基于Youngs-VOF法的垂向二维水流及泥沙输运的数值模拟
|
摘要
对于泥沙的研究,由于三维数学模型的复杂性,通常根据问题的性质以及地形和水流特征进行简化。在研究水力特性沿侧向变化不大而垂向上有明显差异区域的泥沙运动时,垂向二维泥沙模型基本能够满足需求,且相较三维模型而言,输入数据少,计算效率高。
基于Youngs-VOF法,由精度较高的ELVIRA法取代Youngs-VOF法中传统的自由面法向确立方法,耦合Reynolds时均方程、非线性k-ε紊流模型及泥沙输运模型,建立了垂向二维泥沙输运模型。紊流模型和悬沙输运模型采用水平显式,垂向隐式的power-law格式进行求解,而床沙输运模型则采用稳定性较好的欧拉加权基本无振荡迎风格式(Euler-WENO)求解。在底部边界处理上,采用了壁函数法则及网格封闭技术。
利用所建立的垂向二维水流模型对带精确解的一维经典浅水问题、孤立波爬坡问题及带槽沟明渠水流运动问题进行了数值模拟,分析了模型的数值稳定性、和谐性、适应性、激波捕捉能力。在此基础之上,利用建立的泥沙输运模型进对净冲刷、净淤积和深槽回淤的水槽试验进行了数值模拟分析。
由数值分析的结果可知,本文建立的垂向二维泥沙输运模型是有效的,且对自由面非线性有着将强的适应性,对涌潮这类强间断水流作用下的泥沙输运研究有着重要的借鉴意义。
Because of the complexity of the three dimensional mathematical model, usually, the research of sediment is simplified according to the topography, the flow characteristics and the nature of the problem. And the2-D vertical sediment model can do quite well in researching the sediment transport where the hydraulic characteristics change little along the lateral while obviously in the vertical direction. Compared to the3-D model, the2-D model requires fewer dates, and is more efficient.
In this paper, a2-D vertical model of sediment transport was established by coupling with the time-average Reynolds equations, the k-ε nonlinear turbulence model and the sediment transport model based on the Youngs-VOF method that free surface normal was obtained by ELVIRA method. The turbulent model and suspended sediment transport model were discretized with implicit in the vertical coordinate and explicit in the horizontal coordinate based on the power-law scheme, and bed sand transport model was solved by Euler-WENO scheme. The wall function law and the technique of grid-closing were introduced in dealing with the bottom boundary.
Using the established flow model, the1-D shallow water problems having exact solutions, the experiment of solitary wave runup and rundown, and the experiment of steady flow crossing the trench were simulated to analyse the numerical stability, adaptability, shock-capturing property, and the accuracy of the numerical results of the model. On this basis, the experiment of net entrainment from a loose bed, net deposition and evolution of the trench were simulated and analysed by the sediment transport model.
The results indicated that the2-D vertical sediment transport model established was effective, and had strong adaptability for nonlinear free surface, could have a good reference for the research of sediment transport driven by the flow with strong discontinuity.
基于Youngs-VOF法,由精度较高的ELVIRA法取代Youngs-VOF法中传统的自由面法向确立方法,耦合Reynolds时均方程、非线性k-ε紊流模型及泥沙输运模型,建立了垂向二维泥沙输运模型。紊流模型和悬沙输运模型采用水平显式,垂向隐式的power-law格式进行求解,而床沙输运模型则采用稳定性较好的欧拉加权基本无振荡迎风格式(Euler-WENO)求解。在底部边界处理上,采用了壁函数法则及网格封闭技术。
利用所建立的垂向二维水流模型对带精确解的一维经典浅水问题、孤立波爬坡问题及带槽沟明渠水流运动问题进行了数值模拟,分析了模型的数值稳定性、和谐性、适应性、激波捕捉能力。在此基础之上,利用建立的泥沙输运模型进对净冲刷、净淤积和深槽回淤的水槽试验进行了数值模拟分析。
由数值分析的结果可知,本文建立的垂向二维泥沙输运模型是有效的,且对自由面非线性有着将强的适应性,对涌潮这类强间断水流作用下的泥沙输运研究有着重要的借鉴意义。
Because of the complexity of the three dimensional mathematical model, usually, the research of sediment is simplified according to the topography, the flow characteristics and the nature of the problem. And the2-D vertical sediment model can do quite well in researching the sediment transport where the hydraulic characteristics change little along the lateral while obviously in the vertical direction. Compared to the3-D model, the2-D model requires fewer dates, and is more efficient.
In this paper, a2-D vertical model of sediment transport was established by coupling with the time-average Reynolds equations, the k-ε nonlinear turbulence model and the sediment transport model based on the Youngs-VOF method that free surface normal was obtained by ELVIRA method. The turbulent model and suspended sediment transport model were discretized with implicit in the vertical coordinate and explicit in the horizontal coordinate based on the power-law scheme, and bed sand transport model was solved by Euler-WENO scheme. The wall function law and the technique of grid-closing were introduced in dealing with the bottom boundary.
Using the established flow model, the1-D shallow water problems having exact solutions, the experiment of solitary wave runup and rundown, and the experiment of steady flow crossing the trench were simulated to analyse the numerical stability, adaptability, shock-capturing property, and the accuracy of the numerical results of the model. On this basis, the experiment of net entrainment from a loose bed, net deposition and evolution of the trench were simulated and analysed by the sediment transport model.
The results indicated that the2-D vertical sediment transport model established was effective, and had strong adaptability for nonlinear free surface, could have a good reference for the research of sediment transport driven by the flow with strong discontinuity.
引文
[1]Harlow FH, Welch JE. Numerical study of large-amplitude free-surface motions [J]. Physics of Fluids,1966,9(5):842-851.
[2]Hirt CW, Nichols BD. Volume of fluid (VOF) method for the dynamics of free boundariesl [J]. Journal of Computational Physics,1981,39(1):201-225.
[3]Osher S, Sethian JA. Fronts propagating with curvature-dependent speed:algorithms based on Hamilton-Jacobi formulations [J]. Journal of Computational Physics,1988,79(1):12-49.
[4]Youngs DL. Time-dependent multi-material flow with large fluid distortion. In:Morton KW, Baineks MJ (eds), Numerical Methods for Fluid Dynamics, Academic [C]. New York:Academic ,1982.
[5]Ashgriz N, Poo JY. FLAIR:flux line-segment model for advection and interface reconstruction [J]. Journal of Computational Physics,1991,93(2):449-468.
[6]Rudman M. Volume-tracking methods for interfacial flow calculations [J]. International Journal for Numerical Methods in Fluids,1997,24(7):671-691.
[7]van Rijn LC, Tan GL. Sutrench model:two-dimensional vertical mathematical model for sedimentation in dredged channels and trenched by currents and waves [M]. Hague: Rijkswaterstaat communications,1985.
[8]Walstra DJR, van Rijn LC, Hoogewoning SE, et al. Modeling of sedimentation of dredged trenches and channels under the combined action of tidal currents and waves [J]. Coastal Sediments,1999.
[9]Niyyati M F, Maraghei A. Sediment transport and coastline development along the Caspian Sea; Bandar Nowshahr area. The changing coast, EUROCOAST, Portugal,2002.
[10]Celik I, Rodi WG. Modeling suspended sediment transport in nonequilibrium situations [J]. Journal of Hydraulic Engineering, ASCE,1988,114(10):1157-1191.
[11]徐健益,陶学为,方良田等.长江口南支非均匀沙垂向分层的数学模型[J].泥沙研究,1995,2：74-79.
[12]Brors B. Numerical modeling of flow and scour at pipelines [J]. Journal of Hydraulic Engineering,1999,125(5):511-523.
[13]江春波,张庆海,高忠信.河道立面二维非恒定水温及污染物分布预报模型[J].水利学报,2000,9：20-24.
[14]Liang DF, Liang C, Li FJ. Numerical modeling of flow and scour below a pipeline in currents: Part Ⅱ. Scour simulation [J]. Coastal Engineering,2005,52(1):43-62.
[15]Zhang JX, Liu H. A vertical 2-D numerical simulation of suspended sediment transport [J]. Journal of Hydrodynamics,2007,19(2):217-224.
[16]冯小香,小峰,韦直林等.冲刷漏斗纵剖面形态数值模拟技术研究[J].水科学进展,2008,1(19)：19-26.
[17]Wu T, Li XX. Vertical 2-d mathematical model of sediment silting in dredged channel [J]. Journal of Hydrodynamics,2007,22(5):628-632.
[18]Zhang JX, Liu H. Currents induced by vertical varied radiation stress in standing waves and evolution of the bed composed of fine sediments [J]. International Journal of Sediment Research, 2009,24(2):214-226.
[19]Dong P, Zhang KF. Two-phase flow modeling of sediment motions in oscillatory sheet flow [J]. Coastal Engineering,1999,36(2):87-109.
[20]Nguyen KD, Guillou S, Chauchat J, et al. A two-phase numerical model for suspended-sediment transport in estuaries [J]. Advances in Water Resources,2009,32(8):1187-1196.
[21]Bakhtyar R, Yeganeh-Bakhtiary A, Barry DA, et al. Two-phase hydrodynamic and sediment transport modeling of wave-generated sheet flow [J]. Advances in Water Resources,2009,32(8): 1267-1283.
[22]Hsu TJ, Chen SN, Ogston AS. The landward and sea ward mechanisms of fine-sediment transport across intertidal flats in the shallow-water region—A numerical investigation [J]. Continental Shelf Research,2012.
[23]Launder BE, Spalding DB. The numerical computation of turbulent flows [J]. Computer Methods in Applied Mechanics and Engineering,1974,3(2):269-289.
[24]王福军.计算流体动力学分析：CFD软件原理与应用[M].北京：清华大学出版社,2004.
[25]Pilliod JE, Puckett EG. Second-order accurate volume-of-fluid algorithms for tracking material interfaces [J]. Journal of Computational Physics,2004,199(2):465-502.
[26]Alfrink BJ, van Rijn LC. Two-equation turbulent model for flow in trenches[J]. Journal of Hydraulic Engineering,1983,109(7):941-958.
[27]Cebeci T, Bradshaw P. Momentum transfer in boundary Layers [M]. New York:Hemisphere Publishing Corporation,1977.
[28]吴修广,沈永明,王敏等.非静压假定的σ坐标下垂向二维浅水模型的应用研究[J].水力发电学报,2005,24(1)：93-97.
[29]van Rijn LC. Mathematical modeling of morphological processes in the case of suspended sediment transport [D]. Delft:Delft University of Technology,1987.
[30]Phillips BC, Sutherland AJ. Spatial lag effects in bed load sediment transport [J]. Journal of Hydraulic Research,1989,27(1):115-133.
[31]Wu WM, Rodi WG, Wenka T.3D numerical modeling of flow and sediment transport in open channels [J]. Journal of Hydraulic Engineering, ASCE,2000,126(1):4-15.
[32]Long W, Kirby JT, Shao ZY. A numerical scheme for morphological bed level calculations[J]. Coastal Engineering,2008,55:167-180.
[33]Liu XD, Osher S, Chan T. Weighted essentially non-oscillatory schemes [J]. Journal of Computational Physics,1994,115,200:200-212.
[34]van Rijn LC. Sediment transport by currents and waves, Technical Report H461 [R]. Delft Hydraulics:Delft, The Netherlands,1989.
[35]Einstein HA. The bed-load function for sediment transport in open channel flows [M]. Washington DC:U.S. Dept. of Agriculture,1950.
[36]吴修广,沈永明等.非正交曲线坐标下三维弯曲河流湍流数学模型[J].水力发电学报,2005,24(4)：36-42.
[37]张瑞瑾等.河流泥沙动力学(第二版).北京：中国水利水电出版社,1998.
[38]van Rijn LC. Sediment transport, Part II:Suspended load transport [J]. Jounal of Hydraulic Engineering, ASCE,1984,110(11):1613-1641.
[39]van Rijn LC. Sediment transport, Part III:Bed forms and alluvial roughness [J]. Jounal of Hydraulic Engineering, ASCE,1984,110(12):1733-1754.
[40]张洪武,汪家寅.沙石及模型沙水下休止角的试验研究[j].泥沙研究,1989,3：90-96.
[41]陆永军,窦国仁,韩龙喜等.三维紊流悬沙数学模型及应用.中国科学E辑技术科学,2003,34(3)：311-328.
[42]Toro EF. Shocking-capturing methods for free surface shallow waters[M]. UK:Wiley and Sons, United Kingdom,2001.
[43]Alcrudoa F, Benkhaldounb F. Exact solutions to the Riemann problem of the shallow water equations with a bottom step [J]. Computers & Fluids,2001,30(6):643-671.
[44]潘存鸿,林炳尧,毛献忠.一维浅水流动方程的Godunov格式求解[J].水科学进展,2003,14(4)：430-436.
[45]Ying XY, Khan AA, Wang SSY. Upwind conservative scheme for the saint equations [J]. Journal of Hydraulic Engineering, ASCE,2004,130(10):977-987.
[46]Mohapatra PK, Eswaran V, Bhallamudi MS. Two-dimensional analysis of dam break flow in vertical plane [J]. Journal of Hydraulic Engineering, ASCE,2004,125(2):183-192.
[47]Vazquez-Cendon ME. Improved Treatment of Source Terms in upwind schemes for the shallow water equations in channels with irregular geometry [J]. Journal of Computational Physics,1999, 148(2):497-526.
[48]Zhou JG, Causon DM, Mingham CG, et al. The surface gradient method for the treatment of source terms in the shallow-water equations [J]. Journal of Computational Physics,2001,168 (1):1-25.
[49]王志力,耿艳芬,金生.具有复杂计算域和地形的二维浅水流动数值模拟[J].水力学报,2005,35(4)：1-9.
[50]Synolakis CE. The runup of long waves [D]. Pasadena:California Institute of Technology, 1986.
[51]Van Rijn LC. Mathematical modeling of suspended sediment in non-uniform flows [J]. Journal of Hydraulic Engineering, ASCE,1986,112(6):433-455.
[52]夏云峰.感潮河段三维水流泥沙数值模型研究与应用[D].南京：河海大学.
[53]Wang ZB, Ribberink JS. The validity of a depth-integrated model [J]. Journal of Hydraulic Engineering, ASCE,1990,116(10):1270-1288.
[54]Galappatti G, Vreugdenhil CB. A Depth Integrated Mod el for Suspended Sediment Transport [J] Journal of Hydraulic Research,1985,23(4):359-377.
[55]Guo QC, Jin YC. Modeling nonuniform suspended sediment transport in alluvial rivers[J]. Journal of Hydraulic Engineering, ASCE,2002,128(9):839-837.
[2]Hirt CW, Nichols BD. Volume of fluid (VOF) method for the dynamics of free boundariesl [J]. Journal of Computational Physics,1981,39(1):201-225.
[3]Osher S, Sethian JA. Fronts propagating with curvature-dependent speed:algorithms based on Hamilton-Jacobi formulations [J]. Journal of Computational Physics,1988,79(1):12-49.
[4]Youngs DL. Time-dependent multi-material flow with large fluid distortion. In:Morton KW, Baineks MJ (eds), Numerical Methods for Fluid Dynamics, Academic [C]. New York:Academic ,1982.
[5]Ashgriz N, Poo JY. FLAIR:flux line-segment model for advection and interface reconstruction [J]. Journal of Computational Physics,1991,93(2):449-468.
[6]Rudman M. Volume-tracking methods for interfacial flow calculations [J]. International Journal for Numerical Methods in Fluids,1997,24(7):671-691.
[7]van Rijn LC, Tan GL. Sutrench model:two-dimensional vertical mathematical model for sedimentation in dredged channels and trenched by currents and waves [M]. Hague: Rijkswaterstaat communications,1985.
[8]Walstra DJR, van Rijn LC, Hoogewoning SE, et al. Modeling of sedimentation of dredged trenches and channels under the combined action of tidal currents and waves [J]. Coastal Sediments,1999.
[9]Niyyati M F, Maraghei A. Sediment transport and coastline development along the Caspian Sea; Bandar Nowshahr area. The changing coast, EUROCOAST, Portugal,2002.
[10]Celik I, Rodi WG. Modeling suspended sediment transport in nonequilibrium situations [J]. Journal of Hydraulic Engineering, ASCE,1988,114(10):1157-1191.
[11]徐健益,陶学为,方良田等.长江口南支非均匀沙垂向分层的数学模型[J].泥沙研究,1995,2：74-79.
[12]Brors B. Numerical modeling of flow and scour at pipelines [J]. Journal of Hydraulic Engineering,1999,125(5):511-523.
[13]江春波,张庆海,高忠信.河道立面二维非恒定水温及污染物分布预报模型[J].水利学报,2000,9：20-24.
[14]Liang DF, Liang C, Li FJ. Numerical modeling of flow and scour below a pipeline in currents: Part Ⅱ. Scour simulation [J]. Coastal Engineering,2005,52(1):43-62.
[15]Zhang JX, Liu H. A vertical 2-D numerical simulation of suspended sediment transport [J]. Journal of Hydrodynamics,2007,19(2):217-224.
[16]冯小香,小峰,韦直林等.冲刷漏斗纵剖面形态数值模拟技术研究[J].水科学进展,2008,1(19)：19-26.
[17]Wu T, Li XX. Vertical 2-d mathematical model of sediment silting in dredged channel [J]. Journal of Hydrodynamics,2007,22(5):628-632.
[18]Zhang JX, Liu H. Currents induced by vertical varied radiation stress in standing waves and evolution of the bed composed of fine sediments [J]. International Journal of Sediment Research, 2009,24(2):214-226.
[19]Dong P, Zhang KF. Two-phase flow modeling of sediment motions in oscillatory sheet flow [J]. Coastal Engineering,1999,36(2):87-109.
[20]Nguyen KD, Guillou S, Chauchat J, et al. A two-phase numerical model for suspended-sediment transport in estuaries [J]. Advances in Water Resources,2009,32(8):1187-1196.
[21]Bakhtyar R, Yeganeh-Bakhtiary A, Barry DA, et al. Two-phase hydrodynamic and sediment transport modeling of wave-generated sheet flow [J]. Advances in Water Resources,2009,32(8): 1267-1283.
[22]Hsu TJ, Chen SN, Ogston AS. The landward and sea ward mechanisms of fine-sediment transport across intertidal flats in the shallow-water region—A numerical investigation [J]. Continental Shelf Research,2012.
[23]Launder BE, Spalding DB. The numerical computation of turbulent flows [J]. Computer Methods in Applied Mechanics and Engineering,1974,3(2):269-289.
[24]王福军.计算流体动力学分析：CFD软件原理与应用[M].北京：清华大学出版社,2004.
[25]Pilliod JE, Puckett EG. Second-order accurate volume-of-fluid algorithms for tracking material interfaces [J]. Journal of Computational Physics,2004,199(2):465-502.
[26]Alfrink BJ, van Rijn LC. Two-equation turbulent model for flow in trenches[J]. Journal of Hydraulic Engineering,1983,109(7):941-958.
[27]Cebeci T, Bradshaw P. Momentum transfer in boundary Layers [M]. New York:Hemisphere Publishing Corporation,1977.
[28]吴修广,沈永明,王敏等.非静压假定的σ坐标下垂向二维浅水模型的应用研究[J].水力发电学报,2005,24(1)：93-97.
[29]van Rijn LC. Mathematical modeling of morphological processes in the case of suspended sediment transport [D]. Delft:Delft University of Technology,1987.
[30]Phillips BC, Sutherland AJ. Spatial lag effects in bed load sediment transport [J]. Journal of Hydraulic Research,1989,27(1):115-133.
[31]Wu WM, Rodi WG, Wenka T.3D numerical modeling of flow and sediment transport in open channels [J]. Journal of Hydraulic Engineering, ASCE,2000,126(1):4-15.
[32]Long W, Kirby JT, Shao ZY. A numerical scheme for morphological bed level calculations[J]. Coastal Engineering,2008,55:167-180.
[33]Liu XD, Osher S, Chan T. Weighted essentially non-oscillatory schemes [J]. Journal of Computational Physics,1994,115,200:200-212.
[34]van Rijn LC. Sediment transport by currents and waves, Technical Report H461 [R]. Delft Hydraulics:Delft, The Netherlands,1989.
[35]Einstein HA. The bed-load function for sediment transport in open channel flows [M]. Washington DC:U.S. Dept. of Agriculture,1950.
[36]吴修广,沈永明等.非正交曲线坐标下三维弯曲河流湍流数学模型[J].水力发电学报,2005,24(4)：36-42.
[37]张瑞瑾等.河流泥沙动力学(第二版).北京：中国水利水电出版社,1998.
[38]van Rijn LC. Sediment transport, Part II:Suspended load transport [J]. Jounal of Hydraulic Engineering, ASCE,1984,110(11):1613-1641.
[39]van Rijn LC. Sediment transport, Part III:Bed forms and alluvial roughness [J]. Jounal of Hydraulic Engineering, ASCE,1984,110(12):1733-1754.
[40]张洪武,汪家寅.沙石及模型沙水下休止角的试验研究[j].泥沙研究,1989,3：90-96.
[41]陆永军,窦国仁,韩龙喜等.三维紊流悬沙数学模型及应用.中国科学E辑技术科学,2003,34(3)：311-328.
[42]Toro EF. Shocking-capturing methods for free surface shallow waters[M]. UK:Wiley and Sons, United Kingdom,2001.
[43]Alcrudoa F, Benkhaldounb F. Exact solutions to the Riemann problem of the shallow water equations with a bottom step [J]. Computers & Fluids,2001,30(6):643-671.
[44]潘存鸿,林炳尧,毛献忠.一维浅水流动方程的Godunov格式求解[J].水科学进展,2003,14(4)：430-436.
[45]Ying XY, Khan AA, Wang SSY. Upwind conservative scheme for the saint equations [J]. Journal of Hydraulic Engineering, ASCE,2004,130(10):977-987.
[46]Mohapatra PK, Eswaran V, Bhallamudi MS. Two-dimensional analysis of dam break flow in vertical plane [J]. Journal of Hydraulic Engineering, ASCE,2004,125(2):183-192.
[47]Vazquez-Cendon ME. Improved Treatment of Source Terms in upwind schemes for the shallow water equations in channels with irregular geometry [J]. Journal of Computational Physics,1999, 148(2):497-526.
[48]Zhou JG, Causon DM, Mingham CG, et al. The surface gradient method for the treatment of source terms in the shallow-water equations [J]. Journal of Computational Physics,2001,168 (1):1-25.
[49]王志力,耿艳芬,金生.具有复杂计算域和地形的二维浅水流动数值模拟[J].水力学报,2005,35(4)：1-9.
[50]Synolakis CE. The runup of long waves [D]. Pasadena:California Institute of Technology, 1986.
[51]Van Rijn LC. Mathematical modeling of suspended sediment in non-uniform flows [J]. Journal of Hydraulic Engineering, ASCE,1986,112(6):433-455.
[52]夏云峰.感潮河段三维水流泥沙数值模型研究与应用[D].南京：河海大学.
[53]Wang ZB, Ribberink JS. The validity of a depth-integrated model [J]. Journal of Hydraulic Engineering, ASCE,1990,116(10):1270-1288.
[54]Galappatti G, Vreugdenhil CB. A Depth Integrated Mod el for Suspended Sediment Transport [J] Journal of Hydraulic Research,1985,23(4):359-377.
[55]Guo QC, Jin YC. Modeling nonuniform suspended sediment transport in alluvial rivers[J]. Journal of Hydraulic Engineering, ASCE,2002,128(9):839-837.