Instability-wave propagation in boundary-layer flows at subsonic through hypersonic Mach numbers

Direct numerical simulations (DNS) form an important ingredient to physics-based prediction of laminar-turbulent transition in boundary-layer flows, particularly in applications where it is desirable or even essential to model the various stages of transition process in an integrated manner. This paper addresses two building-block issues towards such capability: application to instability-wave propagation in boundary layers over curvilinear surfaces and robust outflow boundary conditions across the speed regime. In particular, detailed comparisons of linear and nonlinear development of instability waves in a range of boundary-layer flows are used to cross-validate a high-order direct numerical simulation algorithm against the approximate but computationally more efficient technique of parabolized stability equations (PSE). Three separate flow configurations are investigated in this study: (i) development of a Tollmien-Schlichting (TS) instability wave over a two-dimensional (2D), symmetric, low-speed airfoil, (ii) both first and second-mode development in a self-similar, flat plate boundary layer at Mach 4.5, and (iii) amplification of first and second modes of Rayleigh instability and a stationary Gortler vortex in the hypersonic, axisymmetric boundary layer over a flared cone. The satisfactory agreement between the DNS and PSE predictions for both amplitudes and mode shapes of the instability waves confirms the overall efficacy of the DNS algorithm, while underscoring the accuracy of predictions based on the PSE approximation.