大吸附雷诺数下胀-缩壁面管道非稳态流动渐近求解

Asymptotic solution for unsteady flow in expanding or contracting channels with large suction Reynolds

研究了大吸附雷诺数下,可渗透、膨胀或收缩的半无限长管道中的层流流动.采用自相似理论,把描述该模型的Navier-Stokes方程转化成一个四阶的非线性微分方程.应用奇异摄动方法,对该方程进行渐近求解.分析了不同的膨胀系数、吸附雷诺数对管道流动的影响.壁面收缩时,边界层变薄;壁面膨胀时,边界层变厚;当膨胀率与雷诺数之比大于1时,管道流动出现回流.

An incompressible laminar flow in a semi-infinite porous channel with expanding or contracting wails is considered. Following the self-similarity transformation, the Navier-Stokes equations are reduced to a fourth-order non-linear differential equation. The resulting equation is then solved asymptotically for large suction Reynolds number. The influences of expansion rate and Reynolds number on the fluid are obtained. When the wall contracts, the boundary layer becomes thinner; and when the wall expands, the boundary layer becomes thicker. It appears that flow reversal begins when the ratio of expansion rate to suction Reynolds number exceeds 1.