Parametric reduced-order modeling of unsteady aerodynamics for hypersonic vehicles

Abstract

A novel parametric reduced-order model (ROM) is proposed for efficiently predicting hypersonic unsteady aerodynamic responses under different flight conditions. The construction of the ROM is realized by computational fluid dynamics (CFD) simulations under the prescribed motion of the structure, while the results are processed via the proper orthogonal decomposition (POD) to obtain the predominant flow modes. Subsequently, to obtain the ROM valid for varying flight conditions, the method of interpolation in a tangent space to a Grassmann manifold is used to generate a new POD modal matrix for the arbitrary operating point in the considered parameter space. Finally, the least squares support vector machine (LS-SVM) is carried out to obtain the nonlinear relations between the applied excitations and the resulting POD coefficients. Once the parametric ROM is constructed, it can behave as a substitution of the full-order CFD flow solver in the considered parameter space. For demonstration purposes, the parametric ROM is used to predict hypersonic unsteady aerodynamic loads, flutter boundaries and limit-cycle oscillations of a double wedge airfoil over a wide range of the flight conditions, respectively. Numerical investigations show a good agreement between the results obtained by the ROM methodology in comparison to the full-order CFD solution over a wide range of the parameters. In addition, the ROM approach yields a significant speedup regarding unsteady aerodynamic calculations, which is beneficial for aeroelastic analysis, control and optimization applications.