Direct Numerical Simulation of Wall Cooling on Hypersonic Boundary-Layer Transition

This paper investigates the influence of wall cooling on boundary-layer instability and transition over a sharp 7-deg half-angle cone at zero angle of attack in a Mach 6 flow representative of the Air Force Research Laboratory Mach-6 Ludwieg Tube. The study uses direct numerical simulations (DNS) with random inflow forcing to examine how wall temperature conditions modify primary disturbance and transition behavior. A side-by-side comparison of DNS results for two isothermal wall conditions are performed: a warm-wall case with Tw = 298 K and a cooled-wall case with Tw = 84 K. Visualization of the boundary-layer transition, evolution of the mean flow, analysis of the turbulent spectra, and development of the turbulent flow are shown. In agreement with previous study using linear stability analysis, the simulations show, for both wall temperature conditions, that Mack’s second mode is the primary instability mechanism responsible for transition. Differences in the instabilities are observed between the cases, with the presence of Mack’s first and second modes in the warm-wall cone, while only second mode is presented in the cold wall cone. Overall, wall cooling leads to a thinner boundary layer and a corresponding shift toward higher second-mode frequencies, diminished oblique waves, a more dominant planar second-mode instability, and a downstream shift in the transition location for the cold wall.