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Pressure gradient effects on the large-scale structure of turbulent boundary layers

Published online by Cambridge University Press:  09 January 2013

Zambri Harun ,
Jason P. Monty ,
Romain Mathis  and
Ivan Marusic
Zambri Harun
Affiliation:
Department of Mechanical Engineering, University of Melbourne, Victoria 3010, Australia Department of Mechanical and Materials Engineering, The National University of Malaysia, 43600 Bangi, Malaysia
Jason P. Monty*
Affiliation:
Department of Mechanical Engineering, University of Melbourne, Victoria 3010, Australia
Romain Mathis
Affiliation:
Department of Mechanical Engineering, University of Melbourne, Victoria 3010, Australia Laboratoire de Mécanique de Lille, UMR CNRS 8107, 59655 Villeneuve d’Ascq, France
Ivan Marusic
Affiliation:
Department of Mechanical Engineering, University of Melbourne, Victoria 3010, Australia
*
†Email address for correspondence: montyjp@unimelb.edu.au
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Abstract

Research into high-Reynolds-number turbulent boundary layers in recent years has brought about a renewed interest in the larger-scale structures. It is now known that these structures emerge more prominently in the outer region not only due to increased Reynolds number (Metzger & Klewicki, Phys. Fluids, vol. 13(3), 2001, pp. 692–701; Hutchins & Marusic, J. Fluid Mech., vol. 579, 2007, pp. 1–28), but also when a boundary layer is exposed to an adverse pressure gradient (Bradshaw, J. Fluid Mech., vol. 29, 1967, pp. 625–645; Lee & Sung, J. Fluid Mech., vol. 639, 2009, pp. 101–131). The latter case has not received as much attention in the literature. As such, this work investigates the modification of the large-scale features of boundary layers subjected to zero, adverse and favourable pressure gradients. It is first shown that the mean velocities, turbulence intensities and turbulence production are significantly different in the outer region across the three cases. Spectral and scale decomposition analyses confirm that the large scales are more energized throughout the entire adverse pressure gradient boundary layer, especially in the outer region. Although more energetic, there is a similar spectral distribution of energy in the wake region, implying the geometrical structure of the outer layer remains universal in all cases. Comparisons are also made of the amplitude modulation of small scales by the large-scale motions for the three pressure gradient cases. The wall-normal location of the zero-crossing of small-scale amplitude modulation is found to increase with increasing pressure gradient, yet this location continues to coincide with the large-scale energetic peak wall-normal location (as has been observed in zero pressure gradient boundary layers). The amplitude modulation effect is found to increase as pressure gradient is increased from favourable to adverse.

JFM classification

Boundary Layers: Boundary Layers Turbulent Flows: Turbulent Flows Turbulent Flows: Turbulent boundary layers
Type
Papers
Information
Journal of Fluid Mechanics , Volume 715 , 25 January 2013 , pp. 477 - 498
Copyright
©2013 Cambridge University Press

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References

Abe, H., Kawamura, H. & Choi, H. 2004 Very large-scale structures and their effects on the wall shear-stress fluctuations in a turbulent channel flow up to ${\mathit{Re}}_{\tau } = 640$. Trans. ASME: J. Fluid Engng 126, 835–843.Google Scholar
Adrian, R. J. 2007 Hairpin vortex organization in wall turbulence. Phys. Fluids 19 (4), 041301.Google Scholar
Adrian, R. J., Meinhart, C. D. & Tomkins, C. D. 2000 Vortex organization in the outer region of a turbulent boundary layer. J. Fluid Mech. 422, 1–53.Google Scholar
del Álamo, J. C. & Jiménez, J. 2003 Spectra of the very large anisotropic scales in turbulent channels. Phys. Fluids 15 (6), L41–L44.CrossRefGoogle Scholar
del Álamo, J. C. & Jiménez, J. 2006 Linear energy amplification in turbulent channels. J. Fluid Mech. 559, 205–213.CrossRefGoogle Scholar
del Álamo, J. C. & Jiménez, J. 2009 Estimation of turbulent convection velocities and corrections to Taylor’s approximation. J. Fluid Mech. 640, 5–26.CrossRefGoogle Scholar
del Álamo, J. C., Jiménez, J., Zandonade, P. & Moser, R. D. 2004 Scaling of the energy spectra of turbulent channels. J. Fluid Mech. 500, 135–144.Google Scholar
Aubertine, C. D. & Eaton, J. K. 2005 Turbulence development in a non-equilibrium turbulent boundary layer with mild adverse pressure gradient. J. Fluid Mech. 532, 345–364.CrossRefGoogle Scholar
Bailey, S. C. C., Hultmark, M., Smits, A. & Schultz, M. P. 2008 Azimuthal structure of turbulence in high Reynolds number pipe flow. J. Fluid Mech. 615, 121–138.Google Scholar
Balakumar, B. J. & Adrian, R. J. 2007 Large and very-large-scale motions in channel and boundary-layer flows. Phil. Trans. R. Soc. A 365, 665–681.CrossRefGoogle ScholarPubMed
Bandyopadhyay, P. R. & Hussain, A. K. M. F. 1984 The coupling between scales in shear flows. Phys. Fluids 27 (9), 2221–2228.Google Scholar
Bourassa, C. & Thomas, F. O. 2009 An experimental investigation of a highly accelerated turbulent boundary layer. J. Fluid Mech. 634, 359–404.Google Scholar
Bradshaw, P. 1967a Inactive motion and pressure fluctuations in turbulent boundary layers. J. Fluid Mech. 30, 241–258.Google Scholar
Bradshaw, P. 1967b The turbulence structure of equilibrium boundary layers. J. Fluid Mech. 29, 625–645.Google Scholar
Chauhan, K., Ng, H. C. H. & Marusic, I. 2010 Empirical mode decomposition and Hilbert transforms for analysis of oil-film interferograms. Meas. Sci. Technol. 21, 105405, 1–13.CrossRefGoogle Scholar
Chung, D. & McKeon, B. J. 2010 Large-eddy simulation of large-scale structures in long channel flow. J. Fluid Mech. 661, 341–364.CrossRefGoogle Scholar
DeGraaff, D. E. & Eaton, J. K. 2000 Reynolds-number scaling of the flat-plate turbulent boundary layer. J. Fluid Mech. 422, 319–346.CrossRefGoogle Scholar
Dengel, P. & Fernholz, H. H. 1990 An experimental investigation of an incompressible turbulent boundary layer in the vicinity of separation. J. Fluid Mech. 212, 615–636.Google Scholar
Dennis, D. J. C. & Nickels, T. B. 2008 On the limitations of Taylor’s hypothesis in constructing long structures in a turbulent boundary layer. J. Fluid Mech. 614, 197–206.Google Scholar
Dixit, S. A. & Ramesh, O. N. 2010 Large-scale structures in turbulent and reverse-transitional sink flow boundary layers. J. Fluid Mech. 649, 233–273.Google Scholar
Fernholz, H. H. & Warnack, D. 1998 The effects of a favourable pressure gradient and of the Reynolds number on an incompressible axisymmetric turbulent boundary layer. Part 1. The turbulent boundary layer. J. Fluid Mech. 359, 329–356.Google Scholar
Ganapathisubramani, B., Hambleton, N., Hutchins, W. T., Longmire, E. K. & Marusic, I. 2005 Investigation of large-scale coherence in a turbulent boundary layer using two-point correlation. J. Fluid Mech. 524, 57–80.CrossRefGoogle Scholar
Ganapathisubramani, B., Longmire, E. K. & Marusic, I. 2003 Characteristics of vortex packets in turbulent boundary layers. J. Fluid Mech. 478, 35–46.CrossRefGoogle Scholar
Grinvald, D. & Nikora, V. 1988 Rechnaya turbulentnost (River Turbulence). Hydrometeoizdat, Russia (in Russian).Google Scholar
Hambleton, W. T., Hutchins, N. & Marusic, I. 2006 Simultaneous orthogonal-plane particular image velocimetry measurements in a turbulent boundary layer. J. Fluid Mech. 560, 53–64.Google Scholar
Hutchins, N. & Marusic, I. 2007a Evidence of very long meandering features in the logarithmic region of turbulent boundary layers. J. Fluid Mech. 579, 1–28.Google Scholar
Hutchins, N. & Marusic, I. 2007b Large-scale influences in near-wall turbulence. Phil. Trans. R. Soc. A 365, 647–664.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, 103–136.CrossRefGoogle Scholar
Jones, M. B., Marusic, I. & Perry, A. E. 2001 Evolution and structure of sink flow turbulent boundary layers. J. Fluid Mech. 428, 1–27.Google Scholar
Jones, W. P. & Launder, B. E. 1972 Some properties of sink-flow turbulent boundary layers. J. Fluid Mech. 56, 337–351.Google Scholar
Kim, K. C. & Adrian, R. J. 1999 Very large-scale motion in the outer layer. Phys. Fluids 11 (2), 417–422.CrossRefGoogle Scholar
Kline, S. J., Reynolds, W. C., Schraub, F. A. & Runstadler, P. W. 1967 The structure of turbulent boundary layers. J. Fluid Mech. 30, 741–773.CrossRefGoogle Scholar
Krogstad, P.-A˚ & Skåre, P. E. 1995 Influence of a strong adverse pressure gradient on the turbulent structure in a boundary layer. Phys. Fluids 7, 2014–2024.Google Scholar
Kunkel, G. & Marusic, I. 2006 Study of the near-wall-turbulent region of the high-Reynolds-number boundary layer using an atmospheric flow. J. Fluid Mech. 548, 375–402.CrossRefGoogle Scholar
Lee, J. H. & Sung, H. J. 2009 Structures in turbulent boundary layers subjected to adverse pressure gradients. J. Fluid Mech. 639, 101–131.Google Scholar
Maciel, Y., Rossignol, K.-S. & Lemay, J. 2006 Self similarity in the outer region of adverse-pressure-gradient turbulent boundary layers. AIAA J. 44 (11), 2450–2464.Google Scholar
Marusic, I. & Heuer, W. D. C. 2007 Reynolds number invariance of the structure inclination angle in wall turbulence. Phys. Rev. Lett. 99, 41–45.CrossRefGoogle ScholarPubMed
Marusic, I. & Hutchins, N. 2007 Study of the log-layer structure in wall turbulence over a very large range of Reynolds number. Flow Turbul. Combust. 81, 115–130.CrossRefGoogle Scholar
Marusic, I., Mathis, R. & Hutchins, N. 2010 High Reynolds number effects in wall turbulence. Int. J. Heat Fluid Flow 31, 418–428.Google 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
Mathis, R., Hutchins, N. & Marusic, I. 2009a Large-scale amplitude modulation of the small-scale structures in turbulent boudary layers. J. Fluid Mech. 628, 311–337.CrossRefGoogle Scholar
Mathis, R., Monty, J. P, Hutchins, N. & Marusic, I. 2009b Comparison of large-scale amplitude modulation in turbulent boundary layers, pipes, and channel flows. Phys. Fluids 21 (11), 111703.Google Scholar
Metzger, M. M. & Klewicki, J. C. 2001 A comparative study of near-wall turbulence in high and low Reynolds number boundary layers. Phys. Fluids 13 (3), 692–701.CrossRefGoogle Scholar
Monty, J. P., Harun, Z. & Marusic, I. 2011 A parametric study of adverse pressure gradient turbulent boundary layers. Int. J. Heat Fluid Flow 32, 575–585.Google Scholar
Monty, J. P., Hutchins, N., Ng, H. C. H. & Chong, M. S. 2009 A comparison of turbulent pipe, channel and boundary layer flows. J. Fluid Mech. 632, 431–442.Google Scholar
Monty, J. P., Stewart, J. A., Williams, R. C. & Chong, M. S. 2007 Large-scale features in turbulent pipe and channel flows. J. Fluid Mech. 589, 147–156.CrossRefGoogle Scholar
Na, Y. & Moin, P. 1998 Direct numerical simulation of a separated turbulent boundary layer. J. Fluid Mech. 374, 379–405.Google Scholar
Nagano, Y., Tagawa, M. & Tsuji, T. 1992 Effects of adverse pressure gradients on mean flows and turbulence statistics in a boundary layer. In Proceedings of Turbulent Shear Flows 8, pp. 7–21Berlin.Google Scholar
Nagano, Y., Tsuji, T. & Houra, T. 1998 Structure of turbulent boundary layer subjected to adverse pressure gradient. Int. J. Heat Fluid Flow 19, 563–572.CrossRefGoogle Scholar
Nagib, H. M. & Chauhan, K. A. 2008 Variations of von Kármán coefficient in canonical flows. Phys. Fluids 20, 101518.Google Scholar
Nickels, T. B., Marusic, I., Hafez, S. & Chong, M. S. 2005 Evidence of the ${ k}_{1}^{\ensuremath{-} 1} $ law in a high-Reynolds-number turbulent boundary layer. Phys. Rev. Lett. 95, 074501.Google Scholar
Nikora, V., Nokes, R., Veale, W., Davidson, M. & Jirka, G. H. 2007 Large-scale turbulent structure of uniform shallow free-surface flows. Environ. Fluid Mech. 7 (2), 159–172.Google Scholar
Perry, A. E., Marusic, I. & Jones, M. B. 2002 On the streamwise evolution of turbulent boundary layers in arbitrary pressure gradients. J. Fluid Mech. 461, 61–91.Google Scholar
Perry, A. E., Marusic, I. & Li, J. D. 1994 Wall turbulence closure based on classical similarity laws and the attached eddy hypothesis. Phys. Fluids 6 (2), 1024.Google Scholar
Pope, S. B. 2000 Turbulent flows. Cambridge University Press.Google Scholar
Rahgozar, S. & Maciel, Y. 2011 Low- and high-speed structures in the outer region of an adverse-pressure-gradient turbulent boundary layer. Experimental Thermal and Fluid Science 35 (8), 1575–1587.Google Scholar
Rao, K. N., Narasimha, R. & Badri Narayanan, M. A. 1971 The ‘bursting’ phenomena in a turbulent boundary layer. J. Fluid Mech. 48, 339–352.Google Scholar
Robinson, S. K. 1991 Coherent motions in the turbulent boundary layer. Annu. Rev. Fluid Mech. 23, 601–639.CrossRefGoogle Scholar
Skote, M. & Henningson, D. S. 2002 Direct numerical simulation of a seperated turbulent boundary layer. J. Fluid Mech. 471, 107–136.Google Scholar
Skote, M., Henningson, D. S. & Henkes, R. A. W. M. 1998 Direct numerical simulation of self-similar turbulent boundary layers in adverse pressure gradients. Flow Turbulence Combustion 60, 47–85.Google Scholar
Skåre, P. E. & Krogstad, P.-A˚. 1994 A turbulent equilibrium boundary layer near separation. J. Fluid Mech. 272, 319–348.CrossRefGoogle Scholar
Spalart, P. R. & Coleman, G. N. 1997 Numerical study of a separation bubble with heat transfer. Eur. J. Mech. B Fluids 16, 169–189.Google Scholar
Spalart, P. R. & Watmuff, J. H. 1993 Experimental and numerical study of a turbulent boundary layer with pressure gradient. J. Fluid Mech. 249, 337–371.Google Scholar
Tomkins, C. D. & Adrian, R. J. 2003 Spanwise structure and scale growth in turbulent boundary layers. J. Fluid Mech. 490, 37–74.CrossRefGoogle Scholar
Townsend, A. A. 1961 Equilibrium layers and wall turbulence. J. Fluid Mech. 11, 97–120.CrossRefGoogle Scholar
Townsend, A. A. 1976 The structure of turbulent shear flow, 2nd edn. Cambridge University Press.Google Scholar