Hostname: page-component-cd9895bd7-q99xh Total loading time: 0 Render date: 2024-12-18T19:02:57.342Z Has data issue: false hasContentIssue false
  • English
  • Français

Thin-airfoil theory applied to hydrofoils with a single finite cavity and arbitrary free-streamline detachment

Published online by Cambridge University Press:  28 March 2006

A. G. Fabula
A. G. Fabula
Affiliation:
U.S. Naval Ordnance Test Station, Pasadena, California
Get access Rights & Permissions [Opens in a new window]

Abstract

Thin-airfoil theory is applied to steady, plane potential flow about vented or cavitating hydrofoils of arbitrary profile when there are two free-streamlines detaching from the foil and bounding the single cavity that extends downstream of the trailing edge. Cavity-termination models employed are the closed, the partly closed and the open models for which the thickness of the implied ’wake’ following the cavity ranges from zero to maximum for the open model. The general solution for given wetted-surface profile, cavity length and particular cavity termination is constructed by superposition of the profile's cusp-closure solution (angle of attack α+) plus the particular flat-plate solution to give the desired angle of attack α. Four related integrals involving the wetted-surface contour slope distribution lead to drag, lift, cavity pressure and α+vs cavity length. A comparison of theoretical and experimental lift and drag for a cavitating hydrofoil shows good agreement until the theoretical cavity closure nears the trailing edge.

Type
Research Article
Information
Journal of Fluid Mechanics , Volume 12 , Issue 2 , February 1962 , pp. 227 - 240
Copyright
© 1962 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

Bateman, H. 1944 Partial Differential Equations of Mathematical Physics, p. 239. New York: Dover.
Biot, M. A. 1942 Some simplified methods in airfoil theory. J. Aero. Sci. 9, 185.Google Scholar
Cheng, H. K. & Rott, N. 1954 Generalizations of the inversion formula of thin airfoil theory. J. Rat. Mech. Anal. 3, 357.Google Scholar
Fabula, A. G. 1960 Application of thin airfoil theory to hydrofoils with cut-off ventilated tailing edge. Nav. Ord. Test Sta. N A V W E P S Rep. no. 7571.Google Scholar
Jones, R. T. & Cohen, Doris 1960 High Speed Wing Theory, p. 23. Princeton University Press. (See also Vol. VII of High Speed Aerodynamics and Jet Propulsion, Princeton University Press).
Kellogg, O. M. 1929 Foundations of Potential Theory, p. 353. Berlin: Springer Verlag.
Lang, T. G. 1959 Base-vented hydrofoils. Nav. Ord. Test Sta. N A V O R D Rep. no. 6606.Google Scholar
Lang, T. G., Daybell, D. A. & Smith, K. E. 1959 Water-tunnel tests of hydrofoils with forced ventilation. Nav. Ord. Test Sta. N A V O R D Rep. no. 7008.Google Scholar
Parkin, B. R. 1956 Experiments on circular arc and flat plate hydrofoils in noncavitating and full cavity flows. Calif. Inst. Tech. Hydro. Lab. Rep. no. 47–6.Google Scholar
Thwaites, B. (Ed.) 1960 Incompressible Aerodynamics. Oxford University Press.
Tulin, M. P. 1953 Steady two-dimensional cavity flows about slender bodies. David Taylor Model Basin Rep. no. 834.Google Scholar
Woods, L. C. 1953 Theory of aerofoils on which occur bubbles of stationary air. Aero. Res. Counc., Lond., Rep. & Mem. no. 3049.Google Scholar
Wu, T. Yau-Tsu 1955 A free streamline theory for two-dimensional fully cavitated hydrofoils. Calf. Inst. Tech. Hydro. Lab. Rep. no. 21–17.Google Scholar
Wu, T. Yao-Tsu 1956 A note on the linear and nonlinear theories for fully cavitated hydrofoils. Calif. Inst. Tech. Hydro. Lab. Rep. no. 21–22.Google Scholar
Wu, T. Yau-Tsu 1957 A simple method for calculating the drag in the linear theory of cavity flows. Calif. Inst. Tech. Engng Div. Rep. no. 85–5.Google Scholar