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In this study, the open water performance of three propellers with diverse rake angles was investigated by computational fluid dynamics method. The objective of this study was to find out the influence of the rake angle on the performance of conventional screw propellers. For this purpose, first, the obtained results for three B-series propellers were validated against the empirical results and then by modifying the rake angle, different models were investigated by the same method. Flow characteristics were examined for the models and the evolvement of vortices on different planes around the propeller were compared. The results suggest that in case of conventional screw propellers with linear rake distribution, while the effect of the rake angle on the propeller efficiency is not significant, the augmentation of this parameter improves the propeller thrust, especially at high propeller loads, but at the same time, the required torque increases, which is not desirable for the propeller design process.
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A study on the effect of the rake angle on the
performance of marine propellers
A N Hayati, S M Hashemi, and M Shams*
Department of Mechanical Engineering, K.N. Toosi University of Technology, Tehran, Iran
The manuscript was received on 11 May 2011 and was accepted after revision for publication on 11 July 2011.
DOI: 10.1177/0954406211418588
Abstract: In this study, the open water performance of three propellers with diverse rake angles
was investigated by computational fluid dynamics method. The objective of this study was to find
out the influence of the rake angle on the performance of conventional screw propellers. For this
purpose, first, the obtained results for three B-series propellers were validated against the empir-
ical results and then by modifying the rake angle, different models were investigated by the same
method. Flow characteristics were examined for the models and the evolvement of vortices on
different planes around the propeller were compared. The results suggest that in case of conven-
tional screw propellers with linear rake distribution, while the effect of the rake angle on the
propeller efficiency is not significant, the augmentation of this parameter improves the propeller
thrust, especially at high propeller loads, but at the same time, the required torque increases,
which is not desirable for the propeller design process.
Keywords: rake angle, marine propellers, computational fluid dynamics methods
1 INTRODUCTION
Computational fluid dynamics (CFD) methods have
been developed remarkably on the basis of Reynolds
averaged Navier–Stokes equations in the analysis of
marine propellers in recent decades. Although the
numerical modelling of flow around various solids
is possible, in case of propellers, it is difficult due to
several factors such as geometry complexity, turbu-
lent flow occurrence, flow separation, boundary layer
effects, wake field, and cavitation incidence.
Uto and Kodama [1] used the CFD method for
modelling the flow around a propeller behind a sub-
merged body. By employing a structured mesh, their
obtained results were restricted to open water condi-
tion. In addition, due to the complexity of the blade
geometry, they were not capable of accurate predic-
tion of the flownear the tipof the blades.Funeno [2, 3]
studied the flow around high-skewed propellers
using an unstructured mesh. Despite the good
compatibility of the obtained results with empirical
results, the approach of mesh generation was very
complicated and time consuming due to the division
of the numerical domain into several regions and
individual mesh generation for each of them.
Martı
´nez-Calle et al. [4] modelled a propeller in
open water condition by employing standard k"tur-
bulence model. Although the results of this that study
were generally acceptable, the average amount of
error in the prediction of propeller torque was 30
per cent. Watanabe et al. [5] modelled a propeller in
both steady and unsteady conditions using the stan-
dard k!turbulence model. The obtained results had
good compatibility with experimental results and the
average amount of error in thrust prediction was
15 per cent. Rhee and Evangelos [6] modelled the
flow around a propeller by two-dimensional simula-
tion with the standard k!turbulence model and the
error percentage in their final results was 13 per cent.
Many other works were carried out on the perfor-
mance prediction of conventional and high-skewed
propellers by CFD method [710].
In spite of several studies done on the performance
prediction of marine propellers, the effect of a specific
*Corresponding author: Department of Mechanical Engineering,
K.N. Toosi University of Technology, Tehran, Iran.
email: shams@kntu.ac.ir
1
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geometrical parameter on the performance has rarely
been investigated. The geometry complexity and the
effect of several geometrical parameters on it are the
main troubles in such studies. Skew angle is a typical
parameter which was taken into consideration in
some literatures such as Abdel-Maksoud et al. [7]
and Ghasemi [11] to compare its effect on the propel-
ler performance. The results of such studies indicated
that the use of high-skewed propellers leads to
more reduction in propeller-excited vibrations on the
full-body and better-performance characteristics
simultaneously.
Rake angle is another important parameter in pro-
peller technology that influences the propeller perfor-
mance; however, no numerical studies on this
parameter have been carried out, especially, to find
out the performance improvement of a propeller by
the modification of the rake angle. The objective of
this study was to examine the effect of the rake angle
alteration on the performance of a typical screw pro-
peller by CFD method. It was supposed that the
results were trustworthy for other screw propellers
with linear rake distribution.
2 RAKE ANGLE
As it was defined by Carlton [12], the propeller rake on
any arbitrary section of a propeller (i
T
(r)) includes two
separate components: the generator rake (i
G
) and the
skew induced rake (i
S
). Therefore, the total rake at
each section can be written as
iTðrÞ¼iGðrÞþiSðrÞð1Þ
As a physical definition, rake angle is a parameter
which determines the blades position against the flow
direction. If the blades are mounted perpendicular to
the hub, then the propeller would have zero rake
angle, but as the blades incline towards or backwards
the flow direction, negative or positive rake appears,
respectively. In standard conventional propeller
series, in which the rake distribution on each propel-
ler section is a linear function of its radial distance
from the propeller centre, the rake angle is defined as
r¼tan1iGr
R¼1

R
 ð2Þ
The general range for the rake angle of conven-
tional standard propellers is between 5(forward)
and þ20(backward). Among various standard series
of propellers, Wageningen B-screw, which was first
developed by Troost [13], is the most well-known
series and its conventional rake angle is equal to 15.
3 PROPELLER MODELS
Three B3-50 propellers with different pitch ratios (0.6,
0.8, and 1) were studied. The models were generated
by the application of GAMBIT 2.3. The principal geo-
metrical parameters of each propeller are presented
in Table 1. The conventional propeller with a pitch
ratio of 0.6 and a rake angle of 15is shown in
Fig. 1(a). By modifying the rake angle of this propeller,
other models with diverse rake angles were repro-
duced and are shown in Fig. 1(b) to (d). The only geo-
metrical distinction between these models is the
amount of the rake angle which was set to 5,15
,
and 20for examining the influence of this parameter
on the performance of screw propellers. Same proce-
dure was carried out for modelling the two other
models with different pitch ratios.
4 NUMERICAL SOLUTION
4.1 Governing equations
The computations were executed by the application
of FLUENT 6.3, which is established on the basis of
CFD codes and is well known as a robust commercial
software package in diverse problems in the analysis
of marine propellers according to several literatures
published in this field of study [4, 5, 14, 15]
The governing equation for mass conservation in
each principal direction can be written as
@
@xi
ðuiÞ¼0ð3Þ
where is the fluid density and u
i
the velocity in each
of the principal directions (x, y, z). In addition,
momentum conservation equation in principal direc-
tions can be written as follows
@
@tðuiÞþ @
@xj
ðuiujÞ¼@p
@xi
þ@ij
@xj
þgiþFið4Þ
Table 1 Main geometrical parameters of the
propellers
Diameter (m) 0.2
Number of blades 3
Expanded area ratio 0.5
Pitch ratio 0.6, 0.8, and 1
Hub ratio 0.169
Chord length (0.7R) (m) 0.0723
Thickness ratio (0.7R) 0.0473
Skew angle ()5
Handedness Right handed
Section type Inner sections: airfoil
Outer sections: segmental
2 A N Hayati, S M Hashemi, and M Shams
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where
ij
is the Reynolds stress tensor defined as
ij ¼@ui
@xj
þ@uj
@xi

2
3@ui
@xi
@ij ð5Þ
where
ij
is the Kronecker delta which is unity when i
and jare the same and zero in other cases.
Considering equations (3) to (5), the Reynolds aver-
aged momentum equations are derived as
@
@tðuiÞþ @
@xj
ðuiujÞ
¼@
@xj
@ui
@xj
þ@uj
@xi

2
3@ui
@xi

@p
@xi
þ@
@xj
ðu0
iu0
jÞ
ð6Þ
For turbulence description, the standard k!
model which was developed by Wilcox [16] was
employed, where kand !represent turbulence
kinetic energy and turbulence dissipation rate,
respectively, and are obtained from the following
equations
@
@tðkÞþ @
@xi
ðkuiÞ
¼ij
@ui
@xj
k!þ@
@xi
þt
k

@k
@xi
ð7Þ
@
@tð!Þþ @
@xi
ð!uiÞ
¼!
kij
@ui
@xj
!2þ@
@xi
þt
!

@k
@xj
ð8Þ
where
k
and
!
indicate turbulent Prandtl numbers for
kand !, respectively, and and
*
obtained from exper-
imental formulations by Wilcox [16]. Furthermore, tur-
bulent viscousity,
t
, is obtained from the combination
of kand !according to the following equation
t¼k
!ð9Þ
The selected solver for the equations was 3D
Segregated. The employed algorithm for pressure–
velocity coupling was SIMPLE with standard discre-
tization for pressure and second-order upwind
discretization for momentum, kand !.
4.2 Grid generation
An unstructured hybrid mesh was employed for grid
generation. Blades surfaces were meshed with trian-
gular cells. Smaller triangles with sides of approxi-
mately 0.001D(where Dis the propeller diameter)
were used for regions near the root, blade edges,
and tip for better monitoring the flow in these
regions. Other surfaces were meshed with larger tri-
angles with sides of approximately 0.1D. In addition,
for better prediction of the flow between the propeller
blades, a moving mesh zone was generated around
the propeller (Fig. 2). Finally, the remaining regions in
the domain were meshed with appropriate growing
rate of 1.1 with tetrahedral cells.
Fig. 1 B3-50 models with P/D¼0.6: (a)
r
¼15; (b)
r
¼5; (c)
r
¼5; and (d)
r
¼20
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4.3. Boundary conditions
In order to investigate the propeller performance in
uniform flow and simulating open water condition, a
cylindrical control volume was assumed around each
propeller with velocity inlet and outflow boundary
conditions for the entry of the flow in front of the
propeller and the flow exit astern the propeller,
respectively (Fig. 3). The domain dimensions
(Table 2) were considered large enough to avoid
external effects on the performance prediction of
the propellers. In order to avoid the occurrence of
the stagnation point at the propeller hub, the blades
were attained to a long shaft along the control volume.
Fig. 2 Generated grid for computational domain
Fig. 3 Arranged control volume for computational solution
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The rotating speed of the propeller shaft was set to
25 r/s (1500 r/min) throughout this study and the flow
velocity through the inlet boundary was varied for
different values of advance ratio.
5 VALIDATION
For the validation of the obtained results, first, the
study of mesh independency was carried out for the
conventional propeller with P/D¼0.6 (
r
¼15) and
the results are presented in Table 3. It was indicated
that the third pattern of mesh generation offered the
least error in the prediction of the thrust coefficient
and as mesh sizes decreased in the last pattern, no
better results were obtained. Therefore, the selected
pattern was executed for the mesh generation of all
the models throughout the study. Second, the open
water performance diagrams for three conventional
models with P/Dequal to 0.6, 0.8, and 1 were com-
pared to the numerical results and are represented in
Fig. 4(a) to (c), respectively. The definitions of the
principle performance parameters of the propellers
are defined as
J¼va
nD ð10Þ
KT¼T
n2D4ð11Þ
KQ¼Q
n2D5ð12Þ
O¼KT
KQ
:J
2ð13Þ
where Jis the advance ratio and is varied by increas-
ing the advance velocity at the propeller inlet, K
T
the
thrust coefficient which indicates the thrust gener-
ated at a determined advance ratio, K
Q
the torque
coefficient which indicates the torque needed for
the propeller rotation at a determined advance
ratio, and finally
O
the propeller efficiency that indi-
cates the ratio of the generated thrust to the required
torque at a determined advance ratio.
There is a good agreement between the numerical
and the experimental results. The average amount of
error in the prediction of the thrust and torque coef-
ficients with the current numerical method are
shown in Fig. 5. In all models, the average percentage
of error in the performance prediction is below 16 per
cent, which is acceptable with respect to similar lit-
eratures. Furthermore, the predicted results for
models with higher pitch ratios (P/D¼1) have less
discrepancy with respect to empirical results, which
implies the capability of standard k!turbulence
model in simulating the performance of higher
twisted propellers very well.
By increasing the propeller load, more thrust and
torque are generated, which is confirmed by numer-
ical solution. At heavy loads (low advance ratios), as
the flow velocity at the propeller inlet decreases, the
difference between static pressure on both sides of
the propeller augments remarkably. Figure 6 indi-
cates that the range of the static pressure on both
sides of the propeller is much higher at heavy loads
(Fig. 6(a) and (b)) compared to normal loads (Fig. 6(c)
and (d)). The static pressure distribution on the blade
surface at the suction side indicates high-pressure
region at the leading edge. This incidence is due to
the position of the leading edge of the blades on the
hub and the direction of the propeller rotation. As
seen from the propeller astern, clockwise rotation
leads to the existence of minimum fluid velocity at
the leading edge (the flow inlet to the blade sections)
and so highest static pressure at this location.
For a better comparison between the static pressure
distribution on the blade surface at heavy and normal
loads, the non-dimensional pressure coefficient is
Table 2 Domain dimensions for the computational solution
Distance from the centre of the propeller to
Inlet boundary Outlet boundary Radial boundary Moving zone
1.5D3.5D1.5D0.525D
Table 3 Mesh independency for conventional B3-50 with P/D¼0.6 at J¼0.4
Row Mesh size at blade surface Mesh size far from blade Total number of cells Thrust coefficient Error (%)
1 0.02D0.1D1 269 273 0.1031 6.1874
2 0.01D0.1D1 436 899 0.1037 5.6415
3 0.001D0.1D1 582 128 0.1078 1.9108
4 0.0001D0.05D3 006 478 0.1055 4.0036
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shown on two inner and outer sections in Fig. 7. The
pressure coefficient is defined as
Cp¼PsP1
1=2Pv2ð14Þ
where P
s
is the static pressure at the propeller
surface, P
1
the pressure remote from the propeller,
vthe local velocity at the propeller inlet, and C
p
the
pressure coefficient which indicates the static pres-
sure with respect to the free stream pressure. The
fluctuations in the pressure coefficient as the flow
proceeds from the leading edge (x/c¼0) to the
trailing edge (x/c¼1) is mainly due to the variations
in the flow regime, turbulent transition occurrence,
and boundary layer effects along the section. By com-
paring Fig. 7(a) and (b), it is inferred that the differ-
ence between the static pressure on both sides of
the propeller is much greater on outer sections
and for inner sections, a great decline occurs in its
range. In addition, according to Fig. 7(a) to (d), at
high propeller loads, the range of the static pressure
on both sides is much greater than that at normal
loads, which indicates more thrust generation at
low advance ratios.
0 0.1 0.2 0.3 0.4 0.5 0.6
0
0.1
0.2
0.3
0.4
0.5
0.6
0.7
0.8
0.9
1
(a)
J
KT, 10KQ, ηO
KT, 10KQ, ηO
KT, 10KQ, ηO
P/D = 0.6
KT (Num.)
10KQ (Num.)
ηO (Num.)
KT (Exp.)
10KQ (Exp.)
ηO (Exp.)
0 0.2 0.4 0.6 0.8 1
0
0.1
0.2
0.3
0.4
0.5
0.6
0.7
0.8
0.9
1
(c)
J
P/D=1
KT (Num.)
10KQ (Num.)
ηO (Num.)
KT (Exp.)
10KQ (Exp.)
ηO (Exp.)
0 0.2 0.4 0.6 0.8
0
0.1
0.2
0.3
0.4
0.5
0.6
0.7
0.8
0.9
1
(b)
J
P/D=0.8
KT (Num.)
10KQ (Num.)
ηO (Num.)
KT (Exp.)
10KQ (Exp.)
ηO (Exp.)
Fig. 4 Comparison between the numerical and the empirical results for B3-50: (a) P/D¼0.6; (b) P/
D¼0.8; and (c) P/D¼1
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Furthermore, the axial velocity distribution on the
pressure side of the propeller blades (Fig. 8) indicates
that maximum fluid velocity occurs at the blade tip
which is obvious due to the furthest distance from the
propeller centre of rotation. Furthermore, the region
with minimum velocity occurs at the blade root and
there is a remarkable increase in the velocity from the
root to the tip of the blades. Comparing two cases of
the propeller loads, at heavy loads (Fig. 8(a)), a small
region with reverse flow is observed around the blade
root near the propeller hub at the pressure side,
which is due to the low flow velocity at the propeller
inlet at low advance ratio.
In order to examine the vortex distribution around
the propeller at different loads, first, the strength
of the vortices are illustrated on two planes parallel
to the propeller plane which are located beside the
suction and the pressure side of the propeller with
distances x/R¼0.3 and 0.3 from the propeller
centre, respectively (Fig. 9). The vorticity magnitude
is defined as
!¼ffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi
@w
@y@v
@z

2
þ@u
@z@w
@x

2
þ@v
@x@u
@y

2
s
ð15Þ
where u, v, and ware the terms of the velocity vector
in principal directions (x, y and z), respectively and !
the vorticity magnitude of the induced vortices in the
rotational flow.
Figure 9(a) and (c) indicate that the evolvement of
vortices originates from the region close to the pro-
peller shaft while the vortices at heavy loads are
developed more than those at normal loads. In the
planes behind the propeller (Fig. 9(b) and (d)) the
Fig. 5 Average error in the performance prediction of
B3-50 with different pitch ratios
Fig. 6 Static pressure distribution for conventional B3-50 with P/D¼0.8: (a) pressure side, J¼0.1;
(b) suction side, J¼0.1; (c) pressure side, J¼0.5; and (d) suction side, J¼0.5
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vortices are well developed throughout the planes
and the regions with maximum strength
are developed through farther distances from the
propeller shaft, while for heavy loads, the overall
vorticity strength is greater than normal propeller
loads.
Second, the vorticity on the propeller plane with x/
R¼0 is illustrated in Fig. 10. At heavy loads (Fig.
10(a)), the region with high vorticity strength is
fully developed from the root to the tip of
the blades, which indicates more energy loss and
consequently poor efficiency, as shown previously
y/c
Pressure coefficient
0.2 0.4 0.6 0.8 1
–50
0
50
100
Pressure side
Suction side
(a) (b)
y/c
Pressure coefficient
00.2 0.4 0.6 0.8 1
–200
(d)
(c)
0
200
400
Pressure side
Suction side
y
/c
Pressure coefficient
00.2 0.4 0.6 0.8 1
–6
–4
–2
0
2
4
6
Pressure side
Suction side
y/c
Pressure coefficient
00.2 0.4 0.6 0.8 1
–2
0
2
4
Pressure side
Suction side
Fig. 7 Chordwise distribution of pressure coefficient for conventional B3-50 with P/D ¼0.8:
(a) r/R¼0.3, J¼0.1; (b) r/R¼0.7, J¼0.1; (c) r/R¼0.3, J¼0.5; and (d) r/R¼0.7, J¼0.5
Fig. 8 Axial velocity distribution for conventional B3-50 with P/D¼0.8 on pressure side:
(a) J¼0.1; (b) J¼0.5
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Fig. 9 Vortex evolvement around B3-50 with P/D¼0.8: (a) x/R¼0.3, J¼0.1; (b) x/R¼0.3, J¼0.1;
(c) x/R¼0.3, J¼0.5; and (d) x/R¼0.3, J¼0.5
Fig. 10 Vorticity distribution at the propeller plane for B3-50 with P/D ¼0.8: (a) J¼0.1; (b) J¼0.245;
(c) J¼0.5; and (d) J¼0.676
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in Fig. 4(b). For higher advance ratios, the region with
maximum vorticity strength declines gradually and
conveys to the root and inner sections of the blades,
which implies less energy loss. Thus, the increase
in the efficiency is expected, as shown in Fig. 4(b).
For low propeller loads (Fig. 10(d)), the region
with maximum vorticity is distributed close to the
blade surface and the overall vorticity strength is
less than the other cases. Consequently, the energy
loss in this load is minimum and the propeller has
maximum efficiency at this advance ratio, as shown
in Fig. 4(b).
6 RESULTS AND DISCUSSION
The effect of the rake angle on the thrust and torque
coefficients and the efficiency of the propellers for a
range of advance ratios are illustrated in Figs 11 to 13.
The overall thrust and torque coefficients for propellers
with higher backward rake angles (
r
¼15and 20)
are greater than those with forward rake angles
(
r
¼5) and lower backward rake angles (
r
¼5).
While an overall increase is shown for different
advance ratios, by increasing the rake angle, the aug-
mentation is more significant at heavy propeller
loads (J¼0.1). In spite of the improvement in the
0 0.1 0.2 0.3 0.4 0.5 0.6
0.04
0.06
0.08
0.1
0.12
0.14
0.16
0.18
0.2
0.22
0.24
(a)
J
KT
KT
KT
P/D=0.6
θr=−5 deg
θr=5 deg
θr=15 deg
θr=20 deg
0 0.2 0.4 0.6 0.8 1
0.05
0.1
0.15
0.2
0.25
0.3
0.35
0.4
0.45
(c)
J
P/D=1
θr=−5 deg
θr=5 deg
θr=15 deg
θr=20 deg
0 0.2 0.4 0.6 0.8
0.05
0.1
0.15
0.2
0.25
0.3
0.35
0.4
(b)
J
P/D=0.8
θr=−5 deg
θr=5 deg
θr=15 deg
θr=20 deg
Fig. 11 Effect of the rake angle on the propeller thrust coefficient: (a) P/D¼0.6; (b) P/D¼0.8; and
(c) P/D¼1
10 A N Hayati, S M Hashemi, and M Shams
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propeller generated thrust for higher rake angles (Fig.
11), more torque and consequently more power is
required for the propeller rotation (Fig. 12), while
the efficiency alteration for different rake angles is
not significant for the range of propeller loads
(Fig. 13); However, for low propeller loads, a slight
augmentation is observed in the propeller efficiency
for models with higher backward rake angles.
This increase is more significant for models with
higher pitch ratios, as observed by comparing
Fig. 13(a) to (c). The overall improvement in the
performance of the propellers by comparing
models with forward and high backward rake
angles (5and 20) is shown in Fig. 14.
For propellers with P/D¼0.8, the performance
improvement was monitored more remarkably
than other models. Therefore, this model was
selected for the rest of the study.
The improvement in the performance of propellers
with high backward rake angles is mainly due to the
arrangement of the propeller sections in different
rake angles which changes the flow characteristics
on each propeller section and especially influences
the static pressure distribution on both sides of the
propellers. The static pressure distribution on the
pressure side of two propellers with low and high
backward rake angles (5and 20, respectively) are
presented for heavy and normal loads (Fig. 15).
0 0.1 0.2 0.3 0.4 0.5 0.6
0.1
0.12
0.14
0.16
0.18
0.2
0.22
0.24
0.26
(a)
J
10*KQ
P/D=0.6
θr=−5 deg
θr=5 deg
θr=15 deg
θr=20 deg
0 0.2 0.4 0.6 0.8 1
0.2
0.25
0.3
0.35
0.4
0.45
0.5
0.55
0.6
0.65
(c)
J
10*KQ
P/D=1
θr=−5 deg
θr=5 deg
θr=15 deg
θr=20 deg
0 0.2 0.4 0.6 0.8
0.1
0.15
0.2
0.25
0.3
0.35
0.4
0.45
0.5
(b)
J
10*KQ
P/D=0.8
θr=−5 deg
θr=5 deg
θr=15 deg
θr=20 deg
Fig. 12 Effect of the rake angle on the propeller torque coefficient: (a) P/D¼0.6; (b) P/D¼0.8;
and (c) P/D¼1
A study on the effect of the rake angle on the performance of marine propellers 11
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Overall increase in the static pressure on the blade
surface is observed for propeller with high backward
rake angle with respect to that with low backward
rake angle at both advance ratios. The region with
high static pressure is developed towards the trailing
edge and inner sections, as shown in Fig. 15(b) and (d).
For better comparison, the chordwise distribution of
the pressure coefficient on a determined propeller
section (r/R¼0.7) is illustrated in Fig. 16 for heavy
and normal propeller loads. As the advance ratio
increases, the range of the pressure coefficient on
both sides of the section decreases significantly, as
shown in Fig. 7, previously. The location of zero
pressure coefficient is considerable in the analysis
of flow characteristics on the section, which shows
the equality of the local pressure at a point to that
of the free stream pressure. By comparing the pres-
sure chordwise distribution on the pressure side of
the section at both advance ratios (Fig. 16(a) to (d)),
it is inferred that for propellers with high backward
rake angles, the minimum pressure coefficient is
greater than those with low backward rake angles
and in the case of high backward rake angle (
r
¼20),
there is no point on the section with zero pressure
coefficient throughout the pressure side. By averag-
ing the pressure coefficient from the leading to the
0 0.1 0.2 0.3 0.4 0.5 0.6
0.1
0.15
0.2
0.25
0.3
0.35
0.4
0.45
0.5
(a)
J
ηO
ηO
ηO
P/D=0.6
θr=−5 deg
θr=5 deg
θr=15 deg
θr=20 deg
0 0.2 0.4 0.6 0.8 1
0.1
0.15
0.2
0.25
0.3
0.35
0.4
0.45
0.5
0.55
0.6
(c)
J
P/D=1
θr=−5 deg
θr=5 deg
θr=15 deg
θr=20 deg
0 0.2 0.4 0.6 0.8
0.1
0.15
0.2
0.25
0.3
0.35
0.4
0.45
0.5
0.55
0.6
(b)
J
P/D=0.8
θr=−5 deg
θr=5 deg
θr=15 deg
θr=20 deg
Fig. 13 Effect of the rake angle on the propeller efficiency: (a) P/D¼0.6; (b) P/D¼0.8;
and (c) P/D¼1
12 A N Hayati, S M Hashemi, and M Shams
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trailing edge on the suction and the pressure side of
the determined section, the average C
p
difference
between the two sides was obtained and is illustrated
in Fig. 17 for heavy and normal propeller loads.
The augmentation in the average C
p
difference
indicates more thrust and torque generation for
propellers with higher backward rake angles.
The axial velocity distribution on the suction side of
the propellers with high and low backward rake
angles is shown in Fig. 18. The overall range of the
axial velocity on the blade surfaces for the propeller
with high rake angle is lower than those with low
values. At heavy propeller loads, this distinction is
better monitored, comparing Fig. 18(a) and (b). The
region with maximum velocity declines from the
blade tip to inner sections, which is mainly due to
the arrangement of the blades as the flow enters the
propeller suction side.
The vorticity distribution on the propeller plane
(x/R¼0) which is perpendicular to the propeller
axis is illustrated in Fig. 19 for heavy and normal pro-
peller loads. The overall strength of the vortices
around the propeller with high backward rake angle
is less than that around the propeller with low value.
Comparing the induced vortices at the tip of the
blades for both models, it is observed that the
region with maximum vorticity declines significantly,
which is well monitored for normal propeller loads
(Fig. 19(c) and (d)). Therefore, the energy loss for pro-
pellers with high backward rake angles is less than
that for models with low backward rake angles,
which implies better performance.
Fig. 14 Overall improvement in the performance of
propellers by the rake angle augmentation
Fig. 15 Static pressure distribution for the selected propeller with: (a)
r
¼5,J¼0.1; (b)
r
¼20,J¼
0.1; (c)
r
¼5,J¼0.5; and (d)
r
¼20,J¼0.5
A study on the effect of the rake angle on the performance of marine propellers 13
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7 CONCLUSION
In this study, the effect of the rake angle on the per-
formance of three typical screw propellers was inves-
tigated by CFD method. It was indicated that
increasing the rake angle improves the performance
and especially the generated thrust of conventional
propellers. The improvement was well monitored at
heavy propeller loads and indicated the remarkable
effect of the rake angle on the propeller performance
y/c
Pressure Coefficient
00.2 0.4 0.6 0.8 1
–200
0
200
400
(a)
Suction side
Pressure side
y/c
Pressure Coefficient
00.2 0.4 0.6 0.8 1
–6
–4
–2
0
2
4
6
(d)
(b)
Pressure side
Suction side
y
/c
Pressure Coefficient
0.2 0.4 0.6 0.8 1
–6
–4
–2
0
2
4
6
(c)
Pressure side
Suction side
y/c
Pressure Coefficient
00.2 0.4 0.6 0.8 1
–200
0
200
400
Pressure side
Suction side
Fig. 16 Chordwise distribution of pressure coefficient on section r/R¼0.7: (a)
r
¼5,J¼0.1;
(b)
r
¼20,J¼0.1; (c)
r
¼5,J¼0.5; and (d)
r
¼20,J¼0.5
Fig. 17 Effect of the rake angle on the average C
p
difference on section r/R¼0.7: (a) J¼0.1;
(b) J¼0.5
14 A N Hayati, S M Hashemi, and M Shams
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Fig. 18 Axial velocity distribution on the suction side: (a)
r
¼5,J¼0.1; (b)
r
¼20,J¼0.1;
(c)
r
¼5,J¼0.5; and (d)
r
¼20,J¼0.5
Fig. 19 Vorticity distribution at the propeller plane: (a)
r
¼5,J¼0.1; (b)
r
¼20,J¼0.1;
(c)
r
¼5,J¼0.5; and (d)
r
¼20,J¼0.5
A study on the effect of the rake angle on the performance of marine propellers 15
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at heavy loads; however, the variation of the propeller
efficiency for different rake angles was not noticeable
in the case of propellers with linear rake distribution.
Furthermore, improvements were shown in the flow
characteristics around the propellers with higher
backward rake angles. As a further study, it would
be interesting to investigate the effect of the propeller
rake modification and progressive rakes on the
improvements of the performance of screw propel-
lers and specifically enhancing the efficiency of
conventional propellers.
ßAuthors 2011
REFERENCES
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APPENDIX
Notation
D= propeller diameter (m)
F= external body forces (N)
g= gravitational acceleration (m/s
2
)
i
G
= generator rake (m)
i
S
= skew-induced rake (m)
i
T
= total rake (m)
J= advance ratio
K
T
= thrust coefficient
K
Q
= torque coefficient
n= rotational speed of the propeller shaft (r/s)
P
s
= local static pressure (KPa)
P
1
= free stream pressure (KPa)
Q= propeller torque (N.m)
R= propeller radius (m)
T= propeller thrust (N)
u=xvelocity (m/s)
v=yvelocity (m/s)
v
a
= advance velocity (m/s)
w=zvelocity (m/s)
O
= open water efficiency
r
= rake angle (deg)
m= fluid viscosity (kg/(m.s))
= fluid density (kg/m
3
)
!= vorticity magnitude (1/s)
16 A N Hayati, S M Hashemi, and M Shams
Proc. IMechE Vol. 0 Part C: J. Mechanical Engineering Science
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... In Figure 1 it is shown the base geometry and the final geometry of the propeller with the complete configuration shown in Table 3. It was selected the rake angle according to the angle used in the B-Series Wageningen propellers, 15° (Hayati, Hashemi, & Shams, 2011). The computational domain is Illustrated in figure 2. It is shown the boundary field, the position, and the dimensions, in meters, of the mesh elements: outer cylinder, middle cylinder, inner cylinder, and the propeller (in this order as show in figure 2). ...
... As the two propellers are the same, the front propeller is used in this paper to analyze the thrust and reaction torque; the hydrodynamics of the rear propeller can be obtained according to those of the front propeller. The thrust and torque of the front propeller can be calculated by (Hayati et al., 2012;Mizzi et al., 2017) ...
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Recently, the simulation technology by CFD (Computational Fluid Dynamics) has made remarkable progress. The method has become to be applied to viscous flow problems around not only various ship hulls but also marine propellers. Consequently many difficult problems on flow analysis on account of remarkable viscous effect are being resolved. There are also many subjects related to viscous effect of the flow around marine propellers. In this paper the author presents the topics about hub vortex and scale effect of propeller performance characteristics. The used analytical method consists of commercial CFD software and multifunctional grid generation software. As a result, the structure of flow around hub vortex and the difference of scale effect due to propeller shapes were revealed. These results show that the method is useful for design of such energy-saving devices as PBCF (Propeller Boss Cap Fins) or Kawasaki RBS-F (Rudder Bulb System with Fins), for ship power estimation with higher accuracy and for improvement of propellers performance.
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Computational fluid dynamics results are presented of four-quadrant flow for marine-propulsor P4381. The solution method is unsteady three-dimensional incompressible Reynolds-averaged Navier-Stokes equations in generalized coordinates with the Baldwin-Lomax turbulence model. The method was used previously for the design condition for marine-propulsor P4119, including detailed verification and validation. Only limited verification is performed for P4381. The validation is limited by the availability of four-quadrant performance data and ring vortex visualizations for the crashback conditions. The predicted performance shows close agreement with the data for the forward and backing conditions, whereas for the crashahead and crashback conditions the agreement is only qualitative and requires an ad hoc cavitation correction. Also, the predicted ring vortices for the crashback conditions are in qualitative agreement with the data. Extensive calculations enable detailed description of flow characteristics over a broad range of propulsor four-quadrant operations, including surface pressure and streamlines, velocity distributions, boundary layer and wake, separation, and tip and ring vortices. The overall results suggest promise for Reynolds-averaged Navier-Stokes methods for simulating marine-propulsor flow, including off-design. However, important outstanding issues include additional verification and validation, time-accurate solutions, and resolution and turbulence modeling for separation and tip and ring vortices.
Article
The authors have been investigating the possibility of the application of CFD to the propeller performance evaluation and optimization. In these previous papers [1,2], the authors presented CFD simulation of non-cavitating and cavitating flow around a marine propeller using a commercial CFD code. A good agreement with the experiment was confirmed for the non-cavitating flow. Various validations were also carried out for the cavitating flow, and the followings were revealed. First, we confirmed that the cavity shape in a uniform flow was qualitatively well estimated, but the difference between two propellers, of which the blade sections were somewhat different, were not reproduced. Secondary, the cavity pattern in the non-uniform flow was also qualitatively well estimated, but the resulting pressure fluctuation was not validated. In this paper, the systematic experiment was carried out using two propellers, whose dimensions were very similar, to study the above issues, and simulation was carried out for the same cases. In the uniform cavitating flow simulation, the discrepancy of cavity shape around two propellers, whose dimension were very similar, was reproduced, and the quantitative validation of the fluid force such as thrust was done. In the non-uniform cavitating flow simulation, the comparison of the cavity pattern with the experiment and the quantitative validation of the fluctuating pressure on the wall of the cavitation tunnel were done.
Article
This paper provides an investigation into the influence of wake and skew on a ship propeller performance, based on the potential Boundary Element Method (BEM). Two types of inflow wake from a ship (i.e. Seiun-Maru and MS689) have been investigated for two propeller types; a Conventional Propeller (CP) and a Highly Skewed Propeller (HSP). The computed results include pressure distribution, open water characteristics and thrust fluctuation for one blade and for all blades of the propeller. Calculations of the unsteady pressure distributions, thrust and torque are in good agreement with experimental data. In addition, the effect of propeller skew angle on the performance of thrust and torque, is investigated.
Conference Paper
The open water model tests technique is well known and commonly used to predict propellers performance. In this paper, a quite different approach is intended and the main propeller variables are numerically modelled using a finite volume commercial code. Particularly, a fishing-boat propeller is numerically treated using a three-dimensional unstructured mesh. Mesh dependency and different turbulent models are considered together with an sliding technique to account for the rotation. Typical turbomachinery boundary conditions for a volume containing the propeller are imposed (inlet velocity and outlet static pressure). In order to get the open water test performance coefficients for the considered propeller (KT , KQ , η), different advance coefficient (J) are imposed as boundary conditions for the numerical model. The results of such simulations are compared with experimental data available for the open water tests of the propeller. Once the model is validated with the experimental data available, a wake field simulation would be possible and would lead to the definition of the fluid-dynamic variables (pressure, iso-velocity maps, etc.) which are needed during any design process. Also some comparisons with real scale thrust measurements are intended.
Article
The paper presents a validation study of a RANS prediction of open water characteristics of a highly skewed propeller in full range advance-ratio. Computational results are compared with open water data, and extensively validated at one loading with paint test, cavitation inception test and PIV measurements. Except at two extreme off-design loads, the difference between prediction and measurement is less than 3% for KT and less than 5% for KQ at a wide range of advance ratios. While this can be considered as good agreement with experiment for KT and KQ, an attempt is made to critically analyze the predicted flow detail and some possible deficiency of the existing RANS method is discussed. Part of the work was carried out within the EU-funded research project “LEADING EDGE2”.
Article
The unsteady flow around a marine propeller blade section embedded in a traveling wave field is simulated and the results are validated against the well-known experimental data. Unstructured dynamic meshing techniques based on smoothing and remeshing are implemented and applied. The Massachusetts Institute of Technology Flapping Foil Experiment is selected for the validation, as it reveals the complex unsteady flow physics on a typical marine propeller blade section. The comparison with experimental data is good in terms of the first harmonic amplitudes and phases of the surface pressure coefficient and streamwise velocity component around and in the boundary layer of the blade section. The validation results suggest that the present computational approach with the unstructured dynamic meshing techniques, which are also available for three-dimensional problems, is both easy to apply and accurate enough for more realistic problems.