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Ocean Engineering 35 (2008) 117130

Computational hydrodynamic analysis of the propellerrudder and the

AZIPOD systems

Hassan Ghassemi, Parviz Ghadimi

Department of Marine Technology, Amirkabir University of Technology, Hafez Ave, No 424, P.O. Box 15875-4413, Tehran, Iran

Received 20 November 2006; accepted 13 July 2007

Available online 27 July 2007

Abstract

A computational method has been developed to predict the hydrodynamic performance of the propellerrudder systems (PRS) and

azimuthing podded drive (AZIPOD) systems. The method employs a vortex-based lifting theory for the propeller and the potential

surface panel method for the steering system. Three propeller models along with three steering systems (rudder and strut, flap and pod

(SFP)) are implemented in the present calculations for the cases of uniform and non-uniform conditions. Computed velocity components

show good agreement with the experimental measurements behind a propeller with or without the rudder. Calculated thrust, torque and

lift also agree well with the experimental results. Computations are also performed for an AZIPOD system in order to obtain the pressure

distributions on the SFP, and the hydrodynamic performance (thrust, torque and lift coefficients). The present method is useful for

examining the performance of the PRS and AZIPOD systems in the hope of estimating the propulsion and the maneuverability

characteristics of the marine vehicles more accurately.

r 2007 Elsevier Ltd. All rights reserved.

Keywords: Hydrodynamic analysis; Propellerrudder; AZIPOD

1. Introduction

Propellerrudder systems (PRS) are located behind a

ships stern where they encounter large wake flow. Due to

the hulls presence, the flow distribution into the propeller

is non-uniform and unsteady. Recent improvements made

in the electrical propulsion by the engine manufacturers

provide the azimuthing podded drive (AZIPOD) systems

which are compact propulsion systems, and give excellent

maneuverability. The most significant hydrodynamic ad-

vantage of the AZIPOD system is that the propeller is setin a more regular flow. It utilizes a smaller rudder, i.e. the

flap, located at the trailing edge of a vertical hydrofoil, and

the strut, situated in a similar arrangement as a flap on an

airplane wing, The flap and strut mechanism provides

greater propulsion efficiency and excellent maneuverabi-

lity. The flap is generally used for high-speed crafts when

the pod needs to be locked in neutral position, but could

also function as a controlling element for the course

keeping task.

Until now, hydrodynamics investigations of the propeller

rudder systems, by virtue of different methodologies, have

mainly concentrated on the PRS propulsors. A theoretical

treatment of the propeller and rudder was initially

conducted by Yamazaki (1968) and later numerically by

Yamazaki et al. (1985). Tamashima et al. (1993) and

Matsui et al. (1994) evaluated the PRS propulsion systems

under uniform flow conditions. Matsui et al. (1994) applied

this method in the context of the ship maneuverabilitytaking into account free surface effects. Molland and

Turnock (1993, 1996) investigated experimentally the

propellerrudder performance in the wind tunnel and

developed the propeller theory and rudder lifting line

theory to predict forces on a rudder in a propeller

slipstream. Li (1996) also investigated the propellerrudder

interactions by applying the lifting line theory for the

propeller and the vortex lattice method for the rudder.

For the AZIPOD systems, efficient numerical schemes

are scarce. Rains et al. (1981) applied empirical formulas to

ARTICLE IN PRESS

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0029-8018/$ - see front matter r 2007 Elsevier Ltd. All rights reserved.

doi:10.1016/j.oceaneng.2007.07.008

Corresponding author. Tel.: +982166419615; fax: +982166413028.

E-mail address: gasemi@aut.ac.ir (H. Ghassemi).

http://www.elsevier.com/locate/oceanenghttp://dx.doi.org/10.1016/j.oceaneng.2007.07.008mailto:gasemi@aut.ac.irmailto:gasemi@aut.ac.irhttp://dx.doi.org/10.1016/j.oceaneng.2007.07.008http://www.elsevier.com/locate/oceaneng

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estimate the drag coefficients of different parts of the strut,

flap, and pod (SFP). Wang et al. (2004) investigated

experimentally and numerically (panel code) the push and

pull configurations of the podded propulsion system andthe effect of the pod geometry on the hydrodynamic

performance of the whole system.

More recently, due to the market needs and in order to

gain more efficiency by the AZIPOD systems, marine

researchers have rigorously pursued this topic and much

effort has been devoted to explore it numerically and

experimentally. During the past two years, the 1st and 2nd

T-Pod conferences have been held at the University of

Newcastle (UK) and Universite de Bretagne Occidentale

Brest (France) in 2004 and 2006, respectively, and many

researchers (like Ma et al., 2004; Mohammed Islam et al.,

2004; Sakir Bal et al., 2006; Zhang Lijun and Wang

Yanyin, 2006) presented their latest findings.

Hydrodynamic design of the propellerpod-strut system

has not thus far been adequately explored. It is indeed

imperative that we use more reliable procedures in the

design of such a propulsion system in order to increase the

propulsion efficiency. In an attempt to meet these needs,

the present paper introduces a numerical procedure which

analyzes the hydrodynamic performance of the PRS

and the AZIPOD systems. The method applies Yamazaki

et al.s (1985) method for the analysis of the propeller and

the potential-based boundary element method (so-called

panel method) for the steering system. This combined

method could not only emulate the hydrodynamic behavior

of the simple PRS systems, but also could quite satisfacto-

rily predict the hydrodynamic performance of the more

complex and involved AZIPOD systems. In this work, the

effect of the steering system is also examined on both typesof the propulsors as well as the interactions occurring at

different operating conditions.

2. Prediction method

2.1. Formulation of the problem

2.1.1. Coordinate system

In order to study the flow fields around a rotating

propeller and steering system in a steady flow, a

rectangular coordinate system O-XYZ and a cylindrical

coordinate system O-Xry are defined in space. The origin is

located at the center of the propeller and the X-axis

coincides with the propeller shaft axis as shown Fig. 1. The

steering post is placed behind the propeller and is parallel

to the Z-axis. The distance between the post and the

propeller is X XRud.

2.1.2. Inflow velocity onto the propeller

The propeller is assumed to rotate with a constant

angular velocity o around the X-axis in the negative

direction ofy. Denoting the components of the steady non-

uniform velocity field towards the propeller in the

Cartesian coordinates by (uPX, uPY, uPZ) and in the

cylindrical coordinates by (vPX, vPr, vPy), they are expressed

ARTICLE IN PRESS

Nomenclature

a0(r) geometric pitch of the propeller

a(r) effective pitch of the propeller

c(r) propeller chord length at r

cM(r) distance from leading edge to maximum thick-ness

CP pressure distribution coefficient

D propeller diameter

FRY rudder lift

h(r) pitch of the free vortex

kN(r) Prandtls tip correction factor

MP radial number of intervals

n revolutions per second

N number of propeller blades

nq normal vector

NP circumferential number of intervals

Pi pressure at center of each panel

P0 atmospheric pressureP propeller pitch

PU upper-side pressure

PL lower-side pressure

Q propeller torque

rB hub radius

R propeller radius

SB body surface (steering system)

SW wake surface

SN

outer control surface

T propeller thrust

tL(r) distance from LE to base line at r

tT(r) distance from TE to base line at rtmax(r) maximum thickness at r

tan ag zero lift angle from the base line~V0 upstream inflow velocityV measured axial mean velocity~Vr induced radial velocity~VP inflow velocity to propeller~VR inflow velocity to rudder~VX induced axial velocity~Vt induced tangential velocityXRud propellerrudder stock distance

dF flap angle

dR rudder angle

fP velocity potential on propellerfR velocity potential on rudder

fR right-side potential

fL left-side potential

r water density

G(r,y) strength of bound vortex

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as components of the vector:

~vP vPX; vPr; vPy uPX; uPY sin y

uPZ cos y; 2prn uPY cos y uPZ sin y. 1

In the case of steady and uniform flow, the inflow

velocity simplifies to

~vP vPX; vPr; vPy V0; 0; 2prn, (2)

where V0 is the speed at which water is moving onto the

propeller and n is the propeller rotational speed.

2.2. Vortex-based lifting theory for the propeller

2.2.1. Vortex and potential calculations

The propeller is represented by the vortex system. This is

composed of the bound vortex arranged in the radial

direction on the propeller (it is assumed that the propeller

is replaced by the infinitely many blade-like actuator discs)

and the free vortex shedding from the bound vortex. The

free vortex is distributed on the helical surface with

pitch 2ph(r) without contraction. The strength of the

bound vortex G(r,y) and the velocity potential fP are

determined by the equations of the propeller theory and the

kinematic boundary condition (KBC). An iterative proce-

dure is used to obtain converged values of h(r) on the bladeradius.

The velocity potential fP due to the bound vortex on the

propeller may be expressed (Yamazaki, 1968) as

fP

ZRrB

r0 dr0Z2p

0

Gr0; y0GPx; r; y; r0; y0 dy0, (3)

where

GPx; r; y; r0; y0

r0

hr0

1

RP

r cos y sin y0 r sin y cos y0

R2P X

21

X

RP 4

and

RP

ffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiX2 Y r0 sin y02 Z r0 cos y02

q.

Other parameters of the Eqs. (3) and (4) are identified in

Fig. 2.

2.2.2. Kinematic boundary condition

The propeller is considered to have a finite number of

blades and a finite chord length. Under these assumptions,

the KBC on the blade is expressed as

2

ffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffir2 ar2

qNk1cr

r2 hr2

2rhrkNr

0@

1AGr; y

qfPqX

P

hr

r

qfPrqy

P

ar

rvPy vPX, 5

where a(r) is the effective pitch angle and is defined by

ar ka0r r tan ag

1 a0r=r tan ag;

tan ag 2k0tr=cr

1:5 cMr=cr

tLr tTr

cr,

tr tmaxr

2 1

cMr

cr

tLr

cMr

crtTr, 6

kNr 2

pcos1 exp N 1

r

R

ffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiR2 hr2q

2hr

8