Abstract

In this paper, we propose an approach based on the topological sensitivity notion for solving an inverse design problem. The presented procedure can be applied for finding the optimal design of cooling holes in a turbine blade. Our proposed method uses a simplified and rigorous mathematical analysis related to the unsteady state heat transfer equation. We start our analysis by establishing a preliminary estimate describing the asymptotic behavior of the heat equation solution with respect to the presence of small hole. The obtained estimate will play a crucial role in the derivation of a topological asymptotic formula valid for a large class of design functions. Based on the derived theoretical results, we build a one-iteration numerical algorithm for solving an inverse design problem. To point out the efficiency and accuracy of the proposed approach, some numerical experiments are presented.

中文翻译：

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一个热问题的拓扑渐近展开

摘要

在本文中，我们提出了一种基于拓扑敏感性概念的解决逆设计问题的方法。所提出的程序可用于寻找涡轮叶片中冷却孔的最佳设计。我们提出的方法使用了与非稳态传热方程有关的简化和严格的数学分析。我们通过建立一个初步的估计来开始我们的分析，该估计描述了关于小孔存在的热方程解的渐近行为。所获得的估计值将在推导对大多数设计函数有效的拓扑渐近公式中起关键作用。基于得出的理论结果，我们建立了一个单迭代数值算法来解决逆设计问题。