 16, with increasing Manning’s coefficient, the canal bed speed decreases. But this deceleration is more noticeable than the deceleration of the higher model, which can be justified by increasing the speed and, of course, increasing the Froude number.
Figure 16Canal diagram with a depth of 3 meters and a flow rate of 5.1 meters per second.
According to Figure 17, it is clear that, with increasing Manning’s coefficient, the canal bed speed decreases. But this deceleration is more noticeable than the deceleration of the higher models, which can be justified by increasing the speed and, of course, increasing the Froude number.
Figure 17Canal diagram with a depth of 3 meters and a flow rate of 5.2 meters per second.
According to Figure 18, with increasing Manning’s coefficient, the canal bed speed decreases. But this deceleration is more noticeable than the deceleration of the higher models, which can be justified by increasing the speed and, of course, increasing the Froude number.
Figure 18Canal diagram with a depth of 3 meters and a flow rate of 5.3 meters per second.
According to Figure 19, it can be seen that the vegetation placed in front of the flow input velocity has negligible effect on the reduction of velocity, which of course can be justified due to the flexibility of the vegetation. The only unusual thing is the unexpected decrease in floor speed of 3 m/s compared to higher speeds. (a) (b) (c) (a) (b) (c)Figure 19Comparison of velocity profiles with the same plant densities (depth 1 m). Comparison of velocity profiles with (a) plant densities of 25%, depth 1 m; (b) plant densities of 50%, depth 1 m; and (c) plant densities of 75%, depth 1 m.
According to Figure 20, by increasing the speed of vegetation, the effect of vegetation on reducing the flow rate becomes more noticeable. And the role of input current does not have much effect in reducing speed. (a) (b) (c) (a) (b) (c)Figure 20Comparison of velocity profiles with the same plant densities (depth 2 m). Comparison of velocity profiles with (a) plant densities of 25%, depth 2 m; (b) plant densities of 50%, depth 2 m; and (c) plant densities of 75%, depth 2 m.
According to Figure 21, it can be seen that, with increasing speed, the effect of vegetation on reducing the bed flow rate becomes more noticeable and the role of the input current does not have much effect. In general, it can be seen that, by increasing the speed of the input current, the slope of the profiles increases from the bed to the water surface and due to the fact that, in software, the roughness coefficient applies to the channel floor only in the boundary conditions, this can be perfectly justified. Of course, it can be noted that, due to the flexible conditions of the vegetation of the bed, this modeling can show acceptable results for such grasses in the canal floor. In the next directions, we may try application of swarm-based optimization methods for modeling and finding the most effective factors in this research [2, 7, 8, 15, 18, 89–94]. In future, we can also apply the simulation logic and software of this research for other domains such as power engineering [95–99]. (a) (b) (c) (a) (b) (c)Figure 21Comparison of velocity profiles with the same plant densities (depth 3 m). Comparison of velocity profiles with (a) plant densities of 25%, depth 3 m; (b) plant densities of 50%, depth 3 m; and (c) plant densities of 75%, depth 3 m.
The effects of vegetation on the flood canal were investigated by numerical modeling with FLOW-3D software. After analyzing the results, the following conclusions were reached:(i)Increasing the density of vegetation reduces the velocity of the canal floor but has no effect on the velocity of the canal surface.(ii)Increasing the Froude number is directly related to increasing the speed of the canal floor.(iii)In the canal with a depth of one meter, a sudden increase in speed can be observed from the lowest speed and higher speed, which is justified by the sudden increase in Froude number.(iv)As the inlet flow rate increases, the slope of the profiles from the bed to the water surface increases.(v)By reducing the Froude number, the effect of vegetation on reducing the flow bed rate becomes more noticeable. And the input velocity in reducing the velocity of the canal floor does not have much effect.(vi)At a flow rate between 3 and 3.3 meters per second due to the shallow depth of the canal and the higher landing number a more critical area is observed in which the flow bed velocity in this area is between 2.86 and 3.1 m/s.(vii)Due to the critical flow velocity and the slight effect of the roughness of the horseshoe vortex floor, it is not visible and is only partially observed in models 1-2-3 and 21.(viii)As the flow rate increases, the effect of vegetation on the rate of bed reduction decreases.(ix)In conditions where less current intensity is passing, vegetation has a greater effect on reducing current intensity and energy consumption increases.(x)In the case of using the flow rate of 0.8 cubic meters per second, the velocity distribution and flow regime show about 20% more energy consumption than in the case of using the flow rate of 1.3 cubic meters per second.
Manning’s roughness coefficient
Chézy roughness coefficient
Depth of water change
Slope of the canal floor
Slope of energy line
Characteristic length of the canal
All data are included within the paper.
Conflicts of Interest
The authors declare that they have no conflicts of interest.
This work was partially supported by the National Natural Science Foundation of China under Contract no. 71761030 and Natural Science Foundation of Inner Mongolia under Contract no. 2019LH07003.
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Probabilistic investigation of cavitation occurrence in chute spillway based on the results of Flow-3D numerical modeling
Amin Hasanalipour Shahrabadi1*, Mehdi Azhdary Moghaddam2
1-University of Sistan and Baluchestan،email@example.com
2-University of Sistan and Baluchestan،Mazhdary@eng.usb.ac.ir
Probabilistic designation is a powerful tool in hydraulic engineering. The uncertainty caused by random phenomenon in hydraulic design may be important. Uncertainty can be expressed in terms of probability density function, confidence interval, or statistical torques such as standard deviation or coefficient of variation of random parameters. Controlling cavitation occurrence is one of the most important factors in chute spillways designing due to the flow’s high velocity and the negative pressure (Azhdary Moghaddam & Hasanalipour Shahrabadi, ۲۰۲۰). By increasing dam’s height, overflow velocity increases on the weir and threats the structure and it may cause structural failure due to cavitation (Chanson, ۲۰۱۳). Cavitation occurs when the fluid pressure reaches its vapor pressure. Since high velocity and low pressure can cause cavitation, aeration has been recognized as one of the best ways to deal with cavitation (Pettersson, ۲۰۱۲). This study, considering the extracted results from the Flow-۳D numerical model of the chute spillway of Darian dam, investigates the probability of cavitation occurrence and examines its reliability. Hydraulic uncertainty in the design of this hydraulic structure can be attributed to the uncertainty of the hydraulic performance analysis. Therefore, knowing about the uncertainty characteristics of hydraulic engineering systems for assessing their reliability seems necessary (Yen et al., ۱۹۹۳). Hence, designation and operation of hydraulic engineering systems are always subject to uncertainties and probable failures. The reliability, ps, of a hydraulic engineering system is defined as the probability of safety in which the resistance, R, of the system exceeds the load, L, as follows (Chen, ۲۰۱۵): p_s=P(L≤R) (۱) Where P(۰) is probability. The failure probability, p_f, is a reliability complement and is expressed as follows: p_f=P[(L>R)]=۱- p_s (۲) Reliability development based on analytical methods of engineering applications has come in many references (Tung & Mays, ۱۹۸۰ and Yen & Tung, ۱۹۹۳). Therefore, based on reliability, in a control method, the probability of cavitation occurrence in the chute spillway can be investigated. In reliability analysis, the probabilistic calculations must be expressed in terms of a limited conditional function, W(X)=W(X_L ,X_R)as follows: p_s=P[W(X_L ,X_R)≥۰]= P[W(X)≥۰] (۳) Where X is the vector of basic random variables in load and resistance functions. In the reliability analysis, if W(X)> ۰, the system will be secure and in the W(X) <۰ system will fail. Accordingly, the eliability index, β, is used, which is defined as the ratio of the mean value, μ_W, to standard deviation, σ_W, the limited conditional function W(X) is defined as follows (Cornell, ۱۹۶۹): β=μ_W/σ_W (۴) The present study was carried out using the obtained results from the model developed by ۱:۵۰ scale plexiglass at the Water Research Institute of Iran. In this laboratory model, which consists of an inlet channel and a convergent thrower chute spillway, two aerators in the form of deflector were used at the intervals of ۲۱۱ and ۲۷۰ at the beginning of chute, in order to cope with cavitation phenomenon during the chute. An air duct was also used for air inlet on the left and right walls of the spillway. To measure the effective parameters in cavitation, seven discharges have been passed through spillway. As the pressure and average velocity are determined, the values of the cavitation index are calculated and compared with the values of the critical cavitation index, σ_cr. At any point when σ≤σ_cr, there is a danger of corrosion in that range (Chanson, ۱۹۹۳). In order to obtain uncertainty and calculate the reliability index of cavitation occurrence during a chute, it is needed to extract the limited conditional function. Therefore, for a constant flow between two points of flow, there would be the Bernoulli (energy) relation as follows (Falvey, ۱۹۹۰): σ= ( P_atm/γ- P_V/γ+h cosθ )/(〖V_۰〗^۲/۲g) (۵) Where P_atm is the atmospheric pressure, γ is the unit weight of the water volume, θ is the angle of the ramp to the horizon, r is the curvature radius of the vertical arc, and h cosθ is the flow depth perpendicular to the floor. Therefore, the limited conditional function can be written as follows: W(X)=(P_atm/γ- P_V/γ+h cosθ )/(〖V_۰〗^۲/۲g) -σ_cr (۶) Flow-۳D is a powerful software in fluid dynamics. One of the major capabilities of this software is to model free-surface flows using finite volume method for hydraulic analysis. The spillway was modeled in three modes, without using aerator, ramp aerator, and ramp combination with aeration duct as detailed in Flow-۳D software. For each of the mentioned modes, seven discharges were tested. According to Equation (۶), velocity and pressure play a decisive and important role in the cavitation occurrence phenomenon. Therefore, the reliability should be evaluated with FORM (First Order Reliable Method) based on the probability distribution functions For this purpose, the most suitable probability distribution function of random variables of velocity and pressure on a laboratory model was extracted in different sections using Easy fit software. Probability distribution function is also considered normal for the other variables in the limited conditional function. These values are estimated for the constant gravity at altitudes of ۵۰۰ to ۷۰۰۰ m above the sea level for the unit weight, and vapor pressure at ۵ to ۳۵° C. For the critical cavitation index variable, the standard deviation is considered as ۰.۰۱. According to the conducted tests, for the velocity random variable, GEV (Generalized Extreme Value) distribution function, and for the pressure random variable, Burr (۴P) distribution function were presented as the best distribution function. The important point is to not follow the normal distribution above the random variables. Therefore, in order to evaluate the reliability with the FORM method, according to the above distributions, they should be converted into normal variables based on the existing methods. To this end, the non-normal distributions are transformed into the normal distribution by the method of Rackwitz and Fiiessler so that the value of the cumulative distribution function is equivalent to the original abnormal distribution at the design point of x_(i*). This point has the least distance from the origin in the standardized space of the boundary plane or the same limited conditional function. The reliability index will be equal to ۰.۴۲۰۴ before installing the aerator. As a result, reliability, p_s, and failure probability, p_f, are ۰.۶۶۲۹ and ۰.۳۳۷۱, respectively. This number indicates a high percentage for cavitation occurrence. Therefore, the use of aerator is inevitable to prevent imminent damage from cavitation. To deal with cavitation as planned in the laboratory, two aerators with listed specifications are embedded in a location where the cavitation index is critical. In order to analyze the reliability of cavitation occurrence after the aerator installation, the steps of the Hasofer-Lind algorithm are repeated. The modeling of ramps was performed separately in Flow-۳D software in order to compare the performance of aeration ducts as well as the probability of failure between aeration by ramp and the combination of ramps and aeration ducts. Installing an aerator in combination with a ramp and aerator duct greatly reduces the probability of cavitation occurrence. By installing aerator, the probability of cavitation occurrence will decrease in to about ۴ %. However, in the case of aeration only through the ramp, the risk of failure is equal to ۱۰%.
확률적 지정은 수력 공학에서 강력한 도구입니다. 유압 설계에서 임의 현상으로 인한 불확실성이 중요할 수 있습니다. 불확실성은 확률 밀도 함수, 신뢰 구간 또는 표준 편차 또는 무작위 매개변수의 변동 계수와 같은 통계적 토크로 표현될 수 있습니다. 캐비테이션 발생을 제어하는 것은 흐름의 높은 속도와 음압으로 인해 슈트 여수로 설계에서 가장 중요한 요소 중 하나입니다(Azhdary Moghaddam & Hasanalipour Shahrabadi, ۲۰۲۰). 댐의 높이를 높이면 둑의 범람속도가 증가하여 구조물을 위협하고 캐비테이션으로 인한 구조물의 파손을 유발할 수 있다(Chanson, ۲۰۱۳). 캐비테이션은 유체 압력이 증기압에 도달할 때 발생합니다. 높은 속도와 낮은 압력은 캐비테이션을 유발할 수 있으므로, 통기는 캐비테이션을 처리하는 가장 좋은 방법 중 하나로 인식되어 왔습니다(Pettersson, ۲۰۱۲). 본 연구에서는 Darian 댐의 슈트 여수로의 Flow-۳D 수치모델에서 추출된 결과를 고려하여 캐비테이션 발생 확률을 조사하고 그 신뢰성을 조사하였다. 이 수력구조의 설계에서 수력학적 불확실성은 수력성능 해석의 불확실성에 기인할 수 있다. 따라서 신뢰성을 평가하기 위해서는 수력공학 시스템의 불확도 특성에 대한 지식이 필요해 보인다(Yen et al., ۱۹۹۳). 따라서 수력 공학 시스템의 지정 및 작동은 항상 불확실성과 가능한 고장의 영향을 받습니다. 유압 공학 시스템의 신뢰성 ps는 저항 R, 시스템의 부하 L은 다음과 같이 초과됩니다(Chen, ۲۰۱۵): p_s=P(L≤R)(۱) 여기서 P(۰)은 확률입니다. 고장 확률 p_f는 신뢰도 보완이며 다음과 같이 표현됩니다. Mays, ۱۹۸۰ 및 Yen & Tung, ۱۹۹۳). 따라서 신뢰성을 기반으로 제어 방법에서 슈트 여수로의 캐비테이션 발생 확률을 조사할 수 있습니다. 신뢰도 분석에서 확률적 계산은 제한된 조건부 함수 W(X)=W(X_L , X_R)은 다음과 같습니다. p_s=P[W(X_L,X_R)≥۰]= P[W(X)≥۰] (۳) 여기서 X는 부하 및 저항 함수의 기본 랜덤 변수 벡터입니다. 신뢰도 분석에서 W(X)> ۰이면 시스템은 안전하고 W(X) <۰에서는 시스템이 실패합니다. 따라서 표준편차 σ_W에 대한 평균값 μ_W의 비율로 정의되는 신뢰도 지수 β가 사용되며, 제한된 조건부 함수 W(X)는 다음과 같이 정의됩니다(Cornell, ۱۹۶۹). β= μ_W/σ_W (۴) 본 연구는 이란 물연구소의 ۱:۵۰ scale plexiglass로 개발된 모델로부터 얻은 결과를 이용하여 수행하였다. 이 실험 모델에서, 입구 수로와 수렴형 투수 슈트 여수로로 구성되며 슈트 중 캐비테이션 현상에 대처하기 위해 슈트 초기에 ۲۱۱과 ۲۷۰ 간격으로 편향기 형태의 2개의 에어레이터를 사용하였다. 여수로 좌우 벽의 공기 유입구에도 공기 덕트가 사용되었습니다. 캐비테이션의 효과적인 매개변수를 측정하기 위해 7번의 배출이 방수로를 통과했습니다. 압력과 평균 속도가 결정되면 캐비테이션 지수 값이 계산되고 임계 캐비테이션 지수 σ_cr 값과 비교됩니다. σ≤σ_cr일 때 그 범위에서 부식의 위험이 있다(Chanson, ۱۹۹۳). 슈트 중 캐비테이션 발생의 불확실성을 구하고 신뢰도 지수를 계산하기 위해서는 제한된 조건부 함수를 추출할 필요가 있다. 따라서 두 지점 사이의 일정한 흐름에 대해 다음과 같은 Bernoulli(에너지) 관계가 있습니다(Falvey, ۱۹۹۰). σ= ( P_atm/γ- P_V/γ+h cosθ )/(〖V_۰〗 ^۲/۲g) (۵) 여기서 P_atm은 대기압, γ는 물의 단위 중량, θ는 수평선에 대한 경사로의 각도, r은 수직 호의 곡률 반경, h cos θ는 바닥에 수직인 흐름 깊이입니다. 따라서 제한된 조건부 함수는 다음과 같이 쓸 수 있습니다. W(X)=(P_atm/γ- P_V/γ+h cosθ )/(〖V_۰〗^۲/۲g) -σ_cr (۶) Flow-۳D는 유체 역학의 강력한 소프트웨어. 이 소프트웨어의 주요 기능 중 하나는 수리학적 해석을 위해 유한 체적 방법을 사용하여 자유 표면 흐름을 모델링하는 것입니다. 방수로는 Flow-۳D 소프트웨어에 자세히 설명된 바와 같이 폭기 장치, 램프 폭기 장치 및 폭기 덕트가 있는 램프 조합을 사용하지 않고 세 가지 모드로 모델링되었습니다. 언급된 각 모드에 대해 7개의 방전이 테스트되었습니다. 식 (۶)에 따르면 속도와 압력은 캐비테이션 발생 현상에 결정적이고 중요한 역할을 합니다. 따라서 확률분포함수에 기반한 FORM(First Order Reliable Method)으로 신뢰도를 평가해야 한다 이를 위해 실험실 모델에 대한 속도와 압력의 확률변수 중 가장 적합한 확률분포함수를 Easy fit을 이용하여 구간별로 추출하였다. 소프트웨어. 확률 분포 함수는 제한된 조건부 함수의 다른 변수에 대해서도 정상으로 간주됩니다. 이 값은 단위 중량의 경우 해발 ۵۰۰ ~ ۷۰۰۰ m 고도에서의 일정한 중력과 ۵ ~ ۳۵ ° C에서의 증기압으로 추정됩니다. 임계 캐비테이션 지수 변수의 표준 편차는 ۰.۰۱으로 간주됩니다. . 수행된 시험에 따르면 속도 확률변수는 GEV(Generalized Extreme Value) 분포함수로, 압력변수는 Burr(۴P) 분포함수가 가장 좋은 분포함수로 제시되었다. 중요한 점은 확률 변수 위의 정규 분포를 따르지 않는 것입니다. 따라서 FORM 방법으로 신뢰도를 평가하기 위해서는 위의 분포에 따라 기존 방법을 기반으로 정규 변수로 변환해야 합니다. 이를 위해, 비정규분포를 Rackwitz와 Fiiessler의 방법에 의해 정규분포로 변환하여 누적분포함수의 값이 x_(i*)의 설계점에서 원래의 비정상분포와 같도록 한다. 이 점은 경계면의 표준화된 공간 또는 동일한 제한된 조건부 함수에서 원점으로부터 최소 거리를 갖습니다. 신뢰성 지수는 폭기 장치를 설치하기 전의 ۰.۴۲۰۴과 같습니다. 그 결과 신뢰도 p_s와 고장확률 p_f는 각각 ۰.۶۶۲۹과 ۰.۳۳۷۱이다. 이 숫자는 캐비테이션 발생의 높은 비율을 나타냅니다. 따라서 캐비테이션으로 인한 즉각적인 손상을 방지하기 위해 폭기 장치의 사용이 불가피합니다. 실험실에서 계획한 대로 캐비테이션을 처리하기 위해, 나열된 사양을 가진 두 개의 폭기 장치는 캐비테이션 지수가 중요한 위치에 내장되어 있습니다. 폭기장치 설치 후 캐비테이션 발생의 신뢰성을 분석하기 위해 Hasofer-Lind 알고리즘의 단계를 반복합니다. 경사로의 모델링은 폭기 덕트의 성능과 경사로에 의한 폭기 및 경사로와 폭기 덕트의 조합 사이의 실패 확률을 비교하기 위해 Flow-۳D 소프트웨어에서 별도로 수행되었습니다. 경사로 및 폭기 덕트와 함께 폭기 장치를 설치하면 캐비테이션 발생 가능성이 크게 줄어듭니다. 에어레이터를 설치하면 캐비테이션 발생 확률이 약 ۴%로 감소합니다. 그러나 램프를 통한 폭기의 경우 실패 위험은 ۱۰%와 같습니다. 폭기 설치 후 캐비테이션 발생의 신뢰성을 분석하기 위해 Hasofer-Lind 알고리즘의 단계를 반복합니다. 경사로의 모델링은 폭기 덕트의 성능과 경사로에 의한 폭기 및 경사로와 폭기 덕트의 조합 사이의 실패 확률을 비교하기 위해 Flow-۳D 소프트웨어에서 별도로 수행되었습니다. 경사로 및 폭기 덕트와 함께 폭기 장치를 설치하면 캐비테이션 발생 가능성이 크게 줄어듭니다. 에어레이터를 설치하면 캐비테이션 발생 확률이 약 ۴%로 감소합니다. 그러나 램프를 통한 폭기의 경우 실패 위험은 ۱۰%와 같습니다. 폭기장치 설치 후 캐비테이션 발생의 신뢰성을 분석하기 위해 Hasofer-Lind 알고리즘의 단계를 반복합니다. 경사로의 모델링은 폭기 덕트의 성능과 경사로에 의한 폭기 및 경사로와 폭기 덕트의 조합 사이의 실패 확률을 비교하기 위해 Flow-۳D 소프트웨어에서 별도로 수행되었습니다. 경사로 및 폭기 덕트와 함께 폭기 장치를 설치하면 캐비테이션 발생 가능성이 크게 줄어듭니다. 에어레이터를 설치하면 캐비테이션 발생 확률이 약 ۴%로 감소합니다. 그러나 램프를 통한 폭기의 경우 실패 위험은 ۱۰%와 같습니다. 경사로의 모델링은 폭기 덕트의 성능과 경사로에 의한 폭기 및 경사로와 폭기 덕트의 조합 사이의 실패 확률을 비교하기 위해 Flow-۳D 소프트웨어에서 별도로 수행되었습니다. 경사로 및 폭기 덕트와 함께 폭기 장치를 설치하면 캐비테이션 발생 가능성이 크게 줄어듭니다. 에어레이터를 설치하면 캐비테이션 발생 확률이 약 ۴%로 감소합니다. 그러나 램프를 통한 폭기의 경우 실패 위험은 ۱۰%와 같습니다. 경사로의 모델링은 폭기 덕트의 성능과 경사로에 의한 폭기 및 경사로와 폭기 덕트의 조합 사이의 실패 확률을 비교하기 위해 Flow-۳D 소프트웨어에서 별도로 수행되었습니다. 경사로 및 폭기 덕트와 함께 폭기 장치를 설치하면 캐비테이션 발생 가능성이 크게 줄어듭니다. 에어레이터를 설치하면 캐비테이션 발생 확률이 약 ۴%로 감소합니다. 그러나 램프를 통한 폭기의 경우 실패 위험은 ۱۰%와 같습니다. 에어레이터를 설치하면 캐비테이션 발생 확률이 약 ۴%로 감소합니다. 그러나 램프를 통한 폭기의 경우 실패 위험은 ۱۰%와 같습니다. 에어레이터를 설치하면 캐비테이션 발생 확률이 약 ۴%로 감소합니다. 그러나 램프를 통한 폭기의 경우 실패 위험은 ۱۰%와 같습니다.
Aerator Probable Failure Reliability Method FORM Flow ۳D.
이 논문은 FLOW-3D를 적용하여 다양한 흐름 배출 및 식생 시나리오가 유속(종방향, 횡방향 및 수직 속도 포함)에 미치는 영향을 조사합니다.
실험적 측정을 통한 검증 후 식생직경, 식생높이, 유출량에 대한 민감도 분석을 수행하였습니다. 종방향 속도의 경우 흐름 구조에 대한 가장 큰 영향은 배출보다는 식생 직경에서 비롯됩니다.
그러나 식생 높이는 수직 분포의 변곡점을 결정합니다. 식생 지역, 즉 상류와 하류의 두 위치에서 횡단 속도를 비교하면 수심을 따라 대칭 패턴이 식별됩니다. 식생 지역의 횡단 및 수직 유체 순환 패턴을 포함하여 흐름 또는 식생 시나리오에 관계없이 수직 속도에서도 동일한 패턴이 관찰됩니다.
또한 식생 직경이 클수록 이러한 패턴이 더 분명해집니다. 상부 순환은 식생 캐노피 근처에서 발생합니다. 식생 지역의 가로 세로 방향 순환에 관한 이러한 발견은 수중 식생을 통한 3차원 흐름 구조를 밝혀줍니다.
This paper applies the Flow-3D to investigate the impacts of different flow discharge and vegetation scenarios on the flow velocity (including the longitudinal, transverse and vertical velocities). After the verification by using experimental measurements, a sensitivity analysis is conducted for the vegetation diameter, the vegetation height and the flow discharge. For the longitudinal velocity, the greatest impact on the flow structure originates from the vegetation diameter, rather than the discharge. The vegetation height, however, determines the inflection point of the vertical distribution. Comparing the transverse velocities at two positions in the vegetated area, i.e., the upstream and the downstream, a symmetric pattern is identified along the water depth. The same pattern is also observed for the vertical velocity regardless of the flow or vegetation scenario, including both transverse and vertical fluid circulation patterns in the vegetated area. Moreover, the larger the vegetation diameter is, the more evident these patterns become. The upper circulation occurs near the vegetation canopy. These findings regarding the circulations along the transverse and vertical directions in the vegetated region shed light on the 3-D flow structure through the submerged vegetation.
Submerged rigid vegetation
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적층 제조(AM) 기술은 복잡한 형상의 3D 부품을 쉽게 만들고 미세 구조 제어를 통해 재료 특성을 크게 제어할 수 있기 때문에 많은 관심을 받았습니다. PBF(Powderbed fusion) 방식의 AM 공정에서는 금속 분말을 레이저나 전자빔으로 녹이고 응고시키는 과정을 반복하여 3D 부품을 제작합니다.
일반적으로 응고 미세구조는 Hunt[Mater. 과학. 영어 65, 75(1984)]. 그러나 CET 이론이 일반 316L 스테인리스강에서도 높은 G와 R로 인해 PBF형 AM 공정에 적용될 수 있을지는 불확실하다.
본 연구에서는 미세구조와 응고 조건 간의 관계를 밝히기 위해 전자빔 조사에 의해 유도된 316L 강의 응고 미세구조를 분석하고 CtFD(Computational Thermal-Fluid Dynamics) 방법을 사용하여 고체/액체 계면에서의 응고 조건을 평가했습니다.
CET 이론과 반대로 높은 G 조건에서 등축 결정립이 종종 형성되는 것으로 밝혀졌다. CtFD 시뮬레이션은 약 400 mm s-1의 속도까지 유체 흐름이 있음을 보여 주며 수상 돌기의 파편 및 이동의 영향으로 등축 결정립이 형성됨을 시사했습니다.
Additive manufacturing（AM）technologies have attracted much attention because it enables us to build 3D parts with complicated geometry easily and control material properties significantly via the control of microstructures. In the powderbed fusion（PBF）type AM process, 3D parts are fabricated by repeating a process of melting and solidifying metal powders by laser or electron beams. In general, the solidification microstructures can be predicted from solidification conditions defined by the combination of temperature gradient G and solidification rate R on the basis of columnar-equiaxed transition（CET）theory proposed by Hunt [Mater. Sci. Eng. 65, 75（1984）]. However, it is unclear whether the CET theory can be applied to the PBF type AM process because of the high G and R, even for general 316L stainless steel. In this study, to reveal relationships between microstructures and solidification conditions, we have analyzed solidification microstructures of 316L steel induced by electronbeam irradiation and evaluated solidification conditions at the solid/liquid interface using a computational thermal-fluid dynamics （CtFD）method. It was found that equiaxed grains were often formed under high G conditions contrary to the CET theory. CtFD simulation revealed that there is a fluid flow up to a velocity of about 400 mm s-1, and suggested that equiaxed grains are formed owing to the effect of fragmentations and migrations of dendrites.
Additive Manufacturing, 316L Stainless Steel, Powder Bed Fusion, Electron Beam Melting, Computational Thermal Fluid Dynamics Simulation
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a State Key Laboratory of Hydraulics and Mountain River Engineering, College of Water Resource and Hydropower, Sichuan University, Chengdu, 610065, China
b State Key Laboratory of Hydraulics and Mountain River Engineering, Sichuan University, College Of Water Resource and Hydropower, Chengdu, 610065, China
c faculty of Engineering & Informatics, University of Bradford, BD7 1DP, UK
The bed slope and the tailwater depth are two important ones among the factors that affect the propagation of the dam-break flood and Favre waves. Most previous studies have only focused on the macroscopic characteristics of the dam-break flows or Favre waves under the condition of horizontal bed, rather than the internal movement characteristics in sloped channel. The present study applies two numerical models, namely, large eddy simulation (LES) and shallow water equations (SWEs) models embedded in the CFD software package FLOW-3D to analyze the internal movement characteristics of the dam-break flows and Favre waves, such as water level, the velocity distribution, the fluid particles acceleration and the bed shear stress, under the different bed slopes and water depth ratios. The results under the conditions considered in this study show that there is a flow state transition in the flow evolution for the steep bed slope even in water depth ratio α = 0.1 (α is the ratio of the tailwater depth to the reservoir water depth). The flow state transition shows that the wavefront changes from a breaking state to undular. Such flow transition is not observed for the horizontal slope and mild bed slope. The existence of the Favre waves leads to a significant increase of the vertical velocity and the vertical acceleration. In this situation, the SWEs model has poor prediction. Analysis reveals that the variation of the maximum bed shear stress is affected by both the bed slope and tailwater depth. Under the same bed slope (e.g., S0 = 0.02), the maximum bed shear stress position develops downstream of the dam when α = 0.1, while it develops towards the end of the reservoir when α = 0.7. For the same water depth ratio (e.g., α = 0.7), the maximum bed shear stress position always locates within the reservoir at S0 = 0.02, while it appears in the downstream of the dam for S0 = 0 and 0.003 after the flow evolves for a while. The comparison between the numerical simulation and experimental measurements shows that the LES model can predict the internal movement characteristics with satisfactory accuracy. This study improves the understanding of the effect of both the bed slope and the tailwater depth on the internal movement characteristics of the dam-break flows and Favre waves, which also provides a valuable reference for determining the flood embankment height and designing the channel bed anti-scouring facility.
댐붕괴 홍수와 파브르 파도의 전파에 영향을 미치는 요인 중 하상경사와 후미수심은 두 가지 중요한 요소이다. 대부분의 선행 연구들은 경사 수로에서의 내부 이동 특성보다는 수평층 조건에서 댐파괴류나 Favre파동의 거시적 특성에만 초점을 맞추었다.
본 연구에서는 CFD 소프트웨어 패키지 FLOW-3D에 내장된 LES(Large Eddy Simulation) 및 SWE(Shallow Water Equation) 모델의 두 가지 수치 모델을 적용하여 댐-파괴 흐름 및 Favre 파도의 내부 이동 특성을 분석합니다.
수위, 속도 분포, 유체 입자 가속도 및 층 전단 응력, 다양한 층 경사 및 수심 비율로. 본 연구에서 고려한 조건하의 결과는 수심비 α = 0.1(α는 저수지 수심에 대한 tailwater 깊이의 비율)에서도 급경사면에 대한 유동상태 전이가 있음을 보여준다. 유동 상태 전이는 파면이 파단 상태에서 비정형으로 변하는 것을 보여줍니다.
수평 경사와 완만한 바닥 경사에서는 이러한 흐름 전이가 관찰되지 않습니다. Favre 파의 존재는 수직 속도와 수직 가속도의 상당한 증가로 이어집니다. 이 상황에서 SWE 모델은 예측이 좋지 않습니다.
분석에 따르면 최대 바닥 전단 응력의 변화는 바닥 경사와 꼬리 수심 모두에 영향을 받습니다. 동일한 바닥 경사(예: S0 = 0.02)에서 최대 바닥 전단 응력 위치는 α = 0.1일 때 댐의 하류에서 발생하고 α = 0.7일 때 저수지의 끝쪽으로 발생합니다.
동일한 수심비(예: α = 0.7)에 대해 최대 바닥 전단 응력 위치는 항상 S0 = 0.02에서 저수지 내에 위치하는 반면, S0 = 0 및 0.003에 대해 흐름이 진화한 후 댐 하류에 나타납니다. 수치적 시뮬레이션과 실험적 측정을 비교한 결과 LES 모델이 내부 움직임 특성을 만족스러운 정확도로 예측할 수 있음을 알 수 있습니다.
본 연구는 댐 파절류 및 Favre파의 내부 이동 특성에 대한 하상 경사 및 후미 수심의 영향에 대한 이해를 향상 시키며, 이는 또한 제방 높이를 결정하고 수로 저반위 설계를 위한 귀중한 참고자료를 제공한다.
A comparative performance analysis of the CFD platforms OpenFOAM and FLOW-3D is presented, focusing on a 3D swirling turbulent flow: a steady hydraulic jump at low Reynolds number. Turbulence is treated using RANS approach RNG k-ε. A Volume Of Fluid (VOF) method is used to track the air–water interface, consequently aeration is modeled using an Eulerian–Eulerian approach. Structured meshes of cubic elements are used to discretize the channel geometry. The numerical model accuracy is assessed comparing representative hydraulic jump variables (sequent depth ratio, roller length, mean velocity profiles, velocity decay or free surface profile) to experimental data. The model results are also compared to previous studies to broaden the result validation. Both codes reproduced the phenomenon under study concurring with experimental data, although special care must be taken when swirling flows occur. Both models can be used to reproduce the hydraulic performance of energy dissipation structures at low Reynolds numbers.
CFD 플랫폼 OpenFOAM 및 FLOW-3D의 비교 성능 분석이 3D 소용돌이치는 난류인 낮은 레이놀즈 수에서 안정적인 유압 점프에 초점을 맞춰 제시됩니다. 난류는 RANS 접근법 RNG k-ε을 사용하여 처리됩니다.
VOF(Volume Of Fluid) 방법은 공기-물 계면을 추적하는 데 사용되며 결과적으로 Eulerian-Eulerian 접근 방식을 사용하여 폭기가 모델링됩니다. 입방체 요소의 구조화된 메쉬는 채널 형상을 이산화하는 데 사용됩니다. 수치 모델 정확도는 대표적인 유압 점프 변수(연속 깊이 비율, 롤러 길이, 평균 속도 프로파일, 속도 감쇠 또는 자유 표면 프로파일)를 실험 데이터와 비교하여 평가됩니다.
모델 결과는 또한 결과 검증을 확장하기 위해 이전 연구와 비교됩니다. 소용돌이 흐름이 발생할 때 특별한 주의가 필요하지만 두 코드 모두 실험 데이터와 일치하는 연구 중인 현상을 재현했습니다. 두 모델 모두 낮은 레이놀즈 수에서 에너지 소산 구조의 수리 성능을 재현하는 데 사용할 수 있습니다.
CFDRANS, OpenFOAM, FLOW-3D ,Hydraulic jump, Air–water flow, Low Reynolds number
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