[LAMPS] Body-fitted topology optimization of an airfoil

Résumé

In a broad sense, shape and topology optimization aims at finding an optimal shape among a set of admissible shapes, constrained in a design space, with respect to a set of prescribed criteria. While originating from solid mechanics and being a mature technology in that field, the ideas of the methodology are extendable to all physics described by a set of Partial Differential Equations (PDE), including fluid dynamics. In order to solve the PDE, one typically relies on Finite Volume (FV) Method rather than Finit Element (FE) Method, classically used in solid mechanics. However, rather than reinventing the wheel, the aim of this work is to use OpenFOAM, a well-known open-source FV solver, within a topology optimization framework. The numerical implementation has been done with the Research and Developpement open source software OpenPISCO. The numerical optimization strategy relies on the level set method, the notion of Hadamard shape deerivative linked to the computation of an advection velocity and an algorithm to handle constrained problems. To enable such coupling, the criteria evaluation and the underlying topology optimization framework and used to enforce a descent direction and advect an interface. By doing so, the boundary fits smoothly the interface by an explicit discretization of the zero isovalue of the implicit domain and provide both a clear definition of the shape and an accurate evaluation of the criteria of interest. This contribution focuses on the general methodology to couple the body-fitted methodology with a FV solver. We also illustrate this coupling in the context of the optimization of a 3D airfoil, which will be presented. Such contribution leverages the benefits of the body-fitted approach regarding external physical solvers coupling and paves the way to even more complex and interesting CFD problems.

Mots clés : topology optimization, level-set, body-fitted, fluid dynamics
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Intervenant

David Danan, Chercheur-Ingénieur IRT-SystemX