表面粗糙度的分形特征及其对微通道内层流流动的影响

基于分形几何学，研究了表面粗糙度的分形特征.采用Weierstrass- Mandelbrot函数对多尺度自仿射的表面粗糙度进行了描述；建立了微通道内层流流动的三维模型并对表面粗糙度的影响进行了数值模拟，分析了雷诺数、相对粗糙度和分形维数对流动阻力特性的影响.研究结果表明，与常规尺度通道不同，粗糙微通道的Poiseuille数不再是常数，而是随雷诺数近似线性增加；相对粗糙度越大，流动产生的回流和分离所导致的流动压降越明显.在相同的相对粗糙度下，粗糙表面的分形维数越大，表面轮廓变化就越频繁，这也将导致流动阻 关键词： 粗糙度 层流阻力系数 微通道 分形

Fractal characteristics of surface roughness and its effect on laminar flow in microchannels

The fractal characteristics of the surface roughness are investigated by using fractal geometry. A three-dimensional model of laminar flow in microchannels with surface roughness characterized by fractal geometry is developed and analyzed numerically. The Weierstrass-Mandelbrot function is introduced to characterize the multiscale self-affine roughness. The effects of Reynolds number Re， relative roughness， and fractal dimension on Poiseuille number are investigated and discussed. The results show that， different from the conventional channels， Poiseuille number in rough microchannels is no longer constant for different Re， but increases approximately linearly with Re， and is larger than the classical value. The flow over roughness features with high relative roughness induces recirculation and flow separation， which plays an important role in flow pressure drop. More specifically， roughness with larger fractal dimension， which yields more frequent variation in the surface profile， also results in a significant increase in pressure loss， even though at the same relative roughness. In addition， the accuracy of Poiseuille number calculated by the present model is verified by the experimental data available in the literature.