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On the interaction of a compliant wall with a turbulent boundary layer

Published online by Cambridge University Press:  23 July 2020

Jin Wang ,
Subhra Shankha Koley  and
Joseph Katz Open the ORCID record for Joseph Katz [Opens in a new window]
Jin Wang
Affiliation:
Department of Mechanical Engineering, Johns Hopkins University, Baltimore, MD 21218, USA
Subhra Shankha Koley
Affiliation:
Department of Mechanical Engineering, Johns Hopkins University, Baltimore, MD 21218, USA
Joseph Katz*
Affiliation:
Department of Mechanical Engineering, Johns Hopkins University, Baltimore, MD 21218, USA
*
†Email address for correspondence: katz@jhu.edu
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Abstract

This study examines the interactions of a compliant wall with a turbulent boundary layer as the deformation scale increases from submicron to several wall units (δν). The friction velocity Reynolds number ranges between 1435 and 5179, and $E/\rho U_0^2$, where E is the Young modulus, varies from 59 to 2.4, $\rho $ is fluid density and $ U_0$ is free-stream velocity. Time-resolved Mach–Zehnder interferometry is used for measuring the spatial distribution of the surface deformation, and two-dimensional (2-D) particle image velocimetry for measuring the velocity in the inner part of the boundary layer. Reynolds stresses and two-point correlations are measured in the log layer. The deformation amplitude increases from 0.02δν at $E/\rho U_0^2 = 59$ to 3.6δν at $E/\rho U_0^2 = 2.4$. Wavenumber–frequency and 2-D spatial spectra show that the deformations consist of two modes: The first is an advected mode that travels downstream at 66 % of U0, has a lattice-like structure and a preferential spanwise alignment. The amplitude and frequency of this mode agree with the Chase (J. Acoust. Soc. Am., vol. 89, no. 6, 1991, pp. 2589–2596) and Benschop et al. (J. Fluid Mech., vol. 859, 2019, pp. 613–658) model predictions. The second mode is a streamwise-aligned wave that travels at the material shear speed (Ct = 7.85 m s−1) in the spanwise direction and has a wavelength of three times the compliant layer thickness. With decreasing $E/\rho U_0^2$, the velocity profiles in the boundary layer increasingly deviate from those of a rigid smooth wall. Yet, these deviations begin when the deformation is 0.02δν. The most prominent features are a sharp decrease in velocity at y < 10δν and an increase in the near-wall turbulence, both consistent, for matching $E/\rho U_0^2$, with the direct numerical simulation results of Rosti and Brandt (J. Fluid Mech., vol. 830, 2017, pp. 708–735).

JFM classification

Turbulent Flows: Turbulent boundary layers
Type
JFM Papers
Information
Journal of Fluid Mechanics , Volume 899 , 25 September 2020 , A20
Copyright
© The Author(s), 2020. Published by Cambridge University Press

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Wang et al. supplementary movie 1

Spatially detrended deformation of a compliant wall at ${\it U_0}=1.2\;m/s$, and ${\it E/\rho U_0^2} = 59.0$
Download Wang et al. supplementary movie 1(Video)
Video 9.7 MB

Wang et al. supplementary movie 2

Spatially detrended deformation of a compliant wall at ${\it U_0}=3.2\;m/s$, and ${\it E/\rho U_0^2} = 8.3$
Download Wang et al. supplementary movie 2(Video)
Video 10.3 MB

Wang et al. supplementary movie 3

Spatially detrended deformation of a compliant wall at ${\it U_0}=5.3\;m/s$, and ${\it E/\rho U_0^2} = 3.0$
Download Wang et al. supplementary movie 3(Video)
Video 10.3 MB