Proceedings of the Thirty-second (2022) International Ocean and Polar Engineering Conference
Shanghai, China, June 5–10, 2022
Copyright © 2022 by the International Society of Offshore and Polar Engineers (ISOPE)
ISBN 978-1-880653-81-4; ISSN 1098-6189

www.isope.org

Numerical Investigation of Propeller-Rudder Interaction Based on Induct Factor Fitting Body Force
MethodMingzhe Wang, Jianhua Wang*, Decheng Wan
Computational Marine Hydrodynamics Lab (CMHL), School of Naval Architecture, Ocean and Civil Engineering,
Shanghai Jiao Tong University, Shanghai, China* Corresponding Author

ABSTRACT

directly involved in solving momentum equation.

Using body force model based on blade element momentum theory
instead of real propeller model can save considerable computational
resources. However, due to the simplification of propeller geometry
and the inapplicability of ideal fluid theory in viscosity solver,correction methods should be put forward to reduce the error. In thispaper, the induct factor distribution is obtained by the projection model,
and the numerical simulation of the propeller-rudder interaction
between KP505 propeller and NACA0018 section rudder is carried out
under five working conditions: J=0.1, 0.3, 0.5, 0.7 and 0.9. The results
show that the body force model can capture the influence of nonuniform inflow, and the pressure distribution of rudder surface obtainedby the two models are similar, which proves the capability of the bodyforce model at different working conditions.

As a body force model with moderate complexity and accuracy, bladeelement momentum theory has great application potential. In viscous
flow CFD solver, there are two main problems to be solved in utilizing
body force model based on traditional blade element momentum theory.
One of the problem is that the airfoil data obtained based on windtunnel tests are for the infinite airfoil with a given Reynolds number,and ignoring the three-dimensional effect. It means that direct
calculation of propeller performance will lead to errors (Benini, 2004),
which need to be corrected in practical application (MacNeill, 2017;Ortolani et al., 2018). Another problem is the way to calculate inflow
velocity. If the foil performance was calculated by “inflow velocity”(far field velocity), the relationship between “local velocity” and“inflow velocity” must be established to get foil performance at
specific working condition because the velocity field at propeller plane
is disturbed by the propeller. This bridging function is assumed byinduct factors. Traditionally, induct factors are derived iteratively basedon ideal thruster theory, and does not consider the viscous effect andthree-dimensional effect of the fluid. Thus, there will be an error
between the result and the actual situation in RANS solver. These twoconstraints make the curve of blade element momentum theory’s error
and advance ratio like a “V” shape. There will be an advance ratio J0
corresponding to the minimum error, and when the advance ratio isabove or lower than J0, the error will increase, which means thismethod can not meet propeller performance in different advance ratio
conditions at the same time (Benini, 2004).

KEY WORDS: Blade element momentum theory; propeller-rudderinteraction; body force; OpenFOAM; numerical simulation.

INTRODUCTION
Rudder is one of the most important appendages for ship maneuvering.
In order to improve the rudder efficiency, the propeller is usuallyplaced in front of the rudder to bring a higher inflow speed. This causes
the inflow region of rudder being disturbed by the propeller. Propeller
and rudder interference study needs a lot of experimental data support,
which is a complex test. Computational Fluid Dynamics (CFD) is a
developed method to research propeller-rudder interaction without
expensive laboratorial equipment (Badoe et al., 2015). However, thetime step and mesh size are limited due to the high rates rotating
motion and complex geometric structure of the real propeller model,
which makes direct numerical simulation very expensive. At the sametime, it is generally not necessary to obtain all the details of the flow
field in the long-time maneuverability test (Broglia et al., 2012), suchas the interaction between the vortices separated by the rotating
propeller and the aligned rudder. Therefore, body force model wasproposed to replace the real propeller model, which as a source termWith the increasing accuracy of real propeller model, a direct
projection model based on radial distribution of real propeller load isbeing widely used. The recent researches show that the body force
model based on the radial distribution of real propeller load can beapplied to some simple simulation (Villa et al., 2018; Bruzzone et al.,2014). However, this method uses two assumptions: The influence offlow field disturbance on propeller load is not considered, and thepropeller load is uniformly distributed in circumferential direction,
which means that this method cannot consider the influence of the3700