Hostname: page-component-78c5997874-dh8gc Total loading time: 0 Render date: 2024-11-09T13:39:27.993Z Has data issue: false hasContentIssue false
  • English
  • Français

A linearized potential flow theory for airfoils with spoilers

Published online by Cambridge University Press:  29 March 2006

G. P. Brown  and
G. V. Parkinson
G. P. Brown
Affiliation:
Department of Mechanical Engineering, University of British Columbia
G. V. Parkinson
Affiliation:
Department of Mechanical Engineering, University of British Columbia
Get access Rights & Permissions [Opens in a new window]

Abstract

Linearized two-dimensional potential flow theory is applied to an airfoil with an upper surface spoiler. The spoiler wake is modelled as a cavity of empirically given constant pressure, and a sequence of conformal transformations maps the linearized physical plane, with a slit on the real axis representing the airfoil plus cavity, onto the upper half of the plane exterior to the unit circle. The complex acceleration potential is used, and its real part is specified on the real axis, repre- senting the cavity boundary, while its imaginary part is specified on the unit semicircle, representing the wetted surface of the airfoil and spoiler. Solutions are found for both the steady-state lift and the transient lift after spoiler actuation for airfoils of arbitrary camber, thickness and incidence, with and without a simple flap, and with spoilers of arbitrary position, height and angle. The empirical cavity pressure is arbitrary for the steady-state solution, but is assumed to have the free-stream value for the transient solutions. Comparisons are made with the results of wind-tunnel experiments, and, for the steady-state solutions, with predictions of an earlier theory. The agreement of the present theoretical predictions with the experimental results is generally good, and is in most cases somewhat better than that of the earlier theory.

Type
Research Article
Information
Journal of Fluid Mechanics , Volume 57 , Issue 4 , 6 March 1973 , pp. 695 - 719
Copyright
© 1973 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

Barnes, C. S. 1965 A developed theory of spoilers on aerofoils. Aero Res. Counc. Current Paper, no. 887.Google Scholar
Biot, M. A. 1942 Some simplified methods in airfoil theory. J. Aero. Sci. 9(5), 185.Google Scholar
Bisplinghoff, R. L., Ashley, H. & Halfman, R. L. 1955 Aeroelastkity, p. 284. Addison-Wesley.
Brown, G. P. 1971 Steady and nonsteady potential flow methods for airfoils with spoilers. Ph.D. thesis, University of British Columbia.
Fabula, A. G. 1962 Thin-airfoil theory applied to hydrofoils with a single finite cavity and arbitrary free streamline detachment. J. Fluid Mech. 12, 227.Google Scholar
Hess, J. L. & Smith, A. M. O. 1966 Calculation of potential flow about arbitrary bodies. Prog. Aero Sci. 8.Google Scholar
Jandali, T. 1970 A potential flow theory for airfoil spoilers. Ph.D. thesis, University of British Columbia.
Jandali, T. & Parkinson, G. V. 1970 A potential flow theory for airfoil spoilers. Trans. C.A.S.I. 3(1), 1.Google Scholar
Maskell, E. C. 1963 A theory of blockage effects on bluff bodies and stalled wings in a closed wind tunnel. Aero Res. Counc. R. & M. no. 3400.Google Scholar
Parkin, B. R. 1959 Linearized theory of cavity flow in two dimensions. Rand Rep. P-1745.Google Scholar
Parkinson, G. V. & Jandali, T. 1970 A wake source model for bluff body potential flow. J. Fluid Mech. 40, 3, 577.Google Scholar
Pope, A. & Harper, J. J. 1966 Low-Speed Wind Tunnel Testing. Wiley.
Song, C. S. 1965 Supercavitating flat plate with an oscillating flap a t zero cavitation number. St Anthony Falls Hydraulic Lab. Tech. Paper, B 52.Google Scholar
Theodorsen, T. 1931 Theory of wing sections of arbitrary shape. N.A.C.A. Rep. no. 411.Google Scholar
Woods, L. C. 1953 Theory of aerofoil spoilers. Aero Res. Coulzc. R. & M. no. 2969.Google Scholar