Skip to main content Accessibility help
×
Home

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

  • Jin Wang (a1), Subhra Shankha Koley (a1) and Joseph Katz (a1)

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).

Copyright

Corresponding author

Email address for correspondence: katz@jhu.edu

References

Hide All
Adrian, R. J. 1991 Particle-imaging techniques for experimental fluid mechanics. Annu. Rev. Fluid Mech. 23 (1), 261304.
Benjamin, T. B. 1960 Effects of a flexible boundary on hydrodynamic stability. J. Fluid Mech. 9, 513532.
Benjamin, T. B. 1963 The threefold classification of unstable disturbances in flexible surfaces bounding inviscid flows. J. Fluid Mech. 16, 436450.
Benschop, H. O. G., Greidanus, A. J., Delfos, R., Westerweel, J. & Breugem, W.-P. 2019 Deformation of a linear viscoelastic compliant coating in a turbulent flow. J. Fluid Mech. 859, 613658.
Blick, E. F. & Walters, R. R. 1968 Turbulent boundary-layer characteristics of compliant surfaces. J. Aircraft 5 (1), 1116.
Brereton, G. J. & Hwang, J. L. 1994 The spacing of streaks in unsteady turbulent wall-bounded flow. Phys. Fluids 6, 24462454.
Burattini, P., Leonardi, S., Orlandi, P. & Antonia, R. A. 2008 Comparison between experiments and direct numerical simulations in a channel flow with roughness on one wall. J. Fluid Mech. 600, 403426.
Carpenter, P. W., Davies, C. & Lucey, A. D. 2000 Hydrodynamics and compliant walls: does the dolphin have a secret? Curr. Sci. 79 (6), 758765.
Carpenter, P. W. & Garrad, A. D. 1985 The hydrodynamic stability of flows over Kramer-type compliant surfaces. Part 1. Tollmien–Schlichting instabilities. J. Fluid Mech. 155, 465510.
Carpenter, P. W. & Garrad, A. D. 1986 The hydrodynamic stability of flows over Kramer-type compliant surfaces. Part 2. Flow-induced surface instabilities. J. Fluid Mech. 170, 199232.
Castellini, P., Martarelli, M. & Tomasini, E. P. 2006 Laser Doppler vibrometry: development of advanced solutions answering to technology's needs. Mech. Syst. Signal Process. 20, 12651285.
Charruault, F., Greidanus, A. & Westerweel, J. 2018 A dot tracking algorithm to measure free surface deformations. In 18th Intl Symp. on Flow Visualization, Zurich, Switzerland. ETH Zurich.
Chase, D. M. 1991 Generation of fluctuating normal stress in a viscoelastic layer by surface shear stress and pressure as in turbulent boundary-layer flow. J. Acoust. Soc. Am. 89 (6), 25892596.
Choi, K.-S., Yang, X., Clayton, B. R., Glover, E. J., Atlar, M., Semenov, B. N. & Kulik, V. M. 1997 Turbulent drag reduction using compliant surfaces. Proc. R. Soc. Lond. A 453, 22292240.
Djenidi, L., Antonia, R. A., Amielh, M. & Anselmet, F. 2008 A turbulent boundary layer over a two-dimensional rough wall. Exp. Fluids 44, 3747.
Duncan, J. H. 1986 The response of an incompressible, viscoelastic coating to pressure fluctuations in a turbulent boundary layer. J. Fluid Mech. 171, 339363.
Endo, T. & Himeno, R. 2002 Direct numerical simulation of turbulent flow over a compliant surface. J. Turbul. 3, 110.
Fisher, D. H. & Blick, E. F. 1966 Turbulent damping by flabby skins. J. Aircraft 3 (2), 163164.
Flack, K. A. & Schultz, M. P. 2014 Roughness effects on wall-bounded turbulent flows. Phys. Fluids 26, 101305.
Gad-El-Hak, M. 1986 The response of elastic and visco-elastic surfaces to a turbulent boundary layer. Trans. ASME E: J. Appl. Mech. 53, 206212.
Gad-El-Hak, M., Blackwelder, R. F. & Riley, J. J. 1984 On the interaction of compliant coatings with boundary layer flows. J. Fluid Mech. 140, 257280.
Gao, J. & Katz, J. 2018 Self-calibrated microscopic dual-view tomographic holography for 3D flow measurements. Opt. Express 26, 1670816725.
Ghiglia, D. C., Mastin, G. A. & Romero, L. A. 1987 Cellular-automata method for phase unwrapping. J. Opt. Soc. Am. A 4, 267280.
Goldstein, R. M., Zebker, H. A. & Werner, C. L. 1988 Radar interferometry: two-dimensional phase unwrapping. Radio Science 23, 713720.
Goody, M. 2004 Empirical spectral model of surface pressure fluctuations. AIAA J. 42 (9), 17881794.
Grant, I. 1997 Particle image velocimetry: a review. Proc. Inst. Mech. Engrs C 211, 5576.
Hansen, R. J. & Hunston, D. L. 1974 An experimental study of turbulent flows over compliant surfaces. J. Sound Vib. 34, 297308.
Hansen, R. J. & Hunston, D. L. 1983 Fluid-property effects on flow-generated waves on a compliant surface. J. Fluid Mech. 133, 161177.
Harris, G. L. & Lissaman, P. B. S. 1969 Turbulent skin friction on compliant surfaces. AIAA J. 7 (8), 16251627.
Hartman, B., Lee, G. F. & Lee, J. D. 1994 Loss factor height and widths for polymer relaxations. J. Acoust. Soc. Am. 95 (1), 226233.
Hess, D. E., Peattie, R. A. & Schwarz, W. H. 1993 A noninvasive method for the measurement of flow-induced surface displacement of a compliant surface. Exp. Fluids 14, 7884.
Hong, J., Katz, J., Meneveau, C. & Schultz, M. P. 2012 Coherent structures and associated subgrid-scale energy transfer in a rough-wall turbulent channel flow. J. Fluid Mech. 712, 92128.
Hong, J., Katz, J. & Schultz, M. P. 2011 Near-wall turbulence statistics and flow structures over three-dimensional roughness in a turbulent channel flow. J. Fluid Mech. 667, 137.
Ikeda, T. & Durbin, P. A. 2007 Direct simulations of a rough-wall channel flow. J. Fluid Mech. 571, 235263.
Jimenez, J. 2003 Turbulent flows over rough walls. Annu. Rev. Fluid Mech. 36, 173196.
Joshi, P., Liu, X. & Katz, J. 2014 Effect of mean and fluctuating pressure gradients on boundary layer turbulence. J. Fluid Mech. 748, 3684.
Kim, E. & Choi, H. 2014 Space-time characteristics of a compliant wall in a turbulent channel flow. J. Fluid Mech. 756, 3053.
Kramer, M. O. 1957 Boundary-layer stabilization by distributed damping. J. Aero. Sci. 24, 459460.
Kramer, M. O. 1962 Boundary-layer stabilization by distributed damping. Naval Engrs J. 74 (2), 341348.
Landahl, M. T. 1962 On the stability of a laminar incompressible boundary layer over a flexible surface. J. Fluid Mech. 13, 609632.
Lee, T., Fisher, M. & Schwarz, W. H. 1993 a Investigation of the stable interaction of a passive compliant surface with a turbulent boundary layer. J. Fluid Mech. 257, 373401.
Lee, T., Fisher, M. & Schwarz, W. H. 1993 b The measurement of flow-induced surface displacement on a compliant surface by optical holographic interferometry. Exp. Fluids 14, 159168.
Lee, S. H. & Sung, H. J. 2007 Direct numerical simulation of the turbulent boundary layer over a rod-roughened wall. J. Fluid Mech. 584, 125146.
Li, Y., Chen, H. & Katz, J. 2017 Measurements and characterization of turbulence in the tip region of an axial compressor rotor. Trans. ASME: J. Turbomach. 139, 121003.
Ling, H., Srinivasan, S., Golovin, K., McKinley, G. H., Tuteja, A. & Katz, J. 2016 High-resolution velocity measurement in the inner part of turbulent boundary layers over super-hydrophobic surfaces. J. Fluid Mech. 801, 670703.
Lucey, A. D. & Carpenter, P. W. 1992 A numerical simulation of the interaction of a compliant wall and inviscid flow. J. Fluid Mech. 234, 121146.
McMichael, J. M., Klebanoff, P. S. & Mease, N. E. 1980 Experimental investigation of drag on a compliant surface. In Viscous Flow Drag Reduction (ed. Hough, G. R.), vol. 72, pp. 410438. AIAA.
Melling, A. 1997 Tracer particles and seeding for particle image velocimetry. Meas. Sci. Technol. 8, 14061416.
Moisy, F., Rabaud, M. & Salsac, K. 2009 A synthetic Schlieren method for the measurement of the topography of a liquid interface. Exp. Fluids 46 (6), 10211063.
Mooney, M. 1940 A theory of large elastic deformation. J. Appl. Phys. 11 (9), 582592.
Naka, Y., Stanislas, M., Foucaut, J., Coudert, S., Laval, J. & Obi, S. 2015 Space–time pressure–velocity correlations in a turbulent boundary layer. J. Fluid Mech. 771, 624675.
Palchesko, R. N., Zhang, L., Yan, S. & Feinberg, A. W. 2012 Development of polydimethylsiloxane substrates with tunable elastic modulus to study cell mechanobiology in muscle and nerve. PLoS ONE 7 (12), e51499.
Panton, R. L., Goldamn, A. L., Lowery, R. L. & Reischman, M. M. 1980 Low- frequency pressure fluctuations in axisymmetric turbulent boundary layers. J. Fluid Mech. 97, 299319.
Perry, A. E., Lim, K. L. & Henbest, S. M. 1987 An experimental study of the turbulence structure in smooth- and rough-wall boundary layers. J. Fluid Mech. 177, 437466.
Piomelli, U. 2019 Recent advances in the numerical simulation of rough-wall boundary layers. Phys. Chem. Earth 113, 6372.
Rivlin, R. S. 1948 Large elastic deformations of isotropic materials. IV. Further developments of the general theory. Phil. Trans. R. Soc. Lond. A 241 (835), 379397.
Rosti, M. E. & Brandt, L. 2017 Numerical simulation of turbulent channel flow over a viscous hyper-elastic wall. J. Fluid Mech. 830, 708735.
Sheng, J., Malkiel, E. & Katz, J. 2006 Digital holographic microscope for measuring three-dimensional particle distributions and motions. Appl. Opt. 45, 38933901.
Smith, C. R. & Metzler, S. P. 1983 The characteristics of low-speed streaks in the near-wall region of a turbulent boundary layer. J. Fluid Mech. 129, 2754.
Tabatabai, H., Oliver, D. E., Rohrbaugh, J. W. & Papadopoulos, C. 2013 Novel applications of laser Doppler vibration measurements to medical imaging. Sens. Imaging 14, 1328.
Talapatra, S. & Katz, J. 2012 Coherent structures in the inner part of a rough-wall channel flow resolved using holographic PIV. J. Fluid Mech. 711, 161170.
Tan, D., Li, Y., Wilkes, I., Vagnonii, E., Miorini, R. L. & Katz, J. 2015 Experimental investigation of the role of large scale cavitating vortical structures in performance breakdown of an axial waterjet pump. Trans. ASME: J. Fluids Engng 137 (11), 111301.
Tsuji, Y., Fransson, J., Alfredsson, P. & Johansson, A. 2007 Pressure statistics and their scaling in high-Reynolds-number turbulent boundary layers. J. Fluid Mech. 585, 140.
Wang, Z., Yeo, K. S. & Khoo, B. C. 2006 On two-dimensional linear waves in Blasius boundary layer over viscoelastic layers. Eur. J. Mech. (B/Fluids) 25, 3358.
Wang, J., Zhang, C. & Katz, J. 2019 GPU-based, parallel-line, omni-directional integration of measured pressure gradient field to obtain the 3D pressure distribution. Exp. Fluids 60, 58.
Westerweel, J., Geelhoed, P. F. & Lindken, R. 2004 Single-pixel resolution ensemble correlation for micro-PIV applications. Exp. Fluids 37, 375384.
Xia, Q. J., Huang, W. X. & Xu, C. X. 2017 Direct numerical simulation of turbulent boundary layer over a compliant wall. J. Fluids Struct. 71, 126142.
Xu, S., Rempfer, D. & Lumley, J. 2003 Turbulence over a compliant surface: numerical simulation and analysis. J. Fluid Mech. 478, 1134.
Zhang, C., Miorini, R. & Katz, J. 2015 Integrating Mach–Zehnder interferometry with TPIV to measure the time - resolved deformation of a compliant wall along with the 3D velocity field in a turbulent channel flow. Exp. Fluids 56, 122.
Zhang, C., Wang, J., Blake, W. & Katz, J. 2017 Deformation of a compliant wall in a turbulent channel flow. J. Fluid Mech. 823, 345390.
MathJax
MathJax is a JavaScript display engine for mathematics. For more information see http://www.mathjax.org.

JFM classification

Type Description Title
VIDEO
Movies

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

 Video (9.7 MB)
9.7 MB
VIDEO
Movies

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

 Video (10.3 MB)
10.3 MB
VIDEO
Movies

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

 Video (10.3 MB)
10.3 MB

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

  • Jin Wang (a1), Subhra Shankha Koley (a1) and Joseph Katz (a1)

Metrics

Full text views

Total number of HTML views: 0
Total number of PDF views: 0 *
Loading metrics...

Abstract views

Total abstract views: 0 *
Loading metrics...

* Views captured on Cambridge Core between <date>. This data will be updated every 24 hours.

Usage data cannot currently be displayed.