The Hydrofoil with Finite Cavity in a Solid-Wall Channel

The asymmetrical fully cavitating linearized flow about an arbitrarily shaped slender hydrofoil placed anywhere in a solid-wall channel is considered as a doubly connected region problem. The method of solution involves conformal mapping and a generalization of the Plemeli formulas to doubly periodic functions. The velocity field is expressed in terms of Jacobi's that a functions with the nome q of these functions related directly to the cavity-length/channel-width ratio. Explicit results are obtained for a fully cavitating flat plate at small angles of attack in a midchannel position. For small q, simple wall effect correction terms are obtained for the cavity length and the lift coefficient as a function of cavitation number. These correction terms are correct up to and including third order in q and require no quadratures. For large values of the cavity-length/channel-width ratio (q close to unity) the asymptotic choked flow solution is used to compute the blockage cavitation number and the lift coefficient for the choked flow.