Hostname: page-component-77c89778f8-rkxrd Total loading time: 0 Render date: 2024-07-18T23:39:14.062Z Has data issue: false hasContentIssue false
  • English
  • Français

Flow development in the vicinity of the sharp trailing edge on bodies impulsively set into motion

Published online by Cambridge University Press:  20 April 2006

James C. Williams
James C. Williams
Affiliation:
Department of Aerospace Engineering, Auburn University, Auburn, Alabama
Get access Rights & Permissions [Opens in a new window]

Abstract

The initial development of the viscous flow in the vicinity of the sharp trailing edge of a symmetrical body, impulsively set into motion is studied within the framework of boundary-layer theory. For a blunt trailing edge there exists a similarity solution for the inviscid outer flow as has been pointed out by Proudman & Johnson (1961). The present work shows that for sharp trailing edges, however, no such solution exists.

For small or moderate trailing-edge angles, a moving singularity occurs in the solution fairly early in the flow development. The flow in the vicinity of this singularity exhibits the characteristics of unsteady separation. For large trailing-edge angles, the boundary layer becomes so thick that solutions must be terminated before there is any evidence of a singularity. For a cusped trailing edge, the solution is arbitrarily terminated to avoid large computational times and with the realization that the trailing edge flow must eventually be influenced by the leading edge at which time the present solutions cease to have meaning.

Type
Research Article
Information
Journal of Fluid Mechanics , Volume 115 , February 1982 , pp. 27 - 37
Copyright
© 1982 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

Blottner, F. G. 1970 Finite-difference methods of solution of the boundary layer equations. A.I.A.A.J. 8, 193.Google Scholar
Dennis, S. C. R. 1972 The motions of a viscous fluid past an impulsively started semi-infinite flat plate. J. Inst. Math. Applic. 10, 105.Google Scholar
Hall, M. G. 1969 The boundary layer over an impulsively started plate. Proc. R. Soc. Lond. A 310, 401.Google Scholar
Nanbu, K. 1971 Unsteady Falkner — Skan flow. Z. angew. Math. Phys. 22, 1167.Google Scholar
Proudman, I. & Johnson, K. 1961 Boundary layer growth near a rear stagnation point. J. Fluid Mech. 12, 161.Google Scholar
Robins, A. J. & Howarth, J. A. 1972 Boundary layer development at a two-dimensional rear stagnation point. J. Fluid Mech. 56, 161.Google Scholar
Smith, S. H. 1967 The impulsive motion of a wedge in a viscous fluid. Z. angew. Math. Phys. 18, 508.Google Scholar
Stewartson, K. 1951 On the impulsive motion of a flat plate in a viscous fluid. Quart. J. Mech. Appl. Math. 4, 182.Google Scholar
Van Dommelen, L. L. & Shen, S. F. 1981 The genesis of separation. In Numerical and Physical Aspects of Aerodynamic Flows, Proc. Symp. January 1981, Long Beach, California (ed. T. Cebeci).
Williams, J. C. & Johnson, W. D. 1974 Semisimilar solutions to unsteady boundary layer flows including separation. A.I.A.A. J. 12, 1388.Google Scholar
Williams, J. C. & Rhyne, T. B. 1980 Boundary layer development on a wedge impulsively set into motion. SIAM J. Appl. Math. 38, 215.Google Scholar