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Full-coverage film cooling. Part 2. Prediction of the recovery-region hydrodynamics

Published online by Cambridge University Press:  19 April 2006

S. Yavuzkurt ,
R. J. Moffat  and
W. M. Kays
S. Yavuzkurt
Affiliation:
Mechanical Engineering Department, Stanford University, CA 94305
R. J. Moffat
Affiliation:
Mechanical Engineering Department, Stanford University, CA 94305
W. M. Kays
Affiliation:
Mechanical Engineering Department, Stanford University, CA 94305
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Abstract

Hydrodynamic data are reported in the companion paper (Yavuzkurt, Moffat & Kays 1980) for a full-coverage film-cooling situation, both for the blown and the recovery regions. Values of the mean velocity, the turbulent shear stress, and the turbulence kinetic energy were measured at various locations, both within the blown region and in the recovery region. The present paper is concerned with an analysis of the recovery region only. Examination of the data suggested that the recovery-region hydrodynamics could be modelled by considering that a new boundary layer began to grow immediately after the cessation of blowing. Distributions of the Prandtl mixing length were calculated from the data using the measured values of mean velocity and turbulent shear stresses. The mixing-length distributions were consistent with the notion of a dual boundary-layer structure in the recovery region. The measured distributions of mixing length were described by using a piecewise continuous but heuristic fit, consistent with the concept of two quasi-independent layers suggested by the general appearance of the data. This distribution of mixing length, together with a set of otherwise normal constants for a two-dimensional boundary layer, successfully predicted all of the observed features of the flow. The program used in these predictions contains a one-equation model of turbulence, using turbulence kinetic energy with an algebraic mixing length. The program is a two-dimensional, finite-difference program capable of predicting the mean velocity and turbulence kinetic energy profiles based upon initial values, boundary conditions, and a closure condition.

Type
Research Article
Information
Journal of Fluid Mechanics , Volume 101 , Issue 1 , 13 November 1980 , pp. 159 - 178
Copyright
© 1980 Cambridge University Press

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References

Abramovich, G. N. 1960 The Theory of Turbulent Jets, p. 544. Massachusetts Institute of Technology Press.
Antonia, R. A. & Luxton, R. E. 1972 The response of a turbulent boundary layer to a step change in surface roughness. Part 2. Rough to smooth. J. Fluid Mech. 53, 737–757.Google Scholar
Boussinesq, J. 1877 Théorie de l’écoulement tourbillant. Mém. prés. div. Sav. Acad Sci Inst. Fr. 23, Paris.Google Scholar
Choe, H., Kays, W. M. & Moffat, R. J. 1975 Turbulent boundary layer on a full-coverage film-cooled surface - An experimental heat transfer study with normal injection. N.A.S.A. Rep. CR-2642. (Also Stanford Univ., Mech. Engng Dept Rep. HMT-22.)Google Scholar
Crawford, M. E. & Kays, W. M. 1975 STAN5 - A program for numerical computation of two-dimensional internal/external boundary-layer flows. Stanford Univ., Mech. Engng Dept Rep. HMT-23.Google Scholar
Crawford, M. E., Kays, W. M. & Moffat, R. J. 1976 Heat transfer to a full-coverage film-cooled surface with 30-deg. slanthole injection. Stanford Univ., Mech. Engng Dept Rep. HMT-25.Google Scholar
Ericksen, V. L., Eckert, E. R. G. & Goldstein, R. J. 1971 A model for analysis of the temperature field downstream of a heated jet injected into an isothermal crossflow at an angle of 90° C., N.A.S.A. Rep. CR-72990.Google Scholar
Goldstein, R. J., Eckert, E. R. G., Erickson, V. L. & Ramsey, J. W. 1969 Film cooling following injection through inclined circular tubes, N.A.S.A Rep. CR-73612.Google Scholar
Herring, H. J. 1975 A method of predicting the behaviour of a turbulent boundary layer with discrete transpiration jets. Trans. A.S.M.E. A, J. Engng Power 97, 214–224.Google Scholar
Kacker, S. C. & Whitelaw, J. H. 1970 Prediction of wall-jet and wall-wake flows. J. Mech. Engng Sci. 12, 404–420.Google Scholar
Kolmogorov, A. N. 1942 Equations of turbulent motion of an incompressible turbulent fluid. Izv. Akad. Nauk S.S.S.R., Ser. Phys. 6, No. 1–2, 56.Google Scholar
Launder, B. E. & Spalding, D. B. 1972 Lectures in Mathematical Models of Turbulence. Academic.
Mayle, R. E. & Camarata, F. J. 1975 Multihole cooling film effectiveness and heat transfer. Trans. A.S.M.E. C, J. Heat Transfer 97, 534–538.Google Scholar
Pai, B. R. & Whitelaw, J. H. 1971 The prediction of wall temperature in the presence of film cooling. Int. J. Heat Mass Transfer 14, 409–426.Google Scholar
Patankar, S. V., Rastogi, A. K. & Whitelaw, J. H. 1973 The effectiveness of three-dimensional film-cooling slots - III. Predictions. Int. J. Heat Mass Transfer 16, 1673–1681.Google Scholar
Prandtl, L. 1945 Über ein neues Formelsystem für die ausgebildete Turbulenz. Nachrichten von der Akad. der Wissenschaft in Göttingen.
Schlichting, H. 1968 Boundary-Layer Theory, 6th edn, p. 533. McGraw-Hill.
Wolfstein, M. 1969 The velocity and temperature distribution in one-dimensional flow with turbulence augmentation and pressure gradient. Int. J. Heat Mass Transfer 12, 301–318.Google Scholar
Yavuzkurt, S., Moffat, R. J. & Kays, W. M. 1977 Full-coverage film-cooling: 3-dimensional measurements of turbulence structure and prediction of recovery region hydrodynamics. Stanford Univ., Mech. Engng Dept Rep. HMT-27.Google Scholar
Yavuzkurt, S., Moffat, R. J. & Kays, W. M. 1980 Full-coverage film cooling. Part 1. Three-dimensional measurements of turbulence structure. J. Fluid Mech. 101, 129–158.Google Scholar