海底管道冲刷势流模型的改进
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摘要
对Li&Cheng的势流模型在数值方法、床面平衡条件及冲刷床面调整技术做出了3方面的改进。采用边界元法代替差分法求解Laplace方程,前者可以准确地拟合地形与管道边界,因而可以准确反映固壁边界对流态的影响,此外,还具有数据准备简单,降低计算维数,计算速度快等优点。Li&Cheng模型以床面水流切应力等于泥沙起动切应力,τ_b=τ_c,作为床面平衡条件,这只适用于清水冲刷。以沿程输沙相同作为平衡剖面条件,理论上,将模型推广到了动床冲刷。此外,为了提高模型的收敛性,提出了最速下降法与牛顿迭代法相结合的床面调整技术。采用实验资料对模型进行了检验,计算的冲刷深度与实验结果符合良好。
The potential flow model proposed by Li & Cheng is improved in the aspects of numerical method, bed surface equilibrium condition and scoured bed surface adjustment technique. The boundary element method(BEM), instead of the method of difference, is used to solve the Laplace equation. The BEM can accurately fit the terrain and pipeline boundary, so that the influence of solid wall boundary on flow pattern can be reflected accurately. In addition, the BEM also has the advantages of simple data preparation, reducing computational dimension, fast calculation speed and the like. In Li and Cheng model, the bed surface equilibrium condition is that the shear stress of water flow on the bed surface is equal to the starting shear stress of sediment, that is, τ_b=τ_c. However, this is just valid for the clear-water scouring. In the present paper, the constant sediment transport along the way is taken as the criterion of bed surface equilibrium, which has, in theory, extended the potential flow model to the moving bed scour. Besides, in order to improve the convergence of the model, a seabed surface adjustment technique is proposed, which is a combination of steepest descent method and Newton iteration technique. This model has been tested by using experimental data, showing that the scouring depth calculated by the model is in a good agreement with the results from experiments.
The potential flow model proposed by Li & Cheng is improved in the aspects of numerical method, bed surface equilibrium condition and scoured bed surface adjustment technique. The boundary element method(BEM), instead of the method of difference, is used to solve the Laplace equation. The BEM can accurately fit the terrain and pipeline boundary, so that the influence of solid wall boundary on flow pattern can be reflected accurately. In addition, the BEM also has the advantages of simple data preparation, reducing computational dimension, fast calculation speed and the like. In Li and Cheng model, the bed surface equilibrium condition is that the shear stress of water flow on the bed surface is equal to the starting shear stress of sediment, that is, τ_b=τ_c. However, this is just valid for the clear-water scouring. In the present paper, the constant sediment transport along the way is taken as the criterion of bed surface equilibrium, which has, in theory, extended the potential flow model to the moving bed scour. Besides, in order to improve the convergence of the model, a seabed surface adjustment technique is proposed, which is a combination of steepest descent method and Newton iteration technique. This model has been tested by using experimental data, showing that the scouring depth calculated by the model is in a good agreement with the results from experiments.
引文
[1] LI F,CHENG L.Numerical model for local scour under offshore pipelines[J].Journal of Hydraulic Engineering,1999,125(4):400-406.
[2] SUMER B M,FREDSOE J.The mechanics of scour in the marine environment[M].Singapore:World Scientific,2002:117-137.
[3] CHIEW Y M.Prediction of maximum scour depth at submarine pipelines[J].Journal of Hydraulic Engineering,1991,117(4):452-466.
[4] KJELDSEN S P,GJOSVIK O,BRINGAKER K G,et al.Local scour near offshore pipelines[C]//Proceeding of 2th International Conference on Port and Ocean Engineering under Arctic Conditions,Iceland:1973:308-331.
[5] IBRAHIM A,NALLURI C.Scour prediction around marine pipelines[C]//Proceeding of 5th International Symposium on Offshore Mechanics and Arctic Engineering,ASME.Tokyo,1986:679-684.
[6] BIJKER E W,LEEUWESTEIN W.Interaction between pipelines and the seabed under the influence of waves and currents[C]//Seabed Mechanics,Proceeding of the International Union of Theoretical and Applied Mechanics Conference,Graham and Trotman,London,1984:235-242.
[7] CHAO J L,HENNESSY P V.Local scour under ocean outfall pipeline[J].Journal of Water Pollution Control Federacy,1972,44(7):1443-1447.
[8] LIANG D,CHENG L,LI F.Numerical modeling of flow and scour below a pipeline in currents Part II.Scour simulation[J].Coastal Engineering,2005,52:43-62.
[9] LU L,LI Y,QIN J.Numerical simulation of the equilibrium profile of local scour around submarine pipelines based on renormalized group turbulence model[J].Ocean Engineering,2005,32:2007-2019.
[10] ZHAO Z,FERNANDO H J S.Numerical simulation of scour around pipelines using an Euler-Euler coupled two-phase model[J].Environmental Fluid Mechanics,2007,7:121-142.
[11] YEGANEH-BAKHTIARY A,KAZEMINEZHAD M H,ETEMAD-SHAHIDI A,et al.Euler-Euler two-phase flow simulation of tunnel erosion beneath marine pipelines[J].Applied Ocean Research,2011,33:137-146.
[12] DUPUIS A,CHOPARD B.Lattice gas modeling of scour formation under submarine pipelines[J].Journal of Computational Physics,2002,178:161-174.
[13] ANG W T.A beginner’s course in boundary element methods[M/OL].[2018-09-24].https://www.ntu.edu.sg/home/mwtang/bem2011.html.
[14] YUAN ZQ,XIAO J,ZHU JL.Object-oriented boundary element method programming[J].Journal of Chongqing University,2003,26(8):130-134.袁政强,肖捷,祝家麟.面向对象的边界元程序设计[J].重庆大学学报,2003,26(8):130-134.
[15] MEYER-PETER E,MULLER R.Formulas for bed-load transport[C]//Report on 2nd Meeting,International Association for Hydraulic Research,1948,3:39-64
[16] VAN RIJN I C.Sediment transport,partⅡ:bed load transport[J].Journal of Hydraulic Engineering,1984,110(11):1431-1456.
[17] XIA H Y,WANG J Q.Boundary element method for calculating the onset of scour beneath marine pipelines under the wave action[J].Coastal Engineering,2017,36(2):9-16.夏华永,王俊勤.波浪作用下管道冲刷暴发计算的边界元方法[J].海岸工程,2017,36(2):9-16.
[18] HANSEN E A,FREDSOE J,MAO Y.Two-dimensional scour below pipelines[C]//Proceeding of 5th International Symposium On Offshore Mechanics And Arctic Engineering,ASME.New York,1986(3):670-678.
[19] MAO Y.The interaction between a pipeline and erodible bed[C]//Lyngby,Denmark:Technical University of Denmark,1986.
[2] SUMER B M,FREDSOE J.The mechanics of scour in the marine environment[M].Singapore:World Scientific,2002:117-137.
[3] CHIEW Y M.Prediction of maximum scour depth at submarine pipelines[J].Journal of Hydraulic Engineering,1991,117(4):452-466.
[4] KJELDSEN S P,GJOSVIK O,BRINGAKER K G,et al.Local scour near offshore pipelines[C]//Proceeding of 2th International Conference on Port and Ocean Engineering under Arctic Conditions,Iceland:1973:308-331.
[5] IBRAHIM A,NALLURI C.Scour prediction around marine pipelines[C]//Proceeding of 5th International Symposium on Offshore Mechanics and Arctic Engineering,ASME.Tokyo,1986:679-684.
[6] BIJKER E W,LEEUWESTEIN W.Interaction between pipelines and the seabed under the influence of waves and currents[C]//Seabed Mechanics,Proceeding of the International Union of Theoretical and Applied Mechanics Conference,Graham and Trotman,London,1984:235-242.
[7] CHAO J L,HENNESSY P V.Local scour under ocean outfall pipeline[J].Journal of Water Pollution Control Federacy,1972,44(7):1443-1447.
[8] LIANG D,CHENG L,LI F.Numerical modeling of flow and scour below a pipeline in currents Part II.Scour simulation[J].Coastal Engineering,2005,52:43-62.
[9] LU L,LI Y,QIN J.Numerical simulation of the equilibrium profile of local scour around submarine pipelines based on renormalized group turbulence model[J].Ocean Engineering,2005,32:2007-2019.
[10] ZHAO Z,FERNANDO H J S.Numerical simulation of scour around pipelines using an Euler-Euler coupled two-phase model[J].Environmental Fluid Mechanics,2007,7:121-142.
[11] YEGANEH-BAKHTIARY A,KAZEMINEZHAD M H,ETEMAD-SHAHIDI A,et al.Euler-Euler two-phase flow simulation of tunnel erosion beneath marine pipelines[J].Applied Ocean Research,2011,33:137-146.
[12] DUPUIS A,CHOPARD B.Lattice gas modeling of scour formation under submarine pipelines[J].Journal of Computational Physics,2002,178:161-174.
[13] ANG W T.A beginner’s course in boundary element methods[M/OL].[2018-09-24].https://www.ntu.edu.sg/home/mwtang/bem2011.html.
[14] YUAN ZQ,XIAO J,ZHU JL.Object-oriented boundary element method programming[J].Journal of Chongqing University,2003,26(8):130-134.袁政强,肖捷,祝家麟.面向对象的边界元程序设计[J].重庆大学学报,2003,26(8):130-134.
[15] MEYER-PETER E,MULLER R.Formulas for bed-load transport[C]//Report on 2nd Meeting,International Association for Hydraulic Research,1948,3:39-64
[16] VAN RIJN I C.Sediment transport,partⅡ:bed load transport[J].Journal of Hydraulic Engineering,1984,110(11):1431-1456.
[17] XIA H Y,WANG J Q.Boundary element method for calculating the onset of scour beneath marine pipelines under the wave action[J].Coastal Engineering,2017,36(2):9-16.夏华永,王俊勤.波浪作用下管道冲刷暴发计算的边界元方法[J].海岸工程,2017,36(2):9-16.
[18] HANSEN E A,FREDSOE J,MAO Y.Two-dimensional scour below pipelines[C]//Proceeding of 5th International Symposium On Offshore Mechanics And Arctic Engineering,ASME.New York,1986(3):670-678.
[19] MAO Y.The interaction between a pipeline and erodible bed[C]//Lyngby,Denmark:Technical University of Denmark,1986.