Second-order supercavitating hydrofoil theory

Abstract

The second-order problem of Helmholtz flow past lifting hydrofoils and symmetric struts has been formulated and solved. The solution involves elementary operations on the known solutions of the first-order problem. The second-order lift and drag coefficients are given in integral form. Results obtained for a flat plate at incidence and a symmetric wedge agree with the exact solutions up to the second order. In terms of quantitative improvements, the present second-order theory predicts a lift coefficient for a flat plate at 45° incidence with an error of 8%, and a drag coefficient for a symmetric wedge of 50° included angle with an error of 5%; the corresponding angles at which the linear theory would predict force coefficients incurring the same errors are 5° and 15° respectively.