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.
Published Version
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