平板微通道壁面粗糙度对流场影响的摄动分析

选取相对粗糙度作为小参数建立了平板微通道流动的摄动方程组,采用傅里叶分析结合数值方法进行求解.计算结果表明:影响流场结构的主要因素为相对粗糙度和粗糙曲线的空间波数.当保持波数不变,增加壁面相对粗糙度时,无量纲流函数扰动峰值将增大,而流场受扰区域不发生变化;当保持相对粗糙度不变,减小空间波数时,流函数扰动峰值和流场受扰区域都将增大;近壁区流场中存在明显的涡结构,涡结构的出现使得流场内部的黏性耗散作用增强,因此导致相同条件下微通道层流的流动损失高于大尺度流动时的阻力损失.

Perturbation Analysis of Wall Roughness Effect on Flow in Micro-Channel Between Two Parallel Plates

By choosing relativity roughness as the small parameter, perturbation equations of laminar flow in micro-channel between two parallel plates were set up. The perturbation equations were analyzed by the method of Fourier analysis and solved numerically. The computing results show that the main factors affecting the flow pattern are relative roughness and spatial wave number of wall rough curve. If the wave number keeps constant and the relative roughness increases, the peak of the disturbed non-dimensional stream function increases and the disturbed area in flow field is invariable. If the relative roughness keeps constant and the spatial wave number decreases, both the peak of disturbed stream function and disturbed area in flow field increase simultaneously. Because of the existence of rough elements, obvious vortex structures occur in the flow field near the wall. The vortex structures make viscous dissipation augment and lead to the friction loss flowing in micro-channels larger than that in macro-channels under the same conditions.