无变形网格下运动参考系求解平动流固耦合问题
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摘要
为模拟平动涡激振动,采用一种无变形网格的计算方法。通过运动参考系模拟整个求解域的运动,结合非结构网格下高精度算法,在NS方程中引入运动参考系引起的对流项及采用新的边界处理方式,通过构造合理的计算求解域,对低雷诺数下(Re=200)圆柱涡激振动进行了模拟,得到了圆柱涡激振动振幅以及详细流场结构,与实验结果和数值结果相比都得到了很好的一致性。并对不同阻尼比、频率比等参数进行研究,详细对比了不同振幅下尾流结构特征。结果证明了该计算方法是可行的、准确的。
A new approach using fixed gird was adopted to simulate the translational motion of solid walls.Combining with a high-accuracy and high-stability algorithm in the condition of non-structured mesh,a solution over entire computational domain was achieved by use of the moving reference frame,which must be taken to consider the convection term of N-S equation. Meanwhile,the boundary conditions of the solid wall were specially treated with a new method. A reasonable computational domain was established to simulate the translational motion of a circular cylinder in the fluid with low Reynolds number of 200 and the vibration amplitude of the cylinder and the detailed flow field structure were obtained. Changing the ratio of the cylinder natural frequency to its wake vortex shedding frequency and the structural damping ratio,the vortex induced vibration amplitudes and the wake flow structures in the condition of different vibration amplitudes were compared and analysed. The results show that the computational method provided tends to be feasible and accurate.
A new approach using fixed gird was adopted to simulate the translational motion of solid walls.Combining with a high-accuracy and high-stability algorithm in the condition of non-structured mesh,a solution over entire computational domain was achieved by use of the moving reference frame,which must be taken to consider the convection term of N-S equation. Meanwhile,the boundary conditions of the solid wall were specially treated with a new method. A reasonable computational domain was established to simulate the translational motion of a circular cylinder in the fluid with low Reynolds number of 200 and the vibration amplitude of the cylinder and the detailed flow field structure were obtained. Changing the ratio of the cylinder natural frequency to its wake vortex shedding frequency and the structural damping ratio,the vortex induced vibration amplitudes and the wake flow structures in the condition of different vibration amplitudes were compared and analysed. The results show that the computational method provided tends to be feasible and accurate.
引文
[1]KOOPMANN G.The vortex wakes of vibrating cylinders at low reynolds numbers[J].Journal of Fluid Mechanics,1967,28(3):501-512.
[2]GRIFFIN O,KOOPMANN G.The vortex-excited lift and reaction forces on resonantly vibrating cylinders[J].Journal of Sound and Vibration,1977,54(3):435-448.
[3]GOVARDHAN R,WILLIAMSON C.Modes of vortex formation and frequency response of a freely vibrating cylinder[J].Journal of Fluid Mechanics,2000,420(1):85-130.
[4]RYAN K,THOMPSON M,HOURIGAN K.Variation in the critical mass ratio of a freely oscillating cylinder as a function of reynolds number[J].Physics of Fluids,2005,17(3):38-106.
[5]MORSE T,WILLIAMSON C.The effect of reynolds number on the critical mass phenomenon in vortex-induced vibration[J].Physics of Fluids,2009,21(4):45-105.
[6]徐枫,欧进萍.低雷诺数下弹性圆柱体涡激振动及影响参数分析[J].计算力学学报,2009,54(5):613-620.XU Feng,OU Jinping.Analysis of vortex-induced vibration of an elastic cylinder and influence parameters at low Reynolds number[J].Chinese Journal of Computational Mechanics,2009,54(5):613-620.
[7]曹淑刚,黄维平,顾恩凯.考虑流固耦合的弹性圆柱体涡激振动研究[J].振动与冲击,2015,34(1):58-63.CAO Shugang,HUANG Weiping,GU Enkai.Study on vortexinduced vibration of an elastic cylinder considering fluidstructure interaction[J].Journal of Vibration and Sound,2015,34(1):58-63.
[8]陈文礼,李惠.基于RANS的圆柱风致涡激振动的CFD数值模拟[J].西安建筑科技大学学报(自然科学版),2006,38(4):509-514.CHEN Wenli,LI Hui.CFD numerical simulation of vortexinduced vibration of a circular cylinder based on a RANS method[J].Journal of Xi’an University of Architecture&Technology,2006,38(4):509-514.
[9]BAHMANI M,AKBARI M.Flow induced vibration characteristics of a cylinder in cross flwo at low-reynolds numbers[C]∥BBAA VI International Colloquium on:Bluff Bodies Aerodynamics and Applications.Milano,Italy,2008:1-5.
[10]方平治,顾明.圆柱两自由度涡激振动的数值模拟研究[J].同济大学学报(自然科学版),2008,36(3):295-299.FANG Pingzhi,GU Ming.Numerical simulation for vortexinduced vibration of circular cylinder with two degree of feedoms[J].Journal of Tongji University(Natural Science),2008,36(3):295-299.
[11]ZHOU C,SO R,LAM K.Vortex-induced vibrations of an elastic circular cylinder[J].Journal of Fluids and Structures,1999,13(2):165-189.
[12]曹丰产,项海帆.圆柱非定常绕流及涡致振动的数值计算[J].水动力学研究与进展,2001,16(1):111-118.CAO Fengchan,XIANG Haifan.Calculation of unsteady flow around circular cylinder and vortex-induced vibration[J].Journal of Hydrodynamics,2001,16(1):111-118.
[13]郭晓玲,唐国强,刘名名,等.低雷诺数下串联双圆柱涡激振动机理的数值研究[J].振动与冲击,2014,33(4):60-69.GUO Xiaoling,TANG Guoqiang,LIU Mingming,et al.Numerical investigation on vortex-induced vibration of twin tandem circular cylinders under low Reynolds number[J].Journal of Vibration and Sound,2014,33(4):60-69.
[14]罗竹梅,张立翔.耦合四圆柱涡激振动的力特性及水动能获取分析[J].振动与冲击,2015,34(17):25-29.LUO Zhumei,ZHANG Lixiang.Force characteristics and hydrokinetic energy harvesting for VIV of four coupling-linked cylinders[J].Journal of Vibration and Sound,2015,34(17):25-29.
[15]战庆亮,周志勇,葛耀君.Re=3 900圆柱绕流的三维大涡模拟[J].哈尔滨工业大学学报,2015,47(12):75-79.ZHAN Qingliang,ZHOU Zhiyong,GE Yaojun.3-Dimensional large eddy simulation of circular cylinder at Re=3 900[J].Journal of Harbin Institute of Technology,2015,47(12):75-79.
[16]李松年.非线性连续统力学[M].北京:北京航空学院出版社,1987.
[17]WERNER H,WENGLE H.Large-eddy simulation of turbulent flow over and around a cube in a plate channel[M].Berlin:Springer,1993:155-168.
[18]DAVIDSON L.A pressure correction method for unstructured meshes with arbitrary control volumes[J].International Journal for Numerical Methods in Fluids,1996,22(4):265-281.
[19]姜华,席光.对流项二次迎风插值格式在非结构化网格中的应用[J].西安交通大学学报,2006,11(1):1246-1251.JIANG Hua,XI Guang.Application of quadratic upwind interpolation of convective kinematics scheme in unstructured grids to solve navier-stokes equations[J].Journal of Xi’an Jiaotong University,2006,11(1):1246-1251.
[20]VENKATAKRISHNAN V.Convergence to steady state solutions of the euler equations on unstructured grids with limiters[J].Journal of Computational Physics,1995,118(1):120-130.
[21]ISSA R I.Solution of the implicitly discretised fluid flow equations by operator-splitting[J].Journal of Computational Physics,1986,62(1):40-65.
[22]GOVARDHAN R,WILLIAMSON C.Defining the‘modified griffin plot’in vortex-induced vibration:revealing the effect of reynolds number using controlled damping[J].Journal of Fluid Mechanics,2006,561(1):147-180.
[23]SKOP R A,BALASUBRAMANIAN S.A new twist on an old model for vortex-excited vibrations[J].Journal of Fluids&Structures,1997,11(4):395-412.
[2]GRIFFIN O,KOOPMANN G.The vortex-excited lift and reaction forces on resonantly vibrating cylinders[J].Journal of Sound and Vibration,1977,54(3):435-448.
[3]GOVARDHAN R,WILLIAMSON C.Modes of vortex formation and frequency response of a freely vibrating cylinder[J].Journal of Fluid Mechanics,2000,420(1):85-130.
[4]RYAN K,THOMPSON M,HOURIGAN K.Variation in the critical mass ratio of a freely oscillating cylinder as a function of reynolds number[J].Physics of Fluids,2005,17(3):38-106.
[5]MORSE T,WILLIAMSON C.The effect of reynolds number on the critical mass phenomenon in vortex-induced vibration[J].Physics of Fluids,2009,21(4):45-105.
[6]徐枫,欧进萍.低雷诺数下弹性圆柱体涡激振动及影响参数分析[J].计算力学学报,2009,54(5):613-620.XU Feng,OU Jinping.Analysis of vortex-induced vibration of an elastic cylinder and influence parameters at low Reynolds number[J].Chinese Journal of Computational Mechanics,2009,54(5):613-620.
[7]曹淑刚,黄维平,顾恩凯.考虑流固耦合的弹性圆柱体涡激振动研究[J].振动与冲击,2015,34(1):58-63.CAO Shugang,HUANG Weiping,GU Enkai.Study on vortexinduced vibration of an elastic cylinder considering fluidstructure interaction[J].Journal of Vibration and Sound,2015,34(1):58-63.
[8]陈文礼,李惠.基于RANS的圆柱风致涡激振动的CFD数值模拟[J].西安建筑科技大学学报(自然科学版),2006,38(4):509-514.CHEN Wenli,LI Hui.CFD numerical simulation of vortexinduced vibration of a circular cylinder based on a RANS method[J].Journal of Xi’an University of Architecture&Technology,2006,38(4):509-514.
[9]BAHMANI M,AKBARI M.Flow induced vibration characteristics of a cylinder in cross flwo at low-reynolds numbers[C]∥BBAA VI International Colloquium on:Bluff Bodies Aerodynamics and Applications.Milano,Italy,2008:1-5.
[10]方平治,顾明.圆柱两自由度涡激振动的数值模拟研究[J].同济大学学报(自然科学版),2008,36(3):295-299.FANG Pingzhi,GU Ming.Numerical simulation for vortexinduced vibration of circular cylinder with two degree of feedoms[J].Journal of Tongji University(Natural Science),2008,36(3):295-299.
[11]ZHOU C,SO R,LAM K.Vortex-induced vibrations of an elastic circular cylinder[J].Journal of Fluids and Structures,1999,13(2):165-189.
[12]曹丰产,项海帆.圆柱非定常绕流及涡致振动的数值计算[J].水动力学研究与进展,2001,16(1):111-118.CAO Fengchan,XIANG Haifan.Calculation of unsteady flow around circular cylinder and vortex-induced vibration[J].Journal of Hydrodynamics,2001,16(1):111-118.
[13]郭晓玲,唐国强,刘名名,等.低雷诺数下串联双圆柱涡激振动机理的数值研究[J].振动与冲击,2014,33(4):60-69.GUO Xiaoling,TANG Guoqiang,LIU Mingming,et al.Numerical investigation on vortex-induced vibration of twin tandem circular cylinders under low Reynolds number[J].Journal of Vibration and Sound,2014,33(4):60-69.
[14]罗竹梅,张立翔.耦合四圆柱涡激振动的力特性及水动能获取分析[J].振动与冲击,2015,34(17):25-29.LUO Zhumei,ZHANG Lixiang.Force characteristics and hydrokinetic energy harvesting for VIV of four coupling-linked cylinders[J].Journal of Vibration and Sound,2015,34(17):25-29.
[15]战庆亮,周志勇,葛耀君.Re=3 900圆柱绕流的三维大涡模拟[J].哈尔滨工业大学学报,2015,47(12):75-79.ZHAN Qingliang,ZHOU Zhiyong,GE Yaojun.3-Dimensional large eddy simulation of circular cylinder at Re=3 900[J].Journal of Harbin Institute of Technology,2015,47(12):75-79.
[16]李松年.非线性连续统力学[M].北京:北京航空学院出版社,1987.
[17]WERNER H,WENGLE H.Large-eddy simulation of turbulent flow over and around a cube in a plate channel[M].Berlin:Springer,1993:155-168.
[18]DAVIDSON L.A pressure correction method for unstructured meshes with arbitrary control volumes[J].International Journal for Numerical Methods in Fluids,1996,22(4):265-281.
[19]姜华,席光.对流项二次迎风插值格式在非结构化网格中的应用[J].西安交通大学学报,2006,11(1):1246-1251.JIANG Hua,XI Guang.Application of quadratic upwind interpolation of convective kinematics scheme in unstructured grids to solve navier-stokes equations[J].Journal of Xi’an Jiaotong University,2006,11(1):1246-1251.
[20]VENKATAKRISHNAN V.Convergence to steady state solutions of the euler equations on unstructured grids with limiters[J].Journal of Computational Physics,1995,118(1):120-130.
[21]ISSA R I.Solution of the implicitly discretised fluid flow equations by operator-splitting[J].Journal of Computational Physics,1986,62(1):40-65.
[22]GOVARDHAN R,WILLIAMSON C.Defining the‘modified griffin plot’in vortex-induced vibration:revealing the effect of reynolds number using controlled damping[J].Journal of Fluid Mechanics,2006,561(1):147-180.
[23]SKOP R A,BALASUBRAMANIAN S.A new twist on an old model for vortex-excited vibrations[J].Journal of Fluids&Structures,1997,11(4):395-412.