Prandtl number effects on the hydrodynamic stability of compressible boundary layers: flow–thermodynamics interactions

• Published in: Journal of fluid mechanics Vol. 948
• Main Authors: Sharma, Bajrang, Girimaji, Sharath S.
• Format: Journal Article
• Language: English
• Published: Cambridge, UK Cambridge University Press 10.10.2022
• Subjects: Adiabatic; Base flow; Boundary conditions; Boundary layer stability; Boundary layers; Compressibility; Cooling; Direct numerical simulation; Energy; Flow profiles; Flow stability; Fluid mechanics; High temperature; Hydrodynamics; JFM Papers; Lagrange multiplier; Linear analysis; Mach number; Mathematical models; Perturbation; Physics; Prandtl number; Reynolds number; Stability; Thermodynamics; Trends; Turbulence; Velocity; compressible boundary layers
• ISSN: 0022-1120; 1469-7645
• DOI: 10.1017/jfm.2022.678

Hydrodynamic stability of compressible boundary layers is strongly influenced by the Mach number ($M$), Prandtl number ($Pr$) and thermal wall boundary condition. These effects manifest on the flow stability via the flow–thermodynamics 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–thermodynamics interactions are examined using linear analysis and direct numerical simulations in the following parameter regime: $0.5 \leq M \leq 8$; and $0.5 \leq Pr \leq 1.3$. For the adiabatic wall boundary condition, increasing Prandtl number has a destabilizing effect. In this work, we characterize the behaviour of production, pressure–strain correlation and pressure dilatation as functions of the 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.