Hostname: page-component-6bf8c574d5-gr6zb Total loading time: 0 Render date: 2025-02-14T10:44:26.670Z Has data issue: false hasContentIssue false
  • English
  • Français

Development and separation of a compressible laminar boundary layer under the action of a very sharp adverse pressure gradiant

Published online by Cambridge University Press:  12 April 2006

N. Curle
N. Curle
Affiliation:
Department of Applied Mathematics, University of St Andrews, Fife, Scotland
Get access Rights & Permissions [Opens in a new window]

Abstract

We consider a compressible laminar boundary layer with uniform pressure when x < x0 and a prescribed large adverse pressure gradient when x > x0. The Illingworth-Stewartson transformation is applied, and the transformed external velocity u1(x) then chosen such that \[ \lambda = -\frac{x_0}{u^2_0}u_1\frac{du_1}{dx}\frac{T_w}{T_s} \] is constant, where Ts is the stagnation temperature.

For large λ, when a thin sublayer exists as the layer reacts to the sharp pressure gradient, inner and outer asymptotic expansions are derived and matched for functions F and S which determine the stream function and the temperature. The equations for F and S are largely uncoupled, in that the first approximation to F is independent of S, the first approximation to S depends only on the first approximation to F, and so on.

Type
Research Article
Information
Journal of Fluid Mechanics , Volume 84 , Issue 2 , 30 January 1978 , pp. 385 - 400
Copyright
© 1978 Cambridge University Press

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

Blasius, H. 1908 Grenzschichten in Flüssigkeiten mit kleiner Reibung. Z. Math. Phys. 56, 1.Google Scholar
Buckmaster, J. 1970 The behaviour of a laminar compressible boundary layer on a cold wall near a point of zero skin friction. J. Fluid Mech. 44, 237.Google Scholar
Curle, N. 1976 Development and separation of a laminar boundary layer, under the action of a very sharp constant adverse pressure gradient. Proc. Roy. Soc. Edin. A 74, 119.Google Scholar
Curle, N. & Davies, H. J. 1971 Modern Fluid Dynamics, vol. II, p. 275. Van Nostrand/Reinhold.Google Scholar
Davies, T. & Walker, G. 1977 On solutions of the compressible laminar boundary-layer equations and their behaviour near separation. J. Fluid Mech. 80, 279.Google Scholar
Goldstein, S. 1948 On laminar boundary layer flow near a position of separation. Quart. J. Mech. Appl. Math. 1, 43.Google Scholar
Illingworth, C. R. 1949 Steady flow in the laminar boundary layer of a gas. Proc. Roy. Soc. A 199, 533.Google Scholar
Pohlhausen, E. 1921 Der Wärmeaustausch zwischen festen Körpern und Flüssigkeiten mit kleiner Reibung und kleiner Wärmeleitung. Z. angew. Math. Mech. 1, 115.Google Scholar
Stewartson, K. 1949 Correlated incompressible and compressible boundary layers. Proc. Roy. Soc. A 200, 84.Google Scholar
Stewartson, K. 1962 The behaviour of a laminar compressible boundary layer near a point of zero skin-friction. J. Fluid Mech. 12, 117.Google Scholar
Stratford, B. S. 1954 Flow in the laminar boundary layer near separation. Aero. Res. Counc. R. & M. no. 3002.Google Scholar