Efficient Computation of Boundary-Layer Instabilities in Highly Three-Dimensional Flows

Abstract

Boundary-layer transition from laminar to turbulent flow critically affects vehicle safety and performance, particularly at hypersonic speeds where heat-transfer rates are extreme. Accounting for transition effects requires robust tools capable of modeling the underlying physical mechanisms that lead to turbulence. Transition is notoriously sensitive to the details of the underlying flow; therefore, any reduced-order models must balance correct physical assumptions with rising computational cost. A major goal of this work is to enable linear disturbance modeling in flows with a rapid streamwise variation at a reduced cost compared to direct numerical simulations. To this end, a tool is developed to solve the harmonic linearized Navier–Stokes (HLNS) equations, which are capable of modeling perturbations in flows with large gradients in two or three spatial directions. The new solver is applied to two locations on a cone with a highly-swept fin in Mach 6 flow: the leading edge of the fin and on the cone near the upstream start of the fin. Prior to investigating the stability characteristics of either location, an in-depth study of the finned cone basic state is performed for a range of freestream and geometric parameters. This provides an enhanced understanding of the basic state within the parameter space explored by previous experiments. The large, stationary vortices present in the flow field require significant computational resources to converge, which introduces possible errors when comparing against experimental data. Particular attention is paid to minimizing all potential sources of error in the basic state, and quantifying errors where this is not possible. The lessons learned in this study inform the generation of all remaining basic states presented in this dissertation. Flow near the leading edge of the fin contains a large component of crossflow velocity, potentially destabilizing the crossflow instability. To investigate this, the two-dimensional HLNS solver is employed to model perturbation growth on the fin. The HLNS approach is required in this case because of reversed flow (in the stability frame of reference) found near the wall due to the large, stationary vortex which exists on the fin. The growth and characteristics of both stationary and travelling disturbances are computed. An investigation on the perturbation sensitivity to slight yaw angles reveals the disturbances follow trends associated with the classic crossflow instability. This gives additional insight into the mechanism driving the perturbation growth on the fin. Finally, the growth of perturbations around the start of the fin-cone junction is considered. Some consideration is given to the possibility of absolute instabilities present in the small separation region which forms upstream of the fin for certain freestream and geometric configurations. The decay rate of an absolute instability is estimated for several Reynolds numbers using the residuals algorithm. Three-dimensional HLNS calculations are used to model the growth of convective disturbances subject to the large spatial gradients present in this region. This work adds to the community’s understanding of how instabilities develop on the surface of the finned cone.