Hostname: page-component-5b777bbd6c-cp4x8 Total loading time: 0 Render date: 2025-06-19T15:46:27.308Z Has data issue: false hasContentIssue false
  • English
  • Français

A structure-based model for turbulent-boundary-layer wall pressures

Published online by Cambridge University Press:  16 March 2010

B.-K. AHN ,
W. R. GRAHAM  and
S. A. RIZZI
B.-K. AHN
Affiliation:
Department of Engineering, Trumpington Street, Cambridge, CB2 1PZ, UK
W. R. GRAHAM*
Affiliation:
Department of Engineering, Trumpington Street, Cambridge, CB2 1PZ, UK
S. A. RIZZI
Affiliation:
NASA Langley Research Center, Hampton, VA 23681-2199, USA
*
‡Email address for correspondence: wrg@eng.cam.ac.uk
Get access Rights & Permissions [Opens in a new window]

Abstract

Practical prediction of structural vibrations due to a turbulent boundary layer currently depends on empirical representations of the unsteady wall pressures. Improvements in these representations would be greatly facilitated if a simple, physically based model were available to test ad hoc assumptions and provide rigorous interpolation of experimental data. A possible candidate is the attached-eddy model, developed from Townsend's initial ideas by Perry and co-workers in the context of turbulence velocity spectra. This approach employs the superposition of contributions from individual ‘eddies’, of varying size, to yield its predictions. It is shown here that the same methodology can be applied for wall pressures, once the field due to an eddy has been obtained via solution of the governing Poisson equation. Comparisons with large-eddy simulation and experimental data, spanning a two-decade Reynolds number range, show remarkably good agreement, given the simplicity of the model. It is concluded that this approach has the potential to provide useful physical insight and, subject to its extension to a time-resolved form, improvements to existing empirical formulations.

Type
Papers
Information
Journal of Fluid Mechanics , Volume 650 , 10 May 2010 , pp. 443 - 478
Copyright
Copyright © Cambridge University Press 2010

Access options

Get access to the full version of this content by using one of the access options below. (Log in options will check for institutional or personal access. Content may require purchase if you do not have access.)

Article purchase

Temporarily unavailable

Footnotes

†

Present address: Department of Naval Architecture and Ocean Engineering, Chungnam National University, 79 Daehangno, Daejeon 305-764, Korea.

References

REFERENCES

Adrian, R. J. 2007 Hairpin vortex organization in wall turbulence. Phys. Fluids 19, 041301-1–041301-16.CrossRefGoogle Scholar
Adrian, R. J., Meinhart, C. D. & Tomkins, C. D. 2000 Vortex organization in the outer region of the turbulent boundary layer. J. Fluid Mech. 422, 1–54.CrossRefGoogle Scholar
Blake, W. K. 1970 Turbulent boundary-layer wall-pressure fluctuations on smooth and rough walls. J. Fluid Mech. 44, 637–660.CrossRefGoogle Scholar
Blake, W. K. 1986 Mechanics of Flow-Induced Sound and Vibration, Vol. 2: Complex Flow-Structure Interactions. Academic.Google Scholar
Bull, M. K. 1967 Wall-pressure fluctuations associated with subsonic turbulent boundary layer flow. J. Fluid Mech. 28, 719–754.CrossRefGoogle Scholar
Bull, M. K. 1969 Mean shear in a constant-pressure turbulent boundary layer. AIAA J. 7, 359–362.CrossRefGoogle Scholar
Dhanak, M. R. & Dowling, A. P. 1995 On the pressure fluctuations induced by coherent vortex motion near a surface. 26th AIAA Fluid Dyn. Conf. paper 95-2240.CrossRefGoogle Scholar
Gradshteyn, I. S. & Rizhik, I. M. 1994 Table of Integrals, Series, and Products. Academic.Google Scholar
Graham, W. R. 1997 A comparison of models for the wavenumber-frequency spectrum of turbulent boundary layer pressures. J. Sound Vib. 206, 541–565.CrossRefGoogle Scholar
Hambleton, W. T., Hutchins, N. & Marusic, I. 2006 Simultaneous orthogonal-plane particle image velocimetry measurements in a turbulent boundary layer. J. Fluid Mech. 560, 53–64.CrossRefGoogle Scholar
Head, M. R. & Bandyopadhyay, P. 1981 New aspects of turbulent boundary-layer structure. J. Fluid Mech. 107, 297–338.CrossRefGoogle Scholar
Howe, M. S. 1989 The rôle of surface shear stress fluctuations in the generation of boundary layer noise. J. Sound Vib. 65, 159–164.CrossRefGoogle Scholar
Hutchins, N., Hambleton, W. T. & Marusic, I. 2005 Inclined cross-stream stereo particle image velocimetry measurements in turbulent boundary layers. J. Fluid Mech. 541, 21–54.CrossRefGoogle Scholar
Hutchins, N. & Marusic, I. 2007 Evidence of very long meandering features in the logarithmic region of turbulent boundary layers. J. Fluid Mech. 579, 1–28.CrossRefGoogle Scholar
Marusic, I. 2001 On the role of large-scale structures in wall turbulence. Phys. Fluids 13, 735–743.CrossRefGoogle Scholar
Marusic, I. & Perry, A. E. 1995 A wall-wake model for the turbulence structure of boundary layers. Part 2. Further experimental support. J. Fluid Mech. 298, 389–407.CrossRefGoogle Scholar
Nickels, T. B., Marusic, I., Hafez, S. & Chong, M. S. 2005 Evidence of the k 1−1 law in a high-Reynolds-number turbulent boundary layer. Phys. Rev. Lett. 95, 074501-1–074501-4.CrossRefGoogle Scholar
Nickels, T. B., Marusic, I., Hafez, S., Hutchins, N. & Chong, M. S. 2007 Some predictions of the attached eddy model for a high Reynolds number boundary layer. Phil. Trans. R. Soc. A 365, 807–822.CrossRefGoogle ScholarPubMed
Perry, A. E. & Chong, M. S. 1982 On the mechanism of wall turbulence. J. Fluid Mech. 119, 173–217.CrossRefGoogle Scholar
Perry, A. E., Henbest, S. & Chong, M. S. 1986 A theoretical and experimental study of wall turbulence. J. Fluid Mech. 165, 163–199.CrossRefGoogle Scholar
Perry, A. E. & Marusic, I. 1995 A wall-wake model for the turbulence structure of boundary layers. Part 1. Extension of the attached eddy hypothesis. J. Fluid Mech. 298, 361–388.CrossRefGoogle Scholar
Rizzi, S. A., Rackl, R. G. & Andrianov, E. V. 2000 Flight test measurements from the Tu-144LL structure/cabin noise experiment. NASA TM 2000-209858.Google Scholar
Schlichting, H. 1979 Boundary-Layer Theory. McGraw-Hill.Google Scholar
Schumann, G. & Corcos, G. M. 1967 The dynamics of turbulence near a wall according to a linear model. J. Fluid Mech. 29, 113–135.Google Scholar
Singer, B. A. 1996 a Large-eddy simulation of turbulent wall-pressure fluctuations. NASA CR 198276.Google Scholar
Singer, B. A. 1996 b Turbulent wall-pressure fluctuations: new model for off-axis cross-spectral density. NASA CR 198297.Google Scholar
Spalart, P. R. 1988 Direct simulation of a turbulent boundary layer up to R θ = 1410. J. Fluid Mech. 187, 61–98.CrossRefGoogle Scholar
Townsend, A. A. 1976 The Structure of Turbulent Shear Flow. Cambridge University Press.Google Scholar
Witting, J. M. 1986 A spectral model of pressure fluctuations at a rigid wall bounding an incompressible fluid, based on turbulent structures in the boundary layer. Noise Control Engng J. 26, 28–43.CrossRefGoogle Scholar
Wu, X. & Moin, P. 2009 Direct numerical simulation of turbulence in a nominally zero-pressure-gradient flat-plate boundary layer. J. Fluid Mech. 630, 5–41.CrossRefGoogle Scholar
Young, A. D. 1989 Boundary Layers. AIAA Education Series.Google Scholar