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

JOURNAL OF COMPUTATIONAL PHYSICS

卷:230

Article

Bourguet, Remi¹  Braza, Marianna²  Dervieux, Alain³ 

[1] MIT, Cambridge, MA 02139 USA

[2] Inst Mecan Fluides Toulouse, F-31400 Toulouse, France

[3] Inst Natl Rech Informat & Automat, F-06902 Sophia Antipolis, France

关键词: Reduced-order modeling;    Navier-Stokes equations;    Hadamard formulation;    Proper Orthogonal Decomposition;    Transonic regime;    Shape deformation;   

DOI  :  10.1016/j.jcp.2010.09.019

来源: Elsevier

【 摘 要 】

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. (C) 2010 Elsevier Inc. All rights reserved.

【 授权许可】

Free