Reduced order modeling of steady flows subject to aerodynamic constraints

Ralf Zimmermann, Alexander Vendl, Stefan Goertz

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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.
Original languageEnglish
JournalAIAA Journal
Issue number2
Pages (from-to)255-266
Number of pages12
Publication statusPublished - 2014
Externally publishedYes


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