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Three-dimensional marginal separation

Published online by Cambridge University Press:  26 April 2006

P. W. Duck
P. W. Duck
Affiliation:
Department of Mathematics, University of Manchester, Manchester M13 9PL, UK
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Abstract

The three-dimensional marginal separation of a boundary layer along a line of symmetry is considered. The key equation governing the displacement function is derived, and found to be a nonlinear integral equation in two space variables. This is solved iteratively using a pseudospectral approach, based partly in double Fourier space, and partly in physical space. Qualitatively the results are similar to previously reported two-dimensional results (which are also computed to test the accuracy of the numerical scheme); however quantitatively the three-dimensional results are much different.

Type
Research Article
Information
Journal of Fluid Mechanics , Volume 202 , May 1989 , pp. 559 - 575
Copyright
© 1989 Cambridge University Press

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References

Bodonyi, R. J. & Duck, P. W., 1988 A numerical method for treating strongly interactive three-dimensional viscous-inviscid flows. Computers Fluids 16, 279.Google Scholar
Brown, S. N.: 1985 Marginal separation of a three-dimensional boundary layer on a line of symmetry. J. Fluid Mech. 158, 95.Google Scholar
Brown, S. N. & Stewartson, K., 1983 On an integral equation of marginal separation. SIAM J. Appl. Maths 43, 1119.Google Scholar
Cebeci, T., Khattab, A. K. & Stewartson, K., 1980 On nose separation. J. Fluid Mech. 97, 435.Google Scholar
Cebeci, T. & Su, W., 1988 Separation of three-dimensional laminar boundary layers on a prolate spheroid. J. Fluid Mech. 191, 47.Google Scholar
Cooley, J. W. & Tukey, J. W., 1965 An algorithm for the machine computation of complex Fourier series. Maths Comp. 19, 297.Google Scholar
Duck, P. W. & Burggraf, O. R., 1986 Spectral solutions for three-dimensional triple-deck flow over surface topography. J. Fluid Mech. 162, 1.Google Scholar
Fornberg, B.: 1980 A numerical study of steady viscous flow past a circular cylinder. J. Fluid Mech. 98, 819.Google Scholar
Fornberg, B.: 1985 Steady viscous flow past a circular cylinder up to a Reynolds number 600. J. Comp. Phys. 61, 297.Google Scholar
Goldstein, S.: 1948 On laminar boundary layer flow near a point of separation. Q. J. Mech. Appl. Maths 1, 43.Google Scholar
Lighthill, M. J.: 1963 Boundary layer theory. In Laminar Boundary Layers (ed. L. Rosenhead), chap. II. Oxford University Press.
Peregrine, D. H.: 1985 A note on the steady high-Reynolds-number flow about a circular cylinder. J. Fluid Mech. 157, 493.Google Scholar
Smith, F. T.: 1979 Laminar flow of a incompressible fluid past a bluff body; the separation, reattachment, eddy properties and drag. J. Fluid Mech. 92, 171.Google Scholar
Smith, F. T.: 1982 Concerning dynamic stall. Aero Q. 33, 331.Google Scholar
Smith, F. T.: 1983 Properties and a finite-difference approach, for three-dimensional interactive boundary layers. UTRC Rep. 83–46. United Technical Res. Cent. East Hertford, CN.
Smith, F. T.: 1985 A structure for laminar flow past a bluff body at high Reynolds number. J. Fluid Mech. 155, 175.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, 163.Google Scholar
Stewartson, K.: 1970 Is the singularity at separation removable? J. Fluid Mech. 44, 347.Google Scholar
Stewartson, K., Smith, F. T. & Kaups, K., 1982 Marginal separation. Stud. Appl. Maths 67, 45.Google Scholar