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arXiv · 2205.05742

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

Bajrang Sharma·Sharath S. Girimaji
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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.

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Bajrang Sharma, Sharath S. Girimaji. 2022-05-11. Prandtl number effects on the hydrodynamic stability of compressible boundary layers: flow-thermodynamic interactions. https://doi.org/10.1017/jfm.2022.678

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