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Trapped waves in supersonic and hypersonic turbulent channel flow over porous walls

Published online by Cambridge University Press:  11 June 2021

Yongkai Chen Open the ORCID record for Yongkai Chen [Opens in a new window]  and
Carlo Scalo Open the ORCID record for Carlo Scalo [Opens in a new window]
Yongkai Chen*
Affiliation:
School of Mechanical Engineering, Purdue University, West Lafayette, IN47906, USA
Carlo Scalo
Affiliation:
School of Mechanical Engineering, Purdue University, West Lafayette, IN47906, USA School of Aeronautics and Astronautics, Purdue University, West Lafayette, IN47906, USA*
*
†Email address for correspondence: chen1305@purdue.edu
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Abstract

This study investigates the effect of an isothermal wall with complex impedance on compressible turbulent channel flow up to bulk Mach numbers of $6.00$. Such investigation is carried out via the time-domain impedance boundary conditions based on auxiliary differential equations method. A three-parameter complex impedance, modelling a frequency-selective porous wall, with tuneable resonating frequency $\omega _{res}$ and variable resistance $R \in [0.10, 1.0]$ is employed. Higher resistance leads to lower wall permeability with $R \rightarrow \infty$ representing the impermeable limit. Three bulk Mach numbers $M_b = \{1.50, 3.50, 6.00\}$ are investigated with a semi-local Reynolds number $Re_\tau ^{*} \approx 220$. It is found that a sufficiently low $R$ could trigger flow instabilities, which comprise streamwise-travelling waves in the near-wall region, akin to spanwise rollers at low subsonic flow conditions and second-mode waves at hypersonic conditions. The probability density function of instantaneous wall-shear stress shows an enhancement in extreme positive cases of wall-shear stress fluctuations, leading to an increase in the mean wall-shear stress due to porous walls. The wave dynamically affects the turbulence, yielding a local peak near the wall in the pre-multiplied spectrum of the production term of turbulence kinetic energy. Linear stability analysis using the turbulent base flow profile confirmed that the finite wall permeability triggers the instability when $R$ is below a threshold $R_{{cr}}$, which shows a sub-linear proportionality on the bulk Mach number $M_b$. The perturbed field exhibits more dilatational nature in high Mach number flows with low permeability.

JFM classification

Aerodynamics: High-speed flow Turbulent Flows: Compressible turbulence Flow Control: Instability control
Type
JFM Papers
Information
Journal of Fluid Mechanics , Volume 920 , 10 August 2021 , A24
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Copyright
© The Author(s), 2021. Published by Cambridge University Press

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Footnotes

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