自然对流问题的拓扑优化
Topology optimisation for natural convection problems
摘要：
本文演示了应用密度为基础的拓扑优化方法的设计散热器和微型泵的基础上自然对流效应。在稳态层流的假设下，使用不可压缩的纳维-斯托克斯方程通过Boussinesq近似耦合到对流扩散方程的问题进行建模。为了便于拓扑优化，采取Brinkman方法来惩罚固体域内部的速度，并对有效热导率进行插值，以适应固相和液相热导率的差异。控制方程离散稳定有限元和拓扑优化进行了两个不同的问题，使用离散伴随灵敏度分析。研究表明，拓扑优化是一种可行的方法来设计散热器的几何形状的自然对流冷却和自然对流驱动的微泵。
英文摘要：
This paper demonstrates the application of the density-based topology optimisation approach for the design of heat sinks and micropumps based on natural convection effects. The problems are modelled under the assumptions of steady-state laminar flow using the incompressible Navier-Stokes equations coupled to the convection-diffusion equation through the Boussinesq approximation. In order to facilitate topology optimisation, the Brinkman approach is taken to penalise velocities inside the solid domain and the effective thermal conductivity is interpolated in order to accommodate differences in thermal conductivity of the solid and fluid phases. The governing equations are discretised using stabilised finite elements and topology optimisation is performed for two different problems using discrete adjoint sensitivity analysis. The study shows that topology optimisation is a viable approach for designing heat sink geometries cooled by natural convection and micropumps powered by natural convection.
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