Computational analysis of receptivity and growth mechanisms in laminar boundary layers
Final Report Abstract
An integrated framework for performing stability analyses of high speed flows over complex geometry including shocks has been developed. The framework consists of a nonlinear, linearized, and adjoint linearized compressible Navier-Stokes solver combined with a matrix-free solver for eigenvalue problems. An unstable global eigenfunction of the flow over a high speed cone was analyzed. The eigenfunction is localized near the curved tip of the cone and shows features similar to that of a Tollmien-Schlichting wave. The corresponding adjoint eigenfunction indicates highly receptive regions upstream of the blunt tip and the bow shock, bounded by the incoming free-stream characteristics. More generally, the framework can form the foundation for far reaching further investigations into the stability of hypersonic vehicles. Specifically, the implementation of an adjoint solver allows the rigorous analysis of the receptivity and sensitivity of high-speed flows. An example of a particularly promising potential application is the direct identification of modifications of the base flow which result in a weakening of the growth of exponential instabilities which are associated with breakdown to turbulence in high-speed flows. Perspectives for the industrial application could be for instance the development of models for laminarturbulent transition. Ongoing discussions explore potential collaborations with partners from industry.
Publications
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Algebraic disturbance growth by interaction of Orr and lift-up mechanisms. J. Fluid Mech. 829 p. 112–126
Hack, M.J.P. & Moin, P.
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Coherent instability in wall-bounded shear. J. Fluid Mech. 844 p. 917–955
Hack, M.J.P. & Moin, P.
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(2020) A variational framework for computing nonlinear optimal disturbances in compressible flows. Journal of Fluid Mechanics, 894 A5
Huang, Z., Flint, T. & Hack, M.J.P.
