Hostname: page-component-76fb5796d-zzh7m Total loading time: 0 Render date: 2024-04-26T21:25:55.118Z Has data issue: false hasContentIssue false
  • English
  • Français

Separation and reattachment near the leading edge of a thin oscillating airfoil

Published online by Cambridge University Press:  21 April 2006

Tuncer Cebeci ,
A. A. Khattab  and
S. M. Schimke
Tuncer Cebeci
Affiliation:
Aerodynamics Research and Technology, Douglas Aircraft Company, Long Beach, CA 90846, USA
A. A. Khattab
Affiliation:
Aerodynamics Research and Technology, Douglas Aircraft Company, Long Beach, CA 90846, USA
S. M. Schimke
Affiliation:
Aerodynamics Research and Technology, Douglas Aircraft Company, Long Beach, CA 90846, USA
Get access Rights & Permissions [Opens in a new window]

Abstract

The evolution of unsteady boundary layers in the vicinity of the leading edge of a thin oscillating airfoil has been examined with a novel numerical method which is able to deal with the movement of the stagnation point and with regions of reverse and separated flow. Solutions to the unsteady boundary-layer equations, with a prescribed pressure distribution which causes flow reversal and separation, demonstrate the importance of numerical steps in distance and time and that a requirement similar to the stability criterion of Courant, Friedrichs and Lewy must be satisfied to avoid numerical errors. At the lower reduced frequencies of the investigation, solutions could not be obtained with this procedure and it was necessary to introduce interaction between the viscous and inviscid flows. The solutions obtained with the interactive method were increasingly different from those without interaction as the reduced frequency was decreased towards zero and, for some combinations of Reynolds number and frequency, exhibited behaviour consistent with the instability of separation bubbles.

Type
Research Article
Information
Journal of Fluid Mechanics , Volume 188 , March 1988 , pp. 253 - 274
Copyright
© 1988 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

Cark, L. W., McAuster, K. W. & McCroskey, W. J. 1977 Analysis of the development of dynamic stall based on oscillating airfoil experiments. NASA TND-8382.Google Scholar
Cebeci, T. 1976 Separated flows and their representation by boundary-layer equations. Mech. Engng Rep. ONR-CR215-234-2. California State University, Long Beach.
Cebeci, T. 1979 The laminar boundary layer on a circular cylinder started impulsively from rest. J. Comp. Phys. 31, 153–172.Google Scholar
Cebeci, T. 1982 Unsteady separation. In Numerical and Physical Aspects of Aerodynamic Flows (ed. T. Cebeci), pp. 265–277. Springer.
Cebeci, T. 1986 Unsteady boundary layers with an intelligent numerical scheme. J. Fluid Mech. 163, 129–140.Google Scholar
Cebeci, T. & Bradshaw, P. 1984 Physical and Computational Aspects of Convective Heat Transfer. Springer.
Cebeci, T. & Carr, L. W. 1981 Prediction of boundary-layer characteristics of an oscillating airfoil. In Unsteady Turbulent Shear Flows (ed. R. Michel, J. Cousteix and R. Houdeville), pp. 145–158. Springer.
Cebeci, T. & Clark, R. W. 1984 An interactive approach to subsonic flows with separation. In Numerical and Physical Aspects of Aerodynamic Flows, II (ed. T. Cebeci), pp. 193–204. Springer.
Cebeci, T., Clark, U. W., Chang, K. C., Halsey, N. D. & Lee, K. 1986 Airfoils with separation and the resulting wakes. J. Fluid Mech. 163, 323–347.Google Scholar
Cebeci, T., Khattab, A. A. & Schimke, S. M. 1984 Can the singularity be removed in time-dependent flows? In Workshop on Unsteady Separated Flow (ed. M. S. Francis and M. W. Luttges), pp. 97–105. Colorado Springs, CO.
Cebeci, T., Stewaetson, K. & Williams, P. G. 1981 Separation and reattachment near the leading edge of a thin airfoil at incidence. AGARD CP 291, Paper 20.Google Scholar
Cowley, S. J. 1983 Computer extension and analytic continuation of Blasius' expansion for impulsive flow past a circular cylinder. J. Fluid Mech. 135, 389–405.Google Scholar
Daley, D. C. & Jumper, E. J. 1984 Experimental investigation of dynamic stall. J. Aircraft 21, 831–832.Google Scholar
Francis, M. S., Keese, J. E. & Retelle, J. P. 1983 An investigation of airfoil dynamic stall with large amplitude motions. FJSRL-TR-83-0010. F. J. Seiler Research Labs, Air Force Academy, Colorado Springs, CO.
Ingham, D. B. 1984 Unsteady separation. J. Comp. Phys. 53, 90–99.Google Scholar
Isaacson, E. & Keller, H. B. 1966 Analysis of Numerical Methods. Wiley.
Keller, H. B. 1974 Accurate difference methods for two-point boundary-value problems. SIAM J. Numer. Anal. 11, 305.Google Scholar
Keller, H. B. 1978 Numerical methods in boundary-layer theory. Ann. Rev. Fluid Mech. 10, 417–433.Google Scholar
Krause, E., Hirschel, E. H. & Bothemann, Th. 1968 Die numerische Integration der Bewegungsgleichungen dreidimensionaler laminarer kompressibler Grenzschichten, Band 3. Fachtagung Aerodynamik, Berlin. D6LR-Fachlinchreike.
Lorber, P. F. & Covert, E. E. 1986 Unsteady airfoil boundary layers - experiment and computation. In Numerical and Physical Aspects of Aerodynamic Flows III (ed. T. Cebeci), pp. 235–251. Springer.
Stewartson, K., Smith, F. T. & Kaups, K. 1982 Marginal separation. Stud. Appl. Maths 67, 45–61.Google Scholar
Van Dommelen, L. L. & Shen, S. F. 1982 The genesis of separation. In Numerical and Physical Aspects of Aerodynamic Flows (ed. T. Cebeci), pp. 293–311. Springer.
Veldman, A. E. P. 1981 New quasi-simultaneous method to calculate interacting boundary layers. AIAA J. 19, 79–85.Google Scholar