A Note on the Linear and Nonlinear Theories for Fully Cavitated Hydrofoils


The lifting problem of fully cavitated hydrofoils has recently received some attention. The nonlinear problem of two-dimensional fully cavitated hydrofoils has been treated by the author, using a generalized free streamline theory. The hydrofoils investigated in Ref. 1 were those with sharp leading and trailing edges which are assumed to be the separation points of the cavity streamlines. Except for this limitation, the nonlinear theory is applicable to hydrofoils of arbitrary geometric profile, operating at any cavitation number, and for almost all angles of attack as long as the cavity wake is fully developed. By using an elegant linear theory, Tulin has treated the problem of a fully cavitated flat plate set at a small angle of attack and operated at arbitrary cavitation number. In the case of hydrofoils of arbitrary profile operating at zero cavitation number, some interesting simple relationships are given by Tulin for the connection between the lift, drag and moment of a supercavitating hydrofoil and the lift, moment and the third moment of an equivalent airfoil (unstalled). In the present investigation, Tulin's linear theory is first extended to calculate the hydrodynamic lift and drag on a fully cavitated hydrofoil of arbitrary camber at arbitrary cavitation number. A numerical example is given for a circular hydrofoil subtending an arc angle of 160, for which the corresponding nonlinear solution is available. A direct comparison between these two theories is made explicitly for the flat plate and the circular arc hydrofoil. Some important aspects of the results are discussed subsequently

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