Abstract
Experimental data for an incompressible turbulent moving surface boundary layer are reviewed and a theoretical extension of their predictions is suggested for the case of finite free stream velocities. It is argued that such a boundary layer provides an incompressible analogue for shock-induced turbulent boundary layers. Coles's transformation is used to predict the behaviour of the shock-induced case from the incompressible analogue. These predictions are used to attempt to correlate the available experimental shock-induced turbulent boundary layer data. It is felt that the correlations are reasonably successful for some of the data. It is suggested that the remaining data have been affected by the premature arrival of the contact region and reflected rarefaction wave.
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Abbreviations
- A, b :
-
constants defined in (27)
- c f :
-
surface friction coefficient defined in (14)
- c h :
-
Stanton number defined in (15)
- h :
-
enthalpy
- H :
-
total enthalpy, h+u 2/2
- M :
-
Mach number based on flow velocity relative to shock
- p :
-
pressure
- Pr :
-
Prandtl number
- q :
-
heat transfer rate in direction of increasing y
- T :
-
temperature
- u, v :
-
velocity component parallel to surface measured relative to shock motion and velocity component normal to surface respectively
- U :
-
u w/u e
- x, y :
-
co-ordinates fixed in shock, x parallel to surface and y normal to surface
- γ :
-
ratio of principal specific heats
- δ :
-
boundary layer thickness
- δ⋆:
-
defined in (5)
- ζ :
-
defined in (26)
- η :
-
defined in (8)
- θ :
-
defined in (6)
- μ :
-
coefficient of viscosity
- ν :
-
μ/ρ
- ξ :
-
defined in (8)
- ρ :
-
density
- σ :
-
defined in (9)
- τ :
-
shear stress
- φ :
-
defined in (7)
- ω :
-
index in viscosity-temperature relation
- Ω :
-
ratio of c f predicted by (35) to that predicted by (36)
- e:
-
flow exterior to boundary layer
- f:
-
outer edge of sublayer
- r:
-
recovery conditions
- w:
-
surface
- δ :
-
outer edge of boundary layer
- τ :
-
characteristic velocity, equations (22)
- l:
-
outer edge of buffer layer
- -:
-
refers to boundary layer flows related to shock-induced flows
References
Duff, R. E., Physics of Fluids 2 (1959) 207.
Mirels, H., Boundary layer behind shock or thin expansion wave moving into stationary fluid. NACA TN 3712, 1956.
Martin, W. A., Journal of the Aero/Space Sciences 25 (1958) 644.
Gooderum, P. B., An experimental study of the turbulent boundary layer on a shock-tube wall. NACA TN 4243, 1958.
Spence, D. A., Journal of Fluid Mechanics 8 (1960) 368.
Bernstein, L., Notes on some experimental and theoretical results for the boundary layer development aft of the shock in a shock-tube. ARC CP 625, 1961.
Coles, D., Physics of Fluids 7 (1964) 1403.
Tsou, F. K., E. M. Sparrow, and R. J. Goldstein, Int. J. of Heat and Mass Transfer 10 (1967) 219.
Crocco, L., AIAA Journal 1 (1963) 2723.
Baronti, P. O. and P. A. Libby, AIAA Journal 4 (1966) 193.
Hooker, W. J., Physics of Fluids 4 (1961) 1451.
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Samuel, T.D.M.A., Ackroyd, J.A.D. Shock-induced turbulent boundary layers. Appl. Sci. Res. 28, 161–184 (1973). https://doi.org/10.1007/BF00413065
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DOI: https://doi.org/10.1007/BF00413065