基于有限元法的二维水翼性能预报
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摘要
随着高性能船的迅速发展,水翼被越来越广泛地运用于这一领域。水翼技术的优势在于其有很大的升阻比,比较容易实现升力控制,同时还有一定的消波作用。由于这些突出特点,水翼可用来对船舶进行姿态控制、减阻、消波等。所以进一步深入研究水翼的水动力性能、几何参数优化、水翼—船体干扰效应等仍十分必要。
本文对水翼绕流计算的数值方法进行了综述和讨论,对有限差分法(FDM)、面元法(PANEL METHOD)、涡格法(VLM)、有限元方法(FEM)及它们的应用作了概括和总结。随着计算机的高速发展,有限元方法成为了船舶水动力计算和性能分析研究非常有效的工具,也适用于水翼绕流计算。
本文基于势流理论,利用有限元方法,对二维水翼绕流问题进行了研究。将流体计算区域划分为若干等参四边形单元,通过拉普拉斯方程建立有限元Galerkin积分表达式,以流场速度势为未知量求解有限元总体方程。本文构建了两种不同的计算模式,即控制流线法和速度势分解法,分别对水翼物理量进行分析计算。具体算例采用了NACA翼型的二维翼,通过对不同计算参数的调整和相应的数值计算,讨论了两种方法各自的特点。控制流线法计算过程较为简单,速度势分解法适用范围更广。本文采用了这两种不同算法计算并与试验数据进行了对比,取得了较为一致的结果,说明了本文方法的有效性和可靠性。本文的计算方法和相应的计算程序为以后带自由面粘性流场中的机翼绕流计算打下了一定的基础。
With the rapid development of high performance ships, the hydrofoil technology has been widely used in this area. The technical advantages of hydrofoil are relatively higher lift-drag ratio, flexible lift force controls. And to some extent, hydrofoil can reduce wave making resistance of ship. Because of these outstanding performances, hydrofoil could be used to control ship motion, reduce resistance and absorb wave energy. So it is necessary for researchers to further discuss the hydrodynamic performance of hydrofoil, the interferential effect between hydrofoil and ship hull, optimization of hydrofoil geometric parameters and so on.
The summary and discussion on the numerical computation methods to tackle the flow around hydrofoil is presented in this article. Furthermore, the typical methods and their application are briefly introduced. They are finite difference method, panel method, vortex lattice method and finite element method. With the rapid development of the computer technology, the finite element method becomes an effective tool to the research and numerical computation on hydrodynamic performance of ship and hydrofoil.
Based on the potential theory and the finite element method, the problem of flow around two-dimension hydrofoil is discussed in detail. The fluid region of calculation is divided into many isoparametric quadrilateral elements. According to Laplace equation, the Galerkin integral expression is derived, and the global finite element equations are solved to get the velocity potential distribution of whole flow field. In this article, two different methods are constructed and used to the calculation on the physical parameters of hydrofoils, they are the stream line control method and the velocity potential decomposition method. The 2-D hydrofoil with NACA aerofoil section is employed, and the characters of two different methods are individually discussed based on the various parameters adjustment and numerical computations. The computation process of stream line control method is easier, while the application scope of velocity potential decomposition method is broader. According to the comparison between numerical results and experiment data, perfect agreement is obtained. The validity and reliability of these methods is proven. In this paper, the numerical methods and computation codes pave the way for the further research on hydrodynamic performance of hydrofoil in viscous fluid flow with free surface.
本文对水翼绕流计算的数值方法进行了综述和讨论,对有限差分法(FDM)、面元法(PANEL METHOD)、涡格法(VLM)、有限元方法(FEM)及它们的应用作了概括和总结。随着计算机的高速发展,有限元方法成为了船舶水动力计算和性能分析研究非常有效的工具,也适用于水翼绕流计算。
本文基于势流理论,利用有限元方法,对二维水翼绕流问题进行了研究。将流体计算区域划分为若干等参四边形单元,通过拉普拉斯方程建立有限元Galerkin积分表达式,以流场速度势为未知量求解有限元总体方程。本文构建了两种不同的计算模式,即控制流线法和速度势分解法,分别对水翼物理量进行分析计算。具体算例采用了NACA翼型的二维翼,通过对不同计算参数的调整和相应的数值计算,讨论了两种方法各自的特点。控制流线法计算过程较为简单,速度势分解法适用范围更广。本文采用了这两种不同算法计算并与试验数据进行了对比,取得了较为一致的结果,说明了本文方法的有效性和可靠性。本文的计算方法和相应的计算程序为以后带自由面粘性流场中的机翼绕流计算打下了一定的基础。
With the rapid development of high performance ships, the hydrofoil technology has been widely used in this area. The technical advantages of hydrofoil are relatively higher lift-drag ratio, flexible lift force controls. And to some extent, hydrofoil can reduce wave making resistance of ship. Because of these outstanding performances, hydrofoil could be used to control ship motion, reduce resistance and absorb wave energy. So it is necessary for researchers to further discuss the hydrodynamic performance of hydrofoil, the interferential effect between hydrofoil and ship hull, optimization of hydrofoil geometric parameters and so on.
The summary and discussion on the numerical computation methods to tackle the flow around hydrofoil is presented in this article. Furthermore, the typical methods and their application are briefly introduced. They are finite difference method, panel method, vortex lattice method and finite element method. With the rapid development of the computer technology, the finite element method becomes an effective tool to the research and numerical computation on hydrodynamic performance of ship and hydrofoil.
Based on the potential theory and the finite element method, the problem of flow around two-dimension hydrofoil is discussed in detail. The fluid region of calculation is divided into many isoparametric quadrilateral elements. According to Laplace equation, the Galerkin integral expression is derived, and the global finite element equations are solved to get the velocity potential distribution of whole flow field. In this article, two different methods are constructed and used to the calculation on the physical parameters of hydrofoils, they are the stream line control method and the velocity potential decomposition method. The 2-D hydrofoil with NACA aerofoil section is employed, and the characters of two different methods are individually discussed based on the various parameters adjustment and numerical computations. The computation process of stream line control method is easier, while the application scope of velocity potential decomposition method is broader. According to the comparison between numerical results and experiment data, perfect agreement is obtained. The validity and reliability of these methods is proven. In this paper, the numerical methods and computation codes pave the way for the further research on hydrodynamic performance of hydrofoil in viscous fluid flow with free surface.
引文
[1]王献孚,韩久瑞.机翼理论.北京:人民交通出版社,1987.
[2]王献孚.船用翼理论.北京:国防工业出版社,1998.
[3]赵连恩.高性能船舶水动力原理与设计.哈尔滨:哈尔滨工程大学出版社,2001.
[4]卢继汉.水翼艇.北京:战士出版社,1983.
[5]张文治.水翼船设计.北京:人民交通出版社,1964.
[6]赵永甫,梁军,韩涛.走向21世纪的高性能船.北京:海潮出版社,2000.
[7]李百齐.21世纪海洋高性能船.北京:国防工业出版社,2001.
[8] Eppler R,Somers D M.A Computer Program for the Design and Analysis Low-Speed Airfoils.NASA TM 80210,1980.
[9] Mandel P.Some hydrodynamics aspects of appendage design,Trans.SNAME,1953,vol 61:464～515.
[10] Patankar SV.Numerical Heat Transfer and Fluid Flow.Washington,Hemisphere,1980.
[11] Noh W F. CEL.A Time-Dependent Two-Space-Dimensional Coupled Eulerian-Lagrangian Code. Methods in Computational Physics 3.New York: A Cadem Icpress, 1964.
[12]李子如.用面元法预报船体兴波阻力.[硕士学位论文].武汉:武汉理工大学交通学院,2006.
[13]喻红霞.鱼形舵定常升力的数值模拟与计算研究.[硕士学位论文].哈尔滨:哈尔滨工程大学,2003.
[14]朱标,宋文萍,袁昌盛.扑翼升力特性的非定常涡格法计算研究.航空计算技术,2005,35(2):13～16.
[15] O Pironneam.Finite Element Methods for Fluid.Chichester, New York, Paris: Wily Massn,1989.
[16] S C Brenner, L R Scott.The Mathematical Theory of Finite Element Methods.北京:世界图书出版公司.
[17] C.Taylor, T.G.Hughes. Finite Element Program of the Navier-Stokes Equations.Swansea, U.K: Pinerdige Press Limited,1981.
[18]章本照,印建安,张宏基.流体力学数值方法.北京:机械工业出版社,2003.
[19] Chorin AJ. Numerical solution of the Navier-Stokes equation. Math. Comput.,1968, 22(104): 745～762.
[20] Ramaswamy B,Kawahara M.Lagrangian finite element analysis applied to viscous free surface fluid flow.Int.j.numer.methods fluids, 1987, 7: 953～984.
[21] Hayashi M, Hatanaka K, Kawahara M. Lagrangian finite element method for free surface Navier-Stokes flow using fractional step methods.Int.j.numer.methods fluids, 1991, 13: 805～840.
[22] Okamoto T, Kaawahr M. Two-dimensional sloshing analysis by Lagrangian finite element method. Int.j.numer.methods fluids, 1990, 11: 453～477.
[23] Hayashi M, Hatanaka K, Kawahar M.Lagrangian finite element method for free surface Navier-Stokes flow using fractional step methods. Int.j.numer.methods fluids, 1991, 13: 805～840.
[24] Tian M, Zhu YNonlinear water waves in Lagrangian coordinates: shallow fluids.Journal of Hydrodynamics, Ser.B, 1996, 8(4): 25～34.
[25] Ushijima S.Three-dimensional arbitrary Lagangian-Eulerian numerical prediction method for non-linear free surface oscillation.Int.j.numer.methods fluids, 1998, 26: 605～623.
[26] Ren G, Utnes T.A finite element solution of the time-dependent incompressible Navier-Stokes equations using a modified velocity correction method.Int.j.numer.methods fluids, 1993, 17: 349～364.
[27] Fan J, Qu DB, Zhang ZX.A finite element and boundary element method of numerical simulation of two dimensional and two phase flow.Journal of Hydrodynamics, 1994, 9(4): 40～47.
[28] Nakayama T, Mori M.An Eulerian finite element method for time-dependent free surface problems in hydrodynamics.Int.j.numer.methods fluids, 1996, 22: 175～194.
[29] Ushijima S. Three-dimensional arbitrary Lagangian-Eulerian numerical prediction method for non-linear free surface oscillation.Int.j.numer.methods fluids, 1998, 26: 605～623.
[30] Hughes TJR, Liu WK, Zimmerman T. Lagrangian-Eulerian finite element formulation for incompressible viscous flow,Comput.Mech.Appl.Mech.Eng.,1981, 29: 329～349.
[31] Ushijima S.Three-dimensional arbitrary Lagangian-Eulerian numerical prediction method for non-linear free surface oscillation.Int.j.numer.methods fluids, 1998, 26: 605～623.
[32] Nomura T. ALE finite element computations of fluid-Structure interaction problems.Comput.Meths.Appl.Mech.Engrg, 1994, 112: 291～308.
[33] Liu WK, Ma DC.Computer implementation aspects for fluid-structure interaction problems.Comput.Meths.Appl.Mech.Engrg, 1982, 31: 129～148.
[34] Nomura T, Hughes TJR.An arbitrary Lagrangian-Eulerian finite element method for interaction of fluid and a rigid body.Comput.Meths.Appl.Mech.Engrg., 1992, 95: 115～138.
[35]张雄,陆明万,王建军.任意拉格朗日—欧拉描述法研究进展.计算力学学报,1997,14(1):91～102.
[36]刘希云,赵润祥.流体力学中的有限元与边界元方法.上海:上海交通大学出版社,1993.
[37] T.J.Chung.流体动力学的有限元分析.张二骏,龚崇准,王木兰,等.北京:电力工业出版社,1980.
[38]章本照.流体力学中的有限元方法.北京:机械工业出版社,1986.
[39]王焕定,焦兆平.有限单元法基础.北京:高等教育出版社,2002.
[40]张涤明.计算流体力学.广州:中山大学出版社,1991.
[41]刘树红,吴玉林,周雪漪,陈庆光.应用流体力学.北京:清华大学出版社,2006.
[42]傅德薰,马延文.计算流体力学.北京:高等教育出版社,2002.
[43]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.
[44] J N Newman.船舶流体动力学.周国树.北京:人民交通出版社,1986.
[45]刘应中,王献孚,周树信,等.计算船舶流体力学.上海:上海交通大学出版社,1992.
[46]董曾南,章梓雄.非粘性流体力学.北京:清华大学出版社,2003.
[47]宋红军,王肇,尹协振.二维翼型非定常运动数值模拟.水动力学研究与进展,2004,19:896-903.
[48]叶建,林国华,邹正平,等.低雷诺数下二维翼型绕流的流场特性分析.航空动力学报,2003,18(1):38～45.
[49]韩忠华,乔志德,熊俊涛,何光洪.Navier-Stokes方程预处理方法及其对翼型绕流数值模拟的应用.西北工业大学学报,2006,24(3):275～280.
[50]王志东,汪德.粘流场数值模拟关键技术研究进展.华东船舶工业学院学报(自然科学版),2002,16(5):1～8.
[51]张新龙.二维粘性流场中自由面波动的有限元算法及数值波浪水池的建立.[硕士学位论文].武汉:华中科技大学.2000.
[52]俞铭华,吴剑国,王林.有限元法与C程序设计.北京:科学出版社,1998.
[53]王载新,曾大亮,杨有安,等.程序设计基础—C语言.北京:人民邮电出版社,2000.
[54] John A Ekaterinaris,Max F P latzer.Computational prediction of airfoil dynamic stall.Prog.Aerospace Sci,1997,33:759～846.
[55] LU X Y,YANG J M and YIN X Z.Propulsive performance and vortex shedding of a foil in flapping flight.Acta Mechanica,2003,165:189～206.
[2]王献孚.船用翼理论.北京:国防工业出版社,1998.
[3]赵连恩.高性能船舶水动力原理与设计.哈尔滨:哈尔滨工程大学出版社,2001.
[4]卢继汉.水翼艇.北京:战士出版社,1983.
[5]张文治.水翼船设计.北京:人民交通出版社,1964.
[6]赵永甫,梁军,韩涛.走向21世纪的高性能船.北京:海潮出版社,2000.
[7]李百齐.21世纪海洋高性能船.北京:国防工业出版社,2001.
[8] Eppler R,Somers D M.A Computer Program for the Design and Analysis Low-Speed Airfoils.NASA TM 80210,1980.
[9] Mandel P.Some hydrodynamics aspects of appendage design,Trans.SNAME,1953,vol 61:464～515.
[10] Patankar SV.Numerical Heat Transfer and Fluid Flow.Washington,Hemisphere,1980.
[11] Noh W F. CEL.A Time-Dependent Two-Space-Dimensional Coupled Eulerian-Lagrangian Code. Methods in Computational Physics 3.New York: A Cadem Icpress, 1964.
[12]李子如.用面元法预报船体兴波阻力.[硕士学位论文].武汉:武汉理工大学交通学院,2006.
[13]喻红霞.鱼形舵定常升力的数值模拟与计算研究.[硕士学位论文].哈尔滨:哈尔滨工程大学,2003.
[14]朱标,宋文萍,袁昌盛.扑翼升力特性的非定常涡格法计算研究.航空计算技术,2005,35(2):13～16.
[15] O Pironneam.Finite Element Methods for Fluid.Chichester, New York, Paris: Wily Massn,1989.
[16] S C Brenner, L R Scott.The Mathematical Theory of Finite Element Methods.北京:世界图书出版公司.
[17] C.Taylor, T.G.Hughes. Finite Element Program of the Navier-Stokes Equations.Swansea, U.K: Pinerdige Press Limited,1981.
[18]章本照,印建安,张宏基.流体力学数值方法.北京:机械工业出版社,2003.
[19] Chorin AJ. Numerical solution of the Navier-Stokes equation. Math. Comput.,1968, 22(104): 745～762.
[20] Ramaswamy B,Kawahara M.Lagrangian finite element analysis applied to viscous free surface fluid flow.Int.j.numer.methods fluids, 1987, 7: 953～984.
[21] Hayashi M, Hatanaka K, Kawahara M. Lagrangian finite element method for free surface Navier-Stokes flow using fractional step methods.Int.j.numer.methods fluids, 1991, 13: 805～840.
[22] Okamoto T, Kaawahr M. Two-dimensional sloshing analysis by Lagrangian finite element method. Int.j.numer.methods fluids, 1990, 11: 453～477.
[23] Hayashi M, Hatanaka K, Kawahar M.Lagrangian finite element method for free surface Navier-Stokes flow using fractional step methods. Int.j.numer.methods fluids, 1991, 13: 805～840.
[24] Tian M, Zhu YNonlinear water waves in Lagrangian coordinates: shallow fluids.Journal of Hydrodynamics, Ser.B, 1996, 8(4): 25～34.
[25] Ushijima S.Three-dimensional arbitrary Lagangian-Eulerian numerical prediction method for non-linear free surface oscillation.Int.j.numer.methods fluids, 1998, 26: 605～623.
[26] Ren G, Utnes T.A finite element solution of the time-dependent incompressible Navier-Stokes equations using a modified velocity correction method.Int.j.numer.methods fluids, 1993, 17: 349～364.
[27] Fan J, Qu DB, Zhang ZX.A finite element and boundary element method of numerical simulation of two dimensional and two phase flow.Journal of Hydrodynamics, 1994, 9(4): 40～47.
[28] Nakayama T, Mori M.An Eulerian finite element method for time-dependent free surface problems in hydrodynamics.Int.j.numer.methods fluids, 1996, 22: 175～194.
[29] Ushijima S. Three-dimensional arbitrary Lagangian-Eulerian numerical prediction method for non-linear free surface oscillation.Int.j.numer.methods fluids, 1998, 26: 605～623.
[30] Hughes TJR, Liu WK, Zimmerman T. Lagrangian-Eulerian finite element formulation for incompressible viscous flow,Comput.Mech.Appl.Mech.Eng.,1981, 29: 329～349.
[31] Ushijima S.Three-dimensional arbitrary Lagangian-Eulerian numerical prediction method for non-linear free surface oscillation.Int.j.numer.methods fluids, 1998, 26: 605～623.
[32] Nomura T. ALE finite element computations of fluid-Structure interaction problems.Comput.Meths.Appl.Mech.Engrg, 1994, 112: 291～308.
[33] Liu WK, Ma DC.Computer implementation aspects for fluid-structure interaction problems.Comput.Meths.Appl.Mech.Engrg, 1982, 31: 129～148.
[34] Nomura T, Hughes TJR.An arbitrary Lagrangian-Eulerian finite element method for interaction of fluid and a rigid body.Comput.Meths.Appl.Mech.Engrg., 1992, 95: 115～138.
[35]张雄,陆明万,王建军.任意拉格朗日—欧拉描述法研究进展.计算力学学报,1997,14(1):91～102.
[36]刘希云,赵润祥.流体力学中的有限元与边界元方法.上海:上海交通大学出版社,1993.
[37] T.J.Chung.流体动力学的有限元分析.张二骏,龚崇准,王木兰,等.北京:电力工业出版社,1980.
[38]章本照.流体力学中的有限元方法.北京:机械工业出版社,1986.
[39]王焕定,焦兆平.有限单元法基础.北京:高等教育出版社,2002.
[40]张涤明.计算流体力学.广州:中山大学出版社,1991.
[41]刘树红,吴玉林,周雪漪,陈庆光.应用流体力学.北京:清华大学出版社,2006.
[42]傅德薰,马延文.计算流体力学.北京:高等教育出版社,2002.
[43]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.
[44] J N Newman.船舶流体动力学.周国树.北京:人民交通出版社,1986.
[45]刘应中,王献孚,周树信,等.计算船舶流体力学.上海:上海交通大学出版社,1992.
[46]董曾南,章梓雄.非粘性流体力学.北京:清华大学出版社,2003.
[47]宋红军,王肇,尹协振.二维翼型非定常运动数值模拟.水动力学研究与进展,2004,19:896-903.
[48]叶建,林国华,邹正平,等.低雷诺数下二维翼型绕流的流场特性分析.航空动力学报,2003,18(1):38～45.
[49]韩忠华,乔志德,熊俊涛,何光洪.Navier-Stokes方程预处理方法及其对翼型绕流数值模拟的应用.西北工业大学学报,2006,24(3):275～280.
[50]王志东,汪德.粘流场数值模拟关键技术研究进展.华东船舶工业学院学报(自然科学版),2002,16(5):1～8.
[51]张新龙.二维粘性流场中自由面波动的有限元算法及数值波浪水池的建立.[硕士学位论文].武汉:华中科技大学.2000.
[52]俞铭华,吴剑国,王林.有限元法与C程序设计.北京:科学出版社,1998.
[53]王载新,曾大亮,杨有安,等.程序设计基础—C语言.北京:人民邮电出版社,2000.
[54] John A Ekaterinaris,Max F P latzer.Computational prediction of airfoil dynamic stall.Prog.Aerospace Sci,1997,33:759～846.
[55] LU X Y,YANG J M and YIN X Z.Propulsive performance and vortex shedding of a foil in flapping flight.Acta Mechanica,2003,165:189～206.