Hypersonic boundary-layer transition over a circular cone in a Mach 8 digital wind tunnel

In conventional hypersonic wind tunnels, tunnel noise is dominated by acoustic radiation from turbulent nozzle-wall boundary layers, which can directly influence the boundary-layer transition (BLT) over the model in the test section. To offer new insights into BLT in conventional ground facilities, direct numerical simulations (DNS) were performed to simulate the receptivity and transition processes of a Mach 8 boundary layer over a nearly sharp $7^\circ$ half-angle cone, with transition triggered by tunnel-like broadband free-stream acoustic disturbances radiated from the nozzle wall of the Sandia hypersonic wind tunnel at Mach 8 (Sandia HWT-8). The DNS captured all the stages of the transition to turbulence caused by tunnel noise, including the passage of broadband free-stream noise through the shock wave, the receptivity process leading to the generation of Mack’s second-mode waves, their nonlinear growth to saturation, the laminar breakdown to turbulence and the post-transitional, fully turbulent flow. The transition location predicted by DNS compared well with that of Pate’s theory and was also consistent with the locations of peak pressure fluctuations as measured in the Sandia HWT-8 facility. The computed skin friction and Stanton number distributions in the initial breakdown region showed an overshoot compared with the turbulent predictions by the van Driest II theory. The wall-pressure spectra in both the transitional and turbulent regions of the cone compared well with those measured in the Sandia HWT-8. The second-mode breakdown amplitude $A_{max}$ predicted by the DNS was also consistent with sharp-cone measurements from multiple conventional wind tunnels.