Numerical modeling of flow around ducted propellers
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An iterative method, coupling a vortex lattice method (VLM) based potential solver and a finite volume method (FVM) based Euler solver, is used to model the flow around ducted propellers. The VLM is applied to the blade inside the duct, solves for the potential flow in the vicinity of the blade and predicts the pressures, forces, moments and cavity patterns. The FVM is applied to the whole fluid domain with the duct. The Euler equations are solved with the pressure difference across the blades being converted into body force terms and the duct being modeled as solid wall boundaries. The effective velocities are then evaluated by subtracting the induced velocities from the total velocities. The VLM is applied again with the updated effective velocities and the iteration between VLM and FVM continues until the thrust and torque converge. The interaction between duct and propeller is included with such an iterative procedure. Some special treatments on the ducted propeller are presented. A simplified image model is applied to account for the nonaxisymmetric duct wall effects. A gap model, based on an orifice equation, is implemented to predict the influence of the viscous gap region on the overall performance of ducted propellers. A computational viscous model is used to assess the discharge coefficient in the current method. Some approaches to predict the effective velocities with accuracy are discussed. Systematic validations for the current method with other numerical methods and experiments are given. Finally an approach to model the tip leakage vortex is presented. The tip leakage vortices are aligned via a free wake relaxation method. Convergence and parameter studies are given for this model.