管内流体交变流动速度的横向分布研究

Transverse distribution of axial velocity on oscillating flow in circular tube

基于线性理论分析,考虑流体的可压缩性、速度横向分布的相位延迟,对微扰项使用Fourier变换,给出充分发展、层流交变流动管内速度分布解析解。给出的解析解适用于描述各种小振幅振型的振荡,体现出流体速度横向分布的相位延迟,并验证了交变流动状态下的“环形效应”。关于流体速度横向分布的解析解给出了流体在谐振状态下的速度分布函数,与肖家华在热声研究中使用常规摄动分析方法假设微扰项以单一频率振荡条件下得到的解析解一致。分析了可压缩流体和不可压缩流体在理论模型上的区别。

The transverse distribution of axial velocity on oscillating flow in circular tube was reported. Based on the linear theory and introducing the assumption of fully developed parallel oscillating flow in circular tube, the transverse distribution of axial velocity has been found using Fourier transform as well as considering the compressibility of the fluid and the phase lag of the velocity along the radius. The analytical solution could describe the mode of low amplitude oscillation and present the phase lag of the axial velocity distribution. The phenomena of annular effect of oscillation flow have also been verified. By the property of Fourier transform, elements of simple harmonic part of the solution are given in the identical form with that of Xiao＇s solution. Moreover, the difference between the compressible and incompressible fluid has been analyzed.