Reduced Order Models for Aerodynamic Applications, Loads and MDO

This work gives an overview of Reduced Order Model (ROM) applications employed within the context of the DLR Digital-X project. The ROM methodology has found widespread application in fluid dynamics. In its direct application to CFD it seeks to reduce the computational complexity of a problem by reducing the number of degrees of freedom rather than simplifying the physical model. Here, parametric aerodynamic ROMs are used to provide pressure distributions based on high-fidelity CFD, but at lower evaluation time and storage than the original CFD model. ROMs for steady aerodynamic applications are presented. We consider ROMs combining proper orthogonal decomposition (POD) and Isomap, which is a manifold learning method, with interpolation methods as well as physics-based ROMs, where an approximate solution is found in the POD-subspace or non-linear manifold by minimizing the corresponding steady or unsteady flow-solver residual. The issue of how to train the ROM with high-fidelity CFD data is also addressed. The steady ROMs are used to predict the static aeroelastic loads in an MDO 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. We also show an approach combining correction of a linear loads analysis model using steady, rigid CFD solutions at various Mach numbers and angles of attack with a ROM of the corrected Aerodynamic Influence Coefficients (AICs). This integrates the results into a complete loads analysis model preserving aerodynamic nonlinearities while allowing fast evaluation across all model parameters. Thus, correction for the major nonlinearities, e.g. depending on Mach number and angle of attack combines with the linearity of the baseline model to yield a large domain of validity across all flow parameters at the expense of a relatively small number of CFD solutions. The different ROM methods are applied to 3D test cases and in particular to a transonic wing-body transport aircraft configuration