Hostname: page-component-669899f699-ggqkh Total loading time: 0 Render date: 2025-04-26T00:24:23.964Z Has data issue: false hasContentIssue false
  • English
  • Français

Dynamic stall due to unsteady marginal separation

Published online by Cambridge University Press:  21 April 2006

J. W. Elliott  and
F. T. Smith
J. W. Elliott
Affiliation:
Department of Applied Mathematics, University of Hull, Hull HU6 7RX, UK
F. T. Smith
Affiliation:
Department of Mathematics, University College London, London WC1E 6BT, UK
Get access Rights & Permissions [Opens in a new window]

Abstract

A theoretical investigation into the next stage of dynamic stall, concerning the beginnings of eddy shedding from the boundary layer near an aerofoil's leading edge, is described by means of the unsteady viscous-inviscid interacting marginal separation of the boundary layer. The fully nonlinear stage studied in the present paper is shown to match with a previous ‘weakly nonlinear’ regime occurring in the earlier development of the typical eddy from its initially slender thin state. Numerical solutions followed by linear and nonlinear analysis suggest that with confined initial conditions the strong instabilities in the present unsteady flow tend to force a breakdown within a finite time. This leads on subsequently to an unsteady predominantly inviscid stage where the eddy becomes non-slender, spans the entire boundary layer and its evolution then is governed by the Euler equations. This is likely to be followed by the shedding of the eddy from the boundary layer.

Type
Research Article
Information
Journal of Fluid Mechanics , Volume 179 , June 1987 , pp. 489 - 512
Copyright
© 1987 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.)

Article purchase

Temporarily unavailable

References

Abramowitz, M. & Stegun, I. A. 1965 Handbook of Mathematical Functions. Dover.
Burggraf, O. R. & Smith, F. T. 1985 On the development of large-sized short-scaled disturbances in boundary layers. Proc. R. Soc. Lond. A 399, 25–55.Google Scholar
Duck, P. W. 1985 Laminar flow over unsteady humps: the formation of waves. J. Fluid Mech. 160, 465–498.Google Scholar
Elliott, J. W., Cowley, S. J. & Smith, F. T. 1983 Breakdown of boundary layers, (i) on moving surfaces, (ii) in semi-similar unsteady flow, (iii) in fully unsteady flow. Geophys. Astrophys. Fluid Dyn. 25, 77–138.Google Scholar
Goldstein, S. 1948 On laminar boundary-layer flow near a position of separation. Q. J. Mech. Appl. Maths 1, 43–69.Google Scholar
Mcallister, K. W. & Carr, I. W. 1979 Trans. ASME I: J. Fluids Engng 10, 376
Mccroskey, W. J. 1982 Unsteady airfoils. Ann. Rev. Fluid Mech. 14, 285–311.Google Scholar
Moore, D. W. 1979 The spontaneous appearance of a singularity in the shape of an evolving vortex sheet. Proc. R. Soc. Lond. A 365, 105–119.Google Scholar
Ryzhov, O. S. & Smith, F. T. 1984 Short-length instabilities, breakdown and initial-value problems in dynamic stall. Mathematika. 31, 163.Google Scholar
Smith, F. T. 1979 On the non-parallel flow stability of the Blasius boundary layer. Proc. R. Soc. Lond. A 360, 91–109.Google Scholar
Smith, F. T. 1982 Concerning dynamic stall. Aero Q. November, 331–352.
Smith, F. T. & Elliott, J. W. 1985 On the abrupt turbulent reattachment downstream of leading-edge laminar separation. Proc. R. Soc. Lond. A401, 1–27.Google Scholar
Smith, F. T. & Merkin, J. H. 1984 Triple-deck solutions for subsonic flow past humps, steps. concave or convex corners and wedged trailing edges. J. Comput. Fluids 10, 7–25.Google Scholar
Stewartson, K. 1970 Is the singularity at separation removable?. J. Fluid Mech. 44, 347–364.Google Scholar
Stewartson, K., Smith, F. T. & Kaups, K. 1982 Marginal separation. Stud. Appl. Maths 67, 45–61.Google Scholar
Telionis, D. P. 1981 Unsteady Viscous Flows. Springer.
Van Dommelen, L. L. 1981 Unsteady boundary layer separation. Ph.D. thesis, Cornell University.