Serife Yurdagul Kumcu−2−KSCE Journal of Civil Engineeringthe use of CFD for the assessment of a design, as well as screeningand optimizing of hydraulic structures and cofferdam layouts. Theyconclude that CFD has been successful in optimizing the finalconceptual configuration for the hydraulics design of the project,but recommend that physical modeling still be used as a finalconfirmation.This paper provides experimental studies performed on Kav akDam and analyses the stability of spillway design by usingFLOW-3D model. It compares the hydraulic model tests withFLOW-3D simulation results and gives information on howaccurately a commercially available Computational Fluid Dynamic(CFD) model can predict the spillway discharge capacity andpressure distribution along the spillway bottom surface. 2. Physical ModelA 1/50-scaled undistorted physical model of the Kavsak Damspillway and stilling basin was built and tested at the HydraulicModel Laboratory of State Hydraulic Works of Turkey (DSI).The model was constructed of plexiglas and was fabricated toconform to the distinctive shape of an ogee crest. The spillwayhas 45.8 m in width and 57 m long with a bottom slope of 125%.The length of the stilling basin is about 90 m. During model tests,flow velocities were measured with an ultrasonic flow meter.Pressures on the spillway were measured using a piezometerssçTable 1. Upstream and Downstream Operating Conditions of theKavsak DamRun Upstream reservoir elevation (m)Downstream tailwater elevation (m)1 306.55 168.002 311.35 174.503 314.00 178.904 316.50 182.55Fig. 1. (a) Original Project Design and Final Project Design after Experimental Investigations and Flow Measurement Sections at theApproach, (b) Top View Experimentally Modified Approach in the Laboratory, (c) Side View of the Experimentally Modified Approachin the Laboratory

Investigation of flow over spillway modeling and comparison between experimental data and CFD analysis

여수로 모델링 및 실험 데이터와 CFD 해석의 비교에 대한 조사

DOI:10.1007/s12205-016-1257-z

Authors:

Serife Yurdagul Kumcu at Necmettin Erbakan Üniversitesi

Serife Yurdagul Kumcu

Abstract and Figures

As a part of design process for hydro-electric generating stations, hydraulic engineers typically conduct some form of model testing. The desired outcome from the testing can vary considerably depending on the specific situation, but often characteristics such as velocity patterns, discharge rating curves, water surface profiles, and pressures at various locations are measured. Due to recent advances in computational power and numerical techniques, it is now also possible to obtain much of this information through numerical modeling. In this paper, hydraulic characteristics of Kavsak Dam and Hydroelectric Power Plant (HEPP), which are under construction and built for producing energy in Turkey, were investigated experimentally by physical model studies. The 1/50-scaled physical model was used in conducting experiments. Flow depth, discharge and pressure data were recorded for different flow conditions. Serious modification was made on the original project with the experimental study. In order to evaluate the capability of the computational fluid dynamics on modeling spillway flow a comparative study was made by using results obtained from physical modeling and Computational Fluid Dynamics (CFD) simulation. A commercially available CFD program, which solves the Reynolds-averaged Navier-Stokes (RANS) equations, was used to model the numerical model setup by defining cells where the flow is partially or completely restricted in the computational space. Discharge rating curves, velocity patterns and pressures were used to compare the results of the physical model and the numerical model. It was shown that there is reasonably good agreement between the physical and numerical models in flow characteristics.

수력 발전소 설계 프로세스의 일부로 수력 엔지니어는 일반적으로 어떤 형태의 모델 테스트를 수행합니다. 테스트에서 원하는 결과는 특정 상황에 따라 상당히 다를 수 있지만 속도 패턴, 방전 등급 곡선, 수면 프로파일 및 다양한 위치에서의 압력과 같은 특성이 측정되는 경우가 많습니다. 최근 계산 능력과 수치 기법의 발전으로 인해 이제는 수치 모델링을 통해 이러한 정보의 대부분을 얻을 수도 있습니다.

본 논문에서는 터키에서 에너지 생산을 위해 건설 중인 Kavsak 댐과 수력발전소(HEPP)의 수력학적 특성을 물리적 모델 연구를 통해 실험적으로 조사하였다. 1/50 스케일의 물리적 모델이 실험 수행에 사용되었습니다. 다양한 흐름 조건에 대해 흐름 깊이, 배출 및 압력 데이터가 기록되었습니다. 실험 연구를 통해 원래 프로젝트에 대대적인 수정이 이루어졌습니다.

배수로 흐름 모델링에 대한 전산유체역학의 능력을 평가하기 위해 물리적 모델링과 전산유체역학(CFD) 시뮬레이션 결과를 이용하여 비교 연구를 수행하였습니다. RANS(Reynolds-averaged Navier-Stokes) 방정식을 푸는 상업적으로 이용 가능한 CFD 프로그램은 흐름이 계산 공간에서 부분적으로 또는 완전히 제한되는 셀을 정의하여 수치 모델 설정을 모델링하는 데 사용되었습니다.

물리적 모델과 수치 모델의 결과를 비교하기 위해 배출 등급 곡선, 속도 패턴 및 압력을 사용했습니다. 유동 특성에서 물리적 모델과 수치 모델 간에 상당히 좋은 일치가 있는 것으로 나타났습니다.

Serife Yurdagul Kumcu−2−KSCE Journal of Civil Engineeringthe use of CFD for the assessment of a design, as well as screeningand optimizing of hydraulic structures and cofferdam layouts. Theyconclude that CFD has been successful in optimizing the finalconceptual configuration for the hydraulics design of the project,but recommend that physical modeling still be used as a finalconfirmation.This paper provides experimental studies performed on Kav akDam and analyses the stability of spillway design by usingFLOW-3D model. It compares the hydraulic model tests withFLOW-3D simulation results and gives information on howaccurately a commercially available Computational Fluid Dynamic(CFD) model can predict the spillway discharge capacity andpressure distribution along the spillway bottom surface. 2. Physical ModelA 1/50-scaled undistorted physical model of the Kavsak Damspillway and stilling basin was built and tested at the HydraulicModel Laboratory of State Hydraulic Works of Turkey (DSI).The model was constructed of plexiglas and was fabricated toconform to the distinctive shape of an ogee crest. The spillwayhas 45.8 m in width and 57 m long with a bottom slope of 125%.The length of the stilling basin is about 90 m. During model tests,flow velocities were measured with an ultrasonic flow meter.Pressures on the spillway were measured using a piezometerssçTable 1. Upstream and Downstream Operating Conditions of theKavsak DamRun Upstream reservoir elevation (m)Downstream tailwater elevation (m)1 306.55 168.002 311.35 174.503 314.00 178.904 316.50 182.55Fig. 1. (a) Original Project Design and Final Project Design after Experimental Investigations and Flow Measurement Sections at theApproach, (b) Top View Experimentally Modified Approach in the Laboratory, (c) Side View of the Experimentally Modified Approachin the Laboratory
Serife Yurdagul Kumcu−2−KSCE Journal of Civil Engineeringthe use of CFD for the assessment of a design, as well as screeningand optimizing of hydraulic structures and cofferdam layouts. Theyconclude that CFD has been successful in optimizing the finalconceptual configuration for the hydraulics design of the project,but recommend that physical modeling still be used as a finalconfirmation.This paper provides experimental studies performed on Kav akDam and analyses the stability of spillway design by usingFLOW-3D model. It compares the hydraulic model tests withFLOW-3D simulation results and gives information on howaccurately a commercially available Computational Fluid Dynamic(CFD) model can predict the spillway discharge capacity andpressure distribution along the spillway bottom surface. 2. Physical ModelA 1/50-scaled undistorted physical model of the Kavsak Damspillway and stilling basin was built and tested at the HydraulicModel Laboratory of State Hydraulic Works of Turkey (DSI).The model was constructed of plexiglas and was fabricated toconform to the distinctive shape of an ogee crest. The spillwayhas 45.8 m in width and 57 m long with a bottom slope of 125%.The length of the stilling basin is about 90 m. During model tests,flow velocities were measured with an ultrasonic flow meter.Pressures on the spillway were measured using a piezometerssçTable 1. Upstream and Downstream Operating Conditions of theKavsak DamRun Upstream reservoir elevation (m)Downstream tailwater elevation (m)1 306.55 168.002 311.35 174.503 314.00 178.904 316.50 182.55Fig. 1. (a) Original Project Design and Final Project Design after Experimental Investigations and Flow Measurement Sections at theApproach, (b) Top View Experimentally Modified Approach in the Laboratory, (c) Side View of the Experimentally Modified Approachin the Laboratory

References

Bureau of Reclamation (1977). Design of small dams, U.S. Government Printing Office, Washington, D.C., U.S.

Bureau of Reclamation (1990). Cavitation in chute and spillways, Engineering Monograph, No.42, U.S. Chanel, P. G. (2008). An evaluation of computational fluid dynamics for

spillway modeling, MSc Thesis, University of Manitoba Winnipeg, Manitoba, Canada.

Chanson, H. (2002). The hydraulics of stepped chutes and spillways,Balkema, Lisse, The Netherlands.

Chanson, H. and Gonzalez, C. A. (2005). “Physical modeling and scale effects of air-water flows on stepped spillways.” Journal of Zhejiang University Science, Vol. 6A, No. 3, pp. 243-250.

Demiroz, E. (1986). “Specifications of aeration structures which are added to the spillways.” DSI Report, HI-754, DSI-TAKK Publications, Ankara, Turkey.

Erfanain-Azmoudeh, M. H. and Kamanbedast, A. A. (2013). “Determine the appropriate location of aerator system on gotvandoliadam’s spillway using Flow 3D.” American-Eurasian J. Agric. & Environ. Sci., Vol. 13, No. 3, pp. 378-383, DOI: 10.5829/idosi.aejaes.2013. 13.03. 458.

Falvey, H. T. (1990). Cavitation in chutes and spillways, Engineering Monograph 42 Water Resources Technical Publication US Printing Office, Bureau of Reclamation, Denver.

Flow-3D User ’s Manual (2012). Flow science, Inc., Santa Fe, N.M.

Hirt, C. W. (1992). “Volume-fraction techniques: Powerful tools for flow

modeling.” Flow Science Report, No. FSI-92-00-02, Flow Science, Inc., Santa Fe, N.M.

Hirt C. W. and Nichols B. D. (1981). “Volume of Fluid (VOF) method for the dynamics of free boundaries.”Jornal of Computational Physics, Vol. 39, pp. 201-225, DOI: 10.1016/0021-9991(81)90145-5.

Hirt, C. W. and Sicilian, J. M. (1985). “A Porosity technique for the definition of obstacles in rectangular cell meshes.” Proceedings of the 4th International Conference on Ship Hydro-dynamics, 24-27 September 1985, National Academic of Sciences, Washington DC.

Ho, D., Boyes, K., Donohoo, S., and Cooper, B. (2003). “Numerical flow analysis for spillways.” 43rd ANCOLD Conference, Hobart, Tas m a nia .

Johnson, M. C. and Savage, B. M. (2006). “Physical and numerical comparison of flow over ogee spillway in the presence of tailwater.”

Journal of Hydraulic Engineering, Vol. 132, No. 12, pp. 1353-135, DOI: 10.1061/(ASCE)0733-9429.

Kim, S. D., Lee, H. J., and An, S. D. (2010). “Improvement of hydraulic stability for spillway using CFD model.” Int. Journal of the Physical Sciences, Vol. 5, No. 6, pp. 774-780.

Kokpinar, M. A. and Gogus, M. (2002). “High speed jet flows over spillway aerators.” Canadian Journal of Civil Engineering, Vol. 29, No. 6, pp. 885-898, DOI: 10.1139/l02-088.

Kumcu, S. Y. (2010). Hydraulic model studies of Kavsak Dam and HEPP, DSI Report, HI-1005, DSI-TAKK Publications, Ankara, Turkey.

Margeirsson, B. (2007). Computational modeling of flow over a spillway, MSc Thesis, Chalmers University of Technology, Gothenburg, Sweden.

Nichols, B. D. and Hirt, C. W. (1975). “Methods for calculating multi-dimensional, transient free surface flows past bodies.” Proc. First Intern. Conf. Num., Ship Hydrodynamics, Gaithersburg, ML.

Savage, B. M. and Johnson, M. C. (2001). “Flow over ogee spillway: Physical and numerical model case study.” Journal of Hydraulic Engineering, ASCE, Vol. 127, No. 8, pp. 640-649, DOI: 10.1061/(ASCE)0733-9429.

Souders, D. T. and Hirt, C. W. (2004). “Modeling entrainment of air at turbulent free surfaces.” Critical Transitions in Water and Environmental resources Management, pp. 1-10.

entürk, F. (1994). Hydraulics of dams and reservoirs, Water Resources Publication Colorado, USA.

Teklemariam, E., Korbaylo, B, Groeneveld, J., Sydor, K., and Fuchs, D. (2001). Optimization of hydraulic design using computational fluid dynamics, Waterpower XII, Salt Lake City, Utah.

Teklemariam, E., Shumilak, B., Sydor, K., Murray, D., Fuchs, D., and Holder, G. (2008). “An integral approach using both physical and computational modeling can be beneficial in addressing the full range of hydraulic design issues.” CDA Annual Conference, Winnipeg, Canada.

Usta, E. (2014). Numerical investigation of hydraulic characteristics of Laleli Dam spillway and comparison with physical model study, Master Thesis, Middle East Technical University, Ankara, Turkey.

Versteeg, H. K. and Malalasekera, W. (1996). An introduction to computational fluid dynamics, Longman Scientific and Technical, Longman Group Limited, Harlow, England.

Vischer, D. L. and Hager, W. H. (1997). Dam hydraulics, J. Wiley & Sons Ltd., England.

Wagner, W. E. (1967). “Glen Canyon diversion tunnel outlets.” J. Hydraulic Division, ASCE, Vol. 93, No. HY6, pp. 113-134.

Willey, J., Ewing, T., Wark, B., and Lesleighter, E. (2012). Comple-mentary use of physical and numerical modeling techniques in spillway design refinement, Commission Internationale Des Grands Barrages, Kyoto, June 2012.

Fig. 1. Averaged error trend.

Assessment of spillway modeling using computational fluid dynamics

전산유체역학을 이용한 여수로 모델링 평가

Authors: Paul G. Chanel and John C. Doering AUTHORS INFO & AFFILIATIONS

Publication: Canadian Journal of Civil Engineering

3 December 2008

Abstract

Throughout the design and planning period for future hydroelectric generating stations, hydraulic engineers are increasingly integrating computational fluid dynamics (CFD) into the process. As a result, hydraulic engineers are interested in the reliability of CFD software to provide accurate flow data for a wide range of structures, including a variety of different spillways. In the literature, CFD results have generally been in agreement with physical model experimental data. Despite past success, there has not been a comprehensive assessment that looks at the ability of CFD to model a range of different spillway configurations, including flows with various gate openings. In this article, Flow-3D is used to model the discharge over ogee-crested spillways. The numerical model results are compared with physical model studies for three case study evaluations. The comparison indicates that the accuracy of Flow-3D is related to the parameter P/Hd.

미래의 수력 발전소를 위한 설계 및 계획 기간 동안 유압 엔지니어는 전산유체역학(CFD)을 프로세스에 점점 더 많이 통합하고 있습니다. 결과적으로 유압 엔지니어는 다양한 여수로를 포함하여 광범위한 구조에 대한 정확한 흐름 데이터를 제공하는 CFD 소프트웨어의 신뢰성에 관심을 갖고 있습니다. 문헌에서 CFD 결과는 일반적으로 물리적 모델 실험 데이터와 일치했습니다. 과거의 성공에도 불구하고 다양한 게이트 개구부가 있는 흐름을 포함하여 다양한 여수로 구성을 모델링하는 CFD의 기능을 살펴보는 포괄적인 평가는 없었습니다. 이 기사에서는 Flow-3D를 사용하여 ogee-crested 방수로의 배출을 모델링합니다. 세 가지 사례 연구 평가를 위해 수치 모델 결과를 물리적 모델 연구와 비교합니다. 비교는 Flow-3D의 정확도가 매개변수 P/Hd와 관련되어 있음을 나타냅니다.

Résumé

Les ingénieurs en hydraulique intègrent de plus en plus la dynamique des fluides numérique (« CFD ») dans le processus de conception et de planification des futures centrales. Ainsi, les ingénieurs en hydraulique s’intéressent à la fiabilité du logiciel de « CFD » afin de fournir des données précises sur le débit pour une large gamme de structures, incluant différents types d’évacuateurs. Les résultats de « CFD » dans la littérature ont été globalement sont généralement en accord avec les données expérimentales des essais physiques. Malgré les succès antérieurs, il n’y avait aucune évaluation complète de la capacité des « CFD » à modéliser une plage de configuration des évacuateurs, incluant les débits à diverses ouvertures de vannes. Dans le présent article, le logiciel Flow-3D est utilisé pour modéliser le débit par des évacuateurs en doucine. Les résultats du modèle de calcul sont comparés à ceux des essais physiques pour trois études de cas. La comparaison montre que la précision du logiciel Flow-3D est associée au paramètre P/Hd.

Fig. 1. Averaged error trend.
Fig. 1. Averaged error trend.

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References

Chanel, P.G., and Doering, J.C. 2007. An evaluation of computational fluid dynamics for spillway modelling. In Proceedings of the 16th Australasian Fluid Mechanics Conference (AFMC), Gold Coast, Queensland, Australia, 3–7 December 2007. pp. 1201–1206.

Google Scholar

Flow Science, Inc. 2007. Flow-3D user’s manuals. Version 9.2. Flow Science, Inc., Santa Fe, N.M.

Google Scholar

Gessler, D. 2005. CFD modeling of spillway performance, EWRI 2005: Impacts of global climate change. In Proceedings of the World Water and Environmental Resources Congress, Anchorage, Alaska, 15–19 May 2005. Edited by R. Walton. American Society of Civil Engineers, Reston, Va.

Google Scholar

Hirt, C.W., and Nichols, B.D. 1981. Volume of fluid (VOF) method for the dynamics of free boundaries. Journal of Computational Physics, 39(1): 201–225.

Crossref

ISI

Google Scholar

Hirt, C.W., and Sicilian, J.M. 1985. A porosity technique for the definition of obstacles in rectangular cell meshes. In Proceedings of the 4th International Conference on Ship Hydro-dynamics, Washington, D.C., 24–27 September 1985. National Academy of Sciences, Washington, D.C.

Google Scholar

Ho, D., Cooper, B., Riddette, K., and Donohoo, S. 2006. Application of numerical modelling to spillways in Australia. In Dams and Reservoirs, Societies and Environment in the 21st Century. Edited by Berga et al. Taylor and Francis Group, London.

Google Scholar

LaSalle Consulting Group Inc. 1992. Conawapa generating station. Sectional model study of the spillway. LaSalle Consulting Group Inc., Montréal, Que.

Google Scholar

Lemke, D.E. 1989. A comparison of the hydraulic performance of an orifice and an overflow spillway in a northern application using physical modeling. M.Sc. thesis, University of Manitoba, Winnipeg, Man.

Google Scholar

Savage, B.M., and Johnson, M.C. 2001. Flow over ogee spillway: Physical and numerical model case study. Journal of Hydraulic Engineering, 127(8): 640–649.

Crossref

ISI

Google Scholar

Teklemariam, E., Korbaylo, B., Groeneveld, J., Sydor, K., and Fuchs, D. 2001. Optimization of hydraulic design using computational fluid dynamics. In Proceedings of Waterpower XII, Salt Lake City, Utah, 9–11 July 2001.

Google Scholar

Teklemariam, E., Korbaylo, B., Groeneveld, J., and Fuchs, D. 2002. Computational fluid dynamics: Diverse applications in hydropower project’s design and analysis. In Proceedings of the CWRA 55th Annual Conference, Winnipeg, Man., 11–14 June 2002. Canadian Water Resources Association, Cambridge, Ontario.

Google Scholar

Western Canadian Hydraulic Laboratories Inc. 1980. Hydraulics model studies limestone generating station spillway/diversion structure flume study. Final report. Western Canadian Hydraulic Laboratories Inc., Port Coquitlam, B.C.

Google Scholar

Sketch of approach channel and spillway of the Kamal-Saleh dam

CFD modeling of flow pattern in spillway’s approach channel

Sustainable Water Resources Management volume 1, pages245–251 (2015)Cite this article

Abstract

Analysis of behavior and hydraulic characteristics of flow over the dam spillway is a complicated task that takes lots of money and time in water engineering projects planning. To model those hydraulic characteristics, several methods such as physical and numerical methods can be used. Nowadays, by utilizing new methods in computational fluid dynamics (CFD) and by the development of fast computers, the numerical methods have become accessible for use in the analysis of such sophisticated flows. The CFD softwares have the capability to analyze two- and three-dimensional flow fields. In this paper, the flow pattern at the guide wall of the Kamal-Saleh dam was modeled by Flow 3D. The results show that the current geometry of the left wall causes instability in the flow pattern and making secondary and vortex flow at beginning approach channel. This shape of guide wall reduced the performance of weir to remove the peak flood discharge.

댐 여수로 흐름의 거동 및 수리학적 특성 분석은 물 공학 프로젝트 계획에 많은 비용과 시간이 소요되는 복잡한 작업입니다. 이러한 수력학적 특성을 모델링하기 위해 물리적, 수치적 방법과 같은 여러 가지 방법을 사용할 수 있습니다. 요즘에는 전산유체역학(CFD)의 새로운 방법을 활용하고 빠른 컴퓨터의 개발로 이러한 정교한 흐름의 해석에 수치 방법을 사용할 수 있게 되었습니다. CFD 소프트웨어에는 2차원 및 3차원 유동장을 분석하는 기능이 있습니다. 본 논문에서는 Kamal-Saleh 댐 유도벽의 흐름 패턴을 Flow 3D로 모델링하였다. 결과는 왼쪽 벽의 현재 형상이 흐름 패턴의 불안정성을 유발하고 시작 접근 채널에서 2차 및 와류 흐름을 만드는 것을 보여줍니다. 이러한 형태의 안내벽은 첨두방류량을 제거하기 위해 둑의 성능을 저하시켰다.

Introduction

Spillways are one of the main structures used in the dam projects. Design of the spillway in all types of dams, specifically earthen dams is important because the inability of the spillway to remove probable maximum flood (PMF) discharge may cause overflow of water which ultimately leads to destruction of the dam (Das and Saikia et al. 2009; E 2013 and Novak et al. 2007). So study on the hydraulic characteristics of this structure is important. Hydraulic properties of spillway including flow pattern at the entrance of the guide walls and along the chute. Moreover, estimating the values of velocity and pressure parameters of flow along the chute is very important (Chanson 2004; Chatila and Tabbara 2004). The purpose of the study on the flow pattern is the effect of wall geometry on the creation transverse waves, flow instability, rotating and reciprocating flow through the inlet of spillway and its chute (Parsaie and Haghiabi 2015ab; Parsaie et al. 2015; Wang and Jiang 2010). The purpose of study on the values of velocity and pressure is to calculate the potential of the structure to occurrence of phenomena such as cavitation (Fattor and Bacchiega 2009; Ma et al. 2010). Sometimes, it can be seen that the spillway design parameters of pressure and velocity are very suitable, but geometry is considered not suitable for conducting walls causing unstable flow pattern over the spillway, rotating flows at the beginning of the spillway and its design reduced the flood discharge capacity (Fattor and Bacchiega 2009). Study on spillway is usually conducted using physical models (Su et al. 2009; Suprapto 2013; Wang and Chen 2009; Wang and Jiang 2010). But recently, with advances in the field of computational fluid dynamics (CFD), study on hydraulic characteristics of this structure has been done with these techniques (Chatila and Tabbara 2004; Zhenwei et al. 2012). Using the CFD as a powerful technique for modeling the hydraulic structures can reduce the time and cost of experiments (Tabbara et al. 2005). In CFD field, the Navier–Stokes equation is solved by powerful numerical methods such as finite element method and finite volumes (Kim and Park 2005; Zhenwei et al. 2012). In order to obtain closed-form Navier–Stokes equations turbulence models, such k − ε and Re-Normalisation Group (RNG) models have been presented. To use the technique of computational fluid dynamics, software packages such as Fluent and Flow 3D, etc., are provided. Recently, these two software packages have been widely used in hydraulic engineering because the performance and their accuracy are very suitable (Gessler 2005; Kim 2007; Kim et al. 2012; Milési and Causse 2014; Montagna et al. 2011). In this paper, to assess the flow pattern at Kamal-Saleh guide wall, numerical method has been used. All the stages of numerical modeling were conducted in the Flow 3D software.

Materials and methods

Firstly, a three-dimensional model was constructed according to two-dimensional map that was prepared for designing the spillway. Then a small model was prepared with scale of 1:80 and entered into the Flow 3D software; all stages of the model construction was conducted in AutoCAD 3D. Flow 3D software numerically solved the Navier–Stokes equation by finite volume method. Below is a brief reference on the equations that used in the software. Figure 1 shows the 3D sketch of Kamal-Saleh spillway and Fig. 2 shows the uploading file of the Kamal-Saleh spillway in Flow 3D software.

figure 1
Fig. 1
figure 2
Fig. 2

Review of the governing equations in software Flow 3D

Continuity equation at three-dimensional Cartesian coordinates is given as Eq (1).

vf∂ρ∂t+∂∂x(uAx)+∂∂x(vAy)+∂∂x(wAz)=PSORρ,vf∂ρ∂t+∂∂x(uAx)+∂∂x(vAy)+∂∂x(wAz)=PSORρ,

(1)

where uvz are velocity component in the x, y, z direction; A xA yA z cross-sectional area of the flow; ρ fluid density; PSOR the source term; v f is the volume fraction of the fluid and three-dimensional momentum equations given in Eq (2).

∂u∂t+1vf(uAx∂u∂x+vAy∂u∂y+wAz∂u∂z)=−1ρ∂P∂x+Gx+fx∂v∂t+1vf(uAx∂v∂x+vAy∂v∂y+wAz∂v∂z)=−1ρ∂P∂y+Gy+fy∂w∂t+1vf(uAx∂w∂x+vAy∂w∂y+wAz∂w∂z)=−1ρ∂P∂y+Gz+fz,∂u∂t+1vf(uAx∂u∂x+vAy∂u∂y+wAz∂u∂z)=−1ρ∂P∂x+Gx+fx∂v∂t+1vf(uAx∂v∂x+vAy∂v∂y+wAz∂v∂z)=−1ρ∂P∂y+Gy+fy∂w∂t+1vf(uAx∂w∂x+vAy∂w∂y+wAz∂w∂z)=−1ρ∂P∂y+Gz+fz,

(2)

where P is the fluid pressure; G xG yG z the acceleration created by body fluids; f xf yf z viscosity acceleration in three dimensions and v f is related to the volume of fluid, defined by Eq. (3). For modeling of free surface profile the VOF technique based on the volume fraction of the computational cells has been used. Since the volume fraction F represents the amount of fluid in each cell, it takes value between 0 and 1.

∂F∂t+1vf[∂∂x(FAxu)+∂∂y(FAyv)+∂∂y(FAzw)]=0∂F∂t+1vf[∂∂x(FAxu)+∂∂y(FAyv)+∂∂y(FAzw)]=0

(3)

Turbulence models

Flow 3D offers five types of turbulence models: Prantl mixing length, k − ε equation, RNG models, Large eddy simulation model. Turbulence models that have been proposed recently are based on Reynolds-averaged Navier–Stokes equations. This approach involves statistical methods to extract an averaged equation related to the turbulence quantities.

Steps of solving a problem in Flow 3D software

(1) Preparing the 3D model of spillway by AutoCAD software. (2) Uploading the file of 3D model in Flow 3D software and defining the problem in the software and checking the final mesh. (3) Choosing the basic equations that should be solved. (4) Defining the characteristics of fluid. (5) Defining the boundary conditions; it is notable that this software has a wide range of boundary conditions. (6) Initializing the flow field. (7) Adjusting the output. (8) Adjusting the control parameters, choice of the calculation method and solution formula. (9) Start of calculation. Figure 1 shows the 3D model of the Kamal-Saleh spillway; in this figure, geometry of the left and right guide wall is shown.

Figure 2 shows the uploading of the 3D spillway dam in Flow 3D software. Moreover, in this figure the considered boundary condition in software is shown. At the entrance and end of spillway, the flow rate or fluid elevation and outflow was considered as BC. The bottom of spillway was considered as wall and left and right as symmetry.

Model calibration

Calibration of the Flow 3D for modeling the effect of geometry of guide wall on the flow pattern is included for comparing the results of Flow 3D with measured water surface profile. Calibration the Flow 3D software could be conducted in two ways: first, changing the value of upstream boundary conditions is continued until the results of water surface profile of the Flow 3D along the spillway successfully covered the measurement water surface profile; second is the assessment the mesh sensitivity. Analyzing the size of mesh is a trial-and-error process where the size of mesh is evaluated form the largest to the smallest. With fining the size of mesh the accuracy of model is increased; whereas, the cost of computation is increased. In this research, the value of upstream boundary condition was adjusted with measured data during the experimental studies on the scaled model and the mesh size was equal to 1 × 1 × 1 cm3.

Results and discussion

The behavior of water in spillway is strongly affected by the flow pattern at the entrance of the spillway, the flow pattern formation at the entrance is affected by the guide wall, and choice of an optimized form for the guide wall has a great effect on rising the ability of spillway for easy passing the PMF, so any nonuniformity in flow in the approach channel can cause reduction of spillway capacity, reduction in discharge coefficient of spillway, and even probability of cavitation. Optimizing the flow guiding walls (in terms of length, angle and radius) can cause the loss of turbulence and flow disturbances on spillway. For this purpose, initially geometry proposed for model for the discharge of spillway dam, Kamal-Saleh, 80, 100, and 120 (L/s) were surveyed. These discharges of flow were considered with regard to the flood return period, 5, 100 and 1000 years. Geometric properties of the conducting guidance wall are given in Table 1.Table 1 Characteristics and dimensions of the guidance walls tested

Full size table

Results of the CFD simulation for passing the flow rate 80 (L/s) are shown in Fig. 3. Figure 3 shows the secondary flow and vortex at the left guide wall.

figure 3
Fig. 3

For giving more information about flow pattern at the left and right guide wall, Fig. 4 shows the flow pattern at the right side guide wall and Fig. 5 shows the flow pattern at the left side guide wall.

figure 4
Fig. 4
figure 5
Fig. 5

With regard to Figs. 4 and 5 and observing the streamlines, at discharge equal to 80 (L/s), the right wall has suitable performance but the left wall has no suitable performance and the left wall of the geometric design creates a secondary and circular flow, and vortex motion in the beginning of the entrance of spillway that creates cross waves at the beginning of spillway. By increasing the flow rate (Q = 100 L/s), at the inlet spillway secondary flows and vortex were removed, but the streamline is severely distorted. Results of the guide wall performances at the Q = 100 (L/s) are shown in Fig. 6.

figure 6
Fig. 6

Also more information about the performance of each guide wall can be derived from Figs. 7 and 8. These figures uphold that the secondary and vortex flows were removed, but the streamlines were fully diverted specifically near the left side guide wall.

figure 7
Fig. 7
figure 8
Fig. 8

As mentioned in the past, these secondary and vortex flows and diversion in streamline cause nonuniformity and create cross wave through the spillway. Figure 9 shows the cross waves at the crest of the spillway.

figure 9
Fig. 9

The performance of guide walls at the Q = 120 (L/s) also was assessed. The result of simulation is shown in Fig. 10. Figures 11 and 12 show a more clear view of the streamlines near to right and left side guide wall, respectively. As seen in Fig. 12, the left side wall still causes vortex flow and creation of and diversion in streamline.

figure 10
Fig. 10
figure 11
Fig. 11
figure 12
Fig. 12

The results of the affected left side guide wall shape on the cross wave creation are shown in Fig. 13. As seen from Fig. 3, the left side guide wall also causes cross wave at the spillway crest.

figure 13
Fig. 13

As can be seen clearly in Figs. 9 and 13, by moving from the left side to the right side of the spillway, the cross waves and the nonuniformity in flow is removed. By reviewing Figs. 9 and 13, it is found that the right side guide wall removes the cross waves and nonuniformity. With this point as aim, a geometry similar to the right side guide wall was considered instead of the left side guide wall. The result of simulation for Q = 120 (L/s) is shown in Fig. 14. As seen from this figure, the proposed geometry for the left side wall has suitable performance smoothly passing the flow through the approach channel and spillway.

figure 14
Fig. 14

More information about the proposed shape for the left guide wall is shown in Fig. 15. As seen from this figure, this shape has suitable performance for removing the cross waves and vortex flows.

figure 15
Fig. 15

Figure 16 shows the cross section of flow at the crest of spillway. As seen in this figure, the proposed shape for the left side guide wall is suitable for removing the cross waves and secondary flows.

figure 16
Fig. 16

Conclusion

Analysis of behavior and hydraulic properties of flow over the spillway dam is a complicated task which is cost and time intensive. Several techniques suitable to the purposes of study have been undertaken in this research. Physical modeling, usage of expert experience, usage of mathematical models on simulation flow in one-dimensional, two-dimensional and three-dimensional techniques, are some of the techniques utilized to study this phenomenon. The results of the modeling show that the CFD technique is a suitable tool for simulating the flow pattern in the guide wall. Using this tools helps the designer for developing the optimal shape for hydraulic structure which the flow pattern through them are important.

References

  • Chanson H (2004) 19—Design of weirs and spillways. In: Chanson H (ed) Hydraulics of open channel flow, 2nd edn. Butterworth-Heinemann, Oxford, pp 391–430Chapter Google Scholar 
  • Chatila J, Tabbara M (2004) Computational modeling of flow over an ogee spillway. Comput Struct 82:1805–1812Article Google Scholar 
  • Das MM, Saikia MD (2009) Irrigation and water power engineering. PHI Learning, New DelhiGoogle Scholar 
  • E, Department Of Army: U.S. Army Corps (2013) Hydraulic Design of Spillways. BiblioBazaar, CharlestonGoogle Scholar 
  • Fattor C, Bacchiega J (2009) Design conditions for morning-glory spillways: application to potrerillos dam spillway. Adv Water Res Hydraul Eng Springer, Berlin, pp 2123–2128Google Scholar 
  • Gessler D (2005) CFD modeling of spillway performance. Impacts Glob Clim Change. doi:10.1061/40792(173)398
  • Kim D-G (2007) Numerical analysis of free flow past a sluice gate. KSCE J Civ Eng 11:127–132Article Google Scholar 
  • Kim D, Park J (2005) Analysis of flow structure over ogee-spillway in consideration of scale and roughness effects by using CFD model. KSCE J Civ Eng 9:161–169Article Google Scholar 
  • Kim S, Yu K, Yoon B, Lim Y (2012) A numerical study on hydraulic characteristics in the ice Harbor-type fishway. KSCE J Civ Eng 16:265–272Article Google Scholar 
  • Ma X-D, Dai G-Q, Yang Q, Li G-J, Zhao L (2010) Analysis of influence factors of cavity length in the spillway tunnel downstream of middle gate chamber outlet with sudden lateral enlargement and vertical drop aerator. J Hydrodyn Ser B 22:680–686Article Google Scholar 
  • Milési G, Causse S (2014) 3D numerical modeling of a side-channel spillway. In: Gourbesville P, Cunge J, Caignaert G (eds) Advances in hydroinformatics. Springer, Singapore, pp 487–498Chapter Google Scholar 
  • Montagna F, Bellotti G, Di Risio M (2011) 3D numerical modeling of landslide-generated tsunamis around a conical island. Nat Hazards 58:591–608Article Google Scholar 
  • Novak P, Moffat AIB, Nalluri C, Narayanan R (2007) Hydraulic structures. Taylor & Francis, LondonGoogle Scholar 
  • Parsaie A, Haghiabi A (2015a) Computational modeling of pollution transmission in rivers. Appl Water Sci. doi:10.1007/s13201-015-0319-6
  • Parsaie A, Haghiabi A (2015b) The effect of predicting discharge coefficient by neural network on increasing the numerical modeling accuracy of flow over side weir. Water Res Manag 29:973–985Article Google Scholar 
  • Parsaie A, Yonesi H, Najafian S (2015) Predictive modeling of discharge in compound open channel by support vector machine technique. Model Earth Syst Environ 1:1–6Article Google Scholar 
  • Su P-L, Liao H-S, Qiu Y, Li CJ (2009) Experimental study on a new type of aerator in spillway with low Froude number and mild slope flow. J Hydrodyn Ser B 21:415–422Article Google Scholar 
  • Suprapto M (2013) Increase spillway capacity using Labyrinth Weir. Procedia Eng 54:440–446Article Google Scholar 
  • Tabbara M, Chatila J, Awwad R (2005) Computational simulation of flow over stepped spillways. Comput Struct 83:2215–2224Article Google Scholar 
  • Wang J, Chen H (2009) Experimental study of elimination of vortices along guide wall of bank spillway. Adv Water Res Hydraul Eng Springer, Berlin, pp 2059–2063Google Scholar 
  • Wang Y, Jiang C (2010) Investigation of the surface vortex in a spillway tunnel intake. Tsinghua Sci Technol 15:561–565Article Google Scholar 
  • Zhenwei MU, Zhiyan Z, Tao Z (2012) Numerical simulation of 3-D flow field of spillway based on VOF method. Procedia Eng 28:808–812Article Google Scholar 

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  1. Department of Water Engineering, Lorestan University, Khorram Abad, IranAbbas Parsaie, Amir Hamzeh Haghiabi & Amir Moradinejad

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Correspondence to Abbas Parsaie.

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Parsaie, A., Haghiabi, A.H. & Moradinejad, A. CFD modeling of flow pattern in spillway’s approach channel. Sustain. Water Resour. Manag. 1, 245–251 (2015). https://doi.org/10.1007/s40899-015-0020-9

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  • Received28 April 2015
  • Accepted28 August 2015
  • Published15 September 2015
  • Issue DateSeptember 2015
  • DOIhttps://doi.org/10.1007/s40899-015-0020-9

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Keywords

  • Approach channel
  • Kamal-Saleh dam
  • Guide wall
  • Flow pattern
  • Numerical modeling
  • Flow 3D software
    Figure 3. FLOW-3D results for Strathcona Dam spillway with all gates fully open at an elevated reservoir level during passage of a large flood. Note the effects of poor approach conditions and pier overtopping at the leftmost bay.

    BC Hydro Assesses Spillway Hydraulics with FLOW-3D

    by Faizal Yusuf, M.A.Sc., P.Eng.
    Specialist Engineer in the Hydrotechnical Department at BC Hydro

    BC Hydro, a public electric utility in British Columbia, uses FLOW-3D to investigate complex hydraulics issues at several existing dams and to assist in the design and optimization of proposed facilities.

    Faizal Yusuf, M.A.Sc., P.Eng., Specialist Engineer in the Hydrotechnical department at BC Hydro, presents three case studies that highlight the application of FLOW-3D to different types of spillways and the importance of reliable prototype or physical hydraulic model data for numerical model calibration.

    W.A.C. Bennett Dam
    At W.A.C. Bennett Dam, differences in the spillway geometry between the physical hydraulic model from the 1960s and the prototype make it difficult to draw reliable conclusions on shock wave formation and chute capacity from physical model test results. The magnitude of shock waves in the concrete-lined spillway chute are strongly influenced by a 44% reduction in the chute width downstream of the three radial gates at the headworks, as well as the relative openings of the radial gates. The shock waves lead to locally higher water levels that have caused overtopping of the chute walls under certain historical operations.Prototype spill tests for discharges up to 2,865 m3/s were performed in 2012 to provide surveyed water surface profiles along chute walls, 3D laser scans of the water surface in the chute and video of flow patterns for FLOW-3D model calibration. Excellent agreement was obtained between the numerical model and field observations, particularly for the location and height of the first shock wave at the chute walls (Figure 1).

    W.A.C에서 Bennett Dam, 1960년대의 물리적 수력학 모델과 프로토타입 사이의 여수로 형상의 차이로 인해 물리적 모델 테스트 결과에서 충격파 형성 및 슈트 용량에 대한 신뢰할 수 있는 결론을 도출하기 어렵습니다. 콘크리트 라이닝 방수로 낙하산의 충격파 크기는 방사형 게이트의 상대적인 개구부뿐만 아니라 헤드워크에 있는 3개의 방사형 게이트 하류의 슈트 폭이 44% 감소함에 따라 크게 영향을 받습니다. 충격파는 특정 역사적 작업에서 슈트 벽의 범람을 야기한 국부적으로 더 높은 수위로 이어집니다. 최대 2,865m3/s의 배출에 대한 프로토타입 유출 테스트가 2012년에 수행되어 슈트 벽을 따라 조사된 수면 프로필, 3D 레이저 스캔을 제공했습니다. FLOW-3D 모델 보정을 위한 슈트의 수면 및 흐름 패턴 비디오. 특히 슈트 벽에서 첫 번째 충격파의 위치와 높이에 대해 수치 모델과 현장 관찰 간에 탁월한 일치가 이루어졌습니다(그림 1).
    Figure 1. Comparison between prototype observations and FLOW-3D for a spill discharge of 2,865 m^3/s at Bennett Dam spillway.
    Figure 1. Comparison between prototype observations and FLOW-3D for a spill discharge of 2,865 m^3/s at Bennett Dam spillway.

    The calibrated FLOW-3D model confirmed that the design flood could be safely passed without overtopping the spillway chute walls as long as all three radial gates are opened as prescribed in existing operating orders with the outer gates open more than the inner gate.

    The CFD model also provided insight into the concrete damage in the spillway chute. Cavitation indices computed from FLOW-3D simulation results were compared with empirical data from the USBR and found to be consistent with the historical performance of the spillway. The numerical analysis supported field inspections, which concluded that deterioration of the concrete conditions in the chute is likely not due to cavitation.

    Strathcona Dam
    FLOW-3D was used to investigate poor approach conditions and uncertainties with the rating curves for Strathcona Dam spillway, which includes three vertical lift gates on the right abutment of the dam. The rating curves for Strathcona spillway were developed from a combination of empirical adjustments and limited physical hydraulic model testing in a flume that did not include geometry of the piers and abutments.

    Numerical model testing and calibration was based on comparisons with prototype spill observations from 1982 when all three gates were fully open, resulting in a large depression in the water surface upstream of the leftmost bay (Figure 2). The approach flow to the leftmost bay is distorted by water flowing parallel to the dam axis and plunging over the concrete retaining wall adjacent to the upstream slope of the earthfill dam. The flow enters the other two bays much more smoothly. In addition to very similar flow patterns produced in the numerical model compared to the prototype, simulated water levels at the gate section matched 1982 field measurements to within 0.1 m.

    보정된 FLOW-3D 모델은 외부 게이트가 내부 게이트보다 더 많이 열려 있는 기존 운영 명령에 규정된 대로 3개의 방사형 게이트가 모두 열리는 한 여수로 낙하산 벽을 넘지 않고 설계 홍수를 안전하게 통과할 수 있음을 확인했습니다.

    CFD 모델은 방수로 낙하산의 콘크리트 손상에 대한 통찰력도 제공했습니다. FLOW-3D 시뮬레이션 결과에서 계산된 캐비테이션 지수는 USBR의 경험적 데이터와 비교되었으며 여수로의 역사적 성능과 일치하는 것으로 나타났습니다. 수치 분석은 현장 검사를 지원했으며, 슈트의 콘크리트 상태 악화는 캐비테이션 때문이 아닐 가능성이 높다고 결론지었습니다.

    Strathcona 댐
    FLOW-3D는 Strathcona Dam 여수로에 대한 등급 곡선을 사용하여 열악한 접근 조건과 불확실성을 조사하는 데 사용되었습니다. 여기에는 댐의 오른쪽 접합부에 3개의 수직 리프트 게이트가 포함되어 있습니다. Strathcona 여수로에 대한 등급 곡선은 경험적 조정과 교각 및 교대의 형상을 포함하지 않는 수로에서 제한된 물리적 수리 모델 테스트의 조합으로 개발되었습니다.

    수치 모델 테스트 및 보정은 세 개의 수문이 모두 완전히 개방된 1982년의 프로토타입 유출 관측과의 비교를 기반으로 했으며, 그 결과 가장 왼쪽 만의 상류 수면에 큰 함몰이 발생했습니다(그림 2). 최좌단 만으로의 접근 흐름은 댐 축과 평행하게 흐르는 물과 흙채움댐의 상류 경사면에 인접한 콘크리트 옹벽 위로 떨어지는 물에 의해 왜곡됩니다. 흐름은 훨씬 더 원활하게 다른 두 베이로 들어갑니다. 프로토타입과 비교하여 수치 모델에서 생성된 매우 유사한 흐름 패턴 외에도 게이트 섹션에서 시뮬레이션된 수위는 1982년 현장 측정과 0.1m 이내로 일치했습니다.

    Figure 2. Prototype observations and FLOW-3D results for a Strathcona Dam spill in 1982 with all three gates fully open.
    Figure 2. Prototype observations and FLOW-3D results for a Strathcona Dam spill in 1982 with all three gates fully open.

    The calibrated CFD model produces discharges within 5% of the spillway rating curve for the reservoir’s normal operating range with all gates fully open. However, at higher reservoir levels, which may occur during passage of large floods (as shown in Figure 3), the difference between simulated discharges and the rating curves are greater than 10% as the physical model testing with simplified geometry and empirical corrections did not adequately represent the complex approach flow patterns. The FLOW-3D model provided further insight into the accuracy of rating curves for individual bays, gated conditions and the transition between orifice and free surface flow.

    보정된 CFD 모델은 모든 게이트가 완전히 열린 상태에서 저수지의 정상 작동 범위에 대한 여수로 등급 곡선의 5% 이내에서 배출을 생성합니다. 그러나 대규모 홍수가 통과하는 동안 발생할 수 있는 더 높은 저수지 수위에서는(그림 3 참조) 단순화된 기하학과 경험적 수정을 사용한 물리적 모델 테스트가 그렇지 않았기 때문에 모의 배출과 등급 곡선 간의 차이는 10% 이상입니다. 복잡한 접근 흐름 패턴을 적절하게 표현합니다. FLOW-3D 모델은 개별 베이, 게이트 조건 및 오리피스와 자유 표면 흐름 사이의 전환에 대한 등급 곡선의 정확도에 대한 추가 통찰력을 제공했습니다.

    Figure 3. FLOW-3D results for Strathcona Dam spillway with all gates fully open at an elevated reservoir level during passage of a large flood. Note the effects of poor approach conditions and pier overtopping at the leftmost bay.
    Figure 3. FLOW-3D results for Strathcona Dam spillway with all gates fully open at an elevated reservoir level during passage of a large flood. Note the effects of poor approach conditions and pier overtopping at the leftmost bay.

    John Hart Dam
    The John Hart concrete dam will be modified to include a new free crest spillway to be situated between an existing gated spillway and a low level outlet structure that is currently under construction. Significant improvements in the design of the proposed spillway were made through a systematic optimization process using FLOW-3D.

    The preliminary design of the free crest spillway was based on engineering hydraulic design guides. Concrete apron blocks are intended to protect the rock at the toe of the dam. A new right training wall will guide the flow from the new spillway towards the tailrace pool and protect the low level outlet structure from spillway discharges.

    FLOW-3D model results for the initial and optimized design of the new spillway are shown in Figure 4. CFD analysis led to a 10% increase in discharge capacity, significant decrease in roadway impingement above the spillway crest and improved flow patterns including up to a 5 m reduction in water levels along the proposed right wall. Physical hydraulic model testing will be used to confirm the proposed design.

    존 하트 댐
    John Hart 콘크리트 댐은 현재 건설 중인 기존 배수로와 저층 배수로 사이에 위치할 새로운 자유 마루 배수로를 포함하도록 수정될 것입니다. FLOW-3D를 사용한 체계적인 최적화 프로세스를 통해 제안된 여수로 설계의 상당한 개선이 이루어졌습니다.

    자유 마루 여수로의 예비 설계는 엔지니어링 수력학 설계 가이드를 기반으로 했습니다. 콘크리트 앞치마 블록은 댐 선단부의 암석을 보호하기 위한 것입니다. 새로운 오른쪽 훈련 벽은 새 여수로에서 테일레이스 풀로 흐름을 안내하고 여수로 배출로부터 낮은 수준의 배출구 구조를 보호합니다.

    새 여수로의 초기 및 최적화된 설계에 대한 FLOW-3D 모델 결과는 그림 4에 나와 있습니다. CFD 분석을 통해 방류 용량이 10% 증가하고 여수로 마루 위의 도로 충돌이 크게 감소했으며 최대 제안된 오른쪽 벽을 따라 수위가 5m 감소합니다. 제안된 설계를 확인하기 위해 물리적 수압 모델 테스트가 사용됩니다.

    Figure 4. FLOW-3D model results for the preliminary and optimized layout of the proposed spillway at John Hart Dam.
    Figure 4. FLOW-3D model results for the preliminary and optimized layout of the proposed spillway at John Hart Dam.

    Conclusion

    BC Hydro has been using FLOW-3D to investigate a wide range of challenging hydraulics problems for different types of spillways and water conveyance structures leading to a greatly improved understanding of flow patterns and performance. Prototype data and reliable physical hydraulic model testing are used whenever possible to improve confidence in the numerical model results.

    다양한 유형의 여수로 및 물 수송 구조로 인해 흐름 패턴 및 성능에 대한 이해가 크게 향상되었습니다. 프로토타입 데이터와 신뢰할 수 있는 물리적 유압 모델 테스트는 수치 모델 결과의 신뢰도를 향상시키기 위해 가능할 때마다 사용됩니다.

    About Flow Science, Inc.
    Based in Santa Fe, New Mexico USA, Flow Science was founded in 1980 by Dr. C. W. (Tony) Hirt, who was one of the principals in pioneering the “Volume-of-Fluid” or VOF method while working at the Los Alamos National Lab. FLOW-3D is a direct descendant of this work, and in the subsequent years, we have increased its sophistication with TruVOF, boasting pioneering improvements in the speed and accuracy of tracking distinct liquid/gas interfaces. Today, Flow Science products offer complete multiphysics simulation with diverse modeling capabilities including fluid-structure interaction, 6-DoF moving objects, and multiphase flows. From inception, our vision has been to provide our customers with excellence in flow modeling software and services.

    Fig. 8. Comparison of the wave pattern for : (a) Ship wave only; (b) Ship wave in the presence of a following current.

    균일한 해류가 존재하는 선박 파도의 수치 시뮬레이션

    Numerical simulation of ship waves in the presence of a uniform current

    CongfangAiYuxiangMaLeiSunGuohaiDongState Key Laboratory of Coastal and Offshore Engineering, Dalian University of Technology, Dalian, 116024, China

    Highlights

    • Ship waves in the presence of a uniform current are studied by a non-hydrostatic model.

    • Effects of a following current on characteristic wave parameters are investigated.

    • Effects of an opposing current on characteristic wave parameters are investigated.

    • The response of the maximum water level elevation to the ship draft is discussed.

    Abstract

    이 논문은 균일한 해류가 존재할 때 선박파의 생성 및 전파를 시뮬레이션하기 위한 비정역학적 모델을 제시합니다. 선박 선체의 움직임을 표현하기 위해 움직이는 압력장 방법이 모델에 통합되었습니다.

    뒤따르거나 반대 방향의 균일한 흐름이 있는 경우의 선박 파도의 수치 결과를 흐름이 없는 선박 파도의 수치 결과와 비교합니다. 추종 또는 반대 균일 전류가 존재할 때 계산된 첨단선 각도는 분석 솔루션과 잘 일치합니다. 추종 균일 전류와 반대 균일 전류가 특성파 매개변수에 미치는 영향을 제시하고 논의합니다.

    선박 흘수에 대한 최대 수위 상승의 응답은 추종 또는 반대의 균일한 흐름이 있는 경우에도 표시되며 흐름이 없는 선박 파도의 응답과 비교됩니다. 선박 선체 측면의 최대 수위 상승은 Froude 수 Fr’=Us/gh의 특정 범위에 대해 다음과 같은 균일한 흐름의 존재에 의해 증가될 수 있음이 밝혀졌습니다.

    여기서 Us는 선박 속도이고 h는 물입니다. 깊이. 균일한 해류를 무시하면 추종류나 반대류가 존재할 때 선박 흘수에 대한 최대 수위 상승의 응답이 과소평가될 수 있습니다.

    본 연구는 선박파의 해석에 있어 균일한 해류의 영향을 고려해야 함을 시사합니다.

    This paper presents a non-hydrostatic model to simulate the generation and propagation of ship waves in the presence of a uniform current. A moving pressure field method is incorporated into the model to represent the movement of a ship hull. Numerical results of ship waves in the presence of a following or an opposing uniform current are compared with those of ship waves without current. The calculated cusp-line angles in the presence of a following or opposing uniform current agree well with analytical solutions. The effects of a following uniform current and an opposing uniform current on the characteristic wave parameters are presented and discussed. The response of the maximum water level elevation to the ship draft is also presented in the presence of a following or an opposing uniform current and is compared with that for ship waves without current. It is found that the maximum water level elevation lateral to the ship hull can be increased by the presence of a following uniform current for a certain range of Froude numbers Fr′=Us/gh, where Us is the ship speed and h is the water depth. If the uniform current is neglected, the response of the maximum water level elevation to the ship draft in the presence of a following or an opposing current can be underestimated. The present study indicates that the effect of a uniform current should be considered in the analysis of ship waves.

    Keywords

    Ship waves, Non-hydrostatic model, Following current, Opposing current, Wave parameters

    1. Introduction

    Similar to wind waves, ships sailing across the sea can also create free-surface undulations ranging from ripples to waves of large size (Grue, 20172020). Ship waves can cause sediment suspension and engineering structures damage and even pose a threat to flora and fauna living near the embankments of waterways (Dempwolff et al., 2022). It is quite important to understand ship waves in various environments. The study of ship waves has been conducted over a century. A large amount of research (Almström et al., 2021Bayraktar and Beji, 2013David et al., 2017Ertekin et al., 1986Gourlay, 2001Havelock, 1908Lee and Lee, 2019Samaras and Karambas, 2021Shi et al., 2018) focused on the generation and propagation of ship waves without current. When a ship navigates in the sea or in a river where tidal flows or river flows always exist, the effect of currents should be taken into account. However, the effect of currents on the characteristic parameters of ship waves is still unclear, because very few publications have been presented on this topic.

    Over the past two decades, many two-dimensional (2D) Boussinesq-type models (Bayraktar and Beji, 2013Dam et al., 2008David et al., 2017Samaras and Karambas, 2021Shi et al., 2018) were developed to examine ship waves. For example, Bayraktar and Beji (2013) solved Boussinesq equations with improved dispersion characteristics to simulate ship waves due to a moving pressure field. David et al. (2017) employed a Boussinesq-type model to investigate the effects of the pressure field and its propagation speed on characteristic wave parameters. All of these Boussinesq-type models aimed to simulate ship waves without current except for that of Dam et al. (2008), who investigated the effect of currents on the maximum wave height of ship waves in a narrow channel.

    In addition to Boussinesq-type models, numerical models based on the Navier-Stokes equations (NSE) or Euler equations are also capable of resolving ship waves. Lee and Lee (20192021) employed the FLOW-3D model to simulate ship waves without current and ship waves in the presence of a uniform current to confirm their equations for ship wave crests. FLOW-3D is a computational fluid dynamics (CFD) software based on the NSE, and the volume of fluid (VOF) method is used to capture the moving free surface. However, VOF-based NSE models are computationally expensive due to the treatment of the free surface. To efficiently track the free surface, non-hydrostatic models employ the so-called free surface equation and can be solved efficiently. One pioneering application for the simulation of ship waves by the non-hydrostatic model was initiated by Ma (2012) and named XBeach. Recently, Almström et al. (2021) validated XBeach with improved dispersive behavior by comparison with field measurements. XBeach employed in Almström et al. (2021) is a 2-layer non-hydrostatic model and is accurate up to Kh=4 for the linear dispersion relation (de Ridder et al., 2020), where K=2π/L is the wavenumber. L is the wavelength, and h is the still water depth. However, no applications of non-hydrostatic models on the simulation of ship waves in the presence of a uniform current have been published. For more advances in the numerical modelling of ship waves, the reader is referred to Dempwolff et al. (2022).

    This paper investigates ship waves in the presence of a uniform current by using a non-hydrostatic model (Ai et al., 2019), in which a moving pressure field method is incorporated to represent the movement of a ship hull. The model solves the incompressible Euler equations by using a semi-implicit algorithm and is associated with iterating to solve the Poisson equation. The model with two, three and five layers is accurate up to Kh= 7, 15 and 40, respectively (Ai et al., 2019) in resolving the linear dispersion relation. To the best of our knowledge, ship waves in the presence of currents have been studied theoretically (Benjamin et al., 2017Ellingsen, 2014Li and Ellingsen, 2016Li et al., 2019.) and numerically (Dam et al., 2008Lee and Lee, 20192021). However, no publications have presented the effects of a uniform current on characteristic wave parameters except for Dam et al. (2008), who investigated only the effect of currents on the maximum wave height in a narrow channel for the narrow relative Froude number Fr=(Us−Uc)/gh ranging from 0.47 to 0.76, where Us is the ship speed and Uc is the current velocity. To reveal the effect of currents on the characteristic parameters of ship waves, the main objectives of this paper are (1) to validate the capability of the proposed model to resolve ship waves in the presence of a uniform current, (2) to investigate the effects of a following or an opposing current on characteristic wave parameters including the maximum water level elevation and the leading wave period in the ship wave train, (3) to show the differences in characteristic wave parameters between ship waves in the presence of a uniform current and those without current when the same relative Froude number Fr is specified, and (4) to examine the response of the maximum water level elevation to the ship draft in the presence of a uniform current.

    The remainder of this paper is organized as follows. The non-hydrostatic model for ship waves is described in Section 2. Section 3 presents numerical validations for ship waves. Numerical results and discussions about the effects of a uniform current on characteristic wave parameters are provided in Section 4, and a conclusion is presented in Section 5.

    2. Non-hydrostatic model for ship waves

    2.1. Governing equations

    The 3D incompressible Euler equations are expressed in the following form:(1)∂u∂x+∂v∂y+∂w∂z=0(2)∂u∂t+∂u2∂x+∂uv∂y+∂uw∂z=−∂p∂x(3)∂v∂t+∂uv∂x+∂v2∂y+∂vw∂z=−∂p∂y(4)∂w∂t+∂uw∂x+∂vw∂y+∂w2∂z=−∂p∂z−gwhere t is the time; u(x,y,z,t), v(x,y,z,t) and w(x,y,z,t) are the velocity components in the horizontal x, y and vertical z directions, respectively; p(x,y,z,t) is the pressure divided by a constant reference density; and g is the gravitational acceleration.

    The pressure p(x,y,z,t) can be expressed as(5)p=ps+g(η−z)+qwhere ps(x,y,t) is the pressure at the free surface, η(x,y,t) is the free surface elevation, and q(x,y,z,t) is the non-hydrostatic pressure.

    η(x,y,t) is calculated by the following free-surface equation:(6)∂η∂t+∂∂x∫−hηudz+∂∂y∫−hηvdz=0where z=−h(x,y) is the bottom surface.

    To generate ship waves, ps(x,y,t) is determined by the following slender-body type pressure field (Bayraktar and Beji, 2013David et al., 2017Samaras and Karambas, 2021):

    For −L/2≤x’≤L/2,−B/2≤y’≤B/2(7)ps(x,y,t)|t=0=pm[1−cL(x′/L)4][1−cB(y′/B)2]exp⁡[−a(y′/B)2]where x′=x−x0 and y′=y−y0. (x0,y0) is the center of the pressure field, pm is the peak pressure defined at (x0,y0), and L and B are the lengthwise and breadthwise parameters, respectively. cL, cB and a are set to 16, 2 and 16, respectively.

    2.2. Numerical algorithms

    In this study, the generation of ship waves is incorporated into the semi-implicit non-hydrostatic model developed by Ai et al. (2019). The 3D grid system used in the model is built from horizontal rectangular grids by adding horizontal layers. The horizontal layers are distributed uniformly along the water depth, which means the layer thickness is defined by Δz=(η+h)/Nz, where Nz is the number of horizontal layers.

    In the solution procedure, the first step is to generate ship waves by implementing Eq. (7) together with the prescribed ship track. In the second step, Eqs. (1)(2)(3)(4) are solved by the pressure correction method, which can be subdivided into three stages. The first stage is to compute intermediate velocities un+1/2, vn+1/2, and wn+1/2 by solving Eqs. (2)(3)(4), which contain the non-hydrostatic pressure at the preceding time level. In the second stage, the Poisson equation for the non-hydrostatic pressure correction term is solved on the graphics processing unit (GPU) in conjunction with the conjugate gradient method. The third stage is to compute the new velocities un+1, vn+1, and wn+1 by correcting the intermediate values after including the non-hydrostatic pressure correction term. In the discretization of Eqs. (2)(3), the gradient terms of the water surface ∂η/∂x and ∂η/∂y are discretized by means of the semi-implicit method (Vitousek and Fringer, 2013), in which the implicitness factor θ=0.5 is used. The model is second-order accurate in time for free-surface flows. More details about the model can be found in Ai et al. (2019).

    3. Model validation

    In this section, we validate the proposed model in resolving ship waves. The numerical experimental conditions are provided in Table 1 and Table 2. In Table 2, Case A with the current velocity of Uc = 0.0 m/s represents ship waves without current. Both Case B and Case C correspond to the cases in the presence of a following current, while Case D and Case E represent the cases in the presence of an opposing current. The current velocities are chosen based on the observed currents at 40.886° N, 121.812° E, which is in the Liaohe Estuary. The measured data were collected from 14:00 on September 18 (GMT + 08:00) to 19:00 on September 19 in 2021. The maximum flood velocity is 1.457 m/s, and the maximum ebb velocity is −1.478 m/s. The chosen current velocities are between the maximum flood velocity and the maximum ebb velocity.

    Table 1. Summary of ship speeds.

    CaseWater depth h (m)Ship speed Us (m/s)Froude number Fr′=Us/gh
    16.04.570.6
    26.05.350.7
    36.06.150.8
    46.06.900.9
    56.07.0930.925
    66.07.280.95
    76.07.4760.975
    86.07.861.025
    96.08.061.05
    106.08.2431.075
    116.08.451.1
    126.09.201.2
    136.09.971.3
    146.010.751.4
    156.011.501.5
    166.012.301.6
    176.013.051.7
    186.013.801.8
    196.014.601.9
    206.015.352.0

    Table 2. Summary of current velocities.

    CaseABCDE
    Current velocity
    Uc (m/s)
    0.00.51.0−0.5−1.0

    Notably, the Froude number Fr′=Us/gh presented in Table 1 is defined by the ship speed Us only and is different from the relative Froude number Fr when a uniform current is presented. According to the theory of Lee and Lee (2021), with the same relative Froude number, the cusp-line angles in the presence of a following or an opposing uniform current are identical to those without current. As a result, for the test cases presented in Table 1Table 2, all calculated cusp-line angles follow the analytical solution of Havelock (1908), when the relative Froude number Fr is introduced.

    As shown in Fig. 1, the dimensions of the computational domain are −420≤x≤420 m and −200≤y≤200 m, which are similar to those of David et al. (2017). The ship track follows the x axis and ranges from −384 m to 384 m. The ship hull is represented by Eq. (7), in which the length L and the beam B are set to 14.0 m and 7.0 m, respectively, and the peak pressure value is pm= 5000 Pa. In the numerical simulations, grid convergence tests reveal that the horizontal grid spacing of Δx=Δy= 1.0 m and two horizontal layers are adequate. The numerical results with different numbers of horizontal layers are shown in the Appendix.

    Fig. 1

    Fig. 2Fig. 3 compare the calculated cusp-line angles θc with the analytical solutions of Havelock (1908) for ship waves in the presence of a following uniform current and an opposing uniform current, respectively. The calculated cusp-line angles without current are also depicted in Fig. 2Fig. 3. All calculated cusp-line angles are in good agreement with the analytical solutions, except that the model tends to underpredict the cusp-line angle for 0.9<Fr<1.0. Notably, a similar underprediction of the cusp-line angle can also be found in David et al. (2017).

    Fig. 2
    Fig. 3

    4. Results and discussions

    This section presents the effects of a following current and opposing current on the maximum water level elevation and the leading wave period in the wave train based on the test cases presented in Table 1Table 2. Moreover, the response of the maximum water level elevation to the ship draft in the presence of a uniform current is examined.

    4.1. Effects of a following current on characteristic wave parameters

    To present the effect of a following current on the maximum wave height, the variations of the maximum water level elevation ηmax with the Froude number Fr′ at gauge points G1 and G2 are depicted in Fig. 4. The positions of gauge points G1 and G2 are shown in Fig. 1. The maximum water level elevation is an analogue to the maximum wave height and is presented in this study, because maximum wave heights at different positions away from the ship track vary throughout the wave train (David et al., 2017). In general, the variations of ηmax with the Froude number Fr′ in the three cases show a similar behavior, in which with the increase in Fr′, ηmax increases and then decreases. The presence of the following currents decreases ηmax for Fr′≤0.8 and Fr′≥1.2. Specifically, the following currents have a significant effect on ηmax for Fr′≤0.8. Notably, ηmax can be increased by the presence of the following currents for 0.9≤Fr′≤1.1. Compared with Case A, at location G1 ηmax is amplified 1.25 times at Fr′=0.925 in Case B and 1.31 times at Fr′=1.025 in Case C. Similarly, at location G2 ηmax is amplified 1.15 times at Fr′=1.025 in Case B and 1.11 times at Fr′=1.075 in Case C. The fact that ηmax can be increased by the presence of a following current for 0.9≤Fr′≤1.1 implies that if a following uniform current is neglected, then ηmax may be underestimated.

    Fig. 4

    To show the effect of a following current on the wave period, Fig. 5 depicts the variation of the leading wave period Tp in the wave train at gauge point G2 with the Froude number Fr′. Similar to David et al. (2017), Tp is defined by the wave period of the first wave with a leading trough in the wave train. The leading wave periods for Fr′= 0.6 and 0.7 were not given in Case B and Case C, because the leading wave heights for Fr′= 0.6 and 0.7 are too small to discern the leading wave periods. Compared with Case A, the presence of a following current leads to a larger Tp for 0.925≤Fr′≤1.1 and a smaller Tp for Fr′≥1.3. For Fr′= 0.8 and 0.9, Tp in Case B is larger than that in Case A and Tp in Case C is smaller than that in Case A. In all three cases, Tp decreases with increasing Fr′ for Fr′>1.0. However, this decreasing trend becomes very gentle after Fr′≥1.4. Notably, as shown in Fig. 5, Fr′=1.2 tends to be a transition point at which the following currents have a very limited effect on Tp. Moreover, before the transition point, Tp in Case B and Case C are larger than that in Case A (only for 0.925≤Fr′≤1.2), but after the transition point the reverse is true.

    Fig. 5

    As mentioned previously, the cusp-line angles for ship waves in the presence of a following or an opposing current are identical to those for ship waves only with the same relative Froude number Fr. However, with the same Fr, the characteristic parameters of ship waves in the presence of a following or an opposing current are quite different from those of ship waves without current. Fig. 6 shows the variations of the maximum water level elevation ηmax with Fr at gauge points G1 and G2 for ship waves in the presence of a following uniform current. Overall, the relationship curves between ηmax and Fr in Case B and Case C are lower than those in Case A. It is inferred that with the same Fr, ηmax in the presence of a following current is smaller than that without current. Fig. 7 shows the variation of the leading wave period Tp in the wave train at gauge point G2 with Fr for ship waves in the presence of a following uniform current. The overall relationship curves between Tp and Fr in Case B and Case C are also lower than those in Case A for 0.9≤Fr≤2.0. It can be inferred that with the same Fr, Tp in the presence of a following current is smaller than that without current for Fr≥0.9.

    Fig. 6
    Fig. 7

    To compare the numerical results between the case of ship waves only and the case of ship waves in the presence of a following current with the same Fr, Fig. 8 shows the wave patterns for Fr=1.2. To obtain the case of ship waves in the presence of a following current with Fr=1.2, the ship speed Us=9.7 m/s and the current velocity Uc=0.5 m/s are adopted. Fig. 8 indicates that both the calculated cusp-line angles for the case of Us=9.2 m/s and Uc=0.0 m/s and the case of Us=9.7 m/s and Uc=0.5 m/s are equal to 56.5°, which follows the theory of Lee and Lee (2021)Fig. 9 depicts the comparison of the time histories of the free surface elevation at gauge point G2 for Fr=1.2 between the case of ship waves only and the case of ship waves in the presence of a following current. The time when the ship wave just arrived at gauge point G2 is defined as t′=0. Both the maximum water level elevation and the leading wave period in the case of Us=9.2 m/s and Uc=0.0 m/s are larger than those in the case of Us=9.7 m/s and Uc=0.5 m/s, which is consistent with the inferences based on Fig. 6Fig. 7.

    Fig. 8
    Fig. 8. Comparison of the wave pattern for Fr=1.2: (a) Ship wave only; (b) Ship wave in the presence of a following current.
    Fig. 9
    Fig. 9. Comparison of the time histories of the free surface elevation at gauge point G2 for between case of ship waves only and case of ship waves in the presence of a following current.

    Fig. 10 shows the response of the maximum water level elevation ηmax to the ship draft at gauge point G2 for Fr′= 1.2 in the presence of a following uniform current. pm ranges from 2500 Pa to 40,000 Pa with an interval of Δp= 2500 Pa pm0= 2500 Pa represents a reference case. ηmax0 denotes the maximum water level elevation corresponding to the case of pm0= 2500 Pa. The best-fit linear trend lines obtained by linear regression analysis for the three responses are also depicted in Fig. 10. In general, all responses of ηmax to the ship draft show a linear relationship. The coefficients of determination for the three linear trend lines are R2= 0.9901, 0.9941 and 0.9991 for Case A, Case B and Case C, respectively. R2 is used to measure how close the numerical results are to the linear trend lines. The closer R2 is to 1.0, the more linear the numerical results tend to be. As a result, the relationship curve between ηmax and the ship draft in the presence of a following uniform current tends to be more linear than that without current. Notably, with the increase in pmpm0, ηmax increases faster in Case B and Case C than Case A. This implies that neglecting the following currents can lead to the underestimation of the response of ηmax to the ship draft.

    Fig. 10

    4.2. Effects of an opposing current on characteristic wave parameters

    Fig. 11 shows the variations of the maximum water level elevation ηmax with the Froude number Fr′ at gauge points G1 and G2 for ship waves in the presence of an opposing uniform current. The presence of opposing uniform currents leads to a significant reduction in ηmax at the two gauge points for 0.6≤Fr′≤2.0. Especially for Fr′=0.6, the decrease in ηmax is up to 73.8% in Case D and 78.4% in Case E at location G1 and up to 93.8% in Case D and 95.3% in Case E at location G2 when compared with Case A. Fig. 12 shows the variations of the leading wave period Tp at gauge point G2 with the Froude number Fr′ for ship waves in the presence of an opposing uniform current. The leading wave periods for Fr′= 0.6 and 0.7 were also not provided in Case D and Case E due to the small leading wave heights. In general, Tp decreases with increasing Fr′ in Case D and Case E for 0.8≤Fr′≤2.0. Tp in Case D and Case E are larger than that in Case A for Fr′≥1.0.

    Fig. 11
    Fig. 12

    Fig. 13 depicts the variations of the maximum water level elevation ηmax with the relative Froude number Fr at gauge points G1 and G2 for ship waves in the presence of an opposing uniform current. Similar to Case B and Case C shown in Fig. 6, the overall relationship curves between ηmax and Fr in Case D and Case E are lower than those in Case A. This implies that with the same Fr, ηmax in the presence of an opposing current is also smaller than that without current. Fig. 14 depicts the variations of the leading wave period Tp in the wave train at gauge point G2 with Fr for ship waves in the presence of an opposing uniform current. Similar to Case B and Case C shown in Fig. 7, the overall relationship curves between Tp and Fr in Case D and Case E are lower than those in Case A for 0.9≤Fr≤2.0. This also implies that with the same Fr, Tp in the presence of an opposing current is smaller than that without current.

    Fig. 13
    Fig. 14

    Fig. 15 shows a comparison of the wave pattern for Fr=1.2 between the case of ship waves only and the case of ship waves in the presence of an opposing current. The case of the ship wave in the presence of an opposing current with Fr=1.2 is obtained by setting the ship speed Us=8.7 m/s and the current velocity Uc=−0.5 m/s. As expected (Lee and Lee, 2021), both calculated cusp-line angles are identical. Fig. 16 depicts the comparison of the time histories of the free surface elevation at gauge point G2 for Fr=1.2 between the case of ship waves only and the case of ship waves in the presence of an opposing current. The maximum water level elevation in the case of Us=9.2 m/s and Uc=0.0 m/s is larger than that in the case of Us=8.7 m/s and Uc=−0.5 m/s, while the reverse is true for the leading wave period. Fig. 16 is consistent with the inferences based on Fig. 13Fig. 14.

    Fig. 15
    Fig. 16

    Fig. 17 depicts the response of the maximum water level elevation ηmax to the ship draft at gauge point G2 for Fr′= 1.2 in the presence of an opposing uniform current. Similarly, the response of ηmax to the ship draft in the presence of an opposing uniform current shows a linear relationship. The coefficients of determination for the three linear trend lines are R2= 0.9901, 0.9955 and 0.9987 for Case A, Case D and Case E, respectively. This indicates that the relationship curve between ηmax and the ship draft in the presence of an opposing uniform current also tends to be more linear than that without current. In addition, ηmax increases faster with increasing pmpm0 in Case D and Case E than Case A, implying that the response of ηmax to the ship draft can also be underestimated by neglecting opposing currents.

    Fig. 17

    5. Conclusions

    A non-hydrostatic model incorporating a moving pressure field method was used to investigate characteristic wave parameters for ship waves in the presence of a uniform current. The calculated cusp-line angles for ship waves in the presence of a following or an opposing uniform current were in good agreement with analytical solutions, demonstrating that the proposed model can accurately resolve ship waves in the presence of a uniform current.

    The model results showed that the presence of a following current can result in an increase in the maximum water level elevation ηmax for 0.9≤Fr′≤1.1, while the presence of an opposing current leads to a significant reduction in ηmax for 0.6≤Fr′≤2.0. The leading wave period Tp can be increased for 0.925≤Fr′≤1.2 and reduced for Fr′≥1.3 due to the presence of a following current. However, the presence of an opposing current leads to an increase in Tp for Fr′≥1.0.

    Although with the same relative Froude number Fr, the cusp-line angles for ship waves in the presence of a following or an opposing current are identical to those for ship waves without current, the maximum water level elevation ηmax and leading wave period Tp in the presence of a following or an opposing current are quite different from those without current. The present model results imply that with the same Fr, ηmax in the presence of a following or an opposing current is smaller than that without current for Fr≥0.6, and Tp in the presence of a following or an opposing current is smaller than that without current for Fr≥0.9.

    The response of ηmax to the ship draft in the presence of a following current or an opposing current is similar to that without current and shows a linear relationship. However, the presence of a following or an opposing uniform current results in more linear responses of ηmax to the ship draft. Moreover, more rapid responses of ηmax to the ship draft are obtained when a following current or an opposing current is presented. This implies that the response of ηmax to the ship draft in the presence of a following current or an opposing current can be underestimated if the uniform current is neglected.

    The present results have implications for ships sailing across estuarine and coastal environments, where river flows or tidal flows are significant. In these environments, ship waves can be larger than expected and the response of the maximum water level elevation to the ship draft may be more remarkable. The effect of a uniform current should be considered in the analysis of ship waves.

    The present study considered only slender-body type ships. For different hull shapes, the effects of a uniform current on characteristic wave parameters need to be further investigated. Moreover, the effects of an oblique uniform current on ship waves need to be examined in future work.

    CRediT authorship contribution statement

    Congfang Ai: Conceptualization, Methodology, Software, Validation, Writing – original draft, Funding acquisition. Yuxiang Ma: Conceptualization, Methodology, Funding acquisition, Writing – review & editing. Lei Sun: Conceptualization, Methodology. Guohai Dong: Supervision, Funding acquisition.

    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.

    Acknowledgments

    This research is financially supported by the National Natural Science Foundation of China (Grant No. 521712485172010501051979029), LiaoNing Revitalization Talents Program (Grant No. XLYC1807010) and the Fundamental Research Funds for the Central Universities (Grant No. DUT21LK01).

    Appendix. Numerical results with different numbers of horizontal layers

    Fig. 18 shows comparisons of the time histories of the free surface elevation at gauge point G1 for Case B and Fr′= 1.2 between the three sets of numerical results with different numbers of horizontal layers. The maximum water level elevations ηmax obtained by Nz= 3 and 4 are 0.24% and 0.35% larger than ηmax with Nz= 2, respectively. Correspondingly, the leading wave periods Tp obtained by Nz= 3 and 4 are 0.45% and 0.55% larger than Tp with Nz= 2, respectively. In general, the three sets of numerical results are very close. To reduce the computational cost, two horizontal layers Nz= 2 were chosen for this study.

    Fig. 18

    Data availability

    Data will be made available on request.

    References

    Ai et al., 2019

    C. Ai, Y. Ma, C. Yuan, G. Dong

    Development and assessment of semi-implicit nonhydrostatic models for surface water waves

    Ocean Model., 144 (2019), Article 101489

    ArticleDownload PDFView Record in ScopusGoogle ScholarAlmström et al., 2021

    B. Almström, D. Roelvink, M. Larson

    Predicting ship waves in sheltered waterways – an application of XBeach to the Stockholm Archipelago, Sweden

    Coast. Eng., 170 (2021), Article 104026

    ArticleDownload PDFView Record in ScopusGoogle ScholarBayraktar and Beji, 2013

    D. Bayraktar, S. Beji

    Numerical simulation of waves generated by a moving pressure field

    Ocean Eng., 59 (2013), pp. 231-239

    Google ScholarBenjamin et al., 2017

    K. Benjamin, B.K. Smelzer, S.A. Ellingsen

    Surface waves on currents with arbitrary vertical shear

    Phys. Fluids, 29 (2017), Article 047102

    Google ScholarDam et al., 2008

    K.T. Dam, K. Tanimoto, E. Fatimah

    Investigation of ship waves in a narrow channel

    J. Mar. Sci. Technol., 13 (2008), pp. 223-230 View PDF

    CrossRefView Record in ScopusGoogle ScholarDavid et al., 2017

    C.G. David, V. Roeber, N. Goseberg, T. Schlurmann

    Generation and propagation of ship-borne waves – solutions from a Boussinesq-type model

    Coast. Eng., 127 (2017), pp. 170-187

    ArticleDownload PDFView Record in ScopusGoogle Scholarde Ridder et al., 2020

    M.P. de Ridder, P.B. Smit, A. van Dongeren, R. McCall, K. Nederhoff, A.J.H.M. Reniers

    Efficient two-layer non-hydrostatic wave model with accurate dispersive behaviour

    Coast. Eng., 164 (2020), Article 103808

    Google ScholarDempwolff et al., 2022

    L.-C. Dempwolff, G. Melling, C. Windt, O. Lojek, T. Martin, I. Holzwarth, H. Bihs, N. Goseberg

    Loads and effects of ship-generated, drawdown waves in confined waterways – a review of current knowledge and methods

    J. Coast. Hydraul. Struct., 2 (2022), pp. 2-46

    Google ScholarEllingsen, 2014

    S.A. Ellingsen

    Ship waves in the presence of uniform vorticity

    J. Fluid Mech., 742 (2014), p. R2

    View Record in ScopusGoogle ScholarErtekin et al., 1986

    R.C. Ertekin, W.C. Webster, J.V. Wehausen

    Waves caused by a moving disturbance in a shallow channel of finite width

    J. Fluid Mech., 169 (1986), pp. 275-292

    View Record in ScopusGoogle ScholarGrue, 2017

    J. Grue

    Ship generated mini-tsunamis

    J. Fluid Mech., 816 (2017), pp. 142-166 View PDF

    CrossRefView Record in ScopusGoogle ScholarGrue, 2020

    J. Grue

    Mini-tsunamis made by ship moving across a depth change

    J. Waterw. Port, Coast. Ocean Eng., 146 (2020), Article 04020023

    View Record in ScopusGoogle ScholarGourlay, 2001

    T.P. Gourlay

    The supercritical bore produced by a high-speed ship in a channel

    J. Fluid Mech., 434 (2001), pp. 399-409 View PDF

    CrossRefView Record in ScopusGoogle ScholarHavelock, 1908

    T.H. Havelock

    The propagation of groups of waves in dispersive media with application to waves on water produced by a travelling disturbance

    Proc. Royal Soc. London Series A (1908), pp. 398-430

    Google ScholarLee and Lee, 2019

    B.W. Lee, C. Lee

    Equation for ship wave crests in the entire range of water depths

    Coast. Eng., 153 (2019), Article 103542

    ArticleDownload PDFView Record in ScopusGoogle ScholarLee and Lee, 2021

    B.W. Lee, C. Lee

    Equation for ship wave crests in a uniform current in the entire range of water depths

    Coast. Eng., 167 (2021), Article 103900

    ArticleDownload PDFView Record in ScopusGoogle ScholarLi and Ellingsen, 2016

    Y. Li, S.A. Ellingsen

    Ship waves on uniform shear current at finite depth: wave resistance and critical velocity

    J. Fluid Mech., 791 (2016), pp. 539-567 View PDF

    CrossRefView Record in ScopusGoogle ScholarLi et al., 2019

    Y. Li, B.K. Smeltzer, S.A. Ellingsen

    Transient wave resistance upon a real shear current

    Eur. J. Mech. B Fluid, 73 (2019), pp. 180-192

    ArticleDownload PDFCrossRefView Record in ScopusGoogle ScholarMa, 2012

    H. Ma

    Passing Ship Effects in a 2DH Non- Hydrostatic Flow Model

    UNESCO-IHE, Delft, The Netherlands (2012)

    Google ScholarSamaras and Karambas, 2021

    A.G. Samaras, T.V. Karambas

    Numerical simulation of ship-borne waves using a 2DH post-Boussinesq model

    Appl. Math. Model., 89 (2021), pp. 1547-1556

    ArticleDownload PDFView Record in ScopusGoogle ScholarShi et al., 2018

    F. Shi, M. Malej, J.M. Smith, J.T. Kirby

    Breaking of ship bores in a Boussinesq-type ship-wake model

    Coast. Eng., 132 (2018), pp. 1-12

    ArticleDownload PDFCrossRefView Record in ScopusGoogle ScholarVitousek and Fringer, 2013

    S. Vitousek, O.B. Fringer

    Stability and consistency of nonhydrostatic free-surface models using the semi-implicit θ-method

    Int. J. Numer. Methods Fluid., 72 (2013), pp. 550-582 View PDF

    CrossRefView Record in ScopusGoogle Scholar

    이종 금속 인터커넥트의 펄스 레이저 용접을 위한 가공 매개변수 최적화

    Optimization of processing parameters for pulsed laser welding of dissimilar metal interconnects

    본 논문은 독자의 편의를 위해 기계번역된 내용이어서 자세한 내용은 원문을 참고하시기 바랍니다.

    NguyenThi TienaYu-LungLoabM.Mohsin RazaaCheng-YenChencChi-PinChiuc

    aNational Cheng Kung University, Department of Mechanical Engineering, Tainan, Taiwan

    bNational Cheng Kung University, Academy of Innovative Semiconductor and Sustainable Manufacturing, Tainan, Taiwan

    cJum-bo Co., Ltd, Xinshi District, Tainan, Taiwan

    Abstract

    워블 전략이 포함된 펄스 레이저 용접(PLW) 방법을 사용하여 알루미늄 및 구리 이종 랩 조인트의 제조를 위한 최적의 가공 매개변수에 대해 실험 및 수치 조사가 수행됩니다. 피크 레이저 출력과 접선 용접 속도의 대표적인 조합 43개를 선택하기 위해 원형 패킹 설계 알고리즘이 먼저 사용됩니다.

    선택한 매개변수는 PLW 프로세스의 전산유체역학(CFD) 모델에 제공되어 용융 풀 형상(즉, 인터페이스 폭 및 침투 깊이) 및 구리 농도를 예측합니다. 시뮬레이션 결과는 설계 공간 내에서 PLW 매개변수의 모든 조합에 대한 용융 풀 형상 및 구리 농도를 예측하기 위해 3개의 대리 모델을 교육하는 데 사용됩니다.

    마지막으로, 대체 모델을 사용하여 구성된 처리 맵은 용융 영역에 균열이나 기공이 없고 향상된 기계적 및 전기적 특성이 있는 이종 조인트를 생성하는 PLW 매개변수를 결정하기 위해 세 가지 품질 기준에 따라 필터링됩니다.

    제안된 최적화 접근법의 타당성은 최적의 용접 매개변수를 사용하여 생성된 실험 샘플의 전단 강도, 금속간 화합물(IMC) 형성 및 전기 접촉 저항을 평가하여 입증됩니다.

    결과는 최적의 매개변수가 1209N의 높은 전단 강도와 86µΩ의 낮은 전기 접촉 저항을 생성함을 확인합니다. 또한 용융 영역에는 균열 및 기공과 같은 결함이 없습니다.

    An experimental and numerical investigation is performed into the optimal processing parameters for the fabrication of aluminum and copper dissimilar lap joints using a pulsed laser welding (PLW) method with a wobble strategy. A circle packing design algorithm is first employed to select 43 representative combinations of the peak laser power and tangential welding speed. The selected parameters are then supplied to a computational fluidic dynamics (CFD) model of the PLW process to predict the melt pool geometry (i.e., interface width and penetration depth) and copper concentration. The simulation results are used to train three surrogate models to predict the melt pool geometry and copper concentration for any combination of the PLW parameters within the design space. Finally, the processing maps constructed using the surrogate models are filtered in accordance with three quality criteria to determine the PLW parameters that produce dissimilar joints with no cracks or pores in the fusion zone and enhanced mechanical and electrical properties. The validity of the proposed optimization approach is demonstrated by evaluating the shear strength, intermetallic compound (IMC) formation, and electrical contact resistance of experimental samples produced using the optimal welding parameters. The results confirm that the optimal parameters yield a high shear strength of 1209 N and a low electrical contact resistance of 86 µΩ. Moreover, the fusion zone is free of defects, such as cracks and pores.

    Fig. 1. Schematic illustration of Al-Cu lap-joint arrangement
    Fig. 1. Schematic illustration of Al-Cu lap-joint arrangement
    Fig. 2. Machine setup (MFQS-150W_1500W
    Fig. 2. Machine setup (MFQS-150W_1500W
    Fig. 5. Lap-shear mechanical tests: (a) experimental setup and specimen dimensions, and (b) two different failures of lap-joint welding.
N. Thi Tien et al.
    Fig. 5. Lap-shear mechanical tests: (a) experimental setup and specimen dimensions, and (b) two different failures of lap-joint welding. N. Thi Tien et al.
    Fig. 9. Simulation and experimental results for melt pool profile. (a) Simulation results for melt pool cross-section, and (b) OM image of melt pool cross-section.
(Note that laser processing parameter of 830 W and 565 mm/s is chosen.).
    Fig. 9. Simulation and experimental results for melt pool profile. (a) Simulation results for melt pool cross-section, and (b) OM image of melt pool cross-section. (Note that laser processing parameter of 830 W and 565 mm/s is chosen.).

    References

    [1]

    G. Santos

    Road transport and CO2 emissions: What are the challenges?

    Transport Policy, 59 (2017), pp. 71-74

    ArticleDownload PDFView Record in ScopusGoogle Scholar[2]

    A. Das, D. Li, D. Williams, D. Greenwood

    Joining technologies for automotive battery systems manufacturing

    World Electric Veh. J., 9 (2) (2018), p. 22 View PDF

    CrossRefGoogle Scholar[3]

    M. Zwicker, M. Moghadam, W. Zhang, C. Nielsen

    Automotive battery pack manufacturing–a review of battery to tab joining

    J. Adv. Joining Process., 1 (2020), Article 100017

    ArticleDownload PDFView Record in ScopusGoogle Scholar[4]

    T. Mai, A. Spowage

    Characterisation of dissimilar joints in laser welding of steel–kovar, copper–steel and copper–aluminium

    Mater. Sci. Eng. A, 374 (1–2) (2004), pp. 224-233

    ArticleDownload PDFView Record in ScopusGoogle Scholar[5]

    S.S. Lee, T.H. Kim, S.J. Hu, W.W. Cai, J. Li, J.A. Abell

    Characterization of joint quality in ultrasonic welding of battery tabs

    International Manufacturing Science and Engineering Conference, vol. 54990, American Society of Mechanical Engineers (2012), pp. 249-261

    Google Scholar[6]

    Y. Zhou, P. Gorman, W. Tan, K. Ely

    Weldability of thin sheet metals during small-scale resistance spot welding using an alternating-current power supply

    J. Electron. Mater., 29 (9) (2000), pp. 1090-1099 View PDF

    CrossRefView Record in ScopusGoogle Scholar[7]

    S. Katayama

    Handbook of laser welding technologies

    Elsevier (2013)

    Google Scholar[8]

    A. Sadeghian, N. Iqbal

    A review on dissimilar laser welding of steel-copper, steel-aluminum, aluminum-copper, and steel-nickel for electric vehicle battery manufacturing

    Opt. Laser Technol., 146 (2022), Article 107595

    ArticleDownload PDFView Record in ScopusGoogle Scholar[9]

    M.J. Brand, P.A. Schmidt, M.F. Zaeh, A. Jossen

    Welding techniques for battery cells and resulting electrical contact resistances

    J. Storage Mater., 1 (2015), pp. 7-14

    ArticleDownload PDFView Record in ScopusGoogle Scholar[10]

    M. Jarwitz, F. Fetzer, R. Weber, T. Graf

    Weld seam geometry and electrical resistance of laser-welded, aluminum-copper dissimilar joints produced with spatial beam oscillation

    Metals, 8 (7) (2018), p. 510 View PDF

    CrossRefView Record in ScopusGoogle Scholar[11]S. Smith, J. Blackburn, M. Gittos, P. de Bono, and P. Hilton, “Welding of dissimilar metallic materials using a scanned laser beam,” in International Congress on Applications of Lasers & Electro-Optics, 2013, vol. 2013, no. 1: Laser Institute of America, pp. 493-502.

    Google Scholar[12]

    P. Schmitz, J.B. Habedank, M.F. Zaeh

    Spike laser welding for the electrical connection of cylindrical lithium-ion batteries

    J. Laser Appl., 30 (1) (2018), Article 012004 View PDF

    CrossRefView Record in ScopusGoogle Scholar[13]

    P. Kah, C. Vimalraj, J. Martikainen, R. Suoranta

    Factors influencing Al-Cu weld properties by intermetallic compound formation

    Int. J. Mech. Mater. Eng., 10 (1) (2015), pp. 1-13

    Google Scholar[14]

    Z. Lei, X. Zhang, J. Liu, P. Li

    Interfacial microstructure and reaction mechanism with various weld fillers on laser welding-brazing of Al/Cu lap joint

    J. Manuf. Process., 67 (2021), pp. 226-240

    ArticleDownload PDFView Record in ScopusGoogle Scholar[15]

    T. Solchenbach, P. Plapper

    Mechanical characteristics of laser braze-welded aluminium–copper connections

    Opt. Laser Technol., 54 (2013), pp. 249-256

    ArticleDownload PDFView Record in ScopusGoogle Scholar[16]

    T. Solchenbach, P. Plapper, W. Cai

    Electrical performance of laser braze-welded aluminum–copper interconnects

    J. Manuf. Process., 16 (2) (2014), pp. 183-189

    ArticleDownload PDFView Record in ScopusGoogle Scholar[17]

    S.J. Lee, H. Nakamura, Y. Kawahito, S. Katayama

    Effect of welding speed on microstructural and mechanical properties of laser lap weld joints in dissimilar Al and Cu sheets

    Sci. Technol. Weld. Join., 19 (2) (2014), pp. 111-118

    Google Scholar[18]

    Z. Xue, S. Hu, D. Zuo, W. Cai, D. Lee, K.-A. Elijah Jr

    Molten pool characterization of laser lap welded copper and aluminum

    J. Phys. D Appl. Phys., 46 (49) (2013), Article 495501 View PDF

    CrossRefView Record in ScopusGoogle Scholar[19]

    S. Zhao, G. Yu, X. He, Y. Zhang, W. Ning

    Numerical simulation and experimental investigation of laser overlap welding of Ti6Al4V and 42CrMo

    J. Mater. Process. Technol., 211 (3) (2011), pp. 530-537

    ArticleDownload PDFView Record in ScopusGoogle Scholar[20]

    W. Huang, H. Wang, T. Rinker, W. Tan

    Investigation of metal mixing in laser keyhole welding of dissimilar metals

    Mater. Des., 195 (2020), Article 109056

    ArticleDownload PDFView Record in ScopusGoogle Scholar[21]

    E. Kaiser, G. Ambrosy, E. Papastathopoulos

    Welding strategies for joining copper and aluminum by fast oscillating, high quality laser beam

    High-Power Laser Materials Processing: Applications, Diagnostics, and Systems IX, vol. 11273, International Society for Optics and Photonics (2020), p. 112730C

    View Record in ScopusGoogle Scholar[22]

    V. Dimatteo, A. Ascari, A. Fortunato

    Continuous laser welding with spatial beam oscillation of dissimilar thin sheet materials (Al-Cu and Cu-Al): Process optimization and characterization

    J. Manuf. Process., 44 (2019), pp. 158-165

    ArticleDownload PDFView Record in ScopusGoogle Scholar[23]

    V. Dimatteo, A. Ascari, E. Liverani, A. Fortunato

    Experimental investigation on the effect of spot diameter on continuous-wave laser welding of copper and aluminum thin sheets for battery manufacturing

    Opt. Laser Technol., 145 (2022), Article 107495

    ArticleDownload PDFView Record in ScopusGoogle Scholar[24]

    D. Wu, X. Hua, F. Li, L. Huang

    Understanding of spatter formation in fiber laser welding of 5083 aluminum alloy

    Int. J. Heat Mass Transf., 113 (2017), pp. 730-740

    ArticleDownload PDFView Record in ScopusGoogle Scholar[25]

    R. Ducharme, K. Williams, P. Kapadia, J. Dowden, B. Steen, M. Glowacki

    The laser welding of thin metal sheets: an integrated keyhole and weld pool model with supporting experiments

    J. Phys. D Appl. Phys., 27 (8) (1994), p. 1619 View PDF

    CrossRefView Record in ScopusGoogle Scholar[26]

    C.W. Hirt, B.D. Nichols

    Volume of fluid (VOF) method for the dynamics of free boundaries

    J. Comput. Phys., 39 (1) (1981), pp. 201-225

    ArticleDownload PDFGoogle Scholar[27]

    W. Piekarska, M. Kubiak

    Three-dimensional model for numerical analysis of thermal phenomena in laser–arc hybrid welding process

    Int. J. Heat Mass Transf., 54 (23–24) (2011), pp. 4966-4974

    ArticleDownload PDFView Record in ScopusGoogle Scholar[28]J. Zhou, H.-L. Tsai, and P.-C. Wang, “Transport phenomena and keyhole dynamics during pulsed laser welding,” 2006.

    Google Scholar[29]

    D. Harrison, D. Yan, S. Blairs

    The surface tension of liquid copper

    J. Chem. Thermodyn., 9 (12) (1977), pp. 1111-1119

    ArticleDownload PDFView Record in ScopusGoogle Scholar[30]

    M. Leitner, T. Leitner, A. Schmon, K. Aziz, G. Pottlacher

    Thermophysical properties of liquid aluminum

    Metall. Mater. Trans. A, 48 (6) (2017), pp. 3036-3045 View PDF

    This article is free to access.

    CrossRefView Record in ScopusGoogle Scholar[31]

    H.-C. Tran, Y.-L. Lo

    Systematic approach for determining optimal processing parameters to produce parts with high density in selective laser melting process

    Int. J. Adv. Manuf. Technol., 105 (10) (2019), pp. 4443-4460 View PDF

    CrossRefView Record in ScopusGoogle Scholar[32]A. Ascari, A. Fortunato, E. Liverani, and A. Lutey, “Application of different pulsed laser sources to dissimilar welding of Cu and Al alloys,” in Proceedings of Lasers in Manufacturing Conference (LIM), 2019.

    Google Scholar[33]

    A. Fortunato, A. Ascari

    Laser welding of thin copper and aluminum sheets: feasibility and challenges in continuous-wave welding of dissimilar metals

    Lasers in Manufacturing and Materials Processing, 6 (2) (2019), pp. 136-157 View PDF

    CrossRefView Record in ScopusGoogle Scholar[34]

    A. Boucherit, M.-N. Avettand-Fènoël, R. Taillard

    Effect of a Zn interlayer on dissimilar FSSW of Al and Cu

    Mater. Des., 124 (2017), pp. 87-99

    ArticleDownload PDFView Record in ScopusGoogle Scholar[35]

    N. Kumar, I. Masters, A. Das

    In-depth evaluation of laser-welded similar and dissimilar material tab-to-busbar electrical interconnects for electric vehicle battery pack

    J. Manuf. Process., 70 (2021), pp. 78-96

    ArticleDownload PDFView Record in ScopusGoogle Scholar[36]

    M. Abbasi, A.K. Taheri, M. Salehi

    Growth rate of intermetallic compounds in Al/Cu bimetal produced by cold roll welding process

    J. Alloy. Compd., 319 (1–2) (2001), pp. 233-241

    ArticleDownload PDFGoogle Scholar[37]

    D. Zuo, S. Hu, J. Shen, Z. Xue

    Intermediate layer characterization and fracture behavior of laser-welded copper/aluminum metal joints

    Mater. Des., 58 (2014), pp. 357-362

    ArticleDownload PDFView Record in ScopusGoogle Scholar[38]

    S. Yan, Y. Shi

    Influence of Ni interlayer on microstructure and mechanical properties of laser welded joint of Al/Cu bimetal

    J. Manuf. Process., 59 (2020), pp. 343-354

    ArticleDownload PDFView Record in ScopusGoogle Scholar[39]

    S. Yan, Y. Shi

    Influence of laser power on microstructure and mechanical property of laser-welded Al/Cu dissimilar lap joints

    J. Manuf. Process., 45 (2019), pp. 312-321

    ArticleDownload PDFView Record in ScopusGoogle Scholar

    Effect of tailwater depth on non-cohesive earth dam failure due to overtopping

    Effect of tailwater depth on non-cohesive earth dam failure due to overtopping

    범람으로 인한 비점착성 흙댐 붕괴에 대한 테일워터 깊이의 영향

    ShaimaaAmanaMohamedAbdelrazek RezkbRabieaNasrc

    Abstract

    본 연구에서는 범람으로 인한 토사댐 붕괴에 대한 테일워터 깊이의 영향을 실험적으로 조사하였다. 테일워터 깊이의 네 가지 다른 값을 검사합니다. 각 실험에 대해 댐 수심 측량 프로파일의 진화, 고장 기간, 침식 체적 및 유출 수위곡선을 관찰하고 기록합니다.

    결과는 tailwater 깊이를 늘리면 고장 시간이 최대 57% 감소하고 상대적으로 침식된 마루 높이가 최대 77.6% 감소한다는 것을 보여줍니다. 또한 상대 배수 깊이가 3, 4, 5인 경우 누적 침식 체적의 감소는 각각 23, 36.5 및 75%인 반면 최대 유출량의 감소는 각각 7, 14 및 17.35%입니다.

    실험 결과는 침식 과정을 복제할 때 Flow 3D 소프트웨어의 성능을 평가하는 데 활용됩니다. 수치 모델은 비응집성 흙댐의 침식 과정을 성공적으로 시뮬레이션합니다.

    The influence of tailwater depth on earth dam failure due to overtopping is investigated experimentally in this work. Four different values of tailwater depths are examined. For each experiment, the evolution of the dam bathymetry profile, the duration of failure, the eroded volume, and the outflow hydrograph are observed and recorded. The results reveal that increasing the tailwater depth reduces the time of failure by up to 57% and decreases the relative eroded crest height by up to 77.6%. In addition, for relative tailwater depths equal to 3, 4, and 5, the reduction in the cumulative eroded volume is 23, 36.5, and 75%, while the reduction in peak discharge is 7, 14, and 17.35%, respectively. The experimental results are utilized to evaluate the performance of the Flow 3D software in replicating the erosion process. The numerical model successfully simulates the erosion process of non-cohesive earth dams.

    Keywords

    Earth dam, Eroded volume, Flow 3D model, Non-cohesive soil, Overtopping failure, Tailwater depth

    Notation

    d50

    Mean partical diameterWc

    Optimum water contentZo

    Dam height (cm)do

    Tailwater depth (cm)Zeroded

    Eroded height of the dam measured at distance of 0.7 m from the dam heel (cm)t

    Total time of failure (sec)t1

    Time of crest width erosion (sec)Zcrest

    The crest height (cm)Vtotal

    Total volume of the dam (m3)Veroded

    Cumulative eroded volume (m3)RMSE

    The statistical variable root- mean- square errord

    Degree of agreement indexyu.s.

    The upstream water depth (cm)yd.s

    The downstream water depth (cm)H

    Water surface elevation over sharp crested weir (cm)Q

    Outflow discharge (liter/sec)Qpeak

    Peak discharge (liter/sec)

    1. Introduction

    Earth dams are compacted structures composed of natural materials that are usually mined or quarried from local locations. The failures of the earth dams have proven to be deadly, destructive, and costly. According to People’s Daily, two earthen dams, Yong’an Dam and Xinfa Dam located in Hulun Buir City in North China’s Inner Mongolia failed on 2021, due to a surge in the water level of the Nuomin River caused by heavy rain. The dam breach affected 16,660 people, flooded 325,622 mu of farmland (21708.1 ha), and destroyed 22 bridges, 124 culverts, and 15.6 km of roadways. Also, the failure of south fork dam (earth and rock fill dam) near Johnstown on 1889 is considered the worst U.S dam disaster in terms of loss of life. The dam was overtopped and washed away due to unexpected heavy rains, releasing 20 million tons of water which destroyed Johnstown and resulted in 2209 deaths, [1][2]. Piping or shear sliding, failure due to natural factors, and failure due to overtopping are all possible causes of earth dam failure. However, overtopping failure is the most frequent cause of dam failure. According to The International Committee on Large Dams (ICOLD, 1995), and [3], more than one-third of the total known dam failures were caused by dam overtopping.

    Overtopping occurs as the result of insufficient flood design or freeboard in some cases. Extreme rainstorms can cause floods which can overtop the dam and cause it to fail. The size and geometry of the reservoir or the dam (side slopes, top width, height, etc.), the homogeneity of the material used in the construction of the dam, overtopping depth, and the presence or absence of tailwater are all elements that influence this type of failure which will be illustrated in the following literature. Overtopping failures of earth dams may be divided into several failure mechanisms based on the material composition and the inner structure of the dam. For cohesive earth dams because of low permeability, no seepage exists on the slopes. Erosion often begins at the earth dam toe during turbulent erosion and moves upstream, undercutting the slope, causing the removal of large chunks of materials. While for non-cohesive earth dams the downstream face of the dam flattens progressively and is often said to rotate around a point near the downstream toe [4][5][6] In the last few decades, the study of failures due to overtopping has gained popularity among researchers. The overtopping failure, in fact, has been widely investigated in coastal and river hydraulics and morpho dynamic. In addition, several laboratory experimental studies have been conducted in this field in order to better understand different involved factors. Also, many numerical types of research have been conducted to investigate the process of overtopping failure as well as the elements that influence this type of failure.

    Tabrizi et al. [5] conducted a series of embankment overtopping tests to find the effect of compaction on the failure of a homogenous sand embankment. A plane breach process occurred across the flume width due to the narrow flume width. They measured the downstream hydrographs and embankment surface profile for every case. They concluded that the peak discharge decreased with a high compaction level, while the time to peak increased. Kansoh et al. [6] studied experimentally the failure of compacted homogeneous non-cohesive earthen embankment due to overtopping. They investigated the influence of different shape parameters including the downstream slope, the crest width, and the height of the embankment on the erosion process. The erosion process was initiated by carving a pilot channel into the embankment crest. They evaluated the time of embankment failure for different shape parameters. They concluded that the failure time increases with increasing the downstream slope and the crest width. Zhu et al. [7] investigated experimentally the breaching of five embankments, one constructed with pure sand, and four with different sand-silt–clay mixtures. The erosion pattern was similar across the flume width. They stated that for cohesive soil mixtures the head cut erosion was the most important factor that affected the breach growth, while for non-cohesive soil the breach erosion was affected by shear erosion.

    Amaral et al. [8] studied experimentally the failure by overtopping for two embankments built from silt sand material. They studied the effect of the degree of compaction of the embankment and the geometry of the pilot channel carved at the centre of the dam crest. They studied two shapes of pilot channel a rectangular shape and triangular shape. They stated that the breach development is influenced by a higher degree of compaction, however, the pilot channel geometry did not influence the breach’s final form. Bereta et al. [9] studied experimentally the breach formation of five dam models, three of them were homogenous clay soil while two were sandy-clay mixtures. The erosion process was initiated by cutting a pilot channel at the centre of the dam crest. They observed the initiation of erosion, flow shear erosion, sidewall bottom erosion, and distinguished the soil mechanical slope mass failure from the head cut vertically and laterally during these tests. Verma et al. [10] investigated experimentally a two-dimensional erosion phenomenon due to overtopping by using a wooden fuse plug model and five different soils. They concluded that the erosion process was affected mostly by cohesiveness and degree of compaction. For cohesive soils, a head cut erosion was observed, while for non-cohesive soils surface erosion occurred gradually. Also, the dimensions of fuse plug, type of fill material, reservoir capacity, and inflow were found to affect the behaviour of the overall breaching process.

    Wu and Qin [11] studied the effect of adding coarse grains to the downstream face of a non-cohesive dam as a result of tailings deposition. The process of overtopping during tailings dam failures is analyzed and its effect on delaying the dam-break process and disaster mitigation are investigated. They found that the tested protective measures decreased the breach area, the maximum breaching flow discharge and flow velocity, and the downstream inundated area. Khankandi et al. [12] studied experimentally the effect of reservoir geometry on dam break flow in case of dry and wet bed conditions. They considered four different reservoir shapes, a long reservoir, a wide, a trapezoidal shaped and one with a 90◦ bend all with identical water volume and horizontal bed. The dam break is simulated by the sudden gate removal using a pneumatic jack. They measured the variation of water level over time with ultrasonic sensors and flow velocity component with an acoustic Doppler velocimeter. Also, the experimental results of water level variation are compared with Ritters solution (1892) [13]. They stated that for dry bed condition the long and 90 bend reservoirs results are close to the analytical solution by ritter also in these two shapes a 1D flow is noticed. However, for wide and trapezoidal reservoirs a 2D effect is significant due to flow contraction at channel entrance.

    Rifai et al. [14] conducted a series of experiments to investigate the effect of tailwater depth on the outflow discharge and breach geometry during non-cohesive homogenous fluvial dikes overtopping failure. They cut an initial notch in the crest at 0.8 m from the upstream end of the dike to initiate overtopping. They compared their results to previous experiments under different main channel inflow discharges combined with a free floodplain. They divided the dike breaching process into three stages: gradual start of overtopping flow resulting in slow initiation of dike erosion, deepening and widening breach due to large flow depth and velocity, finally the flow depth starts stabilizing at its minimal level with or without sustained breach expansion. They stated that breach discharge has lower values than in free floodplain tests. Jiang [15] studied the effect of bed slope on breach parameters and peak discharge in non-cohesive embankment failure. An initial triangular breach with a depth and width of 4 cm was pre-set on one side of the dam. He stated that peak discharge increases with the increase of bed slope and then decreases.

    Ozmen-cagatay et al. [16] studied experimentally flood wave propagation resulted from a sudden dam break event. For dam-break modelling, they used a mechanism that permitted the rapid removal of a vertical plate with a thickness of 4 mm and made of rigid plastic. They conducted three tests, one with dry bed condition and two tests with tailwater depths equal 0.025 m and 0.1 m respectively. They recorded the free surface profile during initial stages of dam break by using digital image processing. Finally, they compared the experimental results with the with a commercially available VOF-based CFD program solving the Reynolds-averaged Navier –Stokes equations (RANS) with the k– Ɛ turbulence model and the shallow water equations (SWEs). They concluded that Wave breaking was delayed with increasing the tailwater depth to initial reservoir depth ratio. They also stated that the SWE approach is sufficient more to represent dam break flows for wet bed condition. Evangelista [17] investigated experimentally and numerically using a depth-integrated two-phase model, the erosion of sand dike caused by the impact of a dam break wave. The dam break is simulated by a sudden opening of an upstream reservoir gate resulting in the overtopping of a downstream trapezoidal sand dike. The evolution of the water wave caused from the gate opening and dike erosion process are recorded by using a computer-controlled camera. The experimental results demonstrated that the progression of the wave front and dike erosion have a considerable influence on each other during the process. In addition, the dike constructed from fine sands was more resistant to erosion than the one built with coarse sand. They also stated that the numerical model can is capable of accurately predicting wave front position and dike erosion. Also, Di Cristo et al. [18] studied the effect of dam break wave propagation on a sand embankment both experimentally and numerically using a two-phase shallow-water model. The evolution of free surface and of the embankment bottom are recorded and used in numerical model assessment. They stated that the model allows reasonable simulation of the experimental trends of the free surface elevation regardeless of the geofailure operator.

    Lots of numerical models have been developed over the past few years to simulate the dam break flooding problem. A one-dimensional model, such as Hec-Ras, DAMBRK and MIKE 11, ect. A two-dimensional model such as iRIC Nay2DH is used in earth embankment breach simulation. Other researchers studied the failure process numerically using (3D) computational fluid dynamics (CFD) models, such as FLOW-3D, and FLUENT. Goharnejad et al. [19] determined the outflow hydrograph which results from the embankment dam break due to overtopping. Hu et al. [20] performed a comparison between Flow-3D and MIKE3 FM numerical models in simulating a dam break event under dry and wet bed conditions with different tailwater depths. Kaurav et al. [21] simulated a planar dam breach process due to overtopping. They conducted a sensitivity analysis to find the effect of dam material, dam height, downstream slope, crest width, and inlet discharge on the erosion process and peak discharge through breach. They concluded that downstream slope has a significant influence on breaching process. Yusof et al. [22] studied the effect of embankment sediment sizes and inflow rates on breaching geometric and hydrodynamic parameters. They stated that the peak outflow hydrograph increases with increasing sediment size and inflow rates while time of failure decreases.

    In the present work, the effect of tailwater depth on earth dam failure during overtopping is studied experimentally. The relation between the eroded volume of the dam and the tailwater depth is presented. Also, the percentage of reduction in peak discharge due to tailwater existence is calculated. An assessment of Flow 3D software performance in simulating the erosion process during earth dam failure is introduced. The statistical variable root- mean- square error, RMSE, and the agreement degree index, d, are used in model assessment.

    2. Material and methods

    The tests are conducted in a straight rectangular flume in the laboratory of Irrigation Engineering and Hydraulics Department, Faculty of Engineering, Alexandria University, Egypt. The flume dimensions are 10 m long, 0.86 m wide, and 0.5 m deep. The front part of the flume is connected to a storage basin 1 m long by 0.86 m wide. The storage basin is connected to a collecting tank for water recirculation during the experiments as shown in Fig. 1Fig. 2. A sharp-crested weir is placed at a distance of 4 m downstream the constructed dam to keep a constant tailwater depth in each experiment and to measure the outflow discharge.

    To measure the eroded volume with time a rods technique is used. This technique consists of two parallel wooden plates with 10 cm distance in between and five rows of stainless-steel rods passing vertically through the wooden plates at a spacing of 20 cm distributed across flume width. Each row consists of four rods with 15 cm spacing between them. Also, a graph board is provided to measure the drop in each rod with time as shown in Fig. 3Fig. 4. After dam construction the rods are carefully rested on the dam, with the first line of rods resting in the middle of the dam crest and then a constant distance of 15 cm between rods lines is maintained.

    A soil sample is taken and tested in the laboratory of the soil mechanics to find the soil geotechnical parameters. The soil particle size distribution is also determined by sieve analysis as shown in Fig. 5. The soil mean diameter d50,equals 0.38 mm and internal friction angle equals 32.6°.

    2.1. Experimental procedures

    To investigate the effect of the tailwater depth (do), the tailwater depth is changed four times 5, 15, 20, and 25 cm on the sand dam model. The dam profile is 35 cm height, with crest width = 15 cm, the dam base width is 155 cm, and the upstream and downstream slopes are 2:1 as shown in Fig. 6. The dam dimensions are set as the flume permitted to allow observation of the dam erosion process under the available flume dimensions and conditions. All of the conducted experiments have the same dimensions and configurations.

    The optimum water content, Wc, from the standard proctor test is found to be 8 % and the maximum dry unit weight is 19.42 kN/m3. The soil and water are mixed thoroughly to ensure consistency and then placed on three horizontal layers. Each layer is compacted according to ASTM standard with 25 blows by using a rammer (27 cm × 20.5 cm) weighing 4 kg. Special attention is paid to the compaction of the soil to guarantee the repeatability of the tests.

    After placing and compacting the three layers, the dam slopes are trimmed carefully to form the trapezoidal shape of the dam. A small triangular pilot channel with 1 cm height and 1:1 side slopes is cut into the dam crest to initiate the erosion process. The position of triangular pilot channel is presented in Fig. 1. Three digital video cameras with a resolution of 1920 × 1080 pixels and a frame rate of 60 fps are placed in three different locations. One camera on one side of the flume to record the progress of the dam profile during erosion. Another to track the water level over the sharp-crested rectangular weir placed at the downstream end of the flume. And the third camera is placed above the flume at the downstream side of the dam and in front of the rods to record the drop of the tip of the rods with time as shown previously in Fig. 1.

    Before starting the experiment, the water is pumped into the storage basin by using pump with capacity 360 m3/hr, and then into the upstream section of the flume. The upstream boundary is an inflow condition. The flow discharge provided to the storage basin is kept at a constant rate of 6 L/sec for all experiments, while the downstream boundary is an outflow boundary condition.

    Also, the required tailwater depth for each experiment is filled to the desired depth. A dye container valve is opened to color the water upstream of the dam to make it easy to distinguish the dam profile from the water profile. A wooden board is placed just upstream of the dam to prevent water from overtopping the dam until the water level rises to a certain level above the dam crest and then the wooden board is removed slowly to start the experiment.

    2.2. Repeatability

    To verify the accuracy of the results, each experiment is repeated two times under the same conditions. Fig. 7 shows the relative eroded crest height, Zeroded / Zo, with time for 5 cm tailwater depth. From the Figure, it can be noticed that results for all runs are consistent, and accuracy is achieved.

    3. Numerical model

    The commercially available numerical model, Flow 3D is used to simulate the dam failure due to overtopping for the cases of 15 cm, 20 cm and 25 cm tailwater depths. For numerical model calibration, experimental results for dam surface evolution are used. The numerical model is calibrated for selection of the optimal turbulence model (RNG, K-e, and k-w) and sediment scour equations (Van Rin, Meyer- peter and Muller, and Nielsen) that produce the best results. In this, the flow field is solved by the RNG turbulence model, and the van Rijn equation is used for the sediment scour model. A geometry file is imported before applying the mesh.

    A Mesh sensitivity is analyzed and checked for various cell sizes, and it is found that decreasing the cell size significantly increases the simulation time with insignificant differences in the result. It is noticed that the most important factor influencing cell size selection is the value of the dam’s upstream and downstream slopes. For example, the slopes in the dam model are 2:1, thus the cell size ratio in X and Z directions should be 2:1 as well. The cell size in a mesh block is set to be 0.02 m, 0.025 m, and 0.01 m in X, Y and Z directions respectively.

    In the numerical computations, the boundary conditions employed are the walls for sidewalls and the channel bottom. The pressure boundary condition is applied at the top, at the air–water interface, to account for atmospheric pressure on the free surface. The upstream boundary is volume flow rate while the downstream boundary is outflow discharge.

    The initial condition is a fluid region, which is used to define fluid areas both upstream and downstream of the dam. To assess the model accuracy, the statistical variable root- mean- square error, RMSE, and the agreement degree index, d, are calculated as(1)RMSE=1N∑i=1N(Pi-Mi)2(2)d=1-∑Mi-Pi2∑Mi-M¯+Pi-P¯2

    where N is the number of samples, Pi and Mi are the models and experimental values, P and M are the means of the model and experimental values. The best fit between the experimental and model results would have an RMSE = 0 and degree of agreement, d = 1.

    4. Results of experimental work

    The results of the total time of failure, t (defined as the time from when the water begins to overtop the dam crest until the erosion reaches a steady state, when no erosion occurs), time of crest width erosion t1, cumulative eroded volume Veroded, and peak discharge Qpeak for each experiment are listed in Table 1. The case of 5 cm tailwater depth is considered as a reference case in this work.

    Table 1. Results of experimental work.

    Tailwater depth, do (cm)Total time of failure, t (sec)Time of crest width erosion, t1 (sec)cumulative eroded volume, Veroded (m3)Peak discharge, Qpeak (liter/sec)
    5255220.2113.12
    15165300.1612.19
    20140340.1311.29
    25110390.0510.84

    5. Discussion

    5.1. Side erosion

    The evolution of the bathymetry of the erosion line recorded by the video camera1. The videos are split into frames (60 frames/sec) by the Free Video to JPG Converter v.5.063 build and then converted into an excel spreadsheet using MATLAB code as shown in Fig. 8.

    Fig. 9 shows a sample of numerical model output. Fig. 10Fig. 11Fig. 12 show a dam profile development for different time steps from both experimental and numerical model, for tailwater depths equal 15 cm, 20 cm and 25 cm. Also, the values of RMSE and d for each figure are presented. The comparison shows that the Flow 3D software can simulate the erosion process of non-cohesive earth dam during overtopping with an RMSE value equals 0.023, 0.0218, and 0.0167 and degree of agreement, d, equals 0.95, 0.968, and 0.988 for relative tailwater depths, do/(do)ref, = 3, 4 and 5, respectively. The low values of RMSE and high values of d show that the Flow 3D can effectively simulate the erosion process. From Fig. 10Fig. 11Fig. 12, it can be noticed that the model is not capable of reproducing the head cut, while it can simulate well the degradation of the crest height with a minor difference from experimental work. The reason of this could be due to inability of simulation of all physical conditions which exists in the experimental work, such as channel friction and the grain size distribution of the dam soil which is surely has a great effect on the erosion process and breach development. In the experimental work the grain size distribution is shown in Fig. 5, while the numerical model considers that the soil is uniform and exactly 50 % of the dam particles diameter are equal to the d50 value. Another reason is that the model is not considering the increased resistance of the dam due to the apparent cohesion which happens due to dam saturation [23].

    It is clear from both the experimental and numerical results that for a 5 cm tailwater depth, do/(do)ref = 1.0, erosion begins near the dam toe and continues upward on the downstream slope until it reaches the crest. After eroding the crest width, the crest is lowered, resulting in increased flow rates and the speeding up of the erosion process. While for relative tailwater depths, do/(do)ref = 3, 4, and 5 erosion starts at the point of intersection between the downstream slope and tailwater. The existence of tailwater works as an energy dissipater for the falling water which reduces the erosion process and prevents the dam from failure as shown in Fig. 13. It is found that the time of the failure decreases with increasing the tailwater depth because most of the dam height is being submerged with water which decreases the erosion process. The reduction in time of failure from the referenced case is found to be 35.3, 45, and 57 % for relative tailwater depth, do /(do)ref equals 3, 4, and 5, respectively.

    The relation between the relative eroded crest height, Zeroded /Zo, with time is drawn as shown in Fig. 14. It is found that the relative eroded crest height decreases with increasing tailwater depth by 10, 41, and 77.6 % for relative tailwater depth, do /(do)ref equals 3, 4, and 5, respectively. The time required for the erosion of the crest width, t1, is calculated for each experiment. The relation between relative tailwater depth and relative time of crest width erosion is shown in Fig. 15. It is found that the time of crest width erosion increases linearly with increasing, do /Zo. The percent of increase is 36.4, 54.5 and 77.3 % for relative tailwater depth, do /(do)ref = 3, 4 and 5, respectively.

    Crest height, Zcrest is calculated from the experimental results and the Flow 3D results for relative tailwater depths, do/(do)ref, = 3, 4, and 5. A relation between relative crest height, Zcrest/Zo with time from experimental and numerical results is presented in Fig. 16. From Fig. 16, it is seen that there is a good consistency between the results of numerical model and the experimental results in the case of tracking the erosion of the crest height with time.

    5.2. Upstream and downstream water depths

    It is noticed that at the beginning of the erosion process, both upstream and downstream water depths increase linearly with time as long as erosion of the crest height did not take place. However, when the crest height starts to lower the upstream water depth decreases with time while the downstream water depth increases. At the end of the experiment, the two depths are nearly equal. A relation between relative downstream and upstream water depths with time is drawn for each experiment as shown in Fig. 17.

    5.3. Eroded volume

    A MATLAB code is used to calculate the cumulative eroded volume every time interval for each experiment. The total volume of the dam, Vtotal is 0.256 m3. The cumulative eroded volume, Veroded is 0.21, 0.16, 0.13, and 0.05 m3 for tailwater depths, do = 5, 15, 20, and 25 cm, respectively. Fig. 18 presents the relation between cumulative eroded volume, Veroded and time. From Fig. 18, it is observed that the cumulative eroded volume decreases with increasing the tailwater depth. The reduction in cumulative eroded volume is 23, 36.5, and 75 % for relative tailwater depth, do /(do)ref = 3, 4, and 5, respectively. The relative remained volume of the dam equals 0.18, 0.375, 0.492, and 0.8 for tailwater depths = 5, 15, 20, and 25 cm, respectively. Fig. 19 shows a relation between relative tailwater depth and relative cumulative eroded volume from experimental results. From that figure, it is noticed that the eroded volume decreases exponentially with increasing relative tailwater depth.

    5.4. The outflow discharge

    The inflow discharge provided to the storage tank is maintained constant for all experiments. The water surface elevation, H, over the sharp-crested weir placed at the downstream side is recorded by the video camera 2. For each experiment, the outflow discharge is then calculated by using the sharp-crested rectangular weir equation every 10 sec.

    The outflow discharge is found to increase rapidly until it reaches its peak then it decreases until it is constant. For high values of tailwater depths, the peak discharge becomes less than that in the case of small tailwater depth as shown in Fig. 20 which agrees well with the results of Rifai et al. [14] The reduction in peak discharge is 7, 14, and 17.35 % for relative tailwater depth, do /(do)ref = 3, 4, and 5, respectively.

    The scenario presented in this article in which the tailwater depth rises due to unexpected heavy rainfall, is investigated to find the effect of rising tailwater depth on earth dam failure. The results revealed that rising tailwater depth positively affects the process of dam failure in terms of preventing the dam from complete failure and reducing the outflow discharge.

    6. Conclusions

    The effect of tailwater depth on earth dam failure due to overtopping is investigated experimentally in this work. The study focuses on the effect of tailwater depth on side erosion, upstream and downstream water depths, eroded volume, outflow hydrograph, and duration of the failure process. The Flow 3D numerical software is used to simulate the dam failure, and a comparison is made between the experimental and numerical results to find the ability of this software to simulate the erosion process. The following are the results of the investigation:

    The existence of tailwater with high depths prevents the dam from completely collapsing thereby turning it into a broad crested weir. The failure time decreases with increasing the tailwater depth and the reduction from the reference case is found to be 35.3, 45, and 57 % for relative tailwater depth, do /(do)ref = 3, 4, and 5, respectively. The difference between the upstream and downstream water depths decreases with time till it became almost negligible at the end of the experiment. The reduction in cumulative eroded volume is 23, 36.5, and 75 % for relative tailwater depth, do /(do)ref = 3, 4, and 5, respectively. The peak discharge decreases by 7, 14, and 17.35 % for relative tailwater depth, do /(do)ref = 3, 4, and 5, respectively. The relative eroded crest height decreases linearly with increasing the tailwater depth by 10, 41, and 77.6 % for relative tailwater depth, do /(do)ref = 3, 4, and 5, respectively. The numerical model can reproduce the erosion process with a minor deviation from the experimental results, particularly in terms of tracking the degradation of the crest height with time.

    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.

    Reference

    [1]

    D. McCullough

    The Johnstown Flood

    Simon and Schuster, NY (1968)

    Google Scholar[2]Rose AT. The influence of dam failures on dam safety laws in Pennsylvania. Association of State Dam Safety Officials Annual Conference 2013, Dam Safety 2013. 2013;1:738–56.

    Google Scholar[3]

    M. Foster, R. Fell, M. Spannagle

    The statistics of embankment dam failures and accidents

    Can Geotech J, 37 (5) (2000), pp. 1000-1024, 10.1139/t00-030 View PDF

    View Record in ScopusGoogle Scholar[4]Pickert, G., Jirka, G., Bieberstein, A., Brauns, J. Soil/water interaction during the breaching process of overtopped embankments. In: Greco, M., Carravetta, A., Morte, R.D. (Eds.), Proceedings of the Conference River-Flow 2004, Balkema.

    Google Scholar[5]

    A. Asghari Tabrizi, E. Elalfy, M. Elkholy, M.H. Chaudhry, J. Imran

    Effects of compaction on embankment breach due to overtopping

    J Hydraul Res, 55 (2) (2017), pp. 236-247, 10.1080/00221686.2016.1238014 View PDF

    View Record in ScopusGoogle Scholar[6]

    R.M. Kansoh, M. Elkholy, G. Abo-Zaid

    Effect of Shape Parameters on Failure of Earthen Embankment due to Overtopping

    KSCE J Civ Eng, 24 (5) (2020), pp. 1476-1485, 10.1007/s12205-020-1107-x View PDF

    View Record in ScopusGoogle Scholar[7]

    YongHui Zhu, P.J. Visser, J.K. Vrijling, GuangQian Wang

    Experimental investigation on breaching of embankments

    Experimental investigation on breaching of embankments, 54 (1) (2011), pp. 148-155 View PDF

    CrossRefView Record in ScopusGoogle Scholar[8]Amaral S, Jónatas R, Bento AM, Palma J, Viseu T, Cardoso R, et al. Failure by overtopping of earth dams. Quantification of the discharge hydrograph. Proceedings of the 3rd IAHR Europe Congress: 14-15 April 2014, Portugal. 2014;(1):182–93.

    Google Scholar[9]

    G. Bereta, P. Hui, H. Kai, L. Guang, P. Kefan, Y.Z. Zhao

    Experimental study of cohesive embankment dam breach formation due to overtopping

    Periodica Polytechnica Civil Engineering, 64 (1) (2020), pp. 198-211, 10.3311/PPci.14565 View PDF

    View Record in ScopusGoogle Scholar[10]

    D.K. Verma, B. Setia, V.K. Arora

    Experimental study of breaching of an earthen dam using a fuse plug model

    Int J Eng Trans A, 30 (4) (2017), pp. 479-485, 10.5829/idosi.ije.2017.30.04a.04 View PDF

    View Record in ScopusGoogle Scholar[11]Wu T, Qin J. Experimental Study of a Tailings Impoundment Dam Failure Due to Overtopping. Mine Water and the Environment [Internet]. 2018;37(2):272–80. Available from: doi: 10.1007/s10230-018-0529-x.

    Google Scholar[12]

    A. Feizi Khankandi, A. Tahershamsi, S. Soares-Frazo

    Experimental investigation of reservoir geometry effect on dam-break flow

    J Hydraul Res, 50 (4) (2012), pp. 376-387 View PDF

    CrossRefView Record in ScopusGoogle Scholar[13]

    A. Ritter

    Die Fortpflanzung der Wasserwellen (The propagation of water waves)

    Zeitschrift Verein Deutscher Ingenieure, 36 (33) (1892), pp. 947-954

    [in German]

    View Record in ScopusGoogle Scholar[14]

    I. Rifai, K. El Kadi Abderrezzak, S. Erpicum, P. Archambeau, D. Violeau, M. Pirotton, et al.

    Floodplain Backwater Effect on Overtopping Induced Fluvial Dike Failure

    Water Resour Res, 54 (11) (2018), pp. 9060-9073 View PDF

    This article is free to access.

    CrossRefView Record in ScopusGoogle Scholar[15]

    X. Jiang

    Laboratory Experiments on Breaching Characteristics of Natural Dams on Sloping Beds

    Advances in Civil Engineering, 2019 (2019), pp. 1-14

    View Record in ScopusGoogle Scholar[16]

    H. Ozmen-Cagatay, S. Kocaman

    Dam-break flows during initial stage using SWE and RANS approaches

    J Hydraul Res, 48 (5) (2010), pp. 603-611 View PDF

    CrossRefView Record in ScopusGoogle Scholar[17]

    S. Evangelista

    Experiments and numerical simulations of dike erosion due to a wave impact

    Water (Switzerland), 7 (10) (2015), pp. 5831-5848 View PDF

    CrossRefView Record in ScopusGoogle Scholar[18]

    C. Di Cristo, S. Evangelista, M. Greco, M. Iervolino, A. Leopardi, A. Vacca

    Dam-break waves over an erodible embankment: experiments and simulations

    J Hydraul Res, 56 (2) (2018), pp. 196-210 View PDF

    CrossRefView Record in ScopusGoogle Scholar[19]Goharnejad H, Sm M, Zn M, Sadeghi L, Abadi K. Numerical Modeling and Evaluation of Embankment Dam Break Phenomenon (Case Study : Taleghan Dam) ISSN : 2319-9873. 2016;5(3):104–11.

    Google Scholar[20]Hu H, Zhang J, Li T. Dam-Break Flows : Comparison between Flow-3D , MIKE 3 FM , and Analytical Solutions with Experimental Data. 2018;1–24. doi: 10.3390/app8122456.

    Google Scholar[21]

    R. Kaurav, P.K. Mohapatra, D. Ph

    Studying the Peak Discharge through a Planar Dam Breach, 145 (6) (2019), pp. 1-8 View PDF

    CrossRef[22]

    Z.M. Yusof, Z.A.L. Shirling, A.K.A. Wahab, Z. Ismail, S. Amerudin

    A hydrodynamic model of an embankment breaching due to overtopping flow using FLOW-3D

    IOP Conference Series: Earth and Environmental Science, 920 (1) (2021)

    Google Scholar[23]

    G. Pickert, V. Weitbrecht, A. Bieberstein

    Breaching of overtopped river embankments controlled by apparent cohesion

    J Hydraul Res, 49 (2) (Apr. 2011), pp. 143-156, 10.1080/00221686.2011.552468 View PDF

    View Record in ScopusGoogle Scholar

    Cited by (0)

    My name is Shaimaa Ibrahim Mohamed Aman and I am a teaching assistant in Irrigation and Hydraulics department, Faculty of Engineering, Alexandria University. I graduated from the Faculty of Engineering, Alexandria University in 2013. I had my MSc in Irrigation and Hydraulic Engineering in 2017. My research interests lie in the area of earth dam Failures.

    Peer review under responsibility of Ain Shams University.

    © 2022 THE AUTHORS. Published by Elsevier BV on behalf of Faculty of Engineering, Ain Shams University.

    Extratropical cyclone damage to the seawall in Dawlish, UK: eyewitness accounts, sea level analysis and numerical modelling

    영국 Dawlish의 방파제에 대한 온대 저기압 피해: 목격자 설명, 해수면 분석 및 수치 모델링

    Extratropical cyclone damage to the seawall in Dawlish, UK: eyewitness accounts, sea level analysis and numerical modelling

    Natural Hazards (2022)Cite this article

    Abstract

    2014년 2월 영국 해협(영국)과 특히 Dawlish에 영향을 미친 온대 저기압 폭풍 사슬은 남서부 지역과 영국의 나머지 지역을 연결하는 주요 철도에 심각한 피해를 입혔습니다.

    이 사건으로 라인이 두 달 동안 폐쇄되어 5천만 파운드의 피해와 12억 파운드의 경제적 손실이 발생했습니다. 이 연구에서는 폭풍의 파괴력을 해독하기 위해 목격자 계정을 수집하고 해수면 데이터를 분석하며 수치 모델링을 수행합니다.

    우리의 분석에 따르면 이벤트의 재난 관리는 성공적이고 효율적이었으며 폭풍 전과 도중에 인명과 재산을 구하기 위해 즉각적인 조치를 취했습니다. 파도 부이 분석에 따르면 주기가 4–8, 8–12 및 20–25초인 복잡한 삼중 봉우리 바다 상태가 존재하는 반면, 조위계 기록에 따르면 최대 0.8m의 상당한 파도와 최대 1.5m의 파도 성분이 나타났습니다.

    이벤트에서 가능한 기여 요인으로 결합된 진폭. 최대 286 KN의 상당한 임펄스 파동이 손상의 시작 원인일 가능성이 가장 높았습니다. 수직 벽의 반사는 파동 진폭의 보강 간섭을 일으켜 파고가 증가하고 최대 16.1m3/s/m(벽의 미터 너비당)의 상당한 오버탑핑을 초래했습니다.

    이 정보와 우리의 공학적 판단을 통해 우리는 이 사고 동안 다중 위험 계단식 실패의 가장 가능성 있는 순서는 다음과 같다고 결론을 내립니다. 조적 파괴로 이어지는 파도 충격력, 충전물 손실 및 연속적인 조수에 따른 구조물 파괴.

    The February 2014 extratropical cyclonic storm chain, which impacted the English Channel (UK) and Dawlish in particular, caused significant damage to the main railway connecting the south-west region to the rest of the UK. The incident caused the line to be closed for two months, £50 million of damage and an estimated £1.2bn of economic loss. In this study, we collate eyewitness accounts, analyse sea level data and conduct numerical modelling in order to decipher the destructive forces of the storm. Our analysis reveals that the disaster management of the event was successful and efficient with immediate actions taken to save lives and property before and during the storm. Wave buoy analysis showed that a complex triple peak sea state with periods at 4–8, 8–12 and 20–25 s was present, while tide gauge records indicated that significant surge of up to 0.8 m and wave components of up to 1.5 m amplitude combined as likely contributing factors in the event. Significant impulsive wave force of up to 286 KN was the most likely initiating cause of the damage. Reflections off the vertical wall caused constructive interference of the wave amplitudes that led to increased wave height and significant overtopping of up to 16.1 m3/s/m (per metre width of wall). With this information and our engineering judgement, we conclude that the most probable sequence of multi-hazard cascading failure during this incident was: wave impact force leading to masonry failure, loss of infill and failure of the structure following successive tides.

    Introduction

    The progress of climate change and increasing sea levels has started to have wide ranging effects on critical engineering infrastructure (Shakou et al. 2019). The meteorological effects of increased atmospheric instability linked to warming seas mean we may be experiencing more frequent extreme storm events and more frequent series or chains of events, as well as an increase in the force of these events, a phenomenon called storminess (Mölter et al. 2016; Feser et al. 2014). Features of more extreme weather events in extratropical latitudes (30°–60°, north and south of the equator) include increased gusting winds, more frequent storm squalls, increased prolonged precipitation and rapid changes in atmospheric pressure and more frequent and significant storm surges (Dacre and Pinto 2020). A recent example of these events impacting the UK with simultaneous significant damage to coastal infrastructure was the extratropical cyclonic storm chain of winter 2013/2014 (Masselink et al. 2016; Adams and Heidarzadeh 2021). The cluster of storms had a profound effect on both coastal and inland infrastructure, bringing widespread flooding events and large insurance claims (RMS 2014).

    The extreme storms of February 2014, which had a catastrophic effect on the seawall of the south Devon stretch of the UK’s south-west mainline, caused a two-month closure of the line and significant disruption to the local and regional economy (Fig. 1b) (Network Rail 2014; Dawson et al. 2016; Adams and Heidarzadeh 2021). Restoration costs were £35 m, and economic effects to the south-west region of England were estimated up to £1.2bn (Peninsula Rail Taskforce 2016). Adams and Heidarzadeh (2021) investigated the disparate cascading failure mechanisms which played a part in the failure of the railway through Dawlish and attempted to put these in the context of the historical records of infrastructure damage on the line. Subsequent severe storms in 2016 in the region have continued to cause damage and disruption to the line in the years since 2014 (Met Office 2016). Following the events of 2014, Network Rail Footnote1 who owns the network has undertaken a resilience study. As a result, it has proposed a £400 m refurbishment of the civil engineering assets that support the railway (Fig. 1) (Network Rail 2014). The new seawall structure (Fig. 1a,c), which is constructed of pre-cast concrete sections, encases the existing Brunel seawall (named after the project lead engineer, Isambard Kingdom Brunel) and has been improved with piled reinforced concrete foundations. It is now over 2 m taller to increase the available crest freeboard and incorporates wave return features to minimise wave overtopping. The project aims to increase both the resilience of the assets to extreme weather events as well as maintain or improve amenity value of the coastline for residents and visitors.

    figure 1
    Fig. 1

    In this work, we return to the Brunel seawall and the damage it sustained during the 2014 storms which affected the assets on the evening of the 4th and daytime of the 5th of February and eventually resulted in a prolonged closure of the line. The motivation for this research is to analyse and model the damage made to the seawall and explain the damage mechanisms in order to improve the resilience of many similar coastal structures in the UK and worldwide. The innovation of this work is the multidisciplinary approach that we take comprising a combination of analysis of eyewitness accounts (social science), sea level and wave data analysis (physical science) as well as numerical modelling and engineering judgement (engineering sciences). We investigate the contemporary wave climate and sea levels by interrogating the real-time tide gauge and wave buoys installed along the south-west coast of the English Channel. We then model a typical masonry seawall (Fig. 2), applying the computational fluid dynamics package FLOW3D-Hydro,Footnote2 to quantify the magnitude of impact forces that the seawall would have experienced leading to its failure. We triangulate this information to determine the probable sequence of failures that led to the disaster in 2014.

    figure 2
    Fig. 2

    Data and methods

    Our data comprise eyewitness accounts, sea level records from coastal tide gauges and offshore wave buoys as well as structural details of the seawall. As for methodology, we analyse eyewitness data, process and investigate sea level records through Fourier transform and conduct numerical simulations using the Flow3D-Hydro package (Flow Science 2022). Details of the data and methodology are provided in the following.

    Eyewitness data

    The scale of damage to the seawall and its effects led the local community to document the first-hand accounts of those most closely affected by the storms including residents, local businesses, emergency responders, politicians and engineering contractors involved in the post-storm restoration work. These records now form a permanent exhibition in the local museum in DawlishFootnote3, and some of these accounts have been transcribed into a DVD account of the disaster (Dawlish Museum 2015). We have gathered data from the Dawlish Museum, national and international news reports, social media tweets and videos. Table 1 provides a summary of the eyewitness accounts. Overall, 26 entries have been collected around the time of the incident. Our analysis of the eyewitness data is provided in the third column of Table 1 and is expanded in Sect. 3.Table 1 Eyewitness accounts of damage to the Dawlish railway due to the February 2014 storm and our interpretations

    Full size table

    Sea level data and wave environment

    Our sea level data are a collection of three tide gauge stations (Newlyn, Devonport and Swanage Pier—Fig. 5a) owned and operated by the UK National Tide and Sea Level FacilityFootnote4 for the Environment Agency and four offshore wave buoys (Dawlish, West Bay, Torbay and Chesil Beach—Fig. 6a). The tide gauge sites are all fitted with POL-EKO (www.pol-eko.com.pl) data loggers. Newlyn has a Munro float gauge with one full tide and one mid-tide pneumatic bubbler system. Devonport has a three-channel data pneumatic bubbler system, and Swanage Pier consists of a pneumatic gauge. Each has a sampling interval of 15 min, except for Swanage Pier which has a sampling interval of 10 min. The tide gauges are located within the port areas, whereas the offshore wave buoys are situated approximately 2—3.3 km from the coast at water depths of 10–15 m. The wave buoys are all Datawell Wavemaker Mk III unitsFootnote5 and come with sampling interval of 0.78 s. The buoys have a maximum saturation amplitude of 20.5 m for recording the incident waves which implies that every wave larger than this threshold will be recorded at 20.5 m. The data are provided by the British Oceanographic Data CentreFootnote6 for tide gauges and the Channel Coastal ObservatoryFootnote7 for wave buoys.

    Sea level analysis

    The sea level data underwent quality control to remove outliers and spikes as well as gaps in data (e.g. Heidarzadeh et al. 2022; Heidarzadeh and Satake 2015). We processed the time series of the sea level data using the Matlab signal processing tool (MathWorks 2018). For calculations of the tidal signals, we applied the tidal package TIDALFIT (Grinsted 2008), which is based on fitting tidal harmonics to the observed sea level data. To calculate the surge signals, we applied a 30-min moving average filter to the de-tided data in order to remove all wind, swell and infra-gravity waves from the time series. Based on the surge analysis and the variations of the surge component before the time period of the incident, an error margin of approximately ± 10 cm is identified for our surge analysis. Spectral analysis of the wave buoy data is performed using the fast Fourier transform (FFT) of Matlab package (Mathworks 2018).

    Numerical modelling

    Numerical modelling of wave-structure interaction is conducted using the computational fluid dynamics package Flow3D-Hydro version 1.1 (Flow Science 2022). Flow3D-Hydro solves the transient Navier–Stokes equations of conservation of mass and momentum using a finite difference method and on Eulerian and Lagrangian frameworks (Flow Science 2022). The aforementioned governing equations are:

    ∇.u=0∇.u=0

    (1)

    ∂u∂t+u.∇u=−∇Pρ+υ∇2u+g∂u∂t+u.∇u=−∇Pρ+υ∇2u+g

    (2)

    where uu is the velocity vector, PP is the pressure, ρρ is the water density, υυ is the kinematic viscosity and gg is the gravitational acceleration. A Fractional Area/Volume Obstacle Representation (FAVOR) is adapted in Flow3D-Hydro, which applies solid boundaries within the Eulerian grid and calculates the fraction of areas and volume in partially blocked volume in order to compute flows on corresponding boundaries (Hirt and Nichols 1981). We validated the numerical modelling through comparing the results with Sainflou’s analytical equation for the design of vertical seawalls (Sainflou 1928; Ackhurst 2020), which is as follows:

    pd=ρgHcoshk(d+z)coshkdcosσtpd=ρgHcoshk(d+z)coshkdcosσt

    (3)

    where pdpd is the hydrodynamic pressure, ρρ is the water density, gg is the gravitational acceleration, HH is the wave height, dd is the water depth, kk is the wavenumber, zz is the difference in still water level and mean water level, σσ is the angular frequency and tt is the time. The Sainflou’s equation (Eq. 3) is used to calculate the dynamic pressure from wave action, which is combined with static pressure on the seawall.

    Using Flow3D-Hydro, a model of the Dawlish seawall was made with a computational domain which is 250.0 m in length, 15.0 m in height and 0.375 m in width (Fig. 3a). The computational domain was discretised using a single uniform grid with a mesh size of 0.125 m. The model has a wave boundary at the left side of the domain (x-min), an outflow boundary on the right side (x-max), a symmetry boundary at the bottom (z-min) and a wall boundary at the top (z-max). A wall boundary implies that water or waves are unable to pass through the boundary, whereas a symmetry boundary means that the two edges of the boundary are identical and therefore there is no flow through it. The water is considered incompressible in our model. For volume of fluid advection for the wave boundary (i.e. the left-side boundary) in our simulations, we utilised the “Split Lagrangian Method”, which guarantees the best accuracy (Flow Science, 2022).

    figure 3
    Fig. 3

    The stability of the numerical scheme is controlled and maintained through checking the Courant number (CC) as given in the following:

    C=VΔtΔxC=VΔtΔx

    (4)

    where VV is the velocity of the flow, ΔtΔt is the time step and ΔxΔx is the spatial step (i.e. grid size). For stability and convergence of the numerical simulations, the Courant number must be sufficiently below one (Courant et al. 1928). This is maintained by a careful adjustment of the ΔxΔx and ΔtΔt selections. Flow3D-Hydro applies a dynamic Courant number, meaning the program adjusts the value of time step (ΔtΔt) during the simulations to achieve a balance between accuracy of results and speed of simulation. In our simulation, the time step was in the range ΔtΔt = 0.0051—0.051 s.

    In order to achieve the most efficient mesh resolution, we varied cell size for five values of ΔxΔx = 0.1 m, 0.125 m, 0.15 m, 0.175 m and 0.20 m. Simulations were performed for all mesh sizes, and the results were compared in terms of convergence, stability and speed of simulation (Fig. 3). A linear wave with an amplitude of 1.5 m and a period of 6 s was used for these optimisation simulations. We considered wave time histories at two gauges A and B and recorded the waves from simulations using different mesh sizes (Fig. 3). Although the results are close (Fig. 3), some limited deviations are observed for larger mesh sizes of 0.20 m and 0.175 m. We therefore selected mesh size of 0.125 m as the optimum, giving an extra safety margin as a conservative solution.

    The pressure from the incident waves on the vertical wall is validated in our model by comparing them with the analytical equation of Sainflou (1928), Eq. (3), which is one of the most common set of equations for design of coastal structures (Fig. 4). The model was tested by running a linear wave of period 6 s and wave amplitude of 1.5 m against the wall, with a still water level of 4.5 m. It can be seen that the model results are very close to those from analytical equations of Sainflou (1928), indicating that our numerical model is accurately modelling the wave-structure interaction (Fig. 4).

    figure 4
    Fig. 4

    Eyewitness account analysis

    Contemporary reporting of the 4th and 5th February 2014 storms by the main national news outlets in the UK highlights the extreme nature of the events and the significant damage and disruption they were likely to have on the communities of the south-west of England. In interviews, this was reinforced by Network Rail engineers who, even at this early stage, were forecasting remedial engineering works to last for at least 6 weeks. One week later, following subsequent storms the cascading nature of the events was obvious. Multiple breaches of the seawall had taken place with up to 35 separate landslide events and significant damage to parapet walls along the coastal route also were reported. Residents of the area reported extreme effects of the storm, one likening it to an earthquake and reporting water ingress through doors windows and even through vertical chimneys (Table 1). This suggests extreme wave overtopping volumes and large wave impact forces. One resident described the structural effects as: “the house was jumping up and down on its footings”.

    Disaster management plans were quickly and effectively put into action by the local council, police service and National Rail. A major incident was declared, and decisions regarding evacuation of the residents under threat were taken around 2100 h on the night of 4th February when reports of initial damage to the seawall were received (Table 1). Local hotels were asked to provide short-term refuge to residents while local leisure facilities were prepared to accept residents later that evening. Initial repair work to the railway line was hampered by successive high spring tides and storms in the following days although significant progress was still made when weather conditions permitted (Table 1).

    Sea level observations and spectral analysis

    The results of surge and wave analyses are presented in Figs. 5 and 6. A surge height of up to 0.8 m was recorded in the examined tide gauge stations (Fig. 5b-d). Two main episodes of high surge heights are identified: the first surge started on 3rd February 2014 at 03:00 (UTC) and lasted until 4th of February 2014 at 00:00; the second event occurred in the period 4th February 2014 15:00 to 5th February 2014 at 17:00 (Fig. 5b-d). These data imply surge durations of 21 h and 26 h for the first and the second events, respectively. Based on the surge data in Fig. 5, we note that the storm event of early February 2014 and the associated surges was a relatively powerful one, which impacted at least 230 km of the south coast of England, from Land’s End to Weymouth, with large surge heights.

    figure 5
    Fig. 5
    figure 6
    Fig. 6

    Based on wave buoy records, the maximum recorded amplitudes are at least 20.5 m in Dawlish and West Bay, 1.9 m in Tor Bay and 4.9 m in Chesil (Fig. 6a-b). The buoys at Tor Bay and Chesil recorded dual peak period bands of 4–8 and 8–12 s, whereas at Dawlish and West Bay registered triple peak period bands at 4–8, 8–12 and 20–25 s (Fig. 6c, d). It is important to note that the long-period waves at 20–25 s occur with short durations (approximately 2 min) while the waves at the other two bands of 4–8 and 8–12 s appear to be present at all times during the storm event.

    The wave component at the period band of 4–8 s can be most likely attributed to normal coastal waves while the one at 8–12 s, which is longer, is most likely the swell component of the storm. Regarding the third component of the waves with long period of 20 -25 s, which occurs with short durations of 2 min, there are two hypotheses; it is either the result of a local (port and harbour) and regional (the Lyme Bay) oscillations (eg. Rabinovich 1997; Heidarzadeh and Satake 2014; Wang et al. 1992), or due to an abnormally long swell. To test the first hypothesis, we consider various water bodies such as Lyme Bay (approximate dimensions of 70 km × 20 km with an average water depth of 30 m; Fig. 6), several local bays (approximate dimensions of 3.6 km × 0.6 km with an average water depth of 6 m) and harbours (approximate dimensions of 0.5 km × 0.5 km with an average water depth of 4 m). Their water depths are based on the online Marine navigation website.Footnote8 According to Rabinovich (2010), the oscillation modes of a semi-enclosed rectangle basin are given by the following equation:

    Tmn=2gd−−√[(m2L)2+(nW)2]−1/2Tmn=2gd[(m2L)2+(nW)2]−1/2

    (5)

    where TmnTmn is the oscillation period, gg is the gravitational acceleration, dd is the water depth, LL is the length of the basin, WW is the width of the basin, m=1,2,3,…m=1,2,3,… and n=0,1,2,3,…n=0,1,2,3,…; mm and nn are the counters of the different modes. Applying Eq. (5) to the aforementioned water bodies results in oscillation modes of at least 5 min, which is far longer than the observed period of 20–25 s. Therefore, we rule out the first hypothesis and infer that the long period of 20–25 s is most likely a long swell wave coming from distant sources. As discussed by Rabinovich (1997) and Wang et al. (2022), comparison between sea level spectra before and after the incident is a useful method to distinguish the spectrum of the weather event. A visual inspection of Fig. 6 reveals that the forcing at the period band of 20–25 s is non-existent before the incident.

    Numerical simulations of wave loading and overtopping

    Based on the results of sea level data analyses in the previous section (Fig. 6), we use a dual peak wave spectrum with peak periods of 10.0 s and 25.0 s for numerical simulations because such a wave would be comprised of the most energetic signals of the storm. For variations of water depth (2.0–4.0 m), coastal wave amplitude (0.5–1.5 m) (Fig. 7) and storm surge height (0.5–0.8 m) (Fig. 5), we developed 20 scenarios (Scn) which we used in numerical simulations (Table 2). Data during the incident indicated that water depth was up to the crest level of the seawall (approximately 4 m water depth); therefore, we varied water depth from 2 to 4 m in our simulation scenarios. Regarding wave amplitudes, we referred to the variations at a nearby tide gauge station (West Bay) which showed wave amplitude up to 1.2 m (Fig. 7). Therefore, wave amplitude was varied from 0.5 m to 1.5 m by considering a factor a safety of 25% for the maximum wave amplitude. As for the storm surge component, time series of storm surges calculated at three coastal stations adjacent to Dawlish showed that it was in the range of 0.5 m to 0.8 m (Fig. 5). These 20 scenarios would help to study uncertainties associated with wave amplitudes and pressures. Figure 8 shows snapshots of wave propagation and impacts on the seawall at different times.

    figure 7
    Fig. 7

    Table 2 The 20 scenarios considered for numerical simulations in this study

    Full size table

    figure 8
    Fig. 8

    Results of wave amplitude simulations

    Large wave amplitudes can induce significant wave forcing on the structure and cause overtopping of the seawall, which could eventually cascade to other hazards such as erosion of the backfill and scour (Adams and Heidarzadeh, 2021). The first 10 scenarios of our modelling efforts are for the same incident wave amplitudes of 0.5 m, which occur at different water depths (2.0–4.0 m) and storm surge heights (0.5–0.8 m) (Table 2 and Fig. 9). This is because we aim at studying the impacts of effective water depth (deff—the sum of mean sea level and surge height) on the time histories of wave amplitudes as the storm evolves. As seen in Fig. 9a, by decreasing effective water depth, wave amplitude increases. For example, for Scn-1 with effective depth of 4.5 m, the maximum amplitude of the first wave is 1.6 m, whereas it is 2.9 m for Scn-2 with effective depth of 3.5 m. However, due to intensive reflections and interferences of the waves in front of the vertical seawall, such a relationship is barely seen for the second and the third wave peaks. It is important to note that the later peaks (second or third) produce the largest waves rather than the first wave. Extraordinary wave amplifications are seen for the Scn-2 (deff = 3.5 m) and Scn-7 (deff = 3.3 m), where the corresponding wave amplitudes are 4.5 m and 3.7 m, respectively. This may indicate that the effective water depth of deff = 3.3–3.5 m is possibly a critical water depth for this structure resulting in maximum wave amplitudes under similar storms. In the second wave impact, the combined wave height (i.e. the wave amplitude plus the effective water depth), which is ultimately an indicator of wave overtopping, shows that the largest wave heights are generated by Scn-2, 7 and 8 (Fig. 9a) with effective water depths of 3.5 m, 3.3 m and 3.8 m and combined heights of 8.0 m, 7.0 m and 6.9 m (Fig. 9b). Since the height of seawall is 5.4 m, the combined wave heights for Scn-2, 7 and 8 are greater than the crest height of the seawall by 2.6 m, 1.6 m and 1.5 m, respectively, which indicates wave overtopping.

    figure 9
    Fig. 9

    For scenarios 11–20 (Fig. 10), with incident wave amplitudes of 1.5 m (Table 2), the largest wave amplitudes are produced by Scn-17 (deff = 3.3 m), Scn-13 (deff = 2.5 m) and Scn-12 (deff = 3.5 m), which are 5.6 m, 5.1 m and 4.5 m. The maximum combined wave heights belong to Scn-11 (deff = 4.5 m) and Scn-17 (deff = 3.3 m), with combined wave heights of 9.0 m and 8.9 m (Fig. 10b), which are greater than the crest height of the seawall by 4.6 m and 3.5 m, respectively.

    figure 10
    Fig. 10

    Our simulations for all 20 scenarios reveal that the first wave is not always the largest and wave interactions, reflections and interferences play major roles in amplifying the waves in front of the seawall. This is primarily because the wall is fully vertical and therefore has a reflection coefficient of close to one (i.e. full reflection). Simulations show that the combined wave height is up to 4.6 m higher than the crest height of the wall, implying that severe overtopping would be expected.

    Results of wave loading calculations

    The pressure calculations for scenarios 1–10 are given in Fig. 11 and those of scenarios 11–20 in Fig. 12. The total pressure distribution in Figs. 1112 mostly follows a triangular shape with maximum pressure at the seafloor as expected from the Sainflou (1928) design equations. These pressure plots comprise both static (due to mean sea level in front of the wall) and dynamic (combined effects of surge and wave) pressures. For incident wave amplitudes of 0.5 m (Fig. 11), the maximum wave pressure varies in the range of 35–63 kPa. At the sea surface, it is in the range of 4–20 kPa (Fig. 11). For some scenarios (Scn-2 and 7), the pressure distribution deviates from a triangular shape and shows larger pressures at the top, which is attributed to the wave impacts and partial breaking at the sea surface. This adds an additional triangle-shaped pressure distribution at the sea surface elevation consistent with the design procedure developed by Goda (2000) for braking waves. The maximum force on the seawall due to scenarios 1–10, which is calculated by integrating the maximum pressure distribution over the wave-facing surface of the seawall, is in the range of 92–190 KN (Table 2).

    figure 11
    Fig. 11
    figure 12
    Fig. 12

    For scenarios 11–20, with incident wave amplitude of 1.5 m, wave pressures of 45–78 kPa and 7–120 kPa, for  the bottom and top of the wall, respectively, were observed (Fig. 12). Most of the plots show a triangular pressure distribution, except for Scn-11 and 15. A significant increase in wave impact pressure is seen for Scn-15 at the top of the structure, where a maximum pressure of approximately 120 kPa is produced while other scenarios give a pressure of 7–32 kPa for the sea surface. In other words, the pressure from Scn-15 is approximately four times larger than the other scenarios. Such a significant increase of the pressure at the top is most likely attributed to the breaking wave impact loads as detailed by Goda (2000) and Cuomo et al. (2010). The wave simulation snapshots in Fig. 8 show that the wave breaks before reaching the wall. The maximum force due to scenarios 11–20 is 120–286 KN.

    The breaking wave impacts peaking at 286 KN in our simulations suggest destabilisation of the upper masonry blocks, probably by grout malfunction. This significant impact force initiated the failure of the seawall which in turn caused extensive ballast erosion. Wave impact damage was proposed by Adams and Heidarzadeh (2021) as one of the primary mechanisms in the 2014 Dawlish disaster. In the multi-hazard risk model proposed by these authors, damage mechanism III (failure pathway 5 in Adams and Heidarzadeh, 2021) was characterised by wave impact force causing damage to the masonry elements, leading to failure of the upper sections of the seawall and loss of infill material. As blocks were removed, access to the track bed was increased for inbound waves allowing infill material from behind the seawall to be fluidised and subsequently removed by backwash. The loss of infill material critically compromised the stability of the seawall and directly led to structural failure. In parallel, significant wave overtopping (discussed in the next section) led to ballast washout and cascaded, in combination with masonry damage, to catastrophic failure of the wall and suspension of the rails in mid-air (Fig. 1b), leaving the railway inoperable for two months.

    Wave Overtopping

    The two most important factors contributing to the 2014 Dawlish railway catastrophe were wave impact forces and overtopping. Figure 13 gives the instantaneous overtopping rates for different scenarios, which experienced overtopping. It can be seen that the overtopping rates range from 0.5 m3/s/m to 16.1 m3/s/m (Fig. 13). Time histories of the wave overtopping rates show that the phenomenon occurs intermittently, and each time lasts 1.0–7.0 s. It is clear that the longer the overtopping time, the larger the volume of the water poured on the structure. The largest wave overtopping rates of 16.1 m3/s/m and 14.4 m3/s/m belong to Scn-20 and 11, respectively. These are the two scenarios that also give the largest combined wave heights (Fig. 10b).

    figure 13
    Fig. 13

    The cumulative overtopping curves (Figs. 1415) show the total water volume overtopped the structure during the entire simulation time. This is an important hazard factor as it determines the level of soil saturation, water pore pressure in the soil and soil erosion (Van der Meer et al. 2018). The maximum volume belongs to Scn-20, which is 65.0 m3/m (m-cubed of water per metre length of the wall). The overtopping volumes are 42.7 m3/m for Scn-11 and 28.8 m3/m for Scn-19. The overtopping volume is in the range of 0.7–65.0 m3/m for all scenarios.

    figure 14
    Fig. 14
    figure 15
    Fig. 15

    For comparison, we compare our modelling results with those estimated using empirical equations. For the case of the Dawlish seawall, we apply the equation proposed by Van Der Meer et al. (2018) to estimate wave overtopping rates, based on a set of decision criteria which are the influence of foreshore, vertical wall, possible breaking waves and low freeboard:

    qgH3m−−−−√=0.0155(Hmhs)12e(−2.2RcHm)qgHm3=0.0155(Hmhs)12e(−2.2RcHm)

    (6)

    where qq is the mean overtopping rate per metre length of the seawall (m3/s/m), gg is the acceleration due to gravity, HmHm is the incident wave height at the toe of the structure, RcRc is the wall crest height above mean sea level, hshs is the deep-water significant wave height and e(x)e(x) is the exponential function. It is noted that Eq. (6) is valid for 0.1<RcHm<1.350.1<RcHm<1.35. For the case of the Dawlish seawall and considering the scenarios with larger incident wave amplitude of 1.5 m (hshs= 1.5 m), the incident wave height at the toe of the structure is HmHm = 2.2—5.6 m, and the wall crest height above mean sea level is RcRc = 0.6–2.9 m. As a result, Eq. (6) gives mean overtopping rates up to approximately 2.9 m3/s/m. A visual inspection of simulated overtopping rates in Fig. 13 for Scn 11–20 shows that the mean value of the simulated overtopping rates (Fig. 13) is close to estimates using Eq. (6).

    Discussion and conclusions

    We applied a combination of eyewitness account analysis, sea level data analysis and numerical modelling in combination with our engineering judgement to explain the damage to the Dawlish railway seawall in February 2014. Main findings are:

    • Eyewitness data analysis showed that the extreme nature of the event was well forecasted in the hours prior to the storm impact; however, the magnitude of the risks to the structures was not well understood. Multiple hazards were activated simultaneously, and the effects cascaded to amplify the damage. Disaster management was effective, exemplified by the establishment of an emergency rendezvous point and temporary evacuation centre during the storm, indicating a high level of hazard awareness and preparedness.
    • Based on sea level data analysis, we identified triple peak period bands at 4–8, 8–12 and 20–25 s in the sea level data. Storm surge heights and wave oscillations were up to 0.8 m and 1.5 m, respectively.
    • Based on the numerical simulations of 20 scenarios with different water depths, incident wave amplitudes, surge heights and peak periods, we found that the wave oscillations at the foot of the seawall result in multiple wave interactions and interferences. Consequently, large wave amplitudes, up to 4.6 m higher than the height of the seawall, were generated and overtopped the wall. Extreme impulsive wave impact forces of up to 286 KN were generated by the waves interacting with the seawall.
    • We measured maximum wave overtopping rates of 0.5–16.1 m3/s/m for our scenarios. The cumulative overtopping water volumes per metre length of the wall were 0.7–65.0 m3/m.
    • Analysis of all the evidence combined with our engineering judgement suggests that the most likely initiating cause of the failure was impulsive wave impact forces destabilising one or more grouted joints between adjacent masonry blocks in the wall. Maximum observed pressures of 286 KN in our simulations are four times greater in magnitude than background pressures leading to block removal and initiating failure. Therefore, the sequence of cascading events was :1) impulsive wave impact force causing damage to masonry, 2) failure of the upper sections of the seawall, 3) loss of infill resulting in a reduction of structural strength in the landward direction, 4) ballast washout as wave overtopping and inbound wave activity increased and 5) progressive structural failure following successive tides.

    From a risk mitigation point of view, the stability of the seawall in the face of future energetic cyclonic storm events and sea level rise will become a critical factor in protecting the rail network. Mitigation efforts will involve significant infrastructure investment to strengthen the civil engineering assets combined with improved hazard warning systems consisting of meteorological forecasting and real-time wave observations and instrumentation. These efforts must take into account the amenity value of coastal railway infrastructure to local communities and the significant number of tourists who visit every year. In this regard, public awareness and active engagement in the planning and execution of the project will be crucial in order to secure local stakeholder support for the significant infrastructure project that will be required for future resilience.

    Notes

    1. https://www.networkrail.co.uk/..
    2. https://www.flow3d.com/products/flow-3d-hydro/.
    3. https://www.devonmuseums.net/Dawlish-Museum/Devon-Museums/.
    4. https://ntslf.org/.
    5. https://www.datawell.nl/Products/Buoys/DirectionalWaveriderMkIII.aspx.
    6. https://www.bodc.ac.uk/.
    7. https://coastalmonitoring.org/cco/.
    8. https://webapp.navionics.com/#boating@8&key=iactHlwfP.

    References

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    Acknowledgements

    We are grateful to Brunel University London for administering the scholarship awarded to KA. The Flow3D-Hydro used in this research for numerical modelling is licenced to Brunel University London through an academic programme contract. We sincerely thank Prof Harsh Gupta (Editor-in-Chief) and two anonymous reviewers for their constructive review comments.

    Funding

    This project was funded by the UK Engineering and Physical Sciences Research Council (EPSRC) through a PhD scholarship to Keith Adams.

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    Authors and Affiliations

    1. Department of Civil and Environmental Engineering, Brunel University London, Uxbridge, UB8 3PH, UKKeith Adams
    2. Department of Architecture and Civil Engineering, University of Bath, Bath, BA2 7AY, UKMohammad Heidarzadeh

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    Correspondence to Keith Adams.

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    Adams, K., Heidarzadeh, M. Extratropical cyclone damage to the seawall in Dawlish, UK: eyewitness accounts, sea level analysis and numerical modelling. Nat Hazards (2022). https://doi.org/10.1007/s11069-022-05692-2

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    • Received17 May 2022
    • Accepted17 October 2022
    • Published14 November 2022
    • DOIhttps://doi.org/10.1007/s11069-022-05692-2

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    Keywords

    • Storm surge
    • Cyclone
    • Railway
    • Climate change
    • Infrastructure
    • Resilience
    Fig. 1. Schematic of lap welding for 6061/5182 aluminum alloys.

    알루미늄 합금 겹침 용접 중 용접 형성, 용융 흐름 및 입자 구조에 대한 사인파 발진 레이저 빔의 영향

    린 첸 가오 양 미시 옹 장 춘밍 왕
    Lin Chen , Gaoyang Mi , Xiong Zhang , Chunming Wang *
    중국 우한시 화중과학기술대학 재료공학부, 430074

    Effects of sinusoidal oscillating laser beam on weld formation, melt flow and grain structure during aluminum alloys lap welding

    Abstract

    A numerical model of 1.5 mm 6061/5182 aluminum alloys thin sheets lap joints under laser sinusoidal oscillation (sine) welding and laser welding (SLW) weld was developed to simulate temperature distribution and melt flow. Unlike the common energy distribution of SLW, the sinusoidal oscillation of laser beam greatly homogenized the energy distribution and reduced the energy peak. The energy peaks were located at both sides of the sine weld, resulting in the tooth-shaped sectional formation. This paper illustrated the effect of the temperature gradient (G) and solidification rate (R) on the solidification microstructure by simulation. Results indicated that the center of the sine weld had a wider area with low G/R, promoting the formation of a wider equiaxed grain zone, and the columnar grains were slenderer because of greater GR. The porosity-free and non-penetration welds were obtained by the laser sinusoidal oscillation. The reasons were that the molten pool volume was enlarged, the volume proportion of keyhole was reduced and the turbulence in the molten pool was gentled, which was observed by the high-speed imaging and simulation results of melt flow. The tensile test of both welds showed a tensile fracture form along the fusion line, and the tensile strength of sine weld was significantly better than that of the SLW weld. This was because that the wider equiaxed grain area reduced the tendency of cracks and the finer grain size close to the fracture location. Defect-free and excellent welds are of great significance to the new energy vehicles industry.

    온도 분포 및 용융 흐름을 시뮬레이션하기 위해 레이저 사인파 진동 (사인) 용접 및 레이저 용접 (SLW) 용접에서 1.5mm 6061/5182 알루미늄 합금 박판 랩 조인트 의 수치 모델이 개발되었습니다. SLW의 일반적인 에너지 분포와 달리 레이저 빔의 사인파 진동은 에너지 분포를 크게 균질화하고 에너지 피크를 줄였습니다. 에너지 피크는 사인 용접의 양쪽에 위치하여 톱니 모양의 단면이 형성되었습니다. 이 논문은 온도 구배(G)와 응고 속도 의 영향을 설명했습니다.(R) 시뮬레이션에 의한 응고 미세 구조. 결과는 사인 용접의 중심이 낮은 G/R로 더 넓은 영역을 가짐으로써 더 넓은 등축 결정립 영역의 형성을 촉진하고 더 큰 GR로 인해 주상 결정립 이 더 가늘다는 것을 나타냅니다. 다공성 및 비관통 용접은 레이저 사인파 진동에 의해 얻어졌습니다. 그 이유는 용융 풀의 부피가 확대되고 열쇠 구멍의 부피 비율이 감소하며 용융 풀의 난류가 완만해졌기 때문이며, 이는 용융 흐름의 고속 이미징 및 시뮬레이션 결과에서 관찰되었습니다. 두 용접부 의 인장시험 은 융착선을 따라 인장파괴형태를인장강도사인 용접의 경우 SLW 용접보다 훨씬 우수했습니다. 이는 등축 결정립 영역이 넓을수록 균열 경향이 감소하고 파단 위치에 근접한 입자 크기가 미세 하기 때문입니다. 결함이 없고 우수한 용접은 신에너지 자동차 산업에 매우 중요합니다.

    Fig. 1. Schematic of lap welding for 6061/5182 aluminum alloys.
    Fig. 1. Schematic of lap welding for 6061/5182 aluminum alloys.
    Fig. 2. Finite element mesh.
    Fig. 2. Finite element mesh.
    Fig. 3. Weld morphologies of cross-section and upper surface for the two welds: (a) sine pattern weld; (b) SLW weld.
    Fig. 3. Weld morphologies of cross-section and upper surface for the two welds: (a) sine pattern weld; (b) SLW weld.
    Fig. 4. Calculation of laser energy distribution: (a)-(c) sine pattern weld; (d)-(f) SLW weld.
    Fig. 4. Calculation of laser energy distribution: (a)-(c) sine pattern weld; (d)-(f) SLW weld.
    Fig. 5. The partially melted region of zone A.
    Fig. 5. The partially melted region of zone A.
    Fig. 6. The simulated profiles of melted region for the two welds: (a) SLW weld; (b) sine pattern weld.
    Fig. 6. The simulated profiles of melted region for the two welds: (a) SLW weld; (b) sine pattern weld.
    Fig. 7. The temperature field simulation results of cross section for sine pattern weld.
    Fig. 7. The temperature field simulation results of cross section for sine pattern weld.
    Fig. 8. Dynamic behavior of the molten pool at the same time interval of 0.004 s within one oscillating period: (a) SLW weld; (b) sine pattern weld.
    Fig. 8. Dynamic behavior of the molten pool at the same time interval of 0.004 s within one oscillating period: (a) SLW weld; (b) sine pattern weld.
    Fig. 9. The temperature field and flow field of the molten pool for the SLW weld: (a)~(f) t = 80 ms~100 ms.
    Fig. 9. The temperature field and flow field of the molten pool for the SLW weld: (a)~(f) t = 80 ms~100 ms.
    Fig. 10. The temperature field and flow field of the molten pool for the sine pattern weld: (a)~(f) t = 151 ms~171 ms.
    Fig. 10. The temperature field and flow field of the molten pool for the sine pattern weld: (a)~(f) t = 151 ms~171 ms.
    Fig. 11. The evolution of the molten pool volume and keyhole depth within one period.
    Fig. 11. The evolution of the molten pool volume and keyhole depth within one period.
    Fig. 12. The X-ray inspection results for the two welds: (a) SLW weld, (b) sine pattern weld.
    Fig. 12. The X-ray inspection results for the two welds: (a) SLW weld, (b) sine pattern weld.
    Fig. 13. Comparison of the solidification parameters for sine and SLW patterns: (a) the temperature field simulated results of the molten pool upper surfaces; (b) temperature gradient G and solidification rate R along the molten pool boundary isotherm from weld centerline to the fusion boundary; (c) G/R; (d) GR.
    Fig. 13. Comparison of the solidification parameters for sine and SLW patterns: (a) the temperature field simulated results of the molten pool upper surfaces; (b) temperature gradient G and solidification rate R along the molten pool boundary isotherm from weld centerline to the fusion boundary; (c) G/R; (d) GR.
    Fig. 14. The EBSD results of equiaxed grain zone in the weld center of: (a) sine pattern weld; (b) SLW weld; (c) grain size.
    Fig. 14. The EBSD results of equiaxed grain zone in the weld center of: (a) sine pattern weld; (b) SLW weld; (c) grain size.
    Fig. 15. (a) EBSD results of horizontal sections of SLW weld and sine pattern weld; (b) The columnar crystal widths of SLW weld and sine pattern weld.
    Fig. 15. (a) EBSD results of horizontal sections of SLW weld and sine pattern weld; (b) The columnar crystal widths of SLW weld and sine pattern weld.
    Fig. 16. (a) The tensile test results of the two welds; (b) Fracture location of SLW weld; (b) Fracture location of sine pattern weld.
    Fig. 16. (a) The tensile test results of the two welds; (b) Fracture location of SLW weld; (b) Fracture location of sine pattern weld.

    Keywords

    Laser welding, Sinusoidal oscillating, Energy distribution, Numerical simulation, Molten pool flow, Grain structure

    References

    Chen, X., 2014. Study on laser-MAG Hybrid Weaving Welding Charateristics. Master
    thesis. Harbin Institute of Technology, China.
    Chen, G., Wang, B., Mao, S., Zhong, P., He, J., 2019. Research on the “∞”-shaped laser
    scanning welding process for aluminum alloy. Opt. Laser Technol. 115, 32–41.
    Cho, W.-I., Na, S.-J., Cho, M.-H., Lee, J.-S., 2010. Numerical study of alloying element
    distribution in CO2 laser–GMA hybrid welding. Comput. Mater. Sci. 49, 792–800.
    Cho, W.-I., Na, S.-J., Thomy, C., Vollertsen, F., 2012. Numerical simulation of molten
    pool dynamics in high power disk laser welding. J. Mater. Process. Technol. 212,
    262–275.
    Das, A., Butterworth, I., Masters, I., Williams, D., 2018. Microstructure and mechanical
    properties of gap-bridged remote laser welded (RLW) automotive grade AA 5182
    joints. Mater. Charact. 145, 697–712.
    Fetzer, F., Sommer, M., Weber, R., Weberpals, J.-P., Graf, T., 2018. Reduction of pores by
    means of laser beam oscillation during remote welding of AlMgSi. Opt. Lasers Eng.
    108, 68–77.
    Geng, S., Jiang, P., Shao, X., Guo, L., Gao, X., 2020. Heat transfer and fluid flow and their
    effects on the solidification microstructure in full-penetration laser welding of
    aluminum sheet. J. Mater. Sci. Technol. 46, 50–63.
    Hagenlocher, C., Sommer, M., Fetzer, F., Weber, R., Graf, T., 2018a. Optimization of the
    solidification conditions by means of beam oscillation during laser beam welding of
    aluminum. Mater. Des. 160, 1178–1185.
    Hagenlocher, C., Weller, D., Weber, R., Graf, T., 2018b. Reduction of the hot cracking
    susceptibility of laser beam welds in AlMgSi alloys by increasing the number of grain
    boundaries. Sci. Technol. Weld. Join. 24, 313–319.
    Hagenlocher, C., Fetzer, F., Weller, D., Weber, R., Graf, T., 2019. Explicit analytical
    expressions for the influence of welding parameters on the grain structure of laser
    beam welds in aluminium alloys. Mater. Des. 174, 107791.
    Han, X., Tang, X., Wang, T., Shao, C., Lu, F., Cui, H., 2018. Role of ambient pressure in
    keyhole dynamics based on beam transmission path method for laser welding on Al
    alloy. Int. J. Adv. Manuf. Technol. 99, 1639–1651.
    Hao, K., Li, G., Gao, M., Zeng, X., 2015. Weld formation mechanism of fiber laser
    oscillating welding of austenitic stainless steel. J. Mater. Process. Technol. 225,
    77–83.
    Hirt, C.W., Nichols, B.D., 1981. Volume of fluid (VOF) method for the dynamics of free
    boundaries. J. Comput. Phys. 39, 201–225.
    Jiang, Z., Chen, X., Li, H., Lei, Z., Chen, Y., Wu, S., Wang, Y., 2020. Grain refinement and
    laser energy distribution during laser oscillating welding of Invar alloy. Mater. Des.
    186, 108195.
    Kaplan, A., 1994. A model of deep penetration laser welding based on calculation of the
    keyhole profile. J. Phys. D Appl. Phys. 27, 1805–1814.
    Kou, S., 2002. Welding Metallurgy, 2nd ed. Wiley-Interscience, New Jersey, USA.
    Kuryntsev, S.V., Gilmutdinov, A.K., 2015. The effect of laser beam wobbling mode in
    welding process for structural steels. Int. J. Adv. Manuf. Technol. 81, 1683–1691.
    Li, P., Nie, F., Dong, H., Li, S., Yang, G., Zhang, H., 2018. Pulse MIG welding of 6061-T6/
    A356-T6 aluminum alloy dissimilar T-joint. J. Mater. Eng. Perform. 27, 4760–4769.
    Liu, T., Mu, Z., Hu, R., Pang, S., 2019. Sinusoidal oscillating laser welding of 7075
    aluminum alloy: hydrodynamics, porosity formation and optimization. Int. J. Heat
    Mass Transf. 140, 346–358.
    Seto, N., Katayama, S., Matsunawa, A., 2000. High-speed simultaneous observation of
    plasma and keyhole behavior during high power CO2 laser welding: effect of
    shielding gas on porosity formation. J. Laser Appl. 12, 245–250.
    Tang, Z., Vollertsen, F., 2014. Influence of grain refinement on hot cracking in laser
    welding of aluminum. Weld. World 58, 355–366.
    Wang, L., Gao, M., Zhang, C., Zeng, X., 2016. Effect of beam oscillating pattern on weld
    characterization of laser welding of AA6061-T6 aluminum alloy. Mater. Des. 108,
    707–717.
    Wang, L., Gao, M., Zeng, X., 2018. Experiment and prediction of weld morphology for
    laser oscillating welding of AA6061 aluminium alloy. Sci. Technol. Weld. Join. 24,
    334–341.
    Yamazaki, Y., Abe, Y., Hioki, Y., Nakatani, M., Kitagawa, A., Nakata, K., 2016.
    Fundamental study of narrow-gap welding with oscillation laser beam. Weld. Int. 30,
    699–707.
    Yuan, Z., Tu, Y., Yuan, T., Zhang, Y., Huang, Y., 2021. Size effects on mechanical
    properties of pure industrial aluminum sheet for micro/meso scale plastic
    deformation: experiment and modeling. J. Alloys. Compd. 859, 157752.
    Zou, J., 2016. Characteristics of laser scanning welding process for 5A06 aluminum alloy
    thick plate with narrow gap. Materials Processing Engineering. Harbin Welding
    Institute, China. Master thesis.

    Fig. 8. Variation of water surface profile (a) α = 0.1; (b) α = 0.3; (c) α = 0.5; (d) α = 0.7.

    Numerical study of the dam-break waves and Favre waves down sloped wet rigid-bed at laboratory scale

    WenjunLiuaBoWangaYakunGuobaState Key Laboratory of Hydraulics and Mountain River Engineering, College of Water Resource and Hydropower, Sichuan University, Chengdu 610065, ChinabFaculty of Engineering & Informatics, University of Bradford, BD7 1DP, UK

    Highlights

    경사진 습윤층에서 댐파괴유동과 FFavre 파를 수치적으로 조사하였다.
    수직 대 수평 속도의 비율이 먼저 정량화됩니다.
    유동 상태는 유상 경사가 큰 후기 단계에서 크게 변경됩니다.
    Favre 파도는 수직 속도와 수직 가속도에 큰 영향을 미칩니다.
    베드 전단응력의 변화는 베드 기울기와 꼬리물의 영향을 받습니다.

    Abstract

    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.

    Fig. 1. Sketch of related variables involved in shallow water model.
    Fig. 1. Sketch of related variables involved in shallow water model.
    Fig. 2. Flume model in numerical simulation.
    Fig. 2. Flume model in numerical simulation.
    Fig. 3. Grid sensitivity analysis (a) water surface profile; (b) velocity profile.
    Fig. 3. Grid sensitivity analysis (a) water surface profile; (b) velocity profile.
    Fig. 4. Sketch of experimental set-up for validating the velocity profile.
    Fig. 4. Sketch of experimental set-up for validating the velocity profile.
    Fig. 5. Sketch of experimental set-up for validating the bed shear stress.
    Fig. 5. Sketch of experimental set-up for validating the bed shear stress.
    Fig. 6. Model validation results (a) variation of the velocity profile; (b) error value of the velocity profile; (c) variation of the bed shear stress; (d) error value of the bed shear stress.
    Fig. 6. Model validation results (a) variation of the velocity profile; (b) error value of the velocity profile; (c) variation of the bed shear stress; (d) error value of the bed shear stress.
    Fig. 7. Schematic diagram of regional division.
    Fig. 7. Schematic diagram of regional division.
    Fig. 8. Variation of water surface profile (a) α = 0.1; (b) α = 0.3; (c) α = 0.5; (d) α = 0.7.
    Fig. 8. Variation of water surface profile (a) α = 0.1; (b) α = 0.3; (c) α = 0.5; (d) α = 0.7.
    Fig. 8. (continued).
    Fig. 8. (continued).
    Fig. 8. (continued).
    Fig. 8. (continued).
    Fig. 8. (continued).
    Fig. 8. (continued).
    Fig. 9. Froude number for α = 0.1 (a) variation with time; (b) variation with wavefront position.
    Fig. 9. Froude number for α = 0.1 (a) variation with time; (b) variation with wavefront position.
    Fig. 10. Characteristics of velocity distribution (a) α = 0.1; (b) α = 0.3; (c) α = 0.5; (d) α = 0.7.
    Fig. 10. Characteristics of velocity distribution (a) α = 0.1; (b) α = 0.3; (c) α = 0.5; (d) α = 0.7.
    Fig. 11. Average proportion of the vertical velocity (a) α = 0.1; (b) α = 0.3; (c) α = 0.5; (d) α = 0.7.
    Fig. 11. Average proportion of the vertical velocity (a) α = 0.1; (b) α = 0.3; (c) α = 0.5; (d) α = 0.7.
    Fig. 12. Bed shear stress distribution (a) α = 0.1; (b) α = 0.3; (c) α = 0.5; (d) α = 0.7.
    Fig. 12. Bed shear stress distribution (a) α = 0.1; (b) α = 0.3; (c) α = 0.5; (d) α = 0.7.
    Fig. 12. (continued).
    Fig. 12. (continued).
    Fig. 13. Variation of the maximum bed shear stress position with time (a) α = 0.1; (b) α = 0.3; (c) α = 0.5; (d) α = 0.7.
    Fig. 13. Variation of the maximum bed shear stress position with time (a) α = 0.1; (b) α = 0.3; (c) α = 0.5; (d) α = 0.7.
    Fig. 14. Time when the maximum bed shear stress appears at different positions (a) α = 0.1; (b) α = 0.3; (c) α = 0.5; (d) α = 0.7.
    Fig. 14. Time when the maximum bed shear stress appears at different positions (a) α = 0.1; (b) α = 0.3; (c) α = 0.5; (d) α = 0.7.
    Fig. 15. Movement characteristics of the fluid particles (a) α = 0.1; (b) α = 0.3; (c) α = 0.5; (d) α = 0.7.
    Fig. 15. Movement characteristics of the fluid particles (a) α = 0.1; (b) α = 0.3; (c) α = 0.5; (d) α = 0.7.
    Fig. 15. (continued).
    Fig. 15. (continued).

    Keywords

    Dam-break flow, Bed slope, Wet bed, Velocity profile, Bed shear stress, Large eddy simulation

    References

    Barnes, M.P., Baldock, T.E. 2006. Bed shear stress measurements in dam break and swash
    flows. Proceedings of International Conference on Civil and Environmental
    Engineering. Hiroshima University, Japan, 28–29 September.
    Biscarini, C., Francesco, S.D., Manciola, P., 2010. CFD modelling approach for dam break
    flow studies. Hydrol. Earth Syst. Sc. 14, 705–718. https://doi.org/10.5194/hess-14-
    705-2010.
    Fig. 15. (continued).
    W. Liu et al.
    Journal of Hydrology 602 (2021) 126752
    19
    Bristeau, M.-O., Goutal, N., Sainte-Marie, J., 2011. Numerical simulations of a nonhydrostatic shallow water model. Comput. Fluids. 47 (1), 51–64. https://doi.org/
    10.1016/j.compfluid.2011.02.013.
    Bung, D.B., Hildebrandt, A., Oertel, M., Schlenkhoff, A., Schlurmann, T. 2008. Bore
    propagation over a submerged horizontal plate by physical and numerical
    simulation. Proc. 31st Intl.Conf. Coastal Eng., Hamburg, Germany, 3542–3553.
    Cantero-Chinchilla, F.N., Castro-Orgaz, O., Dey, S., Ayuso, J.L., 2016. Nonhydrostatic
    dam break flows. I: physical equations and numerical schemes. J. Hydraul. Eng. 142
    (12), 04016068. https://doi.org/10.1061/(ASCE)HY.1943-7900.0001205.
    Castro-Orgaz, O., Chanson, H., 2020. Undular and broken surges in dam-break flows: A
    review of wave breaking strategies in a boussinesq-type framework. Environ. Fluid
    Mech. 154 https://doi.org/10.1007/s10652-020-09749-3.
    Chang, T.-J., Kao, H.-M., Chang, K.-H., Hsu, M.-H., 2011. Numerical simulation of
    shallow-water dam break flows in open channels using smoothed particle
    hydrodynamics. J. Hydrol. 408 (1-2), 78–90. https://doi.org/10.1016/j.
    jhydrol.2011.07.023.
    Chen, H., Xu, W., Deng, J., Xue, Y., Li, J., 2009. Experimental investigation of pressure
    load exerted on a downstream dam by dam-break flow. J. Hydraul. Eng. 140,
    199–207. https://doi.org/10.1061/(ASCE)HY.1943-7900.0000743.
    Favre H. 1935. Etude th´eorique et exp´erimentale des ondes de translation dans les
    canaux d´ecouverts. Dunod, Paris. (in French).
    Flow Science Inc. 2016. Flow-3D User’s Manuals. Santa Fe NM.
    Fraccarollo, L., Toro, E.F., 1995. Experimental and numerical assessment of the shallow
    water model for two-dimensional dam-break type problems. J. Hydraul. Res. 33 (6),
    843–864. https://doi.org/10.1080/00221689509498555.
    Guo, Y., Wu, X., Pan, C., Zhang, J., 2012. Numerical simulation of the tidal flow and
    suspended sediment transport in the qiantang estuary. J Waterw. Port Coastal. 138
    (3), 192–202. https://doi.org/10.1061/(ASCE)WW.1943-5460.0000118.
    Guo, Y., Zhang, Z., Shi, B., 2014. Numerical simulation of gravity current descending a
    slope into a linearly stratified environment. J. Hydraulic Eng. 140 (12), 04014061.
    https://doi.org/10.1061/(ASCE)HY.1943-7900.0000936.
    Khosronejad, A., Kang, S., Flora, K., 2019. Fully coupled free-surface flow and sediment
    transport modelling of flash floods in a desert stream in the mojave desert, california.
    Hydrol. Process 33 (21), 2772–2791. https://doi.org/10.1002/hyp.v33.2110.1002/
    hyp.13527.
    Khosronejad, A., Arabi, M.G., Angelidis, D., Bagherizadeh, E., Flora, K., Farhadzadeh, A.,
    2020a. A comparative study of rigid-lid and level-set methods for LES of openchannel flows: morphodynamics. Environ. Fluid Mech. 20 (1), 145–164. https://doi.
    org/10.1007/s10652-019-09703-y.
    Khosronejad, A., Flora, K., Zhang, Z.X., Kang, S., 2020b. Large-eddy simulation of flash
    flood propagation and sediment transport in a dry-bed desert stream. Int. J.
    Sediment Res. 35 (6), 576–586. https://doi.org/10.1016/j.ijsrc.2020.02.002.
    Khoshkonesh, A., Nsom, B., Gohari, S., Banejad, H., 2019. A comprehensive study of dam
    break over the dry and wet beds. Ocean Eng. 188, 106279.1–106279.18. https://doi.
    org/10.1016/j.oceaneng.2019.106279.
    Kocaman, S., Ozmen-Cagatay, H., 2012. The effect of lateral channel contraction on dam
    break flows: laboratory experiment. J. Hydrol. 432–433, 145–153. https://doi.org/
    10.1016/j.jhydrol.2012.02.035.
    Kocaman, S., Ozmen-Cagatay, H., 2015. Investigation of dam-break induced shock waves
    impact on a vertical wall. J. Hydrol. 525, 1–12. https://doi.org/10.1016/j.
    jhydrol.2015.03.040.
    LaRocque, L.A., Imran, J., Chaudhry, M.H., 2013a. Experimental and numerical
    investigations of two-dimensional dam-break flows. J. Hydraul. Eng. 139 (6),
    569–579. https://doi.org/10.1061/(ASCE)HY.1943-7900.0000705.
    Larocque, L.A., Imran, J., Chaudhry, M.H., 2013b. 3D numerical simulation of partial
    breach dam-break flow using the LES and k-ε turbulence models. J. Hydraul. Res. 51,
    145–157. https://doi.org/10.1080/00221686.2012.734862.
    Lauber, G., Hager, W.H., 1998a. Experiments to dam break wave: Horizontal channel.
    J. Hydraul. Res. 36 (3), 291–307. https://doi.org/10.1080/00221689809498620.
    Lauber, G., Hager, W.H., 1998b. Experiments to dam break wave: Sloping channel.
    J. Hydraul. Res. 36 (5), 761–773. https://doi.org/10.1080/00221689809498601.
    Leal, J.G., Ferreira, R.M., Cardoso, A.H., 2006. Dam-break wave-front celerity.
    J. Hydraul. Eng. 132 (1), 69–76. https://doi.org/10.1061/(ASCE)0733-9429(2006)
    132:1(69).
    Liu, W., Wang, B., Guo, Y., Zhang, J., Chen, Y., 2020. Experimental investigation on the
    effects of bed slope and tailwater on dam-break flows. J. Hydrol. 590, 125256.
    https://doi.org/10.1016/j.jhydrol.2020.125256.
    Marche, C., Beauchemin P. EL Kayloubi, A. 1995. Etude num´erique et exp´erimentale des
    ondes secondaires de Favre cons´ecutives a la rupture d’un harrage. Can. J. Civil Eng.
    22, 793–801, (in French). https://doi.org/10.1139/l95-089.
    Marra, D., Earl, T., Ancey, C. 2011. Experimental investigations of dam break flows down
    an inclined channel. Proceedings of the 34th World Congress of the International
    Association for Hydro-Environment Research and Engineering: 33rd Hydrology and
    Water Resources Symposium and 10th Conference on Hydraulics in Water
    Engineering, Brisbane, Australia.
    Marsooli, R., Wu, W., 2014. 3-D finite-volume model of dam-break flow over uneven
    beds based on vof method. Adv. Water Resour. 70, 104–117. https://doi.org/
    10.1016/j.advwatres.2014.04.020.
    Miller, S., Chaudhry, M.H., 1989. Dam-break flows in curved channel. J. Hydraul. Eng.
    115 (11), 1465–1478. https://doi.org/10.1061/(ASCE)0733-9429(1989)115:11
    (1465).
    Mohapatra, P.K., Chaudhry, M.H., 2004. Numerical solution of Boussinesq equations to
    simulate dam-break flows. J. Hydraul. Eng. 130 (2), 156–159. https://doi.org/
    10.1061/(ASCE)0733-9429(2004)130:2(156).
    Oertel, M., Bung, D.B., 2012. Initial stage of two-dimensional dam-break waves:
    laboratory versus VOF. J. Hydraul. Res. 50 (1), 89–97. https://doi.org/10.1080/
    00221686.2011.639981.
    Ozmen-Cagatay, H., Kocaman, S., 2012. Investigation of dam-break flow over abruptly
    contracting channel with trapezoidal-shaped lateral obstacles. J. Fluids Eng. 134,
    081204 https://doi.org/10.1115/1.4007154.
    Ozmen-Cagatay, H., Kocaman, S., Guzel, H., 2014. Investigation of dam-break flood
    waves in a dry channel with a hump. J. Hydro-environ. Res. 8 (3), 304–315. https://
    doi.org/10.1016/j.jher.2014.01.005.
    Park, I.R., Kim, K.S., Kim, J., Van, S.H., 2012. Numerical investigation of the effects of
    turbulence intensity on dam-break flows. Ocean Eng. 42, 176–187. https://doi.org/
    10.1016/j.oceaneng.2012.01.005.
    Peregrine, D.H., 1966. Calculations of the development of an undular bore. J. Fluid
    Mech. 25 (2), 321–330. https://doi.org/10.1017/S0022112066001678.
    Savic, L.j., Holly, F.M., 1993. Dam break flood waves computed by modified Godunov
    method. J. Hydraul. Res. 31 (2), 187–204. https://doi.org/10.1080/
    00221689309498844.
    Shigematsu, T., Liu, P., Oda, K., 2004. Numerical modeling of the initial stages of dambreak waves. J. Hydraul. Res. 42 (2), 183–195. https://doi.org/10.1080/
    00221686.2004.9628303.
    Smagorinsky, J., 1963. General circulation experiments with the primitive equations.
    Part I: the basic experiment. Mon. Weather Rev. 91, 99–164. https://doi.org/
    10.1126/science.27.693.594.
    Soares-Frazao, S., Zech, Y., 2002. Undular bores and secondary waves – Experiments and
    hybrid finite-volume modeling. J. Hydraul. Res. 40, 33–43. https://doi.org/
    10.1080/00221680209499871.
    Stansby, P.K., Chegini, A., Barnes, T.C.D., 1998. The initial stages of dam-break flow.
    J. Fluid Mech. 370, 203–220. https://doi.org/10.1017/022112098001918.
    Treske, A., 1994. Undular bores (favre-waves) in open channels – experimental studies.
    J. Hydraul. Res. 32 (3), 355–370. https://doi.org/10.1080/00221689409498738.
    Wang, B., Chen, Y., Wu, C., Dong, J., Ma, X., Song, J., 2016. A semi-analytical approach
    for predicting peak discharge of floods caused by embankment dam failures. Hydrol.
    Process 30 (20), 3682–3691. https://doi.org/10.1002/hyp.v30.2010.1002/
    hyp.10896.
    Wang, B., Chen, Y., Wu, C., Peng, Y., Ma, X., Song, J., 2017. Analytical solution of dambreak flood wave propagation in a dry sloped channel with an irregular-shaped
    cross-section. J. Hydro-environ. Res. 14, 93–104. https://doi.org/10.1016/j.
    jher.2016.11.003.
    Wang, B., Chen, Y., Wu, C., Peng, Y., Song, J., Liu, W., Liu, X., 2018. Empirical and semianalytical models for predicting peak outflows caused by embankment dam failures.
    J. Hydrol. 562, 692–702. https://doi.org/10.1016/j.jhydrol.2018.05.049.
    Wang, B., Zhang, J., Chen, Y., Peng, Y., Liu, X., Liu, W., 2019. Comparison of measured
    dam-break flood waves in triangular and rectangular channels. J. Hydrol. 575,
    690–703. https://doi.org/10.1016/j.jhydrol.2019.05.081.
    Wang, B., Liu, W., Zhang, J., Chen, Y., Wu, C., Peng, Y., Wu, Z., Liu, X., Yang, S., 2020a.
    Enhancement of semi-theoretical models for predicting peak discharges in breached
    embankment dams. Environ. Fluid Mech. 20 (4), 885–904. https://doi.org/10.1007/
    s10652-019-09730-9.
    Wang, B., Chen, Y., Peng, Y., Zhang, J., Guo, Y., 2020b. Analytical solution of shallow
    water equations for ideal dam-break flood along a wet bed slope. J. Hydraul. Eng.
    146 (2), 06019020. https://doi.org/10.1061/(ASCE)HY.1943-7900.0001683.
    Wang, B., Liu, W., Wang, W., Zhang, J., Chen, Y., Peng, Y., Liu, X., Yang, S., 2020c.
    Experimental and numerical investigations of similarity for dam-break flows on wet
    bed. J. Hydrol. 583, 124598. https://doi.org/10.1016/j.jhydrol.2020.124598.
    Wang, B., Liu, X., Zhang, J., Guo, Y., Chen, Y., Peng, Y., Liu, W., Yang, S., Zhang, F.,
    2020d. Analytical and experimental investigations of dam-break flows in triangular
    channels with wet-bed conditions. J. Hydraul. Eng. 146 (10), 04020070. https://doi.
    org/10.1061/(ASCE)HY.1943-7900.0001808.
    Wu, W., Wang, S., 2007. One-dimensional modeling of dam-break flow over movable
    beds. J. Hydraul. Eng. 133 (1), 48–58. https://doi.org/10.1061/(ASCE)0733-9429
    (2007)133:1(48).
    Xia, J., Lin, B., Falconer, R.A., Wang, G., 2010. Modelling dam-break flows over mobile
    beds using a 2d coupled approach. Adv. Water Resour. 33 (2), 171–183. https://doi.
    org/10.1016/j.advwatres.2009.11.004.
    Yang, S., Yang, W., Qin, S., Li, Q., Yang, B., 2018a. Numerical study on characteristics of
    dam-break wave. Ocean Eng. 159, 358–371. https://doi.org/10.1016/j.
    oceaneng.2018.04.011.
    Yang, S., Yang, W., Qin, S., Li, Q., 2018b. Comparative study on calculation methods of
    dam-break wave. J. Hydraul. Res. 57 (5), 702–714. https://doi.org/10.1080/
    00221686.2018.1494057.

    Fig. 1. Model geometry with the computational domain, extrusion nozzle, toolpath, and boundary conditions. The model is presented while printing the fifth layer.

    재료 압출 적층 제조에서 증착된 층의 안정성 및 변형

    Md Tusher Mollah Raphaël 사령관 Marcin P. Serdeczny David B. Pedersen Jon Spangenberg덴마크 공과 대학 기계 공학과, Kgs. 덴마크 링비

    2020년 12월 22일 접수, 2021년 5월 1일 수정, 2021년 7월 15일 수락, 2021년 7월 21일 온라인 사용 가능, 기록 버전 2021년 8월 17일 .

    Abstract

    이 문서는 재료 압출 적층 제조 에서 여러 레이어를 인쇄하는 동안 증착 흐름의 전산 유체 역학 시뮬레이션 을 제공합니다 개발된 모델은 증착된 레이어의 형태를 예측하고 점소성 재료 를 인쇄하는 동안 레이어 변형을 캡처합니다 . 물리학은 일반화된 뉴턴 유체 로 공식화된 Bingham 구성 모델의 연속성 및 운동량 방정식에 의해 제어됩니다. . 증착된 층의 단면 모양이 예측되고 재료의 다양한 구성 매개변수에 대해 층의 변형이 연구됩니다. 층의 변형은 인쇄물의 정수압과 압출시 압출압력으로 인한 것임을 알 수 있다. 시뮬레이션에 따르면 항복 응력이 높을수록 변형이 적은 인쇄물이 생성되는 반면 플라스틱 점도 가 높을수록 증착된 레이어에서변형이 커 집니다 . 또한, 인쇄 속도, 압출 속도 의 영향, 층 높이 및 인쇄된 층의 변형에 대한 노즐 직경을 조사합니다. 마지막으로, 이 모델은 후속 인쇄된 레이어의 정수압 및 압출 압력을 지원하기 위해 증착 후 점소성 재료가 요구하는 항복 응력의 필요한 증가에 대한 보수적인 추정치를 제공합니다.

    This paper presents computational fluid dynamics simulations of the deposition flow during printing of multiple layers in material extrusion additive manufacturing. The developed model predicts the morphology of the deposited layers and captures the layer deformations during the printing of viscoplastic materials. The physics is governed by the continuity and momentum equations with the Bingham constitutive model, formulated as a generalized Newtonian fluid. The cross-sectional shapes of the deposited layers are predicted, and the deformation of layers is studied for different constitutive parameters of the material. It is shown that the deformation of layers is due to the hydrostatic pressure of the printed material, as well as the extrusion pressure during the extrusion. The simulations show that a higher yield stress results in prints with less deformations, while a higher plastic viscosity leads to larger deformations in the deposited layers. Moreover, the influence of the printing speed, extrusion speed, layer height, and nozzle diameter on the deformation of the printed layers is investigated. Finally, the model provides a conservative estimate of the required increase in yield stress that a viscoplastic material demands after deposition in order to support the hydrostatic and extrusion pressure of the subsequently printed layers.

    Fig. 1. Model geometry with the computational domain, extrusion nozzle, toolpath, and boundary conditions. The model is presented while printing the fifth layer.
    Fig. 1. Model geometry with the computational domain, extrusion nozzle, toolpath, and boundary conditions. The model is presented while printing the fifth layer.

    키워드

    점성 플라스틱 재료, 재료 압출 적층 제조(MEX-AM), 다층 증착, 전산유체역학(CFD), 변형 제어
    Viscoplastic Materials, Material Extrusion Additive Manufacturing (MEX-AM), Multiple-Layers Deposition, Computational Fluid Dynamics (CFD), Deformation Control

    Introduction

    Three-dimensional printing of viscoplastic materials has grown in popularity over the recent years, due to the success of Material Extrusion Additive Manufacturing (MEX-AM) [1]. Viscoplastic materials, such as ceramic pastes [2,3], hydrogels [4], thermosets [5], and concrete [6], behave like solids when the applied load is below their yield stress, and like a fluid when the applied load exceeds their yield stress [7]. Viscoplastic materials are typically used in MEX-AM techniques such as Robocasting [8], and 3D concrete printing [9,10]. The differences between these technologies lie in the processing of the material before the extrusion and in the printing scale (from microscale to big area additive manufacturing). In these extrusion-based technologies, the structure is fabricated in a layer-by-layer approach onto a solid surface/support [11, 12]. During the process, the material is typically deposited on top of the previously printed layers that may be already solidified (wet-on-dry printing) or still deformable (wet-on-wet printing) [1]. In wet-on-wet printing, control over the deformation of layers is important for the stability and geometrical accuracy of the prints. If the material is too liquid after the deposition, it cannot support the pressure of the subsequently deposited layers. On the other hand, the material flowability is a necessity during extrusion through the nozzle. Several experimental studies have been performed to analyze the physics of the extrusion and deposition of viscoplastic materials, as reviewed in Refs. [13–16]. The experimental measurements can be supplemented with Computational Fluid Dynamics (CFD) simulations to gain a more complete picture of MEX-AM. A review of the CFD studies within the material processing and deposition in 3D concrete printing was presented by Roussel et al. [17]. Wolfs et al. [18] predicted numerically the failure-deformation of a cylindrical structure due to the self-weight by calculating the stiffness and strength of the individual layers. It was found that the deformations can take place in all layers, however the most critical deformation occurs in the bottom layer. Comminal et al. [19,20] presented three-dimensional simulations of the material deposition in MEX-AM, where the fluid was approximated as Newtonian. Subsequently, the model was experimentally validated in Ref. [21] for polymer-based MEX-AM, and extended to simulate the deposition of multiple layers in Ref. [22], where the previously printed material was assumed solid. Xia et al. [23] simulated the influence of the viscoelastic effects on the shape of deposited layers in MEX-AM. A numerical model for simulating the deposition of a viscoplastic material was recently presented and experimentally validated in Refs. [24] and [25]. These studies focused on predicting the cross-sectional shape of a single printed layer for different processing conditions (relative printing speed, and layer height). Despite these research efforts, a limited number of studies have focused on investigating the material deformations in wet-on-wet printing when multiple layers are deposited on top of each other. This paper presents CFD simulations of the extrusion-deposition flow of a viscoplastic material for several subsequent layers (viz. three- and five-layers). The material is continuously printed one layer over another on a fixed solid surface. The rheology of the viscoplastic material is approximated by the Bingham constitutive equation that is formulated using the Generalized Newtonian Fluid (GNF) model. The CFD model is used to predict the cross-sectional shapes of the layers and their deformations while printing the next layers on top. Moreover, the simulations are used to quantify the extrusion pressure applied by the deposited material on the substrate, and the previously printed layers. Numerically, it is investigated how the process parameters (i.e., the extrusion speed, printing speed, nozzle diameter, and layer height) and the material rheology affect the deformations of the deposited layers. Section 2 describes the methodology of the study. Section 3 presents and discusses the results. The study is summarized and concluded in Section 4.

    References

    [1] R.A. Buswell, W.R. Leal De Silva, S.Z. Jones, J. Dirrenberger, 3D printing using
    concrete extrusion: a roadmap for research, Cem. Concr. Res. 112 (2018) 37–49.
    [2] Z. Chen, Z. Li, J. Li, C. Liu, C. Lao, Y. Fu, C. Liu, Y. Li, P. Wang, Y. He, 3D printing of
    ceramics: a review, J. Eur. Ceram. Soc. 39 (4) (2019) 661–687.
    [3] A. Bellini, L. Shor, S.I. Guceri, New developments in fused deposition modeling of
    ceramics, Rapid Prototyp. J. 11 (4) (2005) 214–220.
    [4] S. Aktas, D.M. Kalyon, B.M. Marín-Santib´
    anez, ˜ J. P´erez-Gonzalez, ´ Shear viscosity
    and wall slip behavior of a viscoplastic hydrogel, J. Rheol. 58 (2) (2014) 513–535.
    [5] J. Lindahl, A. Hassen, S. Romberg, B. Hedger, P. Hedger Jr., M. Walch, T. Deluca,
    W. Morrison, P. Kim, A. Roschli, D. Nuttall, Large-scale Additive Manufacturing
    with Reactive Polymers, Oak Ridge National Lab.(ORNL), Oak Ridge, TN (United
    States), 2018.
    [6] V.N. Nerella, V. Mechtcherine, Studying the printability of fresh concrete for
    formwork-free Concrete onsite 3D Printing Technology (CONPrint3D), 3D Concr.
    Print. Technol. (2019) 333–347.
    [7] C. Tiu, J. Guo, P.H.T. Uhlherr, Yielding behaviour of viscoplastic materials, J. Ind.
    Eng. Chem. 12 (5) (2006) 653–662.
    [8] B. Dietemann, F. Bosna, M. Lorenz, N. Travitzky, H. Kruggel-Emden, T. Kraft,
    C. Bierwisch, Modeling robocasting with smoothed particle hydrodynamics:
    printing gapspanning filaments, Addit. Manuf. 36 (2020), 101488.
    [9] B. Khoshnevis, R. Russell, H. Kwon, S. Bukkapatnam, Contour crafting – a layered
    fabrication, Spec. Issue IEEE Robot. Autom. Mag. 8 (3) (2001) 33–42.
    [10] D. Asprone, F. Auricchio, C. Menna, V. Mercuri, 3D printing of reinforced concrete
    elements: technology and design approach, Constr. Build. Mater. 165 (2018)
    218–231.
    [11] J. Jiang, Y. Ma, Path planning strategies to optimize accuracy, quality, build time
    and material use in additive manufacturing: a review, Micromachines 11 (7)
    (2020) 633.
    [12] J. Jiang, A novel fabrication strategy for additive manufacturing processes,
    J. Clean. Prod. 272 (2020), 122916.
    [13] F. Bos, R. Wolfs, Z. Ahmed, T. Salet, Additive manufacturing of concrete in
    construction: potentials and challenges, Virtual Phys. Prototyp. 11 (3) (2016)
    209–225.
    [14] P. Wu, J. Wang, X. Wang, A critical review of the use of 3-D printing in the
    construction industry, Autom. Constr. 68 (2016) 21–31.
    [15] T.D. Ngo, A. Kashani, G. Imbalzano, K.T. Nguyen, D. Hui, Additive manufacturing
    (3D printing): a review of materials, methods, applications and challenges,
    Compos. Part B: Eng. 143 (2018) 172–196.
    [16] M. Valente, A. Sibai, M. Sambucci, Extrusion-based additive manufacturing of
    concrete products: revolutionizing and remodeling the construction industry,
    J. Compos. Sci. 3 (3) (2019) 88.
    [17] N. Roussel, J. Spangenberg, J. Wallevik, R. Wolfs, Numerical simulations of
    concrete processing: from standard formative casting to additive manufacturing,
    Cem. Concr. Res. 135 (2020), 106075.
    [18] R.J.M. Wolfs, F.P. Bos, T.A.M. Salet, Early age mechanical behaviour of 3D printed
    concrete: numerical modelling and experimental testing, Cem. Concr. Res. 106
    (2018) 103–116.
    [19] R. Comminal, M.P. Serdeczny, D.B. Pedersen, J. Spangenberg, Numerical modeling
    of the strand deposition flow in extrusion-based additive manufacturing, Addit.
    Manuf. 20 (2018) 68–76.
    [20] R. Comminal, M.P. Serdeczny, D.B. Pedersen, J. Spangenberg, Numerical modeling
    of the material deposition and contouring precision in fused deposition modeling,
    in Proceedings of the 29th Annual International Solid Freeform Fabrication
    Symposium, Austin, TX, USA, 2018, pp. 1855–1864.
    [21] M.P. Serdeczny, R. Comminal, D.B. Pedersen, J. Spangenberg, Experimental
    validation of a numerical model for the strand shape in material extrusion additive
    manufacturing, Addit. Manuf. 24 (2018) 145–153.
    [22] M.P. Serdeczny, R. Comminal, D.B. Pedersen, J. Spangenberg, Numerical
    simulations of the mesostructure formation in material extrusion additive
    manufacturing, Addit. Manuf. 28 (2019) 419–429.
    [23] H. Xia, J. Lu, G. Tryggvason, A numerical study of the effect of viscoelastic stresses
    in fused filament fabrication, Comput. Methods Appl. Mech. Eng. 346 (2019)
    242–259.
    [24] R. Comminal, W.R.L. da Silva, T.J. Andersen, H. Stang, J. Spangenberg, Influence
    of processing parameters on the layer geometry in 3D concrete printing:
    experiments and modelling, in: Proceedings of the Second RILEM International
    Conference on Concrete and Digital Fabrication, vol. 28, 2020, pp. 852–862.
    [25] R. Comminal, W.R.L. da Silva, T.J. Andersen, H. Stang, J. Spangenberg, Modelling
    of 3D concrete printing based on computational fluid dynamics, Cem. Concr. Res.
    38 (2020), 106256.
    [26] E.C. Bingham, An investigation of the laws of plastic flow, US Bur. Stand. Bull. 13
    (1916) 309–352.
    [27] N. Casson, A flow equation for pigment-oil suspensions of the printing ink type,
    Rheol. Disperse Syst. (1959) 84–104.
    [28] W.H. Herschel, R. Bulkley, Konsistenzmessungen von Gummi-Benzollosungen, ¨
    Kolloid Z. 39 (1926) 291–300.
    [29] “FLOW-3D | We solve The World’s Toughest CFD Problems,” FLOW SCIENCE.
    〈https://www.flow3d.com/〉. (Accessed 27 June 2020).
    [30] S. Jacobsen, R. Cepuritis, Y. Peng, M.R. Geiker, J. Spangenberg, Visualizing and
    simulating flow conditions in concrete form filling using pigments, Constr. Build.
    Mater. 49 (2013) 328–342.
    [31] E.J. O’Donovan, R.I. Tanner, Numerical study of the Bingham squeeze film
    problem, J. Non-Newton. Fluid Mech. 15 (1) (1984) 75–83.
    [32] C.W. Hirt, B.D. Nichols, Volume of fluid (VOF) method for the dynamics of free
    boundaries, J. Comput. Phys. 39 (1) (1981) 201–225.
    [33] R. Comminal, J. Spangenberg, J.H. Hattel, Cellwise conservative unsplit advection
    for the volume of fluid method, J. Comput. Phys. 283 (2015) 582–608.
    [34] A. Negar, S. Nazarian, N.A. Meisel, J.P. Duarte, Experimental prediction of material
    deformation in large-scale additive manufacturing of concrete, Addit. Manuf. 37
    (2021), 101656.

    Fig. 1- Schematic of the general pattern of flow and aeration process in the aerators

    2상 유동 해석을 통한 슈트 폭기 시스템 효율에 대한 램프 각도의 영향 조사

    Investigation of the Effect of Ramp Angle on Chute Aeration System Efficiency by Two-Phase Flow Analysis

    Authors

    1 Associate Professor, Civil Engineering Department, Jundi-Shapur University of Technology, Dezful, Iran

    2 Instructor in Civil Engineering Department Jundi-Shapur University of Technology, Dezful,Iran.

     10.22055/JISE.2021.37743.1980

    Abstract

    Flow aeration in chute spillway is one of the most effective and economic ways to prevent cavitation damage. Surface damage is significantly reduced when very small values of air are scattered in a water prism. A structure known as an aerator may be used for this purpose. Besides, ramp angle is one of the factors influencing aerator efficiency. In this research, the value of air entraining the flow through the Jarreh Dam’s spillway at the ramp angles of 6, 8 and 10 degrees, as three different scenarios, was simulated using the Flow-3D software. In order to validate the results of the inlet air into the flowing fluid at a ramp angle of 6 degrees, the observational results of the dam spillway physical model from the laboratory of TAMAB Company in Iran were used. According to the results, raising the ramp angle increases the inlet air to the water jet nappe, and a ten-degree ramp angle provides the best aeration efficiency. The Flow-3D model can also simulate the two-phase water-air flow on spillways, according to the results.

    슈트 여수로의 흐름 폭기는 캐비테이션 손상을 방지하는 가장 효과적이고 경제적인 방법 중 하나입니다. 수중 프리즘에 아주 작은 양의 공기가 흩어지면 표면 손상이 크게 줄어듭니다. 이를 위해 폭기 장치로 알려진 구조를 사용할 수 있습니다. 또한, 램프 각도는 폭기 효율에 영향을 미치는 요인 중 하나입니다. 이 연구에서는 FLOW-3D 소프트웨어를 사용하여 3가지 다른 시나리오인 6, 8 및 10도의 램프 각도에서 Jarreh 댐의 방수로를 통해 흐름을 동반하는 공기의 값을 시뮬레이션했습니다. 6도의 경사각에서 유동 유체로 유입되는 공기의 결과를 검증하기 위해이란 TAMAB Company의 실험실에서 댐 방수로 물리적 모델의 관찰 결과를 사용했습니다. 결과에 따르면 램프 각도를 높이면 워터제트 기저귀로 유입되는 공기가 증가하고 10도 램프 각도는 최고의 폭기 효율을 제공합니다. Flow-3D 모델은 결과에 따라 여수로의 2단계 물-공기 흐름을 시뮬레이션할 수도 있습니다.

    Keywords

    Fig. 1- Schematic of the general pattern of flow and aeration process in the aerators
    Fig. 1- Schematic of the general pattern of flow and aeration process in the aerators
    (a) The full-scale map of the Jarreh spillway’s plan and profile.
    (a) The full-scale map of the Jarreh spillway’s plan and profile.
    Fig. 2- Experimental setup (Shamloo et al., 2012)
    Fig. 2- Experimental setup (Shamloo et al., 2012)

    References

    1- Baharvand, S., & Lashkar-Ara, B. (2021). Hydraulic design criteria of the modified meander C-type
    fishway using the combined experimental and CFD models. Ecological Engineering, 164.
    https://doi.org/10.1016/j.ecoleng.2021.106207
    2- Bayon, A., Toro, J. P., Bombardelli, F. A., Matos, J., & López-Jiménez, P. A. (2018). Influence of VOF
    technique, turbulence model and discretization scheme on the numerical simulation of the non-aerated,
    skimming flow in stepped spillways. Journal of Hydro-Environment Research, 19, 137–149.
    https://doi.org/10.1016/j.jher.2017.10.002
    3- Brethour, J. M., & Hirt, C. W. (2009). Drift Model for Two-Component Flows. Flow Science, Inc., FSI09-TN83Rev, 1–7.
    4- Chanson, H. (1989). Study of air entrainment and aeration devices. Journal of Hydraulic Research, 27(3),
    301–319. https://doi.org/10.1080/00221688909499166
    5- Dong, Z., Wang, J., Vetsch, D. F., Boes, R. M., & Tan, G. (2019). Numerical simulation of air-water twophase flow on stepped spillways behind X-shaped flaring gate piers under very high unit discharge. Water
    (Switzerland), 11(10). https://doi.org/10.3390/w11101956
    6- Flow-3D, V. 11. 2. (2017). User Manual. Flow Science Inc.: Santa Fe, NM, USA;
    7- Hirt, C. W. (2003). Modeling Turbulent Entrainment of Air at a Free Surface. Flow Science, Inc., FSI-03-
    TN6, 1–9.
    8- Hirt, C. W. (2016). Dynamic Droplet Sizes for Drift Fluxes. Flow Science, Inc., 1–10.
    9- Hirt, C. W., & Nichols, B. D. (1981). Volume of fluid (VOF) method for the dynamics of free boundaries.
    Journal of Computational Physics, 39(1), 201–225. https://doi.org/10.1016/0021-9991(81)90145-5
    10- Kherbache, K., Chesneau, X., Zeghmati, B., Abide, S., & Benmamar, S. (2017). The effects of step
    inclination and air injection on the water flow in a stepped spillway: A numerical study. Journal of
    Hydrodynamics, 29(2), 322–331. https://doi.org/10.1016/S1001-6058(16)60742-4
    11- Kramer, M., & Chanson, H. (2019). Optical flow estimations in aerated spillway flows: Filtering and
    discussion on sampling parameters. Experimental Thermal and Fluid Science, 103, 318–328.
    https://doi.org/10.1016/j.expthermflusci.2018.12.002
    12- Mahmoudian, Z., Baharvand, S., & Lashkarara, B. (2019). Investigating the Flow Pattern in Baffle
    Fishway Denil Type. Irrigation Sciences and Engineering (JISE), 42(3), 179–196.
    13- Meireles, I. C., Bombardelli, F. A., & Matos, J. (2014). Air entrainment onset in skimming flows on
    steep stepped spillways: An analysis. Journal of Hydraulic Research, 52(3).
    https://doi.org/10.1080/00221686.2013.878401
    14- Parsaie, A., & Haghiabi, A. H. (2019). Inception point of flow aeration on quarter-circular crested stepped
    spillway. Flow Measurement and Instrumentation, 69.
    https://doi.org/10.1016/j.flowmeasinst.2019.101618
    15- Richardson, J. F., & Zaki W N. (1979). Sedimentation and Fluidisation. Part 1. Trans. Inst. Chem. Eng,
    32, 35–53.
    16- Shamloo, H., Hoseini Ghafari, S., & Kavianpour, M. (2012). Experimental study on the effects of inlet
    flows on aeration in chute spillway (Case study: Jare Dam, Iran). 10th International Congress on
    Advances in Civil Engineering, Middle East Technical University, Ankara, Turkey.
    17- Wang, S. Y., Hou, D. M., & Wang, C. H. (2012). Aerator of stepped chute in Murum Hydropower
    Station. Procedia Engineering, 28, 803–807. https://doi.org/10.1016/j.proeng.2012.01.813.
    18- Wei, W., Deng, J., & Zhang, F. (2016). Development of self-aeration process for supercritical chute
    flows. International Journal of Multiphase Flow, 79, 172–180.
    https://doi.org/10.1016/j.ijmultiphaseflow.2015.11.003
    19- Wu, J., QIAN, S., & MA, F. (2016). A new design of ski-jump-step spillway. Journal of Hydrodynamics,
    05, 914–917.
    20- Xu, Y., Wang, W., Yong, H., & Zhao, W. (2012). Investigation on the cavity backwater of the jet flow from the chute aerators. Procedia Engineering, 31, 51–56. https://doi.org/10.1016/j.proeng.2012.01.989
    21- Yakhot, V., & Orszag, S. A. (1986). Renormalization group analysis of turbulence. I. Basic theory.
    Journal of Scientific Computing, 1(1), 3–51. https://doi.org/10.1007/BF01061452
    22- Yang, J., Teng, P., & Lin, C. (2019). Air-vent layouts and water-air flow behaviors of a wide spillway
    aerator. Theoretical and Applied Mechanics Letters, 9(2), 130–143.
    https://doi.org/10.1016/j.taml.2019.02.009
    23- Zhang, G., & Chanson, H. (2016). Interaction between free-surface aeration and total pressure on a
    stepped chute. Experimental Thermal and Fluid Science, 74, 368–381.
    https://doi.org/10.1016/j.expthermflusci.2015.12.011

    Fig. 2- Experimental setup (Shamloo et al., 2012)

    2상 유동 해석을 통한 슈트 폭기 시스템 효율에 대한 램프 각도의 영향 조사

    1 Associate Professor, Civil Engineering Department, Jundi-Shapur University of Technology, Dezful, Iran

    2 Instructor in Civil Engineering Department Jundi-Shapur University of Technology, Dezful,Iran.

     10.22055/JISE.2021.37743.1980

    Abstract

    슈트 여수로의 흐름 폭기는 캐비테이션 손상을 방지하는 가장 효과적이고 경제적인 방법 중 하나입니다. 수중 프리즘에 아주 작은 양의 공기가 흩어지면 표면 손상이 크게 줄어듭니다. 이를 위해 폭기 장치로 알려진 구조를 사용할 수 있습니다. 또한, 램프 각도는 폭기 효율에 영향을 미치는 요인 중 하나입니다. 이 연구에서는 Flow-3D 소프트웨어를 사용하여 3가지 다른 시나리오인 6, 8 및 10도의 램프 각도에서 Jarreh 댐의 방수로를 통해 흐름을 동반하는 공기의 값을 시뮬레이션했습니다. 6도의 경사각에서 유동 유체로 유입되는 공기의 결과를 검증하기 위해이란 TAMAB Company의 실험실에서 댐 방수로 물리적 모델의 관찰 결과를 사용했습니다. 결과에 따르면 램프 각도를 높이면 워터제트 기저귀로 유입되는 공기가 증가하고 10도 램프 각도는 최고의 폭기 효율을 제공합니다. Flow-3D 모델은 결과에 따라 여수로의 2단계 물-공기 흐름을 시뮬레이션할 수도 있습니다.

    Flow aeration in chute spillway is one of the most effective and economic ways to prevent cavitation damage. Surface damage is significantly reduced when very small values of air are scattered in a water prism. A structure known as an aerator may be used for this purpose. Besides, ramp angle is one of the factors influencing aerator efficiency. In this research, the value of air entraining the flow through the Jarreh Dam’s spillway at the ramp angles of 6, 8 and 10 degrees, as three different scenarios, was simulated using the Flow-3D software. In order to validate the results of the inlet air into the flowing fluid at a ramp angle of 6 degrees, the observational results of the dam spillway physical model from the laboratory of TAMAB Company in Iran were used. According to the results, raising the ramp angle increases the inlet air to the water jet nappe, and a ten-degree ramp angle provides the best aeration efficiency. The Flow-3D model can also simulate the two-phase water-air flow on spillways, according to the results.

    Fig. 1- Schematic of the general pattern of flow and aeration process in the aerators
    Fig. 1- Schematic of the general pattern of flow and aeration process in the aerators
    Fig. 2- Experimental setup (Shamloo et al., 2012)
    Fig. 2- Experimental setup (Shamloo et al., 2012)
    Fig. 3- Results of numerical model validation in determining a) mean flow depth, b) mean velocity, and c) static pressure in various discharges vs (Shamloo et al., 2012) research under a 6 degree ramp angle
    Fig. 3- Results of numerical model validation in determining a) mean flow depth, b) mean velocity, and c) static pressure in various discharges vs (Shamloo et al., 2012) research under a 6 degree ramp angle
    Fig. 4- Location of data extraction stations after aeration on a scale model of 1:50
    Fig. 4- Location of data extraction stations after aeration on a scale model of 1:50
    Fig.7- Changes in cavitation index in different discharges with changes in ramp angle: a) 6 degrees, b) 8 degrees and c) 10 degrees
    Fig.7- Changes in cavitation index in different discharges with changes in ramp angle: a) 6 degrees, b) 8 degrees and c) 10 degrees

    Keywords

    Aeration system Ramp angle Aeration coefficient Two-phase flow Flow-3D model

    참고문헌

    • Baharvand, S., & Lashkar-Ara, B. (2021). 실험 모델과 CFD 모델을 결합한 수정 사행 C형 어로의 수력학적 설계기준. 생태 공학 , 164 . https://doi.org/10.1016/j.ecoleng.2021.106207

    2- Bayon, A., Toro, JP, Bombardelli, FA, Matos, J., & López-Jiménez, PA(2018). VOF 기술, 난류 모델 및 이산화 방식이 계단식 배수로에서 폭기되지 않은 스키밍 흐름의 수치 시뮬레이션에 미치는 영향. 수력 환경 연구 저널 , 19 , 137–149. https://doi.org/10.1016/j.jher.2017.10.002

    3- Brethour, JM, & Hirt, CW (2009). 2성분 흐름에 대한 드리프트 모델. Flow Science, Inc. , FSI – 09 – TN83Rev , 1–7.

    4- Chanson, H. (1989). 공기 유입 및 폭기 장치 연구. 수력학 연구 저널 , 27 (3), 301–319. https://doi.org/10.1080/00221688909499166

    5- Dong, Z., Wang, J., Vetsch, DF, Boes, RM, & Tan, G. (2019). 매우 높은 단위 배출에서 X자형 플레어링 게이트 교각 뒤의 계단식 배수로에서 공기-물 2상 흐름의 수치 시뮬레이션. 물(스위스) , 11 (10). https://doi.org/10.3390/w11101956

    6- Flow-3D, V. 11. 2. (2017). 사용자 매뉴얼. Flow Science Inc.: Santa Fe, NM, USA;

    7- Hirt, CW (2003). 자유 표면에서 공기의 난류 동반 모델링. Flow Science, Inc. , FSI – 03 – TN6 , 1–9.

    8- Hirt, CW (2016). 드리프트 플럭스에 대한 동적 액적 크기. Flow Science, Inc. , 1–10.

    9- Hirt, CW, & Nichols, BD (1981). 자유 경계의 역학에 대한 VOF(유체 체적) 방법. 전산 물리학 저널 , 39 (1), 201–225. https://doi.org/10.1016/0021-9991(81)90145-5

    10- Kherbache, K., Chesneau, X., Zeghmati, B., Abide, S., & Benmamar, S. (2017). 계단식 배수로의 물 흐름에 대한 계단식 경사 및 공기 주입의 영향: 수치 연구. 유체 역학 저널 , 29 (2), 322–331. https://doi.org/10.1016/S1001-6058(16)60742-4

    11- Kramer, M., & Chanson, H. (2019). 폭기된 여수로 흐름에서 광학 흐름 추정: 샘플링 매개변수에 대한 필터링 및 논의. 실험적 열 및 유체 과학 , 103 , 318–328. https://doi.org/10.1016/j.expthermflusci.2018.12.002

    12- Mahmoudian, Z., Baharvand, S., & Lashkarara, B. (2019). Baffle Fishway Denil Type의 흐름 패턴 조사. 관개 과학 및 공학(JISE) , 42 (3), 179–196.

    13- Meireles, IC, Bombardelli, FA 및 Matos, J. (2014). 가파른 계단식 배수로의 스키밍 흐름에서 공기 유입 시작: 분석. 수력학 연구 저널 , 52 (3). https://doi.org/10.1080/00221686.2013.878401

    14- Parsaie, A., & Haghiabi, AH (2019). 1/4 원형 볏이 있는 계단식 배수로에서 흐름 폭기의 시작 지점. 유량 측정 및 계측 , 69 . https://doi.org/10.1016/j.flowmeasinst.2019.101618

    15- Richardson, JF, & Zaki W N. (1979). 침전 및 유동화. 파트 1. 트랜스. Inst. 화학 영어 , 32 , 35–53.

    16- Shamloo, H., Hoseini Ghafari, S., & Kavianpour, M. (2012). 슈트 여수로의 폭기에 대한 유입구 흐름의 영향에 대한 실험적 연구(사례 연구: 이란 Jare Dam). 제10차 토목 공학 발전에 관한 국제 회의, 중동 기술 대학, 앙카라, 터키 .

    17- Wang, SY, Hou, DM, & Wang, CH (2012). Murum 수력 발전소의 계단식 슈트의 폭기 장치. 프로시디아 엔지니어링 , 28 , 803–807. https://doi.org/10.1016/j.proeng.2012.01.813.

    18- Wei, W., Deng, J., & Zhang, F. (2016). 초임계 슈트 흐름에 대한 자체 폭기 공정 개발. 다상 흐름의 국제 저널 , 79 , 172–180. https://doi.org/10.1016/j.ijmultiphaseflow.2015.11.003

    19- Wu, J., QIAN, S., & MA, F. (2016). 스키점프 스텝 배수로의 새로운 디자인. 유체 역학 저널 , 05 , 914–917.

    20- Xu, Y., Wang, W., Yong, H., & Zhao, W. (2012). 슈트 폭기 장치에서 제트 흐름의 공동 역류에 대한 조사. 프로시디아 엔지니어링 , 31 , 51–56. https://doi.org/10.1016/j.proeng.2012.01.989

    21- Yakhot, V., & Orszag, SA (1986). 난류의 재정규화 그룹 분석. I. 기본 이론. 과학 컴퓨팅 저널 , 1 (1), 3–51. https://doi.org/10.1007/BF01061452

    22- Yang, J., Teng, P., & Lin, C. (2019). 넓은 여수로 폭기장치의 통풍구 배치 및 물-기류 거동. Theoretical and Applied Mechanics Letters , 9 (2), 130–143. https://doi.org/10.1016/j.taml.2019.02.009

    23- Zhang, G., & Chanson, H. (2016). 자유 표면 폭기와 계단식 슈트의 총 압력 사이의 상호 작용. 실험적 열 및 유체 과학 , 74 , 368–381. https://doi.org/10.1016/j.expthermflusci.2015.12.011

    Fig. 1. A typical Boiling Water Reactor (BWR) and selected segment of study for simulation

    Understanding dry-out mechanism in rod bundles of boiling water reactor

    끓는 물 원자로 봉 다발의 건조 메커니즘 이해

    Liril D.SilviaDinesh K.ChandrakercSumanaGhoshaArup KDasb
    aDepartment of Chemical Engineering, Indian Institute of Technology, Roorkee, India
    bDepartment of Mechanical Engineering, Indian Institute of Technology, Roorkee, India
    cReactor Engineering Division, Bhabha Atomic Research Centre, Mumbai, India

    Abstract

    Present work reports numerical understanding of interfacial dynamics during co-flow of vapor and liquid phases of water inside a typical Boiling Water Reactor (BWR), consisting of a nuclear fuel rod bundle assembly of 7 pins in a circular array. Two representative spacings between rods in a circular array are used to carry out the simulation. In literature, flow boiling in a nuclear reactor is dealt with mechanistic models or averaged equations. Hence, in the present study using the Volume of Fluid (VOF) based multiphase model, a detailed numerical understanding of breaking and making in interfaces during flow boiling in BWR is targeted. Our work will portray near realistic vapor bubble and liquid flow dynamics in rod bundle scenario. Constant wall heat flux for fuel rod and uniform velocity of the liquid at the inlet patch is applied as a boundary condition. The saturation properties of water are taken at 30 bar pressure. Flow boiling stages involving bubble nucleation, growth, merging, local dry-out, rewetting with liquid patches, and complete dry-out are illustrated. The dry-out phenomenon with no liquid presence is numerically observed with phase fraction contours at various axial cut-sections. The quantification of the liquid phase fraction at different axial planes is plotted over time, emphasizing the progressive dry-out mechanism. A comparison of liquid-vapor distribution for inner and outer rods reveals that the inner rod’s dry-out occurs sooner than that of the outer rod. The heat transfer coefficient to identify the heat dissipation capacity of each case is also reported.

    현재 작업은 원형 배열에 있는 7개의 핀으로 구성된 핵연료봉 다발 어셈블리로 구성된 일반적인 끓는 물 원자로(BWR) 내부의 물의 증기 및 액체상의 동시 흐름 동안 계면 역학에 대한 수치적 이해를 보고합니다.

    원형 배열의 막대 사이에 두 개의 대표적인 간격이 시뮬레이션을 수행하는 데 사용됩니다. 문헌에서 원자로의 유동 비등은 기계론적 모델 또는 평균 방정식으로 처리됩니다.

    따라서 VOF(Volume of Fluid) 기반 다상 모델을 사용하는 본 연구에서는 BWR에서 유동 비등 동안 계면의 파괴 및 생성에 대한 자세한 수치적 이해를 목표로 합니다.

    우리의 작업은 막대 번들 시나리오에서 거의 사실적인 증기 기포 및 액체 흐름 역학을 묘사합니다. 연료봉에 대한 일정한 벽 열유속과 입구 패치에서 액체의 균일한 속도가 경계 조건으로 적용됩니다. 물의 포화 특성은 30bar 압력에서 취합니다.

    기포 핵 생성, 성장, 병합, 국소 건조, 액체 패치로 재습윤 및 완전한 건조를 포함하는 유동 비등 단계가 설명됩니다. 액체가 존재하지 않는 건조 현상은 다양한 축 단면에서 위상 분율 윤곽으로 수치적으로 관찰됩니다.

    다른 축 평면에서 액상 분율의 정량화는 점진적인 건조 메커니즘을 강조하면서 시간이 지남에 따라 표시됩니다. 내부 막대와 외부 막대의 액-증기 분포를 비교하면 내부 막대의 건조가 외부 막대보다 더 빨리 발생함을 알 수 있습니다. 각 경우의 방열 용량을 식별하기 위한 열 전달 계수도 보고됩니다.

    Fig. 1. A typical Boiling Water Reactor (BWR) and selected segment of study for simulation
    Fig. 1. A typical Boiling Water Reactor (BWR) and selected segment of study for simulation
    Fig. 2. (a-c) dimensions and mesh configuration for G = 6 mm; (d-f) dimensions and mesh configuration for G = 0.6 mm
    Fig. 2. (a-c) dimensions and mesh configuration for G = 6 mm; (d-f) dimensions and mesh configuration for G = 0.6 mm
    Fig. 3. Simulating the effect of spacer (a) Spacer configuration around rod bundle (b) Mesh structure in spacer zone (c) Distribution of vapor bubbles in a rod bundle with spacer (d) Liquid phase fraction comparison for geometry with and without spacer (e,f,g) Wall temperature comparison for geometry with and without spacer; WS: With Spacer, WOS: Without Spacer; Temperature in the y-axis is in (f) and (g) is same as (e).
    Fig. 3. Simulating the effect of spacer (a) Spacer configuration around rod bundle (b) Mesh structure in spacer zone (c) Distribution of vapor bubbles in a rod bundle with spacer (d) Liquid phase fraction comparison for geometry with and without spacer (e,f,g) Wall temperature comparison for geometry with and without spacer; WS: With Spacer, WOS: Without Spacer; Temperature in the y-axis is in (f) and (g) is same as (e).
    Fig. 4. Validation of the present numerical model with crossflow boiling over a heated cylindrical rod [40]
    Fig. 4. Validation of the present numerical model with crossflow boiling over a heated cylindrical rod [40]
    Fig. 5. Grid-Independent study in terms of vapor volume in 1/4th of computational domain
    Fig. 5. Grid-Independent study in terms of vapor volume in 1/4th of computational domain
    Fig. 6. Interface contour for G = 6 mm; ul = 1.2 m/s; q˙ w = 396 kW/m2; they are showing nucleation, growth, merging, and pseudo-steady-state condition.
    Fig. 6. Interface contour for G = 6 mm; ul = 1.2 m/s; q˙ w = 396 kW/m2; they are showing nucleation, growth, merging, and pseudo-steady-state condition.
    Fig. 7. Interface contours for G = 0.6 mm; ul = 1.2 m/s; q˙ w = 396 kW/m2; It shows dry-out at pseudo-steady-state near the exit
    Fig. 7. Interface contours for G = 0.6 mm; ul = 1.2 m/s; q˙ w = 396 kW/m2; It shows dry-out at pseudo-steady-state near the exit
    Fig. 8. Vapor-liquid distribution across various distant cross-sections (Black color indicates liquid; Gray color indicates vapor); Magnification factor: 1 × (for a and b), 1.5 × (for c and d)
    Fig. 8. Vapor-liquid distribution across various distant cross-sections (Black color indicates liquid; Gray color indicates vapor); Magnification factor: 1 × (for a and b), 1.5 × (for c and d)
    Fig. 21. Two-phase flow mixture velocity (u¯z); for G = 6 mm, r = 5 means location at inner heated wall and r = 25 means location at outer adiabatic wall; for G = 0.66 mm, r = 5 means location at inner heated wall and r = 16.6 mm means location at outer adiabatic wall.
    Fig. 21. Two-phase flow mixture velocity (u¯z); for G = 6 mm, r = 5 means location at inner heated wall and r = 25 means location at outer adiabatic wall; for G = 0.66 mm, r = 5 means location at inner heated wall and r = 16.6 mm means location at outer adiabatic wall.

    References

    [1] J. Würtz, An Experimental and Theoretical Investigation of Annular Steam-Water Flow in Tubes and Annuli at 30 to 90 Bar, Risø National Laboratory,
    Roskilde, 1978.
    [2] W. Tian, A. Myint, Z. Li, S. Qiu, G.H. Su, D. Jia, Experimental study on dryout point in vertical narrow annulus under low flow conditions, in: International Conference on Nuclear Engineering, 4689, 2004, pp. 643–648. Jan
    1Vol.
    [3] K.M. Becker, C.H. Ling, S. Hedberg, G. Strand, An experimental investigation of
    post dryout heat transfer, R. Inst. Technol. (1983).
    [4] K.M. Becker, A Burnout Correlation for Flow of Boiling Water in Vertical Rod
    Bundles, AB Atomenergi, 1967.
    [5] Jr J.R. Barbosa, G.F. Hewitt, S.M. Richardson, High-speed visualisation of nucleate boiling in vertical annular flow, Int. J. Heat Mass Transf. 46 (26) (2003)
    5153–5160 1, doi:10.1016/S0017-9310(03)00255-2.
    [6] Y. Mizutani, A. Tomiyama, S. Hosokawa, A. Sou, Y. Kudo, K. Mishima, Twophase flow patterns in a four by four rod bundle, J. Nucl. Sci. Technol. 44 (6)
    (2007) 894–901 1, doi:10.1080/18811248.2007.9711327.
    [7] S.S. Paranjape, Two-Phase Flow Interfacial Structures in a Rod Bundle Geometry, Purdue University, 2009.
    [8] D. Lavicka, J. Polansky, Model of the cooling of a nuclear reactor fuel rod, Multiph. Sci. Technol. 25 (2-4) (2013), doi:10.1615/MultScienTechn.v25.i2-4.90.
    [9] M. Thurgood, J. Kelly, T. Guidotti, R. Kohrt, K. Crowell, Tech. rep., Pacific Northwest National Laboratory, 1983.
    [10] S. Sugawara, Droplet deposition and entrainment modeling based on the
    three-fluid model, Nucl. Eng. Des. 122 (1-3) (1990) 67–84, doi:10.1016/
    0029-5493(90)90197-6.
    [11] C. Adamsson, J.M. Le Corre, Modeling and validation of a mechanistic tool
    (MEFISTO) for the prediction of critical power in BWR fuel assemblies, Nucl.
    Eng. Des. 241 (8) (2011) 2843–2858, doi:10.1016/j.nucengdes.2011.01.033.
    [12] S. Talebi, H. Kazeminejad, A mathematical approach to predict dryout in a rod
    bundle, Nucl. Eng. Des. 249 (2012) 348–356, doi:10.1016/j.nucengdes.2012.04.
    016.
    [13] H. Anglart, O. Nylund, N. Kurul, M.Z. Podowski, CFD prediction of flow and
    phase distribution in fuel assemblies with spacers, Nucl. Eng. Des. 177 (1-3)
    (1997) 215–228, doi:10.1016/S0029-5493(97)00195-7.
    [14] H. Li, H. Anglart, CFD model of diabatic annular two-phase flow using the
    Eulerian–Lagrangian approach, Ann. Nucl. Energy 77 (2015) 415–424, doi:10.
    1016/j.anucene.2014.12.002.
    [15] G. Sorokin, A. Sorokin, Experimental and numerical investigation of liquid metal boiling in fuel subassemblies under natural circulation conditions, Prog. Nucl. Energy 47 (1-4) (2005) 656–663, doi:10.1016/j.pnucene.2005.
    05.069.
    [16] W.D. Pointer, A. Tentner, T. Sofu, D. Weber, S. Lo, A. Splawski, Eulerian
    two-phase computational fluid dynamics for boiling water reactor core analysis, Joint International Topical Meeting on Mathematics and Computation and
    Supercomputing in Nuclear Applications (M and C± SNA), 2007.
    [17] K. Podila, Y. Rao, CFD modelling of supercritical water flow and heat transfer
    in a 2 × 2 fuel rod bundle, Nucl. Eng. Des. 301 (2016) 279–289, doi:10.1016/j.
    nucengdes.2016.03.019.
    [18] H. Pothukuchi, S. Kelm, B.S. Patnaik, B.V. Prasad, H.J. Allelein, Numerical investigation of subcooled flow boiling in an annulus under the influence of eccentricity, Appl. Therm. Eng. 129 (2018) 1604–1617, doi:10.1016/j.applthermaleng.
    2017.10.105.
    [19] H. Pothukuchi, S. Kelm, B.S. Patnaik, B.V. Prasad, H.J. Allelein, CFD modeling of
    critical heat flux in flow boiling: validation and assessment of closure models,
    Appl. Therm. Eng. 150 (2019) 651–665, doi:10.1016/j.applthermaleng.2019.01.
    030.
    [20] W. Fan, H. Li, H. Anglart, A study of rewetting and conjugate heat transfer
    influence on dryout and post-dryout phenomena with a multi-domain coupled CFD approach, Int. J. Heat Mass Transf. 163 (2020) 120503, doi:10.1016/j.
    ijheatmasstransfer.2020.120503.
    [21] R. Zhang, T. Cong, G. Su, J. Wang, S. Qiu, Investigation on the critical heat
    flux in typical 5 by 5 rod bundle at conditions prototypical of PWR based
    on CFD methodology, Appl. Therm. Eng. 179 (2020) 115582, doi:10.1016/j.
    applthermaleng.2020.115582.

    [22] L.D. Silvi, A. Saha, D.K. Chandraker, S. Ghosh, A.K. Das, Numerical analysis of
    pre-dryout sequences through the route of interfacial evolution in annular gasliquid two-phase flow with phase change, Chem. Eng. Sci. 212 (2020) 115356,
    doi:10.1016/j.ces.2019.115356.
    [23] L.D. Silvi, D.K. Chandraker, S. Ghosh, A.K. Das, On-route to dryout through sequential interfacial dynamics in annular flow boiling around temperature and
    heat flux controlled heater rod, Chem. Eng. Sci. 229 (2021) 116014, doi:10.1016/
    j.ces.2020.116014.
    [24] J.U. Brackbill, D.B. Kothe, C. Zemach, A continuum method for modeling surface
    tension, J. Comput. Phys. 100 (2) (1992) 335–354, doi:10.1016/0021-9991(92)
    90240-Y.
    [25] B. Lafaurie, C. Nardone, R. Scardovelli, S. Zaleski, G. Zanetti, Modelling merging
    and fragmentation in multiphase flows with SURFER, J. Comput. Phys. 113 (1)
    (1994) 134–147, doi:10.1006/jcph.1994.1123.
    [26] I. Tanasawa, Advances in condensation heat transfer, Ad. Heat Transf. 21 (1991)
    55–139 Vol, doi:10.1016/S0065-2717(08)70334-4.
    [27] V.H. Del Valle, D.B. Kenning, Subcooled flow boiling at high heat flux, Int.
    J. Heat Mass Transf. 28 (10) (1985) 1907–1920, doi:10.1016/0017-9310(85)
    90213-3.
    [28] B. Matzner, G.M. Latter, Reduced pressure drop space for boiling water reactor
    fuel bundles, US Patent US5375154A, (1993)
    [29] C. Unal, O. Badr, K. Tuzla, J.C. Chen, S. Neti, Pressure drop at rod-bundle spacers
    in the post-CHF dispersed flow regime, Int. J. Multiphase Flow 20 (3) (1994)
    515–522, doi:10.1016/0301-9322(94)90025-6.
    [30] D.K. Chandraker, A.K. Nayak, V.P. Krishnan, Effect of spacer on the dryout of
    BWR fuel rod assemblies, Nucl. Eng. Des. 294 (2015), doi:10.1016/j.nucengdes.
    2015.09.004.
    [31] S.K Verma, S.L. Sinha, D.K. Chandraker, A comprehensive review of the spacer
    effect on performance of nuclear fuel bundle using computational fluid dynamics methodology, Mater. Today: Proc. 4 (2017) 100030–110034, doi:10.
    1016/j.matpr.2017.06.315.
    [32] S.K Verma, S.L. Sinha, D.K. Chandraker, Experimental investigation on the effect
    of space on the turbulent mixing in vertical pressure tube-type boiling water
    reactor, Nucl. Sci. Eng. 190 (2) (2018), doi:10.1080/00295639.2017.1413874.
    [33] T. Zhang, Y. Liu, Numerical investigation of flow and heat transfer characteristics of subcooled boiling in a single rod channel with/without spacer grid,
    Case Stud. Therm. Eng. 20 (2020) 100644, doi:10.1016/j.csite.2020.100644.
    [34] K.M. Becker, G. Hernborg, M. Bode, O. Eriksson, Burnout data for flow of boiling water in vertical round ducts, annuli and rod clusters, AB Atomenergi
    (1965).
    [35] A. Saha, A.K. Das, Numerical study of boiling around wires and influence of
    active or passive neighbours on vapour film dynamics, Int. J. Heat Mass Transf.
    130 (2019) 440–454, doi:10.1016/j.ijheatmasstransfer.2018.10.117.
    [36] M. Reimann, U. Grigull, Heat transfer with free convection and film boiling in
    the critical area of water and carbon dioxide, Heat Mass Transf. 8 (1975) 229–
    239, doi:10.1007/BF01002151.
    [37] M.S. Plesset, S.A. Zwick, The growth of vapor bubbles in superheated liquids, J.
    Appl. Phys. 25 (4) (1954) 493–500, doi:10.1063/1.1721668.
    [38] N. Samkhaniani, M.R. Ansari, Numerical simulation of superheated vapor bubble rising in stagnant liquid, Heat Mass Transf. 53 (9) (2017) 2885–2899,
    doi:10.1007/S00231-017-2031-6.
    [39] N. Samkhaniani, M.R. Ansari, The evaluation of the diffuse interface method
    for phase change simulations using OpenFOAM, Heat Transf. Asian Res. 46 (8)
    (2017) 1173–1203, doi:10.1002/htj.21268.
    [40] P. Goel, A.K. Nayak, M.K. Das, J.B. Joshi, Bubble departure characteristics in a
    horizontal tube bundle under cross flow conditions, Int. J. Multiph. Flow 100
    (2018) 143–154, doi:10.1016/j.ijmultiphaseflow.2017.12.013.
    [41] K.M. Becker, J. Engstorm, B.Scholin Nylund, B. Sodequist, Analysis of the dryout
    incident in the Oskarshamn 2 boiling water reactor, Int. J. Multiph. Flow 16 (6)
    (1990) 959–974, doi:10.1016/0301-9322(90)90101-N.
    [42] H.G. Weller, A New Approach to VOF-Based Interface Capturing Methods
    for Incompressible and Compressible Flow, A New Approach to VOF-Based
    Interface Capturing Methods for Incompressible and Compressible Flow, 4,
    OpenCFD Ltd., 2008 Report TR/HGW.
    [43] G. Boeing, Visual analysis of nonlinear dynamical systems: chaos, fractals, selfsimilarity and the limits of prediction, Systems 4 (4) (2016) 37, doi:10.3390/
    systems4040037.

    What’s New – FLOW-3D 2022R1

    FLOW-3D 제품의 새로운 2022R1 버전은 Flow Science가 FLOW-3D , FLOW-3D CAST 및 FLOW-3D HYDRO 에 대해 동일한 버전명을 채택 했음을 의미합니다. 2022R1은 FLOW-3D 제품을 위한 통합 코드 베이스로의 전환을 나타내며, 이를 통해 사용자는 최신 버전 개발이 준비되는 즉시 더 빠른 릴리스 버전을 만나실 수 있습니다.

    2022R1 릴리스는 상세한 cutcell 표현이라고 하는 FAVOR™ 방법의 확장, 테마 솔버 기본값이 있는 시뮬레이션 템플릿 도입, 이동하는 액적/기포 소스, 새로운 축 펌프 모델, 능동 시뮬레이션 제어 기능에 대한 확장, 사용자는 두 개의 독립 변수를 기반으로 복잡한 속성 종속성을 지정하고 VOF-to-particle 개발과 같은 추가 수치 기능을 지정하여 분해되는 유체 영역의 질량 보존을 개선할 수 있습니다. 간소화된 GUI 개선 사항에는 재설계된 물리 대화 상자, 새로운 초기 조건 위젯, 더 쉽고 빠르고 오류 없는 시뮬레이션 설정을 위해 재설계된 출력 및 지오메트리 위젯이 포함됩니다.

    상세한 Cutcell 표현 – FAVOR ™ 의 확장

    FAVOR™ 방법은 일반 데카르트 그리드에서 면적 및 부피 분율을 사용하여 솔리드 형상을 구현하는 방법입니다. 이를 통해 FLOW-3D 는 구조화되지 않은 body-fitted mesh에 의존하지 않고 솔리드의 복잡한 형상과 주변의 유체 흐름을 효율적으로 시뮬레이션할 수 있습니다. 상당한 계산상의 이점에도 불구하고 FAVOR™ 방법의 한 가지 문제는 고체 표면을 따라 벽 전단 응력을 계산할 때는 문제가 발생할 수도 있었습니다. 그러나, 상세한 cutcell  표현이라고 하는 FAVOR™의 확장은 벽 전단 응력 계산을 크게 개선하여 솔리드 표면 근처의 유체 유동 해석에서 상당한 개선을 가져옵니다.

    detailed cutcell 표현 의 검증뿐만 아니라 advanced numerics 에 대해 자세히 알아보십시오 .

    정체점으로부터의 각도
    상세한 컷셀 표현

    Tabular Properties

    점도 및 표면 장력과 같은 재료 속성은 온도, 밀도, 변형률 또는 오염 물질 농도와 같은 것을 나타내는 사용자 정의 스칼라 양과 같은 흐름 조건에 따라 달라질 수 있습니다. 이러한 속성을 기능적 형태에 맞추려면 특히 속성이 둘 이상의 독립 변수에 종속되는 경우 복잡한 곡선 맞춤이 필요할 수 있습니다. FLOW-3D 의 새로운 Tabular Properties 기능은  사용자가 최대 2개의 독립 변수를 사용하여 테이블 형식으로 유체 속성을 정의할 수 있습니다. 예를 들어, 표면 장력은 오염 물질 농도 및 온도에 대한 복잡한 비선형 종속성을 설명하기 위해 실험 데이터에서 표로 만들 수 있으며, 점도는 변형률 속도 및 온도에 대한 종속성을 나타내기 위해 실험 데이터에서 표로 만들 수 있습니다. 사용자는 표 속성 대화 상자에서 단일 변수 또는 두 개의 변수 종속성을 입력할 수 있습니다.

    점도는 고체 함량(밀도)과 변형률의 함수로 정의됩니다. 이 예에서 조밀한 유체 영역은 시간이 0일 때 조밀한 침전된 유체 영역과 위쪽에 맑은 물이 있는 정지된 풀로 미끄러져 내려갑니다.

    표 속성
    이 대화 상자는 표 속성 기능을 사용하여 변형률 및 온도의 함수로 점도를 정의하는 방법을 보여줍니다. 세 가지 다른 온도에 대한 변형률의 함수로서의 점도에 대한 값이 대화 상자의 오른쪽에 표시되고 그래프로 표시됩니다.

    Expanded Active Simulation Control

    능동 시뮬레이션 제어(ASC) 는 Probe로 지정한 부분의 흐름 정보를 기반으로 시뮬레이션을 제어하는 ​​데 매우 유용합니다. 이번 릴리스에서 ASC는 일반 이력 데이터, 플럭스 표면 및 sampling volumes의 흐름 정보를 기반으로 추가 제어를 허용하도록 확장되었습니다.

    포인트 프로브에 비해 플럭스 표면 및 샘플링 볼륨의 장점 중 하나는 포인트 기반이 아닌 표면 또는 볼륨에 대해 평균화된 정보를 제공할 수 있다는 것입니다. 어떤 상황에서는 표면 기반 및 볼륨 기반 정보가 시뮬레이션에서 관심 있는 동작을 더 잘 나타낼 수 있습니다.

    이 새로운 기능을 통해 사용자는 다음을 수행할 수 있습니다.

    • 제어 볼륨의 온도가 임계값을 초과하거나 아래로 떨어지면 시뮬레이션을 종료합니다.
    • 샘플링 볼륨의 난류 에너지를 기반으로 노즐에서 충전 속도를 제어합니다.
    • 자속 평면의 평균 속도를 기반으로 출력 주파수를 제어합니다.
    • 샘플링 볼륨의 채우기 비율이 사용자가 지정한 값에 도달하면 시뮬레이션을 종료합니다.

    이 예에서 극저온 탱크 공급 파이프의 펌프(진한 회색 직사각형)는 일정한 유속으로 추진제 탱크에서 액체 산소를 끌어옵니다. 액체 산소가 배출됨에 따라 얼리지의 압력이 지정된 값 아래로 떨어질 때 활성 시뮬레이션 제어에 의해 질량/운동량 소스(상단의 회색 막대)가 트리거됩니다. 얼리지 압력이 지정된 값 이상으로 상승하면 가압이 꺼집니다.

    VOF to Particles

    FLOW-3D 에서 복잡한 자유표면을 추적하는 VOF 방법의 정확성과 견고성은 유체 입자와 결합하여 향상되었습니다. VOF 입자라고 하는 새로운 입자 종류는 VOF 기능 대신 사용되어, 계산 영역에서 작은 유체 인대와 액적을 추적하여 유체 부피와 운동량을 더 잘 보존할 수 있습니다. 중력 제어 프로세스에서 더 높은 시간 단계 크기도 예상할 수 있습니다. VOF 유체는 특정 조건이 충족되면 특정 시간과 위치에서 자동으로 VOF 입자로 변환됩니다. 그런 다음 입자 모션은 Lagrangian 입자 모델을 사용하여 계산되고 입자는 유체에 다시 들어갈 때 VOF 표현으로 다시 변환됩니다.

    입자-FLOW-3D 2022R1에 대한 VOF
    입자에 대한 VOF

    Axial Pump Model

    FLOW-3D의 새로운 Axial Pump Model을 통해 사용자는 시뮬레이션에서 Axial Pump의 실제 효과를 구현할 수 있습니다. 펌프 동작과 관련하여 두 가지 옵션이 있습니다. 첫 번째 옵션은 유체가 지정된 속도로 이동하도록 펌프를 통한 체적 유량 또는 유속을 규정하는 것입니다. 이 옵션은 펌프에 작동 유량이 제공될 때 적합합니다. 두 번째 옵션은 펌프 성능 곡선을 기반으로 펌프 작동에 대한 보다 완전한 정의를 제공합니다. 이 경우 사용자는 펌프 성능 곡선의 선형 근사치를 정의하여 펌프를 통과하는 유량이 펌프 전체의 압력 강하에 따라 달라지도록 할 수 있습니다. 이 구성에서 펌프의 일반적인 동작은 다음과 같이 표시됩니다.

    축 펌프 설정
    GUI의 팬/임펠러 구성요소
    축 펌프 설정
    GUI의 축 펌프 구성 요소

    Droplet/Bubble Source Model | 액적/기포 소스 모델

    FLOW-3D 는 처음 개발된 이후 로 표면 장력 작용에 따라 진화하는 유체 모양을 시뮬레이션하기 위해 노즐 및 기타 오리피스 모양에서 분사되는 액적을 모델링하는 데 사용되었습니다. 그러나 기판에 대한 액적의 영향만 관심이 있기 때문에 노즐을 떠날 때 액적의 모양을 시뮬레이션할 필요가 없는 경우가 있습니다. 또한, 유체에서 기포의 이동을 모델링하는 것은 흥미로울 수 있지만 기포의 시작은 아닙니다. 새로운 액적/기포 소스 모델은 이와 같은 경우에 유용합니다.

    이 예에서 액적 소스는 원형 패턴으로 이동하면서 액적을 10m/s의 속도로 다공성 매체로 아래쪽으로 토출하여 링 모양 디자인을 만듭니다.

    방울/거품 설정
    사용자 인터페이스에서 액적/기포 소스 설정

    Simulation Templates

    새로운 시뮬레이션 템플릿은 자유 표면이 있는 하나의 유체에 대해 비압축성 흐름 또는 2개의 유체 압축성 시뮬레이션과 같은 주어진 모델링 프레임워크를 기반으로 중요한 매개변수를 미리 로드합니다. 새로운 시뮬레이션이 생성되면 FLOW-3D 에서 가장 일반적으로 모델링된 사례를 다루는 6개의 템플릿이 포함된 대화 상자가 사용자에게 표시됩니다 . ‘없음’ 옵션을 사용하면 고급 사용자가 특수 수치 설정을 적용할 수 있도록 빈 슬레이트로 시작할 수 있습니다. 템플릿을 사용하면 모델 설정 프로세스를 신속하게 처리하고 사용자가 실수를 하거나 매개변수 정의를 잊어버리는 것을 방지할 수 있습니다.

    시뮬레이션 템플릿
    GUI의 새로운 시뮬레이션 템플릿

    추가 솔버 기능

    추가 솔버 기능에는 비뉴턴 유체에 대한 Herschel-Bulkley 모델 및 분해되기 쉬운 유체 영역에 대한 질량 보존을 개선하기 위한 기체-공동 변환, 다중 이벤트 동작 및 이벤트 옵션 지원을 포함한 확장된 질량-운동량 소스 프로브 이벤트가 포함됩니다. 동반된 공기의 부피 분율과 용질 농도에 대한 것입니다.

    솔버 기능
    Herschel-Bulkley 모델
    솔버 기능
    활성 시뮬레이션 질량 운동량 소스 이벤트

    GUI 개선

    WSIWYN 설계 접근 방식을 사용한 간소화된 GUI 개선에는 재설계된 물리 및 초기 조건 대화 상자, 더 쉽고 빠르며 오류 없는 시뮬레이션 설정을 위해 재설계된 출력 및 지오메트리 위젯이 포함됩니다.

    초기 조건 위젯

    초기 조건 위젯은 초기 유체 및 기체 영역 설정을 개선하여 더 쉽고 빠르게 만듭니다. 새로운 디자인에서는 전역, 영역 및 포인터 개체가 별도의 탭에 배치되어 설정을 훨씬 더 명확하게 볼 수 있습니다.

    초기 조건
    초기 조건 – 지역
    초기 조건 - 정수압
    초기 조건 – 정수압
    초기 조건
    초기 조건 – 포인터

    출력 위젯

    재설계된 출력 위젯을 통해 사용자는 시뮬레이션 결과 파일에서 어떤 출력을 사용할 수 있는지 정확히 확인할 수 있으며, 하나의 간결한 보기에서 다시 시작 및 선택한 데이터 출력을 명확히 알 수 있습니다.

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    Fig. 5. The predicted shapes of initial breach (a) Rectangular (b) V-notch. Fig. 6. Dam breaching stages.

    Investigating the peak outflow through a spatial embankment dam breach

    공간적 제방댐 붕괴를 통한 최대 유출량 조사

    Mahmoud T.GhonimMagdy H.MowafyMohamed N.SalemAshrafJatwaryFaculty of Engineering, Zagazig University, Zagazig 44519, Egypt

    Abstract

    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.

    Keywords

    Spatial dam breach; FLOW-3D; Overtopping erosion; Computational fluid dynamics (CFD)

    1. Introduction

    There are many purposes for dam construction, such as protection from flood disasters, water storage, and power generationEmbankment 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 [1]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 [2]. Alhasan et al. [3] 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 [4] 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. [5] 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. [6] 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 [7].

    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 [8][9], but Y. Yang et al. [10] 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 [11].

    Zhang et al. [12] 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. [13] 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. [14] 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. [15] 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. [16] 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 [7] 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. [17] 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. [18] 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. [19] 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. [20] and Wu et al. [21] 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. [22] 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 [23]. 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 [24]. Therefore, 3D models are preferred. Larocque et al. [25] and Yang et al. [26] 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.

    2. Numerical simulation

    The current study for spatial dam breach is simulated by using (FLOW-3D) software [27], which is a powerful computational fluid dynamics (CFD) program.

    2.1. Geometric presentations

    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 continuity equation:(2)∂ui∂xi=0

    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. [28] 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 (AxAyAz) 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 [29]. 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 [30]. 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 [7] 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 [1], 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. [11], 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

    4. Conclusions

    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 [7] 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.

    References

    [1]V. SinghDam breach modeling technologySpringer Science & Business Media (1996)Google Scholar[2]Wahl TL. Prediction of embankment dam breach parameters: a literature review and needs assessment. 1998.Google Scholar[3]Z. Alhasan, J. Jandora, J. ŘíhaStudy of dam-break due to overtopping of four small dams in the Czech RepublicActa Universitatis Agriculturae et Silviculturae Mendelianae Brunensis, 63 (3) (2015), pp. 717-729 View PDFCrossRefView Record in ScopusGoogle Scholar[4]D. FreadBREACH, an erosion model for earthen dam failures: Hydrologic Research LaboratoryNOAA, National Weather Service (1988)Google Scholar[5]J. Říha, S. Kotaška, L. PetrulaDam Break Modeling in a Cascade of Small Earthen Dams: Case Study of the Čižina River in the Czech RepublicWater, 12 (8) (2020), p. 2309, 10.3390/w12082309 View PDFView Record in ScopusGoogle Scholar[6]E. Goodarzi, L. Teang Shui, M. ZiaeiDam overtopping risk using probabilistic concepts–Case study: The Meijaran DamIran Ain Shams Eng J, 4 (2) (2013), pp. 185-197ArticleDownload PDFView Record in ScopusGoogle Scholar[7]L. Schmocker, W.H. HagerPlane dike-breach due to overtopping: effects of sediment, dike height and dischargeJ Hydraul Res, 50 (6) (2012), pp. 576-586 View PDFCrossRefView Record in ScopusGoogle Scholar[8]J.S. Walder, R.M. Iverson, J.W. Godt, M. Logan, S.A. SolovitzControls on the breach geometry and flood hydrograph during overtopping of noncohesive earthen damsWater Resour Res, 51 (8) (2015), pp. 6701-6724View Record in ScopusGoogle Scholar[9]H. Wei, M. Yu, D. Wang, Y. LiOvertopping breaching of river levees constructed with cohesive sedimentsNat Hazards Earth Syst Sci, 16 (7) (2016), pp. 1541-1551 View PDFCrossRefView Record in ScopusGoogle Scholar[10]Y. Yang, S.-Y. Cao, K.-J. Yang, W.-P. LiYang K-j, Li W-p. Experimental study of breach process of landslide dams by overtopping and its initiation mechanismsJ Hydrodynamics, 27 (6) (2015), pp. 872-883ArticleDownload PDFCrossRefView Record in ScopusGoogle Scholar[11]G.G.D. Zhou, M. Zhou, M.S. Shrestha, D. Song, C.E. Choi, K.F.E. Cui, et al.Experimental investigation on the longitudinal evolution of landslide dam breaching and outburst floodsGeomorphology, 334 (2019), pp. 29-43ArticleDownload PDFView Record in ScopusGoogle Scholar[12]J. Zhang, Z.-x. Guo, S.-y. CaoYang F-g. Experimental study on scour and erosion of blocked damWater Sci Eng, 5 (2012), pp. 219-229ArticleDownload PDFView Record in ScopusGoogle Scholar[13]K. Höeg, A. Løvoll, K. VaskinnStability and breaching of embankment dams: Field tests on 6 m high damsInt J Hydropower Dams, 11 (2004), pp. 88-92View Record in ScopusGoogle Scholar[14]H. Hakimzadeh, V. Nourani, A.B. AminiGenetic programming simulation of dam breach hydrograph and peak outflow dischargeJ Hydrol Eng, 19 (4) (2014), pp. 757-768View Record in ScopusGoogle Scholar[15]A.R. Refaiy, N.M. AboulAtta, N.Y. Saad, D.A. El-MollaModeling the effect of downstream drain geometry on seepage through earth damsAin Shams Eng J, 12 (3) (2021), pp. 2511-2531ArticleDownload PDFView Record in ScopusGoogle Scholar[16]Y. Zhu, P.J. Visser, J.K. Vrijling, G. WangExperimental investigation on breaching of embankmentsScience China Technological Sci, 54 (1) (2011), pp. 148-155 View PDFCrossRefView Record in ScopusGoogle Scholar[17]M.-H. Yu, H.-Y. Wei, Y.-J. Liang, Y. ZhaoInvestigation of non-cohesive levee breach by overtopping flowJ Hydrodyn, 25 (4) (2013), pp. 572-579ArticleDownload PDFCrossRefView Record in ScopusGoogle Scholar[18]S. Wu, M. Yu, H. Wei, Y. Liang, J. ZengNon-symmetrical levee breaching processes in a channel bend due to overtoppingInt J Sedim Res, 33 (2) (2018), pp. 208-215ArticleDownload PDFView Record in ScopusGoogle Scholar[19]O. Saberi, G. ZenzNumerical investigation on 1D and 2D embankment dams failure due to overtopping flowInt J Hydraulic Engineering, 5 (2016), pp. 9-18View Record in ScopusGoogle Scholar[20]M. Guan, N.G. Wright, P.A. Sleigh2D Process-Based Morphodynamic Model for Flooding by Noncohesive Dyke BreachJ Hydraul Eng, 140 (7) (2014), p. 04014022, 10.1061/(ASCE)HY.1943-7900.0000861 View PDFView Record in ScopusGoogle Scholar[21]W. Wu, R. Marsooli, Z. HeDepth-Averaged Two-Dimensional Model of Unsteady Flow and Sediment Transport due to Noncohesive Embankment Break/BreachingJ Hydraul Eng, 138 (6) (2012), pp. 503-516View Record in ScopusGoogle Scholar[22]Z. Wang, D.S. BowlesThree-dimensional non-cohesive earthen dam breach model. Part 1: Theory and methodologyAdv Water Resour, 29 (10) (2006), pp. 1528-1545ArticleDownload PDFView Record in ScopusGoogle Scholar[23]Říha J, Duchan D, Zachoval Z, Erpicum S, Archambeau P, Pirotton M, et al. Performance of a shallow-water model for simulating flow over trapezoidal broad-crested weirs. J Hydrology Hydromechanics. 2019;67:322-8.Google Scholar[24]C.B. VreugdenhilNumerical methods for shallow-water flowSpringer Science & Business Media (1994)Google Scholar[25]L.A. Larocque, J. Imran, M.H. Chaudhry3D numerical simulation of partial breach dam-break flow using the LES and k–∊ turbulence modelsJ Hydraul Res, 51 (2) (2013), pp. 145-157 View PDFCrossRefView Record in ScopusGoogle Scholar[26]C. Yang, B. Lin, C. Jiang, Y. LiuPredicting near-field dam-break flow and impact force using a 3D modelJ Hydraul Res, 48 (6) (2010), pp. 784-792 View PDFCrossRefView Record in ScopusGoogle Scholar[27]FLOW-3D. Version 11.1.1 Flow Science, Inc., Santa Fe, NM. https://wwwflow3dcom.Google Scholar[28]C.W. Hirt, B.D. NicholsVolume of fluid (VOF) method for the dynamics of free boundariesJ Comput Phys, 39 (1) (1981), pp. 201-225ArticleDownload PDFGoogle Scholar[29]S.V. PatankarNumerical heat transfer and fluid flow, Hemisphere PublCorp, New York, 58 (1980), p. 288View Record in ScopusGoogle Scholar[30]M. Alemi, R. MaiaNumerical simulation of the flow and local scour process around single and complex bridge piersInt J Civil Eng, 16 (5) (2018), pp. 475-487 View PDFCrossRefView Record in ScopusGoogle Scholar

    Figure 8: Instantaneous flow structures extracted using the Q-criterion (Qcriterion=1200) and colored by the magnitude of flow velocity.

    Hybrid modeling on 3D hydraulic features of a step-pool unit

    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 (chendinorthwest@163.com) and Mengzhen Xu (mzxu@mail.tsinghua.edu.cn)

    Abstract

    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.

    Figure 1: Workflow of the hybrid modeling. SfM-MVS refers to the technology of Structure from Motion with Multi View Stereo. DSM is short for digital surface model. RNG-VOF is short for Renormalized Group (RNG) k-ε turbulence model coupled with Volume of Fluid method.
    Figure 1: Workflow of the hybrid modeling. SfM-MVS refers to the technology of Structure from Motion with Multi View Stereo. DSM is short for digital surface model. RNG-VOF is short for Renormalized Group (RNG) k-ε turbulence model coupled with Volume of Fluid method.
    Figure 2: Flume experiment settings in Zhang et al., (2020): (a) the artificially built-up step-pool model using natural stones, with stone number labelled; (b) the unsteady hydrograph of the run of CIFR (continually-increasing-flow-rate) T2 used in this study.
    Figure 2: Flume experiment settings in Zhang et al., (2020): (a) the artificially built-up step-pool model using natural stones, with stone number labelled; (b) the unsteady hydrograph of the run of CIFR (continually-increasing-flow-rate) T2 used in this study.
    Figure 3: Setup of the CFD model: (a) three-dimensional digital surface model (DSM) of the step-pool unit by structure from motion with multi view stereo (SfM-MVS) method as the input to the 3D computational fluid dynamics (CFD) modeling; (b) extruded bed 160 surface model connected to the extra downstream component (in purple blue) and rectangular columns to fill leaks (in green), with the boundary conditions shown on mesh planes; (c) recognized geometry with mesh grids of two mesh blocks shown where MS is short for mesh size; (d) sampling volumes to capture the flow forces acting on each step stone at X, Y, and Z directions; and (e) an example for the simulated 3D flow over the step-pool unit colored by velocity magnitude at the discharge of 49.9 L/s. The abbreviations for boundary conditions in (b) are: V for specified velocity; C for continuative; P for specific pressure; and W for wall 165 condition. The contraction section in Figure (e) refers to the edge between the jet and jump at water surface.
    Figure 3: Setup of the CFD model: (a) three-dimensional digital surface model (DSM) of the step-pool unit by structure from motion with multi view stereo (SfM-MVS) method as the input to the 3D computational fluid dynamics (CFD) modeling; (b) extruded bed 160 surface model connected to the extra downstream component (in purple blue) and rectangular columns to fill leaks (in green), with the boundary conditions shown on mesh planes; (c) recognized geometry with mesh grids of two mesh blocks shown where MS is short for mesh size; (d) sampling volumes to capture the flow forces acting on each step stone at X, Y, and Z directions; and (e) an example for the simulated 3D flow over the step-pool unit colored by velocity magnitude at the discharge of 49.9 L/s. The abbreviations for boundary conditions in (b) are: V for specified velocity; C for continuative; P for specific pressure; and W for wall 165 condition. The contraction section in Figure (e) refers to the edge between the jet and jump at water surface.
    Figure 4: Distribution of time-averaged velocity magnitude (VM_mean) and vectors in three longitudinal sections. The section at Y = 0 cm goes across the keystone while the other two (Y = -18 and 13.5 cm) are located at the step stones beside the keystone with 265 lower top elevations. Q refers to the discharge at the inlet of the computational domain. The spacing for X, Y, and Z axes are all 10 cm in the plots.
    Figure 4: Distribution of time-averaged velocity magnitude (VM_mean) and vectors in three longitudinal sections. The section at Y = 0 cm goes across the keystone while the other two (Y = -18 and 13.5 cm) are located at the step stones beside the keystone with lower top elevations. Q refers to the discharge at the inlet of the computational domain. The spacing for X, Y, and Z axes are all 10 cm in the plots.
    Figure 5: Distribution of time-averaged flow velocity at five cross sections which are set according to the reference section (x0). The reference cross section x0 is located at the downstream end of the keystone (KS). The five sections are located at 18 cm and 6 cm upstream of the reference section (x0-18 and x0-6), and 2 cm, 15 cm and 40 cm downstream of the reference section (x0+2, x0+15, x0+40). The spacing for X, Y, and Z axes are all 10 cm in the plots.
    Figure 5: Distribution of time-averaged flow velocity at five cross sections which are set according to the reference section (x0). The reference cross section x0 is located at the downstream end of the keystone (KS). The five sections are located at 18 cm and 6 cm upstream of the reference section (x0-18 and x0-6), and 2 cm, 15 cm and 40 cm downstream of the reference section (x0+2, x0+15, x0+40). The spacing for X, Y, and Z axes are all 10 cm in the plots.
    Figure 6: Distribution of the time-averaged turbulence kinetic energy (TKE) at the five cross sections same with Figure 3.
    Figure 6: Distribution of the time-averaged turbulence kinetic energy (TKE) at the five cross sections same with Figure 3.
    Figure 7: Boxplots for the distributions of the mass-averaged flow kinetic energy (KE, panels a-f), turbulence kinetic energy (TKE, panels g-l), and turbulent dissipation (εT, panels m-r) in the pool for all the six tested discharges (the plots at the same discharge are in the same row). The mass-averaged values were calculated every 2 cm in the streamwise direction. The flow direction is from left to right in all the plots. The general locations of the contraction section for all the flow rates are marked by the dashed lines, except for Q = 5 L/s when the jump is located too close to the step. The longitudinal distance taken up by negative slope in the pool for the inspected range is shown by shaded area in each plot.
    Figure 7: Boxplots for the distributions of the mass-averaged flow kinetic energy (KE, panels a-f), turbulence kinetic energy (TKE, panels g-l), and turbulent dissipation (εT, panels m-r) in the pool for all the six tested discharges (the plots at the same discharge are in the same row). The mass-averaged values were calculated every 2 cm in the streamwise direction. The flow direction is from left to right in all the plots. The general locations of the contraction section for all the flow rates are marked by the dashed lines, except for Q = 5 L/s when the jump is located too close to the step. The longitudinal distance taken up by negative slope in the pool for the inspected range is shown by shaded area in each plot.
    Figure 8: Instantaneous flow structures extracted using the Q-criterion (Qcriterion=1200) and colored by the magnitude of flow velocity.
    Figure 8: Instantaneous flow structures extracted using the Q-criterion (Qcriterion=1200) and colored by the magnitude of flow velocity.
    Figure 9: Time-averaged dynamic pressure (DP_mean) on the bed surface in the step-pool model under the two highest discharges, with the step numbers marked. The negative values in the plots result from the setting of standard atmospheric pressure = 0 Pa, whose absolute value is 1.013×105 Pa.
    Figure 9: Time-averaged dynamic pressure (DP_mean) on the bed surface in the step-pool model under the two highest discharges, with the step numbers marked. The negative values in the plots result from the setting of standard atmospheric pressure = 0 Pa, whose absolute value is 1.013×105 Pa.
    Figure 10: Time-averaged shear stress (SS_mean) on bed surface in the step-pool model, with the step numbers marked. The standard atmospheric pressure is set as 0 Pa.
    Figure 10: Time-averaged shear stress (SS_mean) on bed surface in the step-pool model, with the step numbers marked. The standard atmospheric pressure is set as 0 Pa.
    Figure 11: Variation of fluid force components and magnitude of resultant flow force acting on step stones with flow rate. The stone 4 is the keystone. Stone numbers are consistent with those in Fig. 9-10. The upper limit of the sampling volumes for flow force calculation is higher than water surface while the lower limit is set at 3 cm lower than the keystone crest.
    Figure 11: Variation of fluid force components and magnitude of resultant flow force acting on step stones with flow rate. The stone 4 is the keystone. Stone numbers are consistent with those in Fig. 9-10. The upper limit of the sampling volumes for flow force calculation is higher than water surface while the lower limit is set at 3 cm lower than the keystone crest.
    Figure 12: Variation of drag (CD) and lift (CL) coefficient of the step stones along with flow rate. Stone numbers are consistent with those in Fig. 8-9. KS is short for keystone. The negative values of CD correspond to the drag forces towards the upstream while the negative values of CL correspond to lift forces pointing downwards.
    Figure 12: Variation of drag (CD) and lift (CL) coefficient of the step stones along with flow rate. Stone numbers are consistent with those in Fig. 8-9. KS is short for keystone. The negative values of CD correspond to the drag forces towards the upstream while the negative values of CL correspond to lift forces pointing downwards.
    Figure 13: Longitudinal distributions of section-averaged and -integral turbulent kinetic energy (TKE) for the jump and wake vortexes at the largest three discharges. The flow direction is from left to right in all the plots. The general locations of the contraction sections under the three flow rates are marked by dashed lines in figures (d) to (f).
    Figure 13: Longitudinal distributions of section-averaged and -integral turbulent kinetic energy (TKE) for the jump and wake vortexes at the largest three discharges. The flow direction is from left to right in all the plots. The general locations of the contraction sections under the three flow rates are marked by dashed lines in figures (d) to (f).
    Figure A1: Water surface profiles of the simulations with different mesh sizes at the discharge of 43.6 L/s at the longitudinal sections at: (a) Y = 24.5 cm (left boundary); (b) Y = 0.3 cm (middle section); (c) Y = -24.5 cm (right boundary). MS is short for mesh size. The flow direction is from left to right in each plot.
    Figure A1: Water surface profiles of the simulations with different mesh sizes at the discharge of 43.6 L/s at the longitudinal sections at: (a) Y = 24.5 cm (left boundary); (b) Y = 0.3 cm (middle section); (c) Y = -24.5 cm (right boundary). MS is short for mesh size. The flow direction is from left to right in each plot.
    Figure A2: Contours of velocity magnitude in the longitudinal section at Y = 0 cm at different mesh sizes (MSs) under the flow condition with the discharge of 43.6 L/s: (a) 0.50 cm; (b) 0.375 cm; (c) 0.30 cm; (d) 0.27 cm; (e) 0.25 cm; (f) 0.24 cm. The flow direction is from left to right.
    Figure A2: Contours of velocity magnitude in the longitudinal section at Y = 0 cm at different mesh sizes (MSs) under the flow condition with the discharge of 43.6 L/s: (a) 0.50 cm; (b) 0.375 cm; (c) 0.30 cm; (d) 0.27 cm; (e) 0.25 cm; (f) 0.24 cm. The flow direction is from left to right.
    Figure A3: Measurements of water surfaces (orange lines) used in model verification: (a) water surface profiles from both sides of the flume; (b) upstream edge of the jump regime from top view. KS refers to keystone in figure (b).
    Figure A3: Measurements of water surfaces (orange lines) used in model verification: (a) water surface profiles from both sides of the flume; (b) upstream edge of the jump regime from top view. KS refers to keystone in figure (b).
    Figure A15. Figure (a) shows the locations of the cross sections and target coarse grains at Q = 49.9 L/s. Figures (b) to (e) show the distribution of velocity magnitude (VM_mean) in the four chosen cross sections: (a) x0+8.0; (b) x0+14.0; (c) x0+21.5; (d) x0+42.5. G1 to G6 refer to 6 protruding grains in the micro-bedforms in the pool.
    Figure A15. Figure (a) shows the locations of the cross sections and target coarse grains at Q = 49.9 L/s. Figures (b) to (e) show the distribution of velocity magnitude (VM_mean) in the four chosen cross sections: (a) x0+8.0; (b) x0+14.0; (c) x0+21.5; (d) x0+42.5. G1 to G6 refer to 6 protruding grains in the micro-bedforms in the pool.
    Figure A16. The distribution of turbulent kinetic energy (TKE) in the same cross sections as in figure S15: (a) x0+8.0; (b) x0+14.0; (c) x0+21.5; (d) x0+42.5.
    Figure A16. The distribution of turbulent kinetic energy (TKE) in the same cross sections as in figure S15: (a) x0+8.0; (b) x0+14.0; (c) x0+21.5; (d) x0+42.5.

    References

    720 Aberle, J. and Smart, G. M: The influence of roughness structure on flow resistance on steep slopes, J. Hydraul. Res., 41(3),
    259-269, https://doi.org/10.1080/00221680309499971, 2003.
    Abrahams, A. D., Li, G., and Atkinson, J. F.: Step-pool streams: Adjustment to maximum flow resistance. Water Resour. Res.,
    31(10), 2593-2602, https://doi.org/10.1029/95WR01957, 1995.
    Adrian, R. J.: Twenty years of particle image velocimetry. Exp. Fluids, 39(2), 159-169, https://doi.org/10.1007/s00348-005-
    725 0991-7 2005.
    Chanson, H.: Hydraulic design of stepped spillways and downstream energy dissipators. Dam Eng., 11(4), 205-242, 2001.
    Chartrand, S. M., Jellinek, M., Whiting, P. J., and Stamm, J.: Geometric scaling of step-pools in mountain streams:
    Observations and implications, Geomorphology, 129(1-2), 141-151, https://doi.org/10.1016/j.geomorph.2011.01.020,
    2011.
    730 Chen, Y., DiBiase, R. A., McCarroll, N., and Liu, X.: Quantifying flow resistance in mountain streams using computational
    fluid dynamics modeling over structure‐from‐motion photogrammetry‐derived microtopography, Earth Surf. Proc.
    Land., 44(10), 1973-1987, https://doi.org/10.1002/esp.4624, 2019.
    Church, M. and Zimmermann, A.: Form and stability of step‐pool channels: Research progress, Water Resour. Res., 43(3),
    W03415, https://doi.org/10.1029/2006WR005037, 2007.
    735 Cignoni, P., Callieri, M., Corsini, M., Dellepiane, M., Ganovelli, F., and Ranzuglia, G.: Meshlab: an open-source mesh
    processing tool, in: Eurographics Italian chapter conference, Salerno, Italy, 2-4 July 2008, 129-136, 2008.

    Comiti, F., Andreoli, A., and Lenzi, M. A.: Morphological effects of local scouring in step-pool streams, Earth Surf. Proc.
    Land., 30(12), 1567-1581, https://doi.org/10.1002/esp.1217, 2005.
    Comiti, F., Cadol, D., and Wohl, E.: Flow regimes, bed morphology, and flow resistance in self‐formed step-pool
    740 channels, Water Resour. Res., 45(4), 546-550, https://doi.org/10.1029/2008WR007259, 2009.
    Dudunake, T., Tonina, D., Reeder, W. J., and Monsalve, A.: Local and reach‐scale hyporheic flow response from boulder ‐
    induced geomorphic changes, Water Resour. Res., 56, e2020WR027719, https://doi.org/10.1029/2020WR027719, 2020.
    Flow Science.: Flow-3D Version 11.2 User Manual, Flow Science, Inc., Los Alamos, 2016.
    Gibson, S., Heath, R., Abraham, D., and Schoellhamer, D.: Visualization and analysis of temporal trends of sand infiltration
    745 into a gravel bed, Water Resour. Res., 47(12), W12601, https://doi.org/10.1029/2011WR010486, 2011.
    Hassan, M. A., Tonina, D., Beckie, R. D., and Kinnear, M.: The effects of discharge and slope on hyporheic flow in step‐pool
    morphologies, Hydrol. Process., 29(3), 419-433, https://doi.org/10.1002/hyp.10155, 2015.
    Hirt, C. W. and Nichols, B. D.: Volume of Fluid (VOF) method for the dynamics of free boundaries. J. Comput. Phys., 39,
    201-225, https://doi.org/10.1016/0021-9991(81)90145-5, 1981.
    750 Javernick L., Brasington J., and Caruso B.: Modeling the topography of shallow braided rivers using structure-from-motion
    photogrammetry, Geomorphology, 213(4), 166-182, https://doi.org/10.1016/j.geomorph.2014.01.006, 2014.
    Lai, Y. G., Smith, D. L., Bandrowski, D. J., Xu, Y., Woodley, C. M., and Schnell, K.: Development of a CFD model and
    procedure for flows through in-stream structures, J. Appl. Water Eng. Res., 1-15,
    https://doi.org/10.1080/23249676.2021.1964388, 2021.
    755 Lenzi, M. A.: Step-pool evolution in the Rio Cordon, northeastern Italy, Earth Surf. Proc. Land., 26(9), 991-1008,
    https://doi.org/10.1002/esp.239, 2001.
    Lenzi, M. A.: Stream bed stabilization using boulder check dams that mimic step-pool morphology features in Northern
    Italy, Geomorphology, 45(3-4), 243-260, https://doi.org/10.1016/S0169-555X(01)00157-X, 2002.
    Lenzi, M. A., Marion, A., and Comiti, F.: Local scouring at grade‐control structures in alluvial mountain rivers, Water Resour.
    760 Res., 39(7), 1176, https://doi:10.1029/2002WR001815, 2003.
    Li, W., Wang Z., Li, Z., Zhang, C., and Lv, L.: Study on hydraulic characteristics of step-pool system, Adv. Water Sci., 25(3),
    374-382, https://doi.org/10.14042/j.cnki.32.1309.2014.03.012, 2014. (In Chinese with English abstract)
    Maas, H. G., Gruen, A., and Papantoniou, D.: Particle tracking velocimetry in three-dimensional flows, Exp. Fluids, 15(2),
    133-146. https://doi.org/10.1007/BF00223406, 1993.

    765 Montgomery, D. R. and Buffington, J. M.: Channel-reach morphology in mountain drainage basins, Geol. Soc. Am. Bul., 109(5), 596-611, https://doi.org/10.1130/0016-7606(1997)109<0596:CRMIMD>2.3.CO;2, 1997. Morgan J. A., Brogan D. J., and Nelson P. A.: Application of structure-from-motion photogrammetry in laboratory flumes, Geomorphology, 276(1), 125-143, https://doi.org/10.1016/j.geomorph.2016.10.021, 2017. Recking, A., Leduc, P., Liébault, F., and Church, M.: A field investigation of the influence of sediment supply on step-pool 770 morphology and stability. Geomorphology, 139, 53-66, https://doi.org/10.1016/j.geomorph.2011.09.024, 2012. Roth, M. S., Jähnel, C., Stamm, J., and Schneider, L. K.: Turbulent eddy identification of a meander and vertical-slot fishways in numerical models applying the IPOS-framework, J. Ecohydraulics, 1-20, https://doi.org/10.1080/24705357.2020.1869916, 2020. Saletti, M. and Hassan, M. A.: Width variations control the development of grain structuring in steep step‐pool dominated 775 streams: insight from flume experiments, Earth Surf. Proc. Land., 45(6), 1430-1440, https://doi.org/10.1002/esp.4815, 2020. Smith, D. P., Kortman, S. R., Caudillo, A. M., Kwan‐Davis, R. L., Wandke, J. J., Klein, J. W., Gennaro, M. C. S., Bogdan, M. A., and Vannerus, P. A.: Controls on large boulder mobility in an ‘auto-naturalized’ constructed step-pool river: San Clemente Reroute and Dam Removal Project, Carmel River, California, USA, Earth Surf. Proc. Land., 45(9), 1990-2003, 780 https://doi.org/10.1002/esp.4860, 2020. Thappeta, S. K., Bhallamudi, S. M., Fiener, P., and Narasimhan, B.: Resistance in Steep Open Channels due to Randomly Distributed Macroroughness Elements at Large Froude Numbers, J. Hydraul. Eng., 22(12), 04017052, https://doi.org/10.1061/(ASCE)HE.1943-5584.0001587, 2017. Thappeta, S. K., Bhallamudi, S. M., Chandra, V., Fiener, P., and Baki, A. B. M.: Energy loss in steep open channels with step785 pools, Water, 13(1), 72, https://doi.org/10.3390/w13010072, 2021. Turowski, J. M., Yager, E. M., Badoux, A., Rickenmann, D., and Molnar, P.: The impact of exceptional events on erosion, bedload transport and channel stability in a step-pool channel, Earth Surf. Proc. Land., 34(12), 1661-1673, https://doi.org/10.1002/esp.1855, 2009. Vallé, B. L. and Pasternack, G. B.: Air concentrations of submerged and unsubmerged hydraulic jumps in a bedrock step‐pool 790 channel, J. Geophys. Res.-Earth, 111(F3), F03016. https://doi:10.1029/2004JF000140, 2006. Waldon, M. G.: Estimation of average stream velocity, J. Hydraul. Eng., 130(11), 1119-1122. https://doi.org/10.1061/(ASCE)0733-9429(2004)130:11(1119), 2004. Wang, Z., Melching, C., Duan, X., and Yu, G.: Ecological and hydraulic studies of step-pool systems, J. Hydraul. Eng., 135(9), 705-717, https://doi.org/10.1061/(ASCE)0733-9429(2009)135:9(705), 2009

    795 Wang, Z., Qi, L., and Wang, X.: A prototype experiment of debris flow control with energy dissipation structures, Nat. Hazards, 60(3), 971-989, https://doi.org/10.1007/s11069-011-9878-5, 2012. Weichert, R. B.: Bed Morphology and Stability in Steep Open Channels, Ph.D. Dissertation, No. 16316. ETH Zurich, Switzerland, 247pp., 2005. Wilcox, A. C., Wohl, E. E., Comiti, F., and Mao, L.: Hydraulics, morphology, and energy dissipation in an alpine step‐pool 800 channel, Water Resour. Res., 47(7), W07514, https://doi.org/10.1029/2010WR010192, 2011. Wohl, E. E. and Thompson, D. M.: Velocity characteristics along a small step–pool channel. Earth Surf. Proc. Land., 25(4), 353-367, https://doi.org/10.1002/(SICI)1096-9837(200004)25:4<353::AID-ESP59>3.0.CO;2-5, 2000. Wu, S. and Rajaratnam, N.: Impinging jet and surface flow regimes at drop. J. Hydraul. Res., 36(1), 69-74, https://doi.org/10.1080/00221689809498378, 1998. 805 Xu, Y. and Liu, X.: 3D computational modeling of stream flow resistance due to large woody debris, in: Proceedings of the 8th International Conference on Fluvial Hydraulics, St. Louis, USA, 11-14, Jul, 2346-2353, 2016. Xu, Y. and Liu, X.: Effects of different in-stream structure representations in computational fluid dynamics models—Taking engineered log jams (ELJ) as an example, Water, 9(2), 110, https://doi.org/10.3390/w9020110, 2017. Zeng, Y. X., Ismail, H., and Liu, X.: Flow Decomposition Method Based on Computational Fluid Dynamics for Rock Weir 810 Head-Discharge Relationship. J. Irrig. Drain. Eng., 147(8), 04021030, https://doi.org/10.1061/(ASCE)IR.1943- 4774.0001584, 2021. Zhang, C., Wang, Z., and Li, Z.: A physically-based model of individual step-pool stability in mountain streams, in: Proceedings of the 13th International Symposium on River Sedimentation, Stuttgart, Germany, 801-809, 2016. Zhang, C., Xu, M., Hassan, M. A., Chartrand, S. M., and Wang, Z.: Experimental study on the stability and failure of individual 815 step-pool, Geomorphology, 311, 51-62, https://doi.org/10.1016/j.geomorph.2018.03.023, 2018. Zhang, C., Xu, M., Hassan, M. A., Chartrand, S. M., Wang, Z., and Ma, Z.: Experiment on morphological and hydraulic adjustments of step‐pool unit to flow increase, Earth Surf. Proc. Land., 45(2), 280-294, https://doi.org/10.1002/esp.4722, 2020. Zimmermann A., E.: Flow resistance in steep streams: An experimental study, Water Resour. Res., 46, W09536, 820 https://doi.org/10.1029/2009WR007913, 2010. Zimmermann A. E., Salleti M., Zhang C., Hassan M. A.: Step-pool Channel Features, in: Treatise on Geomorphology (2nd Edition), vol. 9, Fluvial Geomorphology, edited by: Shroder, J. (Editor in Chief), Wohl, E. (Ed.), Elsevier, Amsterdam, Netherlands, https://doi.org/10.1016/B978-0-12-818234-5.00004-3, 2020.

    Figure 1 Location map of barrier lakes, Sichuan-Tibet region, China

    Barrier Lake의 홍수 침수 진행 및 평가지역 생태 시공간 반응 사례 연구 (쓰촨-티베트 지역)

    Flood Inundation Evolution of Barrier Lake and Evaluation of Regional Ecological Spatiotemporal Response — A Case Study of Sichuan-Tibet Region

    Abstract

    중국 쓰촨-티베트 지역은 댐 호수의 발생과 붕괴를 동반한 지진 재해가 빈번한 지역이었습니다. 댐 호수의 붕괴는 하류 직원의 생명과 재산 안전을 심각하게 위협합니다.

    동시에 국내외 학자들은 주변의 댐 호수에 대해 우려하고 있으며 호수에 대한 생태 연구는 거의 없으며 댐 호수가 생태에 미치는 영향은 우리 호수 건설 프로젝트에서 매우 중요한 계몽 의의를 가지고 있습니다.

    이 기사의 목적은 방벽호의 댐 붕괴 위험을 과학적으로 예측하고 생태 환경에 대한 영향을 조사하며 통제 조치를 제시하는 것입니다. 본 논문은 쓰촨-티베트 지역의 Diexihaizi, Tangjiashan 댐호, Hongshihe 댐의 4대 댐 호수 사건을 기반으로 원격 감지 이미지에서 수역을 추출하고 HEC-RAS 모델을 사용하여 위험이 있는지 여부를 결정합니다.

    댐 파손 여부 및 댐의 경로 예측; InVEST 모델을 이용하여 1990년부터 2020년까지 가장 작은 행정 구역(군/구)이 위치한 서식지를 평가 및 분석하고, 홍수 침수 결과를 기반으로 평가합니다. 결과는 공학적 처리 후 안정적인 댐 호수(Diexi Haizi)가 서식지 품질 지수에 안정화 효과가 있음을 보여줍니다.

    댐 호수의 형성은 인근 토지 이용 유형과 지역 경관 생태 패턴을 변화 시켰습니다. 서식지 품질 지수는 사이 호수 주변 1km 지역에서 약간 감소하지만 3km 지역과 5km 지역에서 서식지 품질이 향상됩니다. 인공 홍수 방류 및 장벽 호수의 공학적 보강이 필요합니다.

    이 논문에서 인간의 통제가 강한 지역은 다른 지역의 서식지 질 지수보다 더 잘 회복될 것입니다.

    The Sichuan-Tibet region of China has always been an area with frequent earthquake disasters, accompanied by the occurrence and collapse of dammed lakes. The collapse of dammed lakes seriously threatens the lives and property safety of downstream personnel.

    At the same time, domestic and foreign scholars are concerned about the surrounding dammed lake there are few ecological studies on the lake, and the impact of the dammed lake on the ecology has very important enlightenment significance for our lake construction project. It is the purpose of this article to scientifically predict the risk of dam break in a barrier lake, explore its impact on the ecological environment and put forward control measures.

    Based on the four major dammed lake events of Diexihaizi, Tangjiashan dammed lake, and Hongshihe dammed lake in the Sichuan-Tibet area, this paper extracts water bodies from remote sensing images and uses the HEC-RAS model to determine whether there is a risk of the dam break and whether Forecast the route of the dam; and use the InVEST model to evaluate and analyze the habitat of the smallest administrative district (county/district) where it is located from 1990 to 2020 and make an evaluation based on the results of flood inundation.

    The results show that the stable dammed lake (Diexi Haizi) after engineering treatment has a stabilizing effect on the habitat quality index. The formation of the dammed lake has changed the nearby land-use types and the regional landscape ecological pattern.

    The habitat quality index will decrease slightly in the 1 km area around Sai Lake, but the habitat quality will increase in the 3 km area and the 5 km area. Artificial flood discharge and engineering reinforcement of barrier lakes are necessary. In this paper, the areas with strong human control will recover better than other regions’ habitat quality index.

    Fengshan Jiang (  florachaing@mail.ynu.edu.cn )
    Yunnan University https://orcid.org/0000-0001-6231-6180
    Xiaoai Dai
    Chengdu University of Technology https://orcid.org/0000-0003-1342-6417
    Zhiqiang Xie
    Yunnan University
    Tong Xu
    Yunnan University
    Siqiao Yin
    Yunnan University
    Ge Qu
    Chengdu University of Technology
    Shouquan Yang
    Yunnan University
    Yangbin Zhang
    Yunnan University
    Zhibing Yang
    Yunnan University
    Jiarui Xu
    Yunnan University
    Zhiqun Hou
    Kunming institute of surveying and mapping

    Keywords

    dammed lake, regional ecology, flood simulation, habitat quality

    Figure 1 Location map of barrier lakes, Sichuan-Tibet region, China
    Figure 1 Location map of barrier lakes, Sichuan-Tibet region, China
    Figure 8 Habitat quality changes in Maoxian County
    Figure 8 Habitat quality changes in Maoxian County
    Figure 9 Habitat quality changes in Beichuan County
    Figure 9 Habitat quality changes in Beichuan County
    Figure 10 Habitat quality change map of Qingchuan County
    Figure 10 Habitat quality change map of Qingchuan County

    References

    1. Chaoying Hu H S, Tianming Zhang. 2017. Environmental impact assessment of barrier lake treatment project based on
      ecological footprint[J]. People’s Yangtze River, 48: 30-32
    2. Dai F C, Lee C F, Deng J H, et al. 2004. The 1786 earthquake-triggered landslide dam and subsequent dam-break flood on
      the Dadu River, southwestern China[J]. Geomorphology, 65.
    3. Dongjing Chen Z X 2002. Research on Ecological Security Evaluation of Inland River Basin in Northwest China——A Case
      Study of Zhangye Region in the Middle Reaches of Heihe River Basin[J]. Arid zone geography: 219-224
    4. Dongsheng Chang L Z, Yao Xu, Runqiu Huang. 2009. Risk Assessment of Overtopping Dam Burst in Hongshi River Barrier
      Lake[J]. Journal of Engineering Geology, 17: 50-55
    5. Fan X, Yunus Ali P, Jansen John D, et al. 2019. Comment on ‘Gigantic rockslides induced by fluvial incision in the Diexi
      area along the eastern margin of the Tibetan Plateau’ by Zhao et al. (2019) Geomorphology 338, 27–42[J].
      Geomorphology.
    6. Feng Yu X L, Hong Wang, Hongjing Yu. 2006. Land Use Change and Ecological Security Evaluation in Huangfuchuan
      Watershed[J]. Acta Geographica Sinica: 645-653.
    7. Hafiyyan Q, Adityawan M B, Harlan D, et al. 2021. Comparison of Taylor Galerkin and FTCS models for dam-break
      simulation[J]. IOP Conference Series: Earth and Environmental Science, 737.
    8. Haiwen Li X B 2020. Comprehensive Evaluation of the Restoration Status of Damaged Ecological Space along the
      Plateau Fragile Area of the Sichuan-Tibet Railway[J]. Journal of Railway Science and Engineering, 17: 2412-2422.
    9. Haohao Li X R, Huabin Yang. 2008. Rescue construction and thinking of Hongshihe dammed lake in Qingchuan
      County[J]. Water Conservancy and Hydropower Technology (Chinese and English): 50-51+62
    10. Hejun Chai, Runqiu Huang, Hanchao Liu I O E G, Chengdu University of Technology 1997. Analysis and Evaluation of the
      Dangerous Degree of Landslide Blocking the River[J]. Chinese Journal of Geological Hazard and Control: 2-8+16
    11. Hong Wang Y L, Lili Song, Yun Chen. 2020. Comparison of characteristics of thunderstorm and gale activity and
      environmental factors in Sichuan-Tibet area[J]. Journal of Applied Meteorology, 31: 435-446.
    1. Hongyan X, Xu H, Jiang H, et al. 2020. Potential pollen evidence for the 1933 M 7.5 Diexi earthquake and implications for
      post-seismic landscape recovery[J]. Environmental Research Letters, 15.
    2. Hui Xu J C, Zhijiu Cui, Pei Guo. 2019. Analysis of Grain Size Characteristics of Sediment in Dammed Lake——Taking Diexi
      Ancient Dammed Lake in the Upper Minjiang River as an Example[J]. Acta Sedimentologica Sinica, 37: 51-61
    3. Jian Yang B P, Min Zhao. 2014. Research on Ecological Restoration Technology in Wenchuan Earthquake-Stricken Area
      ——Taking Tangjiashan Barrier Lake Area as an Example[J]. Sichuan Building Science Research, 40: 164-167.
    4. Jian Yang B P 2017. Evaluation of Ecological Quality of Tangjiashan Dammed Lake Region in Beichuan County[J].
      People’s Yangtze River, 48: 27-32
    5. Jianfeng Chen Y W, Yang Li. 2006. Application of HEC-RAS model in flood simulation[J]. Northeast Water Resources and
      Hydropower: 12-13+42+71.
    6. Jiankang Liu Z C, Tao Yu. 2016. Dam failure risk and its impact of Hongshiyan dammed lake in Ludian, Yunnan[J].
      Journal of Mountain Science, 34: 208-215
    7. Jianrong Fan B T, Genwei Cheng, Heping Tao, Jianqiang Zhang,Dong Yan, Fenghuan Su. 2008. Information extraction of
      dammed bodies induced by the May 12 Wenchuan earthquake based on multi-source remote sensing data[J]. Journal of
      Mountain Science: 257-262.
    8. Jinghuan Tian K Z, Meng Chen, Fuxin Chai. 2012. Research on the application of HEC-RAS model in flood risk analysis
      and assessment[J]. Hydropower Energy Science, 30: 23-25
    9. Juan He X W 2015. Dam-break flood analysis based on HEC-RAS and HEC-GeoRAS[J]. Journal of Water Resources and
      Water Transport Engineering: 112-116
    10. Junwei Gan L Y, Jinjun Li. 2017. Research on the Influencing Factors of Sichuan-Tibet Tourism Industry Competitiveness
      Based on DEMATEL[J]. Arid Land Resources and Environment, 31: 197-202
    11. Lansheng Wang L Y, Xiaoqun Wang, Liping Duan 2005. Discovery of the ancient dammed lake in Diexi, Minjiang River[J].
      Journal of Chengdu University of Technology (Natural Science Edition): 1-11
    12. Ma S, Zhu J, Ya. H. Year. Construction of Risk Assessment System of Dam-break in Barrier Lake Based on Collaborative
      Workflow: 9.
    13. Ming Zeng Y C, Bingyu Zou. 2019. Discussion on the Method of Forecasting the Flood Evolution of Barrier Lake Burst——
      Taking “11·3” Jinsha River Baige Barrier Lake as an Example[J]. Water Resources and Hydropower Express, 40: 11-14
    14. Ouyang C, An H, Zhou S, et al. 2019. Insights from the failure and dynamic characteristics of two sequential landslides at
      Baige village along the Jinsha River, China Landslides[J]. 16.
    15. Peng M, Zhang L M 2012. Analysis of human risks due to dam-break floods—part 1: a new model based on Bayesian
      networks[J]. Natural Hazards, 64.
    16. Qianfeng Li Y L, Gang Liu, Zhiyun Ouyang, Hua Zheng. 2013. The Impact of Land Use Change on Ecosystem Service
      Function——Taking Miyun Reservoir Watershed as an Example[J]. Acta Ecologica Sinica, 33: 726-736.
    17. Qiang Xu G Z, Weile Li, Zhaoyang He, Xiujun Dong, Chen Guo, Wenkai Feng. 2018. Analysis and study of two landslides
      and dams blocking the river in Baige on the Jinsha River in October and November 2018[J]. Journal of Engineering
      Geology, 26: 1534-1551
    18. Qin Ji J Y, Hongju Chen, Man Li. 2019. Analysis of Economic Differences Along the Sichuan-Tibet Railway from the
      Perspective of Spatial and Industrial Decomposition[J]. Glacier permafrost: 1-14
    19. Qingchun Li Y H, Yubing Shi. 2020. Study on the stability of the residual dam in Tangjiashan dammed lake[J]. Journal of
      Underground Space and Engineering, 16: 993-998
    20. Qiwen Xiang J P, Guangze Zhang, Zhengxuan Xu, Dingkai Zhang, Wenli Tu. 2020. Monitoring and Analysis of Surface
      Deformation in Zheduo Mountain Area of Sichuan-Tibet Railway Based on SBAS Technology[J]. Surveying Engineering,
      29: 48-54+59
    1. Shangfu Kuang X W, Jinchi Huang, Yinqi Wei 2008. Analysis and Evaluation of Dam-Break Risk of Barred Lake and Its
      Influence[J]. China Water Resources: 17-21.
    2. Sheng-Hsueh Y, Yii-Wen P, Jia-Jyun D, et al. 2013. A systematic approach for the assessment of flooding hazard and risk
      associated with a landslide dam[J]. Natural Hazards, 65.
    3. Sun L 2021. Research on Fast Perception and Simulation Calculation Method of Landslide Dam in Alpine and Gorge
      Area: Taking Baige Dammed Lake as an Example[J]. Water Conservancy and Hydropower Technology (Chinese and
      English), 52: 44-52
    4. Tamiru H, O. D M 2021. Application of ANN and HEC-RAS model for flood inundation mapping in lower Baro Akobo River
      Basin, Ethiopia[J]. Journal of Hydrology: Regional Studies, 36.
    5. Tao Pan S W, Erfu Dai, Yujie Liu. 2013. Spatio-temporal changes of water supply services in the ecosystem of the Three
      Rivers Source Region based on InVEST model[J]. Journal of Applied Ecology, 24: 183-189
    6. Vera K, Sergey C, Inna K, et al. 2017. Modeling potential scenarios of the Tangjiashan Lake outburst and risk assessment
      in the downstream valley[J]. Frontiers of Earth Science, 11.
    7. Wang Z 1985. Preliminary Discussion on the Evaluation of Ecological Environment Quality in Minjiang River Basin[J].
      Journal of ecology: 29-32
    8. Wei Chen Z S, Hui Guo,Hao Wang, Ting Wei, Nan Li, Kaiyi Zhang Shuxiang Yang, Kaijia Dai. 2007. Analysis of Bird
      Resources and Habitats in Wuhan Urban Lakes and Urban Wetlands in Winter[J]. Forestry Investigation and Planning: 46-
      50
    9. Wei G, Gaohong X, Jun S, et al. 2020. Simulation of Flood Process Based on the Model of Improved Barrier Lake’s
      Gradual Dam Break Model %J Journal of Coastal Research[J]. 104.
    10. Wei X, Jiang H, Xu H, et al. 2021. Response of sedimentary and pollen records to the 1933 Diexi earthquake on the
      eastern Tibetan Plateau[J]. Ecological Indicators, 129.
    11. Wei Xu M L, Jie Yang, Chunzhi Li, Xiaojuan Shang. 2011. Risk Analysis of Flood Overflow in Huainan Section of Huaihe
      River Based on HEC-RAS[J]. Journal of Yangtze River Scientific Research Institute, 28: 13-18
    12. Weiwei Zhan R H, Xiangjun Pei, Weile Li. 2017. Research on empirical prediction model of channel type landslide-debris
      flow movement distance[J]. Journal of Engineering Geology, 25: 154-163
    13. Xianju Zheng H L, Wenhai Huang. 2015. Numerical Simulation of Reconstruction of Natural Dams Induced by Heavy Rain
      ——An Example of Tangjiashan Dammed Lake[J]. Business story: 62-63
    14. Xiao-Qun W, Xin H, Man S, et al. 2020. Possible relatedness between the outburst of the Diexi ancient dammed lake and
      ancient Chengdu’s cultural change[J]. Journal of Mountain Science, 17: 2497-2511.
    15. Xingbo Zhou X D, Yu Yao. 2019. Analysis of the dam-break flood of the Baige dammed lake on the Jinsha River[J].
      Hydroelectric Power, 45: 8-12+32
    16. Xinhua Zhang R X, Ming Wang, Zhiqiu Yu, Bingdong Li, Bo Wang. 2020. Investigation and analysis of flood disaster
      caused by dam break of Baige landslide on Jinsha River[J]. Engineering Science and Technology, 52: 89-100
    17. Xinxiao Yu B Z, Xizhi Lv, Zhige Yang. 2012. Evaluation of Forest Water Conservation Function of Beijing Mountainous
      Area Based on InVEST Model[J]. Forestry Science, 48: 1-5
    18. Xu J, Guo J, Zhang J, et al. 2021. Route choice model based on cellular automata and cumulative prospect theory: Case
      analysis of transportation network in Sichuan-Tibet region[J]. Journal of Intelligent & Fuzzy Systems, 40.
    19. Xuan Liang Z Z 2021. Research on the Influence of Numerical Simulation of Tailings Pond Based on FLOW-3D on
      Downstream[J]. Jiangxi Water Conservancy Science and Technology, 47: 11-20
    20. Yu Zheng P Z, Feng Tang, Li Zhao, Xu Zhao. 2018. Research on the Impact of Land Use Change on Habitat Quality in
      Changli County Based on InVEST Model[J]. China’s Agricultural Resources and Regionalization, 39: 121-128
    21. Yuanyuan Yang E D, Hua Fu. 2012. Research Framework of Value Evaluation of Ecosystem Service Function Based on
      InVEST Model[J]. Journal of Capital Normal University (Natural Science Edition), 33: 41-47
    1. Yunfei Ma T L, Jinbiao Xiong. 2021. Numerical simulation of dam-break flow based on VOF method and DFBI model[J].
      Applied Technology, 48: 23-28
    2. Zhe Wu X C, Beibei Liu, Jinfeng Chu, Lixu Peng. 2013. Research progress of InVEST model and its application[J]. Tropical
      Agriculture Science, 33: 58-62
    3. Zhengpeng Li Y H, Yilun Li, Yuehong Ying, Zehua Huangfu. 2021. Numerical simulation of dam-break flood in Qianping
      Reservoir based on BIM+GIS technology[J]. People’s Yellow River, 43: 160-164
    4. Zhenming Shi X X, Ming Peng, Minglang Lin. 2015. Analysis of Seepage Stability of Barrier Dam with High Permeability
      Area——Taking Hongshihe Barrier Dam as an Example[J]. Journal of Hydraulic Engineering, 46: 1162-1171.
    5. Zhu J, Qi H, Hu Y, et al. 2012. A DVGE service system for risk assessment of dam-break in barrier lake[J]. International
      Conference on Automatic Control and Artificial Intelligence (ACAI 2012).
    6. Zhu Y, Peng M, Cai S, et al. 2021. Risk-Based Warning Decision Making of Cascade Breaching of the Tangjiashan
      Landslide Dam and Two Smaller Downstream Landslide Dams[J]. Frontiers in Earth Science.
    7. Zuyu Chen G H, Qiang Zhang, Shuaifeng Wu. 2020. Disaster Mitigation Analysis of Cascade Hydropower Stations on the
      Jinsha River in “11.03” Baige Barrier Lake Emergency Treatment[J]. Hydropower, 46: 59-63
    8. Zuyu Chen S C, Lin Wang, Qiming Zhong, Qiang Zhang, Songli Jin. 2020. Inversion analysis of the “11.03” Baige barrier
      lake burst flood in the upper reaches of the Jinsha River[J]. Science in China: Technological Science, 50: 763-774.
    Figure 1 | Original Compound Broad Crested Weir Model (PVC cast).

    복합 광대보의 방류계수 예측을 위한 실험적 해석과 CFD 해석의 비교연구

    Comparative study of experimental and CFD analysis for predicting discharge coefficient of compound broad crested weir

    ABSTRACT

    Present study highlights the behavior of weir crest head and width parameter on the discharge coefficient of compound broad crested (CBC) weir. Computational fluid dynamics model (CFD) is validated with laboratory experimental investigations.

    In the discharge analysis through broad crested weirs, the upstream head over the weir crest (h) is crucial, where the result is mainly dependent upon the weir crest length (L) in transverse direction to flow, water depth from channel bed. Currently, minimal investigations are known for CFD validations on compound broad crested weirs.

    The hydraulic research for measuring discharge numerically is carried out using FLOW 3D software. The model applies renormalized group (RNG) using volume of fluid (VOF) method for improved accuracy in free surface simulations. Structured hexagonal meshes of cubic elements define discretized meshing.

    The comparative analysis of the numerical simulations and experimental observations confirm the performance of CBC weir for precise measurement of a wide range of discharges. Series of CFD model studies and experimental validation have led to constant range of discharg coefficients for various head over weir crest. The correlation coefficient of discharge predictions is 0.999 with mean error of 0.28%.

    현재 연구에서는 CBC(compound broad crested) 위어의 배출 계수에 대한 위어 볏 머리 및 너비 매개변수의 거동을 강조합니다. 전산 유체 역학 모델(CFD)은 실험실 실험 조사를 통해 검증되었습니다.

    넓은 볏이 있는 둑을 통한 유출 분석에서 둑 마루의 상류 수두(h)가 중요합니다. 여기서 결과는 주로 흐름에 대한 횡 방향의 둑 마루 길이(L), 수로 바닥에서 수심에 따라 달라집니다. . 현재 복합 넓은 볏 둑에 대한 CFD 검증에 대해 최소한의 조사가 알려져 있습니다.

    수압 연구는 FLOW 3D 소프트웨어를 사용하여 수치적으로 측정합니다. 이 모델은 자유 표면 시뮬레이션의 정확도 향상을 위해 VOF(유체 체적) 방법을 사용하여 RNG(재정규화 그룹)를 적용합니다. 정육면체 요소의 구조화된 육각형 메쉬는 이산화된 메쉬를 정의합니다.

    수치 시뮬레이션과 실험적 관찰의 비교 분석을 통해 광범위한 배출의 정확한 측정을 위한 CBC 둑의 성능을 확인했습니다. 일련의 CFD 모델 연구와 실험적 검증을 통해 다양한 head over weir crest에 대한 일정한 범위의 방전 계수가 나타났습니다. 방전 예측의 상관 계수는 0.999이고 평균 오차는 0.28%입니다.

    Figure 1 | Original Compound Broad Crested Weir Model (PVC cast).
    Figure 1 | Original Compound Broad Crested Weir Model (PVC cast).
    Figure 4 | CFD Simulation for max discharge (y2 ¼ 13.557 cm, Qmax ¼ 10 lps) and min discharge (y2 ¼ 6.56 cm, Qmin ¼ 2 lps).
    Figure 4 | CFD Simulation for max discharge (y2 ¼ 13.557 cm, Qmax ¼ 10 lps) and min discharge (y2 ¼ 6.56 cm, Qmin ¼ 2 lps).
    Figure 5 | (a, b) Velocity profiles corresponding to max discharge (10 lps) and min discharge (2 lps).
    Figure 5 | (a, b) Velocity profiles corresponding to max discharge (10 lps) and min discharge (2 lps).
    Table 8 | Range of Froude number, Reynold number and Weber number
    Table 8 | Range of Froude number, Reynold number and Weber number

    Key words

    compound weir, flow 3D, flow measurement, numerical technique, open channel

    HIGHLIGHTS

    • The Head-Discharge relation is established for discharge measurement using compound broad crested weir, experimentally and numerically.
    • Assessment of head over weir crest for different step widths of proposed weir on discharge coefficient is executed.
    • Experimental and CFD results of weir performance demonstrate good agreement between the theoretical discharges by traditional rectangular weir formulae keeping Cd constant.

    CONCLUSION

    1. The head discharge relationship established for compound rectangular broad crested weir for various discharge ranges was validated by CFD technique. A three dimensional simulation software FLOW 3D was used for this purpose.
    2. Original theoretical compound weir model depicts the relative average error between discharge predictions with Flow 3D simulation as 4.96% which is found less than the predictions made by graphical interpolation technique which is 5.33%.
    3. The standard deviation in Cd parameter for CFD simulation model is less i.e. 0.0146 as compared to experimental output of 0.0502.
    4. The correlation coefficient for physical and CFD studies for modified compound weir model is high, around 0.999 with
      error in discharge predictions being 0.28% as compared to the accuracy limits of about +3–5% stated in literature so far.
    5. Discharge coefficient by experimental and CFD approach is maintained constant and equal to design input value of 0.6.
      Thus, the proposed CBC weir can be operated for various discharge ranges by maintaining constant discharge coefficients.
      Good agreement between the theoretical, experimental and CFD simulation results for obtaining discharge through compound broad crested weir ascertains the fact that CFD model can be used as an effective tool towards modeling flow through compound broad crested weir.

    REFERENCES

    Abd El-Hady Rady, R. M. 2011 2D 3D modeling of flow over sharp crested weirs. Journal of Applied Sciences Research 7 (12), 2495–2505.
    ISSN 1819-544X.
    Ackers, P., White, W. R. & Harrison, A. J. M. 1978 Weirs and Flumes for Flow Measurement. Wiley, New York.
    Aydin, M. C. 2016 Investigation of a sill effect on rectangular side-weir flow by using CFD. Journal of Irrigation and Drainage Engineering
    142 (2), 04015043.
    Azimi, A. H. & Rajaratnam, N. 2009 Discharge characteristics of weirs of finite crest length. Journal of Hydraulic Engineering 135 (12),
    1081–1085.
    Bijankhan, M., Di Stefano, C., Ferro, V. & Kouchakzadeh, S. 2014 New stage discharge relationship for weirs of finite crest length. Journal of
    Irrigation and Drainage Engineering 140 (3), 06013006.
    Boiten, W. & Pitlo, H. R. 1982 The V- shaped broad-crested weir. Journal of Irrigation and Drainage Engineering 108 (2), 142–160.
    Bos, M. G. 1989 Discharge Measurement Structures, 3rd edn. International Institute for Land Reclamation and Improvement, Publication 20,
    Wageningen, The Netherlands.
    Gogus, M., Defne, Z. & Ozkandemir, V. 2006 Broad-crested weirs with rectangular compound cross sections. Journal of Irrigation and
    Drainage Engineering 132 (3), 272–280.

    Gogus, M., Al-Khatib, I. A., Atalay, A. E. & Khatib, J. I. 2016 Discharge prediction in flow measurement flumes with different downstream
    transition slopes. Flow Measurement and Instrumentation 47, 28–34.
    Hager, W. H. & Schwalt, M. 1994 Broad – crested weir. Journal of Irrigation and Drainage Engineering 120 (1), 13–25.
    Harrison, A. J. M. 1967 The streamlined broad-crested weir. Proceedings of the Institution of Civil Engineers 38, 657–678.
    Hinge, G. A., Balkrishna, S. & Khare, K. C. 2010 Improved design of stilling basin for deficient tail water. Journal of Basic and Applied
    Scientific Research 1 (1), 31–40.
    Hinge, G. A., Balkrishna, S. & Khare, K. C. 2011 Experimental and numerical study of compound broad crested weir. International Journal of
    Fluids Engineering 3 (2), 197–202.
    Horton, R. E. 1907 Weir Experiments, Coefficients, and Formulas. Dept. of the Interior, U.S. Geological Survey, Water-Supply and Irrigation
    Paper 200. Government Printing Office, Washington, DC.
    Khan, L. A., Wicklein, E. A. & Teixeira, E. C. 2006 Validation of a three-dimensional computational fluid dynamics model of a contact tank.
    Journal of Hydraulic Engineering 132 (7), 741–746.
    Kindsvater, C. E. & Carter, R. W. 1959 Discharge characteristics of rectangular thin-plate weirs. Paper No. 3001, Transactions, American
    Society of Civil Engineers 124.
    Kulin, G. & Compton, P. R. 1975 A Guide to Methods and Standards for the Measurement of Water Flow. Special Publication 421, National
    Bureau of Standards.
    Kulkarni, K. H. & Hinge, G. A. 2017 Compound broad crested weir for measurement of discharge – a novel approach. In: Proceedings
    International Conference Organized by Indian Society of Hydraulics – ISH HYDRO, 21–23 Dec 2017, India, pp. 678–687.
    Kulkarni, K. H. & Hinge, G. A. 2020 Experimental study for measuring discharge through compound broad crested weir. Flow Measurement
    Instrumentation 75, 101803. ISSN 0955-5986.
    Man, C., Zhang, G., Hong, V., Zhou, S. & Feng, Y. 2019 Assessment of turbulence models on bridge-pier scour using flow-3D. World Journal
    of Engineering and Technology 7, 241–255. ISSN Online: 2331-4249.
    Omer, B., Cihan, A. M., Emin, E. M. & Miller, C. J. 2018 Experimental and CFD analysis of circular labyrinth weirs. Journal of Irrigation and
    Drainage Engineering 144 (6), 04018007.
    RangaRaju, K. G. 1981 Flow Through Open Channels. McGraw-Hill, New York.
    Roushangar, K., Nouri, A., Shahnazi, S. & Azamathulla, H. M. 2021 Towards design of compound channels with minimum overall cost
    through grey wolf optimization algorithm. IWA – Journal of Hydroinformatics (In – press).
    Safarzadeh, A. & Mohajeri, S. H. 2018 Hydrodynamics of rectangular broad-crested porous weir. Journal of Irrigation and Drainage
    Engineering 144 (10), 04018028.
    Salmasi, F., Poorescandar, S., Dalir, A. H. & Zadeh, D. F. 2012 Discharge relations for rectangular broad crested weirs. Journal of
    Agricultural Sciences 17, 324–336.
    Samadi, A. & Arvanaghi, H. 2014 CFD simulation of flow over contracted compound arched rectangular sharp crested weirs. International
    Journal of Optimization in Civil Engineering 4 (4), 549–560.
    Savage, B. M. & Johnson, M. C. 2001 Flow over ogee spillway: physical and numerical model case study. Journal of Hydraulic Engineering
    127 (8), 640–649.
    Swamee, P. K. 1988 Generalized rectangular weir equations. Journal of Hydraulic Engineering 945–952. doi:10.1061/(ASCE),0733-9429
    114:8(945).
    The United States Bureau of Reclamation (USBR) 2001 Water Measurement Manual, Chapter 7 – Weirs. U.S. Government Printing Office,
    Washington, DC, p. 20402. Available from: http://www/usbr.gov/pmts/hydraulics_lab/pubs/wmm.
    Zahiri, A. & Azamathulla, H. M. 2014 Comparison between linear genetic programming and M5 tree models to predict flow discharge in
    compound channels. Neural Computing and Application 24, 413–420.

    Figure 15. Localized deformations on revetment due to run-down and sliding of armor from body laboratory model (left) and numerical modeling (right).

    지속 가능한 해안 보호 구조로서 굴절식 콘크리트 블록 매트리스의 손상 메커니즘의 수치적 모델링

    Numerical Modeling of Failure Mechanisms in Articulated Concrete Block Mattress as a Sustainable Coastal Protection Structure

    Author

    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)

    Abstract

    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.

    Figure 1.  Armor  geometric  characteristics  and  drawing  three-dimensional  geometry  of  a  breakwater section  in SolidWorks software.
    Figure 1. Armor geometric characteristics and drawing three-dimensional geometry of a breakwater section in SolidWorks software.
    Figure  5.  Wave  overtopping on  concrete block  mattress in (a)  laboratory  and (b)  numerical  model.
    Figure 5. Wave overtopping on concrete block mattress in (a) laboratory and (b) numerical model.
    Figure  7.  Mesh  block  for  calibrated  numerical  model  with  686,625  cells  and  utilization  of  FAVOR  tab to assess figure geometry.
    Figure 7. Mesh block for calibrated numerical model with 686,625 cells and utilization of FAVOR tab to assess figure geometry.
    Figure  10.  How to place different layers  (core, filter,  and revetment)  of the structure on slope.
    Figure 10. How to place different layers (core, filter, and revetment) of the structure on slope.

    Suggested Citation

    Figure 11. Wave run-up on ACB Mat blocks in (a) laboratory model and (b) numerical modeling.
    Figure 11. Wave run-up on ACB Mat blocks in (a) laboratory model and (b) numerical modeling.
    Figure  15.  Localized  deformations  on  revetment  due  to  run-down  and  sliding  of  armor  from  body  laboratory  model  (left) and  numerical  modeling (right).
    Figure 15. Localized deformations on revetment due to run-down and sliding of armor from body laboratory model (left) and numerical modeling (right).

    References

    1. Capobianco, V.; Robinson, K.; Kalsnes, B.; Ekeheien, C.; Høydal, Ø. Hydro-Mechanical Effects of Several Riparian Vegetation Combinations on the Streambank Stability—A Benchmark Case in Southeastern Norway. Sustainability 2021, 13, 4046. [CrossRef]
    2. MarCom Working Group 113. PIANC Report No 113: The Application of Geosynthetics in Waterfront Areas; PIANC: Brussels, Belgium, 2011; p. 113, ISBN 978-2-87223-188-1.
    3. Hunt, W.F.; Collins, K.A.; Hathaway, J.M. Hydrologic and Water Quality Evaluation of Four Permeable Pavements in North Carolina, USA. In Proceedings of the 9th International Conference on Concrete Block Paving, Buenos Aires, Argentina, 18–21 October 2009.
    4. Kirkpatrick, R.; Campbell, R.; Smyth, J.; Murtagh, J.; Knapton, J. Improvement of Water Quality by Coarse Graded Aggregates in Permeable Pavements. In Proceedings of the 9th International Conference on Concrete Block Paving, Buenos Aires, Argentina, 18–21 October 2009.
    5. Chinowsky, P.; Helman, J. Protecting Infrastructure and Public Buildings against Sea Level Rise and Storm Surge. Sustainability 2021, 13, 10538. [CrossRef]
    6. Breteler, M.K.; Pilarczyk, K.W.; Stoutjesdijk, T. Design of alternative revetments. Coast. Eng. 1998 1999, 1587–1600. [CrossRef]
    7. Pilarczyk, K.W. Design of Revetments; Dutch Public Works Department (Rws), Hydraulic Engineering Division: Delft, The Netherlands, 2003.
    8. Hughes, S.A. Combined Wave and Surge Overtopping of Levees: Flow Hydrodynamics and Articulated Concrete Mat Stability; Engineer Research and Development Center Vicksburg Ms Coastal and Hydraulics Lab: Vicksburg, MS, USA, 2008.
    9. Gier, F.; Schüttrumpf, H.; Mönnich, J.; Van Der Meer, J.; Kudella, M.; Rubin, H. Stability of Interlocked Pattern Placed Block Revetments. Coast. Eng. Proc. 2012, 1, Structures-46. [CrossRef]
    10. Najafi, J.A.; Monshizadeh, M. Laboratory Investigations on Wave Run-up and Transmission over Breakwaters Covered by Antifer Units; Scientia Iranica: Tehran, Iran, 2010.
    11. Oumeraci, H.; Staal, T.; Pförtner, S.; Ludwigs, G.; Kudella, M. Hydraulic Performance, Wave Loading and Response of Elastocoast Revetments and their Foundation—A Large Scale Model Study; Leichtweiß Institut für Wasserbau: Braunschweig, Germany, 2010.
    12. Tripathy, S.K. Significance of Traditional and Advanced Morphometry to Fishery Science. J. Hum. Earth Future 2020, 1, 153–166. [CrossRef]
    13. Nut, N.; Mihara, M.; Jeong, J.; Ngo, B.; Sigua, G.; Prasad, P.V.V.; Reyes, M.R. Land Use and Land Cover Changes and Its Impact on Soil Erosion in Stung Sangkae Catchment of Cambodia. Sustainability 2021, 13, 9276. [CrossRef]
    14. Xu, C.; Pu, L.; Kong, F.; Li, B. Spatio-Temporal Change of Land Use in a Coastal Reclamation Area: A Complex Network Approach. Sustainability 2021, 13, 8690. [CrossRef]
    15. Mousavi, S.; Kavianpour, H.M.R.; Yamini, O.A. Experimental analysis of breakwater stability with antifer concrete block. Mar. Georesour. Geotechnol. 2017, 35, 426–434. [CrossRef]
    16. Yamini, O.; Aminoroayaie, S.; Mousavi, H.; Kavianpour, M.R. Experimental Investigation of Using Geo-Textile Filter Layer In Articulated Concrete Block Mattress Revetment On Coastal Embankment. J. Ocean Eng. Mar. Energy 2019, 5, 119–133. [CrossRef]
    17. Ghasemi, A.; Far, M.S.; Panahi, R. Numerical Simulation of Wave Overtopping From Armour Breakwater by Considering Porous Effect. J. Mar. Eng. 2015, 11, 51–60. Available online: http://dorl.net/dor/20.1001.1.17357608.1394.11.22.8.4 (accessed on 21 October 2021).
    18. Nourani, O.; Askar, M.B. Comparison of the Effect of Tetrapod Block and Armor X block on Reducing Wave Overtopping in Breakwaters. Open J. Mar. Sci. 2017, 7, 472–484. [CrossRef]
    19. Aminoroaya, A.O.; Kavianpour, M.R.; Movahedi, A. Performance of Hydrodynamics Flow on Flip Buckets Spillway for Flood Control in Large Dam Reservoirs. J. Hum. Earth Future 2020, 1, 39–47.
    20. Milanian, F.; Niri, M.Z.; Najafi-Jilani, A. Effect of hydraulic and structural parameters on the wave run-up over the berm breakwaters. Int. J. Nav. Archit. Ocean Eng. 2017, 9, 282–291. [CrossRef]
    21. Yamini, O.A.; Kavianpour, M.R.; Mousavi, S.H. Experimental investigation of parameters affecting the stability of articulated concrete block mattress under wave attack. Appl. Ocean Res. 2017, 64, 184–202. [CrossRef]
    22. Yakhot, V.; Orszag, S.A.; Thangam, S.; Gatski, T.B.; Speziale, C.G. Development of turbulence models for shear flows by a double expansion technique. Phys. Fluids 1992, 4, 1510–1520. [CrossRef]
    23. Bayon, A.; Valero, D.; García-Bartual, R.; López-Jiménez, P.A. Performance assessment of OpenFOAM and FLOW-3D in the numerical modeling of a low Reynolds number hydraulic jump. Environ. Model. Softw. 2016, 80, 322–335. [CrossRef]
    24. Jin, J.; Meng, B. Computation of wave loads on the superstructures of coastal highway bridges. Ocean Eng. 2011, 38, 2185–2200. [CrossRef]
    25. Yang, S.; Yang, W.; Qin, S.; Li, Q.; Yang, B. Numerical study on characteristics of dam-break wave. Ocean Eng. 2018, 159, 358–371. [CrossRef]
    26. Ersoy, H.; Karahan, M.; Geli¸sli, K.; Akgün, A.; Anılan, T.; Sünnetci, M.O.; Yah¸si, B.K. Modelling of the landslide-induced impulse waves in the Artvin Dam reservoir by empirical approach and 3D numerical simulation. Eng. Geol. 2019, 249, 112–128. [CrossRef]
    27. Zhan, J.M.; Dong, Z.; Jiang, W.; Li, Y.S. Numerical simulation of wave transformation and runup incorporating porous media wave absorber and turbulence models. Ocean Eng. 2010, 37, 1261–1272. [CrossRef]
    28. Owen, M.W. The Hydroulic Design of Seawall Profiles, Proceedings Conference on Shoreline Protection; ICE: London, UK, 1980; pp. 185–192.
    29. Pilarczyk, K.W. Geosythetics and Geosystems in Hydraulic and Coastal Engineering; CRC Press: Balkema, FL, USA, 2000; p. 913, ISBN 90.5809.302.6.
    30. Van der Meer, J.W.; Allsop, N.W.H.; Bruce, T.; De Rouck, J.; Kortenhaus, A.; Pullen, T.; Schüttrumpf, H.; Troch, P.; Zanuttigh, B. (Eds.) Manual on Wave Overtopping of Sea Defences and Related Structures–Assessment Manual; EurOtop.: London, UK, 2016; Available online: www.Overtopping-manual.com (accessed on 21 October 2021).
    31. Battjes, J.A. Computation of Set-up, Longshore Currents, Run-up and Overtopping Due to Wind-Generated Waves; TU Delft Library: Delft, The Netherlands, 1974.
    32. Van der Meer, J.W. Rock Slopes and Gravel Beaches under Wave Attack; Delft Hydraulics: Delft, The Netherlands, 1988.
    33. Ten Oever, E. Theoretical and Experimental Study on the Placement of Xbloc; Delft Hydraulics: Delft, The Netherlands, 2006.
    34. Flow Science, Inc. FLOW-3D User Manual Version 9.3; Flow Science, Inc.: Santa Fe, NM, USA, 2008.
    35. Lebaron, J.W. Stability of A-Jacksarmored Rubble-Mound Break Waters Subjected to Breaking and Non-Breaking Waves with No Overtopping; Master of Science in Civil Engineering, Oregon State University: Corvallis, OR, USA, 1999.
    36. McLaren RW, G.; Chin, C.; Weber, J.; Binns, J.; McInerney, J.; Allen, M. Articulated Concrete Mattress block size stability comparison in omni-directional current. In Proceedings of the OCEANS 2016 MTS/IEEE Monterey, Monterey, CA, USA, 19–23 September 2016; pp. 1–6. [CrossRef]
    Hydraulic Analysis of Submerged Spillway Flows and Performance Evaluation of Chute Aerator Using CFD Modeling: A Case Study of Mangla Dam Spillway

    CFD 모델링을 이용한 침수 배수로 흐름의 수리학적 해석 및 슈트 폭기장치 성능 평가: Mangla Dam 배수로 사례 연구

    Hydraulic Analysis of Submerged Spillway Flows and Performance Evaluation of Chute Aerator Using CFD Modeling: A Case Study of Mangla Dam Spillway

    Muhammad Kaleem SarwarZohaib NisarGhulam NabiFaraz ul HaqIjaz AhmadMuhammad Masood & Noor Muhammad Khan 

    Abstract

    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.

    Keywords

    • Aerator
    • CFD
    • FLOW 3D
    • Froude number
    • Submerged spillway
    • Fig. 1extended data figure 1Fig. 2extended data figure 2Fig. 3extended data figure 3Fig. 4extended data figure 4Fig. 5extended data figure 5Fig. 6extended data figure 6Fig. 7extended data figure 7Fig. 8

    References

    1. Aydin MC (2018) Aeration efficiency of bottom-inlet aerators for spillways. ISH J Hydraul Eng 24(3):330–336. https://doi.org/10.1080/09715010.2017.1381576Article Google Scholar 
    2. Bennett P, Chesterton J, Neeve D, Ucuncu M, Wearing M, Jones SEL (2018) Use of CFD for modelling spillway performance. Dams Reserv 28(2):62–72. https://doi.org/10.1680/jdare.18.00001Article Google Scholar 
    3. Bhosekar VV, Jothiprakash V, Deolalikar PB (2012) Orifice Spillway Aerator: Hydraulic Design. J Hydraul Eng 138(6):563–572. https://doi.org/10.1061/(ASCE)HY.1943-7900.0000548Article Google Scholar 
    4. Chanel PG, Doering JC (2008) Assessment of spillway modeling using computational fluid dynamics. Can J Civ Eng 35(12):1481–1485. https://doi.org/10.1139/L08-094Article Google Scholar 
    5. Flow Sciences, Inc. (2013) FLOW 3D user manual version 10.1.
    6. Gadge PP, Jothiprakash V, Bhosekar VV (2018) Hydraulic investigation and design of roof profile of an orifice spillway using experimental and numerical models. J Appl Water Eng Res 6(2):85–94. https://doi.org/10.1080/23249676.2016.1214627Article Google Scholar 
    7. Gadge PP, Jothiprakash V, Bhosekar VV (2019) Hydraulic design considerations for orifice spillways. ISH J Hydraul Eng 25(1):12–18. https://doi.org/10.1080/09715010.2018.1423579Article Google Scholar 
    8. Gu S, Ren L, Wang X, Xie H, Huang Y, Wei J, Shao S (2017) SPHysics simulation of experimental spillway hydraulics. Water 9(12):973. https://doi.org/10.3390/w9120973Article Google Scholar 
    9. Gurav NV (2015) Physical and Numerical Modeling of an Orifice Spillway. Int J Mech Prod Eng 3(10):71–75Google Scholar 
    10. Hirt CW, Nichols BD (1981) Volume of fluid (VOF) method for the dynamics of free boundaries. J Comput Phys 39(1):201–225. https://doi.org/10.1016/0021-9991(81)90145-5Article MATH Google Scholar 
    11. Ho DKH, Riddette KM (2010) Application of computational fluid dynamics to evaluate hydraulic performance of spillways in Australia. Aust J Civ Eng 6(1):81–104. https://doi.org/10.1080/14488353.2010.11463946Article Google Scholar 
    12. Jothiprakash V, Bhosekar VV, Deolalikar PB (2015) Flow characteristics of orifice spillway aerator: numerical model studies. ISH J Hydraul Eng 21(2):216–230. https://doi.org/10.1080/09715010.2015.1007093Article Google Scholar 
    13. Kumcu SY (2017) Investigation of flow over spillway modeling and comparison between experimental data and CFD analysis. KSCE J Civ Eng 21(3):994–1003. https://doi.org/10.1007/s12205-016-1257-zArticle Google Scholar 
    14. Lian J, Qi C, Liu F, Gou W, Pan S, Ouyang Q (2017) Air entrainment and air demand in the spillway tunnel at the Jinping-I Dam. Appl Sci 7(9):930. https://doi.org/10.3390/app7090930Article Google Scholar 
    15. Luo M, Khayyer A, Lin P (2021) Particle methods in ocean and coastal engineering. Appl Ocean Res 114:102734Article Google Scholar 
    16. Moreira A, Leroy A, Violeau D, Taveira-Pinto F (2019) Dam spillways and the SPH method: two case studies in Portugal. J Appl Water Eng Res 7(3):228–245. https://doi.org/10.1080/23249676.2019.1611496Article Google Scholar 
    17. Moreira AB, Leroy A, Violeau D, Taveira-Pinto FA (2020) Overview of large-scale smoothed particle hydrodynamics modeling of dam hydraulics. J Hydraul Eng 146(2):03119001. https://doi.org/10.1061/(ASCE)HY.1943-7900.0001658Article Google Scholar 
    18. O’Connor J, Rogers BD (2021) A fluid–structure interaction model for free-surface flows and flexible structures using smoothed particle hydrodynamics on a GPU. J Fluids Struct. https://doi.org/10.1016/j.jfluidstructs.2021.103312Article Google Scholar 
    19. Sarwar MK, Bhatti MT, Khan NM (2016) Evaluation of air vents and ramp angles on the performance of orifice spillway aerators. J Eng Appl Sci 35(1):85–93Google Scholar 
    20. Sarwar MK, Ahmad I, Chaudary ZA, Mughal H-U-R (2020) Experimental and numerical studies on orifice spillway aerator of Bunji Dam. J Chin Inst Eng 43(1):27–36. https://doi.org/10.1080/02533839.2019.1676652Article Google Scholar 
    21. Saunders K, Prakash M, Cleary PW, Cordell M (2014) Application of smoothed particle hydrodynamics for modelling gated spillway flows. Appl Math Model 38(17–18):4308–4322. https://doi.org/10.1016/j.apm.2014.05.008Article MATH Google Scholar 
    22. Savage BM, Johnson MC (2001) Flow over ogee spillway: physical and numerical model case study. J Hydraul Eng 127(8):640–649. https://doi.org/10.1061/(ASCE)0733-9429(2001)127:8(640)Article Google Scholar 
    23. Shadloo MS, Oger G, le Touzé D (2016) Smoothed particle hydrodynamics method for fluid flows, towards industrial applications: Motivations, current state, and challenges. Comput Fluids. https://doi.org/10.1016/j.compfluid.2016.05.029MathSciNet Article MATH Google Scholar 
    24. Shao Z, Jahangir Z, MuhammadYasir Q, Atta-ur-Rahman, Mahmood S (2020) Identification of potential sites for a multi-purpose dam using a dam suitability stream model. Water 12(11):3249. https://doi.org/10.3390/w12113249Article Google Scholar 
    25. Shimizu Y, Khayyer A, Gotoh H, Nagashima K (2020) An enhanced multiphase ISPH-based method for accurate modeling of oil spill. Coast Eng J 62(4):625–646. https://doi.org/10.1080/21664250.2020.1815362Article Google Scholar 
    26. Teng P, Yang J (2016) CFD modeling of two-phase flow of a spillway chute aerator of large width. J Appl Water Eng Res 4(2):163–177. https://doi.org/10.1080/23249676.2015.1124030Article Google Scholar 
    27. Teng P, Yang J, Pfister M (2016) Studies of two-phase flow at a chute aerator with experiments and CFD modelling. Model Simul Eng 2016:1–11. https://doi.org/10.1155/2016/4729128Article Google Scholar 
    28. Wapda (2004) Mangla dam raising project-sectional physical model study report of main spillway: Wapda model study cell, Gujrawala, Pakistan
    29. Yang J, Andreasson P, Teng P, Xie Q (2019) The past and present of discharge capacity modeling for spillways—a Swedish perspective. Fluids 4(1):10. https://doi.org/10.3390/fluids4010010Article Google Scholar 
    30. Yang J, Teng P, Xie Q, Li S (2020) Understanding water flows and air venting features of spillway—a case study. Water 12(8):2106. https://doi.org/10.3390/w12082106Article Google Scholar 
    31. Ye T, Pan D, Huang C, Liu M (2019) Smoothed particle hydrodynamics (SPH) for complex fluid flows: recent developments in methodology and applications. Phys Fluids 31(1):011301Article Google Scholar 
    32. Zhan X, Qin H, Liu Y, Yao L, Xie W, Liu G, Zhou J (2020) Variational Bayesian neural network for ensemble flood forecasting. Water 12(10):2740. https://doi.org/10.3390/w12102740Article Google Scholar 

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    Fig. 11. Velocity vectors along x-direction through the center of the box culvert for B0, B30, B50, and B70 respectively.

    Numerical investigation of scour characteristics downstream of blocked culverts

    막힌 암거 하류의 세굴 특성 수치 조사

    NesreenTahabMaged M.El-FekyaAtef A.El-SaiadaIsmailFathya
    aDepartment of Water and Water Structures Engineering, Faculty of Engineering, Zagazig University, Zagazig 44519, Egypt
    bLab Manager, Faculty of Engineering, Zagazig University, Zagazig 44519, Egypt

    Abstract

    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.

    1. Introduction

    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 [1]. 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 [2][3][4][5][6]. Cesar Mendoza [6] found a good correlation between the scour depth and the discharge Intensity (Qg−.5D−2.5). Breusers and Raudkiv [7] used shear velocity in the outlet-scour prediction procedure. Ali and Lim [8] used the densimetric Froude number in estimation of the scour depth [1][8][9][10][11][12][13][14]. “The densimetric Froude number presents the ratio of the tractive force on sediment particle to the submerged specific weight of the sediment” [15](1)Fd=uρsρ-1gD50

    Ali and Lim [8] pointed to the consequence of tailwater depth on scour behavior [1][2][8][13]. Abida and Townsend [2] 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 [2]. Ruff et al. [16] 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. [4] 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 [1][2][4][9][17][18]. Abt et al [3][19] 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 [16][20]. The scour hole dimension was also effected by the culvert slope. Abt et al. [3][21] 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. [21][22] 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 [23][24]. The blockage phenomenon through was studied experimentally and numerical [15][25][26][27][28][29][30][31][32][33]. Jaeger and Lucke [33] 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. [26] 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. [32] 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 [34][35][36][37][38]. Epely-Chauvin et al. [36] 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. [35] 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. [14][15] 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 [39]. 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 [40].1.

    Governing equations

    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 [41].

    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 [41]:(8)θcr=τcrgd50(ρs-ρ)

    The Soulsby–Whitehouse [42] 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 [43].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.

    Boundary condition

    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.

    Casehb cmB = hb/hQ lit/sSFdd50 mmds/h measuredls/hdd/hld/hds/h estimated
    B000351.261.692.50.581.500.275.000.46
    B3060.30351.261.682.50.481.250.274.250.40
    B50100.50351.221.742.50.451.100.244.000.37
    B70140.70351.231.732.50.431.500.165.500.33

    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 [44] and Abt [4] are so closed to the present study data.

    Table 2. Comparison of some previous scour formula.

    ResearchersFdCulvert shaped50(mm)Proposed equationSubmerged ratio
    Present study0.9–2.11square2.75dsh=0.56Fd-0.20B+0.45S-1.051.25–1.75
    Lim [44]1–10Circular1.65dsh=0.45Fd0.47
    Abt [4]Fd ≥ 1Circular0.22–7.34-dsh=3.67Fd0.57∗D500.4∗σ-0.4

    10. Conclusions

    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.

    References

    [1]P. Sarathi, M. Faruque, R. BalachandarInfluence of tailwater depth, sediment size and densimetric Froude number on scour by submerged square wall jetsJ. Hydraul. Res., 46 (2) (2008), pp. 158-175CrossRefView Record in ScopusGoogle Scholar[2]H. Abida, R. TownsendLocal scour downstream of box-culvert outletsJ. Irrig. Drain. Eng., 117 (3) (1991), pp. 425-440CrossRefView Record in ScopusGoogle Scholar[3]S.R. Abt, C.A. Donnell, J.F. Ruff, F.K. DoehringCulvert Slope and Shape Effects on Outlet ScourTransp. Res. Rec., 1017 (1985), pp. 24-30View Record in ScopusGoogle Scholar[4]S.R. Abt, R.L. Kloberdanz, C. MendozaUnified culvert scour determinationJ. Hydraul. Eng., 110 (10) (1984), pp. 1475-1479CrossRefView Record in ScopusGoogle Scholar[5]J.P. Bohan, Erosion And Riprap Requirements At Culvert And Storm-Drain Outlets, ARMY ENGINEER WATERWAYS EXPERIMENT STATION VICKSBURG MISS1970.Google Scholar[6]C. Mendoza, S.R. Abt, J.F. RuffHeadwall influence on scour at culvert outletsJ. Hydraul. Eng., 109 (7) (1983), pp. 1056-1060CrossRefView Record in ScopusGoogle Scholar[7]H. Breusers, A. Raudkivi, Scouring, hydraulic structures design manual, vol. 143, IAHR, AA Balkema, Rotterdam, 1991.Google Scholar[8]K. Ali, S. LimLocal scour caused by submerged wall jetsProc. Inst. Civ. Eng., 81 (4) (1986), pp. 607-645CrossRefView Record in ScopusGoogle Scholar[9]O. Aderibigbe, N. RajaratnamEffect of sediment gradation on erosion by plane turbulent wall jetsJ. Hydraul. Eng., 124 (10) (1998), pp. 1034-1042View Record in ScopusGoogle Scholar[10]F.W. Blaisdell, C.L. AndersonA comprehensive generalized study of scour at cantilevered pipe outletsJ. Hydraul. Res., 26 (4) (1988), pp. 357-376CrossRefView Record in ScopusGoogle Scholar[11]Y.-M. Chiew, S.-Y. LimLocal scour by a deeply submerged horizontal circular jetJ. Hydraul. Eng., 122 (9) (1996), pp. 529-532View Record in ScopusGoogle Scholar[12]R.A. Day, S.L. Liriano, W.R. WhiteEffect of tailwater depth and model scale on scour at culvert outletsProc. Instit. Civil Eng. – Water Marit. Eng., 148 (3) (2001), pp. 189-198http://www.icevirtuallibrary.com/doi/10.1680/wame.2001.148.3.18910.1680/wame.2001.148.3.189View Record in ScopusGoogle Scholar[13]S. Emami, A.J. SchleissPrediction of localized scour hole on natural mobile bed at culvert outletsScour and Erosion (2010), pp. 844-853CrossRefView Record in ScopusGoogle Scholar[14]S. Sorourian, A. Keshavarzi, J. Ball, B. SamaliStudy of Blockage Effect on Scouring Pattern Downstream of a Box Culvert under Unsteady FlowAustr. J Water Resor. (2013)Google Scholar[15]S. Sorourian, Turbulent Flow Characteristics At The Outlet Of Partially Blocked Box Culverts, in: 36th IAHR World Congress, The Hague, the Netherlands, 2015.Google Scholar[16]J. Ruff, S. Abt, C. Mendoza, A. Shaikh, R. KloberdanzScour at culvert outlets in mixed bed materialsUnited States. Federal Highway Administration. Office of Research and Development (1982)Google Scholar[17]S.A. Ansari, U.C. Kothyari, K.G.R. RajuInfluence of cohesion on scour under submerged circular vertical jetsJ. Hydraul. Eng., 129 (12) (2003), pp. 1014-1019View Record in ScopusGoogle Scholar[18]B. Crookston B. Tullis, Scour and Riprap Protection in a Bottomless Arch Culvert, in: World Environmental and Water Resources Congress 2008: Ahupua’A, 2008, pp. 1–10.Google Scholar[19]S.R. Abt, J. Ruff, F. Doehring, C. DonnellInfluence of culvert shape on outlet scourJ. Hydraul. Eng., 113 (3) (1987), pp. 393-400View Record in ScopusGoogle Scholar[20]Y.H. Chen, Scour at outlets of box culverts, Colorado State University, 1970.Google Scholar[21]S. Abt, P. Thompson, T. LewisEnhancement of the culvert outlet scour estimation equationsTransp. Res. Rec. J. Transp. Res. Board, 1523 (1996), pp. 178-185View Record in ScopusGoogle Scholar[22]F.K. Doehring, S.R. AbtDrop height influence on outlet scourJ. Hydraul. Eng., 120 (12) (1994), pp. 1470-1476CrossRefView Record in ScopusGoogle Scholar[23]W. Weeks, A. Barthelmess, E. Rigby, G. Witheridge, R. Adamson, Australian rainfall and runoff revison project 11: blockage of hydraulic structures, 2009.Google Scholar[24]W. Weeks, G. Witheridge, E. Rigby, A. BarthelmessProject 11: blockage of hydraulic structuresEngineers Australia (2013)Google Scholar[25]S.R. Abt, T.E. Brisbane, D.M. Frick, C.A. McKnightTrash rack blockage in supercritical flowJ. Hydraul. Eng., 118 (12) (1992), pp. 1692-1696View Record in ScopusGoogle Scholar[26]E. Rigby, M. Boyd, S. Roso, P. Silveri, A. Davis, Causes and effects of culvert blockage during large storms, in: Global solutions for urban drainage, 2002, pp. 1–16.Google Scholar[27]S. Roso, M. Boyd, E. Rigby, R. VanDrie“Prediction of increased flooding in urban catchments due to debris blockage and flow diversionsProceedings Novatech (2004), pp. 8-13View Record in ScopusGoogle Scholar[28]C.-D. Jan, C.-L. ChenDebris flows caused by Typhoon Herb in Taiwanin Debris-Flow Hazards and Related Phenomena, Springer (2005), pp. 539-563CrossRefGoogle Scholar[29]L.W. Zevenbergen, P.F. Lagasse, P.E. Clopper, Effects of debris on bridge pier scour, in: World Environmental and Water Resources Congress 2007: Restoring Our Natural Habitat, 2007, pp. 1–10.Google Scholar[30]A. Barthelmess, E. Rigby, Estimating Culvert and Bridge Blockages-a Simplified Procedure, in: Proceedings of the 34th World Congress of the International Association for Hydro-Environment Research and Engineering: 33rd Hydrology and Water Resources Symposium and 10th Conference on Hydraulics in Water Engineering, Engineers Australia, 2011, pp. 39.Google Scholar[31]E. Rigby, A. Barthelmess, Culvert Blockage Mechanisms and their Impact on Flood Behaviour, in: Proceedings of the 34th World Congress of the International Association for Hydro-Environment Research and Engineering: 33rd Hydrology and Water Resources Symposium and 10th Conference on Hydraulics in Water Engineering, Engineers Australia, 2011, pp. 380.Google Scholar[32]G. Streftaris, N. Wallerstein, G. Gibson, S. ArthurModeling probability of blockage at culvert trash screens using Bayesian approachJ. Hydraul. Eng., 139 (7) (2012), pp. 716-726Google Scholar[33]R. Jaeger, T. LuckeInvestigating the relationship between rainfall intensity, catchment vegetation and debris mobilityInt. J. GEOMATE, 12 (33) (2017), pp. 22-29 Download PDFView Record in ScopusGoogle Scholar[34]S. Amiraslani, J. Fahimi, H. Mehdinezhad, The Numerical Investigation of Free Falling Jet’s Effect On the Scour of Plunge Pool, in: XVIII International conference on water resources, Tehran University, Iran, 2008.Google Scholar[35]A.W. Nielsen, X. Liu, B.M. Sumer, J. FredsøeFlow and bed shear stresses in scour protections around a pile in a currentCoast. Eng., 72 (2013), pp. 20-38ArticleDownload PDFView Record in ScopusGoogle Scholar[36]G. Epely-Chauvin, G. De Cesare, S. SchwindtNumerical modelling of plunge pool scour evolution in non-cohesive sedimentsEng. Appl. Comput. Fluid Mech., 8 (4) (2014), pp. 477-487 Download PDFCrossRefView Record in ScopusGoogle Scholar[37]H. Karami, H. Basser, A. Ardeshir, S.H. HosseiniVerification of numerical study of scour around spur dikes using experimental dataWater Environ. J., 28 (1) (2014), pp. 124-134CrossRefView Record in ScopusGoogle Scholar[38]S.-H. Oh, K.S. Lee, W.-M. JeongThree-dimensional experiment and numerical simulation of the discharge performance of sluice passageway for tidal power plantRenew. Energy, 92 (2016), pp. 462-473ArticleDownload PDFView Record in ScopusGoogle Scholar[39]M.A. Khodier, B.P. TullisExperimental and computational comparison of baffled-culvert hydrodynamics for fish passageJ. Appl. Water Eng. Res. (2017), pp. 1-9CrossRefView Record in ScopusGoogle Scholar[40]F.S. Inc., FLOW-3D user’s manual, Flow Science, Inc., 2009.Google Scholar[41]G. Wei, J. Brethour, M. Grünzner, J. BurnhamSedimentation scour modelFlow Science Report, 7 (2014), pp. 1-29View Record in ScopusGoogle Scholar[42]R. Soulsby, R. Whitehouse, Threshold of sediment motion in coastal environments, in: Pacific Coasts and Ports’ 97: Proceedings of the 13th Australasian Coastal and Ocean Engineering Conference and the 6th Australasian Port and Harbour Conference, vol. 1, Centre for Advanced Engineering, University of Canterbury, 1997, pp. 145.Google Scholar[43]L.C.v. RijnSediment transport, part II: suspended load transportJ. Hydraul. Eng., 110 (11) (1984), pp. 1613-1641View Record in ScopusGoogle Scholar[44]S Y LIMScour below unsubmerged full-flowing culvert outletsProc. Instit. Civil Eng. – Water Marit. Energy, 112 (2) (1995), pp. 136-149http://www.icevirtuallibrary.com/doi/10.1680/iwtme.1995.2765910.1680/iwtme.1995.27659View Record in ScopusGoogle Scholar

    Peer review under responsibility of Faculty of Engineering, Alexandria University.

    Figure 1- Schematic diagram of pooled stepped spillway conducted by Felder et al. (2012A): Notes: h step height (10 cm): w pool height (3.1 cm): l horizontal step length (20 cm): lw pool weir length (1.5 cm): d' is the water depth above the crest; y' is the distance normal to the crest invert

    Study of inception point, void fraction and pressure over pooled stepped spillways using Flow-3D

    Khosro Morovati , Afshin Eghbalzadeh 
    International Journal of Numerical Methods for Heat & Fluid Flow

    ISSN: 0961-5539

    Article publication date: 3 April 2018

    Abstract

    많은 계단식 배수로 지오메트리 설계 지침이 평평한 단계를 위해 개발되었지만 통합 단계를 설계하는 것이 더 효율적으로 작동하는 배수로에 대한 적절한 대안이 될 수 있습니다.

    이 논문은 POOL의 다른 높이에서 공기 연행과 보이드 비율의 시작점을 다루는 것을 목표로 합니다. 그 후, FLOW-3D 소프트웨어를 사용하여 POOL과 경사면의 높이를 다르게 하여 폭기된 지역과 폭기되지 않은 지역에서 압력 분포를 평가했습니다.

    얻어진 수치 결과와 실험 결과의 비교는 본 연구에 사용된 모든 방류에 대해 잘 일치했습니다. POOL 높이는 시작 지점 위치에 미미한 영향을 미쳤습니다. 공극률의 값은 높은 방류에 비해 낮은 방전에서 더 많은 영향을 받았습니다.

    여수로의 마루(통기되지 않은 지역)에서는 음압이 나타나지 않았으며 각 방류에서 마루를 따라 높이가 15cm인 수영장에서 최대 압력 값이 얻어졌습니다.

    모든 사면에서 웅덩이 및 평평한 계단형 여수로의 계단층 부근에서는 음압이 형성되지 않았습니다. 그러나 평단식 여수로에 비해 평단식 여수로의 수직면 부근에서 음압이 더 많이 형성되어 평단식 슈트에서 캐비테이션 현상이 발생할 확률이 증가하였습니다.

    Study of inception point, void fraction and pressure over pooled
    stWhile many stepped spillways geometry design guidelines were developed for flat steps, designing pooled steps might be an appropriate alternative to spillways working more efficiency. This paper aims to deal with the inception point of air-entrainment and void fraction in the different height of the pools. Following that, pressure distribution was evaluated in aerated and non-aerated regions under the effect of different heights of the pools and slopes through the use of the FLOW-3D software. Comparison of obtained numerical results with experimental ones was in good agreement for all discharges used in this study. Pools height had the insignificant effect on the inception point location. The value of void fraction was more affected in lower discharges in comparison with higher ones. Negative pressure was not seen over the crest of spillway (non-aerated region), and the maximum pressure values were obtained for pools with 15 cm height along the crest in each discharge. In all slopes, negative pressure was not formed near the step bed in the pooled and flat stepped spillways. However, negative pressure was formed in more area near the vertical face in the flat stepped spillway compared with the pooled stepped spillway which increases the probability of cavitation phenomenon in the flat stepped chute.

    Design/methodology/approach

    압력, 공극률 및 시작점을 평가하기 위해 POOL된 계단식 여수로가 사용되었습니다. 또한 POOL의 다른 높이가 사용되었습니다. 이 연구의 수치 시뮬레이션은 Flow-3D 소프트웨어를 통해 수행되었습니다. 얻어진 결과는 풀이 압력, 공극률 및 시작점을 포함한 2상 유동 특성에 영향을 미칠 수 있음을 나타냅니다.

    Findings

    마루 위에는 음압이 보이지 않았습니다. 압력 값은 사용된 모든 높이와 15cm 높이에서 얻은 최대 값에 대해 다릅니다. 또한, 풀링 스텝은 플랫 케이스에 비해 음압점 감소에 더 효과적인 역할을 하였습니다. 시작 지점 위치는 특히 9 및 15cm 높이에 대해 스키밍 흐름 영역과 비교하여 낮잠 및 전환 흐름 영역에서 더 많은 영향을 받았습니다.

    Keywords

    Citation

    Morovati, K. and Eghbalzadeh, A. (2018), “Study of inception point, void fraction and pressure over pooled stepped spillways using Flow-3D”, International Journal of Numerical Methods for Heat & Fluid Flow, Vol. 28 No. 4, pp. 982-998. https://doi.org/10.1108/HFF-03-2017-0112

    Figure 1- Schematic diagram of pooled stepped spillway conducted by Felder et al. (2012A): Notes: h  step height (10 cm): w pool height (3.1 cm): l horizontal step length (20 cm): lw pool weir length (1.5 cm):  d' is the water depth above the crest; y' is the distance normal to the crest invert
    Figure 1- Schematic diagram of pooled stepped spillway conducted by Felder et al. (2012A): Notes: h step height (10 cm): w pool height (3.1 cm): l horizontal step length (20 cm): lw pool weir length (1.5 cm): d’ is the water depth above the crest; y’ is the distance normal to the crest invert
    Figure 2- meshing domain and distribution of blocks
    Figure 2- meshing domain and distribution of blocks
    Figure 3- Comparison of numerical simulation with experimental data by Felder et al. (2012A);  mesh convergence analysis; pooled stepped spillway (slope: 26.6 0 )
    Figure 3- Comparison of numerical simulation with experimental data by Felder et al. (2012A); mesh convergence analysis; pooled stepped spillway (slope: 26.6 0 )
    Figure 4- Comparison of numerical simulation with experimental data by Felder et al. (2012A);  Flat stepped spillway (slope: 0 26 6. )
    Figure 4- Comparison of numerical simulation with experimental data by Felder et al. (2012A); Flat stepped spillway (slope: 0 26 6. )
    Figure 5-Comparison of numerical simulation with experimental data by Felder et al. (2012B); pooled  and flat stepped spillways (slope: 0 9.8 )
    Figure 5-Comparison of numerical simulation with experimental data by Felder et al. (2012B); pooled and flat stepped spillways (slope: 0 9.8 )
    Figure 6- TKE distribution on steps 8, 9 and 10 for four different mesh numbers: 261252 (model 1),  288941 (model 2), 323578 (model 3) and 343154 (model 4)
    Figure 6- TKE distribution on steps 8, 9 and 10 for four different mesh numbers: 261252 (model 1), 288941 (model 2), 323578 (model 3) and 343154 (model 4)
    Figure 7- Comparison of obtained Void fraction distribution on step 10 in numerical simulation with  experimental work conducted by Felder et al. (2012A); (slope 26.60 )
    Figure 7- Comparison of obtained Void fraction distribution on step 10 in numerical simulation with experimental work conducted by Felder et al. (2012A); (slope 26.60 )
    Figure 8- Results of inception point of air entrainment in different height of the pools: comparison with  empirical correlations (Eqs 8-9), experimental (Felder et al. (2012A)) and numerical data
    Figure 8- Results of inception point of air entrainment in different height of the pools: comparison with empirical correlations (Eqs 8-9), experimental (Felder et al. (2012A)) and numerical data
    Figure 9- Void fraction distribution for different pool heights on steps 10; slope 26.6 0
    Figure 9- Void fraction distribution for different pool heights on steps 10; slope 26.6 0
    Figure 10- Comparison of pressure distribution between numerical simulation and experimental work  conducted by Zhang and Chanson (2016); flat stepped spillway (slope: 0 45 )
    Figure 10- Comparison of pressure distribution between numerical simulation and experimental work conducted by Zhang and Chanson (2016); flat stepped spillway (slope: 0 45 )
    Figure 11- A comparison of the pressure distribution above the crest of the spillway; B comparison of the  free surface profile along the crest of the spillway.  Note: x' indicates the longitudinal distance from the starting point of the crest.
    Figure 11- A comparison of the pressure distribution above the crest of the spillway; B comparison of the free surface profile along the crest of the spillway. Note: x’ indicates the longitudinal distance from the starting point of the crest.
    Figure 12- pressure distribution along crest of spillway in different discharges; slope 26.6
    Figure 12- pressure distribution along crest of spillway in different discharges; slope 26.6
    Figure 13- Pressure distribution near the last step bed for different slopes and discharges: x'' indicatesthe  longitudinal distance from the intersection of the horizontal and vertical faces of step 10; y" is the distance from the intersection of the horizontal and vertical faces in the vertical direction
    Figure 13- Pressure distribution near the last step bed for different slopes and discharges: x” indicatesthe longitudinal distance from the intersection of the horizontal and vertical faces of step 10; y” is the distance from the intersection of the horizontal and vertical faces in the vertical direction
    Figure 14- Pressure distribution adjacent the vertical face of step 9 for different discharges and slopes
    Figure 14- Pressure distribution adjacent the vertical face of step 9 for different discharges and slopes
    Table1- Used discharges for assessments of mesh convergence analysis and hydraulic  characteristics
    Table1- Used discharges for assessments of mesh convergence analysis and hydraulic characteristics

    Conclusion

    본 연구에서는 자유표면을 모사하기 위해 VOF 방법과 k -ε (RNG) 난류 모델을 활용하여 FLOW-3D 소프트웨어를 사용하였고, 계단식 배수로의 유동을 모사하기 위한 목적으로 난류 특성을 모사하였다. 얻은 결과는 수치 모델이 시작점 위치, 보이드 비율 및 압력을 적절하게 시뮬레이션했음을 나타냅니다. 풀의 높이는 공기 유입 위치에 미미한 영향을 미치므로 얻은 결과는 이 문서에서 제시된 상관 관계와 잘 일치했습니다. 즉, 사용 가능한 상관 관계를 서로 다른 풀 높이에 사용할 수 있습니다. 공극률의 결과는 스텝 풀 근처의 나프 유동 영역에서 공극율 값이 다른 배출보다 더 큰 것으로 나타났다. 더욱이 고방출량 .0 113m3/s에서 수영장 높이를 변경해도 수영장 표면 근처의 공극률 값에는 영향을 미치지 않았습니다.

    낮잠 및 전환 체제의 압력 분포에 대한 0 및 3cm 높이의 수영장 효과는 많은 지점에서 대부분 유사했습니다. 더욱이 조사된 모든 높이에서 여수로의 마루를 따라 부압이 없었습니다. 여수로 끝단의 바닥 부근의 압력 결과는 평평하고 고인 경우 부압이 발생하지 않았음을 나타냅니다. 수직면 부근의 음압은 웅덩이에 비해 평평한 계단형 여수로의 깊이(w=0 cm)의 대부분에서 발생하였다. 또한 더 큰 사면에 대한 풀링 케이스에서 음압이 제거되었습니다. 평단식 여수로에서는 계단의 수직면에 인접한 더 넓은 지역에서 음압이 발생하였기 때문에 이 여수로에서는 고형단식여수로보다 캐비테이션 현상이 발생할 가능성이 더 큽니다.

    In this study, the FLOW-3D software was used through utilizing the VOF method and k −ε (RNG) turbulence model in order to simulate free surface, and turbulence characteristics for the purpose of simulating flow over pooled stepped spillway. The results obtained indicated that the numerical model properly simulated the inception point location, void fraction, and pressure. The height of the pools has the insignificant effect on the location of air entrainment, so that obtained results were in good agreement with the correlations presented in this paper. In other words, available correlations can be used for different pool heights. The results of void fraction showed that the void fraction values in nappe flow regime near the step pool were more than the other discharges. Furthermore in high discharge, 0.113m3/s, altering pool height had no effect on the value of void fraction near the pool surface.

    The effect of the pools with 0 and 3 cm heights over the pressure distribution in nappe and transition regimes was mostly similar in many points. Furthermore, in all examined heights there was no negative pressure along the crest of the spillway. The pressure results near the bed of the step at the end of the spillway indicated that negative pressure did not occur in the flat and pooled cases. Negative pressure near the vertical face occurred in the most part of the depth in the flat stepped spillway (w=0 cm) in comparison with the pooled case. Also, the negative pressure was eliminated in the pooled case for the larger slopes. Since negative pressure occurred in a larger area adjacent the vertical face of the steps in the flat stepped spillways, it is more likely that cavitation phenomenon occurs in this spillway rather than the pooled stepped spillways.

    References

    1. André, S. (2004), “High velocity aerated flows on stepped chutes with macro-roughness elements.” Ph.D. thesis,
      Laboratoire de Constructions Hydraulics (LCH), EPFL, Lausanne, Switzerland, 272 pages.
    2. Attarian, A. Hosseini, Kh. Abdi, H and Hosseini, M. (2014), “The Effect of the Step Height on Energy
      Dissipation in Stepped Spillways Using Numerical Simulation”. Arabian Journal for Science and
      Engineering, 39(4), 2587-2594.
    3. Bombardelli, F.A. Meireles. I. Matos, J. (2011), “Laboratory measurements and multi-block numerical
      simulations of the mean flow and turbulence in the non-aerated skimming flow region of steep stepped
      spillways”. Environmental fluid mechanics, 11(3) 263-288.
    4. Chakib, B. (2013), “Numerical Computation of Inception Point Location for Flat-sloped Stepped Spillway”.
      International Journal of Hydraulic Engineering; 2(3): 47-52.
    5. Chakib, B. Mohammed, H. (2015), “Numerical Simulation of Air Entrainment for Flat-Sloped Stepped Spillway.
      Journal of computational multiphase flows”, Volume 7. Number 1.
    6. Chanson, H. Toombes, L. (2002), “Air–water flows down stepped chutes: turbulence and flow structure
      observations”. International Journal of Multiphase Flow, 28(11) 1737-1761
    7. Chen, Q. Dai, G. Liu, H. (2002), “Volume of Fluid Model for Turbulence Numerical Simulation
      of Stepped Spillway Overflow”. DOI: 10.1061/(ASCE)0733-9429128:7(683).
    8. Cheng, X. Chen, Y. Luo, L. (2006), “Numerical simulation of air-water two-phase flow over stepped spillways”.
      Science in China Series E: Technological Sciences, 49(6), 674-684.
    9. Cheng, X. Luo, L. Zhao, W. (2004), “Study of aeration in the water flow over stepped spillway”. In: Proceedings
      of the world water congress.
    10. Chinnarasri, Ch. Kositgittiwong, D. Julien, Y. (2013), “Model of flow over spillways by computational fluid
      dynamics”. Proceedings of the ICE – Water Management, Volume 167(3) 164 –175.
    11. Dastgheib, A. Niksokhan, M.H. and Nowroozpour, A.R. (2012), “Comparing of Flow Pattern and Energy
      Dissipation over different forms of Stepped Spillway”. World Environmental and Water Resources
      Congress ASCE.
    12. Eghbalzadeh, A. Javan, M. (2012), “Comparison of mixture and VOF models for numerical simulation of air
      entrainment in skimming flow over stepped spillway”. Procedia Engineering, 28. 657-660.
    13. Felder, S, Chanson, H. (2012), “Free-surface Profiles, Velocity and Pressure Distributions on a
      Broad-Crested Weir: a Physical study “Free-surface Profiles, Velocity and Pressure Distributions on a
      Broad-Crested Weir: a Physical study
    14. Felder, S. Fromm, Ch. Chanson, H. (2012B), “Air entrainment and energy dissipation on a 8.9 slope stepped
      spillway with flat and pooled steps”, School of Civil Engineering, The University of Queensland,.
      Brisbane, Australia.
    15. Felder, S. Chanson, H. (2014A), Triple decomposition technique in air–water flows: application to instationary
      flows on a stepped spillway. International Journal of Multiphase Flow, 58, 139-153.
    16. Felder, S. Chanson, H. (2014B), Effects of step pool porosity upon flow aeration and energy dissipation on
      pooled stepped spillways. Journal of Hydraulic Engineering, 140(4), 04014002.
    17. Felder, S. Chanson, H. (2013A), “Air entrainment and energy dissipation on porous pooled stepped spillways”.
      Paper presented at the International Workshop on Hydraulic Design of Low-Head Structures.
    18. Felder, S. Chanson, H. (2013B), “Aeration, flow instabilities, and residual energy on pooled stepped spillways of
      embankment dams”. Journal of irrigation and drainage engineering, 139(10) 880-887.
    19. Felder, S. Guenther, Ph. Chanson, H. (2012A). “Air-water flow properties and energy dissipation on stepped
      spillways: a physical study of several pooled stepped configurations”, School of Civil Engineering, The
      University of Queensland,. Brisbane, Australia.
    20. Flow Science, (2013). “FLOW-3D user’s manual”, version 10.1. Flow Science, Inc, Los Alamos.
    21. Frizell, K.W. Renna, F.M. Matos, J. (2012), “Cavitation potential of flow on stepped spillways”. Journal of
      Hydraulic Engineering, 139(6), 630-636.
    22. Gonzalez, C. (2005), “An experimental study of free-surface aeration on embankment stepped chutes”,
      department of civil engineering, Brisbane, Australia, Phd thesis.
    23. Gonzalez, C.A. Chanson, H. (2008), “Turbulence manipulation in air–water flows on a stepped chute: An
      experimental study”. European Journal of Mechanics-B/Fluids, 27(4), 388-408.
    24. Guenther, Ph.. Felder, S. Chanson, H. (2013), “Flow aeration, cavity processes and energy dissipation on flat and
      pooled stepped spillways for embankments”. Environmental fluid mechanics, 13(5) 503-525.
    25. Hamedi, A. Mansoori, A. Malekmohamadi, I. Roshanaei, H. (2011), “Estimating Energy Dissipation in Stepped
      Spillways with Reverse Inclined Steps and End Sill”. World Environmental and Water Resources
      Congress, ASCE.
    26. Hirt, C.W. (2003), “Modeling Turbulent Entrainment of Air at a Free Surface”. Flow Science Inc.
    27. Hunt, S.L. Kadavy, K.C. (2013), “Inception point for enbankment dam stepped spillway”. J. Hydraul. Eng.,
      139(1), 60–64.
    28. Hunt, S.L. Kadavy, K.C. (2010), “Inception Point Relationship for Flat-Sloped Stepped
      Spillways”. DOI: 10.1061/ASCEHY.1943-7900.0000297.
    29. Matos, J. Quintela, A. (2000), “Air entrainment and safety against cavitation damage in stepped spillways over
      RCC dams. In: Proceeding Intl. Workshop on Hydraulics of Stepped Spillways”, VAW, ETH-Zurich, H.E.
      Minor and W.H. Hager. Balkema. 69–76.
    30. Meireles, I. Matos, J. (2009), “Skimming flow in the nonaerated region of stepped spillways over embankment
      dams”. J. Hydraul. Eng., 135(8), 685–689.
    31. Miang-liang, ZH. Yong-ming, SH. (2008), “Three dimentional simulation of meandering river basin on 3-D
      RNG k − ε turbulence model”. Journal of hydrodynamics, 20(4): 448-455.
    32. Morovati, Kh. Eghbalzadeh, A. Javan, M. (2015), “Numerical investigation of the configuration of the pools on
      the flowPattern passing over pooled stepped spillway in skimming flow regime. Acta Mech, DOI
      10.1007/s00707-015-1444-x
    33. Morovati, Kh. Eghbalzadeh, A. Soori, S. (2016), “Numerical Study of Energy Dissipation of Pooled Stepped
      spillway”. Civil Engineering Journal. Vol. 2, No. 5.
    34. Nikseresht, A.H. Talebbeydokhti, N. and Rezaei, M.J. (2013), “Numerical simulation of two-phase flow on steppool spillways”. Scientia Iranica, A 20 (2), 222–230.
    35. Peyras, L. Royet, P. Degoutte, G. (1990), “Flow and energy dissipation over stepped gabion weirs”. ASCE
      Convention.
    36. Qun, Ch. Guang-qing, D. Feu-qing, Zh. Qing, Y. (2004). “Three-dimensional turbulence numerical simulation of
      a stepped spillway overflow”. Journal of hydrodynamics, Ser. B, 1, 74-79.
    37. Relvas, A. T. Pinheiro, A. N. (2008), Inception point and air concentration in flows on stepped chutes lined with
      wedge-shaped concrete blocks. Journal of Hydraulic Engineering, 134(8), 1042-1051
    38. Sanchez, M. (2000), “Pressure field in skimming flow over a stepped spillways”. In: Proceeding Intl. Workshop
      on Hydraulics of Stepped Spillways, VAW, ETH-Zurich, H.E. Minor and W.H. Hager. Balkema,
      137–146.
    39. Sarfaraz, M. Attari, J. Pfister, M. (2012), “Numerical Computation of Inception Point Location for Steeply
      Sloping Stepped Spillways”. 9th International Congress on Civil Engineering, May 8-10. Isfahan
      University of Technology (IUT), Isfahan, Iran.
    40. Savage, Bruce M. Michael C. Johnson. (2001), “Flow over ogee spillway: Physical and numerical model case
      study.” Journal of Hydraulic Engineering 127.8:640-649.
    41. Shahhedari, H. Jafari Nodoshan, E. Barati, R. Azhdary moghadam, M. (2014). “Discharge coeficient and energy
      dissipation over stepped spillway under skimming flow regime”. KSCE Journal of Civil Engineering, DOI
      10.1007/s12205-013-0749-3.
    42. Tabbara, M. Chatila, J. Awwad, R. (2005), “Computational simulation of flow over stepped spillways”.
      Computers & structures, 83(27) 2215-2224.
    43. Thorwarth, J. (2008), “Hydraulisches Verhalten der Treppengerinne mit eingetieften Stufen—Selbstinduzierte
      Abflussinstationaritäten und Energiedissipation” [Hydraulics of pooled stepped spillways— Self-induced
      unsteady flow and energy dissipation]. Ph.D. thesis, Univ. of Aachen, Aachen, Germany (in German).
    44. WeiLin, XU. ShuJing, LUO, QiuWen, ZH. Jing, LUO. (2015), “Experimental study on pressure and aeration
      characteristics in stepped chute flows. SCIENCE CHINA. Vol.58 No.4: 720–726. doi: 10.1007/s11431-015-
      5783-6.
    45. Xiangju, Ch. Yongcan, C. Lin, L. (2006), “Numerical simulation of air-water two-phase flow over stepped
      spillways”. Science in China Series E: Technological Sciences, 49(6), 674-684.
    46. Zare, K.H. Doering, J.C. (2012), “Inception Point of Air Entrainment and Training Wall
      Characteristics of Baffles and Sills on Stepped Spillways”. DOI: 10.1061/(ASCE)HY
      .1943-7900.0000630.
    47. Zhan, J. Zhang, J. Gong, Y. (2016), “Numerical investigation of air-entrainment in skimming flow over stepped
      spillways”. Theoretical and Applied Mechanics Letters. Volume 6. Pages 139–142.
    48. Zhang, G. Chanson, H. (2016), Hydraulics of the developing flow region of stepped spillways. II: Pressure and
      velocity fields. Journal of Hydraulic Engineering, 142(7).
    49. Zhenwei, M. Zhiyan, Zh. Tao, Zh. (2012), “Numerical Simulation of 3-D Flow Field of Spillway based on VOF
      Method”. Procedia Engineering, 28, 808-812.
    50. Zhi-yong, D. Hun-wei, L.J. (2006), “Numerical simulation of skimming flow over mild stepped channel”.
      Journal of Hydrodynamics, Ser. B, 18(3) 367-371.
    51. ZhongDong, Q. XiaoQing, H. WenXin, H. António, A. (2009), “Numerical simulation and analysis of water
      flow over stepped spillways”. Science in China Series E: Technological Sciences, 52(7) 1958-1965.
    Fig. 1  Layout of spillway tunnel

    Experimental study and numerical simulation of hydraulic characteristics of ogee spillway tunnel

    WU Jingxia1
    , ZHANG Chunjin2,3
    (1. Xi’an Water Conservancy Survey Design Institute, Xi’an  710054, Shaanxi, China; 2. Key Laboratory of
    Yellow River Sediment Research, M. W. R. , Yellow River Institute of Hydraulic Research, Zhengzhou 
    450003, Henan, China; 3. State Key Laboratory of Hydrology-Water Resources and Hydraulic
    Engineering, Hohai University, Nanjing  210098, Jiangsu, China)

    수치 시뮬레이션을 통해 오지 여수로 터널의 수리적 특성 연구의 타당성을 탐색하기 위해 황하 Xiaolangdi 수질 관리 프로젝트의 2번 오지 여수로 터널을 연구 대상으로 취한 다음 오지의 수리 특성 설계 및 점검 홍수 수준 조건에서 여수로 터널은 RNG k-ε 난류 모델을 사용하여 배출 용량, 터널 크라운 잔류 공간, 단면 유속, 압전 수두, 유동 캐비테이션 수, 제트 흐름 범위 및 1 ∶ 40의 일반 수리 모델과 결합된 세굴 구덩이 깊이, 시뮬레이션 값과 실험 값 모두 비교됩니다.

    연구결과 모의실험값이 실험값과 일치하여 오지 여수로터널의 수리적 특성을 수치모사를 통해 탐색할 수 있음을 확인하였다. 여수로터널 내부의 흐름은 안정적이고 터널 크라운 잔류 공간은 개방 흐름과 완전 흐름의 교대 흐름 패턴이 없는 25% 이상입니다.

    체크 홍수 수위에서 시뮬레이션 값과 유량 계수의 실험 값은 모두 설계에서보다 높으므로 배출 용량은 홍수 제어 관련 설계 요구 사항을 충족할 수 있습니다. 오지 단면과 플립 단면의 유동 캐비테이션 수는 캐비테이션 손상이 발생할 가능성이 작기 때문에 캐비테이션 침식을 줄이기 위한 적절한 적절한 조치가 채택될 필요가 있습니다.

    유압 모델의 고르지 않은 표면에 부압이 발생하면 표면 구조에 관련주의를 기울일 필요가 있습니다. 연구 결과는 여수로 터널의 설계 및 건설에 대한 관련 참고 및 이론적 근거를 제공할 수 있습니다.

    Keywords

    Xiaolangdi Water Control Project; ogee spillway tunnel; simulative calculation; hydraulic characteristics; turbulent
    model

    Fig. 1  Layout of spillway tunnel
    Fig. 1  Layout of spillway tunnel
    Fig. 4  Hydraulic modeling
    Fig. 4  Hydraulic modeling
    Fig. 6  Sectional surface profile distributions
    Fig. 6  Sectional surface profile distributions
    Fig. 7  Comparison between simulated results and experimental results for flow velocity of section-cross
    Fig. 7  Comparison between simulated results and experimental results for flow velocity of section-cross

    参考文献(References)

    [1]  谢省宗, 吴一红, 陈文学. 我国高坝泄洪消能新技术的研究和创
    新[J]. 水利学报, 2016, 47(3): 324-336.
    XIE Shengzong, WU Yihong, CHEN Wenxue. New technology and
    innovation on flood discharge and energy dissipation of high dams in
    China [J]. Journal of Hydraulic Engineering, 2016, 47( 3): 324-
    336.
    [2]  刘嘉夫, 齐昕. 龙抬头水电站泄洪洞水力特性研究[ J]. 水利水
    电技术, 2019, 50(2): 139-143.
    LIU Jiafu, QI Xin. Study on hydraulic characteristics of ogee spillway
    tunnel of hydropower station [ J]. Water Resources and Hydropower
    Engineering, 2019, 50(2): 139-143.
    [3]  范灵, 张宏伟, 刘之平, 等. 明流泄洪洞布置形式对水力特性影
    响的数值研究[J]. 水力发电学报, 2009, 28(3): 126-131.
    FAN Ling, ZHANG Hongwei, LIU Zhiping, et al. Numerical study
    on hydraulic characteristic of free surface flow in spillway tunnel with
    different configuration [ J ]. Journal of Hydroelectric Engineering,
    2009, 28(3): 126-131.
    [4]  张春晋, 李永业, 孙西欢. 明流泄洪洞水力特性的二维数值模拟
    与试验研究[J]. 长江科学院院报, 2016, 33(1): 54-60.
    ZHANG Chunjin, LI Yongye, SUN Xihuan. Two-dimensional numerical simulation and experimental research of hydraulic characteristics
    in spillway tunnel with free water surface [ J]. Journal of Yangtze
    River Scientific Research Institute, 2016, 33(1): 54-60.
    [5]  徐国宾, 章环境, 刘昉, 等. 龙抬头泄洪洞水力特性的数值模拟
    [J]. 长江科学院院报, 2015, 32(1): 84-87.
    XU Guobin, ZHANG Huanjing, LIU Fang, et al. Numerical simulation on hydraulic characteristic of high head ogee spillway tunnel [J].
    Journal of Yangtze River Scientific Research Institute, 2015, 32(1):
    84-87.
    [6]  陈瑞华, 杨吉健, 马麟, 等. 小湾水电站泄洪洞洞身数值模拟
    [J]. 排灌机械工程学报, 2017, 35(6): 488-494.
    CHEN Ruihua, YANG Jijian, MA Lin, et al. Numerical simulation
    of tunnel of Xiaowan Hydropower Station [ J]. Journal of Drainage
    and Irrigation Machinery Engineering, 2017, 35(6): 488-494.
    [7]  翟保林, 刘亚坤. 高水头明流泄洪洞三维数值模拟[ J]. 水利与
    建筑工程学报, 2017, 15(3): 31-34.
    ZHAI Baolin, LIU Yakun. 3-D Numerical simulation of high water
    head spillway tunnel with free surface [ J ]. Journal of Water
    Resources and Architectural Engineering, 2017, 15(3): 31-34.
    [8]  姜 攀, 尹进步, 何武全, 等. 有压泄洪洞弯道压力特性数值模拟
    与试验研究[J]. 水力发电, 2016, 42(2): 49-53.
    JIANG Pan, YIN Jinbu, HE Wuquan, et al. Numerical simulation
    and experimental research on pressure characteristic of curved section
    of pressure spillway tunnel [J]. Water Power, 2016, 42(2): 49-53.
    [9]  邓 军, 许唯临, 雷军, 等. 高水头岸边泄洪洞水力特性的数值模
    拟[J]. 水利学报, 2005(10): 1209-1212.
    DENG Jun, XU Weilin, LEI Jun, et al. Numerical simulation of
    hydraulic characteristics of high head spillway tunnel [J]. Journal of
    Hydraulic Engineering, 2005(10): 1209-1212.
    [10] 史晓薇, 王长新, 李琳. 高流速泄洪隧洞水力特性的三维数值模
    拟[J]. 新疆农业大学学报, 2015, 38(6): 495-501.
    SHI Xiaowei, WANG Changxin, LI Lin. Three dimensional numerical
    simulation of hydraulic characteristics of spillway tunnel with high flow
    velocity [ J]. Journal of Xinjiang Agricultural University, 2015, 38
    (6): 495-501.
    [11] 叶茂, 伍平, 王波, 等. 泄洪洞掺气水流的数值模拟研究[J]. 水
    力发电学报, 2014, 33(4): 105-110.
    YE Mao, WU Ping, WANG Bo, et al. Numerical simulation of
    aerated flow in hydraulic tunnel [ J ]. Journal of Hydroelectric
    Engineering, 2014, 33(4): 105-110.
    [12] 胡涛, 王均星, 杜少磊. 大流量泄洪洞掺气坎水力特性数值模拟
    [J]. 武汉大学学报(工学版), 2014, 47(5): 615-620.
    HU Tao, WANG Junxing, DU Shaolei. Numerical simulation of
    hydraulic characteristics of aerators in spillway tunnel with large
    discharge [J]. Engineering Journal of Wuhan University, 2014, 47
    (5): 615-620.
    [13] 孙鹏飞, 姜哲, 崔维成, 等. 基于 CFD 的全海深载人潜水器直航
    阻力性能研究[J]. 中国造船, 2019, 60(2): 77-87.
    SUN Pengfei, JIANG Zhe, CUI Weicheng, et al. Numerical simulation of a full ocean depth manned submersible based on CFD method
    [J]. Shipbuilding of China, 2019, 60(2): 77-87.
    [14] 宛鹏翔, 范俊, 韩省思, 等. 冲击射流流动换热超大涡模拟研究
    [J]. 推进技术, 2020, 41(10): 2237-2247.
    WAN Pengxiang, FAN Jun, HAN Xingsi, et al. Very-large eddy
    simulation of impinging jet flow and heat transfer [ J]. Journal of
    Propulsion Technology, 2020, 41(10): 2237-2247.
    [15] 李国杰, 黄萌, 陈斌. 基于 PISO 算法的非结构化网格 VOF 算法
    [J]. 工程热物理学报, 2013, 34(3): 476-479.
    LI Guojie, HUANG Meng, CHEN Bing. VOF method on unstructured
    grid using PISO algorithm [ J]. Journal of Engineering Thermophysics, 2013, 34(3): 476-479.
    [16] 董玮, 何庆南, 梁武科, 等. 双蜗壳离心泵泵腔轴向宽度与流动

    DONG Wei, HE Qingnan, LIANG Wuke, et al. Relationship
    between axial width and flow characteristics of pump chamber in
    double volute centrifugal pump [ J ]. Journal of Northwestern
    Polytechnical University, 2020, 38(6): 1322-1329.
    [17] 陈恺, 张震宇, 王同光, 等. 基于 CFD 的水平轴风力机叶尖小翼
    增功研究[J]. 太阳能学报, 2021, 42(1): 272-278.
    CHEN Kai, ZHANG Zhenyu, WANG Tongguang, et al. CFD-Based
    power enhancement of winglets for horizontal-axis wind turbines [ J].
    Acta Energiae Solaris Sinica, 2021, 42(1): 272-278.
    [18] 张志君, 金柱男, 辛相锦, 等. 基于 VOF 方法的湿式离合器润滑
    油路 CFD 数值模拟[J]. 东北大学学报(自然科学版), 2020, 41
    (5): 716-722.
    ZHANG Zhijun, JIN Zhunan, XIN Xiangjin, et al. VOF method
    based CFD numerical simulation for wet clutch lubricating oil passage
    [ J]. Journal of Northeastern University (Natural Science), 2020, 41
    (5): 716-722.
    [19] 罗永钦, 刁明军, 何大明, 等. 高坝明流泄洪洞掺气减蚀三维数
    值模拟分析[J]. 水科学进展, 2012, 23(1): 110-116.
    LUO Yongqin, DIAO Mingjun, HE Daming, et al. Numerical simulation of aeration and cavitation in high dam spillway tunnels [ J].
    Advances in Water Science, 2012, 23(1): 110-116.
    [20] 许文海, 党彦, 李国栋, 等. 双洞式溢洪洞三维流动的数值模拟
    [J]. 水力发电学报, 2007(1): 56-60.
    XU Wenhai, DANG Yan, LI Guodong, et al. Three dimensional
    numerical simulation of the bi-tunnel spillway flow [ J]. Journal of
    Hydroelectric Engineering, 2007(1): 56-60.
    [21] 李爱华, 王腾, 刘沛清. 溪洛渡坝区岩石河床冲刷过程数值模拟
    [J]. 水力发电学报, 2012, 31(5): 154-158.
    LI Aihua, WANG Teng, LIU Peiqing. Numerical simulation of rock
    bed scour behind the dam of Xiluodu hydropower station [J]. Journal
    of Hydroelectric Engineering, 2012, 31(5): 154-15

    Flow velocity profiles for canals with a depth of 3 m and flow velocities of 5–5.3 m/s.

    Optimization Algorithms and Engineering: Recent Advances and Applications

    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

    Abstract

    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.

    1. Introduction

    Considering the impact of each variable is a very popular field within the analytical and statistical methods and intelligent systems [114]. 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 [1527]. Consequently, it is necessary to study the effects of the passive factors on the active domain [2836]. Because of the effect of vegetation on reducing the discharge capacity of rivers [37], 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 [3841].

    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 [42], 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 [4345]. 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 [46]. 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 [4748].

    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. [49], the Manning roughness coefficient for plants was calculated according to the Kouwen and Unny [50] 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 [51].

    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 [52]. 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 [53].

    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 nf, 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 [54].

    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 [4555].

    One of the works that has been done on the effect of vegetation on the roughness coefficient is Darby [56] 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 [475758] and the other method is to increase the canal bed roughness (Manning-Strickler coefficient) [455961]. These two methods provide acceptable results in models designed to simulate floodplain flow. Wang et al. [62] 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. [49] provided equations for determining the coefficient of vegetation roughness under different conditions. Lee et al. [63] 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 [496366] 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. [63] 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 [67]. 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 xyz and  are viscosity accelerations in the directions xyz 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 [68]. 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 1 The 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 1 The 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 [69] 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 [69] 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 [7077]. Determination and true implementation of such parameters is one of the key steps of any simulation [237881] and computing procedure [8286]. 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 [8788]. 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 2 Modeling the plant with cylindrical tubes at the bottom of the canal.

    Figure 3 Velocity 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 414 ). The total number of experiments in this study was 48 due to the limitations of modeling.(a)
    (a)(b)
    (b)(c)
    (c)(d)
    (d)(a)
    (a)(b)
    (b)(c)
    (c)(d)
    (d)Figure 4 Flow 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 5 Canal diagram with a depth of 1 meter and a flow rate of 3 meters per second.

    Figure 6 Canal diagram with a depth of 1 meter and a flow rate of 3.1 meters per second.

    Figure 7 Canal diagram with a depth of 1 meter and a flow rate of 3.2 meters per second.

    Figure 8 Canal diagram with a depth of 1 meter and a flow rate of 3.3 meters per second.(a)
    (a)(b)
    (b)(c)
    (c)(d)
    (d)(a)
    (a)(b)
    (b)(c)
    (c)(d)
    (d)Figure 9 Flow 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 10 Canal diagram with a depth of 2 meters and a flow rate of 4 meters per second.

    Figure 11 Canal diagram with a depth of 2 meters and a flow rate of 4.1 meters per second.

    Figure 12 Canal diagram with a depth of 2 meters and a flow rate of 4.2 meters per second.

    Figure 13 Canal diagram with a depth of 2 meters and a flow rate of 4.3 meters per second.(a)
    (a)(b)
    (b)(c)
    (c)(d)
    (d)(a)
    (a)(b)
    (b)(c)
    (c)(d)
    (d)Figure 14 Flow 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 510, 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 58 and 1011), 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 15 Canal 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 16 Canal 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 17 Canal 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 18 Canal 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)
    (a)(b)
    (b)(c)
    (c)(a)
    (a)(b)
    (b)(c)
    (c)Figure 19 Comparison 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)
    (a)(b)
    (b)(c)
    (c)(a)
    (a)(b)
    (b)(c)
    (c)Figure 20 Comparison 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 [27815188994]. In future, we can also apply the simulation logic and software of this research for other domains such as power engineering [9599].(a)
    (a)(b)
    (b)(c)
    (c)(a)
    (a)(b)
    (b)(c)
    (c)Figure 21 Comparison 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.

    3. Conclusion

    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.

    Nomenclature

    n:Manning’s roughness coefficient
    C:Chézy roughness coefficient
    f:Darcy–Weisbach coefficient
    V:Flow velocity
    R:Hydraulic radius
    g:Gravitational acceleration
    y:Flow depth
    Ks:Bed roughness
    A:Constant coefficient
    :Reynolds number
    y/∂x:Depth of water change
    S0:Slope of the canal floor
    Sf:Slope of energy line
    Fr:Froude number
    D:Characteristic length of the canal
    G:Mass acceleration
    :Shear stresses.

    Data Availability

    All data are included within the paper.

    Conflicts of Interest

    The authors declare that they have no conflicts of interest.

    Acknowledgments

    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.

    References

    1. H. Yu, L. Jie, W. Gui et al., “Dynamic Gaussian bare-bones fruit fly optimizers with abandonment mechanism: method and analysis,” Engineering with Computers, vol. 20, pp. 1–29, 2020.View at: Publisher Site | Google Scholar
    2. X. Zhao, D. Li, B. Yang, C. Ma, Y. Zhu, and H. Chen, “Feature selection based on improved ant colony optimization for online detection of foreign fiber in cotton,” Applied Soft Computing, vol. 24, pp. 585–596, 2014.View at: Publisher Site | Google Scholar
    3. J. Hu, H. Chen, A. A. Heidari et al., “Orthogonal learning covariance matrix for defects of grey wolf optimizer: insights, balance, diversity, and feature selection,” Knowledge-Based Systems, vol. 213, Article ID 106684, 2021.View at: Publisher Site | Google Scholar
    4. C. Yu, M. Chen, K. Chen et al., “SGOA: annealing-behaved grasshopper optimizer for global tasks,” Engineering with Computers, vol. 4, pp. 1–28, 2021.View at: Publisher Site | Google Scholar
    5. W. Shan, Z. Qiao, A. A. Heidari, H. Chen, H. Turabieh, and Y. Teng, “Double adaptive weights for stabilization of moth flame optimizer: balance analysis, engineering cases, and medical diagnosis,” Knowledge-Based Systems, vol. 8, Article ID 106728, 2020.View at: Google Scholar
    6. J. Tu, H. Chen, J. Liu et al., “Evolutionary biogeography-based whale optimization methods with communication structure: towards measuring the balance,” Knowledge-Based Systems, vol. 212, Article ID 106642, 2021.View at: Publisher Site | Google Scholar
    7. Y. Zhang, R. Liu, X. Wang et al., “Towards augmented kernel extreme learning models for bankruptcy prediction: algorithmic behavior and comprehensive analysis,” Neurocomputing, vol. 430, 2020.View at: Google Scholar
    8. H.-L. Chen, G. Wang, C. Ma, Z.-N. Cai, W.-B. Liu, and S.-J. Wang, “An efficient hybrid kernel extreme learning machine approach for early diagnosis of Parkinson׳s disease,” Neurocomputing, vol. 184, pp. 131–144, 2016.View at: Publisher Site | Google Scholar
    9. J. Xia, H. Chen, Q. Li et al., “Ultrasound-based differentiation of malignant and benign thyroid Nodules: an extreme learning machine approach,” Computer Methods and Programs in Biomedicine, vol. 147, pp. 37–49, 2017.View at: Publisher Site | Google Scholar
    10. C. Li, L. Hou, B. Y. Sharma et al., “Developing a new intelligent system for the diagnosis of tuberculous pleural effusion,” Computer Methods and Programs in Biomedicine, vol. 153, pp. 211–225, 2018.View at: Publisher Site | Google Scholar
    11. X. Xu and H.-L. Chen, “Adaptive computational chemotaxis based on field in bacterial foraging optimization,” Soft Computing, vol. 18, no. 4, pp. 797–807, 2014.View at: Publisher Site | Google Scholar
    12. M. Wang, H. Chen, B. Yang et al., “Toward an optimal kernel extreme learning machine using a chaotic moth-flame optimization strategy with applications in medical diagnoses,” Neurocomputing, vol. 267, pp. 69–84, 2017.View at: Publisher Site | Google Scholar
    13. L. Chao, K. Zhang, Z. Li, Y. Zhu, J. Wang, and Z. Yu, “Geographically weighted regression based methods for merging satellite and gauge precipitation,” Journal of Hydrology, vol. 558, pp. 275–289, 2018.View at: Publisher Site | Google Scholar
    14. F. J. Golrokh, G. Azeem, and A. Hasan, “Eco-efficiency evaluation in cement industries: DEA malmquist productivity index using optimization models,” ENG Transactions, vol. 1, 2020.View at: Google Scholar
    15. D. Zhao, L. Lei, F. Yu et al., “Chaotic random spare ant colony optimization for multi-threshold image segmentation of 2D Kapur entropy,” Knowledge-Based Systems, vol. 8, Article ID 106510, 2020.View at: Google Scholar
    16. Y. Zhang, R. Liu, X. Wang, H. Chen, and C. Li, “Boosted binary Harris hawks optimizer and feature selection,” Engineering with Computers, vol. 517, pp. 1–30, 2020.View at: Publisher Site | Google Scholar
    17. L. Hu, G. Hong, J. Ma, X. Wang, and H. Chen, “An efficient machine learning approach for diagnosis of paraquat-poisoned patients,” Computers in Biology and Medicine, vol. 59, pp. 116–124, 2015.View at: Publisher Site | Google Scholar
    18. L. Shen, H. Chen, Z. Yu et al., “Evolving support vector machines using fruit fly optimization for medical data classification,” Knowledge-Based Systems, vol. 96, pp. 61–75, 2016.View at: Publisher Site | Google Scholar
    19. X. Zhao, X. Zhang, Z. Cai et al., “Chaos enhanced grey wolf optimization wrapped ELM for diagnosis of paraquat-poisoned patients,” Computational Biology and Chemistry, vol. 78, pp. 481–490, 2019.View at: Publisher Site | Google Scholar
    20. Y. Xu, H. Chen, J. Luo, Q. Zhang, S. Jiao, and X. Zhang, “Enhanced Moth-flame optimizer with mutation strategy for global optimization,” Information Sciences, vol. 492, pp. 181–203, 2019.View at: Publisher Site | Google Scholar
    21. M. Wang and H. Chen, “Chaotic multi-swarm whale optimizer boosted support vector machine for medical diagnosis,” Applied Soft Computing Journal, vol. 88, Article ID 105946, 2020.View at: Publisher Site | Google Scholar
    22. Y. Chen, J. Li, H. Lu, and P. Yan, “Coupling system dynamics analysis and risk aversion programming for optimizing the mixed noise-driven shale gas-water supply chains,” Journal of Cleaner Production, vol. 278, Article ID 123209, 2020.View at: Google Scholar
    23. H. Tang, Y. Xu, A. Lin et al., “Predicting green consumption behaviors of students using efficient firefly grey wolf-assisted K-nearest neighbor classifiers,” IEEE Access, vol. 8, pp. 35546–35562, 2020.View at: Publisher Site | Google Scholar
    24. H.-J. Ma and G.-H. Yang, “Adaptive fault tolerant control of cooperative heterogeneous systems with actuator faults and unreliable interconnections,” IEEE Transactions on Automatic Control, vol. 61, no. 11, pp. 3240–3255, 2015.View at: Google Scholar
    25. H.-J. Ma and L.-X. Xu, “Decentralized adaptive fault-tolerant control for a class of strong interconnected nonlinear systems via graph theory,” IEEE Transactions on Automatic Control, vol. 66, 2020.View at: Google Scholar
    26. H. J. Ma, L. X. Xu, and G. H. Yang, “Multiple environment integral reinforcement learning-based fault-tolerant control for affine nonlinear systems,” IEEE Transactions on Cybernetics, vol. 51, pp. 1–16, 2019.View at: Publisher Site | Google Scholar
    27. J. Hu, M. Wang, C. Zhao, Q. Pan, and C. Du, “Formation control and collision avoidance for multi-UAV systems based on Voronoi partition,” Science China Technological Sciences, vol. 63, no. 1, pp. 65–72, 2020.View at: Publisher Site | Google Scholar
    28. C. Zhang, H. Li, Y. Qian, C. Chen, and X. Zhou, “Locality-constrained discriminative matrix regression for robust face identification,” IEEE Transactions on Neural Networks and Learning Systems, vol. 99, pp. 1–15, 2020.View at: Publisher Site | Google Scholar
    29. X. Zhang, D. Wang, Z. Zhou, and Y. Ma, “Robust low-rank tensor recovery with rectification and alignment,” IEEE Transactions on Pattern Analysis and Machine Intelligence, vol. 43, no. 1, pp. 238–255, 2019.View at: Google Scholar
    30. X. Zhang, J. Wang, T. Wang, R. Jiang, J. Xu, and L. Zhao, “Robust feature learning for adversarial defense via hierarchical feature alignment,” Information Sciences, vol. 560, 2020.View at: Google Scholar
    31. X. Zhang, R. Jiang, T. Wang, and J. Wang, “Recursive neural network for video deblurring,” IEEE Transactions on Circuits and Systems for Video Technology, vol. 03, p. 1, 2020.View at: Publisher Site | Google Scholar
    32. X. Zhang, T. Wang, J. Wang, G. Tang, and L. Zhao, “Pyramid channel-based feature attention network for image dehazing,” Computer Vision and Image Understanding, vol. 197-198, Article ID 103003, 2020.View at: Publisher Site | Google Scholar
    33. X. Zhang, T. Wang, W. Luo, and P. Huang, “Multi-level fusion and attention-guided CNN for image dehazing,” IEEE Transactions on Circuits and Systems for Video Technology, vol. 3, p. 1, 2020.View at: Publisher Site | Google Scholar
    34. L. He, J. Shen, and Y. Zhang, “Ecological vulnerability assessment for ecological conservation and environmental management,” Journal of Environmental Management, vol. 206, pp. 1115–1125, 2018.View at: Publisher Site | Google Scholar
    35. Y. Chen, W. Zheng, W. Li, and Y. Huang, “Large group Activity security risk assessment and risk early warning based on random forest algorithm,” Pattern Recognition Letters, vol. 144, pp. 1–5, 2021.View at: Publisher Site | Google Scholar
    36. J. Hu, H. Zhang, Z. Li, C. Zhao, Z. Xu, and Q. Pan, “Object traversing by monocular UAV in outdoor environment,” Asian Journal of Control, vol. 25, 2020.View at: Google Scholar
    37. P. Tian, H. Lu, W. Feng, Y. Guan, and Y. Xue, “Large decrease in streamflow and sediment load of Qinghai-Tibetan Plateau driven by future climate change: a case study in Lhasa River Basin,” Catena, vol. 187, Article ID 104340, 2020.View at: Publisher Site | Google Scholar
    38. A. Stokes, C. Atger, A. G. Bengough, T. Fourcaud, and R. C. Sidle, “Desirable plant root traits for protecting natural and engineered slopes against landslides,” Plant and Soil, vol. 324, no. 1, pp. 1–30, 2009.View at: Publisher Site | Google Scholar
    39. T. B. Devi, A. Sharma, and B. Kumar, “Studies on emergent flow over vegetative channel bed with downward seepage,” Hydrological Sciences Journal, vol. 62, no. 3, pp. 408–420, 2017.View at: Google Scholar
    40. G. Ireland, M. Volpi, and G. Petropoulos, “Examining the capability of supervised machine learning classifiers in extracting flooded areas from Landsat TM imagery: a case study from a Mediterranean flood,” Remote Sensing, vol. 7, no. 3, pp. 3372–3399, 2015.View at: Publisher Site | Google Scholar
    41. L. Goodarzi and S. Javadi, “Assessment of aquifer vulnerability using the DRASTIC model; a case study of the Dezful-Andimeshk Aquifer,” Computational Research Progress in Applied Science & Engineering, vol. 2, no. 1, pp. 17–22, 2016.View at: Google Scholar
    42. K. Zhang, Q. Wang, L. Chao et al., “Ground observation-based analysis of soil moisture spatiotemporal variability across a humid to semi-humid transitional zone in China,” Journal of Hydrology, vol. 574, pp. 903–914, 2019.View at: Publisher Site | Google Scholar
    43. L. De Doncker, P. Troch, R. Verhoeven, K. Bal, P. Meire, and J. Quintelier, “Determination of the Manning roughness coefficient influenced by vegetation in the river Aa and Biebrza river,” Environmental Fluid Mechanics, vol. 9, no. 5, pp. 549–567, 2009.View at: Publisher Site | Google Scholar
    44. M. Fathi-Moghadam and K. Drikvandi, “Manning roughness coefficient for rivers and flood plains with non-submerged vegetation,” International Journal of Hydraulic Engineering, vol. 1, no. 1, pp. 1–4, 2012.View at: Google Scholar
    45. F.-C. Wu, H. W. Shen, and Y.-J. Chou, “Variation of roughness coefficients for unsubmerged and submerged vegetation,” Journal of Hydraulic Engineering, vol. 125, no. 9, pp. 934–942, 1999.View at: Publisher Site | Google Scholar
    46. M. K. Wood, “Rangeland vegetation-hydrologic interactions,” in Vegetation Science Applications for Rangeland Analysis and Management, vol. 3, pp. 469–491, Springer, 1988.View at: Publisher Site | Google Scholar
    47. C. Wilson, O. Yagci, H.-P. Rauch, and N. Olsen, “3D numerical modelling of a willow vegetated river/floodplain system,” Journal of Hydrology, vol. 327, no. 1-2, pp. 13–21, 2006.View at: Publisher Site | Google Scholar
    48. R. Yazarloo, M. Khamehchian, and M. R. Nikoodel, “Observational-computational 3d engineering geological model and geotechnical characteristics of young sediments of golestan province,” Computational Research Progress in Applied Science & Engineering (CRPASE), vol. 03, 2017.View at: Google Scholar
    49. G. E. Freeman, W. H. Rahmeyer, and R. R. Copeland, “Determination of resistance due to shrubs and woody vegetation,” International Journal of River Basin Management, vol. 19, 2000.View at: Google Scholar
    50. N. Kouwen and T. E. Unny, “Flexible roughness in open channels,” Journal of the Hydraulics Division, vol. 99, no. 5, pp. 713–728, 1973.View at: Publisher Site | Google Scholar
    51. S. Hosseini and J. Abrishami, Open Channel Hydraulics, Elsevier, Amsterdam, Netherlands, 2007.
    52. C. S. James, A. L. Birkhead, A. A. Jordanova, and J. J. O’Sullivan, “Flow resistance of emergent vegetation,” Journal of Hydraulic Research, vol. 42, no. 4, pp. 390–398, 2004.View at: Publisher Site | Google Scholar
    53. F. Huthoff and D. Augustijn, “Channel roughness in 1D steady uniform flow: Manning or Chézy?,,” NCR-days, vol. 102, 2004.View at: Google Scholar
    54. M. S. Sabegh, M. Saneie, M. Habibi, A. A. Abbasi, and M. Ghadimkhani, “Experimental investigation on the effect of river bank tree planting array, on shear velocity,” Journal of Watershed Engineering and Management, vol. 2, no. 4, 2011.View at: Google Scholar
    55. A. Errico, V. Pasquino, M. Maxwald, G. B. Chirico, L. Solari, and F. Preti, “The effect of flexible vegetation on flow in drainage channels: estimation of roughness coefficients at the real scale,” Ecological Engineering, vol. 120, pp. 411–421, 2018.View at: Publisher Site | Google Scholar
    56. S. E. Darby, “Effect of riparian vegetation on flow resistance and flood potential,” Journal of Hydraulic Engineering, vol. 125, no. 5, pp. 443–454, 1999.View at: Publisher Site | Google Scholar
    57. V. Kutija and H. Thi Minh Hong, “A numerical model for assessing the additional resistance to flow introduced by flexible vegetation,” Journal of Hydraulic Research, vol. 34, no. 1, pp. 99–114, 1996.View at: Publisher Site | Google Scholar
    58. T. Fischer-Antze, T. Stoesser, P. Bates, and N. R. B. Olsen, “3D numerical modelling of open-channel flow with submerged vegetation,” Journal of Hydraulic Research, vol. 39, no. 3, pp. 303–310, 2001.View at: Publisher Site | Google Scholar
    59. U. Stephan and D. Gutknecht, “Hydraulic resistance of submerged flexible vegetation,” Journal of Hydrology, vol. 269, no. 1-2, pp. 27–43, 2002.View at: Publisher Site | Google Scholar
    60. F. G. Carollo, V. Ferro, and D. Termini, “Flow resistance law in channels with flexible submerged vegetation,” Journal of Hydraulic Engineering, vol. 131, no. 7, pp. 554–564, 2005.View at: Publisher Site | Google Scholar
    61. W. Fu-sheng, “Flow resistance of flexible vegetation in open channel,” Journal of Hydraulic Engineering, vol. S1, 2007.View at: Google Scholar
    62. P.-f. Wang, C. Wang, and D. Z. Zhu, “Hydraulic resistance of submerged vegetation related to effective height,” Journal of Hydrodynamics, vol. 22, no. 2, pp. 265–273, 2010.View at: Publisher Site | Google Scholar
    63. J. K. Lee, L. C. Roig, H. L. Jenter, and H. M. Visser, “Drag coefficients for modeling flow through emergent vegetation in the Florida Everglades,” Ecological Engineering, vol. 22, no. 4-5, pp. 237–248, 2004.View at: Publisher Site | Google Scholar
    64. G. J. Arcement and V. R. Schneider, Guide for Selecting Manning’s Roughness Coefficients for Natural Channels and Flood Plains, US Government Printing Office, Washington, DC, USA, 1989.
    65. Y. Ding and S. S. Y. Wang, “Identification of Manning’s roughness coefficients in channel network using adjoint analysis,” International Journal of Computational Fluid Dynamics, vol. 19, no. 1, pp. 3–13, 2005.View at: Publisher Site | Google Scholar
    66. E. T. Engman, “Roughness coefficients for routing surface runoff,” Journal of Irrigation and Drainage Engineering, vol. 112, no. 1, pp. 39–53, 1986.View at: Publisher Site | Google Scholar
    67. M. Feizbahr, C. Kok Keong, F. Rostami, and M. Shahrokhi, “Wave energy dissipation using perforated and non perforated piles,” International Journal of Engineering, vol. 31, no. 2, pp. 212–219, 2018.View at: Publisher Site | Google Scholar
    68. M. Farzadkhoo, A. Keshavarzi, H. Hamidifar, and M. Javan, “Sudden pollutant discharge in vegetated compound meandering rivers,” Catena, vol. 182, Article ID 104155, 2019.View at: Publisher Site | Google Scholar
    69. V. T. Chow, Open-channel Hydraulics, Mcgraw-Hill Civil Engineering Series, Chennai, TN, India, 1959.
    70. X. Zhang, R. Jing, Z. Li, Z. Li, X. Chen, and C.-Y. Su, “Adaptive pseudo inverse control for a class of nonlinear asymmetric and saturated nonlinear hysteretic systems,” IEEE/CAA Journal of Automatica Sinica, vol. 8, no. 4, pp. 916–928, 2020.View at: Google Scholar
    71. C. Zuo, Q. Chen, L. Tian, L. Waller, and A. Asundi, “Transport of intensity phase retrieval and computational imaging for partially coherent fields: the phase space perspective,” Optics and Lasers in Engineering, vol. 71, pp. 20–32, 2015.View at: Publisher Site | Google Scholar
    72. C. Zuo, J. Sun, J. Li, J. Zhang, A. Asundi, and Q. Chen, “High-resolution transport-of-intensity quantitative phase microscopy with annular illumination,” Scientific Reports, vol. 7, no. 1, pp. 7654–7722, 2017.View at: Publisher Site | Google Scholar
    73. B.-H. Li, Y. Liu, A.-M. Zhang, W.-H. Wang, and S. Wan, “A survey on blocking technology of entity resolution,” Journal of Computer Science and Technology, vol. 35, no. 4, pp. 769–793, 2020.View at: Publisher Site | Google Scholar
    74. Y. Liu, B. Zhang, Y. Feng et al., “Development of 340-GHz transceiver front end based on GaAs monolithic integration technology for THz active imaging array,” Applied Sciences, vol. 10, no. 21, p. 7924, 2020.View at: Publisher Site | Google Scholar
    75. J. Hu, H. Zhang, L. Liu, X. Zhu, C. Zhao, and Q. Pan, “Convergent multiagent formation control with collision avoidance,” IEEE Transactions on Robotics, vol. 36, no. 6, pp. 1805–1818, 2020.View at: Publisher Site | Google Scholar
    76. M. B. Movahhed, J. Ayoubinejad, F. N. Asl, and M. Feizbahr, “The effect of rain on pedestrians crossing speed,” Computational Research Progress in Applied Science & Engineering (CRPASE), vol. 6, no. 3, 2020.View at: Google Scholar
    77. A. Li, D. Spano, J. Krivochiza et al., “A tutorial on interference exploitation via symbol-level precoding: overview, state-of-the-art and future directions,” IEEE Communications Surveys & Tutorials, vol. 22, no. 2, pp. 796–839, 2020.View at: Publisher Site | Google Scholar
    78. W. Zhu, C. Ma, X. Zhao et al., “Evaluation of sino foreign cooperative education project using orthogonal sine cosine optimized kernel extreme learning machine,” IEEE Access, vol. 8, pp. 61107–61123, 2020.View at: Publisher Site | Google Scholar
    79. G. Liu, W. Jia, M. Wang et al., “Predicting cervical hyperextension injury: a covariance guided sine cosine support vector machine,” IEEE Access, vol. 8, pp. 46895–46908, 2020.View at: Publisher Site | Google Scholar
    80. Y. Wei, H. Lv, M. Chen et al., “Predicting entrepreneurial intention of students: an extreme learning machine with Gaussian barebone harris hawks optimizer,” IEEE Access, vol. 8, pp. 76841–76855, 2020.View at: Publisher Site | Google Scholar
    81. A. Lin, Q. Wu, A. A. Heidari et al., “Predicting intentions of students for master programs using a chaos-induced sine cosine-based fuzzy K-Nearest neighbor classifier,” Ieee Access, vol. 7, pp. 67235–67248, 2019.View at: Publisher Site | Google Scholar
    82. Y. Fan, P. Wang, A. A. Heidari et al., “Rationalized fruit fly optimization with sine cosine algorithm: a comprehensive analysis,” Expert Systems with Applications, vol. 157, Article ID 113486, 2020.View at: Publisher Site | Google Scholar
    83. E. Rodríguez-Esparza, L. A. Zanella-Calzada, D. Oliva et al., “An efficient Harris hawks-inspired image segmentation method,” Expert Systems with Applications, vol. 155, Article ID 113428, 2020.View at: Publisher Site | Google Scholar
    84. S. Jiao, G. Chong, C. Huang et al., “Orthogonally adapted Harris hawks optimization for parameter estimation of photovoltaic models,” Energy, vol. 203, Article ID 117804, 2020.View at: Publisher Site | Google Scholar
    85. Z. Xu, Z. Hu, A. A. Heidari et al., “Orthogonally-designed adapted grasshopper optimization: a comprehensive analysis,” Expert Systems with Applications, vol. 150, Article ID 113282, 2020.View at: Publisher Site | Google Scholar
    86. A. Abbassi, R. Abbassi, A. A. Heidari et al., “Parameters identification of photovoltaic cell models using enhanced exploratory salp chains-based approach,” Energy, vol. 198, Article ID 117333, 2020.View at: Publisher Site | Google Scholar
    87. M. Mahmoodi and K. K. Aminjan, “Numerical simulation of flow through sukhoi 24 air inlet,” Computational Research Progress in Applied Science & Engineering (CRPASE), vol. 03, 2017.View at: Google Scholar
    88. F. J. Golrokh and A. Hasan, “A comparison of machine learning clustering algorithms based on the DEA optimization approach for pharmaceutical companies in developing countries,” ENG Transactions, vol. 1, 2020.View at: Google Scholar
    89. H. Chen, A. A. Heidari, H. Chen, M. Wang, Z. Pan, and A. H. Gandomi, “Multi-population differential evolution-assisted Harris hawks optimization: framework and case studies,” Future Generation Computer Systems, vol. 111, pp. 175–198, 2020.View at: Publisher Site | Google Scholar
    90. J. Guo, H. Zheng, B. Li, and G.-Z. Fu, “Bayesian hierarchical model-based information fusion for degradation analysis considering non-competing relationship,” IEEE Access, vol. 7, pp. 175222–175227, 2019.View at: Publisher Site | Google Scholar
    91. J. Guo, H. Zheng, B. Li, and G.-Z. Fu, “A Bayesian approach for degradation analysis with individual differences,” IEEE Access, vol. 7, pp. 175033–175040, 2019.View at: Publisher Site | Google Scholar
    92. M. M. A. Malakoutian, Y. Malakoutian, P. Mostafapour, and S. Z. D. Abed, “Prediction for monthly rainfall of six meteorological regions and TRNC (case study: north Cyprus),” ENG Transactions, vol. 2, no. 2, 2021.View at: Google Scholar
    93. H. Arslan, M. Ranjbar, and Z. Mutlum, “Maximum sound transmission loss in multi-chamber reactive silencers: are two chambers enough?,,” ENG Transactions, vol. 2, no. 1, 2021.View at: Google Scholar
    94. N. Tonekaboni, M. Feizbahr, N. Tonekaboni, G.-J. Jiang, and H.-X. Chen, “Optimization of solar CCHP systems with collector enhanced by porous media and nanofluid,” Mathematical Problems in Engineering, vol. 2021, Article ID 9984840, 12 pages, 2021.View at: Publisher Site | Google Scholar
    95. Z. Niu, B. Zhang, J. Wang et al., “The research on 220GHz multicarrier high-speed communication system,” China Communications, vol. 17, no. 3, pp. 131–139, 2020.View at: Publisher Site | Google Scholar
    96. B. Zhang, Z. Niu, J. Wang et al., “Four‐hundred gigahertz broadband multi‐branch waveguide coupler,” IET Microwaves, Antennas & Propagation, vol. 14, no. 11, pp. 1175–1179, 2020.View at: Publisher Site | Google Scholar
    97. Z.-Q. Niu, L. Yang, B. Zhang et al., “A mechanical reliability study of 3dB waveguide hybrid couplers in the submillimeter and terahertz band,” Journal of Zhejiang University Science, vol. 1, no. 1, 1998.View at: Google Scholar
    98. B. Zhang, D. Ji, D. Fang, S. Liang, Y. Fan, and X. Chen, “A novel 220-GHz GaN diode on-chip tripler with high driven power,” IEEE Electron Device Letters, vol. 40, no. 5, pp. 780–783, 2019.View at: Publisher Site | Google Scholar
    99. M. Taleghani and A. Taleghani, “Identification and ranking of factors affecting the implementation of knowledge management engineering based on TOPSIS technique,” ENG Transactions, vol. 1, no. 1, 2020.View at: Google Scholar
    Fig. 5 Comparison of experimental SEM image and CtFD simulated melt pool with beam diameters of(a)700 μm,(b)1000 μm, and(c)1300 μm and an absorption rate of 0.3. Electron beam power and scan speed are 900 W and 100 mm s-1, respectively

    추가 생산용 전자빔 조사에 의한 316L 스테인리스 용융 · 응고 거동

    Melting and Solidification Behavior of 316L Steel Induced by Electron-Beam Irradiation for Additive Manufacturing

    付加製造用電子ビーム照射による 316L ステンレス鋼の溶融・凝固挙動

    奥 川 将 行*・宮 田 雄一朗*・王     雷*・能 勢 和 史*
    小 泉 雄一郎*・中 野 貴 由*
    Masayuki OKUGAWA, Yuichiro MIYATA, Lei WANG, Kazufumi NOSE,
    Yuichiro KOIZUMI and Takayoshi NAKANO

    Abstract

    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 형