· PDF fileIJRAET DESIGN AND SIMULATION OF A MARINE PROPELLER ... surfaces of the airfoil ......
Transcript of · PDF fileIJRAET DESIGN AND SIMULATION OF A MARINE PROPELLER ... surfaces of the airfoil ......
Volume 5, Issue 1 SEP 2015
IJRAET
DESIGN AND SIMULATION OF A MARINE PROPELLER
1 T. CHITTARANJAN KUMAR REDDY, 2 K.NAGARAJA RAO
1 PG Scholar, Department of MECH, VIVEKANANDA GROUP OF INSTITUTIONS, Ranga Reddy, Telangana, India.
2 Associate Professor (HOD), Department of MECH, VIVEKANANDA GROUP OF INSTITUTIONS, Ranga Reddy,
Telangana, India.
Abstract—
A propeller is a type of fan that transmits power by
converting rotational motion into thrust. A pressure
difference is produced between the forward and rear
surfaces of the airfoil-shaped blade, and a fluid (such as air
or water) is accelerated behind the blade. Propeller
dynamics can be modelled by both Bernoulli's principle
and Newton's third law. A marine propeller is sometimes
colloquially known as a screw propeller or screw.
The present work is directed towards the study of marine
propeller working and its terminology,simulation and flow
simulation of marine propeller has been performed.The
von misses stresses ,resultant deformation ,strain and areas
below factor of safety has been displayed.
The velocity and pressure with which the propeller blades
pushes the water has been displayed in the results.
KEYWORDS: Propeller, Design, Analysis, Static, CDF
(Computational Flow Dynamics)
INTRODUCTION
INTRODUCTION TO PROPELLER:
A propeller is a type of fan that transmits power by
converting rotational motion into thrust. A pressure
difference is produced between the forward and rear
surfaces of the airfoil-shaped blade, and a fluid (such as air
or water) is accelerated behind the blade. Propeller
dynamics can be modelled by both Bernoulli's principle
and Newton's third law. A marine propeller is sometimes
colloquially known as a screw propeller or screw.
Marine propeller
HISTORY AND DEVELOPMENT:
The concept of a propulsion device resembling what is
now called the screw propeller is certainly not new. The
experience of ancients with sculling oars, coupled with the
later development of rotary engines, obviously suggested a
combination of a series of inclined plates secured to a
rotary hub. In 945 B.C., the Egyptians used a screw-like
device for irrigation purposes. Archimedes (287-212 BC),
the first scientist whose work had a lasting effect on the
history of naval architecture and ship propulsion, has been
credited with the invention of the screw.Hecreated the
screw to pump out flooded ships.
The screw pump, designed by Archimedes for supplying
irrigation ditches, was the forerunner of the screw
propeller. Drawings done by Leonardo DA Vinci (1452-
1519) (Figure 1-1 below) contain pictures of water screws
Volume 5, Issue 1 SEP 2015
IJRAET
for pumping. However, his famous helicopter rotor more
nearly resembles a marine screw.
Despite this knowledge, application of screw propulsion to
boats and ships didn't take place until the advent of steam
power. Due to greater suitability with the slow-turning,
early steam engines, the first powered boats used paddle
wheels for a form of water propulsion. In 1661, Toogood
and Hays adopted the Archimedian screw as a ship
propeller, although their boat design appears to have
involved a type of water jet propulsion.
At the beginning of the 19th century, screw propulsion was
considered a strictly second-rate means of moving a ship
through the water. However, it was during this century that
screw propulsion development got underway. In 1802,
Colonel John Stevens built and experimented with a
single-screw, and later a twin-screw, steam-driven boat.
Unfortunately, due to a lack of interest, his ideas were not
accepted in America.
The Invention of the Screw Propeller
The credit for the invention of the screw propeller narrows
down to two men, Francis Petit Smith and John Ericsson.
In 1836, Smith and Ericsson obtained patents for screw
propellers, marking the start of modern development.
Ericsson's patent covered a contra-rotating bladed wheel,
as well as twin-screw and single-screw installations.
Ericsson's propeller design took advantage of many of the
unique benefits of the bladed wheel. With the wheel, it was
possible to obtain the increased thrust of a large number of
blades in a small diameter without cluttering up the area
adjacent to the hub.
Yet, both the inner and outer elements supplied propulsive
thrust. The wheel design was inherently strong, without
much unnecessary material to interfere with its basic
action. The outer ring also served to keep lines, ice, and
debris away from the blades. There is no clear-cut
evolution of the bladed wheel into the modern screw
propeller, although the bladed wheel possessed most of the
elements of a successful propulsive device. It seems to
have been used in the original Ericsson form and then
dropped in favor of the conventional screw.
BASIC PROPELLER PARTS :
The first step to understanding propellers and how they
work is familiarizing your-self with the basic parts of a
boat propeller.
A. Blade Tip: The maximum reach of the blade from the
center of the propeller hub. It separates the leading edge
from the trailing edge.
B. Leading Edge: The part of the blade nearest the boat,
which first cuts through the water. It extends from the hub
to the tip.
Volume 5, Issue 1 SEP 2015
IJRAET
C. Trailing Edge: The part of the blade farthest from the
boat. The edge from which the water leaves the blade. It
extends from the tip to the hub (near the diffuser ring on
through-hub exhaust propellers).
D. Cup: The small curve or lip on the trailing edge of the
blade, permitting the propeller to hold water better and
normally adding about 1/2" (12.7 mm) to 1" (25.4 mm) of
pitch.
E. Blade Face: The side of the blade facing away from the
boat, known as the positive pressure side of the blade.
F. Blade Back: The side of the blade facing the boat,
known as the negative pressure (or suction) side of the
blade.
G. Blade Root: The point where the blade attaches to the
hub.
H. Inner Hub: This contains the Flo-Torq rubber hub or
Flo-Torq II Delrin® Hub System (Figures 2-2 above and
2-3). The forward end of the inner hub is the metal surface
which generally transmits the propeller thrust through the
forward thrust hub to the propeller shaft and in turn,
eventually to the boat.
I. Outer Hub: For through-hub exhaust propellers. The
exterior surface is in direct contact with the water. The
blades are attached to the exterior surface. Its inner surface
is in contact with the exhaust passage and with the ribs
which attach the outer hub to the inner hub.
J. Ribs: For through-hub exhaust propellers. The
connections between the inner and outer hub. There are
usually three ribs, occasionally two, four, or five. The ribs
are usually either parallel to the propeller shaft ("straight"),
or parallel to the blades ("helical").
K. Shock-Absorbing Rubber Hub: Rubber molded to an
inner splined hub to protect the propeller drive system
from impact damage and to flex when shifting the engine,
to relieve the normal shift shock that occurs between the
gear and clutch mechanism - generally used with low
horsepower applications.
L. Diffuser Ring: Aids in reducing exhaust back pressure
and in preventing exhaust gas from feeding back into
propeller blades.
M. Exhaust Passage: For through-hub exhaust propellers.
The hollow area between the inner hub and the outer hub
through which engine exhaust gases are discharged into
the water. In some stern drive installations using a
through-transom exhaust system, this passage carries air.
N. Performance Vent System (PVS): PVS, is a patented
Mercury ventilation system, allows the boater to custom
tune the venting of the propeller blades for maximum
planing performance. On acceleration, exhaust is drawn
out of the vent hole located behind each blade.
When the next propeller blade strikes this aerated water,
less force is required to push through this water allowing
the engine RPM to rise more rapidly.
Water flows over the vent holes once the boat is on plan
sending exhaust through the exhaust passage. Varying the
size of the exhaust holes engine RPM can be controlled,
outboards perform better with venting and stern drives
typically require less venting if any at all.
Hub Configurations :
At the center of the propeller is the hub. If exhaust gases
are discharged into the water through the hub, the propeller
is called a through-hub exhaust (or Jet-Prop™ exhaust)
propeller.
If the exhaust gases are not discharged into the water
through a passage in the hub, but rather over the hub, the
propeller is called an over-the-hub exhaust propeller.
Volume 5, Issue 1 SEP 2015
IJRAET
through the propeller's hub. This is accomplished by
extending the drive shaft out through the very bottom of
the transom. When running properly only one blade of a
two bladed propeller is actually in the water. The surface
propeller is very efficient at minimizing or eliminating
cavitation by replacing it with ventilation. With each
stroke, the propeller blade brings a bubble of air into what
would otherwise be the vacuum cavity region.
SOLIDWORKS
Solid Works is mechanical design automation software
that takes advantage of the familiar Microsoft Windows
graphical user interface.
It is an easy-to-learn tool which makes it possible for
mechanical designers to quickly sketch ideas, experiment
with features and dimensions, and produce models and
detailed drawings.
A Solid Works model consists of parts, assemblies, and
drawings.
Typically, we begin with a sketch, create a base feature,
and then add more features to the model. (One can also
begin with an imported surface or solid geometry).
We are free to refine our design by adding, changing, or
reordering features.
Associativity between parts, assemblies, and drawings
assures that changes made to one view are automatically
made to all other views.
We can generate drawings or assemblies at any time in
the design process.
The SolidWorks software lets us customize functionality
to suit our needs.
MODELLING OF MARINE PROPELLER
Modeling of marine propeller :
First sketching the outer hub on right plane as shown
below:
Figure : sketch of outer hub
Then by using revolve option outer hub is generated as
shown
Figure : revolve of outer hub
Now blade profile is sketched on reference plane which is
taken by 30 deg angle to right plane .
sketching of blade profile
Then blade extrusion of 5mm is performed as shown
Volume 5, Issue 1 SEP 2015
IJRAET
Extrusion of blade
By using flex operation bending of blade is generated as
shown
Figure : Bending of blade
Next extrusion of inner hub is performed as shown below
Extrusion of inner hub
Now blades are circularly patterned on the outer hub
.here we are generating three blade propeller as shown
circular pattern of blades
Now Ribs are extruded as shown
Extrusion of ribs
Necessary filleting and chamfering is done and the final
marine propeller is as follows:
Marine propeller
Four different views of marine propeller as shown below :
Volume 5, Issue 1 SEP 2015
IJRAET
Different views of marine propeller
FINITE ELEMENT MODELLING
INTRODUCTION TO FEM
Many problems in engineering and applied science are
governed by differential or integral equations. The
solutions to these equations would provide an exact, closed
form solution to the particular problem being studied.
However, complexities in the geometry, properties and in
the boundary conditions that are seen in most real world
problems usually means that an exact solution cannot be
obtained in a reasonable amount of time. They are content
to obtain approximate solutions that can be readily
obtained in a reasonable time frame and with reasonable
effort. The FEM is one such approximate solution
technique.
The FEM is a numerical procedure for obtaining
approximate solutions to many of the problems
encountered in engineering analysis. In the FEM, a
complex region defining a continuum is discretised into
simple geometric shapes called elements. The properties
and the governing relationships are assumed over these
elements and expressed mathematically in terms of
unknown values at specific points in the elements called
nodes. An assembly process is used to link the individual
elements to the linked system. When the effects of loads
and boundary conditions are considered, a set of linear or
nonlinear algebraic equations is usually obtained. Solution
of these equations gives the approximate behaviour of the
continuum or system. The continuum has an infinite
number of degrees of freedom (DOF), while the discretised
model has a finite number of DOF. This is the origin of the
name, finite element method.
SIMULATION OF MARINE PROPELLERThe static
analysis is performed on marine propeller .When the ice
block of 2000N hits the marine propeller the effects have
been observed .
Naming the static analysis as marine propeller simulation
Marine propeller simulation
ADDITION OF MATERIAL TO PROPELLER:
Adding 6061 alloy material to the propeller as shown
below.
Figure : Addition of alloy steel to propeller
FIXING OF GEOMETRY :
Volume 5, Issue 1 SEP 2015
IJRAET
Shaft diameter is kept fixed in propeller becase it connects
the propeller and engine.
Figure : fixing of geometry
APPLICATION OF LOAD :Loads are applied to the
blades ,outerhub,inner hub and ribs of the propeller.
Figure : Application of load of 2000N
MESHING:
Fine Meshing of size 6mm is performed on the propeller
then the meshing modelled is shown below:
Fine meshing of size 6mm
SOLVE :
Then running the simulation of propeller to see the von
misses stresses,resultant displacement and areas below
Factor of safety.
running the simulation
RESULTS :
Volume 5, Issue 1 SEP 2015
IJRAET
von misses stresses for fine meshing
The yield strength for the material is 620.4MPa and the
maximum stress obtained is 699.4(Mesh size 6mm) MPa.
It means that if the stress is greater than the yield stress
the material will not break but will deform plastically.
Deflection for fine meshing of size 6mm
Figure : strain produced on propeller
areas below factor of safety
A factor of safety less than 1 at a location indicates that the
material at that location has failed.A factor of safety of 1 at
a location indicates that the material at that location has
just started to fail. A factor of safety greater than 1 at a
location indicates that the material at that location is safe.
COMPARISION OF RESULTS:
Volume 5, Issue 1 SEP 2015
IJRAET
Figure :comparision of results
FLOW SIMULATION
SOLIDWORKS FLOWSIMULATION
INTRODUCTION :
SolidWorks Flow Simulation 2010 is a fluid flow analysis
add-in package that is available forSolidWorks in order to
obtain solutions to the full Navier-Stokes equations that
govem the motion of fluids. Other packages that can be
added to SolidWorks include SolidWorks Motion and
SolidWorks Simulation. A fluid flow analysis using Flow
Simulation involves a number of basic steps that are shown
in the following flowchart in figure.
Flowchart for fluid flow analysis using Solidworks Flow
Simulation
INSERTING BOUNDARV CONDITIONS: boundary
conditions are required for both the inflow and outflow
faces of internal flow regions with the exception of
enclosures subjected to natural convection. Visualization
of boundary conditions can be shown with anows of
different colors indicating the type and direction of the
boundary condition. The boundary conditions are divided
in three different types: flow openings, pressure openings
and walls.
List of available boundary conditions in Solid Works Flow
Simulation
Each boundary condition has a number of parameters
related to it that can be set to different values. The
available parameters for each boundary condition are
shown in table below:
List of available parameters for different boundary
conditions in Solid Works Flow Simulation
The flow parameter depends on the boundary condition but
includes velocity, Mach number and mass and volume
flow rate. The direction of the flow vector can be specified
Volume 5, Issue 1 SEP 2015
IJRAET
as normal to the face, as s'wirl or as a 3D vector. The
thermodynamic parameters include temperature and
pressure. For the turbulence parameters you can choose
between speci[ing the turbulence intensity and length or
the turbulence energy and dissipation (k-e turbulence
model). The boundary layer is set to either laminar or
turbulent. You can also specify velocity and thermal
boundary layer thickness for the inlet velocity boundary
condition as well as speciry the core velocity and
temperature. For the real wall boundary condition you can
speciry the wall roughness together with wall temperature
and heat transfer coefficient. The real wall
also has an option for motion in the form of translational or
angular velocity.
CHOOSING GOALS:
Goals are criteria used to stop the iterative solution
process. The goals are chosen from the physical
parameters of interest to the user of Flow Simulation. The
use of goals minimizes errors in the calculated parameters
and shortens the total solution time for the solver. There
are five different types of goals:
Global goals, point goals, surface goals, volume goals and
equation goals. The global goal is based on parameter
values determined everywhere in the flow field whereas a
point goal is related to a specific point inside the
computational domain. Surface goals are determined on
specific surfaces and volume goals are determined within a
specific subset of the computational domain as specified
by the user. Finally, equation goals are defined by
mathematical expressions. Table is showing 48 different
parameters that can be chosen by the different types of
goals.
Figure : List of available parameters for different goals in
SolidWorks Flow Simulation
VIEWING RESULTS
Results can be visualized in a number of different ways as
indicated by table :
List of available results in SolidWorks Flow Simulation
ADVANTAGES OF FLOW SIMULATION :
Low Cost:
Volume 5, Issue 1 SEP 2015
IJRAET
The most important advantage of computational prediction
is its low cost. In most applications, the cost of a computer
run is many orders of magnitude lower than the cost of
corresponding experimentation. This can reduce or even
eliminate the need for expensive or large-scale physical
test facilities. This factor assumes increasing importance
as the physical situation to be studied becomes larger and
more complicated. Further whereas the prices of most
items are increasing, computing cost is likely to be even
lower in the future.
Speed:
A computational investigation can be performed with
remarkable speed. A designer can study the implication of
hundreds of different configurations in less than a day and
choose the optimum design process; rapid evaluation of
design alternatives can be made. On the other hand, a
corresponding experimental investigating would take a
long time.
Complete information:
A computer solution of problem gives detailed and
complete information. It can provide the values of all
relevant variables (such as velocity, pressure, temperature,
concentration, turbulence intensity) throughout the domain
interest. This provides a better understanding of the flow
phenomenon and the product performance. For this
reason, even when an experiment is performed, there is
great value in obtaining a companion computer solution to
supplement the experimental information.
Ability to stimulate Realistic Conditions:
In theoretical calculation, realistic conditions can be easily
stimulated. There is no need to resort to small scale or
cold models. Through a computer program, there is little
difficulty in having a very large or very small dimension,
in treating very low or very high temperatures, in handling
toxic or flammable substances, or in following very fast or
very slow processes.
Ability to stimulate Ideal Conditions: A prediction
method is sometimes used to study a basic phenomenon,
rather than a complex engineering application. In the
study of phenomenon, one wants to focus attention on a
few essential parameters and eliminates all irrelevant
features. Thus many idealizations are desirable for
example: two dimensionally constant densities an adiabatic
surface of an infinite reaction rate. In a computation
approach, such conditions can be setup with case and
precision, whereas even careful experimental can barely
approximate the idealization.
Reduction of Failure risks: CFD can also be used to
investigate configurations that may be too large to test or
which pose a significant safety risk including pollutant
spread and nuclear accident scenarios. This can often
provide confidence in operation, reduce or eliminate the
cost of problem solving during installations, reduce
product liability risks.
APPLICATIONS OF FLOW SIMULATION :
Automobile and Engine Applications:
To improve performance means environmental quality,
fuel economy of modern trucks and cars. It is study of the
external flow over the body of a vehicle, or the internal
flow through the internal combustion engines.
Industrial Manufacturing Applications:
A mould being filed with liquid modular cast iron is a
good example. The liquid flow fields are calculated as a
function of time. Another example is manufacture of
ceramics.
Volume 5, Issue 1 SEP 2015
IJRAET
Civil engineering Applications:
Problems involving the theology of rivers, lakes etc are
also subject of investigations using CFD. Example is
filling of mud from an underwater mud capture reservoir.
Environmental Engineering Applications:
The discipline of heating, air conditioning and general air
circulation through buildings are some of the examples of
the application situations. The example is fluid burning in
furnaces.
Product design:
The ultimate functionality of a product depends on its cost,
efficiency, robustness, and acceptance in the commercial
market. In products that are developed to improve the
environment through energy conservation; fluid-flow, heat
and mass transfer plays an important role. CFD now with
its multitude capabilities serves as an essential tool for
modeling these phenomena in the design of such products.
Product improvement:
Many of the current industrial products have been
developed in pre-CFD periods. As we become more
energy efficient conscious, we find that the products
involving thermal-fluid systems can be redesigned to
reduce their energy consumption. Successfully redesigned
products not only can lower the operating cost but remain
competitive in the market place. In addition they may be
introduced as new lines of products to stimulate the growth
of the business.
Bio medical engineering:
Flow modeling with computational fluid dynamics (CFD)
software lets you visualize and predict physical
phenomena related to the flow of any substance. It is
widely used in medical, pharmaceutical, and biomedical
applications.
FLOW SIMULATION OF MARINE PROPELLER
The purpose of the flow simulation is to see the flow
trajectories of the fluid that is moved by propeller .In this
flow simulation no velocity and pressure conditions are
given but aim is to calculate them.
First rotating region has to be extruded around the
propeller that is the volume that will be rotated,
Figure : Extrusion of rotating region
On solidworks flow simulation menu creating new study
name “Marine propeller flow simulation” as shown.
Volume 5, Issue 1 SEP 2015
IJRAET
creating study name
Then selecting SI units , external analysis and rotation
region as shown.
Setting external analysis and rotation region
Adding water as a project fluid from the liquids
water as project fluid
By using default wall conditions and default initial
conditions and setting result resolution as shown.
setting result resolution
Then flow simulation tree will appear on left side of the
screen. The computational domain
is adjusted as shown by editing it.
Volume 5, Issue 1 SEP 2015
IJRAET
editing of computational domain
Then adding rotational region by selecting the boss extrude
of marine propeller’s rotational region and the speed is
2000 rpm.
Addition of rotational region of speed 2000 rpm.
Then running the flow simulation
running of flow simulation
RESULTS :On the results tree flow trajectories has been
inserted by selecting the surfaces which are in contact
with the fluid i.e, water.
inserting flow trajectories
flow trajectories of water [velocity]
The water velocity has been displayed on the above figure.
The water leaves with 14m/s velocity from the marine
propeller blades as shown above.
Volume 5, Issue 1 SEP 2015
IJRAET
flow trajectories of water [ pressure]
The pressure increases with in the rotating region and then
decreases as shown
CONCLUSIONS
The marine propeller working and terminology
has been studied.
The marine propeller with 3 blades has been
modeled in solidworks 2014.
The solidworks simulation has been studied and
the marine propeller simulation has been
performed.
The maximum induced stresses i.e, 699.4Mpa in
propeller is greater than the material yield
strength 620.4Mpa.This means that if the stress is
greater than the yield stress the material will not
break but will deform plastically.
The resultant deformation, strain and areas below
factor of safety has been displayed.
The solidworks flow simulation has been studied
and the velocity and pressure with the blades of
the propeller has been calculated.
The flow trajectories for velocity and pressure
have been displayed.
REFERENCES:
[1] Bloor, M. I. G. and Wilson, M.J. Generating blend surfaces using partial differential equations. CAD, 21(3):165-171, 1989.
[2] Mortenson, M. E. Geometric modeling. Wiley-Interscience, New York, 1985.
[3] Kerwin, J. E. and Lee, C-S. Prediction of steady and unsteady marine propeller performance by numerical lifting-surface theory. Trans. Society of Naval Architects and Marine Engineers, 86, 1978.
[4] Hess, J. L. Calculation of potential flow about arbitrary three-dimensional lifting bodies. Technical Report MDCJ5679-01, McDonell Douglas, Oct 1972.
[5] Friesch, J. Possibilities of model tests for energy saving devices. In Marine Jubilee Meeting, Wageningen, The Netherlands, 1992.
[6] Young, F. R. Cavitation. McGraw-Hill Book Company Limited, Maidenhead, England, 1989.
[7] Rossignac, A. R. and Requicha, A. A. G. Constant radius blending and solid modelling. Computers in Mechanical Engineering, pages 65-73, 1984.
[8] Elliot, W. S. Computer-aided mechanical engineering: 1958 to 1988. CAD,21(5):274- 288,1989.
[9] Bezier, P. Style, Mathematics and NC. CAD, 22(9):524-526, 1990.
[10] Woodwark, J. Computing shape. Butterworths, London, 1986.
[11] do Carmo, M. P. Differential geometry of curves and surfaces. Prentice-Hall, Inc., New Jersey, 1976.
[12] Nowacki, H. and Reese, D. Design and fairing of ship surfaces. Surfaces in CAGD, pages 121-134, 1983. 186 Bibliography 187
[13] Piegl, L. Key development in Computer-Aided Geometric Design. CAD,21(5):262- 274, 1989.
[14] Bezier, P. Emploi des machines a commande numerique. Masson and Cie, Paris, France, 1970.
[15] Bernstein, S. N. Demonstration du theoreme de Weierstrass fondee sur Ie calcul des probabilities. Commun. Soc. Math., 13(2):1-2, 1912.
[16] Weierstrass, K. Uber die analytische Darstellbarkeit Sogenannter willkurlicher Funktionen einer reellen Veranderlichen. Sitsungsberichte der Akad., Berlin, 1885.
[17] Faux, I. D. and Pratt, M. J. Computational geometry for design and manufacture. Ellis Horwood, Chicester, UK, 1979.
Volume 5, Issue 1 SEP 2015
IJRAET
[18] Barnhill, R. E., Farin, G., Fayard, L. and Hagen, H. Twists, curvatures and surface interrogation. CAD, 20(6):341-346, 1988.
[19] Hockfield, H. and Ahlers, M. Role of Bezier curves and surfaces in the Volkswagen CAD approach from 1967 to today. CAD, 22(9):598-607, 1990.
[20] Gorden, W. and Riesenfeld, R. B-spline curves and surfaces. Computer Aided Geometric Design, pages 95-126, 1974.
[21] Boehm, W. Inserting new knots into B-spline curves. CAD, 12(4):199-201, 1980.
[22] Bloor, M.I. G. and Wilson, M. J. Generating N-sided patches with partial differential equations. Computer graphics international '89, pages 129-145,1989.
[23] Bloor, M. I. G. and Wilson, M. J. Using partial differential equations to generate free-form surfaces. CAD, 22(4):202-212,1990.
[24] Brown, J. M. The design and properties of surfaces generated using partial differential equations. PhD thesis, Dept of Applied Mathematics, University of Leeds, England, 1992.
[25] Collatz, L. The numerical treatment of differential equations. Springer-Verlag, Berlin, 1960.
[26] Smith, D. R. and Slater, J. E. The geometry of marine propellers. Technical Report 88/214, Defence Research Establishment Atlantic, Canada, 1988. Bibliography 188
[27] Eckhardt, M. K. and Morgen, W. B. A propeller design method. Trans. Society of Naval Architects and Marine Engineers, 63:325-374, 1955.
[28] Saunders, H. E. In discussion at end of paper of Eckhardt and Morgen.
[29] Troost, L. Open water test series with modern propeller forms. Trans. North East Coast institution of Engineers and Shipbuilders, 67, 1952.
[30] Abbott, I. H. and von Doenhoff, A. E. Theory of wing sections. McGraw-Hill Book Company, Inc., New York, 1949.
[31] Woodward, C. D. Methods for cross-sectional design of B-spline surfaces. In Recquicha, A. A. G, editor, Eurographics 86, pages 129-142. Elsevier Science Publishers, 1986.
[32] Nittel, M. F. Numerically controlled machining of propeller blades. Marine Technology, 26, 1989.
[33] Choi, B. K. and Ju, S. Y. Constant-radius blending in surface modeling. CAD, 21( 4):213-220,1989.
[34] Patience, G. Propeller surface roughness and fuel economy. Technical report, Stone Manganese Marine Limited, 1983.
[35] Grigson, C. W. B. Propeller roughness, its nature and its effect upon the drag coefficients of blades and ship power. Technical report, R.I.N .A., 1982.
[36] Struik, D. J. Lectures on classical differential geometry. Dover Publications, Inc., New York, 1961.
[37] Falcao de Campos, J. A. C., van Gent, W. and Holtrop, J. Modelling of propulsors in design, theory and experiment. In Marine Jubilee Meeting, Wageningen, The Netherlands, 1992.
[38] Demy, S. B., Puckette, L. T. et al. A new usable propeller series. Marine Technology, 26(3), 1989.
[39] Kinnas, S. A. and Coney, W. B. The generalized image model - an application to the design of ducted propellers. to be published, 1990.
[40] Betz, A. Schraubenpropeller mit geringstem energieverlust. K. Ges. Wiss. Gottingem Nachr. Math.-Phys., pages 193-217,1919. Bibliography 189
[41] Prandtl, L. Application of modern hydrodynamics to aeronautics. Natl. Advis. Comm. Aeronaut. Ann. Rep., 7:157-215, 1921.
[42] Lerbs, H. W. Moderately loaded propellers with a finite number of blades and an arbitrary distribution of circulation. Trans. Society of Naval Architects and Marine Engineers, 60:73-123, 1952.
[43] Morgan, W. B., Silovic, V. and Denny, S. B. Propeller lifting-surface corrections. Trans. Society of Naval Architects and Marine Engineers, 76:309-47, 1968.
Volume 5, Issue 1 SEP 2015
IJRAET
[44] Greeley, D. S. and Kerwin, J. E. Numerical methods for propeller design and analysis in steady flow. Trans. Society of Naval Architects and Marine Engineers, 90(14):415- 453, 1982.
[45J Szantyr, J. A. and Glover, E. J. The analysis of unsteady propeller cavitation and hull surface pressures for ducted propellers. In The Royal Institution of Naval Architects, 1989.
[46] Lighthill, M. J. A new approach to thin aerofoil theory. Aerodynamics Quarterly, pages 193-210, 1951.
[47] Lamb, H. Hydrodynamics. Cambridge University Press, London, 1932.
[48] Hess, J. L. and Smith, A. M. O. Calculation of potential flow about arbitrary bodies. Progress in Aeronautical Sciences, 8:1-138, 1967.
[49] Kinnas, S. A. and Fine, N. E. Non-linear analysis of the flow around partially or super-cavitating hydrofoils by a potential based panel method. In IABEM-90 symposium of the international association for boundary element methods, Rome, 1990.
[50] Cheng, H. M. and Hadler, J. B. Analysis of NSMB wake surveys on victory ship models. Marine Technology, 3(1):1-22, 1966.
[51] Ligtelijn, J. T., van der Kooij, J. Kuiper, G. and van Gent, W. Research on propellerhull interaction in the depressurized towing tank. In Marine Jubilee Meeting, Wageningen, The Netherlands, 1992.
[52] Kinnas, S. A. and Hsin, C-Y. A boundary element method for the analysis of the unsteady flow around extreme propeller geometries. to be published, 1990. Bibliography 190
[53] Larsson, L., Kim, K. J., Esping, E. and Holm, D. Hydrodynamic optimisation using shipflow. In Caldwell, J. B. and Ward, G., editor, PRADS 92: Practical design of ships and mobile units, pages 1.1-1.17, 1992.
[54] Dekanski, C. W., Bloor, M. 1. G., Nowacki, H. and Wilson, M. J. The geometric design of marine propeller blades using the pde method. In Caldwell, J. B. and Ward, G., editor, PRADS 92: Practical design of ships and mobile units, pages 1.596-1.610, 1992.
[55] Houghton, P. and Mullane, U. Geometric modelling and manufacture of marine propeller blades. Technical report, Dept. Mech. Eng., University of Leeds, England, 1992.
[56] A. E. Turbines. Victoria Way, Yeadon, Bradford.
[57] Munchmeyer, F. Shape interrogation: A case study. In Farin, G., editor, Geometric modelling, pages 291-301. SIAM, 1987.
[58] Bloor, M. I. G. and Wilson, M. J. Local control of surfaces generated using partial differential equations. to be published, 1993.
[59] Petrie, J. A. H. Development of an efficient and versatile panel method for aerodynamic problems. PhD thesis, Department of Applied Mathematical Studies, University of Leeds, England, 1979.
[60] Greig, D. M. Optimisation. Longman, 1980.
[61] Imam, M. H. Three dimensional shape optimisation. International Journal for Numerical Methods in Engineering, 18:661-673, 1982.
[62] Lowe, T. W. Functionality in computer aided geometric design. PhD thesis, Dept. of Applied Mathematics, University of Leeds, England, 1992.
[63] Fletcher, R. and Powell, M. J. D. A rapidly convergent descent method for minimisation. Computer Journal, 6:163-168, 1963.
[64] Powell, M. J. D. An efficient method for finding the minimum of a function of several variables without calculating derivatives. The Computer Journal, 7:155-162, 1964.
[65] Kruppe, C. F. L. High speed propellers - Hydrodynamics and design. The Univesity of Michigan, 1967. Bibliography 191
[66] Bloor, M. I. G. and Wilson, M. J. Blend design as a boundary-value problem. Geometric modeling: Theory and practise, pages 221-234, 1989.
[67] Smith, G. D. Numerical solutions of partial differential equations. Oxford University Press, London, 1971.
Volume 5, Issue 1 SEP 2015
IJRAET
[68] Boyce, W. E. and DiPrima, R. C. Elementary differential equations and boundary value problems. Wiley-Interscience, New York, 1992.
[69] Cheng, S. Y. Blending and fairing using partial differential equations. PhD thesis, Dept. of Applied Mathematics, University of Leeds, England, 1992.
[70] Clancy, L. J. Aerodynamics. Pitman Publishing, Inc, New York, 1975.
[71] Umlauf, U. Propellergeometrieentwurf liber Formparameter, 1990. Private communication.
[72] Ortega, J. M. and Poole, W. G. An introduction to numerical methods for differential equations. Pitman Publishing, Inc, New York, 1981