Hostname: page-component-78c5997874-fbnjt Total loading time: 0 Render date: 2024-11-10T05:12:03.705Z Has data issue: false hasContentIssue false
  • English
  • Français

Spectral solutions for three-dimensional triple-deck flow over surface topography

Published online by Cambridge University Press:  21 April 2006

P. W. Duck  and
O. R. Burggraf
P. W. Duck
Affiliation:
Department of Mathematics, University of Manchester, Manchester M139PL
O. R. Burggraf
Affiliation:
Department of Aeronautical and Astronautical Engineering, The Ohio State University, Columbus, Ohio 43210
Get access Rights & Permissions [Opens in a new window]

Abstract

The effect of surface topography on an otherwise two-dimensional boundary-layer flow is investigated. The flow is assumed to be steady, laminar and incompressible, and is described by triple-deck theory. The basic problem reduces to the solution of a form of the nonlinear three-dimensional boundary-layer equations, together with an interaction condition. The solutions are obtained by a spectral method, with the computations carried out iteratively in Fourier-transform space. Numerical results are presented for several cases including three-dimensional separation. Comparison is made with the predictions of linearized theory. The decay corridor observed by Smith is confirmed for one localized configuration, but not for another having a broader height distribution.

Type
Research Article
Information
Journal of Fluid Mechanics , Volume 162 , January 1986 , pp. 1 - 22
Copyright
© 1986 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

Burggraf, O. R. 1976 The three-dimensional triple deck. In Workshop on Viscous Interaction and Boundary-layer Separation, Ohio State University, 16—17 August 1976.
Burggraf, O. R. & Duck, P. W. 1981 Spectral computation of triple-deck flows. In Numerical and Physical Aspects of Aerodynamic Flows (ed T. Cebeci). Springer.
Cooley, J. W. & Tukey, J. W. 1965 Math.Comp. 19, 297.
Duck, P. W. 1980 Z. angew. Math. Phys. 32, 24.
Jobe, C. E. & Burggraf, O. R. 1974 Proc. R. Soc. Lond. A 340, 91.
Lighthill, M. J. 1963 Introduction. Boundary layer theory. In Laminar Boundary Layers (ed. L. Rosenhead), chap II. Oxford University Press.
Messiter, A. F. 1970 SIAM J. Appl. Maths 18, 241.
Neiland, V. Ya. 1969 Izv. Akad. Nauk SSSR, Mekh. Zhidk. Gaza 4, 40.
Rizzetta, D. P., Burggraf, O. R. & Jenson, R. 1978 J. Fluid Mech. 89, 535.
Smith, F. T. 1976 Mathematika 23, 62.
Smith, F. T. 1980 J. Fluid Mech. 99, 185.
Smith, F. T., Sykes, R. I. & Brighton, P. W. M. 1977 J. Fluid Mech. 83, 163.
Sneddon, I. M. 1979 Intl J. Engng Sci. 17, 185.
Stewartson, K. 1969 Mathematika 16, 106.
Stewartson, K. 1974 Adv. Appl. Mech. 14, 145.
Stewartson, K. 1981 SIAM Rev. 23, 308.
Stewartson, K. & Williams, P. G. 1969 Proc. R. Soc. Land. A 312, 181.
Sykes, R. I. 1978 Proc. R. Soc. Lond. A 361, 225.
Sykes, R. I. 1980 Proc. R. Soc. Land. A 373, 311.