Model hierarchy for the shape optimization of a microchannel cooling system,ZAMM - Journal of Applied Mathematics and Mechanics

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Model hierarchy for the shape optimization of a microchannel cooling system
ZAMM - Journal of Applied Mathematics and Mechanics ( IF 2.3 ) Pub Date : 2020-11-04 , DOI: 10.1002/zamm.202000166
Sebastian Blauth _{1,

2} , Christian Leithäuser ₁ , René Pinnau ₂

Affiliation

We model a microchannel cooling system and consider the optimization of its shape by means of shape calculus. A three‐dimensional model covering all relevant physical effects and three reduced models are introduced. The latter are derived via a homogenization of the geometry in 3D and a transformation of the three‐dimensional models to two dimensions. A shape optimization problem based on the tracking of heat absorption by the cooler and the uniform distribution of the flow through the microchannels is formulated and adapted to all models. We present the corresponding shape derivatives and adjoint systems, which we derived with a material derivative free adjoint approach. To demonstrate the feasibility of the reduced models, the optimization problems are solved numerically with a gradient descent method. A comparison of the results shows that the reduced models perform similarly to the original one while using significantly less computational resources.

中文翻译：

用于微通道冷却系统形状优化的模型层次结构

我们对微通道冷却系统进行建模，并考虑通过形状演算来优化其形状。介绍了一个涵盖所有相关物理效应的三维模型和三个简化模型。后者是通过3D几何形状的均质化和将三维模型转换为二维而得出的。制定了基于冷却器跟踪热量吸收和通过微通道的流量均匀分布的形状优化问题，并将其应用于所有模型。我们介绍了相应的形状导数和伴随系统，它们是使用无材料导数的伴随方法得出的。为了证明简化模型的可行性，采用梯度下降法对优化问题进行了数值求解。

更新日期：2020-11-04

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