Reduced-order modeling of transonic flows around an airfoil submitted to small deformations

  • Authors:

  • Rémi Bourguet;Marianna Braza;Alain Dervieux

  • Affiliations:

  • Massachusetts Institute of Technology, 77 Massachusetts Avenue, Cambridge, MA 02139-4307, USA;Institut de Mécanique des Fluides de Toulouse, 6 Allée du Professeur C. Soula, Toulouse 31400, France;Institut National de Recherche en Informatique et en Automatique, 2004 Route des Lucioles - BP 93, Sophia-Antipolis 06902, France

  • Venue:
  • Journal of Computational Physics
  • Year:
  • 2011

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Abstract

A reduced-order model (ROM) is developed for the prediction of unsteady transonic flows past an airfoil submitted to small deformations, at moderate Reynolds number. Considering a suitable state formulation as well as a consistent inner product, the Galerkin projection of the compressible flow Navier-Stokes equations, the high-fidelity (HF) model, onto a low-dimensional basis determined by Proper Orthogonal Decomposition (POD), leads to a polynomial quadratic ODE system relevant to the prediction of main flow features. A fictitious domain deformation technique is yielded by the Hadamard formulation of HF model and validated at HF level. This approach captures airfoil profile deformation by a modification of the boundary conditions whereas the spatial domain remains unchanged. A mixed POD gathering information from snapshot series associated with several airfoil profiles can be defined. The temporal coefficients in POD expansion are shape-dependent while spatial POD modes are not. In the ROM, airfoil deformation is introduced by a steady forcing term. ROM reliability towards airfoil deformation is demonstrated for the prediction of HF-resolved as well as unknown intermediate configurations.