Hostname: page-component-8448b6f56d-qsmjn Total loading time: 0 Render date: 2024-04-18T10:30:55.547Z Has data issue: false hasContentIssue false
  • English
  • Français

A more general effective-viscosity hypothesis

Published online by Cambridge University Press:  29 March 2006

S. B. Pope
S. B. Pope
Affiliation:
Department of Mechanical Engineering, Imperial College, London
Get access Rights & Permissions [Opens in a new window]

Abstract

A discussion of the applicability of an effective-viscosity approach to turbulent flow suggests that there are flow situations where the approach is valid and yet present hypotheses fail. The general form of an effective-viscosity formulation is shown to be a finite tensor polynomial. For two-dimensional flows, the coefficients of this polynomial are evaluated from the modelled Reynolds-stress equations of Launder, Reece & Rodi (1975). The advantage of the proposed effective-viscosity formulation, equation (4.3), over isotropie-viscosity hypotheses is that the whole velocity-gradient tensor affects the predicted Reynolds stresses. Two notable consequences of this are that (i) the complete Reynolds-stress tensor is realistically modelled and (ii) the influence of streamline curvature on the Reynolds stresses is incorporated.

Type
Research Article
Information
Journal of Fluid Mechanics , Volume 72 , Issue 2 , 25 November 1975 , pp. 331 - 340
Copyright
© 1975 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

Boussinesq, T. V. 1877 Mém. pres. Acad. Sci., 3rd edn, Paris XXIII, p. 46.
Bradshaw, P. 1973 Effects of streamline curvature on turbulent flow. AGARDograph, no. 169.
Bradshaw, P., Ferriss, D. H. & Atwell, N. P. 1967 Calculation of boundary-layer development using the turbulent energy equation. J. Fluid Mech. 28, 593–616.Google Scholar
Champagne, F. M., Harris, V. G. & Corrsin, S. 1970 Experiments on nearly homogeneous turbulent shear flow. J. Fluid Mech. 41, 81–139.Google Scholar
Launder, B. E., Reece, G. J. & Rodi, W. 1975 Progress in the development of a Reynolds-stress turbulence closure. J. Fluid Mech. 68, 537–566.Google Scholar
Launder, B. E. & Spalding, D. B. 1972 Mathematical Models of Turbulence. Academic.
Lumley, J. L. 1970 Towards a turbulent constitutive relation. J. Fluid Mech. 41, 413–434.Google Scholar
Ng, K. H. 1971 Predictions of turbulent boundary-layer developments using a two-equation model of turbulence. Ph.D. thesis, University of London.
Spencer, A. J. M. & Rivlin, R. S. 1959 The theory of matrix polynomials and its application to the mechanics of isotropic continua. Arch. Rat. Mech. Anal. 2, 309–336.Google Scholar
Spencer, A. J. M. & Rivlin, R. S. 1960 Further results in the theory of matrix polynomials. Arch. Rat. Mech. Anal. 4, 214–230.Google Scholar
Rodi, W. 1972 The prediction of free turbulent boundary layers by use of a two-equation model of turbulence. Ph.D. thesis, University of London. (See also Imperial College, Mech. Engng Dept. Rep. HTS/72/24.)
Runchal, A. K. & Spalding, D. B. 1971 Steady turbulent flow and heat transfer downstream of a sudden enlargement in a pipe of circular cross-section. Imperial College, Mech. Engng Dept. Rep. EF/TN/A/39.Google Scholar