A THEORY OF THE DUCTED PROPELLER WITH A FINITE NUMBER OF BLADES
CALIFORNIA UNIV BERKELEY INST OF ENGINEERING RESEARCH
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A theory for the ducted propeller is developed which is based on a linearized annular airfoil theory and a lifting-line propeller theory. The flow field of the annular airfoil is represented by a distribution of ring vortices and ring sources on a cylinder and where necessary a trailing vortex system. This approach allows the airfoil section to have an arbitrary shape although the annular airfoil itself is assumed to be axisymmetric. The ring source strength is shown to be a function of only the duct thickness while the ring vortex strength is a function of camber, thickness and the radial velocity induced on the cylinder by the propeller and duct trailing vortex system. In the presence of the propeller, two coupled singular integral equations are derived for the vortex strength which are reduced to two coupled Fredholm equations of the second kind. The flow field of the propeller is represented by a lifting line and a helicoidal trailing vortex system. By this approach, the problem reduces essentially to the propeller problem solved by Lerbs. The hub is treated by slender body theory which allows it to have an arbitrary axisymmetric shape. One consequence of using this theory is that the hub induces no tangential velocities.
- Marine Engineering