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

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。

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.