半圆形管道中的脉冲流动
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摘要
在半圆形管道中,周期振荡的压力梯度驱动不可压粘性牛顿流体的流动,运用分离变量法求解了半圆形管道内N-S(Navier-Stokes)方程,得到了速度解析解.在此基础上,我们研究了无量纲压强梯度有关的参数A和震荡雷诺数Re对速度剖面f的影响.结果说明速度振幅随参数A减少而减少,随Re减少而增加,而且出现脉动流速度的"环形效应".
A periodic oscillatory pressure-driven flow of viscous incompressible Newtonian fluid is studied.The Navier-Stokes equation is solved by using the method of separation of variables. Based on this,the effects of the nondimensional parameters,such as parameter A and Reynolds number Re regarding pressure gradient,on the velocity are investigated. The results show that the velocity amplitude decreases with A and increases with the decrease in Re. In addition, " toroidal effect" of oscillatory velocity is observed.
A periodic oscillatory pressure-driven flow of viscous incompressible Newtonian fluid is studied.The Navier-Stokes equation is solved by using the method of separation of variables. Based on this,the effects of the nondimensional parameters,such as parameter A and Reynolds number Re regarding pressure gradient,on the velocity are investigated. The results show that the velocity amplitude decreases with A and increases with the decrease in Re. In addition, " toroidal effect" of oscillatory velocity is observed.
引文
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[15]Mateescu D,Pa1¨doussis M P,Bélanger F.A theoretical model compared with experiments for the unsteady pressure on a cylinder oscillating in turbulent annular flow[J].J.Sound Vib.,1989,135(3):487-498.
[16]Sato Y,Kanki H.Formulas for compression wave and oscillating flow in circular pipe[J].Appl.Acoust.,2008,69(1):1-11.
[17]Mastikhin I V,Hetherington N L,Emms R.Oscillating gradient measurements of fast oscillatory and rotational motion in the fluids[J].J.Magn.Reson.,2012,214:189-199.
[18]苏霄燕,章本照,陈华军.圆柱形旋转弯曲管道内脉冲流动的二次流动[J].浙江大学学报(工学版),2003,37(5):602-607.
[2]Deng J,Shao X,Ren A.Vanishing of three-dimensionality in the wake behind a rotationally oscillating circular cylinder[J].J.Hydrodyn.,2007,19(6):751-755.
[3]Liang B,Li H,Lee D.Bottom shear stress under wavecurrent interaction[J].Journal of Hydrodynamics,2008,20(1):88-95.
[4]Jensen O,Heil M.High-frequency self-excited oscillations in a collapsible-channel flow[J].J.Fluid Mech.,2003,481:235-268.
[5]长龙,刘全生,菅永军,等.具有正弦粗糙度的环形微管道中脉冲流动[J].应用数学和力学,2016,37(10):1118-1128.
[6]Peng X X.Analysis and measurement of stokes layer flow in an oscillating narrow channel[J].Journal of Hydrodynamics,2008,20(6):770-775.
[7]Mihailo R.Jovanovic'.Turbulence suppression in channel flows by small amplitude transverse wall oscillations[J].American Control Conference,2008,20(1):6.
[8]Thomas A M,Thich G K,Narayanan R.Low Reynolds number flow in a channel with oscillating wavy-walls:An analytical study[J].Chemical Engineering Science,2006,61(18):6047-6056.
[9]刘雅鹏,菅永军,布仁满都拉.粗糙微管道壁面振荡的磁流体流动[J].内蒙古大学学报,2015,46(4):363-369.
[10]Nomura T,Suzuki Y,Uemura M,Kobayashi N.Aerodynamic forces on a square cylinder in oscillating flow with mean velocity[J].J.Wind Eng.Ind.Aerod.,2003,91(1-2):199-208.
[11]Ibrahim M,Hashim W.Oscillating flow in channels with a sudden change in cross section[J].Comput.Fluids,1994,23(1):211-24.
[12]Richardson E G,Tyler E.The transverse velocity gradient near the mouths of pipes in which an alternating or continuous flow of air is established[J].Proc.Phys.Soc.,1929,42(1):1-15.
[13]Uchida S.The pulsating viscous flow superposed on the steady laminar motion of incompressible fluid in a circular pipe[J].Z.Angew.Math.Phys.,1956,7(5):403-422.
[14]Denison E B,Stevenson W H,Fox R W.Pulsating laminar flow measurements with a directionally sensitive laser velocimeter[J].AICh E Journal,1971,17(4):781-787.
[15]Mateescu D,Pa1¨doussis M P,Bélanger F.A theoretical model compared with experiments for the unsteady pressure on a cylinder oscillating in turbulent annular flow[J].J.Sound Vib.,1989,135(3):487-498.
[16]Sato Y,Kanki H.Formulas for compression wave and oscillating flow in circular pipe[J].Appl.Acoust.,2008,69(1):1-11.
[17]Mastikhin I V,Hetherington N L,Emms R.Oscillating gradient measurements of fast oscillatory and rotational motion in the fluids[J].J.Magn.Reson.,2012,214:189-199.
[18]苏霄燕,章本照,陈华军.圆柱形旋转弯曲管道内脉冲流动的二次流动[J].浙江大学学报(工学版),2003,37(5):602-607.