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Numerical analysis of turbulent end-wall boundary layers of intense vortices

Published online by Cambridge University Press:  12 April 2006

Joseph Chi
Joseph Chi
Affiliation:
National Bureau of Standards, Washington, D.C. 20234
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Abstract

After a careful consideration of the laws of generation, advection, diffusion and dissipation of turbulent kinetic energy proposed by Prandtl (1945) and Emmons (1954), equations of motion and turbulent kinetic energy for the vortex flow near a solid end wall are established. These equations are then evaluated by a numerical procedure. Care is taken to specify boundary conditions such that satisfactory matching of the solution with the main vortex is assured. The agreement between the predicted mean velocity distribution and the experimental data is remarkably good. In addition, several interesting characteristics are predicted by the theory: (i) the vertical distribution of horizontal velocity is oscillatory in the inner region, whilst it is of the ordinary boundary-layer type in the outer region; (ii) the maximum velocity in the boundary layer can exceed that in the main vortex by a considerable amount and (iii) the minimum pressure of the vortex does not occur in the vortex-core root as has been generally believed.

Type
Research Article
Information
Journal of Fluid Mechanics , Volume 82 , Issue 2 , 7 September 1977 , pp. 209 - 222
Copyright
© 1977 Cambridge University Press

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References

Ames, W. F. 1965 Nonlinear Partial Differential Equations in Engineering, p. 377. Academic Press.
Bödewadt, W. T. 1940 Die Drehströmung über festem Grunde. Z. angew. Math. Mech. 20, 241.Google Scholar
Chi, S. W. 1974 Numerical modelling of the three dimensional flows in the ground boundary layer of an intense axisymmetrical vortex. Proc. S.E.S. 10 (to be published).Google Scholar
Chi, S. W. & Chang, C. C. 1969 Effective viscosity in a turbulent boundary layer. A.I.A.A. J. 10, 2032.Google Scholar
Chi, S. W. & Costopoulos, T. 1974 Measurements of mean velocity in turbulent vortex boundary layers. Rep. to N.S.F. GK 41469, 1974.
Chi, S. W. & Glowacki, W. J. 1974 Applicability of mixing length theory to turbulent boundary layers beneath intense vortices. J. Appl. Mech. 41, 15.Google Scholar
Chi, S. W. & Jih, J. 1974 Numerical modeling of the three-dimensional flows in the ground boundary layer of a maintained axisymmetrical vortex. Tellus 26, 444.Google Scholar
Chi, S. W., Ying, S. J. & Chang, C. C. 1969 The ground boundary layer of a stationary tornedolike vortex. Tellus 21, 693.Google Scholar
Deissler, R. G. & Perlmutter, M. 1960 Analysis of the flow and energy separation in a turbulent vortex. J. Heat Mass Transfer 1, 173.Google Scholar
Emmons, H. W. 1954 Shear flow turbulence. Proc. U.S. Nat. Cong. Appl. Mech. 2, 1.Google Scholar
Glushko, G. S. 1965 Turbulent boundary layer on a flat plate in an incompressible fluid. Izv. Akad. Nauk SSSR, Mekh. 4, 13.Google Scholar
Gosman, A. D. Et Al. 1969 Heat and Mass Transfer in Recirculating Flows. Academic Press.
Hinze, J. O. 1959 Turbulence, p. 492. McGraw-Hill.
Klebanoff, P. S. 1955 Characteristics of turbulence in a boundary layer with zero pressure gradient. N.A.C.A. Tech. Rep. no. 1247.Google Scholar
Kuo, H. L. 1971 Axisymmetric flows in the boundary layer of a maintained vortex. J. Atmos. Sci. 28, 20.Google Scholar
Lewellen, W. S. 1962 A solution for three-dimensional vortex flow with strong circulation. J. Fluid Mech. 14, 420.Google Scholar
Mack, L. M. 1964 The laminar boundary layer on a rotating disk of finite radius in a rotating flow. JPL Space Prog. Summ. no. 37–18, p. 43.Google Scholar
Prandtl, L. 1945 Über ein neues Formelsystem für die ausgebildete Turbulenz. Nachr. Akad. Wiss. Göttingen, Mathphys. no. 6.
Schubauer, G. B. & Klebanoff, P. S. 1951 Investigation of separation of the turbulent boundary layer. N.A.C.A. Rep. no. 1030.Google Scholar
Spalding, D. B. 1967 Heat transfer from turbulent separated flows. J. Fluid Mech. 27, 97.Google Scholar
Stewartson, K. 1957 On rotating laminar boundary layers. Proc. Symp. Boundary Layer Res. p. 59. Springer.
Townsend, A. A. 1961 Equilibrium layer and wall turbulence. J. Fluid Mech. 11, 97.Google Scholar