ThesisR4

FLOW VISUALIZATION OF THE VENTILATED CAVITIES AND SPRAY

PATTERN GENERATED BY A SURFACE PIERCING PROPELLER

by

Luis Altamirano

A Thesis Submitted to the Faculty of

The College of Engineering and Computer Science

in Partial Fulfillment of the Requirements for the Degree of

Master of Science

Florida Atlantic University

Dania Beach, Florida

May 2010

ii

FLOW VISUALIZATION OF THE VENTILATED CAVITIES AND SPRAY

PATTERN GENERATED BY A SURFACE PIERCING PROPELLER

by

Luis Altamirano

This thesis was prepared under the direction of the candidate’s thesis advisor, Dr. Karl von Ellenrieder, Department of Ocean & Mechanical Engineering, and has been approved by the members of his supervisory committee. It was submitted to the faculty of the College of Engineering and Computer Science and was accepted in partial fulfillment of the requirements for the degree of Master of Science.

SUPERVISORY COMMITTEE:

___________________________Karl von Ellenrieder, Ph.D. Thesis Advisor

___________________________Manhar Dhanak, Ph.D. Director of Seatech

___________________________P. Ananthakrishnan, Ph.D. Associate Professor

______________________________________ Manhar Dhanak, Ph.D. Chair, Department of Ocean & Mechanical Engineering

______________________________________ Karl K. Stevens, Ph.D., P.E. Dean, College of Engineering and Computer Science

______________________________________ ________________________Barry T. Rosson, Ph.D. Date Dean, Graduate College

iii

ACKNOWLEDGEMENTS

I would like express my gratitude to my advisor Dr. Karl von Ellenrieder as well

as my supervisory committee who guided me to become a better engineer. I would like

to thank Justin Lorio for sharing his valuable effort in the process of designing the test

apparatus. I am truly thankful to Luis Padilla for patiently sharing his knowledge with

me in the machine shop. I would also like to thank Tom Furfaro for his substantial

contributions in the development of the code for taking measurement. Also to Phillip

Duerr as well as Dr. Raju Datla and Mike Morabito and the Stevens Institute of

Technology for all their important contributions to make this study possible.

iv

ABSTRACT

Author: Luis Altamirano

Title: Flow visualization of the ventilated cavities and spray pattern

generated by a surface piercing propeller

Institution: Florida Atlantic University

Thesis Advisor: Dr. Karl von Ellenrieder

Degree: Master of Science

Year: 2010

In the present study, images and videos of a surface piercing propeller tested at

yaw angles 0-30 degrees, pitch angles 0-15 degrees and propeller immersion ratios of

0.33 and 0.5 are analyzed. A complete sequence of image analysis is described based on

an existing method used to measure various parameters of the propeller wake. The

provided sequence is applied to experimentally obtained images through the use of a

computer algorithm written for this study. The values obtained from these

measurements are plotted and the results are compared with expectations based on

theory and past observations. Conclusions are made based on results as to the

importance of this study.

DEDICATION

This thesis is dedicated to my family who was always remembered even though

they were physically far away. To Aniko Bahr for all her support during two years of

research and to Pony for all her patience and love.

v

TABLE OF CONTENTS

LIST OF TABLES ........................................................................................................................... viii

LIST OF FIGURES ........................................................................................................................... ix

NOMENCLATURE......................................................................................................................... xv

1. INTRODUCTION .........................................................................................................................1

1.1 Motivation and Approach .................................................................................................. 1

The motivation of the present study is to contribute to existing knowledge of SPPs as part a

collective effort with other scientists in the search for a reliable performance prediction

method that can be used as the new basis for SPP design. In ................................................. 1

particular, the present investigation started with ONR’s interest of using SPPs as an

alternative method of propulsion for the T-craft [4] which is a high speed vessel. The

approach is to conduct open water tests of variable orientations of the SPP with respect to

the water surface as defined in section 1.2: I, γ as in [5], Ψ and to produce flow depiction

and footage of these tests for further analysis. It is certain that flow visualizations of a SPP at

work will guide the development of a prediction method of SPPs.......................................... 2

1.2 Present Study ..................................................................................................................... 2

vi

...............................................4

1.3 Thesis Goals........................................................................................................................ 5

The first goal of the present thesis is to gather images of the wake of a SPP under various

conditions of...........................................................................................................5

The second goal is to produce video footage of the SPP in order to provide a description of the

spray pattern created at different testing conditions. Both images and footage

will be compared with expectations developed in chapter 3. Conclusions and

recommendations will be made based on the results obtained............................5

2. EXPERIMENTAL METHOD ..........................................................................................................6

2.1 Facility................................................................................................................................. 6

2.2 Testing Conditions .............................................................................................................. 7

2.3 Visualization System Setup................................................................................................. 7

2.3.1 Components ................................................................................................................ 7

vii

2.3.1.1 Cameras and Flash................................................................................................ 8

2.3.1.2 Video cameras.................................................................................................... 10

2.3.2 Camera Triggering System......................................................................................... 12

2.3.3 Video Triggering System............................................................................................ 14

2.4 Description of a Testing Run............................................................................................. 14

3. DATA PROCESSING ..................................................................................................................18

3.1 Expected Outcomes.......................................................................................................... 18

3.1.1 Expectations Based on a Theoretical Approach........................................................ 18

3.1.2 Expectations Based on Existing Observations........................................................... 21

3.2. Image Analysis................................................................................................................. 22

3.2.1. Image Analysis Sequence ......................................................................................... 23

3.2.2 Measurement of Wake Parameters .......................................................................... 25

3.2.2.1 Measurement of Cavity Width........................................................................... 25

3.2.2.2 Measurement of Wake Pitch, Wake Diameter and Wake Pitch ........................ 27

3.2.3 The Measuring Algorithm.......................................................................................... 28

3.3 Video Analysis................................................................................................................... 33

4. RESULTS AND DISCUSSION......................................................................................................35

4.1 Wake Pitch, Wake Diameter and Wake Pitch Angle Measurement Results .................... 35

viii

LIST OF TABLES

Error! No table of contents entries found.

ix

LIST OF FIGURES

Error! No table of contents entries found.

x

NOMENCLATURE

d Ventilated cavity width

Cavity speed of closure

D Propeller diameter

Dw Diameter of trailing wake

I Immersion ratio

J Advance coefficient

Jscaled Advance coefficient scaled by velocity component along propeller shaft

n Propeller rate of revolution [Hz]

U Speed of advance of propeller

Pw Pitch of trailing edge

X Distance for triggering camera

γ Shaft inclination

Angular position of propeller blade

Φw Pitch angle of trailing wake

Ψ Yaw angle

1

1. INTRODUCTION

A surface-piercing propeller (SPP) is a propeller positioned so that each propeller

blade is out of the water for part of each revolution. A SPP is often recognized as one of

the most efficient propulsive devices for high-speed vessels. Its efficiency is primarily

attributed to the reduction of appendage drag, because most of the propeller assembly is

elevated above the water [1]. An additional advantage of using a SPP is that it eliminates

cavitation by replacing it with ventilation; the cyclic blade entry from air into the water

opens a ventilated cavity around the propeller which almost completely prevents the

occurrence of vapor cavitation [2] [3].

A drawback of using SPPs is that a complete performance prediction method is

still under development and even though SPPs are used largely in the boat racing

community, the design of SPPs is often performed in a trial-and-error basis.

1.1 Motivation and Approach

The motivation of the present study is to contribute to existing knowledge of

SPPs as part a collective effort with other scientists in the search for a reliable

performance prediction method that can be used as the new basis for SPP design. In

2

particular, the present investigation started with ONR’s interest of using SPPs as an

alternative method of propulsion for the T-craft [4] which is a high speed vessel. The

approach is to conduct open water tests of variable orientations of the SPP with

respect to the water surface as defined in section 1.2: I, γ as in [5], Ψ and to produce

flow depiction and footage of these tests for further analysis. It is certain that flow

visualizations of a SPP at work will guide the development of a prediction method of

SPPs.

1.2 Present Study

The present work is a joint research effort with master student Justin Lorio [6]. It

consists of 4 stages. The first stage is the design of a SPP testing apparatus that

automatically controls I , γ, and Ψ using fours motors as shown in figure 1.3. The

definition of the propeller parameters can be seen in figure 1.1. A more in depth

description of the design and functionality of the SPP testing apparatus can be found in

3

[6] and [7]. Based on the dimensions of the SPP used given in table 1.1 and those of the

towing tank used given in section 2.1, the effect of blockage can be neglected for the

present experiment according to [8].

(a) (b) (c)

Figure 1.1 - Definitions of (a) yaw angle Ψ and immersion ratio I = h/D, (b) shaft inclination angle γ,

and (c) SPP rate of revolution.

The second stage of the present project is the fabrication of the parts that form the

CAD model developed in stage 1. Three months of manufacturing are necessary to create

more than 75 parts that are assembled in stage three of the process. The finished assembly

is then mounted on a towing carriage described in section 2.1 as shown in figure 1.4.

Testing the assembly is the fourth stage and it is described in detail in chapter 2. The final

stage of the present study is data analysis and it is discussed in chapters 3 and 4. The SPP

used can be seen in figure 1.2 and table 1.1 shows the SPP specifications.

4

Figure 1.2 - Front and section profile of the SPP.

Table 1.1: SPP properties

Figure 1.3 - CAD drawing of the SPP test apparatus. From Lorio [7].

Figure 1.4 - The SPP test apparatus mounted on towing carriage at Stevens Institute of Technology. December 11, 2009.

Diameter: 9.7 in.Material: Stainless steelAverage Pitch: 18.312”Blades: 4Rotation: Left

Inclination Motor

Spray Shield

Supporting Arm

Yaw Motor

Heave Motor Propeller Motor

SPP

Carriage

Linear Stage

5

1.3 Thesis Goals

The first goal of the present thesis is to gather images of the wake of a SPP under

various conditions of I , γ, Ψ, and . Using an existing model, the wake diameter,

wake pitch and wake pitch angle (explained in section 3.2.2.2) will be measured in order

to quantify the behavior of the ventilated cavities of a SPP under different conditions. A

computer algorithm will be written in order to accurately determine the dimensions of

these parameters so they can be plotted and compared between the different testing

conditions. Additionally, measurements of the width of ventilated cavities in the wake of

a SPP will be taken and related to an existing theoretical work.

The second goal is to produce video footage of the SPP in order to provide a

description of the spray pattern created at different testing conditions. Both images and

footage will be compared with expectations developed in chapter 3. Conclusions and

recommendations will be made based on the results obtained.

6

2. EXPERIMENTAL METHOD

2.1 Facility

The Stevens Institute of Technology collaborates with the research team by

making its towing tank facility available for the current project. It is a straight tank, 16 ft

(3.66 m) wide by 8 ft (1.83 m) deep by 313 ft (95.40 m) long as seen in figure 2.1. Its

towing carriage can go up to 100 ft/s with a speed-resolution of 0.01 ft/s. Another

desirable feature is its holding weight capability; it can hold approximately 500 pounds of

weight [9].

Figure 2.1 - Towing tank at Stevens Institute of Technology.

7

2.2 Testing Conditions

The test condition matrix is shown in table 2.1. Note that there is an overlap with

some of the conditions tested by Olofsson 1996 [10] in order to validate experimental

results obtained in the present study. A total of 95 combinations of this matrix were

executed.

Table 2.1: Testing conditions

I (%)

γ (degrees) J Ψ (degrees)

33 0, 7.5, 15 0.8-1.6 0, 15, 3050 0 0.8-1.6 0

2.3 Visualization System Setup

2.3.1 Components

The equipment for flow visualizations consists of two cameras, five flashes, an

underwater mirror and two video recorders. The Davidson Laboratory is equipped with a

test section window midway through its length. At this location, two cameras are located.

Camera 1 is an underwater camera pointing to a mirror on the bottom of the tank,

allowing it to take underwater images of the trailing wake of the propeller. Camera 2

8

photographs the side view of the propeller as it passed through the tank’s section window

as in figure 2.2.

Figure 2.2 - Location of cameras and mirror.

2.3.1.1 Cameras and Flash

Two Canon EOS Digital Rebel XTi cameras with EFS 18-55 mm lenses and five

Vivitar 285 HV flashes are used (figure 2.3). Camera 1 is set to a focal length of 27.0

mm, shutter speed of 1/320 s, aperture value of 9.0 and ISO speed of 1600. It is placed

inside an underwater housing, pointing at the center of an inclined mirror on the bottom

TOP VIEW

FRONT VIEW

Mirror

Camera 2

Camera 1SPP

Flashes

Length ofviewingwindow

9

of the tank (figure 2.4) producing mirror images of the bottom of the trailing wake of the

SPP, with a resolution of 3888 x 2592 pixels. Camera 2 is set to a focal length of 24.0

mm, shutter speed of 1/320 s, aperture value of 9.0 and ISO speed of 1600. It is located

outside the tank focused through the viewing window (figure 2.5), producing side view

images of the trailing wake.

Figure 2.3 - Camera and flash used to record side and bottom view images.

Figure 2.4 - Camera 1 pointing at mirror.

Underwater mirror

Camera 1

10

Figure 2.5 - Camera 2 and flash at viewing window.

One of the flashes is mounted on camera 2 and the four remaining flashes are

placed two each in two watertight boxes located at 8 ft apart at the upstream and

downstream sides of the mirror on the bottom of the tank. The cameras have the

capability to simultaneously store JPEG and RAW files. This feature is used because

RAW files store minimally processed data, preserving greater detail than JPEG images.

The triggering system used for the cameras is given in section 2.3.2.

2.3.1.2 Video cameras

The laboratory has a National Electronics Digital Video camera (video 1) with a

frame rate of 33 Hz. and a minimum required illumination of 0.25 lux. It is a 1/3” high

resolution color camera with a CCTV lens of 3.5-8 mm. It is mounted on the carriage in

order to follow the SPP system maintaining the same focal length on every run. This

camera is useful for capturing splashing patterns around the propeller. It also allows the

researchers to check the SPP performance at any point along each run. Video 2, a camera

Camera 2 and flash

11

Aiptek ISDV2.4 with video resolution of 720 x 480 pixels and a focus range of 40cm~∞

is mounted on the carriage 5.25 ft directly in front and 2 feet above the waterline. Video

2 is used to get a more focused view of the splash around the SPP. It is covered with a zip

bag to make it water proof. This setup is shown in figure 2.6.

(a)

(b)Figure 2.6 - Video cameras mounted on carriage. (a) Schematic of the top view. (b) View in

Perspective.

Video 1

Video 2

SPP

Carriage

31°

SPP

VIDEO 1VIDEO 2

6 ft5.25 ft

12

2.3.2 Camera Triggering System

The triggering sequence used to activate the cameras at the desired position is

summarized below in figure 2.7.

Figure 2.7 - Diagram of the process to trigger the cameras and flashes.

Step 1: The carriage is moved to the desired position within the viewing window

of the tank where it is going to be photographed. This distance is measured to

be from the starting carriage position. This value corresponds to zero

carriage speed. In order to obtain different values of , the value of is varied. It is

known that there is a time delay of seconds for the cameras and flash to go off

13

from the time the trigger signal is sent by an encoder. Thus, to ensure the same position

of the propeller assembly in the viewing window when the pictures are taken, a relative

distance needs to be subtracted from . The distance the carriage travels while the

triggering signal goes from the encoder to the cameras, , can be calculated by

. Thus the input camera distance is given by: .

For example, for ,

feet. The different values for can be seen in table 2.2. These values are entered in a

Dynapar Master Controller for each set of runs (figure 2.8).

Table 2.2: Triggering Distances for Cameras

Figure 2.8 - Dynapar Master Controller.

Step 2: An optical limit switch (figure 2.9) of 1” resolution measures the input

position given by . Once this distance is reached, the optical limit switch outputs a

signal to the Dynapar Master Controller which triggers the cameras. Cables from the

RPM = 1325J U (ft/s) (ft)

0.8 14.19 154.901 17.67 154.00

1.2 21.15 153.201.4 24.64 152.301.6 28.12 151.50

14

flash boxes go to a central distribution box, which 1) provides power to recharge them, 2)

triggers them at the same time as the cameras are triggered and 3) provides an indicator

light to show if they were charged.

Figure 2.9 - Optical limit switch.

Step 3: Images are captured and stored temporarily in the memory of the camera.

Then through a USB hub connected from both cameras to a laptop, the images are sent to

the laptop.

Step 4: Images are saved on the laptop. All files are stored automatically in

ascending numbers. The numbers of the pictures are recorded in a lab book with their

respective run numbers and conditions for later use.

2.3.3 Video Triggering System

Video 1 is triggered using computer software Turtle Beach which allows starting

and stopping recording of the run. It also allows projecting the view of Video 1 on a

computer screen. Video 2 is triggered manually for each run.

2.4 Description of a Testing Run

Metal Teeth

Optical Limit Switch

Carriage

15

First the SPP testing apparatus is mounted on the laboratory’s carriage. Then,

before each test run condition the SPP is positioned at the desired parameters (I, ϕ and

Ψ). I is measured using guide lines previously drawn on the propeller blades. ϕ is

measured using an inclinometer built-in the SPP testing apparatus. Ψ is measured using a

protractor1. Before each run condition, the SPP is placed in the desired position according

to the testing matrix given in table 2.1. Then the desired value for X is input into Master

1 Originally a built-in compass located in the SPP testing apparatus measures the yaw angle. However due to the presence of many metal objects in the facility, the readings from this device are not consistent.

16

Controller as given in table 2.2. A count-down is given in order to activate video footage.

The run starts and cameras 1 and 2 simultaneously take images of the bottom and side

view of the SPP wake at the specified distance X. Figure 2.10 shows side and bottom

images obtained with cameras 1 and 2 after the process shown in figure 2.7.

(a)

(b)

Figure 2.10 - Original images of (a) side view with camera 1 and (b) bottom view with camera 2, of SPP wake for condition I = 33%, γ = 0°, Ψ = 0°, J = 1.176, 1.176.

By the end of the experimental approach, 348 images are obtained including side

and bottom views in both JPEG and RAW format. Additionally, using video 1, 90 video

clips (.avi) of the conditions tested are taken for further analysis of the spray generated by

17

the SPP. Using Video 2, 15 video clips (.asf) of the front view of the SPP are taken also

for spray generation analysis.

18

3. DATA PROCESSING

3.1 Expected Outcomes

3.1.1 Expectations Based on a Theoretical Approach

From the definition of propeller pitch given in [11] and in [12]it is known that a

propeller can be thought of a helix inside a cylinder. In figure 3.1 an unrolled section of

this helix is shown where the horizontal axis is the rate at which the propeller travels to

its rpm.

Figure 3.1 - An Unrolled Propeller.

19

From figure 3.8 and the parameters defined in section 3.2.2.2, it can be seen that:

And:

From the definition of advance coefficient:

Thus, according to equation 3.1, the wake pitch angle is expected to change

proportionally as the advance ratio changes, within the same condition.

Dividing by :

It can be expressed as:

Therefore, it can be expected from expression 3.2 that the ratio of the wake pitch

divided by the SPP diameter be directly proportional to the advance ratio.

is defined as the distance between the center of the SPP hub and the edge of

the cavity of interest along a horizontal line (section 3.2.2.2). This means that in the same

viewing window, higher values of produce less number of cavities. Thus, equation

3.2 implies that a comparison between two images of the SPP wake of a similar

condition tested at different values of is expected to show that low values of produce

more ventilated cavities (provided that the images have equal size in pixels).

Given that a ventilated cavity is full of air [13], it is understood that an amount of

water equal to the amount of air occupying the cavity is displaced. A sheet of spray is the

amount of spray corresponding to one ventilated cavity. This means that more cavities

will produce more sheets of spray. This is consistent with observations made by [10].

20

Since we know that low values of are expected to produce more ventilated cavities,

then it is also expected that low values of produce more spray sheets.

Consider figure 3.8 so that:

Figure 3.2 - Wake parameters in an unrolled propeller.

From figure 3.8, let:

Where:

For example, at the third ventilated cavity:

So in figure 3.2:

Recall from equation 3.1:

Equating the tangents of the angles:

21

Dividing by D:

In equation 3.3, the quantities in the parenthesis are dimensionless numbers. This

expression indicates that the ratio of wake diameter over SPP diameter is inversely

proportional to the value of advance ratio. Table 3.1 summarizes all the theoretical

expectations.

Table 3.1: Theoretical Expectations

Number Expectation

1 Wake pitch angles change proportionally to the advance ratio.

2The ratio wake pitch over SPP diameter is directly proportional to the advance ratio.

3 Low values of advance ratio produce more ventilated cavities.

4 Low values of advance ratio produce more spray sheets.

5The ratio wake diameter over SPP diameter is inversely proportional to the value of advance ratio.

3.1.2 Expectations Based on Existing Observations

As the value of J drops, some expectations can be outlined [14]:

- Transition to fully ventilation occurs at a region of J.

22

- The amount of spray grows to cover SPP by a solid layer or water.

An expectation from the observations made by [15] is that:

- Most spray should come from the exit side of the propeller.

From [13]:

Figure 3.3 - Vent path. From Vorus 2008 [13].

At the entry side, the propeller blade cuts through producing some spray and as it

continues, creating an air cavity, the blade pushes water in its way which is expulsed at

the exit side in the form of spray, producing most of the spray. This explains the

observation made by [15].

Observations made in [10] are summarized:

- varies linearly as a function of the angular position of the SPP.

- has no dependence of Ψ.

- behaves inversely proportional to Ψ.

3.2. Image Analysis

AIR

EXIT ENTRY

WATERBLADE

23

As Camera 1 is located farther from the SPP than camera 2, there is a slight

difference magnification and resolution between bottom and side images recorded.

Therefore it is crucial to calibrate the image magnifications.

During testing trials, two 36-inch rulers are attached at right angles to one another

to the propeller shaft and mounted as shown in figure 3.4. The SPP assembly with the

rulers attached is positioned at and pictures are taken. The ratio of a ruler

measurement in the bottom view to one in the side view is found to be 0.69 referred to as

calibration scaling in section 3.2.1.

Figure 3.4 - Ruler test showing a different magnification between images.

3.2.1. Image Analysis Sequence

The region of interest is the wake created by the SPP so the images need to be

cropped. It is desired to obtain a composite image of the every side view image with their

Waterline

SPP

SPP

Rulers

Rulers

BOTTOM VIEW

SIDE VIEW

24

respective bottom view images. Finally, a label of the condition tested is given to every

image. The diagram in figure 3.5 shows this process.

Figure 3.5 - Sequence used to analyze images.

To accomplish steps 1 through 3, Imagemagick software was used through a DOS

window allowing to process batch file images reducing the time needed for these actions.

To obtain the desired focused view of the wake software Canon Utilities File Viewer

Utility version 1.3.2.11 is used. Using this software the pixel coordinates of the cursor’s

location is displayed on the screen which is used to determine the size (in pixels) of the

desired viewing window where only the SPP wake will be seen. The cropping offsets for

locating this viewing window are determined similarly. The latter is important to know

since the SPP wake is not in the same location as Ψ and γ vary.

25

Finally in step 3 of the process shown in figure 3.5, the resulting side and bottom

cropped images are merged into one compound image with their corresponding label for

each condition. After this step, 63 composited-labeled images are ready to be analyzed. A

sample image obtained, after step 3 is completed, is shown in figure 3.6. The DOS code

used for steps 1 through 3 is shown in appendix A.1. In step 4, a new folder is created in

a convenient location containing all the resultant images from the previous steps. Step 5

is described in detail in section 3.2.2.

Figure 3.6 - Composite-labeled image of condition I = 33%, γ = 0°, Ψ = 0°, J = 1.176, 1.176.

3.2.2 Measurement of Wake Parameters

3.2.2.1 Measurement of Cavity Width

One of the parameters of interest is cavity width measured at the entry side of

the propeller blade. A particular interest of this study is to compare experimental results

of the width of the ventilated cavities with the work developed by [13]. To obtain the

26

measurement of , three tangent points to the walls of the ventilated cavity at the blade

entry side are picked and a circle is drawn based on the points picked as shown in figure

3.7. All diameters lie in the same horizontal line.

The dimensions of the diameters are recorded as ventilated cavity widths. For an

accurate measurement of , a ventilated cavity must stand alone. By inspection, the

cases where cavities stand alone are when γ = 0°, and is greater or equal than

1.363. In all other conditions the ventilated cavities collapse with each other, making it

difficult to measure in a consistent manner.

Figure 3.7 - Measurement of the width of 4 ventilated cavities of condition I = 33%, γ = 0°, Ψ = 0°,

1.927 made in AutoCAD 2008.

Cavity widths

27

3.2.2.2 Measurement of Wake Pitch, Wake Diameter and Wake Pitch Angle

The present study uses a method published in 1996 by [10] to measure various

parameters of the trailing wake of a SPP working at different conditions. To measure the

shape of the cavities in the trailing wake of the propeller, three parameters are introduced.

The wake pitch, , is defined to be the distance from the blade spindle axis to the

upstream edge of the ventilated cavity along a horizontal drawn at the blade spindle axis.

The original definition of in [10] is the distance from the blade spindle axis

to the “tip” of the ventilated cavities. However, the cavities in the present study had fat-

ends making it hard to consistently pick a cavity tip.

The angular position of the blade is used to indicate the cavity of interest. The

second parameter is the wake diameter which measures the width of the trailing

wake in the horizontal plane at a distance downstream of the propeller. The final

parameter is the wake pitch angle , defined to be the angle between the vertical plane

perpendicular to the free-stream velocity and the tangent of the cavity at a distance

downstream of the propeller. These parameters can be seen in figure 3.8.

28

Figure 3.8 - Olofsson’s nomenclature for trailing wake parameters [10].

3.2.3 The Measuring Algorithm

A Matlab algorithm that semi-automatically measures the desired wake

parameters as described in section 3.2.2.2 is developed for the present study (shown in

appendices A.3-A.6). The code has four parts:

Parser Code: It is a function able to take the name of the image files given in a

specific format and break it down to extract information within the name of the file such

are the values of I, γ, Ψ, and J. It was written as a function so other programs can call it

and use it.

= 2π

π

0

Pw

ΦwVortex Sheet or cavity

Dw

Boundary to trailing wake

View from Bellow

U

29

Wake Profile Code: It runs a loop through all the images to pick points around

the wake profile with a click of the mouse. The program stores the coordinates of each

pair of points of the profile picked. A sample image is shown in figure 3.9 after the wake

profile points are picked. Note that the composite image is cropped for measurement

taking so only the bottom view image is displayed.

Wake Pitch and Angle Code: This code runs a loop for all the images which first

converts the image in grayscale and then allows picking a point at the blade spindle axis

as shown in figure 3.10.

Figure 3.9 - Wake profile of condition I = 33%, γ = 0°, Ψ = 0°, J = 1.176, 1.176.

Wake Profile

30

Figure 3.10 - Picking a point for blade spindle axis for condition I = 33%, γ = 0°, Ψ = 0°, J = 1.176, 1.176.

Then, the program converts the grayscale image into a binary image so that the

ventilated cavities can be seen more easily. The resultant image replaces all pixels in the

input image with luminance greater than the threshold value specified, with 1 or white

and all other pixels with 0 or black. The function to calculate the threshold value uses

Otsu’s [16] method which selects an optimal threshold value automatically and stably,

not based on differentiation but on integration of the histogram. A horizontal line is

drawn at the blade spindle axis point as seen in figure 3.11.

Blade spindle axis point

31

Figure 3.11 - Binary image of condition I = 33%, γ = 0°, Ψ = 0°, J = 1.176, 1.176.

As shown in figure 3.11 the intersections between the horizontal line with the

upstream edges of the ventilated cavities can be selected. A point near the desired

intersection is selected by a click and the program automatically identifies the closest

point where there is a differential in pixel value in the binary image along the horizontal

line. This is possible since along the upstream edge of the cavity there are pixels of value

0 to one side and 1 to the opposite side. The desired amount of ventilated cavities and

corresponding intersections are picked and the result is shown in figure 3.12.

Ventilated cavities

Horizontal line

32

Figure 3.12 - Automatic recognition of edge-horizontal plane intersections for condition I = 33%, γ =

0°, Ψ = 0°, J = 1.176, 1.176.

The values for the intersection points are saved in a new file with the

corresponding name by calling the function parser code. Using the intersection and blade

spindle axis points the value of Pw is calculated. A linear interpolation between the

points picked with the wake profile code and the edge-horizontal intersection points is

used to calculate Dw. Finally, using the diagram of an unrolled propeller given in figure

Intersections of cavity edges with horizontal line

33

3.1 and distance Pw, the value of is obtained. In the cases where Ψ > 0, Ψ is

subtracted from this calculation to obtain the final value of . Note that all distance

measurements are given in pixels. The ruler image is measured in Canon Utilities File

Viewer Utility version 1.3.2.11and the ratio inches to pixels is found to be 5/209. This

conversion number is used to convert the values of the parameters to inches.

Plotter Code: It makes the plots of the measured parameters. It uses the function

parser to accurately label the plots. The results from this code can be seen in chapter 4.

3.3 Video Analysis

As discussed in section 3.1.1, there is a relationship between the value of advance

ratio and the amount of spray generated by the SPP. In order to observe if this

relationship is valid, video clips taken from video 1 are used to look for such a pattern. A

frame of each of the movies is taken at 13.6 seconds corresponding to about half way of

the testing run time to be able to simultaneously compare patterns between videos of the

same condition but at different values of J. A quantification of the amount of spray is not

34

directed in the present study as that pertains to a more in depth study of spray caused by a

SPP.

35

4. RESULTS AND DISCUSSION

4.1 Wake Pitch, Wake Diameter and Wake Pitch Angle Measurement Results

The measurements taken for these parameters were taken as described in section

3.2.2.2. Two samples of typical results at high and low values of for each testing

conditions are shown in figures 4.1 – 4.20 (the complete set of images and their results

can be seen in Appendix B). In the case of low values of , the ratio Dw/D

increases with respect to the angular position of the SPP while when is higher,

this ratio seems to remain constant. For all testing conditions, the value of the ratio Dw/D

at angular speed 3π/2 is higher when is lower in agreement with theoretical

expectation number 5 from table 3.1. At low values of a higher number of

36

ventilated cavities are visible which is what is expected from expectation 3 of table 3.1.

For all the conditions, the range of values for the wake pitch angle is higher for higher

values of . This behaves as expected from expectation 2 of table 3.1. Additionally,

the range of values for change inversely proportionally to Ψ. This result is

in agreement with observations made by [10]. The ratio Pw/D varies almost linearly with

respect to ϕ and this behavior does not seem to change as Ψ changes also in agreement

with [10]. The range of values for the ratio Pw/D is higher when the values of are

37

higher for all testing conditions in conformity with expectation 2 of table 3.1. For all

conditions it seems that there is a region where the SPP experiences a fully ventilated

regime (a ventilated region made up of many merged ventilated cavities). For all cases,

the average region of for fully ventilated condition was calculated to be 0.905 –

0.721. This region is in the neighborhood of the region observed by [14].

From the side view images it is possible to see that the ventilated cavities have the

shape of a bowl which means that the tip of the ventilated cavity travels downstream with

a lower speed than the center of the wake. This agrees with observations made by [10]

and [17] and it may be explained based on the propeller jet flow [12] where because of

the pressure gradient, there is more pressure further into the boundary region of the

actuator disk flow than in the outer boundaries [18].

38

Figure 4.1 - Results for condition I = 33%, γ = 0°, Ψ = 0°, J = 0.767, 0.767.

39


40


41


42


43


44


45


46


43


44


45


46

Figure 4.13 - Results for condition I = 33%, γ = 7.5°, Ψ = 0°, J = 0.803, 0.796.

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48


49


50


51

Figure 4.18 - Results for condition I = 33%, γ = 7.5°, Ψ = 30°, J = 1.747, 1.

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53


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4.2 Cavity Width Measurement Results

The measurements of d are taken as described in section 3.2.2.1. A quadratic fit

is applied to the results of the ratio d/D plotted versus the angular position of the SPP as

this behavior is expected from a theoretical work in [13]given in the form:

And the relationship between t and ϕ is:

The velocity component of this expression is of interest since it represents the

speed with which the ventilated cavities close after the trailing edge of the SPP passes

through the vent path (figure 3.3). Results of for conditions given in figures 4.21-4.24

are displayed in table 4.1 using U = 28.7 ft/s (from table 2.2).

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Table 4.1: Velocity component from cavity width measurements.

The values seem to vary linearly with respect to values for the

conditions given. This seems plausible since at lower values of the SPP blade

spends more time in the vent duct which delays the time of collapse of the cavity. On the

other hand, at higher values of , the SPP blade passes by the vent faster allowing

the cavity walls to close faster. Independent of the influence of , the value of

does not seem to vary when immersion ratio is varied. When values of Ψ are varied, the

linear relationship between and still seems to hold.

Condition (in/s)

I = 33%, γ = 0°, Ψ = 0°, J = 1.927, 1.927 0.119

I = 50%, γ = 0°, Ψ = 0°, J = 1.441, 1.441 0.112

I = 33%, γ = 0°, Ψ = 15°, J = 1.574, 1.363

0.004

I = 33%, γ = 0°, Ψ = 30°, J = 1.772, 1.535

0.05

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Figure 4.21 - Width results for condition I = 33%, γ = 0°, Ψ = 0°, J = 1.927, 1.927.


57



58

4.3 Video Analysis Results

When the testing run stars, the SPP is partially wetted and as it reaches the value

of the SPP starts producing spray sheets that elevate downstream of the SPP. At

high values of these spray sheets remain downstream away from the SPP but as

the value of drops spray progresses to covering the entire SPP. This agrees with

expectations mentioned in section 3.1.2. In order to be able to compare between different

spray patterns, the videos obtained for each testing condition are analyzed as described in

section 3.3. At high values of videos show that most of the spray produced comes

from the exit side of the SPP in concurrence with expectations mentioned in section

3.1.2.

Additionally, it is found that at low values of more spray sheets were

generated in accord with expectation 4 of table 3.1. Substantial amount of spray is

generated at the entry side of the blade at low values of which may be explained

by considering figure 3.3. When the blade enters the water, it produces spray due the

impact and also some spray is produced as the ventilated cavities close [19][20].

At high values of the spray pattern has a more uniform direction straight

downstream from the SPP. At low values of , the spray pattern increases in

progressively downstream of the SPP. This finding is consistent with the measurements

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of Dw/D which are almost constant at high values of and have increasing values

when is low.

The spray generated seems to change its volume proportional to γ. This seems to

be mainly caused by the bottom assembly of the SPP testing apparatus which is

submerged when γ > 0. The shape of the spray pattern does not seem to change as γ is

varied. As Ψ changes, the spray pattern seems to change orientation so it is always

aligned along the SPP shaft. This is counter-intuitive since the orientation of the

ventilated cavities with respect to a horizontal line does not change as Ψ is varied. One

reason for this may be that the spray generation depends on the blade position only

(which is always the same with respect to the SPP shaft) whereas the orientation of the

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ventilated cavities seems to be affected by the direction of U.

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5. CONCLUSIONS AND RECOMMENDATIONS

The first goal of the present thesis was to gather images of the wake of a SPP

under various conditions of I , γ, Ψ, J , and to measure 4 wake parameters based on an

existing model using a computer algorithm and plot the measurements. The images

obtained after the experiments were conducted were of great quality: they showed a great

amount of detail of the wake SPP at each tested condition. Only for a small number of

images, one of the flashes did not charge properly and so the side view image of the

condition tested was not available. The existing model to measure SPP wake parameters

had to be redefined since it assumed that ventilated cavities had a thin tip at the exit side

of the propeller which is was not the case for the images obtained. Also, a background of

the theory of an unrolled propeller needed to be written in order to fully understand the

way the parameters were defined in the existing model.

A MATLAB algorithm was written to measure 3 of the 4 desired wake

parameters. The amount of preparation of the code was extensive but overall it was

definitely worth it since it allowed taking measurements more rapidly and more

accurately than using AUTOCAD which was the original program to be

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used to take measurements. The only inconvenience with the first proposed goal was that

the width of ventilated cavities could be measured only when they did not collapse with

each other which only happened at high values of and also when γ > 0. It is

recommended to execute experiments with γ = 0 and a large range of low values of

in order to get more measurements of d. Also, having more images where d can

be clearly identified, a MATLAB program could be written based on the one produced in

this thesis. Overall the first goal aimed by this thesis was successful.

A second goal was to produce video footage of the spray pattern created by the

SPP in order to give a description of them. Frames of the videos were taken at a specified

time which seemed to be an effective way to compare many conditions at the same time

in order to find commonalities between the frames. Many observations were made of the

relationship between the value of and the wake parameters including the spray

generated. Video footage seemed to be a valuable tool for describing the spray patterns

generated. For future studies, a method to quantify the amount of spray generated by the

SPP should be executed aiming to observe the relationship between d for a ventilated

cavity and the amount of spray generated by it.

After conducting data analysis of images and videos it was found that the

experimental results are in agreement with the theoretical predictions developed for this

thesis. This thesis aimed to contribute to existing knowledge of SPPs by showing that a

theoretically relationship between the wake parameters , , d, and with the

value of can be validated with experimental results obtained with an computer

algorithm made for this study. These findings are useful to provide a more complete

63

description of the wake created by a SPP in effort to guide the development of a method

for performance prediction of SPPs.

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APPENDICES

65

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APPENDIX A: COMPUTER CODE

A.1 ImageMagick code through DOS window for resizing, crop andappend side and bottom view images.

:: Open file where all images are located.C:\users\laltamir

:: Resize all side view images using calibration scaling number.FOR %a in (*_side*.jpg) DO convert %a -resize 69% r_%a

:: Cropping offsets found using Canon Utilities File Viewer Utility version:: 1.3.2.11 as mentioned in section 3.2.1.

:: Crop ruler images.FOR %%a in ruler*.jpg) DO convert %%a -crop 1188x676+140+000 c_%%a

:: Crop all images of inclination 0 deg. and yaw 0 deg.FOR %%a in (*P00Y00*.jpg) DO convert %%a -crop 1188x676+140+000 c_%%a

:: Crop all images of inclination 7.5 deg. and yaw 15 deg.FOR %%a in (*P7p5Y15*.jpg) DO convert %%a -crop 1188x676+214+000 c_%%a


:: Crop all images of inclination 7.5 deg. and yaw 0 deg.FOR %%a in (*P7P5Y00*.jpg) DO convert %%a -crop 1188x676+214+000 c_%%a


: crop all 0 deg. Pitch and 15 deg yawFOR %%a in (*P00Y15*.jpg) DO convert %%a -crop 1188x676+140+000 c_%%a


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:: Crop all images of inclination 7.5 deg. and yaw30 deg.FOR %%a in (*P7p5Y30*.jpg) DO convert %%a -crop 1188x676+214+48 c_%%a

:: Append side and bottom images to make composite image. FOR %%a in (.jpg) DO convert c_%%a_side.jpg c_%%a_bottom.jpg -append a_%a

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A.2 MATLAB code to label composite image.

%Read in desired file.I = imread ('H33P00Y00J0p8N1325_sb7.jpg');

%Label image.TEXt(10,10,’I=33% \gamma=0ô\psi=0ô J=0.767,J_{scaled}=0.767');

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A.3 MATLAB code to get information within name of file.

function FileInfo = parser(filename)%fn_parser Takes filename of form 'HaaPbbYccJdPe_Runf.jpg' % and returns structure containing numeric fields:% % H = aa;% P = bb;% Y = cc;% J = d + e/10;% Run = f;%% and the string fields:% fn = filename;% H = str2num(filename(2:3)); P = str2num([filename(5:6)]); Y = str2num(filename(8:9)); J = str2num([filename(11) '.' filename(13)]); Run = str2num(filename(18)); FileInfo.H = H; FileInfo.P = P; FileInfo.Y = Y; FileInfo.J = J; FileInfo.Run = Run; FileInfo.fn = filename;

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A.4 MATLAB code for obtaining wake profile.

% Clean all previous information. clear, clc, clf, close all

% Folder where images are located.input_dir = 'C:\Users\laltamir\Desktop\image_measure\';

% Folder where results will be saved. output_dir = 'C:\Users\laltamir\Desktop\image_measure\wake\';

% Read only JPEG files from folder. files = dir(strcat(input_dir, '*.jpg'));

% Start a loop that takes every JPEG file in current folder. for k = 1 : length(files) % Read in file

I = imread(strcat(input_dir, files(k).name));

% Get height and width dimensions of image. [h w] = size(I);

% Crops image so only bottom view is displayed based on h % and w. I = imcrop(I, [0 h/2 w h]);

%Allows to pick a polygon area using mouse. Coordinates of %points are xi, yi.[mask xi yi] = roipoly(I);

% Save values of xi, yi. New file with results is named % as the original image file with “Wake_Dia” at begging.save(strcat(output_dir, 'Wake_Dia', strrep(files(k).name, '.jpg', '.mat')), 'xi', 'yi');

end % End of loop.

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A.5 MATLAB code for measuring wake pitch and wake pitch angle


% Select folder where images are located.img_home_dir = 'C:\Users\laltamir\Desktop\image_measure\';

% Select folder where results will be saved. output_dir = 'C:\Users\laltamir\Desktop\image_measure\';

% Select folder with wake profile results are located.wake_dir = 'C:\Users\laltamir\Desktop\image_measure\wake\';

filter_radius = 4; %Radius of filterD = 9.7; %Radius of SPP [in]mkdir(output_dir); %Creates destination folder

%Find all files in working directory that are JPEGS.files = dir(strcat(img_home_dir, '*.jpg'));

%Set parameter p used in loop. Open a figure to display image.p = 1;figure, set(gcf, 'WindowStyle', 'Docked')

%Start a loop that goes through all the images in the directory.while p <= length(files)

%Load wake profile coordinates.load(strcat(wake_dir, 'Wake_Dia', strrep(files(p).name, '.jpg', '.mat')))

%Call parser function to get information within name of %file.

FileInfo = parser(files(p).name); %Read the current image number given by parameter 'p'. I = (imread(strcat(img_home_dir, files(p).name)));

%convert image to gray scaleI = rgb2gray(I);

%Crop image so only bottom view is displayed

[height width] = size(I);%Give crop window sizeI_new = imcrop(I, [0 height/2 width height]);

%Increase intensity of new image. I_new = imadjust(I_new);

%Constant number for threshold value.c_thresh = 0.9/0.5;

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%Apply Otsu's threshold method. Multiply by constant. thresh = graythresh(I_new)*c_thresh;

%Round up edges of cavities (filter) and rotate image.

%Create round filter of filter_radius.f = fspecial('disk',filter_radius);

%Apply filter to image.J = imfilter(I_new,f);

%Equalize histogram.Increase the contrast of J J = imadjust(J);

%Display processed image.imshow(J, 'InitialMagnification', 'fit');

%Pick hub location.disp('Please click once on hub location')

[xh yh] = ginput(1); %Pick one point for hub location.

%Rounds value of points xh and yh to nearest integer.xh = round(xh);

yh = round(yh); %Convert rotated image to binary image. N = im2bw(J, thresh);

%Grab size of image into an array.[n m] = size(N);

%Show line along SPP shaft at height yh.

%Make a matrix with 0s and 1s.A = [zeros([yh-1,m]);ones([1,m]);zeros([n-yh,m])];

cl = logical(A); %Get diagonal elements of A negative = xor(N, cl); %Find 0s and 1s along shaft line

%Draw 1s when 0s and visceversaimshow(negative, 'InitialMagnification', 'fit')

%Display messages.num = input('How many cavities do you want to consider?\n');disp(sprintf('Pick close to shaft line and cavity edge.\n')) %Read cavities walls and surroundings as 0s and 1s.

%Select points close to edges.[x_close y_close] = ginput(num);

%Get row of 0s and 1s around edges.

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line1 = negative(yh,:);

%Difference between 0s and 1s everywhere in image.%Absolute value of difference to get only 1s.

%Finds all nonzeros (1s) at all edges of all cavities.intersections = find(abs(diff(line1)));

%Find positions of tangent ends at cavity (from ginput).

%Create one column of zeros of max-x_close-rowsInd = zeros(length(x_close),1);

%Show and imageimshow(J, 'InitialMagnification', 'fit'), hold on

%Start loop that repeats for each cavity selected.

for k = 1:length(x_close)

%grab 1s closest to points picked [C, Ind] = min(abs(x_close(k) - intersections));

%show edges of cavitiesplot(intersections(Ind), yh, 's', 'MarkerSize', 14), hold on

interesting_intersections(k) = intersections(Ind); %Calculate wake pitch angle c = interesting_intersections(k) - xh;

%Normalize to obtain pixels only and do calculation. %a is based on distances on an unrolled propeller.a = ((k*(pi/2)*D)*(209/5)); phi(k) = atand(abs(c)/abs(a));

%Get wake pitch in inches. Pw(k) = c*(5/209);

%Upper part of wake profile. Xi1 = 1:(round (length(xi)/2)-1); Yi1 = 1:(round (length(yi)/2)-1);

%Bottom part of wake profile.Xi2 = round(length(xi)/2):length(xi)-1;

Yi2 = round(length(yi)/2):length(yi)-1;

%Use interpolation to find points above and below %interesting_intersection points

yw1(k)=interp1(xi(Xi1),yi(Yi1),interesting_intersections(k)); %upper part of wake profile

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yw2(k)=interp1(xi(Xi2),yi(Yi2),interesting_intersections(k)); %bottom part of wake profile

%Calculate wake diameter in inches Dw(k) = abs(abs(yw2(k))-abs(yw1(k)))*(5/209); end %End of for loop.

disp(sprintf('Hit any key to continue.\n')) pause

%Name results to be saved.

Results.p = p; Results.yh = yh; Results.xh = xh; Results.P_x = interesting_intersections; Results.FileInfo = FileInfo; Results.c_Thresh = c_thresh; Results.phi = phi; Results.Pw = Pw; Results.Dw = Dw;

%Prompt user if save work or not.answer = input('Save results? [y/n]\n', 's');

%Start a loop that either saves results or not, then repeats %while loop for same condition, for next condition or exits %while loop. %Option that saves results in mat file in destination folder. %Displays name of file saved. if strcmp(answer, 'y') || strcmp(answer, 'Y')

fn_output = strrep(files(p).name, '.jpg', '.mat'); save(strcat(output_dir, fn_output), 'Results') disp(sprintf('Saved as %s in %s...\n',

fn_output, output_dir));

%Option that does not save resultselseif ~(strcmp(answer, 'N') || strcmp(answer, 'n'))

disp(sprintf('How can I know what you want if you yourself are unsure?\n'))

end %End of if loop

%Prompt to repeat or exit from while loop. answer = input('Repeat, continue, or exit? [R/C/E]\n','s');

%Option executes while loop for next file. if strcmp(answer, 'C') || strcmp(answer, 'c')

p = p + 1;

%Option that executes while loop for same file.

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elseif strcmp(answer, 'R') || strcmp(answer, 'r') continue;

%Option that exits while loop. elseif strcmp(answer, 'E') || strcmp(answer, 'e')

break;

else disp(sprintf('How can I know what you wReant if you yourself are unsure?\n'))

end %Ends if loop.

%Clears all storage information from previous executed file. clear Results I_new P I J Dw Pw interesting_intersections n m xh yhc_thresh x_close phi

end %Ends while loop.

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A.6 MATLAB code plotting parameters


% Select folder where images are located.home_dir = 'C:\Users\laltamir\Desktop\image_measure\';

% Select folder where results will be saved.output_dir = 'C:\Users\laltamir\Desktop\image_measure\graphs\';

% Select folder with wake profile results are located.wake_dir = 'C:\Users\laltamir\Desktop\image_measure\wake\';

%Find only .mat filesfiles = dir(strcat(home_dir, '*.mat'));

%Create output directorymkdir(output_dir);p = 1;D = 9.7; %prop. diameter in inches

%Values for J and Jscaled J.value = [0.767 0.975 1.176 1.36 1.328 1.316 1.481 1.927,… 0.758 0.95 1.15 1.302 1.445 1.491 1.531 1.574 1.804 0.773,… 0.957 1.134 1.34 1.479 1.772 0.85 1.051 1.239 1.487 1.537,… 1.982 1.027 1.2 1.4 1.745 1.717 0.918 1.120 1.356 1.358,… 1.412 1.552 0.803 1.006 1.206 1.197 1.395 0.806 1.023 1.219,… 1.41 1.638 1.814 1.326 0.805 0.994 1.187 1.301 1.49 1.747,… 0.913 1.19 1.419 1.421 1.441];

J.scaled = [0.767 0.975 1.176 1.36 1.328 1.316 1.481 1.927,… 0.656 0.823 0.996 1.127 1.251 1.292 1.326 1.363 1.562 0.67,… 0.829 0.982 1.161 1.281 1.535 0.822 1.016 1.197 1.436 1.485,… 1.914 0.859 1.004 1.171 1.46 1.437 0.768 0.937 1.135 1.136,… 1.181 1.298 0.796 0.997 1.196 1.186 1.383 0.692 0.879 1.047,… 1.211 1.406 1.558 1.139 0.691 0.853 1.019 1.117 1.28 1.5,…0.913 1.19 1.419 1.421 1.441];

%Starts loop that plots wake parameters versus SPP angular %rotation in 2 subplots with respective name of file in title.while p <= length(files)

%load the wake measure.load(strcat(wake_dir, 'Wake_Dia', strrep(files(p).name, '.jpg', '.mat'))) load(strcat(home_dir, ' ' , %

%Load pitch and angle measure.strrep(files(p).name, '.jpg','.mat')))

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%Call the function FileInfo to break filename info and get %angles.

FileInfo = parser(files(p).name); %Convert values of phi wrt to horizontal. phi_h = Results.phi - FileInfo.Y; %Values for Angular Position of Propeller.

ap = (pi/2)*[1:length(Results.Dw)]; %Open a figure.

figure(p)

%Plot of wake pitch and diameter as a function of angular %position.

subplot(2,1,1),plot(ap, Results.Dw/D, 'bo-'), hold on plot( ap, Results.Pw/D, 'gs-'), hold off

%Label meaningful values.set(gca,'XTick',pi/2:pi/2:(pi*length(Results.Dw)));set(gca,'XTickLabel',{'pi/2','pi','3pi/2','2pi','5pi/2',…'3pi','7pi/2’,'4pi','9pi/2','5pi','11pi/2','6pi','13pi/2’,…','7pi','15pi/2','8pi'});

%Change form of inclination angle given as bb to b.b.

if FileInfo.P == 75 FileInfo.P = 7.5; end

%Using parser function, title plot same as name of file. title (['I = ',num2str(FileInfo.H),'%,...

\gamma = ',num2str(FileInfo.P),... 'ô, \psi = ',num2str(FileInfo.Y), 'ô,...

J = ',num2str(J.value(p)),... ', J_{scaled }= ',num2str(J.scaled(p))]);

%Label axis of plot. xlabel ('\phi');

ylabel ('Pw/D, Dw/D');

%Plot of wake pitch angle as a function of angular %position subplot(2,1,2),plot(ap, phi_h, 'rv-'); %Label meaningful values

set(gca,'XTick',pi/2:pi/2:(pi*length(Results.Dw))); set(gca,'XTickLabel',{'pi/2','pi','3pi/2','2pi','5pi/2',...'3pi','7pi/2','4pi','9pi/2','5pi','11pi/2','6pi','13pi/2','7pi','15pi/2','8pi'});

%Label axis of plot. xlabel ('\phi');

ylabel ('\Phiw'); disp ('Select Dw/D then Pw/D locations');

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%Pick location to display a tag for Dw and Pw lines. gtext ({'Dw/D';'Pw/D'});

%Prompt user if save work or not.

answer = input('Save results? [y/n]\n', 's');

%Start a loop that either saves results or not, then repeats %while loop for same condition, for next condition or exits %while loop. %Option that saves results as JPEGS file in destination %folder. Displays name of file saved. if strcmp(answer, 'y') || strcmp(answer, 'Y')

fn_output = strrep(files(p).name, '.mat', '.jpg'); save(strcat(output_dir, fn_output), 'Results') disp(sprintf('Saved as %s in %s...\n',

fn_output, output_dir));

%Option that does not save resultselseif ~(strcmp(answer, 'N') || strcmp(answer, 'n'))

disp(sprintf('How can I know what you want if you yourself are unsure?\n'))

end %End of if loop

%Prompt to repeat or exit from while loop. answer = input('Repeat, continue, or exit? [R/C/E]\n','s');

%Option executes while loop for next file. if strcmp(answer, 'C') || strcmp(answer, 'c')

p = p + 1;

%Option that executes while loop for same file. elseif strcmp(answer, 'R') || strcmp(answer, 'r')

continue; %Option that exits while loop. elseif strcmp(answer, 'E') || strcmp(answer, 'e')

break;

else disp(sprintf('How can I know what you wReant if you yourself are unsure?\n'))

end %Ends if loop. %Clears all storage information from previous executed file.

clear Results Pw Dw phi fig FileInfo.Y FileInfo.P FileInfo.HFileInfo.fn

end %Ends while loop.

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APPENDIX B: COMPLETE SET OF IMAGES AND WAKE PARAMETER MEASUREMENTS

B.1 Results for immersion 50%, inclination 0 degrees and yaw 0 degrees with descending values of Jscaled.

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B.2 Results for immersion 33%, inclination 7.5 degrees and yaw 30 degrees. images are shown with descending values of Jscaled.

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B.3 Results for immersion 33%, inclination 7.5 degrees and yaw 15 degrees. Images are shown with descending values of Jscaled.

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B.4 Results for immersion 33%, inclination 7.5 degrees and yaw 0 degrees. Images are shown with descending values of Jscaled.

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B.5 Results for immersion 33%, inclination 15 degrees and yaw 30 degrees. Images are shown with descending values of Jscaled.

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90

91


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93


94

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B.9 Results for immersion 33%, inclination 0 degrees and yaw 15 degrees. Images are shown with descending values of J scaled.

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B.10 Results for immersion 33%, inclination 0 degrees and yaw 0 degrees. Images are shown with descending values of J scaled.

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REFERENCES

[1] Young, Yin L., and Spyros A. Kinnas. "Performance Prediction of Surface-Piercing Propellers." Journal of Ship Research 2004,Vol. 28: pp. 288-304.

[2] Kamen, Paul. "Surface-Piercing Propellers." Boatbuilder Magazine 1995: 1-8.

[3] The Propulsion Commitee, “Proceedings of the 23rd ITTC.” 23th International Towing Tank Conference 2002, Volume I: pp. 90-142.

[4] Office of Naval Research. “Broad Agency Announcement (BAA).” Department of the Navy Sciency & Technology 2005: pp.1-13.

[5] Hecker, Richard. “Experimental Performance of a Partially Submerged Propeller in Inclined Flow.” The Society of Naval Architects and Marine Engineers 1973: pp.1-9.

[6] Lorio, Justin. Open Water Testing of a Surface-Piercing Propeller with Varying Submergence, Yaw Angle and Inclination Angle 2008, Master Thesis: 1-40.

[7] Lorio, J. M., L. M. Altamirano, M. H. Tall & K. D. von Ellenrieder. “Design of a Next Generation Surface-Piercing Propeller Test Stand.” Paper presented at Oceans ’09 MTS/IEEE Biloxi, October 26-29, 2009.

[8] The Specialist Committee on Model Test of High Speed Marine Vehicles Final Report and Recommendations to the 22nd ITTC, Annapolis, USA, November 1998.

[9] Schaefer, Charles V. “Our Research Facilities.” The Center for Maritime Systems2004: 14 March 2009 <http://www.stevens.edu/ses/cms/Facilities/index.html >.

[10] Olofsson, Niclas. Force and Flow Characteristics of a Partially Submerged Propeller. Goteborg: Department of Naval Architecture and Ocean Engineering -Chalmers University of Technology, 1996.

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[11] Carlton, John S., Marine propellers and propulsion. Great Britain: MPG Books Ltd. 2nd ed. 2007

[12] Gillmer, Thomas C., and Bruce Johnson. Introduction to Naval Architecture. Annapolis, Maryland: Naval Institute Press, 1982.

[13] Vorus, William S. “Surface Piercing Propellers: Design and Testing” ONR T-Craft Meeting. January 8 and 9, 2008

[14] Brandt, H., “Modellversuche mit Schiffspropellern an der Wasseroberfläche.” Dissertation 1972/1973, TU Berlin.

[15] Hadler, J.B., and R. Hecker. “Performance of Partially Submerged Propellers.” 7th

ONR Symposium on Naval Hydrodynamics 1968: pp. 1449-1496.

[16] Otsu, Nobuyuki., “A threshold selection method from gray-level histograms.” IEEE Transactions on systems, man and cybernetics 1979: Vol. 9: pp. 62-66.

[17] Hoshino, T., “Hydrodynamic analysis of propellers in steady flow using a surface panel method.” Journal of the Society of Naval Architects of Japan 1989: Vol. 165: pp. 55- 70.

[18] Ananthakrishnan, P. “Actuator-Disk Model” Hydrodynamic Aspects of Ship Design. Class notes. 2009: Florida Atlantic University, Dania Beach.

[19] Truscott, Tadd and Alexandra H. Techet. "Cavity formation in the wake of a spinning sphere impacting the free surface." Physics of Fluids 2006: pp.18.

[20] Worthington, A.M. and R.S. Cole. “Impact with a liquid surface studied by the aid of instantaneous photography” Philosophical Transactions of the Royal Society of London 1900, Vol.194: pp 175-199

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