Hostname: page-component-cd9895bd7-q99xh Total loading time: 0 Render date: 2024-12-22T11:02:42.407Z Has data issue: false hasContentIssue false

An appraisal of ‘flat plate’ closure for the approximate solution of boundary layer problems

Published online by Cambridge University Press:  04 July 2016

D. I. A. Poll
Affiliation:
Aerodynamics Division, College of Aeronautics, Cranfield Institute of Technology
C. M. Hellon
Affiliation:
Aerodynamics Division, College of Aeronautics, Cranfield Institute of Technology

Summary

The usefulness of zero pressure gradient, flat plate closure relations in providing approximate solutions for the boundary layer momentum and energy integral equations is examined. Expressions are obtained for skin friction, surface heat transfer rate and local Reynolds analogy factor under general compressible flow conditions. For laminar flows the predictions are compared with well known similarity solutions, with some exact solutions for non-similar flows and with experimental heat transfer data for high speed flow over a blunt cone. Consideration is also given to situations in which the surface temperature is a function of position. For turbulent flow situations comparisons are made with experimental data obtained from two-dimensional and axi-symmetric tests. Conditions vary from low Mach number incompressible flows through to high Mach number compressible flows with highly cooled walls. Some comparisons are also made with other prediction techniques.

Type
Research Article
Copyright
Copyright © Royal Aeronautical Society 1987 

Access options

Get access to the full version of this content by using one of the access options below. (Log in options will check for institutional or personal access. Content may require purchase if you do not have access.)

References

1. Von Kármán, T. Über laminare und turbulente reibung Zeitschrift fur Angewandte Mathematik und Mechanik, 1921, 1, 223252.Google Scholar
2. Squire, H. B. Heat transfer. Modern Developments in Fluid Dynamics — High Speed Flow Vol. II, Oxford University Press, 1953.Google Scholar
3. Ambrok, G. S. The effect of surface temperature variability on heat exchange in laminar flow in a boundary layer. Soviet Physics, 1957, 2, No 4, 1978.Google Scholar
4. Stewartson, K. The theory of laminar boundary layers in compressible fluids. Oxford University Press, 1964.Google Scholar
5. Stollery, J. L. Supersonic turbulent boundary layers: Some comparisons between experiment and a simple theory. The Aeronautical Quarterly, May 1976, XXVII, 8798.Google Scholar
6. Stollery, J. L. Turbulent boundary layer growth at hypersonic speeds. Imperial College Aero Report 73-04, May 1973.Google Scholar
7. Stollery, J. L. and Bates, L. Turbulent hypersonic viscous interaction. Journal of Fluid Mechanics, 1974, 63, part 1, 145156.Google Scholar
8. Cebeci, T. and Smith, A. M. O. Analysis of turbulent boundary layers, Volume 15, Applied Mathematics and Mechanics Series Academic Press, 1974.Google Scholar
9. Cebeci, T. and Bradshaw, P. Physical and computation aspects of convective heat transfer. Springer-Verlag, 1984.Google Scholar
10. Thwaites, B. Approximate calculation of the laminar boundary layer. The Aeronautical Quarterly, 1949, 1, 249.Google Scholar
11. Head, M. R. Entrainment in the turbulent boundary layer. ARC R&M 3152, 1958. 10.Google Scholar
12. Luxton, R. E. and Young, A. D. Generalised methods for the calculation of the laminar compressible boundary layer characteristics with heat transfer and non-uniform pressure distribution. ARC R&M 3233, 1962.Google Scholar
13. Curle, N. The laminar boundary layer equations. Oxford University Press, 1962.Google Scholar
14. Green, J. E., Weeks, D. J. and Brooman, J. W. F. Prediction of turbulent boundary layers and wakes in compressible flow by a lag-entrainment method. ARC R&M 3791, 1973.Google Scholar
15. Green, J. E. Application of Head’s entrainment method to the prediction of turbulent boundary layers and wakes in compressible flow. ARC R&M 3788, 1972.Google Scholar
16. Winter, K. G., Gaudet, L. and Bell, T. Experience with a steady state heat transfer technique in a large wind tunnel. ARC R&M 3797, 1975.Google Scholar
17. Eckert, E. R. G. Engineering relations for friction and heat transfer to surfaces in high velocity flows. Journal of the Aeronautical Sciences, August 1955, 22, 585587.Google Scholar
18. Spence, D. A. Velocity and enthalpy distributions in the compressible turbulent boundary layer on a flat plate. Journal of Fluid Mechanics, 1960, 8, 368387.Google Scholar
19. Colburn, A. P. A method of correlating forced convection heat transfer data and a comparison with fluid friction. Transactions of the American Institute of Chemical Engineers, 1933, 29, 174210.Google Scholar
20. Spence, D. A. The growth of compressible turbulent boundary layers on isothermal and adiabatic walls. ARC R&M 3191, June 1959.Google Scholar
21. Walker, G. K. A particular solution to the turbulent boundary-layer equations. Journal of the Aerospace Sciences, September 1960, 27, No. 10, 715716.Google Scholar
22. Falkner, V. M. and Skan, S. W. Some approximate solutions of the boundary layer equations. ARC R&M 1314, 1930. See also Philosophical Magazine, 1931, 12, 865896.Google Scholar
23. Hartree, D. R. On an equation occurring in Falkner and Skan’s approximate treatment of the equations of the boundary layer. Proceedings of the Cambridge Philosophical Society, 1937, 33, Part II, 223239.Google Scholar
24. Fage, A. and Falkner, V. M. Relations between heat transfer and surface friction for laminar flow. ARC R&M 1408, 1931.Google Scholar
25. Cohen, C. B. and Reshotko, E. Similar solutions for the compressible laminar boundary layer with heat transfer and pressure gradient. NACA Report 1293, 1956.Google Scholar
26. Beasley, J. A. Calculation of the laminar boundary layer and prediction of transition on a sheared wing. ARC R&M 3787, October 1973.Google Scholar
27. Smith, A. G. and Spalding, D. B. Heat transfer in a laminar boundary layer with constant fluid properties and constant wall temperature. Journal of the Royal Aeronautical Society, 1958, 62, 60.Google Scholar
28. Widhopf, G. F. Laminar, transitional and turbulent heat transfer measurements on a yawed blunt conical nosetip. Aerospace Corporation Report No. TR-0073 (S3450-60)-1.Google Scholar
29. Holden, M. S. Studies of potential fluid mechanical mechanisms for enhanced stagnation-region heating. AIAA Paper No. 85-1002, 20th Thermophysics Conference, Williamsburg, Virginia, June 1985.Google Scholar
30. Buri, A. A method of calculation for the turbulent boundary layer with accelerated or retarded basic flow. Ministry of Aircraft Production, RTP Translation 2073.Google Scholar
31. Newman, B. G. Some contributions to the study of the turbulent boundary layer near separation. Australian Department of Supply Report ACA-53, 1951.Google Scholar
32. Moretti, P. M. and Kays, W. M. Heat transfer to a turbulent boundary layer with varying freestream velocity and varying surface temperature, an experimental study. International Journal of Heat and Mass Transfer, 1965, 8, 11871202.Google Scholar
33. Tetervin, N. Approximate calculation of Reynolds analogy for turbulent boundary layer with pressure gradient. AIAA Journal, June 1969, 7, No 6, 10791085.Google Scholar
34. Nakayama, A., Koyama, H. and Ohsawa, S. Momentum/heat transfer analogy for turbulent boundary layers in mild pressure gradients. AIAA Journal, June 1984, 22, No 6, 841844.Google Scholar
35. Lewis, J. E., Gran, R. L. and Kubota, T. An experiment on the adiabatic compressible turbulent boundary layer in adverse and favourable pressure gradients. Journal of Fluid Mechanics, 1972, 51, 657672.Google Scholar
36. Johnston, L. J. A calculation method for two-dimensional wall-bounded turbulent flows. The Aeronautical Journal, May 1986, 90, No. 895, 174184.Google Scholar
37. Gran, R. L., Lewis, J. E. and Kubota, T. The effect of wall cooling on a compressible turbulent boundary layer. Journal of Fluid Mechanics, 1974, 66, 507528.Google Scholar
38. Thoman, H. Effect of streamwise wall curvature on heat-transfer in a turbulent boundary layer. Journal of Fluid Mechanics, 1968, 33, Part 2, 283292.Google Scholar
39. Fernholz, H. H. and Finlay, P. J. A critical compilation of compressible turbulent boundary layer data. AGARDograph No. 223, June 1977.Google Scholar
40. Hoydeysh, W. G. and Zakkay, V. An experimental investigation of hypersonic turbulent boundary layers in adverse pressure gradient. AIAA Journal, January 1969, 7, No. 1, 105116.Google Scholar
41. Kussoy, M. I. and Horstman, C. C. An experimental documentation of a hypersonic shock-wave turbulent boundary layer interaction flow — with and without separation. NASA TM X-62412, February 1975.Google Scholar
42. Marvin, J. G., Horstman, C. C, Rubesin, M. W., Coakley, T. J. and Kussoy, M. I. An experimental and numerical investigation of shock-wave induced turbulent boundary-layer separation at hypersonic speeds. Paper No. 25, AGARD CP 168, 1975.Google Scholar