Reduced-order models for aerodynamic applications, loads and MDO

This article gives an overview of reduced-order modeling work performed in the DLR project Digital-X. Parametric aerodynamic reduced-order models (ROMs) are used to predict surface pressure distributions based on high-fidelity computational fluid dynamics (CFD), but at lower evaluation time and storage than the original CFD model. ROMs for steady aerodynamic applications are built using proper orthogonal decomposition and Isomap, a manifold learning method. Approximate solutions in the so-obtained low-dimensional representations of the data are found with interpolation techniques, or by minimizing the corresponding steady flow-solver residual. The latter approach produces physics-based ROMs driven by the governing equations. The steady ROMs are used to predict the static aeroelastic loads in a multidisciplinary design and optimization context, where the structural model is to be sized for the (aerodynamic) loads. They are also used in a process where an a priori identification of the critical load cases is of interest and the sheer number of load cases to be considered does not lend itself to high-fidelity CFD. An approach to correct a linear loads analysis model using steady CFD solutions at various Mach numbers and angles of attack and a ROM of the corrected aerodynamic influence coefficients is also shown. This results in a complete loads analysis model preserving aerodynamic nonlinearities while allowing fast evaluation across all model parameters. The different ROM methods are applied to a 3D test case of a transonic wing-body transport aircraft configuration.