中文摘要：

基于边界层理论，建立边界速度数学模型研究矩形管道中Rayleigh声流现象。此数学模型采用3阶的谱元方法求解，驻波声场对流体流动的影响采用壁面处的声边界速度来表达，同时引入雷诺数来分析非线性项和黏性项的重要性。数值结果表明：在2维和3维情况下，声边界速度模型均与近似解相符。声边界速度模型和近似解的差异来源于对非线性项的处理。与近似解相比，声边界速度模型的优势在于能考虑流体流动的非线性效应且仅要求矩形管道的特征尺寸的2倍小于波长。在2维情况下，回流区的涡心位于管道高度的1／4；而在3维情况下，回流区的涡心则靠近壁面。在壁面附近，非线性项的影响不能忽略；而在上下2个涡心的中间位置，非线性项比黏性项更加重要。

英文摘要：

Based on the boundary-layer theory, a mathematical model about acoustic boundary-velocity was developed to investigate Rayleigh acoustic streaming in a rectangular pipe. The governing equations were solved by a three-order spectral element method, and the effect of standing acoustic wave on the fluid flow was described by the acoustic boundary-velocity near the wall. Further, Reynolds number was introduced to compare the importance of the nonlinear term with that of the viscous term. Numerical results show that the predicted fluid flow by the acoustic boundary-velocity model conforms with the approximate solution. And the difference between the acoustic boundary-velocity model and the approximate solution comes from the treatment for the nonlinear term. Compared with the approximate solution, the acoustic boundary-velocity model has two advantages. The first advantage is that it considers the nonlinear effect of fluid flow, and the second is that the characteristic length of rectangular pipe is only less than half of the wavelength. On the two-dimensional condition, the center of the circulation zone is near a quarter of height of the pipe. But on the three-dimension condition, the center of the circulation zone is close to the wall. Near the wall, the effect of the nonlinear term can not be ignored. And in the middle of the vortex center for the upper and lower recirculation zones, the effect of the nonlinear term is more important than that of the viscous term.