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  • Letter
  • Open Access

Instability of mixing layers: Momentum and thermal transport in the continuum breakdown regime

Vishnu Mohan*

A. Sameen

Balaji Srinivasan

Sharath S. Girimaji

  • School of Engineering, Newcastle University, Newcastle-upon-Tyne NE1 7RU, United Kingdom

  • Department of Aerospace Engineering, Indian Institute of Technology Madras, Chennai 600036, India

  • Department of Mechanical Engineering, Indian Institute of Technology Madras, Chennai 600036, India

  • Department of Ocean Engineering, Texas A&M University, College Station, Texas 77843, USA

  • *Corresponding author: vishnu.mohan@newcastle.ac.uk
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Phys. Rev. E 108, L053101 – Published 8 November, 2023

DOI: https://doi.org/10.1103/PhysRevE.108.L053101

Abstract

We examine the momentum and thermal transport in the continuum breakdown regime of a mixing layer flow, which exhibits Kelvin-Helmholtz instability under ideal continuum conditions. The Grad 13 moment model is used as it provides an adequate description of the flow physics (second-order accurate in Knudsen number) in the transition regime. Analytical solutions are developed under breakdown conditions for two-dimensional, compressible, parallel shear flows. It is shown that the deviation of viscous stress and heat flux from the Navier-Stokes-Fourier system follows two different scaling regimes depending upon the Mach number. At low Mach numbers, the departure of all stress and heat-flux components depends only upon the Knudsen number. At high Mach number, the scaling of shear stress and transverse heat flux depends on the product of the Knudsen and Mach numbers. The normal stresses depend individually on the Knudsen and Mach number. The scaling results are verified against numerical simulations of compressible mixing layers performed using the unified gas kinetic scheme for various degrees of rarefaction.

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Outline

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Phys. Rev. E 108, L053101– Published 8 November, 2023
  • Received 30 July 2023
  • Accepted 4 October 2023
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Published by the American Physical Society under the terms of the Creative Commons Attribution 4.0 International license. Further distribution of this work must maintain attribution to the author(s) and the published article's title, journal citation, and DOI.

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