A Lifting-Line Theory of a Wing in Exponential Shear Flow and Application to Supercavitating Hydrofoil

A lifting line theory of a wing in exponential shear flow is presented. The governing equation due to Chen et al. is reduced to two ordinary differential equations by separation of variables, and a general solution is obtained by linearly combining the fundamental solutions. Induced attack angle is derived from the general solution and the condition of far downstream, and relation of lift force to effective attack angle is described by the Taylor series expansion in the vicinity of geometrical attack angle. From the induced attack angle and the lift force, a lifting-line equation is derived, and solved by Gaussian elimination method. By applying the theory to supercavitating hydrofiol, the effects of shear parameter, cavitation number and aspect ratio are clarified through some numerical calculations.