Receptivity and instability of the hypersonic flow over moderately blunt cones

TL;DR

This study uses resolvent analysis to investigate the receptivity and instability mechanisms in hypersonic flow over a blunt cone, revealing how wall temperature and entropy-layer effects influence mode amplification and transition processes.

Contribution

It provides new insights into the linear receptivity and amplification mechanisms in hypersonic blunt cone flows, highlighting the role of entropy-layer effects and wall temperature conditions.

Findings

Stationary streak modes are most amplified in isothermal conditions.

The first Mack mode dominates in adiabatic conditions.

Entropy-layer disturbances significantly influence receptivity structures.

Abstract

With a view to identifying and understanding the linear receptivity and amplification mechanisms that underpin laminar-to-turbulent transition over blunt bodies in hypersonic flow, we use resolvent analysis to study the flow over a blunt cone with 7{\deg} half-angle at Mach number $M_{\infty} = 6$, zero angle of attack, and nose-radius-based Reynolds number $Re_{R_n} = 90000$. Optimal forcing and responses are obtained for frequencies up to 330 kHz and azimuthal wavenumbers between 0 and 200. Wall-temperature effects are accounted for by considering both isothermal ($T_w =$ 300 K) and adiabatic wall conditions. The resolvent analysis shows that stationary streak modes are the most amplified in the isothermal case, followed by entropy-layer modes between 20 and 140 kHz. In the adiabatic case, the $1^{st}$ Mack mode is the most amplified. The entropy layer, caused by the nose-tip bluntness, has a profound influence on the receptivity structures. For the optimal streak mode, the most intense receptivity structures lie deep in the entropy layer, further away from the boundary-layer edge compared to the equivalent sharp-cone streak mode. This indicates that atmospheric disturbances may excite streak-like instability without fully penetrating the boundary layer. For the entropy-layer modes, the dominant receptivity and fluctuation signatures are located within the entropy layer. An energy-budget analysis reveals that these modes are most susceptible to kinetic disturbances and they sign the most on temperature fluctuations. These modes are found to leverage a temperature mixing mechanism that exploits the baseflow's wall-normal temperature gradient in the entropy layer to grow.