4. List of Tables iii
List of Tables
3.1 Geometry of the Wageningen B-screw series[4]. . . . . . . . . . . . . . 9
3.2 Values of V 1 for use in the equations.[4] . . . . . . . . . . . . . . . . 11
3.3 Values of V 2 for use in the equations.[4] . . . . . . . . . . . . . . . . 11
3.4 Coefficients for the KT and KQ polynomials representing the Wa-
geningen B-screen series for a Reynolds number of 2 × 106
.[4] . . . . . 14
4.1 Extent of the Wageningen B-screw series[1]. . . . . . . . . . . . . . . 17
5. 1 Introduction 1
1 Introduction
1.1 Background and context
Being developed for more than one hundred years, propellers have been equipped
by most vessels all over the world as the major propulsion system because of its
relatively high efficiency and simple driving structure. However, due to the highly
twisted geometry and numerous variable parameters, it is hard to operate the de-
sign and optimization loops manually, which is time consuming. Additionally, the
traditional two-dimensional drawing, like figure: 3.3, cannot demonstrate the real
geometry of the propellers. Thus, traditional design method can hardly cooperate
with some advanced manufactural technology, for example 3-D printing.
A new Computer Aided Design (CAD) method called parametric design has be-
come a strong trend in contemporary architecture design practise.
As its name implies, such term means that to digitally model a series of design vari-
ants ,through one or several mathematical connections,whose relationships to each
other are defined. Then, numerous related but distinct structures can be formed.[2]
1.2 Scope and objectives
The main objective of the project is to investigate the feasibility of introducing
parametric design into the design and optimization procedures of propeller. The
project will focus on one propeller series of B-screw which is one of the most widely
used propeller series.
The propeller model is build with the utilization of the software Grasshopper,
which can be projected and changed by just modifying its parameters. Moreover, the
characteristics can be calculated with these parameters and some other coefficients
from the propeller model. Finally the optimization loops can be set just by using
the repeating function.
1.3 Introduction to Grasshopper
Rhinoceros is quite popular among architecture designers, especially those with a
focus on formal design considerations which is used in multiple design industries due
to its ease of use and processing speed.
The Grasshopper is a graphical algorithm editor as a plug-in for Rhinoceros. With-
out formal scripting experience, designers can quickly generate parametric forms
with the plug-in ([2]). As shown in figure 1.1, the functions of Rhinoceros repre-
6. 1.3 Introduction to Grasshopper 2
sented by a number of nodes within Grasshopper, and the relationships of parameters
the connecting lines.
Figure 1.1: The Example of the usage of Grasshopper
Additionally, as several coding languages, such as Visual Basic and Visual C#,
can be used inside Grasshoppers working panel, not only the parametric geometry
design, but also the analysis can be implemented.
Eventually, since the propellers’ structural factors and performance characteristics
depend on several parameters. So, it is suitable to operate design and optimization
with the utilization of Grasshopper, which can dramatically shorten the working
time of designing loop and improve the efficiency.
7. 2 Literature review of the topic area 3
2 Literature review of the topic area
2.1 Ship propellers and propulsion
Paper citation: Carlton, J.S.(2007). Marine propellers and propulsion. – 2nd ed.
Elsevier Ltd. All, 2007.
This book demonstrates almost all aspects of propeller. In it, Carlton(2007)
attempt to balance theoretical and practical considerations in each chapter of the
book. Therefore, the material presented will be valuable for the practitioner in
marine science. For innovative studies, particularly of a theoretical nature, the data
presented here will act as a starting point for further research.
There are twenty-five chapters included by this book. The first two chapters are
the introduction of the subject, chapter three the geometry and the fourth and fifth
the working environment of the propeller and the wake field. Chapters six to fifteen
deal with propulsion hydrodynamics, and the chapters from the seventeenth to the
twentieth deal with the mechanical aspects of propellers. The final five chapters
discuss various practical aspects of propeller technology, starting with design, then
continuing to operational problems, service performance and, finally, to propeller
inspection, repair and maintenance.
This thesis focuses on the third, sixth and twenty-second chapters from the whole
book. The following is the brief introduction and some comments of these chapters.
Chapter three is the beginning of the main component of this book, which con-
siders propeller geometry. Additionally, the part is the foundation of the rest of the
book on which the rest of the book. Without a thorough knowledge of propeller ge-
ometry, the subject will not be fully understood. From which, I acquired a detailed
knowledge about how a propeller model is structure. However, only the traditional
two dimensional cartography is recorded here, which may not suitable for digital
design, consequently it should be modified to attain the requirement of parametric
design.
Chapter six has the name of propeller performance characteristics, which is the
basic knowledge of the propulsion hydrodynamics. To discuss the performance char-
acteristics of a propeller, Carlon(2007) divided the topic into open water and behind-
hull properties. As the open water characteristics is the description of the forces and
moments acting on the propeller when operating in a uniform fluid stream, these
are steady loadings by definition. But, the behind-hull characteristics are those gen-
erated by the propeller when operating in a mixed wake field behind a body, hence
these have both a steady and unsteady part by the very nature of the environment
in which the propeller operates. The author treated both types of characteristics
8. 2.2 OpenProp: An open-source parametric design and analysis tool for propellers4
separately in this chapter, especially for some propeller series. After thoroughly
read this chapter, the propeller of Wageningen B-screw series is chosen as the objec-
tive propeller. The information of such propeller in this book is not detailed, more
specific data should be found.
Each of chapters except this one in this book has considered different aspects
of the propeller in detail. But, in chapter twenty-two, Carlon(2007) attempts to
provide a basis for drawing together the various threads of the subject, so that the
propeller and its design process can be considered as an integrated entity. The real
propeller design is the loop that contains different phases of design and optimization,
which can be seen from the figure below (fig: 2.1). Actually, the whole propeller
design procedures should comprise information from vessels that is not derived. So,
the project only includes part of the design loop.
Figure 2.1: The phases of propeller design[1]
2.2 OpenProp: An open-source parametric design
and analysis tool for propellers
Epps, B., Chalfant, J., Kimball, R., Techet, A., Flood, K., & Chryssostomidis, C.
(2009). OpenProp: An open-source parametric design and analysis tool for pro-
pellers. In Proceedings of the 2009 Grand Challenges in Modeling & Simulation
Conference (pp. 104-111). Society for Modeling & Simulation International.
OpenProp is a suite of open-source propeller and turbine design codes written
in the MATLAB programming language[2]. The methodology of these codes is the
9. 2.2 OpenProp: An open-source parametric design and analysis tool for propellers5
same as what utilized by the US Navy for parametric design of marine propellers.
Being a GUI-based user-friendly tool, OpenProp can be used by both propeller
design professionals as well as beginners to it.
Started from 2001, a team of researchers at MIT, Marine Maritime Academy and
Univeresity of Marine have contributed to the OpenProp code.
In OpenProp, the input parameters, design, geometry, and operating states of a
propeller are collected with the usage of data structures. iIn the figure 2.2, the data
flow is illuminated. From this figure, it can be seen that after the data (diameter,
rotation rate) is inputted and optimised, the procedures go into two parts. In the
one part (the right part) the consequential propeller design is analysed at off-design
conditions in the analyser to determine off-design operating states. The other part,
the crafter than draw the three dimensional geometry and prepare rapid prototyping
files for producing the propeller. The total design loop of the recent project is based
on such data flow structure. But, the methodology of this is a little bit not suitable
for the usage of the propeller of Wageningen B-screw series.
Figure 2.2: OpenProp information flow chart[2]
10. 2.3 Further computer-analysed data of the Wageningen B-screw series 6
2.3 Further computer-analysed data of the
Wageningen B-screw series
Oosurveld, M.W.C., & Van Oossanen, P. (1975). Further computer-analysed data of
the Wageningen B-screw series.
This paper illustrates the detailed polynomials that give the open-water character-
istics of the Wageningen B-series propellers. With the help of a multiple regression
analysis of the original open-water test data of the 120 propeller models comprising
the B-series, these polynomials were derived. Than, all test data was corrected for
Reynolds effects via an equivalent profile method developed by Lerbs.
The open-water characteristics of such propeller series can be derived by polyno-
mials, which can be easily employed by coding software. Because loads of propeller
characteristics can only be derived with graphs that may be hard to be applied
digitally. Furthermore, dislike the description of the characteristics of Wageningen
B-series propellers from the book ’Marine propellers and propulsion’, the information
of it here is detailed, for example, each of the parameters appears in the polynomials
are explained specifically.
11. 3 Preliminary analysis 7
3 Preliminary analysis
3.1 Fundamental parameters
A number of parameters should be utilized when designing a propeller. The following
paragraphs define the fundamental parameters can be utilized in either geometry or
optimization.
VA is the advance velocity, D the diameter of propellers and Z the blade number.
N is the rotation ratio per minute with the unit of round/min, which usually
transferred to the rotation ratio per second n = N/60.
Pitch ratio is P/D, where D is the diameter of the propeller and P is the pitch.
Here the meaning of pitch is shown by the figure 3.1. Assume a point P locating
on the surface of a cylinder of radius r being at some initial point P0.Then it moves
towards the direction of the blade profile as the figure shows which forms a helix over
the cylinder surface and the points P1,P2,...,Pn illustrates the helical track. Then,
pitch is the axial distance of two nearby points which have the same circumferential
position on the cylinder surface, such as the distance of the points P0,P12 from the
picture 3.1.
Figure 3.1: Definition of pitch .[1]
Blade area ratio (AE/AO or BAR) is the ratio of expanded area (AE) to the area
of the roundness(AO) with the diameter which equals to the propeller diameter D.
From the fig:3.2, the expanded area is the area surrounded by the expanded outline
which is the outline of the blade profiles on the plane.
12. 3.2 Characteristics of Wageningen B-screw series 8
Figure 3.2: Outline definition.[1]
The thrust coefficient, torque coefficient, advance coefficient are illustrated in
following equations:KT = T
ρn2D4 , KQ = Q
ρn2D5 and J = VA
n·D
, where T and Q are the
propeller thrust and torque. And all the other coefficients in those equations have
already be shown in the previous paragraphs.
3.2 Characteristics of Wageningen B-screw series
Wageningen B-screw series is perhaps the most extensive and widely used propeller
series which is a comprehensive fixed pitch, non-ducted propeller series with general
purposes.
3.2.1 Geometry
The fig3.3 shows the geometry of the B-screw propeller series with five blades. From
the figure, it can be identified that the propeller geometry is built by using expanded
profiles which are the surfaces of a blade cut by the cylinder surface with different
radius. The rake here is fifteen degrees.
Figure 3.3: The Geometry of B5-screw series[1]
The following texts inside the section illustrate the geometry factors of blade
sections from 0.2R to 1.0R (R is the radial of the propeller). The table below (3.1)
gives the general dimensions, such as the chords and maximum thickness of each
sections.
13. 3.2 Characteristics of Wageningen B-screw series 9
Table 3.1: Geometry of the Wageningen B-screw series[4].
Dimensions of four-, five-, six- and seven-bladed
seven-bladed B-screw series.
r/R c
D
· Z
AE/AO
a/c b/c t/D = Ar − Br · Z
Ar Br
0.2 1.662 0.617 0.350 0.0526 0.0040
0.3 1.882 0.613 0.350 0.0464 0.0035
0.4 2.050 0.601 0.351 0.0402 0.0030
0.5 2.152 0.586 0.355 0.0340 0.0025
0.6 2.187 0.561 0.389 0.0278 0.0020
0.7 2.144 0.524 0.443 0.0216 0.0015
0.8 1.970 0.463 0.479 0.0154 0.0010
0.9 1.582 0.351 0.500 0.0092 0.0005
1.0 0.000 0.000 0.000 0.0030 0.0000
Dimensions of three-bladed propellers.
r/R c
D
· Z
AE/AO
a/c b/c t/D = Ar − Br · Z
Ar Br
0.2 1.633 0.616 0.350 0.0526 0.0040
0.3 1.832 0.611 0.350 0.0464 0.0035
0.4 2.000 0.599 0.350 0.0402 0.0030
0.5 2.120 0.583 0.355 0.0340 0.0025
0.6 2.186 0.558 0.389 0.0278 0.0020
0.7 2.168 0.526 0.442 0.0216 0.0015
0.8 2.127 0.481 0.478 0.0154 0.0010
0.9 1.657 0.400 0.500 0.0092 0.0005
1.0 0.000 0.000 0.000 0.0030 0.0000
Ar, Br = constants in equation for t/D.
a = distance between leading edge and generator line at r.
b = distance between leading edge and location of maximum thickness.
c = chord length of blade section ar radius r.
t = maximum blade section thickness at radius r.
The diagram (2.1) shows a typical blade section. By it, the detailed meaning of
each of the parameters recorded in this section is illustrated.
Then, by combing the equations of 3.1 and 3.1 with the data of V1 and V2 which
are kept in the table 3.2 and 3.3 respectively, the Y-coordinates of the face and back
line of a profile are derived. Finally, the plane sections of a propeller blade can be
gained by linking it with the coefficients.
14. 3.2 Characteristics of Wageningen B-screw series 10
Figure 3.4: The sketch diagram of the profile of B5-screw series[4]
Yface = V1(tmax − tt.e.)
Yback = (V1 + V2)(tmax − tt.e.) + tt.e.
for P ≤ 0. (3.1)
Yface = V1(tmax − tl.e.)
Yback = (V1 + V2)(tmax − tl.e.) + tl.e.
for P ≥ 0. (3.2)
Referring to the diagram 3.4, notice the following:
Yface, Yback are vertical ordinate of a point on a blade section on the face and on
the back with respect to the pitch line. tmax is the maximum thickness of blade
section. tt.e., tl.e. are extrapolated blade section thickness at the trailing and leading
edges. V1, V2 are tabulated functions dependent on r/R and P. P is non-dimensional
coordinate along pitch line from position of maximum thickness to leading edge
(where P = 1), and from position of maximum thickness to trailing edge (where
P = −1).
16. 3.2 Characteristics of Wageningen B-screw series 12
3.2.2 Analysis
Oosterveld and van Oossanen (1975)[4] reported the results of their experiments
in which the open-water characteristics of the B-screw series are represented. The
polynomials (3.7 and 3.6 in the advance ratio J, the pitch ratio P/D, the blade area
ratio AE/AQ, and the blade number Z express the thrust and torque coefficients KT
and KQ of the screws for the Reynolds number Rn equals to 2 × 106
. Additionally,
Rn is regarded as 2 × 106
when it is less the 2 × 106
.
KQ =
47
i=1
Cn(J)sn
(P/D)tn
(AE/AO)un
(Z)vn
(3.3)
KT =
39
i=1
Cn(J)sn
(P/D)tn
(AE/AO)un
(Z)vn
(3.4)
The coefficients of Cn,sn,,tn,un and vn are replicated in Table 3.4. After the
calculation, KT and KQ can be derived.
However, when the Reynolds number is more than 2×106
, The effect of a Reynolds
number variation on the test results has been taken into account by using the method
developed Lerbs([3]).
This is the origin formula to predict Reynolds number: Rn = V ·L
ν
. According to
the Lerbs([3]) equivalent profile method, the blade section at 0.75R can be assumed
to be equivalent for the whole blade. Here, the Reynolds number is defined by using
the following equation (3.5) given by Lerbs([3]):
Rn =
c0.75R · V 2
A + (0.75πnD)2
ν
(3.5)
where, c0.75R is the chord length at 0.75R and ν the kinematical viscosity.
To extend the work, to predict KT and KQ, further to be suitable for larger
Reynolds number, Oosterveld and van Oossanen(1975)[4] have performed more ex-
ercises for Reynolds numbers equal to 2 × 107
, 2 × 108
and 2 × 109
for a chosen set
of J, P/D, Z and AE/AQ values. In cooperation with the values for Rn = 2 × 106
,
those KT and KQ values developed the input for the determination of a KT and
KQ polynomial for the extra effect of Reynolds number more above 2 × 106
. These
polynomials are given in equation 3.6 and 3.7.
19. 4 Realization of parametric propeller design with Grasshopper 15
4 Realization of parametric propeller design
with Grasshopper
This chapter introduces main steps of the realization of the parametric propeller
design and optimization. The left part of figure 4.1 shows the final working panel in
Grasshopper, and the right part the finished propeller design. From the left part of
it, it can be seen that there are three parts in the project represented by different
colors of blue, green and yellow. The blue part is the part of general parameters,
the green part the geometry of the propeller,and the yellow part the analysis. The
chapter separately describes the procedures of building these three segments.
Figure 4.1: The finished in Grasshopper
4.1 general parameters
All the parameters illustrated in the section:3.1 are some quite basic parameters
which may not be used by the geometry or analysis procedures directly. Thus, what
should be introduced in this section is the introduction of these data into the plug-in
software Grasshopper and some simple transformation.
To be a unique component in the project, the General Parameters is the begin-
ning of the programme. As can be seen in the figure 4.2, there are three kinds of
parameters in this component, the variables, the fix quantities and the value derived
by using the variables or fix quantities with some mathematical equations.
20. 4.1 general parameters 16
Figure 4.2: The part of general parameters
Number slider is used to represent the changeable values which can be floating
point number, integer number, even or odd number. It is obviously shown in the
picture 4.3a that the advance velocity, diameter, pitch ratio, and rotation ratio per
minute are defined with such way.
(a) The Variables in Grasshopper (b) The fix quantities in Grasshopper
But, it may looks odd that the blade number (Z) and blade area ratio (BAR)
are defined together with a integer number slider from 1 to 20. From the book
’Marine propellers and propulsion’ [1], The extent of the series in terms of a blade
number versus blade area ratio matrix is given in table ??, from which it can be seen
that there are twenty blade area-blade number configurations in the series. Hence,
to make the discontinuous variables be capable of the automatic optimisation, the
slider of Z-BAR is combined with a Python script to give formal blade area-blade
number configurations. For example, if Z-BAR is 1 the Python will show Z=2 and
21. 4.2 Geometry of the propeller 17
Table 4.1: Extent of the Wageningen B-screw series[1].
Blade number(Z) Blade area ratio AE/AO
2 0.3
3 0.35 0.5 0.65 0.80
4 0.4 0.55 0.70 0.85 1.00
5 0.45 0.60 0.75 1.05
6 0.5 0.65 0.80
7 0.55 0.70 0.85
BAR=0.3, and than 2 means B3-35, 3 B3-50,..., 20 B7-85. In this way, the whole
information in this table is given.
From the figure 4.3b, the fix quantities in the table 3.1 in the previous section 3.2
is stored by the panels of notes and values. In each panel the values are arranged
with the order of the radius of the cylinders, on which the sections located, from
0.2R to1.0R.
After having these two kinds of values, the data, which can be applied by either
geometry or analysis, can be derived with some mathematical procedures. The
procedures to get such parameters is shown in the figure 4.4.
Figure 4.4: Calculated parameters
4.2 Geometry of the propeller
The figure below (4.5) mainly create the plate coordinates to build the blade. For
example, the middle yellow panels are the V1 and V2 values from the table 3.2 and
3.3. By using the equation 3.1 and 3.2, the y-ordinates of both the face and back of
the blades can be obtained.
22. 4.2 Geometry of the propeller 18
Figure 4.5: The part of geometry
However, the main procedures to build blades are within a order node caller
Cluster, which is used to simplify the appearance of the software because if there
are too many nodes existed it may be very hard to distinguish the relationship of
these order nodes. The figures from 4.6 gives the outside and inside aspects of
the Cluster of geometry building, which are shown in the left and right pictures
respectively. The rest of this section introduces the detailed way to build an unique
blade profile.
Figure 4.6: The outside and inside aspects of the Cluster of geometry building.
The procedures to position points is showing in the figures of 4.7. The left picture
shows the points on plate constructed with the coordinates originally imported by
using the order node ’Construct Point’. Then, the points are rotated to a have
suitable angle to the advance direction. As B-screw propeller series are all fixed
pitch, the angle is determined by the following equation 4.1:
θ =
P
2πr
(4.1)
After that, the points should be putted on the cylinder with the radius of r.
The coordinates of points are derived by using the order of ’Deconstruct Point’.
Then, with these coordinates, the real points on the cylinder with radius of r can
be constructed by using the cylindrical points constructor ’Point Cylindrical’.
23. 4.3 Analysis of the propeller 19
Figure 4.7: The procedures to position points
The lines of each section can be organized with these located points. Finally, one
single blade can be built by using the loft order, which is shown in 4.8.
Here, one B-screw propeller blade consists of nine sections, and sections should
be dealt by the same orders. Hence, the working panels are usually filled with
connecting lines and order nodes, which may make it hard to understand or further
develop the whole programme even for the developer him/her-self. To deal with
such problem, the tree system in Grasshopper, which can utilize parallel operation
to deal with multiple data.
Figure 4.8: The geometry of single blade
4.3 Analysis of the propeller
The figure 4.9 shows working panel of the analysis part. The equations in the
subsection 3.2.2 have been utilized here to derive the propeller thrust and torque
coefficient (KT , KQ), then the value of propeller thrust (T), torque (Q) and open-
24. 4.4 Automatic optimisation 20
water efficiency (ηO) can be obtained by using the equations of3.6, 3.6 and 3.9
respectively.
Figure 4.9: The part of analysis
4.4 Automatic optimisation
The the function of ’Galapagos Genetic Input’ (Genome) in Grasshopper can operate
on any number of slider objects. Certain sliders should be assigned to the Galapagos
object for them to become part of ’Genome’.[5]
Figure 4.10: The tool of Genome
From the figure 4.10, the usage of Genome is illustrated. The ’Genome’ end
should be connected to the parameter sliders which are wanted to be taken into
optimisation. Whilst the ’Fitness’ end should be connected to the target which
should be the maximum or minimum.
As the optimisation procedure may contains the loop of ’changing-analysis’ for
thousands times, the geometry component should be excepted to avoid wasting to
much time on it. So the data dam (4.11),was used. It can barrier the data when it
25. 4.5 The test of the programme 21
has changed until the start bottom, the small triangle located in the center of it, is
clicked.
Figure 4.11: Data dam
4.5 The test of the programme
In the programme, the only optimisation judgement is the open-water efficiency.
Usually the advance velocity, diameter and required effective power are set. And
pitch ratio, rotate ratio and Z-BAR will be changeable. The example is shown below.
Figure 4.12: The usage of the programme
Figure 4.13: The running of the optimisation
26. 5 Conclusions and further discussion 22
5 Conclusions and further discussion
5.1 Achievement of the programme
This project has experience the whole parametric design and the optimization of the
propeller. First, it is obvious Grasshopper is a excellent parametric design plug-in
software, which permits guests perform geometry design as coding a programme. In
this way the models can be parametrically variable, which means one parametric
design equals to the design of a series of similar geometries.
Furthermore, when mathematical measurement functions be introduced in to the
parametric design, the digital analysis can link visual design directly. Such advantage
is perfectly shown on the parametric design of propeller, because the propeller’s
performance greatly relies on its shape parameter.
5.2 The shortages of this programme
Although great achievements exist in this programme, there still are some shortages.
Firstly, the analysis and optimisation are only based on the open-water perfor-
mance and only B-screw propeller are applied. So, the programme cannot be used
prevalently.
Secondly, when the effective power is limited, it may be hard for the loop solver
to find a set of valid values.
5.3 Further discussion
To look into the further, the optimization solver should be specifically designed
which should have higher efficiency and reliability.
Moreover, the analysis component should be suitable to more propellers, and the
finite element method should be taken account if possible.
Finally, the parametric design and optimization should be extended vessels which
can combine with propeller design and analysis to make all the geometry design
around ship automatic.
27. Bibliography 23
Bibliography
[1] J. S. Carlton. Marine Propellers and Propulsion.-2nd ed. Elsevier Ltd. All, 2007.
(document), 2.1, 3.1, 3.2, 3.3, 4.1
[2] Chalfant J. Kimball R. Techet A. Flood K. Chryssostomidis C. Epps, B. Open-
prop: An open-source parametric design and analysis tool for propellers. In
Proceedings of the 2009 Grand Challenges in Modeling & Simulation Conference
(pp. 104-111)., 2009. (document), 1.1, 1.3, 2.2, 2.2
[3] H.W. Lerbs. ’on the effect of scale and roughness on free running propellers. In
Journal ASME, 1951. 3.2.2
[4] Oossanen P.V. Oosurveld, M.W.C. Further computer-analysed data of the wa-
geningen b-screw series. International Shipbuilding Progress & Shipbuilding and
Marine Engineering Monthly, Vol. 22:No. 251, 1975. (document), 3.1, 3.4, 3.2,
3.3, 3.2.2, 3.2.2, 3.4
[5] Issa R. Payne, A. Grasshopper Primer for Version 0.6.0007. 4.4
