Effects of Optimized Vortex Generators on Mack Mode-Dominated Boundary Layer Transition*

The primary purpose of this study is to examine the potential for Mack mode stabilization and transition delay of an optimized vortex generator (VG) shape on a circular cone at hypersonic flight conditions. The configuration of interest corresponds to a selected trajectory point from the ascent phase of the HiFIRE-1 flight experiment. Both experimental and numerical studies have shown Mack mode amplification to be the leading mechanism of laminar to turbulent transition in hypersonic boundary layers. Calculations with streamwise streaks generated by VGs have shown that they can reduce the net amplification of Mack modes, effectively delaying boundary-layer transition. The shape of the VGs used in this study is optimized by using SU2's adjoint solver for mean streak amplitude along the wake of the VGs. The optimized VGs are found to yield mean streak amplitude values that are several times larger than those corresponding to the baseline design. A grid refinement study is performed to determine the effect of grid resolution on the optimized shape and streak amplitude evolution. The stability of the VG wake is examined using the plane-marching parabolized stability equations (PSE) to establish the potential of the VGs for transition delay and establish the benefit of the VG optimization.