平板自由下落的数值模拟
|
摘要
采用动网格技术,通过耦合求解N-S方程和运动方程的方法进行数值模拟,研究二维平板的自由下落运动。选取了不同质量分布的二维平板作为研究对象,研究初始角度、转动惯量和质心位置等因素对其自由下落运动轨迹的影响,以及其中的流体力学和动力学机理。数值模拟结果显示了二维平板的自由下落运动,除了摆动运动、翻滚运动和定常下落等经典运动轨迹外,随着质心位置的偏移还会衍生出非对称摆动、摆翻运动等特殊运动轨迹。研究结果表明:无量纲转动惯量和质心位置是决定二维平板自由下落运动方式的重要参数,但两者对下落运动影响的物理机制存在差异。这些结果对相关物理问题,特别是低雷诺数流体力学和动力学研究,具有一定的指导意义。
In this paper,2-Dimension freely falling plates with different mass distributions are simulated by numerically solving the equations of motion coupling with the Navier-Stokes equations.With moving mesh,the motions related to different parameters are studied.The trajectories are identified and the unsteady dynamics are given by considering different dimensionless moments of inertia,and the initial falling angle and centroid positions.The results show that,except the three known classical trajectories:fluttering,tumbling,steady descent,we also observe two new motions.These motions are asymmetrical-fluttering and fluttertumbling trajectories.They are caused by the centroid position deviating from the center of the plate and the dimensionless moment of inertia in the range of 0～0.95.These motions turn to the tumbling when the centroid position is beyond 0.13 L.It indicates that the dimensionless moment of inertia and centroid position are important parameters in freely falling plates,but the physical mechanisms are different in falling motions.The present results can provide academic reference in study of low Reynolds number problems.
In this paper,2-Dimension freely falling plates with different mass distributions are simulated by numerically solving the equations of motion coupling with the Navier-Stokes equations.With moving mesh,the motions related to different parameters are studied.The trajectories are identified and the unsteady dynamics are given by considering different dimensionless moments of inertia,and the initial falling angle and centroid positions.The results show that,except the three known classical trajectories:fluttering,tumbling,steady descent,we also observe two new motions.These motions are asymmetrical-fluttering and fluttertumbling trajectories.They are caused by the centroid position deviating from the center of the plate and the dimensionless moment of inertia in the range of 0～0.95.These motions turn to the tumbling when the centroid position is beyond 0.13 L.It indicates that the dimensionless moment of inertia and centroid position are important parameters in freely falling plates,but the physical mechanisms are different in falling motions.The present results can provide academic reference in study of low Reynolds number problems.
引文
[1] BELMONTE A,EISENBERG H,MOSES E.From flutter to tumble:inertial drag and froude similarity in falling paper[J].Physical Review Letters,1998,81(2):345-348.
[2] ANDERSEN A,PESAVENTO U, WANG Z J.Unsteady aerodynamics of fluttering and tumbling plates[J].J Fluid Mech,2005,541:65-90.
[3] PESAVENTO U,WANG Z J.Falling paper:Navier-Stokes solutions,model of fluid forces,and center of mass elevation[J].Physical Review Letters,2004,93(14):4501.
[4] WAN H,DONG H,LIANG Z.Vortex formation of freely falling plates[R].AIAA 2012-1079,2012.
[5] TIAN R,SHU F.Experimental study of the fluid and structure interaction for gravity driven falling plates[C]//Aps Division of Fluid Dynamics Meeting,2014.
[6] TIAN R.Experimental and theoretical study of fluid-structure interactions in plunging hydrofoils and gravity-driven falling plates[D].New Mexico State University,2015:77-85.
[7] KUBOTAL Y,MOCHIZUKI O.Numerical investigation of aerodynamic characteristics by a rotating thin plate[J].World Journal of Mechanics,2015,(5):42-47.
[8] HU R,WANG L.Motion transitions of falling plates via quasisteady aerodynamics[J].Physical Review E,2014,90:013020.
[9] ZHONG H J,LEE C B.The wake of falling disks at low Reynolds numbers[J].Acta Mech Sin,2012,28(2):367-371.
[10]ZHONG H J,YCHEN S,LEEC B.Experimental study of freely falling thin disks:transition from planar zigzag to spiral[J].Physics of Fluids,2011,23(1):011702.
[11]周琪.自由下落平板非定常致力机理研究[D].上海交通大学,2012.ZHOU Q.The study of unsteady aerodynamics of freely falling plates[D].Shanghai Jiao Tong University,2012.
[12]孙茂.动物飞行的空气动力学[J].空气动力学学报,2018,36(1):122-128.SUN M.Aerodynamics of animal flight[J].Acta Aerodynamica Sinica,2018,36(1):122-128.(in Chinese)
[13]SUN M,TANG J.Unsteady aerodynamic force generation by a model fruit fly wing in flapping motion[J].The Journal of Experimental Biology,2002,205:55-70.
[14]ROGERS S E,KWAK D.Upwind differencing scheme for the time-accurate incompressible Navier-Stokes equations[J].AIAA Journal,1990,28(2):253-262.
[15]ROGERS S E,KWAK D,KIRIS C.Numerical solution of the incompressible Navier-Stokes equations for steady-state and time-dependent problems[C]//AIAA 27th Aerospace Sciences Meeting.Washington,D.C:American Institute of Aeronautics and Astronautics,1989:89-0463.
[16]LIANG B,SUN M.Nonlinear flight dynamics and stability of hovering model insects[J].J R Soc Interface,2013,10:20130269.
[2] ANDERSEN A,PESAVENTO U, WANG Z J.Unsteady aerodynamics of fluttering and tumbling plates[J].J Fluid Mech,2005,541:65-90.
[3] PESAVENTO U,WANG Z J.Falling paper:Navier-Stokes solutions,model of fluid forces,and center of mass elevation[J].Physical Review Letters,2004,93(14):4501.
[4] WAN H,DONG H,LIANG Z.Vortex formation of freely falling plates[R].AIAA 2012-1079,2012.
[5] TIAN R,SHU F.Experimental study of the fluid and structure interaction for gravity driven falling plates[C]//Aps Division of Fluid Dynamics Meeting,2014.
[6] TIAN R.Experimental and theoretical study of fluid-structure interactions in plunging hydrofoils and gravity-driven falling plates[D].New Mexico State University,2015:77-85.
[7] KUBOTAL Y,MOCHIZUKI O.Numerical investigation of aerodynamic characteristics by a rotating thin plate[J].World Journal of Mechanics,2015,(5):42-47.
[8] HU R,WANG L.Motion transitions of falling plates via quasisteady aerodynamics[J].Physical Review E,2014,90:013020.
[9] ZHONG H J,LEE C B.The wake of falling disks at low Reynolds numbers[J].Acta Mech Sin,2012,28(2):367-371.
[10]ZHONG H J,YCHEN S,LEEC B.Experimental study of freely falling thin disks:transition from planar zigzag to spiral[J].Physics of Fluids,2011,23(1):011702.
[11]周琪.自由下落平板非定常致力机理研究[D].上海交通大学,2012.ZHOU Q.The study of unsteady aerodynamics of freely falling plates[D].Shanghai Jiao Tong University,2012.
[12]孙茂.动物飞行的空气动力学[J].空气动力学学报,2018,36(1):122-128.SUN M.Aerodynamics of animal flight[J].Acta Aerodynamica Sinica,2018,36(1):122-128.(in Chinese)
[13]SUN M,TANG J.Unsteady aerodynamic force generation by a model fruit fly wing in flapping motion[J].The Journal of Experimental Biology,2002,205:55-70.
[14]ROGERS S E,KWAK D.Upwind differencing scheme for the time-accurate incompressible Navier-Stokes equations[J].AIAA Journal,1990,28(2):253-262.
[15]ROGERS S E,KWAK D,KIRIS C.Numerical solution of the incompressible Navier-Stokes equations for steady-state and time-dependent problems[C]//AIAA 27th Aerospace Sciences Meeting.Washington,D.C:American Institute of Aeronautics and Astronautics,1989:89-0463.
[16]LIANG B,SUN M.Nonlinear flight dynamics and stability of hovering model insects[J].J R Soc Interface,2013,10:20130269.