传热结构摄动敏度分析及动态拓扑优化

摘要/Abstract

摘要： 针对传热强化拓扑优化过程中新形成的孔洞边界对拓扑优化影响的问题，研究了考虑孔洞影响的拓扑导数分析技术，并提出了优化过程中对新形成孔洞边界进行处理的自适应动态边界处理方法。应用Lebesgue微分理论，基于域摄动敏度分析和局部极限定律，推导了Poisson方程控制系统在三类边界条件下不同目标函数的拓扑导数计算公式；最后通过数值分析实例验证了采用该方法直接设计高效换热器的可行性和有效性。

关键词: 传热结构, 拓扑优化, 摄动敏度分析, 拓扑导数

Abstract: Aimed at the effects of the generated new hole boundaries on the topology optimization in the processes of heat transfer enhancement topology optimization, a topological derivative analysis with respect to the new holes was studied , and an adaptive dynamic boundary treatment method was proposed for the new boundaries in the optimization processes. By using Lebesgue differential theory, based on the domain perturbation technique and local limit law, the topological derivative formulas with different objective functions subjected to three kinds of boundary conditions were derived for the control system of Poisson equation. Finally, a number of numerical examples were presented to demonstrate the feasibility and effectiveness of the proposed method for designing the efficient heat exchangers.

Key words: heat transfer structure, topology optimization, perturbation sensitivity analysis, topological derivative

中图分类号:

TH122

邹中妃, 何林, 李家春, 陈跃威. 传热结构摄动敏度分析及动态拓扑优化[J]. 中国机械工程.

ZOU Zhongfei, HE Lin, LI Jiachun, CHEN Yuewei. Perturbation Sensitivity Analysis and Dynamic Topology Optimization for Heat Transfer Structures[J]. China Mechanical Engineering.

参考文献

[1]GAO X J, MA H T. Topology Optimization of Continuum Structures under Buckling Constraints [J]. Computers & Structures, 2015, 157:142-152.
[2]ZHENG L, XIE R L, WANG Y, et al. Topology Optimization of Constrained Layer Damping on Plates Using Method of Moving Asymptote (MMA) Approach [J]. Journal of Vibration and Shock, 2014, 33(8):165-170.
[3]PENG Y, LIU W Y, LIU B, et al. The Performance of the Novel Vapor Chamber Based on the Leaf Vein System [J]. International Journal of Heat and Mass Transfer, 2015, 86:656-666.
[4]SOPRANI S, HAERTEL J H K, LAZAROV B S, et al. A Design Approach for Integrating Thermoelectric Devices Using Topology Optimization [J]. Applied Energy, 2016, 176:49-64.
[5]CHEN K, WANG S F, SONG M X. Optimization of Heat Source Distribution for Two-dimensional Heat Conduction Using Bionic Method [J]. International Journal of Heat and Mass Transfer, 2016, 93:108-117.
[6]BEJAN A. From Heat Transfer Principles to Shape and Structure in Nature:Construct Theory [J]. International Journal of Heat and Mass Transfer, 2000, 122(3):430-449.
[7]AKIHIRO T, GIL H Y, SEUNG H J, et al. Structural Topology Optimization with Strength and Heat Conduction Constraints [J]. Computer Methods in Applied Mechanics and Engineering, 2014, 276:341-361.
[8]ZHUANG C G, XIONG Z H, DING H. Topology Optimization of Multi-material for the Heat Conduction Problem Based on the Level Set Method[J]. Engineering Optimization, 2010, 42(9):811-831.
[9]左孔天, 陈立平, 张云清, 等. 用拓扑优化方法进行热传导散热体的结构优化设计[J]. 机械工程学报, 2005, 41(4):13-16.
ZUO Kongtian, CHEN Liping, ZHANG Yunqing, et al. Structural Optimal Design of Heat Conductive Body with Topology Optimization Method [J]. Journal of Mechanical Engineering, 2005, 41(4):13-16.
[10]吴晶，程新广，孟继安，等.层流对流换热中的势容耗散极值与最小熵产[J].工程热物理学报，2006，27(1)：100-102.
WU Jing, CHENG Xinguang, MENG Jian, et al. Potential Capacity Dissipation Extremum and Entropy Generation Minimization in Laminar Convective Heat Transfer [J]. Journal of Engineering Thermophysics, 2006, 27(1):100-102.
[11]顾元宪, 刘涛, 亢战, 等. 热结构瞬态响应的耦合灵敏度分析方法与优化设计[J]. 力学学报, 2004, 36(1):37-42.
GU Yuanxian, LIU Tao, KANG Zhan, et al. Coupling Sensitivity Analysis and Design Optimization of Thermo-structural Transient Responses [J]. Acta Mechanica Sinica, 2004, 36(1):37-42.
[12] LI Q, STEVEN G P, XIE Y M, et al. Evolutionary Topology Optimization for Temperature Reduction of Heat Conducting Domain[J]. International Journal of Heat and Mass Transfer, 2004, 47(23):5071-5083.
[13] ZDEMIR I. Topological Derivative Based Optimization of 3D Porous Elastic Microstructures [J]. Computational Materials Science, 2014, 81:319-325.
[14]GIUSTI S M, NOVOTNY A A. Topological Derivative for an Anisotropic and Heterogeneous Heat Diffusion Problem [J]. Mechanics Research Communications, 2012, 46:26-33.
[15]ABDEL W M, HASSINE M, MASMOUDI M. Optimal Shape Design for Fluid Flow Using Topological Perturtation Technique[J]. Journal of Mathematical Analysis and Application, 2009, 356:548-563.
[16]周筑宝.最小耗能原理及其应用[M]. 北京:科学出版社, 2001:8-12.
ZHOU Zhubao. Principle of Minimum Energy Dissipation and Application [M]. Beijing:Science Press, 2001:8-12.