Hostname: page-component-cd9895bd7-dk4vv Total loading time: 0 Render date: 2024-12-18T10:13:07.776Z Has data issue: false hasContentIssue false
  • English
  • Français

Turbulence statistics in fully developed channel flow at low Reynolds number

Published online by Cambridge University Press:  21 April 2006

John Kim ,
Parviz Moin  and
Robert Moser
John Kim
Affiliation:
NASA Ames Research Center, Moffett Field, CA 94035, USA
Parviz Moin
Affiliation:
NASA Ames Research Center, Moffett Field, CA 94035, USA
Robert Moser
Affiliation:
NASA Ames Research Center, Moffett Field, CA 94035, USA
Get access Rights & Permissions [Opens in a new window]

Abstract

A direct numerical simulation of a turbulent channel flow is performed. The unsteady Navier-Stokes equations are solved numerically at a Reynolds number of 3300, based on the mean centreline velocity and channel half-width, with about 4 × 106 grid points (192 × 129 × 160 in x, y, z). All essential turbulence scales are resolved on the computational grid and no subgrid model is used. A large number of turbulence statistics are computed and compared with the existing experimental data at comparable Reynolds numbers. Agreements as well as discrepancies are discussed in detail. Particular attention is given to the behaviour of turbulence correlations near the wall. In addition, a number of statistical correlations which are complementary to the existing experimental data are reported for the first time.

Type
Research Article
Information
Journal of Fluid Mechanics , Volume 177 , April 1987 , pp. 133 - 166
Copyright
© 1987 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

Alfredsson, P. H. & Johansson, A. V. 1984 On the detection of turbulence-generating events. J. Fluid Mech. 139, 325.Google Scholar
Barlow, R. S. & Johnston, J. P. 1985 Structure of turbulent boundary layers on a concave surface. Rep. MD-47, Department of Mechanical Engineering, Stanford University, Stanford, California, USA.Google Scholar
Brodkey, R. S., Wallace, J. M. & Eckelmann, H. 1974 Some properties of truncated turbulence signals in bounded shear flows. J. Fluid Mech. 63, 209.Google Scholar
Chapman, D. R. & Kuhn, G. D. 1984 Computational models of the viscous sublayer and limiting behaviour of turbulence near a wall. NEAR TR 334, Nielsen Engineering & Research, Inc., Mountain View, California, USA.Google Scholar
Clark, J. A. 1968 A study of incompressible turbulent boundary layers in channel flow. Trans. ASME D: J. Basic Engng 90, 455Google Scholar
Comte-Bellot, G. 1963 Contribution a l’étude de la turbulence de conduite. Doctoral thesis, University of Grenoble, France.
Dean, R. B. 1978 Reynolds number dependence of skin friction and other bulk flow variables in two-dimensional rectangular duct flow. Trans. ASME I: J. Fluids Engng 100, 215Google Scholar
Dean, R. B. & Bradshaw, P. 1976 Measurements of interacting turbulent shear layers in a duct. J. Fluid Mech. 78, 641.Google Scholar
Deardorff, J. W. 1970 A numerical study of three-dimensional turbulent channel flow at large Reynolds number. J. Fluid Mech. 41, 453.Google Scholar
Eckelmann, H. 1070 Mitteilungen aus dem MPI für Strömungsforschung und der AVA, Göttingen, no. 48.
Eckelmann, H. 1974 The structure of the viscous sublayer and the adjacent wall region in a turbulent channel flow. J. Fluid Mech. 65, 439.Google Scholar
Falco, R. E. 1980 The production of turbulence near a wall. AIAA Paper 80–1356.Google Scholar
Finnicum, D. S. & Hanratty, T. J. 1985 Turbulent normal velocity fluctuations close to a wall. Phys. Fluids 28, 1654.Google Scholar
Gottlieb, D. & Orszag, S. A. 1977 Numerical Analysis of Spectral Methods: Theory and Applications. CBMS-NSF, Society for Industrial and Applied Mathematics. Philadelphia, PA, USA.
Gupta, A. K. & Kaplan, R. E. 1972 Statistical characteristics of Reynolds stress in a turbulent boundary layer. Phys. Fluids 15, 981.Google Scholar
Hanjalic, K. & Launder, B. E. 1976 Contribution towards a Reynolds-stress closure for low-Reynolds-number turbulence. J. Fluid Mech. 74, 593.Google Scholar
Hanratty, T. J., Chorn, L. G. & Hatziavramidis, D. T. 1977 Turbulent fluctuations in the viscous wall region for Newtonian and drag reducing fluids. Phys. Fluids 20, S112.Google Scholar
Hinze, J. O. 1975 Turbulence, 2nd edn, p. 621. McGraw-Hill.
Hussain, A. K. M. F. & Reynolds, W. C. 1975 Measurements in fully developed turbulent channel flow. Trans. ASME I: J. Fluids Engng 97, 568Google Scholar
Johansson, A. V. & Alfredsson, P. H. 1982 On the structure of turbulent channel flow. J. Fluid Mech. 122, 295.Google Scholar
Johansson, A. V. & Alfredsson, P. H. 1983 Effects of imperfect spatial resolution on measurement of wall-bounded turbulent shear flows. J. Fluid Mech. 137, 409.Google Scholar
Kastrinakis, E. G. & Eckelmann, H. Measurement of streamwise vorticity fluctuations in a turbulent channel flow. J. Fluid Mech. 137, 165.
Kim, J. 1983 On the structure of wall-bounded turbulent flows. Phys. Fluids 26, 2088.Google Scholar
Kim, J. 1985 Turbulence structures associated with the bursting event. Phys. Fluids 28, 52.Google Scholar
Kim, J. & Moin, P. The structure of the vorticity field in turbulent channel flow. Part 2. Study of ensemble-averaged fields. J. Fluid Mech. 162, 339.
Kim, H. T., Kline, S. J. & Reynolds, W. C. 1971 The production of turbulence near a smooth wall in a turbulent boundary layer. J. Fluid Mech. 50, 133.Google Scholar
Kreplin, H. & Eckelmann, H. 1979 Behavior of the three fluctuating velocity components in the wall region of a turbulent channel flow. Phys. Fluids 22, 1233.Google Scholar
Lanczos, C. 1956 Applied Analysis. Prentice-Hall.
Laufer, J. 1951 Investigation of turbulent flow in a two-dimensional channel. NACA Rep. 1053.Google Scholar
Leonard, A. & Wray, A. A. 1982 A numerical method for the simulation of three-dimensional flow in a pipe. Proc. 8th Intl Conf. on Numerical Methods in Fluid Dynamics, Aachen, Germany, 28 June-2 July, 1982, pp. 335–342. Springer.
Moin, P. 1984 Probing turbulence via large eddy simulation. AIAA Paper 84–0174.Google Scholar
Moin, P. & Kim, J. 1980 On the numerical solution of time-dependent viscous incompressible fluid flows involving solid boundaries. J. Comp. Phys. 35, 381.Google Scholar
Moin, P. & Kim, J. 1982 Numerical investigation of turbulent channel flow. J. Fluid Mech. 118, 341.Google 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.Google Scholar
Moser, R. D. & Moin, P. 1984 Direct numerical simulation of curved turbulent channel flow. NASA TM 85974. Also, Rep. TF-20, Department of Mechanical Engineering, Stanford University, Stanford, California, USA.Google Scholar
Nikuradse, J. 1929 Untersuchungen über die Strömungen des Wassers in konvergenten und divergenten Kanälen. Forsch. Geb. Ing. Wes., Heft 289.Google Scholar
Ohji, M. 1967 Statistical theory of wall turbulence. Phys. Fluids Suppl. 10, S153.Google Scholar
Orszag, S. A. & Patera, A. T. 1981 Subcritical transition to turbulence in planar shear flows. Proc. Symp. of The Mathematics Research Center, University of Wisconsin-Madison, 13–15 October 1980 (ed. R. E. Meyer), pp. 127–146. Academic.
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, 7–9 August 1985, Cornell University, Ithaca, NY, pp. 9.29–9.34.
Reichardt, H. 1938 Messungen turbulenter Schwankungen. Naturwissenschaften, Jahrg. 26, Heft 24/25, p. 404.
Rogallo, R. S. & Moin, P. 1984 Numerical simulation of turbulent flows. Ann. Rev. Fluid Mech. 16, 99.Google Scholar
Sabot, J. & Comte-Bellot, G. 1976 Intermittency of coherent structures in the core region of fully developed turbulent pipe flow. J. Fluid Mech. 74, 767.Google Scholar
Schumann, U. 1973 Ein Verfahren zur direkten numerischen Simulation turbulenter Strömungen in Platten- und Ringspaltkanälen und über seine Anwendung zur Untersuchung von Turbulenzmodellen. Dissertation, University of Karlsruhe (NASA Tech. Translation, NASA TTF 15391).
Smith, C. R. & Schwartz, S. P. 1983 Observation of streamwise rotation in the near-wall region of a turbulent boundary layer. Phys. Fluids 26, 641.Google Scholar
Smith, C. R. & Metzler, S. P. 1983 The characteristics of low-speed streaks in the near-wall region of a turbulent boundary layer. J. Fluid Mech. 129, 27.Google Scholar
Spalart, P. R. 1985 Numerical simulations of boundary layers. NASA TM 88220–88222.Google Scholar
Tennekes, H. & Lumley, J. L. 1972 A First Course in Turbulence. MIT Press.
Wallace, J. M., Eckelmann, H. & Brodkey, R. S. 1972 The wall region in turbulent shear flow. J. Fluid Mech. 54, 39.Google Scholar
Willmarth, W. W. 1975 Pressure fluctuations beneath turbulent boundary layers. Ann. Rev. Fluid Mech. 5, 13.Google Scholar
Willmarth, W. W. & Lu, S. S. 1972 Structure of the Reynolds stress near the wall. J. Fluid Mech. 55, 65.Google Scholar