Numerical investigation of nonlinear entropy-layer instability waves for hypersonic boundary-layers

Direct Numerical Simulations (DNS) were carried out to investigate the laminar-turbulent transition for a blunt (right) cone (7^◦ half-angle) at Mach 5.9 and zero angle of attack. First, (linear) stability calculations were carried out employing the same DNS 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) approach. Secondly, a highly-resolved nonlinear breakdown simulation was performed using high-fidelity DNS. The DNS results showed that linearly unstable oblique disturbance waves, when excited with large enough amplitudes, lead to a rapid breakdown and complete laminar-turbulent transition in the entropy layer just downstream of the blunted nose.