基于蒙特卡洛法和分形理论的接触导热计算
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摘要
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.
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.
引文
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[16]李小彭,刘洋,王雪,等.三维分形接触热导的建模与多参数影响分析[J].振动与冲击,2018,37(5):1-6.
[17]古亮,尹泽龙,王帅,等.基于三维分形的尖板间隙放电现象的研究[J].重庆理工大学学报(自然科学),2018(8):182-186.
[2] MUTLU M,KILIC M. Three-dimensional conjugate numerical analysis of fin and tube heat exchangers with various fin thermal conductivity values and geometric parameters[J]. Journal of Thermal Science and Technology,2016,36(1):85-98.
[3]方文振,任兴杰,陶文铨.基于多块格子Boltzmann方法模拟接触热阻[J].工程热物理学报,2017,38(3):595-600.
[4]王安良,赵剑锋.接触热阻预测的研究综述[J].中国科学:技术科学,2011,41(5):545-556.
[5] MIKIC B B. Thermal contact conductance:theoretical considerations[J]. Journal of Heat and Mass Transfer,1974,17(2):205-214.
[6] YOVANOVICH M M. Thermal contact correlations[C]//AIAA 16th Thermophysics Conference,Palo Alto,California,USA,1981,83-95.
[7]陈剑楠,毛章明,罗小兵.基于CMY模型改进的界面热阻模型及应用[J].工程热物理学报,2012,16(4):305-308.
[8] KUMAR S,RAMAMURTHI K. Prediction of Thermal Contact Conductance in Vacuum Using Monte Carlo Simulation[J]. Journal of Thermophysics and Heat Transfer,,2001,15(1):27-33.
[9] MAIUMDAR A,TIEN C L. Fractal network model for contact conductance[J]. Journal of Heat Transfer,1991,113(8):516-525.
[10] WARREN T L,KRAJCINOVIC D. Random cantor set models for the elastic-perfectly plastic contact of rough surfaces[J]. Wear,1996,196:1-15.
[11]赵兰萍.低温固体界面间接触传热的研究[D].上海:上海交通大学,2000.
[12]徐瑞萍.基于Cantor集分形的固体接触界面热阻研究[D].上海:上海交通大学,2005.
[13] ZOU M Q,YU B M,CAI J C,et al. Fractal model for thermal contact conductance[J]. Journal of Heat Transfer,2008,130:101301.
[14] JI Cuicui,ZHU Hua,JIANG Wei. Fractal Prediction Model of Thermal Contact Conductance of Rough Surfaces[J]. Journal of Heat and Mass Transfer,2013,26(1):128-135.
[15]马丽娜.弹塑性接触变形下的接触热导分形模型[J].太原科技大学学报,2014,35(6):438-442.
[16]李小彭,刘洋,王雪,等.三维分形接触热导的建模与多参数影响分析[J].振动与冲击,2018,37(5):1-6.
[17]古亮,尹泽龙,王帅,等.基于三维分形的尖板间隙放电现象的研究[J].重庆理工大学学报(自然科学),2018(8):182-186.