关键词: 表面功能结构, 分形, 微观形貌, 微通道, 流动特性

Abstract:

In order to implement the multiscale digital design of metal functional surface structures,a mathematical method combining the Weierstrass-Mandelbrot fractal geometry and the three-dimension parametric surface is developed based on the self-affine fractal characteristics of the microtopography of machined metal surfaces. With this method,the coarse microtopography of three-dimension structures can be well integrated with macroscopic models,so that a multiscale microtopographic model of functional surface structures can be established. For experimental investigation,a multiscale 3D solid model is created to simulate the flow characteristics of fluid in a ploughed Vshaped microchannel,and the influences of the Reynolds number,the surface height scale coefficient and the fractal dimension on the flow characteristics are analyzed. The results show that ( 1) the frictional resistance coefficient decreases with the increase in the Reynolds number,but increases with the surface height scale coefficient; ( 2) the influence of the fluid vortex due to surface roughness,which becomes significant with the roughness increase,is non-neglectable; and ( 3) the frictional resistance coefficient of microchannels decreases with the increase of the Weierstrass-Mandelbrot fractal dimension.

Key words: functional surface structure, fractal, microtopography, microchannel, flow characteristic