Hostname: page-component-7b7567c8c-wxvwp Total loading time: 0 Render date: 2026-11-14T16:02:59.538Z Has data issue: false hasContentIssue false
  • English
  • Français

A linearized theory for rotational supercavitating flow

Published online by Cambridge University Press:  28 March 2006

Robert L. Street
Robert L. Street
Affiliation:
Department of Civil Engineering, Stanford University
Get accessRights & Permissions [Opens in a new window]

Abstract

In this paper methods are given for establishing qualitative and quantitative measures of the effects of rotation in supercavitating flows past slender bodies. A linearized theory is developed for steady, two-dimensional flow under the assumption that the flow has a constant rotation throughout. The stream function of the rotational flow satisfies Poisson's equation. By using a particular solution of this equation, the rotational problem is reduced to a problem involving Laplace's equation and harmonic perturbation velocities. The resulting boundary-value problem is solved by use of conformal mapping and singularities from thinairfoil theory. The theory is then applied to asymmetric shear flow past wedges and hydrofoils and to symmetric shear flow past wedges. The presence of rotation is shown to create significant changes in the forces acting on the slender bodies and in the shape and size of the trailing cavities.

Information

Type
Research Article
Information
Journal of Fluid Mechanics , Volume 17 , Issue 4 , December 1963, pp. 513 - 545
Copyright
© 1963 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

Acosta, A. J. 1961 The effect of a longitudinal gravitational field on the supercavitating flow over a wedge. J. Appl. Mech. 28, 188.Google Scholar
Chen, C. F. 1962 Second-order supercavitating hydrofoil theory. J. Fluid Mech. 13, 321.Google Scholar
Fabula, A. G. 1962 Thin-aerofoil theory applied to hydrofoils with a single finite cavity and arbitrary free-streamline detachment. J. Fluid Mech. 12, 227.Google Scholar
Geurst, J. A. 1961 Linearized theory of two-dimensional cavity flows. Doct. Diss., Technische Hogeschool Te Delft.
Geurst, J. A. and Timman, R. 1956 Linearized theory of two-dimensional cavitational flow around a wing section. IXth International Congress of Appl. Mech., Brussels.
Parkin, B. R. 1957 A note on the cavity flow past a hydrofoil in a liquid with gravity. Calif. Inst. Tech. Engng Div. Rev. no. 47-9.Google Scholar
Parkin, B. R. 1959 Linearized theory of cavity flow in two-dimension. RAND Corp. Rep. no. P-1745.Google Scholar
Street, R. L. 1962 A linearized theory for rotational, supercavitating flow. Stanford Univ. Civil Engng Dept. Rep. no. 16.Google Scholar
Tsien, H.-S. 1943 Symmetrical Joukowsky airfoils in shear flow. Quart. Appl. Math. 1, 130.Google Scholar
Tulin, M. P. 1953 Steady two-dimensional cavity flows about slender bodies. David Taylor Model Basin Rep. no. 834.Google Scholar
Wu, T. Y. 1956 A note on the linear and nonlinear theories for fully cavitated hydrofolis. Calif. Inst. Tech. Hydro. Lab. Rep. no. 21-22.Google Scholar
Wu, T. Y. 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
Yih, C-S. 1959 Two solutions of inviscid rotational flow with corner eddies. J. Fluid Mech. 5, 36.Google Scholar