基于伪密度的对流换热热沉结构拓扑优化  

Topology Optimization of Convection Heat Sink Based on Pseudo-density Method

作　　者：吴璇 陈群[1] WU Xuan;CHEN Qun(Key Laboratory for Thermal Science and Power Engineering of Ministry of Education,Department of Engineering Mechanics,Tsinghua University,Beijing 100084,China)

机构地区：[1]清华大学工程力学系,热科学与动力工程教育部重点实验室,北京100084

出　　处：《工程热物理学报》2022年第3期763-769,共7页Journal of Engineering Thermophysics

基　　金：国家自然科学基金资助项目(No.51836004)。

摘　　要：强制对流换热热沉的拓扑优化对提升热沉换热性能有重要意义。本文以热源边界平均温度最小为优化目标,对三维方管和扁管内层流强制对流热沉结构进行拓扑优化。通过分析对流换热过程,构造拉格朗日泛函,导出优化准则及相应伴随方程。基于开源计算流体力学软件OpenFOAM,利用SIMPLE算法开发伴随方程求解器,获得灵敏度信息。基于伪密度法描述热沉结构,构造不动点迭代格式,优化热沉的几何结构。结果显示,三维层流强制对流换热模型最优热沉为多花瓣状结构,对应流场为多纵向涡结构;当截面形状长宽比增加时,截面上纵向涡数量也会增加。Topology optimization of forced convection heat sink is of great significance to improve the heat transfer performance. In this paper, the topology optimization of a three-dimensional forced convection heat sink in a square tube and a flat tube with the aim of minimizing the average temperature of the heat source boundary is carried out. By analyzing the process of convective heat transfer, a Lagrangian functional is constructed, and optimization criteria and the adjoint equations are derived. Based on the open source computational fluid dynamics software OpenFOAM, the SIMPLE algorithm is used to develop an adjoint equation solver to obtain sensitivity information.Based on the pseudo-density method to describe the heat sink structure, a fixed point iteration scheme for solving the optimal heat sink structure is derived. The results show that the optimal heat sink of the three-dimensional laminar forced convection heat transfer model is a multi-petal structure,corresponding to a flow field with a multi-longitudinal vortex structure;when the aspect ratio of the section shape increases, the number of longitudinal vortices on the section will also increase.

关 键 词：对流换热热沉 优化准则法 伪密度法 拓扑优化 伴随方程 

分 类 号：TK124[动力工程及工程热物理—工程热物理]