A NEW PARADIGM FOR GENERATING SURFACE-NORMAL FORCES FOR

HULL-CLEANING ROBOTS

By

Kristina Maria Kamensky

A DISSERTATION

Michigan State University

in partial fulfillment of the requirements

Submitted to

for the degree of

Mechanical Engineering – Doctor of Philosophy

2020

ABSTRACT

A NEW PARADIGM FOR GENERATING SURFACE-NORMAL FORCES FOR

HULL-CLEANING ROBOTS

By

Kristina Maria Kamensky

A Bernoulli pad uses an axial jet to produce radial outflow between the pad and a proximally located
parallel surface, which may be either a mobile workpiece or a fixed wall. The flow field produces
a force between the surfaces which depends upon their spacing Ò. The direction of this force is
repulsive for large and small h, but two equilibria exist between these limits. The nearer equilibrium
point (Òeq) is stable, and this distance is dependent on the direction and magnitude of the force
the pad is required to apply. Increasing the flow rate increases the strength of the contactless grip,
subject to cavitation or compressibility constraints, depending on the working fluid. Industry has
created devices of this type to grip and transport a variety of workpieces without contact. The
present research is inspired by the need to keep a submerged ship hull free of biofouling organisms.
Preventative maintenance during idle periods of operations can improve efficiency while prolonging
the original surface properties of the hull. The Bernoulli pad for this application is significantly
larger and uses the surrounding water as the working fluid. In the present work, the flow field was
investigated computationally and experimentally. Field tests were also performed to determine the
ability of the device to mitigate biofouling.

The computational work, which was validated with experimental results found in literature,
indicates that a power-law relationship exists between Òeq and the inlet fluid power required to sus-
tain this equilibrium spacing when each is appropriately scaled. This scaling is derived principally
from the wall shear; an additional term incorporating the inlet Reynolds number is used to account
for the force applied to the system. The relationship is valid over a range of forces acting on the
system, geometric, and material properties. Major and minor geometry alterations provide insight
to customizing pressure or wall shear stress profiles.

The biofouling removal ability of a shear-based device was field tested on two submerged surface

types, Garolite G-10 and AkzoNobel’s Intersleek 1100SR. The latter is a fouling-release coating.
Each surface was groomed at four frequencies along with a control group during a seven-week
grooming study conducted in Narragansett Bay in Rhode Island. An image-processing algorithm
was developed and used to assess the effectiveness of the various grooming protocols, along with
direct measurements of chlorophyll a per surface area. The image-processing data showed that
the grooming resulted in approximately 50% cleanliness on the Garolite at the end of the study
whereas the Intersleek was continuously restored to nearly its initial clean state. Chlorophyll a
data supported these overall conclusions. These results indicate that surface cleanliness can be
maintained effectively on Intersleek using frequent shear-based grooming. The key to success is
to match or supersede the critical wall shear stress of settled biofouling organisms whose adhesive
strength is exponential in time.

Particle Tracking Velocimetry (PTV) measurements were also taken on the flow field. This La-
grangian measurement approach uses an iterative particle reconstruction technique in combination
with high seeding density to reconstruct a 4D (x, y, z, t) flow field. This 4D reconstruction allows
the pressure field to be reconstructed using the Navier-Stokes equations. Various experiments
have been conducted on confined radial outflow but PTV measurements are presented here for the
first time. The PTV measurements were compared with computational results and while there is
reasonable agreement in the velocity field data, there are discrepancies is the pressure field data.
Recommendations are provided for future work that can reconcile these differences.

Copyright by
KRISTINA MARIA KAMENSKY
2020

Dedicated to Michael Anthony Donegan, who never let my confidence run dry.

v

ACKNOWLEDGEMENTS

I would like to express my gratitude and thanks to my advisor, Dr. Ranjan Mukherjee, for his
guidance and patience during my career at Michigan State University. Together, we have worked
on more than just the research presented in this paper. He has fostered an incredible lab where he
encourages my lab mates and myself to push ourselves while we push the boundaries on scientific
knowledge. I would also like to thank my Navy mentor, Dr. Aren Hellum, who has provided insight
at every step. He also has been an exceptional role model, and I am proud of my career trajectory.
I also want to thank Dr. John Foss for his earlier investigation into confined radial flow, which
definitely was the seed of inspiration for this research. Thank you Dr. Ricardo Mejia for being
on my committee and letting me use your fluid flow visualization setup. Your help when I would
get stuck at processing and evaluating the data was also instrumental in my research. Thank you
Richard Prevost, from LaVision, for taking the time to lend your expertise on operating the Particle
Tracking Velocimetry setup efficiently to get results within the first few tries. Thank you Dr. James
Klausner for being on my committee. Your passion for sustainable engineering helps to give me
critical feedback on my own research.

Thank you Office of Naval Research, and in particular Maria Medeiros, for funding and sup-
porting me through the Naval Undersea Research Program (NURP). I benefited highly from such a
unique graduate school experience. I pursued engineering in order to make a difference in the world,
in particular to make systems more energy efficient in order to reduce environmental footprint. It
is not a coincidence that this dissertation reflects that goal.

The biggest thank you to my parents, Martin and Lydia Kamensky, who loved and nurtured
the curious scientist in me from a very early age. My dad instilled gardening in me, as well as a
passion for tinkering with tools to fix and build things. I have so many memories of books with my
mom. Not only did she buy me books (science, insect, and animal books were my favorites), but
she also took me on countless library visits. I love books and the pursuit of knowledge more than
ever. Thank you to my brother, Martin Ernest Kamensky, who was born first. By choosing your

vi

college and major before me, I was able to learn from you what engineering was truly all about.
A shout-out to all my aunts, uncles, and cousins for their love and support. I also want to thank
my best friend and sister that I always wanted, Kimberly June "Bug" Moody. You have always
encouraged me to be my weird self.

I cannot thank my partner, Michael Anthony Donegan, enough. We met in Flint, Michigan
when were were both pursuing our Bachelors of Science in Electrical (him) and Mechanical (me).
I’ve been infatuated with him ever since. Michael has been an endless source of strength and
support for me while I continued being a professional student. His immediate and extended family
has also been a blessing. They have never stopped cheering me on.

There are so many people at MSU that I want to thank. I am glad I somehow sat next to Andrew
Hess at a campus-wide teaching assistant orientation. I thought I was getting too old to make new
best friends, but he thankfully proved me wrong. I am grateful of my research lab family for being
who they are; Mahmoud Abdullatif, Amer Allafi, Sanders Aspelund, Connor Boss, Sheryl Chau,
and Nilay Kant. Pursuing a PhD is an individual journey, but it is less daunting with people like
them. Many thanks to the various faculty that welcomed my questions when I knocked on their
office door or emailed them, regardless if I was taking a course with them. A huge thanks to the
Division of Engineering Computing Services (DECS), who without them I would not have the
resources or support to be successful. I also can not thank the people who run the Department
Mechanical Engineering enough.
I want to thank Roy Bailiff and Mike Koschmider from the
Manufacturing Teaching Laboratory for all the random help and 3D printing they have provided. A
huge thanks to Dr. Katy Colbry for her help and words of encouragement. I have so much gratitude
toward Dr. Percy Pierre and the Sloan Engineering Program that he created. I am also thankful for
Julie Rojewski and MSU BEST (Broadening Experiences in Scientific Training) for empowering
me to make the most of my time on campus.

A huge thanks to the various people who helped me with my field test studies in Newport,
Rhode Island. Thanks to the Center of Corrosion and Biofouling Control at the Florida Institute
of Technology for inviting me to visit their group and providing the special paint. Thanks to Dr.

vii

Mark Menesses from Boston University who was a fellow graduate student in NURP. He shared
his knowledge of biofouling and experience in field test studies. Thanks to Natasha Dickinson
from NUWC for regularly visiting me at the dock and identifying the invertebrates that were living
on my experimental setup. Thanks to Dr. Pia Moisander and Abhishek Naik from University of
Massachusetts Dartmouth for your collaboration. Thanks to Dr. Christin Murphy for taking an
interest in me and becoming one of my newest mentors.

Thanks to everyone who gave me a chance prior to my time at MSU, especially Dr. Homayun
Navaz. When I visited his office to talk about joining his research group as an undergraduate
student at Kettering University in 2007, I never could imagine how far that interview would take
me. Not only did I write my first thesis on evaporation and vapor transport models within porous
materials with him as my advisor, but I stayed in Flint to pursue a Masters. Dr. Navaz and I started
a company to do consulting on optimizing commercial refrigeration. I wrote another thesis based
on our own research on quantifying and visualizing the infiltration/exfiltration process in walk-in
coolers. Within a few weeks of having my Masters degree in hand, I was asked by Dr. Craig Hoff
and Dr. Henry Kowalski if I wanted to teach an undergraduate mechanical engineering course.
Thank you for the opportunity, because my love for learning and new found love for teaching led me
to applying to MSU’s PhD program. There are so many more people from Kettering that played a
critical role and I want to name a few more. Thanks to Dr. Patrick Atkinson, Dr. Theresa Atkinson,
Professor Reginald Bell, Dr. Susan Farhat, Dr. Gianfranco DiGiuseppe, Dr. Mary Gilliam, Dr.
Ruben Hayrapetyan, Nick Keehn, Brenda Lemke, Dr. Massoud Tavakoli, and Dr. Ali Zand.

Flint, Michigan has been my year round home since 2010. I feel as though I have been adopted
by various people in this tight knit community. I wholeheartedly thank Dawn Hibbard for befriend-
ing me and introducing me to the Rotary Club of Flint. Not only did I get the chance to meet the
leaders and business owners of this tenacioius city, but I was invited to join their diverse group.

At the time of this writing, we are in the midst a modern pandemic, ecological turmoil, and
civil unrest. A last thank you for everyone that helped me to keep moving forward and focused
during what had already been the most stressful time in my life.

viii

TABLE OF CONTENTS

LIST OF TABLES .
LIST OF FIGURES .
CHAPTER 1

.
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.
INTRODUCTION .

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. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . xiii
1
. . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

xi

CHAPTER 2 POWER SCALING OF RADIAL OUTFLOW: BERNOULLI PADS IN

.
.

.
.

. .
.
.

Introduction .
.

2.1
2.2 Approach .

EQUILIBRIUM .
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7
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7
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7
. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
7
2.2.1 Description of computations . . . . . . . . . . . . . . . . . . . . . . . . .
8
2.2.2 Validation using published results
. . . . . . . . . . . . . . . . . . . . . .
Finding Òeq using interpolation . . . . . . . . . . . . . . . . . . . . . . . .
2.2.3
9
Fluid power measurement . . . . . . . . . . . . . . . . . . . . . . . . . . . 11
2.2.4
. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 12
. 16
. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 19
Scaling based on wall shear . . . . . . . . . . . . . . . . . . . . . . . . . . 19
Scaling modified to account for 
a . . . . . . . . . . . . . . . . . . . . . . 21
.
. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 22
. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 22

2.5.1
2.5.2
2.5.3 Corner Effects .
.

2.3 Results .
2.4 Sample Calculations of Discretization Error
2.5 Discussion .

. . . . . . . . . . . . . . . . . . . .

2.6 Concluding Remarks

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CHAPTER 3 UNDERWATER SHEAR-BASED GROOMING OF MARINE BIOFOUL-

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. .

Introduction .

3.1
.
3.2 Materials and Methods
3.3 Experimental Design .
.

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. . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
.

ING USING A NON-CONTACT BERNOULLI PAD . . . . . . . . . . . . 26
. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 26
. 26
. 29
3.3.1 Test Site .
. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 29
3.3.2 Experimental Design - Year 1 . . . . . . . . . . . . . . . . . . . . . . . . 29
3.3.3 Experimental Design - Year 2 . . . . . . . . . . . . . . . . . . . . . . . . 31
3.3.4 Grooming Procedure . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 33
3.3.5 Data Acquisition . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 35
3.3.6
. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 37
3.3.7 Chlorophyll a Processing . . . . . . . . . . . . . . . . . . . . . . . . . . . 38
. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 39
Preliminary Findings - Year 1 . . . . . . . . . . . . . . . . . . . . . . . . 39
Image Analysis - Year 2 . . . . . . . . . . . . . . . . . . . . . . . . . . . . 42
. 44
3.5 Temperature, Light, and Salinity Data
. . . . . . . . . . . . . . . . . . . . . . . . 48
3.6 Biofouling Organisms Observed . . . . . . . . . . . . . . . . . . . . . . . . . . . 50
. 53

3.4.1
3.4.2
3.4.3 Chlorophyll a - Year 2 . . . . . . . . . . . . . . . . . . . . . . . . . . . .

. . . . . . . . . . . . . . . . . . . . . . . .

Image Setup and Collection

Image Processing .

3.4 Results . .

3.6.1

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ix

.
3.7 Discussion . .
3.8 Concluding Remarks

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. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 54
.
. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 57

CHAPTER 4

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. .

Imaging .

Introduction .

4.1
.
4.2 Description of Experiment

. .

3D PARTICLE TRACKING VELOCIMETRY OF RADIAL OUTFLOW
BETWEEN TWO PARALLEL PLATES . . . . . . . . . . . . . . . . . . . 58
. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 58
. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 58
4.2.1 Bernoulli pad in water tank . . . . . . . . . . . . . . . . . . . . . . . . . . 58
. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 60
4.2.2
. . . . . . . . . . . . . . . . . . . . . . . . . . . 62
4.2.3 Experimental Procedure
. 63
. . . . . . . . . . . . . . . . . . . . . . . . 67
. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 68
.
4.5.1 Ensemble Average
. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 68
4.5.2 Azimuthal Average . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 69
Pressure Distribution . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 70
4.5.3
. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 71
.
. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 84

. . . . . . . . . . . . . . . . . . . . . . . . . . . .

4.3 Experimental Measurements
4.4 Computational Fluid Dynamics Model
4.5 Results .

4.6 Analysis .
.
4.7 Concluding Remarks

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CHAPTER 5 CONCLUSIONS .
APPENDIX .
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BIBLIOGRAPHY .

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. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 88
. 92
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.
. 132

. . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

x

LIST OF TABLES

Table 2.1: Sample discretization errors in pressure computations plotted in Figure 2.1 (a)

for 
 = 4 mm, 
 = 40 mm, Ò = 0.4 mm and (cid:164)
 = 5.1 × 10−4 kg/s.

. . . . . . . . 17

Table 2.2: Sample discretization errors in force computations plotted in Figure 2.1 (b) for


 = 4 mm, 
 = 40 mm and (cid:164)
 = 5.1 × 10−4 kg/s.

. . . . . . . . . . . . . . . . . 18

Table 2.3: Sample discretization errors in power computations at equilibrium plotted in

Figure 2.8 for 
 = 4 mm and 
 = 40 mm.

. . . . . . . . . . . . . . . . . . . . . 19

Table 3.1: Results of rmANOVA testing the effects of grooming on the concentration of
chlorophyll a in fouling material growing on Garolite and Intersleek plates.
This data and table was provided by Abhishek Naik.

. . . . . . . . . . . . . . . 47

Table 3.2: Effects of grooming on chlorophyll a on fouled plates. Values represent
Cohen’s d estimates of effect size, a standardized mean difference between chl
a on control and groomed plates across 3 replicate plates each. Cohen’s d
values < 0 imply decreased chl a on groomed plates. Cohen’s d > 0 implies
increased chl a on groomed plates. This data and table was provided by
Abhishek Naik.

. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 48

. .

. .

Table A.1: Detailed legend for the following tables displaying all photos used in image
analysis. The field study was initiated on a Wednesday in order to consistently
distribute the labor throughout the week. . . . . . . . . . . . . . . . . . . . . . . 93

.

Table A.2: 3× Garolite. .
Table A.3: 2× Garolite. .
Table A.4: 1× Garolite. .
.
Table A.5: 0.5× Garolite. .

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. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 96

. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 103

. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 110

. .

. .

. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 112

.

Table A.6: Control Garolite.
Table A.7: 3× Intersleek. .
Table A.8: 2× Intersleek. .
Table A.9: 1× Intersleek. .
.
Table A.10:0.5× Intersleek. .

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. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 114

. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 121

. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 128

. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 130

xi

Table A.11:Control Intersleek.

.

.

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. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 131

xii

LIST OF FIGURES

Figure 1.1:

(a) Parameters characterizing radial outflow between a Bernoulli pad and a
proximal parallel surface. The embodiments (b)-(e) correspond to a work-
piece being lifted, a workpiece being levitated, the pad being levitated, and
the pad being lifted, respectively. The applied force 

 is the sum of all
forces acting on the freely moving component (pad or surface) which are not
produced by the fluid flow between the pad and surface. The convention used
here is that 

 > 0 (

 < 0) attempts to increase (decrease) the gap between
the pad and the proximal surface.

. . . . . . . . . . . . . . . . . . . . . . . . .

1

Figure 2.1: Comparison of CFD simulation results with experimental results in [1]: (a)
pressure 
 as a function of radius 
 for 
 = 4 mm, 
 = 40 mm, Ò = 0.4 mm
and (cid:164)
 = 5.1 × 10−4 kg/s, analytical results available for 
 = 0 mm [1] are
also presented (b) fluid force on workpiece 
 as a function of gap height Ò
for a mass flow rate of (cid:164)
 = 5.1 × 10−4 kg/s. Stable and unstable equilibrium
points are found at Ò = 0.29 mm and Ò = 5.1 mm respectively. The insets
are provided to indicate the magnitude of the error bars where it would not
be visible otherwise. .

. . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

.

9

Figure 2.2: Example of interpolation to find equilibrium gap height Òeq for zero and a

non-zero value of the applied force 
a.

. . . . . . . . . . . . . . . . . . . . . . 10

Figure 2.3: Fluid power (cid:164)
m,in required to maintain an equilibrium height Òeq for 
a = 0.
The nominal dataset is 
 = 4 mm, 
 = 40 mm, 
s = 0.04 mm, based on air as
the working fluid; each other dataset varies one parameter from this baseline.
The dotted line is the best fit to the nominal dataset.

. . . . . . . . . . . . . . . 12

Figure 2.4: Ratio of inlet fluid pressure to inlet momentum as a function of equilibrium
height Òeq for 
a = 0. The nominal dataset is 
 = 4 mm, 
 = 40 mm,

s = 0.04 mm, based on air as the working fluid; each other dataset varies one
parameter from this baseline. The dotted line is the best fit to the nominal dataset. 13

Figure 2.5: Non-dimensional fluid power (cid:164)
∗ required to maintain a given non-dimensional
equilibrium height Ò∗. The nominal dataset is 
 = 4 mm, 
 = 40 mm,

s = 0.04 mm, based on air as the working fluid; each other dataset varies
one parameter from this baseline. The dotted line is the best fit to all data.

. . . 14

Figure 2.6: Non-dimensional fluid power (cid:164)
∗ required to maintain a given non-dimensional
equilibrium height Ò∗ for different values of 
∗ when the force correction
term in Eq.(2.5) is not used. The nominal dataset is 
 = 4 mm, 
 = 40 mm,

s = 0.04 mm, using air as the working fluid. The dotted line is the best fit to
the 
∗ = 0 dataset. .

. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 15

.

xiii

Figure 2.7: Non-dimensional fluid power (cid:164)
∗corr required to maintain a given non-dimensional

equilibrium height Ò∗ for different values of 
∗ when the force correction term
in Eq.(2.5) is used with 
 = 2/5. The nominal dataset is 
 = 4 mm, 
 = 40
mm, 
s = 0.04 mm, using air as the working fluid. The dotted line is the best
fit to the 
∗ = 0 dataset. Points associated with 
∗ = +6 at Ò∗ > 0.25 are not
visible in the present spread.

. . . . . . . . . . . . . . . . . . . . . . . . . . . 16

Figure 2.8: Fluid power

(cid:164)
m,in required to maintain an equilibrium height Òeq for the
nominal data set: 
 = 4 mm, 
 = 40 mm, 
s = 0.04 mm, and air as the
working fluid with 
a = 0. The GCI errors bars are included with sample
calculations shown in Table 2.3. . . . . . . . . . . . . . . . . . . . . . . . . . . 17

Figure 2.9:

Illustration of corner geometries: (a) 

 = 0, (b) 

 > 0, (c) 

 < 0.
Comparison of CFD simulation results with experimental results in [1]. . . . .

(d)

. 23

Figure 2.10: The pressure contour plots and pressure profile of a Bernoulli pad with a mass
flow rate of 2 kg/s pulled 5 mm away from the wall; (a) shows the simple
geometry with a 90 degree corner generating 21 N of suction and (b) shows a
pintle physically turning the axial flow to radial flow generating 45 N of suction. 24

Figure 2.11: The velocity contour plots and resulting wall shear profiles of a Bernoulli pad
with a mass flow rate of 2 kg/s pulled 5 mm away from the wall; (a) shows
the simple geometry with a 90 degree corner generating a larger peak wall
shear stress sooner and (b) shows a pintle generating a lower peak wall shear
stress at a larger radial location. . . . . . . . . . . . . . . . . . . . . . . . . . . 24

Figure 3.1:

(a) Half of the cross-sectional view of radial outflow between a Bernoulli pad
and a proximal parallel surface such as a hull with a magnified gap, (b) and
(c) normal and tangential stresses on the vessel hull generated by a pad of
dimensions 
 = 200 mm and 
 = 31.75 mm, operating at Òeq = 0.91 mm
resulting from an inlet jet velocity of 1.9 m/s.

. . . . . . . . . . . . . . . . . . 27

Figure 3.2: The shear stress range generated by the Bernoulli pad as implemented in this
study, shown in the context of literature data. Critical shear stress (Pa) required
for biofouling removal are shown as a function of time for biofilm or biofouling
development prior to exposure to shear. With the flow rate generating a
maximum wall shear stress of 5000 Pa and a minimum of 0 Pa on clean
plates, significant biofouling mitigation is expected between the minimum
and maximum (2 days to 2 weeks) time elapsed between all frequencies of
grooming. This is shown with a dark grey box overlay. Previously published
and adapted with permission from both the author and publisher (Menesses
et al. 2017).

. .

. .

. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 28

Figure 3.3: An aerial view of the Naval Undersea Warfare Center (NUWC) Division

Newport where both Year 1 and Year 2 studies were conducted.

. . . . . . . .

. 30

xiv

Figure 3.4:

(a) Pier at Stillwater Basin showing the suspended frames with plates sub-
merged under water. (b) A frame hauled up to remove a plate scheduled for
grooming.
(c) Using a tote filled partially with ocean water to keep plate
submerged while in transit to and from the grooming tank. (d) Suspended
test design used in Year 1. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 31

Figure 3.5: Suspended test design used in Year 2, shown here in two rows for ease of
illustration. The water level remained at least 0.3 meters above the top of the
grooming frame during the lowest tide.

. . . . . . . . . . . . . . . . . . . . . . 32

Figure 3.6: Grooming operation on a set of 4 Intersleek plates flush-mounted in the
Garolite grooming frame; the clear acrylic Bernoulli pad is difficult to discern
and is therefore outlined.

. . . . . . . . . . . . . . . . . . . . . . . . . . . . . 34

Figure 3.7: Picture of the sheltered space taken with the Canon EOS Digital Rebel XT
used for data acquisition, which is why there is no camera fixed into the
mount. The photographing platform for the assembled grooming frame is
directly underneath the point of view of the camera. The middle cutout
was to provide addition contact prevention on the plates. The accent light
is currently directed to the tank during the water exchange before scheduled
grooming.

. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 35

. .

.

.

. .

Figure 3.8: The sampling device was sanitized in between plate sampling with isopropyl
alcohol. (a) A plate slides into a slot designed into the bottom piece. Contact
on the front plate was avoided by holding only the permanently installed tab.
The top piece was carefully set down on the plate with the well containing
the single o-ring targeted on the area not yet sampled. Engaging the clamp
compresses the o-ring to create a leak-proof seal. The plastic top piece was
constrained from ever coming into contact with the plate by resting completely
on the flat face of the bottom piece of the sampling device. (b) 1 mL of 0.2
µm-filtered seawater was added to the well. (c) An overhead view in to show
the water sitting in the sealed well. (d) The biofouling in the well was scraped
off with a sterile plastic pestle before collected with a pipette.

. . . . . . . . . . 36

Figure 3.9: The top row shows raw images of Garolite and Intersleek plates before and
after grooming. The middle row shows computer generated images of Garolite
and Intersleek plates before and after grooming. The pixels of the computer-
generated images have colors that correspond to the entries of 




+; the
thin black contour indicates entries of 
+ = 4.5. The bottom row shows the
measure of cleanliness 
(
) for different values of 
; as expected, the plates
. . . . . . . . . . . . . . . . . . . . . . . . . . .
are cleaner after grooming.

. 39

xv

Figure 3.10: (a) The view from above during static grooming levitating the Garolite plate.
(b) Select results of static grooming of Garolite plates in Year 1. The plates are
shown before and after grooming in weeks 3 and 5 after they were submerged,
for four different grooming frequencies. . . . . . . . . . . . . . . . . . . . . . . 40

Figure 3.11: Select results of scanned grooming of Garolite plates in Year 1. The plates
are shown before and after grooming in weeks 1, 3 and 5 after they were
submerged, for four different grooming frequencies.

. . . . . . . . . . . . . . . 41

Figure 3.12: “Cleanliness” measured using 
(
) with 
 = 4.5 for (a) Garolite and (b)
Intersleek plates for four different grooming frequencies over a period of
seven weeks. The terms “before” and “after” indicate the pair of results
obtained before and after grooming on a particular day. The points linked by
the dotted lines in (a) correspond to the Garolite plates shown in Figure 3.9
(a). Similarly, the points linked by the dotted lines in (b) correspond to the
Intersleek plates shown in Figure 3.9 (b).

. . . . . . . . . . . . . . . . . . . . . 43

Figure 3.13: Chlorophyll a concentrations (µg cm−2) at 5 time points post-deployment.
(a) Garolite plates; (b) Intersleek plates. For the Garolite 0.5×/wk groomed
plates, samples were not collected on day 37 due to hard fouling growth. This
data and figure was provided by Abhishek Naik.

. . . . . . . . . . . . . . . . . 45

Figure 3.14: Effects of grooming on Garolite and Intersleek plates. Each point is a Cohen’s
d estimate representing a standardized mean difference between chl a on
control and groomed plates across 3 replicate plates each. Each estimate
summarizes the effect size for one plate type, grooming frequency, and day.
A Cohen’s d < 0 implies decreased chl a on groomed plates. A Cohen’s d
> 0 implies increased chl a on groomed plates. For the 0.5×/wk groomed
plates, samples were not collected on day 37 due to hard fouling growth. For
Intersleek plates, Cohen’s d values could not be calculated for the day 9 time
points due to negligible averages and zero standard deviations among chl a
concentrations of groomed plates and control plates. The red lines indicate
large Cohen’s d effect size of 0.8. This data and figure was provided by
Abhishek Naik.

. .

. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 46

Figure 3.15: The temperature and light intensity was logged in 15 minute intervals locally
with a HOBO pendant sensor that was mounted on one of the submersible
frames. The raw data points for temperature were plotted individually, with a
moving mean overlay.

. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 49

Figure 3.16: The water quality stations from the T-Warf located at the southern point of
Prudence Island represent the open bay water near the field test site. Water
salinity data was collected at both surface and bottom stations every 15
minutes using YSI 6600 V2 and EXO2 data loggers. Each data point is
plotted for the duration of the study along with a moving mean.

. . . . . . . . . 49

xvi

Figure 3.17: The front (top) and back (bottom) of the Garolite control plates at day 43
of the field test study. The box shows a close up picture of the area when
submerged to better show the mussel that is attached. The top also shows
circular areas that were used for sampling for chl a. Since the front of the
plates had a significant amount of biomass by day 35, the sampling device
could not maintain a seal for the circular well even if there were no hard
fouling in the way. The samples for that day was taken with a sterilized cell
lifter, the most noticeable resulting patch being on the front of the second
plate from the left. .

.

.

. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 51

Figure 3.18: The back of the control set of Garolite plates installed in its submersible frame
is shown, revealing a variety of macrofouling at day 51 which is after the end
of the 7 week study. The last extensive scraping of the back happened 2 weeks
prior. .

. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 52

.

.

.

.

.

.

.

.

Figure 3.19: Photos taken of (a) the back of the grooming frame after a group of 4 duplicate
plates are installed, and (b) the front. A paper note was used to document the
details and time of what was photographed. . . . . . . . . . . . . . . . . . . . . 54

Figure 4.1: The Bernoulli pad assembled with a plenum and flow straighteners. . . . . . . . 59

Figure 4.2: The BPA is mounted on a beam with roller wheels that allow the pad to be
placed in close proximity to the tank wall. Double arrows indicate the direc-
tion of movement of the BPA permitted by the roller wheels; this movement
allows the pad to find its equilibrium configuration.

. . . . . . . . . . . . . . . 59

Figure 4.3: A top view of the experimental setup showing the imaging hardware com-
prised of four ultra high-speed cameras and a dual-head pulsing laser. The
cameras are placed in an arc-like arrangement and focused on a volume that
lies between the pad and the tank wall. The dual-head laser is located in the
middle of the four cameras.

. . . . . . . . . . . . . . . . . . . . . . . . . . . . 61

Figure 4.4:

(a) CAD model illustrating where the laser illumination is directed to on
the BPA. Defined edges indicate where the image was masked in the flow
visualization software.
(b) The Bernoulli pad showing the matte surface
finish and three equally spaced nylon-tipped set screws installed. These set
screws help avoiding perturbations of the uniform equilibrium gap between
the pad and the tank wall. (c) Side view of the laser illuminating the area of
interest in the gap and partially into the jet outlet.

. . . . . . . . . . . . . . . . 62

Figure 4.5: A single representative image at time T (taken from the set of 100,000 images)

from the four cameras is shown. . . . . . . . . . . . . . . . . . . . . . . . . . . 64

Figure 4.6: Overlay of all 100,000 images are shown for each camera. These images (left

to right) correspond to the cameras (left to right) shown in figure 4.3.

. . . . . . 64

xvii

Figure 4.7: a) Straight-on view of measurement volume that includes a small portion of
the jet. b) and c) Tracks of the particles (Lagrangian) visible in the four
images in figure 2.6 over 8 additional frames (equivalent to 400
s). d) Vector
fields (Eulerian) of the particles visible in the four images in Figure 2.6.

. . . . 66

Figure 4.8: The force generated at different gap heights and four different mass flow
rates (left). The force versus mass flow rate at a gap height of 1.25 mm
with equilibrium shown with a dashed line (right). The maximum velocity
generated at this equilibrium point in the fluid flow field at 1.25 mm is 8.4
m/s, which is below the limits of the hardware. . . . . . . . . . . . . . . . . . . 67

Figure 4.9: Portion of the inlet is visible on the bottom left, and the intermediate outlet
of the experiment window is at the top of these plots. (a) Raw z-component
of velocity, (b) Raw theta-component of velocity, (c) Raw radial-component
of velocity, (d) refined radial-component of velocity, e) radial-component of
velocity from CFD run at the same boundary conditions. . . . . . . . . . . . . . 69

Figure 4.10: (a) Raw pressure, (b) refined pressure, c) Pressure from CFD run at the same

boundary conditions.

. . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

Figure 4.11: An illustration to show the boundaries of the data after completing the az-

. 71

. 72

. 72

imuthal average.

. . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

Figure 4.12: Mass flow rate calculated for every radial location using raw and refined radial

velocity data. .

.

.

. . . . . . . . . . . . . . . . . . . . . . . . . . . . .

.

.

.

.

.

.

Figure 4.13: The experimental radial velocity at different axial locations within the fluid
gap (
/Òeq), where zero is at the glass wall. The discretized PTV data is
overlaid on the original unstructured PTV data. . . . . . . . . . . . . . . . . . . 73

Figure 4.14: The CFD radial velocity at different axial locations within the fluid gap
(
/Òeq), where zero is at the glass wall. The discretized CFD is overlaid on
the original unstructured PTV data. . . . . . . . . . . . . . . . . . . . . . . . . 74

Figure 4.15: The experimental axial velocity at different axial locations within the fluid
gap (
/Òeq), where zero is at the glass wall. The discretized PTV data is
overlaid on the original unstructured PTV data. . . . . . . . . . . . . . . . . . . 75

Figure 4.16: The CFD axial velocity at different axial locations within the fluid gap (
/Òeq),
where zero is at the glass wall. The discretized CFD is overlaid on the original
unstructured PTV data.

. . . . . . . . . . . . . . . . . . . . . . . . . . . . .

. 76

xviii

Figure 4.17: The experimental discretized and tangential velocity at different axial loca-
tions within the fluid gap (
/Òeq), where zero is at the glass wall. The dis-
cretized PTV data is overlaid on the original unstructured PTV undiscretized
data.

. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 77

.

.

.

.

.

.

.

.

.

Figure 4.18: The experimental pressure at different axial locations within the fluid gap
(
/Òeq), where zero is at the glass wall. The discretized PTV data is overlaid
on the original unstructured PTV data.

. . . . . . . . . . . . . . . . . . . . . . 78

Figure 4.19: The CFD pressure at different axial locations within the fluid gap (
/Òeq),
where zero is at the glass wall. The discretized CFD is overlaid on the original
unstructured PTV data.

. . . . . . . . . . . . . . . . . . . . . . . . . . . . .

. 79

Figure 4.20: The discretized pressure curve along the bottom of the glass overlaid over all
the unstructured pressure data in the entire height of the gap. The vertical
dashed lines indicate the original data region from 10.8 mm and 64.4 mm.

. . . 81

Figure 4.21: The discretized pressure curve along the bottom of the glass with an offset of
+0.82 kPa overlaid over all the unstructured pressure data in the entire height
of the gap. The vertical dashed lines indicate the original data region from
10.8 mm and 64.4 mm.

. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 81

Figure 4.22: The discretized pressure curve along the bottom of the glass with an overshoot
of +0.82 kPa overlaid over all the unstructured pressure data in the entire height
of the gap. The vertical dashed lines indicate the original data region from
10.8 mm and 64.4 mm.

. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 82

Figure 4.23: The cumulative summation of the force along the glass. Pressure at a radial
location was multiplied with the annular surface area. The vertical dashed
lines indicate the original data region from 10.8 mm and 64.4 mm.

. . . . . .

. 82

Figure 4.24: Normalized Radial velocity for multiple flow rates of water with the pad
dimensions used in the PTV experiment. The velocity near the glass wall
(top) shows no negative flow due to being between the separation bubble and
glass, where the velocity near the pad (bottom) does capture the recirculation
that occurs in the separation bubble.

. . . . . . . . . . . . . . . . . . . . . .

. 84

Figure 4.25: Normalized pressure for both PTV and CFD data of the water Bernoulli pad
based on equation 4.5. The air case is included with the previously published
experimental data measured with a traversing pressure tap.

. . . . . . . . . . . 85

xix

Figure 5.1: Modeling a water Bernoulli pad (
 = 31.75 mm, 
 = 200 mm) with a mass
flow rate of 1.5 kg/s resulting in an equilibrium gap height of 0.9 mm. Only
a portion of geometry is shown from 
 ≈ 10 mm to 50 mm. The top contour
plot shows the radial velocity in a torrid-shaped fluid space, if the flow did
not have axial flow to turn the corner. The bottom contour plot shows how the
recirculation bubble (indicated by the region with negative radial velocity)
constricts the turning flow to achieve a higher values of velocities near the corner. 90

Figure A.1: Illustration of the location of each of the 4 duplicate plates and how the group

looked before and after scheduled grooming on that day in the proceeding tables. 94

Figure A.2: Picture taken of Garolite plates after grooming, with points hand selected to

analyze the pixels within the resulting polygon. . . . . . . . . . . . . . . . . . . 95

Figure A.3: A close up of the generated polygon of the plate that was never subject to
biological sampling. Drop down menus for grooming details were available
on the top left. The coating type can be selected on the top middle. The
"continue" button on the top right proceeds to the next full image to repeat
the point selection process.

. . . . . . . . . . . . . . . . . . . . . . . . . . . . 95

xx

CHAPTER 1

INTRODUCTION

A confined radial outflow can be produced by forcing a jet of fluid out from the center of a pad
towards a proximally located parallel surface - see Figure 1.1 (a). Per Livesey [2], interest in this
flow field grew out of application to lubricating films [3] away from the Re (cid:28) 1 limit, as inertial
effects become equal in importance to viscous terms. Despite the apparent simplicity of the flow, it
is not amenable to exact solution of the Navier-Stokes equations. A perturbation expansion which
achieves reasonable agreement sufficiently far from the jet has been found [4], but the development
region near 
 = 
/2 precludes a solution over the entire footprint of the pad. This lack of tractability
engendered a strong tradition of experimental work on the topic [5, 6], which has continued to the
present day for classical [1, 7] and perturbed [8, 9] geometries. Because the flow geometry is
relatively simple, simulations have also been used to effectively model the system [10, 11].

Figure 1.1: (a) Parameters characterizing radial outflow between a Bernoulli pad and a proximal
parallel surface. The embodiments (b)-(e) correspond to a workpiece being lifted, a workpiece
being levitated, the pad being levitated, and the pad being lifted, respectively. The applied force


 is the sum of all forces acting on the freely moving component (pad or surface) which are not
produced by the fluid flow between the pad and surface. The convention used here is that 

 > 0
(

 < 0) attempts to increase (decrease) the gap between the pad and the proximal surface.

1

Devices exhibiting this flow field see widespread use in the semiconductor industry [12], where
their ability to manipulate delicate components without contact is valuable. A rich patent literature
focused on this application has also been developed [13, 14, 15]. Because these devices are able
to exert force to grip soft and pliable workpieces, they have also been explored in medical [16],
apparel [8], and meat processing [17] applications.

The magnitude and direction of the normal force produced are strongly dependent upon the
distance between the pad and the surface. The reason this force changes direction can be intuitively
understood as follows. In the limit where the pad contacts the surface, the repulsive force is equal
to the product of the jet’s area and feed pressure.
In the limit of very large distances, the jet
is unconfined, and the repulsive force is proportional to the jet momentum. An attractive force
is produced at intermediate distances, which can be understood in the context of the Bernoulli
equation. Although this framework is not quantitatively accurate owing to the presence of large
shear forces, it is useful for illustration. In combination with mass conservation, the result

(cid:34) 

2
in

(cid:35)2


(
) = 
(0) − 

2

8
Ò


(1.1)

is readily found, where Ò represents the gap between the pad and the surface. For small values of
the product Ò
, a net attractive force is produced. Because the force is repulsive in the limits of
large and small Ò, with attractive forces produced in the middle, there exist two equilibrium points
where the net force is zero; one stable and the other unstable [1].

The fact that equilibrium points exist is intuitively obvious, but this appears to have been dis-
cussed for the first time in [12] and has since received limited attention [1]. In various embodiments
of the system (see Figure 1.1), this equilibrium height is produced by the balance between the ap-
plied force and the force generated by the pressure field. The applied force 
a is the sum of all
forces acting on the freely moving component (pad or surface) which are not produced by the fluid
flow between the pad and the surface. It is assumed to be positive (negative) when it attempts to
increase (decrease) the gap between the pad and the proximal parallel surface. The equilibrium
height is important in a variety of applications. The second chapter of this dissertation utilizes a
parametric study to find equilibrium points in order to find a scaling relationship of fluid power.

2

For example, the equilibrium height is important in levitated mobile robot applications [18] where
a sufficiently prominent surface feature could make undesired contact with the robot. In material
handling applications such as the one described in [19], point contacts with a levitated workpiece
prevent the workpiece from inadvertent lateral sliding motion; a sufficiently small equilibrium
height is therefore required to engage these contacts.

This work is motivated by an application in which a mobile robot moves around the submerged
hull of a stationary marine vessel to groom in order to maintain peak efficiency when underway.
Microorganisms, plants, and animals responsible for biofouling are ubiquitous in all bodies of water
and have impacted human activities as long as maritime and aquatic industries have existed. If an
initially clean surface submerged in the marine environment is left undisturbed, bacteria readily
form a biofilm on it, followed by other attaching microorganisms, with the various subsequently
colonizing species contributing to formation of a complex biofouling community [20]. A vessel
hull that is continuously immersed in seawater experiences biofouling pressure that depends on
the season, location, and the duration for which it remains idle [21, 22]. The degree to which
the hull becomes fouled from this pressure is also dependent upon its surface characteristics and
maintenance protocols. In the absence of a strategy that prevents fouling, the hull experiences the
full extent of the fouling pressure. The resulting biofouling that accumulates on the hull produces
significantly more drag, increasing fuel consumption by as much as 50% and reducing the vessel’s
top speed by as much as 10% [23, 24]. Universally deployed and efficient anti-fouling protection
would save the world’s merchant fleet an estimated $180 billion in 2020 [21]. For the destroyer class
ships of the US Navy alone, the overall cost associated with combating biofouling is around $56
million per year [25, 26]. Apart from the economic losses, biofouling also results in a higher carbon
footprint [27] and facilitates the spread of invasive species [28, 29, 30, 31]. These impacts continue
to drive interest in the development of effective biofouling removal technology and management
plans.

Surface coatings have been developed to prevent or reduce biofouling and the most effective
coatings are biocidal. Such coatings based on tributyltin (TBT) or other organotin compounds

3

have been banned [32, 33], while coatings based on copper have been scrutinized [34, 35, 20]
because of their environmental impact. With more than 1.1 million 
2 of the US Navy’s hull
area is coated with self-polishing copper coatings, it is important to consider both the positive
and negative long term effects of a hull husbandry strategy [36]. To avoid harmful environmental
impacts from leaching metal, non-biocidal anti-fouling coatings have come into use as a common
way of mitigating the fouling pressure on vessel hulls. So-called fouling-release and slime-release
coatings are currently the most commercially available option [37, 38]. These coatings are ideal
for fast vessels that are frequently underway, which assists with the release of biofouling organisms
that accumulated while the vessel was stationary [21].

Biofouling is not completely preventable using currently available surface treatments; therefore,
supplementary cleaning or treatment is common even on coated surfaces. There are two different
approaches to either treatments or cleaning, proactive and reactive [39]. The more established the
biofouling, the more aggressive the reactive response needs to be, since the adhesive strength of
biofouling organisms is exponential in nature as it physically localizes onto a surface [40] using
different adhesion phases and a variety of adhesion mechanisms [41]. The heavier the fouling pres-
sure, the more aggressive the proactive response needs to be to impede the dynamics of biofouling
colonization. Fouling pressure often has a seasonality depending on location, therefore requiring
different levels of responses at different times of the year. The following methods lie somewhere on
the proactive and reactive spectrum: mechanical grooming [42, 43], continuous aeration curtains
[44, 40], ultraviolet (UV) light [45], lasers [46], steam [47], and ultrasonic sound waves that create
resonance on the hull [48, 49, 50, 51]. Even if a method is successful at combating biofouling,
there is the potential to degrade the efficacy of the anti-fouling properties of the surface coating
over extended periods of time, depending on the frequency and aggressiveness of the treatment.
Less aggressive and less abrasive cleaning, even if conducted more frequently, reduces damage to
surface coatings [42, 52]. This gentler approach, required to prolong the life of current anti-fouling
coatings, is typically referred to as “grooming” instead of “cleaning”. Another consequence of
biofouling is the corrosion products created in a biofilm, which can accelerate the corrosion already

4

occurring or even induce biocorrosion in materials and surfaces that are typically expected to not
experience corrosion such as stainless steel [53].

Technical improvements to the grooming process can also be made to further reduce damage
to the coating. A recently-commercialized system [54, 55] for improving coating longevity uses
a rotating brush co-developed with a self-polishing coating. A one-year study performed with
immersed water jets shows that contactless cleanings done at a frequency of 0.5 × /month and
1 × /month was sufficient to maintain both anti-fouling and foul-release coatings without damage
[56]. The grooming method described in the present work is produced entirely without surface
contact. It is anticipated to improve hull performance while extending the life cycle of the coating
relative to more abrasive cleaning methods.

The focus of third chapter is to present field test study results of a biofouling mitigation device
that produces both wall shear and contactless grip using a unique radial jet flow. The potential of
the method was recently demonstrated computationally in the second chapter. The wall shear is
used to dislodge nascent fouling communities, while the contactless grip keeps the device levitating
near the hull. A test protocol is presented that was used to establish the efficacy of the grooming
device, along with site details, testing procedures, image acquisition and biological surveys per-
formed. The results of these field tests from two field seasons are presented and discussed, along
with an image-processing algorithm used to objectively discern the level of cleanliness of surfaces
subjected to biofouling pressure. Comparison between Intersleek®-coated and uncoated Garolite
plates using both image-analysis and chlorophyll a measurements bounds the grooming frequency
requirements. Finally, the potential of the described grooming approach and some directions for
future study/development are presented.

For the fourth chapter, the pad dimensions from the field test study in operation with the sub-
mersible pump is the basis of an experiment to capture the unique fluid flow field in equilibrium.
Using the latest hardware and software, along with techniques and algorithms in fluid flow field
visualization, the Lagrangian tracks captured by using tracer particles can be converted to a vec-
tor field on a regular grid for more convenient analyses [57]. Shake-the-Box is a time-resolved

5

Particle Tracking Velocimetry (4D PTV) that maps more densely seeded flows when compared to
Particle Image Velocimetry (PIV) by incorporating as much as possible the temporal and spacial
information available [58]. Multiple cameras synced to a laser volume can accurately achieve a
3D representation of the measured data after successful volume self-calibration (VSC) [59, 60, 61]
enhanced by an Optical Transfer Function (OTF) to account for voxel pulse spreading to reduce the
occurrence of ghost particles [60, 58]. STB leverages Iterative particle reconstruction (IPR) to find
and triangulate a particle in 3D space by ’shaking’ the particle in space, where in every iteration the
particle track is linearly extrapolated outwards to predict particle positions. From densely seeded
flow, only some of the particles will be successfully tracked in the first iteration, leaving residual
particles found from back-projection of the already tracked particles to repeat the ’shaking’ and
extrapolation [62]. Processing the particle data using FlowFit optimizes the velocity field and
consequently the pressure field, while Vortex-in-Cell-plus (VIC+) optimizes the vorticity field,
velocity boundary, and accelaration boundary. The VIC+ method further achieves an accurate and
ghostless reconstruction, but is more computationally intensive when compared to the approach of
tomographic PIV [63]. Increasing the spatial resolution by a factor of 2 also doubles the grid nodes
in each direction (23 = 8), thereby the total computation time increases in proportion. To optimize
the processing while avoiding error at the computation boundary, VIC+ utilizes a multi-grid ap-
proximation that is popular in the PIV community by providing an approximate solution quickly
with a coarse grid before converging with every sequentially finer grid [63].

Since microfouling and macrofouling can occur on any submerged surface, the broader appli-
cations of a contactless grooming device are discussed in the fifth and concluding chapter. The
highest environmental and economic impacts from biofouling occur to the maritime vessels; which
includes industry, private, and military. The proposed device can work in both saltwater and
freshwater to maintain an initially clean and smooth surface of a vessel hull by utlizing the shear
forces created by the confined radial outflow. Future work in terms of experiments and prototypes
to increase the peak wall shear stress, and therefore the cleaning ability, is also discussed in this
final chapter.

6

POWER SCALING OF RADIAL OUTFLOW: BERNOULLI PADS IN EQUILIBRIUM

CHAPTER 2

2.1 Introduction

This chapter is in large part from what became an article published in Journal of Fluids [64].
For a mobile robot-based grooming strategy to work, the equilibrium distance Òeq must be large
enough to avoid interference with surface features on the hull, such as rivets. To remain at this
equilibrium distance, some amount of power must be expended to accelerate ambient fluid to the jet
velocity 
in and to overcome losses in the system. The present computational study indicates that
Òeq and this required power (cid:164)
m,in are closely related, with the latter varying over several orders of
magnitude. When both quantities are appropriately scaled, a power-law describes the relationship
between (cid:164)
m,in and Òeq. A derivation for this power law is provided, which indicates that the work
added to the system is primarily needed to overcome shear at the wall, and that the force applied
to the system can be accounted for using a term incorporating the inlet Reynolds number. This
relationship is valid over a range of applied forces, geometric and material parameters.

2.2 Approach

2.2.1 Description of computations

Computations validated by published experimental results have been employed in the present work.
This approach was taken because of the large parameter space being investigated. The parameter
space produces more than 200 equilibrium points, each of which is obtained by the interpolation
of multiple non-equilibrium configurations. Analytical models are not reliable near the jet exit
[4], making them a poor choice for comparing different geometries. The numerical results in this
chapter were computed using ANSYS-Fluent. To reduce run time, a 2D axisymmetric geometry
was used. The flow conditions were steady-state. A four-equation Transition-SST model, based

7

on the k-
 transport equations coupled with intermittency and transition transport equations, was
used to model turbulence. Pressure-velocity coupling was performed via the SIMPLE algorithm.
Second-order spatial discretization was used for pressure, density, momentum, energy, dissipation
rate and intermittency. The turbulent intensity at the inlet was fixed at 5%. The turbulent viscosity
ratio was limited to 10 during solution.

The parameters in the validation dataset [1] were chosen to avoid local compressibility effects
anywhere in the flow field. Incompressible and compressible solvers had similar solutions to that
set of parameters. For all of the data points presented in the present work, a compressible solver
was employed to preserve a consistent working method. Supersonic and transonic velocities were
not observed in any of the data presented in the present work.

A roughness value characteristic of commercial steel (
p = 0.04 mm) was used for the pad
throughout this study. This roughness value was also used for the surface (
s = 0.04 mm) for
most of the data sets. Two sets were run using roughness values characteristic of smooth plastic
(
s = 0.007 mm) and galvanized iron (
s = 0.15 mm) to determine the effect of surface roughness.
Air was used as the working fluid for each case, save for a single set where 
2 was used to confirm
an interesting non-dimensional feature of the system.

2.2.2 Validation using published results

A comparison between measurements of surface pressure and forces due to fluid flow from a set
of experiments in [1, 7] and our CFD calculations is presented in Figure 2.1. The experimental
apparatus in [1, 7] used a sliding tap to acquire high-resolution pressure data on a plate opposite
the Bernoulli pad. The radial pressure distribution and total force were measured over gap heights
ranging from 0.21 mm to 1.40 mm. The flow velocities used in the experiment were selected to
avoid compressibility effects within the domain. The set of parameters being used in both the
experiment and simulation are 
 = 4 mm, 
 = 40 mm, 
p = 
s = 0.04 mm, and air as the working
fluid. These values represent the nominal parameter set in the present work. The variation of
surface pressure on the workpiece with radial distance is compared in Figure 2.1 (a) for a fixed gap

8

height. The variation of fluid force on the workpiece as a function of gap height is compared in
Figure 2.1 (b) for a constant mass flow rate. Both figures show error bars calculated from the fine
grid convergence index (GCI) [65]; sample discretization error calculations are provided in Tables
2.1 and 2.2. As shown in Figures 2.1 (a) and (b), the simulations show a reasonable agreement with
experiment with a small grid convergence error. The discrepancy with experimental data may be
attributable to small uncatalogued differences in inflow development or geometry [66]. Figure 2.1
(a) also presents the single data point for the pressure at 
 = 0 mm that was derived analytically [1];
the analytical approach oversimplifies the complex flow behavior and under-predicts the pressure,
making it an inappropriate choice for predicting the fluid power.

Figure 2.1: Comparison of CFD simulation results with experimental results in [1]: (a) pressure 

as a function of radius 
 for 
 = 4 mm, 
 = 40 mm, Ò = 0.4 mm and (cid:164)
 = 5.1×10−4 kg/s, analytical
results available for 
 = 0 mm [1] are also presented (b) fluid force on workpiece 
 as a function of
gap height Ò for a mass flow rate of (cid:164)
 = 5.1 × 10−4 kg/s. Stable and unstable equilibrium points
are found at Ò = 0.29 mm and Ò = 5.1 mm respectively. The insets are provided to indicate the
magnitude of the error bars where it would not be visible otherwise.

2.2.3 Finding Òeq using interpolation

As shown in Figure 2.1 (b), and consistent with the literature [6, 12, 7], the force produced by a
Bernoulli pad for a given mass flow is dictated largely by the gap height Ò. In the present study, this
dimension is considered to be a dependent parameter, rather than an independent one, as is typically

9

done. This is consistent with the contactless nature of these devices, as commonly deployed; a
high-pressure source is used to provide the fluid power, and the height of the gap is determined by
the applied force 
a.

To determine the equilibrium point, a geometry with a specific gap height Ò was drawn and
meshed, then multiple mass flow rates were simulated. This gap height will be the equilibrium gap
height Òeq for some value of the inlet mass flow rate (cid:164)
, at which the total force is equal to zero,
such that


a + 
 = 0,


 = 2



(0, 
) 




Þ 
/2

0

Each computational geometry (including the gap height Ò) is an equilibrium configuration for some
value of inlet mass flow rate (cid:164)
, which is found by survey and interpolation as illustrated in Figure
2.2. This permits the equilibrium configurations to be found with much less user input and repeated
meshing than would be required by the alternative, in which the inlet conditions are fixed and Ò is
varied until Òeq is found.

Figure 2.2: Example of interpolation to find equilibrium gap height Òeq for zero and a non-zero
value of the applied force 
a.

The error associated with this interpolation process was estimated as follows. The interpolation
process at a given gap height Ò predicts a mass flow rate (cid:164)
 at which Ò = Òeq. The simulations

10

are then re-run at that predicted (cid:164)
 and the actual force produced by the pad is compared to the
predicted value 
 = 0. For the nominal parameter set, the maximum normalized error associated
with interpolation of the non-dimensional force


∗ =



(1/2) 
in
2

in (

2)/4

was 2.32 × 10−3; this is three orders of magnitude smaller than the values of the non-dimensional
force investigated.

2.2.4 Fluid power measurement

It is common in treatments of this radial flow field to produce the relationship between force
generated by the flow in the gap and the gap height as a figure of merit. A different metric is
required at equilibrium because the total force is zero. A practical choice is power, which is easy to
measure and is relevant for engineering applications. The fluid power delivered to the inlet based
on mass, has been employed instead of making assumptions about a prime mover or internal energy.
For the geometry presented in Figure 1.1, the fluid power at the defined control surface, is given by
the expression

(cid:164)
m,in = 2



(
) 




(2.1)

Þ 
/2

0

(cid:20)1
2 
 [
(
)]2 + 
(
)

(cid:21)

This fluid power is either lost or is convected out of the domain. The “stem” of the device, from
the inlet to the corner, has been kept short to minimize shear losses in that region. In Eq.(2.1), the
ratio of the two bracketed terms forms the following non-dimensional “fluid power ratio”:


 =

2



2

(2.2)

This is the ratio of fluid power needed to overcome losses and that needed to add kinetic energy to
the fluid. This quantity also appears in [6], less the constant multiplier, where it is referred to as a
non-dimensional plenum pressure.

11

2.3 Results

Figure 2.3 provides the relationship between the equilibrium gap height Òeq and the required inlet
power (cid:164)
m,in for 
a = 0, as calculated in Eq.(2.1). The data for 
a ࣔ 0 will be discussed separately
for better visualization. The nominal set of parameters is: 
 = 4 mm, 
 = 40 mm, 
p = 
s = 0.04
mm, and air as the working fluid. These parameters are the same as those used for validation in
section 2.2.2. Each other dataset varies these parameters one at a time. A linear least squares
method was used to find the best fit to the nominal dataset. The variation in required fluid power is
observed to be approximately six orders of magnitude over the entire corpus of data. An estimate
of the grid convergence error in power is provided for the nominal geometry in Table 2.3.

Figure 2.3: Fluid power (cid:164)
m,in required to maintain an equilibrium height Òeq for 
a = 0. The
nominal dataset is 
 = 4 mm, 
 = 40 mm, 
s = 0.04 mm, based on air as the working fluid; each
other dataset varies one parameter from this baseline. The dotted line is the best fit to the nominal
dataset.

It is immediately clear that the power required at a given Òeq is most dramatically dependent
upon the pad diameter, such that increasing 
 by a factor of four increases the required power by
≈ 3.5 orders of magnitude. In contrast, the inner diameter 
 and surface roughness 
s are only

12

marginally influential. The relative importance of 
 indicates that the power requirements are
dominated by the need to overcome losses (
 in Eq.(2.1)), rather than by the need to add kinetic
energy to the fluid (

2/2 in Eq.(2.1)). This may be visualized in Figure 2.4, in which the ratio of
these terms (
 in Eq.(2.2)) is displayed as a function of Òeq.

Figure 2.4: Ratio of inlet fluid pressure to inlet momentum as a function of equilibrium height Òeq
for 
a = 0. The nominal dataset is 
 = 4 mm, 
 = 40 mm, 
s = 0.04 mm, based on air as the
working fluid; each other dataset varies one parameter from this baseline. The dotted line is the
best fit to the nominal dataset.

The nominal dataset in Figure 2.4 is the same as that in Figure 2.3 (
 = 4 mm, 
 = 40 mm,

s = 0.04 mm, air), and the displayed dotted line is the best linear least squares fit to this dataset.
The relative contribution of pressure drop to the power is large at small Òeq, but declines to parity
with the kinetic energy at large Òeq. In contrast with Figure 2.3 (where (cid:164)
m,in depends primarily on

), the power ratio 
 is primarily dependent upon the jet diameter 
 at a given Òeq. The variation
in 
 at a fixed Òeq is considerably less than the variation in power (cid:164)
m,in. Although not described
as a ratio of relative power expenditures, the ratio 
 was also shown to have a strong dependence
on 
 in [6].

There is also a set of scaling relationships which causes the (cid:164)
m,in versus Òeq data to collapse to

13

a single trend. In Figure 2.5, the nondimensional power (cid:164)
∗ is plotted against the non-dimensional
equilibrium height Ò∗, where

(cid:34)

(cid:35)

(cid:164)
∗ =

(cid:164)
m,in
in
(
/
)


 
2

,

Ò∗ =

Òeq



(2.3)

For the data presented in Figure 2.5, the applied force 

 = 0. The dotted line displayed in Figure
2.5 is the best linear least squares fit to all data. A derivation for this non-dimensional group,
representing the measured fluid power at the inlet, is provided in section 2.5.1, with associated
discussion.

Figure 2.5: Non-dimensional fluid power (cid:164)
∗ required to maintain a given non-dimensional equi-
librium height Ò∗. The nominal dataset is 
 = 4 mm, 
 = 40 mm, 
s = 0.04 mm, based on air as
the working fluid; each other dataset varies one parameter from this baseline. The dotted line is the
best fit to all data.

Figure 2.6 provides the relationship between Ò∗ and (cid:164)
∗ for seven values of the non-dimensional
external force 
∗, defined below, when 

 ࣔ 0. For each case, the nominal geometry was employed.
The non-dimensional force is defined as the ratio of the applied force and the inlet momentum, i.e.


∗ =




(1/2) 
in 
2
in (

2/4)

14

(2.4)

Figure 2.6: Non-dimensional fluid power (cid:164)
∗ required to maintain a given non-dimensional equi-
librium height Ò∗ for different values of 
∗ when the force correction term in Eq.(2.5) is not used.
The nominal dataset is 
 = 4 mm, 
 = 40 mm, 
s = 0.04 mm, using air as the working fluid. The
dotted line is the best fit to the 
∗ = 0 dataset.

It is clear from Figure 2.6 that the scaling relationship which collapses the data for the unloaded
system does not do so when the system is loaded (

 ࣔ 0). In particular, a dramatic spread is visible
in the data for 
∗ < 0 at large Ò∗. To account for the effect of the applied force, the non-dimensional
fluid power is redefined as

(cid:34)

(cid:164)
∗corr =

(cid:164)
m,in
in
(
/
)
8 
∗Rein


 
2
= (cid:164)
∗ − 


(cid:35)(cid:20)
in
in 


(cid:21)(cid:34)
2

(cid:35)





2




in(

2/4)
(1/2) 
in
2

(cid:34)

(cid:35)
(cid:34)
2

− 

8

(cid:35)





2




(2.5)

When the force correction is applied, the data collapse is largely recovered, with some spread for
Ò∗ > 0.25 - see Figure 2.7. The empirical constant 
 = 2/5 was used to provide this fit. A
derivation for this force correction, including and a proposed reason for the scaling breakdown at

∗ < 0 above Ò∗ ≈ 0.25, is provided in section 2.5.2.

15

(cid:164)
∗corr required to maintain a given non-dimensional
Figure 2.7: Non-dimensional fluid power
equilibrium height Ò∗ for different values of 
∗ when the force correction term in Eq.(2.5) is used
with 
 = 2/5. The nominal dataset is 
 = 4 mm, 
 = 40 mm, 
s = 0.04 mm, using air as the
working fluid. The dotted line is the best fit to the 
∗ = 0 dataset. Points associated with 
∗ = +6
at Ò∗ > 0.25 are not visible in the present spread.

2.4 Sample Calculations of Discretization Error

Ansys Fluent Workbench 17.1 was utilized for all steps of the CFD modeling process. For
determining grid independence, three different mesh sizes were used with high orthogonal quality
and low orthogonal skew. The ratios between the fine and medium mesh elements and the medium
and coarse mesh elements are denoted by 
21 and 
32. Mesh inflation was selected at the walls to
capture the boundary effects. For the residual errors, the condition for iterative convergence was set
to 1.0 × 10−5. The discretization error was computed using the Richardson extrapolation method
described in [65]; the tables provided in this section are based on the nomenclature used in [65].
Tables 2.1 and 2.2 provide sample discretization errors for pressure and force computations used
for comparison with experimental data - see section 2.2.2.

For the pressure profile at a single gap height, 0.35 % of the total number of 570 points indicated

16

Table 2.1: Sample discretization errors in pressure computations plotted in Figure 2.1 (a) for 
 = 4
mm, 
 = 40 mm, Ò = 0.4 mm and (cid:164)
 = 5.1 × 10−4 kg/s.


 (mm)

21

32

1 (Pa)

2 (Pa)

3 (Pa)



21
e

 (Pa)

21



21
e




 
21
f




10.101
1.34503
1.33196
0.03449
0.03423
0.03447
0.186
0.03232

5.068
1.34503
1.33196
-0.38839
-0.39636
-0.42685
4.735
-0.39403

19.852
0.000
1.34503
1.34503
1.33196
1.33196
0.00061
5.64860
0.00059
5.76250
0.00061
5.81960
0.168
2.177
0.00453
5.64884
2.016% 2.052% 0.753% 0.481% 3.641%
0.004% 1.431% 6.722% 1.496% 86.437%
2.17%
3.91%

15.134
1.34503
1.33196
0.02486
0.02474
0.02466
1.188
0.02524

2.21%

0.81%

0.52%

Figure 2.8: Fluid power (cid:164)
m,in required to maintain an equilibrium height Òeq for the nominal data
set: 
 = 4 mm, 
 = 40 mm, 
s = 0.04 mm, and air as the working fluid with 
a = 0. The GCI
errors bars are included with sample calculations shown in Table 2.3.

17

Table 2.2: Sample discretization errors in force computations plotted in Figure 2.1 (b) for 
 = 4
mm, 
 = 40 mm and (cid:164)
 = 5.1 × 10−4 kg/s.

Ò (mm)

21

32

1 (N)

2 (N)

3 (N)



21
e

 (N)

21
a

21
e




 
21
f




0.24

0.27

0.4

1.32772
1.34405
0.03835
0.03369
0.03203
3.890
0.04066

1.34503
1.31687
1.33196
1.32476
-0.05752
0.11858
-0.05825
0.11200
-0.06103
0.11442
4.706
3.683
-0.05728
0.12232
5.55% 12.13% 1.27%
0.42%
3.06%
3.15%
0.64%

5.69%
6.56%

0.5

1.34745
1.34106
-0.06312
-0.06332
-0.06479
6.805
-0.06309
0.32%
0.05%
0.16%

0.9

1.35303
1.36832
-0.04372
-0.04376
-0.04405
6.531
-0.04372
0.08%
0.01%
0.04%

1.3

1.37792
1.37460
-0.03161
-0.03155
-0.03117
5.929
-0.03162
0.19%
0.03%
0.08%

oscillatory convergence. The local order of accuracy 
 ranges from 0.013 to 19.7, with an average
value of 
a

 = 2.6, which is used to calculate the GCI error bars in Figure 2.1 (a). In Table 2.1,
the highest extrapolated error, 
21
e

, is relative to the pressure near the outer diameter, where the
gage pressure goes to zero.

Taking the integral of the pressure profile gives a value of the force generated by the fluid flow.
When the mass flow rate is kept constant, the force is a function of gap height. The force plot had
38% of the 16 points exhibit oscillatory convergence. The local order of accuracy 
 ranges from
0.21 to 12.9, with an average value of 
a

 = 4.2, which is used to calculate the GCI error bars in
Figure 2.1 (b).

The main focus of the second chapter of this dissertation is to derive a scaling relationship for
the fluid power and Table 2.3 provides sample discretization errors for power computations. For the
nominal data set of the parametric study 65% of the 17 points indicated oscillatory convergence.
The local order of accuracy 
 ranges from 0.60 to 18.9, with an average value of 
a

 = 8.3. There
are no GCI error bars for the power plot in Figure 2.3 since the percent error is visibly negligible
on the log scale used. The nominal data set in Figure 2.3, when replotted in Figure 2.8 using a
regular scale, shows that the errors are minimal.

18

Table 2.3: Sample discretization errors in power computations at equilibrium plotted in Figure 2.8
for 
 = 4 mm and 
 = 40 mm.

Ò (mm)

21

32

1 (W)

2 (W)

3 (W)



21
e

 (W)

21
a

21
e




 
21
f




0.24

1.31687
1.32476
13.4581
13.8643
14.5747
1.929

12.87804
3.02%
4.50%
0.50%

0.27

1.32772
1.34405
6.30099
6.07708
6.13503
4.940
6.37426
3.55%
1.15%
0.54%

0.4

1.34503
1.33196
0.75723
0.75714
0.73827
18.885
0.75723
0.01%
0.00%
0.00%

0.5

1.34745
1.34106
0.24350
0.23537
0.23296
3.990
0.24706
3.34%
1.44%
0.45%

0.9

1.35303
1.36832
0.00523
.00519
0.00461
8.112
0.00524
0.86%
0.08%
0.11%

1.3

1.37792
1.37460
0.00049
0.00049
0.00049
9.148
0.00049
0.04%
0.00%
0.00%

2.5 Discussion

2.5.1 Scaling based on wall shear

Figure 2.4 indicates that the dominant contributor to the power required by the system at equilibrium
is the pressure drop from the inlet to the outlet. The trends in Figure 2.3 show that the power required
at a given Òeq is strongly dependent on 
. Therefore, a relationship based on the wall shear within
the gap might reasonably be expected to collapse the data, and the non-dimensional groups in the
first term of Eq.(2.3) can indeed be derived on this basis.

Consider the expression below for (cid:164)
s, the work expended to oppose the wall shear 
w:

(cid:164)
s = 
w 



 = 






 ∝ 





ࡁ








(2.6)

where the terms ࡁ
, 

 and 

 correspond to the characteristic length, area and velocity scales,
respectively. Mass conservation between the inlet and the gap yields

(cid:20) 




(cid:21)





(cid:21)2

(cid:20) 


2

2


 Òeq 

 = 



in

(2.7)

where 

 is a characteristic radius. Choosing 

 ∝ 
 yields 

 ∝ (
/Òeq)
in. Since the total wall
shear force should increase with decreasing gap height and increasing pad area, we choose ࡁ
 = Òeq

19

and 

 = 
2. Substituting these characteristic scales into Eq.(2.6) yields

(cid:34) 
 
2

in
2



(cid:35)(cid:20) Òeq

(cid:21)−3




(cid:164)
s ∝ 



 
in
Ò2
eq


2 
 
in
Òeq

∝

(cid:20) Òeq

(cid:21)−3




(2.8)

⇒

(cid:164)
s
in
(
/
) ∝

 
2

These non-dimensional groups, found by a shear-based derivation are the same as those observed
in Figure 2.5. Furthermore, the value of the derived exponent is a close approximation to the linear
least squares best fit indicated in Figures 2.5-2.7. The range of the observed best fit exponent 
 was
found to vary over the range 3.12 ≤ 
 ≤ 3.24 depending on the subset of data being examined. The
scaling relationship provided in Eq.(9) indicates that the scaling is dependent upon the dynamic
viscosity 
. To test this, a set of simulations using 
2 as the working fluid was performed.
These data follow the same trend as the data using air when the power and gap height are made
non-dimensional.

A “cleaner" derivation may be apparent to the reader, in which the characteristic values of

velocity, gradient, and area are instead taken at the generic location 
 such that



 =


in
(
/2)2

2

 Òeq

,






ࡁ


=




Òeq

These may be integrated to form a characteristic shear work

,




 = 






(2.9)

Þ 2


0



Òeq

(cid:34)
in
(
/2)2

2

 Òeq

(cid:35)2








(2.10)

(cid:164)
s =


w

 


 =

Þ




(cid:20)

Þ 
/2
(cid:21)−3
(cid:19)(cid:21)(cid:20) Òeq


/2

(cid:18) 


The result of this integration yields the characteristic work

(cid:164)
s ∝


 
2

in 
 ln







⇒

(cid:164)
s
in 
 ln(
/
) ∝

 
2

(cid:20) Òeq

(cid:21)−3




(2.11)

Making the power data in Figure 2.3 non-dimensional using the non-dimensional groups in Eq.(2.11)
does not collapse the data. A comparison between the two derivations makes it clear that the power
required for a given Òeq is fixed by “worst-case” choices of characteristic parameters - largest
velocity, largest gradient, and largest area - rather than by using averaged parameters or the values
of the parameters at a fixed value of 
.

20

2.5.2 Scaling modified to account for 
a

The scaling correction for non-zero force shown in Eq.(2.3) can be derived as follows. Consider
the expression

(cid:164)
∗corr =

(cid:164)
m,in


(
2/
) −


2






in(
2/
)



2

(2.12)

(cid:34)

where 

 is a characteristic velocity. The sign convention used in this work, where 

 < 0 attempts
to decrease the gap between the pad and the proximal parallel surface, produces the sign of the force
correction term 



 in Eq.(2.12). This can be understood physically as follows. If an applied
force is helping to lift or levitate the free component at a given gap height Òeq, the flow field in the
gap does not need to produce as much force to bring the free component into equilibrium. This
smaller force is achieved by reducing the velocity of the working fluid, which reduces the fluid
power required. Both the inlet kinetic energy and pressure are reduced, such that the dependence
of 
 on 
∗ is minimal relative to the overall trend shown in Figure 2.4. Because the fluid power
required at equilibrium is less than that required by an unassisted workpiece, the force correction
is positive for 

 < 0. The converse of these arguments holds for 

 > 0, where the applied force
is attempting to increase the gap between the pad and the parallel surface.

The force correction term in Eq.(2.12) can be manipulated to form four non-dimensional groups
corresponding to a non-dimensional force, the inlet Reynolds number, an area ratio, and a velocity
ratio:

(cid:35)(cid:20)
in
in 


(cid:21)(cid:34)
2

(cid:35)(cid:20)
c

(cid:21)





2


in

(2.13)






in(
2/
) =



2



8




in(

2/4)
(1/2) 
in
2

In Figure 2.7, the characteristic velocity ratio 
c = 
 
in where 
 = 2/5 was found to give a
satisfactory fit to the data. It is not obvious a priori that this form of 
c is most appropriate - in
particular, if 
c is a velocity within the gap, 
c ∝ 
in/Ò∗ rather than the form observed. Velocity
ratios in this form did not successfully scale the data.

It is notable that the scaling is less successful for 
∗ > 0 above Ò∗ ≈ 0.25. Comparing the area

in the gap at the corner point 
 = 
/2 to the inlet area yields the ratio


g
 


in

=



Ò



2/4 = 4Ò∗

21

meaning that for Ò∗ < 0.25, the flow geometry contracts at the corner, whereas at Ò∗ > 0.25, the
geometry expands at the corner. This has several consequences on the ability of the pad to support
or lift a load. First, because a supporting force is provided primarily by the central pressure near

 = 0, the 
∗ < 0 points are less problematic at large values of Ò∗. Second, because the area
is expanding at the corner for Ò∗ > 0.25, the pressure gradient predicted by an inviscid analysis
is positive at the corner; the recirculation bubble [66] prevents this from being strictly true, but
it suffices to say that the first-order analysis of the problem no longer favors suction. This being
the case, very large velocities (inlet Mach number greater than 0.5) are required to produce large
amounts of lifting force at these values of Ò∗. As such, some of the deviation from the predicted
scaling may be related to compressibility effects.

2.5.3 Corner Effects

The pressure field near the centerline of the pad is quite sensitive to the geometry near the stem-pad
corner, so I have provided several corner geometries for context in 2.9. Surface pressures produced
by the nominal square corner geometry, a geometry with a radius at the corner (

 > 0), and a
reentrant geometry (

 < 0) are provided.

Industry favors the pintle design for the increase in load capacity [67] with no drawback to the
reduced wall shear stress since cleaning is not a need. In regards to underwater grooming, the most
effective grooming happens from the directly impinging flow as in Figures 2.10(a) and 2.11(a).
Since the jet never directly impinges on the hull, there is no positive pressure generated as seen in
Figures 2.10(b), but because of the distance it takes to turn the flow while keeping the initial radius
of the stem the same as in the simple geometry causes the maximum velocity to happen at a larger
radial location in the gap as seen in 2.11(b).

2.6 Concluding Remarks

A computational study of Bernoulli pads has been performed, with the intention of determining
the input power required to maintain stable equilibrium. At the stable equilibrium, some gap exists

22

Figure 2.9: Illustration of corner geometries: (a) 

 = 0, (b) 

 > 0, (c) 

 < 0. (d) Comparison of
CFD simulation results with experimental results in [1].

between the pad and the workpiece; the size of this gap depends on the magnitude and direction of
the applied forces as well as the pressure and mass flow at the inlet. The applied forces and inlet
flow characteristics determine the inlet power required to operate the pad at equilibrium.

The current work presents a set of scaling relationships that collapses the power requirements
of a large number of pad geometries and operating conditions onto a single curve. This set of
scaling relationships is derived initially for the case of zero applied force and extended to the case
of non-zero applied force. The present work is the first to treat the inlet power as a parameter of
interest, and the scaling relationships derived have not appeared in the literature.

Over 200 realizations of equilibrium were used to derive these scaling relationships. This

23

Figure 2.10: The pressure contour plots and pressure profile of a Bernoulli pad with a mass flow
rate of 2 kg/s pulled 5 mm away from the wall; (a) shows the simple geometry with a 90 degree
corner generating 21 N of suction and (b) shows a pintle physically turning the axial flow to radial
flow generating 45 N of suction.

Figure 2.11: The velocity contour plots and resulting wall shear profiles of a Bernoulli pad with a
mass flow rate of 2 kg/s pulled 5 mm away from the wall; (a) shows the simple geometry with a 90
degree corner generating a larger peak wall shear stress sooner and (b) shows a pintle generating a
lower peak wall shear stress at a larger radial location.

24

large number or working geometries and conditions, coupled with the relatively simple geometry,
makes it an ideal problem to study computationally rather than experimentally. Analytical models
described in the literature do not accurately predict the inlet conditions, and therefore cannot be
trusted to provide a good estimate of the inlet power. Two recommendations can be made to
researchers wishing to perform computational studies of Bernoulli pads at equilibrium. First,
because local velocities near the jet corner can be a large multiple of the inlet velocity, particularly
for small gap heights, we recommend that compressible codes be used throughout any survey.
Second, for a given pad geometry, it is better to create a single mesh for each Òeq and adjust the inlet
conditions until equilibrium is reached. The alternate method, in which the inlet mass flow is fixed
and the gap height is varied, requires a new mesh to be created for every gap height. The scheme we
recommend significantly reduces the time required as it eliminates the need to repeatedly change
the computational grid.

The scaling relationships show that the primary contributor to the power requirement is related
to the fluid losses in the system rather than the kinetic energy. Therefore, significant power reduction
may be possible by reducing these losses. An analogy to pipe flow may be instructive, wherein the
shear associated with the confined flow in the gap is equivalent to the “major losses”, and losses
near the corner are the “minor losses”. Future work is envisioned to further investigate each of
these types of loss in the flow field. Work is underway to more closely characterize the operation of
the pad in equilibrium using water as the working fluid in the envisioned hull grooming application.

25

CHAPTER 3

UNDERWATER SHEAR-BASED GROOMING OF MARINE BIOFOULING USING A

NON-CONTACT BERNOULLI PAD

3.1 Introduction

The following chapter is the result of two summer internships through the Naval Research Enterprise
Internship Program (NREIP) that allowed field tests to be conducted off the coast of Rhode Island.
While biofilms and biofouling occurs from ubiquitous microorganisms in any body of water resulting
in mitigation and repair costs to various industries, biofouling mitigation in an ocean environment
was the focus in this research.

3.2 Materials and Methods

The basis of the grooming device is a Bernoulli pad that uses an axial jet at its inlet to produce
radial outflow between the pad and a proximally located parallel surface such as a hull. One-half
of the cross-sectional area of this arrangement is shown in Figure 3.1a. As the flow moves from
the jet region to the exit, the increasing area at each radius r causes the velocity to decrease. This
flow field produces a force between the surfaces, which depends upon the gap height Ò. The total
force can be calculated by taking the integral of the pressure curve shown in Figure 3.1b. The
direction of this force changes sign, such that a stable equilibrium point exists for some spacing
Ò = Òeq [1, 64]. The wall shear also changes radially, with the peak wall shear occurring beyond
the stagnation area, when the pure axial flow turns into radial flow. A similar trend is also observed
in unconfined radial outflow generated by an immersed water jet for hull-grooming [68].

The flow field in this work has potential use for hull-grooming applications for several reasons.
First, the pad will remain levitating parallel to the hull without additional forces, given a consistent
source of fluid power (Kamensky et al. 2019). Second, because the radial outflow is confined to
a thin gap, it will reliably produce shear forces on the hull surface, which will remove biofouling

26

Figure 3.1: (a) Half of the cross-sectional view of radial outflow between a Bernoulli pad and a
proximal parallel surface such as a hull with a magnified gap, (b) and (c) normal and tangential
stresses on the vessel hull generated by a pad of dimensions 
 = 200 mm and 
 = 31.75 mm,
operating at Òeq = 0.91 mm resulting from an inlet jet velocity of 1.9 m/s.

organisms (Menesses et al. 2017). Finally, grooming performed using fluid shear does not require
contact with the hull, alleviating potential damage to the coating. Figures 3.1b and 3.1c show the
predicted normal and shear stresses on the vessel hull generated by the Bernoulli pad in Figure 3.1
of outer diameter 
 = 200 mm and inner diameter 
 = 31.75, operating at its equilibrium gap
height of Òeq = 0.91 mm, achieved with an inlet jet velocity of 1.9 m/s [64]. Because the pad is
in equilibrium, the integral of the normal stress over the total area covered by the pad is zero. The
peak shear stress occurs near the jet exit and reaches a magnitude of 5 kPa; this is expected to be
sufficient to remove recently attached bacteria, diatoms, and larvae using a reasonable grooming

27

frequency to prevent any organism from reaching maturity - see Figure 3.2 used with permission
by Menesses et al. [40]. The wall shear stress is zero at the center of the jet and near the outer
diameter of the pad. The shear forces produced by the Bernoulli pad result brackets a range of
expected effectiveness when projected on natural marine biofouling organisms in Figure 3.2, based

Figure 3.2: The shear stress range generated by the Bernoulli pad as implemented in this study,
shown in the context of literature data. Critical shear stress (Pa) required for biofouling removal
are shown as a function of time for biofilm or biofouling development prior to exposure to shear.
With the flow rate generating a maximum wall shear stress of 5000 Pa and a minimum of 0 Pa on
clean plates, significant biofouling mitigation is expected between the minimum and maximum (2
days to 2 weeks) time elapsed between all frequencies of grooming. This is shown with a dark grey
box overlay. Previously published and adapted with permission from both the author and publisher
(Menesses et al. 2017).

28

on published data on the organisms’ adhesion strength on various surface types shows the trend
in adhesive strength of biofouling tends to be exponential in time. The expected produced shear
force at the beginning of the study could not be maintained with the electrical input to the pump
held constant, because the peak shear in the system will decrease with the increase in both the gap
height and the thickness of biofouling. Other data on the adhesion strength of microfouling specific
to foul-release coatings show that a shear stress of at least 300 Pa from an immersed water jet is
sufficient to maintain a clean surface [41].

3.3 Experimental Design

3.3.1 Test Site

Field tests were conducted at the same location and time of the year as Menesses et al. 2017 [40];
off a pier at Stillwater Basin (latitude 41°32(cid:48)06.8(cid:48)(cid:48) N and longitude 71°18(cid:48)49.8(cid:48)(cid:48) W) in Narragansett
Bay, Rhode Island, USA (see Figure 3.4). Both studies were completed within the most active
season of biofouling (approximately from May to August). Bordered by the Atlantic Ocean, the
study area is characterized by a moist continental climate. A stone breakwater shelters the pier
where the study was conducted. The deployed plates were suspended such that they remained
completely submerged even during low tide (Figures 3.4 and 3.5). For the second year, the average
water temperature logged by a HOBO MX2202 pendant attached to one of the submersible frames
during the study period (June 12 to July 29) was 211.7°C. For the same time period, the average
salinity range from a nearby surface water quality monitor station (latitude 41°3442.10 N and
longitude 71°1916.05 W) was 29.20.5 parts per thousand (ppt) [69]. More detail on the logged
temperature, light intensity, and salinity data can be found in section 3.4.

3.3.2 Experimental Design - Year 1
During the summer of 2018, five plates (30.5 × 30.5 cm) of fiber-reinforced plastic, commercially
known as Garolite, were fixed to PVC frames (Figure 3.4). When submerged, the PVC frames
flooded with water and held the panels vertically facing the sun (Figure 3.4a). Four panels were

29

Figure 3.3: An aerial view of the Naval Undersea Warfare Center (NUWC) Division Newport
where both Year 1 and Year 2 studies were conducted.

subjected to different grooming frequencies established by the Center for Corrosion and Biofouling
Control (CCBC) at Florida Institute of Technology (FIT): 3× per week, 2× per week, 1× per week
and 0.5×/wk [43]. The fifth panel was the control, which was not groomed for the entire duration
of the study. Based on the grooming schedule, individual plates were removed from their frames
and transported to an acrylic tank in a laboratory for grooming; the acrylic tank was filled with
300 liters of dechlorinated tap water mixed with 10.9 kg of Instant Ocean® for a final salinity of
approximately 30 parts per thousand (ppt). For an unobstructed view of the contactless grooming
process, the Bernoulli pad was machined out of clear acrylic and fixed 2 cm below the water
surface. The pad was connected to a pump with a maximum flow rate of 150 liters per minute
(LPM). Each plate was held proximally below the pad and the pump was turned on. The fluid
flow field then generated normal forces to levitate the plate and shear forces to groom without
contact. The pump was operated for approximately one minute, resulting in “static grooming”
with no relative motion between the plate and the pad. Before and after grooming, the plates were

30

Figure 3.4: (a) Pier at Stillwater Basin showing the suspended frames with plates submerged under
water. (b) A frame hauled up to remove a plate scheduled for grooming. (c) Using a tote filled
partially with ocean water to keep plate submerged while in transit to and from the grooming tank.
(d) Suspended test design used in Year 1.

transported between the pier and the acrylic tank in a plastic tub filled with ocean water. The results
from this static grooming experiment were used to inform a second test during Year 1, in which the
pad was "scanned" over the surface to be cleaned. These preliminary results of Year 1 test informed
the design and test protocol of the Year 2 experiment.

3.3.3 Experimental Design - Year 2

In this study, we investigated the efficacy of combining our grooming method with a fouling-release
paint treatment on the surfaces, similar to the protocol described in [42, 43] that were using different
grooming technologies. To this end, two types of plate surfaces were compared: bare Garolite®

31

G101 plates in factory condition and Garolite plates painted on one side with Intersleek® 1100SR2
coating. These two surface types will be hereafter simply referred to as Garolite and Intersleek.
Garolite was chosen for its resemblance to a smooth epoxy/fiberglass surface, and is expected to
handle biofouling pressure worse than the Intersleek surface. A sponge and dish soap was used to
eliminate any initial residue on the Garolite that occurred from the manufacturing process. Four
plates of each surface type were exposed. A single plate was reserved for image analysis, and
three dedicated replicate plates were included for biological sampling for every combination of
surface type (Garolite and Intersleek) and grooming frequency (3×/wk, 2×/wk, 1×/wk, 0.5×/wk,
and control, bringing the total number of plates that needed to be submerged to 40 (Figure 3.5). The

Figure 3.5: Suspended test design used in Year 2, shown here in two rows for ease of illustration.
The water level remained at least 0.3 meters above the top of the grooming frame during the lowest
tide.

1This is an epoxy-grade industrial laminate and phenolic material manufactured by Accurate

Plastics, Inc in Yonkers, NY.

dam, Netherlands.

2This is a patented slime release fluoropolymer technology from AkzoNobel based in Amster-

32

grooming frequency protocol developed by CCBC [37] and previously used for year 1, was used
again for year 2. Our 0.32 cm thick plates were chosen to have the dimensions of 10.2 by 10.2 cm to
fit a custom biofouling sampling device previously used by University of Massachusetts Dartmouth
(UMass-D).
To mitigate the possibility of a shading bias from the pilings and pier structure,
the locations of every set of plates were shifted every grooming day during the entire duration of
the field test study. Shading was the most likely reason for less biofouling on the lowest grooming
frequency plates as seen in Figure 3.10 from static grooming in Year 1. Since the back and edges
of each plate did not experience any contactless grooming, biofouling did build up significantly to
warrant removal every biological sampling day starting at week 3 (See Figures 3.15 and 3.16).

3.3.4 Grooming Procedure

Grooming was carried out on the pier in a tank freshly filled with ocean water. The process of
removal of the plates from the submersible rig to replacement in the rig did not exceed twenty
minutes and the plates were never held out of ocean water for more than 30 seconds. The plates
were transported between the rig and the grooming tank in a tote filled with clean ocean water,
which was at a sufficient level to submerge the plates during transport. To simultaneously groom
each set of 4 plates (that had the same grooming frequency and surface type), a neutrally buoyant
Garolite frame was fabricated to flush-mount the plates (Figure 3.6). Only the tabs, edges and
backsides experienced contact during the swap from the submersible frame to the grooming frame
and back. The Bernoulli pad was coupled to a submersible pump with a maximum flow rate of
150 Liters/minute (LPM) and a self-excited flowmeter was placed in-line to measure the flow rate
during operation. For an unobstructed view of the contactless grooming process, the Bernoulli pad
was machined out of clear rigid acrylic with the dimensions previously modelled computationally
(Figure 3.1). The water level was maintained to be 2 cm above the pad.

When the pump was operated, the Garolite frame with a set of 4 plates automatically finds
its equilibrium position under the pad and was manually moved laterally for scanned grooming
for approximately one minute. The flow rate was chosen at the beginning of the study to be

33

the maximum with which no cavitation occurred with the plates in their pristine condition; this
corresponded to a no-load flow rate of 84 LPM using a pulse width modulation (PWM) circuit to
allow some form of flow rate adjustment of the pump. All grooming operations were performed
by keeping the duty cycle of the PWM circuit fixed. As the study progressed this resulted in
a gradual increase in the flow rate during grooming as there was an increase in the level of
biofouling growth on the surfaces; this is due to the fact that heavier biofouling increases the drag
and in turn the equilibrium gap height. The combination of the drag and larger gap height also
decreases the maximum velocity, which correlates directly with maximum wall shear. The key
to this proactive grooming is to stay ahead of biofouling pressure in order to maintain the peak
wall shear stress. Consistency of the act of grooming was more crucial than the duration of shear
exposure. Prolonging the scan by either multiple passes or slowing the lateral scanning movement
is not expected to affect the amount of biofouling removed since the critical wall shear to biofouling
removal is the threshold that is or is not reached with the constant electrical power supplied to the
pump.

Figure 3.6: Grooming operation on a set of 4 Intersleek plates flush-mounted in the Garolite
grooming frame; the clear acrylic Bernoulli pad is difficult to discern and is therefore outlined.

34

3.3.5 Data Acquisition

Pictures of the plates were taken before and after grooming using a Canon EOS Digital Rebel XT
for the first year. The second year the Canon Rebel was mounted and accompanied with an Ikan
Piatto PL90 Accent Light as seen in Figure 3.7. The mount provided more consistent straight on
shots of the set of plates. The time that elapsed between pictures before and after grooming was
no more than two minutes. At each grooming frequency, one plate was never sampled biologically.
Pictures of this plate were fed into an image-processing algorithm, described in subsection 3.3.2.
Chlorophyll a (chl a) concentration per unit surface area was used as a biological measure for
grooming effect. Samples for chl a were collected once a week on the same day of the week for the
duration of the experiment, on a day with no scheduled grooming. Triplicate plates were sampled
per grooming frequency and plate type, along with triplicate non-groomed control plates. A custom

Figure 3.7: Picture of the sheltered space taken with the Canon EOS Digital Rebel XT used for data
acquisition, which is why there is no camera fixed into the mount. The photographing platform
for the assembled grooming frame is directly underneath the point of view of the camera. The
middle cutout was to provide addition contact prevention on the plates. The accent light is currently
directed to the tank during the water exchange before scheduled grooming.

35

3D printed sampling device was used to collect chl a samples from the plate surfaces and can be seen
in Figure 3.8. The complete assembly included two adjustable steel “Hold-Down Toggle Clamps”
installed on the bottom piece and a single “Oil-Resistant Buna-N O-Rings” press fitted into one of
the eight shallow cylindrical cavities. No additional o-rings were installed to prevent contact on
any area that is not scheduled to be sampled. Only the edges and back experienced contact during
the handling and sampling procedure. The device created leak-proof 16 mm diameter wells on the
plate surface that could be quantitatively sampled without spill-over to surroundings. To sample
for chl a, a plate was affixed into the sampling device (Figure 3.8a-b), 1 mL of 0.2 µm-filtered

Figure 3.8: The sampling device was sanitized in between plate sampling with isopropyl alcohol.
(a) A plate slides into a slot designed into the bottom piece. Contact on the front plate was avoided
by holding only the permanently installed tab. The top piece was carefully set down on the plate
with the well containing the single o-ring targeted on the area not yet sampled. Engaging the clamp
compresses the o-ring to create a leak-proof seal. The plastic top piece was constrained from ever
coming into contact with the plate by resting completely on the flat face of the bottom piece of the
sampling device. (b) 1 mL of 0.2 µm-filtered seawater was added to the well. (c) An overhead view
in to show the water sitting in the sealed well. (d) The biofouling in the well was scraped off with
a sterile plastic pestle before collected with a pipette.

36

seawater was added to the well (Figure 3.8b-c), and the biofouling in the well scraped off with a
sterile plastic pestle (Figure 3.8d). On day 35, plates groomed 0.5×/week could not be sampled due
to hard fouling that prevented leak-proof attachment of the sampling device. From the suspended
biofilm, 200 µL was collected into a microcentrifuge tube, centrifuged, the supernatant discarded,
and the pellets stored at −20°C until analysis. Chlorophyll a was extracted from the thawed pellets
with 90% acetone overnight, and concentrations measured using a non-acidification method and
narrow band-pass filters (Welschmeyer 1994) with a Turner-10AU fluorometer calibrated with pure
chlorophyll a standards and stability checked daily with a solid standard (Turner Designs, San Jose,
CA).

3.3.6

Image Processing

Although the human eye can qualitatively determine whether a surface is covered with biofouling,
we developed an image-processing tool for year 2 in order to affix a quantitative value to the amount
of visible fouling. This tool is amenable to integration with an automated grooming system. Each
pixel within a selected section of an image has a value for its Red, Green, and Blue (RGB) channels.
For an image section with N pixels, this yields the matrix:







1



2
· · ·











1



2
· · ·


 


P =

,

,





1



2
· · ·









(cid:110) (cid:174)

,

=

(cid:111)

(cid:174)

,

(cid:174)



(3.1)



(cid:110)
(cid:110)

Note that the selected portion of each image may contain a different number of pixels. Using
a section of a clean plate (that has not been fouled), we first compute the mean 
 and standard
deviation 
 of the RGB channels:

(cid:111)
(cid:111)

−→
 




 =
−→
 




 =



, 

, 





, 

, 

















37

(3.2)

(3.3)

These vectors are representative of the plate material to which we can compare the plates, which
are submerged. A separate “clean” vector-pair is computed for each coating type. For a raw image
of a submerged plate (top row of Figure 3.9), the vector




+ =

1
3

|

1−

|
|

2−

|









+ |

1−

|
+ |

2−

|





+ |

1−

|
+ |

2−

|












· · ·





|


−

|





+ |

 
−

|

+ |


−

|







(3.4)

is a measure of the difference between each pixel’s color and the mean value for that channel
observed on the clean plate, normalized by the standard deviation associated with that channel.
This is illustrated by the colored contour maps (computer generated images) shown in the middle
row of Figure 3.9. In each image, some number of the pixels fall under the threshold 




+ < 
.
These pixels are considered “clean”, and the fraction of clean pixels is given by the value of the
cumulative density function at 
, 
(
). By analogy, a pixel is fouled above 




+ > 
, and the
fraction of fouled pixels is given by 1 − 
(
). The threshold 
 = 4.5 was trained using user input
on a subset of the images. In the bottom row of Figure 3, the effect of 
 on 
(
) is provided for the
sample image.

3.3.7 Chlorophyll a Processing

During year 2, Chlorophyll a (chl a) concentrations in controls and groomed plates over time were
compared using a two-way repeated measures ANOVA (rmANOVA) in SPSS (v26.0.0). Cohen’s
d effect sizes were calculated for each grooming frequency and time point to estimate how chl a
concentration differed on the surfaces of control and groomed plates [70]. Cohen’s d values of 0.2,
0.5, and 0.8 were interpreted as small, medium, and large effect sizes, respectively. Graphs were
created using RStudio (v1.1.456) using ggplot2 (v3.2.1). Sampling and processing the data was
completed by Abhishek Naik from University of Massachusetts - Dartmouth. More details the chl
a can be found in [71], which was the result of the collaboration between MSU, UMass-D, and

38

Figure 3.9: The top row shows raw images of Garolite and Intersleek plates before and after
grooming. The middle row shows computer generated images of Garolite and Intersleek plates
before and after grooming. The pixels of the computer-generated images have colors that correspond
to the entries of 




+; the thin black contour indicates entries of 
+ = 4.5. The bottom row
shows the measure of cleanliness 
(
) for different values of 
; as expected, the plates are cleaner
after grooming.

NUWC.

3.4 Results

3.4.1 Preliminary Findings - Year 1

Results from static grooming confirmed that the maximum shear forces are generated near the jet
outlet on the plate. Although a significant portion of the biofouling was removed in the initial
weeks, some organisms remained attached to the plates in the region below the outer diameter of

39

the pad. This remnant biofouling increased the surface roughness, causing reduction in the efficacy
of the grooming operation. Over time, the Bernoulli pad failed to generate sufficient forces for
both levitation and grooming. Some results from static grooming are shown in Figure 3.10. It is
clear from these figures that grooming was effective in week 3 but less effective in week 5. Also,
grooming was most effective in the central region where the shear forces were the highest. Another
observation was that the sun exposure was non-uniform on the submerged plates, which is likely
to have resulted in less biofouling of the plates groomed with the lowest frequency. To mitigate
the shading bias, the locations of the plates were rotated every grooming day during the second
experiment in Year 1. In addition, the mode of grooming was changed to “scanned grooming”
in the second experiment to alleviate the problems associated with static grooming. In scanned
grooming, which was also performed for one minute, the plate was moved laterally relative to
the pad such that the entire surface of the plate was subjected to the maximum shear forces. To
facilitate scanned grooming, the outer diameter of the pad was reduced to 
 = 200 mm from its
original size of 
 = 300 mm. This reduction in size was performed after simulations confirmed

Figure 3.10: (a) The view from above during static grooming levitating the Garolite plate. (b)
Select results of static grooming of Garolite plates in Year 1. The plates are shown before and after
grooming in weeks 3 and 5 after they were submerged, for four different grooming frequencies.

40

that the peak shear stress and the pressure profiles were marginally affected. Although scanned
grooming was more effective than static grooming, it was not possible to completely dislodge
all organisms. Scanned grooming kept the plate surfaces cleaner for a longer duration of time
but was eventually rendered ineffective similar to static grooming. Some results from scanned
grooming are shown in Figure 3.11. Similar to the results obtained with static grooming, these
results also indicate that the effectiveness of grooming reduces over time. Scanned grooming,
however, removed organisms more uniformly from the entire surface area of the plates. Also, as
evident from the results of week 3 before grooming, uniform sun exposure through rotation of the
plates achieved the expected difference in biofouling for different grooming frequencies. After
both rounds of tests were completed, it was concluded that it is difficult to quantify the level of
biofouling and hence objectively evaluate the effectiveness of grooming. This indicated the need
for normalized image-based analysis and more detailed biological testing. During Year 1 it was
also determined that the time taken to transport the plates between the pier and the laboratory was

Figure 3.11: Select results of scanned grooming of Garolite plates in Year 1. The plates are
shown before and after grooming in weeks 1, 3 and 5 after they were submerged, for four different
grooming frequencies.

41

not optimal. The grooming was done directly on the pier during Year 2 in order to reduce the
potential biases to the experiment resulting from extended time the plates were out of the ocean
environment.

3.4.2

Image Analysis - Year 2

The image-processing method was used to assess the effectiveness of grooming undertaken at
four different frequencies compared to controls, over a period of seven weeks. The processed
“cleanliness” data are shown in Figure 3.12a and b for the Garolite and Intersleek plates, respectively.
There is no statistical testing of these data since the image analysis was limited to a single plate for
every grooming frequency and surface type.

For Garolite, at the beginning of the study (first two weeks), 
(
) 1 for plates both before
and after grooming. This was true regardless of the grooming frequency. After this initial period,
during which the plates became colonized by biofouling organisms, the trend in 
(
) before
grooming essentially tracked that of the Garolite control, and 
(
) after grooming was (with
isolated exceptions) higher than that observed before grooming. While this was expected, it was
not anticipated that the grooming effect would be larger on the 2 × /

 and 1 × /

 plates than on
the 3×/

 plates. More frequent grooming seemed to promote a robust monoculture of a tenacious
biofilm [37], and it is hypothesized that more frequent grooming facilitates the growth of either
a more tenacious species or promotes an alternative compact growth habit that can better tolerate
the grooming frequency. A similar trend has been observed in industrial water systems, where
turbulent flows promote homogeneous and slimy biofilms which are significantly more robust and
harder to eradicate than biofilms that develop in laminar flow [53].

The data for the Intersleek plates indicate that up to day 46, grooming frequencies of 1× and
more frequent grooming per week were capable of maintaining the plates to the clean state, such that

(
)1 even for plates before grooming (Figure 3.12). On the plate which was groomed 0.5×/wk,
the 
(
) for the plate before grooming began to track that of the control plate on day 29, although
it appears that grooming was able to reduce the plate back to the clean state. A similar result was

42

observed when the control plate was groomed for the first time on day 48, which was the last day
of the study. The before and after photographs of this control plate grooming are shown at the top
right of Figure 3.11 and the complete set of four plates are shown at the bottom of Table A.11 in
the Appendix. It is also notable that the 
(
) for the 0.5×/wk groomed Intersleek plate, prior to
grooming, was decreasing over the test. This may have been caused by a rise in temperature over

Figure 3.12: “Cleanliness” measured using 
(
) with 
 = 4.5 for (a) Garolite and (b) Intersleek
plates for four different grooming frequencies over a period of seven weeks. The terms “before”
and “after” indicate the pair of results obtained before and after grooming on a particular day. The
points linked by the dotted lines in (a) correspond to the Garolite plates shown in Figure 3.9 (a).
Similarly, the points linked by the dotted lines in (b) correspond to the Intersleek plates shown in
Figure 3.9 (b).

43

the duration of the experiment, given that 0.5×/wk grooming was apparently effective in removing
the biofouling of the Intersleek plates.

It is also apparent that the biofouling prevention characteristics of the Intersleek and Garolite
control plates were not substantially different when judged on the basis of the image data. This
appears to confirm the proposed working method of the Intersleek formulation. As designed, the
surface does not simply passively prevent the growth of macroscopic biofouling, but acts as a
fouling-release coating only under the action of fluid shear, such as that produced by a moving
vessel.

3.4.3 Chlorophyll a - Year 2

Increase in chl a over time was observed on all plate types, although the degree of growth varied
across plate types and grooming treatments (Figures 3.13 and 3.14). Overall, chl a concentrations
were always substantially lower on the Intersleek vs. Garolite plates. This is a different result from
that obtained via image processing. In particular, image-processing data indicated that the passive
fouling prevention characteristics on the control plates were not sensitive to plate surface type.

On the Garolite plates, the chl a concentration of control plates increased from 0.03 ± 0.001
µg cm−2 at 9 days post-deployment to 3.61.27 µg cm−2 at 37 days post-deployment (Figure 3.13a).
Changes in chl a concentration were dependent on grooming frequency. Cohen’s d estimates
suggest that grooming of bare plates was associated with reduction of chl a until day 30 for plates
groomed 0.5×/wk, 1×/wk and 3×/wk (dashed lines of Figure 3.14, Table 3.2). However, compared
to control plates, there were no statistically significant reductions in chlorophyll a on groomed
Garolite plates when considering the entire duration of growth (37 days) (Table 3.2). Among the
0.5×/wk-groomed Garolite plates, there was a statistically significant reduction in chl a concentra-
tions compared to control plates only for the first 30 days, after which they could not be sampled
due to hard fouling growth (rmANOVA; F = 15.34, p < 0.05). While 0.5×/wk grooming visibly
removed some soft fouling from Garolite plates (Table A.5 in Appendix). However, the 0.5×/wk
groomed plates could not be sampled at day 37 due to hard fouling growth. These results suggest

44

that 0.5×/wk grooming may remove soft fouling, it may have simultaneously allowed hard fouling
to accumulate. For Garolite plates groomed 2×/wk and 1×/wk, there was some soft fouling removal
(Tables A.4 and A.3 in the Appendix), but no statistically significant difference in chl a concen-
trations between control and groomed plates (Figure 3.13a). At 3×/wk grooming frequency, there
was a significant difference in chl a concentrations between control and groomed bare plates only
until day 30 (F = 26.255, p < 0.05), but not when considering all 37 days (F = 0.706, p = 0.448). On
day 37, chl a concentrations were higher on groomed plates compared to control plates (positive
effect size, Figure 3.14, bottom right). Hence, despite low post-grooming cleanliness based on
image analysis, 3×/wk grooming may have removed chlorophyll-rich biomass from bare plates, but

Figure 3.13: Chlorophyll a concentrations (µg cm−2) at 5 time points post-deployment. (a) Garolite
plates; (b) Intersleek plates. For the Garolite 0.5×/wk groomed plates, samples were not collected
on day 37 due to hard fouling growth. This data and figure was provided by Abhishek Naik.

45

Figure 3.14: Effects of grooming on Garolite and Intersleek plates. Each point is a Cohen’s d
estimate representing a standardized mean difference between chl a on control and groomed plates
across 3 replicate plates each. Each estimate summarizes the effect size for one plate type, grooming
frequency, and day. A Cohen’s d < 0 implies decreased chl a on groomed plates. A Cohen’s d >
0 implies increased chl a on groomed plates. For the 0.5×/wk groomed plates, samples were not
collected on day 37 due to hard fouling growth. For Intersleek plates, Cohen’s d values could not be
calculated for the day 9 time points due to negligible averages and zero standard deviations among
chl a concentrations of groomed plates and control plates. The red lines indicate large Cohen’s d
effect size of 0.8. This data and figure was provided by Abhishek Naik.

only until day 30. However, there was a grooming frequency-dependent increase in light green and
apparently shear-tolerant macroalgae (Tables A.2 and A.3 in the Appendix). The visually observed
high abundance of this community appears to be correlated with lower post-grooming cleanliness
at 2×/wk and 3×/wk grooming on bare plates (Figure 3.12a). The presence of this community
would likely also have influenced measured chl a concentrations.

On Intersleek control plates, chl a concentrations were from 0 µg cm−2 at 9 days post-

46

deployment, increased to 0.82 ± 0.19 µg cm−2 on day 30, and decreased to 0.266 ± 0.16 µg
cm−2 at day 37 (Figure 3.14b). Fouling growth on Intersleek control plates was loosely attached,
hence the lower final concentration may be a result of natural fouling removal by in situ shear
stresses. There was a significant reduction of chl a concentration due to grooming at all frequencies
on Intersleek plates, relative to the control plates (all rmANOVA tests p < 0.02). Grooming was
consistently associated with large reduction in chl a concentrations on Intersleek plates (negative
Cohen’s d, solid lines of Figure 3.14 and Table 3.2). However, the effects were generally not con-
sistent across time, with effect size decreasing between day 30 and 37 due to the low concentrations
of chl a concentrations on the control plate at 37 days post-deployment.
Table 3.1: Results of rmANOVA testing the effects of grooming on the concentration of chlorophyll
a in fouling material growing on Garolite and Intersleek plates. This data and table was provided
by Abhishek Naik.

47

Table 3.2: Effects of grooming on chlorophyll a on fouled plates. Values represent Cohen’s d
estimates of effect size, a standardized mean difference between chl a on control and groomed
plates across 3 replicate plates each. Cohen’s d values < 0 imply decreased chl a on groomed
plates. Cohen’s d > 0 implies increased chl a on groomed plates. This data and table was provided
by Abhishek Naik.

3.5 Temperature, Light, and Salinity Data

A HOBO MX2202 pendant to log temperature and light intensity every 15 minutes was attached
to one of the submersible frames 10 days into the field test study. For the complete data logged
shown in Figure 3.15, the average was 21 ±1.7 °C. The salinity from a water quality monitor station
5 km from the submersible rig was acquired from the National Estuarine Research Reserve System
(NERRS) in partnership with the National Oceanic and Atmospheric Administration (NOAA). The
complete data logged for the time period of the field test study is shown in Figure 3.16. The average
surface salinity range was 29.2 ±0.5 parts per thousand (ppt) is representative to what the plates
experienced.

48

Figure 3.15: The temperature and light intensity was logged in 15 minute intervals locally with a
HOBO pendant sensor that was mounted on one of the submersible frames. The raw data points
for temperature were plotted individually, with a moving mean overlay.

Figure 3.16: The water quality stations from the T-Warf located at the southern point of Prudence
Island represent the open bay water near the field test site. Water salinity data was collected at both
surface and bottom stations every 15 minutes using YSI 6600 V2 and EXO2 data loggers. Each
data point is plotted for the duration of the study along with a moving mean.

49

3.6 Biofouling Organisms Observed

The scheduled grooming occurring only on the front, which by orientation from being suspended
off the pier and restricted from rotating resulted in more direct sun exposure. Due to the shading
effect, the back and edges of all plates experienced the biofouling pressure differently from that of
the front. The combination of the shade and no grooming promoted a completely different array
of organisms, to the point where the back and edges of all plates had to be scraped weekly once
significant biofouling accumulated. On the sun-side of Garolite plates that were subject to grooming,
sampling, and imaging, the fouling community was soft for the first 5 weeks; consisting of green
and brown algae, biofilm, and intermittent arborescent bryozoans. After 5 weeks, hard fouling
appeared in the form of tubeworms and slipper snails. The sun-side of the Garolite control plates
experienced the highest level of hard fouling in the form of bryozoans, slipper snails, tubeworms
and mussels. Some of these organisms can be seen in Figure 3.17 of the set of Garolite control plates
in the grooming frame. Figure 3.18 shows the same set installed in the submersible frame where
the plates are kept physically separated. Keeping the plates underwater allowed us to gently move
the buoyant soft fouling aside to better investigate the community. On the sun-side of all Intersleek
plates, the fouling community was soft; consisting of green and brown algae, and noticeable biofilm
where there was no algae attached. The biofouling on Intersleek also was significantly less dense
when compared to the Garolite counterparts of the same grooming frequency, demonstrating the
effectiveness of the slime release coating. The Intersleek control did have most biofouling coverage
compared to any of the groomed Intersleek but was still significantly less fouled than the Garolite
control.

To mitigate the possibility of a shading bias on the front of plates from the pilings and pier
structure itself, the locations of every set of plates were shifted away from the coast during every
grooming day (M, W, F) since the beginning of the field study. This was conveniently and quickly
accomplished using threaded connecting links made from stainless steel installed on the ropes to
detach and re-secure the individual submersible frames. All of these types of interactions with
the plates were completed as much as possible in submerged conditions with the help of multiple

50

ocean water filled totes. The grooming test tank was set up in a shack at the deployment dock that
provided protection from the elements, such as sun and rain.

The observed organisms that established themselves on all the exposed surfaces of the plate

Figure 3.17: The front (top) and back (bottom) of the Garolite control plates at day 43 of the field
test study. The box shows a close up picture of the area when submerged to better show the mussel
that is attached. The top also shows circular areas that were used for sampling for chl a. Since the
front of the plates had a significant amount of biomass by day 35, the sampling device could not
maintain a seal for the circular well even if there were no hard fouling in the way. The samples for
that day was taken with a sterilized cell lifter, the most noticeable resulting patch being on the front
of the second plate from the left.

51

Figure 3.18: The back of the control set of Garolite plates installed in its submersible frame is
shown, revealing a variety of macrofouling at day 51 which is after the end of the 7 week study.
The last extensive scraping of the back happened 2 weeks prior.

(which comprises of the sun-side, edges, and back) is in agreement to what Menesees et al. [40]
observed on Garolite plates that were free of any coating. The plates in that study were 15.2× 22.9
cm and suspended at a 22.5° angle from the vertical to both mimic the non-vertical portion of a
hull and ensure continuously generated wall shear stress created by the bubbles as they rose along
the Garolite surface. The single stream of bubbles created a distinctly clean region. Moving away
from the bubble stream, the fouling growth gradually increases.

Since the back and edges of each plate in the presented study did not experience any contactless
grooming, substantial biofouling did build up, warranting removal during every biological sampling
day (Thursday) starting at week 3. The method of carefully scraping with a small putty knife was
accomplished by holding the plate only by the permanently mounted tab to maintain no physical

52

contact to the front side. The scraping allowed the plates to fit into the chlorophyll a sampling device
while maintaining no direct contact with the groomed-side other than the o-ring that created a seal
for the sampling well as described in the earlier section regarding data acquisition. The scraping
also prevented any biofouling that started on the edges or back of the plate from influencing or
encroaching onto the sun side. Based on visual observations that occurred while handling plates,
the same variety and rate of biofouling was observed on the back of all plates, which was expected
since the Intersleek plates had the slime release coating only on the front side, leaving the back
surface in original Garolite condition. Thus, the edges and back of all 40 plates in this study had
the same surface type and same level of light exposure, and consisted of mainly colonial tunicates,
arborescent bryozoans and encrusting bryozoans (as previously seen in Figures 3.17 and 3.18).

Image Setup and Collection

3.6.1
Four 10.2× 10.2 cm plates were lined up in order and secured flush to a grooming frame. To begin
assembly, the grooming frame was positioned upside down on spacers in the corners to prevent the
sample plates from coming into contact with anything on the sun-side. Touching was strictly on
the tabs and the back or shade-side if needed to ensure flushness. A set of four duplicate plates
was labeled on the back with frequency and duplicate number. They were consistently placed in
decreasing order (Figure 3.19) so that when the grooming frame was flipped, they were in increasing
order. Figure 3.19b shows the flush side that was exposed to contactless grooming via shear stress.
The pink foam visible in Figure 3.19a was attached to achieve neutral buoyancy of the assembled
grooming frame when submerged in the grooming tank. The fasteners were permanently mounted
to the frame. On the other side of the grooming frame, the screws acted like a fixture to mount the
plates consistently.

53

Figure 3.19: Photos taken of (a) the back of the grooming frame after a group of 4 duplicate plates
are installed, and (b) the front. A paper note was used to document the details and time of what
was photographed.

3.7 Discussion

The biofouling mitigation effectiveness of a Bernoulli pad grooming device was tested on a Garolite
and Intersleek surfaces. The tests took place over a 48-day period at four different grooming

54

frequencies, during which image and chl a data were acquired. An image-processing algorithm
was developed to produce a quantitative measure of cleanliness.

For the Garolite plates, the image analysis indicates that grooming rendered the plate cleaner
than the control plate at the end of the test for all grooming frequencies, but ultimately did not
restore the plates to a nearly clean state after 20 days. The chl a data support this observation,
and indicates that grooming was minimally effective for all grooming frequencies. The chl a data
also suggests only 0.5× and 3×/wk grooming had less biofouling than the control up to day 28.
Both visual and biological methods suggest that the higher grooming frequencies removed the less
tenacious fouling organisms. Note the before and after grooming difference in C(
) is consistently
smaller for the 3×/wk compared to the other grooming frequencies indicating a the peak wall shear
was below critical threshold for a significant portion of the biofouling present, which is why both
the 0.5× and 1×/wk appear to be cleanest on day 43. This is consistent with previous observations
that stress on the organism produced by turbulent flow or grooming influences the structure of
biofouling community [72, 53, 37].

To the extent that there are differences between the methods’ findings, we offer the following
possible explanations. First, the image-processing threshold 
 was calibrated visually, such that the
notably clean and fouled areas were consistent between the raw and processed images, as shown in
3.12. In contrast, the chl a data records only photosynthetic biofouling, including that found within
the growing layer. A plate with significant thickness of fouling will produce elevated levels in the
chl a survey compared to the image analysis. Second, the image-processing algorithm considers
the plate to be either clean or dirty at a given location. This means that the "dirtiness" of the plate
at that location is saturated. This is not the case for the chl a data, where the thickness of fouling
buildup can yield additional chl a. Finally, not all biofouling organisms produce chl a, meaning that
the approaches will diverge when the surface is under biofouling pressure from non-photosynthetic
organisms.

On the Intersleek plates, grooming was able to restore the plate to a nearly-clean state at all
treatment frequencies, as measured by both the image-processing and chl a methods. By day 42,

55

some fouling was visible on the 0.5×/wk plate prior to the grooming step, indicating that whatever
residual organisms not dislodged by the previous grooming action were able to recover to a visually
measurable level in the interim two weeks. The results demonstrate that it is considerably easier
to remove biofouling from the Intersleek plates than the Garolite surfaces using the fluid shear
grooming protocol.
It is also notable that the Intersleek control plate was groomed to a nearly
clean state at the end of the study, indicating that a 48-day or longer grooming frequency may be
appropriate for this surface type under the in situ conditions prevailing during this study.

The Bernoulli pad uses fluid shear stress as a cleaning mechanism. The images therefore
fully corroborate fouling-release as Intersleek’s mode of action from wall shear stress generated
by an underway vessel, whereas the chl a data suggest that this coating also limits attachment
and/or buildup in a to-be-determined manner. There is a range of other foul-release coatings from
a variety of manufacturers that rely on the shortest possible idle periods to prevent the required
critical shear stress for removal to surpass the generated fluid shear stress [21]. The most successful
and thereby most popular foul-release coatings on the market all use surface properties to make
the surface either more hydrophilic to increase resistance to cell adhesion and protein adsorption
[73] or hydrophobic to lower the surface energy that prevents an organism from forming a strong
adhesive bond [74]. When polymers are formulated to be simultaneously both hydrophilic and
hydrophobic, the result is a coating such as the Intersleek 1100SR used in this study [75]. We
therefore expect that the main results in the present work will be generalizable to other fouling
release coatings.

For future field test studies of this method, both the gap height and input electrical power to the
pump should be measured and logged in real-time. The input electrical power should be varied to
allow the device to compensate for events where biofouling has become sufficiently abundant to
cause drag in the fluid flow field. Using the gap height and the flow rate data, the maximum velocity
in the gap can be calculated, and we can estimate the generated wall shear stress. This information
can be incorporated into a feedback loop so that the flow rate can be adjusted to generate sufficient
force to match the adhesion strength of biofouling present. This approach of force matching will

56

ensure optimal grooming while extending the life of the anti-fouling or foul-release coating. The
electrical input can also be used to determine how restricted the flow is during grooming. A
duplicate contactless grooming device machined from clear acrylic could be dedicated to study the
cavitation bubbles generated when the flow rate is high enough to generate extreme low pressure
region immediately after the corner of the stem-pad interface where the axial flow from the jet
begins to turn into radial flow. Such an investigation will determine the location and extent of
cavitation erosion (potentially on both pad and contactlessly groomed surface) as well as quantify
the improvement on biofouling mitigation when the maximum possible wall shear stress is generated
consistently.

3.8 Concluding Remarks

A Bernoulli-based grooming device is capable of effectively removing fouling from an Intersleek
surface without damaging or abrading the Intersleek surface material. The same cannot be said of
the Garolite surface. The method of cleaning is fluid shear stress, which is the same mechanism
used to produce fouling release when a vessel is underway [21] and can help maintain a vessel hull
that experiences biofouling pressure when idle, by preventing biofouling before it gets too strongly
attached (Figure 3.2). One shortfall of relying on the speed of the vessel to shed biofouling is that
the generated wall shear stress will vary depending on the location on the hull. This grooming
effect, produced entirely without surface contact, is anticipated to improve hull performance while
extending the life cycle of the coating relative to more abrasive cleaning methods.

The image-processing algorithm described here offers a way to achieve immediate feedback
in an automated grooming system. Furthermore, the radial outflow supplied by the Bernoulli pad
enforces a self-equilibrating gap between the pad and the hull. This removes any need to sense
contact pressure on the hull, which might ordinarily be required to remain attached while not
creating excessive shear force on the hull surface. We therefore believe that this type of grooming
system is well-suited to incorporation in an automated or remotely operated system, and we plan
to explore this in future work.

57

CHAPTER 4

3D PARTICLE TRACKING VELOCIMETRY OF RADIAL OUTFLOW BETWEEN TWO

PARALLEL PLATES

4.1 Introduction

For the Bernoulli pad to be effective as a cleaning device, there needs to be sufficient wall shear
stress generated by the radial fluid flow to remove organisms that settle on the surface of a vessel
hull. Since the flow rate and equilibrium height have an inverse relationship; with increasing the
flow rate directly increases the generated suction force, which decreases the equilibrium gap height.
The CFD model has been validated with previously published experimental data using air as the
working fluid as previously presented in Chapter 2, but only in terms of radial pressure profiles
and the suction force generated at different gap heights. There was no information available on
experimentally measured velocity field and the derived pressure to compare to CFD. With water as
a working fluid, an experiment was conducted in a glass tank with a Bernoulli pad fabricated with
the dimensions used previously in the field test study as discussed in Chapter 3.

4.2 Description of Experiment

4.2.1 Bernoulli pad in water tank

The Bernoulli pad used in our experiments had an inner diameter of 31.75 mm and an outer diameter
of 200 mm. The pad was made of opaque matte black acrylic to block the view of particles on the
other side of the pad and reduce glare within the measurement volume. The pad was connected to a
flow conditioning system comprised of a plenum chamber, a honeycomb, a series of meshes (coarse
mesh with 46% opening area; medium mesh with 36% opening area, fine mesh with 31% opening
area), and a converging nozzle [76]. This flow conditioning system produced a very close to
homogeneous velocity distribution at the inlet of the Bernoulli pad. Figure 4.1 shows the Bernoulli
pad together with the flow conditioning unit in exploded and assembled views. This assembly will

58

Figure 4.1: The Bernoulli pad assembled with a plenum and flow straighteners.

Figure 4.2: The BPA is mounted on a beam with roller wheels that allow the pad to be placed in
close proximity to the tank wall. Double arrows indicate the direction of movement of the BPA
permitted by the roller wheels; this movement allows the pad to find its equilibrium configuration.

henceforth be called the Bernoulli pad assembly (BPA).

Our experiment was conducted in a glass water tank of dimensions 1.22 m× 0.305 m× 0.762 m.
The water tank was placed on an optical table. A modular frame with tracks was secured to the
optical table to mount the BPA on rollers and with its pad parallel to one of the tank walls. When
water flows radially outward between the pad and the wall, the BPA would move freely toward or
away from the wall to find the equilibrium gap between the wall and the pad. As shown in figure

59

wire screen mesheshoneycomb structureconverging nozzleBernoulli padacrylic chamberend capinlet frompump(a) exploded view(b) assembled view(a) top view(b) side viewBernoulli padglass water tankmodular framebeam with roller wheelspumproller wheelsbeam4.2, a submersible pump (1/3 HP) is connected to the Bernoulli pad assembly to drive the flow.
This setup is shown in figure 4.2.

4.2.2

Imaging

For imaging, we used four Phantom v2512 cameras (maximum frame rate at full resolution: 25,700
fps at 1280 pixel x 800 pixel); they were placed in an arc-like pattern (see figure 2.2) such that
the optical axes of their lenses were coplanar and converged to a single point located in the gap
between the BPA and the tank wall. Each camera utilized a Scheimpflug mount to keep the entire
image plane in focus. A dual head Photonics Industries class IV laser, DM30-527DH, (maximum
energy: 70 mJ/pulse at 527 nm, maximum pulsing rate: 10 kHz/head) was used to illuminate a
volume encompassing the focal point. A programmable timing unit (PTU) was used to synchronize
the cameras with the laser for data acquisition. This imaging setup was implemented with DaVis
software by LaVision, Inc.

We used Time-resolved 3D Particle Tracking Velocimetry (4D-PTV) for flow characterization.
This method is based on syncing multiple cameras to look at a laser-illuminated volume from
different angles simultaneously, to track the motion of individual particles suspended in the fluid.
It uses an Iterative Particle Reconstruction (IPR) technique in combination with a 4D algorithm
using time-information of the particles for track reconstruction (assuming that tracer particles track
fluid particles sufficiently well, a track can be defined as a surrogate path-line).

To increase our signal-to-noise ratio, premixed fluorescent-coated microspheres (38 − 45
 m),
which fluoresce at a wavelength of 606 nm peak emission upon excitation with green light (527 nm
in our case) were used to seed the water in the tank. Because the light fluoresced off the particles
was of a different frequency, any stray laser light was filterd out by notch filters centered at the
fluorescent wavelength. With 50 mm lenses and a 1.5 magnification factor, particle images were
typically around 2 pixels in diameter. To minimize peak-locking, diffuser optical filters were in-
stalled in the Scheimpflug mounts to broaden the point-spread function of particle images.

60

Figure 4.3: A top view of the experimental setup showing the imaging hardware comprised of
four ultra high-speed cameras and a dual-head pulsing laser. The cameras are placed in an arc-like
arrangement and focused on a volume that lies between the pad and the tank wall. The dual-head
laser is located in the middle of the four cameras.

Spatial calibration was performed with a dual-plane target with a distance of 1 mm between
planes. Once the laser volume and cameras were aligned with the target, the camera view was
masked to the area of interest in order to reduce memory requirements and disk space. The target
was used to make the cameras look approximately at the same field of view and to obtain an
initial coarse spatial calibration. Since the depth of the volume of interest was ∼ 1 mm, it was
unnecessary to traverse the target along the depth to construct the initial spatial calibration. The
spatial calibration was then refined with a self-calibration algorithm applied to particle images [?].
After volumetric self-calibration and refinement were performed to reduce disparities, the optic
transfer function was generated. The resulting fit model was a third-order polynomial with an
RMS of fit of 0.0013 pixel and a scale factor of 14.11 pixel/mm. The final dewarped image was
227 × 851 pixels in size.

61

4.2.3 Experimental Procedure

After removing the calibration target, the resulting laser volume between the wall and the BPA was
as shown in figure 4.4. This laser volume captured a portion of the incoming axial flow and a radial
strip that extends beyond half the radius of the pad, where the average flow has become purely
radial. Given the arc-like camera distribution, and to achieve optimal focus by using the smallest
possible angle between the cameras, the orientation of the laser volume was chosen to be vertical.

Figure 4.4: (a) CAD model illustrating where the laser illumination is directed to on the BPA.
Defined edges indicate where the image was masked in the flow visualization software. (b) The
Bernoulli pad showing the matte surface finish and three equally spaced nylon-tipped set screws
installed. These set screws help avoiding perturbations of the uniform equilibrium gap between the
pad and the tank wall. (c) Side view of the laser illuminating the area of interest in the gap and
partially into the jet outlet.

Each laser head was run at 10 kHz, and the two were combined in cavity stacking mode to
achieve a laser pulse frequency of 20 kHz. A total of 100,000 sets of four images each were
acquired over a time interval of 5 s.

With the purpose of reducing loss of pairs and peak locking due to exceedingly large or small
displacements respectively, flow conditions were adjusted at the maximum acquisition rate to
obtain particle displacements no greater than 10 pixels between frames [77]. This was achieved
by finding an optimal combination of equilibrium height Òeq and 


. For the present experiment,
a configuration based on simulations indicated Òeq ≈ 1.25 mm, 


 ≈ 0.77 m/s, resulting in

max ≈ 8.4 m/s. These simulation-derived parameters were found to satisfy the above-mentioned

62

requirement for pixel displacement, and the process is discussed more in Section 4.4. Higher values
of 
max were avoided because they would induce cavitation and would also result in very small
equilibrium gaps.

The equilibrium gap was maintained by first adjusting the nylon-tipped set screws (see Figure
4.4b-c) to provide the nominally correct gap as defined by our simulation. The electrical power
delivered to the pump was then increased until the support force provided by the screws was
approximately zero. The screws were then retracted slightly to confirm that the pad was indeed in
equilibrium, then replaced to make gentle contact with the tank wall.

The aforementioned simulations indicated that the mean radial velocity ¯
(
) = 2 m/s at the
outermost radial location within the measurement volume. The total time 
t = 5 s duration of data
acquisition corresponds to 
t ¯
(
)/






 = 4.2 times the radial distance of the measurement
volume. This duration of data acquisition was deemed likely to provide a sufficient number of
statistically independent data samples to ensure convergence.

4.3 Experimental Measurements

In this section, the raw images from the four cameras to obtain the velocity vector field in the
volume of measurement are outlined. This experiment was carried out with a relatively low seeding
density, requiring a large number of instantaneous realizations (100,000) to ensure convergence of
flow statistics. For illustration, a single particle image taken from the set of 100,000 is shown in
Figure 4.5, which we will refer subsequently as time 
 = 
. Figure 4.6 shows an overlay of all
raw images. This composite particle field was used to detect if there were any large regions of the
volume of interest consistently devoid of tracers in the course of our experiment. A region like that
would be unable to yield statistically significant data. While there are a few narrow gaps that were
not visited by tracers, their azimuthal extent is small enough to be taken care by data interpolation
after converting the track field into a structured-grid velocity field.

Each set of four 2D particle images, like the set shown in figure 4.5, is used to determine the in-
stantaneous location of each particle in the 3D volume of measurement. The particle distribution of

63

Figure 4.5: A single representative image at time T (taken from the set of 100,000 images) from
the four cameras is shown.

Figure 4.6: Overlay of all 100,000 images are shown for each camera. These images (left to right)
correspond to the cameras (left to right) shown in figure 4.3.

64

the next time step is then predicted based on the current particle distribution. The errors introduced
with the prediction are then corrected with image matching before repeating the prediction for the
following time step. This algorithm also avoids the problem of creating ghost particles. Following
this prediction-matching approach, the motion of each individual particle is tracked using subse-
quent instantaneous realizations until the particle exits the field of view. The time delay and particle
displacement between instantaneous realizations are used to determine instantaneous velocity. The
set of all instantaneous velocities and positions of a single particle define particle tracks (path-line
surrogates). When the entire set of 100,000 images is processed, the particle-tracking algorithm
produces a large set of particle tracks that define a flow field based on a Lagrangian description.
This PTV technique was implemented using LaVision-DaVis. Reference [57] presents a detailed
description of this algorithm. The particle-tracking algorithm was performed to the entire illumi-
nated volume multiple times for refinement, where the total volume consisted of the gap and the
bottom portion of the jet flow 15 mm into the stem. To keep both the processing time and file size
reasonable, the final volume of interest was defined to be 13 mm azimuthally by 53 mm radially, by
1.5 mm axially from the glass tank wall.
Transforming the data from the Langrangian specification of the field (Figure 4.7b) to the Eulerian
specification (Figure 4.7c) requires converting the tracks to a vector field on a structured grid. The
PTV data had vector fields computed for every time step with the following specifications: collect
tracks inside sub-volumes sized 4 voxels with 75% overlap resulting in a grid spacing of 1 voxel
(which was equivalent to a cube of size 0.07 mm in our experimental setup) using a third-order
spatial polynomial. The collected tracks are then converted using a filter length of 5 time steps
and a second-order polynomial fit. This interpolation resulted in 100,000 sparse velocity fields that
were ensemble-averaged to obtain the average velocity field. Given their sparsity, grid points with
no velocity information were excluded from the calculation. Ensemble averaging and any further
calculation on the vector fields were implemented with MATLAB as explained in the following
sections.

65

Figure 4.7: a) Straight-on view of measurement volume that includes a small portion of the jet. b)
and c) Tracks of the particles (Lagrangian) visible in the four images in figure 2.6 over 8 additional
frames (equivalent to 400
s). d) Vector fields (Eulerian) of the particles visible in the four images
in Figure 2.6.

66

4.4 Computational Fluid Dynamics Model

To help with both the setup and analysis, a 2D axisymmetric CFD model was created and run in
ANSYS-Fluent with steady-state flow conditions. A four-equation Transition-SST model, based
on the k-
 transport equations coupled with intermittency and transition transport equations, was
used to model turbulence. For more detail on the setup of the CFD, please refer to section 2.2.1.
The pad outer diameter and jet diameter corresponded to both the device used in the field test study
from Chapter 3, as well as the black acrylic pad machined specifically for the PTV experiment in
this Chapter. The 31.75 mm stem diameter in the CFD model and experimental both had a length
of 25 mm, where a MFR boundary condition in CFD produced top hat velocity profile to match the
top hat velocity profile of water created by the flow straightener entering the clear acrylic stem of
the BPA. In both cases, the flow was allowed to develop past the initial entrance of the stem.

With the limit of the hardware being 10 m/s in order to prevent a seed particle from moving
more than 10 pixels in a single time step, the gap height had to be set to an approximate gap
height and flow rate. Otherwise, significant error will be introduced during the cross-correlation to
achieve particle track reconstruction. To find a suitable pair of parameters, a parametric sweep was
done with 4 different mass flow rates and 8 gap heights as seen in Figure 4.8. The MFR needed to

Figure 4.8: The force generated at different gap heights and four different mass flow rates (left).
The force versus mass flow rate at a gap height of 1.25 mm with equilibrium shown with a dashed
line (right). The maximum velocity generated at this equilibrium point in the fluid flow field at
1.25 mm is 8.4 m/s, which is below the limits of the hardware.

67

be significant enough to generate enough suction (negative force) with a steep F/h slope to allow
the suspended BPA to overcome rolling friction on the rails. Based on the preliminary results, The
equilibrium gap height needed to be larger than the experimental study, which a smaller flow rate
would achieve. Since the experiment will have outliers in regards to the maximum velocity, the
CFD model indicates that a mass flow rate of 0.605 kg/s will result in an equilibrium gap height of
1.25 mm with a peak velocity magnitude of 8.4 m/s.

4.5 Results

Radial outflow has a unique fluid flow field, where the initial axial flow transitions into radial flow.
This involves separation of the flow at the corner of the stem/pad interface before reattaching on the
pad-side further downstream. The DaVis Software has the ability of converting the particle tracks
into a vector field and calculating the pressure field.

4.5.1 Ensemble Average

The above mentioned conversion from particle tracks to vector fields in an unstructured mesh,
and then to vector fields in a structured rectangular mesh, produced a total of 
 = 100, 000 3-
dimensional vector fields of grid size 
 = 171 × 
 = 756 × 
 = 22; with velocity components at
each grid point (
, 
, 
) given by (

, 
,
 , 

, 
,
 , 

, 
,
). The value at each grid point of the ensemble
average of each velocity component (
, 
, and 
), is defined as the average velocity value across
all 
 instantaneous realizations at each grid point. That is:









=1


=1



, 
,
 =









=1


=1


, 
,



(
)

(
)


, 
,


, 

, 
,
 =


, 
,



(
)

(
)


, 
,


, 

, 
,
 =


, 
,



(
)

(
)


, 
,


(4.1)









=1


=1

Where 
(
)

, 
,
 = 1 if the (
, 
, 
)−th grid point of the 
−th instantaneous realization has data, and

(
)

, 
,
 = 0 if it does not. Equations (4.1) were used by DaVis software to generate an average
efficiently without having to store the individual vector fields for every time step.

68

4.5.2 Azimuthal Average

Utilizing the nature of the axis-symmetric flow, both the Cartesian coordinate system and the
corresponding data were transformed onto a cylindrical frame of reference and collapsed onto the
rz-plane. To focus on the longest particle tracks that originally generated the data, a wedge that
starts at the origin of the jet and intersects with the bottom of the experimental window was defined
from 4.64 to 4.78 radians, where 3
/2 radians is the center of the wedge that was illuminated at
the bottom of the BPA. The transition from the 3D (
, 
, 
) space to a 2D (
, 
) plane resulted in the
data remaining structured in the z-direction, but became unstructured in the r-direction. Bins of the
size 0.07 mm were used to preserve the resolution, and were used to sort and average the number of
instances that occurred in each bin. The resulting fluid flow field on a 2D plane is shown in Figure
4.9a-c.

Figure 4.9: Portion of the inlet is visible on the bottom left, and the intermediate outlet of the
experiment window is at the top of these plots. (a) Raw z-component of velocity, (b) Raw theta-
component of velocity, (c) Raw radial-component of velocity, (d) refined radial-component of
velocity, e) radial-component of velocity from CFD run at the same boundary conditions.

With the nature of flow visualization using seeding particles, there were instances in which no

69

seed passed through a voxel in space nearest the walls, even after binning. The velocity was forced
to be zero m/s at the walls, and a shape-preserving piecewise cubic spline interpolation algorithm
in MATLAB called ’pchip’ was used to fill in the gaps near the wall as shown in Figure 4.9d. With
an estimated 0.59 kg/s mass flow rate in CFD that will be discussed in more detail the next section,
there is good agreement of the radial velocity contour plots between PTV and CFD (Figure 4.9d
and e).

4.5.3 Pressure Distribution

From the LaVision DaVis software that was used to conduct the experiment and process the
captured images, the pressure was directly computed using LaVision Pressure from PIV, a 4D
pressure solver based on the method of computing the pressure gradient from the velocity field
and using Poisson’s equation to spatially integrate [78]. Using the velocity field generated from
the average of all 100k images as described previously, the time-averaged pressure was calculated
from the following parameters; working fluid was defined as water at room temperature with the
boundary condition set using gauge pressure equal to 0
 

 at point 
 = 60

, 
 = 0.637, which
this solver treats as a Dirichlet boundary condition. The 4D pressure solver developed in part by
NIOPLEX (Non-Intrusive Optical Pressure and Loads Extraction for Aerodynamic Analysis) [79]
where the 4D spatio-temporal blocks consist of multiple 3D domains as well as their Lagrangian
connections in the time domain. Boundary conditions are defined by the user to the first time step,
and the calculated pressure is used in the next time step.

The resulting pressure field from PTV is shown in Figure 4.10, with the main discrepancy being

the pressure generated in the central region.

70

Figure 4.10: (a) Raw pressure, (b) refined pressure, c) Pressure from CFD run at the same boundary
conditions.

4.6 Analysis

Once the PTV data had been collapsed onto the rz-plane, the mass flow rate was estimated at every
radial location using the following summation

22



=1

(cid:164)
(
) =


2

 


(
, 
)

(4.2)

where L is the grid spacing between the 19 points within the gap in the axial direction. There
were 3 additional points that include data captured in the stem, where 
 > 1.275

 as seen in
Figure 4.11, and were not included in this calculation. This summation is shown in Figure 4.12
was repeated with the refined PTV data, and shows that the radial velocity near the wall can be
better estimated. The focus of this chapter is the velocity and pressure field that was well defined
by enough instances of particles in the 100k sets of images. The estimation of a MFR of 0.7 kg/s
was used in CFD.

71

Figure 4.11: An illustration to show the boundaries of the data after completing the azimuthal
average.

Figure 4.12: Mass flow rate calculated for every radial location using raw and refined radial velocity
data.

To better visualize the different components of velocity and the pressure field in the gap, scatter
plots with each z-location was color coded. The axial velocities for PTV and CFD are shown in
Figures 4.13 and 4.14 respectively. The axial velocity before the corner of the stem/pad interface
has good agreement. The axial velocity does achieve a larger negative values after the corner when
compared to CFD. The flow that occurred near the glass wall experienced only positive radial
velocity and near 0 m/s axial flow. At the corner of the pad/stem interface, the flow separation

72

Figure 4.13: The experimental radial velocity at different axial locations within the fluid gap
(
/Òeq), where zero is at the glass wall. The discretized PTV data is overlaid on the original
unstructured PTV data.

73

Figure 4.14: The CFD radial velocity at different axial locations within the fluid gap (
/Òeq), where
zero is at the glass wall. The discretized CFD is overlaid on the original unstructured PTV data.

74

Figure 4.15: The experimental axial velocity at different axial locations within the fluid gap (
/Òeq),
where zero is at the glass wall. The discretized PTV data is overlaid on the original unstructured
PTV data.

75

Figure 4.16: The CFD axial velocity at different axial locations within the fluid gap (
/Òeq), where
zero is at the glass wall. The discretized CFD is overlaid on the original unstructured PTV data.

76

Figure 4.17: The experimental discretized and tangential velocity at different axial locations within
the fluid gap (
/Òeq), where zero is at the glass wall. The discretized PTV data is overlaid on the
original unstructured PTV undiscretized data.

77

Figure 4.18: The experimental pressure at different axial locations within the fluid gap (
/Òeq),
where zero is at the glass wall. The discretized PTV data is overlaid on the original unstructured
PTV data.

78

Figure 4.19: The CFD pressure at different axial locations within the fluid gap (
/Òeq), where zero
is at the glass wall. The discretized CFD is overlaid on the original unstructured PTV data.

79

results in a region of recirculation. This seperation bubble appears to be larger in the PTV
visualization as evidenced by the locations 0.67 < 
/Ò

 < 0.94 to reach negative radial velocity
values whereas only the locations 0.83 < 
/Ò

 < 0.94 in the CFD reach negative radial velocity
values as seen in Figures 4.15 and 4.16 respectively. This recirculation region also where the
highest tangential velocities occur as seen in Figure 4.17. The mean of the discretized points is
-0.04 m/s. CFD results of the tangential velocity is omitted due to being zero everywhere in the
gap, even with axis-symmetric swirl allowed.

After the negative pressure peak is generated, the pressure asymptotically goes to zero gauge
pressure by the end of the experimental window as seen in Figure 4.18. While there is discrepancy
in peak positive pressure between the PTV and CFD Figures 4.18 and 4.19 respectively, both reach
near zero gauge pressure by D/2 = 50 mm. This confirms the initial boundary condition used in
the DaVis pressure solver was a reasonable one. Further investigation to the pressure at this point
is discussed at the end of this section.

Since only a portion of the radial flow was captured, the pressure gradient beyond 64.4 mm is
unknown. Based on the tail spread of available undiscretized data seen, the shape of the remaining
pressure curve is unknown. Integrating the pressure curve at the glass, over the radially growing
surface area, the force can be estimated if the data is extended from 0 mm to 10.8 mm and from
64.4 mm to 100 mm as seen in Figure 4.20. From past CFD cases as well as the experimental
data set from Li and Kagawa [1] used in the CFD model validation in Chapter 2, the asymptotic
portion of the pressure curve has been observed to slightly overshoot the ambient pressure before
the outlet. Since the DaVis pressure solver calculates the pressure gradient, the earlier estimation
of 0 kPa at 60 mm can be modified in such a way to achieve F = 0 N when the entire pressure curve
is integrated as seen in Figure 4.21. With 0 kPa at 100 mm, the data points in between 64.4 and
100 mm was populated with data using a shape-preserving piecewise cubic spline interpolation
algorithm. Plotting the cumulative summation of force along the radial length does confirm that
the pressure gradient still had an upwards trajectory as seen at the second vertical dashed line in
Figure 4.23, but even modifying how the pressure profile extends by folowing the trend before 64.4

80

mm would not achieve a total force of 0 N even with an overshoot to 0.82 kPa as seen in 4.22. The
offset of 0.82 kPa does preserve the pressure gradient and makes a reasonable estimation of the
shape of both the pressure curve and the force summation after the end of the experimental window.
The offset also falls within the spread of the tail end of the unstructured data.

Figure 4.20: The discretized pressure curve along the bottom of the glass overlaid over all the
unstructured pressure data in the entire height of the gap. The vertical dashed lines indicate the
original data region from 10.8 mm and 64.4 mm.

Figure 4.21: The discretized pressure curve along the bottom of the glass with an offset of +0.82
kPa overlaid over all the unstructured pressure data in the entire height of the gap. The vertical
dashed lines indicate the original data region from 10.8 mm and 64.4 mm.

81

Figure 4.22: The discretized pressure curve along the bottom of the glass with an overshoot of
+0.82 kPa overlaid over all the unstructured pressure data in the entire height of the gap. The
vertical dashed lines indicate the original data region from 10.8 mm and 64.4 mm.

Figure 4.23: The cumulative summation of the force along the glass. Pressure at a radial location
was multiplied with the annular surface area. The vertical dashed lines indicate the original data
region from 10.8 mm and 64.4 mm.

82

To normalize the captured and processed PTV data, the maximum radial velocity, 




 is
unique to the fluid field flow since keeping the velocity at the inlet constant will generate different
maximum radial velocity at every different gap height. The radial velocity is normalized as follows:


∗

 =



(
, 
)







with the radial location normalized with respect to the radius of the jet outlet.

where the normalized pressure, 
∗, is based on the pressure forces and inertial forces.


∗ =




 



∗ =


(
, 
)


2






(4.3)

(4.4)

(4.5)

Each data set was defined in non-dimensional terms of its own Euler and Reynold’s numbers:



 =






(
, 0)


2








 =







 
 





(4.6)

(4.7)

The near the walls of the gap show reasonable agreement of the normalized radial velocities in
Figure 4.24. The case previously validated in Chapter 2 where the air was the working fluid and
the pad was 
 = 4

, 
 = 40

 is also shown in red. The discrepancy between the pressure
near the centerline of the jet still exists after normalization as seen in Figure 4.25, but there is good
agreement between the three CFD cases of water (green, grey, and cyan) and the CFD of air (red).
The experimental data with air (magenta) measured a higher pressure than what was predicted with
CFD, further confirming that the flow is complex, and any change to the size in th seperation bubble
impacts the pressure field.

83

Figure 4.24: Normalized Radial velocity for multiple flow rates of water with the pad dimensions
used in the PTV experiment. The velocity near the glass wall (top) shows no negative flow due
to being between the separation bubble and glass, where the velocity near the pad (bottom) does
capture the recirculation that occurs in the separation bubble.

4.7 Concluding Remarks

Confined radial outflow has never been imaged before using PTV, but the current hardware and
software made it possible to capture at an acceptable level of accuracy and provide insight to the

84

Figure 4.25: Normalized pressure for both PTV and CFD data of the water Bernoulli pad based on
equation 4.5. The air case is included with the previously published experimental data measured
with a traversing pressure tap.

region of separation and reattachment. The annular recirculation bubble is advantageous in our
application of a contactless grooming device because of the direct correlation to the maximum
velocity that is induced between the bubble and the glass wall. After processing the data and
converting to grid, the gap height was measured to be 1.275 mm, providing supporting evidence
that the pad was indeed levitating without contact when the pump was in operation.

The setup can be improved by incorporating a mass flow meter in line at the inlet and several
pressure taps embedded in the pad; such as after the corner and before the outer diameter. Rolling
friction in the suspended rail configuration was could prevent the pad from finding the exact point of
equilibrium. As seen in Figure 4.8, the slope of the force curve is steep near the stable equilibrium
point, and would still indicate the results presented in this Chapter to be near equilibrium. The
set screws were mainly to provide stability and prevent any oscillations of the levitating pad to
keep a fixed gap as the reattachment point has been observed to fluctuate [66] which in turn would

85

slightly fluctuate the force gnerated by the fluid flow field. Another major improvement would be
to add a precision laser sensor to measure the gap height. Ideally in multiple locations to ensure
the pad is indeed parallel to the glass wall. The seeding density was at the minimum desirable level
and should be increased in the future. Once the experimental setup is robust, multiple data sets at
different flow rates and different gap heights can be analyzed to see the development of the turbulent
and transition region. The stable equilibrium point with no applied force, 

 = 0 will continue to
be the main aspect of intereset due to the final application of the contactless hull grooming device
described in Chapter 3.

Another shortcoming of the research presented here is that only a portion of the radial length
was captured. The relative pressure at the outlet in the experiment could not be confirmed. It was
assumed that the pressure had reached 0 gauge pressure at the outlet, but looking at the raw PTV
data before descretization in Figure 4.18 a range of pressures measured in the experimental window
contracts from 20 mm to 55 mm before spreading out at the end of the experimental window.
Discretization did result in an average pressure with minimal fluctuation in the last portion of the
radial outflow. Having a complete pressure profile curve would allow for the force to be accurately
calculated through integration. Reducing the size of the pad is not recommended since a shallower
experimental window would occur at equilibrium with no applied Force, 

. Holding the gap with
some 

 would still be of some interest. Keeping the current size of the Bernoulli pad, the fluid
flow along entire diameter can be captured by stitching data from multiple data sets from several
different experimental windows. This can be accomplished without moving the cameras or laser
volume if the radial outflow in the horizontal is the focus, and the BPA can still move laterally as in
the original experimental setup as seen in Figure 4.2. The resulting pressure versus radial location
can be integrated to determine the total force generated by the flow field at specific parameters and
operating conditions.

With the recommended improvements to the PTV setup, the larger variety of acquired data will
serve as a better benchmark for refining the CFD model. With only the velocity field and pressure
gradient from the experiment, there was no efficient way to investigate the Reynolds-averaged

86

Navier-Stokes (RANS) equations and how they impact the region of separation and reattachment.
Another turbulent flow simulation method should also be investigated in future studies, such as
Scale Resolving Simulations (SRS). The main disadvantage of SRS is how computationally ex-
pensive the modeling is since both high grid resolution and small times steps are required for this
inherently unsteady method.

87

CHAPTER 5

CONCLUSIONS

The oceans cover 71% of the Earth’s surface which the international seaborne trade navigated to
transport 11 billion tons of cargo in 2018 [80]. As stated in the introduction, optimal fuel efficiency
can be achieved with a clean hull of transport vessels. This results in a cost savings and a reduced
carbon footprint. The other important aspect to consider is that every vessel has the potential to
transport invasive species, which is why it is essential to prevent biofouling in order to stop these
biological hitchhikers from spreading further.

The lessons learned from this research is not just for the ocean environment and the US Navy.
Increasing the efficiency of any system that is submerged in salt or fresh water is significant. Even
stationary systems, such as a power plant, highly benifits from biofouling prevention. For mobile
surfaces that experience submersion, such as a boat or vessel, cleaning reduces or eliminates the
unintentional transportation of invasive species to another waterway. The state of Michigan has
been dealing with the consequences of the non-native zebra mussel (Dreissena polymorpha) that
have been first detected in Lake St. Clair in 1988 and found to be established in all of the Great
Lakes by 1990 [81]. The zebra mussel was indigenous to the lakes of southern Russia and Ukraine,
but has spread globally as a result of discharged transoceanic ship ballast water contaminated with
mussels [81]. Juveniles tend to settle on surfaces that experience flow rates less than 1.5 m/sec
[82]. Once established, they can grow so densely that they block pipelines and screens; resulting
in clogged water intakes of hydroelectric companies, municipal water plants, and other industries.
Zebra mussels causes accelerated corrosion of concrete and steel, which impacts structural integrity
[81]. For a vessel of any size, zebra mussels can encrust the hull which results in significant drag or
restrict the passages of the engine cooling system which results in overheating [81]. The national
economical impact has been estimated to be $1 billion per year [83], with the cost of damage and
management of zebra mussels in the Great Lakes alone exceeds $500 million per year [84, 85].
Another side effect of invasive species is how they impact ecosystems by disrupting the food chain

88

and out-compete native species.

Since the gap between prevention and removal of biofouling organisms is continuous, the key
is early and continuous attention. A custom solution by combining several or more biofouling
prevention tactics holds the most promise long term. As part of the maintenance and repair
schedule, there are three categories: passive (such as the fouling-release paint that was used in
Chapter 2), active (such as the contactless grooming proposed by this dissertation operated by a
SCUBA diver), and active but autonomous (such as developing the contactless grooming device into
a autonomous robot). The biofouling mitigation schedule is recommended to utilize more active
tools and approaches during the peak of the local biofouling season.
Investigating larger sizes
of Bernoulli pads with flexible material or an array of Bernoulli pads to conform to underwater
surfaces with noticeable curvature would increase the power and versatility of the non-contact
grooming device. The geometry of the stem and pad holds the most potential for creating the
optimal fluid flow field, but from early studies there are often trade-offs. Both the force of suction
and the size of the levitation window can be increased by using a pintle to help turn the flow from
axial to radial, but at the cost of reducing the peak wall shear as seen in Figure 2.11.

Directly impinging flow with out being confined has demonstrated successful removal of bio-
fouling while the adhesion strength is still under the threshold of the peak wall shear stress generated
by the flow [41, 68, 56]. When compared to the confined radial outflow approach in this research,
fluid power of the unconfined radial outflow is reduced due to entrainment of the ambient water.
The other benefit the Bernoulli pad has is that the device will automatically self equilibriate the
gap as it is moved across a surface. The main limitation to the Bernoulli pad approach are surface
features that protrude more than the gap height or inaccessible areas of a ship such as the side
thrusters. The bulbous bow and stern have the most extreme variances in geometry. Creating an
array of Bernoulli pad devices would increase the effective surface area cleaned, and would allow
for more physical flexibility even with rigid pads while providing stability when cleaning portions
of the hull with extreme variances. If one pad of the array reaches the unstable equilibrium point,
the pads that remain levitating can help re-orientate the dislodged pad to find the stable equilibrium

89

point and continue grooming operations. An aspect of operation that has potential to be beneficial
or detrimental to the groomed surface is when cavitation is induced with higher flow rates. Inves-
tigating caviation with another field test study would provide insight to the durability of both the
device and the groomed surface.

Physically constraining an impinging jet to a confined gap has several interesting attributes.
The corner geometry determines how quickly the axial flow is turned into radial flow. There also
is a flow separation induced at this corner, which does reattach downstream based on the main
operating conditions of flow rate and gap height. The larger the outer diameter, the more room
there is for reattachment. With this in mind the gap can be made larger before levitation ceases
when the unstable equilibrium point is reached. In between the separation and reattachment point
on the surface of the pad, lies the annular recirculation bubble. This region . Not only is the cross
sectional area reduced from the jet diameter (
(
/2)2) to the first instance of the cross-sectional
area in the gap (
Ò
/2), but the presence of the recirculation bubble artificially reduces the cross-
sectional area that the majority of the flow passes though after the corner as seen in Figure 5.1. The
maximum velocity in the entire fluid flow filed can be found in this specific region. The maximum
wall shear stress on the surface parallel to the pad correlates directly to this maximum velocity. The
jet still generates a stagnation region where the maximum pressure and minimum velocity of zero
occur. After the axial flow turns into radial flow, the velocity also quickly diminishes with respect

Figure 5.1: Modeling a water Bernoulli pad (
 = 31.75 mm, 
 = 200 mm) with a mass flow rate
of 1.5 kg/s resulting in an equilibrium gap height of 0.9 mm. Only a portion of geometry is shown
from 
 ≈ 10 mm to 50 mm. The top contour plot shows the radial velocity in a torrid-shaped fluid
space, if the flow did not have axial flow to turn the corner. The bottom contour plot shows how the
recirculation bubble (indicated by the region with negative radial velocity) constricts the turning
flow to achieve a higher values of velocities near the corner.

90

to 
 due to increasing cross-sectional area in the gap. The flow does recover after the separation
bubble, and becomes purely radial as seen in Figure 5.1.

Since wall shear stress is the critical feature of this Bernoulli pad device for contactless grooming
applications, additional experiments using a hot film sensor to find the wall shear profile generated
along 
. The hot film probe can be mounted from the back-side of a test plate with the surface
flush to the front-side that would be parallel to the pad.
Including a force torque sensor to
ensure equilibrium, where 
 = 0, and a laser measurement device to determine the gap height at
equilibrium conditions. A flow rate sensor can be incorporated to measure fluid power as defined
in Chapter 2. Electrical power to the pump should also be monitored and recorded in real-time.
There is potential to reverse-engineer a wall shear stress profile, by creating the desired wall shear
stress profile first to steer the design and operating conditions. Only the center of a pad can be
designed this way since there is no effective way to counter the increasing cross-sectional area in
the radial direction without affecting the desired clearance of the pad relative to a surface.

91

APPENDIX

92

APPENDIX

YEAR 2 FIELD TEST STUDY DETAILS AND COMPLETE COLLECTION OF RAW

IMAGES USED FOR IMAGE ANALYSIS

Table A.1 is a legend for the tables A.2 to A.11. The images are arranged in pairs where the top
picture is the ‘before’, while the bottom is the ‘after’ as seen in Figure A.1. In the subsequent pages,
note that position 4 was left untouched for image processing, while positions 1,2,3 are the sampled
plates where little circles free from biofouling were the result of sample collection as described
earlier, in Chapter 3.

Table A.1: Detailed legend for the following tables displaying all photos used in image analysis.
The field study was initiated on a Wednesday in order to consistently distribute the labor throughout
the week.

The Garolite is originally slightly transparent, as seen in the first few weeks after the initial
submersion. The vertical grey portion in the middle of the plates are the mounting tabs that fit
in both the submersible rig and the grooming frame. The vertical red potion is an intermediate
gasket material between the back of the plate and additional standalone tabs as seen on the top
of Figure 3.19. The tab that was physically and permanently mounted onto the back of the plates
using stainless steel hex drive flat head screws (82 Degree Countersink Angle, 2-56 Thread Size)
flush with the front surface and stainless steel locknuts. The diameter of the screw heads was 5


and were not included in the image analysis as seen in Figures A.2 and A.3 generated by the code
written and run in MATLAB. If there was glare from light or overhanging algae that grew from the
head of the screw, this code had the flexibility to make a polygon with more than 4 points to omit

93

Figure A.1: Illustration of the location of each of the 4 duplicate plates and how the group looked
before and after scheduled grooming on that day in the proceeding tables.

areas that would skew the 
+ number, also referred to as the measure of cleanliness. The original
pictures were 1728 by 1152 pixels. The polygon made manually on the fourth plate ended up being
only 3 to 6% of the original amount of pixels depending on how much the mounted camera was
zoomed in.

94

Figure A.2: Picture taken of Garolite plates after grooming, with points hand selected to analyze
the pixels within the resulting polygon.

Figure A.3: A close up of the generated polygon of the plate that was never subject to biological
sampling. Drop down menus for grooming details were available on the top left. The coating type
can be selected on the top middle. The "continue" button on the top right proceeds to the next full
image to repeat the point selection process.

95

Table A.2: 3× Garolite.

96

Table A.2 (cont’d)

97

Table A.2 (cont’d)

98

Table A.2 (cont’d)

99

Table A.2 (cont’d)

100

Table A.2 (cont’d)

101

Table A.2 (cont’d)

102

Table A.3: 2× Garolite.

103

Table A.3 (cont’d)

104

Table A.3 (cont’d)

105

Table A.3 (cont’d)

106

Table A.3 (cont’d)

107

Table A.3 (cont’d)

108

Table A.3 (cont’d)

109

Table A.4: 1× Garolite.

110

Table A.4 (cont’d)

111

Table A.5: 0.5× Garolite.

112

Table A.6: Control Garolite.

113

Table A.7: 3× Intersleek.

114

Table A.7 (cont’d)

115

Table A.7 (cont’d)

116

Table A.7 (cont’d)

117

Table A.7 (cont’d)

118

Table A.7 (cont’d)

119

Table A.7 (cont’d)

120

Table A.8: 2× Intersleek.

121

Table A.8 (cont’d)

122

Table A.8 (cont’d)

123

Table A.8 (cont’d)

124

Table A.8 (cont’d)

125

Table A.8 (cont’d)

126

Table A.8 (cont’d)

127

Table A.9: 1× Intersleek.

128

Table A.9 (cont’d)

129

Table A.10: 0.5× Intersleek.

130

Table A.11: Control Intersleek.

131

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