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The calculation of three-dimensional turbulent boundary layers in incompressible flow

Published online by Cambridge University Press:  29 March 2006

J. F. Nash
J. F. Nash
Affiliation:
Lockheed Georgia Research Laboratory, Marietta, Georgia
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Abstract

A method is described for calculating the development of a three-dimensional turbulent boundary layer, over a flat or developable surface, in incompressible flow. The method involves the numerical integration of the equations of motion by an explicit finite-difference method. The shear stress is determined by a parallel integration of the turbulent energy equation modified by the inclusion of empirical functions of a form which has proved successful in two dimensions, and the additional assumption is made that the turbulent shear stress acts in the direction of the rate of strain of the mean motion. The treatment of the turbulent energy equation follows closely the work of Bradshaw, Ferriss & Atwell (1967) in two dimensions.

Comparison with experiment is found to be substantially more difficult than in two dimensions. Particular difficulty is encountered in translating the recorded details of the experiment into boundary conditions for the calculation. The comparisons submitted here give some indication that the method as a whole performs satisfactorily, but they do not provide a definitive assessment of the validity of the basic assumptions. A plea is made for an experiment to supply data in a suitable form for making a more careful assessment of methods of this type.

Type
Research Article
Information
Journal of Fluid Mechanics , Volume 37 , Issue 4 , 28 July 1969 , pp. 625 - 642
Copyright
© 1969 Cambridge University Press

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References

Bradshaw, P., Ferriss, D. H. & Atwell, N. P. 1967 Calculation of boundary-layer development using the turbulent energy equation J. Fluid Mech. 28, 593.Google Scholar
Cumpsty, N. A. 1967 The calculation of three-dimensional turbulent boundary layers. Ph.D. Thesis, University of Cambridge.CrossRefGoogle Scholar
Francis, G. P. & Pierce, F. J. 1967 An experimental study of skewed turbulent boundary layers in low speed flows. J. Basic. Eng. 89, 597.Google Scholar
Hornung, H. G. & Joubert, P. N. 1963 The mean velocity profile in three-dimensional turbulent boundary layers. J. Fluid Mech. 15, 368.Google Scholar
Joubert, P. N., Perry, A. E. & Brown, K. C. 1967 Critical review and current developments in three-dimensional turbulent boundary layers. Fluid Mechanics of Internal Flows. Amsterdam: Elsevier.Google Scholar
Mcdonald, H. 1968 The departure from equilibrium of turbulent boundary layers. Aero. Quart. 19, 1.CrossRefGoogle Scholar
Nash, J. F. 1968 A finite-difference method for the calculation of incompressible turbulent boundary layers in two dimensions. Lockheed-Georgia Co., Rep. ER-9655.Google Scholar
Perry, A. E. & Joubert, P. N. 1965 A three-dimensional turbulent boundary layer J. Fluid Mech. 22, 285.Google Scholar
Rosenhead, L. (ed.) 1963 Laminar Boundary Layers. Oxford: Pergamon.Google Scholar
Townsend, A. A. 1955 The Structure of Turbulent Shear Flow. Cambridge University Press.Google Scholar
Tucker, H. J. & Reynolds, A. J. 1968 The distortion of turbulence by irrotational plane strain. J. Fluid Mech. 32, 657.Google Scholar
Winter, K. G., Smith, K. G. & Rotta, J. C. 1965 Turbulent boundary-layer studies on a waisted body of revolution in subsonic and supersonic flow. Agardograph, 97.Google Scholar