Numerical studies on receptivity and transition of Gortler instabilities in hypersonic boundary layers

The transition of hypersonic boundary layer flow is one of the fundamental problems in fluid mechanics, and Görtler instability is one of many boundary layer instability mechanisms. The study of the Görtler vortices and their role in laminar-turbulent transition of hypersonic boundary layers has practical significance because many engineering designs, such as hypersonic engine inlets, involve concave surfaces. In general, Görtler vortices become turbulent in four steps: (1) the receptivity of disturbances, (2) the linear growth of the spanwise disturbances, (3) the nonlinear development of the vortices, and (4) the secondary instabilities. Although there have been extensive studies on the Görtler instabilities in incompressible flow, there are only a few studies in hypersonic flows based on LST (linear stability theory) or asymptotic studies only.; In this research, linear and nonlinear development and receptivity of the hypersonic Görtler vortices are studied using both the spatial DNS (direct numerical simulation) and LST approaches. At the same time, the properties of the Görtler are also analyzed by linear stability analysis and are compared with the DNS results. Specifically, Görtler vortices in a Mach 15 flow over a blunt wedge with a concave surface are investigated by solving the full Navier-Stokes equations in a spatially developing computational domain bounded by the bow shock wave and the solid wall.; It is found that DNS results of linear development of hypersonic Görtler vortices agree well with those from LST which shows that the linear region of hypersonic Görtler vortices can be predicted by LST analysis. The DNS results of the nonlinear development of the hypersonic Görtler vortices show the overall results of the nonlinear development of Görlter instability at hypersonic flow are similar to those in incompressible flow, with the exception that higher harmonic modes as well as the fundamental change significantly compared to the linear solution. Leading edge receptivity to free stream standing vorticity waves shows that there are two growing mechanisms inside hypersonic boundary layers induced by the vorticity waves which are the early spatial transient growth near the leading edge due to the coupling of non-orthogonal eigenvectors and Görlter instability in concave region. While the early transient growth is due to the superposition of different non-orthogonal modes, Görlter instability is the growth of a single mode. However, it is found that these mechanisms have the similar characteristics which implies the growing mechanism due to the early transient is closely related with the one in Görtler instability. It may be because two different growing mechanisms are originated from the same lift-up effects of counter rotating vortices.