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The unsteady laminar boundary layer on an axisymmetric body subject to small-amplitude fluctuations in the free-stream velocity

Published online by Cambridge University Press:  26 April 2006

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

The effect of small-amplitude, time-periodic, free-stream disturbances on an otherwise steady axisymmetric boundary layer on a circular cylinder is considered. Numerical solutions to the problem are presented, and an asymptotic solution to the flow, valid far downstream along the axis of the cylinder is detailed. Particular emphasis is placed on the unsteady eigensolutions that occur far downstream, which turn out to be very different from the analogous planar eigensolutions. These axisymmetric eigensolutions are computed numerically and also are described by asymptotic analyses valid for low and high frequencies of oscillation.

Type
Research Article
Information
Journal of Fluid Mechanics , Volume 232 , November 1991 , pp. 415 - 438
Copyright
© 1991 Cambridge University Press

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References

Abramowitz, M. & Stegun, I. A. 1964 Handbook of Mathematical Functions, with Formulas, Graphs and Mathematical Tables. Washington DC: US Government Printing Office.
Ackerberg, R. C. & Phillips, J. H. 1972 The unsteady laminar boundary layer on a semi-infinite plate plate due to small fluctuations in the magnitude of the freestream velocity. J. Fluid Mech. 51, 137.Google Scholar
Brown, S. N. & Stewartson, K. 1973a On the propagation of disturbances in a laminar boundary layer I. Proc. Camb. Phil. Soc. 73, 493.Google Scholar
Brown, S. N. & Stbwaktson, K. 1973b On the propagation of disturbances in a laminar boundary layer II. Proc. Camb. Phil. Soc. 73, 503.Google Scholar
Bush, W. B. 1976 Axial incompressible viscous flow past a slender body of revolution. Rocky Mount. J. Maths 6, 527.Google Scholar
Duck, P. W. 1984 The effect of a surface discontinuity on an axisymmetric boundary layer. Q. J. Mech. Appl. Maths 37, 57.Google Scholar
Duck, P. W. 1989 A numerical method for treating time-periodic boundary layers. J. Fluid Mech. 204, 544.Google Scholar
Duck, P. W. & Bodonyi, R. J. 1986 The wall jet on an axisymmetric body. Q. J. Mech. Appl. Maths 34, 407.Google Scholar
Duck, P. W. & Hall, P. 1989 On the interaction of axisymmetric Tollmien-Schlichting waves in supersonic flow. Q. J. Mech. Appl. Maths 42, 115 (also ICASE Rep. 88–10).Google Scholar
Glauert, M. B. & Lighthill, M. J. 1955 The axisymmetric boundary layer on a long thin cylinder. Proc. R. Soc. Lond. A 230, 188.Google Scholar
Goldstein, M. E. 1983 The evolution of Tollmien-Schlichting waves near a leading edge. J. Fluid Mech. 127, 59.Google Scholar
Goldstein, M. E., Sockol, P. M. & Sanz, J. 1983 The evolution of Tollmien—Schlichting waves near a leading edge. Part 2. Numerical determination of amplitudes. J. Fluid Mech. 129, 443.Google Scholar
Hartman, R. J. 1964 Ordinary Differential Equations. John Wiley.
Keller, H. B. & Cebeci, T. 1971 Accurate numerical methods for boundary-layer flows. Part 1. Two-dimensional laminar flows. In Proc. 2nd Intl Conf. on Numerical Methods in Fluid Dynamics (ed. M. Holt). Lecture Notes in Physics, vol. 8. Springer.
Lam, S. H. & Rott, N. 1960 Theory of linearised time-dependent boundary layers. Cornell University GSAE Rep. AFOSR. TN-60–1100.Google Scholar
Lighthill, M. J. 1954 The response of laminar skin friction and heat transfer to fluctuations in the stream velocity. Proc. R. Soc. Lond. A 224, 1.Google Scholar
Pedley, T. J. 1972 Two-dimensional boundary layers in a free stream which oscillate without reversing. J. Fluid Mech. 55, 359.Google Scholar
Phillips, J. H. & Ackerberg, R. C. 1973 A numerical method for integrating the unsteady boundary-layer equations when there are regions of backflow. J. Fluid Mech. 58, 561.Google Scholar
Rott, N. & Rosenweig, M. L. 1980 On the response of the laminar boundary layer to small fluctuations of the free-stream velocity. J. Aero. Sci. 27, 741.Google Scholar
Seban, R. A. & Bond, R. 1951 Skin friction and heat transfer characteristics of a laminar boundary layer on a cylinder in axial incompressible flow. J. Aero. Sci. 10, 171.Google Scholar
Stewabtson, K. 1955 The asymptotic boundary layer on a circular cylinder in axial incompressible flow Q Appl. Maths 13, 113.Google Scholar