Hostname: page-component-6dbcb7884d-wnk8j Total loading time: 0 Render date: 2025-02-14T00:03:39.500Z Has data issue: false hasContentIssue false
  • English
  • Français

Three-dimensional vortex organization in a high-Reynolds-number supersonic turbulent boundary layer

Published online by Cambridge University Press:  11 February 2010

G. E. ELSINGA ,
R. J. ADRIAN ,
B. W. VAN OUDHEUSDEN  and
F. SCARANO
G. E. ELSINGA*
Affiliation:
Department of Aerospace Engineering, Delft University of Technology, 2629HS Delft, The Netherlands
R. J. ADRIAN
Affiliation:
Department of Mechanical and Aerospace Engineering, Arizona State University, Tempe, AZ85287, USA
B. W. VAN OUDHEUSDEN
Affiliation:
Department of Aerospace Engineering, Delft University of Technology, 2629HS Delft, The Netherlands
F. SCARANO
Affiliation:
Department of Aerospace Engineering, Delft University of Technology, 2629HS Delft, The Netherlands
*
†Present address: Laboratory for Aero and Hydrodynamics, Delft University of Technology, 2628CA Delft, The Netherlands. Email address for correspondence: [email protected]
Get access Rights & Permissions [Opens in a new window]

Abstract

Tomographic particle image velocimetry was used to quantitatively visualize the three-dimensional coherent structures in a supersonic (Mach 2) turbulent boundary layer in the region between y/δ = 0.15 and 0.89. The Reynolds number based on momentum thickness Reθ = 34000. The instantaneous velocity fields give evidence of hairpin vortices aligned in the streamwise direction forming very long zones of low-speed fluid, consistent with Tomkins & Adrian (J. Fluid Mech., vol. 490, 2003, p. 37). The observed hairpin structure is also a statistically relevant structure as is shown by the conditional average flow field associated to spanwise swirling motion. Spatial low-pass filtering of the velocity field reveals streamwise vortices and signatures of large-scale hairpins (height > 0.5δ), which are weaker than the smaller scale hairpins in the unfiltered velocity field. The large-scale hairpin structures in the instantaneous velocity fields are observed to be aligned in the streamwise direction and spanwise organized along diagonal lines. Additionally the autocorrelation function of the wall-normal swirling motion representing the large-scale hairpin structure returns positive correlation peaks in the streamwise direction (at 1.5δ distance from the DC peak) and along the 45° diagonals, which also suggest a periodic arrangement in those directions. This is evidence for the existence of a spanwise–streamwise organization of the coherent structures in a fully turbulent boundary layer.

Type
Papers
Information
Journal of Fluid Mechanics , Volume 644 , 10 February 2010 , pp. 35 - 60
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.)

References

REFERENCES

Adrian, R. J. 1996 Stochastic estimation of the structure of turbulent fields. In Eddy Structure Identification (ed. Bonnet, J. P.), pp. 145–195. Springer-Verlag.CrossRefGoogle Scholar
Adrian, R. J. 2007 Hairpin vortex organization in wall turbulence. Phys. Fluids 19, 041301.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
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
Blackwelder, R. F. & Kovasznay, L. S. G. 1972 Time scales and correlations in a turbulent boundary layer. Phys. Fluids 15, 1545.CrossRefGoogle Scholar
Chakraborty, P., Balachandar, S. & Adrian, R. J. 2005 On the relationship between local vortex identification schemes. J. Fluid Mech. 535, 189–214.CrossRefGoogle Scholar
Christensen, K. T. & Adrian, R. J. 2001 Statistical evidence of hairpin vortex packets in wall turbulence. J. Fluid Mech. 431, 433–443.CrossRefGoogle Scholar
Delo, C. J., Kelso, R. M. & Smits, A. J. 2004 Three-dimensional structure of a low-Reynolds-number turbulent boundary layer. J. Fluid Mech. 512, 47–83.CrossRefGoogle Scholar
Elsinga, G. E. 2008 Tomographic particle image velocimetry and its application to turbulent boundary layers. Ph.D. dissertation, Delft University of Technology, Delft (http://repository.tudelft.nl/file/1003861/379883).Google Scholar
Elsinga, G. E., Kuik, D. J., van Oudheusden, B. W. & Scarano, F. 2007 Investigation of the three-dimensional coherent structures in a turbulent boundary layer. In Forty-fifth AIAA Aerospace Sciences Meeting, Reno, NV, AIAA-2007-1305.Google Scholar
Elsinga, G. E., van Oudheusden, B. W. & Scarano, F. 2006 a Experimental assessment of tomographic-PIV accuracy. In Thirteenth Intl Symp. on Laser Techniques to Fluid Mech., Lisbon, Portugal, Paper 20.5.Google Scholar
Elsinga, G. E., Scarano, F., Wieneke, B. & vanOudheusden, B. W. Oudheusden, B. W. 2006 b Tomographic particle image velocimetry. Exp. Fluids 41, 933–947.CrossRefGoogle Scholar
Falco, R. E. 1977 Coherent motions in the outer region of turbulent boundary layers. Phys. Fluids 20, S124–S132.CrossRefGoogle Scholar
Ganapathisubramani, B., Clemens, N. T. & Dolling, D. S. 2006 Large-scale motions in a supersonic turbulent boundary layer. J. Fluid Mech. 556, 271–282.CrossRefGoogle Scholar
Ganapathisubramani, B., Clemens, N. T. & Dolling, D. S. 2007 a Effects of upstream boundary layer on the unsteadiness of shock-induced separation. J. Fluid Mech. 585, 369–394.CrossRefGoogle Scholar
Ganapathisubramani, B., Clemens, N. T. & Dolling, D. S. 2007 b Effects of upstream coherent structures on low-frequency motion of shock-induced turbulent separation. In Forty-fifth AIAA Aerospace Sciences Meeting, Reno, NV, AIAA-2007-1141.Google Scholar
Ganapathisubramani, B., Longmire, E. K. & Marusic, I. 2003 Characteristics of vortex packets in the turbulent boundary layer. J. Fluid Mech. 478, 35–46.CrossRefGoogle Scholar
Garg, S. & Settles, G. S. 1998 Measurements of a supersonic turbulent boundary layer by focusing schlieren deflectometry. Exp. Fluids 25, 254–264.CrossRefGoogle Scholar
Guala, M., Hommema, S. E. & Adrian, R. J. 2006 Large-scale and very-large-scale motions in turbulent pipe flow. J. Fluid Mech. 554, 521–542.CrossRefGoogle Scholar
Head, M. R. & Bandyopadhyay, P. 1981 New aspects of the turbulent boundary layer structure. J. Fluid Mech. 107, 297–338.CrossRefGoogle Scholar
Humble, R. A., Elsinga, G. E., Scarano, F. & vanOudheusden, B. W. Oudheusden, B. W. 2009 Three-dimensional unsteady flow organization of shock wave/turbulent boundary layer interaction. J. Fluid Mech. 622, 33–62.CrossRefGoogle Scholar
Humble, R. A., Scarano, F. & vanOudheusden, B. W. Oudheusden, B. W. 2007 Particle image velocimetry measurements of shock wave/turbulent boundary layer interaction. Exp. Fluids 43, 173–183.CrossRefGoogle Scholar
Humble, R. A., Scarano, F., VanOudheusden, B. W. Oudheusden, B. W. & Tuinstra, M. 2006 PIV measurements of Shock Wave/Turbulent Boundary Layer Interaction. In Thirteenth Intl Symp. on Laser Techniques to Fluid Mechanics, Lisbon, Portugal, Paper 14.2.Google Scholar
Hunt, J. C. R., Wray, A. A. & Moin, P. 1988 Eddies, stream, and convergence zones in turbulent flows. Tech. Rep. Report CTR-S88. Centre for Turbulence Research, pp. 193–208.Google 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
Kim, K. C. & Adrian, R. J. 1999 Very large-scale motion in the outer layer. Phys. Fluids 11, 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
Martin, M. P. 2007 Direct numerical simulation of hypersonic turbulent boundary layers. Part 1. Initialization and comparison with experiments. J. Fluid Mech. 570, 347–364.CrossRefGoogle Scholar
Meinhart, C. D. & Adrian, R. J. 1995 On the existence of uniform momentum zones in a turbulent boundary layer. Phys. Fluids 7, 694–696.CrossRefGoogle Scholar
Perry, A. E., Lim, T. T. & Teh, E. W. 1981 A visual study of turbulent spots. J. Fluid Mech. 104, 387–405.CrossRefGoogle Scholar
Ringuette, M. J., Wu, M. & Martin, M. P. 2008 Coherent structures in direct numerical simulation of turbulent boundary layers at Mach 3. J. Fluid Mech. 594, 59–69.CrossRefGoogle Scholar
Robinson, S. K. 1991 Coherent motions in the turbulent boundary layer. Annu. Rev. Fluid Mech. 23, 601–639.CrossRefGoogle Scholar
Savitzky, A. & Golay, M. J. E. 1964 Smoothing and differentiation of data by simplified least squares procedures. Anal. Chem. 36, 1627–1639.CrossRefGoogle Scholar
Scarano, F. & Riethmuller, M. L. 2000 Advances in iterative multigrid PIV image processing. Exp. Fluids 29, 51–60.CrossRefGoogle Scholar
Schrijer, F. F. J. & Scarano, F. 2007 Particle slip compensation in steady compressible flows. Seventh Intl Symp. on Particle Image Velocimetry, Rome, Italy.Google Scholar
Schröder, A., Geisler, R., Elsinga, G. E., Scarano, F. & Dierksheide, U. 2007 Investigation of a turbulent spot and a tripped turbulent boundary layer using time-resolved tomographic PIV. Exp. Fluids 44, 305–316.CrossRefGoogle Scholar
Smits, A. J. & Dussauge, J. P. 2006 Turbulent shear layers in supersonic flow, 2nd edn. Springer.Google Scholar
Smits, A. J., Hayakawa, K. & Muck, K. C. 1983 Constant temperature hot-wire anemometry practice in supersonic flows; Part 1. The normal wire. Exp. Fluids 1, 83–92.CrossRefGoogle Scholar
Smith, M. W. & Smits, A. J. 1995 Visualization of the structure of supersonic turbulent boundary layers. Exp. Fluids 18, 288–302.CrossRefGoogle Scholar
Spina, E. F., Donovan, J. F. & Smits, A. J. 1991 On the structure of high-Reynolds-number supersonic turbulent boundary layers. J. Fluid Mech. 222, 293–327.CrossRefGoogle Scholar
Spina, E. F., Smits, A. J. & Robinson, S. K. 1994 The physics of supersonic boundary layers. Annu. Rev. Fluid Mech. 26, 287–319.CrossRefGoogle Scholar
Stanislas, M., Perret, L. & Foucaut, J. M. 2008 Vortical structures in the turbulent boundary layer: a possible route to a universal representation. J. Fluid Mech. 602, 327–382.CrossRefGoogle Scholar
Theodorsen, T. 1952 Mechanism of turbulence. In Proceedings of Second Midwestern Conference on Fluid Mechanics, Ohio State University, Columbus, OH, pp. 1–19.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
Wieneke, B. 2008 Volume self-calibration for 3D particle image velocimetry. Exp. Fluids 45, 549–556.CrossRefGoogle Scholar
Zhou, J., Adrian, R. J., Balachandar, S. & Kendall, T. M. 1999 Mechanisms for generating coherent packets of hairpin vortices in channel flow. J. Fluid Mech. 387, 353–396.CrossRefGoogle Scholar