Reduced-order models for aerodynamic applications, loads and MDO

Abstract

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 (POD) 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 (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. 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 (AICs) 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. Keywords reduced order model • proper orthogonal decomposition • isomap • manifold learning • multidisciplinary design and optimization • aerodynamic influence coefficients • loads analysis • CFD

A Hybrid Reduced-Order Model for the Aeroelastic Analysis of Flexible Subsonic Wings—A Parametric Assessment

“…Oswald's efficiency factor [83] is finally used to write the lift coefficient derivative for the entire wing; the unified LLT [86] shall be employed for slender wings with significant sweep angle. Within a proper orthogonal decomposition (POD) perspective [26], scaling function and aerofoil differential pressure coefficient distribution may be interpreted as the dominant (normalised) modes of the load in the spanwise and chordwise directions, respectively, with the angle of attack driving their amplitude.…”

“…A hybrid reduced-order model (ROM) [22][23][24][25][26] for the aeroelastic analysis of subsonic wings in unsteady incompressible flow is presented here within a generalised quasi-analytical formulation. A modified strip theory (MST) is adopted for the aerodynamic load [27,28], tuned (TST) and standard (SST) strip theories being readily resumed for comparison [29].…”

Model order reduction in aerodynamics: Review and applications

“…25 The DLR has also researched a method using Isomap for basis creation. 26,27 In Ripepi et al., 27 the efforts carried out by DLR under the project Digital-X on MOR are summarized, which include POD- and Isomap-based ROMs.…”

Impact of POD modes energy redistribution on flow reconstruction for unsteady flows of impulsively started airfoils and wings

“…This might happen when relying for example on Proper Orthogonal Decomposition (POD) (Weller, Lombardi and Iollo 2009;Cazemier 1998) to identify the RBM modes. POD was introduced for the analysis of turbulent flows by Lumley (Lumley 1967) and it has been widely used in literature for both steady and unsteady problems (Stabile and Rozza 2018;Ripepi et al 2018;Stabile et al 2017;Ripepi and Goertz 2015;Zhan, Habashi and Fossati 2015;Iuliano and Quagliarella 2013;Carlberg and Farhat 2008;Lieu, Farhat and Lesoinne 2005;Bui-Thanh 2003;Legresley and Alonso 2000), since it allows to describe most of the information of the initial data set with the lowest number of modes possible (Holmes et al 2012). It identifies a basis, which is the closest to the set of snapshots in terms of an average projection error based on an energy norm.…”