Prandtl number effects on the hydrodynamic stability of compressible boundary layers: flow-thermodynamic interactions

TL;DR

This study investigates how Prandtl number and Mach number influence the stability of compressible boundary layers through flow-thermodynamic interactions, using linear analysis and DNS to reveal destabilizing effects and mode-specific physics.

Contribution

It provides a detailed analysis of Prandtl number effects on flow stability and elucidates the underlying physics for different instability modes in compressible boundary layers.

Findings

Increasing Prandtl number destabilizes the flow for adiabatic walls.

First and second instability modes show opposite underlying physics.

Prandtl number effects are linked to base flow profile and perturbation modes.

Abstract

Hydrodynamic stability of compressible boundary layers is strongly influenced by Mach number ($M$), Prandtl number ($Pr$) and thermal wall boundary condition. These effects manifest on the flow stability via the flow-thermodynamic interactions. Comprehensive understanding of stability flow physics is of fundamental interest and important for developing predictive tools and closure models for integrated transition-to-turbulence computations. The flow-thermodynamic interactions are examined using linear analysis and direct numerical simulations (DNS) in the following parameter regime: $0.5 \leq M \leq 8$; and, $0.5 \leq Pr \leq 1.3$. For adiabatic wall boundary condition, increasing Prandtl number has a destabilizing effect. In this work, we characterize the behavior of production, pressure-strain correlation and pressure-dilatation as functions of Mach and Prandtl numbers. First and second instability modes exhibit similar stability trends but the underlying flow physics is shown to be diametrically opposite. The Prandtl-number influence on instability is explicated in terms of the base flow profile with respect to the different perturbation mode shapes.