Reduced-Order Modeling of Steady Flows Subject to Aerodynamic Constraints

Abstract

A novel reduced-order modeling method based on proper orthogonal decomposition for predicting steady, turbulent flows subject to aerodynamic constraints is introduced. Model-order reduction is achieved by replacing the governing equations of computational fluid dynamics with a nonlinear weighted least-squares optimization problem, which aims at finding the flow solution restricted to the low-order proper orthogonal decomposition subspace that features the smallest possible computational fluid dynamics residual. As a second and new ingredient, aerodynamic constraints are added to the nonlinear least-squares problem. It is demonstrated that the constrained nonlinear least-squares problem can be solved almost as efficiently as its unconstrained counterpart and outperforms all alternative approaches known to the authors. The method is applied to data fusion, seeking to combine the use of computational fluid dynamics with wind-tunnel or flight testing to improve the prediction of aerodynamic loads. It is also demonstrated that it can be used to compute aerodynamic loads for a given aerodynamic configuration subject to aerodynamic design or performance targets. Exemplary results considering both applications are computed for the NACA 64A010 airfoil and the DLR-F15 high-lift configuration.