DUCTED SHIP PROPELLERS IN RADIALLY SHEARED FLOWS

We consider the linearized Euler equations and the continuity equation by the assumptions of a large shear and small perturbation velocities of ducted propeller.;We treat integral equations as linear simultaneous equations using the far field boundary condition.;Duct and propeller are treated separately to obtain perturbation velocities of each with and without shear flow and these are then combined for the design problem of ducted propellers.;The loading on the duct is taken as the roof-top distribution and loading on the propeller disk is assumed to be an arbitrary distribution with the proviso that the combined loading can produce the designed thrust coefficient.;Manipulating the Euler equations and the continuity equation in cylindrical coordinates for axisymmetric shear flow a Poisson type equation involving the disturbance pressure can be obtained. A formal reduction of this equation yields an integral equation in the pressure, which can be converted to a manageable non-homogeneous integral equation by means of a Fourier transform.;Each component of the induced velocities is calculated from the original Euler equations and continuity equation and the pressure distribution in the absence and presence of shear. Duct thickness effects with shear are discussed.;A design method for ducts is provided for flows with and without shear from the exact second order kinematic boundary condition on the duct surface for given propeller thrust coefficients and duct thrust coefficients are calculated in both with- and without-shear-flow cases. Significant effects of shear are noted in the derived duct geometry.