This paper presents two numerical methods, a Vortex-Lattice Method (VLM) based potential solver (named MPUF3A) coupled with a Finite Volume Method (FVM) based Euler solver (named GBFLOW), and a Boundary Element Method (BEM) based potential solver (named PROPCAV), which can predict the wetted and cavitating performance of ducted propellers. For the first approach, VLM is applied to model the propeller, and FVM is used to analyze the whole flow field with the duct. Those two methods are coupled together to include the interaction between duct and propeller. By distributing the line vortices and the line sources on the camber surface, MPUF3A solves the potential flow around the propeller, and as a result the pressure and cavitation patterns on the blade surface are determined. The duct is modeled as a solid boundary in GBFLOW which solves the Euler equations with body force term converted from pressures evaluated in MPUF3A. The solution of the Euler equation would bring the total velocity distribution. An effective wake field is determined by subtracting the induced velocity from the total velocity, and the predicted effective velocity is used by MPUF3A to predict the updated pressure distributions. In this way, both the duct (as solid boundary) and propeller (as body forces) are included in the fluid domain simultaneously and the flow and body forces are updated iteratively. The solution converges when the predicted thrust is stabilized within an acceptable tolerance. A general image model is applied to include the duct wall effect, and the viscous effect is modeled by the discharge model when the gap region between duct inner surface and propeller tip is small. For the second approach, a Boundary Element Method is applied to predict the cavitating performance of ducted propeller, in which the propeller and duct are paneled and solved simultaneously by applying the appropriate boundary conditions. The blade sheet cavity is determined by applying the dynamic and the kinematic boundary conditions on the cavity surface. The potential on the cavity surface is known from the dynamic boundary condition and the relation between cavitation number and cavity velocity. Once the boundary value problem is solved for the unknowns, i.e. the potentials on the wetted blade surface and the normal derivative of potentials on the cavity surface, the new cavity shape is adjusted by using the normal derivative of the potential. The procedure is repeated until the cavity shape converges and the pressure on the cavity becomes constant and equals to the vapor pressure. The present methods have been validated by comparing the predicted forces with those measured in experiments, and the cavity patterns and forces predicted from the two methods have been compared to each other.
Numerical Modeling of Ducted Propellers
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Kinnas, SA, Lee, H, & Gu, H. "Numerical Modeling of Ducted Propellers." Proceedings of the ASME 2005 Fluids Engineering Division Summer Meeting. Volume 1: Symposia, Parts A and B. Houston, Texas, USA. June 19–23, 2005. pp. 1115-1125. ASME. https://doi.org/10.1115/FEDSM2005-77047
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