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Engineers, Part M: Journal of Engineering for Proceedings of the Institution of Mechanical
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: [email protected]
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.
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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
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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
Technique for improvement of open water propeller performance 3
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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.
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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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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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