Application of the One-Way Navier-Stokes (OWNS) Equations to Hypersonic Boundary Layers

Abstract

Prediction of linear amplification of disturbances in hypersonic boundary layers is challenging due to the presence and interactions of discrete modes (e.g. Tollmien-Schlichting and Mack) and continuous modes (entropic, vortical, and acoustic). While DNS and global analysis can be used, the large grids required make the computation of optimal transient and forced responses expensive, particularly when a large parameter space is required. At the same time, parabolized stability equations are non-convergent and unreliable for problems involving multi-modal and non-modal interactions. In this work, we apply the One-Way Navier-Stokes (OWNS) equations to hypersonic boundary layers. OWNS is based on a rigorous, approximate parabolization of the equations of motion that removes disturbances with upstream group velocity using a high-order recursive filter. We extend the original algorithm by considering non-orthogonal body-fitted curvilinear coordinates and incorporate full compressibility with temperature-dependent fluid properties. We validate the results by comparing to DNS data for a flat plate and sharp cone, and to LST results for local disturbances on the centerline of the HIFiRE-5 elliptic cone. OWNS provides DNS-quality results for the former flows at a small fraction of the computational expense.