Hostname: page-component-cd9895bd7-gvvz8 Total loading time: 0 Render date: 2024-12-28T06:55:39.141Z Has data issue: false hasContentIssue false
  • English
  • Français

Direct numerical simulation of turbulence in a nominally zero-pressure-gradient flat-plate boundary layer

Published online by Cambridge University Press:  10 July 2009

XIAOHUA WU  and
PARVIZ MOIN
XIAOHUA WU
Affiliation:
Department of Mechanical Engineering, Royal Military College of Canada, Kingston, Ontario, Canada, K7K 7B4
PARVIZ MOIN*
Affiliation:
Centre for Turbulence Research, Stanford University, Stanford, CA 94305-3035, USA
*
†Email address for correspondence: [email protected]
Get access Rights & Permissions [Opens in a new window]

Abstract

A nominally-zero-pressure-gradient incompressible boundary layer over a smooth flat plate was simulated for a continuous momentum thickness Reynolds number range of 80 ≤ Reθ ≤ 940. Transition which is completed at approximately Reθ = 750 was triggered by intermittent localized disturbances arising from patches of isotropic turbulence introduced periodically from the free stream at Reθ = 80. Streamwise pressure gradient is quantified with several measures and is demonstrated to be weak. Blasius boundary layer is maintained in the early transitional region of 80 < Reθ < 180 within which the maximum deviation of skin friction from the theoretical solution is less than 1%. Mean and second-order turbulence statistics are compared with classic experimental data, and they constitute a rare DNS dataset for the spatially developing zero-pressure-gradient turbulent flat-plate boundary layer. Our calculations indicate that in the present spatially developing low-Reynolds-number turbulent flat-plate boundary layer, total shear stress mildly overshoots the wall shear stress in the near-wall region of 2–20 wall units with vanishing normal gradient at the wall. Overshoots as high as 10% across a wider percentage of the boundary layer thickness exist in the late transitional region. The former is a residual effect of the latter. The instantaneous flow fields are vividly populated by hairpin vortices. This is the first time that direct evidence (in the form of a solution of the Navier–Stokes equations, obeying the statistical measurements, as opposed to synthetic superposition of the structures) shows such dominance of these structures. Hairpin packets arising from upstream fragmented Λ structures are found to be instrumental in the breakdown of the present boundary layer bypass transition.

Type
Papers
Information
Journal of Fluid Mechanics , Volume 630 , 10 July 2009 , pp. 5 - 41
Copyright
Copyright © Cambridge University Press 2009

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

Acarlar, M. S. & Smith, C. R. 1987 A study of hairpin vortices in a laminar boundary layer. Part 2. Hairpin vortices generated by fluid injection. J. Fluid Mech. 175, 43–83.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
Alfredsson, P. H., Johansson, A. V., Haritonidis, J. H. & Eckelmann, H. 1988 The fluctuation wall-shear stress and the velocity field in the viscous sublayer. Phys. Fluids 31, 1026–1033.CrossRefGoogle Scholar
Barenblatt, G. I. & Chorin, A. J. 1998 Scaling of the intermediate region in wall-bounded turbulence: the power law. Phys. Fluids 10, 1043–1044.CrossRefGoogle Scholar
Brandt, L., Schlatter, P. & Henningson, D. S. 2004 Transition in boundary layers subject to free-stream turbulence. J. Fluid Mech. 517, 167–198.CrossRefGoogle Scholar
Chakraborty, P., Balachandar, S. & Adrian, R. 2005 On the relationships between local vortex identification schemes. J. Fluid Mech. 535, 189–214.CrossRefGoogle Scholar
Choi, H. & Moin, P. 1990 On the space–time characteristics of wall-pressure fluctuations. Phys. Fluids 2, 1450–1460.CrossRefGoogle Scholar
Coles, D. 1956 The law of the wake in the turbulent boundary layer. J. Fluid Mech. 1, 191–226.CrossRefGoogle Scholar
De Graaff, D. B. & Eaton, J. K. 2000 Reynolds-number scaling of the flat-plate turbulent boundary layer. J. Fluid Mech. 422, 319–346.CrossRefGoogle Scholar
Erm, L. P. & Joubert, P. N. 1991 Low Reynolds number turbulent boundary layers. J. Fluid Mech. 230, 1–44.CrossRefGoogle Scholar
Erm, L. P., Smits, A. J. & Joubert, P. N. August 7–9, 1985 Low Reynolds number turbulent boundary layers on a smooth flat surface in a zero pressure gradient. In Proceedings of fifth Symposium on Turbulent Shear Flows, Ithaca, NY.Google Scholar
Favre, A. J., Gaviglio, J. J. & Dumas, R. J. 1957 Space–time double correlations and spectra in a turbulent boundary layer. J. Fluid Mech. 2, 313–342.CrossRefGoogle Scholar
Head, M. R. & Bandyopadhyay, P. 1981 New aspects of turbulent boundary layer structure. J. Fluid Mech. 107, 297–338.CrossRefGoogle Scholar
Herbert, T. 1988 Secondary instability of boundary layers. Annu. Rev. Fluid Mech. 20, 487–526.CrossRefGoogle Scholar
Honkan, A. & Andreopoulos, Y. 1997 Vorticity, strain-rate and dissipation characteristics in the near-wall region of turbulent boundary layers. J. Fluid Mech. 350, 29–96.CrossRefGoogle Scholar
Hunt, J. C. R., Wray, A. A. & Moin, P. 1988 Eddies, streams, and convergence zones in turbulent flows. In Proceedings of Summer Program, pp. 9–14. Centre for Turbulence Research, Stanford University.Google 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
Jacobs, R. G. & Durbin, P. A. 2001 Simulation of bypass transition. J. Fluid Mech. 428, 185–212.CrossRefGoogle Scholar
Khurajadze, G. & Oberlack, M. 2004 DNS and scaling laws from new symmetry groups of zpg turbulent boundary layer flow. Theor. Comput. Fluid Dyn. 18, 391441.Google Scholar
Kim, J., Moin, P. & Moser, R. D. 1987 Turbulence statistics in fully developed channel flow at low Reynolds number. J. Fluid Mech. 177, 133–166.CrossRefGoogle Scholar
Kim, K., Sung, H. J. & Adrian, R. J. 2008 Effects of background noise on generating coherent packets of hairpin vortices. Phys. Fluids 20, 105107.CrossRefGoogle Scholar
Lund, T. S., Wu, X. & Squires, K. D. 1998 Generation of turbulent inflow data for spatially-developing boundary layer simulations. J. Comput. Phys. 140, 233–258.CrossRefGoogle Scholar
Moin, P. & Kim, J. 1985 The structure of the vorticity field in turbulent channel flow. Part 1. Analysis of instantaneous fields and statistical correlations. J. Fluid Mech. 155, 441–464.CrossRefGoogle Scholar
Monkewitz, P., Chauhan, K. A. & Nagib, H. M. 2007 Self-consistent high-Reynolds-number asymptotic for zero-pressure-gradient turbulent boundary layers. Phys. Fluids 19, 115101.CrossRefGoogle Scholar
Murlis, J., Tsai, H. M. & Bradshaw, P. 1982, The structure of turbulent boundary layers at low Reynolds numbers. J. Fluid Mech. 122, 13–56.CrossRefGoogle Scholar
Nagib, H. M., Chauhan, K. & Monkewitz, P. 2007 Approach to an asymptotic state for zero pressure gradient turbulent boundary layers. Phil. Trans. R. Soc. A 365, 755–770.CrossRefGoogle Scholar
Ovchinnikov, V., Piomelli, U. & Choudhari, M. M. 2006 Numerical simulations of boundary-layer transition induced by a cylinder wake. J. Fluid Mech. 547, 413–441.CrossRefGoogle Scholar
Pauley, L. L., Moin, P. & Reynolds, W. C. 1990 The structure of two-dimensional separation. J. Fluid Mech. 220, 397–411.CrossRefGoogle Scholar
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, 163–200.CrossRefGoogle Scholar
Pierce, C. D. & Moin, P. 2001 Progress variable approach for large-eddy simulation of turbulent combustion. Report No. TF-80, Stanford University.Google Scholar
Pierce, C. D. & Moin, P. 2004 Progress variable approach for large-eddy simulation of non-premixed turbulent combustion. J. Fluid Mech. 504, 73–97.CrossRefGoogle Scholar
Purtell, L. P., Klebanoff, P. S. & Buckley, F. T. 1981 Turbulent boundary layer at low Reynolds number. Phys. Fluids 24, 802–811.CrossRefGoogle Scholar
Rai, M. M. & Moin, P. 1993 Direct numerical simulation of transition and turbulence in a spatially evolving boundary layer. J. Comput. Phys. 109, 169–192.CrossRefGoogle Scholar
Roach, P. E. & Brierley, D. H. 1990 The influence of a turbulent frees-stream on zero pressure gradient transitional boundary layer development. Part I. Test Cases T3A and T3B. In Numerical Simulation of Unsteady Flows and Transition to Turbulence, pp. 319–347, Cambridge University Press.Google Scholar
Robinson, S. K. 1991 Coherent motion in the turbulent boundary layer. Annu. Rev. Fluid Mech. 23, 601–639.CrossRefGoogle Scholar
Schubauer, G. B. & Skramstad, H. K. 1947 Laminar boundary layer oscillations and stability of laminar flow. J. Aero. Sci. 14, 69–78.CrossRefGoogle Scholar
Singer, B. A. & Joslin, R. D. 1994 Metamorphosis of a hairpin vortex into a young turbulent spot. Phys. Fluids 11, 3724–3736.CrossRefGoogle Scholar
Smith, R. W. 1994 Effect of Reynolds number on the structure of turbulent boundary layers. PhD thesis, Department of Mechanical and Aerospace Engineering, Princeton University.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
Spalart, P. R. & Watmuff, J. H. 1993 Experimental and numerical study of a turbulent boundary layer with pressure gradients. J. Fluid Mech. 249, 337–371.CrossRefGoogle 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
Turan, O., Azad, R. S. & Kassab, S. Z. 1987 Experimental and theoretical evaluation of the k 1−1 spectral law. Phys. Fluids 30, 3463–3474.CrossRefGoogle Scholar
Willmarth, W. W. 1975 Pressure fluctuations beneath turbulent boundary layers. Annu. Rev. Fluid Mech. 7, 13–38.CrossRefGoogle Scholar
Wu, X., Jacobs, R., Hunt, J. C. R. & Durbin, P. A. 1999 Simulation of boundary layer transition induced by periodically passing wakes. J. Fluid Mech. 398, 109–153.CrossRefGoogle Scholar
Wu, X. & Moin, P. 2008 A direct numerical simulation study on the mean velocity characteristics in turbulent pipe flow. J. Fluid Mech. 608, 81–112.CrossRefGoogle Scholar
Zagarola, M. & Smits, A. J. 1998 A new mean velocity scaling for turbulent boundary layers. In Proceedings of ASME Fluids Engineering Division Summer Meeting, June 21–25, Washington DC.Google Scholar
Zaki, T. A. & Durbin, P. A. 2005 Mode interaction and the bypass route to transition. J. Fluid Mech. 531, 85–111.CrossRefGoogle Scholar