Sixth International Symposium on Marine Propulsors

smp’19, Rome, Italy, May 2019

Marine Propeller Optimization Design

Kang Han1, Chao Wang1

1College of Shipbuilding Engineering, Harbin Engineering University, Harbin, PR China

ABSTRACT by turbulent pulsation, viscous effects, and vortex motion,

The propeller is a crucial component of the ship resulting in the severe uneven flow after the boat (Liu et
propulsion system, and its design is related to the safety al 2010). Propellers are working in the wake of the boats,
and economy of the ship. Since the actual propeller is so the cavitation and noise performance of propellers are
operated in an uneven flow field behind the ship, the affected severely by the uneven flow after the boat. In
uneven flow field has an essential influence on the 1963, Beveridge and John L designed wake-adapted
cavities, noise, vibration and hydrodynamic performance propellers using Eckhardt-Morgan method based on Lerps
of the propeller. The purpose of the wake-adapted theory, and they obtained ideal performance in both open-
propeller design and parameter optimization design is to water and wake-flow conditions (Beveridge & John L
design the propeller reasonably under the condition of 1963). Donald MacPherson proposed that it is possible to
accurately predicting the flow field of the ship. This paper design customized propeller for ships with more and more
takes the HSP propeller as an example, and the stern flow plants achieving digital construction when he analyzes the
field is hypothetical, combined with the accompanying wake-adapted design of propellers (Donald MacPherson
flow harmonic analysis method, the lifting line program, 2010). Ding et al. analyzed the differences between the
the lifting surface program, the unsteady surface element flow of single-propeller ships and that of twin-propeller
program and the optimization design software iSIGHT. ships and researched with the account of the tangential
Then the wake-adapted propeller design and parameter wake (Ding et al 2011).
optimization design system is established. Moreover, in The purpose of the wake-adapted propeller design and
this paper, the HSP paddle is redesigned to verify the parameter optimization design is to design the propeller
effectiveness of the system. parameters reasonably so that the propeller would have
Keywords good hydrodynamic performances as well as cavitation
Propeller, Wake-adapted, Propeller Theoretical Design, performance. This paper introduced the process of wake-
Performance, Parameter Optimization Design adapted propeller design and parameter optimization
design firstly. Then the parameterized model is
1 INTRODUCTION introduced. Finally, the paper verifies the feasibility of the
With modern detection equipment and weapons (missile, optimization design process according to the redesign of
torpedo, mine) developing to high precision and long the HSP propeller.
distance, the possibility of submarine exposure and attack
increases dramatically, and survivability, as well as 2 THE PROCESS OF WAKE-ADAPTED PROPELLER
combat effectiveness, is seriously threatened. Submarine DESIGN AND PARAMETER OPTIMIZATION DESIGN
low-noise navigation not only keeps the action hidden and This paper combines the theoretical design and
avoid being detected but also increases its detection optimization design to form a relatively complete
distance. This would make the submarine maintain the propeller design process. The process consists of the
initiative of the war. resonance analysis method of the accompanying flow
field and the selection method of the number of blades,
A submarine usually navigates with high speed and has pitch distribution, and skew distribution. Also, lifting line
large scale, so its length Reynolds number is much larger and lifting surface design programs, hydrodynamic
than its critical Reynolds number when sailing performances forecasting program (using unsteady panel
underwater, and the flow field around the submarine is a method), an optimization design program and iSIGHT
turbulent flow field. Also, the submarine has several software are all involved in this process.
appendages and complex lines, which makes the
submarine wake become complex flow field characterized With the continuous development of ship design and
construction technology, the shortcomings of the

*
Corresponding author. E-mail address: zaniso@163.com (Kang Han)
National Natural Science Foundation of China (51679052), National Defense Basic Research Project Funding Project
(JCKY2016604B001).
propeller design under open-water conditions are START
gradually exposed, and wake-adapted propeller design
methods become the mainstream idea. To achieve the
purpose of customized propeller design and parameter Initialize the Particle Swarm
optimization, the design process should contain these
procedures as follows: Calculating the Target Value of Each
1) Initialization theory wake-adapted design of the Particle
propeller: According to ship type characteristics and
design requirements, determine the input parameters of Update the Speed and Position of Each
the lifting line program, including propeller rotation Particle
speed, diameter, thrust, horsepower received by the
propeller and wake fraction et al. Among them, the wake Update Individual Optimal Position
fraction can be estimated based on the characteristics of Values and Global Optimal Positions
the ship and the experienced formula. Then, carry out the
propeller design process that does not consider the
influence of skew and rake distribution. Whether the Convergence
Condition Is Met NO
2) According to the principle of selection of rake and
skew, combined with initialization pitch angle, resonance YES
analysis the wake and choose reasonable rake and skew END
distribution. Fig. 2 Propeller wake-adapted optimization design process
3) Wake-adapted propeller design: Carry out lifting line 3 PARAMETERIZED MODLE OF THE PROPELLER
and lifting surface design process with the influence of The B-spline curve is flexible for curve control (LAXMI
rake and skew. Then, take advantage of hydrodynamic PARI DA 1993). If the geometric parameters of the
performances forecasting program to predict the paddle are parameterized based on the B-spline curve,
performance of the propeller and estimate whether the smooth geometric parameter distributions in the radial
propeller satisfied the instruction, otherwise, redesign the direction can be obtained with fewer control points. The
wake-adapted propeller. specific expression of the B-spline curve of the radial
4) Optimized design of wake-adapted propeller: This step distribution of the propeller geometry is as follows:
is to improve the performance of some aspects of the n
propeller further. Take the theoretical design paddle as the pu    d i N i ,k u  0  u  1 (1)
parent type, and explore the range of variation of the i 0
design variables. Then, optimization program, iSIGHT
software and unsteady panel method program are used to Where p  u  is the geometric parameter distribution;
di  i  1, , n  are the control vertices of the curve
optimize the parameters of the propeller.

Ni ,k  u  is the basis function of k-order

START
shape;
Resonance Analysis of the Wake to Select the
Appropriate Number of Blades
normalized B-spline.
In the optimization design process of the propeller, the
Lifting Line and Surface Program
Wake-adapted geometric parameters of the propeller have different
Design Initial Propeller Initial Design
values at a different distance in radial directions. When
Combined with Geometric Pitch Angel, the geometric parameters are optimized, the geometric
Analysis theWake to Select Skew and Rake parameters of different radial distance need to be
regained, which is represented by a curve. The new
Considering the Influence of Skew and geometric parameter distribution obtained by changing
Rake, Carry Out Theoretical Design the control vertices cannot control the transformation
Predict the Hydrodynamic Performance,
range of the geometric parameters well. Therefore, for
Adjust Design
Strength, Noise and Cavitation of the Propeller Parameters
designers, the geometric parameter distribution on the
curve should be considered directly rather than
controlling the shape of the polygon. From the initial
Whether the Performance curve, calculating the control polygon and finding a
Meets the Requirements NO
reasonable curve shape are reasonable (Hu Zhigang et al
2000). Specifically, the geometric parameters along the
YES
radial direction of the B-spline curve are known, and
END
p1 , p2 , , p n are selected along the curve, then, control
Fig. 1 Propeller wake-adapted theory design process
vertices d1 , d2 , , d n , d n1 , d n2 are calculated
inversely. According to these control vertices, the B-
spline curve is fitted, and the geometric parameter values expression program of this paper can be used to express
at a different radial distance are obtained. The governing the geometric parameter of the propeller.
equations and boundary conditions are listed as follows
(Hu Jian 2006): 4 CASE ANALYSIS
3.1 Input of Design Parameters
 di  di 1  di 2   p i  1，
2 n (2)
In order to verify the validity of the theoretical design and
i
6 optimization design process of the marine propeller in this
paper, the redesigned HSP propeller is taken as an
d1  d2 , dn1  dn2 (3) example. The experimental values of the geometric
Combining the above B-spline curve theory, this paper parameters, accompanying flow field and hydrodynamic
compiled related programs to express geometric performance of the HSP paddle are described in the
parameter based on FORTRAN, and take the P4382 literature (Hu Jian 2006). According to the test conditions
paddle as an example to verify the feasibility of the of the HSP paddle, partial input parameters of lifting line
program, using the program to express the distribution of design program are given, as shown in Table 1. Axial
chord length, pitch, skew and rake. wake distribution information is presented in a table in the
1.6
literature, and Fig.5 originate from the table to make axial
0.4
1.5
wake information visual. Moreover, the average axial data
0.3
1.4 at each radius is obtained, as shown in Table 2, where r/R
1.3

0.2 1.2
is the dimensionless radius, and this is also applicable to
B/D

OriginalPropeller
P/D

Original Propeller
B-spline 1.1
B-spline
the following.
0.1
1.0

0.0 0.9

0.8
0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1.0 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1.0 0
r/R r/R
1.0 330 30 0.000

0.1078
(a) Chord length ratio (b) Pitch ratio 0.8 0.2155

0.3232
40
0.12 0.6 300 60 0.4310

0.5387
0.10 30 0.4
0.6465
0.08 Original Propeller
B-spline 0.7542
20
0.2
0.06 0.8620
S(°)
Ra/D

0.04
0.0 270 90
10

0.02 Original Propeller 0.2

0 B-spline
0.00
0.4
-0.02
-10
0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1.0 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1.0 0.6 240 120
r/R r/R
0.8

(c) Rake (d) Skew 1.0 210 150

180
Fig. 3 Comparison of geometric parameters of the original
paddle and parametrically expressed paddle
1.0
Fig. 5 Axial wake distribution
Original KT
0.8
Original
B-spline
10KQ
KT
Table 1 HSP paddle lift line input parameters
B-spline 10KT

0.6
Propeller Diameter
KT,10KQ

3.6 Boss Ratio rh/R 0.2

0.4
D(m)
0.2 Rotational Speed Ship Speed
n(rps) 3.0 Vs(m/s) 9.604
0.0
0.3 0.4 0.5 0.6 0.7 0.8 0.9 1.0

J Delivered Power
Thrust T(N) 66016.23 353.66
PD(kw)
Fig. 4 Comparison of the open-water performance curves of the
original paddle and the parameterized expression paddle Table 2 The circumferential average of the axial flow of the
HSP paddle
Given the advantages of the B-spline curve, four control
points are selected in this paper. The specific location of r/R 0.2 0.3 0.4 0.5 0.6
the four control points depends on the distribution of the Axial Flow 0.4568 0.3471 0.2697 0.2192 0.1899
geometric parameters. As shown in Fig. 3, the chord
length, pitch, thickness, camber, rake, and skew of the r/R 0.7 0.8 0.9 1
parameterized paddle are consistent with the original data. Axial Flow 0.1761 0.1722 0.1726 0.1717
The hydrodynamic performance of the paddle after the
3.2 The Selection of Skew and Rake Distribution
parameterized expression is calculated and compared to
Since the wake flow fields of different ships are different,
the hydrodynamic performance of the original paddle. As
it is necessary to select the appropriate skew distribution
shown in Figure 4, the open water performance curves are
according to the specific wake of ships. Before the
basically consistent between these two propellers. It can
theoretical design process, the harmonic analysis method
be seen that the inverse B-spline parameterized
is used to analyze the normal wake of the ship, and the
skew distribution is rationally selected to avoid the step force of the main blade can be obtained. It can be
various sections of the propeller rotating to the high flow seen from Fig. 6 that the main pulsation amplitude of the
velocity area simultaneously. And the skew distribution HSP propeller corresponding to the balanced and rear
must be considered together with the harmonic skew distribution is smaller than that of the original
components of the accompanying flow field, regardless of propeller and the balanced reduction is larger. Besides,
the radial accompanying flow, and the normal the average thrust coefficient of the main blade of the rear
accompanying flow for each profile is: skew HSP paddle (the thrust amplitude of the 0th order) is
wN  wx cos  p  w sin  p (4) larger than that of the original paddle, while the balanced
HSP paddle has reverse performance. However, the
Where wN = normal accompanying flow; wx = axial magnitude of the reduction is not large. Therefore, in
accompanying flow; wθ = circumferential accompanying order to ensure the strength characteristics, under the
flow; and βp = pitch angle. condition of satisfying the thrust of the propeller, the
Before the theoretical design process, it is necessary to balanced skew distribution form should be selected as
initialize the designed propeller and obtain the pitch angle much as possible. If the strength of the paddle is
to carry out the resonance analysis of the normal guaranteed, in order to improve the thrust coefficient of
accompanying flow field. This step is omitted because the the propeller the rear skew distribution can be selected.
geometric pitch angle of the original HSP paddle is
known. Through the resonance analysis, the maximum
normal phase angle of the 5th order is obtained as shown
in Table 3. Table 3 also shows the original skew
distribution of the original HSP paddle. The design
principle of the skew distribution is that the skew
distribution curve should have a relatively large
intersection angle with the normal accompanying flow
phase distribution curve. According to this principle, the
authors initially selected two modes of HSP propellers in
the form of balanced and rear skew forms along with the
radial distribution. Fig. 6 The amplitude of the thrust coefficient of the main blade
Table 3 The maximum normal phase and three kinds of the of three propellers of a rotation
lateral distribution of flow field in HSP impellers The main purpose of the rake distribution is to increase
Maximum the distance between the blade and the hull and reduce the
Skew of washing effect to the hull, and thus the vibration could be
normal Balanced Rear Skew
Original
r/R Distribution Distribution reduced, however, the designers usually design the
phase angle propeller
(°)
(°) (°) propeller in isolation and consider the wake of the hull to
(°) account for the effect of the speed field on the propeller
0.1 -37.38 0 0 0 after the hull. The rake distribution patterns include the
972 blade inner radius front and outer radius rear distribution,
0.2 -36.6 -0.21 -0.32 0.01
the front rake and the rear rake. From the perspective of
0.3 -13.02 -3.93 -7.82 1.18 strength, the rear rake should not be too large to reduce
0.4 2.83 -2.94 -8.61 3.82 the centrifugal force bending moment; and the front rake
is beneficial to the strength of the large skew propeller
0.5 10.94 -0.06 -4.22 7.76
and can effectively reduce the stress level of the paddle.
0.6 6.77 4.31 3.8 12.85 From the perspective of hydrodynamic performance, the
0.7 3.94 11.1 13.94 18.94 thrust coefficient and torque coefficient of rear rake
propeller will increase with the increase of the rake angle,
0.8 3.48 20.06 24.64 25.86
and the front rake can improve the efficiency of the
0.9 2.29 30.45 34.38 33.48 propeller. From the perspective of the cavitation, the rear
0.9 1.43 35.97 38.41 37.49 rake can improve the three-dimensional flow of the tip,
5 thereby delaying the initiation of the tip vortex.
0.9 0.92 38.78 40.13 39.54
75 Considering the hydrodynamic performance, cavitation,
1 0.38 41.62 41.62 41.62
noise, and strength of the propeller, the rake distribution
Under the condition of other geometric parameters that inner radius front and outer radius rear can be
keeping accordant, the unsteady hydrodynamic selected.
performance of different HSP propellers was predicted,
including original skew, balanced and rear skew versions. In this example, the HSP paddle selects the five-blade in
Based on the Fourier analysis method, the unsteady thrust the redesigned process. The rake and skew distribution
coefficient of the main blade of the HSP paddle in three options are shown in Table 4 as the input parameters for
skew modes can be analyzed, and the amplitude of each the lifting line program.
3.3 Theoretical Design Result Table 6 Comparison of hydrodynamic performance between
After the selection of the rake and skew, the wake- original HSP propeller and designed propeller
adapted theory design of the HSP paddle can be carried
out. Table 5 shows the geometric parameters of the KT KQ
designed propeller, where B/D is chord length ratio; P/D Original Propeller 0.172 0.02687
is pitch ratio; T/D is thickness ratio, and f/B is camber Designed Propeller 0.168 0.0261
chord length ratio. The pitch of the blade root and blade
Error 2.33% 2.87%
tip is smaller than that of the original paddle, which is
beneficial to reduce the hub vortex and tip vortex of the
propeller.
0.10
Designed Propeller KT
Figure 7 shows a three-dimensional model of the Designed Propeller 10KQ
propeller with a smoother geometry. The stress 0.08
Original Propeller KT
distribution prediction of the designed propeller is based Original Propeller 10KQ
on the program developed by the laboratory using panel 0.06
method and the cantilever beam method, as shown in Fig.

Kt,10Kq
8. The maximum stress value of the paddle is 2.5*107 Pa
0.04
(255.1 kgf/cm2), which is less than the allowable stress of
the material of 637kgf/cm2, and the strength meets the
0.02
requirements.
Table 5 Geometric parameters of the designed propeller 0.00
0 60 120 180 240 300 360
0
r/R B/D P/D T/D f/B ( )
0.2 0.173 0.708
Oj 0.037 -
0.3 8
0.208 RRRr
0.925 8
0.032 0.0074
0.0175 Fig. 9 The thrust coefficient and torque coefficient of the
0.4 2
0.241 9
1.036 2
0.025 0.0253 original HSP propeller and the design master blade
0.5 9
0.272 2
1.069 0.017 0.0291
0.6 7
0.295 1.014 8
0.013 0.029
0.7 5
0.303 7
0.889 4
0.011 0.0258
0.8 1
0.292 6
0.754 2
0.009 0.0202
0.9 4
0.237 9
0.637 4
0.007 0.0095
0.95 0.163 3
0.578 8
0.007 0.0047
1 90 1
0.510 0.006 0
8

Fig. 10 The amplitude of the thrust coefficient of the main blade

of two propellers of a rotation
It can be seen from Table 6 that the designed propeller
provides 2.3% lower thrust and this is aimed to give the
same thrust and better noise performance in unsteady flow
Fig. 7 Designed paddle schematic filed. As can be seen from Figure 9, the thrust coefficients
Y Z
Y
and torque factors of the main blade of these two
X
Z X propellers are relatively consistent during one revolution.
2.5E+0
7
At the same time, as can be seen from Figure 10, the
2E+07 thrust amplitude of the designed paddle is slightly smaller
1.5E+0
than the original paddle, and this is beneficial to reducing
2.5E+0 7
vibration and noise according to design experience. Noise
7
performance comparison should be carried out to verify
1E+07
the design results, and this will be improved in later
2E+0
5E+06 study.
(a)Blade face 7
(b) Blade back
Fig. 8 Designed paddle stress profile 0 3.4Optimization Design Result
1.5E+0
In this example, the wake-adapted theoretical designed
In order to better analyze the performance of the
7
-5E+06

HSP propeller is considered as the parent type, and the

redesigned propeller, unsteady panel method is used to
1E+0
-1E+07
feasibility of the optimized design method is established.
predict its performance, and performance comparison is
7 - Under the designed speed coefficient, the chord, pitch,
carried out, as shown in Table 6 and Figure 10. 1.5E+0 skew, rake, and camber are optimized by iSIGHT
5E+0

7
6

-2E+07
0

-
-

2.5E+0
5E+0

7
6

-3E+07
-
 Y

software to reduce the maximum thrust coefficient and the Z

Z
Y

maximum unsteady thrust amplitude of the main blade. 3.5E+07

X X

3.5E+07

Moreover the maximum stress of the propeller is limited 3E+07

2.5E+07
2E+07
1.5E+07
3E+07
2.5E+07
2E+07
1.5E+07

to 637kgf/cm2. Specifically, the propeller stress 1E+07

5E+06
0
1E+07
5E+06
0
-5E+06 -5E+06

calculation is calculated by the cantilever beam method in -1E+07

-1.5E+07
-2E+07
-1E+07
-1.5E+07
-2E+07
-2.5E+07 -2.5E+07

order to save time in the optimizing process, and the -3E+07

-3.5E+07
-4E+07
-3E+07
-3.5E+07
-4E+07

number of populations is set to 30, and the number of

iterations is 12 times when searching for the target paddle.
The unsteady thrust amplitude of the largest main blade of (a)Blade face (b) Blade back
the optimized paddle is designed as the abscissa and the
Fig. 12 The blade stress distribution of propeller 1
average thrust coefficient is set as ordinate, which
Y

constitutes the Pareto Graph as shown in Figure 11. The Z

Z
Y

point which respects parent type is separated in the Pareto X

3E+07
X

3E+07

Graph. It can be seen that after the optimization design, 2.5E+07

2E+07
1.5E+07
1E+07
2.5E+07
2E+07
1.5E+07
1E+07

the performance of the propeller is further improved. 5E+06

0
-5E+06
-1E+07
5E+06
0
-5E+06
-1E+07

Although the 2ed thrust amplitude of the theoretical -1.5E+07

-2E+07
-2.5E+07
-3E+07
-1.5E+07
-2E+07
-2.5E+07
-3E+07

propeller is larger than that of optimized propellers, the -3.5E+07

-4E+07
-3.5E+07
-4E+07

average thrust coefficient is much smaller, and the main

reason is that the theoretical propeller designing depends
on experience in some extent, so it is not the optimum
(a)Blade face (b) Blade back
solution in real condition. Each coordinate point in the
Pareto Graph represents an optimization scheme that Fig. 13 The blade stress distribution of propeller 2
allows the ship designer to select the appropriate solution Table 7 shows the unsteady thrust amplitude and average
paddle for a different ship. thrust coefficient of the maximum main blade of the two
optimized paddles, theoretical designed paddle and
0.28 original paddle. As is shown from Table 7 and FIG.14,
Optimized Propeller Pareto Graph
Theoretical Propeller the unsteady thrust amplitude of the main maximum blade
Average Thrust Coefficient

0.26
of propeller 1 and propeller 2 are both lower than that of
0.24 original HSP propeller while the average thrust
coefficients are higher. Therefore, the rapidity and
0.22 vibration performance of the propeller 1 and the propeller
2 are better than those of the original HSP in the wake of
0.20
the ship.
0.18 Table 7 Comparison of Hydrodynamic Performance
0.16 The amplitude of Average thrust
thrust of the main coefficient
0.0124 0.0128 0.0132 0.0136 0.0140 0.0144 blade
the 2ed Amplitude of Thrust of the Main Blade Original Propeller 0.01408 0.172
Theoretical Propeller 0.1287 0.168
Fig. 11 Propeller Proper Flow Optimization Design
Propeller Pareto Frontier Propeller 1 0.01292 0.2362
Select two suitable optimization scheme from the Pareto Propeller 2 0.01239 0.229
Graph to analysis, starting now referred to as the propeller
1 and propeller 2. Figures 12 and 13 show the stress
prediction results for the two options. The maximum
stress of the propeller 1 is 3.5*107Pa (357.1 kgf/cm2), and
the maximum stress of the propeller 2 is 3*107 Pa (306.1
kgf). /cm2). It can be seen that the maximum stress of the
two schemes does not exceed 637kgf/cm2, and the
strength meets the requirements.

Fig. 14 Unsteady thrust coefficient of primary blades of primary

and design propellers
 0.40 1.4 occurrence of cavitation. However, the strength of the
0.35

0.30
1.2 whole blade is unfavorable in such condition. The camber
0.25
1.0 at the blade root of these three propellers is much smaller
0.20

P/D
than that of the original HSP paddle, which is
B/D

0.8
0.15 Original HSP Propeller
Theoretical Designed peopeller Original HSP Propeller
0.10

0.05
Propeller 1
Propeller 2 0.6
Theoretical Designed Propeller
Propeller 1
Propeller 2
advantageous for the strength and the hub vortex at the
0.00
0.4 blade root; the camber distribution in the middle of the
-0.05
0.2 0.3 0.4 0.5 0.6
r/R
0.7 0.8 0.9 1.0 0.2 0.3 0.4 0.5 0.6
r/R
0.7 0.8 0.9 1.0
blades of two optimized propellers is larger than that of
the theoretically designed propeller which is useful for
(a) Chord length ratio (b) Pitch ratio improving the thrust of the propeller. The trend of the
0.06
50 skew distribution of all these four propellers are similar,
0.05

0.04
40
but these three propellers have larger skew at the blade tip
30 Original HSP Propeller
0.03

20
Theoretical Designed Propeller
Propeller 1
Propeller 2
than that of the original HSP paddle. This is advantageous
0.02
for reducing the unsteady thrust amplitude of the largest
S(°)
f/B

10
0.01

0.00
Original HSP Propeller
Theoretical Designed Propeller
Propeller 1
0 main blade. For rake, the rake of the blade root of the
-0.01
Propeller 2 -10
optimized paddles is reduced, and the rake near the blade
-0.02 -20
0.2 0.3 0.4 0.5 0.6
r/R
0.7 0.8 0.9 1.0 0.2 0.3 0.4 0.5 0.6
r/R
0.7 0.8 0.9 1.0
tip is increased. Actually, the rake distribution of these
three propellers is quite different from the original paddle,
(c)Camber ratio (d) Skew and this form of distribution is advantageous for the
0.06
strength of the propeller.
Original HSP Propeller 5 CONCLUSIONS
0.04 Theoretical Designed Propeller
Propeller 1 In this paper, the resonance analysis method of the flow
Propeller 2
field, the selection method of the number of blades, skew
0.02
and rake distribution, lifting line and lifting surface
Ra/D

programs, hydrodynamic performance predicting program

0.00
and iSIGHT software are combined to form a relative
complete propeller optimization design process, and some
-0.02
conclusions are listed as follows:
0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1.0 1) B-spline curve is used in the propeller parameterized
r/R
expression process, and the geometric parameter
distribution of the smooth propeller can be obtained with
(e) Rake fewer reasonably selected control points, and the chord
Fig. 15 Comparison of geometric parameters of the original length, pitch, thickness, camber, skew and rake
paddle and design paddle distributions are consistent with the original paddle and
can be applied to the parameter optimization design
Figure 15 shows the chord length, pitch, camber, skew, process of the propeller.
and rake distribution of the original paddle, theoretical
designed paddle and two optimized paddles. Compared 2) The theoretically designed propeller should have such
with the original paddle, the distribution curves of these effect that the hydrodynamic performance is consistent
geometric parameters of the optimized paddles are both with the original propeller, and the strength meets the
smoother than the original paddle, and the distribution requirements, and the vibration and noise performance is
trend is also different from that of the original paddle. The better than the original propeller. Moreover, the propeller
chord lengths at the inner radius of the theoretically described in this paper has realized such effect, verifying
designed propeller and two optimized propellers are the effectiveness of the method.
reduced compared with the original paddle, and thereby 3) The optimized propeller should have better thrust and
the open water efficiency is improved. The pitch of blade vibration performance than the theoretically designed
root and blade tip of these three propellers is smaller than propeller. Also, the result has proved that the optimization
the original paddle, while the pitch of the middle of the process is feasible.
blade is larger than the original paddle, which is
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