具有正弦粗糙度的环形微管道中脉冲流动

长龙; 刘全生; 菅永军; 布仁满都拉; 孙艳军

doi:10.21656/1000-0887.370116

具有正弦粗糙度的环形微管道中脉冲流动

doi: 10.21656/1000-0887.370116

¹内蒙古大学数学科学学院, 呼和浩特 010021;²内蒙古财经大学统计与数学学院, 呼和浩特 010071;³北京航空航天大学航空科学与工程学院, 北京 100191;⁴赤峰学院数学与统计学院, 内蒙古赤峰 024000

基金项目: 国家自然科学基金(11562014;11472140);内蒙古自然科学基金(2015MS0113;2015MS0110;2016MS0106);内蒙古自治区草原英才资助项目(12000-12102013);内蒙古自治区高等学校科学技术研究项目(NJZY14109);内蒙古自治区研究生科研创新资助项目(11200-12110201)

详细信息

作者简介:
长龙(1979—)，男，讲师，博士生(E-mail: suolunga@163.com);刘全生(1979—)，男，副教授，博士,硕士生导师(通讯作者. E-mail: smslqs@imu.edu.cn).

中图分类号: O357.1
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- 被引次数: 0
出版历程
- 收稿日期: 2016-04-14
- 修回日期: 2016-05-25
- 刊出日期: 2016-10-15

Oscillating Flow in Annular Microchannels With Sinusoidally Corrugated Walls

¹School of Mathematical Sciences, Inner Mongolia University, Hohhot 010021, P.R.China;²School of Statistics and Mathematics, Inner Mongolia University of Finance and Economics, Hohhot 010071, P.R.China;³School of Aeronautic Science and Engineering, Beihang University, Beijing 100191, P.R.China;

Funds: The National Natural Science Foundation of China(11562014;11472140)

摘要

摘要: 研究了具有正弦粗糙度的环形微管道中脉冲流动, 其中壁面粗糙度用小振幅的正弦波表示, 不可压缩粘性脉冲流动由周期振荡的压力梯度驱动, 运用摄动展开法求解了柱坐标系下的动量方程, 获得了环形微管道内脉冲流动的近似解析速度及其体积流率.在此基础上, 研究了相关无量纲参数, 如Reynolds(雷诺)数Re、压力梯度振幅A、正弦波状粗糙的小振幅ε、内外半径之比α、相位差β及其波数λ对速度u及平均体积流率Φ_m的影响.结果表明, 剖面速度随A的增大而增大, 随Re的增大而减小，相位滞后χ随振荡Reynolds数Re的增大而增大
- 压力梯度振荡 /
- 摄动法 /
- 正弦波状壁面 /
- 环形微管道
Abstract: Oscillating flow in annular microchannels with sinusoidal wall roughness was investigated. The oscillating flow of incompressible viscous fluid was driven by a time-periodically oscillating pressure gradient. Approximate solutions of the velocity and flow rate in the annular microchannel were obtained through computation of the momentum conservation equations in the cylindrical coordinate system with the perturbation method. Based on these approximate solutions, the effects of the relevant nondimensional parameters, such as Reynolds number Re, pressure gradient amplitude A, sinusoidal roughness amplitude ε, ratio of the inner radius to the outer radius α, phase difference β and wave number λ, on velocity u and flow rate Φ_m, were analyzed. The results show that the velocity increases with A and decreases with Re, and phase lag χ increases with Re.
- pressure gradient oscillation /
- perturbation method /
- sinusoidally corrugated wall /
- annular microchannel

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参考文献(29)

[1]	DENG Jian, SHAO Xue-ming, REN An-lu. Vanishing of three-dimensionality in the wake behind a rotationally oscillating circular cylinder[J]. Journal of Hydrodynamics,2007,19(6): 751-755.
[2]	LIANG Bing-chen, LI Hua-jun, Lee D. Bottom shear stress under wave-current interaction[J]. Journal of Hydrodynamics,2008,20(1): 88-95.
[3]	Jensen O E, Heil M. High-frequency self-excited oscillations in a collapsible-channel flow[J]. Journal of Fluid Mechanics,2003,481: 235-268.
[4]	PENG Xiao-xing, Hsu C T. Analysis and measurement of Stokes layer flow in an oscillating narrow channel[J]. Journal of Hydrodynamics,2008,20(6): 770-775.
[5]	Nazar M, Zulqarnain M, Akram M S, Asif M. Flow through an oscillating rectangular duct for generalized Maxwell fluid with fractional derivatives[J]. Communications in Nonlinear Science and Numerical Simulation,2012,17(8): 3219-3234.
[6]	Nomura T, Suzuki Y, Uemura M, Kobayashi N. Aerodynamic forces on a square cylinder in oscillating flow with mean velocity[J]. Journal of Wind Engineering and Industrial Aerodynamics,2003,91(1/2): 199-208.
[7]	Ibrahim M B, Hashim W. Oscillating flow in channels with a sudden change in cross section[J]. Computers & Fluids,1994,23(1): 211-224.
[8]	Bellhouse B J, Bellhouse F H, Curl C M,MacMillan T I, Gunning A J, Spratt E H, MacMurray S B, Nelems J M. A high efficiency membrane oxygenator and pulsatile pumping system, and its application to animal trials[J]. ASAIO Journal,1973,19(1): 72-79.
[9]	Yin D, Ma H B. Analytical solution of oscillating flow in a capillary tube[J]. International Journal of Heat and Mass Transfer,2013,66: 699-705.
[10]	Yin D, Ma H B. Analytical solution of heat transfer of oscillating flow at a triangular pressure waveform[J]. International Journal of Heat and Mass Transfer, 2014,70: 46-53.
[11]	ZHENG Lian-cun, LI Chun-rui, ZHANG Xin-xin, GAO Ying-tao. Exact solutions for the unsteady rotating flows of a generalized Maxwell fluid with oscillating pressure gradient between coaxial cylinders[J]. Computers & Mathematics With Applications,2011,62(3): 1105-1115.
[12]	Sato Y, Kanki H. Simplification of formulas for compression wave and oscillating flow in circular pipe[J].Applied Acoustics,2008,69(10): 901-912.
[13]	Placzek A, Sigrist J F, Hamdouni A. Numerical simulation of an oscillating cylinder in a cross-flow at low Reynolds number: forced and free oscillations[J]. Computers & Fluids,2009,38(1): 80-100.
[14]	Shah S B H, LU Xi-yun. Numerical simulation of an oscillating flow past a circular cylinder in the vicinity of a plane wall[J]. Journal of Hydrodynamics,2008,20(5): 547-552.
[15]	Nam K, Jeong S. Novel flow analysis of regenerator under oscillating flow with pulsating pressure[J].Cryogenics,2005,45(5): 368-379.
[16]	G·C·夏玛, M·简妮, M·察尼特拉. 磁场对具有压力梯度的低频振荡自然对流的影响[J]. 应用数学和力学, 2003,24(3): 245-252.(Sharma G C, Jain M, Chandra M. The effect of magnetic fields on low frequency oscillating natural convection with pressure gradient[J]. Applied Mathematics and Mechanics,2003,24(3): 245-252.(in Chinese))
[17]	陆夕云, 凌国灿. 圆柱振荡绕流的三维不稳定性研究[J]. 应用数学和力学, 2003,24(7): 699-707.(LU Xi-yun, LING Guo-chan. Three-dimensional instability of an oscillating viscous flow past a circular cylinder[J]. Applied Mathematics and Mechanics,2003,24(7): 699-707.(in Chinese))
[18]	Wang C Y. On Stokes flow between corrugated plates[J]. Journal of Applied Mechanics,1979,46(2): 462-464.
[19]	王昊利, 王元, 刘江. 平板微通道壁面粗糙度对流场影响的摄动分析[J]. 西安交通大学学报, 2005,39(5): 540-543.(WANG Hao-li, WANG Yuan, LIU Jiang. Perturbation analysis of wall roughness effect on flow in micro-channel between two parallel plates[J]. Journal of Xi’an Jiaotong University,2005,39(5): 540-543.(in Chinese))
[20]	张春平, 唐大伟, 韩鹏, 祝捷. 粗糙度对微细圆管内流动特性影响的摄动分析[J]. 工程热物理学报, 2008,29(5): 849-852.(ZHANG Chun-ping, TANG Da-wei, HAN Peng, ZHU Jie. A perturbation analysis of wall roughness effects on flow in microtube[J]. Journal of Engineering Thermophysics,2008,29(5): 849-852.(in Chinese))
[21]	焦云龙, 刘小君, 逄明华, 刘焜. 液滴平壁铺展过程中的滞后效应及力学机制研究[J]. 应用数学和力学，2016,37(1): 14-26.(JIAO Yun-long, LIU Xiao-jun, PANG Ming-hua, LIU Kun. Study of contact angle hysteresis at moving contact lines based on CFD simulation and mechanical analysis[J]. Applied Mathematics and Mechanics,2016,37(1): 14-26.(in Chinese))
[22]	Chu Z K H. Slip flow in an annulus with corrugated walls[J]. Journal of Physics D: Applied Physics,2000,33(6): 627-631.
[23]	Tsikata J M, Tachie M F. Effects of roughness and adverse pressure gradient on the turbulence structure[J]. International Journal of Heat and Fluid Flow,2013,44: 239-257.
[24]	Tsikata J M, Tachie M F. Adverse pressure gradient turbulent flows over rough walls[J]. International Journal of Heat and Fluid Flow,2013,39: 127-145.
[25]	Sisavath S, Al-Yaaruby A, Pain C C, Zimmerman R W. A simple model for deviations from the cubic law for a fracture undergoing dilation or closure[J]. Pure and Applied Geophysics,2003,160(5/6): 1009-1022.
[26]	Buren M, Jian Y J, Chang L. Electromagnetohydrodynamic flow through a microparallel channel with corrugated walls[J]. Journal of Physics D: Applied Physics,2014,47(42): 425501.
[27]	Buren M,Jian Y. Electromagnetohydrodynamic(EMHD) flow between two transversely wavy microparallel plates[J]. Electrophoresis,2015,36(14): 1539-1548.
[28]	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.
[29]	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(自然科学版), 2015,46(4): 363-369.(LIU Ya-peng, JIAN Yong-jun, Burenmandula. Magnetohydrodynamic(MHD) flow through two parallel microchannels with oscillating corrugated walls[J]. Journal of Inner Mongolia University(Natural Science Edition),2015,46(4): 363-369.(in Chinese))