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Shear-free turbulent boundary layers. Part 1. Physical insights into near-wall turbulence

Published online by Cambridge University Press:  26 April 2006

Blair Perot  and
Parviz Moin
Blair Perot
Affiliation:
Department of Mechanical Engineering, Stanford University, Stanford, CA 94305 USA Currently at Los Alamos National Laboratory, NM 87545, USA.
Parviz Moin
Affiliation:
Department of Mechanical Engineering, Stanford University, Stanford, CA 94305 USA Also with NASA-Ames Research Center, Moffett Field, CA 94035, USA.
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Abstract

Direct numerical simulation is used to examine the interaction of turbulence with a wall in the absence of mean shear. The influence of a solid wall on turbulence is analysed by first considering two ‘simpler’ types of boundaries. The first boundary is an idealized permeable wall. This boundary isolates and elucidates the viscous effects created by the wall. The second boundary is an idealized free surface. This boundary complements the first by allowing one to isolate and investigate the kinematic effects that occur near boundaries. The knowledge gained from these two simpler flows is then used to understand how turbulence is influenced by solid walls where both viscous and kinematic effects occur in combination.

Examination of the instantaneous flow fields confirms the presence of previously hypothesized structures (splats), and reveals an additional class of structures (antisplats). Statistical analysis of the Reynolds stresses and Reynolds stress transport equations indicates the relative importance of dissipation, intercomponent energy transfer, and energy transport. It is found that it is not the structures themselves, but the imbalance between structures which leads to intercomponent energy transfer. Remarkably, this imbalance (and hence near-wall intercomponent energy transfer) is controlled by viscous processes such as dissipation and diffusion. The analysis presented herein is a departure from past notions of how boundaries influence turbulence. The efficacy of these qualitative physical concepts is demonstrated in Part 2 where improved near-wall turbulence models are derived based on these ideas.

Type
Research Article
Information
Journal of Fluid Mechanics , Volume 295 , 25 July 1995 , pp. 199 - 227
Copyright
© 1995 Cambridge University Press

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References

Batchelor, G. K. 1956 The Theory of Homogeneous Turbulence, p. 47. Cambridge University Press.
Biringen, S. & Reynolds, W. C. 1981 Large-eddy simulation of the shear-free turbulent boundary layer. J. Fluid Mech. 103, 53–63.Google Scholar
Bradshaw, P. & Bott, D. M. 1993 A moving-floor test section for simulating high free-stream turbulence. AFOSR Contractors Meeting – August 1993, p. 4.1–1.Google Scholar
Brumley, B. 1984 Turbulence measurements near the free surface in stirred grid experiments. In Gas Transfer at Water Surfaces (ed. W. Brutsaert & G. H. Jirka), pp. 83–92. Reidel.
Durbin, P. A. 1993 A Reynolds stress model for near-wall turbulence. J. Fluid Mech. 249, 465–498.Google Scholar
Falco, R. E. 1988 Vortex ring/viscous wall layer interaction model of the turbulence production process near walls. Exps. Fluids 6, 305–315.Google Scholar
Falco, R. E. 1991 A coherent structure model of the turbulent boundary layer and its ability to predict Reynolds number dependence. Phil. Trans. R. Soc. Lond. A 336, 103–129.Google Scholar
Hallback, M. & Johansson, A. V. 1992 Modeling of pressure-strain in homogeneous turbulence. Advances in Turbulence 4 (ed. F. T. M. Nieuwstadt). Springer.
Harlow, F. H. & Welch, J. E. 1965 Numerical calculation of time-dependent viscous incompressible flow of fluid with free surface. Phys. Fluids 8, 2182–2189.Google Scholar
Hunt, J. C. R. 1984a Turbulence structure and turbulent diffusion near gas–liquid interfaces. In Gas Transfer at Water Surfaces (ed. W. Brutsaert & G. H. Jirka), pp. 67–82. Reidel.
Hunt, J. C. R. 1984b Turbulence structure in thermal convection and shear-free boundary layers. J. Fluid Mech. 138, 161–184.Google Scholar
Hunt, J. C. R. & Graham, J. M. R. 1978 Free-stream turbulence near plane boundaries. J. Fluid Mech. 84, 209–235.Google Scholar
Jimenez, J. & Moin, P. 1991 The minimal flow unit in near wall turbulence. J. Fluid Mech. 225, 213.Google Scholar
Kim, J. & Moin, P. 1985 Application of a fractional-step method to incompressible Navier–Stokes equations. J. Comput. Phys. 59, 308–323.Google 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.Google Scholar
Le, H. 1994 Direct numerical simulation of turbulent flow over a backward facing step. PhD thesis, Dept of Mech. Engng, Stanford University.
Lee, M. J., Kim, J. & Moin, P. 1990 Structure of turbulence at high shear rate. J. Fluuid Mech. 216, 561–583.Google Scholar
Lilly, D. K. 1965 Mon. Weather Rev. 93, 11.
Maday, Y., Patera, A. T. & Ronquist, E. M. 1990 An operator-integration-factor splitting method for time-dependent problems: application to incompressible fluid flow. J. Sci. Comput. 5, 263–292.Google Scholar
Malan, P. & Johnston, J. P. 1993 Heat transfer in shear-free turbulent boundary layers. Rep. MD-64. Department of Mechanical Engineering, Stanford University.
Moin, P. 1987 Analysis of turbulence data generated by numerical simulations. AIAA 25th Aerospace Sciences Meeting, January 1987, Reno, Nevada. AIAA Paper 87–0194.
Orlandi, P. & Verzicco, R. 1993 Vortex rings impinging on walls: axisymmetric and three-dimensional simulations. J. Fluid Mech. 256, 615–646.Google Scholar
Perot, J. B. 1992 Direct numerical simulation of turbulence on the Connection Machine. In Parallel Computational Fluid Dynamics ’92 (ed. R. Pelz, A. Ecer & J. Hauser), pp. 325–336. North-Holland.
Perot, J. B. 1993 An analysis of the fractional step method. J. Comput. Phys. 108, 51–58.Google Scholar
Perot, J. B. & Moin, P. 1993 Shear-free turbulent boundary layers. Rep. TF-60. Dept. of Mech. Engng, Stanford University.
Perot, J. B. & Moin, P. 1995 Shear-free turbulent boundary layers. Part 2. New concepts of Reynolds stress transport equation modelling of inhomogeneous flows. J. Fluid Mech. 295, 229–245.Google Scholar
Prandtl, L. 1925 Über die ausgebildete Turbulenz. Z. Angew. Math. Mech. 5, 136.Google Scholar
Reynolds, W. C. 1991 The potential and limitations of direct and large eddy simulations. In Whither Turbulence (ed. J. L. Lumley). Lecture Notes in Physics, vol. 357, pp. 313–315. Springer.
Robinson, S. K. 1991 Coherent motions in the turbulent boundary layer. Ann. Rev. Fluid Mech. 23, 601.Google Scholar
Rotta, J. 1951 Statistical Theory of inhomogeneous turbulence. Part I. Z. Phys. 129, 257–572.Google Scholar
Thomas, N. H. & Hancock, P. E. 1977 Grid turbulence near a moving wall. J. Fluid Mech. 82, 481–496.Google Scholar
Uzkan, T. & Reynolds, W. C. 1967 A shear-free turbulent boundary layer. J. Fluid Mech. 28, 803–821.Google Scholar