基于蒙特卡洛法和分形理论的接触导热计算

Prediction of Thermal Contact Conductance Based on Monte Carlo Simulation and Fractal Theory

根据固体粗糙表面的随机特性和分形特性,结合蒙特卡洛法和Weierstrass-Mandelbrot分形函数,对粗糙表面的形貌和接触进行了模拟,在此基础上建立了接触热阻的计算模型,并研究了表面分形参数对固体界面间接触导热的影响。研究结果表明:基于蒙特卡洛法和表面分形理论建立的接触热阻计算模型与实验结果基本一致,能够较为准确地预测接触热阻,具有较高的工程应用价值;分形参数能够唯一确定地表征固体粗糙表面的形貌,从而使得接触热阻的计算具有确定性;在一定的接触压力下,接触界面间的热导率随着分形维数D的增大而增大,随着分形参数G的增大而减小。

According to the random and fractal characteristics of rough surfaces,a reasonable thermal contact resistance model is developed based on the combination of Weierstrass-Mandelbrot fractal function and Monte-Carle method.Fractal parameters which have influence on the thermal contact resistance are further discussed.Theoretical calculation shows,the thermal contact resistance model proposed in the paper is consistent with experimental data,so the feasibility and engineering application value of the model is verified.Results show that:profile of a certain rough surface can be described by fractal parameters;and under the same contact pressure,as dimension D go higher the thermal contact conductance goes greater,and as the scale factor G goes greater the thermal contact conductance goes smaller.