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The wall-pressure spectrum of high-Reynolds-number turbulent boundary-layer flows over rough surfaces

Published online by Cambridge University Press:  09 March 2015

Timothy Meyers
Affiliation:
Department of Aerospace and Ocean Engineering, Virginia Polytechnic Institute and State University, Blacksburg, VA 24061, USA
Jonathan B. Forest
Affiliation:
Department of Aerospace and Ocean Engineering, Virginia Polytechnic Institute and State University, Blacksburg, VA 24061, USA
William J. Devenport*
Affiliation:
Department of Aerospace and Ocean Engineering, Virginia Polytechnic Institute and State University, Blacksburg, VA 24061, USA
*
Email address for correspondence: [email protected]

Abstract

Experiments have been performed on a series of high-Reynolds-number flat-plate turbulent boundary layers formed over rough and smooth walls. The boundary layers were fully rough, yet the elements remained a very small fraction $({<}1.4\,\%)$ of the boundary-layer thickness, ensuring conditions free of transitional effects. The wall-pressure spectrum and its scaling were studied in detail. One of the major findings is that the rough-wall turbulent pressure spectrum at vehicle relevant conditions is comprised of three scaling regions. These include a newly discovered high-frequency region where the pressure spectrum has a viscous scaling controlled by the friction velocity, adjusted to exclude the pressure drag on the roughness elements.

Type
Papers
Copyright
© 2015 Cambridge University Press 

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References

Aupperle, F. & Lambert, R. 1970 Effects of roughness on measured wall-pressure fluctuations beneath a turbulent boundary layer. J. Acoust. Soc. Am. 47, 359370.CrossRefGoogle Scholar
Bearman, P. W. 1971 Corrections for the effect of ambient temperature drift on hot-wire measurements in incompressible flow. DISA Information 11, 2530.Google Scholar
Bennington, J. L.2004 Effects of various shaped roughness elements in two-dimensional high Reynolds number turbulent boundary layers. PhD dissertation, Aerospace and Ocean Engineering, Virginia Tech., http://scholar.lib.vt.edu/theses/available/etd-09032004-165611/.CrossRefGoogle Scholar
Blake, W. 1970 Turbulent boundary layer wall-pressure fluctuations on smooth and rough walls. J. Fluid Mech. 44, 637660.CrossRefGoogle Scholar
Blake, W.1971 Turbulent velocity and pressure fields in boundary-layer flows over rough surfaces. In Proceedings of the Symposium on Turbulence in Liquids. 4–6 October 1971. University of Missouri-Rolla, edited by J. L. Zakin, 1971.Google Scholar
Blake, W. K. 1986 Mechanics of Flow Induced Sound and Vibration. Academic.Google Scholar
Bradshaw, P. 1967 ‘Inactive’ motion and pressure fluctuations in turbulent boundary layers. J. Fluid Mech. 30, 241258.CrossRefGoogle Scholar
Bull, M. K. 1996 Wall pressure fluctuations beneath turbulent boundary layers: some reflections on forty years of research. J. Sound Vib. 190, 299315.CrossRefGoogle Scholar
Chase, D. M. 1980 Modeling the wavevector-frequency spectrum of turbulent boundary layer wall pressure. J. Sound Vib. 70, 2967.CrossRefGoogle Scholar
Choi, H. & Moin, P. 1990 On the space-time characteristics of wall-pressure fluctuations. Phys. Fluids A 2 (8), 14501460.CrossRefGoogle Scholar
Cipolla, K. M. & Keith, W. L. 2000 Effects of pressure gradients on turbulent boundary layer wave number frequency spectra. AIAA J. 38 (10), 18321836.CrossRefGoogle Scholar
Corcos, G. M. 1963 Resolution of pressure in turbulence. J. Acoust. Soc. Am. 35 (2), 192199.CrossRefGoogle Scholar
Corcos, G. M. 1967 The resolution of turbulent pressures at the wall of a boundary layer. J. Sound Vib. 6 (1), 5970.CrossRefGoogle Scholar
DeGraaff, D. B. & Eaton, J. 2000 Reynolds-number scaling of the flat-plate turbulent boundary layer. J. Fluid Mech. 422, 319346.CrossRefGoogle Scholar
Devenport, W. J., Burdisso, R. A., Borgoltz, A., Ravetta, P. A., Barone, M. F., Brown, K. A. & Morton, M. A. 2013 The Kevlar-walled anechoic wind tunnel. J. Sound Vib. 332 (17), 39713991.CrossRefGoogle Scholar
Devenport, W. J., Grissom, D. L., Nathan Alexander, W., Smith, B. S. & Glegg, S. A. L. 2011 Measurements of roughness noise. J. Sound Vib. 330 (17), 42504273.CrossRefGoogle Scholar
Dvorak, F. A. 1969 Calculation of turbulent boundary layers on rough surfaces in pressure gradient. AIAA J. 7, 17521759.CrossRefGoogle Scholar
Farabee, T. & Casarella, M. 1991 Spectral features of wall pressure fluctuations beneath turbulent boundary layers. Phys. Fluids A 3 (10), 24102420.CrossRefGoogle Scholar
Farabee, T. M. & Geib, F. E. 1991 Measurements of boundary layer pressure fluctuations at low wavenumbers on smooth and rough walls. In ASME Symposium on Flow Noise Modeling Measurement and Control, NCA, vol. 11, pp. 55–68.Google Scholar
Fernholz, H.-H. & Finley, P. J. 1996 The incompressible zero-pressure-gradient turbulent boundary layer: an assessment of the data. Prog. Aerosp. Sci. 32, 245311.CrossRefGoogle Scholar
Flack, K. A., Schultz, M. P. & Shapiro, T. A. 2005 Experimental support for Townsend’s Reynolds number similarity hypothesis on rough walls. Phys. Fluids 17, 035102.CrossRefGoogle Scholar
Forest, J.2012 The wall pressure spectrum of high Reynolds number rough-wall turbulent boundary layer. MS thesis, Aerospace and Ocean Engineering Department, Virginia Tech.CrossRefGoogle Scholar
George, J. & Simpson, R. L.2000 Some effects of sparsely distributed roughness elements on two-dimensional turbulent boundary layers. AIAA Paper 2000-0915.CrossRefGoogle Scholar
Goody, M. 2004 Empirical spectral model of surface pressure fluctuations. AIAA J. 42 (9), 17881794.CrossRefGoogle Scholar
Gravante, S. P., Naguib, A. M., Wark, C. E. & Nagib, H. M. 1998 Characterization of the pressure fluctuations under a fully developed turbulent boundary layer. AIAA J. 36 (10), 18081816.CrossRefGoogle Scholar
Hersh, A. S.1983 Surface roughness generated flow noise. AIAA Paper 83-0786.Google Scholar
Hutchins, N., Nickels, T. B., Marusic, I. & Chong, M. S. 2009 Hot-wire spatial resolution issues in wall-bounded turbulence. J. Fluid Mech. 635, 103168.CrossRefGoogle Scholar
Jiménez, J. 2004 Turbulent flows over rough walls. Annu. Rev. Fluid Mech. 36, 173196.CrossRefGoogle Scholar
Jiménez, J. & Hoyas, S. 2008 Turbulent fluctuations above the buffer layer of wall-bounded flows. J. Fluid Mech. 611, 215236.CrossRefGoogle Scholar
Killen, J. M. & Almo, J. A.1971 The influence of drag reducing polymer additives on surface pressure fluctuations on rough surfaces. Project Rep. 119. University of Minnesota, St Anthony Falls Hydraulic Laboratory.Google Scholar
Klewicki, J. 2013 Self-similar mean dynamics in turbulent wall flows. J. Fluid Mech. 718, 596621.CrossRefGoogle Scholar
Klewicki, J., Fife, P. & Wei, T. 2009 On the logarithmic mean profile. J. Fluid Mech. 638, 7393.CrossRefGoogle Scholar
Klewicki, J. C., Priyadarshana, P. J. A. & Metzger, M. M. 2008 Statistical structure of the fluctuating wall pressure and its in-plan gradients at high Reynolds number. J. Fluid Mech. 609, 195220.CrossRefGoogle Scholar
Ligrani, P. M. & Bradshaw, P. 1987 Spatial resolution and measurement of turbulence in the viscous sublayer using subminiature hot-wire probes. Exp. Fluids 5, 407417.CrossRefGoogle Scholar
Marusic, I., Monty, J. P., Hultmark, M. & Smits, A. J. 2013 On the logarithmic region in wall turbulence. J. Fluid Mech. 716, R3.CrossRefGoogle Scholar
McGrath, B. E. & Simpson, R. L.1987 Some features of surface pressure fluctuations in turbulent boundary layers with zero and favorable pressure gradients. NASA CR 4051.Google Scholar
Mehdi, F., Klewicki, J. C. & White, C. M. 2010 Mean momentum balance analysis of rough-wall turbulent boundary layers. Physica D 239 (14), 13291337.CrossRefGoogle Scholar
Mehdi, F., Klewicki, J. & White, C. M. 2013 Mean force structure and its scaling in rough-wall turbulent boundary layers. J. Fluid Mech. 731, 682712.CrossRefGoogle Scholar
Meneveau, C. & Marusic, I. 2013 Generalized logarithmic law for high-order moments in turbulent boundary layers. J. Fluid Mech. 719, R1.CrossRefGoogle Scholar
Meyers, T. W.2014 Wall pressure spectrum of high Reynolds number turbulent boundary layer flow over rough walls. MS thesis, Aerospace and Ocean Engineering Department, Virginia Tech.CrossRefGoogle Scholar
Morton, M. A.2012 Rotor inflow noise caused by a boundary layer: inflow measurements and noise predictions. MS thesis, Aerospace and Ocean Engineering Department, Virginia Tech.CrossRefGoogle Scholar
Mulhearn, P. J. 1976 Turbulent boundary layer wall-pressure fluctuations downstream from an abrupt change in surface roughness. Phys. Fluids 19, 796801.CrossRefGoogle Scholar
Nikuradse, J.1950 Laws of flow in rough pipes. NACA Tech. Mem. 1292.Google Scholar
Oweis, G. F., Winkel, E. S., Cutbrith, J. M., Ceccio, S. L., Perlin, M. & Dowling, D. R. 2010 The mean velocity profile of a smooth-flat-plate turbulent boundary layer at high Reynolds number. J. Fluid Mech. 665, 357381.CrossRefGoogle Scholar
Panton, R. & Linebarger, J. 1974 Wall pressure spectra calculations for equilibrium boundary layers. J. Fluid Mech. 65 (2), 261287.CrossRefGoogle Scholar
Panton, R. L., Goldman, A. L., Lowery, R. L. & Reischman, M. M. 1980 Low-frequency pressure fluctuations in axisymmetric turbulent boundary layers. J. Fluid Mech. 97, 299319.CrossRefGoogle Scholar
Raupach, M. R., Antonia, R. A. & Rajagopalan, S. 1991 Rough-wall turbulent boundary layers. Appl. Mech. Rev. 44 (1), 125.CrossRefGoogle Scholar
Schewe, G. 1983 On the structure and resolution of wall-pressure fluctuations associated with turbulent boundary-layer flow Journal. J. Fluid Mech. 134, 311328.CrossRefGoogle Scholar
Schlichting, H 1979 Boundary-Layer Theory. McGraw-Hill.Google Scholar
Schloemer, H. H. 1967 Effects of pressure gradients on turbulent-boundary-layer wall-pressure fluctuations. J. Acoust. Soc. Am. 42 (1), 93113.CrossRefGoogle Scholar
Schultz, M. P. & Flack, K. A. 2007 The rough-wall turbulent boundary layer from the hydraulically smooth to the fully rough regime. J. Fluid Mech. 580, 381405.CrossRefGoogle Scholar
Simpson, R. L. 1973 A generalized correlation of roughness density effects on the turbulent boundary layer. AIAA J. 11, 242244.CrossRefGoogle Scholar
Smith, B. S.2008 Wall jet boundary layer flows over smooth and rough surfaces. PhD dissertation, Aerospace and Ocean Engineering Department, Virginia Tech.Google Scholar
Tsuji, Y., Fransson, J. H. M., Alfredsson, P. H. & Johansson, A. V. 2007 Pressure statistics and their scaling in high-Reynolds-number turbulent boundary layers. J. Fluid Mech. 585, 140.CrossRefGoogle Scholar
Varano, N. D2010 Fluid dynamics and surface pressure fluctuations of turbulent boundary layers over sparse roughness. PhD dissertation, Aerospace and Ocean Engineering Department, Virginia Tech.Google Scholar
Willmarth, W. W. 1975 Pressure fluctuations beneath turbulent boundary layers. Annu. Rev. Fluid Mech. 7, 1338.CrossRefGoogle Scholar
Willmarth, W. W. & Wooldridge, C. E. 1962 Measurements of the fluctuating pressure at the wall beneath a thick turbulent boundary layer. J. Fluid Mech. 14, 187210.CrossRefGoogle Scholar
Wittmer, K. S., Devenport, W. J. & Zsoldos, J. S. 1998 A four sensor hot wire probe system for three component velocity measurements. Exp. Fluids 24, 416423; see also vol. 27, no. 4, pp. U1, September 1999.CrossRefGoogle Scholar
Yang, Q. & Wang, M. 2013 Boundary-layer noise induced by arrays of roughness elements. J. Fluid Mech. 727, 282317.CrossRefGoogle Scholar