Hostname: page-component-cd9895bd7-7cvxr Total loading time: 0 Render date: 2024-12-22T06:32:35.439Z Has data issue: false hasContentIssue false
  • English
  • Français

A method for integrating the boundary-layer equations through a region of reverse flow

Published online by Cambridge University Press:  29 March 2006

J. B. Klemp  and
Andreas Acrivos
J. B. Klemp
Affiliation:
Department of Chemical Engineering, Stanford University, Stanford, California Present Address: National Center for Atmospheric Research, Boulder, Colorado.
Andreas Acrivos
Affiliation:
Department of Chemical Engineering, Stanford University, Stanford, California
Get access Rights & Permissions [Opens in a new window]

Abstract

If a region of reverse flow remains confined within a boundary layer the conventional boundary-layer equations should continue to apply downstream of the point of detachment of the surface streamline (ω = 0). Nevertheless, standard numerical techniques fail in the presence of backflow since these methods become highly unstable and, in addition, neglect the upstream flow of information. A procedure for numerically integrating the boundary-layer equations through a region of reverse flow which takes downstream influence into account is therefore presented. This method is then applied to the problem of uniform flow past a parallel flat plate of finite length whose surface has a constant velocity directed opposite to that of the main stream. Although singularities occur at both the point of detachment (xs) and reattachment (xr) of the ω = 0 streamline, this integration technique provides a solution which ceases to apply only in the close proximity of these singular points. From this solution it is evident that, throughout a large portion of the separated region, the flow is strongly affected by conditions near xr, thereby demonstrating the importance of allowing information to be transmitted upstream in a region of backflow. Near (xs), however, it is found that, in spite of the presence of reverse flow, the solution has a self-similar form in this particular example.

Type
Research Article
Information
Journal of Fluid Mechanics , Volume 53 , Issue 1 , 9 May 1972 , pp. 177 - 191
Copyright
© 1972 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

Briley, W. R. 1971 A numerical study of laminar separation bubbles using the Navier-Stokes equations. J. Fluid Mech. 47, 713.Google Scholar
Catherall, D. & Manqler, K. W. 1966 Integration of the two-dimensional laminar boundary-layer equations past the point of vanishing skin friction. J. Fluid Mech. 26, 163.Google Scholar
Emmons, E. W. & Leigh, D. C. 1954 Tabulation of the Blasius function with blowing and suction. Aero. Res. Counc. Current Paper, no. 157.Google Scholar
Kassoy, D. R. 1971 On laminar boundary-layer blow-off. Part 2. J. Fluid Mech. 48, 209.Google Scholar
Klemp, J. B. & Acrivos, A. 1972 High Reynolds number flow past a flat plate with strong blowing. J. Fluid Mech. 51, 337.Google Scholar
Leal, L. G. Q., Acrnos, A. 1969 Structure of steady closed streamline flows within a boundary layer. Phys. Fluids, 2 (suppl.), 105.Google Scholar
Robillard, L. 1971 On a series solution for the laminar boundary layer on a moving wall. Trans. A.S.M.E. E 38, 550.Google Scholar
Rosenhead, L.(ed.)1963 Laminar Boundary Layers. Oxford University Press.