Numerical investigation of transition for a cone at Mach 3.5: Oblique breakdown

The transition process initiated by one or multiple pairs of oblique waves is studied for a 7°-cone using direct numerical simulation (DNS). The simulations were performed under the experimental conditions of the NASA Langley Mach 3.5 Quiet Tunnel. In particular, we investigated two scenarios: (i) the transition process initiated by a single pair of oblique waves with azimuthal mode number k_c = 12 and (ii) the transition process initiated by first a single and then by multiple pairs of oblique waves with azimuthal mode number k_c = 32. The first case (k_c = 12) corresponds to planned experiments at NASA Langley with a controlled disturbance input, whereas the latter case (k_c = 32) attempts to mimic 'natural' transition by superimposing waves with a broad frequency spectrum (but only a single azimuthal wave number) at the in flow. The amplitudes of these waves correspond to their N{factors (e^N- method) obtained from precursor simulations of the linear regime. Qualitative similarities and differences have been documented. In particular, the intermittency resulting from the superposition of waves with a broad frequency spectrum causes the transition location to vary in time. Moreover, the results in this paper indicate that if transition is initiated by multiple pairs of oblique waves with a broad frequency spectrum, nonlinear mechanisms are enhanced when compared to the case, where transition was initiated by a single pair of oblique waves. Therefore, in the time average, the transition location for the case with multiple pairs of oblique waves is located upstream of the transition location for the case with a single pair of oblique waves.