Hypersonic boundary layer transition control over a 3$^{\circ}$ half-angle sharp cone via distributed porosity

The effectiveness of ultrasonic absorptive coatings (UACs) in achieving delay in turbulent transition on a hypersonic boundary layer over a 3 $^\circ$ half-angle cone was investigated under flight-like free-stream disturbance conditions. Tests were conducted at the Boeing/AFOSR Mach 6 Quiet Tunnel at Purdue University for four free-stream Reynolds numbers ranging from $9.0\times 10^6\,$ to $14.3 \times 10^6\,\rm m^{-1}$ . Silicon-carbide-coated carbon foams with pore densities of 60, 100 and 200 pores per inch (X0.6, X1, X2) were fabricated as three frustums to vary streamwise location and porous section length. Solid–porous configurations were constructed to analyse the effect of foam length and position. Axisymmetric direct numerical simulations (DNS) and linear-stability theory (LST) analysis were performed to support the experimental findings, modelling the porous foams as time-domain impedance boundary conditions. The UACs influence boundary-layer transition primarily by modifying wall impedance and providing acoustic absorption to weaken second-mode resonance. All porous foams exhibited this behaviour, with the X1 foam achieving the most effective transition delay, strongly dependent on placement. Downstream positioning (59.2–74.3 cm) produced a 13.6 % relative delay, whereas upstream extension (44.1–74.3 cm) led to initial stabilisation followed by a downstream overshoot in second-mode amplitude. The X0.6 and X2 foams showed similar trends. Both LST and DNS predict attenuation of the high-frequency second-mode band and delayed amplification of adjacent low-frequency modes, explaining the overshoot and placement sensitivity. A detailed comparison of $N$ -factors shows excellent agreement among experiment, LST and DNS, reinforcing the validity of the combined methodology and the consistency of the identified instability mechanisms.