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Marginal separation of a three-dimensional boundary layer on a line of symmetry

Published online by Cambridge University Press:  20 April 2006

S. N. Brown
Affiliation:
Department of Mathematics, University College London, Gower Street, London WC1E 6BT

Abstract

The marginal separation of a laminar incompressible boundary layer on the line of symmetry of a three-dimensional body is discussed. The interaction itself is taken to be quasi-two-dimensional but the results differ from those for a two-dimensional boundary layer in that the effect of the gradient of the crossflow is included. Solutions of the resulting integral equation are computed for two values of the additional parameter, and comparisons made with an analytical prediction of the asymptotic form as the length of the separation bubble tends to infinity. The occurrence of the phenomenon is confirmed by an examination of the results of an existing numerical integration of the boundary-layer equations for the line of symmetry of a paraboloid.

Type
Research Article
Copyright
© 1985 Cambridge University Press

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References

Brown, S. N. & Stewartson K. 1983 On an integral equation of marginal separation. SIAM J. Appl. Maths 43, 11191126.Google Scholar
Cebeci T., Khattab, A. K. & Stewartson K. 1980 On nose separation. J. Fluid Mech. 97, 435454.Google Scholar
Cebeci T., Stewartson, K. & Brown S. N. 1983 Non-similar boundary layers on the leeside of cones at incidence. Comp. Fluids 11, 175186.Google Scholar
Duck P. W. 1984 The effect of a surface discontinuity on an axi-symmetric boundary layer. Q. J. Mech. Appl. Maths 37, 5774.Google Scholar
Goldstein S. 1948 On laminar boundary-layer flow near a point of separation. Q. J. Mech. Appl. Maths 1, 4369.Google Scholar
Kluwick A., Gittler, P. & Bodonyi R. J. 1984 Viscous-inviscid interactions on axisymmetric bodies of revolution in supersonic flow. J. Fluid Mech. 140, 281301.Google Scholar
Nishikawa, N. & Yasui Y. 1984 Separation of three-dimensional boundary layers on elliptic paraboloids. Theoretical & Appl. Mech. 32, 7990.Google Scholar
Rhyzhov, O. & Smith F. T. 1985 Short-length instabilities, breakdown and initial value problems in dynamic stall. (To appear in Mathematika.)
Smith F. T. 1977 The laminar separation of an incompressible fluid streaming past a smooth surface Proc. R. Soc. Lond. A 356, 433463.Google Scholar
Smith F. T. 1978 Three-dimensional viscous and inviscid separation of a vortex sheet from a smooth non-slender body. RAE Tech. Rep. 78095.Google Scholar
Smith F. T. 1982 Concerning dynamic stall. Aero. Q. 331352.Google Scholar
Smith, F. T. & Gajjar J. 1984 Flow past wing-body junctions. J. Fluid Mech. 144, 191215.Google Scholar
Smith F. T., Sykes, R. I. & Brighton P. W. M. 1977 A two-dimensional boundary layer encountering a three-dimensional obstacle. J. Fluid Mech. 83, 163176.Google Scholar
Stewartson K. 1970 Is the singularity at separation removable? J. Fluid Mech. 44, 347364.Google Scholar
Stewartson, K. & Simpson C. J. 1982 On a singularity initiating a boundary-layer collision. Q. J. Mech. Appl. Maths 35, 116.Google Scholar
Stewartson K., Smith, F. T. & Kaups K. 1982 Marginal separation. Stud. Appl. Maths 67, 4561.Google Scholar
Stewartson, K. & Williams P. G. 1969 Self-induced separation Proc. R. Soc. Lond. A 312, 181206.Google Scholar
Sychev V. V. 1972 On laminar separation. Izv. Akad. Nauk SSSR, Mekh. Zhid. Gaza 3, 4759.Google Scholar
Vatsa, V. N. & Werle M. J. 1977 Quasi-three-dimensional boundary-layer separation in supersonic flow. Trans. ASME I: J. Fluids Engng 99, 634000.Google Scholar