An Experimental Investigation of Pressure of a
Simple Dam Break Generated Wave Impacting a
Plate
ARCHNE8
MASSACHUSETTS INSTITUTE
OF rECHNOLOLGY
by
JUN 2 4 2015
Anne M. LaBine
LIBRARIES
Submitted to the Department of Mechanical Engineering
in partial fulfillment of the requirements for the degree of
Bachelor of Science in Mechanical Engineering
at the
MASSACHUSETTS INSTITUTE OF TECHNOLOGY
June 2015
@ Massachusetts Institute of Technology 2015. All rights reserved.
The author hereby grants to MIT permission to reproduce and to
distribute publicly paper and electronic copies of this thesis document
in whole or in part in any medium now known or hereafter created.
I
Author...........
/77
Signature redacted
Department of Mechanical Engineering
M ay 8, 2015
Certified by.........
Signature redacted_
Alexandra Techet
Associate Professor of Mechanical and Ocean Engineering
10
Accepted by ...
Thesis Supervisor
Signature redacted.................
Annette Hosoi
Associate Professor of Mechanical Engineering, Undergraduate Officer
2
An Experimental Investigation of Pressure of a Simple Dam
Break Generated Wave Impacting a Plate
by
Anne M. LaBine
Submitted to the Department of Mechanical Engineering
on May 8, 2015, in partial fulfillment of the
requirements for the degree of
Bachelor of Science in Mechanical Engineering
Abstract
It is desirable to measure pressure of a wave striking a vertical surface because this
information can be used to determine the strength needed in the building materials
of marine structures that may be struck by tall waves. These waves may be caused
by storms, tsunamis, or dam breaks and can cause serious damage. This thesis
presents two experiments aimed at measuring the pressure exerted by a wave. In
both experiments, a series of water waves are released from a reservoir. One wave is
released at a time and the waves vary in the initial height of water in the reservoir. In
the first experiment, pressure is calculated using a force sensor to determine the force
on a paddle and a high-speed camera to determine the contact area. It was found
that wave pressure increases as the initial height increases. The pressures ranged from
5 2kPa at 25 1cm initial water height and 12t2kPa at 45 1cm initial water height.
In the second experiment, pressure is measured at multiple vertical and horizontal
locations on a vertical cantilevered plate. A sensor located in the middle of the plate
horizontally and 1.25in from the bottom recorded the highest maximum pressure for
all trials. The pressures from this sensor for this experiment ranged from 1.6 0.1kPa
at 20 1cm initial water height and 7.4 .4kPa at 45 1cm initial water height.
Thesis Supervisor: Alexandra Techet
Title: Associate Professor of Mechanical and Ocean Engineering
3
4
Acknowledgments
I would like to acknowledge the personnel from my lab. I would like to thank Juliana
Wu, Emma Nelson, Aliza Abraham, and Corbin Foucart for help with the design and
construction of the experimental tank and Leah Mendelson, Barry Scharfman, and
Jeff Dusek, for helping me with the data collection and analysis challenges. I'd like
to thank Sterling Harper for helping me run the experimental trials. Additionally, I'd
like to thank Dr. Barbara Hughey for helping with many aspects of this experiment
and the writing of this paper and Professor Nicholas Patrikalakis for feedback on both
the experiment and drafts of this paper. Many thanks to Professor Alexandra Techet
for being my advisor for the entire project. Without these people this paper would
be much shorter.
5
6
Contents
9
List of Figures
1
Introduction
13
2
Force Derived Pressure
17
4
17
2.2
Dam Break Release System Design
. . .
18
2.3
Measurement of Force and Contact Area
19
2.4
Results and Discussion . . . . . . . . . .
.
Wave Pressure Measurement . . . . . . .
.
22
25
Discrete Wave Pressure
Pressure Sensors
. . . . . . . . . . . . .
. . . . . . .
25
3.2
Dam Break Design with Pressure Sensors
. . . . . . .
26
3.3
Results and Discussion . . . . . . . . . .
. . . . . . .
27
.
.
3.1
.
3
2.1
.
11
.
List of Tables
37
Conclusion
Appendices
38
A Tables
39
B Figures
41
5
51
Bibliography
7
8
List of Figures
1-1
Sequence of high-speed images of the gate rising and the flow exits. The
wave travels from left to right in these images (as previously published
in [41 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
2-1
Schematic diagram of the dam break system (as previously published
in [4]). . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
2-2
18
Shows 10 trials of uncalibrated force data and the average for a wave
with an initial water height of 41cmilcm.
2-3
15
. . . . . . . . . . . . . . .
20
Plot of the calibrated forces from the force sensor versus time as the
wave hits the paddle. This shows the average of the trials at each given
initial water height (as previously published in [4j).
2-4
20
Sample image from Phantom high-speed camera (as previously pub-
lished in [4]).
2-5
. . . . . . . . . .
. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
21
Plot of the area of contact over time as the wave hits the paddle. The
area is a sample from the trials determined from the high-speed camera
frames (as previously published in [41).
2-6
. . . . . . . . . . . . . . . . .
21
Plot of pressure versus time for each of the initial water heights. Found
at each time step by dividing the force by the area of contact at each
time step (as previously published in [41). . . . . . . . . . . . . . . . .
2-7
2-8
22
Maximum Pressure versus initial water height (as previously published
in [4]). . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
23
. . . . . . . . . . . . .
23
Force versus contact area for each time step.
9
3-1
Circuit Diagram of the power supply decoupling and output filtering
.
used with the Freescale MPXV7007GC6U-ND pressure sensors [6]. .
Schematic diagram of the dam break system for directly measuring
pressure.
3-3
......
.. .....
........
27
. . . ....
Schematic diagram of the pressure sensor plate with location of the
sensors. ...
3-4
......
...
..
..
.. ..
..
...
28
........ . .. . . . . . ..
Shows 10 trials of pressure data for a wave with an initial water height
of 35 1cm for sensor E.
. . . . . . . . . . . . . . . . . . . . . . . .
.
3-2
25
29
3-5
Shows 10 trials of pressure data for all initial water heights for all sensors 30
3-6
Plot of pressure of off axis sensors (B, D and E) to show horizontal
.
uniform ity. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
3-7
Plot of the average pressure from A, B and C for an initial water height
.
of 35 5cm . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
.
heights.
3-9
32
Plot of pressure versus time of sensor B for each of the initial water
33
Maximum pressure versus initial water height at sensor B. Data is
. . . . . . . . .
34
.
shown in blue and the trend line is shown in black.
.
3-8
31
35
B-1 Arduino code . . . . . . . . . . . . . . . . . . .
. . . . . . . . . . .
42
B-2
Plot of all Sensor D trials sorted by height.....
. . . . . . . . . . .
43
B-3
Plot of all Sensor E trials sorted by height.....
. . . . . . . . . . .
44
B-4 Plot of all Sensor B trials sorted by height.....
. . . . . . . . . . .
45
B-5 Plot of all Sensor A trials sorted by height.....
. . . . . . . . . . .
46
B-6
Plot of all Sensor C trials sorted by height.....
. . . . . . . . . . .
47
B-7
Plot of pressure of off axis sensors (B, D and E) to show horizontal
. . . .
uniform ity. . . . . . . . . . . . . . . . . . . . . .
48
B-8
Plot of the average pressure from A, B and C
.
49
B-9
Plot of each sensor for all heights and maximum for each sensor for
. . . . . . . . . . . . . . . . . . . .
.
each height
.
.
.
3-10 Maximum pressure versus initial water height at all sensors.
10
50
List of Tables
2.1
Table of initial water heights and there respective number of trials for
the force and area trials. . . . . . . . . . . . . . . . . . . . . . . . . .
3.1
19
Table of initial water heights and their respective number of trials for
. . . . . . . . . . . . . . . . . . . .
27
3.2
Average maximum pressure from Sensor B. . . . . . . . . . . . . . . .
34
A.1
Values of maximum pressure for every initial water height and every
the discrete pressure experiment.
sensor. . . . . . . . . . . . . . . . . . . . . ... . . . . . . . . . . . . . .
11
40
12
Chapter 1
Introduction
Measuring the force of a wave is important in understanding how to build structures
that will need to withstand strong impulse waves. In situations like a dam breaking
or a tsunami, the forces acting on affected boats and structures can be dangerous.
Impact loads are crucial when designing both off-shore and coastal structures. Some
examples of structures that must account for strong impulse waves in their design
include ships, off-shore rigs, and large, sloshing tanks [1]. The experiment performed
in this paper represents a scaled model of some of these larger wave events. Determining the pressure that a wave of a given height can produce can influence design
decisions of manufactured material properties. The objective of this experiment is
to relate the initial height of a reservoir of water to the pressure exerted by a wave
released from the reservoir.
L. Lobovsky et al. performed an experiment which measured pressures exerted by
waves at different points in the wave [2]. Their experimental setup involved releasing
water from a reservoir with varying initial heights and using applied pressure sensors
fixed to a vertical wall. The experiment took point pressures, not an average pressure
of the wave.
This paper presents two experiments, which attempt to confirm the
trends found by L. Lobovsky et al. The second experiment presented in this paper
closely matches L. Lobovsky's setup, but the first experiment records pressure in a
different method. The first experiment presented in this paper uses force sensors to
calculate time-dependent pressure curves, which revealed a similar pressure profile
13
to data from L. Lobovsky et al.
The second experiment uses pressure sensors at
various heights and various initial wave heights that are different from those found in
L. Lobovsky et al.
Both experiments presented in this paper involve a volume of water from a reservoir tank being released into an acrylic channel that is flush with the sides and bottom
of the reservoir tank. The surface of the water touches air on the top and acrylic on
the sides and bottom. The wave release is shown in Figure 1-1. The focus of this
experiment is the pressure exerted by the wave.
Pressure is tested in two ways in these experiments.
The first method uses a
force sensor and the force of a wave is transmitted through a paddle. The second
method uses pressure sensors where the pressure is transmitted through small tubes
filled with air. The first experiment measures average pressure over a large area; the
second experiment measures pressure at spatially discrete points. The pressure cannot
be measured directly because no waterproof sensors are available.
More expensive
sensors were rated for splashing, not underwater applications and were much larger
and heavier than the sensors used in the second experiment. Therefore, in the first
experiment the pressure is calculated by measuring the force exerted on a paddle
submerged in the wave. In order to convert the force on the paddle into a pressure,
a high-speed camera images the wave so that the area of the paddle in contact with
the wave can be measured. The calibrated force and the area are used to find the
pressure for each initial wave height. The results suggest that a larger initial water
height will produce a larger maximum pressure. Propagation of uncertainty analysis
is done to determine the uncertainty on the final pressures. In the second experiment
the pressure is measured through a hose network filled with air, which is assumed to
be incompressible.
Chapter 2 discusses the experimental setup using force and area to determine
pressure. In this chapter, Section 2.1 introduces the theory, Section 2.2 details the
experimental design, 2.3 discusses the force and area measurements and results are
presented in Section 2.4. Chapter 3 discusses the experimental setup in which the
pressure is measured directly.
In this chapter, Section 3.1 introduces the theory,
14
k
Wave Exit Sequence
I
I
I
Figure 1-1: Sequence of high-speed images of the gate rising and the flow exits. The
wave travels from left to right in these images (as previously published in [4]
15
Section 3.2 details the experimental design, and results are presented in Section 3.4.
Finally, conclusions surrounding both experiments are drawn in Chapter 4.
16
Chapter 2
Force Derived Pressure
2.1
Wave Pressure Measurement
The method explored in this chapter uses force and contact area of the downstream
wave to determine pressure. The wave pressure measurement depends on the assumption that the height of the wave is sufficiently small and therefore gravitational effects
of pressure can be neglected. The force is calibrated using a known force applied
to the paddle so that the force of the wave can be determined without theoretical
analysis such as a force balance computation.
The quantity of interest in this report is the pressure exerted by the wave. Pressure
_F(t
)
as a function of time, P(t), is given by the formula,
)
P(t) = F~)(2.1)
A(t
where F(t) is the force exerted by the wave as a function of time and A(t) is the
contact area of the wave as a function of time. Area is calculated using the formula
A(t) = W - H(t)
(2.2)
where W is the width of the paddle and H(t) is the height of the water (with respect
to the bottom of the paddle) as a function of time.
17
2.2
Dam Break Release System Design
The wave in this experiment was generated by opening a gate on a reservoir tank,
allowing water to flow into a dry acrylic channel. The reservoir tank has dimensions of
34.0 0.5inches wide by 28 0.5 inches long by 48 0.5inches deep and can hold 197.8
gallons of water. The initial water height in the tank is varied in this experiment,
with 10 trials performed at each height, except for 35 1cm which had 5 trials. The
reduction of the number of trials at this height is due to a mechanical complication.
The number of trials was chosen to ensure accuracy in the data. The initial heights
ranged from 25 1cm to 45 1cm as shown in Table 2.2. One side of the reservoir
is a sluice gate that is raised vertically by a pneumatic actuator at a velocity of
1503.2cm/s with a maximum deviation of 30 %
13].
The pneumatic cylinder is a
Parker DXPSR with a 30in stroke. The acrylic channel lines up flush to the walls and
bottom of the reservoir in order to minimize the effects of the entrance head loss. To
collect the force data, a paddle on a lever arm is used to transfer the force out of the
water to a
50N dual-range force sensor. The force paddle is located 1.25 0.01m
from the gate and has a width of 102.57 0.08mm and a height of 103.04 0.04mm.
The force paddle is located just above the bottom of the acrylic channel and is not
moved between trials or changes in initial water height for consistency. A schematic
of the dam break system is shown in Figure 2-1.
Reservoir Tank
Force Sensor
Figure 2-1: Schematic diagram of the dam break system (as previously published in
[4]).
The wave height measurements were taken using a Phantom V341 high-speed
18
Force and Area Trials
Initial Water Height Number of Trials
25+1cm
10
30 1cm
10
35 1cm
5
41 1cm
10
45+1cm
10
Table 2.1: Table of initial water heights and there respective number of trials for the
force and area trials.
camera. The camera was focused on the force paddle, and images were captured at
2000 frames per second. Two strobes were used to backlight the experiment.
2.3
Measurement of Force and Contact Area
For each wave trial a pump is used to transfer water into the reservoir. The water is
pumped until the acrylic channel is dry and the water level in the reservoir reaches
the specified height as listed in Table 2.2. After the desired water level is achieved,
the pneumatics are actuated and the gate opens. The released wave hits the sensor
paddle and the data of the wave force over time is recorded.
The force data is collected using the
50N dual-range force sensor. The data
is zeroed and calibrated using a constant found by applying a known force to the
force paddle and recording the force measured by the
50N dual-range force sensor.
An example of the force data trials is shown in Figure 2-2. This figure shows the
repeatability of the force data. Note the black line which shows the averaged response.
This force data has an initial peak and then trails off as backsplash hits the paddle.
At that time, the wave has bounced off the far wall of the tank and decreased the
effective force from the wave. In this experiment the forces of interest occur before
the backsplash, from 0 to less than 0.5s.
The average pressure of each trial is plotted in Figure 2-3. As the initial water
height increases, the force also increases which is expected.
In order to find the pressure exerted by a wave, its area of contact with the paddle
must be known. This contact area is found from images collected by the high-speed
19
40
35
30
25
Aveg
20
L,15
5
1
0.s
-0
1.s
1
Tkm
2
2.s
(s)
Figure 2-2: Shows 10 trials of uncalibrated force data and the average for a wave with
an initial water height of 41cm lcm.
40
35
25
20
IL
s
Inital Height
-25cm
-30cm
30
Inital Height
35cm Initial Height
41cm Initial Height
Initial Height
1-45cm
10
5
0
-s
1 l0.5
Time
1.5
2
.5
Figure 2-3: Plot of the calibrated forces from the force sensor versus time as the wave
hits the paddle. This shows the average of the trials at each given initial water height
(as previously published in [4]).
camera. Water heights in pixels are determined from these images and converted
into physical units, e.g. mm, with a calibration constant obtained by measuring the
pixel size of an object in the image with a known physical dimension. The height
data is calculated from the time when a wave first strikes the paddle. An example
image taken at this time is shown in Figure 2-4. The height is then calculated until
the backsplash obstructs the view of the camera.
The height of the water on the
paddle is then multiplied by the measured width of the paddle, 102.57t0.08mm, as
20
per Equation 2.2 to obtain the contact area as a function of time.
Figure 2-4: Sample image from Phantom high-speed camera (as previously published
in [4]).
The contact area as a function of time determined from the high-speed images is
shown in Figure 2-5. The figure shows that the contact area increases and then begins
to level-off as the wave strikes the paddle. A larger initial water height tends to lead
to a larger area of contact. The 30+1cm trial is smoother because of the accidental
slower sampling rate of the camera in that trial.
9000
8000
-25cm
7000
-30cm Initial Height
3Scm Initial Heht
-41cm Initial Heigh
6000
Initial Height
500
~4000
3000
2000
1000
0
0
0.05
0.1
0.15
0.2 0.25
Time (s)
0.3
0.35
0.4
0.45
Figure 2-5: Plot of the area of contact over time as the wave hits the paddle. The
area is a sample from the trials determined from the high-speed camera frames (as
previously published in [41).
21
2.4
Results and Discussion
The force at each time step is multiplied by a contact area at 'the time step to find
the pressure using Equation 2.1. The initial pressures have the same slope, and after
the peak the pressures fall off to a constant non-zero value. The peak pressures of
the waves occur less than 0.14s after the wave first contacts the paddle. The peak
pressure of the wave with the initial height of 45+1cm is 12000 2000Pa and the
peak pressure of the wave with the initial height of 25 1cm is 5000 2000Pa. The
maximum pressure of the initial wave heights of 25 1cm is lower than the maximum
pressure of the wave with the initial height of 45 1cm. The pressure over time of
waves with different initial water heights is shown in Figure 2-6.
14
-25cm
-30cm
35cm
-41cm
-45cm
12
10
8
Initial Height
Initial Height
Initial Height
Initial Height
Initial Height
4
2
0
0
0.05
-2
0.1
0.15
0.2
0.25
0.3
0.35
0.4
lime (s)
Figure 2-6: Plot of pressure versus time for each of the initial water heights. Found
at each time step by dividing the force by the area of contact at each time step (as
previously published in [41).
The maximum pressure of waves that is created from each height of the reservoir
tank is shown in Figure 2-7.
The wave with a larger initial height has a larger volume of water and more
potential energy while in the reservoir tank. This experiment shows the larger height
has more force, more area, and more force per area (pressure). The force rises to its
max force at a relatively low contact area and then the force levels off as the area
continues to increase. This is shown in Figure 2-8.
22
.20
S15
101
0
20
25
30
35
40
45
50
Initial Height (cm)
Figure 2-7: Maximum Pressure versus initial water height (as previously published
in [4]).
35
30
25
W 26.
20
u
10*
#A r &M
* 25cm
25m
ni4eih
Initial Height
* 30cm Initial Height
35cm Initial Height
41cm Initial Height
5
0
-
0.001
0.002
0.003
0.004
0.005
45cm Initial Height
0.006
0.007
0.008
.5
Figure 2-8: Force versus contact area for each time step.
These results for the pressure curves of the waves agree with the pressure curves
found by L. Lobovsky et al. The pressure curves rise rapidly to a peak pressure and
then decrease back down to a constant non-zero pressure. L. Lobovsky et al. also
found that at every sensor the pressure of the wave with the larger initial height was
larger than the pressure of the wave with a smaller initial height. L. Lobovsky et
al. conclusions also agree with the current experiment's results, which show that as
the initial water height increases average pressure also increases 12]. The 41+1cm
trial was inconsistent with the increasing pressure trend. This discrepancy may be
because of a problem with the area calculation or calibration. The force data behaves
23
as expected while the area data shows the 41t1cm initial water height having larger
area than expected at every time step.
24
Chapter 3
Discrete Wave Pressure
3.1
Pressure Sensors
The pressure data is collected using the Freescale MPXV7007GC6U-ND
pressure
sensor. This pressure sensor is a temperature compensated on-chip integrated sensor.
This sensor was chosen because of its pressure range ( 7kPa), its short acquisition
time, and small physical dimensions. The sensor has 5.0% maximum error between
0 and 85 degrees Celsius. It outputs a signal between 0.5 and 4.5V. Figure 3-1 shows
the data acquisition circuit using the Freescale pressure sensor.
+5v
VOIA
OUTPUT
IPM
1.0 pF
0.01 IF
GND
470 pF
Figure 3-1: Circuit Diagram of the power supply decoupling and output filtering used
with the Freescale MPXV7007GC6U-ND pressure sensors [61.
25
A conversion factor is needed to transform the voltage from the sensor into a
pressure value. The transfer function of the pressure sensor is given by Equation 3.1.
Vout = Vs(0.057P + 0.5)
where Vs is 5.OV
(3.1)
0.25Vdc, Vo0 t is the output voltage recorded in V and P is the
pressure in kPa. This equation solved for P is given in Equation 3.2 (from [6]).
P=
Vt - 0.5
0.057 (Vs
The error of the pressure reading from the sensor is t
3.2
(3.2)
5.0 % [6].
Dam Break Design with Pressure Sensors
The same setup as the previous experiment is used for wave generation; see Section
2.2.
The initial heights for this experiment ranged from 20 1cm to 45
1cm as
shown in Table 3.2. After the desired water level is achieved, the pneumatic cylinder
is actuated and the gate opens. A vertical cantilevered plate that is assumed to be
infinitely stiff is placed 1.25
0.Olm from the reservoir entrance. The pressure sensors
are not waterproof, so it was necessary for the sensors to be situated outside of the
tank. Therefore, the pressure applied to various points on the cantilevered plate is
transmitted to the sensors via plastic tubing filled with air. The air inside the tubing
is assumed to be incompressible for analytic purposes. A similar setup was used by
A. Gao in [5]. These pressure sensors are used detect the average pressure of a much
smaller area than the force paddle used previously. Therefore, the pressure sensors
are much more sensitive to pressure changes that occur in specific area of the wave.
Rather than the method presented in Chapter 2 where pressure was assumed spatially
constant over the paddle, this experiment measures pressure at various small points
spaced vertically and horizontally within the wave. A schematic of the dam break
system is shown in Figure 3-2 and the physical location of the sensors on the plate is
shown in Figure 3-3. The data of the wave pressure over time is recorded using an
26
Arduino and processed in Matlab. The Arduino code is reproduced in Figure B-1.
Discrete Pressure Trials
Initial Water Height Number of Trials
10
20 1cm
10
25
1cm
10
1cm
30
10
35 1cm
10
40 1cm
10
45 1cm
Table 3.1: Table of initial water heights and their respective number of trials for the
discrete pressure experiment.
Reservoir
Tank &m
Pressure
senors
7"SwPlate
77
Figure 3-2: Schematic diagram of the dam break system for directly measuring pressure.
3.3
Results and Discussion
The raw data was recorded for each trial and then calibrated in post-processing using
Equation 3.2. The zero point in the time series for each dataset was manually adjusted
until the data between trials overlapped. An example of the pressure data trials from
Sensor E is shown for the 35cm Height in Figure 3-4. In every trial, the wave hits the
plate shortly after time 0 and immediately rises to the max pressure. The pressure
decreases after the peak and shows some slight oscillation as water continues to hit
the plate and run up the plate. The wave then continues to decrease pressure against
27
in
7in
Figure 3-3: Schematic diagram of the pressure sensor plate with location of the sensors.
the plate as the wave is pulled back due to the backsplash. At around 2 seconds,
a second pressure peak occurs due to the reflection of the backsplash wave in the
same direction as the original wave. The 20 1cm does not have this second wave
because it did not have enough energy to slosh in the tank. This data shows that the
experiment and the wave generated are very repeatable. Sensor data for all 5 Sensors
and all 6 trials is show in Figures B-2, B-3, B-4, B-5, B-6.
The results show that changes in reservoir water height more strongly affect pressure readings than sensor position. This can be seen in Figure 3-5. By looking at the
data from the sensors of one wave height and the data from all of the wave heights,
there is a larger distinction between a 5cm initial height difference than between any
of the sensors for a given initial height.
The average pressure across the wave with an initial water height of 35 1cm at
sensors B, D, and E, which are located at the same height on the plate, is plotted
in Figure 3-6. Average pressure is calculated by taking the mean across all trials (at
28
8
7
6 5
-_
Trial 1
Trial 2
Trial 3
Trial 4
Trial 5
Trial 6
Trial 7
Trial 8
Trial 9
Trial 10
-
CL
2
0
0
0.5
1
1.5
Time [3]
2
2.5
3
Figure 3-4: Shows 10 trials of pressure data for a wave with an initial water height
of 35 1cm for sensor E.
a given height) for each time step. In the horizontal direction the wave exhibits the
same pressure, both in curve and magnitude, as is shown the similarity of the curves
in the figure. The pressure at sensor B, D, and E, for all initial water heights is shown
in Figure B-7. This figure also shows the pressure exerted across the wave is the same
curve and magnitude for each initial water height.
The average pressure measured with an initial water height of 35 1cm at sensors
A, B, and C is shown in Figure 3-7. Sensor A is the topmost sensor as shown in
Figure 3-3. The pressure is expected to increase closer to the bottom of the wave
because of the weight of the water above, which would cause the highest pressure
reading at C and the lowest at A. After the peak of the wave, t > 0.2 s, the pressure
follows this expected order. However, this expected order is broken during the actual
peak of the wave where B measures the maximum value. This trend may be due to a
pressure loss at the heigh of Sensor C due to friction and other dynamic interactions
29
20 cm Height Ml Sensors
8
8
SensorA
Sensor B
Sensor C
SensorD
SensorE
6
10
O)
25cm Height MI Sensors
4
6
0
C,
a-
4
2
0
l
0.2
0.6
0.4
Time [s]
0.8
1
0
0.4
0.2
0.6
0.8
1
0.8
1
Time [s]
35 cm Height Ml Sensors
30cm Height Al Sensors
6
6
0~
0-
0)
4
4
0,
0)
0)
C)
0.
2
2
0
0
0
0.2
0.6
0.4
Time [s]
0.8
0
1
0.4
0.2
0.6
Time [s]
45 cm Height M Sensors
40 cm Height Al Sensors
8-
8
6iA
6
a-
W0)
0)
4
4-
0)
0,
a)
4')
2
a- 2
0
0
0
0.2
0.4
0.6
0.8
0
1
77
V
0.2
0.4
0.6
0.8
1
Time [s]
Time [s]
Figure 3-5: Shows 10 trials of pressure data for all initial water heights for all sensors
with the bottom of the channel. The pressure at sensor A, B, and C, for all initial
water heights is shown in Figure B-8.
The average pressure of sensor B for the 6 height trials is plotted in Figure 3-8.
The pressure curve shows that pressure increases with initial water height.
30
Senor B
SensorD
Sensor E
8
7-
6
5-
4
2
1
0
0
I
I
I
I
0.1
0.2
0.3
0.4
I
0.5
Time [s]
I
I
I
I
I
0.6
0.7
0.8
0.9
1
Figure 3-6: Plot of pressure of off axis sensors (B, D and E) to show horizontal
uniformity.
The maximum pressure of waves created from each height of the reservoir tank is
shown in Figure 3-9. The maximum pressure always occurs at sensor B as shown in
Figure 3-10. Figure 3-10 shows the maximum average pressure from all sensors. The
error in these measurement is
5% due to the error in the sensors [6]. The wave with
a larger initial height has a larger volume of water and more potential energy while
in the reservoir tank, which should result in a larger max pressure with a larger wave.
This is demonstrated in the results of this experiment. As the initial water height
increases the peak pressure of the water increases.
The maximum pressure increases with initial water height. The relationship between initial height and maximum pressure can be approximated as linear with a
slope of 0.23kPa/cm initial water height. The maximum pressure for Sensor B at the
20+1cm initial water height is 1.56+0.08 and at the 45 1cm initial water height is
7.42 0.37.
31
SensorA
Sensor B
SensorC
8
765
0
_U
CL
3
2
0
I
0
0.1
I
I
I
0.2
0.3
0.4
I
0.5
Time[s]
I
I
I
I
I
0.6
0.7
0.8
0.9
1
Figure 3-7: Plot of the average pressure from A, B and C for an initial water height
of 35 5cm.
One source of error in the system could be from transferring the pressure along
tubes to the sensor. There is a potential for pressure loss at the tube entrance and
exit as well as error due to tube movement and air compressibility. The release of the
wave has error due to the variable speed of the raising of the gate of 1503.2cm/s with
a maximum deviation of 30 % [3]. The speed of the gate could change the shape of the
wave and the speed the wave travels down the tank which could effect the pressure.
The sensors also have a pressure error of t 5.0 % [6] and trials were completed with
a unique sensor at each sensor location which were constant throughout the trials.
Maximum pressure is the same order of magnitude as the results from the experiment in Chapter 2. The maximum pressure from the discrete pressure experiment
for Sensor B at all initial height values is shown in Table 3.3 and of all the sensors in
Table A.1. The shape of the wave is similar to the general shape of the wave from the
experiment in Chaper 2 where the wave hits the plate and the pressure rises extremely
32
20cm
25cm
8
30cm
35cm
40cm
7
45cm
-
6
5
0~
4
0)
a)
-
3
2
0
0
0.1
0.2
0.3
0.4
0.5
0.6
0.7
0.8
0.9
I
1
Time [s]
Figure 3-8: Plot of pressure versus time of sensor B for each of the initial water
heights.
rapidly to its maximum value and then falls off again. The difference in time of the
peak of the data could be due to the nature of the force experiment and pressure
experiment setup. The force data was taken using a movable paddle and the pressure
was taken using a rigid plate. That means as the force increased the paddle moved
away from the tank and this could cause a shift in time to the maximum pressure
reading.
33
8
7
I
6
5
I
"a
CL
rum
4
CL
2
-
3
01
20
25
35
30
Height [cm]
I
i
40
45
50
Figure 3-9: Maximum pressure versus initial water height at sensor B. Data is shown
in blue and the trend line is shown in black.
Maximum Average Pressure of Sensor 5
Initial Water Height [cm] Pressure kPa]
1.6 0.1
1
20
2.9 0.1
1
25
4.7 .2
1
30
5.9 .3
1
35
6.2 .3
1
40
7.4 .4
45 t 1
Table 3.2: Average maximum pressure from Sensor B.
34
8SensorA
SensorB
SensorC
SensorD
Sensor E
7
6
-
-
5
0
0
25
30
35
40
45
Height [cm]
Figure 3-10: Maximum pressure versus initial water height at all sensors.
35
36
Chapter 4
Conclusion
The goal of this experiment is to find the maximum pressure of a wave given the initial
height of water in the reservoir. The experiment found that as the initial height of
water in a reservoir tank increases, the wave released from the tank increases in
exerted force, contact area, and maximum pressure. The maximum pressures range
from 5 2kPa at 25 1cm to 12k 2kPa at 45 1cm using force and area measurements
and 1.6
0.lkPa at 20
1cm to 7.4 .4 at 45 1cm when taken directly as a pressure
at Sensor B. Data was gathered at several initial heights yielding a dataset that can
be used to create and validate models of pressure on marine structures due to waves.
Future work could include taking pressure data over a longer time frame to guarantee the pressure found in this time frame is the largest force created. To do this
more time before backsplash would need to be created, either by lengthening the tank
or moving the paddle closer to the reservoir.
Future work could also include mak-
ing the force sensor a more realistic model of a ship hull. The metal plate could be
cantilevered and flexible instead of braced and assumed infinitely stiff. The reaction
of the plate to the forces could be recorded and the deflection of the plate could be
scaled to represent a full ship.
Rather than just measuring the height of the wave at the force paddle, the entire
surface of the wave could be characterized and the changing form could be plotted
over time to compare the maximum forces to the wave shape.
37
Appendices
38
Appendix A
Tables
39
Table A.1:
sensor.
Values of maximum pressure for every initial water height and every
Sensor
20
25
30
35
40
45
A
1.4
1.2
2.0
3.7
4.4
6.5
0.1
0.1
0.10
0.2
0.2
0.3
B
1.6
2.9
4.7
5.9
6.2
7.4
40
0.1
0.1
0.2
0.3
0.3
0.4
C
0.9
2.5
3.6
4.3
4.1
5.6
0.1
0.1
0.2
0.2
0.2
0.3
D
1.1
2.0
4.0
5.5
5.9
7.1
0.1
0.1
0.2
0.3
0.3
0.4
E
1.3
2.5
4.1
5.1
5.4
7.2
0.1
0.1
0.2
0.2
0.3
0.4
Appendix B
Figures
41
sensorPini = Al;
sensorPin2 = A2;
sensorPin3 = A3;
sensorPin4 = A4;
sensorPin5 = A5;
sensoriValue = 0;
sensor2Value = 0;
sensor3Value = 0;
sensor4Value = 0;
int sensor5Value = 0;// variable to store the value coming from the sensor
int powerPin = A0;
int powerValue = 0;
float thingi = 0; //pressure
float thing2 = 0; //pressure
float thing3 = 0; //pressure
float thing4 = 0; //pressure
float thing5 = 0; //pressure
int
int
int
int
int
int
int
int
int
void setupO {
Serial.begin(9600);
}
void loopo {
// read the value from the sensor:
sensoriValue = analogRead(sensorPinl);
sensor2Value = analogRead(sensorPin2);
sensor3Value = analogRead(sensorPin3);
sensor4Value = analogRead(sensorPin4);
sensor5Value = analogRead(sensorPin5);//-analogRead(sensorPinneg);
powerValue = analogRead(powerPin);
thingl=((sensorlValue/powerValue)-.5)/0.057;
thing2=((sensor2Value/powerValue)-.5)/0.057;
thing3=((sensor3Value/powerValue)-.5)/0.057;
thing4=((sensor4Value/powerValue)-.5)/0.057;
thing5=((sensor5Value/powerValue)-.5)/0.057;
Serial. print(thingl);
Serial.print(",");
Serial.print(thing2);
Serial.print(",");
Serial. print(thing3);
Serial.print(",");
Serial. print(thing4);
Serial.print(",");
Serial.println(thing5);
delay(100);
I
Figure B-1: Arduino code
42
20cm Height SensorD Trals
8
6
a.
Trial I
Trial 2
Trial 3
Trial 4
Trial 5
Tial 6
25cm Height SensorD Trials
8
6
Trial 7
4
Trial 8
Trial 9
Tr Ii6 1
-
0L2
S4
2
0
0
2
I
3
2
I
3
Time [s]
Time [s]
30cm Height Sens orD Tials
35cm Height SensorD Tdals
8
8
6
6
4
4
CL
1
0
0
2
1
1
3
2
3
Time [s]
Time [s]
45cm Height Sens orD Trials
40cm Height SensorD Trials
8
8
6
6
04,
0
4
0
0
4
4,
0-
2
0
0
0
2
II
3
0
II
2
Time [s]
Time [s]
Figure B-2: Plot of all Sensor D trials sorted by height.
43
3
Trial 1
Trial 2
Trial 3
20cm Height Sensor E Trials
8
-
4
9,
9,
2
I
r
0
8
- Trial 4
Trial 5
Trial 6
Trial 7
Tri__ 8
Trial 9
Trial 10
6
0~
4,
0~
25cm Height Sensor E Trials
6
07
CL
4
9,L
2
i
0
I
0.5
1
1.5
Time Is]
2
2.5
3
I
0.5
1
1.5
2
2.5
3
2.5
3
2.5
3
Time[s]
35cm Height Sensor E Tris
30cm Height Sensor E Triais
8
8
6
6
4
4
0u
A,
0
0
0.5
wF
CIL
1
1.5s
2
2.5
0.5
3
1
1.5
2
Time [a]
Time [s]
40cm Height Sensor E Trials
45cm Height Sensor E Trials
8
8
6
6
4
4
2
2
0
0
0
0.5
1
1.5
Time [s]
2
2.5
0
3
0.5
1
1.5
Time [s]
Figure B-3: Plot of all Sensor E trials sorted by height.
44
2
20cm Height Sensor B Trials
8
6
4
2
Trial 1
Trial 2
Trdal 3
Trial 4
Trial 5
Trial 6
Trial 7
Trial 8
Trial 9
Trial 10
25cm Height Sensor B Trials
8
.g6
4
2
0
0
1
2
3
2
3
Time [s]
Time [s]
35cm Height Sensor BTdals
30cm Height Sensor BTrials
8
8
6
6
10
4.
4
0L,
0
0
1
2
2
3
3
Time [s]
Time rs]
45cm Height Sensor B Trials
40cm Height Sensor BTrials
8
8
6
76
0.
0,
4)
01
0
0
0
1
2
3
2
I
Time [s]
Time [s]
Figure B-4: Plot of all Sensor B trials sorted by height.
45
3
20cm Height SensorATrils
8
Trial 1
25cm Height SensorATris
Tria 2
Trial 3
8
-- Trial 4
Trial 5
6
1-
Trial 7
Trial 8
Trial 9
Teia 10
4
6
9_,
94
0
0
I
2
1
I
3
2
3
Time Is]
Time [s)
35cm Height Sensor ATrials
30cm Height Sensor A Trials
8
8
6
6
4
4
2-
A-
0
0
2
1
3
3
I
Time [s]
Time [s]
45cm Height Sensor A Trials
40cm Height Sensor A Trials
8
8
6
6
-2
4
00
0
2
1
3
2
1
Time [s
Time [s]
Figure B-5: Plot of all Sensor A trials sorted by height.
46
3
Trial 1
Trial 2
20cm Height SensorC Trials
8
Trial 4
Trial5
Trial 6
Trial 7
Trial 8
Trial S
Trial 10
6
0,
25cm Height SensorC Trials
Trial 3
8
4
2
6
a
4
OL 7
0
0
0.5
0
1
1.5
2
2.5
0.5
3
1
Time [a]
1.5
2
2.5
3
2.5
3
2.5
3
Time [s]
35cm Height SensorC Trials
30cm Height Sensor C Trials
8
8
6
6
C-
0z
0,
4,
4
0)
0
0
1.5]
I
0.5
1
1.5
Time [3]
2
2.5
0.5
3
[
2
Time [3]
45cm Height Sensor C Trials
40cm Height Sensor C Trials
8
8
6
6
24
0
0
~iL~
0
0.5
1
1.5
Time [a]
2
2.5
0
3
0.5
1
1.5
Time []
Figure B-6: Plot of all Sensor C trials sorted by height.
47
2
20cm Height Trial Averages
25cm Height Trial Averages
8[
8
-
___
SensorDB
6
a-
SensorD
SensorE
6
Sensor E
Sensor B
a-
4
4)
0
0
4)
a- 2
0
0
0
0.2
0.6
0.4
Time [s]
0.8
0.2
1
.
0.6
0.8
1
Time [s]
30cm Height Trial Averages
8
0.4
35cm Height Trial Averages
8
Sensor B
---
Sensor B
---
Sens orD
-SenorDi
6
6
Sensor E
-
Sensor E
--
C-
O
0,
4
4
2)
0
0
0.2
0.4
0.6
Time [s]
0.8
0.2
1
8
-Sensor B
--Sens orD
-
08
1
45cm Height Trial Averages
40cm Height Trial Averages
8
0.6
0.4
Time [s]
- -Sensor B
- -Sens orD
- -Sensor E
6
Sensor E
4
0
0w
4
OL2
0
0
0
0.2
0.4
0.6
Time [s]
0.8
0
1
0.2
0.6
0.4
Time [s]
0.8
1
Figure B-7: Plot of pressure of off axis sensors (B, D and E) to show horizontal
uniformity.
48
25cm Height Trial Averages
20cm Height Trial Averages
8
-
8
Sensor A
Sensor B
SensorC
6
_-Sensor A
Sensor B
--
6
- -Sensor C
0L
4
4
0
0
0
0.2
0.8
0.6
0.4
Time [s]
8
1
0.2
35cm Height Tdial Averages
30cm Height Trial Avemges
8
Sensor A
Sensor B
6
0.8
0.6
0.4
Time [s
--
6
- -Sensor C
Sensor A
B
- -Sensor
- -Sensor C
0
4
0
0
0.2
0.8
0.6
0.4
Time [s]
1
1
.
---
0.8
0.6
0.4
Time [s]
45cm Height Tiel Averages
40cm Height Triel Averages
8
0.2
8
Sensor A
B
Sensor C
- -Sensor A
- -Sensor B
- -Sensor
6
-
---
6
--
Sensor C
4
4
0
0
0
0.2
0.4
0.6
0.8
0
1
Time [s]
0.2
0.6
0.4
Time [s
Figure B-8: Plot of the average pressure from A, B and C
49
0.8
20cm
25cm
30cm
35cm
40cm
45cm
Sens orD Average of Tis for each Height
0.
6
U)
2~
0
0.
0
0.2
-
4
0,
0)
U)
0.4
0.6
Sens orD Max Pressure each Height
0)
0)
U)
64
2-
0~
A
0.
U)
5
20
40
35
30
height
Sensor E Max Press ure each Height
45
50
5
20
45
40
35
30
height
Sensor BMax Pressure each Height
50
8
6
4.
2.
0r
15
20
40
35
30
height
Sensor AMax Pressure each Height
45
50
1
0.8
Time [s]
Sensor EAverage of Trials for each Height
8
6
0e
4
C,
CL
S0
0
0.8
0.6
0.4
Time [s1
Sensor BAverage of Trials for each Height
8
0e
6
CL
2
0L
CL
0
0.8
0.6
Time [s]
Sensor A Average of Trials for each Height
0.2
0.4
~~
1
8
0.
0.
6
0.
0,
0,
U)
2
0
0.2
0.4
Time [s]
S ens or C Average of Trials
U)
0,
0,
U)
0.
2
0
25
25
8
6-
4
2
4
0.
0
0.
4
U)
U)
0,
0,
U)
8
6
1
0.2
25
0.6
0.8
1
15
30
35
40
45
50
45
50
Sensor C Max Pressure each Height
f or ew h H ei ght
0.
U)
0)
2
U)
0.
0
0.2
25
height
8
6
4
0
20
0.6
0.4
Time [s]
0.8
1
8.
642
0
15
20
25
35
30
height
40
Figure B-9: Plot of each sensor for all heights and maximum for each sensor for each
height
50
Chapter 5
Bibliography
[1] K. Abdolmaleki, K. P. Thiagarajan and M. T. Morris-Thomas,"Simulation of
The Dam Break Problem and Impact Flows Using a Navier-Stokes Solver," The
University of Western Australia, December, 2004 (15th Australasian Fluid Mechanics Conference, Crawley, WA, 6009 AUSTRALIA) also available online at
http://www.ae.su.oz.au/15afmc/proceedings/papers/AFMC0003 1.pdf
[2] L. Lobovsky,
et al.,
"Experimental investigation of dynamic pressure loads during dam break." Journal of Fluids and Structures
http://dx.doi.org/10.1016/j.jfluidstructs.2014.03.009i
[31 J. Wu, "Characterizing the Dam Break Release," Undergraduate Thesis
at Massachusetts Institute of Technology, 2014, also available online at
HTTP://HDL.HANDLE.NET/1721.1/92213.
[41 A. Techet, T. C. Fu, T. T O'Shea, A. LaBine, C. Foucart, and K. A. Brucker, "An
Experimental and Computational Investigation of a Simple Dam Break Generated
Wave Impinging on a Flexible Plate," 30th Symposium on Naval Hydrodynamics.
Hobart, Tasmania, Australia, November 2-7, 2014.
[5] A. Gao, and M. Triantafyllou, "Bio-Inspired Pressure Sensing for Active Yaw
Control of Underwater Vehicles," In Proc. of IEEE Oceans, 2012
[61 Freescale Semiconductor. "Integrated Silicon Pressure Sensor On-Chip Signal Conditioned, Temperature Compensated and Calibrated," MPXV7007 datasheet, Oc-
tober 2012.
51