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The entrainment function in turbulent boundary-layer and wall-jet calculations

Published online by Cambridge University Press:  28 March 2006

M. P. Escudier  and
W. B. Nicoll
M. P. Escudier
Affiliation:
Imperial College of Science and Technology, Department of Mechanical Engineering, Exhibition Road, London, S.W. 7
W. B. Nicoll
Affiliation:
Imperial College of Science and Technology, Department of Mechanical Engineering, Exhibition Road, London, S.W. 7
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Abstract

Some of the proposals made by Spalding (1964a) in his ‘Unified theory of friction, heat transfer, and mass transfer’ are examined. The two-component velocity-profile family proposed by Spalding is compared with measured boundary-layer and wall-jet velocity profiles and is shown to be adequate for flows with moderate wake components. The drag law implicit in the velocity-profile family is shown to be in good agreement with experimental data.

Recommendations are provided for entrainment functions for both boundary layers and wall jets.

Predictions of boundary-layer and wall-jet development, based on the recommended entrainment functions, are presented and compared with experiment. The predictions are in good agreement with experiment except in the vicinity of separation.

Information

Type
Research Article
Information
Journal of Fluid Mechanics , Volume 25 , Issue 2 , June 1966 , pp. 337 - 366
Copyright
© 1966 Cambridge University Press

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References

Bradshaw, P. & Ferriss, D. H. 1965 The response of a retarded equilibrium turbulent boundary layer to the sudden removal of pressure gradient. NPL Aero. Rep. no. 1145.Google Scholar
Chi, S. W. 1962 Unpublished work at Imperial College.
Clauser, F. H. 1954 Turbulent boundary layers in adverse pressure gradients. J. Aero. Sci. 21, 91.Google Scholar
Clauser, F. H. 1956 The turbulent boundary layer. Advances in Applied Mechanics, iv, no. 1. New York: Academic Press.
Coles, D. 1956 The law of the wake in the turbulent boundary layer. J. Fluid Mech. 1, 191.Google Scholar
Coles, D. E. 1962 The turbulent boundary layer in a compressible fluid. Rand Corp. Rep. no. R–403–PR.Google Scholar
Doenhoff, A. E. Von & Tetervin, N. 1943 Determination of general relations for the behaviour of turbulent boundary layers. NACA TR, no. 772.Google Scholar
Fage, A. 1938 Profile and skin-friction aerofoil drags. Aero. Res. Counc. R. & M. no. 1852.Google Scholar
Fage, A. & Falkner, V. M. 1930 An experimental determination of the intensity of friction on the surface of an aerofoil. Aero. Res. Counc. R. & M. no. 1315.Google Scholar
Gartshore, I. S. 1964 Jets and wall jets in uniform streaming flow. McGill Univ., Mech. Eng. Res. Lab. Rep. no. 64–4.Google Scholar
Head, M. R. 1960 Entrainment in the turbulent boundary layer. Aero. Res. Counc. R. & M. no. 3152.Google Scholar
Herring, H. J. & Norbury, J. F. 1963 Some experiments on equilibrium turbulent boundary layers in favourable pressure gradients. Princeton Univ., Dept. Aerospace & Mech. Sci. FLD, no. 15.Google Scholar
Hinze, J. O. 1959 Turbulence. New York: McGraw Hill.
Klebanoff, P. S. 1955 Characteristics of turbulence in a boundary layer with zero pressure gradient. NACA Rep. no. 1247.Google Scholar
Klebanoff, P. S. & Diehl, Z. W. 1952 Some features of artificially thickened fully developed turbulent boundary layers with zero pressure gradient. NACA Rep. no. 1110.Google Scholar
Kruka, V. & Eskinazi, S. 1964 The wall-jet in a moving stream. J. Fluid Mech. 20, 555.Google Scholar
Ludwieg, H. & Tillmann, W. 1949 Untersuchungen über die Wandschubspannung in turbulenten Reibungsschichten. Ing.-Arch. 17, 288. (Trans. 1950 Investigations of the wall shearing stress in turbulent boundary layers. NACA TM, no. 1285.)Google Scholar
Mellor, G. J. & Gibson, D. M. 1963 Equilibrium turbulent boundary layers. Princeton Univ., Dept. Aerospace & Mech. Sci. FLD, no. 13.Google Scholar
Nash, J. F. 1965 Turbulent-boundary-layer behaviour and the auxiliary equation. AGARDograph, no. 97, part 1, 245.Google Scholar
Newman, B. G. 1951 Some contributions to the study of the turbulent boundary layer near separation. Aust. Dept. Supply Rep. no. ACA–53.Google Scholar
Nicoll, W. B. 1965 Wall jet velocity profiles and entrainment. Imperial College, Mech. Eng. Dept. Rep. no. IC/HRJ/23.Google Scholar
Patel, R. P. & Newman, B. G. 1961 Self-preserving, two-dimensional turbulent jets and wall jets in a moving stream. McGill Univ., Mech. Eng. Res. Lab. Rep. no. Ae5.Google Scholar
Reynolds, W. C., Kays, W. M. & Kline, S. J. 1958 Heat transfer in the turbulent incompressible boundary layer. I Constant wall temperature. NASA Memo, no. 12–1–58 W.Google Scholar
Schubauer, G. B. & Klebanoff, P. S. 1951 Investigation of separation of the turbulent boundary layer. NACA Rep. no. 1030.Google Scholar
Schultz-Grunow, F. 1940 Neues Reibungswiderstandsgesetz für glatte Platten. Luftfahrtforschung, 17, 239. (Trans. 1941 New frictional resistance law for smooth plates. NACA TM no. 986.)Google Scholar
Seban, R. A. & Back, L. H. 1961 Velocity and temperature profiles in a wall jet. Int. J. Heat & Mass Trans. 3, 255.Google Scholar
Smith, D. W. & Walker, J. H. 1959 Skin-friction measurements in incompressible flow. NASA TR, no. R–26.Google Scholar
Spalding, D. B. 1964a A unified theory of friction, heat transfer and mass transfer in the turbulent boundary layer and wall jet. Aero. Res. Counc. Rep. no. 25,925.Google Scholar
Spalding, D. B. 1964b A unified theory of friction, heat transfer and mass transfer in the turbulent boundary layer and wall jet. Imperial College, Mech. Eng. Dep. Rep. (Annotated version of previous reference.)Google Scholar
Spalding, D. B. 1965 The kinetic-energy-deficit equation of the turbulent boundary layer. AGARDograph, no. 97, part 1, 191.Google Scholar
Stratford, B. S. 1959 An experimental flow with zero skin friction throughout its region of pressure rise. J. Fluid Mech. 5, 17.Google Scholar
Thompson, B. G. J. 1964 A critical review of existing methods of calculating the turbulent boundary layer. Aero. Res. Coun. Rep. no. 26,109.Google Scholar
Wieghardt, K. 1944 Zum Reibungswiderstand rauher Platten. ZWB KWI U & M, 6612.Google Scholar