Dynamic mode decomposition of trip-induced hypersonic boundary layer transition

We study the transition of a Mach 5.65 laminar boundary layer tripped by an array of diamond shaped roughness elements using large-scale direct numerical simulations. A low Reynolds number experiment conducted at the Actively Controlled Expansion Hypersonic Wind Tunnel, Texas A & M University National Aerothermochemistry Laboratory is used to validate our simulation. Planar acoustic disturbances are applied at the in flow boundary to mimic the wind tunnel ambient environment. To accurately capture flow physics, a high- order, low-dissipation scheme for the convection terms in the Navier-Stokes equations is used. Visualizations and statistics of the flow explore the dominant and dynamically significant flow structures : the upstream vortex system, the shock system, and the downstream separated shear layer/wake region which originates from the top and sides of the roughness elements. Three-dimensional snapshots of pressure were considered to select dominant dynamic mode decomposition modes using Chu's disturbance energy norm. A coupled system at 30 kHz consisting of the shock system, the separated shear layer/wake region and the upstream vortex system is determined to have the most disturbance energy. The origin of disturbances is observed to be the upstream vortex system while the wake region acts as a dominant amplifier. Comparison of the flow structures and modes of transition between an isolated cylindrical roughness element and the array of diamond shaped roughness elements is performed.