Linear stability of high-speed boundary layer flows at varying Prandtl numbers

Abstract

Accurate prediction of laminar to turbulent transition at hypersonic velocities is a challenging task. The high temperature and low pressure encountered in such applications can lead to large variations in physical and transport properties of the gas. This can result in significant changes in the effective Prandtl number. In this paper, we study the physical effects of Prandtl number on the stability of high Mach number boundary layer flows. Prandtl number values in the range of 0.3 to 1.2 are chosen and a temporal linear stability problem is formulated. The resulting eigenvalue problem is solved using Chebyshev spectral collocation method. We study the effect of Prandtl number on the eigenspectrum for a range of Mach number, Reynolds number and disturbance wave number. It is found that certain combinations of these parameters lead to synchronization between the fast and the slow modes, which can contribute to the peak growth rate. Two types of branching patterns are observed depending on the Prandtl number, where either the fast or the slow mode can be destabilized due to mode-synchronization. The stability diagrams plotted for a range of Reynolds number and wavenumber show a destabilizing role for increasing the Prandtl number, leading to larger regions of instability, and increased growth rates. This also leads to a significant reduction in the critical Reynolds number specifically at intermediate Mach numbers. High-speed flat plate boundary layer flow is thus found to be highly sensitive to slight changes in the Prandtl number.