A Topology Optimized Design Method for High-performance Structures with Fluid-thermal-mechanics Coupling

doi:10.3969/j.issn.1004-132X.2024.03.011

Abstract

Abstract: The rapid advancement of topology optimization and additive manufacturing technology provided efficient methods for designing and manufacturing high-performance complex equipment. However, current topology optimization techniques for high-performance structures only considered the design of thermal-mechanics coupling or fluid-thermal coupling, and were mostly limited to simple structures. The design under the combined effects of fluid-thermal-mechanics fields was not considered, which restricted the enhancement of structural performance. This paper tackled the challenge of designing high-performance complex structures under multi-physics fields, encompassing fluid-thermal-mechanics interactions. A topology optimization method was proposed to enhance the ability to withstand temperature of intricate structures. Firstly, the governing equations of flow field, temperature field and structural displacement field were introduced to provide a unified description of the fluid-solid materials within the computational domain. Secondly, the topology optimization model was formulated with fluid-thermal-mechanics coupling. The objective function was set to minimize the average temperature, while flow energy dissipation and structural compliance served as constraint functions. Sensitivity analysis of design variables was carried out by using a combination of the variational method and Lagrangian function. Finally, the established topology optimization model was applied to the structural design of a turbine, resulting in a structure suitable for additive manufacturing with excellent heat dissipation performance and well-balanced flow channel distribution.

Key words: topology optimization, variable density method, multiphysics field, high-performance structure

摘要： 拓扑优化和增材制造技术的快速发展为高性能复杂装备提供了高效的产品设计和制造方法。目前高性能结构拓扑优化只考虑热力耦合或者流热耦合的设计，且大多局限于简单结构，未考虑流热力三场共同作用下的设计，限制了结构性能的提升。针对流热力多物理场工况下的高性能复杂结构设计这一挑战，提出了一种流热力耦合拓扑优化方法，以提高复杂结构的承温能力。首先引入流场、温度场和结构位移场的控制方程，对计算域的流固材料进行统一表征；然后以最小化平均温度为目标，以流动能量耗散和结构柔度为约束，建立了流热力耦合的拓扑优化模型，并结合变分法和拉格朗日函数开展了设计变量的灵敏度分析；最后将所建立的拓扑优化模型应用于涡轮的结构设计，得到了散热性能良好、流道分布合理的可增材制造结构。

关键词: 拓扑优化, 变密度法, 多物理场, 高性能结构

CLC Number:

LI Rongqi, YAN Tao, HE Zhicheng, MI Dong, JIANG Chao, ZHENG Jing. A Topology Optimized Design Method for High-performance Structures with Fluid-thermal-mechanics Coupling[J]. China Mechanical Engineering, 2024, 35(03): 487-497.

李荣启, 闫涛, 何智成, 米栋, 姜潮, 郑静. 流-热-力耦合的高性能结构拓扑优化设计方法[J]. 中国机械工程, 2024, 35(03): 487-497.

References

［1］LIU Jikai, GAYNOR A T, CHEN Shikui, et al. Current and Future Trends in Topology Optimization for Additive Manufacturing［J］. Structural and Multidisciplinary Optimization, 2018, 57(6):2457-2483.
［2］刘成颖, 谭锋, 王立平, 等. 面向机床整机动态性能的立柱结构优化设计研究［J］. 机械工程学报, 2016, 52(3):161-168.
LIU Chengying, TAN Feng, WANG Liping, et al. Research on Optimization of Column Structure Design for Dynamic Performance of Machine Tool［J］. Journal of Mechanical Engineering, 2016, 52(3):161-168.
［3］DU PLESSIS A, BROECKHOVEN C, YADROITSAVA I, et al. Beautiful and Functional:a Review of Biomimetic Design in Additive Manufacturing［J］. Additive Manufacturing, 2019, 27:408-427.
［4］刘伟, 李能, 周标, 等. 复杂结构与高性能材料增材制造技术进展［J］. 机械工程学报, 2019, 55(20):128-151.
LIU Wei, LI Neng, ZHOU Biao, et al. Progress in Additive Manufacturing on Complex Structures and High-performance Materials［J］. Journal of Mechanical Engineering, 2019, 55(20):128-151.
［5］朱继宏, 周涵, 王创, 等. 面向增材制造的拓扑优化技术发展现状与未来［J］. 航空制造技术, 2020, 63(10):24-38.
ZHU Jihong, ZHOU Han, WANG Chuang, et al. Status and Future of Topology Optimization for Additive Manufacturing［J］. Aeronautical Manufacturing Technology, 2020, 63(10):24-38.
［6］SIGMUND O, MAUTE K. Topology Optimization Approaches［J］. Structural and Multidisciplinary Optimization, 2013, 48(6):1031-1055.
［7］IGA A, NISHIWAKI S, IZUI K, et al. Topology Optimization for Thermal Conductors Considering Design-dependent Effects, Including Heat Conduction and Convection［J］. International Journal of Heat and Mass Transfer, 2009, 52(11/12):2721-2732.
［8］SUBRAMANIAM V, DBOUK T, HARION J L. Topology Optimization of Conductive Heat Transfer Devices:an Experimental Investigation［J］. Applied Thermal Engineering, 2018, 131:390-411.
［9］BORRVALL T, PETERSSON J. Topology Optimization of Fluids in Stokes Flow［J］. International Journal for Numerical Methods in Fluids, 2003, 41(1):77-107.
［10］DHRING M B, JENSEN J S, SIGMUND O. Acoustic Design by Topology Optimization［J］. Journal of Sound and Vibration, 2008, 317(3/4/5):557-575.
［11］RUPP C J, EVGRAFOV A, MAUTE K, et al. Design of Phononic Materials/Structures for Surface Wave Devices Using Topology Optimization［J］. Structural and Multidisciplinary Optimization, 2007, 34(2):111-121.
［12］SUTRADHAR A, PAULINO G H, MILLER M J, et al. Topological Optimization for Designing Patient-specific Large Craniofacial Segmental Bone Replacements［J］. Proceedings of the National Academy of Sciences of the United States of America, 2010, 107(30):13222-13227.
［13］PARK J, LEE Damian, SUTRADHAR A. Topology Optimization of Fixed Complete Denture Framework［J］. International Journal for Numerical Methods in Biomedical Engineering, 2019, 35(6):e3193.
［14］FERRARI F, SIGMUND O. A New Generation 99 Line Matlab Code for Compliance Topology Optimization and Its Extension to 3D［J］. Structural and Multidisciplinary Optimization, 2020, 62(4):2211-2228.
［15］WU Jun, CLAUSEN A, SIGMUND O. Minimum Compliance Topology Optimization of Shell–infill Composites for Additive Manufacturing［J］. Computer Methods in Applied Mechanics and Engineering, 2017, 326:358-375.
［16］WANG Hui, CHENG Wenming, DU Run, et al. Improved Proportional Topology Optimization Algorithm for Solving Minimum Compliance Problem［J］. Structural and Multidisciplinary Optimization, 2020, 62(2):475-493.
［17］KRIEGESMANN B, LDEKER J K. Robust Compliance Topology Optimization Using the First-order Second-moment Method［J］. Structural and Multidisciplinary Optimization, 2019, 60(1):269-286.
［18］RODRIGUES H, FERNANDES P. A Material Based Model for Topology Optimization of Thermoelastic Structures［J］. International Journal for Numerical Methods in Engineering, 1995, 38(12):1951-1965.
［19］YANG Xiongwei, LI Yueming. Topology Optimization to Minimize the Dynamic Compliance of a Bi-material Plate in a Thermal Environment［J］. Structural and Multidisciplinary Optimization, 2013, 47(3):399-408.
［20］PARK J, NGUYEN T H, SHAH J J, et al. Conceptual Design of Efficient Heat Conductors Using Multi-material Topology Optimization［J］. Engineering Optimization, 2019, 51(5):796-814.
［21］DEATON J D, GRANDHI R V. Stiffening of Restrained Thermal Structures via Topology Optimization［J］. Structural and Multidisciplinary Optimization, 2013, 48(4):731-745.
［22］ZHU Xuefeng, ZHAO Chao, WANG Xuan, et al. Temperature-constrained Topology Optimization of Thermo-mechanical Coupled Problems［J］. Engineering Optimization, 2019, 51(10):1687-1709.
［23］TAKEZAWA A, YOON G H, JEONG S H, et al. Structural Topology Optimization with Strength and Heat Conduction Constraints［J］. Computer Methods in Applied Mechanics and Engineering, 2014, 276:341-361.
［24］DEATON J D, GRANDHI R V. Stress-based Design of Thermal Structures via Topology Optimization［J］. Structural and Multidisciplinary Optimization, 2016, 53(2):253-270.
［25］ZHENG Jing, CHEN Hong, JIANG Chao. Robust Topology Optimization for Structures under Thermo-mechanical Loadings Considering Hybrid Uncertainties［J］. Structural and Multidisciplinary Optimization, 2022, 65(1):29.
［26］YOON G H. Topology Optimization for Stationary Fluid-structure Interaction Problems Using a New Monolithic Formulation［J］. International Journal for Numerical Methods in Engineering, 2010, 82(5):591-616.
［27］PICELLI R, VICENTE W M, PAVANELLO R, et al. Evolutionary Topology Optimization for Natural Frequency Maximization Problems Considering Acoustic-structure Interaction［J］. Finite Elements in Analysis and Design, 2015, 106(C):56-64.
［28］LI Hao, KONDOH T, JOLIVET P, et al. Three-dimensional Topology Optimization of a Fluid–Structure System Using Body-fitted Mesh Adaption Based on the Level-set Method［J］. Applied Mathematical Modelling, 2022, 101:276-308.
［29］YOON G H. Topological Design of Heat Dissipating Structure with Forced Convective Heat Transfer［J］. Journal of Mechanical Science and Technology, 2010, 24(6):1225-1233.
［30］YU Minghao, RUAN Shilun, WANG Xinyu, et al. Topology Optimization of Thermal–fluid Problem Using the MMC-based Approach［J］. Structural and Multidisciplinary Optimization, 2019, 60(1):151-165.
［31］YAJI K, YAMADA T, KUBO S, et al. A Topology Optimization Method for a Coupled Thermal–fluid Problem Using Level Set Boundary Expressions［J］. International Journal of Heat and Mass Transfer, 2015, 81:878-888.
［32］ZHAO Xi, ZHOU Mingdong, LIU Yichang, et al. Topology Optimization of Channel Cooling Structures Considering Thermomechanical Behavior［J］. Structural and Multidisciplinary Optimization, 2019, 59(2):613-632.
［33］PANTON R L. Incompressible Flow［M］. Hoboken:Wiley, 2013.
［34］于明豪. 液冷散热器流道与热源分布拓扑优化研究［D］. 大连:大连理工大学, 2021.
YU Minghao. Research on Topology Optimization of Cooling Channels and Heat Sources Distribution for Liquid-cooled Heat Sink［D］. Dalian:Dalian University of Technology, 2021.
［35］LAZAROV B S, SIGMUND O. Filters in Topology Optimization Based on Helmholtz-type Differential Equations［J］. International Journal for Numerical Methods in Engineering, 2011, 86(6):765-781.
［36］XU Shengli, CAI Yuanwu, CHENG Gengdong. Volume Preserving Nonlinear Density Filter Based on Heaviside Functions［J］. Structural and Multidisciplinary Optimization, 2010, 41(4):495-505.

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