Adjoint high-dimensional aircraft shape optimization using a CAD-ROM parameterization

Abstract

A gradient-based aeroelastic shape optimization framework making use of a reduced order model to substitute a parameterization based on computer-aided design software is presented. This parameterization concept is not novel in principle, but it is embedded here in a complex high-fidelity optimization process and proven for a high-dimensional design space. The design software is used initially to generate a parametric model of a three-dimensional transport aircraft configuration. To streamline the actual optimization process, the computer-aided design model is replaced with a parametric reduced order model based on proper orthogonal decomposition that is capable of predicting discrete surface displacement fields as a function of the design parameters. During the optimization, surface displacements are computed according to the current design parameters and applied on the baseline shape. In every optimization step, the aircraft's steady-state equilibrium of forces and moments are satisfied by a trimming algorithm and the Reynolds-averaged Navier-Stokes solver TAU is coupled with a linear structural finite-element method model. Gradients are computed analytically using geometric sensitivities provided by the reduced order model and by applying the adjoint method to the flow solver and the mesh deformation tool. The workflow is embedded within FlowSimulator, a multiphysics environment for high performance computing. The optimization process is demonstrated for a high-dimensional wing parameterization with 126 degrees of freedom. The aircraft cruise drag could be significantly reduced by 6% on a series of three continuously refined meshes for the aerodynamic analysis. For an accurate representation of the optimal shape by the computer-aided design software after the optimization, the approximation error introduced by the reduced order modelling approach must be sufficiently small. Therefore, the accuracy of the predictions was analyzed. The results identify the main source of the geometric error and quantify their effect on the drag reduction gained by the optimization. We dedicate this article to the memory of our colleague and friend Arno Ronzheimer, whose devotion to CAD modeling was unsurpassed.