A theory for hydrofoils of finite span

Abstract

The program of this report is as follows: After a brief survey of the available theoretical and experimental information on the characteristics of hydrofoils, the theory for a hydrofoil of finite span will be formulated. The liquid medium is assumed to be incompressible and nonviscous and of infinite depth. The basic concept of the analysis is patterned after the famous Prandtl wing theory of modern aerodynamics in that the hydrofoil of large aspect ratio may be replaced by a lifting line. The lift distribution along the lifting line is the same as the lift distribution, integrated with respect to the chord of the hydrofoil, along the span direction. The induced velocity field of the lifting line is then calculated by proper consideration of lift distribution along the lifting line, free water surface pressure condition and wave formation. The "local velocity" so determined for flow around each local section perpendicular to the span of the hydrofoil can be considered as that of a two-dimensional flow around a hydrofoil without free water surface. The only additional feature of the flow in this sectional plane is the modification of the geometric angle of attack, as defined by the undisturbed flow, to the so-called effective angle of attack on account of the local induced velocity. Thus the local sectional characteristics to be used can be taken as those of a hydrofoil section in two-dimensional flow without free water surface but may involve cavitation. More precisely, the hydrofoil section at any location of the span has the same hydrodynamic characteristics as if it were a section of an infinite span hydrofoil in a fluid region of infinite extent at a geometric angle of attack equal to ae, together with proper modification of the free stream velocity. Such characteristics may be obtained by theory or by experiment and should be taken at the same Reynolds number and cavitation number. With this separation of the three-dimensional effects and the two-dimensional effects, the effects of Froude number are singled out. Thus a systematic and efficient analysis of the hydrofoil properties can be made.