Dynamic large-eddy simulation of hypersonic transition delay over broadband wall impedance

Abstract

Three-dimensional numerical simulations of hypersonic boundary layer transition delay due to porosity representative of carbon-fibre-reinforced carbon-matrix ceramics (C/C) were carried out on a 7 $^{\circ {}}$ half-angle cone for unit Reynolds numbers $Re_m=2.43 \times 10^6$ – $6.40\times 10^6\ \text {m}^{-1}$ , at the free-stream Mach number $M_\infty =7.4$ , for both sharp and 2.5 mm nose tip radii. A broadband time-domain impedance boundary condition was used to model the acoustic effects of the porous surface on the flow field. A quasi-spectral sub-filter-scale dynamic closure was adopted to stabilize the computations upon turbulent breakdown under extreme cooling conditions, with wall-to-adiabatic temperature ratio of $T_{w}/ T_{ad} \simeq 0.08 $ , while accurately recovering the growth rates of the unstable modes present in the early transition stages. Good agreement is observed with the reference experimental data, both in terms of the predicted extent of the transition delay and the measured second-mode frequency spectrum. The latter is strongly modulated by the formation of near-wall low-temperature three-dimensional streaks. Pressure disturbances concentrate in corridors of locally thickened boundary layer, with frequencies lower than what predicted by linear theory. Here, trapped wavetrains are formed, which can persist long into the turbulent region. Finally, it is shown that the presence of a porous wall simply shifts the onset of turbulence downstream, without affecting its structure.