Hostname: page-component-745bb68f8f-5r2nc Total loading time: 0 Render date: 2025-01-09T21:59:53.906Z Has data issue: false hasContentIssue false
  • English
  • Français

Direct simulation of a turbulent boundary layer up to Rθ = 1410

Published online by Cambridge University Press:  21 April 2006

Philippe R. Spalart
Philippe R. Spalart
Affiliation:
NASA Ames Research Center, Moffett Field, CA 94035, USA
Get access Rights & Permissions [Opens in a new window]

Abstract

The turbulent boundary layer on a flat plate, with zero pressure gradient, is simulated numerically at four stations between Rθ = 225 and Rθ = 1410. The three-dimensional time-dependent Navier-Stokes equations are solved using a spectral method with up to about 107 grid points. Periodic spanwise and streamwise conditions are applied, and a multiple-scale procedure is applied to approximate the slow streamwise growth of the boundary layer. The flow is studied, primarily, from a statistical point of view. The solutions are compared with experimental results. The scaling of the mean and turbulent quantities with Reynolds number is compared with accepted laws, and the significant deviations are documented. The turbulence at the highest Reynolds number is studied in detail. The spectra are compared with various theoretical models. Reynolds-stress budget data are provided for turbulence-model testing.

Type
Research Article
Information
Journal of Fluid Mechanics , Volume 187 , February 1988 , pp. 61 - 98
Copyright
© 1988 Cambridge University Press

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

Bandyopadhyay, P. R. 1987 Resonant flow in a row of small transverse cavities submerged in a turbulent boundary layer. AIAA-87–1235.
Bradshaw, P. 1967 'Inactive' motion and pressure fluctuations in turbulent boundary layers. J. Fluid Mech. 30, 241–258.Google Scholar
Clauser, F. 1954 Turbulent boundary layers in adverse pressure gradients. J. Aero. Sci. 21, 91–108.Google Scholar
Coles, D. E. 1956 The law of the wake in the turbulent boundary layer. J. Fluid Mech. 1, 191–226.Google Scholar
Coles, D. E. 1962 The turbulent boundary layer in a compressible fluid. Rand. Rep. R403-PR, ARC 24473: Appendix A: A manual of experimental practice for low-speed flow.
Coles, D. E. 1978 A model for flow in the viscous sublayer. Workshop on Coherent Structures of Turbulent Boundary Layers AFOSR/Lehigh University, Bethlehem, PA., pp. 462–475.
Deardorff, J. W. 1970 A numerical study of three-dimensional turbulent channel flow at large Reynolds numbers. J. Fluid Mech. 41, 453–480.Google Scholar
Erm, L. P., Smits, A. J. & Joubert, P. N. 1985 Low Reynolds number turbulent boundary layers on a smooth flat surface in a zero pressure gradient. Proc. 5th Symp. on Turbulent Shear Flows, Ithaca, NY, August 7–9, 1985.
Falco, R. E. 1977 Coherent motions in the outer region of turbulent boundary layers. Phys. Fluids Suppl. 20, 124–132.Google Scholar
Head, M. R. & Bandyopadhyay, P. 1981 New aspects of turbulent boundary layer structures. J. Fluid Mech. 107, 297–338.Google Scholar
Hinze, J. O. 1975, Turbulence. 2nd edn. McGraw-Hill.
Kim, H. T., Kline, S. J. & Reynolds, W. C. 1968 An experimental study of turbulence production near a smooth wall in a turbulent boundary layer with zero pressure gradient. Report MD-20, Stanford University, CA.
Klebanoff, P. S. 1954 Characteristics of turbulence in a boundary layer with zero pressure gradient. NACA TN-3178.
Li, J. D., Henbest, S. M. & Perry, A. E. 1986 The difficulties in the measurements of Reynolds stresses in smooth-and rough-wall turbulent boundary layers. Proc. 9th Australasian Fluid Mechanics Conf., Auckland, New Zealand, Dec. 8–12, 1986.
Moin, P. & Kim, J. 1982 Numerical investigation of turbulent channel flow. J. Fluid Mech. 118, 341–377.Google Scholar
Moser, R. D. & Moin, P. 1984 Direct numerical simulation of curved turbulent channel flow. NASA TM-85974. Also 1987 J. Fluid Mech. 175, 479.
Murlis, J., Tsai, H. M. & Bradshaw, P. 1982 The structure of turbulent boundary layers at low Reynolds numbers. J. Fluid Mech. 122, 13–56.Google Scholar
Pelz, R. B., Yakhot, V., Orszag, S. A., Shtilman, L. & Levich, E. 1985 Velocity-vorticity patterns in turbulent flow. Phys. Rev. Lett. 54, 2505.Google Scholar
Perry, A. E., Lim, K. L. & Henbest, S. M. 1985 A spectral analysis of smooth flat-plate boundary layers. Proc. 5th Symp. on Turbulent Shear Flows, Ithaca, NY, August 7–9, 1985.
Perry, A. E., Henbest, S. & Chong, M. S. 1986 A theoretical and experimental study of wall turbulence. J. Fluid Mech. 165, 163–199.Google Scholar
Preston, J. H. 1957 The minimum Reynolds number for a turbulent boundary layer and the selection of a transition device. J. Fluid Mech. 3, 373–384.Google Scholar
Purtell, L. P., Klebanoff, P. S. & Buckley, F. T. 1981 Turbulent boundary layers at low Reynolds numbers. Phys. Fluids 24, 802–811.Google Scholar
Rogallo, R. S. 1981 Numerical experiments in homogeneous turbulence. NASA TM-81315.
Rogallo, R. S. & Moin, P. 1984 Numerical simulation of turbulent flows. Ann. Rev. Fluid Mech. 16, 99–138.Google Scholar
Schewe, G. 1983 On the structure and resolution of wall-pressure fluctuations associated with turbulent boundary-layer flow. J. Fluid Mech. 134, 311–328.Google Scholar
Schlichting, H. 1979 Boundary Layer Theory. 7th edn. McGraw-Hill.
Schumann, U. 1975 Subgrid scale models for finite difference simulations of turbulent flows in plane channels and annuli. J. Comp. Phys. 18, 376–404.Google Scholar
Simpson, R. L. 1970 Characteristics of turbulent boundary layers at low Reynolds numbers with and without transpiration. J. Fluid Mech. 42, 769–802.Google Scholar
Spalart, P. R. 1986a Numerical simulation of boundary layers: Part 1. Weak formulation and numerical method. NASA TM-88222.
Spalart, P. R. 1986b Numerical study of sink-flow boundary layers. J. Fluid Mech. 172, 307–328.Google Scholar
Spalart, P. R. & Leonard, A. 1985 Direct numerical simulation of equilibrium turbulent boundary layers. Proc. 5th Symp. on Turbulent Shear Flows, Ithaca, NY, August 7–9, 1985 (bound volume, 234).
Townsend, A. A. 1956 The Structure of Turbulent Shear Flow, 1st edn. Cambridge University Press.
Townsend, A. A. 1961 Equilibrium layers and wall turbulence. J. Fluid Mech. 11, 97–120.Google Scholar
Townsend, A. A. 1976 The Structure of Turbulent Shear Flow, 2nd edn. Cambridge University Press.
Willmarth, W. W. 1975 Pressure fluctuations beneath turbulent boundary layers. Ann. Rev. Fluid Mech. 7, 13–38.Google Scholar
Wray, A. A. 1987 Minimal storage time-advancement schemes for spectral methods. J. Comp. Phys. (in press).Google Scholar