Marcelet, Meryem (2008) Shape optimization of a fluid-structure system. PhD thesis Mécanique, Département de Simulation Numérique pour la Mécanique des FLuides, ENSAM 2008ENAM0039 p.202.

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Abstract

This work is mainly dedicated to the sensitivity analysis of a static aeroelastic system with respect to design parameters governing its jig-shape. First, a framework able to predict the static aeroelastic equilibrium has been set up. The fluid behavior can be governed either by the nonlinear Euler equations or by the Navier-Stokes Reynolds averaged (RANS) equations. They are numerically solved by an ONERA CFD solver: elsA. The structural behavior is governed by the Euler-Bernoulli equations within the context of beam theory. The aerodynamic loads are transferred to the structure using the matrix of the influence coefficients, also called the flexibility matrix. Only the bending and the twisting aerodynamic load components are consistently transmitted to the structure, and only the bending and the torsional displacements of the structure are calculated under the small displacement hypothesis. The deformation induced on the fluid domain mesh is analytically prescribed using an analogy to solid mechanics. Finally, the resulting coupled aeroelastic system of equations is solved by an iterative process inspired from the fixed-point algorithm. Second, a framework aiming at computing the gradients of the functions of interest (objective and constraints) with respect to a vector of shape parameters related to the jig-shape of the aeroelastic system previously depicted, has been raised. These gradients can be computed either by the discrete direct differentiation method or by the discrete adjoint vector method. In both cases, a coupled linear system of equations has to be solved, which is carried out using a doubly lagged iterative process. Finally, this framework has been applied to the computation of the gradients of the drag and lift aerodynamic coefficients with respect to different shape parameters for three aerodynamic configurations of growing complexity: Euler equations solved on a multiblock mesh with matching boundaries, RANS equations on a monoblock mesh, and, at last, RANS equations solved on a multiblock mesh with non-matching boundaries. The analytical gradients have been validated through the comparison with the finite difference gradients. A last part of this work has been dedicated to the evaluation of the performances of four surrogate models within the shape optimization of a bidimensional turbomachinery configuration.

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