采用有限体积法的自然对流换热拓扑优化数值方法

杜飞; 田镇熊; 刘宏磊; 郭书哲; 郭俊康; 李宝童

doi:10.7652/xjtuxb202408011

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采用有限体积法的自然对流换热拓扑优化数值方法

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- 采用有限体积法的自然对流换热拓扑优化数值方法
- A Numerical Method for Topology Optimization of Natural Convection Heat Transfer Based on Finite Volume Method
- 西安交通大学学报 2024年58卷第8期页码：103-113
- 作者机构：
  
  1. 西北工业大学航天学院,西安,710072
  2. 浙江大学流体动力与机电系统国家重点实验室,杭州,310027
  3. 西安交通大学机械工程学院,西安,710049
- 作者简介：
  
  : 2023-10-03。作者简介: 杜飞(1984—),男,助理教授
  刘宏磊(通信作者),男,助理教授。基金项目: 国家自然科学基金资助项目(52075445)
- 基金信息：
  
  : 2023-10-03。作者简介: 杜飞(1984—),男,助理教授;刘宏磊(通信作者),男,助理教授。基金项目: 国家自然科学基金资助项目(52075445);流体动力与机电系统国家重点实验室开放基金课题资助(GZKF-202123);陕西省留学人员科技活动择优资助项目(2022001)。
- DOI：10.7652/xjtuxb202408011
  中图分类号： TH122
- 网络首发：2024-08-10，
  
  纸质出版：2024
- 稿件说明：
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杜飞, 田镇熊, 刘宏磊, 等. 采用有限体积法的自然对流换热拓扑优化数值方法[J]. 西安交通大学学报, 2024,58(8):103-113.

DU Fei, TIAN Zhenxiong, LIU Honglei, et al. A Numerical Method for Topology Optimization of Natural Convection Heat Transfer Based on Finite Volume Method[J]. 2024, 58(8): 103-113.
杜飞, 田镇熊, 刘宏磊, 等. 采用有限体积法的自然对流换热拓扑优化数值方法[J]. 西安交通大学学报, 2024,58(8):103-113. DOI： 10.7652/xjtuxb202408011.

DU Fei, TIAN Zhenxiong, LIU Honglei, et al. A Numerical Method for Topology Optimization of Natural Convection Heat Transfer Based on Finite Volume Method[J]. 2024, 58(8): 103-113. DOI： 10.7652/xjtuxb202408011.

摘要

针对基于有限体积法的热-流耦合数值分析缺乏拓扑优化框架问题

建立了采用有限体积法的自然对流换热拓扑优化方法。建立了流体固体统一描述的自然对流换热数学模型

提出了基于有限体积法的自然对流求解方法; 通过引入基于结构的离散化描述方法

搭建了结构的描述框架并构建了流体与固体间的材料属性插值模型; 针对自然对流中增强散热能力与增强物质传输能力问题

提出了拓扑优化的数学模型

明确了设计变量、目标函数以及约束条件

建立了自然对流拓扑优化方法框架; 通过3个算例

验证了提出的数学模型和求解方法

并与商业软件COMSOL进行了对比。结果表明:提出的自然对流求解方法与COMSOL计算结果相比

压力、速度、温度的数值误差均小于3%; 对于增强散热能力问题

采用提出的拓扑优化方法获得的最高温度优于COMSOL结果。所提基于有限体积法的自然对流拓扑优化方法的可行性和有效性得到了验证。

Abstract

A topology optimization method for natural convection heat transfer based on the finite volume method(FVM)is established to address the lack of a topology optimization framework in numerical analysis of thermal-fluid coupling based on the FVM. A fluid-solid unified mathematical model of natural convection heat transfer is first established

and a solution algorithm based on the FVM is proposed. By introducing a structure-based discrete description method

a structure description framework and a material attribute interpolation model between the fluid and the solid are constructed. In addition

mathematical models of topology optimization for heat dissipation enhancement and material transport enhancement are proposed

and the design variables

objective functions and constraints are clarified. A framework of natural convection topology optimization algorithm is established. Finally

three examples are given to verify the proposed mathematical models and algorithm

and a comparison is made with the commercial software COMSOL. The results show that the numerical differences of pressure

speed and temperature between the natural convection algorithm proposed in this paper and COMSOL are less than 3%. For enhancing heat dissipation capacity

the maximum temperature obtained by the proposed topology optimization method is superior to the COMSOL optimization result. The results verify the feasibility and effectiveness of the proposed natural convection topology optimization method based on the FVM.

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references

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