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1967•Journal of Fluid MechanicsRequires access

Two supercavitating hydrofoils near a free surface

T. Green, Robert L. Street

Open publisher page 18 citations

Abstract

A two-dimensional, incompressible, irrotational, linearized flow model is employed in this analysis of two supercavitating, flat-plate hydrofoils in the presence of a free surface. The cavities are taken to have finite lengths, and gravity is neglected. The ensuing boundary-value problem is converted, by means of conformal mapping, to a mixed-boundary-value problem for the complex velocity in the upper half-plane. This altered problem is solved by use of the methods of thin-aerofoil theory and the solution involves digital-computer evaluation of a large number of incomplete elliptic integrals of the first and third kinds. Typical results are presented in graphs, and the results of the present work are compared with Yim's (1964) theory for a single supercavitating body near a free surface.

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What this paper is about

A two-dimensional, incompressible, irrotational, linearized flow model is employed in this analysis of two supercavitating, flat-plate hydrofoils in the presence of a free surface. The cavities are taken to have finite lengths, and gravity is neglected. The ensuing boundary-value problem is converted, by means of conformal mapping, to a mixed-boundary-value problem for the complex velocity in the upper half-plane. This altered problem is solved by use of the methods of thin-aerofoil theory and the solution involves digital-computer evaluation of a large number of incomplete elliptic integrals of the first and third kinds. Typical results are presented in graphs, and the results of the present work are compared with Yim's (1964) theory for a single supercavitating body near a free surface.

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Available abstract

A two-dimensional, incompressible, irrotational, linearized flow model is employed in this analysis of two supercavitating, flat-plate hydrofoils in the presence of a free surface. The cavities are taken to have finite lengths, and gravity is neglected. The ensuing boundary-value problem is converted, by means of conformal mapping, to a mixed-boundary-value problem for the complex velocity in the upper half-plane. This altered problem is solved by use of the methods of thin-aerofoil theory and the solution involves digital-computer evaluation of a large number of incomplete elliptic integrals of the first and third kinds. Typical results are presented in graphs, and the results of the present work are compared with Yim's (1964) theory for a single supercavitating body near a free surface.

Key concepts: Supercavitation, Free surface, Conservative vector field, Airfoil, Velocity potential, Conformal map, Surface (topology), Potential flow

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