1. Oscillating Hydrofoil Prototype
Field-Testing and CFD
Comparisons
by
Aryssa Medina
B. S, Brown University, Providence, RI, 02912
A Dissertation submitted in partial fulfillment of the
requirements for the Degree of Bachelor of Science
in the School of Engineering at Brown University.
Prepared under the direction of Prof. Jennifer Franck, advisor.
Providence, Rhode Island
May 2016
2. Acknowledgements
I would like to extend my appreciation and gratitude to Dr. Jennifer Franck,
my thesis advisor. Dr. Franck has acted as my constant advisor, teacher mentor
during my last two years at Brown. She has always had great patience and given
support throughout my research and thesis development. I would not have been
able to complete my work without Dr. Franck’s guidance and knowledge in the fluid
mechanics field.
I would also like to show my appreciate to the team members of Leading Edge and
BluSource Energy who envisioned and designed the Oscillating Hydrofoil Prototype
I device. I would like to especially thank Tom Derecktor and his knowledge and
guidance during the testing-rig design and prototype assembly.
In addition, I would like to thank the many teachers and professors throughout
my career who have given me guidance and encouragement to fulfill my academic
goals. Last but not least, I would like to thank my family and friends for believing
in me and supporting me.
ii
3. Contents
Acknowledgements ii
1. Introduction 1
1.1. Project Background 1
1.2. Hydrokinetic Energy Harvesting with Turbines versus Hydrofoils 1
1.3. Leading Edge - Brown University’s Oscillating Hydrofoil Project 5
1.4. Evaluating the Performance of Prototype I 6
1.5. Organization of Thesis 8
2. Design and Assembly of Prototype I 9
2.1. Designing and Constructing the Leading Edge Prototype I Device 9
2.2. Design and Modification of the Testing-Rig for Prototype I 10
3. Field-Testing and Prototype I Device Results 12
3.1. Field-Testing Methods 12
3.2. Field-Testing Results 13
4. Methods 16
4.1. OpenFoam as a Case Study Tool 16
4.2. Case Study Parameters 16
4.3. Computational Method 16
4.4. Mesh Generation 17
4.5. Resolution 19
5. Results 22
5.1. Case Studies 22
5.2. Single Foil Geometry 22
5.3. Stacked 2 Foil Configuration 24
6. Conclusions 28
iii
5. Abstract of “Oscillating Hydrofoil Prototype Field-Testing and CFD Comparisons”
by Aryssa Medina, Brown University, May 2016
This paper discusses several CFD simulation comparisons and field-tests that
Leading Edge collected for their Oscillating Hydrofoil Prototype I device. This study
includes comparisons of efficiency, power, and the forces associated with the Proto-
type I’s hydrofoil geometry and foil configurations. In previous simulations a single
elliptical geometry was used to simulate the physical hydrofoil which would be de-
signed and placed on Prototype I. However, this model geometry did not accurately
describe the resulting hydrofoil that was used on the Prototype I device.
After field-testing completed, clear differences in CFD case studies, ellipse flume
data and field-test results were observed. Determining if these discrepancies caused
inaccuracies and further analyzing the CFD field-testing efficiency differences, which
appeared at 80◦
pitch, will lead to a better understanding of the hydrofoil device. In
addition, this analysis will equip Brown researchers and engineers with the proper
knowledge and tools to more accurately design and predict the hydrokinetic device’s
behavior as development is continued. This understanding and ability to characterize
the flow physics in the Prototype I device will also aid researchers and engineers in the
design, fabrication, and testing of prototype II, which is currently being developed.
The results from the single biconvex versus ellipse comparison study indicated
that foil geometry does influence efficiency data trends at higher reduced frequency
values. Both CFD efficiency results were in agreement for lower frequency ranges.
Differences between the cases arose at higher frequencies ranging from 0.1-0.16 for
70◦
pitch and 0.14-0.16 for 80◦
, when the single biconvex case produced lower efficiency
values and a steeper declining efficiency trend for both 70◦
and 80◦
pitch. This decline
in efficiency more accurately predicted the field-test results. The results of the stacked
2 foil configuration comparison study also indicated that foil configuration influences
the flow physics of the prototype I device. Once again, steeper declining frequency
trends were produced for both 70◦
and 80◦
pitch. A increase in efficiency was also
v
6. apparent in the 70◦
pitch case due to constructive interference between the top and
bottom foils. More importantly, at 80◦
pitch, there was a complete shift in peak
efficiency from 0.13 to 0.12. This shift and the more dramatic efficiency declines at
higher frequencies resulted in a much more accurate optimal reduced frequency value
with respect to the field-test data, which was determined to be approximately 0.11.
7. 1. Introduction
1.1. Project Background. It is universally acknowledged that the future global
economy will consume increasing amounts of energy to meet rising energy demands
observed in countries such as India and China. Currently, the world is searching for
reliable and renewable energy sources to help meet these demands. One viable option
is tidal and river flows, which offer a large amount of kinetic and potential energy.
1.2. Hydrokinetic Energy Harvesting with Turbines versus Hydrofoils.
The first hydrokinetic turbines were modeled after wind turbines and many radial
turbines contain the same designs to this day. They are very expensive to fabricate
and install and are very location specific. A hydrokinetic turbine’s placement is
limited by their required flow speeds, their large size and the shallowness of waterways
[1-2]. Radial turbines can also restrict access to open water; they can change tidal
levels, negatively impact the marine life and environment, and capture debris drifting
in waterways [3].
Other hydrokinetic turbines include the Gorlov helical turbine [4], which utilizes
curved foil blades mounted longitudinally to a rotating shaft [Figure 1(b)]. There
have also been many attempts to recreate the Savonius turbine [Figure 2] for tidal
energy extraction [5]. This turbine is a drag-type device, which utilizes two scooped
blades rotating about a central rotating shaft.
Another hydrokinetic turbine design [Figure 3] is called the Flipwing pivoting
turbine [6]. This device uses pivoting foil blades that revolve around individual axles
of rotation, which all revolve about a central rotating shaft. Each of these turbines
exhibits the same problematic chopping motion and placement issues as described for
the common radial turbine. More importantly, the most prominent issue that all of
these hydrokinetic devices have is the fact that they are all based on wind turbine
designs. Water is 1000 times denser than air; therefore the same turbine designs are
plausible but raise a more difficult engineering feat for tidal wave energy extraction.
1
8. (a) Example of traditional radial water turbine
(13).
(b) Example of Gorlov water turbine (14)
Figure 1. Examples of helical and radial turbines.
Figure 2. Savonius single-stage turbine scheme: a) elevation view and
b) plane view [5]
As an alternative to the rotation-based turbine, oscillating hydrofoil turbines uti-
lize hydrofoils, which undergo a combined heave-pitch motion about their individual
pitching axis. This thesis explores the efficiency and performance of an oscillating
hydrofoil turbine. An oscillating hydrofoil turbine has a very different motion when
compared to traditional radial turbines. Radial turbines consist of foils originating at
2
9. Figure 3. Schematics depicting the motion of a single Flipwing in
reference to a fixed base [11].
one point then protruding radially outward [Figure 1(a)]. However, oscillating hydro-
foil turbines consist of foils that periodically pitch and heave resulting in an upstroke
and downstroke [Figure 4]. This motion is represented as:
H(t) = h sin(ωt) (1)
θ(t) = α cos(ωt) (2)
where h and α are the heave and pitch amplitudes respectively and ω is the oscillation
frequency.
Figure 4. Depiction of the motion of a hydrofoil during an oscillation [9].
In order to generate power, the device’s hydrofoils must have positive lift forces,
which contribute to the power of the overall system. Torque forces can also contribute
to the power, however, harnessing the power from torque is more challenging from a
design perspective. Optimizing these forces lead to optimal power extraction. The
3
10. instantaneous power equation for a single hydrofoil is expressed as
P(t) = Py(t) + Pθ(t) = Y (t)Vy(t) + M(t)Ω(t) (3)
where Py and Pθ depict the heave and pitch power contributions, respectively. Y
represents the lift force exerted on the hydrofoil, and Vy is the instantaneous heaving
velocity. M is the torque about the pitching axis and Ω represents the instantaneous
pitching angular velocity.The overall efficiency of a single hydrofoil can be calculated
using the equation below:
η = P/0.5ρU3
A (4)
where P is the average power for the cycle, ρ is the density of the water, U is the free
stream velocity, and A is the area swept by the foil.
This sinusoidal pitching and heaving motion of amplitude 50◦
-80◦
and where c is
the chord length of the foil, combined with a π/2 phase difference has been previously
validated to obtain the most optimal maximal power-extraction efficiency for a low
velocity oscillating foil based on a study preformed by Mckinney and DeLaurier [7].
This study investigated the influence of the pitch and heave phase difference with
respect to power extraction from an airflow. An analytical and experimental study
was conducted on a windmill which utilized a harmonically oscillating wing. The
analytical case study was performed using unsteady-wing aerodynamics from aeroe-
lasticity and the results were used to aid in the design of an experimental model.
The results concluded that the wingmill was capable of efficiencies comparable to
traditional radial turbines.
Mckinney’s and DeLaurier’s investigation was later supported by K.D. Jones,
K. Lindsey and M.F. Platzer [8] who conducted numerical simulations (panel-code
and Navier-Stokes simulations) on cases of single oscillation airfoil operation in the
power-extraction regime. This study also consisted of experimental components. The
modeled generator consisted of tandem wings that oscillated in a combined pitch-
plunge motion with a 90◦
phase difference. Two-dimensional inviscid and viscous
flow models were used to predict the flow fields and power transfer in the analytical
4
11. studies. As a result, comparisons were made between the measured and predicted
power outputs.
1.3. Leading Edge - Brown University’s Oscillating Hydrofoil Project.
A group of Brown scientists, engineers, ecologists and entrepreneurs (Leading Edge)
have been working to capture tidal energy using a hydrofoil device with funding from
Advanced Research Project Agency-Energy (ARPAe). In conjunction with laboratory
experiments in a water flume, computational fluid dynamics (CFD) case studies,
and theory investigations, the Leading Edge team launched their first prototype and
conducted field testing in the summer of 2015.
This hydrokinetic device, or prototype I, exhibits special features, which set it
apart from other conventional tidal energy devices such as the radial turbine. This
oscillating hydrofoil device has been engineered to capture the kinetic energy produced
by tidal waves. The device utilizes a pitching and heaving motion where two offset
hydrofoils will move out of phase allowing for the foil to move through the top and
bottom dead centers of their sinusoidal motion. This phase difference between the
pitching and heaving motions is held constant at a value of π/2.
The Leading Edge oscillating hydrofoil device takes advantage of the vortices that
shed off of the leading and trailing edges of each hydrofoil. At high angles of attack,
the boundary layer becomes detached at the leading edge and forms a ”Leading Edge
Vortex”. Inside the core of these vortices low-pressure regions occur. These pressure
regions create gradients that produce an increase in lift forces. The extra lift provides
a boost in power and performance, and thus this fluid phenomena has inspired the
team name ”Leading Edge”
Other key features of the Leading Edge hydrokinetic device include fewer gear-
boxes, as compared to radial turbines, which reduces the probability of failure. The
device’s modular design also allows for efficient energy harnessing in a wider range
of environments including shallow and low free-stream velocities. Due to a lower tip
speed or foil velocity, the expected disturbance to the environment and wildlife is
minimal. It is has also been predicted that an array of these devices will harness
5
12. additional energy as downstream hydrofoils take advantage of the wake created by
vortices shedding off of the upstream foils.
1.4. Evaluating the Performance of Prototype I. The results of the design,
fabrication and field-tests of the first Leading Edge hydrokinetic prototype resulted in
several weeks of data collections. These data collections consisted of recorded values
for the heave and pitch settings, resistance settings, test time, generated voltage, gen-
erated current, and the encoder frequency. Adjusting the encoder frequency, allowed
for the adjustment of the reduced frequency of the hydrofoils. The reduced frequency
is defined as follows:
f∗
= fc/U (5)
where f is the flapping frequency, c is the chord length of the foil, and U is the
free-stream velocity. This nondimensionalized frequency is used in order to compare
results across many length scales and flow velocities. These length scales ranged from
the 10cm chord flume model to the 23.97cm chord prototype tested at 2.1m/s. The
CFD, flume and prototype device also operated at different Reynolds numbers. CFD
simulations utilized Re=1000, flume tests used Re=50000 and field-tests were taken
with a Reynold’s number of approximately 1million.
In order to predict the flow physics and power efficiency versus reduced frequency
results for the prototype I device, multiple CFD simulations were conducted using a
10% thick elliptical foil geometry displayed in Figure 5(a). However, the geometry
that was manufactured and implemented on the prototype I device was a 15% bi-
convex foil shape [Figure 5(b)]. This geometry was a result of both manufacturing
and structural limitations. After all field-tests were completed there were significant
(a) Single foil ellipse geometry used for initial CFD
simulations.
(b) Single foil biconvex geometry used for prior
to testing CFD simulations.
Figure 5. Foil geometries used in CFD simulations.
6
13. discrepancies observed in the original flow physics predictions. The single ellipse foil
CFD case studies and flume test data did not thoroughly describe the field-test re-
sults. These discrepancies could have resulted from Reynolds number differences, foil
configurations, foil geometry shapes, 3d effects or turbulence effects in the freestream.
The goal of this thesis is to help determine, through CFD, if these discrepancies can
be better explained with more accurate CFD case studies. In particular, these studies
will utilize the field-test biconvex foil geometry and a stacked 2 foil configuration [Fig-
ure 6]. Furthermore, this investigation will focus on case comparisons between field
data, flume tests, previous single foil ellipse predictions and single foil biconvex sim-
ulations. In addition, another case comparison will involve the field data, single foil
biconvex and stacked 2 foil biconvex case studies. Determining if these two variables
play a role in these efficiency discrepancies could play a significant role in the design
of future prototypes and help us better understand the field-test data collected from
the summer of 2015 and play a significant role in the design of future prototypes.
4c
Figure 6. Stacked 2 foil configuration with biconvex foil geometry.
7
14. 1.5. Organization of Thesis. The outline of this thesis is as follows:
• chapter 2 will discuss the Design and Assembly of Prototype I
• chapter 3 will discuss Field-Testing and Prototype I Device Results
• chapter 4 will discuss Computational Methods
• chapter 5 will discuss Results
• chapter 6 will discuss Conclusions
8
15. 2. Design and Assembly of Prototype I
2.1. Designing and Constructing the Leading Edge Prototype I Device.
The Leading Edge Hydrokinetic Prototype I device is a 1kW unit that was designed to
harness tidal energy while being mounted to a Sylvan 1989 pontoon boat with a flow
speed of about 2.1m/s. The Figure 7 displays a CAD model of the prototype I device
designed and constructed by the Leading Edge team in conjunction with BluSource
Energy. Figure 7 also indicates several key features of the device. Prototype I is a
Figure 7. CAD Model of Prototype I Device and key features.
robust mechanism [Figure 8] which utilizes multiple belts, gears, and cables to oscillate
two sets of hydrofoils offset by a phase difference of ninety degrees. The device consists
of a pair of mechanically coupled hydrofoils, which operate at a ninety degree phase
difference Figure 2.1. This mechanical couple [Figure 8(a)] drives the pitching motion
by using the heaving motion of the hydrofoils. The hydrofoils have a chord length
of c=0.24m and an effective span of b=1.026m. The manner in which the hydrofoils
were coupled with the phase difference allows the device to overcome dead spots in the
power cycle, located at the top dead center and bottom dead center of the operation
cycle. This configuration also allows the device to begin operation unassisted. An
9
16. adjustable resistive load is used to control the operating frequency of the hydrofoils
at a specific speed. The electric generator [Figure 8(b)], also connected to a resistive
load, is driven by the hydrofoils’ oscillation. A pulse width modulation is used to
adjust the resistive load based on a 0-5V DC input signal. The Prototype I available
heave amplitude settings include 1c, 1.25c, and 1.5c. The available pitch amplitudes
consist of 70◦
and 80◦
. It is important to note that these values were determined
through multiple flume and CFD computations to provide close to optimal power
extraction. End plates were also considered, tested and implemented in order to
further increase power extraction.
(a) CAD model of the prototype I device and
its mechanical coupling system.
(b) Prototype I Device and its generator.
Figure 8. CAD model and prototype I of oscillating hydrofoil device.
2.2. Design and Modification of the Testing-Rig for Prototype I. The
deployment mechanism used for field-testing the Prototype I device was a 1989 Syl-
van pontoon boat [Figure 9] modified by BluSource. A moon pool was cut into the
deck and lined with aluminum and a subframe was installed for reinforcement. The
subframe was an essential modification in order for the boat to be capable of housing
10
17. the 600lbs Prototype I device. A splash guard and aluminum housing was also con-
structed to protect the deck and power conversion technology. A quadrant and winch
system was installed and used to raise and lower the Prototype I device for storage
and testing purposes. Railing and safety lines were also added and the pontoon deck
was sanded and repaired before field-testing commenced.
Figure 9. Prototype I and Testing-Rig.
11
18. 3. Field-Testing and Prototype I Device Results
3.1. Field-Testing Methods. During field-testing, the device was lowered to a
90◦
angle below the boat deck. The boat was then driven on specific routes and at a
range of suitable speeds for testing. A speedometer was also installed on the driver’s
console and enabled scientists to control the relative flow speed of water and retrieve
adequate testing data. A sonar detector was also used to ensure the device was not
lowered and tested in shallow waters.
During data collection, an incremental encoder was used to determine the position
and frequency of the hydrofoils during their oscillation cycles. An AcuDC 243 power
meter was used to measure the generated voltage and current. The relative flow
speed of the water on the device was recorded using the Nortek Vectrino field probe,
which is an acoustic Doppler velocimeter. The signals from these instruments were
monitored and recorded with a National Instruments USB-6341 device and processed
using MATLAB. Data was collected at a rate of 100Hz.
Each test run was conducted in a series of steps. After the device was properly
deployed, the boat speed was gradually increased with no load applied on the gen-
erator. Once the speed hit 0.5 m/s, the device began oscillating. The boat’s speed
is then driven within the range of 1-2.1 m/s. During that time, the 0-5V DC signal
controlling the pulse width modulated resistance is increased in order to incremen-
tally increase the generator load and adjust the reduced frequency of the hydrofoils.
These trials were held for 15-20 cycles for each frequency.
The heave and pitch settings, resistance settings, test time, generated voltage, gen-
erated current, and the encoder frequency were recorded for each trial. The stream-
wise, cross, and pitch flow speeds were recorded, as well as the water temperature
during the test. The three prototype I heave amplitudes that were tested included
1 chord (c) length 1.25c, and 1.5c. The tested pitch amplitudes included 70◦
and
80◦
. Tested flow speeds were within the range of 1-2.5m/s. During each test, two
important parameters were held fixed, the heave amplitude and the pitch angle. How-
ever, the resistive load was varied for each constant flow speed, which is equivalent
12
19. to varying the oscillating frequency of the hydrofoils. The data was compiled into a
set of plots depicting the efficiency versus the reduced frequency.
3.2. Field-Testing Results. The average power output for each cycle was cal-
culated by numerically integrating the product of the generated voltage and generated
current. The following plots depict the results of field-testing conducted during the
month of August in 2015 in comparison with flume testing and previous CFD case
studies. Figure 10 displays the power-extraction efficiency versus the reduced fre-
quency obtained experimentally in a scaled-down single foil ellipse version of the
prototype I device in the flume. The figure also illustrates each heave and pitch
configuration field-tested on the prototype I device and the results acquired in pre-
vious ellipse CFD simulations for 70◦
and 70◦
pitch. Note that the flume tests were
conducted at a Reynold’s number of Re=50000, field tests were run at a Reynold’s
number of approximately 1million and CFD simulations were computed at a Reynold’s
number of Re=1000.
Figure 10(a) Figure 10(b) both depict ellipse CFD and flume efficiency data agree-
ment. Flume data, at 70 degrees pitch, displayed a peak efficiency value of approxi-
mately 0.26 at a reduced frequency value of about 0.13. For both pitch amplitudes,
ellipse CFD and flume results indicated similar efficiency trends, peak efficiency val-
ues, and optimal reduced frequencies as a result of both the flume and CFD utilizing
an elliptical geometry. The results of the field-test data produced an optimal effi-
ciency of η = 17% was reached at h/c = 1, 70◦
pitch and f∗
= 0.13 without end-
plates. Field-tests with endplates resulted in an optimal efficiency of approximately
η = 23% was reached at h/c = 1, 70◦
pitch and approximately f∗
= 0.13. Overall,
higher efficiencies were achieved at pitch amplitudes of 70◦
compared to 80◦
. Also,
heave amplitude values played a key role in influencing peak efficiency values. An
estimated 4% increase in peak efficiency values was observed for the 1c versus 1.25c
tests at 70◦
pitch.
While comparing elliptical foil data (flume and CFD) with field-tests, it was ev-
ident that there were overall decreases in efficiency values, which is to be expected
13
20. due to the greater mechanical losses on the prototype I device compared to flume
tests and CFD, which did not account for frictional losses. It is also apparent that
flume data in Figure 10(b) and Figure 10(d) display very different efficiency trends
in comparison to prototype I field testing at both 1c and 1.25c heave amplitudes. At
1c heave and 80 degree pitch, ellipse flume data indicated a peak efficiency value at
approximately 0.15 reduced frequency. Field-tests concluded a peak efficiency value
at approximately 0.1 reduced frequency. Further, in the higher frequency range, el-
lipse flume efficiency values leveled off but field-tests displayed clear and relatively
steep efficiency decreases. Peak efficiency for the ellipse CFD data, at 70◦
pitch Fig-
ure 10(a), was obtained at a reduced frequency of approximately 0.12. This value is
very similar to the previously stated field-testing optimal frequency value of 0.13.
However at 1c heave and 80◦
pitch, as frequency increased, there were evident
differences in peak efficiency values and corresponding frequency values between pre-
diction cases and field-testing results. Flume and CFD data begins to show efficiency
values leveling off. CFD predicted a platueing efficiency of approximately 0.27 and
Flume depicted a very slow decrease in efficiency at higher frequencies. Test data
displays clear and dramatic efficiency decreases at higher frequencies. As previously
mentioned, these losses and differences could have resulted from Reynold’s number
differences, foil configurations, foil geometry shapes, 3d effects or turbulence effects
in the freestream. The goals of this thesis is to help determine, through CFD, if the
biconvex foil geometry and foil configuration differences contribute to the discrepan-
cies illustrated in Figure 10. In order to evaluate these differences, this thesis will
focus on the field-test kinematics of 1c at 70◦
and 80◦
pitch.
14
21. f*
0.04 0.06 0.08 0.1 0.12 0.14 0.16 0.18 0.2
Efficiency
0
0.05
0.1
0.15
0.2
0.25
0.3
Efficiency vs. f* Reduced Frequency, 1c Heave 70 deg
(a) Kinematics: 1c Heave, 70 Pitch Amplitude
f*
0.04 0.06 0.08 0.1 0.12 0.14 0.16 0.18 0.2
Efficiency
0
0.05
0.1
0.15
0.2
0.25
0.3
Efficiency vs. f* Reduced Frequency, 1c Heave 80 deg
(b) Kinematics: 1c Heave, 80 Pitch Amplitude
(c) Kinematics: 1.25c Heave, 70 Pitch Ampli-
tude
(d) Kinematics: 1.25c Heave, 80 Pitch Ampli-
tude
Figure 10. Efficiency vs. f* Reduced Frequency data plots: light blue
data represents test data without endplates, dark blue data corresponds
to test data with endplates, green data represents ellipse flume data,
and the red data illustrates the ellipse CFD data
15
22. 4. Methods
4.1. OpenFoam as a Case Study Tool. This analysis utilized the Open-
FOAM, a C++ toolbox for the development of customized numerical solvers, and
pre-/post-processing utilities for the solution of continuum mechanics problems, in-
cluding computational fluid dynamics (CFD), to study the power-extraction efficien-
cies of hydrofoils.
4.2. Case Study Parameters. The first case study began with a single-foil
resolved mesh frequency sweep from 0.08-0.16 at 70◦
and 80◦
pitch angles with a 1c
heave amplitude. The second case study involved a stacked 2 foil resolved mesh over
the same frequency sweep with a 1c heave amplitude. Case studies with a 1.25c heave
amplitude were not conducted because the same efficiency trends were depicted in
the 1c heave amplitude cases. It was therefore, deemed sufficient enough to focus on
the 1c heave amplitude case studies.
Fixed parameters included the foil separation distance of 4c, the foil chord length
of 1c, a phase difference of 90◦
, geometry, and the three pitch and heave configurations
built into prototype I. The pitch and heave angles were varied and a frequency sweep
was conducted in order to obtain a range of efficiency values. Several kinematic
parameters were varied during the CFD case studies, which coincide with the first
two row values, listed in the following table, which displays all CFD simulations
conducted in this analysis.
h/c alpha Foil Configuration
1 70 single
1 80 single
1 70 stacked
1 80 stacked
4.3. Computational Method. The OpenFoam code solves the complete un-
steady incompressible Navier-Stokes equations on a finite volume mesh using a direct
numerical simulation. A dynamic mesh algorithm was also implemented in order
16
23. to account for the motion of the hydrofoil in a uniform freestream [12]. It is also
important to note that CFD simulations were performed at a Reynold’s number of
Re=1000 in order to ensure a reasonable computational runtime. This Re value was
also chosen based on previous CFD results, which have shown little difference be-
tween 1000-50000. To analyze the CFD, forces from pressure and viscous stresses are
calculated to obtain lift, drag and the moment on each foil as a function of time.
Pressure, velocity and span-wise vorticity can also be plotted as a function of time in
Tecplot.
4.4. Mesh Generation. Gmsh was used to generate the necessary meshes for
this analysis. Gmsh is a 3D finite element grid generator with a build-in CAD engine
and post-processor. It is a user-friendly meshing tool with parametric input and
advanced visualization capabilities. Gmsh contains four modules including geometry,
meshing, a solver and post-processing.
All single foil cases were contained in a 70cx70c outer boundary with the foil in
the center in order to minimize the influence of the outer computational domain on
the forces and moments. Stacked two foil cases were contained in a 74cx70c outer
boundary There was also an inner rectangle immediately surrounding the foil, in which
the mesh resolution was significantly increased with respect to the outer boundaries.
The inner mesh dimensions for the single foil studies are depicted in Figure 11.
A two-foil stacked resolved mesh [Figure 12] was also created in order to more
accurately model the Leading Edge Prototype I configuration. This mesh was created
by stitching together two single meshes and increasing the resolution between the foils
to ensure that vortex interactions are fully resolved.
17
25. 4.5. Resolution. The resolution of a mesh significantly influences the results of
any CFD case study. The less refined a mesh is, the more information lost, or the less
accurate the results. Taking this into consideration, a more refined mesh was created
for the single foil configuration to ensure that mesh quality was excluded as a cause
for any discrepancies observed in the results. After a number of test cases were run at
70◦
and 80◦
pitch using both the refined and unrefined meshes, it was concluded that
there were slight differences in efficiency values [Figure 13]. At a pitch amplitude of
70◦
there was a 0.05-1.54% difference range. At a pitch amplitude of 80◦
there was
a 0.53-3.46% difference range. These differences and previous CFD simulations, lead
the conclusion that the more refined mesh [Figure 14] was adequate for this thesis
analysis. However, in order to do a full mesh resolution study, it is recommended
that one or more additional mesh refinements should be tested to verify the selected
refined mesh.
f*
0.08 0.09 0.1 0.11 0.12 0.13 0.14 0.15 0.16
Efficiency
0.16
0.18
0.2
0.22
0.24
0.26
0.28
Efficiency vs. f* Reduced Frequency, 1c Heave 70 deg
(a) Kinematics: 1c Heave, 70 Pitch Amplitude
f*
0.08 0.09 0.1 0.11 0.12 0.13 0.14 0.15 0.16
Efficiency
0.12
0.14
0.16
0.18
0.2
0.22
0.24
0.26
0.28
0.3
Efficiency vs. f* Reduced Frequency, 1c Heave 80 deg
(b) Kinematics: 1c Heave, 80 Pitch Amplitude
Figure 13. Efficiency vs. f* Reduced Frequency data plots: black
data illustrates unrefined biconvex CFD results and the magenta data
represents refined biconvex CFD results
A more refined mesh was also created for the stacked foil configuration but upon
further analysis, the increased fineness of the second mesh proved unnecessary. The
results proved equivalent with respect to lift, drag, and torque forces. Efficiency
19
26. Figure 14. Single Foil Inner Mesh
values were also found to be equivalent. Therefore, the initial mesh [Figure 15] was
used for the stacked 2 foil configuration cases.
Figure 15. Single Foil Inner Mesh
20
27. The estimated element size and the number of elements per chord length, along
the mesh boundaries, are listed in Table 1.1 for each of the single and stacked biconvex
foil case studies.
Outer Inner Rectangle Foil
Element Size: 5c .1c 0.01c
Element Number/Chord: .2 10 100
21
28. 5. Results
5.1. Case Studies. This investigation focused on two key parameters, foil con-
figuration (single versus stacked two foil) and foil geometry (elliptical versus bicon-
vex). The following section discusses the results collected for both case studies at a
heave amplitude of 1c.
5.2. Single Foil Geometry. The results of the single foil comparison [Figure 16]
have concluded that foil geometry does have an effect on the flow physics prediction
of the prototype I device in the range of tested frequencies. However in Figure 16(a)
at 70◦
pitch, it is important to note that at lower frequencies of 0.08-0.1, both the
ellipse and biconvex CFD results are in agreement. The results differed only in the
frequency range of 0.1-0.16. In this range the ellipse CFD and flume results exhibited
a larger peak efficiency value of 0.28 and at an optimal reduced frequency value of
0.12. The biconvex CFD results indicated an optimal reduced frequency value of
approximately 0.12 and a peak efficiency of 0.26. These data results concluded in
0.36-7.40% differences.
As shown in Figure 16(a) field-tests at 70◦
resulted in a peak efficiency of .17 at
a frequency of 0.13. This optimal frequency value is very similar to both the ellipse
and the biconvex CFD results, indicating that the frequency is not largely dependent
on foil shape when the pitch amplitude is 70◦
. However, the biconvex results showed
a steeper decrease in the high frequency range of 0.14-0.16, which coincides with the
field-test data trends. Ellipse data did not produce the same declining efficiencies for
the higher frequency range. Thus, the high frequency efficiencies are better predicted
by the biconvex shape than by the ellipse shaped foil.
At a pitch amplitude of 80 degrees [Figure 16(b)], ellipse and biconvex results were
also in agreement at a lower range of reduced frequencies. The frequency values ranged
from 0.08-0.13 and similar peak efficiency values of 0.28 at 0.13 reduced frequency
were reached in both the ellipse and biconvex results. Ellipse and biconvex results
22
29. only differed in the high frequency range of 0.14-0.16. These results produced 0.29-
8.50% differences. The field-test data, biconvex CFD results more accurately modeled
the trends of the prototype than the previous ellipse CFD model. Biconvex results
exhibited a steeper decline in efficiency, similar to the field-test results.
f*
0.04 0.06 0.08 0.1 0.12 0.14 0.16 0.18 0.2
Efficiency
0
0.05
0.1
0.15
0.2
0.25
0.3
Efficiency vs. f* Reduced Frequency, 1c Heave 70 deg
(a) Kinematics: 1c Heave, 70 Pitch Amplitude
f*
0.04 0.06 0.08 0.1 0.12 0.14 0.16 0.18 0.2
Efficiency
0
0.05
0.1
0.15
0.2
0.25
0.3
Efficiency vs. f* Reduced Frequency, 1c Heave 80 deg
(b) Kinematics: 1c Heave, 80 Pitch Amplitude
Figure 16. Efficiency vs. f* Reduced Frequency data plots: light blue
data represents field-test data without endplates, green data represents
flume results, data illustrates previous ellipse CFD results and red data
represents biconvex CFD results
In order to fully understand why the ellipse and biconvex results exhibited dif-
ferences, several plots containing the lift force, torque, instantaneous efficiency, and
cycle-average efficiency. After reviewing these plots, it was determined that the dis-
crepancies between the two data were most directly correlated to both the lift force
and torque. Discrepancies between the ellipse and biconvex results, for a pitch am-
plitude of 70◦
and reduced frequency range of 0.11-0.16 all depicted the same lift and
torque trends displayed in Figure 17. In particular, the lift force for the biconvex
foil always remained lower than that of the ellipse foil. The torque for the biconvex
remained slightly higher at peak torque, which occurred on the foils downward pitch.
Figure 17 is an example of how the lift force and torque results, over three steady-
state cycles, behaved for each of the frequencies listed previously. Please note that
all displayed data begins on the foil’s downstroke.
23
30. Time (s)
10 15 20 25 30
LiftForce
-3
-2
-1
0
1
2
3
Lift vs Time
Single Biconvex
Single Ellipse
(a) Lift Force vs. Time
Time (s)
10 15 20 25 30
Torque
-1
-0.8
-0.6
-0.4
-0.2
0
0.2
0.4
0.6
0.8
1
Torque vs Time
Single Biconvex
Single Ellipse
(b) Torque vs. Time
Figure 17. Kinematics: 1c Heave, 70 Pitch Amplitude and f*=0.11;
green data depicts single biconvex foil results, black data represents
single ellipse foil
At an 80◦
pitch amplitude and frequency range of 0.14-0.16, the observed discrep-
ancies between the ellipse and biconvex results were also a result of lift force and
torque differences. At 80◦
pitch, the same trend observed in the 70◦
pitch amplitude
case appears again. The torque of the biconvex foil remains lower at downward pitch
and the lift force remains smaller than the ellipse foil. Furthermore, these lift force
decreases are a result of the pressure regions forming around the hydrofoil. Figure 18
depicts these pressure regions visually and represent the observed differences in lift
and torque. This figure displays a slightly larger pressure gradient across the under-
side and topside of the hydrofoil. A high pressure region appears on the ellipse foil’s
underside and is larger than the region that appears for the biconvex case.
5.3. Stacked 2 Foil Configuration. Figure 19 illustrates the averaged stacked
2 foil biconvex data in comparison to the single biconvex data. Figure 19(a) illus-
trates agreement between the 2 foil and single foil biconvex cases for the frequency
range of 0.08-0.10. Higher frequencies depicted distinct disagreements. The 2 foil
biconvex data produced higher efficiency than the single biconvex foil but had the
same declining trend. A shift in optimal reduced frequency occurred for the averaged
2 foil biconvex case. Note that this averaged efficiency is the average between the top
24
31. (a) Single Ellipse (b) Single Biconvex
Figure 18. Pressure snap shots of single hydrofoil cases at f*=0.15
and 80 degree pitch
and bottom foil, as would be reported by the field-test data, which cannot distinguish
between top and bottom foil results. In addition to a lower frequency peak, there is
a steeper decreases in efficiency were observed in the higher frequency range for both
cases. For the 80◦
pitch case, the shifted peak in optimal frequency from 0.13 to 0.12
is more accurately predicting the optimal frequency obtained from prototype testing.
f*
0.04 0.06 0.08 0.1 0.12 0.14 0.16 0.18 0.2
Efficiency
0
0.05
0.1
0.15
0.2
0.25
0.3
Efficiency vs. f* Reduced Frequency, 1c Heave 70 deg
(a) Kinematics: 1c Heave, 70 Pitch Amplitude
f*
0.04 0.06 0.08 0.1 0.12 0.14 0.16 0.18 0.2
Efficiency
0
0.05
0.1
0.15
0.2
0.25
0.3
Efficiency vs. f* Reduced Frequency, 1c Heave 80 deg
(b) Kinematics: 1c Heave, 80 Pitch Amplitude
Figure 19. Efficiency vs. f* Reduced Frequency data plots: light
data represents field-test data without endplates, black data depicts
the averaged 2 foil biconvex configuration results, red data represents
the single biconvex case results
25
32. Several plots containing the lift force, torque, instantaneous efficiency, and cycle-
average efficiency were created in order to determine why the single biconvex and
stacked 2 foil biconvex results exhibited differences. After reviewing these plots, it
was determined that the discrepancies between the two data sets were also directly
correlated to the lift force. At 70◦
pitch [Figure 21(b)], top foil data produced higher
lift forces and bottom foil data produced slightly lower lift forces with respect to the
single biconvex case results. Furthermore, the top and bottom foils clearly perform
differently and this is due to the vortex to vortex interactions [Figure 20] influencing
the flow field.
This increase in lift produced by the top foil resulted in the previously described
higher averaged stacked 2 foil efficiency values. In regards to the 80◦
pitch case
[Figure 21(b)], both the top and bottom foils produced lower lift forces, similarly
described in previous studies. Figure 21(b) depicts these lift forces for both 70◦
and 80◦
degrees pitch at a reduced frequency of 0.15. It is important to note that
this reduced frequency is past the peak efficiency for the 70◦
case and at a reduced
frequency under 0.12 the lift forces would be reversed. The average 2 foil case would
produce higher lift forces and the single case would produce the lower forces. It is
also important to note that for the 80◦
study, if a plot of the lift forces for any of the
frequencies within the range of 0.08-0.13, the plot would be very similar to the 70◦
pitch case where the top foil obtained higher lift forces.
26
33. Figure 20. Depiction of the vortex interactions in the stacked 2 foil
case. Colors indicate vortices of various magnitudes.
Time (s)
5 10 15 20 25
LiftForce
-3
-2
-1
0
1
2
3
Lift vs Time
(a) Lift Force vs. Time 70 Pitch Amplitude
Time (s)
5 10 15 20 25
LiftForce
-3
-2
-1
0
1
2
3
Lift vs Time
(b) Lift vs. Time 80 Pitch Amplitude
Figure 21. Kinematics: 1c Heave, f*=0.15; red data represents bicon-
vex top foil results, blue data illustrated biconvex bottom foil results,
and the black data represents the single biconvex case results
27
34. 6. Conclusions
Results of this analysis have determined that both foil geometry and foil config-
uration are important parameters that effect the prediction of flow physics for the
stacked 2 foil Leading Edge Oscillating Hydrofoil Prototype I device. Specifically,
the foil geometry plays a key role in predicting the flow physics of the prototype I at
higher frequencies. Both single ellipse and single biconvex results were in agreement
at lower frequency values for 70 and 80 degree pitch. In both single foil cases at each
pitch amplitude, the biconvex case produced lower efficiency values at a higher de-
cline rate for reduced frequencies 0.13 and above. When compared to field-test data,
biconvex CFD data produced more accurate results than the elliptical CFD data for
the prototype I device.
The stacked 2 foil case study at a 70 degree pitch amplitude proved to agree with
the previous single foil ellipse CFD case. However, the results of the stacked 2 foil
configuration comparison study also indicated that foil configuration influences the
flow physics of the prototype I device for higher frequencies ranging from 0.11-0.16
and larger pitch amplitudes. Once again, steeper declining frequency trends were
produced for both 70◦
pitch and pitch amplitudes of 80◦
. In addition, at 80 degree
pitch, there was a complete shift in peak efficiency. This shift resulted in a more
accurate optimal reduced frequency value with respect to the field-test data. This
significant different is a very clear indication of the interference of shedding vortices
detaching from the top and bottom foils that was not captured with previous single
ellipse CFD case studies.
These results prove that accurate foil geometry and foil configuration play key
roles in the CFD predictions of the flow physics for the Leading Edge Oscillating
Hydrofoil Prototype I device. In the future, the Leading Edge research group will
now have a better understanding of the prototype I device results. Specifically, these
CFD comparisons prove that foil geometry determines efficiency trends at higher
frequencies and also at larger angles of attack (angle at which a freestream flows
28
35. past a hydrofoil). These conclusions will inevitably aid in the future prototypes and
development of the Leading Edge Oscillating Hydrofoil device.
29
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