扇形截面流道Stokes流速度场的解析解  

Analytical Solution of Stokes Flow Velocity Field in the Fan-shaped Cross Section Channel

作　　者：王宗勇[1] 赵家瑜[1] 吴剑华[1,2] 田瑞[1] 朱军[1] 王舒婷[1] 

机构地区：[1]沈阳化工大学能源与动力工程学院,沈阳110142 [2]天津大学化工学院,天津300072

出　　处：《机械工程学报》2014年第18期193-202,共10页Journal of Mechanical Engineering

基　　金：辽宁省'百千万人才工程'(2013921047);辽宁省高校优秀人才支持计划(LJQ2012036)资助项目

摘　　要：基于圆柱坐标下Stokes流的泊松方程和双调和方程,对任意角度扇形截面流道内的流体速度分布进行解析研究。采用分离变量法得到各角度扇形截面流道的轴向速度及流函数解析表达式,并利用配置点法确定流道横截面内周向及径向速度分布规律。利用数值模拟方法分析不同雷诺数下Stokes方程解析解与N-S方程数值解之间的相对偏差。研究结果表明,在低雷诺数下扇形流道内的三维Stokes流可以分解为两个二维流动,即压力降推动的轴向流及圆弧外壁旋转诱发的扇形腔内截面流;流道内的轴向速度和周向速度与扇形角平分线成对称分布关系,而径向速度成反对称关系;雷诺数Re<1的条件下,解析解与数值解相对偏差小于2%,随着雷诺数增大两者结果的偏差显著增大,但雷诺数在100以下时最大偏差不超过10%,表明本文的解析解不但可以应用在雷诺数极低的Stokes流,还可以应用到雷诺数较小的部分层流。Based on the Poisson’s equation and the biharmonic equation, the fluid velocity distribution in the fan-shaped channel with different angle are studied analytically. The analytic expressions of axial velocity and stream function are obtained in the sectorial channel with different angle by the method of separation of variables, and the distributions of the circumferential and radial velocity components in the cross section of the channel are determined by the method collocation points. By numerical simulation method, the relative deviations between analytic solutions of Stokes equation and simulated solutions of N-S equation are analyzed at different Reynolds number. The conclusion indicates that the 3D Stokes flow at low Reynolds number within the fan-shaped channel can be decomposed into two 2D flows, namely the axial flow in the straight duct driven by pressure drop and the sectional flow in the fan-shaped cavity induced by circular wall rotation. In the condition of Re〈1, the relative deviations between analytic solutions and simulated solutions are all less than 2%. The deviations increase greatly with Reynolds number enhancing,but maximum deviations of three velocity components are not larger than 10%as Re〈100, which implies the analytic solutions can not only be used in Stokes flow at very low Reynolds number, but also be applied in laminar flow at lower Reynolds number.

关 键 词：扇形截面 分离变量法 STOKES流 解析解 数值模拟 

分 类 号：TH12[机械工程—机械设计及理论]