Aneesh Kumar J1, a, K. Krishnakumar1, b and S. Savithri2, c 1 Department of Mechanical Engineering, College of Engineering, Thiruvananthapuram, Kerala, 2 Computational Modelling& Simulation Division, Process Engineering & Environmental Technology Division CSIR-National Institute for Interdisciplinary Science & Technology Thiruvananthapuram, Kerala, India. a aneesh82kj@gmail.com, b kkk@cet.ac.in, c sivakumarsavi@gmail.com, ssavithri@niist.res.in Key words: Mold filling, centrifugal casting process, computer simulation, FLOW- 3D™
Abstract
원심 주조 공정은 기능적으로 등급이 지정된 재료, 즉 구성 요소 간에 밀도 차이가 큰 복합 재료 또는 금속 재료를 생산하는 데 사용되는 잠재적인 제조 기술 중 하나입니다. 이 공정에서 유체 흐름이 중요한 역할을 하며 복잡한 흐름 공정을 이해하는 것은 결함 없는 주물을 생산하는 데 필수입니다. 금형이 고속으로 회전하고 금형 벽이 불투명하기 때문에 흐름 패턴을 실시간으로 시각화하는 것은 불가능합니다. 따라서 현재 연구에서는 상용 CFD 코드 FLOW-3D™를 사용하여 수직 원심 주조 공정 중 단순 중공 원통형 주조에 대한 금형 충전 시퀀스를 시뮬레이션했습니다. 수직 원심주조 공정 중 다양한 방사 속도가 충전 패턴에 미치는 영향을 조사하고 있습니다.
Centrifugal casting process is one of the potential manufacturing techniques used for producing functionally graded materials viz., composite materials or metallic materials which have high differences of density among constituents. In this process, the fluid flow plays a major role and understanding the complex flow process is a must for the production of defect-free castings. Since the mold spins at a high velocity and the mold wall being opaque, it is impossible to visualise the flow patterns in real time. Hence, in the present work, the commercial CFD code FLOW-3D™, has been used to simulate the mold filling sequence for a simple hollow cylindrical casting during vertical centrifugal casting process. Effect of various spinning velocities on the fill pattern during vertical centrifugal casting process is being investigated.
Figure 1: (a) Mold geometry and (b) Computational meshFigure 2: Experimental data on height of vertex formed [8]/Figure 3: Vertex height as a function of timeFigure 4: Free surface contours for water model at 10 s, 15 s and 20 s. Figure 5: 3D & 2D views of simulated fill sequence of a hollow cylinder at 1000 rpm and 1500 rpm at various time intervals during filling.
References
[1] W. Shi-Ping, L. Chang-yun, G. Jing-jie, S. Yan-qing, L. Xiu-qiao, F. Heng-zhi, Numerical simulation and experimental investigation of two filling methods in vertical centrifugal casting, Trans. Nonferrous Met. Soc. China 16 (2006) 1035-1040. 10.1016/s1003-6326(06)60373-7 [2] G. Chirita, D. Soares, F.S. Silva, Advantages of the centrifugal casting technique for the production of structural components with Al-Si alloys, Mater. Des. 29 (2008) 20-27. 10.1016/j.matdes.2006.12.011 [3] A. Kermanpur, Sh. Mahmoudi, A. Hajipour, Numerical simulation of metal flow and solidification in the multi-cavity casting moulds of automotive components, J. Mater. Proc. Tech. 206 (208) 62-68. 10.1016/j.jmatprotec.2007.12.004 [4] D. McBride et. al. Complex free surface flows in centrifugal casting: Computational modelling and validation experiments, Computers & Fluids 82 (2013) 63-72. 10.1016/j.compfluid.2013.04.021
Modeling of Mesh Screen for Use in Surface TensionTankUsing Flow-3d Software
Hyuntak Kim․ Sang Hyuk Lim․Hosung Yoon․Jeong-Bae Park*․Sejin Kwon†
ABSTRACT
Mesh screen modeling and liquid propellant discharge simulation of surface tension tank wereperformed using commercial CFD software Flow-3d. 350 × 2600, 400 × 3000 and 510 × 3600 DTW mesh screen were modeled using macroscopic porous media model. Porosity, capillary pressure, and drag coefficient were assigned for each mesh screen model, and bubble point simulations were performed. The mesh screen model was validated with the experimental data. Based on the screen modeling, liquidpropellant discharge simulation from PMD tank was performed. NTO was assigned as the liquidpropellant, and void was set to flow into the tank inlet to achieve an initial volume flowrate of liquid propellant in 3 × 10-3 g acceleration condition. The intial flow pressure drop through the meshscreen was approximately 270 Pa, and the pressure drop increased with time. Liquid propellant discharge was sustained until the flow pressure drop reached approximately 630 Pa, which was near the estimated bubble point value of the screen model.
초 록
상용 CFD 프로그램 Flow-3d를 활용하여, 표면 장력 탱크 적용을 위한 메시 스크린의 모델링 및 추진제 배출 해석을 수행하였다. Flow-3d 내 거시적 다공성 매체 모델을 사용하였으며, 350 × 2600, 400× 3000, 510 × 3600 DTW 메시 스크린에 대한 공극률, 모세관압, 항력계수를 스크린 모델에 대입 후, 기포점 측정 시뮬레이션을 수행하였다.
시뮬레이션 결과를 실험 데이터와 비교하였으며, 메시 스크린 모델링의 적절성을 검증하였다. 이를 기반으로 스크린 모델을 포함한 PMD 구조체에 대한 추진제 배출 해석을 수행하였다. 추진제는 액상의 NTO를 가정하였으며, 3 × 10-3 g 가속 조건에서 초기 유량을만족하도록 void를 유입시켰다. 메시 스크린을 통한 차압은 초기 약 270 Pa에서 시간에 따라 증가하였으며, 스크린 모델의 예상 기포점과 유사한 630 Pa에 이르기까지 액상 추진제 배출을 지속하였다.
Key Words
Surface Tension Tank(표면장력 탱크), Propellant Management Device(추진제 관리 장치), Mesh Screen(메시 스크린), Porous Media Model(다공성 매체 모델), Bubble Point(기포점)
서론
우주비행체를 미소 중력 조건 내에서 운용하 는 경우, 가압 기체가 액상의 추진제와 혼합되어 엔진으로 공급될 우려가 있으므로 이를 방지하 기 위한 탱크의 설계가 필요하다.
다이어프램 (Diaphragm), 피스톤(Piston) 등 다양한 장치들 이 활용되고 있으며, 이 중 표면 장력 탱크는 내 부의 메시 스크린(Mesh screen), 베인(Vane) 등 의 구조체에서 추진제의 표면장력을 활용함으로 써 액상 추진제의 이송 및 배출을 유도하는 방 식이다.
표면 장력 탱크는 구동부가 없는 구조로 신뢰성이 높고, 전 부분을 티타늄 등의 금속 재 질로 구성함으로써 부식성 추진제의 사용 조건 에서도 장기 운용이 가능한 장점이 있다. 위에서 언급한 메시 스크린(Mesh screen)은 수 십 마이크로미터 두께의 금속 와이어를 직조한 다공성 재질로 표면 장력 탱크의 핵심 구성 요소 중 하나이다.
미세 공극 상 추진제의 표면장력에 의해 기체와 액체 간 계면을 일정 차압 내에서 유지시킬 수 있다. 이러한 성질로 인해 일정 조 건에서 가압 기체가 메시 스크린을 통과하지 못 하게 되고, 스크린을 탱크 유로에 설치함으로써 액상의 추진제 배출을 유도할 수 있다.
메시 스크린이 가압 기체를 통과시키기 직전 의 기체-액체 계면에 형성되는 최대 차압을 기포 점 (Bubble point) 이라 칭하며, 메시 스크린의 주 요 성능 지표 중 하나이다. IPA, 물, LH2, LCH4 등 다양한 기준 유체 및 추진제, 다양한 메시 스 크린 사양에 대해 기포점 측정 관련 실험적 연 구가 이루어져 왔다 [1-3].
위 메시 스크린을 포함하여 표면 장력 탱크 내 액상의 추진제 배출을 유도하는 구조물 일체 를 PMD(Propellant management device)라 칭하 며, 갤러리(Gallery), 베인(Vane), 스펀지(Sponge), 트랩(Trap) 등 여러 종류의 구조물에 대해 각종 형상 변수를 내포한다[4, 5].
따라서 다양한 파라미터를 고려한 실험적 연구는 제약이 따를 수 있으며, 베인 등 상대적으로 작은 미소 중력 조건에서 개방형 유로를 활용하는 경우 지상 추진제 배출 실험이 불가능하다[6]. 그러므로 CFD를 통한 표면장력 탱크 추진제 배출 해석은 다양한 작동 조건 및 PMD 형상 변수에 따른 추진제 거동을 이해하고, 탱크를 설계하는 데 유용하게 활용될 수 있다.
상기 추진제 배출 해석을 수행하기 위해서는 핵심 요소 중 하나인 메시 스크린에 대한 모델링이 필수적이다. Chato, McQuillen 등은 상용 CFD 프로그램인 Fluent를 통해, 갤러리 내 유동 시뮬레이션을 수행하였으며, 이 때 메시 스크린에 ‘porous jump’ 경계 조건을 적용함으로써 액상의 추진제가 스크린을 통과할 때 생기는 압력 강하를 모델링하였다[7, 8].
그러나 앞서 언급한 메시 스크린의 기포점 특성을 모델링한 사례는 찾아보기 힘들다. 이는 스크린을 활용하는 표면 장력 탱크 내 액상 추진제 배출 현상을 해석적으로 구현하기 위해 반드시 필요한 부분이다. 본 연구에서는 자유표면 해석에 상대적으로 강점을 지닌 상용 CFD 프로그램 Flow-3d를 사용하여, 메시 스크린을 모델링하였다.
거시적 다공성 매체 모델(Macroscopic porous mediamodel)을 활용하여 메시 스크린 모델 영역에 공극률(Porosity), 모세관압(Capillary pressure), 항력 계수(Drag coefficient)를 지정하고, 이를 기반으로 기포점 측정 시뮬레이션을 수행, 해석 결과와 실험 데이터 간 비교 및 검증을 수행하였다.
이를 기반으로 메시 스크린 및 PMD구조체를 포함한 탱크의 추진제 배출 해석을 수행하고, 기포점 특성의 반영 여부를 확인하였다.
Fig. 1 Real geometry-based mesh screen model (left)
and mesh screen model based on macroscopic
porous media model in Flow-3d (righFig. 2 Modeling of bubble point test apparatus (left) and computational grid (righ)Fig. 3 Modeling of sump in a tank (left) and lower part
of the sump structure (right)
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Pages 541-551 | Received 03 Mar 2020, Accepted 07 May 2020, Published online: 21 May 2020
ABSTRACT
Dams fall in ‘installations containing dangerous forces’ because of their massive impact on the environment and civilian life and property as per International humanitarian law. As such, it becomes vital for hydraulic engineers to refurbish various solutions for dam rehabilitation. This paper presents a review of a new type of weir installation called Piano Key Weir (PKW), which is becoming popular around the world for its higher spillway capacity both for existing and new dam spillway installations. This paper reviews the geometry along with structural integrity, discharging capacity, economic aspects, aeration requirements, sediment transport and erosion aspects of Piano Key Weir (PKW) as compared with other traditional spillway structures and alternatives from literature. The comparison with other alternatives shows PKW to be an excellent alternative for dam risk mitigation owing to its high spillway capabilities and economy, along with its use in both existing and new hydraulic structures.
댐은 국제 인도법에 따라 환경과 민간인 생활 및 재산에 막대한 영향을 미치기 때문에 ‘위험한 힘을 포함하는 시설물’에 속합니다. 따라서 유압 엔지니어는 댐 복구를 위한 다양한 솔루션을 재정비해야 합니다.
이 백서에서는 PKW(Piano Key Weir)라는 새로운 유형의 둑 설치에 대한 검토를 제공합니다. PKW는 기존 및 신규 댐 방수로 설치 모두에서 더 높은 방수로 용량으로 전 세계적으로 인기를 얻고 있습니다.
이 백서에서는 구조적 무결성, 배출 용량, 경제적 측면, 폭기 요구 사항, 퇴적물 운반 및 PKW(Piano Key Weir)의 침식 측면과 함께 다른 전통적인 여수로 구조 및 문헌의 대안과 비교하여 기하학을 검토합니다.
다른 대안과의 비교는 PKW가 높은 여수로 기능과 경제성으로 인해 댐 위험 완화를 위한 탁월한 대안이며 기존 및 새로운 수력 구조물 모두에 사용됨을 보여줍니다.
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Beom-Jin Kim 1, Jae-Hong Hwang 2 and Byunghyun Kim 3,* 1 Advanced Structures and Seismic Safety Research Division, Korea Atomic Energy Research Institute, Daejeon 34057, Korea 2 Korea Water Resources Corporation (K-Water), Daejeon 34350, Korea 3 Department of Civil Engineering, Kyungpook National University, Daegu 41566, Korea
Hydraulic structures installed in rivers inevitably create a water level difference between upstream and downstream regions. The potential energy due to this difference in water level is converted into kinetic energy, causing high-velocity flow and hydraulic jumps in the river. As a result, problems such as scouring and sloping downstream may occur around the hydraulic structures. In this study, a FLOW-3D model was constructed to perform a numerical analysis of the ChangnyeongHaman weir in the Republic of Korea. The constructed model was verified based on surface velocity measurements from a field gate operation experiment. In the simulation results, the flow discharge differed from the measured value by 9–15 m3/s, from which the accuracy was evaluated to be 82–87%. The flow velocity was evaluated with an accuracy of 92% from a difference of 0.01 to 0.16 m/s. Following this verification, a flow analysis of the hydraulic structures was performed according to boundary conditions and operation conditions for numerous scenarios. Since 2018, the ChangnyeongHaman weir gate has been fully opened due to the implementation of Korea’s eco-environmental policy; therefore, in this study, the actual gate operation history data prior to 2018 was applied and evaluated. The evaluation conditions were a 50% open gate condition and the flow discharge of two cases with a large difference in water level. As a result of the analysis, the actual operating conditions showed that the velocity and the Froude number were lower than the optimal conditions, confirming that the selected design was appropriate. It was also found that in the bed protection section, the average flow velocity was high when the water level difference was large, whereas the bottom velocity was high when the gate opening was large. Ultimately, through the reviewed status survey data in this study, the downstream flow characteristics of hydraulic structures along with adequacy verification techniques, optimal design techniques such as procedures for design, and important considerations were derived. Based on the current results, the constructed FLOW-3D-based model can be applied to creating or updating flow analysis guidelines for future repair and reinforcement measures as well as hydraulic structure design.
하천에 설치되는 수력구조물은 필연적으로 상류와 하류의 수위차를 발생시킨다. 이러한 수위차로 인한 위치에너지는 운동에너지로 변환되어 하천의 고속유동과 수압점프를 일으킨다. 그 결과 수력구조물 주변에서 하류의 세굴, 경사 등의 문제가 발생할 수 있다.
본 연구에서는 대한민국 창녕함안보의 수치해석을 위해 FLOW-3D 모델을 구축하였다. 구축된 모델은 현장 게이트 작동 실험에서 표면 속도 측정을 기반으로 검증되었습니다.
시뮬레이션 결과에서 유량은 측정값과 9~15 m3/s 차이가 나고 정확도는 82~87%로 평가되었다. 유속은 0.01~0.16m/s의 차이에서 92%의 정확도로 평가되었습니다.
검증 후 다양한 시나리오에 대한 경계조건 및 운전조건에 따른 수리구조물의 유동해석을 수행하였다. 2018년부터 창녕함안보 문은 한국의 친환경 정책 시행으로 전면 개방되었습니다.
따라서 본 연구에서는 2018년 이전의 실제 게이트 운영 이력 데이터를 적용하여 평가하였다. 평가조건은 50% open gate 조건과 수위차가 큰 2가지 경우의 유수방류로 하였다. 해석 결과 실제 운전조건은 속도와 Froude수가 최적조건보다 낮아 선정된 설계가 적합함을 확인하였다.
또한 베드보호구간에서는 수위차가 크면 평균유속이 높고, 수문개구가 크면 저저유속이 높은 것으로 나타났다. 최종적으로 본 연구에서 검토한 실태조사 자료를 통해 적정성 검증기법과 함께 수력구조물의 하류 유동특성, 설계절차 등 최적 설계기법 및 중요 고려사항을 도출하였다.
현재의 결과를 바탕으로 구축된 FLOW-3D 기반 모델은 수력구조 설계뿐만 아니라 향후 보수 및 보강 조치를 위한 유동해석 가이드라인 생성 또는 업데이트에 적용할 수 있습니다.
Figure 1. Effect of downstream riverbed erosion according to the type of weir foundation.Figure 2. Changnyeong-Haman weir depth survey results (June 2015)Figure 4. Field gate discharge experiment.Figure 16. Analysis results for Case 7 and Case 8
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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
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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.
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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 2015a, b; 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 characterist–ics 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.
Fig. 1Fig. 2
Review of the governing equations in software Flow 3D
Continuity equation at three-dimensional Cartesian coordinates is given as Eq (1).
where u, v, z are velocity component in the x, y, z direction; Ax, Ay, Az cross-sectional area of the flow; ρ fluid density; PSOR the source term; vf is the volume fraction of the fluid and three-dimensional momentum equations given in Eq (2).
where P is the fluid pressure; Gx, Gy, Gz the acceleration created by body fluids; fx, fy, fz viscosity acceleration in three dimensions and vf 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.
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
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.
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.
Fig. 4Fig. 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.
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.
Fig. 7Fig. 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.
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.
Fig. 10Fig. 11Fig. 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.
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.
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.
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.
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.
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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.
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.
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.
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.
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.
Hydraulic model test was used to analyze the rapidly varied flow on the spillway. But, it has some shortcomings such as error of scale effect and expensive costs. Recently, through the development of three dimensional computational fluid dynamics (CFD), rapidly varied flow and turbulence can be simulated. In this study, the applicability of CFD model to simulate flow on the spillway was reviewed. The Karian dam in Indonesia was selected as the study area. The FLOW-3d model, which is well known to simulate a flow having a free surface, was used to analyze flow. The flow stability in approach channel was investigated with the initial plan design, and the results showed that the flow in approach channel is unstable in the initial plan design. To improve flow stability in the spillway, therefore, the revised plan design was formulated. The appropriateness of the revised design was examined by a numerical modeling. The results showed that the flow in spillway is stable in the revised design.
여수로의 급격하게 변화하는 흐름을 분석하기 위해 수리학적 모델 테스트를 사용했습니다. 그러나 스케일 효과의 오차와 고가의 비용 등의 단점이 있다. 최근에는 3차원 전산유체역학(CFD)의 발달로 급변하는 유동과 난류를 모사할 수 있다. 본 연구에서는 여수로의 흐름을 시뮬레이션하기 위한 CFD 모델의 적용 가능성을 검토했습니다. 인도네시아의 Karian 댐이 연구 지역으로 선정되었습니다. 자유표면을 갖는 유동을 모의하는 것으로 잘 알려진 FLOW-3d 모델을 유동해석에 사용하였다. 접근수로의 흐름 안정성은 초기 계획설계와 함께 조사한 결과 초기 계획설계에서 접근수로의 흐름이 불안정한 것으로 나타났다. 따라서 방수로의 흐름 안정성을 향상시키기 위해 수정된 계획 설계가 공식화되었습니다. 수정된 설계의 적합성을 수치모델링을 통해 검토하였다. 결과는 수정된 설계에서 여수로의 흐름이 안정적이라는 것을 보여주었습니다.
Figure 6. Two dimensional flow velocity distribution at the
approach channel (Flow velocity distribution at depth EL. 68.12 m).Figure 7. Flow distribution at the approach channel in PMF.
A. Hydraulic model test; B. Numerial simulatio
C. Cross section view.Figure 8. Revised approach channel section.
A. Initial plan design; B. Revised plan design.Figure 9. Two dimensional flow velocity distribution at the approach channel
based on revised plan design (Flow velocity distribution at depth EL. 68.12 m).Figure 10. Flow distribution at the approach channel in PMF based on revised plan design.
A. Hydarulic model test; B. Numerical simulation; C. Section view.
REFERENCES
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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.
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, 2017, 2020). 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., 2021; Bayraktar and Beji, 2013; David et al., 2017; Ertekin et al., 1986; Gourlay, 2001; Havelock, 1908; Lee and Lee, 2019; Samaras and Karambas, 2021; Shi 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, 2013; Dam et al., 2008; David et al., 2017; Samaras and Karambas, 2021; Shi 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 (2019, 2021) 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., 2017; Ellingsen, 2014; Li and Ellingsen, 2016; Li et al., 2019.) and numerically (Dam et al., 2008; Lee and Lee, 2019, 2021). 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.
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.
Case
Water depth h (m)
Ship speed Us (m/s)
Froude number Fr′=Us/gh
1
6.0
4.57
0.6
2
6.0
5.35
0.7
3
6.0
6.15
0.8
4
6.0
6.90
0.9
5
6.0
7.093
0.925
6
6.0
7.28
0.95
7
6.0
7.476
0.975
8
6.0
7.86
1.025
9
6.0
8.06
1.05
10
6.0
8.243
1.075
11
6.0
8.45
1.1
12
6.0
9.20
1.2
13
6.0
9.97
1.3
14
6.0
10.75
1.4
15
6.0
11.50
1.5
16
6.0
12.30
1.6
17
6.0
13.05
1.7
18
6.0
13.80
1.8
19
6.0
14.60
1.9
20
6.0
15.35
2.0
Table 2. Summary of current velocities.
Case
A
B
C
D
E
Current velocity Uc (m/s)
0.0
0.5
1.0
−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 1, Table 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. 2, Fig. 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. 2, Fig. 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).
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 1, Table 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.
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.
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.
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. 6, Fig. 7.
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. 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.
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. 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. 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. 13, Fig. 14.
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.
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.
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. 52171248, 51720105010, 51979029), 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.
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 arrangementFig. 2. Machine setup (MFQS-150W_1500WFig. 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.).
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.
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
Experimental investigation on the effect of spot diameter on continuous-wave laser welding of copper and aluminum thin sheets for battery manufacturing
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.
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.
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. 1, Fig. 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. 3, Fig. 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)
5
255
22
0.21
13.12
15
165
30
0.16
12.19
20
140
34
0.13
11.29
25
110
39
0.05
10.84
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. 10, Fig. 11, Fig. 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. 10, Fig. 11, Fig. 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.
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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.
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.
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.
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
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:
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).
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).
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.
Fig. 5Fig. 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:
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.
Fig. 7
Table 2 The 20 scenarios considered for numerical simulations in this study
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.
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.
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. 11, 12 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).
Fig. 11Fig. 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).
Fig. 13
The cumulative overtopping curves (Figs. 14, 15) 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.
Fig. 14Fig. 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:
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.
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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
Department of Civil and Environmental Engineering, Brunel University London, Uxbridge, UB8 3PH, UKKeith Adams
Department of Architecture and Civil Engineering, University of Bath, Bath, BA2 7AY, UKMohammad Heidarzadeh
The authors have no relevant financial or non-financial interests to disclose.
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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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Graduate Research Assistant, Dept. of Civil Engineering, New Mexico State Univ., P.O. Box 30001, MSC 3CE, Las Cruces, NM 88003-8001 (corresponding author). Email: samanmzf@nmsu.edu
Professor, Dept. of Civil Engineering, New Mexico State Univ., P.O. Box 30001, MSC 3CE, Las Cruces, NM 88003-8001. Email: zsamani@nmsu.edu
Abstract
추상적인 암거 끝에서 나오는 고속 흐름으로 인한 하류 침식 및 세굴은 수력 엔지니어가 직면한 주요 문제 중 하나입니다. 본 논문의 주요 목적은 일반적인 암거 단부에서 나오는 고속 흐름으로 인한 하류 침식 및 세굴의 위험을 줄일 수 있는 분산 암거 단부 설계를 개발하는 것이었습니다. 이를 위해 전산 유체 역학(CFD) 플랫폼 FLOW-3D 버전 11.1.0 코드를 실험 실행[결정 계수 R2>0.90 및 평균 제곱근 오차(RMSE)<1.9 cm]을 기반으로 보정 및 검증했습니다. 그런 다음 코드를 사용하여 두 가지 대안적인 소멸 암거 끝 설계(ALT 1 및 ALT 2)를 개발하고 하류 침식 및 세굴 완화 가능성을 분석했습니다. 각각의 출수유속과 운동에너지를 측정하여 전형적인 암거단부(대조)유량과 비교하였다. 결과에 따르면 제어 흐름에서의 질량 평균 유체 평균 운동 에너지는 1.37 j/kg2로 기록되었으며, ALT 1 및 ALT 2 흐름에서 각각 0.83 및 0.73 j/kg2로 측정되었습니다. 따라서 제어 흐름 하에서 하류 샌드박스 매스의 제거는 ALT 1 및 ALT 2 흐름에 비해 각각 약 11.1% 및 4.2% 더 높았습니다. FLOW-3D 코드는 암거 끝 흐름과 하류 침식을 예측하고 하류 침식을 줄일 수 있는 잠재적 소산 암거 끝을 설계하는 데 사용할 수 있습니다.
Downstream erosion and scouring caused by high-velocity flow issuing from culvert ends are one of the main problems faced by hydraulic engineers. The main objective of this paper was to develop a dissipating culvert end design that can reduce the risk of downstream erosion and scour caused by high-velocity flow issuing from typical culvert ends. For this purpose, the computational fluid dynamics (CFD) platform FLOW-3D version 11.1.0 code was calibrated and validated based on the experimental runs [coefficient of determination R2>0.90R2>0.90 and root mean square error (RMSE)<1.9 cm(RMSE)<1.9 cm]. Two alternative dissipating culvert end designs (ALT 1 and ALT 2) were then developed using the code, and their potential in mitigation of downstream erosion and scouring was analyzed. The issuing flow velocity and kinetic energy for each were measured and compared with typical culvert end (control) flow. According to the results, mass averaged fluid mean kinetic energy in the control flow was recorded at 1.37 j/kg21.37 j/kg2 and was measured at 0.83 and 0.73 j/kg20.73 j/kg2 in ALT 1 and ALT 2 flows, respectively. Accordingly, the removal of downstream sandbox mass under control flow was approximately 11.1% and 4.2% higher compared with ALT 1 and ALT 2 flows, respectively. FLOW-3D code can be used to predict culvert end flow and downstream erosion and to design potential dissipating culvert ends that can reduce downstream erosion.
Dissipating Culvert End Design for Erosion Control Using CFD Platform FLOW-3D Numerical Simulation Modeling
The tidal bore overflow and scour behind the spur dike are investigated. The overflow water depth under tidal bore is affected by dike height and Froude number after bore. The scour depth behind the spur dike is mainly influenced by the flow intensity, dike height and water depth before bore. An empirical equation predicting scour depth behind the spur dike is established.
Abstract
In estuaries with strong tidal bore, the scour behind the spur dike induced by tidal bore overflow has significant influence on the dike safety. In this study, an experiment study of the local scour induced by tidal bore overflow behind the spur dike was carried out in a physical flume. In addition, the process of the tidal bore overflow on the dike was numerically simulated with the boundary generation method. The stable overflow water depth on the spur dike (hts), unit overflow discharge (qts) and the scour hole characteristics were analyzed based on the experimental and numerical results. It is found that the relative stable overflow water depth (hts/h1) increases with the increase of the Froude number after bore (Fr1) and decreases with the increase of relative dike height (hd/h1). While the relative stable unit overflow discharge (qts/q1) is mainly affected by the relative dike height. Additionally, the results of scour pit behind the spur dike show that the scour depth (s/h1) is directly proportional to the relative current intensity (u1/uc) and the dike height (hd/h1), but inversely proportional to the water depth before bore (h0/h1). An empirical equation for predicting relative maximum scour depth is obtained by fitting the experimental results and the field measured data, and the prediction accuracy is within 30%. The conclusions of this paper can provide technical support for the engineering design and operation evaluation of spur dikes in estuaries with the strong tidal bore.
갯벌이 강한 하구에서는 갯벌 범람에 의해 유발되는 둑 뒤 세굴이 둑 안전에 큰 영향을 미친다. 본 연구에서는 물리수로에서 박차둑 뒤의 조수간만의 범람에 의해 유발되는 국지세굴에 대한 실험연구를 수행하였다. 또한 경계 생성법을 이용하여 제방 위의 조수간만의 범람 과정을 수치적으로 모사하였다. 실험적 및 수치적 결과를 바탕으로 평제방의 안정적인 범람 수심(hts), 단위 범람 방류량(qts) 및 세굴공 특성을 분석하였다. 상대적으로 안정적인 범람 수심(hts/h1)은 굴착 후 Froude 수(Fr1)가 증가함에 따라 증가하고 상대 제방 높이(hd/h1)가 증가함에 따라 감소하는 것으로 나타났습니다. 상대적으로 안정적인 단위 오버플로 방전(qts/q1)은 주로 상대적 제방 높이의 영향을 받습니다. 또한, 스퍼 둑 뒤의 세굴 구덩이 결과는 세굴 깊이(s/h1)가 상대 전류 강도(u1/uc) 및 둑 높이(hd/h1)에 정비례하고 물에 반비례함을 보여줍니다. 보어 전 깊이(h0/h1). 실험결과와 현장 실측자료를 피팅하여 상대 최대 세굴깊이를 예측하는 실증식을 구하였으며, 예측정확도는 30% 이내이다. 본 논문의 결론은 갯벌이 강한 하구에서 Spur dike의 공학적 설계 및 운영 평가에 대한 기술적 지원을 제공할 수 있다.
Hydrodynamics of tidal bore overflow on the spur dike and its influence on the local scour
Keywords
Spur dike, Tidal bore overflow, Overflow water depth, Unit overflow discharge, Maximum scour depth
추상적인:저수지 제방 산사태는 일반적인 지질학적 위험으로, 제때에 미리 경고하지 않으면 하천에 해일파가 발생하여 하천 교통이나 인근 수자원 보호 시설의 안전을 위험에 빠뜨릴 수 있습니다. 저수지 제방 산사태로 인한 해일파 전파 전파 Flow-3D를 이용하여 하류 댐과의 상호작용을 시뮬레이션 하였다. 수리학적 물리적 모델 시험의 타당성과 정확성을 검증하기 위하여 3차원 산사태 해지 모델을 구축하였다. 수면 높이 변화와 서지의 전파 과정에 대한 수리학적 물리적 모델 테스트. 그 동안,가장 위험한 수심과 입사각 조건은 다양한 조건에서 댐과 산사태 해일 사이의 상호 작용을 분석하여 얻었습니다. 엔지니어링 사례는 최대 동적 수두가 해일 높이의 수두보다 작고 물을 따라 감소한다는 것을 보여주었습니다. 이 경우, 서지의 정적 최대 수두에 따라 계산된 댐의 응력은 안전합니다.
As a common geological hazard,reservoir bank landslide would most probably induce surge waves in river if not prewarned in time,endangering river traffic or the safety of nearby water conservancy facilities.The propagation of surge wave induced by the landslide of curved river bank in reservoir and its interaction with downstream dam were simulated by using Flow-3D.A three-dimensional landslide surge model was constructed to verify the validity and accuracy of hydraulic physical model test.The result of the three-dimensional numerical simulation was in good agreement with that of hydraulic physical model test in terms of the water surface height change and the propagation process of the surge.In the mean time,the most dangerous water depth and incident angle conditions were obtained by analyzing the interaction between the dam and the landslide surge under different conditions.Engineering examples demonstrated that the maximum dynamic water head was smaller than the water head of surge height,and reduced along the water depth direction.In such cases,the stress of the dam calculated according to the static maximum water head of the surge is safe.
Abstract해저 협곡에서 탁도의 장거리 이동은 많은 양의 퇴적물을 심해 평원으로 운반할 수 있습니다. 이전 연구에서는 5.9~28.0m/s 범위의 다중 케이블 손상 이벤트에서 파생된 탁도 전류 속도와 0.15~7.2m/s 사이의 현장 관찰 결과에서 명백한 차이가 있음을 보여줍니다. 따라서 해저 환경의 탁한 유체가 해저 협곡을 고속으로 장거리로 흐를 수 있는지에 대한 질문이 남아 있습니다. 연구실 시험의 결합을 통해 해저협곡의 탁류의 고속 및 장거리 운동을 설명하기 위해 약안정 퇴적물 기반의 새로운 모델(약안정 퇴적물에 대한 파손 전파 모델 제안, 줄여서 WSS-PFP 모델)을 제안합니다. 및 수치 아날로그. 이 모델은 두 가지 메커니즘을 기반으로 합니다. 1) 원래 탁도류는 약하게 안정한 퇴적층의 불안정화를 촉발하고 연질 퇴적물의 불안정화 및 하류 방향으로의 이동을 촉진하고 2) 원래 탁도류가 협곡으로 이동할 때 형성되는 여기파가 불안정화로 이어진다. 하류 방향으로 약하게 안정한 퇴적물의 수송. 제안된 모델은 심해 퇴적, 오염 물질 이동 및 광 케이블 손상 연구를 위한 동적 프로세스 해석을 제공할 것입니다.
The long-distance movement of turbidity currents in submarine canyons can transport large amounts of sediment to deep-sea plains. Previous studies show obvious differences in the turbidity current velocities derived from the multiple cables damage events ranging from 5.9 to 28.0 m/s and those of field observations between 0.15 and 7.2 m/s. Therefore, questions remain regarding whether a turbid fluid in an undersea environment can flow through a submarine canyon for a long distance at a high speed. A new model based on weakly stable sediment is proposed (proposed failure propagation model for weakly stable sediments, WSS-PFP model for short) to explain the high-speed and long-range motion of turbidity currents in submarine canyons through the combination of laboratory tests and numerical analogs. The model is based on two mechanisms: 1) the original turbidity current triggers the destabilization of the weakly stable sediment bed and promotes the destabilization and transport of the soft sediment in the downstream direction and 2) the excitation wave that forms when the original turbidity current moves into the canyon leads to the destabilization and transport of the weakly stable sediment in the downstream direction. The proposed model will provide dynamic process interpretation for the study of deep-sea deposition, pollutant transport, and optical cable damage.
Keyword
turbidity current
excitation wave
dense basal layer
velocity
WSS-PFP model
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We thank Hanru WU from Ocean University of China for his help in thesis writing, and Hao TIAN and Chenxi WANG from Ocean University of China for their helps in the preparation of the experimental materials. Guohui XU is responsible for the development of the initial concept, processing of test data, and management of coauthor contributions to the paper; Yupeng REN for the experiment setup and drafting of the paper; Yi ZHANG and Xingbei XU for the simulation part of the experiment; Houjie WANG for writing guidance; Zhiyuan CHEN for the experiment setup.
Author information
Authors and Affiliations
Shandong Provincial Key Laboratory of Marine Environment and Geological Engineering, Qingdao, 266100, ChinaYupeng Ren, Yi Zhang, Guohui Xu, Xingbei Xu & Zhiyuan Chen
Shandong Provincial Key Laboratory of Marine Environment and Geological Engineering, Ocean University of China, Qingdao, 266100, ChinaYupeng Ren & Houjie Wang
Key Laboratory of Marine Environment and Ecology, Ocean University of China, Ministry of Education, Qingdao, 266100, ChinaYi Zhang, Guohui Xu, Xingbei Xu & Zhiyuan Chen
Supported by the National Natural Science Foundation of China (Nos. 41976049, 41720104001) and the Taishan Scholar Project of Shandong Province (No. TS20190913), and the Fundamental Research Funds for the Central Universities (No. 202061028)
Data Availability Statement
The datasets generated and/or analyzed during the current study are available from the corresponding author upon reasonable request.
Ren, Y., Zhang, Y., Xu, G. et al. The failure propagation of weakly stable sediment: A reason for the formation of high-velocity turbidity currents in submarine canyons. J. Ocean. Limnol. (2022). https://doi.org/10.1007/s00343-022-1285-0
TianLiabJ.M.T.DaviesaXiangzhenZhuc aUniversity of Birmingham, Birmingham B15 2TT, United Kingdom bGrainger and Worrall Ltd, Bridgnorth WV15 5HP, United Kingdom cBrunel Centre for Advanced Solidification Technology, Brunel University London, Kingston Ln, London, Uxbridge UB8 3PH, United Kingdom
Abstract
An entrainment defect (also known as a double oxide film defect or bifilm) acts a void containing an entrapped gas when submerged into a light-alloy melt, thus reducing the quality and reproducibility of the final castings. Previous publications, carried out with Al-alloy castings, reported that this trapped gas could be subsequently consumed by the reaction with the surrounding melt, thus reducing the void volume and negative effect of entrainment defects. Compared with Al-alloys, the entrapped gas within Mg-alloy might be more efficiently consumed due to the relatively high reactivity of magnesium. However, research into the entrainment defects within Mg alloys has been significantly limited. In the present work, AZ91 alloy castings were produced under different carrier gas atmospheres (i.e., SF6/CO2, SF6/air). The evolution processes of the entrainment defects contained in AZ91 alloy were suggested according to the microstructure inspections and thermodynamic calculations. The defects formed in the different atmospheres have a similar sandwich-like structure, but their oxide films contained different combinations of compounds. The use of carrier gases, which were associated with different entrained-gas consumption rates, affected the reproducibility of AZ91 castings.
연행 결함(이중 산화막 결함 또는 이중막이라고도 함)은 경합금 용융물에 잠길 때 갇힌 가스를 포함하는 공극으로 작용하여 최종 주물의 품질과 재현성을 저하시킵니다. Al-합금 주물을 사용하여 수행된 이전 간행물에서는 이 갇힌 가스가 주변 용융물과의 반응에 의해 후속적으로 소모되어 공극 부피와 연행 결함의 부정적인 영향을 줄일 수 있다고 보고했습니다. Al-합금에 비해 마그네슘의 상대적으로 높은 반응성으로 인해 Mg-합금 내에 포집된 가스가 더 효율적으로 소모될 수 있습니다. 그러나 Mg 합금 내 연행 결함에 대한 연구는 상당히 제한적이었습니다. 현재 작업에서 AZ91 합금 주물은 다양한 캐리어 가스 분위기(즉, SF6/CO2, SF6/공기)에서 생산되었습니다. AZ91 합금에 포함된 연행 결함의 진화 과정은 미세 조직 검사 및 열역학 계산에 따라 제안되었습니다. 서로 다른 분위기에서 형성된 결함은 유사한 샌드위치 구조를 갖지만 산화막에는 서로 다른 화합물 조합이 포함되어 있습니다. 다른 동반 가스 소비율과 관련된 운반 가스의 사용은 AZ91 주물의 재현성에 영향을 미쳤습니다.
As the lightest structural metal available on Earth, magnesium became one of the most attractive light metals over the last few decades. The magnesium industry has consequently experienced a rapid development in the last 20 years [1,2], indicating a large growth in demand for Mg alloys all over the world. Nowadays, the use of Mg alloys can be found in the fields of automobiles, aerospace, electronics and etc.[3,4]. It has been predicted that the global consumption of Mg metals will further increase in the future, especially in the automotive industry, as the energy efficiency requirement of both traditional and electric vehicles further push manufactures lightweight their design [3,5,6].
The sustained growth in demand for Mg alloys motivated a wide interest in the improvement of the quality and mechanical properties of Mg-alloy castings. During a Mg-alloy casting process, surface turbulence of the melt can lead to the entrapment of a doubled-over surface film containing a small quantity of the surrounding atmosphere, thus forming an entrainment defect (also known as a double oxide film defect or bifilm) [7], [8], [9], [10]. The random size, quantity, orientation, and placement of entrainment defects are widely accepted to be significant factors linked to the variation of casting properties [7]. In addition, Peng et al. [11] found that entrained oxides films in AZ91 alloy melt acted as filters to Al8Mn5 particles, trapping them as they settle. Mackie et al. [12] further suggested that entrained oxide films can act to trawl the intermetallic particles, causing them to cluster and form extremely large defects. The clustering of intermetallic compounds made the entrainment defects more detrimental for the casting properties.
Most of the previous studies regarding entrainment defects were carried out on Al-alloys [7,[13], [14], [15], [16], [17], [18], and a few potential methods have been suggested for diminishing their negative effect on the quality of Al-alloy castings. Nyahumwa et al.,[16] shows that the void volume within entrainment defects could be reduced by a hot isostatic pressing (HIP) process. Campbell [7] suggested the entrained gas within the defects could be consumed due to reaction with the surrounding melt, which was further verified by Raiszedeh and Griffiths [19].The effect of the entrained gas consumption on the mechanical properties of Al-alloy castings has been investigated by [8,9], suggesting that the consumption of the entrained gas promoted the improvement of the casting reproducibility.
Compared with the investigation concerning the defects within Al-alloys, research into the entrainment defects within Mg-alloys has been significantly limited. The existence of entrainment defects has been demonstrated in Mg-alloy castings [20,21], but their behaviour, evolution, as well as entrained gas consumption are still not clear.
In a Mg-alloy casting process, the melt is usually protected by a cover gas to avoid magnesium ignition. The cavities of sand or investment moulds are accordingly required to be flushed with the cover gas prior to the melt pouring [22]. Therefore, the entrained gas within Mg-alloy castings should contain the cover gas used in the casting process, rather than air only, which may complicate the structure and evolution of the corresponding entrainment defects.
SF6 is a typical cover gas widely used for Mg-alloy casting processes [23], [24], [25]. Although this cover gas has been restricted to use in European Mg-alloy foundries, a commercial report has pointed out that this cover is still popular in global Mg-alloy industry, especially in the countries which dominated the global Mg-alloy production, such as China, Brazil, India, etc. [26]. In addition, a survey in academic publications also showed that this cover gas was widely used in recent Mg-alloy studies [27]. The protective mechanism of SF6 cover gas (i.e., the reaction between liquid Mg-alloy and SF6 cover gas) has been investigated by several previous researchers, but the formation process of the surface oxide film is still not clearly understood, and even some published results are conflicting with each other. In early 1970s, Fruehling [28] found that the surface film formed under SF6 was MgO mainly with traces of fluorides, and suggested that SF6 was absorbed in the Mg-alloy surface film. Couling [29] further noticed that the absorbed SF6 reacted with the Mg-alloy melt to form MgF2. In last 20 years, different structures of the Mg-alloy surface films have been reported, as detailed below.(1)
Single-layered film. Cashion [30,31] used X-ray Photoelectron Spectroscopy (XPS) and Auger Spectroscopy (AES) to identify the surface film as MgO and MgF2. He also found that composition of the film was constant throughout the thickness and the whole experimental holding time. The film observed by Cashion had a single-layered structure created from a holding time from 10 min to 100 min.(2)
Double-layered film. Aarstad et. al [32] reported a doubled-layered surface oxide film in 2003. They observed several well-distributed MgF2 particles attached to the preliminary MgO film and grew until they covered 25–50% of the total surface area. The inward diffusion of F through the outer MgO film was the driving force for the evolution process. This double-layered structure was also supported by Xiong’s group [25,33] and Shih et al. [34].(3)
Triple-layered film. The triple-layered film and its evolution process were reported in 2002 by Pettersen [35]. Pettersen found that the initial surface film was a MgO phase and then gradually evolved to the stable MgF2 phase by the inward diffusion of F. In the final stage, the film has a triple-layered structure with a thin O-rich interlayer between the thick top and bottom MgF2 layers.(4)
Oxide film consisted of discrete particles. Wang et al [36] stirred the Mg-alloy surface film into the melt under a SF6 cover gas, and then inspect the entrained surface film after the solidification. They found that the entrained surface films were not continues as the protective surface films reported by other researchers but composed of discrete particles. The young oxide film was composed of MgO nano-sized oxide particles, while the old oxide films consist of coarse particles (about 1 µm in average size) on one side that contained fluorides and nitrides.
The oxide films of a Mg-alloy melt surface or an entrained gas are both formed due to the reaction between liquid Mg-alloy and the cover gas, thus the above-mentioned research regarding the Mg-alloy surface film gives valuable insights into the evolution of entrainment defects. The protective mechanism of SF6 cover gas (i.e., formation of a Mg-alloy surface film) therefore indicated a potential complicated evolution process of the corresponding entrainment defects.
However, it should be noted that the formation of a surface film on a Mg-alloy melt is in a different situation to the consumption of an entrained gas that is submerged into the melt. For example, a sufficient amount of cover gas was supported during the surface film formation in the studies previously mentioned, which suppressed the depletion of the cover gas. In contrast, the amount of entrained gas within a Mg-alloy melt is finite, and the entrained gas may become fully depleted. Mirak [37] introduced 3.5%SF6/air bubbles into a pure Mg-alloy melt solidifying in a specially designed permanent mould. It was found that the gas bubbles were entirely consumed, and the corresponding oxide film was a mixture of MgO and MgF2. However, the nucleation sites (such as the MgF2 spots observed by Aarstad [32] and Xiong [25,33]) were not observed. Mirak also speculated that the MgF2 formed prior to MgO in the oxide film based on the composition analysis, which was opposite to the surface film formation process reported in previous literatures (i.e., MgO formed prior to MgF2). Mirak’s work indicated that the oxide-film formation of an entrained gas may be quite different from that of surface films, but he did not reveal the structure and evolution of the oxide films.
In addition, the use of carrier gas in the cover gases also influenced the reaction between the cover gas and the liquid Mg-alloy. SF6/air required a higher content of SF6 than did a SF6/CO2 carrier gas [38], to avoid the ignition of molten magnesium, revealing different gas-consumption rates. Liang et.al [39] suggested that carbon was formed in the surface film when CO2 was used as a carrier gas, which was different from the films formed in SF6/air. An investigation into Mg combustion [40] reported a detection of Mg2C3 in the Mg-alloy sample after burning in CO2, which not only supported Liang’s results, but also indicated a potential formation of Mg carbides in double oxide film defects.
The work reported here is an investigation into the behaviour and evolution of entrainment defects formed in AZ91 Mg-alloy castings, protected by different cover gases (i.e., SF6/air and SF6/CO2). These carrier gases have different protectability for liquid Mg alloy, which may be therefore associated with different consumption rates and evolution processes of the corresponding entrained gases. The effect of the entrained-gas consumption on the reproducibility of AZ91 castings was also studied.
2. Experiment
2.1. Melting and casting
Three kilograms AZ91 alloy was melted in a mild steel crucible at 700 ± 5 °C. The composition of the AZ91 alloy has been shown in Table 1. Prior to heating, all oxide scale on the ingot surface was removed by machining. The cover gases used were 0.5%SF6/air or 0.5%SF6/CO2 (vol.%) at a flow rate of 6 L/min for different castings. The melt was degassed by argon with a flow rate of 0.3 L/min for 15 min [41,42], and then poured into sand moulds. Prior to pouring, the sand mould cavity was flushed with the cover gas for 20 min [22]. The residual melt (around 1 kg) was solidified in the crucible.
Table 1. Composition (wt.%) of the AZ91 alloy used in this study.
Al
Zn
Mn
Si
Fe
Ni
Mg
9.4
0.61
0.15
0.02
0.005
0.0017
Residual
Fig. 1(a) shows the dimensions of the casting with runners. A top-filling system was deliberately used to generate entrainment defects in the final castings. Green and Campbell [7,43] suggested that a top-filling system caused more entrainment events (i.e., bifilms) during a casting process, compared with a bottom-filling system. A melt flow simulation (Flow-3D software) of this mould, using Reilly’s model [44] regarding the entrainment events, also predicted that a large amount of bifilms would be contained in the final casting (denoted by the black particles in Fig. 1b).
Shrinkage defects also affect the mechanical properties and reproducibility of castings. Since this study focused on the effect of bifilms on the casting quality, the mould has been deliberately designed to avoid generating shrinkage defects. A solidification simulation using ProCAST software showed that no shrinkage defect would be contained in the final casting, as shown in Fig. 1c. The casting soundness has also been confirmed using a real time X-ray prior to the test bar machining.
The sand moulds were made from resin-bonded silica sand, containing 1wt. % PEPSET 5230 resin and 1wt. % PEPSET 5112 catalyst. The sand also contained 2 wt.% Na2SiF6 to act as an inhibitor [45]. The pouring temperature was 700 ± 5 °C. After the solidification, a section of the runner bars was sent to the Sci-Lab Analytical Ltd for a H-content analysis (LECO analysis), and all the H-content measurements were carried out on the 5th day after the casting process. Each of the castings was machined into 40 test bars for a tensile strength test, using a Zwick 1484 tensile test machine with a clip extensometer. The fracture surfaces of the broken test bars were examined using Scanning Electron Microscope (SEM, Philips JEOL7000) with an accelerating voltage of 5–15 kV. The fractured test bars, residual Mg-alloy solidified in the crucible, and the casting runners were then sectioned, polished and also inspected using the same SEM. The cross-section of the oxide film found on the test-bar fracture surface was exposed by the Focused Ion Beam milling technique (FIB), using a CFEI Quanta 3D FEG FIB-SEM. The oxide film required to be analysed was coated with a platinum layer. Then, a gallium ion beam, accelerated to 30 kV, milled the material substrate surrounding the platinum coated area to expose the cross section of the oxide film. EDS analysis of the oxide film’s cross section was carried out using the FIB equipment at accelerating voltage of 30 kV.
2.2. Oxidation cell
As previously mentioned, several past researchers investigated the protective film formed on a Mg-alloy melt surface [38,39,[46], [47], [48], [49], [50], [51], [52]. During these experiments, the amount of cover gas used was sufficient, thus suppressing the depletion of fluorides in the cover gas. The experiment described in this section used a sealed oxidation cell, which limited the supply of cover gas, to study the evolution of the oxide films of entrainment defects. The cover gas contained in the oxidation cell was regarded as large-size “entrained bubble”.
As shown in Fig. 2, the main body of the oxidation cell was a closed-end mild steel tube which had an inner length of 400 mm, and an inner diameter of 32 mm. A water-cooled copper tube was wrapped around the upper section of the cell. When the tube was heated, the cooling system created a temperature difference between the upper and lower sections, causing the interior gas to convect within the tube. The temperature was monitored by a type-K thermocouple located at the top of the crucible. Nie et al. [53] suggested that the SF6 cover gas would react with the steel wall of the holding furnace when they investigated the surface film of a Mg-alloy melt. To avoid this reaction, the interior surface of the steel oxidation cell (shown in Fig. 2) and the upper half section of the thermocouple were coated with boron nitride (the Mg-alloy was not in contact with boron nitride).
During the experiment, a block of solid AZ91 alloy was placed in a magnesia crucible located at the bottom of the oxidation cell. The cell was heated to 100 °C in an electric resistance furnace under a gas flow rate of 1 L/min. The cell was held at this temperature for 20 min, to replace the original trapped atmosphere (i.e. air). Then, the oxidation cell was further heated to 700 °C, melting the AZ91 sample. The gas inlet and exit valves were then closed, creating a sealed environment for oxidation under a limited supply of cover gas. The oxidation cell was then held at 700 ± 10 °C for periods of time from 5 min to 30 min in 5-min intervals. At the end of each holding time, the cell was quenched in water. After cooling to room temperature, the oxidised sample was sectioned, polished, and subsequently examined by SEM.
3. Results
3.1. Structure and composition of the entrainment defects formed in SF6/air
The structure and composition of the entrainment defect formed in the AZ91 castings under a cover gas of 0.5%SF6/air was observed by SEM and EDS. The results indicate that there exist two types of entrainment defects which are sketched in Fig. 3: (1) Type A defect whose oxide film has a traditional single-layered structure and (2) Type B defect, whose oxide film has two layers. The details of these defects were introduced in the following. Here it should be noticed that, as the entrainment defects are also known as biofilms or double oxide film, the oxide films of Type B defect were referred to as “multi-layered oxide film” or “multi-layered structure” in the present work to avoid a confusing description such as “the double-layered oxide film of a double oxide film defect”.
Fig. 4(a-b) shows a Type A defect having a compact single-layered oxide film with about 0.4 µm thickness. Oxygen, fluorine, magnesium and aluminium were detected in this film (Fig. 4c). It is speculated that oxide film is the mixture of fluoride and oxide of magnesium and aluminium. The detection of fluorine revealed that an entrained cover gas was contained in the formation of this defect. That is to say that the pores shown in Fig. 4(a) were not shrinkage defects or hydrogen porosity, but entrainment defects. The detection of aluminium was different with Xiong and Wang’s previous study [47,48], which showed that no aluminium was contained in their surface film of an AZ91 melt protected by a SF6 cover gas. Sulphur could not be clearly recognized in the element map, but there was a S-peak in the corresponding ESD spectrum.
Fig. 5(a-b) shows a Type B entrainment defect having a multi-layered oxide film. The compact outer layers of the oxide films were enriched with fluorine and oxygen (Fig. 5c), while their relatively porous inner layers were only enriched with oxygen (i.e., poor in fluorine) and partly grew together, thus forming a sandwich-like structure. Therefore, it is speculated that the outer layer is the mixture of fluoride and oxide, while the inner layer is mainly oxide. Sulphur could only be recognized in the EDX spectrum and could not be clearly identified in the element map, which might be due to the small S-content in the cover gas (i.e., 0.5% volume content of SF6 in the cover gas). In this oxide film, aluminium was contained in the outer layer of this oxide film but could not be clearly detected in the inner layer. Moreover, the distribution of Al seems to be uneven. It can be found that, in the right side of the defect, aluminium exists in the film but its concentration can not be identified to be higher than the matrix. However, there is a small area with much higher aluminium concentration in the left side of the defect. Such an uneven distribution of aluminium was also observed in other defects (shown in the following), and it is the result of the formation of some oxide particles in or under the film.
Figs. 4 and 5 show cross sectional observations of the entrainment defects formed in the AZ91 alloy sample cast under a cover gas of SF6/air. It is not sufficient to characterize the entrainment defects only by the figures observed from the two-dimensional section. To have a further understanding, the surface of the entrainment defects (i.e. the oxide film) was further studied by observing the fracture surface of the test bars.
Fig. 6(a) shows fracture surfaces of an AZ91 alloy tensile test bar produced in SF6/air. Symmetrical dark regions can be seen on both sides of the fracture surfaces. Fig. 6(b) shows boundaries between the dark and bright regions. The bright region consisted of jagged and broken features, while the surface of the dark region was relatively smooth and flat. In addition, the EDS results (Fig. 6c-d and Table 2) show that fluorine, oxygen, sulphur, and nitrogen were only detected in the dark regions, indicating that the dark regions were surface protective films entrained into the melt. Therefore, it could be suggested that the dark regions were an entrainment defect with consideration of their symmetrical nature. Similar defects on fracture surfaces of Al-alloy castings have been previously reported [7]. Nitrides were only found in the oxide films on the test-bar fracture surfaces but never detected in the cross-sectional samples shown in Figs. 4 and 5. An underlying reason is that the nitrides contained in these samples may have hydrolysed during the sample polishing process [54].
Table 2. EDS results (wt.%) corresponding to the regions shown in Fig. 6 (cover gas: SF6/air).
In conjunction with the cross-sectional observation of the defects shown in Figs. 4 and 5, the structure of an entrainment defect contained in a tensile test bar was sketched as shown in Fig. 6(e). The defect contained an entrained gas enclosed by its oxide film, creating a void section inside the test bar. When the tensile force applied on the defect during the fracture process, the crack was initiated at the void section and propagated along the entrainment defect, since cracks would be propagated along the weakest path [55]. Therefore, when the test bar was finally fractured, the oxide films of entrainment defect appeared on both fracture surfaces of the test bar, as shown in Fig. 6(a).
3.2. Structure and composition of the entrainment defects formed in SF6/CO2
Similar to the entrainment defect formed in SF6/air, the defects formed under a cover gas of 0.5%SF6/CO2 also had two types of oxide films (i.e., single-layered and multi-layered types). Fig. 7(a) shows an example of the entrainment defects containing a multi-layered oxide film. A magnified observation to the defect (Fig. 7b) shows that the inner layers of the oxide films had grown together, presenting a sandwich-like structure, which was similar to the defects formed in an atmosphere of SF6/air (Fig. 5b). An EDS spectrum (Fig. 7c) revealed that the joint area (inner layer) of this sandwich-like structure mainly contained magnesium oxides. Peaks of fluorine, sulphur, and aluminium were recognized in this EDS spectrum, but their amount was relatively small. In contrast, the outer layers of the oxide films were compact and composed of a mixture of fluorides and oxides (Fig. 7d-e).
Fig. 8(a) shows an entrainment defect on the fracture surfaces of an AZ91 alloy tensile test bar, which was produced in an atmosphere of 0.5%SF6/CO2. The corresponding EDS results (Table 3) showed that oxide film contained fluorides and oxides. Sulphur and nitrogen were not detected. Besides, a magnified observation (Fig. 8b) indicated spots on the oxide film surface. The diameter of the spots ranged from hundreds of nanometres to a few micron meters.
To further reveal the structure and composition of the oxide film clearly, the cross-section of the oxide film on a test-bar fracture surface was onsite exposed using the FIB technique (Fig. 9). As shown in Fig. 9a, a continuous oxide film was found between the platinum coating layer and the Mg-Al alloy substrate. Fig. 9 (b-c) shows a magnified observation to oxide films, indicating a multi-layered structure (denoted by the red box in Fig. 9c). The bottom layer was enriched with fluorine and oxygen and should be the mixture of fluoride and oxide, which was similar to the “outer layer” shown in Figs. 5 and 7, while the only-oxygen-enriched top layer was similar to the “inner layer” shown in Figs. 5 and 7.
Except the continuous film, some individual particles were also observed in or below the continuous film, as shown in Fig. 9. An Al-enriched particle was detected in the left side of the oxide film shown in Fig. 9b and might be speculated to be spinel Mg2AlO4 because it also contains abundant magnesium and oxygen elements. The existing of such Mg2AlO4 particles is responsible for the high concentration of aluminium in small areas of the observed film and the uneven distribution of aluminium, as shown in Fig. 5(c). Here it should be emphasized that, although the other part of the bottom layer of the continuous oxide film contains less aluminium than this Al-enriched particle, the Fig. 9c indicated that the amount of aluminium in this bottom layer was still non-negligible, especially when comparing with the outer layer of the film. Below the right side of the oxide film shown in Fig. 9b, a particle was detected and speculated to be MgO because it is rich in Mg and O. According to Wang’s result [56], lots of discrete MgO particles can be formed on the surface of the Mg melt by the oxidation of Mg melt and Mg vapor. The MgO particles observed in our present work may be formed due to the same reasons. While, due to the differences in experimental conditions, less Mg melt can be vapored or react with O2, thus only a few of MgO particles formed in our work. An enrichment of carbon was also found in the film, revealing that CO2 was able to react with the melt, thus forming carbon or carbides. This carbon concentration was consistent with the relatively high carbon content of the oxide film shown in Table 3 (i.e., the dark region). In the area next to the oxide film.
Table 3. EDS results (wt.%) corresponding to the regions shown in Fig. 8 (cover gas: SF6/ CO2).
This cross-sectional observation of the oxide film on a test bar fracture surface (Fig. 9) further verified the schematic of the entrainment defect shown in Fig. 6(e). The entrainment defects formed in different atmospheres of SF6/CO2 and SF6/air had similar structures, but their compositions were different.
3.3. Evolution of the oxide films in the oxidation cell
The results in Section 3.1 and 3.2 have shown the structures and compositions of entrainment defects formed in AZ91 castings under cover gases of SF6/air and SF6/CO2. Different stages of the oxidation reaction may lead to the different structures and compositions of entrainment defects. Although Campbell has conjectured that an entrained gas may react with the surrounding melt, it is rarely reported that the reaction occurring between the Mg-alloy melt and entrapped cover gas. Previous researchers normally focus on the reaction between a Mg-alloy melt and the cover gas in an open environment [38,39,[46], [47], [48], [49], [50], [51], [52], which was different from the situation of a cover gas trapped into the melt. To further understand the formation of the entrainment defect in an AZ91 alloy, the evolution process of oxide films of the entrainment defect was further studied using an oxidation cell.
Fig. 10 (a and d) shows a surface film held for 5 min in the oxidation cell, protected by 0.5%SF6/air. There was only one single layer consisting of fluoride and oxide (MgF2 and MgO). In this surface film. Sulphur was detected in the EDS spectrum, but its amount was too small to be recognized in the element map. The structure and composition of this oxide film was similar to the single-layered films of entrainment defects shown in Fig. 4.
After a holding time of 10 min, a thin (O, S)-enriched top layer (around 700 nm) appeared upon the preliminary F-enriched film, forming a multi-layered structure, as shown in Fig. 10(b and e). The thickness of the (O, S)-enriched top layer increased with increased holding time. As shown in Fig. 10(c and f), the oxide film held for 30 min also had a multi-layered structure, but the thickness of its (O, S)-enriched top layer (around 2.5 µm) was higher than the that of the 10-min oxide film. The multi-layered oxide films shown in Fig. 10(b-c) presented a similar appearance to the films of the sandwich-like defect shown in Fig. 5.
The different structures of the oxide films shown in Fig. 10 indicated that fluorides in the cover gas would be preferentially consumed due to the reaction with the AZ91 alloy melt. After the depletion of fluorides, the residual cover gas reacted further with the liquid AZ91 alloy, forming the top (O, S)-enriched layer in the oxide film. Therefore, the different structures and compositions of entrainment defects shown in Figs. 4 and 5 may be due to an ongoing oxidation reaction between melt and entrapped cover gas.
This multi-layered structure has not been reported in previous publications concerning the protective surface film formed on a Mg-alloy melt [38,[46], [47], [48], [49], [50], [51]. This may be due to the fact that previous researchers carried out their experiments with an un-limited amount of cover gas, creating a situation where the fluorides in the cover gas were not able to become depleted. Therefore, the oxide film of an entrainment defect had behaviour traits similar to the oxide films shown in Fig. 10, but different from the oxide films formed on the Mg-alloy melt surface reported in [38,[46], [47], [48], [49], [50], [51].
Similar with the oxide films held in SF6/air, the oxide films formed in SF6/CO2 also had different structures with different holding times in the oxidation cell. Fig. 11(a) shows an oxide film, held on an AZ91 melt surface under a cover gas of 0.5%SF6/CO2 for 5 min. This film had a single-layered structure consisting of MgF2. The existence of MgO could not be confirmed in this film. After the holding time of 30 min, the film had a multi-layered structure; the inner layer was of a compact and uniform appearance and composed of MgF2, while the outer layer is the mixture of MgF2 and MgO. Sulphur was not detected in this film, which was different from the surface film formed in 0.5%SF6/air. Therefore, fluorides in the cover gas of 0.5%SF6/CO2 were also preferentially consumed at an early stage of the film growth process. Compared with the film formed in SF6/air, the MgO in film formed in SF6/CO2 appeared later and sulphide did not appear within 30 min. It may mean that the formation and evolution of film in SF6/air is faster than SF6/CO2. CO2 may have subsequently reacted with the melt to form MgO, while sulphur-containing compounds accumulated in the cover gas and reacted to form sulphide in very late stage (may after 30 min in oxidation cell).
4. Discussion
4.1. Evolution of entrainment defects formed in SF6/air
HSC software from Outokumpu HSC Chemistry for Windows (http://www.hsc-chemistry.net/) was used to carry out thermodynamic calculations needed to explore the reactions which might occur between the trapped gases and liquid AZ91 alloy. The solutions to the calculations suggest which products are most likely to form in the reaction process between a small amount of cover gas (i.e., the amount within a trapped bubble) and the AZ91-alloy melt.
In the trials, the pressure was set to 1 atm, and the temperature set to 700 °C. The amount of the cover gas was assumed to be 7 × 10−7 kg, with a volume of approximately 0.57 cm3 (3.14 × 10−8 kmol) for 0.5%SF6/air, and 0.35 cm3 (3.12 × 10−8 kmol) for 0.5%SF6/CO2. The amount of the AZ91 alloy melt in contact with the trapped gas was assumed to be sufficient to complete all reactions. The decomposition products of SF6 were SF5, SF4, SF3, SF2, F2, S(g), S2(g) and F(g) [57], [58], [59], [60].
Fig. 12 shows the equilibrium diagram of the thermodynamic calculation of the reaction between the AZ91 alloy and 0.5%SF6/air. In the diagram, the reactants and products with less than 10−15 kmol have not been shown, as this was 5 orders of magnitude less than the amount of SF6 present (≈ 1.57 × 10−10 kmol) and therefore would not affect the observed process in a practical way.
This reaction process could be divided into 3 stages.
Stage 1: The formation of fluorides. the AZ91 melt preferentially reacted with SF6 and its decomposition products, producing MgF2, AlF3, and ZnF2. However, the amount of ZnF2 may have been too small to be detected practically (1.25 × 10−12 kmol of ZnF2 compared with 3 × 10−10 kmol of MgF2), which may be the reason why Zn was not detected in any the oxide films shown in Sections 3.1–3.3. Meanwhile, sulphur accumulated in the residual gas as SO2.
Stage 2: The formation of oxides. After the liquid AZ91 alloy had depleted all the available fluorides in the entrapped gas, the amount of AlF3 and ZnF2 quickly reduced due to a reaction with Mg. O2(g) and SO2 reacted with the AZ91 melt, forming MgO, Al2O3, MgAl2O4, ZnO, ZnSO4 and MgSO4. However, the amount of ZnO and ZnSO4 would have been too small to be found practically by EDS (e.g. 9.5 × 10−12 kmol of ZnO,1.38 × 10−14 kmol of ZnSO4, in contrast to 4.68 × 10−10 kmol of MgF2, when the amount of AZ91 on the X-axis is 2.5 × 10−9 kmol). In the experimental cases, the concentration of F in the cover gas is very low, whole the concentration f O is much higher. Therefore, the stage 1 and 2, i.e, the formation of fluoride and oxide may happen simultaneously at the beginning of the reaction, resulting in the formation of a singer-layered mixture of fluoride and oxide, as shown in Figs. 4 and 10(a). While an inner layer consisted of oxides but fluorides could form after the complete depletion of F element in the cover gas.
Stages 1- 2 theoretically verified the formation process of the multi-layered structure shown in Fig. 10.
The amount of MgAl2O4 and Al2O3 in the oxide film was of a sufficient amount to be detected, which was consistent with the oxide films shown in Fig. 4. However, the existence of aluminium could not be recognized in the oxide films grown in the oxidation cell, as shown in Fig. 10. This absence of Al may be due to the following reactions between the surface film and AZ91 alloy melt:(1)
Mg + MgAl2O4 = MgO + Al, △G(700 °C) =-106.34 kJ/molwhich could not be simulated by the HSC software since the thermodynamic calculation was carried out under an assumption that the reactants were in full contact with each other. However, in a practical process, the AZ91 melt and the cover gas would not be able to be in contact with each other completely, due to the existence of the protective surface film.
Stage 3: The formation of Sulphide and nitride. After a holding time of 30 min, the gas-phase fluorides and oxides in the oxidation cell had become depleted, allowing the melt reaction with the residual gas, forming an additional sulphur-enriched layer upon the initial F-enriched or (F, O)-enriched surface film, thus resulting in the observed multi-layered structure shown in Fig. 10 (b and c). Besides, nitrogen reacted with the AZ91 melt until all reactions were completed. The oxide film shown in Fig. 6 may correspond to this reaction stage due to its nitride content. However, the results shows that the nitrides were not detected in the polished samples shown in Figs. 4 and 5, but only found on the test bar fracture surfaces. The nitrides may have hydrolysed during the sample preparation process, as follows [54]:(3)
Mg3N2 + 6H2O =3Mg(OH)2 + 2NH3↑(4)
AlN+ 3H2O =Al(OH)3 + NH3↑
In addition, Schmidt et al. [61] found that Mg3N2 and AlN could react to form ternary nitrides (Mg3AlnNn+2, n= 1, 2, 3…). HSC software did not contain the database of ternary nitrides, and it could not be added into the calculation. The oxide films in this stage may also contain ternary nitrides.
4.2. Evolution of entrainment defects formed in SF6/CO2
Fig. 13 shows the results of the thermodynamic calculation between AZ91 alloy and 0.5%SF6/CO2. This reaction processes can also be divided into three stages.
Stage 1: The formation of fluorides. SF6 and its decomposition products were consumed by the AZ91 melt, forming MgF2, AlF3, and ZnF2. As in the reaction of AZ91 in 0.5%SF6/air, the amount of ZnF2 was too small to be detected practically (1.51 × 10−13 kmol of ZnF2 compared with 2.67 × 10−10 kmol of MgF2). Sulphur accumulated in the residual trapped gas as S2(g) and a portion of the S2(g) reacted with CO2, to form SO2 and CO. The products in this reaction stage were consistent with the film shown in Fig. 11(a), which had a single layer structure that contained fluorides only.
Stage 2: The formation of oxides. AlF3 and ZnF2 reacted with the Mg in the AZ91 melt, forming MgF2, Al and Zn. The SO2 began to be consumed, producing oxides in the surface film and S2(g) in the cover gas. Meanwhile, the CO2 directly reacted with the AZ91 melt, forming CO, MgO, ZnO, and Al2O3. The oxide films shown in Figs. 9 and 11(b) may correspond to this reaction stage due to their oxygen-enriched layer and multi-layered structure.
The CO in the cover gas could further react with the AZ91 melt, producing C. This carbon may further react with Mg to form Mg carbides, when the temperature reduced (during solidification period) [62]. This may be the reason for the high carbon content in the oxide film shown in Figs. 8–9. Liang et al. [39] also reported carbon-detection in an AZ91 alloy surface film protected by SO2/CO2. The produced Al2O3 may be further combined with MgO, forming MgAl2O4[63]. As discussed in Section 4.1, the alumina and spinel can react with Mg, causing an absence of aluminium in the surface films, as shown in Fig. 11.
Stage 3: The formation of Sulphide. the AZ91 melt began to consume S2(g) in the residual entrapped gas, forming ZnS and MgS. These reactions did not occur until the last stage of the reaction process, which could be the reason why the S-content in the defect shown Fig. 7(c) was small.
In summary, thermodynamic calculations indicate that the AZ91 melt will react with the cover gas to form fluorides firstly, then oxides and sulphides in the last. The oxide film in the different reaction stages would have different structures and compositions.
4.3. Effect of the carrier gases on consumption of the entrained gas and the reproducibility of AZ91 castings
The evolution processes of entrainment defects, formed in SF6/air and SF6/CO2, have been suggested in Sections 4.1 and 4.2. The theoretical calculations were verified with respect to the corresponding oxide films found in practical samples. The atmosphere within an entrainment defect could be efficiently consumed due to the reaction with liquid Mg-alloy, in a scenario dissimilar to the Al-alloy system (i.e., nitrogen in an entrained air bubble would not efficiently react with Al-alloy melt [64,65], however, nitrogen would be more readily consumed in liquid Mg alloys, commonly referred to as “nitrogen burning” [66]).
The reaction between the entrained gas and the surrounding liquid Mg-alloy converted the entrained gas into solid compounds (e.g. MgO) within the oxide film, thus reducing the void volume of the entrainment defect and hence probably causing a collapse of the defect (e.g., if an entrained gas of air was depleted by the surrounding liquid Mg-alloy, under an assumption that the melt temperature is 700 °C and the depth of liquid Mg-alloy is 10 cm, the total volume of the final solid products would be 0.044% of the initial volume taken by the entrapped air).
The relationship between the void volume reduction of entrainment defects and the corresponding casting properties has been widely studied in Al-alloy castings. Nyahumwa and Campbell [16] reported that the Hot Isostatic Pressing (HIP) process caused the entrainment defects in Al-alloy castings to collapse and their oxide surfaces forced into contact. The fatigue lives of their castings were improved after HIP. Nyahumwa and Campbell [16] also suggested a potential bonding of the double oxide films that were in contact with each other, but there was no direct evidence to support this. This binding phenomenon was further investigated by Aryafar et.al.[8], who re-melted two Al-alloy bars with oxide skins in a steel tube and then carried out a tensile strength test on the solidified sample. They found that the oxide skins of the Al-alloy bars strongly bonded with each other and became even stronger with an extension of the melt holding time, indicating a potential “healing” phenomenon due to the consumption of the entrained gas within the double oxide film structure. In addition, Raidszadeh and Griffiths [9,19] successfully reduced the negative effect of entrainment defects on the reproducibility of Al-alloy castings, by extending the melt holding time before solidification, which allowed the entrained gas to have a longer time to react with the surrounding melt.
With consideration of the previous work mentioned, the consumption of the entrained gas in Mg-alloy castings may diminish the negative effect of entrainment defects in the following two ways.
(1) Bonding phenomenon of the double oxide films. The sandwich-like structure shown in Fig. 5 and 7 indicated a potential bonding of the double oxide film structure. However, more evidence is required to quantify the increase in strength due to the bonding of the oxide films.
(2) Void volume reduction of entrainment defects. The positive effect of void-volume reduction on the quality of castings has been widely demonstrated by the HIP process [67]. As the evolution processes discussed in Section 4.1–4.2, the oxide films of entrainment defects can grow together due to an ongoing reaction between the entrained gas and surrounding AZ91 alloy melt. The volume of the final solid products was significant small compared with the entrained gas (i.e., 0.044% as previously mentioned).
Therefore, the consumption rate of the entrained gas (i.e., the growth rate of oxide films) may be a critical parameter for improving the quality of AZ91 alloy castings. The oxide film growth rate in the oxidization cell was accordingly further investigated.
Fig. 14 shows a comparison of the surface film growth rates in different cover gases (i.e., 0.5%SF6/air and 0.5%SF6/CO2). 15 random points on each sample were selected for film thickness measurements. The 95% confidence interval (95%CI) was computed under an assumption that the variation of the film thickness followed a Gaussian distribution. It can be seen that all the surface films formed in 0.5%SF6/air grew faster than those formed in 0.5%SF6/CO2. The different growth rates suggested that the entrained-gas consumption rate of 0.5%SF6/air was higher than that of 0.5%SF6/CO2, which was more beneficial for the consumption of the entrained gas.
It should be noted that, in the oxidation cell, the contact area of liquid AZ91 alloy and cover gas (i.e. the size of the crucible) was relatively small with consideration of the large volume of melt and gas. Consequently, the holding time for the oxide film growth within the oxidation cell was comparatively long (i.e., 5–30 min). However, the entrainment defects contained in a real casting are comparatively very small (i.e., a few microns size as shown in Figs. 3–6, and [7]), and the entrained gas is fully enclosed by the surrounding melt, creating a relatively large contact area. Hence the reaction time for cover gas and the AZ91 alloy melt may be comparatively short. In addition, the solidification time of real Mg-alloy sand castings can be a few minutes (e.g. Guo [68] reported that a Mg-alloy sand casting with 60 mm diameter required 4 min to be solidified). Therefore, it can be expected that an entrained gas trapped during an Mg-alloy melt pouring process will be readily consumed by the surrounding melt, especially for sand castings and large-size castings, where solidification times are long.
Therefore, the different cover gases (0.5%SF6/air and 0.5%SF6/CO2) associated with different consumption rates of the entrained gases may affect the reproducibility of the final castings. To verify this assumption, the AZ91 castings produced in 0.5%SF6/air and 0.5%SF6/CO2 were machined into test bars for mechanical evaluation. A Weibull analysis was carried out using both linear least square (LLS) method and non-linear least square (non-LLS) method [69].
Fig. 15(a-b) shows a traditional 2-p linearized Weibull plot of the UTS and elongation of the AZ91 alloy castings, obtained by the LLS method. The estimator used is P= (i-0.5)/N, which was suggested to cause the lowest bias among all the popular estimators [69,70]. The casting produced in SF6/air has an UTS Weibull moduli of 16.9, and an elongation Weibull moduli of 5.0. In contrast, the UTS and elongation Weibull modulus of the casting produced in SF6/CO2 are 7.7 and 2.7 respectively, suggesting that the reproducibility of the casting protected by SF6/CO2 were much lower than that produced in SF6/air.
In addition, the author’s previous publication [69] demonstrated a shortcoming of the linearized Weibull plots, which may cause a higher bias and incorrect R2 interruption of the Weibull estimation. A Non-LLS Weibull estimation was therefore carried out, as shown in Fig. 15 (c-d). The UTS Weibull modulus of the SF6/air casting was 20.8, while the casting produced under SF6/CO2 had a lower UTS Weibull modulus of 11.4, showing a clear difference in their reproducibility. In addition, the SF6/air elongation (El%) dataset also had a Weibull modulus (shape = 5.8) higher than the elongation dataset of SF6/CO2 (shape = 3.1). Therefore, both the LLS and Non-LLS estimations suggested that the SF6/air casting has a higher reproducibility than the SF6/CO2 casting. It supports the method that the use of air instead of CO2 contributes to a quicker consumption of the entrained gas, which may reduce the void volume within the defects. Therefore, the use of 0.5%SF6/air instead of 0.5%SF6/CO2 (which increased the consumption rate of the entrained gas) improved the reproducibility of the AZ91 castings.
However, it should be noted that not all the Mg-alloy foundries followed the casting process used in present work. The Mg-alloy melt in present work was degassed, thus reducing the effect of hydrogen on the consumption of the entrained gas (i.e., hydrogen could diffuse into the entrained gas, potentially suppressing the depletion of the entrained gas [7,71,72]). In contrast, in Mg-alloy foundries, the Mg-alloy melt is not normally degassed, since it was widely believed that there is not a ‘gas problem’ when casting magnesium and hence no significant change in tensile properties[73]. Although studies have shown the negative effect of hydrogen on the mechanical properties of Mg-alloy castings [41,42,73], a degassing process is still not very popular in Mg-alloy foundries.
Moreover, in present work, the sand mould cavity was flushed with the SF6 cover gas prior to pouring [22]. However, not all the Mg-alloy foundries flushed the mould cavity in this way. For example, the Stone Foundry Ltd (UK) used sulphur powder instead of the cover-gas flushing. The entrained gas within their castings may be SO2/air, rather than the protective gas.
Therefore, although the results in present work have shown that using air instead of CO2 improved the reproducibility of the final casting, it still requires further investigations to confirm the effect of carrier gases with respect to different industrial Mg-alloy casting processes.
7. Conclusion
Entrainment defects formed in an AZ91 alloy were observed. Their oxide films had two types of structure: single-layered and multi-layered. The multi-layered oxide film can grow together forming a sandwich-like structure in the final casting.2.
Both the experimental results and the theoretical thermodynamic calculations demonstrated that fluorides in the trapped gas were depleted prior to the consumption of sulphur. A three-stage evolution process of the double oxide film defects has been suggested. The oxide films contained different combinations of compounds, depending on the evolution stage. The defects formed in SF6/air had a similar structure to those formed in SF6/CO2, but the compositions of their oxide films were different. The oxide-film formation and evolution process of the entrainment defects were different from that of the Mg-alloy surface films previous reported (i.e., MgO formed prior to MgF2).3.
The growth rate of the oxide film was demonstrated to be greater under SF6/air than SF6/CO2, contributing to a quicker consumption of the damaging entrapped gas. The reproducibility of an AZ91 alloy casting improved when using SF6/air instead of SF6/CO2.
Acknowledgements
The authors acknowledge funding from the EPSRC LiME grant EP/H026177/1, and the help from Dr W.D. Griffiths and Mr. Adrian Carden (University of Birmingham). The casting work was carried out in University of Birmingham.
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. 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. 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. 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. 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. 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. 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. 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. 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
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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. 2. Flume model in numerical simulation. 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. 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. 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. (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. 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. 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. 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. 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).
Keywords
Dam-break flow, Bed slope, Wet bed, Velocity profile, Bed shear stress, Large eddy simulation
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A. Safarzadeh1*, P. Mohsenzadeh2, S. Abbasi3 1 Professor of Civil Eng., Water Engineering and Mineral Waters Research Center, Univ. of Mohaghegh Ardabili,Ardabil, Iran 2 M.Sc., Graduated of Civil-Hydraulic Structures Eng., Faculty of Eng., Univ. of Mohaghegh Ardabili, Ardabil, Iran 3 M.Sc., Graduated of Civil -Hydraulic Structures Eng., Faculty of Eng., Univ. of Mohaghegh Ardabili, Ardabil, Iran Safarzadeh@uma.ac.ir
Highlights
유체 이동에 의해 생성된 RBF는 Ls-Dyna에서 Fluent, ICFD ALE 및 SPH 방법으로 시뮬레이션되었습니다. RBF의 과예측은 유체가 메인 도메인에서 고속으로 분리될 때 발생합니다. 이 과잉 예측은 요소 크기, 시간 단계 크기 및 유체 모델에 따라 다릅니다. 유체 성능을 검증하려면 최대 RBF보다 임펄스가 권장됩니다.
Abstract
Dam break is a very important problem due to its effects on economy, security, human casualties and environmental consequences. In this study, 3D flow due to dam break over the porous substrate is numerically simulated and the effect of porosity, permeability and thickness of the porous bed and the water depth in the porous substrate are investigated. Classic models of dam break over a rigid bed and water infiltration through porous media were studied and results of the numerical simulations are compared with existing laboratory data. Validation of the results is performed by comparing the water surface profiles and wave front position with dam break on rigid and porous bed. Results showed that, due to the effect of dynamic wave in the initial stage of dam break, a local peak occurs in the flood hydrograph. The presence of porous bed reduces the acceleration of the flood wave relative to the flow over the solid bed and it decreases with the increase of the permeability of the bed. By increasing the permeability of the bed, the slope of the ascending limb of the flood hydrograph and the peak discharge drops. Furthermore, if the depth and permeability of the bed is such that the intrusive flow reaches the rigid substrate under the porous bed, saturation of the porous bed, results in a sharp increase in the slope of the flood hydrograph. The maximum values of the peak discharge at the end of the channel with porous bed occurred in saturated porous bed conditions.
댐 붕괴는 경제, 보안, 인명 피해 및 환경적 영향으로 인해 매우 중요한 문제입니다. 본 연구에서는 다공성 기재에 대한 댐 파괴로 인한 3차원 유동을 수치적으로 시뮬레이션하고 다공성 기재의 다공성, 투과도 및 다공성 층의 두께 및 수심의 영향을 조사합니다. 단단한 바닥에 대한 댐 파괴 및 다공성 매체를 통한 물 침투의 고전 모델을 연구하고 수치 시뮬레이션 결과를 기존 실험실 데이터와 비교합니다. 결과 검증은 강체 및 다공성 베드에서 댐 파단과 수면 프로파일 및 파면 위치를 비교하여 수행됩니다. 그 결과 댐파괴 초기의 동적파동의 영향으로 홍수수문곡선에서 국부첨두가 발생하는 것으로 나타났다. 다공성 베드의 존재는 고체 베드 위의 유동에 대한 홍수파의 가속을 감소시키고 베드의 투과성이 증가함에 따라 감소합니다. 베드의 투수성을 증가시켜 홍수 수문곡선의 오름차순 경사와 첨두방류량이 감소한다. 더욱이, 만약 층의 깊이와 투과성이 관입 유동이 다공성 층 아래의 단단한 기질에 도달하는 정도라면, 다공성 층의 포화는 홍수 수문곡선의 기울기의 급격한 증가를 초래합니다. 다공층이 있는 채널의 끝단에서 최대 방전 피크값은 포화 다공층 조건에서 발생하였다.
Keywords
Keywords: Dams Break, 3D modeling, Porous Bed, Permeability, Flood wave
Reference
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NadhiraKarimaaIkhaMagdalenaabIndrianaMarcelaaMohammadFaridbaFaculty of Mathematics and Natural Sciences, Bandung Institute of Technology, 40132, IndonesiabCenter for Coastal and Marine Development, Bandung Institute of Technology, Indonesia
Highlights
•A new three-layer model for n-block submerged porous breakwaters is developed.
•New analytical approach in finding the wave transmission coefficient is presented.
•A finite volume method successfully simulates the wave attenuation process.
•Porous media blocks characteristics and configuration can optimize wave reduction.
Abstract
높은 파도 진폭은 해안선에 위험한 영향을 미치고 해안 복원력을 약화시킬 수 있습니다. 그러나 다중 다공성 매체는 해양 생태계의 환경 친화적인 해안 보호 역할을 할 수 있습니다.
이 논문에서 우리는 n개의 잠긴 다공성 미디어 블록이 있는 영역에서 파동 진폭 감소를 계산하기 위해 3층 깊이 통합 방정식을 사용합니다. 수학적 모델은 파동 전달 계수를 얻기 위해 여러 행렬 방정식을 포함하는 변수 분리 방법을 사용하여 해석적으로 해결됩니다.
이 계수는 진폭 감소의 크기에 대한 정보를 제공합니다. 또한 모델을 수치적으로 풀기 위해 지그재그 유한 체적 방법이 적용됩니다.
수치 시뮬레이션을 통해 다공성 매질 블록의 구성과 특성이 투과파 진폭을 줄이는 데 중요하다는 결론을 내렸습니다.
High wave amplitudes may cause dangerous effects on the shoreline and weaken coastal resilience. However, multiple porous media can act as environmental friendly coastal protectors of the marine ecosystem. In this paper, we use three-layer depth-integrated equations to calculate wave amplitude reduction in a domain with n submerged porous media blocks. The mathematical model is solved analytically using the separation of variables method involving several matrix equations to obtain the wave transmission coefficient. This coefficient provides information about the magnitude of amplitude reduction. Additionally, a staggered finite volume method is applied to solve the model numerically. By conducting numerical simulations, we conclude that porous media blocks’ configuration and characteristics are crucial in reducing transmitted wave amplitude.
Fig. 1. Sketch of the problem configuration.Fig. 6. Experiment of waves passing through a single block of porous medium.
References
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ArticleDownload PDFView Record in ScopusGoogle Scholar[9]F. Hajivalie, S. M. Mahmoudof, Experimental study of energy dissipation at rectangular submerged breakwater, Proceedings of the 8th International Conference on Fluid Mechanics.
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Finite element simulation on the convective double diffusive water-based copper oxide nanofluid flow in a square cavity having vertical wavy surfaces in presence of hydro-magnetic field
Yong Cheng, Yude Song, Chunye Liu, Wene Wang * and Xiaotao Hu Key Laboratory of Agricultural Soil and Water Engineering in Arid and Semiarid Areas, Ministry of Education, Northwest A&F University, Yangling 712100, China
Correspondence: wangwene@nwsuaf.edu.cn
Abstract
개방 채널 분기점은 관개 지역에서 가장 일반적인 물 전환 구조입니다. 관개용수 운반에서는 물 운반 효율과 침전이 주요 관심사입니다. 따라서 이 연구는 관개 지역의 물 공급에 대한 개방 채널 분기점의 영향을 분석합니다.
여기에서 FLOW-3D 소프트웨어를 사용하고 15 세트의 작업 조건을 포함하는 수치 시뮬레이션을 통해 개방 채널 분기점에서의 3차원 유동을 연구했습니다. 개수로 분기점 부근의 재순환 구역 및 유동 구조의 수리학적 특성을 분석하였다.
그런 다음 사다리꼴 채널에서 표면 및 바닥층의 흐름 전환 폭에 대한 방정식을 얻었습니다. 수심에 따른 흐름 전환 폭은 사다리꼴 채널과 직사각형 채널에서 다른 것으로 나타났습니다. 결과는 또한 개방 수로 분기점이 주 수로의 유속에 상당한 영향을 미친다는 것을 보여줍니다.
개방 채널 분기점의 재순환 영역에서의 유속은 작았지만 맥동 속도와 난류 운동 에너지는 컸다. 이 지역에서 소산되는 에너지는 상대적으로 커서 수로 물 전달에 도움이 되지 않았습니다.
이 연구는 관개구역의 수로 최적화 및 운영 관리에 대한 참고 자료를 제공합니다.
Open-channel bifurcations are the most common water diversion structures in irrigation districts. In irrigation water conveyance, water transport efficiency and sedimentation are primary concerns. This study accordingly analyzes the influence of open-channel bifurcations on water delivery in irrigation areas. Herein, the three-dimensional flow at an open-channel bifurcation was studied via numerical simulations using FLOW-3D software and including 15 sets of working conditions. The hydraulic characteristics of the recirculation zone and flow structures in the vicinity of the open-channel bifurcation were analyzed. Equations for the flow diversion width of the surface and bottom layers in the trapezoidal channel were then obtained. The flow diversion widths along the water depth were found to differ between trapezoidal and rectangular channels. The results also show that open-channel bifurcations considerably influence the flow velocity in the main channel. The flow velocity in the recirculation zone of open-channel bifurcations was small, but the pulsation velocity and the turbulent kinetic energy were large. The energy dissipated in this area was relatively large, which was not conducive to channel water delivery. This study provides a reference for channel optimization and operation management in irrigation districts.
Keywords
trapezoidal open channel; numerical simulation; the recirculation zone; flow diversion width; turbulence kinetic energy
Figure 1. Experimental plan and section measurement layout. Note: Red points in the figure represent
the measurement point arrangement, and Roman numerals represent measurement section numbers.Figure 5. Froude number (Fr) contour map at different water depths. Note: Q1 = 40 L/s; b = 30 cm. X* and Y* are obtained by dimensionless processing of X-axis and Y-axis coordinates. (a) depth of water below the sill height; (b) depth of water above the sill height.
130m 높이의 Ilarion 댐은 그리스 북부의 Aliakmon 강에 건설되었습니다. 2개의 여수로에는 플런지 풀의 중심을 향해 고속 제트를 빗나가게 하는 스키 점프가 장착되어 있습니다. 최근 몇 년 동안 두 번의 주요 홍수 동안 수영장에서 상당한 수중 작업이 발생했습니다.
신뢰할 수 있는 보호 조치를 조사하기 위해 FLOW-3D®를 사용하여 1:55 스케일 물리적 모델과 수치 모델을 만들었습니다. 플런지 풀과 여수로에서의 유체역학적 거동과 제트의 궤적을 결정할 수 있었습니다.
수치 모델은 플런지 풀의 흐름이 고도로 비대칭이고 두 개의 배수로 중 하나만 있는 회전 흐름이 작동한다는 것을 보여주었습니다.
이 회전 흐름은 여수로의 흐름 속도보다 3배 더 큰 국부적으로 효과적인 흐름 속도를 초래합니다. 시뮬레이션을 통해 이 문제에 대한 한 가지 해결책은 두 방수로의 대칭 작동임을 확인했습니다.
The 130 m high Ilarion Dam is built on the Aliakmon River in northern Greece. Its two spillways are equipped with ski jumps to deflect high-velocity jets towards the centre of the plunge pool. Significant scouring occurred in the pool during two major floods in recent years. To investigate reliable protection measures, a 1:55 scale physical model and a numerical model with FLOW-3D® were created. The hydrodynamic behaviour of the flow in the plunge pool and in the spillways as well as the trajectory of the jets could be determined. The numerical model showed, that the flow in the plunge pool is highly asymmetric and a rotational flow forms with only one of the two spillways is operational. This rotational flow results in locally effective flow rates three times greater than the flow rate from the spillway. Simulations confirm, that one solution to this problem is the symmetrical operation of both spillways.
Details
TitlePlunge pool scour and bank erosion: assessment of protection measures for Ilarion dam by physical and numerical modelling
Shen Zhen-dong*1, 2, Zhang Yang1, 2 1Zhejiang Guangchuan Engineering Consultation Co., Ltd., Hangzhou, 310020, Zhejiang, China 2Zhejiang Institute of Hydraulics &Estuary, Hangzhou 310020, Zhejiang, China E-mail: zdshen1991@126.com
Abstract
최근 몇 년 동안 생태학적 수자원 보존 공학의 발전으로 많은 새로운 댐 디자인이 등장했습니다. 본 논문에서는 체계적인 소면보 연구와 조사를 바탕으로 새로운 종류의 입상 혼합물 위어를 제시하였습니다.
입상보의 수치해석은 Flow-3D를 이용하여 수행하였으며, 그 결과를 물리적 모델 실험결과와 비교하였습니다. 유속, 유속 분포 및 둑의 파손에 대한 수치 시뮬레이션 결과는 실험 결과와 잘 일치하며, 이는 3차원 수학적 모델이 물리적 모델 실험과 결합되어 모든 입상 혼합물 둑을 시뮬레이션할 수 있음을 나타냅니다.
이 방법을 이용하여 특성 및 수리학적 매개변수를 분석하면 생태보의 후속 연구를 위한 기술적 지원을 제공할 수 있습니다.
In recent years, with the development of ecological water conservancy engineering, many new weir designs have also emerged. This paper has put forward a new kind of granular mixtures weir based on the systematic carding weir researches, combined with investigation. The numerical simulation of granular weir is carried out by using Flow-3D,and the results are compared with the physical model experiment results. The numerical simulation results of the flow velocity, flow distribution and the failure of the weir are in good agreement with the experimental results, which indicates that the 3-D mathematical model can be combined with physical model experiments to simulate the granular mixtures weir in all directions. Using this method to analysis the characteristics and hydraulic parameters can provide technical support for the follow-up research of ecological weir.
Figure 1 Mitochondrial Weir Dam Table 1 Numerical simulation programme table Figure 4 Final Damage of Weir in Different Projects
References
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•The limitation of increasing the rotational speed in decreasing powder size was clarified.
•Cooling and disturbance effects varied with the gas flowing rate.
•Inclined angle of the residual electrode end face affected powder formation.
•Additional cooling gas flowing could be applied to control powder size.
Abstract
The plasma rotating electrode process (PREP) is rapidly becoming an important powder fabrication method in additive manufacturing. However, the low production rate of fine PREP powder limits the development of PREP. Herein, we investigated different factors affecting powder formation during PREP by combining experimental methods and numerical simulations. The limitation of increasing the rotation electrode speed in decreasing powder size is attributed to the increased probability of adjacent droplets recombining and the decreased tendency of granulation. The effects of additional Ar/He gas flowing on the rotational electrode on powder formation is determined through the cooling effect, the disturbance effect, and the inclined effect of the residual electrode end face simultaneously. A smaller-sized powder was obtained in the He atmosphere owing to the larger inclined angle of the residual electrode end face compared to the Ar atmosphere. Our research highlights the route for the fabrication of smaller-sized powders using PREP.
플라즈마 회전 전극 공정(PREP)은 적층 제조 에서 중요한 분말 제조 방법으로 빠르게 자리잡고 있습니다. 그러나 미세한 PREP 분말의 낮은 생산율은 PREP의 개발을 제한합니다. 여기에서 우리는 실험 방법과 수치 시뮬레이션을 결합하여 PREP 동안 분말 형성에 영향을 미치는 다양한 요인을 조사했습니다. 분말 크기 감소에서 회전 전극 속도 증가의 한계는 인접한 액적 재결합 확률 증가 및 과립화 경향 감소에 기인합니다.. 회전 전극에 흐르는 추가 Ar/He 가스가 분말 형성에 미치는 영향은 냉각 효과, 외란 효과 및 잔류 전극 단면의 경사 효과를 통해 동시에 결정됩니다. He 분위기에서는 Ar 분위기에 비해 잔류 전극 단면의 경사각이 크기 때문에 더 작은 크기의 분말이 얻어졌다. 우리의 연구는 PREP를 사용하여 더 작은 크기의 분말을 제조하는 경로를 강조합니다.
Keywords
Plasma rotating electrode process
Ti-6Al-4 V alloy, Rotating speed, Numerical simulation, Gas flowing, Powder size
Introduction
With the development of additive manufacturing, there has been a significant increase in high-quality powder production demand [1,2]. The initial powder characteristics are closely related to the uniform powder spreading [3,4], packing density [5], and layer thickness observed during additive manufacturing [6], thus determining the mechanical properties of the additive manufactured parts [7,8]. Gas atomization (GA) [9–11], centrifugal atomization (CA) [12–15], and the plasma rotating electrode process (PREP) are three important powder fabrication methods.
Currently, GA is the dominant powder fabrication method used in additive manufacturing [16] for the fabrication of a wide range of alloys [11]. GA produces powders by impinging a liquid metal stream to droplets through a high-speed gas flow of nitrogen, argon, or helium. With relatively low energy consumption and a high fraction of fine powders, GA has become the most popular powder manufacturing technology for AM.
The entrapped gas pores are generally formed in the powder after solidification during GA, in which the molten metal is impacted by a high-speed atomization gas jet. In addition, satellites are formed in GA powder when fine particles adhere to partially molten particles.
The gas pores of GA powder result in porosity generation in the additive manufactured parts, which in turn deteriorates its mechanical properties because pores can become crack initiation sites [17]. In CA, a molten metal stream is poured directly onto an atomizer disc spinning at a high rotational speed. A thin film is formed on the surface of the disc, which breaks into small droplets due to the centrifugal force. Metal powder is obtained when these droplets solidify.
Compared with GA powder, CA powder exhibits higher sphericity, lower impurity content, fewer satellites, and narrower particle size distribution [12]. However, very high speed is required to obtain fine powder by CA. In PREP, the molten metal, melted using the plasma arc, is ejected from the rotating rod through centrifugal force. Compared with GA powder, PREP-produced powders also have higher sphericity and fewer pores and satellites [18].
For instance, PREP-fabricated Ti6Al-4 V alloy powder with a powder size below 150 μm exhibits lower porosity than gas-atomized powder [19], which decreases the porosity of additive manufactured parts. Furthermore, the process window during electron beam melting was broadened using PREP powder compared to GA powder in Inconel 718 alloy [20] owing to the higher sphericity of the PREP powder.
In summary, PREP powder exhibits many advantages and is highly recommended for powder-based additive manufacturing and direct energy deposition-type additive manufacturing. However, the low production rate of fine PREP powder limits the widespread application of PREP powder in additive manufacturing.
Although increasing the rotating speed is an effective method to decrease the powder size [21,22], the reduction in powder size becomes smaller with the increased rotating speed [23]. The occurrence of limiting effects has not been fully clarified yet.
Moreover, the powder size can be decreased by increasing the rotating electrode diameter [24]. However, these methods are quite demanding for the PREP equipment. For instance, it is costly to revise the PREP equipment to meet the demand of further increasing the rotating speed or electrode diameter.
Accordingly, more feasible methods should be developed to further decrease the PREP powder size. Another factor that influences powder formation is the melting rate [25]. It has been reported that increasing the melting rate decreases the powder size of Inconel 718 alloy [26].
In contrast, the powder size of SUS316 alloy was decreased by decreasing the plasma current within certain ranges. This was ascribed to the formation of larger-sized droplets from fluid strips with increased thickness and spatial density at higher plasma currents [27]. The powder size of NiTi alloy also decreases at lower melting rates [28]. Consequently, altering the melting rate, varied with the plasma current, is expected to regulate the PREP powder size.
Furthermore, gas flowing has a significant influence on powder formation [27,29–31]. On one hand, the disturbance effect of gas flowing promotes fluid granulation, which in turn contributes to the formation of smaller-sized powder [27]. On the other hand, the cooling effect of gas flowing facilitates the formation of large-sized powder due to increased viscosity and surface tension. However, there is a lack of systematic research on the effect of different gas flowing on powder formation during PREP.
Herein, the authors systematically studied the effects of rotating speed, electrode diameter, plasma current, and gas flowing on the formation of Ti-6Al-4 V alloy powder during PREP as additive manufactured Ti-6Al-4 V alloy exhibits great application potential [32]. Numerical simulations were conducted to explain why increasing the rotating speed is not effective in decreasing powder size when the rotation speed reaches a certain level. In addition, the different factors incited by the Ar/He gas flowing on powder formation were clarified.
Fig. 1. Schematic figure showing the PREP with additional gas flowing on the end face of electrode.
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천해 방정식을 기반으로 하는 2차원 흐름 모델은 댐 붕괴 흐름을 모델링하기 위해 개발되었습니다. 공간 이산화는 유한 체적 셀 중심 유형 방법에 의해 얻어집니다.
수치 시스템은 명시적인 방식으로 해결됩니다. 플럭스 모델링은 시간과 공간 모두에서 2차 정확도로 TVD WAF 방식으로 배포되었습니다. 로컬 리만 문제는 셀 인터페이스에서 HLLC 방법으로 해결됩니다. 수치 모델은 모델 결과와 해석 솔루션을 비교하여 검증합니다.
그런 다음 수치 모델의 결과는 90° 및 180° 편차 각도를 갖는 수로 및 삼각형 바텀 씰 위의 직선 수로에서 사용 가능한 실험 데이터와 비교됩니다. 결과는 댐 파괴파를 예측하는 현재 모델의 합리적인 성능을 확인합니다.
A two-dimensional flow model based on shallow water equations is developed for modeling dam-break flows. The spatial discretization is obtained by the finite volume cell centered type method. The numerical system is solved in explicit way. The flux modeling has been deployed by TVD WAF scheme with a second-order accuracy in both time and space. The local Riemann problem is solved by the HLLC method in the interface of the cells. The numerical model is verified by comparison of model results and analytical solutions. Then the results of numerical model are compared with available experimental data of dam-break waves in a channel with 90° and 180° deviation angle and in a straight channel over a triangular bottom sill. The results confirm the reasonable performance of the present model in predicting dam-break waves.
Fig. 2 Generic control volume and notationsFig. 1 The generated grid for a channel with a 180° bendFig. 4 a Water surface profle and b velocity profle of dam-break
problem with left dry bedFig. 5 a Water surface profle and b velocity profle of appearance
dry regionFig. 6 Comparison of the
present model results and exact
solution for transcritical fow
over a bump with a shockFig. 7 Geometry of the reservoir and L-shaped channel: plan
view (Soares-Frazao et al. 2019)Fig. 9 Test facility a plan view, b the bottom elevation of the reservoir to the channel (Bell et al. 1992)
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피기백 파이프라인은 2개의 파이프로 구성되어 2차 라인이 2개의 파이프 사이의 길이가 고정된 거리로 메인 파이프에 탑승합니다. 새로운 전략은 단일 흐름 라인 대신 연안 지역에서 활용됩니다.
이와 관련하여 정상 전류에서 피기백 파이프라인 아래의 세굴 효과를 조사하는 실험 및 수치 연구는 소수에 불과합니다. 따라서 본 연구에서는 수치모사 및 실험적 실험을 통해 관직경, 관간격 등 정류에 의한 세굴에 영향을 미치는 요인을 살펴보고자 합니다.
따라서 연구의 첫 번째 단계에서 단일 파이프를 설치하고 실험식의 결과와 결과를 비교하기 위해 실험실에서 테스트했습니다. 실험적 검증을 마친 후, 피기백 파이프라인도 조립하여 안정된 전류 조건에서 정련을 연구했습니다. 파이프 사이의 간격을 늘리면 최대 세굴 깊이가 감소한다는 결론이 내려졌습니다.
그러나 작은 파이프의 직경이 증가하면 최대 세굴 깊이가 커집니다. 둘째, 본 연구의 수치적 조사에 적합한 도구인 FLOW-3D 소프트웨어를 사용하여 수치해석을 수행하였습니다.
마지막으로, 수치 결과를 해당 실험 데이터와 비교했으며, 이들 사이에 비교적 좋은 일치가 달성되었습니다.
A piggyback pipeline consists of two pipes such that the secondary line rides on the main pipe with a fixed distance between two pipes in length. The novel strategy is utilized in offshore areas instead of a single flow line. In this regard, there are only a handful of experimental and numerical studies investigating the effect of scour below a piggyback pipeline under steady current. Hence, this study focuses on examining the influential factors on scouring due to steady current including the pipe diameter and the gap between pipes through numerical simulations and experimental tests. Accordingly, at the first phase of the research, a single pipe was established and tested in laboratory to compare the results with those of an empirical equation. After finishing experimental verifications, piggyback pipelines were also assembled to study the scouring under steady current conditions. It was concluded that by increasing the gap distance between the pipes, the maximum scour depth decreases; however, an increase in the small pipe’s diameter results in a larger maximum scour depth. Secondly, numerical simulations were carried out using the FLOW-3D software which was found to be a suitable tool for the numerical investigation of this study. Finally, the numerical results have been compared with the corresponding experimental data and a relatively good agreement was achieved between them.
Fig. 1. (a) Arrangement of piggyback pipeline, (b) Plan view of experimental flume.Fig. 3. Initial photos of two mounted piggyback pipelines in experimental setup for d/D=0.25.Fig. 9. Simulated separation regions for surface mounted cylinder
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본 논문은 경사가 완만한 수로에서 손상되거나 손상되지 않은 교각 주변의 유동 패턴을 분석했습니다. 실험은 길이가 12m이고 기울기가 0.008인 직선 수로에서 수행되었습니다. Acoustic Doppler Velocimeter(ADV)를 이용하여 3차원 유속 데이터를 수집하였고, 그 결과를 PIV(Particle Image Velocimetry) 데이터와 분석하여 비교하였습니다.
다중 블록 옵션이 있는 취수구의 퇴적물 시뮬레이션(SSIIM)은 이 연구에서 흐름의 수치 시뮬레이션을 위해 통합되었습니다. 일반적으로 비교에서 얻은 결과는 수치 데이터와 실험 데이터 간의 적절한 일치를 나타냅니다. 결과는 모든 경우에 수로 입구에서 2m 거리에서 기복적 수압 점프가 발생했음을 보여주었습니다.
경사진 수로의 최대 베드 전단응력은 2개의 손상 및 손상되지 않은 교각을 설치하기 위한 수평 수로의 12배였습니다. 이와 같은 경사수로 교각의 위치에 따라 상류측 수위는 수평수로의 유사한 조건에 비해 72.5% 감소한 반면, 이 감소량은 경사면에서 다른 경우에 비해 8.3% 감소하였다. 채널 또한 두 교각이 있는 경우 최대 Froude 수는 수평 수로의 5.7배였습니다.
This paper analyzed the flow pattern around damaged and undamaged bridge piers in a channel with a mild slope. The experiments were carried out on a straight channel with a length of 12 meters and a slope of 0.008. Acoustic Doppler velocimeter (ADV) was employed to collect three-dimensional flow velocity data, and the results were analyzed and compared with particle image velocimetry (PIV) data. Sediment Simulation in Intakes with Multiblock option (SSIIM) was incorporated for the numerical simulation of the flow in this study. Generally, the results obtained from the comparisons referred to the appropriate agreement between the numerical and the experimental data. The results showed that an undular hydraulic jump occurred at a distance of two meters from the channel entrance in every case; the maximum bed shear stress in the sloped channel was 12 times that in a horizontal channel for installing two damaged and undamaged piers. With this position of the piers in the sloped channel, the upstream water level underwent a 72.5% reduction compared to similar conditions in a horizontal channel, while the amount of this water level decrease was equal to 8.3% compared to the other cases in a sloped channel. In addition, with the presence of both piers, the maximum Froude number was 5.7 times that in a horizontal channel.
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2 Dep. of Water Engineering, Faculty of Water and Soil, Gorgan University of Agricultural Sciences and Natural Resources, Golestan.
3 Assistant Professor, Department of Irrigation and Reclamation Engineering, Faculty of Agricultural Engineering and Technology, University College of Agriculture and Natural Resources, University of Tehran, P. O. Box 4111, Karaj, 31587-77871, Iran.
Abstract
The exchange of surface and subsurface flows in riverbeds, especially upstream of control structures as an important ecological area, is very important and noteworthy. The natural morphology of rivers and various in-stream structures along the flow path are important factors in the formation of such flows. Since the in-stream structures in the flow path have a more controlled and effective role than the morphology of rivers in the formation of these exchanges, in this study the effect of the penetration depth of these structures in the porous bed on the characteristics of exchange flows through experiments and Numerical simulation has been investigated. The experiments were performed in a flume with a length of 10 m, width of 20 cm, depth of 30 cm and a slope of 0.01, for three different penetration depths. Potassium permanganate detector was used for tracking the flow. In addition, to obtain exchange flow characteristics; the mainstream and the exchange pattern were simulated by particle tracking method using Flow 3D software. The results showed that in the Reynolds range 1020 to 3450, with increasing the penetration depth of the structure from 0.09 to 0.13 m, the retention time of the exchange flow increases up to 6.6%. In addition, the length of the effect of the structure up to 9%, the length of the exchange path up to 4.6% and the penetration depth of the exchange increases up to 7.7% while the exchange rate decreases to 22%. Therefore, in order to increase the exchange rate, it is recommended to use a structure with a lower penetration depth and to increase the retention time, a structure with a greater penetration depth is recommended.
중요한 생태 지역으로서 특히 제어 구조물의 상류 하천 바닥에서 지표 및 지하 흐름의 교환은 매우 중요하고 주목할 만합니다. 하천의 자연적 형태와 유동 경로를 따라 흐르는 다양한 하천 구조는 이러한 유동 형성에 중요한 요소입니다.
흐름 경로의 유류 구조는 이러한 교환의 형성에서 강의 형태보다 더 제어되고 효과적인 역할을 하기 때문에 본 연구에서는 다공성 층에서 이러한 구조의 침투 깊이가 교환의 특성에 미치는 영향 실험과 수치 시뮬레이션을 통한 흐름이 조사되었습니다.
실험은 길이 10m, 너비 20cm, 깊이 30cm, 기울기 0.01의 수로에서 세 가지 다른 침투 깊이에 대해 수행되었습니다. 흐름을 추적하기 위해 과망간산 칼륨 검출기가 사용되었습니다. 또한, 교환 흐름 특성을 얻기 위해; Flow 3D 소프트웨어를 사용하여 입자 추적 방법으로 주류 및 교환 패턴을 시뮬레이션했습니다.
결과는 Reynolds 범위 1020 ~ 3450에서 구조물의 침투 깊이가 0.09에서 0.13m로 증가함에 따라 교환 흐름의 체류 시간이 최대 6.6%까지 증가함을 보여주었습니다. 또한 구조의 효과 길이는 최대 9%, 교환 경로의 길이는 최대 4.6%, 교환의 침투 깊이는 최대 7.7%까지 증가하는 반면 환율은 22%로 감소합니다.
따라서 환율을 높이기 위해서는 침투깊이가 낮은 구조를 사용하는 것이 좋으며, 머무름 시간을 늘리기 위해서는 침투깊이가 큰 구조를 사용하는 것이 좋습니다.
N.M.T De Silva University of Colombo School of Computing 2018
Abstract
산사태가 발생하기 쉬운 구릉 지역 근처에서 발생하는 최근 인구 증가 및 개발은 취약성을 증가시킵니다. 기후 변화의 영향은 산사태 위험의 가능성을 더욱 높입니다. 따라서 인명 및 재산 피해를 방지하기 위해서는 불안정한 경사면 거동에 대한 적절한 관찰과 분석이 중요합니다.
산사태 흐름 경로 예측은 산사태 흐름 경로를 결정하는 데 중요하며 위험 매핑의 필수 요소입니다. 그러나 현상의 복잡한 특성과 관련 매개변수의 불확실성으로 인해 흐름 경로 예측은 어려운 작업입니다. 이 작업에서는 Kegalle 지역의 Aranayaka 지역의 주요 산사태 사고를 흐름 경로를 모델링하기 위한 사례 연구로 사용합니다.
위치에서 디지털 고도 모델을 기반으로 잠재적 소스 영역이 식별되었습니다. 확산 영역 평가는 D8 및 다중 방향 흐름 알고리즘이라는 두 가지 흐름 방향 알고리즘을 기반으로 했습니다. 이 프로토타입 모델을 사용하여 사용자는 슬라이드의 최대 너비, 런아웃 거리 및 슬립 표면적과 같은 산사태 관련 통계를 대화식으로 얻을 수 있습니다.
모델에서 얻은 결과는 실제 Aranayaka 산사태 데이터 세트와 해당 지역의 산사태 위험 지도와 비교되었습니다. D8 알고리즘을 사용하여 구현된 도구에서 생성된 산사태 흐름 경로는 65% 이상의 일치를 나타내고 다중 방향 흐름 알고리즘은 실제 흐름 경로 및 기타 관련 통계와 69% 이상의 일치를 나타냅니다.
또한, 생성된 유동 경로 방향과 예상되는 산사태 시작 지점이 실제 산사태 경계 내부에 잘 일치합니다.
Recent population growth and developments taking place close to landslides prone hilly areas increase their vulnerability. Climate change impacts further raise the potential of landslide hazard. Therefore, to prevent loss of lives and damage to property, proper observation and analysis of unstable slope behavior is crucial. Landslide flow path forecasting is important for determining a landslide flow route and it is an essential element in hazard mapping. However, due to the complex nature of the phenomenon and the uncertainties of associated parameters flow path prediction is a challenging task. In this work, the major landslide incident at Aranayaka area in Kegalle district is taken as the case study to model the flow path. At the location, potential source areas were identified on the basis of the Digital Elevation Model. Spreading area assessment was based on two flow directional algorithms namely D8 and Multiple Direction Flow Algorithm. Using this prototype model, a user can interactively get landslide specific statistics such as the maximum width of the slide, runout distance, and slip surface area. Results obtained by the model were compared with the actual Aranayaka landslide data set the landslide hazard map of the area. Landslide flow paths generated from the implemented tool using D8 algorithm shows more than 65% agreement and Multiple Direction Flow Algorithm shows more than 69% agreement with the actual flow paths and other related statistics. Also, the generated flow path directions and predicted possible landslide initiation points fit inside the actual landslide boundary with good agreement.
Figure 2.1: Types of Landslides[2]Figure 2.2: Landslide Glossary [2]
References
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Xianqi Zhanga,b,c, Tao Wanga,* and Xiaobin Lua a Water Conservancy College, North China University of Water Resources and Electric Power, Zhengzhou 450046, China b Collaborative Innovation Center of Water Resources Efficient Utilization and Protection Engineering, Zhengzhou 450046, China c Technology Research Center of Water Conservancy and Marine Traffic Engineering, Henan Province, Zhengzhou 450046, China *Corresponding author. E-mail: 1124149584@qq.com
Abstract
하천을 가로지르는 교각의 형태는 하천의 역류에 영향을 미치는 중요한 요인 중 하나이다. 교각 형상이 강의 흐름 패턴에 미치는 영향에 대한 연구는 교량 설계 및 하천 범람에 가치가 있습니다. Mike 21 Flow Model 유체역학 모델을 기반으로 동적 수치 시뮬레이션을 수행하여 다양한 형태의 교각이 물 흐름에 미치는 영향을 조사했습니다. 그 결과 직사각형, 원형 및 타원형 교각이 하천에 물 차단 효과가 있음을 보여줍니다. 교각 근처의 지역에서 흐름 패턴이 변경되었습니다. 동일한 유속에서 직사각형 교각의 역류가 가장 컸고 원형 교각이 그 뒤를 이었고 타원형 교각이 가장 작았다. 직사각형 교각으로 인한 역류량 값은 타원형 교각의 1.95배였다. 타원형 교각 교각은 기본적으로 강의 전반적인 흐름 패턴을 변경하지 않으며 하천 체제에 거의 영향을 미치지 않습니다. 하천 교각의 배치에 대한 참조를 제공합니다.
Figure 1 | Location of the proposed bridgeFigure 2 | Distribution map of detection points.Figure 3 | (a) Elevation contour map of water surface near the rectangular pier in the working condition 1, (b) Elevation contour
map of water surface near the round pier in the working condition 1 and (c) Elevation contour map of water surface near the
oval pier in the working condition 1.Figure 9 | Monitoring section backwater changes; (a) Once in ten years traffic, (b) Yearly average flow, (c) Lowest water level
(p ¼ 95%)
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1Ph.D Student, Dept. of Civil & Environmental Engineering, Hongik University 2Director, Water Resources & Environment Department, HECOREA 3Director, Water Resources Department, ISAN 4Professor, Dept. of Civil & Environmental Engineering, Hongik University
1홍익대학교 건설환경공학과 박사과정 2㈜헥코리아 수자원환경사업부 이사 3㈜이산 수자원부 이사 4홍익대학교 건설환경공학과 교수
ABSTRACT
최근 기후변화로 인해 강우강도 및 빈도의 증가에 따른 집중호우의 영향 및 기존 여수로의 노후화에 대비하여 홍수 시 하류 하천의 영향을 최소화할 수 있는 보조 여수로 활용방안 구축이 필요한 실정이다. 이를 위해, 수리모형 실험 및 수치모형 실험을 통하여 보조 여수로 운영에 따른 흐름특성 변화 검토에 관한 연구가 많이 진행되어 왔다. 그러나 대부분의 연구는 여수로에서의 흐름특성 및 기능성에 대한 검토를 수행하였을 뿐 보조 여수로의 활용방안에 따른 하류하천 영향 검토 및 호안 안정성 검토에 관한 연구는 미비한 실정이다. 이에 본 연구에서는 기존 여수로 및 보조 여수로 방류 조건에 따른 하류영향 분석 및 호안 안정성 측면에서 최적 방류 시나리오 검토를 3차원 수치모형인 FLOW-3D를 사용하여 검토하였다. 또한 FLOW-3D 수치모의 수행을 통한 유속, 수위 결과와 소류
![Figure 2: Experimental data on height of
vertex formed [8] / Figure 3: Vertex height as a function of time](https://flow3d.co.kr/wp-content/uploads/Figure-3-Vertex-height-as-a-function-of-time-.png)
![Fig. 1. (a) Dimensions of the casting with runners (unit: mm), (b) a melt flow simulation using Flow-3D software together with Reilly's model[44], predicted that a large amount of bifilms (denoted by the black particles) would be contained in the final casting. (c) A solidification simulation using Pro-cast software showed that no shrinkage defect was contained in the final casting.](https://flow3d.co.kr/wp-content/uploads/Fig.-1.-a-Dimensions-of-the-casting-with-runners.png)
![Fig. 1. (a) Dimensions of the casting with runners (unit: mm), (b) a melt flow simulation using Flow-3D software together with Reilly's model[44], predicted that a large amount of bifilms (denoted by the black particles) would be contained in the final casting. (c) A solidification simulation using Pro-cast software showed that no shrinkage defect was contained in the final casting.](https://ars.els-cdn.com/content/image/1-s2.0-S2213956721001791-gr1_lrg.jpg)
![Figure 2.1: Types of Landslides[2]](https://flow3d.co.kr/wp-content/uploads/Figure-2.1-Types-of-Landslides2.png)
![Figure 2.2: Landslide Glossary [2]](https://flow3d.co.kr/wp-content/uploads/Figure-2.2-Landslide-Glossary-2.png)
