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http://pim.sagepub.com/content/early/2011/08/27/1475090211413957The online version of this article can be found at:

DOI: 10.1177/1475090211413957

published online 12 September 2011Proceedings of the Institution of Mechanical Engineers, Part M: Journal of Engineering for the Maritime Environment

S BalA practical technique for improvement of open water propeller performance

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A practical technique for improvement ofopen water propeller performanceS Bal

Department of Naval Architecture and Marine Engineering, Istanbul Technical University, Maslak-Sariyer, Istanbul,

34469, Turkey. email: sbal@itu.edu.tr

The manuscript was received on 31 January 2011 and was accepted after revision for publication on 26 May 2011.

DOI: 10.1177/1475090211413957

Abstract: A practical technique for the improvement of open water propeller performancehas been described by using a vortex lattice lifting line method together with a lifting surfacemethod. First, the optimum circulation distribution, giving the maximum thrust–torqueratio, has been computed along the radius of the propeller for given thrust and chordlengths, by adopting a vortex lattice solution to the lifting line problem. Then, by using thelifting surface method, the blade sectional properties such as pitch-to-diameter ratio andcamber ratio, have been calculated for obtaining the desired circulation distribution. Theeffects of skew and rake on propeller performance have been ignored. The blades have beendiscretized by a number of panels extending from hub to tip. The radial distribution ofbound circulation can be computed by a set of vortex elements having constant strengths.Discrete trailing free vortex lines are shed at each panel boundary, and their strengths areequal to the differences in strength of the adjacent bound vortices. The vortex system hasbeen built from a set of horseshoe vortex elements, and they consist of a bound vortex seg-ment and two free vortex lines of constant strengths. Each set of horseshoe vortex elementsinduces an axial and tangential velocity at a specified control point on the blades. An alge-braic equation system can be formed by using the influencial coefficients. Once this equa-tion system has been solved for unknown vortex strengths and specified thrust, the optimumcirculation distribution and the forces can be computed by using Betz–Lerbs method. Whenthe radial distributions of optimum circulation (loading) and chord lengths have beenreached, the lifting surface method can be applied to determine the blade pitch and camberdistribution. DTMB 4119 and DTMB 4381 propellers have been adopted for calculations andtheir hydrodynamic characteristics have been found in their open literature. A very goodcomparison has been obtained between the results of this practical technique and theexperimental measurements.

Keywords: optimum ship propeller, propeller design, propeller analysis, vortex lattice method,

lifting surface method, lifting line method, Betz–Lerbs condition

1 INTRODUCTION

A ship (marine) propeller giving the highest propul-

sion efficiency (h= ðJs=2pÞðKT=KQ), i.e. maximum

thrust-to-torque ratio for a given advance coefficient),

is referred to as an optimal one. The objective of a

ship propeller design is to obtain the highest efficiency

(optimum propeller) subject to prescribed require-

ments from the hydrodynamic point of view if other

design principles are not set. It is also necessary to

have an optimized propeller for the optimal propul-

sion of ships. Thus, a reliable and effective numerical

technique is crucial for propeller design. This paper

addresses the calculation of pitch and camber distri-

butions along the radius of an optimum propeller in

steady flow by using a vortex lattice lifting line

method, together with a lifting surface method. The

effects of skew and rake on the propeller are ignored.

1

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A literature review on the design for a ship pro-

peller working in open water can be summarized as

follows. The actuator disc was one of the earliest

and simplest theories for propeller analysis and is

the limit case of a propeller with the highest effi-

ciency at a specified thrust [1]. It corresponds to the

case of no hub with infinite number of blades and

infinitesimally small advance coefficient and chord

lengths. The optimum circulation distribution on a

propeller with a duct of finite length was deter-

mined by Sparenberg [2]. He discussed the effects of

tip clearances and hub diameter. Yim [3] later

included frictional drag and cavity drag in his analy-

sis of optimum radial load distribution. A vortex

lattice method to analyse and design a marine pro-

peller was used in references [4] and [5], respec-

tively. The continuous singularities on the lifting

surfaces (blades) are represented by a set of vortex/

source lattices. The blade loading and vorticity in the

trailing wake were represented by vortex lattices dis-

tributed on the mean camber surface while the blade

thickness was accounted for by adding thickness

source panels. A review of the hydrodynamic aspects

of marine propellers up to the mid-1980s (1986) was

published by Kerwin [6]. An extensive overview of

the hydrodynamics of ship propellers was presented

in the book by Breslin and Andersen [7].

Coney [8] later developed a design method for

optimal circulation distribution based on variational

optimization. He represented the propeller by con-

centrated lifting lines (horseshoe vortex elements)

and described the thrust and torque as functions

of horseshoe strengths that were solved for con-

strained optimization. The method was applicable

to multi-component propulsors, such as ducted

propellers and the propeller–stator combination.

The method was furthermore easily extended to

include the effects of hub and duct by using the

generalized image method [9]. An unsteady propel-

ler design method which was intended to optimize

the cavitation inception speed was developed in ref-

erence [10]. Kuiper and Jessup [10] focused on

blade section design. An artificial intelligence for the

preliminary propeller design was used by Dai et al.

[11]. They discussed the numerical optimization

and genetic algorithms [11]. On the other hand, the

axisymmetric RANS (Reynolds averaged Navier–

Stokes) calculation and the vortex lattice design

method was coupled by Kerwin et al. [12]. In this

method, while the effective wake input for the vor-

tex lattice design method is provided by RANS com-

putation, the propeller force is transferred as the

body force to the RANS domain. Mishima and

Kinnas [13, 14] developed a numerical method to

determine the blade geometry with the best

efficiency for specified thrust and cavity size con-

straints. The propeller performance was described

as a function of design variables whose combination

determined the blade geometry. The unsteady pro-

peller analysis algorithm was coupled with a con-

strained non-linear optimization algorithm. Griffin

and Kinnas [15] further improved the propeller

analysis and design methods. In particular, the anal-

ysis method was improved in such a way that the

cavity search algorithm was included along the

blade section. The design method was also extended

to include the skew distribution and minimum pres-

sure constraint. The coupled axisymmetric RANS

calculation and vortex/source lattice method were

later applied to design ducted propellers in refer-

ence [16]. The further anlysis and design techniques

on ducted propulsors and viscous/inviscid interac-

tion can be found in references [17] and [18],

respectively.

In the present study, however, the hydrodynamic

improvement of the performance of a marine pro-

peller working in open water has been carried out in

two steps. First, a lifting line model has been used

to determine the optimum radial distribution of cir-

culation over the blades that produce the desired

thrust with the highest propulsion efficiency.

Second, the shape of the blades (pitch and camber

distributions) that produce this desired distribution

of circulation, has been determined. The effects of

skew and rake have not been considered in this

stage of the present study. The vortex lattice solu-

tion (PVL code [1]) to the lifting line problem of the

propeller, in which the blades have been considered

to have concentrated lines of bound vortices, has

been used to predict the optimum circulation distri-

bution over the blades in this study [1]. However,

the lifting line theory cannot alone provide the

actual blade geometry, which produces the desired

circulation distribution. A more elaborate repre-

sentation of the propeller should be employed to

determine the blade pitch, chord, and camber distri-

bution in order to produce the desired circulation

over the blade. A lifting surface method which is

very similar to the one applied for the podded

propulsors in reference [19] has been used here for

this purpose. The blades have been modelled as

sheets of vortex/source singularities with unknown

strengths. The strengths can then be found by

applying the appropriate boundary conditions on

the blades. The steady loading as well as the unstea-

dy forces and cavitation characteristics on the

blades can also be predicted by this lifting surface

method. In the following sections, first the design

and analysis methods of the propeller are explained

in detail and later the application of these methods

2 S Bal

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to DTMB 4119 and DTMB 4381 propellers is shown

and the results are compared with those given in

the open literature.

2 PROPELLER DESIGN METHOD

The lifting line theory has been employed here to

represent the propeller as a set of number of blades

(NB), and straight and radial lifting lines. The lifting

lines represent the blades of the propeller. The blades

are equally loaded. The geometry (i.e. pitch, camber,

and chord) of the actual propeller is replaced by a

radial distribution of circulation. The lifting lines

rotate with angular velocity v around the x axis. The

lifting line starts at a hub radius rh and extends to the

propeller radius R. A cylindrical coordinate system (x,

r, u) is assumed to be rotating with the propeller.

Refer to references [1] and [8] for the details.

The strength of bound vortices on the blades is the

circulation distribution over the blades, G(r). The

shape of the free vortex wake is, however, assumed

to be helical. By the linear lifting line method, the

pitch (b(r)) of the helices can be determined by the

propeller’s rotation and undisturbed inflow

b rð Þ= tan�1 Va rð Þ

vr +Vt rð Þ

� �

(1)

where Va(r) is an effective axial inflow and Vt(r) is

the effective tangential inflow for each radius over

the blades. The shape of the helices can also be

aligned with the induced velocities at the lifting line.

For a propeller with optimum radial load distribu-

tion according to Betz condition [1], the efficiency

for each blade section should be constant and equal

tan b(r)

tan bi(r)= constant (2)

Here, bi is the hydrodynamic pitch angle and can

be given as

bi rð Þ = tan�1 Va rð Þ+u�a rð Þ

vr +Vt rð Þ

� �

(3)

where u�a rð Þ is the axially induced velocity due to

helical free vortex system. Similarly, the Betz condi-

tion can be extended to the case of non-uniform

axial inflow according to Lerbs condition [1]

tanb rð Þ

tanbi rð Þ= g

ffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi

1�wx rð Þp

(4)

Here, wx(r) = 1 2 [Va(r)/Vs], Vs is the ship speed,

and g is an unknown constant.

Expressions, on the other hand, for the forces act-

ing on radius r on the lifting line can be developed

from a local application of Kutta–Joukowsky’s law.

These forces can then be resolved into components

in the axial and tangential directions, integrated

over the radius, and summed over the number of

blades to produce the total propeller thrust and tor-

que values. Refer to references [1] and [8] for details

about the lifting line theory of propellers.

2.1 The vortex lattice solution to

lifting line problem

The continuous distribution of vortices along the

lifting line is discretized by vortex lattice elements

with constant strengths. The element arrangement

along the lifting line employs both uniform spacing

and cosine spacing. The induced velocity is calcu-

lated at control points located at mid-radius of each

panel. Thus the radius of each lifting line is divided

into M panels of length Dr and the continuous dis-

tribution of circulation over the radius can be

replaced by a stepped-like distribution. The value of

the circulation in each panel, G(i) is set equal to the

value of the continuous distribution at the control

points. Since the circulation is piecewise constant,

the helical free wake vortex sheet is replaced by a

set of concentrated, helical vortex lines shed from

each panel boundary. The strength of these trailing

vortices is equal to the difference in bound vortex

strength across the boundary. Therefore, it can be

considered that the continuous vortex distribution

is replaced by a set of vortex horseshoes. Each of

these horseshoes consists of a bound vortex fila-

ment and two helical trailing vortices.

The velocity induced at the lifting line by this sys-

tem of vortices can be computed using the very effi-

cient formulas given in reference [1]. They are not

repeated here. The velocity induced at a given point

is the summation of the velocities induced by each

of the vortex horseshoes

u�a½r(i)�[u

�a(i) =

X

M

m= 1

G(m)�u�a(i,m) (5)

u�t ½r(i)�[u�

t (i) =X

M

m= 1

G(m)�u�t (i,m) (6)

where u�a and u�

t are the axial and tangential compo-

nents of induced velocity, respectively. �u�a and �u�

t are

the axial and tangential components of induced

velocity at the control point at radius r(i) by a unit,

helical horseshoe vortex surrounding the control

point at r(m). Under this discrete model, the

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integrations for the total forces are replaced by the

summations over the number of panels. The code

PVL (propeller vortex lattice) is based on this

method and uses Betz–Lerbs condition to obtain the

optimum circulation distribution over the blades.

Here it is used to obtain the optimum circulation

distribution (i.e. maximum thrust-to-torque ratio)

for a given thrust. Refer to reference [1] for details of

the vortex lattice solution to the lifting line model

and PVL code.

3 PROPELLER ANALYSIS METHOD

A lifting surface method has been developed and

used to calculate the propulsive performance and

induced velocities due to the propeller as similar to

the one given in reference [19]. This model is based

on appropriate vortex and source–sink distribution.

The singularities are distributed on the mean lines

of the propeller blade sections. Thus, this method is

classified as a lifting surface method since the sin-

gularities (vortices and sources) are distributed on

the mean camber surface.

The vortices distributed over the blades are

divided into two parts: bound and trailing vortices.

The bound vortices, located in the radial direction,

are to simulate the load distribution on the propel-

ler blade. The trailing vortices are placed in the

direction of the flow, obtained from the different

intensities of adjacent bound vortex elements. A

number of source elements are taken at the adjacent

bound vortex to simulate the thickness of the blade.

The vortex strengths are calculated by solving a set

of simultaneous equations which satisfy the flow

tangency (kinematic boundary) condition at the

blade control points. The discretized form of the

kinematic boundary condition can be written asX

G

G vG � nm = � vin � nm �X

QB

QB vQ � nm

�X

QC

QC vQ � nm

(7)

where vG is the velocity vector induced by each unit

strength vortex element, vQ is the velocity vector

induced by each unit strength source element, nm is

the unit vector normal to the mean camber line or

trailing wake surface. The induced velocities due to

vortex elements of the lifting surface are calculated

using Biot–Savart’s law expressed as

V G =G

4p:Lxd

d3 (8)

where V G is induced velocity, G is circulation, L is

vortex length element, and d is distance between

the element and the field point. The induced veloci-

ties due to sources/sinks are also computed on the

basis of given source/sink intensity.

In the lifting surface method, the formation and

decay of the cavity can also occur instantaneously

depending only on whether the pressure exceeds the

vapour pressure. It is assumed that the cavity starts

at the leading edge of the blade and vanishes at the

cavity trailing edge. Cavity thickness varies linearly

along each cavity panel in the chord-wise direction.

However, the cavity characteristics of the propellers

(given in section 5) are not considered here. The

propellers here are assumed to be working under non-

cavitating conditions. It is also assumed that the vis-

cous force is computed based on the frictional drag

coefficient, Cf, which is applied uniformly on the

wetted surfaces of blades. Once the bound vortex ele-

ments intensity is obtained, then the velocity

induced by the propeller in any point in space can

be computed using five angular positions of the pro-

peller blade. Finally, the arithmetic average of these

five values becomes the induced velocity at the cor-

responding point. The forces on the propeller blade

are found by adopting the law of Kutta–Joukowsky. If

the propeller is working in a steady-state condition,

the forces on all blades are the same. Hence, the

force on the entire propeller is found by multiplying

each blade force by the number of blades. The hub

effect using the method of images can also be

included in the calculations. Refer to references [1],

[8], and [9] for details of the lifting surface method of

solution to the propeller analysis problem.

4 COMBINING PROPELLER DESIGN AND

ANALYSIS METHODS

The steps of hydrodynamic improvement of a

marine propeller performance can be simply

accomplished as follows.

1. First, the radial distribution of circulation over

the blades that will produce the required total

thrust with the maximum efficiency is estab-

lished using the propeller design method (PVL

code) for a given chord distribution. The radial

distribution of chord length is a necessary input

to the viscous force calculations of the circula-

tion optimization. In order to minimize viscous

drag forces it is desirable to keep propeller chord

length as short as possible. However, the

strength and cavitation considerations limit how

short these chord lengths may become. The

selection of these quantities, however, is not dis-

cussed at this stage of the present study. It is

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assumed that the initial chord length distribu-

tion is taken from the original propellers and

kept fixed during the calculations.

2. Then, the actual shape of the blade (pitch and

camber distribution over the blade) that will

produce the prescribed distribution of circula-

tion can be developed using the propeller analy-

sis method (lifting surface solution). A code for

the propeller analysis method (lifting surface

solution), is developed for this purpose. This

code changes automatically (in a systematic

way) the pitch distribution and camber distribu-

tion to produce the desired (optimum) circula-

tion distribution for given chord lengths. The

code runs very fast. It should however be noted

that the number of blades and the chord distri-

bution can be changed to produce the required

thrust value and to minimize the cavity forma-

tion in step one.

5 VALIDATION AND NUMERICAL RESULTS

5.1 DTMB 4119 propeller

First, the lifting surface method is applied for valida-

tion to a non-cavitating DTMB 4119 propeller [20].

The DTMB 4119 propeller has the following geo-

metric characteristics and working conditions.

1. The propeller inflow is uniform.

2. The propeller has three blades, NB=3.

3. The hub-to-diameter ratio is 0.2.

4. The blade geometries from reference [20] in

terms of radial distribution of the chord length

(c), camber (f), thickness (t), and pitch (P) are

shown in Table 1.

5. The blade sections are designed using NACA 66

modified profiles and a= 0.8 camber line [21].

6. The propeller has no skew and no rake.

The lifting surface analysis program is run for the

propeller under the above-mentioned conditions.

There are (N= 20) vortex lattices used along the

chord-wise direction and (M= 18) vortex lattices

used along the radius of the blades. The frictional

drag coefficient, Cf= 0.004, is used in the calcula-

tions. The perspective view of the DTMB 4119 pro-

peller with its wakes and the vortex elements used

in the lifting surface analysis program are shown in

Fig. 1. The thrust and torque coefficients (KT and

KQ) and efficiency h= Js=2pð Þ KT=KQ

� �

of the propel-

ler versus advance coefficients (Js) computed from

the analysis program are compared with those given

in reference [20], as shown in Fig. 2. The agreement

between the results of the analysis program and

those in reference [20] is satisfactory. Therefore, the

developed propeller analysis program is validated

Table 1 DTMB 4119 propeller geometry from refer-

ence [20]

r/R c/D P/D tmax/c fmax/c

0.20 0.3200 1.1050 0.2055 0.01430.30 0.3635 1.1022 0.1553 0.02320.40 0.4048 1.0983 0.1180 0.02300.50 0.4392 1.0932 0.0902 0.02180.60 0.4610 1.0879 0.0696 0.02070.70 0.4622 1.0839 0.0542 0.02000.80 0.4347 1.0811 0.0421 0.01970.90 0.3613 1.0785 0.0332 0.01820.95 0.2775 1.0770 0.0323 0.01630.98 0.2045 1.0761 0.0321 0.01451.00 0.0800 1.0750 0.0316 0.0118

XY

Z

BladesWakes

Fig. 1 Perspective view of DTMB 4119 propellerblades and wakes

JS

KT,

η

10KQ

0.4 0.5 0.6 0.7 0.8 0.9 1 1.1 1.20

0.1

0.2

0.3

0.4

0.5

0.6

0.7

0.8

0.9

1

0

0.05

0.1

0.15

0.2

0.25

0.3

0.35

0.4

0.45

0.5

0.55

0.6

0.65

0.7

0.75

0.8KT(Present Study)

10KQ(Present Study)

η (Present Study)

KTin [20]

10KQin [20]

η in [20]

Fig. 2 Comparison of KT, KQ, and h values with thosegiven in reference [20]

Technique for improvement of open water propeller performance 5

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for the DTMB 4119 propeller. The pressure contours

for advance coefficient value, Js= 0.8, are also shown

in Fig. 3 for completeness of the results. Note that

for this propeller, the pressure contours on all

blades and for all blade angles are identical, owing

to the steady and uniform incoming flow. In addi-

tion, the radial circulation distributions which are

non-dimensionalized by 2pRVR, (here VR is the

resulting velocity, VR =

ffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi

V 2S+ (0:7Dp n)2

h i

r

), are

given for various Js values in Fig. 4.

Then, the design technique is applied to the

DTMB 4119 propeller to check whether it is the

optimum one. The advance coefficient (Js) is

assumed to be equal to 0.833 (the design value). The

blade sections are designed with NACA 66 modified

profiles and a=0.8 camber line [21], as mentioned

above. The vortex lattice lifting line design program

(PVL code in reference [1]) is run for the DTMB 4119

propeller at the above given conditions. The radial

optimum circulation distribution for design Js=0.833

is shown in Fig. 5. The thrust and torque coefficients

are also included in the same figure. The frictional

drag coefficient, Cf= 0.004 is used. Then, the lifting

surface analysis program is run to obtain the opti-

mum radial circulation distribution for the same

chord length distribution as in PVL code. The radial

circulation distribution computed from the analysis

program is compared with those from the PVL code,

as shown in Fig. 5. The differences between the

results of the analysis program and the design pro-

gram are small. Thus, it can be stated that the blade

geometry given in Table 1 for DTMB 4119 propeller

is almost optimum under the above design condi-

tions. The thrust and torque coefficients from both

analysis and design programs are also included in

Fig. 5. Note that the thrust and torque coefficients

are also very close to each other. The pressure distri-

butions for strip number 10 by the propeller analysis

program are presented with various advance coeffi-

cients in Fig. 6. The strip number 10 is very close to

the section at r= 0.7R.

5.2 DTMB 4381 propeller

Later, the design technique is applied to the DTMB

4381 propeller for which the hydrodynamic

Z

r/R

0 0.5 1 1.5

0.2

0.4

0.6

0.8

1

1.2

1.4

1.6

1.8-Cp

0.525

0.356

0.186

0.016

-0.154

-0.324

-0.494

-0.664

-0.834

-1.004

-1.174

-1.344

-1.514

-1.684

-1.854

Back Side Face Side

Js=0.8

Fig. 3 Pressure contours on both sides of the bladesfor DTMB 4119 propeller at Js=0.8

AA A A A A A A A A A A A A A A

AA

r/R

100

Γ

0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 10

0.25

0.5

0.75

1

1.25

1.5

1.75

2

2.25

2.5

2.75

3

Js=0.5

Js=0.6

Js=0.7

Js=0.8

Js=0.9

Js=1.0

Js=1.1A

Fig. 4 Non-dimensional circulation distribution fordifferent advance coefficients for DTMB 4119propeller

r/R

100

Γ

0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1 1.10

0.1

0.2

0.3

0.4

0.5

0.6

0.7

0.8

0.9

1

1.1

1.2

Lifting Surface Method

PVL

Js=0.833

Lifting Surface Method PVLKT=0.1468 K

T=0.1500

KQ=0.0264 K

Q=0.0262

Fig. 5 Comparison of circulation distribution withPVL for the DTMB 4119 propeller

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characteristics and design conditions are given in

reference [20]. The DTMB 4381 propeller has the

following geometric characteristics and working

conditions.

1. The propeller is working under uniform inflow.

2. The propeller has five blades, NB=5.

3. The hub-to-diameter ratio is 0.2.

4. The blade geometries from reference [20] in

terms of radial distribution of the chord length

(c), camber (f), thickness (t), and pitch (P) are

shown in Table 2.

5. The blade sections are designed using NACA 66

modified profiles and a= 0.8 camber line [21].

6. The propeller has no skew and no rake.

The lifting surface analysis program is run for the

DTMB 4381 propeller under the above-mentioned

conditions. There are (N= 20) vortex lattices used

along the chord-wise direction and (M= 18) vortex

lattices used along the radius of the blades, similar

to the case of the DTMB 4119 propeller. The fric-

tional drag coefficient, Cf= 0.0035, is used in the cal-

culations. The perspective views of the propeller

with their wakes and the vortex elements used in

the lifting surface analysis program are shown in

Figs 7 and 8, respectively. The thrust and torque

coefficients (KT and KQ) and efficiency h=

Js=2pð Þ KT=KQ

� �

of the propeller versus advance

coefficients (Js) computed from the analysis pro-

gram are compared with those given in reference

[20], as shown in Fig. 9. The agreement between the

results of the analysis program and those in refer-

ence [20] is satisfactory, similar to the case of

the DTMB 4119 propeller. The radial circulation dis-

tributions which are non-dimensionalized by

2pRVR (here VR is the resulting velocity, VR =ffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi

V 2S + (0:7Dp n)2

� �

q

), are given for various advance

coefficients in Fig. 10.

The vortex lattice lifting line design program

(PVL code in reference [1]) is then run for the

DTMB 4381 propeller at the above given condi-

tions. The radial optimum circulation distribution

for the design Js = 0.889 is shown in Fig. 11. The

frictional drag coefficient, Cf = 0.0035 is used.

Then, the lifting surface analysis program is run to

obtain the optimum radial circulation distribution

for the same chord length distribution as in the

PVL code. The radial circulation distribution

computed from the analysis program is compared

with those from the PVL code, as shown in Fig. 11.

The differences between the results of the analysis

program and the design program are now signifi-

cantly higher. Thus, it can be stated that the blade

x/c

-Cp

0 0.25 0.5 0.75 1

-2

-1.5

-1

-0.5

0

0.5

1

1.5

Js=0.5

Js=0.7

Js=0.9

Strip 10

Fig. 6 Pressure distribution on strip 10 for differentadvance coefficients for the DTMB 4119propeller

Table 2 DTMB 4381 propeller geometry from refer-

ence [20]

r/R c/D P/D tmax/c fmax/c

0.20 0.1740 1.3320 0.2494 0.03510.25 0.2020 1.3380 0.1960 0.03690.30 0.2290 1.3450 0.1563 0.03680.40 0.2750 1.3580 0.1069 0.03480.50 0.3120 1.3360 0.0769 0.03070.60 0.3370 1.2800 0.0567 0.02450.70 0.3470 1.2100 0.0421 0.01910.80 0.3340 1.1370 0.0314 0.01480.90 0.2800 1.0660 0.0239 0.01230.95 0.2100 1.0310 0.0229 0.01281.00 0.0010 0.9950 0.0160 0.0123

X

Y

Z

Blades

Wakes

Fig. 7 Perspective view of the DTMB 4381 propellerblades and wakes

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geometry given in Table 2 for DTMB 4381 is not

an optimum propeller under the above design

conditions.

The code that calls the propeller analysis method

repeatedly was then run. This code changes

automatically (in a systematic way) the pitch distri-

bution to produce the desired circulation distribu-

tion for the given chord lengths over the blades. The

camber distribution was assumed to be fixed as a

first step in this specific application. The new

0 1V2

V1

1

X Y

Z

0

1

V2

V3

0V1

X

Y

Z

V2

-1

1

0V1

Y X

Z

-0.75 -0.5 -0.25 0.25 0.5 0.75

-0.20

-1

0.5

-10

-0.5

0.5

-0.2 0.201

0.5

0 V3

-0.5

V30

Fig. 8 Different views of the DTMB 4381 propeller and panels used on the blades

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circulation distribution is given as compared with

those of the PVL code in Fig. 12. Now, the agree-

ment between the results of the analysis program

and the design program is very satisfactory. It can

be said that the propeller with this new pitch distri-

bution, which is given in Fig. 13 (as compared with

those of original DTMB 4381 propeller), is the opti-

mum one. Note that the pitch distribution for the

original DTMB 4381 propeller increases slightly up

to r/R= 0.4 and then decreases gradually until the

tip of the blade. On the other hand, the pitch distri-

bution for the optimum propeller modified from

DTMB 4381 is increases up to r/R= 0.9 and then

decreases until the tip of the blade. Note also

that the pitch values are different for both original

and optimum propellers. The thrust and torque

coefficients from both the analysis and design pro-

grams are also included in Fig. 12. Note also that

the thrust and torque coefficients are very close to

each other. Moreover, the pressure distributions on

the optimum propeller for strip number 10 by the

propeller analysis program are presented as com-

pared with those of original DTMB 4381 propeller in

Fig. 14. The strip number 10 corresponds to the

same location on the blade as in the previous

Js

KT,

η

10KQ

0.4 0.5 0.6 0.7 0.8 0.9 1 1.10

0.1

0.2

0.3

0.4

0.5

0.6

0.7

0.8

0.9

1

0

0.1

0.2

0.3

0.4

0.5

0.6

0.7

0.8

0.9

1

KT(Present Study)

10KQ(Present Study)

η (Present Study)

KTin [20]

10KQin [20]

η in [20]

Fig. 9 Comparison of KT, KQ, and h values with thosegiven in reference [20]

r/R

100

Γ

0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1 1.10

0.1

0.2

0.3

0.4

0.5

0.6

0.7

0.8

0.9

1

1.1

1.2

1.3

1.4

1.5

Optimal Propeller (Present Technique)

PVL

Original DTMB 4381

Js=0.889

Lifting Surface MethodKT=0.1985

KQ=0.0386

PVLKT=0.1999

KQ=0.0372

Fig. 12 Circulation distribution compared by presentdesign technique and PVL for the DTMB 4381propeller

r/R

100

Γ

0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 10

0.5

1

1.5

2

2.5

3

Js=0.5

Js=0.6

Js=0.7

Js=0.8

Js=0.9

Js=1.0

Fig. 10 Non-dimensional circulation distribution fordifferent advance coefficients for the DTMB4381 propeller

r/R

100

Γ

0.2 0.4 0.6 0.8 1 1.20

0.1

0.2

0.3

0.4

0.5

0.6

0.7

0.8

0.9

1

1.1

1.2

PVL

Lifting Surface Method

Js=0.889

Fig. 11 Comparison of circulation distribution withPVL for the DTMB 4381 propeller

Technique for improvement of open water propeller performance 9

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example (DTMB 4119 propeller). Note that for the

optimum propeller the pressure difference near the

trailing edge of the blade sections is smaller than

that of the DTMB 4381 propeller. This is consistent

with the circulation distribution of the optimum

propeller given in Fig. 12. The pressure contours for

both DTMB 4381 propeller and optimum propeller

are also shown in Figs 15 and 16, respectively, for

the sake of completeness of the results. Note that,

especially on the back side of the optimum propel-

ler, the negative non-dimensional pressure values

increased slightly. Note also that the distribution of

pressure on the back side is largely uniform. The

thrust and torque coefficients (KT and KQ) and effi-

ciency (h) of the DTMB 4381 propeller versus

advance coefficients (Js) computed from the analysis

program are compared with those of the optimum

propeller, as shown in Fig. 17. The optimum propel-

ler performance for all the advance coefficients is

slightly better than that of the original DTMB 4381

propeller since the torque coefficients are less than

those of the DTMB 4381 propeller.

Z

r/R

0 0.5 1 1.50.2

0.3

0.4

0.5

0.6

0.7

0.8

0.9

1

1.1

1.2

1.3

1.4

1.5

1.6

1.7

1.8-Cp

1.109

0.863

0.618

0.373

0.128

-0.118

-0.363

-0.608

-0.854

-1.099

-1.344

-1.589

-1.835

-2.080

-2.325

Back Side Face Side

Js=0.889 Optimum

Propeller

Fig. 16 Pressure contours on both sides of the bladesfor the optimum propeller at design Js=0.889

r/R

P/D

0.2 0.4 0.6 0.8 10.5

0.6

0.7

0.8

0.9

1

1.1

1.2

1.3

1.4

1.5

Original DTMB 4381

Optimum Propeller

Fig. 13 The pitch distribution over the blade for boththe DTMB 4381 propeller and the optimumpropeller at design Js=0.889

x/c

-Cp

0 0.25 0.5 0.75 1-1

-0.9

-0.8

-0.7

-0.6

-0.5

-0.4

-0.3

-0.2

-0.1

0

0.1

0.2

0.3

0.4

0.5

0.6

0.7

Optimum Propeller

DTMB 4381

Strip 10

Fig. 14 Comparison of pressure distribution on strip10 for the DTMB 4381 propeller and the opti-mum propeller

Z

r/R

0 0.5 1 1.50.2

0.4

0.6

0.8

1

1.2

1.4

1.6-Cp

0.471

0.371

0.271

0.170

0.070

-0.030

-0.130

-0.231

-0.331

-0.431

-0.531

-0.632

-0.732

-0.832

-0.932

Back Side Face Side

Js=0.889 DTMB 4381

Propeller

Fig. 15 Pressure contours on both sides of the bladesfor the DTMB 4381 propeller at design Js=0.889

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6 CONCLUSIONS

A practical design technique for the improvement of

open water propeller performance has been described.

The findings can be summarized as follows.

1. The lifting surface analysis method used in the

design technique has been first validated in the

case of DTMB 4119 and DTMB 4381 propellers

for which the geometric and hydrodynamic

characteristics were given in the open literature.

The design technique was then applied to the

same propellers to check whether they were

optimum or not. It was found that the agree-

ment between the results (thrust, torque, opti-

mum circulation, and pressure distribution over

the blades) of the present design technique and

those given in literature is very satisfactory.

2. It can be concluded that the DTMB 4119 is an

optimum propeller while DTMB 4381 is not.

However, the modified propeller (from the

DTMB 4381 propeller) with the new pitch distri-

bution is optimum while keeping all other geo-

metric characteristics fixed.

3. The technique is very fast and effective and can

be used as a reliable tool for many practical

applications.

4. The effects of skew and rake will be included in

the calculations in the near future.

5. It is also planned to apply the present design

technique to podded propellers. The main

sources of information and data on podded pro-

pulsors are given in the references [22–24].

FUNDING

This research received no specific grant from any

funding agency in the public, commercial, or not-

for-profit sectors.

� Author 2011

REFERENCES

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2 Sparenberg, J. A. On optimum propellers with aduct of finite lengths. J. Ship Res., 1969, 13, 129–136.

3 Yim, B. Optimum propellers with cavity-drag andfrictional-drag effects. J. Ship Res., 1976, 20, 118–123.

4 Kerwin, J. E. and Lee, C. S. Prediction of steadyand unsteady marine propeller performance bynumerical lifting-surface theory. Trans. SNAME,1978, 86, 218–253.

5 Greely, D. S. and Kerwin, J. E. Numerical methodsfor propeller design and analysis in steady flow.Trans. SNAME, 1982, 90, 415–453.

6 Kerwin, J. E. Marine propellers. Ann. Rev. FluidMechanics, 1986, 18, 367–403.

7 Breslin, J. P. and Andersen, P. Hydrodynamics ofship propellers, 1994 (Cambridge University Press,Cambridge, UK).

8 Coney, W. B. Optimum circulation distributionsfor a class of marine propulsors. J. Ship Res., 1992,36, 210–222.

9 Kinnas, S. A. and Coney W. B. The generalizedimage model – an application to the design ofducted propellers. J. Ship Res., 1992, 36, 197–209.

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11 Dai, C., Hambric, S., Mulvihill, L., Tong, S. S., andPowell, D. A prototype marine propulsor designtool using artificial intelligence and numerical opti-mization techniques. Trans. SNAME, 1994, 102,57–69.

12 Kerwin, J. E., Keenan, D. P., Black, S. D., andDiggs, J. D. A coupled viscous/potential flowdesign method for wake-adapted, multi-stage,ducted propulsors using generalized geometry.Trans. SNAME, 1994, 102, 23–56.

13 Mishima, S. and Kinnas, S. A. A numerical optimi-zation technique applied to the design of two-dimensional cavitating hydrofoil sections. J. ShipRes., 1996, 40, 28–38.

14 Mishima, S. and Kinnas, S. A. Application of anumerical optimization technique to the design ofcavitating propellers in non-uniform flow. J. ShipRes., 1997, 41, 93–107.

15 Griffin, P. E. and Kinnas, S. A. A design methodfor high-speed propulsor blades. J. Fluids Engng,1998, 120, 556–562.

Js

KT,

η

10KQ

0.4 0.5 0.6 0.7 0.8 0.9 1 1.10.1

0.2

0.3

0.4

0.5

0.6

0.7

0.8

0.9

1

0.2

0.25

0.3

0.35

0.4

0.45

0.5

0.55

0.6

0.65

0.7

0.75

0.8KT(DTMB 4381)

10KQ(DTMB 4381)

η (DTMB 4381)

KT(Optimum Propeller)

10KQ(Optimum Propeller)

η (Optimum Propeller)

Fig. 17 Comparison of thrust, torque, and efficiencyvalues for the optimum and DTMB 4381propellers

Technique for improvement of open water propeller performance 11

Proc. IMechE Vol. 000 Part M: J. Engineering for the Maritime Environment

at Istanbul Teknik Universitesi on September 12, 2011pim.sagepub.comDownloaded from

16 Kerwin, J. E. The preliminary design of advancedpropulsors. In Proceedings of the Propellers/Shaft-ing 2003 Symposium, SNAME, Virginia Beach, Vir-ginia, USA, 16–17 September 2003.

17 Kinnas, S. A., Lee, H. S., Gu, H., and Deng, Y. Pre-diction of performance and design via optimizationof ducted propellers subject to non-axisymmetricinflows. Trans. SNAME, 2005, 113, 99–121.

18 Sun, H. Performance prediction of cavitating pro-pulsors using a viscous/inviscid interaction method.PhD Thesis, Ocean Engineering Group, The Uni-versity of Texas at Austin, USA, 2008.

19 Bal, S. and Guner, M. Performance analysis ofpodded propulsors. Ocean Engng, 2009, 36, 556–563.

20 Brizzolara, S., Villa, D., and Gaggero, S. A systema-tic comparison between RANS and panel methodsfor propeller analysis. In Proceedings of the 8thInternational Conference on Hydrodynamics,Nantes, France, 30 September–3 October 2008.

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22 Atlar, M., Clarke, D., Glover, E. J., McLean, D.,Sampson, R., and Woodward, M. D. (Eds) In Pro-ceedings of T-POD, the 1st International Confer-ence on Technological advances in poddedpropulsion, University of Newcastle, UK, 2004.

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24 Abu Sharkh, S. M., Turnock, S. R., and Hughes, A.W. Design and performance of an electric tip-dri-ven thruster. Proc. IMechE, Part M: J. Engineeringfor the Maritime Environment, 2003, 217, 133–147.

APPENDIX

Notation

a NACA camber (mean) line constant

c(r) chord length along blade

Cf frictional drag coefficient

Cp(Pi) pressure coefficient

d distance between vortex element and field

point

D propeller diameter

f camber parameter for blade section

fmax maximum camber of each blade section

Js advance coefficient =Vs/(nD)

KQ torque coefficient of propeller =Q/(rn2D5)

KT thrust coefficient of propeller =T/(rn2D4)

M number of radial vortex lattice elements

n propeller rotational speed (r/s)

nm unit vector normal to the mean camber or

trailing wake surface

NB number of blades

P(r) pitch of blade section

PVL propeller vortex lattice

Q propeller torque

rh radius of hub

R radius of propeller

t thickness parameter for blade sections

tmax maximum thickness of each blade section

T propeller thrust

ua*(r) axial induced velocity along blade

ut*(r) tangential induced velocity along blade

vG velocity vector induced by each unit

strength vortex element

vQ velocity vector induced by each unit

strength source element

Va effective axial inflow

VRresulting velocity =

ffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi

V 2S + 0:7Dpnð Þ2

h i

r

VS uniform incoming flow velocity

Vt effective tangential inflow

wx axial wake fraction

x, r, u cylindrical coordinates rotating with blade

b(r) pitch angle of blade section

G circulation

h propeller efficiency = Js/(2p)KT/KQ

r density of water

v angular velocity = 2pn

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