自由面湍流场的数值模拟及其应用
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摘要
自由面流动广泛存在，人类的生存和发展与它有着紧密的联系，对自由面流动的研究不仅有很广泛的实际工程意义，而且在物理和数学上有重要的理论意义。由于自由面问题的复杂性，纯粹理论分析受到了很大的限制，同时实验研究在实施过程中也遇到了很多困难。随着计算机技术的进步，现代数值模拟技术有了很大发展，利用数值方法研究自由面问题已经成为当前水动力学研究的一个热点和难点。本论文基于FLUENT软件，利用VOF(流体体积)方法，结和RNG(重正化群)κ-ε模型分别对椭球体在自由面附近运动，二维圆柱出入水引起的自由面变形，水池摇板造波进行了数值模拟。主要内容如下：
在椭球体在自由面附近运动的数值模拟中，本论文一方面较详细地考察了潜椭球体在不同潜深情况下运动引起的自由面形状，阻力系数以及阻力系数与潜深的关系，另一方面较详细地考察了潜椭球体在不同傅汝德数下运动引起的自由面形状，阻力系数以及阻力系数与傅汝德数的关系。
对于水池摇板造波的数值模拟，本论文根据摇板造波原理，针对哈尔滨工程大学水池摇板式造波机的实例，利用VOF方法和动网格技术，在数值水池中模拟了带有波前的高品质二阶Stokes波，并考察了数值水池中不同位置处波面的历时曲线，典型的波浪形态以及局部流场的速度分布。
在二维圆柱穿越水面出入水的数值模拟中，本论文较详尽地考察了二维圆柱穿越水面垂直出水，垂直入水，斜入水过程中自由面形状的变化，并分析了自由面形状变化的原因。
数值计算结果表明：本论文利用VOF方法结合RNGκ-ε模型来模拟自由面问题是切实可行的。
The existence and development of human has close relations with free-surface flows, the research of which has both widely practical engineering significance and important theoretic value. Due to the complication of free-surface flows, pure theoretic analysis is limited substantially and the experimental research also has many difficulties in the process of application. With the advancement of computer technique, modern numerical simulation has been greatly developed and the numerical research on free-surface flows has become one of the focuses and difficulties in hydrodynamics. In the dissertation, based on FLUENT software, the VOF(Volume of Fluid) method in combination with RNG(renormalization group) k-εmodel was used in the simulation of the motion of an ellipsoid near the free-surface, the deformation of free-surface caused by water entry and exit of the 2-D circular cylinder and the stokes waves generated by rocker-flap wave maker in a tank. The main part of the dissertation is shown as follows:
In the numerical simulation of the motion of an ellipsoid near the free-surface, on the one hand, the free-surface shape and drag coefficient caused by the motion of an ellipsoid in different depth and the relationship between drag coefficient and depth were studied in detail. On the other hand, both the free-surface shape and drag coefficient caused by the motion of an ellipsoid in different Froude numbers and the relationship between drag coefficient and Froude numbers were also researched detailedly.
In the numerical simulation of waves generated by rocker-flap wave maker in a tank, according to the principle of wave generation by rocker-flap, taking example for rocker-flap wave maker in Harbin Engineering University, high quality stokes wave in accuracy of second order was simulate in numerical wave tank with VOF method and dynamic mesh technique. And time series of surface elevation in different place in numerical tank, typical waves and velocity in local flow field were also researched.
In the numerical simulation of water entry and exit of the 2-D circular cylinder, the free-surface deformations caused by the cylinder moving vertically upwards, vertically downwards, and obliquely downwards were investigated as well as the reasons for these deformations.
The computational results showed that VOF method in combination with RNG k-εmodel was effective on the numerical simulation of free-surface flows.
在椭球体在自由面附近运动的数值模拟中，本论文一方面较详细地考察了潜椭球体在不同潜深情况下运动引起的自由面形状，阻力系数以及阻力系数与潜深的关系，另一方面较详细地考察了潜椭球体在不同傅汝德数下运动引起的自由面形状，阻力系数以及阻力系数与傅汝德数的关系。
对于水池摇板造波的数值模拟，本论文根据摇板造波原理，针对哈尔滨工程大学水池摇板式造波机的实例，利用VOF方法和动网格技术，在数值水池中模拟了带有波前的高品质二阶Stokes波，并考察了数值水池中不同位置处波面的历时曲线，典型的波浪形态以及局部流场的速度分布。
在二维圆柱穿越水面出入水的数值模拟中，本论文较详尽地考察了二维圆柱穿越水面垂直出水，垂直入水，斜入水过程中自由面形状的变化，并分析了自由面形状变化的原因。
数值计算结果表明：本论文利用VOF方法结合RNGκ-ε模型来模拟自由面问题是切实可行的。
The existence and development of human has close relations with free-surface flows, the research of which has both widely practical engineering significance and important theoretic value. Due to the complication of free-surface flows, pure theoretic analysis is limited substantially and the experimental research also has many difficulties in the process of application. With the advancement of computer technique, modern numerical simulation has been greatly developed and the numerical research on free-surface flows has become one of the focuses and difficulties in hydrodynamics. In the dissertation, based on FLUENT software, the VOF(Volume of Fluid) method in combination with RNG(renormalization group) k-εmodel was used in the simulation of the motion of an ellipsoid near the free-surface, the deformation of free-surface caused by water entry and exit of the 2-D circular cylinder and the stokes waves generated by rocker-flap wave maker in a tank. The main part of the dissertation is shown as follows:
In the numerical simulation of the motion of an ellipsoid near the free-surface, on the one hand, the free-surface shape and drag coefficient caused by the motion of an ellipsoid in different depth and the relationship between drag coefficient and depth were studied in detail. On the other hand, both the free-surface shape and drag coefficient caused by the motion of an ellipsoid in different Froude numbers and the relationship between drag coefficient and Froude numbers were also researched detailedly.
In the numerical simulation of waves generated by rocker-flap wave maker in a tank, according to the principle of wave generation by rocker-flap, taking example for rocker-flap wave maker in Harbin Engineering University, high quality stokes wave in accuracy of second order was simulate in numerical wave tank with VOF method and dynamic mesh technique. And time series of surface elevation in different place in numerical tank, typical waves and velocity in local flow field were also researched.
In the numerical simulation of water entry and exit of the 2-D circular cylinder, the free-surface deformations caused by the cylinder moving vertically upwards, vertically downwards, and obliquely downwards were investigated as well as the reasons for these deformations.
The computational results showed that VOF method in combination with RNG k-εmodel was effective on the numerical simulation of free-surface flows.
引文
[1] 洪方文．自由面附近运动物体流场的数值与实验研究．中国船舶科学研究中心博士学位论文．2001：1页，8-10页，16-17页，75页，84页，88页，93页，113-129页
[2] 刘儒勋，王志峰等编著．数值模拟方法和运动界面追踪．中国科技大学出版社，2001：30-33页，36-37页
[3] Harlow F.H., Welch J.E. Numerical calculation of time-dependent viscous incompressible flow fluid with free surface. Phys. Fluids, 1964, 8(12): 2182-2189P
[4] Hirt C.W., Nichols B.D. SOLA-A numerical solution algorithm for transient fluid flows. Los Alamos Scientific Laboratory report,1975, LA-5852P
[5] Hirt C. W. ,Nichols B. D. Volume of Fluid(VOF) method for the study of free boundaries. J. Comput. Phys. 1981,39:201-225P
[6] Ashgriz and Poo J.Y. FLAIR:Flux line-segment model for advection and interfacereconstruction. J. Comput. Phys. 1991, 449-468P
[7] Youngs D.L. Time-dependent multi-material flow with large fluid distortion numerical method for fluid dynamics. Academic, New York, 1982, 273-285P
[8] Monaghan J. Smoothed particle hydrodynamics. Ann, Rev.Astron. Astrophys. 1992, 30:543-574P
[9] Sussman M. ,Smereka P. Axisymmetric free boundary problems. Fluid Mech. 1997,341:269-294P
[10] Mei,C. C. Numerical methods in water-waves diffraction and radiation. Ann. Rev. Fluid Mech. 1978,10:393-416P
[11] Chappelear J.E. Shallow-water waves. J. Geophys. Res. 1962,67: 4693-4704P
[12] Yeung,R. W. Numerical Methods in free-surface flows. Ann. Rev. Fluid Mech. 1982,14: 395-442P
[13] Floryan J. M. ,Rasmussen H. Numerical methods for viscous flows with moving boundaries. Appl. Mech. Rev. 1989,42:323-341P
[14] Tsai W.T. ,Yue D.K. Computation of nonlinear free surface flows. Appl. Mech. Rev. 1996,28 : 249-278P
[15] Scardovelli R. ,Zaleski S. Direct numerical simulation of free-surface and interfacial flow. Ann. Rev. Fluid Mech. 1999, 31 : 567-603P
[16] McHyman J. Numerical methods for tracking interfaces. Physics 1984, D 12:296-407P
[17] Boris J.P. New directions in computational fluid dynamics. Ann. Rev. Fluid Mech. 1989, 21:345-385P
[18] 王福军编著．计算流体动力学分析—CFD软件原理与应用．北京：清华大学出版社，2004：21-22页，185页，7-12页，51-54页，75页，114-132页
[19] 李人宪编著．有限体积法基础．北京：国防工业出版社．2005：10-13页，146-152页
[20] 王志东．三维自由面湍流场数值模拟及其在水利工程中的应用．河海大学博士学位论文．2004年，22-31页
[21] R. I. Issa. Solution of the implicitly discretised fluid flow equations by operator-splitting. J. Comput. Phys. 1986,62: 40-65P
[22] Wu G X, Taylor R E. Radiation and diffraction of water waves by a submerged sphere at forward speed. Proceeding of the Royal Society of London. London, UK, 1998, A146, 115-147P
[23] WU J P, ZOU Z J, WANG R K. Numerical simulation of the nonlinear waves generated by a submerged ellipsoid. Journal of Ship Mechanics, 2004, 8(1) : 56-62P
[24] Yeung R.W, Vaidhyanathan M. Highly Separated Flow Near A Free Surface. Proceeding, International Conf. on Hydradynamics, Wuxi, China. 1994, 118-128P
[25] Yoon B. S., Jung R. T. A Wake Filed Control Technique for Blunt Body Drag Reduction. Proceeding, China-Korea Marine Hydrodynamics Meeting, Shanghai, China, 1997: 187-201P
[26] 韩占忠，王敬，兰小平等编著．北京：北京理工大学出版社，2004：151页
[27] Frank M．White．Fluid Mechanics．5th ed．北京：清华大学出版社，2004：485页
[28] 贺五州，范明顺．Stokes波的数值生成．清华大学学报(自然科学版)．1999年，第39卷第11期，34-39页
[29] LI Ben-xia, YU Xi-ping. A 2-D numerical irregular wave tank and its verification. Journal of Hydrodynamics, 2005,17(2): 222-227P
[30] 刘桦，林怡若，张灼等．基于高阶边界元的三维数值波浪港池．海洋工程，2004，22(2)：1-6页
[31] WAND Yong-xue. Numerical wave channel with absorbed wave maker. China Ocean Eng,1995,9(2): 149-160P
[32] WANG Yong-xue. Wave slamming on offshore structure. Proceedings of the 6th International offshore and Polar Engineering Conference. Los Angeles, 1996. Vol 3,192-196P
[33] 齐鹏，王永学．三维数值波浪水池技术与应用．大连理工大学学报，2003，43(6)：825-830页
[34] 贺五州，袁亨良，耿进柱．摇板式造波机生成的长峰规则波．水力发电学报．2002年第1期，146-152页
[35] 张军，李英浩，金朋寿等．垂直及斜出水流场的二维及三维TR-PIV实验．船舶力学．2005(4)：9-17页
[36] Wagner H. Uber stoss und gleitvorgange an der boerflache von flussigkeiten. ZAMM,1932,12: 193-215P
[37] Zhao R ,Faltinsen O. Water entry of 2D bodies. J. Fluid Mech. 1993, 246: 593-612P
[38] Korobkin A A, Pukhnachov V V. Initial Stage of Water impact. Anu. Rev. of Fluid Mech. 1980,20: 85-159P
[39] Korobkin A A, Pukhnachov V V. Initial asymptotic in contact hydrodynamics ' problem. Proc. 4th Inter. Conf. Numer.Ship Hydradynamics, Washington D. C. ,USA, 1985.138-151P
[40] Pukhnachov V V, Korobkin A A. Initial Asymptotic in problem of blunt body entrance into liquid. Proc. 3rd. Inter. Conf. Numer. Ship Hydradynamics, paris, France, 1981.579-591P
[41] 张志荣，洪方文，张军，徐洁．入水初期流场测量方法．水动力学研究与进展．2001，A辑，第16卷第3期：274-278页
[42] Greeenhow & Moyo. Water entry and exit of horizontal circular cylinders. Phil. Trans. R. Soc. Lond. 1997,551-563P
[43] G.X. Wu, H. Sun, Y. S. He. Numerical simulation and experimental study of water entry of a wedge in free fall motion. Journal of Fluids and Structures. 2004,277-289P
[44] 张军，张志荣，洪方文，赵峰等．楔形体入水初期流场的数值模拟．船舶力学．2003，Vol．7，No．4：29-35P
[2] 刘儒勋，王志峰等编著．数值模拟方法和运动界面追踪．中国科技大学出版社，2001：30-33页，36-37页
[3] Harlow F.H., Welch J.E. Numerical calculation of time-dependent viscous incompressible flow fluid with free surface. Phys. Fluids, 1964, 8(12): 2182-2189P
[4] Hirt C.W., Nichols B.D. SOLA-A numerical solution algorithm for transient fluid flows. Los Alamos Scientific Laboratory report,1975, LA-5852P
[5] Hirt C. W. ,Nichols B. D. Volume of Fluid(VOF) method for the study of free boundaries. J. Comput. Phys. 1981,39:201-225P
[6] Ashgriz and Poo J.Y. FLAIR:Flux line-segment model for advection and interfacereconstruction. J. Comput. Phys. 1991, 449-468P
[7] Youngs D.L. Time-dependent multi-material flow with large fluid distortion numerical method for fluid dynamics. Academic, New York, 1982, 273-285P
[8] Monaghan J. Smoothed particle hydrodynamics. Ann, Rev.Astron. Astrophys. 1992, 30:543-574P
[9] Sussman M. ,Smereka P. Axisymmetric free boundary problems. Fluid Mech. 1997,341:269-294P
[10] Mei,C. C. Numerical methods in water-waves diffraction and radiation. Ann. Rev. Fluid Mech. 1978,10:393-416P
[11] Chappelear J.E. Shallow-water waves. J. Geophys. Res. 1962,67: 4693-4704P
[12] Yeung,R. W. Numerical Methods in free-surface flows. Ann. Rev. Fluid Mech. 1982,14: 395-442P
[13] Floryan J. M. ,Rasmussen H. Numerical methods for viscous flows with moving boundaries. Appl. Mech. Rev. 1989,42:323-341P
[14] Tsai W.T. ,Yue D.K. Computation of nonlinear free surface flows. Appl. Mech. Rev. 1996,28 : 249-278P
[15] Scardovelli R. ,Zaleski S. Direct numerical simulation of free-surface and interfacial flow. Ann. Rev. Fluid Mech. 1999, 31 : 567-603P
[16] McHyman J. Numerical methods for tracking interfaces. Physics 1984, D 12:296-407P
[17] Boris J.P. New directions in computational fluid dynamics. Ann. Rev. Fluid Mech. 1989, 21:345-385P
[18] 王福军编著．计算流体动力学分析—CFD软件原理与应用．北京：清华大学出版社，2004：21-22页，185页，7-12页，51-54页，75页，114-132页
[19] 李人宪编著．有限体积法基础．北京：国防工业出版社．2005：10-13页，146-152页
[20] 王志东．三维自由面湍流场数值模拟及其在水利工程中的应用．河海大学博士学位论文．2004年，22-31页
[21] R. I. Issa. Solution of the implicitly discretised fluid flow equations by operator-splitting. J. Comput. Phys. 1986,62: 40-65P
[22] Wu G X, Taylor R E. Radiation and diffraction of water waves by a submerged sphere at forward speed. Proceeding of the Royal Society of London. London, UK, 1998, A146, 115-147P
[23] WU J P, ZOU Z J, WANG R K. Numerical simulation of the nonlinear waves generated by a submerged ellipsoid. Journal of Ship Mechanics, 2004, 8(1) : 56-62P
[24] Yeung R.W, Vaidhyanathan M. Highly Separated Flow Near A Free Surface. Proceeding, International Conf. on Hydradynamics, Wuxi, China. 1994, 118-128P
[25] Yoon B. S., Jung R. T. A Wake Filed Control Technique for Blunt Body Drag Reduction. Proceeding, China-Korea Marine Hydrodynamics Meeting, Shanghai, China, 1997: 187-201P
[26] 韩占忠，王敬，兰小平等编著．北京：北京理工大学出版社，2004：151页
[27] Frank M．White．Fluid Mechanics．5th ed．北京：清华大学出版社，2004：485页
[28] 贺五州，范明顺．Stokes波的数值生成．清华大学学报(自然科学版)．1999年，第39卷第11期，34-39页
[29] LI Ben-xia, YU Xi-ping. A 2-D numerical irregular wave tank and its verification. Journal of Hydrodynamics, 2005,17(2): 222-227P
[30] 刘桦，林怡若，张灼等．基于高阶边界元的三维数值波浪港池．海洋工程，2004，22(2)：1-6页
[31] WAND Yong-xue. Numerical wave channel with absorbed wave maker. China Ocean Eng,1995,9(2): 149-160P
[32] WANG Yong-xue. Wave slamming on offshore structure. Proceedings of the 6th International offshore and Polar Engineering Conference. Los Angeles, 1996. Vol 3,192-196P
[33] 齐鹏，王永学．三维数值波浪水池技术与应用．大连理工大学学报，2003，43(6)：825-830页
[34] 贺五州，袁亨良，耿进柱．摇板式造波机生成的长峰规则波．水力发电学报．2002年第1期，146-152页
[35] 张军，李英浩，金朋寿等．垂直及斜出水流场的二维及三维TR-PIV实验．船舶力学．2005(4)：9-17页
[36] Wagner H. Uber stoss und gleitvorgange an der boerflache von flussigkeiten. ZAMM,1932,12: 193-215P
[37] Zhao R ,Faltinsen O. Water entry of 2D bodies. J. Fluid Mech. 1993, 246: 593-612P
[38] Korobkin A A, Pukhnachov V V. Initial Stage of Water impact. Anu. Rev. of Fluid Mech. 1980,20: 85-159P
[39] Korobkin A A, Pukhnachov V V. Initial asymptotic in contact hydrodynamics ' problem. Proc. 4th Inter. Conf. Numer.Ship Hydradynamics, Washington D. C. ,USA, 1985.138-151P
[40] Pukhnachov V V, Korobkin A A. Initial Asymptotic in problem of blunt body entrance into liquid. Proc. 3rd. Inter. Conf. Numer. Ship Hydradynamics, paris, France, 1981.579-591P
[41] 张志荣，洪方文，张军，徐洁．入水初期流场测量方法．水动力学研究与进展．2001，A辑，第16卷第3期：274-278页
[42] Greeenhow & Moyo. Water entry and exit of horizontal circular cylinders. Phil. Trans. R. Soc. Lond. 1997,551-563P
[43] G.X. Wu, H. Sun, Y. S. He. Numerical simulation and experimental study of water entry of a wedge in free fall motion. Journal of Fluids and Structures. 2004,277-289P
[44] 张军，张志荣，洪方文，赵峰等．楔形体入水初期流场的数值模拟．船舶力学．2003，Vol．7，No．4：29-35P
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