3D global optimal forcing and response of the supersonic boundary layer
Résumé
3D optimal forcing and response of a 2D supersonic boundary layer are obtained by
computing the largest singular value and the associated singular vectors of the global
resolvent matrix. This approach allows to take into account both convective-type and
component-type non-normalities responsible for the non-modal growth of perturbations
in noise selective amplifier flows. It is moreover a fully non-parallel approach that does
not require any particular assumptions on the baseflow. The numerical method is based
on the explicit calculation of the Jacobian matrix proposed by Mettot et al. [1] for 2D
perturbations. This strategy uses the numerical residual of the compressible Navier-Stokes
equations imported from a finite-volume solver that is then linearised employing a finite
difference method. Extension to 3D perturbations, which are expanded into modes of wave
number, is here proposed by decomposing the Jacobian matrix according to the direction of
the derivatives contained in its coefficients. Validation is performed on a Blasius boundary
layer and a supersonic boundary layer, in comparison respectively to global and local
results. Application of the method to a boundary layer at M = 4.5 recovers three regions
of receptivity in the frequency-transverse wave number space. Finally, the energy growth
of each optimal response is studied and discussed.
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