Direct Numerical Simulations of laminar-turbulent boundary-layer transition for blunt cones at Mach 6: Effect of Varying Nose Bluntness

Direct Numerical Simulations (DNS) were carried out to investigate laminar-turbulent boundary-layer transition for a straight cone (7^◦ half-angle) with varying nose radii at Mach 6 and zero angle of attack. First, a conventional Linear Stability Theory (LST) solver was used in order to determine the critical Reynolds number for amplification of second mode disturbances for each of the cases considered here. Next, (linear) stability calculations were carried out by employing a high-order Navier-Stokes solver and using very small disturbance amplitudes in order to capture the linear disturbance development. Contrary to standard Linear Stability Theory results, these investigations revealed a strong “linear” instability in the entropy layer region for a very short downstream distance for oblique disturbance waves with spatial growth rates far exceeding those of second mode disturbances. This linear instability behavior was not captured with conventional LST and/or the Parabolized Stability Equations (PSE). Nonlinear breakdown simulations were performed using high-fidelity DNS for three different cases. The DNS results showed that linearly unstable oblique disturbance waves, when excited with large enough amplitudes, lead to a rapid breakdown and the onset of laminar-turbulent transition in the entropy layer just upstream of the second-mode instability region.