Executive Summary : | Laminar to turbulent tansition delay of high speed boundary layers will be studied in the presence of both hydrodynamic and acoustic mode perturbations using direct numerical simulations (DNS). To conduct the DNS studies, an in-house high-order spectral difference solver for compressible Navier-Stokes equations will be developed and coupled with a linear thermoacoustic wave equation solver. The coupled numerical tool will be used on flat plate and conical geometries to understand the combined effect of hydrodynamic and acoustic mode perturbations in both linear and nonlinear regimes. While the hydrodynamic modes (oblique modes) are responsible for transition at low Mach numbers, acoustic modes (second mode) have been discovered to be more unstable at high Mach numbers. Transition due to oblique modes results in large offshoot of skin friction and wall heat transfer compared to the second mode induced transition, rendering the control of oblique modes in high speed boundary layers more important compared to the acoustic modes. In this study, passive control techniques of both the modes will be explored numerically to determine the optimal perturbations which yield least skin friction coefficient and heat transfer over a surface in a high-speed flow. Semi-analytical models will be developed and validated against the DNS to analyze the generation these optimal perturbations through porous surfaces, whose effect only on acoustic mode instabilities has been studied in the literature. Linear and nonlinear perturbation energy budgets will be develop to derive these semi-analytical models. |