Investigation on Propeller-Rudder Interaction by Numerical Methods

The axial forces in a propeller-rudder interactive system working in uniform flow are theoretically studied: In a steady linear method the propeller is represented by bound and free vortex systems, the rudder by vortex and source filaments and the rudder wake by free vortex filaments. A lifting-line analysis method predicts the propeller characteristics. A vortex lattice method determines the rudder vortex strengths. Comparisons of the axial forces with systematic experiments show a qualitative agreement. A thick rudder located in the accelerating flow just behind a propeller experiences a pressure drag. It is shown that this drag is an internal force which is counterbalanced by part of the increased propeller thrust. Due to the tangential velocities in the propeller slipstream a rudder thrust is created. The rudder in the test cases recovers 39% of the rotational energy, transforms 14% into radial energy and leaves 26% behind. The remaining 21% should in principle have transformed into axial energy but is missing according to the linear method. The drawback of the linear method is that the boundary conditions at the free vortex system of the propeller are not satisfied. A semi-nonlinear method is developed where the boundary condition that the static pressure is the same on the two sides of the free vortex sheet of a simplified propeller is fulfilled. As a result the strength-density variations of the propeller free vortex sheet due to the rudder disturbance are taken into account. The rudder thrust computed by the method is 4% lower than that given by a corresponding linear method for a propeller at CT=1.1. A nonlinear method is developed where also the boundary conditions of zero normal velocity at the propeller free vortex sheet is satisfied, resulting in a deformed slipstream. A smaller, improved rudder thrust is obtained. For a propeller at CT=1.1, the rudder thrust is 8% lower than that obtained by a corresponding linear method; For another propeller at CT=3.0, the rudder thrust is 21% lower than that obtained by a linear method.