Sensitivity analysis on supersonic-boundary-layer stability: Parametric influence, optimization, and inverse design

Abstract

Perturbations of flow control parameters may yield a significant alteration in the boundary layer stability. Based on the previously established parameter-associated sensitivity, the present work derives the optimal minor parameter perturbation analytically under the constraint of base flow energy variation. Specifically, the steady blowing-suction factor and the generalized Hartree parameter are examined at Mach number 4.5 to stabilize the mode S. Good agreement between the linear stability theory calculation, sensitivity theory, and Lagrangian approach is achieved for the optimal parametric state. The optimal state occurs if the contribution of the base velocity distortion has the greatest advantage over the temperature counterpart. Contributions of various physical sources to the growth rate behave similarly and collapse onto one correlation if normalized by the maximum, particularly for the major four: advection, mean shear, base temperature gradient, and pressure gradient. When the parameter perturbation further becomes finite, the optimal state is found on the constraint border of control parameters. Although the favorable pressure gradient and wall suction stabilize the broadband mode S, an unusual opposite tendency may occur for a single-frequency disturbance. In this unusual parametric range, positive contributions of both the major and minor physical sources to the growth rate are promoted. The contributive increase in major and minor sources are attributed to the enhancement of mean shear and viscous effect, respectively. Whether the parametric influence is stabilization or destabilization is intrinsically determined by the sensitivities, and the intermediate process is analyzed. Finally, given the modification to the critical Reynolds number, the input control parameter perturbation is inversely obtained and verified.