直角明渠水流交汇流动特性的数值模拟研究
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摘要
明渠交汇流动是水利工程中常见的水力现象。研究交汇段水流流动特性对城市防洪、河床冲刷、泥沙输运以及污染物质的混合输移等问题具有十分重要的工程及理论意义。明渠水流交汇流动特性十分复杂,受到交汇口几何特征和流动特征两大类因素的影响。其中,交汇口几何特征包括渠道尺寸、形状、底坡和两交汇渠道间的角度等,流动特征包括流动的 Fr 数、渠道糙率、交汇口上游主支流流量比和流体本身的属性等。明渠交汇水流特性受如此多的因素影响,因而,很难考虑所有因素,通过理论分析或者试验研究的方法来解决这个问题。数值模拟可以方便灵活的改变边界条件,对不同的水流工况进行模拟,随着计算技术的发展,数值模拟成为研究交汇水流特性的主要手段。
本文将水深平均二维流动方程与显式代数应力模型相结合,对平底直角明渠交汇流动特性进行了数值模拟。采用交错网格上的有限体积法对方程进行离散,使用 SIMPLE 算法进行压力-速度的校正,并采用逐行扫描的 TDMA 法求解离散后的代数方程组,对四种不同流量比工况的流动进行了模拟,并与实测资料进行比较。比较结果表明,水深平均二维显式代数应力模型能够较好的模拟交汇口下游分离区的形态以及水面沿程变化。
同时,本文还采用显式代数应力模型对三维流动进行计算,采用 Hirt-VOF方法来求解自由水面。方程的离散和求解与水深平均二维流动的求解方法类似,同样的,也对四种工况下的流动进行了数值模拟。模拟结果表明,采用显式代数应力模型进行三维计算能够很好的模拟明渠交汇水流的三维水力特性,对流动的分离区和水面变化等特征的模拟要优于水深平均二维显式代数应力模型的模拟结果。并且,由于采用显式代数应力模型,三维计算能够较好的模拟交汇口下游横断面上存在的二次流现象。
本文模型可以为工程问题提供依据,修改边界条件后,可以用于更加复杂边界问题的计算。并可以作为研究交汇口泥沙输运及污染物质的混合输移等问题的基础。
Open-channel junction flow often occurs in hydraulic engineering. Itgenerates theoretical and practice interest for urban flood control, bed erosion,sediment transport and pollutant transport. Detailed hydrodynamics ofjunction flow is found to be complex and there exists two kinds of factors thatcharacterize the flow physics: geometry character and flow character. Theformer includes the size, shape, slope and angle between the two combiningchannels, and the latter includes the flow Reynolds number, channelroughness, discharge ratio, and fluid properties. So many variables make itdifficult to solve the problem through experimental studies. Numericalsimulation can fit the variable boundaries flexibly. With the development ofcomputational fluid dynamics, Numerical Simulation evolves as the primaryway for solving the open-channel junction flow.
In this thesis, the depth-averaged equations combined with the explicitalgebraic stress turbulence model were applied to the simulation of 90oopen-channel junction with horizontal slope. The governing equations werediscretized on staggered grids by finite volume method. SIMPLE algorithmwas used to complete the velocity-pressure correction. The algebraicequations were solved by TDMA method. Computation was performed forfour different flow conditions. The numerical results were compared with theexperiment data. It showed good agreements for the separation zone and watersurface elevation simulation.
In addition, three-dimensional equations coupled with the explicitalgebraic stress turbulence model were also applied to the model. The solutionprocedure was similar with that in the depth-averaged equations. The resultsshowed advantageous results for the separation zone and water surfaceelevation simulation. Furthermore, secondary flow phenomena in the crosssection downstream the junction were found owning to the use of the explicit
algebraic stress turbulence model.The numerical model applied in the paper can be employed to morecomplex problem occurred in the engineering, it also can work as a foundationto study bed erosion, sediment transport and pollutant transport.
本文将水深平均二维流动方程与显式代数应力模型相结合,对平底直角明渠交汇流动特性进行了数值模拟。采用交错网格上的有限体积法对方程进行离散,使用 SIMPLE 算法进行压力-速度的校正,并采用逐行扫描的 TDMA 法求解离散后的代数方程组,对四种不同流量比工况的流动进行了模拟,并与实测资料进行比较。比较结果表明,水深平均二维显式代数应力模型能够较好的模拟交汇口下游分离区的形态以及水面沿程变化。
同时,本文还采用显式代数应力模型对三维流动进行计算,采用 Hirt-VOF方法来求解自由水面。方程的离散和求解与水深平均二维流动的求解方法类似,同样的,也对四种工况下的流动进行了数值模拟。模拟结果表明,采用显式代数应力模型进行三维计算能够很好的模拟明渠交汇水流的三维水力特性,对流动的分离区和水面变化等特征的模拟要优于水深平均二维显式代数应力模型的模拟结果。并且,由于采用显式代数应力模型,三维计算能够较好的模拟交汇口下游横断面上存在的二次流现象。
本文模型可以为工程问题提供依据,修改边界条件后,可以用于更加复杂边界问题的计算。并可以作为研究交汇口泥沙输运及污染物质的混合输移等问题的基础。
Open-channel junction flow often occurs in hydraulic engineering. Itgenerates theoretical and practice interest for urban flood control, bed erosion,sediment transport and pollutant transport. Detailed hydrodynamics ofjunction flow is found to be complex and there exists two kinds of factors thatcharacterize the flow physics: geometry character and flow character. Theformer includes the size, shape, slope and angle between the two combiningchannels, and the latter includes the flow Reynolds number, channelroughness, discharge ratio, and fluid properties. So many variables make itdifficult to solve the problem through experimental studies. Numericalsimulation can fit the variable boundaries flexibly. With the development ofcomputational fluid dynamics, Numerical Simulation evolves as the primaryway for solving the open-channel junction flow.
In this thesis, the depth-averaged equations combined with the explicitalgebraic stress turbulence model were applied to the simulation of 90oopen-channel junction with horizontal slope. The governing equations werediscretized on staggered grids by finite volume method. SIMPLE algorithmwas used to complete the velocity-pressure correction. The algebraicequations were solved by TDMA method. Computation was performed forfour different flow conditions. The numerical results were compared with theexperiment data. It showed good agreements for the separation zone and watersurface elevation simulation.
In addition, three-dimensional equations coupled with the explicitalgebraic stress turbulence model were also applied to the model. The solutionprocedure was similar with that in the depth-averaged equations. The resultsshowed advantageous results for the separation zone and water surfaceelevation simulation. Furthermore, secondary flow phenomena in the crosssection downstream the junction were found owning to the use of the explicit
algebraic stress turbulence model.The numerical model applied in the paper can be employed to morecomplex problem occurred in the engineering, it also can work as a foundationto study bed erosion, sediment transport and pollutant transport.
引文
[1] 武蓉.明渠交汇口水流流动特性的数值模拟研究.[硕士学位论文].北京:清华大学,2002
[2] Best J L. and Reid, I. Separation zone at open-channel junctions. Journal of Hydraulic Engineering, 1984, 110(11): 1588-1594
[3] Taylor E H., Flow characteristics at rectangular open-channel junctions. Trans, 1944,109:893-902
[4] 倪晋仁,王光谦,张国生.交汇河段水力计算探讨.水利学报,1992,7:51-56
[5] Gurram S K, Karki K S, Hager W H. Subcritical junction flow. Journal of Hydraulic Engineering, 1997, 123(5): 447-455
[6] Hsu C C, Wu F S, and Lee W J. Flow at 90o equal-width open channel junction. Journal of Hydraulic Engineering, 1998, 124(2): 186-191
[7] Hsu C C, Lee W J and Chang C H. Subcritical open-channel junction flow. Journal of Hydraulic Engineering, 1998, 124(8): 847-855
[8] 茅泽育,罗昇,赵升伟.明渠等宽交汇口一维数学模型.水利学报,2004,8:26-32
[9] Webber N B, Greated C A. An investigation of flow behavior at the junction of rectangular channels. Proc. Instn. Of Civ. Engrs., London: Thomas Telford Ltd., 1966.321-334
[10] Mamedov A S. Hydraulic calculation of a confluence. Hydro technical construction, 1989, 23(9): 553-556
[11] 茅泽育,赵升伟,罗昇,张磊.明渠交汇口分离区研究.水科学进展,2005,16(1):7-12
[12] 茅泽育,赵升伟,张磊,黄继汤.明渠交汇口三维水力特性试验研究.水利学报,2004,2:1-7
[13] Mcguirk J J, Rodi W. A depth-averaged mathematical model for the near field of side discharges into open-channel flow. Journal of Fluid Mechanics, 1978, 86(4): 761-781
[14] Weerakoon S B, Tamai N. Three-dimensional calculation of flow in river confluences using boundary fitted co-ordinates. Journal of Hydroscience and Hydraulic Engineering, 1989, 6: 51-62
[15] Bradbrook K F, Lane S N, Richards K S. Role of bed discordance at asymmetrical river confluences. Journal of Hydraulic Engineering, 2001, 127(5): 351-368
[16] Huang J C, Weber L J, Lai Y J. Three-deminsional numerical study of flows in open-channel junctions. Journal of Hydraulic Engineering, 2002, 128(3): 268-280
[17] 程亮,倪汉根. 二维正交渠道交接部流动的直接模拟.全国第一届计算水力学学术讨论会论文集.大连,1991.117-124
[18] 是勋刚.湍流.天津:天津大学出版社,1994.213-214
[19] 陈义良.湍流计算模型.合肥:中国科学技术大学出版社,1991.23-24
[20] 余常昭.环境流体力学导论.北京:清华大学出版社,1992.98-102
[21] 朱自强.应用计算流体力学.北京:北京航空航天大学出版社,1998.122-123
[22] Wilcox D C. Turbulence modeling for CFD. Calif.: DCW Industries Inc., 1998.83-87
[23] 倪浩清.工程湍流模式理论综述及展望.力学进展.1996,26(2):145-165
[24] 张兆顺.湍流.北京:国防工业出版社,2002.203-204
[25] 刘 儒 勋 .数 值 模 拟 方 法 和 运 动 界 面 追 踪 .合 肥 : 中 国 科 学 技 术 大 学 出 版社,2001.31-35
[26] Zalesak S T. Fully multi-dimensional flux corrected transport algorithms for fluid flow. Journal of Computational Physics, 1979, 31:335-362
[27] Hirt C W, Nichols B D. Volume of fluid (VOF) method for the dynamics of free boundaries. Journal of Computational Physics, 1981, 39:201-225
[28] Ashgriz N and Poo J Y. FLAIR: flux line-segment model for advection and interface reconstruction. Journal of Computational Physics, 1991, 93:449-468
[29] Youngs D L. Time-dependent multi-material flow with large fluid distortion. Numerical Methods for Fluid Dynamics, New York: Academic Press.1982, 273–285
[30] Ubbink O and Issay I. A method for capturing sharp fluid interfaces on arbitrary meshes. Journal of Computational Physics, 1999, 153:26-50
[31] Gatski T B and Speziale C G. On explicit algebraic stress models for complex turbulent flows. J. Fluid Mech., 1993,254:59-78
[32] Jongen T and Gatski T B. General explicit algebraic stress relations and best approximation for three-dimensional flows. International Journal of Engineering Science, 1998,36: 739-763
[33] Rhie C M, Chow W L. A numerical study of the turbulent flow past an isolated airfoil with trailing edge separation. AIAA Journal, 1983, 21:1525-1532
[34] Majumdar S. Role of underrelaxation in momentum interpolation for calculation of flow with nonstaggered grids. Numerical Heat Transfer, 1988,13(1): 125-132
[35] Miller T F and Schmidt F W. Use of a pressure-weighted interpolation method for the solution of the incompressible Navier-Stokes equations on a nonstaggered grid system. Numerical Heat Transfer, 1988,14: 213-233
[36] Date A W. Complete pressure correction algorithm for solution of imcompressible Navier-Stokes equations on a nonstaggered grid. Numerical Heat Transfer, 1996,29: 441-458
[37] 倪浩清,沈永明.工程湍流流动、传热及传质的数值模拟.北京:中国水利水电出版社,1996.20-21
[38] 帕坦卡.传热与流体流动的数值计算.北京:科学出版社,1984.116-117
[39] 陶文铨.数值传热学.西安:西安交通大学出版社,1995.285-290
[40] Rudman M. A volume-tracking method for incompressible multifluid flows with large density variations. Int. J. Numer. Meth. Fluids, 1998, 28: 357–378.
[41] Torreymd, Mjolsnessrc, Steinlr. NASA-VOF3D: A three-dimensional computer program for incompressible flow with free surfaces. LosAlamos National Laboratory Report, LA-10612-MS[R]. LosAlamos: [sn], 1987.
[2] Best J L. and Reid, I. Separation zone at open-channel junctions. Journal of Hydraulic Engineering, 1984, 110(11): 1588-1594
[3] Taylor E H., Flow characteristics at rectangular open-channel junctions. Trans, 1944,109:893-902
[4] 倪晋仁,王光谦,张国生.交汇河段水力计算探讨.水利学报,1992,7:51-56
[5] Gurram S K, Karki K S, Hager W H. Subcritical junction flow. Journal of Hydraulic Engineering, 1997, 123(5): 447-455
[6] Hsu C C, Wu F S, and Lee W J. Flow at 90o equal-width open channel junction. Journal of Hydraulic Engineering, 1998, 124(2): 186-191
[7] Hsu C C, Lee W J and Chang C H. Subcritical open-channel junction flow. Journal of Hydraulic Engineering, 1998, 124(8): 847-855
[8] 茅泽育,罗昇,赵升伟.明渠等宽交汇口一维数学模型.水利学报,2004,8:26-32
[9] Webber N B, Greated C A. An investigation of flow behavior at the junction of rectangular channels. Proc. Instn. Of Civ. Engrs., London: Thomas Telford Ltd., 1966.321-334
[10] Mamedov A S. Hydraulic calculation of a confluence. Hydro technical construction, 1989, 23(9): 553-556
[11] 茅泽育,赵升伟,罗昇,张磊.明渠交汇口分离区研究.水科学进展,2005,16(1):7-12
[12] 茅泽育,赵升伟,张磊,黄继汤.明渠交汇口三维水力特性试验研究.水利学报,2004,2:1-7
[13] Mcguirk J J, Rodi W. A depth-averaged mathematical model for the near field of side discharges into open-channel flow. Journal of Fluid Mechanics, 1978, 86(4): 761-781
[14] Weerakoon S B, Tamai N. Three-dimensional calculation of flow in river confluences using boundary fitted co-ordinates. Journal of Hydroscience and Hydraulic Engineering, 1989, 6: 51-62
[15] Bradbrook K F, Lane S N, Richards K S. Role of bed discordance at asymmetrical river confluences. Journal of Hydraulic Engineering, 2001, 127(5): 351-368
[16] Huang J C, Weber L J, Lai Y J. Three-deminsional numerical study of flows in open-channel junctions. Journal of Hydraulic Engineering, 2002, 128(3): 268-280
[17] 程亮,倪汉根. 二维正交渠道交接部流动的直接模拟.全国第一届计算水力学学术讨论会论文集.大连,1991.117-124
[18] 是勋刚.湍流.天津:天津大学出版社,1994.213-214
[19] 陈义良.湍流计算模型.合肥:中国科学技术大学出版社,1991.23-24
[20] 余常昭.环境流体力学导论.北京:清华大学出版社,1992.98-102
[21] 朱自强.应用计算流体力学.北京:北京航空航天大学出版社,1998.122-123
[22] Wilcox D C. Turbulence modeling for CFD. Calif.: DCW Industries Inc., 1998.83-87
[23] 倪浩清.工程湍流模式理论综述及展望.力学进展.1996,26(2):145-165
[24] 张兆顺.湍流.北京:国防工业出版社,2002.203-204
[25] 刘 儒 勋 .数 值 模 拟 方 法 和 运 动 界 面 追 踪 .合 肥 : 中 国 科 学 技 术 大 学 出 版社,2001.31-35
[26] Zalesak S T. Fully multi-dimensional flux corrected transport algorithms for fluid flow. Journal of Computational Physics, 1979, 31:335-362
[27] Hirt C W, Nichols B D. Volume of fluid (VOF) method for the dynamics of free boundaries. Journal of Computational Physics, 1981, 39:201-225
[28] Ashgriz N and Poo J Y. FLAIR: flux line-segment model for advection and interface reconstruction. Journal of Computational Physics, 1991, 93:449-468
[29] Youngs D L. Time-dependent multi-material flow with large fluid distortion. Numerical Methods for Fluid Dynamics, New York: Academic Press.1982, 273–285
[30] Ubbink O and Issay I. A method for capturing sharp fluid interfaces on arbitrary meshes. Journal of Computational Physics, 1999, 153:26-50
[31] Gatski T B and Speziale C G. On explicit algebraic stress models for complex turbulent flows. J. Fluid Mech., 1993,254:59-78
[32] Jongen T and Gatski T B. General explicit algebraic stress relations and best approximation for three-dimensional flows. International Journal of Engineering Science, 1998,36: 739-763
[33] Rhie C M, Chow W L. A numerical study of the turbulent flow past an isolated airfoil with trailing edge separation. AIAA Journal, 1983, 21:1525-1532
[34] Majumdar S. Role of underrelaxation in momentum interpolation for calculation of flow with nonstaggered grids. Numerical Heat Transfer, 1988,13(1): 125-132
[35] Miller T F and Schmidt F W. Use of a pressure-weighted interpolation method for the solution of the incompressible Navier-Stokes equations on a nonstaggered grid system. Numerical Heat Transfer, 1988,14: 213-233
[36] Date A W. Complete pressure correction algorithm for solution of imcompressible Navier-Stokes equations on a nonstaggered grid. Numerical Heat Transfer, 1996,29: 441-458
[37] 倪浩清,沈永明.工程湍流流动、传热及传质的数值模拟.北京:中国水利水电出版社,1996.20-21
[38] 帕坦卡.传热与流体流动的数值计算.北京:科学出版社,1984.116-117
[39] 陶文铨.数值传热学.西安:西安交通大学出版社,1995.285-290
[40] Rudman M. A volume-tracking method for incompressible multifluid flows with large density variations. Int. J. Numer. Meth. Fluids, 1998, 28: 357–378.
[41] Torreymd, Mjolsnessrc, Steinlr. NASA-VOF3D: A three-dimensional computer program for incompressible flow with free surfaces. LosAlamos National Laboratory Report, LA-10612-MS[R]. LosAlamos: [sn], 1987.