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Calculation of boundary-layer development using the turbulent energy equation: compressible flow on adiabatic walls

Published online by Cambridge University Press:  29 March 2006

P. Bradshaw  and
D. H. Ferriss
P. Bradshaw
Affiliation:
Aerodynamics Division, National Physical Laboratory, Teddington Department of Aeronautics, Imperial College, London
D. H. Ferriss
Affiliation:
Aerodynamics Division, National Physical Laboratory, Teddington
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Abstract

The basic method described by Bradshaw, Ferriss & Atwell (1967) is extended to compressible flow in two-dimensional boundary layers in arbitrary pressure gradient (excluding shock waves and expansion fans) by invoking Morkovin's hypothesis (Favre 1964) that the turbulence structure is unaffected by compressibility. Using the same empirical functions as in incompressible flow, skin friction in zero pressure gradient is predicted to within 3% of Spalding & Chi's (1964) correlation for free-stream Mach numbers less than 5. Comparisons with experiments in pressure gradient are restricted by the lack of data, but, since Morkovin's hypothesis does not depend on pressure gradient, methods which use it (of which the present method seems to be the first) can be checked fairly adequately by comparisons with data in zero pressure gradient.

No ‘compressibility transformations’ are needed, although the Crocco relation is used, provisionally, for the temperature: since the calculations take only about 20% longer than in incompressible flow, Morkovin's hypothesis does as much as any transformation could do. It is pointed out that, in supersonic flow, surface curvature which is large enough to induce a significant longitudinal pressure gradient is also large enough to have a very significant effect on the turbulence structure.

Type
Research Article
Information
Journal of Fluid Mechanics , Volume 46 , Issue 1 , 15 March 1971 , pp. 83 - 110
Copyright
© 1971 Cambridge University Press

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References

Bertram, M. H. (ed.) 1969 N.A.S.A. SP-216.
Bradshaw, P. 1969a J. Fluid Mech. 35, 387.
Bradshaw, P. 1969b J. Fluid Mech. 36, 177.
Bradshaw, P. & Ferriss, D. H. 1965 Nat. Phys. Lab. Aero Rep. 1145.
Bradshaw, P. & Ferriss, D. H. 1968 Nat. Phys. Lab. Aero Rep. 1271.
Bradshaw, P. & Ferriss, D. H. 1970 Nat. Phys. Lab. Aero Rep. 1325.
Bradshaw, P., Ferriss, D. H. & Atwell, N. P. 1967 J. Fluid Mech. 28, 593.
Bradshaw, P., Sivasegaram, S. & Whitelaw, J. H. 1970 Imperial College Mech. Engng. Dept. Rep. BL/TN/A/34.
Cebeci, T., Smith, A. M. O. & Mosinskis, G. 1970 A.I.A.A.J. 8, 1974.
Clutter, D. W. & Kaups, K. 1964 Douglas Aircraft Co. Rep. LB-31425.
Coles, D. 1962 Rand Corp. Rep. R-403-PR.
Coles, D. 1964 Phys. Fluids, 7, 1403.
Demetriades, A. 1968 Phys. Fluids, 11, 1841.
Favre, A. (ed.) 1964 The Mechanics of Turbulence. New York: Gordon and Breach.
Favre, A. 1965 J. de Mec. 4, 361, 391.
Ferriss, D. H. 1969 Nat. Phys. Lab. Aero Rep. 1295.
Ferriss, D. H. & Bradshaw, P. 1968 Nat. Phys. Lab. Aero. Rep. 1269.
Firmin, M. C. P. & Cook, J. 1968 R.A.E. Tech. Memo. Aero. 1076.
Green, J. E. 1968 J. Fluid Mech. 31, 753.
Hastings, R. C. & Sawyer, W. G. 1970 R.A.E. Tech. Rep. 70040.
Head, M. R. 1958 Aero. Res. Counc. R. & M. 3152.
Herring, H. J. & Mellor, G. L. 1968 N.A.S.A. CR-1144 and N.A.S.A. SP-216 (1969).
Howarth, L. (ed.) 1953 Modern Developments in Fluid Dynamics: High-Speed Flow, vol. 1. Oxford: Clarendon Press.
Kistler, A. L. 1959 Phys. Fluids, 2, 290.
Kline, S. J., Morkovin, M. V., Sovran, G. & Cockrell, D. J. 1969 1968 AFOSR-IFP-Stanford Conference. Stanford University Press.
Maise, G. & McDonald, H. 1968 A.I.A.A.J. 6, 73.
McLafferty, G. H. & Barber, R. E. 1962 J. Aero/Space Sci. 29, 1.
Michel, R., Quemard, C. & Elena, M. P. 1969 Rech. Aerosp. no. 128, 33.
Myring, D. F. & Young, A. D. 1968 Aero. Quart. 19, 105.
Ng, K. H. & Sivasegaram, S. 1970 Aero. Res. Course. Paper no. 32048.
Ng, K. H. & Spalding, D. B. 1970 Imperial College Mech. Engng. Dept. Rep. BL/TN/A/25.
Pasiuk, L., Hastings, G. M. & Chatham, R. 1964 U.S. Nav. Ord. Lab. Rep. NOL TR 64–200.
Rotta, J. C. 1960 AGARD Rep. 281.
Rotta, J. C. 1965 AGARD ograph 97.
Rotta, J. C. 1967 Phys. Fluids Suppl. 12, S 174.
Simpson, R. L. 1970 J. Fluid Mech. 42, 769.
Sivasegaram, S. 1970 Ph.D. Thesis, Imperial College, London University.
Spalding, D. B. & Chi, S. W. 1964 J. Fluid Mech. 18, 117.
Spalding, D. B. & Patankar, S. V. 1967 Heat and Mass Transfer in Boundary Layers. London: Morgan-Grampian.
Squire, L. C. 1969 J. Fluid Mech. 37, 449.
Townsend, A. A. 1956 The Structure of Turbulent Shear Flow. Cambridge University Press.
Townsend, A. A. 1961 J. Fluid Mech. 11, 97.
Tritton, D. J. 1961 J. Fluid Mech. 11, 440.
Winter, K. G. & Gaudet, L. 1968 R.A.E. Tech. Memo. 1115 and N.A.S.A. SP-216 (1969).
Winter, K. G., Rotta, J. C. & Smith, K. G. 1968 R.A.E. Rep. 68215.