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Approximate calculation of the interaction of supersonic flow with a laminar layer in the flow separation region

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Abstract

The distributions of the pressure, friction, and heat transfer coefficients in the separation zone of a laminar boundary layer ahead of a wedge on a plate are calculated approximately. The integral method of Cohen and Reshotko is used to calculate the flow in the boundary layer.

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Abbreviations

x:

distance along the plate

y:

surface ordinate

s:

distance along the wedge

β:

wedge angle

δ:

boundary layer thickness

δ* :

displacement thickness

δ** :

momentum thickness

u:

velocity

M:

Mach number

R:

Reynolds number

ρ:

density

p:

pressure

τ:

friction

Cp :

pressure coefficient

C f :

friction coefficient

α:

heat transfer coefficient

0:

beginning of interaction region

1:

separation of the boundary layer

2:

vertex of wedge

3:

teattachment of separated layer

4:

end of interaction region

w:

flow parameters at the wall

References

  1. L. Crocco and L. Lees “A mixing theory for the interaction between dissipative flows and nearly isentropic streams”, J. Aeronaut. Sci., vol. 19, no. 10, 1952.

  2. K. N. C. Bray, G. E. Gadd, and M. Woodger, “Some calculations by the Crocco-Lees and other methods of interactions between shock waves and laminar boundary layers, including effects of heat transfer and suction”, ARC C. P., no. 556, 1961.

  3. Makofski, “A two-parameter method for shock wave-laminar boundary layer interaction and flow separation”, Proc. Heat Transfer and Fluid Mechanics Institute, Stanford, California, 1963.

  4. Yu. G. El'kin and V. Ya. Neiland, “On the calculation of the characteristics of laminar separation zones”, Inzh. zh., vol. 5, no. 5, 1961.

  5. L. Lees and B. L. Reeves, “Supersonic separated and reattaching laminar flow: 1, General theory and application to adiabatic boundary layer; Shock-wave interactions”, AIAA Journ., vol. 2, no. 11, 1964.

  6. C. B. Cohen and E. Reshotko, “The compressible laminar boundary layer with heat transfer and arbitrary pressure gradients”, NACA Rep., p. 1294, 1956.

  7. D. R. Chapman, D. M. Kuehn, and H. K. Larson, “Investigation of separated flows in supersonic and subsonic streams with emphasis on the effect of transition”, NACA, Rep, p. 1356, 1958.

  8. D. W. Holder and G. E. Gadd, “The interaction between shock waves and boundary layers and its relation to base pressure: Boundary layers effects in aerodynamics, “Proceedings of a Symposium Held at the NPL on 31 March–1 April, 1955.

  9. D. M. Kuehn, “Laminar boundary layer separation induced by flares on cylinders at zero angle of attack”, NACA Rep. R., p. 146, 1962.

  10. D. W. Holder, “Interaction between shock waves and boundary layers”, JAS Preprint, no. 550, 1955.

  11. D. S. Miller, R, Hyman, and M. E. Childs, “Mach 8 to 22 studies of flow separations due to deflected control surfaces”, AIAA, vol. 2, no. 2, 1964.

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Authors and Affiliations

  1. Moscow

    E. N. Bondarev

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  1. E. N. Bondarev
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Bondarev, E.N. Approximate calculation of the interaction of supersonic flow with a laminar layer in the flow separation region. Fluid Dyn 1, 81–83 (1966). https://doi.org/10.1007/BF01022159

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  • DOI: https://doi.org/10.1007/BF01022159

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