A new nonlinear vortex model is proposed to simulate flow around an arbitrarily loaded marine propeller. It uses a continuously distributed vorticity over the blade and hub surfaces, and free vortex: sheets representing the propeller wake. The definition of "nonlinear" implies that there are both load and geometrical nonlinearities: the propeller. load is arbitrary, including static operation; and the thickness of the blades is not small if compared with chord length. As a result, the bound vortices are not perpendicular to the incoming velocity vector but orthogonal to the local vector of resultant velocity (incoming + induced velocities). As for free vorticity, its vector is collinear with the resultant velocity everywhere in the propeller wake. The second nonlinearity leads to the necessity of the distribution of vortices over the blade surface (instead of chord surface). Because vortex singularities are used, the problem is formulated in terms of a vector potential. It is shown here that an additional component of induced velocity (so-called "relative eddy" component) occurs due to the rotation of the blade system. The introduction of this term is illustrated by the example of steady-state propeller motion in an unbounded inviscid fluid.
Flow Around Marine Propeller: Nonlinear Theory Based on Vector Potential
Mishkevich, Victor. "Flow Around Marine Propeller: Nonlinear Theory Based on Vector Potential." Paper presented at the SNAME 8th Propeller and Shafting Symposium, Virginia Beach, Virginia, USA, September 1997. doi: https://doi.org/10.5957/PSS-1997-23
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