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Model order reduction for steady aerodynamics of high-lift configurations

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Abstract

In aerodynamic applications, many model reduction methods use proper orthogonal decomposition (POD). In this work, a POD-based method, called missing point estimation (MPE), is modified and applied to steady-state flows with variation of the angle of attack. The main idea of MPE is to select a subset of the computational grid points (control volumes) and to limit the governing equations to this subset. Subsequently, the limited equations are projected onto the POD subspace. This approach has the advantage that the nonlinear right-hand side of the governing equations has to be evaluated only for a small number of points (control volumes) in contrast to POD, for which the full right-hand side has to be evaluated. An error estimation for MPE in the continuous ODE setting is tackled. Numerical results are presented for the Navier–Stokes equations for two different industrially relevant, two-element high-lift airfoils, one which is normally adopted during landing and the other during take-off.

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Notes

  1. Note that the scaling with the volume matrix \(\tilde{V}\) is not included in the matrix, since in [5, 6] the Euclidean scalar product instead of the \(L_2\) scalar product is used.

  2. Note that the chord of the main element with stowed flap was 0.6 grid units.

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Acknowledgments

The research of the first author was supported by the German Federal Ministry of Economics and Technology (BMWi), Grant No. 20A0801D. The work of the German Aerospace Center (DLR) was supported in part by the European Regional Development Fund, Economic Development Fund of the Federal German State of Lower Saxony, Contract/Grant Number: W3-80026826, and also by the German Federal Ministry of Economics and Technology (BMWi), Grant No. 20A0801A.

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Authors and Affiliations

  1. Technische Universität Braunschweig, Institut Computational Mathematics, AG Numerik, Fallersleber-Tor-Wall 23, 38100, Braunschweig, Germany

    Alexander Vendl & Heike Faßbender

  2. German Aerospace Center (DLR), Institute of Aerodynamics and Flow Technology, Lilienthalplatz 7, 38108, Braunschweig, Germany

    Stefan Görtz, Ralf Zimmermann & Michael Mifsud

Authors
  1. Alexander Vendl
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  2. Heike Faßbender
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  3. Stefan Görtz
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  4. Ralf Zimmermann
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  5. Michael Mifsud
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Corresponding author

Correspondence to Alexander Vendl.

Additional information

Present address for the author Ralf Zimmermann is Technische Universität Braunschweig, Institut Computational Mathematics, AG Numerik, Fallersleber-Tor-Wall 23, 38100 Braunschweig, Germany.

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Vendl, A., Faßbender, H., Görtz, S. et al. Model order reduction for steady aerodynamics of high-lift configurations. CEAS Aeronaut J 5, 487–500 (2014). https://doi.org/10.1007/s13272-014-0116-1

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  • DOI: https://doi.org/10.1007/s13272-014-0116-1

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