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Plate-injection into a separated supersonic boundary layer

  • F. T. Smith (a1) (a2) and K. Stewartson (a1)

Abstract

The structure of a supersonic laminar boundary layer near a flat plate is examined when fluid is injected into it with velocity of O3U*) over a distance of O(L). Here U* is the undisturbed fluid velocity, L the length of the plate and ε−8 is a representative Reynolds number. An essential requirement of the theory is that separation must have occurred upstream of the blow through a free interaction. It is assumed that between separation and the blow the reversed flow region has a wedge-like shape, of semi-angle in which O2), the fluid velocity has decayed to insignificant values at points just upstream of the blowing region. The blown fluid fills this wedge and the favourable pressure gradient necessary to drive this fluid downstream causes the boundary of the wedge to curve until at the end of the blow it is parallel to the plate. Explicit expressions for the pressure variation and boundary-layer thickness are worked out using a (crucially) modified form of the Cole-Aroesty theory. The relation. between the strong injection studied here and massive injection, when the blowing velocity is of O(U*), is also discussed.

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References

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Belcher, R. J., Burggraf, O. R. & Stewartson, K. 1972 J. Fluid Xech. 52, 753.
Birkhoff, G. 1960 Hydrodynamics. Princeton University Press.
Bott, J. F. 1968 A.I.A.A. J. 6, 613.
Catherall, D., Stewbrtson, K. & Williams, P. G. 1965 Proc. Roy. SOC. A 284, 370.
Cebeci, T. & Keller, H. B. 1971 J. Comp. Phys. 7, 289.
Chapman, D. R., Kuehn, D. M. & Larson, H. K. 1958 N.A.C.A. Rep. no. 1356.
Cole, J. D. & Aroesty, J. 1968 Int. J. Heat. Mass Tram. 11, 1167.
Fernandez, F. L. & Lees, L. 1970 A.I.A.A. J. 8, 1256.
Fernandez, F. L. & Zueoski, E. E. 1969 A.I.A.A. J. 7, 1759.
Fluuge-Lotz, I. & Reyhner, T. A. 1968 Int. J. Nonlinear Mech. 3, 173.
Gadd, G. E., Jones, C. W. & Watson, E. J. 1963 In Laminar Boundary Layers (ed. L, Rosenhead), chap. 5. Oxford University Press.
Hartunian, R. A. & Spencer, D. J. 1967 A.I.A.A. J. 5, 1379.
Inger, C. R. & Gaitatzes, G. A. 1971 A.I.A.A. J. 9, 436.
Libby, P. A. 1962 J. Aerospace X c i. 29, 48.
Smith, F. T. 1972 D.Phil. thesis, Oxford University.
Smith, F. T. & Stewartson, K. 1973 Proc. Roy. SOC. A 332, 1
Stewartson, K. 1954 Proc. Camb. Phil. SOC. 49, 561.
Stewartson, K. & Williams, P. G. 1969 Proc. Roy. SOC. A 312, 181.
Stewartson, K. & Williams, P. G. 1973 Submitted to Mathematika.
Taylor, T. D., Masson, B. S. & Foster, R. M. 1969 A.I.A.A. J. 7, 1686.
Thomas, P. D. 1969 A.I.A.A. J. 7, 681.
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Plate-injection into a separated supersonic boundary layer

  • F. T. Smith (a1) (a2) and K. Stewartson (a1)

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