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A New Solution of the Turbulent Near-Wake Recompression Problem

Published online by Cambridge University Press:  07 June 2016

S J Shamroth  and
H McDonald
S J Shamroth
Affiliation:
United Aircraft Research Laboratories, East Hartford, Connecticut
H McDonald
Affiliation:
United Aircraft Research Laboratories, East Hartford, Connecticut
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Summary

A method is presented for predicting the behaviour of a two-dimensional supersonic turbulent near-wake during the recompression process. In contrast to most previous extensions of Crocco-Lees strong interaction theory, the proposed analysis includes a transverse momentum integral equation. In addition, a modified strip method for conservation of streamwise momentum replaces the usual integral equations. Although a straightforward treatment of the equations results in the appearance of a singularity analogous to the well-known Crocco-Lees critical point, it is shown that solutions can be obtained which do not exhibit a singular behaviour, either by posing the problem as a boundary-value problem rather than an initial-value problem or by making a suitable approximation which suppresses the quasi-elliptic behaviour of the equations. Both procedures lead to an unambiguously defined uniqueness condition for the near-wake recompression solution.

Type
Research Article
Information
Aeronautical Quarterly , Volume 23 , Issue 2 , May 1972 , pp. 121 - 130
Copyright
Copyright © Royal Aeronautical Society. 1972

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References

1. Nash, J F Discussion of two-dimensional turbulent base flows. ARC R & M 3468, 1967.Google Scholar
2. Crocco, L Lees, L A mixing theory for interaction between dissipative flows and nearly isentropic streams. Journal of the Aeronautical Sciences, Vol 19, pp 649-676, October 1962.CrossRefGoogle Scholar
3. Reeves, B Lees, L Theory of laminar near wake of blunt bodies in hypersonic flow. AIAA Journal, Vol 3, pp 2061-2074, November 1965.Google Scholar
4. Baum, E Denison, R Interacting supersonic laminar wake calculations by a finite difference method. AIAA Paper 6645, New York, 1966.Google Scholar
5. Webb, W H Golik, R J Vogenitz, F W Lees, L A multimoment theory for the laminar supersonic near wake. Proceedings of the 1965 Heat Transfer and Fluid Mechanics Institute, Stanford University, pp 168-189, 1965.Google Scholar
6. Ai, D K On the hypersonic laminar near wake critical point of the Crocco-Lees mixing theory. AIAA Paper 67-60, New York, 1967.CrossRefGoogle Scholar
7. Alber, I Lees, L Integral theory for supersonic turbulent base flow. AIAA Journal, Vol 6, pp 1343-1351, July 1968.Google Scholar
8. Weinbaum, S Near wake uniqueness and a re-examination of the throat concept in laminar mixing theory. AIAA Paper 67-61, New York, 1967.Google Scholar
9. Garvine, R W Upstream influence on viscous interaction problems. The Physics of Fluids, Vol 11, pp 1413-1422, July 1968.CrossRefGoogle Scholar
10. Weinbaum, S Garvine, R W On the two-dimensional viscous counterpart of the one-dimensional sonic throat. Journal of Muid Mechanics, Vol 39, Part I, pp 57-85, 1969.Google Scholar
11. Weinbaum, S, Garvine, R W The pressure field in compressible boundary layer theory – A critical re-examination and treatment. R66SD13, Space Sciences Laboratory, General Electric Company, King of Prussia, Pa., 1967.Google Scholar
12. Myring, D F Young, A D The isobars in boundary layers at supersonic speeds. Aeronautical Quarterly, Vol 19, pp 105-126, May 1968.Google Scholar
13. Demetriades, A Bauer, A B Supersonic wind tunnel experiments with axisymmetric wakes. AIAA Paper 66453, New York, 1966.Google Scholar
14. Michel, R Résultats sur la couche limite turbulence aux grandes vitesses.. ONERA Technical Memo 22, 1961.Google Scholar
15. Townsend, A A The Structure of Turbulent Shear Flow, Chapter 8, Cambridge University Press, 1956.Google Scholar
16. Mueller, T N Robertson, J M A study of the mean motion and turbulence downstream of a roughnesss element. Modern Developments in Theoretical and Applied Mechanics, Vol 1, Plenum Press, 1963 Google Scholar
17. Goldberg, P Upstream history and apparent stress in turbulent boundary layers. Gas Turbine Laboratory Report 85, Massachusetts Institute of Technology, 1966.Google Scholar
18. Shamroth, S J On integral methods for predicting shear layer behavior. Journal of Applied Mechanics, Vol 36, pp 673-681, December 1969.Google Scholar
19. Badrinarayanan, M A An experimental investigation of base flows at supersonic speeds. Journal of the Royal Aeronautical Society, Vol 65, pp 475-482, July 1961.Google Scholar
20. Nash, J F An analysis of two-dimensional turbulent base flow, including the effects of the approaching boundary layer. ARC R & M 3344, 1963.Google Scholar