Input/Output Analysis of Hypersonic Boundary Layers using the One-Way Navier-Stokes (OWNS) Equations

Abstract

Accurate prediction of linear amplification of disturbances in hypersonic boundary layers is computationally challenging. While direct numerical simulations and global analysis can be used to compute optimal (worst-case) forced responses, their large computational expense render these tools less practical for large design parameter spaces. At the same time, parabolized stability equations can be unreliable for problems involving multi-modal and non-modal interactions. To bridge this gap, we apply an approximate fast marching technique, the One-Way Navier-Stokes (OWNS) Equations, in iterative fashion to solve for optimal disturbances. OWNS approximates a rigorous parabolization of the equations of motion by removing disturbances with upstream group velocity using a higher-order recursive filter. Using OWNS, we aim to characterize disturbances of flat-plate and complex-geometry hypersonic boundary layers over a range of Mach numbers, and find optimal disturbances under different cost functions that define corresponding receptivity problems. The calculation of optimal disturbances reveals multi-modal transition scenarios depending on the spatial support, frequency, and physical nature of the external disturbances.