fluid behaviour in microgravity - utorweb · specifically, fluids of air, kerosene, and vegetable...

Fluid Behaviour in Microgravity

Iman Datta

Kobtham Chotruangprasert

A thesis submitted in partial fulfillment

of the requirements for the degree of

BACHELOR OF APPLIED SCIENCE

Supervisor: Prof. N. Ashgriz

Department of Mechanical and Industrial Engineering University of Toronto

March 2010

Abstract

Induced accelerations used for the separation of disparate fluid particles as well as acceleration effects known as g-jitter in microgravity systems have been the subject of extensive numerical analysis and physical study. However, a full understanding of the exact nature of the effect of these accelerations on fluids has not yet been achieved. The purpose of this experiment was to study a physical system that imitates these accelerations on a system of an oscillating bubble in a surrounding fluid. Specifically, fluids of air, kerosene, and vegetable oil were inserted into an oscillating tank of water from which motion of these bubbles could be analyzed. The motions of each of these types of bubbles were compared with one another as well as with a computational fluid dynamics model of such a system. The results of this experiment showed a regular motion of these bubbles in response to the oscillation which was not predicted by the computational model. A correlation was also found between the amount of bubble deformation from the oscillation and the density difference between the bubble and surrounding fluid. It was also found that the motion of the bubbles strongly follow that of the forced oscillation frequency. However, due to discrepancies in the conditions that were tested, it was found that more testing at similar conditions should further be conducted to obtain more accurate results.

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Acknowledgements We would like to thank the following people in the Department of Mechanical and Industrial Engineering at the University of Toronto, whose help was invaluable at various stages of the project:

Nasser Ashgriz, our professor. Professor Ashgriz gave us guidance at every step from the formation of the test through to its analysis. Without his help, the test would not have been possible.

Mohammad Movassat, Mechanical Engineering Graduate Student. We worked closely with Mohammad throughout the duration of the project. Without his input at every stage as well as his explanation of the mathematical formulation for the test, this project would not have succeeded.

Ryan Mendell, MIE Machine Shop Manager. Ryan’s help was instrumental in designing the tank for this test and he was also responsible for its fabrication.

Tomas Bernreiter – MIE Lab Engineer and Manager. Tomas gave us very important input as to the use of the mechanical shaker and is the person who gave us access to this device.

Reza Karami – Mechanical Engineering Graduate Student. Reza graciously lent us the high speed camera and trained us to work with it. Without this, data extraction would have not been possible.

Amirreza Amighi – Mechanical Engineering Graduate Student. Amirreza’s help was instrumental in obtaining fluids used in bubble testing.

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Table of Contents Acknowledgements .................................................................................................................................. i

List of Symbols ....................................................................................................................................... iv

List of Figures .......................................................................................................................................... v

List of Tables .......................................................................................................................................... vi

Chapter 1: Overview and Motivation ...................................................................................................... 1

1.1 Introduction and Background ................................................................................................... 1

1.2 Origin of G-Jitter....................................................................................................................... 1

1.3 Induced Vibration for Fluid Separation As Well As G-Jitter ........................................................ 3

1.4 Experimentation Method Overview.......................................................................................... 4

Chapter 2: Experimental Design and Setup ............................................................................................. 5

2.1 Original Testing Specifications .................................................................................................. 5

2.2 Experiment Alternatives ........................................................................................................... 6

2.3 Design Requirements and Challenges ....................................................................................... 7

2.4 Fabrication of Parts and Adjustments to Design Specification ................................................... 9

Chapter 3: Testing Methods and Procedure .......................................................................................... 13

3.1 Testing Procedure .................................................................................................................. 13

3.1.1 Camera Setup: ................................................................................................................ 13

3.1.2 Tank: .............................................................................................................................. 14

3.1.3 Shaker Setup: ................................................................................................................. 14

3.1.4 Levitation Attempt: ........................................................................................................ 15

3.2 Testing ................................................................................................................................... 16

3.2.1 Levitation during Testing ................................................................................................ 17

Chapter 4: Analysis ............................................................................................................................... 20

4.1 Analysis Method .................................................................................................................... 20

4.2 Analysis .................................................................................................................................. 23

4.2.1 Center of Mass Motion ................................................................................................... 23

4.2.2 Shape Deformation ........................................................................................................ 26

4.3 Differences between Fluids ................................................................................................ 29

Chapter 5: Recommendations and Conclusions .................................................................................... 32

5.1 Recommendations ................................................................................................................. 32

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5.1.1 Recommendation 1 ........................................................................................................ 32

5.1.2 Recommendation 2 ........................................................................................................ 33

5.1.3 Recommendation 3 ........................................................................................................ 34

5.1.4 Recommendation 4 ........................................................................................................ 35

5.2 Conclusions ............................................................................................................................ 36

Bibliography .......................................................................................................................................... 38

Chapter 6: Figures and Tables ............................................................................................................... 39

Appendix A: Tested Conditions ............................................................................................................... A

Appendix B: Shaker Oscillation Parameter Calculations ........................................................................... B

Appendix C: Levitation Calculations ........................................................................................................D

Appendix D: Calculations Used for Tank Dimensions and Forces Needed from Shaker (Table 4) .............. E

Appendix E: Bubble Calculations for Centre of Mass, Diameter, and Spline Length ................................. F

Appendix F: Group Work Allocation ....................................................................................................... H

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List of Symbols

𝐹𝐹 Force on bubble 𝑚𝑚 Mass of bubble 𝜔𝜔 Angular frequency of vibration 𝑋𝑋 Amplitude of displacement 𝑎𝑎 Acceleration 𝐹𝐹𝑏𝑏 Buoyant force 𝜌𝜌𝑤𝑤 Water density 𝑔𝑔 Gravitational acceleration 𝑉𝑉 Volume 𝑑𝑑 Position 𝑑𝑑0 Initial position 𝑣𝑣 Velocity 𝑡𝑡 Time 𝐹𝐹𝑔𝑔 Gravitational force 𝜌𝜌𝑏𝑏 Bubble density 𝐹𝐹𝑠𝑠𝑡𝑡𝑠𝑠𝑎𝑎𝑑𝑑𝑠𝑠 Net force on bubble in absense of oscillation 𝐹𝐹𝑛𝑛𝑠𝑠𝑡𝑡 Net force on bubble in presence of oscillation

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List of Figures FIGURE 1: SCHEMATIC DIAGRAM OF STATIONARY BUBBLES IN AN ACOUSTIC STANDING WAVE FIELD [4] ........................................... 39 FIGURE 2: SCHEMATIC DIAGRAM OF EXPERIMENTAL APPARATUS [4] ...................................................................................... 39 FIGURE 3: ALTERNATIVE #2 EXPERIMENTAL APPARATUS ..................................................................................................... 40 FIGURE 4: LARGE AIR BUBBLE STILL PHOTOS AT 2000 FRAMES / SECOND FOR 1 CYCLE.............................................................. 41 FIGURE 5: SMALL AIR BUBBLE STILL PHOTOS AT 2000 FRAMES / SECOND OF EVERY 10 CYCLES FOR 6 CYCLES ................................ 42 FIGURE 6: VEGETABLE OIL BUBBLE STILL PHOTOS AT 2000 FRAMES / SECOND FOR 1 CYCLE ....................................................... 43 FIGURE 7: KEROSENE BUBBLE STILL PHOTOS AT 2000 FRAMES / SECOND FOR 1 CYCLE .............................................................. 43 FIGURE 8: CENTER OF MASS POSITION RELATIVE TO FRONT OF FRAME FOR 3 OSCILLATIONS FOR LARGE AIR BUBBLE......................... 44 FIGURE 9: CENTER OF MASS POSITION RELATIVE TO FRONT OF FRAME FOR 3 OSCILLATIONS FOR VEGETABLE OIL BUBBLE ................... 44 FIGURE 10: CENTER OF MASS POSITION RELATIVE TO FRONT OF FRAME FOR 3 OSCILLATIONS FOR KEROSENE BUBBLE ....................... 44 FIGURE 11: CENTER OF MASS POSITION FOR 3 OSCILLATIONS FOR LARGE AIR BUBBLE AFTER CONSTANT ACCELERATION CORRECTION WITH

SINUSOIDAL FIT ............................................................................................................................................... 45 FIGURE 12: CENTER OF MASS POSITION FOR 3 OSCILLATIONS FOR VEGETABLE OIL BUBBLE AFTER CONSTANT ACCELERATION CORRECTION

WITH SINUSOIDAL FIT........................................................................................................................................ 45 FIGURE 13: CENTER OF MASS POSITION FOR 3 OSCILLATIONS FOR KEROSENE BUBBLE AFTER CONSTANT ACCELERATION CORRECTION WITH

SINUSOIDAL FIT ............................................................................................................................................... 45 FIGURE 14: LARGE AIR BUBBLE CENTRE OF MASS / AVERAGE DIAMETER ................................................................................ 46 FIGURE 15: VEGETABLE OIL BUBBLE CENTRE OF MASS / AVERAGE DIAMETER ......................................................................... 46 FIGURE 16: KEROSENE BUBBLE CENTRE OF MASS / AVERAGE DIAMETER ................................................................................ 46 FIGURE 17: AVERAGE 1/4 CYCLE SPLINE LENGTHS AS PERCENTAGE OF OVERALL AVERAGE SPLINE LENGTHS FOR ALL TESTED BUBBLES... 47 FIGURE 18: LARGE AIR BUBBLE SURFACE SPLINE LENGTH AT 0, 1/4, 1/2, AND 3/4 POINTS OF 3 SUCCESSIVE CYCLES ....................... 47 FIGURE 19: VEGETABLE OIL BUBBLE SURFACE SPLINE LENGTH AT 0, 1/4, 1/2, AND 3/4 LENGTH POINTS AT 5 CYCLE INTERVALS ......... 48 FIGURE 20: KEROSENE BUBBLE SURFACE SPLINE LENGTH AT 0, 1/4, 1/2, AND 3/4 LENGTH POINTS OF 3 SUCCESSIVE CYCLES ............ 48 FIGURE 21: SMALL AIR BUBBLE SURFACE SPLINE LENGTH AT 0, 1/4, 1/2, AND 3/4 LENGTH POINTS AT 10 CYCLE INTERVAL .............. 48 FIGURE 22: LARGE AIR BUBBLE SPLINE FIT FOR EACH QUARTER OF 3 CONSECUTIVE CYCLES ........................................................ 49 FIGURE 23: VEGETABLE OIL BUBBLE SPLINE FIT FOR EACH QUARTER OF 3 CONSECUTIVE CYCLES .................................................. 50 FIGURE 24: KEROSENE BUBBLE SPLINE FIT FOR EACH QUARTER OF 3 CONSECUTIVE CYCLES ........................................................ 51 FIGURE 25: SMALL AIR BUBBLE SPLINE FIT FOR EACH QUARTER OF EVERY 10 CYCLES ................................................................ 52 FIGURE 26: AVERAGE 1/4 CYCLE SPLINE LENGTHS FOR ALL TESTED BUBBLES ........................................................................... 53 FIGURE 27: AVERAGE 1/4 CYCLE DIAMETERS FOR ALL TESTED BUBBLES ................................................................................. 53 FIGURE 28: AVERAGE 1/4 CYCLE SPLINE LENGTHS AS PERCENTAGE OF OVERALL AVERAGE SPLINE LENGTHS FOR ALL TESTED BUBBLES... 54 FIGURE 29: AVERAGE 1/4 CYCLE SPLINE LENGTHS AS PERCENTAGE OF OVERALL AVERAGE DIAMETERS FOR ALL TESTED BUBBLES ......... 54 FIGURE 30: 3D SOLIDWORKS RENDERING OF THE EXPERIMENTAL APPARATUS ......................................................................... 55 FIGURE 31: ENGINEERING DRAWING OF THE CYLINDRICAL TANK ........................................................................................... 56

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List of Tables TABLE 1: MAXIMUM DIFFERENCE (DELTA) BETWEEN MEASURED SPLINE LENGTHS VS AVERAGE OVERALL DIAMETER AND SPLINE LENGTHS

FOR CYCLE QUARTER POINTS OF ALL BUBBLES......................................................................................................... 57 TABLE 2: AVERAGE DIAMETERS AND SPLINE LENGTHS FOR QUARTER CYCLES OF ALL BUBBLES ..................................................... 58 TABLE 3: SINE CURVE FITTING EQUATION VALUES AND MINIMUM AND MAXIMUM DIFFERENCES BETWEEN FITS AND ACTUAL VALUES . 59 TABLE 4: TABLE OF DIMENSIONS CONSIDERED FOR TANK AND FORCES NEEDED FROM SHAKER .................................................... 60

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Chapter 1: Overview and Motivation

1.1 Introduction and Background

The separation of fluid particles of deferring densities on space systems, such as the

International Space Station (ISS), has posed much difficulty in the absence of gravity. This has

created the need for testing and experimentation within these systems to solve this problem.

Many of these tests have been carried out both in space and on the ground. Also, the

phenomenon known as g-jitter, which is a residual gravity effect that is sometimes found in

space, can cause an arbitrary oscillation on fluid particles that can add a level of complexity to

the process of fluid separation and can make other zero-gravity experiments conducted very

difficult to perform with accuracy.

The purpose of this project is to investigate the effect of forced accelerations on disparate

fluid particles as they are being separated as well as when they are subject to the acceleration of

g-jitter. Even though the acceleration characteristics of these two conditions are different (as

will be explained further below), both follow the same physical laws [1], and can be tested in the

same manner with adjustments made only to the frequency of vibration and amplitude of

acceleration.

1.2 Origin of G-Jitter

Zero gravity environments on satellites such as the ISS come from the fact that they are

in a constant state of freefall, which keeps them in orbit around the earth. This is because the

speed of these satellites are so high perpendicular to the earth’s curvature, they never actually hit

the earth but ‘miss’ the ground and continue to go around in a continuous orbit. This constant

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state of freefall causes a zero gravity environment within the satellite, which provides an ideal

laboratory for various zero-gravity experiments that can be performed, ranging from biological

and electrical applications to processing of alloys and composites [2].

Although ideally these spacecraft can be thought of as zero-gravity test-cells, in reality

this description is not entirely true. Due to various external factors, acceleration may not be

completely zero. Instead, it is often observed that there is a very small oscillatory residual

acceleration. This phenomenon is what is known as g-jitter. This acceleration can be as much as

6 magnitudes lower than that of gravitational acceleration on earth [2], which may be good

enough to perform many experiments. However some experiments may require a very high

degree of precision and even this low acceleration may be enough to void results from such tests.

Various factors contribute to this jitter phenomenon. One of which is that an object in

some spacecraft will feel an acceleration if the centre of mass of the object and the centre of

mass of the spacecraft are not at the same point in space with respect to the earth. For fluids, this

acceleration between two particles can cause natural convection where the denser fluid particles

will move towards the centre of mass of the craft with respect to the less dense fluid particles.

This effect is called the gravity gradient effect, and can be steady or time-dependent, depending

on the movement of the centre of mass of the particles and the orientation of the spacecraft [2].

The value of this acceleration is usually between 0.1 to 0.5μg (acceleration due to gravity on

earth equals 1g). Atmospheric drag also acts on spacecraft orbiting the earth, which can cause

acceleration as much as 10μg at an altitude of 250 km above the earth’s surface. However, this

diminishes at higher altitudes. Other effects such as a Coriolis force for a rotating craft as well

as solar radiation pressure can also induce various accelerations acting on fluid particles that can

cause oscillations depending on movement of their acceleration vectors. Finally, movement of

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astronauts working in and around a space station, operation of pumps and mechanical devices,

and firings of thrusters in order to keep a spacecraft on a specific trajectory, as well as vibration

effects that may accompany this, all contribute to a time-dependent oscillation experienced by

fluid particles that may be subjected to zero-gravity testing [2]. An understanding of these

effects has been desired and various methods of testing this phenomenon have been carried out

in the past. However, due to all of the variables involved as have been mentioned, it has been

difficult to fully understand the nature of the oscillation. Nonetheless, this experiment was an

attempt to gain an understanding of how this oscillation affects the motion of fluids.

1.3 Induced Vibration for Fluid Separation As Well As G-Jitter

To separate dissimilar fluid particles, an oscillation of amplitude much greater than that

of g-jitter must be induced. This is a forced oscillation that can be controlled. As mentioned

previously, even though the acceleration for fluid separation may be much larger than that of g-

jitter (of the order of 10g versus much less than 1g for g-jitter), the physics of the motion in

either case is similar.

There are various ways to induce this vibration, including using centrifugal forces

produced by rotation or using thermo-capillary and surface tension forces inherent in gas-liquid

mixtures. Other forces that have been employed range from magnetic and electro-hydrodynamic

forces to vibration-induced acceleration [1]. This last method is what was employed for the

experiment, and will be discussed in detail in later sections. The method for inducing g-jitter and

fluid separation accelerations were the same for the experiment.

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1.4 Experimentation Method Overview

The vibration-induced acceleration method which was employed involves using a

mechanical shaker to oscillate a water-filled tank in which there is a single air bubble. In

general, the bubble oscillates with the forced oscillatory motion created by the shaker that causes

a shape deformation when force is above a certain value. This shape deformation leads to a

shape oscillation which is coupled with the translational motion of the bubble [1]. These two

oscillations have proved to be very complex and highly non-linear, due to the various factors of

forces and boundary conditions inherent in the motion [3].

Numerical Computational Fluid Dynamics (CFD) analysis of this system has been the

work of a PhD candidate working in the Department of Mechanical and Industrial Engineering at

the University of Toronto. This model has been used to describe the motion of a single bubble

under the forced oscillation under g-jitter conditions as well as those of forced fluid separation.

The model has also been used to describe the interaction between two bubbles in close proximity

subject to the same oscillation.

The experiments that were performed attempted to confirm the numerical results with

data obtained from physical testing.

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Chapter 2: Experimental Design and Setup

2.1 Original Testing Specifications

To simulate fluid separation vibration conditions, an air bubble was to be shaken in a tank

of water at an acceleration of 10g at 100 Hz. The acceleration was induced by the vibration

shaker and regulated by a function generator (VibeLab Software) which creates a sine force

wave (which means the induced vibration acts according to a sine function). At these conditions,

the displacement of the bubble can be easily calculated from the equation:

𝐹𝐹 = 𝑚𝑚𝜔𝜔2𝑋𝑋

In this equation, 𝜔𝜔 represents angular frequency and 𝑋𝑋 represents the amplitude of displacement.

This is equivalent to Newton’s 2nd Law (𝐹𝐹=𝑚𝑚𝑎𝑎) for the case of force that varies sinusoidally

with time. In this case, 𝑎𝑎 (acceleration) is equivalent to 𝜔𝜔2𝑋𝑋. For an acceleration of 10g at 100

Hz, the corresponding displacement is about 0.25 mm.

The conditions for g-jitter vibration require a displacement of 0.1 mm at 1 Hz frequency.

Rearranging the above equation, it can be seen that this corresponds to an acceleration of about

0.004 m/s2, or 0.0004g. This is 25000 times smaller than the 10g acceleration for fluid

separation. Nonetheless, since the physics of the oscillations are basically the same, the nature of

bubble motion in either case can be observed by testing the other. Specifically, a shaker was

employed that could produce the higher acceleration for the fluid separation, from which

something could be learned about either system.

Another control for the experiment was the size of the bubble, which influences the shape

distortion at various oscillations. The CFD model was based on a bubble diameter of 4 mm, for

which the original aim of the test was to imitate. It was assumed that a syringe could be

employed such that a specific amount of fluid (and hence bubble volume) could be injected

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consistently. However, upon testing, it was found that this was not the case and that a consistent

single bubble injection was not possible. This will be explained further in later sections. It was

also preferred that the injection point would be near the bottom of the tank, so that the maximum

number of oscillations could be observed before the bubble reached the top.

2.2 Experiment Alternatives Aside from the proposed experimental procedure, there are many other alternatives to test

the bubble motion in fluid. The first alternative is to study the bubble motion using an acoustic

wave field. Following research done by Abe, Kawaji, and Watanabe [4] the acoustic wave setup

would be comprised of the ultrasonic transducers, liquid column, bubble injecting system, and

horn as shown in Figure 1 and more detailed in Figure 2.

As shown in Figure 1, the bubble is stationary as an ultrasonic standing wave was created

by the ultrasonic transmitters. A pair of these transmitters was then used to alter the standing

wave and control the bubble in the equilibrium position. After experimenting with buoyancy

force on earth, the experiment would then be held under reduced-gravity conditions aboard the

plane, which would fly parabolic trajectories creating a microgravity environment for a short

period of time (10 – 30 seconds). While this type of test would be ideal for the study of bubble

dynamics under the forced oscillation, it is not a method that is feasible for the experiment due to

the excess in time and cost that would be incurred if performed.

Another alternative to do the experiment is to directly install the whole setup on the

parabolic flight, for which pool boiling could be used to induce the bubbles. In a study done by

Kawanami and his colleagues [5], bubble behaviour in microgravity is studied by boiling the

pool to introduce the bubble and putting the setup onto the parabolic flight in which the

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microgravity environment is attained. The illustration of this experimental concept is shown in

Figure 3.

This experimental method has proved to be quite popular as many scholars in the field

have chosen to use similar fundamental ideas with small adjustments to fit the experimental

purposes such as attaching magnets to see the effects of magnetic fields on the bubble [6].

However this test again is not feasible on a cost and time basis as it requires aircraft for parabolic

flights to produce a microgravity environment. Problems with isolating a single bubble would

also be inherent due to the boiling procedure needed that would produce many bubbles of

unknown sizes.

2.3 Design Requirements and Challenges

By examining the size of the bubble and displacement characteristics of the two

oscillatory systems, it can be easily seen that the testing involves dealing with a small bubble and

yet smaller amplitude of vibration. To capture this, it was essential to measure with precision the

motion of the bubble. However, this cannot be done directly with the bubble inside the tank.

There must be some way of measuring bubble size directly while it is being captured on camera.

Also, a major difference between the experiment and space conditions is that in the

experiment there is an added constant gravitational acceleration, which causes a buoyant force

represented by the equation:

𝐹𝐹𝑏𝑏 = 𝜌𝜌𝑤𝑤𝑔𝑔𝑉𝑉

where 𝜌𝜌𝑤𝑤 represents the density of the water surrounding the bubble, g equals gravitational

acceleration, and V is the volume displaced by the bubble. This causes an upward motion of the

bubble during testing until it reaches the top of the surface of the tank. This poses a very

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restrictive limitation on the test as there will only be enough time to gather data from the time of

bubble injection to the time it reaches the top of the tank, which depending on its height, is only

a matter of seconds. But after consultation with the professor and the graduate student, it was

decided that a 20cm x 20cm x 20cm box was sufficient to obtain enough data of bubble

oscillation since at 100 Hz, it was assumed that data could be gathered for a hundred cycles of

vibration.

Plexiglas (Acrylic) plastic was then chosen as the material for the box, due to visibility

requirements needed for examining the motion of the bubble as well as its resistance to

mechanical failure. After conducting research on local businesses that sell Plexiglas, a company

in Toronto was found that could make a Plexiglas box that fit the dimensional requirements for

$75. However, one major design requirement for this test is that the box should be completely

filled with water with the only air pocket consisting of the vibrating bubble. This means that it

had to be ensured that the box will not leak, which the manufacturer was not able to guarantee.

Therefore, fabrication of the box was held off until a suitable shaker was found.

The shaker, which is the most expensive piece of equipment needed for this experiment,

took the most amount of time to obtain. The professor was unsure of where to find one and a

few weeks were spent in contacting companies both locally and internationally along with

various faculty members in the Department of Mechanical and Industrial Engineering who might

know where to obtain a shaker in the university that could be used for the test. For a 20cm x

20cm x 20cm Plexiglas box filled with water, a weight of almost 20 lbs was calculated, assuming

a water density of about 1000 kg/m3 [7]. This is a very high load to be shaken and requires a

very high-powered (and expensive) shaker. This weight also does not include the weight of a

fixture to be placed on the shaker that would mount the box. Accounting for the 10g acceleration

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of only the box weight, it was found that this requires a shaker that can produce a sine force of

about 200 lbs, for which there are shakers that are made to supply 250 lbs. However, when the

weight of the fixture was taken into account, total force needed was likely to go over 250 lbs, so

the next step up would be a shaker that can output 500 lbs sine force. These shakers cost over

$20,000, not including the function generator, which was significantly above the budget for the

project. Options at this point were to either make a shaker in-house or continue searching the

university for something that could be used. After contacting various people in the faculty, the

exact 500 lb force shaker that was needed was found to already exist within the department. The

model of this shaker is the ET-127 Electrodynamic Transducer, which outputs 500 lb peak sine

force with 1-inch maximum continuous peak to peak displacement amplitude of vibration. It can

produce up to 100g acceleration with no load and up to 20g acceleration for a load of 20 lbs.

Since the projected box load at this point was 20 lbs, this shaker was taken to be sufficient for the

test as long as the fixture used to mount the box to the shaker did not reduce the acceleration to

less than 10g.

2.4 Fabrication of Parts and Adjustments to Design Specification Once the use of the mechanical shaker was secured, focus was shifted toward completion

of the fabrication of the tank that would be used for the test. Consultation with the MIE Machine

Shop Manager and the Lab Engineer regarding the tank’s construction and mount setup with the

shaker caused certain fundamental design changes. The most important aspects considered

included the actual load the shaker could handle and produce consistent data for, the method to

be used for securing it to the armature of the shaker so that it cannot get wet from any water

spillage from the tank (the vibration-inducing mechanism in the shaker is a solenoid that could

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be damaged if wet), and selecting a tank for which materials would be easily available and for

which fabrication would be most conducive for the manufacturing techniques of the machine

shop.

With these factors in mind, the Lab Engineer indicated from his experience with the

shaker that operation at a condition near its limit will not yield stable acceleration and vibration

frequencies. The 20 lb tank (not including the fixture) that was to be used would have been

subjected to 10g acceleration, which represents the high end of the operating range of the shaker.

Even though it is rated according to specifications that it will handle this load, it would have

been difficult to set a specific frequency of vibration and acceleration with precision during the

test. Also, according to the machine shop manager, it is typically easier to fabricate a tank that is

cylindrical than to make a box. In addition, sealing the edges of the box so that it is not porous

could pose potential problems. Instead, columns can be readily obtained and do not have as

many edges that are spots for potential water leakage.

Material for the tank was also reconsidered. The original idea was to use Plexiglas

(Acrylic), as it is light weight and a clear plastic that works well for observations. However,

based on consultation with the machine shop manager, it was found that polycarbonate would be

a better material for the job, due to its similar optical properties and weight but higher strength.

However due to the higher availability of acrylic plastic from vendors, this material was finally

used for the project.

With these restrictions in place, the design of the tank could then be finalized. The aim

was to make the total weight of the tank and fixture no more than 10 lbs in weight. Based on

this, the set limit for the weight of the tank was made to 5 lbs with the assumption that the fixture

would be of similar weight. Also, the cylindrical tank’s diameter needed to be less than that of

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the shaker table’s mounting surface, which is 6 inches. Along with this, it was desired to

maximize the height of the column to give the bubble a relatively long period from which data

could be extracted before reaching the top of the tank. However, the column could not be made

so high as to make it difficult for a camera to capture its motion.

With these parameters in mind, it was decided with the graduate student on a cylindrical

tank 8 cm in diameter and 40 cm in height. Based on these dimensions, the cylinder would

weigh 4.6 lbs when completely filled with water (refer to Table 4 and Appendix D). Assuming

this weight along with that of the fixture comes to about 10 lbs, the shaker output would have to

be about 100 lbs to produce the 10g level of acceleration that needed to be achieved, which is

well within the range of the 500 lb force shaker.

The last parameter for control is the size of the bubble, which was to be kept to a

diameter of 4mm. A pump injection system was to be obtained from the Department of

Mechanical and Industrial Engineering, which could help in injecting a bubble of consistent

volume into the tank during oscillation. Unfortunately, there was no one in the department who

could provide the system. Instead, a medical syringe and needle was used for the test, for which

manual bubble injection was performed for each trial.

With all of these parameters specified, the tank was fabricated to the above

specifications. A cap screw was placed at the top so that water could be manually poured into it.

A hole with a nylon cap for sealing was placed about 5 cm from the bottom of the tank for the

needle injection. The seal was to allow for air bubble injection with minimal leakage and its low

position was to give the bubble the maximum cycles of oscillation before reaching the top of the

tank. Along with the tank, a plastic base was fabricated that would be used to mount the tank to

the shaker. Another thin plastic board was used and attached underneath, which has a surface

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area greater than the shaker top, so that any water leakage would flow off this board and away

from the shaker.

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Chapter 3: Testing Methods and Procedure

3.1 Testing Procedure

3.1.1 Camera Setup: Once the shaker was obtained for use and the tank was finally fabricated, testing could be

performed. A high speed camera was obtained from the Department of Mechanical and

Industrial Engineering, which could take pictures at speeds of 2000 frames per second. At this

rate, for a bubble oscillating at 100 Hz, 20 frames could be recorded for a single oscillation,

which is enough to get a clear picture of bubble motion under the forced oscillation. Using an

external Data Acquisition Box for the camera, still photos could be obtained for each frame

recorded. This could then be converted to video. Bright external lighting was used for image

generation due to the low exposure inherent in a shutter speed setting for generating 2000

pictures per second.

An unfortunate consequence that came from the high-speed camera that was used was

that it could only accurately take pictures of a small portion of the cylinder. This is because the

total file size of the pictures is very large (2000 per second), so that there is a limit on the amount

of data that can be collected at specific frame rates, which means that as this frame rate

increases, the area of photo taken decreases. Thus, a balance had to be achieved between a

suitable frame rate to examine the bubble and the amount of cycles that can be seen due to screen

size. Also, the relative size of the bubble on the screen had to be considered so that reasonable

measurements could be accurately taken later based on still pictures. For this reason, only a

limited window could be used for high speed pictures.

14

3.1.2 Tank: For testing, the cylindrical tank was attached to the shaker via a plastic mounting plate

and a thin board, using screws. The finished tank was of a height of 40cm at a radius of 8cm, as

illustrated in Figures 30 and 31. In calculations based on size and acrylic density estimations, the

total weight of the tank filled to the top with water was about 4.6 lbs. This did not include the

weight of the two mounting plates, although these were relatively small compared to the weight

of the filled cylinder. The finished parts together actually totaled 7.7 lbs. This, along with the

shaker armature weight, represents the entire load that is subjected to oscillation by the shaker.

3.1.3 Shaker Setup: Prior to testing, time was spent with familiarization with the shaker and the function

generator system (VibeLab Software). As explained earlier, the shaker is rated to 500 lbs and a

maximum peak to peak displacement of 1 in. With these parameters, testing could be performed

at any condition within the requirements. The armature weight of the shaker is 5 lbs. This along

with the 7.7 lbs of the filled tank gives a total load of 12.7 lbs. The three operating parameters

for the test are displacement, acceleration, and frequency. Any two can be chosen to calculate

the third parameter as well as the force that the shaker needs to exert. By choosing the particular

parameters, calculations were made for various conditions to check if they cause smaller than 1

inch peak-to-peak displacement and a force of less than 500 lbs. If a condition does not fall

below these constraints, it could not be performed. As an added precaution, performing

conditions above 350 lbs or 0.5 in displacement were avoided. The formulas used to check these

variables are given in Appendix B.

15

The preferred condition of 10g at 100 Hz of air bubbles in water was the first condition

considered, though problems with this as explained later inhibited full analysis of bubble

behavior at this state. However, as the calculations show in Appendix B, this condition was well

within the range of the shaker, generating a force of 127 lbs at a peak-to-peak displacement of

about 0.02 in.

3.1.4 Levitation Attempt: After fabrication of the tank, it was proposed that a bubble levitation system be put in

place such that instead of dealing with the constant upward motion of the bubble due to the force

of gravity, the bubble would be allowed to hover in one spot so that pictures could be taken of

the bubble indefinitely. To do this, standing waves would have to be created. This means that

the height of the cylinder must be a multiple of the wavelength produced by the oscillation. This

produces a standing wave in which a bubble can find itself stuck in the node of two intersecting

waves. Calculating the parameters needed to do this is not difficult. The assumed wavelength

was the height of the tank, which is 0.4 m. The speed of the wave propagation in the tank can be

taken as the speed of sound in water (or 1500 m/s) [7]. The time for the wave to travel through

the tank can be calculated, and thus the frequency of oscillation needed for this wavelength,

which turns out to be 3750 Hz, is within the range of the shaker’s specs. At this frequency and

with a weight of 12.7 lbs, the maximum acceleration that can be achieved by this shaker is just

under 40g. At this level, the displacement is on the scale of a millionth of an inch (Appendix C).

This is not a displacement that the shaker can produce accurately or even a value that could be

measured with precision. Due to this, any attempt to create a levitating condition in this way was

ceased.

16

3.2 Testing

The first tests were of air bubbles in the tank of water at 10g and 100 Hz. The VibeLab

function generator controls the shaker that slowly sweeps up to this condition from zero

oscillation. Once the tank reaches this oscillation, the bubbles are injected via the syringe.

There were a few problems observed in the bubble formation upon injection. Firstly, in non-

oscillatory conditions, the size of the bubble injected into the water was not due to the amount of

fluid in the syringe. At different needle sizes, the characteristic bubble volumes changed, most

likely based on the volume of the needle. This made it impossible to make a bubble of a

predetermined size, although it could be made consistent according to the needle size. However,

an even more serious problem was that the nature of the bubble injection was inconsistent when

performed under oscillatory conditions. When injected during a condition of induced vibration,

bubbles seemed to break up within the needle ahead of the injection. This led to the injection of

a number of smaller bubbles at a time instead of one larger bubble. This very possibly led to

some external effects such as the Bjerknes forces [8] that cause attractions between bubbles that

are close together. This may have an effect on the motion and shape deformation of the bubbles

that are being studied.

Another strange phenomenon that occurred at the original condition (as well as at various

other conditions) was that the various bubbles that were injected would coalesce into one large

swarm of bubbles that would oscillate at some frequency much smaller than the forced

oscillation by the shaker. Its magnitude of displacement from this oscillation was also quite

large, in between anywhere from ¼ to ½ of the height of the cylindrical tank. The reason for this

is unclear. The attraction of the various bubbles into the larger swarm could be from the

Bjerknes force between them. The walls of the tank could have also played a role in attracting

17

the bubbles together. In addition, the large displacement and small oscillation frequency of the

swarm may have something to do with the bubbles being caught in nodes causing levitation.

While it has already been shown that it is difficult to accurately set a condition for this, it may be

possible that this might be a state that wave nodes are close enough to each other for the large

swarm of bubbles to get stuck in between them. For whatever reason that this happens, accurate

measurements of a single bubble subject to the oscillation was not possible when this condition

was experienced. Other conditions were then performed (within the 500 lb, 1 in displacement

constraint) to find a point where this was not happening. One condition that was typically free of

this phenomenon was of an oscillation of 50 Hz at 10g acceleration. This keeps the same level

of acceleration but at half the frequency. At this condition, it was possible to consistently

produce conditions where single bubbles could be observed as they moved up along the length of

the cylinder.

3.2.1 Levitation during Testing

After the first observations of air bubbles, it was concluded that due to the net upward

motion of the bubbles in the small camera reference screen (usually on the order of 4 cm), there

were not enough oscillations from each set of pictures to see many transient effects in the motion

of the bubbles. Indeed many of the first set of still photos for air bubbles only showed 4 or 5

oscillations before the bubble moved outside of the screen. In order to get more oscillations for

one set of screen shots, it was proposed to use a different fluid than air. The reason why air

bubbles move so quickly out of the screen is due to the difference in density between air and

water. Typically, air has a density of 1.2 kg / m3 while the density of water is 1000 kg / m3 [7].

This vast difference is why the air bubbles rise to the surface so fast. If another fluid was used

18

for the bubble with closer density to water, the rise would be much slower and more cycles of

oscillation could be observed.

With this in mind, alternative fluids with densities similar to that of water were

researched. The most readily available fluid that fit this description was regular vegetable oil,

which has a density of about 910 kg / m3 [9]. However, as can be seen in the Figure 6, the

deformation of the oil in subsequent trials was very small. This was possibly due to its high

viscosity and surface tension at room temperature [7]. It may also have something to do with the

buoyant force on the bubble, which will be elaborated on in the next chapter. Another fluid that

was experimented with was kerosene, which has a density of approximately 800 kg / m3 [10],

and is much less viscous than the vegetable oil. As can be seen in Figure 7, there is also much

smaller distortion of this fluid than either case of air as shown in Figures 4 and 5. Analysis of

the entire set of still frames though of the bubbles moving across the screen show that it does

take significantly more time (and many more cycles) for both the kerosene and the vegetable oil

to move across the screen of the camera than it does for the air bubbles. However, each case

poses its own problems. For the air, a large amount of cycles for data extraction were not

available due to the low density of the bubbles, while for the bubbles of higher density, many

more cycles were seen but with much less deformation in shape, for which investigation is the

main object of the project. Another fuel that was tested was a methanol-based fuel used to power

RC airplanes. However, upon injection, this fluid dissolved into the surrounding water. This

was because methanol is not immiscible in water, so was not a testable fluid for the project.

Among these other three fluids that were tested (vegetable oil, kerosene, and methanol),

kerosene seemed the most promising, as it showed the best deforming characteristics with low

buoyancy force. More trials were run with this fluid. However, in the continuation of these

19

tests, data for air bubbles that are characterized by higher deformation were obtained. The

reason for this was that when kerosene was injected into the tank from the syringe, there would

invariably be air bubbles as well that would come out with the kerosene. A run at this condition

produced a few long images of air bubbles that were actually nearly levitating. The reason for

this was that upon injection, as the kerosene bubbles slowly moved upward, the swarm of air

bubbles was again generated. However, in this case it was confined to the bottom of the tank and

not vibrating at the low frequency that was seen in earlier trials. The kerosene bubbles seemed to

be unaffected by the swarm. The air bubbles however, while experiencing a higher buoyant

force toward the top of the tank, also experienced the Bjerknes force downward from the large

air bubble swarm. It could actually be seen that the smaller bubbles were moving downward

toward the swarm, which means that the Bjerknes force between these bubbles was actually

higher than the buoyant force on them. This would make sense especially for the smaller

bubbles since the buoyant force decreases with decreasing volume. For the project, this created a

condition for air bubbles that were close to a levitation state, for which still pictures were taken

for around 60 cycles. The reason that more cycles could not be observed was that the bubble

moved off the screen from horizontal drift instead of vertical. This trial then provided the

longest observation period that was achieved for air.

After this condition, a few more trials were done with limited success. In many cases the

vibrating swam appeared and leakage problems were observed with the tank.

20

Chapter 4: Analysis

4.1 Analysis Method After testing was completed, analysis of vibrational bubble dynamics was performed. It

was intended that direct comparisons could be made with the CFD analysis performed by the

graduate student, however this could not be accurately carried out due to various factors. The

main reason for this was that in the simulations, the bubble behaviour was analyzed from time

zero, which means that the equivalent physical test had to have data from the beginning of the

bubble injection point. However, the way that the camera was setup during tests, initial

conditions of the bubbles were unobtainable, and that still photos that were taken were not from

the beginning of the bubble formation. However, similar generalizations to the ones that the

CFD analysis shows could be made for the experiments as well, even though direct comparisons

were not possible.

There were a few specific modes of dynamical analysis that were performed. The first

aspect was the motion of the centre of mass of the bubble during the oscillation. Analysis of this

could give insight as to the way the bubble behaves relative to the forced oscillation. For a

bubble that stays perfectly spherical during an oscillation, the position of the centre of mass

should oscillate in a manner that is the same as of the induced acceleration [11]. In the case of

the experiment, the induced oscillation was of a sinusoidal nature. So for a perfectly spherical

bubble, the centre of mass should stay at the bubble’s geometric centre and oscillate in a

perfectly sinusoidal manner. For a bubble that is deforming during the oscillation, it was

expected that this sinusoidal motion would be overlapped with motion of the centre of mass

within the bubble. Measuring the degree of this motion throughout an oscillation period yields a

quantitative method of determining bubble deformation behaviour in the system.

21

Finding the centre of mass of a bubble and showing its motion, however for the physical

test was not straightforward. This information had to be extracted from the still photos that were

taken, for which no automated method was available. To do this, the shape and size of the

bubble had to be extracted and the mass distribution of the bubble had to be integrated based on

the volume profile. To do this from the photos, two major assumptions were made. The first

was that the density of the fluid in the bubble was constant, so that the centre of mass could be

calculated purely from the geometry. Secondly, it was assumed that the centre of mass could be

determined from the 2-dimensional profiles of the bubbles, which is all that the still photos could

show. Based on these assumptions, the centre of mass of a bubble was found by the following

method. First, a profile of the surface of the bubble in a single frame was mapped out by one of

two methods. In the first method, the photo was inlaid onto a grid system from which

coordinates of the surface were taken. These coordinates were then exported into Solidworks

CAD software, which made a spine fit for the surface shape of the bubble. Alternatively, the

second method that was used was to import the entire photo first into Solidworks, for which a

spline fit could be manually drawn from the picture. The first method was more accurate since a

high resolution grid was used to map out the contour of the bubble. However, this process was

impractical when applied to many frames so the slightly less accurate spline-fit method was used

later on. Once a spline was created, the Solidworks software ‘section properties’ feature was

used to find the centroid of the shape. Because of the constant density assumption, this centroid

could also be taken as the centre of mass. It should be also noted that the x-coordinate of the

centre of mass was the extracted quantity. This corresponds to the ‘up-and-down’ motion of the

centre of mass of the bubble. The lateral motion with respect to the tube wall was not examined.

The diameter of the Solidworks model spline was also taken. With this information along with

22

the length of the frame and measurement of the bubble’s relative size within the photo frame, the

actual diameter of the bubble in a particular frame could be measured (refer to Appendix E for

calculations). With this, the true position of the centre of mass could be found, relative to a

specific point on the frame (taken at its front edge). For consistency, the diameter in a frame was

measured as the widest distance between either ends of the bubble in the x-direction (up-down

motion direction). These parameters were taken for a bubble at different frames. How these

changed with oscillation were analyzed. Specifically, four conditions were measured, two with

air bubbles (50 Hz and 10g over 3 cycles for a large air bubble; 100 Hz and 25g over 60 cycles

for a small air bubble; vegetable oil at 0.01 peak to peak displacement and 10g over 3 cycles; and

kerosene at 100 Hz and 20g over 3 cycles). These conditions are also summarized in Appendix

A.

Another parameter that was examined was a more direct way of measuring deformation

of the bubble surface. Since the volume of the bubble does not change during the oscillation (the

amount of the fluid in the bubble over time has to stay constant) the surface area changes as the

bubble deforms. A measure of this change during the oscillation is a direct way of observing the

deformation characteristics. The way that this was done was to take the splines that had already

been created of a bubble at different points in its oscillation and measure their lengths (Appendix

E). Analysis was then performed to see if the deformation could be viewed as being ‘regular’ or

‘irregular.’ Regular deformation means that the shape of a bubble at specific points in the

oscillation period remains the same over time. For example, the spline length of a bubble at a

specific point in an oscillation can be observed over a number of cycles to see if it is changing.

If it is not, it can be concluded that a regular oscillation of the bubble is taking place. The actual

shape can also be observed so that a qualitative examination can be used to confirm this. This is

23

what was done on the bubbles that were analyzed. Specifically, spline lengths were compared

between the starts of oscillations, between the quarter points, between the half points, and

between the three-quarter points. It must be noted that these specific points were only compared

with each other and not with other points in the oscillation. This is because the bubbles are

going through a motion that is repeating according to the oscillation frequency, so that what is

being examined is whether a single point in the oscillation is changing over many successive

oscillations.

4.2 Analysis

4.2.1 Center of Mass Motion Analysis of the centre of mass movement was performed by plotting this point over three

oscillations for the large air bubble, kerosene bubble, and the vegetable oil bubble. Comparisons

were made between the three by showing how well the motion of each bubble fit into a

sinusoidal plot. Before this was done however, the effect of gravity was needed to be removed

to show the true sinusoidal nature of the centre of mass vibration. The method used for this was

to use a 2nd degree polynomial fit for the plot and subtract this from the centre of mass position

curve. The reasoning for this is that any particular bubble experiencing the oscillation in this test

also feels a net upward force resulting in the difference between the buoyant and gravitational

forces (this will be further explained below). Both the oscillation and linear forces show up in

Figures 8 to 10. However, the object of the test is to examine centre of mass motion irrespective

of this acceleration. According to Newtonian dynamics, for a constant acceleration system:

𝑑𝑑 = 𝑑𝑑0 + 𝑣𝑣𝑡𝑡 +12 𝑎𝑎𝑡𝑡2

24

where 𝑑𝑑 is the displacement of the object, 𝑑𝑑0 is its initial position, 𝑣𝑣 is its velocity, 𝑎𝑎 is the

acceleration, and 𝑡𝑡 is the time. This is a 2nd order polynomial which can be subtracted from the

equation to observe the sinusoidal motion without the constant acceleration effect. The

polynomial for each trial was taken from an excel curve fit, which was then subtracted to show

the sine curves in Figures 11 to 13. From these plots, a sinusoidal plot fitting was performed

according to the following equation:

𝑠𝑠 = 𝑎𝑎 + 𝑏𝑏cos(𝑐𝑐𝑐𝑐 + 𝑑𝑑)

Each of the four parameters was fitted in each case to give a perfect sinusoidal curve overlay of

the actual curve of the centre of mass motion. Using this, observations were made regarding

how the actual plots deviated from the perfect sine curves.

By visual inspection of these graphs, it is easy to see a fairly strong fit between the

experimental curves and the sinusoidal fits in each case. Before the test, it had been proposed

that bubbles that experienced high amounts of shape deformation should have the highest

deviation from a perfect sine curve. However this does not appear to be the case as comparison

between the air, kerosene and oil curves shows no appreciable difference as far as the level of

this deviation. Even though the air bubble showed much more deformation than the kerosene

and oil bubbles, its centre of mass deviation was roughly around the same order of magnitude for

each case. Specifically, comparison of the offset between minimum and maximum points and

the sine-fitted curve showed no more than 20% of the amplitude difference in any case, with

most being around 10% (refer to Table 3). This, aided with the visual inspection of the curves,

shows a relatively low correlation between the deformation motion and its effect on the centre of

mass motion curve.

25

There may be a few reasons why there was only a weak correlation seen between the

bubble deformation and the sine curve offset of the centre of mass motion. One major reason

may be due to errors in the spline fits. The centre of mass calculation depended entirely on the

spline fits that were made. These fits however were based on points manually overlaid onto the

bubble for any particular frame. This manual method could easily lead to errors especially in

cases where the division between the skin of the bubble and the surrounding water was not

obvious in the picture. Also, in between each point, a Bessel function is splined which does not

necessarily follow the profile of the bubble surface. These errors however, are not likely to

affect the centre of mass position so much overall due to the high amount of frames that were

splined for each case. Also, errors at this step are more likely to cause deviations away from a

perfect spline curve, whereas the results show a strong correlation for each bubble type.

Also, the fact that these plots only show three oscillations for each bubble may not be

enough oscillations to fully see the centre of mass deviations in each case. Also, according to

numerical simulations [11], the centre of mass motion seems to show more of an irregular

upward or downward shift of the centre of mass curve over a period of oscillations, rather than

any large deviations within a cycle. This suggests that the deformations do not affect the small-

scale centre of mass deviation greatly. To check this, the position of the centre of mass within

the bubble normalized by the average diameter was plotted over time for each of the cases as

well. For vegetable oil the centre of mass falls in between 49 to 51.5 % of the average diameter,

while for kerosene, this falls between 47 and 53%, as can be seen from Figures 14 to 16. For the

large air bubble, the range is much higher, from below 40% to over 80%, which is consistent

with the higher deformations that are achieved by the air bubble. So it is clear that the motion of

26

the centre of mass in the air bubble is much higher than the others, even if its motion curve is not

largely affected.

Based on these results, it can be seen that the deformation level does not significantly

affect the sinusoidal motion of the centre of mass. However, analysis of more cycles would give

more insight into this behavior.

4.2.2 Shape Deformation

Shape deformation analysis revolved around capturing motion of the bubble surface, as

was explained in the previous section. The overall spline shape of the surface was examined

along with the spline lengths over a number of cycles for each bubble, as can be seen in Figures

18 to 21. Spline length variations for each bubble test at the quarter cycles were calculated by

first taking their largest difference for a particular quarter from these figures and then

normalizing them with the average spline length seen during the particular cycle. This gives an

indication of how these lengths varied through the cycles relative to the overall size of the

bubble. As Table 1 indicates, for each quarter cycle, the highest normalized spline length

difference was found for the small air bubble, which has a variation of between 11.79% for the ½

cycle and 19.50% for the ¾ cycles. The large bubble in most cases experiences the 2nd highest

amount of variation, ranging from 6.49% for the ¾ cycles to 14.28% in the ¼ cycle. In general,

the vegetable oil shows the next highest amount of variation, although this only peaks at 5.35%

of its average spline length. For the 0, ¼ and ½ cycles, kerosene shows the lowest variation,

between 1.22% and 3.90%. However, at ¾ cycles, its variation jumps to 9.75%, surpassing both

that of the vegetable oil and the large air bubble.

27

The variation can also be seen visually by examining the actual photos at the different

stages. Comparing the splines for each quarter cycle through the cycles also illustrates this

hypothesis in Figures 22 to 25. From these splines, it is easy to see that the air splines seem to

show the most amount of variation throughout the cycles. The vegetable oil splines show very

little variation at all quarter stages throughout the course of twenty cycles as it can be seen that

the circular profile never appreciably changes. The kerosene shows higher variation (even for

only 3 cycles of data) and is characterized by a more elliptical shape, with the minor axis in the

direction that it is being shaken and also of the tank surface.

It is also interesting to note that, especially in the air bubble cases in Figures 22 and 25,

each quarter cycle state seems to hold its own characteristic shape (although somewhat weakly),

both from one cycle to the next (as shown by the large bubble) and over many cycles (as shown

by the small bubble). As can be seen, the zero quarter for both of these bubbles shows an

eccentric shape that ‘points’ toward the top of the tank. The ¼ stage shows a ‘squeezed’ state

with the major axis of the bubble being perpendicular to the vibration motion. In the ½ frame,

the bubbles go back to a similar orientation of the 0 quarter but seems to point, although less

strongly, in the opposite direction. In the ¾ frame it goes back to a similar orientation as the ¼

frame. While the shape may not be exactly the same for a particular quarter frame from one

cycle to the next, the overall shape appears to stay the same. When comparing the large and

small air bubbles, it can be seen that they both exhibit these same states at the various quarter

lengths although there may be some differences. The zero state for the large bubble appears

more eccentric (‘more pointy’) than for the small bubble for this stage. The ¼ and ¾ squeezed

states appear quite similar, while the ½ state for the large bubble seems less eccentric than the

corresponding frame of the smaller one. This is confirmed by Figure 17, which shows the large

28

bubble spline length at 10% higher than the overall average at this point. This is about 6%

higher than that of the small bubble for this frame. It can also be seen from this graph that the

range of quarter frame spline length averages for the large bubble is slightly higher than that of

the small bubble, between -5% for the ¼, ½, and ¾ quarter frames and 10% for the 0 frame for

the large bubble, and between 4% at the 0 frame and -6% on the ¾ frame for the small bubble.

However, to accurately make any significant comparison between the two situations, data over a

higher number of oscillations for the large bubble would be needed to obtain more stable values

for the spline length averages. Analysis of spline lengths at more points in the oscillation cycle

could also help in mapping out how it changes. In these experiments a high speed camera was

used at 2000 frames per second, which means that for one oscillation of the large bubble

(oscillated at 50 Hz) 40 frames could be captured, while for the small bubble (oscillated at 100

Hz) 20 frames could be captured.

Nevertheless, it is quite clear that the bubbles experience some periodic motion even at

different oscillation conditions (notice that even at the differing frequencies, the characteristic

shapes at the various quarter frames for air are similar). Examination of the videos confirms this,

as it can be seen that there is clearly a pattern of shape deformation along each cycle. This

indicates that there is a regular motion in the bubble oscillation. This observation agrees with a

similar experiment conducted by Lauterborn and Parlitz [12] where bubbles were oscillated by

an acoustical device at various frequencies. In this test, bubble radius was mapped with

oscillation in a similar way that spline length was mapped in this test. The results of this

experiment showed a strong regular periodic behaviour in the radius change in the same way that

has been seen in this experiment.

29

The results of the experiments however, do not fully agree with the CFD simulations

performed by the graduate student. As was already mentioned, regular motion of the air bubbles

were seen at both at accelerations of both 10 and 25g. However, the CFD simulations found the

shapes of the bubbles to visibly change between oscillations at these accelerations, although a

more regular motion was observed at lower accelerations. One reason for the difference may be

that in the experiments, long term observations were made which did not include the start

conditions. However, the CFD simulations took data from the initial conditions and were a more

short term analysis. It is quite possible the experimental observations were of the bubble after

some steady state had been reached, whereas this was not the case for the CFD simulations that

had the more transient analysis from initial conditions. Based on this, it is clear that more work

would need to be done to simulate the exact conditions tested in the numerical simulations before

direct comparisons could be made between the testing and CFD.

4.3 Differences between Fluids

As has already been shown, it can also be clearly seen from still photos, splines, and the

accompanying plots that both the kerosene and the vegetable oil showed very little deformation

compared with the air bubbles. There may be a few reasons for this. Firstly, it is expected that

the viscosity of the fluid has a high impact on the deformation, as mentioned earlier. The higher

the viscosity of the fluid, the more resistant it should be to any erratic motion that the oscillation

forces.

It has also been noticed that the bubble density may have an effect on the range of bubble

deformation. If a free body diagram is drawn out around a particular bubble at a point during an

30

oscillation, three forces are experienced. First there is a buoyant force (as explained earlier)

given by:

𝐹𝐹𝑏𝑏 = 𝜌𝜌𝑤𝑤𝑔𝑔𝑉𝑉

where 𝜌𝜌𝑤𝑤 is the density of the displaced fluid, which is water in all tests. This force acts

upwards. The bubble also experiences the force of gravity, given by:

𝐹𝐹𝑔𝑔 = 𝜌𝜌𝑏𝑏𝑔𝑔𝑉𝑉

where 𝜌𝜌𝑏𝑏 is the density of the fluid inside of the bubble. These forces can be summed into the

following expression for net steady force:

𝐹𝐹𝑠𝑠𝑡𝑡𝑠𝑠𝑎𝑎𝑑𝑑𝑠𝑠 = (𝜌𝜌𝑤𝑤 − 𝜌𝜌𝑏𝑏)𝑔𝑔𝑉𝑉

This relates the force on the bubble in the absence of any forced oscillation. From this it can be

seen that the force increases as the difference between 𝜌𝜌𝑤𝑤 and 𝜌𝜌𝑏𝑏 increases. For the case of

water and air, where water is the more dense fluid by a factor of one thousand, the net upward

force is very high, which explains the speed that these bubbles move up through the tank. For

fluids such as vegetable oil and kerosene, whose densities are closer to that of water, this force

becomes smaller, increasing the time for these bubbles to reach the top surface. Up to this point,

the steady assumption has been used, which neglects the third oscillatory force caused by the

induced vibration. This force can be incorporated into the above expression by noticing that it

acts on both of the fluids together, which means that the gravitational acceleration term is

changed by the addition of this acceleration as follows:

𝐹𝐹𝑛𝑛𝑠𝑠𝑡𝑡 = (𝜌𝜌𝑤𝑤 − 𝜌𝜌𝑏𝑏)(𝑔𝑔 + 𝑎𝑎)𝑉𝑉

The magnitude acceleration (denoted as 𝑎𝑎) changes sinusoidally as forced by the shaker. At any

point in time this could be positive or negative, depending on the point in the oscillation. It is

this continuous back and forth movement that causes the force that induces the deformation of

31

the bubble. From the equation, it can be seen that as the magnitude of 𝜌𝜌𝑤𝑤 − 𝜌𝜌𝑏𝑏 increases, the

magnitude of the net force increases, and thus the deformation. Therefore, it should make sense

that a bubble with a much smaller density than of water, such as air, would experience much

higher deformation than a bubble that is of kerosene or vegetable oil, where the magnitude of the

density difference would not be so high.

32

Chapter 5: Recommendations and Conclusions

5.1 Recommendations

The experiments yielded useful data for analysis, however there were many difficulties

that were encountered that could be improved. These included apparatus setup, human error, as

well as experimental and data analysis methodological errors. This section exploits each

problem in detail as well as recommends useful actions should any further pursuit of the same

experiment be performed in the future.

5.1.1 Recommendation 1

The first experimental setup recommendation point worth mentioning regards the bubble

injection system. Inconsistency in the bubble sizes injected into the water-filled cylinder is a

problem that would first need to be addressed, as the system used could not produce a single

bubble of a predictable size. The method used in this experiment, using a syringe and a needle to

inject the bubble into the cylinder, does not provide constant sizes of bubbles, especially in the

current case that many types of fluids are tested. Also, the manual injection adds human error in

that the force inputted for injection is not constant. For example, the same size of needle did not

supply the same sizes of bubbles for air, kerosene, and veggie oil, and it also did not deliver the

same bubble sizes for different vibration states; e.g. vibrating frequencies, gravitational force,

and/or displacement. Inconsistencies of bubble sizes injected make the data analysis of multiple

bubbles hard to compare. The recommendation for this issue is that a more reliable bubble

injection system (perhaps automatic or commercially available) should be used.

Another issue with the bubble injection system is that the needle fitting attached to the

cylinder had some clearance with the outside diameter of the needle, thus creating leakage and

33

allowing air to go into the water-filled cylinder. Even though this leakage may not be

significant, it still caused undesired air bubbles in the system especially when fluids other than

air were being injected. This issue further justifies the recommendation of changing the bubble

injection system, and that the new one should have a better seal to prevent leakage in the future.

The real leakage problem, however, came from the base of the tank. After about every

15 to 20 consecutive oscillations, the resin seal at the base of the cylinder would start to break

and thus created some leakage. The leakage at this position drains water out of the tank faster

than the leakage from the needle fitting, and which slows down the experiments as the resin seal

would need at least 24 hours to cure before any experiments start again. There are two

recommendations for this issue. Firstly, the base of the tank could be made with a stronger

material before securing it to the tank portion that holds the water. This method would make it

easy for the current overall design of the tank to stay the same, and would also benefit on the

ease of cleaning the tank whenever further types of fluids, rather than air, kerosene, or vegetable

oil, were to be injected. The second recommendation assumes that the type of video camera is

used. This alternative would change the physical design of the current tank to a smaller one in

height such that it does not affect the bubble motion as well as the motion capture from the

camera. This alternative recommendation for this issue, however, may not be the right approach

since the purpose of this experiment is to study the motion of the bubbles for the maximum time

possible.


The second recommendation point of this experiment regards the inside of the tank. The

current design of the tank has one screw on top for water to be input. However, that caused

34

trouble in thoroughly cleaning the cylinder from dust, oil used from the experiment, and even

soap used to clean oil after a trial, as the dust and leftover particles could induce undesired

interaction with bubbles as well as reduce captured video and picture quality of the data. To

make sure data is as accurate as possible and to save time, the cap of the tank should be

redesigned such that it is easy to open or close to allow fast and thorough cleaning of the

cylinder.

A further issue regarding the inside of the tank is the fact that gas bubbles tend to stick to

the inner surface of the cylinder. As one may notice this from any transparent water containers,

air bubbles tend to stick to the surface. In some cases this could void a trial as a bubble may hit a

wall or affect the motion of other bubbles inside the tank, which can greatly affect the nature of

the bubble deformation. Although in most cases this was not a problem because the injection

needle was placed sufficiently close to the centre so that wall effects were minimal, it may be

beneficial in later runs to use a higher diameter tank to completely eliminate this phenomenon or

possibly use a material with even less surface roughness, which could possibly decrease the

interaction between bubbles and the wall surface.


The third recommendation point is about the captured data and camera. Only one camera

was used in the procedure which did not capture any bubble at the initial point after injection.

Also, the data extracted by the photos were two-dimensional in nature and the refraction of light

through the wall of the tank was not taken into account for the analysis of the bubbles. This lack

of dimension and completeness in the observed shape of any bubble could have significant

effects during the analysis of the data, especially if the bubbles do change shape dramatically.

35

Also, analysis of centre of mass position from 2D capture is only based on the assumptions that

the analyzed bubble only moved vertically and that was not always the case. Another issue with

the camera was the limitation of the captured window sizes. From the result analyzed in the

sections above, it can be seen that the size of the captured window one camera can capture is not

very large. One recommendation to this issue is to try using multiple cameras at different angles

around the tank to capture motions at these different angles as well as having more cameras at

higher distance. For example, the first camera can be placed to focus at the point where the

bubble is injected while a second camera recording at the same height but at 90 degrees around

the outside of the tank can be used to view the bubble from this alternative angle. Two more

cameras at the same angle but at higher distance from the ground could also be used to capture

more data. Another alternative is to use some other camera system that can capture broader

views of the tank.


The last point of recommendation deals with experimental or data analysis

methodological issues. One goal of this experiment was to maximize the time of bubble

levitation such that the study of shape changes of the bubbles can be easily performed. However,

as indicated already, this became almost impossible since all the fluids ejected into the tank

system (air, kerosene, and vegetable oil) had lower densities than water, while an acoustic wave

setup exceeded the limitation of the shaker. The recommendation for this issue could be to try to

find a more desirable tank structure or design such that the use of an acoustic wave to induce

vibration becomes possible. Another issue that would also need to be addressed is about the set

of conditions of experimental data. The experimental procedure for each of the three fluids was

36

conducted at a combination of different vibrating frequencies, forces and displacements that

were not necessarily the same for each. This was done out of necessity because the parameters

often changed between tests of differing fluids which made it difficult to test each at the same

conditions. However this made analysis and comparisons between each fluid difficult. Future

experiments should be set to three or more common sets of testing conditions for all cases such

that data from each case can be most easily compared.

5.2 Conclusions Based on the experiments that were performed on the two sizes of air bubbles as well as

on the kerosene and vegetable oil, a few generalizations could be made. Firstly, bubble

deformation caused by the oscillatory force tends to increase for fluids less viscous and dense

than the surrounding fluid. The less viscous the fluid, the less resistant it is to change shape,

while the higher density difference between the fluids will increase the amplitude of the

deformation. It was also found that bubbles closely follow the sinusoidal nature of the induced

oscillation, even in extreme deformation circumstances where it was otherwise expected that the

centre of mass position would not follow this oscillation as well as in the case where deformation

is small.

A regular motion was also found under forced oscillation (although weak). This shows

that a bubble, at least for a certain amount of oscillations, behaves in a predictable manner. This

does not completely agree with the CFD analysis that has been previously performed, which

finds an irregular motion at high accelerations similar to the tested conditions. However, the

limited amount of conditions actually tested produced an insufficient amount of data to make

accurate comparisons between the simulations and the actual test.

37

Overall, while this test produced some interesting results, it was observed that certain

aspects of the experiments could be adjusted and more trials could be performed to obtain more

accurate comparisons between the CFD simulations and the actual tested nature of bubble

vibration.

38

Bibliography [1] Mohammad Movassat, "PhD Thesis Proposal: Numerical Modeling of Bubble Dynamics in

Microgravity," Toronto, ON, 2009. [2] R. Shankar Subramanian, The Motion of Bubbles and Drops in Reduced Gravity.

Cambridge, United Kingdom: Cambridge University Press, 2001. [3] M. Kawaji, N. Ashgriz, and M. Bussmann, "Application of Controlled Vibrations to

Separate Phases in Fluid Mixtures and Segregate Particles in Solid-Fluid Mixtures under Microgravity," Toronto, ON,.

[4] Yutaka Abe, Masahiro Kawaji, and Tadashi Watanabe, "Study on the bubble motion control by ultrasonic wave," Experimental Thermal and Fluid Science, vol. 26, pp. 817-826, 2002.

[5] Osamu Kawanami et al., "Heat transfer and bubble behaviors in microgravity pool boiling in esa parabolic flight experiment," Microgravity Science and Technology, vol. 21, pp. S3-S8, August 2009.

[6] Thilanka Munasinghe, "Studying the Characteristics of Bubble Motion in Pool Boiling in Microgravity Conditions Under the Influence of a Magnetic Field," 2009.

[7] Bruce R. Munson, Donald F. Young, and Theodore H. Okiishi, Fundamentals of Fluid Mechanics, 5th ed. Hoboken, NJ, United States of America: John Wiley & Sons, Inc., 2006.

[8] Lawrence A. Crum, "Bjerknes Forces on Bubbles in A Stationary Sound Field," Acoustical Society of America, vol. 57, no. 6, pp. 1363-1369, 1975.

[9] Glenn Elert. (2000) The Physics Factbook Web site. [Online]. http://hypertextbook.com/facts/2000/IngaDorfman.shtml

[10] VEE GEE Scientific, Inc. (2004, December) MSDS No. M1002. [Online]. http://www.veegee.com/msds/m1002.pdf

[11] Timothy J. Friesen, Hiroyuki Takahira, Lisa Allegro, Yoshitaka Yasuda, and Masahiro Kawaji, "Numerical Simulations of Bubble Motion in a Vibrated Cell Under Microgravity Using Level Set and VOF Algorithms," New York Academy of Sciences, p. 299, 2002.

[12] W. Lauterborn and U. Parlitz, "Methods of Chaos Physics and Their Application to Acoustics," Acoustical Society of America, p. 1984, 1988.

http://hypertextbook.com/facts/2000/IngaDorfman.shtml�

http://www.veegee.com/msds/m1002.pdf�

39

Chapter 6: Figures and Tables

FIGURE 1: SCHEMATIC DIAGRAM OF STATIONARY BUBBLES IN AN ACOUSTIC STANDING WAVE FIELD [4]

FIGURE 2: SCHEMATIC DIAGRAM OF EXPERIMENTAL APPARATUS [4]

40

FIGURE 3: ALTERNATIVE #2 EXPERIMENTAL APPARATUS

41

FIGURE 4: LARGE AIR BUBBLE STILL PHOTOS AT 2000 FRAMES / SECOND FOR 1 CYCLE

42

0 / 12 10 / 212 20 / 412 30 / 612 40 / 812 60 / 1012

0.25 / 17 10.25 / 217 20.25 / 417 30.25 / 617 40.25 / 817 60.25 / 1017

0.5 / 22 10.5 / 222 20.5 / 422 30.5 / 622 40.5 / 822 60.5 / 1022

0.75 / 27 10.75 / 227 20.75 / 427 30.75 / 627 40.75 / 827 60.75 / 1027 FIGURE 5: SMALL AIR BUBBLE STILL PHOTOS AT 2000 FRAMES / SECOND OF EVERY 10 CYCLES FOR 6 CYCLES (CYCLE / FRAME LISTED BELOW EACH PHOTO)

43

FIGURE 6: VEGETABLE OIL BUBBLE STILL PHOTOS AT 2000 FRAMES / SECOND FOR 1 CYCLE

FIGURE 7: KEROSENE BUBBLE STILL PHOTOS AT 2000 FRAMES / SECOND FOR 1 CYCLE

44

FIGURE 8: CENTER OF MASS POSITION RELATIVE TO FRONT OF FRAME FOR 3 OSCILLATIONS FOR LARGE AIR BUBBLE

FIGURE 9: CENTER OF MASS POSITION RELATIVE TO FRONT OF FRAME FOR 3 OSCILLATIONS FOR VEGETABLE OIL BUBBLE

FIGURE 10: CENTER OF MASS POSITION RELATIVE TO FRONT OF FRAME FOR 3 OSCILLATIONS FOR KEROSENE BUBBLE

x = -85.16t2 - 9.767t + 2.973

1.5

2

2.5

3

3.5

0 0.01 0.02 0.03 0.04 0.05 0.06 0.07

Dis

tanc

e fr

om B

egin

ning

of F

ram

e (c

m)

Time (s)

y = -67.33x2 - 8.683x + 1.802

1.55

1.6

1.65

1.7

1.75

1.8

1.85

0 0.005 0.01 0.015 0.02 0.025Dis

tanc

e fr

om B

egin

ning

of F

ram

e (c

m)

Time (s)

x = -57.07t2 - 7.362t + 2.292

1.95

2

2.05

2.1

2.15

2.2

2.25

2.3

2.35

0 0.005 0.01 0.015 0.02 0.025 0.03 0.035

Dis

tanc

e fr

om B

egin

ning

of

Fram

e (c

m)

Time (s)

45

FIGURE 11: CENTER OF MASS POSITION FOR 3 OSCILLATIONS FOR LARGE AIR BUBBLE AFTER CONSTANT ACCELERATION CORRECTION WITH SINUSOIDAL FIT

FIGURE 12: CENTER OF MASS POSITION FOR 3 OSCILLATIONS FOR VEGETABLE OIL BUBBLE AFTER CONSTANT ACCELERATION CORRECTION WITH SINUSOIDAL FIT

FIGURE 13: CENTER OF MASS POSITION FOR 3 OSCILLATIONS FOR KEROSENE BUBBLE AFTER CONSTANT ACCELERATION CORRECTION WITH SINUSOIDAL FIT

-0.5

-0.3

-0.1

0.1

0.3

0.5

0 0.01 0.02 0.03 0.04 0.05 0.06 0.07

Posi

tion

(cm

)

Time (s)

Air [Experimental] Air [Curve Fit] x=0.39cos(313t-2.6)

-0.03

-0.02

-0.01

0

0.01

0.02

0.03

0 0.005 0.01 0.015 0.02 0.025

Posi

tion

(cm

)

Time (s)

Veggie Oil [Experimental] Veggie Oil [Curve Fit]x = 0.02cos(863t-2.5)

-0.07

-0.05

-0.03

-0.01

0.01

0.03

0.05

0.07

0 0.005 0.01 0.015 0.02 0.025 0.03 0.035

Posi

tion

(cm

)

Time (s)

Kerosene [Experimental] Kerosene [Curve Fit] x = 0.0542cos(632t-2.75)

46

FIGURE 14: LARGE AIR BUBBLE CENTRE OF MASS / AVERAGE DIAMETER

FIGURE 15: VEGETABLE OIL BUBBLE CENTRE OF MASS / AVERAGE DIAMETER

FIGURE 16: KEROSENE BUBBLE CENTRE OF MASS / AVERAGE DIAMETER

0.3

0.4

0.5

0.6

0.7

0.8

0.9

0 0.01 0.02 0.03 0.04 0.05 0.06 0.07

Cent

er o

f Mas

s /

Dia

met

er

Time (s)

0.49

0.495

0.5

0.505

0.51

0.515

0 0.005 0.01 0.015 0.02 0.025

Cent

er o

f Mas

s /

Dia

met

er

Time (s)

0.460.470.480.49

0.50.510.520.530.54

0 0.005 0.01 0.015 0.02 0.025 0.03 0.035

Cent

er o

f Mas

s /

Dia

met

er

Time (s)

47

FIGURE 17: AVERAGE 1/4 CYCLE SPLINE LENGTHS AS PERCENTAGE OF OVERALL AVERAGE SPLINE LENGTHS FOR ALL TESTED BUBBLES

FIGURE 18: LARGE AIR BUBBLE SURFACE SPLINE LENGTH AT 0, 1/4, 1/2, AND 3/4 POINTS OF 3 SUCCESSIVE CYCLES

92.00%

94.00%

96.00%

98.00%

100.00%

102.00%

104.00%

106.00%

108.00%

110.00%

112.00%

0 0.25 0.5 0.75

1/4

Cycl

e A

vera

ge S

plin

e Le

ngth

s / O

vera

ll A

vg S

plin

e Le

ngth

1/4 CycleLarge Air Bubble Kerosene Veggie Oil Small Air Bubble

1.3

1.35

1.4

1.45

1.5

1.55

1.6

1.65

1.7

1.75

1.8

0 0.5 1 1.5 2 2.5 3 3.5

Splin

e Le

ngth

(cm

)

Cycle

Length at 0

Length at 1/4

Length at 1/2

Lenth at 3/4

48

FIGURE 19: VEGETABLE OIL BUBBLE SURFACE SPLINE LENGTH AT 0, 1/4, 1/2, AND 3/4 LENGTH POINTS AT 5 CYCLE INTERVALS

FIGURE 20: KEROSENE BUBBLE SURFACE SPLINE LENGTH AT 0, 1/4, 1/2, AND 3/4 LENGTH POINTS OF 3 SUCCESSIVE CYCLES

FIGURE 21: SMALL AIR BUBBLE SURFACE SPLINE LENGTH AT 0, 1/4, 1/2, AND 3/4 LENGTH POINTS AT 10 CYCLE INTERVAL

1.121.131.141.151.161.171.181.19

1.2

0 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20

Splin

e Le

ngth

(cm

)

Cycle

Length at 1/4

Length at 1/2

Length at 3/4

Length at 0

0.78

0.8

0.82

0.84

0.86

0.88

0.9

0 0.5 1 1.5 2 2.5 3 3.5

Splin

e Le

ngth

(cm

)

Cycle

Length at 0

Length at 1/4

Length at 1/2

Length at 3/4

0.3

0.35

0.4

0.45

0.5

0 10 20 30 40 50 60

Splin

e Le

ngth

(cm

)

Cycle

0 Length

1/4 Length

1/2 Length

3/4 Length

49

0 / 290 1 / 330 2 / 370 3 / 410

0.25 / 300 1.25 / 340 2.25 / 380

0.5 / 310 1.5 / 350 2.5 / 390

0.75 / 320 1.75 / 360 2.75 / 400

FIGURE 22: LARGE AIR BUBBLE SPLINE FIT FOR EACH QUARTER OF 3 CONSECUTIVE CYCLES (CYCLE / FRAME LISTED BELOW EACH SPLINE)

50

0 / 165 5 / 225 10 / 300 15 / 375 20 /450

0.25 / 168 5.25 / 228 10.25 / 303 15.25 / 378 20.25 / 453

0.5 / 172 5.5 / 232 10.5 / 307 15.5 / 382 20.5 / 457

0.75 / 176 5.75 / 236 10.75 / 311 15.75 / 386 20.75 / 461

FIGURE 23: VEGETABLE OIL BUBBLE SPLINE FIT FOR EACH QUARTER OF 3 CONSECUTIVE CYCLES (CYCLE / FRAME LISTED BELOW EACH SPLINE)

51

0 / 153 1 / 172 2 / 192 3 / 212

0.25 / 157 1.25 / 177 2.25 / 197

0.5 / 162 1.5 / 182 2.5 / 202

0.75 / 167 1.75 / 187 2.75 / 207

FIGURE 24: KEROSENE BUBBLE SPLINE FIT FOR EACH QUARTER OF 3 CONSECUTIVE CYCLES (CYCLE / FRAME LISTED BELOW EACH SPLINE)

52

0 / 12 10 / 212 20 / 412 30 / 612 40 / 812 50 / 1012

0.25 / 17 10.25 / 217 20.25 / 417 30.25 / 617 40.25 / 817 50.25 / 1017

0.5 / 22 10.5 / 222 20.5 / 422 30.5 / 622 40.25 / 822 50.5 / 1022

0.75 / 27 10.75 / 227 20.75 / 427 30.75 / 627 40.75 / 827 50.75 / 1027 FIGURE 25: SMALL AIR BUBBLE SPLINE FIT FOR EACH QUARTER OF EVERY 10 CYCLES (CYCLE / FRAME LISTED BELOW EACH SPLINE)

53

FIGURE 26: AVERAGE 1/4 CYCLE SPLINE LENGTHS FOR ALL TESTED BUBBLES

FIGURE 27: AVERAGE 1/4 CYCLE DIAMETERS FOR ALL TESTED BUBBLES

0.2

0.4

0.6

0.8

1

1.2

1.4

1.6

1.8

0 0.25 0.5 0.75

1/4

Ave

rage

Spl

ine

Leng

ths (

cm)

1/4 Cycle

Large Air Bubble Kerosene Veggie Oil Small Air Bubble

0

0.1

0.2

0.3

0.4

0.5

0.6

0.7

0 0.25 0.5 0.75

1/$

Cycl

e A

vera

ge D

iam

ater

s (c

m)

1/4 Cycle


54

FIGURE 28: AVERAGE 1/4 CYCLE SPLINE LENGTHS AS PERCENTAGE OF OVERALL AVERAGE SPLINE LENGTHS FOR ALL TESTED BUBBLES

FIGURE 29: AVERAGE 1/4 CYCLE SPLINE LENGTHS AS PERCENTAGE OF OVERALL AVERAGE DIAMETERS FOR ALL TESTED BUBBLES

92%

94%

96%

98%

100%

102%

104%

106%

108%

110%

112%

0 0.25 0.5 0.751/4

Cycl

e A

vera

ge S

plin

e Le

ngth

s / O

vera

ll A

vg

Splin

e Le

ngth

1/4 Cycle


70%

80%

90%

100%

110%

120%

130%

140%

150%

160%

0 0.25 0.5 0.751/4

Cycl

e A

vera

ge D

iam

ater

s /

Ove

rall

Avg

Dia

mat

er

1/4 Cycle


55

FIGURE 30: 3D SOLIDWORKS RENDERING OF THE EXPERIMENTAL APPARATUS

Transparent Acrylic Cylindrical

Metal Needle Fitting

Metal Waterproofing Plate

Plastic Shaker Fixture

56

FIGURE 31: ENGINEERING DRAWING OF THE CYLINDRICAL TANK

57

Large Air Bubble

Kerosene

Veggie Oil

Small Air Bubble

d avg 0.40202

d avg 0.218056

d avg 0.359861

d avg 0.122708

L avg 1.540278

L avg 0.820605

L avg 1.177969

L avg 0.441047

0

0

0

0

delta (cm) 0.148

delta (cm) 0.032

delta (cm) 0.051

delta (cm) 0.07

%d 36.81%

%d 14.68%

%d 14.17%

%d 57.05%

%L 9.61%

%L 3.90%

%L 4.33%

%L 15.87%

0.25

0.25

0.25

0.25

delta (cm) 0.22

delta (cm) 0.01

delta (cm) 0.063

delta (cm) 0.071

%d 54.72%

%d 4.59%

%d 17.51%

%d 57.86%

%L 14.28%

%L 1.22%

%L 5.35%

%L 16.10%

0.5

0.5

0.5

0.5

delta (cm) 0.116

delta (cm) 0.032

delta (cm) 0.051

delta (cm) 0.052

%d 28.85%

%d 14.68%

%d 14.17%

%d 42.38%

%L 7.53%

%L 3.90%

%L 4.33%

%L 11.79%

0.75

0.75

0.75

0.75

delta (cm) 0.1

delta (cm) 0.08

delta (cm) 0.054

delta (cm) 0.086

%d 24.87%

%d 36.69%

%d 15.01%

%d 70.08%

%L 6.49%

%L 9.75%

%L 4.58%

%L 19.50%

TABLE 1: MAXIMUM DIFFERENCE (DELTA) BETWEEN MEASURED SPLINE LENGTHS VS AVERAGE OVERALL DIAMETER AND SPLINE LENGTHS FOR CYCLE QUARTER POINTS OF ALL BUBBLES

58

Large Air Bubble

Kerosene

Veggie Oil

Small Air Bubble

d (cm) L (cm)

d (cm) L (cm)

d (cm) L (cm)

d (cm) L (cm) 0 0.595556 1.702488

0.214583 0.804813

0.356444 1.166001

0.146667 0.459658

0.25 0.343704 1.468891

0.209259 0.808457

0.355556 1.16388

0.1 0.44443 0.5 0.416296 1.466767

0.221296 0.821431

0.354667 1.165537

0.146667 0.445857

0.75 0.312593 1.468895

0.227778 0.852982

0.355556 1.158673

0.0975 0.414241

Overall avg 0.40202 1.540278

0.218056 0.820605

0.359861 1.177969

0.122708 0.441047

d/davg L/Lavg

d/davg L/Lavg

d/davg L/Lavg

d/davg L/Lavg 0 148.14% 110.53%

98.41% 98.08%

99.05% 98.98%

119.52% 104.22%

0.25 85.49% 95.37%

95.97% 98.52%

98.80% 98.80%

81.49% 100.77% 0.5 103.55% 95.23%

101.49% 100.10%

98.56% 98.94%

119.52% 101.09%

0.75 77.76% 95.37%

104.46% 103.95%

98.80% 98.36%

79.46% 93.92%

TABLE 2: AVERAGE DIAMETERS AND SPLINE LENGTHS FOR QUARTER CYCLES OF ALL BUBBLES

59

Vegetable Oil oil

Kerosene

Large Air

Sinusoidal Fit: y=a+b*cos(cx+d) Sinusoidal Fit: y=a+b*cos(cx+d) Sinusoidal Fit: y=a+b*cos(cx+d)

Coefficient Data:

Coefficient Data:

Coefficient Data: a = 0

a = 0

a = 0

b = 0.02

b = 0.05423

b = 0.39 c = 862.7523

c = 631.8773

c = 313.1835

d = -2.5

d = -2.75

d = -2.6

max 0.021876

max 0.059517

max 0.466466 max % 9.38%

max % 9.75%

max % 19.61%

min -0.02169

min -0.05104

min -0.42945 min % 8.45%

min % -5.88%

min % 10.12%

Note: % Values are maximum or minimum normalized by spline amplitude (or parameter b) TABLE 3: SINE CURVE FITTING EQUATION VALUES AND MINIMUM AND MAXIMUM DIFFERENCES BETWEEN FITS AND ACTUAL VALUES

60

Outer Do [cm]

Inner Di [cm]

Height, h [cm]

Tank Weight, Wt [g]

Water Weight, Ww [g]

Total Weight, W [kg]

Total Weight, W [lb]

Force Needed, F [N]

Force Needed, F [Lbs]

5 4.365 50 277.90 748.22 1.03 2.26 100.46 22.59

5 4.365 100 555.80 1496.44 2.05 4.51 200.93 45.17

5 4.365 110 611.38 1646.08 2.26 4.97 221.02 49.69

6 5.365 50 337.25 1130.31 1.47 3.23 143.68 32.30

6 5.365 65 438.42 1469.41 1.91 4.20 186.79 41.99

6 5.365 80 539.60 1808.50 2.35 5.17 229.89 51.68

7 6.365 35 277.62 1113.67 1.39 3.06 136.22 30.62

7 6.365 45 356.94 1431.86 1.79 3.94 175.13 39.37

7 6.365 55 436.26 1750.05 2.19 4.81 214.05 48.12

7 6.365 60 475.92 1909.14 2.39 5.25 233.51 52.50

8 7.365 30 273.57 1278.08 1.55 3.41 151.92 34.15

8 7.365 35 319.16 1491.09 1.81 3.98 177.24 39.84

8 7.365 40 364.76 1704.10 2.07 4.55 202.55 45.54

8 7.365 45 410.35 1917.11 2.33 5.12 227.87 51.23

9 8.365 25 257.65 1373.92 1.63 3.59 159.74 35.91

9 8.365 30 309.18 1648.71 1.96 4.31 191.69 43.09

9 8.365 35 360.71 1923.49 2.28 5.03 223.64 50.28

10 9.365 20 229.86 1377.64 1.61 3.54 157.38 35.38

10 9.365 25 287.32 1722.05 2.01 4.42 196.73 44.23

10 9.365 30 344.79 2066.46 2.41 5.30 236.08 53.07

12 11.365 15 208.00 1521.67 1.73 3.81 169.35 38.07

12 11.365 20 277.34 2028.89 2.31 5.07 225.79 50.76

15 14.365 10 174.28 1620.69 1.79 3.95 175.74 39.51

15 14.365 13 226.56 2106.90 2.33 5.13 228.46 51.36

15 14.365 30 522.83 4862.08 5.38 11.85 527.22 118.52

Acrylic (ρa) Water (ρw)

Density 1.19 1 g/cm^3 Thickness 0.3175

cm

TABLE 4: TABLE OF DIMENSIONS CONSIDERED FOR TANK AND FORCES NEEDED FROM SHAKER

// Limiting total weight of cylinder & water to 5lbs; assuming the fixture has the weight of 5 lbs // Shaker mounting plate has the diameter of 6 in (12.54 cm) //Bolded figures indicate possible scenarios of maximum allowable weight //Highlighted conditions represent the dimensions we will be using in the experiment

A

Appendix A: Tested Conditions Large Air Bubble: 10g acceleration at 50 Hz Vegetable Oil 10g acceleration at 0.01 in peak to peak displacement Kerosene 20g acceleration at 100 Hz Small Air Bubble 25g acceleration at 100 Hz

B

Appendix B: Shaker Oscillation Parameter Calculations Parameters 𝐹𝐹, 𝑎𝑎, 𝑐𝑐𝑝𝑝𝑝𝑝 , 𝑓𝑓 Where 𝐹𝐹 = Force [lbs] 𝑎𝑎 = Acceleration [ft/s2] 𝑐𝑐𝑝𝑝𝑝𝑝= Displacement from peak to peak [in] and 𝑓𝑓 = Frequency [Hz] Constraints

𝑐𝑐𝑝𝑝𝑝𝑝 ≤ 1 𝑖𝑖𝑛𝑛 𝐹𝐹 ≤ 500 𝑙𝑙𝑏𝑏𝑠𝑠

Constants 𝑊𝑊 = Weight of filled tank and armature = 12.7 𝑙𝑙𝑏𝑏𝑠𝑠 𝑚𝑚 = Mass of filled tank and armature

𝑚𝑚 =𝑊𝑊

32.2 𝑓𝑓𝑡𝑡/𝑠𝑠2 = 0.394 𝑙𝑙𝑏𝑏𝑚𝑚

Controlling Parameters

𝑎𝑎,𝑐𝑐𝑝𝑝𝑝𝑝 ,𝑓𝑓 Controlling any of the two parameters will yield a result in the third. Related Equations

𝐹𝐹 = 𝑚𝑚𝑎𝑎 𝑐𝑐𝑝𝑝𝑝𝑝 = 2𝑐𝑐 𝜔𝜔 = 2𝜋𝜋𝑓𝑓

Control Cases

Case 1: Control 𝑐𝑐𝑝𝑝𝑝𝑝 ,𝑓𝑓

𝑎𝑎 = 𝜔𝜔2𝑐𝑐 = (2𝜋𝜋𝑓𝑓)2𝑐𝑐 = 2(2𝜋𝜋𝑓𝑓)2𝑐𝑐𝑝𝑝𝑝𝑝 Applying 𝐹𝐹 = 𝑚𝑚𝑎𝑎;

𝐹𝐹 = 𝑚𝑚�2(2𝜋𝜋𝑓𝑓)2𝑐𝑐𝑝𝑝𝑝𝑝 � Case 2: Control 𝑓𝑓,𝑎𝑎

𝑐𝑐 =𝑎𝑎𝜔𝜔2 =

𝑎𝑎(2𝜋𝜋𝑓𝑓)2

𝑐𝑐𝑝𝑝𝑝𝑝 = 2𝑐𝑐 = 2𝑎𝑎

(2𝜋𝜋𝑓𝑓)2

Applying 𝐹𝐹 = 𝑚𝑚𝑎𝑎; 𝐹𝐹 = 𝑚𝑚�2(2𝜋𝜋𝑓𝑓)2𝑐𝑐𝑝𝑝𝑝𝑝 �

C

Case 3: Control 𝑐𝑐,𝑎𝑎

𝑓𝑓 =𝜔𝜔2𝜋𝜋 =

12𝜋𝜋

�𝑎𝑎𝑐𝑐 =

12𝜋𝜋�

2𝑎𝑎𝑐𝑐𝑝𝑝𝑝𝑝

Applying 𝐹𝐹 = 𝑚𝑚𝑎𝑎; 𝐹𝐹 = 𝑚𝑚�2(2𝜋𝜋𝑓𝑓)2𝑐𝑐𝑝𝑝𝑝𝑝 �

For all equations involving acceleration and displacement, the appropriate unit was utilized between feet and inches: 1 ft = 12 inches. Also, to express 𝑎𝑎 in terms of 𝑔𝑔’s, divide 𝑎𝑎 by 32.2 ft / s2.

D

Appendix C: Levitation Calculations

𝜆𝜆 = 𝑉𝑉𝑡𝑡 𝑉𝑉𝑠𝑠𝑠𝑠𝑠𝑠𝑛𝑛𝑑𝑑 𝑖𝑖𝑛𝑛 𝑤𝑤𝑎𝑎𝑡𝑡𝑠𝑠𝑤𝑤 = 1500 𝑚𝑚/𝑠𝑠

𝑡𝑡 =𝜆𝜆

𝑉𝑉𝑠𝑠𝑠𝑠𝑠𝑠𝑛𝑛𝑑𝑑 𝑖𝑖𝑛𝑛 𝑤𝑤𝑎𝑎𝑡𝑡𝑠𝑠𝑤𝑤=

0.4 𝑚𝑚1500 𝑚𝑚/𝑠𝑠 = 0.000267 𝑠𝑠

𝑓𝑓 =1𝑡𝑡 =

10.000267 𝑠𝑠 = 3750 𝐻𝐻𝐻𝐻

𝑎𝑎 = 𝜔𝜔2𝑐𝑐

𝑐𝑐 =

𝑎𝑎𝜔𝜔2

For 𝑎𝑎 = 1 𝑔𝑔;

𝑐𝑐 = �32 𝑓𝑓𝑡𝑡 𝑠𝑠2⁄

[2𝜋𝜋(3750 𝐻𝐻𝐻𝐻)]2� �12 𝑖𝑖𝑛𝑛1 𝑓𝑓𝑡𝑡 � = 6.92 × 10−7𝑖𝑖𝑛𝑛 = 0.692 𝜇𝜇𝑖𝑖𝑛𝑛

Need 𝑎𝑎𝑚𝑚𝑎𝑎𝑐𝑐 in terms of 𝑔𝑔: Max force = 500 𝑙𝑙𝑏𝑏𝑓𝑓 System weight 𝑊𝑊 = 12.7 𝑙𝑙𝑏𝑏𝑓𝑓

𝑚𝑚 =𝑊𝑊𝑔𝑔 =

12.7 𝑙𝑙𝑏𝑏𝑓𝑓32.2 𝑓𝑓𝑡𝑡 𝑠𝑠2⁄ = 0.394 𝑙𝑙𝑏𝑏𝑚𝑚

∴ 𝑎𝑎𝑚𝑚𝑎𝑎𝑐𝑐 =500 𝑙𝑙𝑏𝑏𝑓𝑓

0.394 𝑙𝑙𝑏𝑏𝑚𝑚 = 1267.7 𝑓𝑓𝑡𝑡/𝑠𝑠2 ×1 𝑔𝑔

32.2 𝑓𝑓𝑡𝑡/𝑠𝑠2

𝑎𝑎𝑚𝑚𝑎𝑎𝑐𝑐 = 39.4 𝑔𝑔 At 39.4 𝑔𝑔;

𝑐𝑐 = �1267.7 𝑓𝑓𝑡𝑡 𝑠𝑠2⁄

�2𝜋𝜋(3750 𝐻𝐻𝐻𝐻)�2� �12 𝑖𝑖𝑛𝑛1 𝑓𝑓𝑡𝑡 � = 2.74 × 10−5 𝑖𝑖𝑛𝑛 = 27.4 𝜇𝜇𝑖𝑖𝑛𝑛

E

Appendix D: Calculations Used for Tank Dimensions and Forces Needed from Shaker (Table 4) Equations Used: 𝑊𝑊𝑡𝑡 = 𝜋𝜋

4(𝐷𝐷𝑠𝑠2 − 𝐷𝐷𝑖𝑖2)𝜌𝜌𝑎𝑎ℎ

𝑊𝑊𝑤𝑤 = 𝜋𝜋4𝐷𝐷𝑖𝑖2𝜌𝜌𝑤𝑤ℎ

𝑊𝑊 = 𝑊𝑊𝑡𝑡 + 𝑊𝑊𝑤𝑤 𝐹𝐹 = 𝑚𝑚𝜔𝜔2𝑋𝑋 Where 𝑚𝑚 = 𝑊𝑊 (kg) 𝜔𝜔 = 2𝜋𝜋𝑓𝑓

𝑋𝑋 = 𝑑𝑑𝑖𝑖𝑠𝑠𝑝𝑝𝑙𝑙𝑎𝑎𝑐𝑐𝑠𝑠𝑚𝑚𝑠𝑠𝑛𝑛𝑡𝑡 = 𝐹𝐹𝜔𝜔2

𝑚𝑚

Condition Used (Fluid Separation Condition):

𝑎𝑎 = 𝐹𝐹𝑚𝑚

= 10g

𝑓𝑓 = 100 Hz

F

Appendix E: Bubble Calculations for Centre of Mass, Diameter, and Spline Length The following calculations are based on inputs taken from use of spline fitting of bubbles in SolidWorks and comparing with still photo dimensions using Microsoft Word. Note: X coordinates are taken as the upward / downward motion of bubble Inputs: 𝑐𝑐𝑐𝑐𝑚𝑚→𝑠𝑠𝑤𝑤 = X coordinate for Centre of Mass in Solidworks (calculated by Solidworks Section Properties tool). 𝑑𝑑𝑠𝑠𝑤𝑤 = Diameter of bubble in SolidWorks coordinate system (measured) 𝑠𝑠𝑙𝑙𝑠𝑠𝑤𝑤 = Spline length of bubble in SolidWorks (calculated by SolidWorks measuring tool) 𝑙𝑙 = Length of photo frame in x direction (measured) 𝐿𝐿 = Length of photo frame expanded to scale in word document (=9 in) 𝑆𝑆 = Start position of bubble on word document expanded frame (measured) 𝐸𝐸 = End position of bubble on word document expanded frame (measured) With these inputs, the true centre of mass position, true diameter, and true spline length can be calculated in the following manner: First use proportions to find the true start and end positions of the bubble. This can be done by taking the length of a bubble photo and comparing the relative size of the bubble in this frame to the relative size in the actual test. This is because the length of the photo frame is known from measurements in the test. This true photo length was usually between 2 and 4.5 cm while the pictures are stretched to length L, which was arbitrarily chosen to be 9 cm on the Microsoft Word page. So we can use proportions of the following:

𝑐𝑐𝑠𝑠𝑙𝑙 =

𝑆𝑆𝐿𝐿

𝑐𝑐𝑠𝑠𝑙𝑙 =

𝐸𝐸𝐿𝐿

Where 𝑐𝑐𝑠𝑠 and 𝑐𝑐𝑠𝑠 are the actual start and end positions of the bubble in the frame that is being solved for. The true bubble diameter is then simply:

𝑑𝑑 = 𝑐𝑐𝑠𝑠 − 𝑐𝑐𝑠𝑠 To find the centre of mass of the bubble in relation to the start bubble coordinate, 𝑐𝑐𝑐𝑐𝑚𝑚∗ , use proportion the proportion between SolidWorks centre of mass position over diameter equaling actual centre of mass position / diameter:

G

𝑐𝑐𝑐𝑐𝑚𝑚→𝑠𝑠𝑤𝑤

𝑑𝑑𝑠𝑠𝑤𝑤=𝑐𝑐𝑐𝑐𝑚𝑚∗

𝑑𝑑

Finally, the actual 𝑐𝑐𝑐𝑐𝑚𝑚 in the frame can easily be calculated by adding the position of the start of the bubble:

𝑐𝑐𝑐𝑐𝑚𝑚 = 𝑐𝑐𝑐𝑐𝑚𝑚∗ + 𝑐𝑐𝑠𝑠 Similarly, we can use the Solidworks spline length and use proportions with the diameter to find the actual spline length, 𝑠𝑠𝑙𝑙:

𝑠𝑠𝑙𝑙𝑠𝑠𝑤𝑤𝑑𝑑𝑠𝑠𝑤𝑤

= 𝑠𝑠𝑙𝑙𝑑𝑑

H

Appendix F: Group Work Allocation

Section/Responsibility Iman D. Kobtham C.

Chapter 1

Chapter 2

Chapter 3

Chapter 4

Chapter 5

Chapter 6

Appendix A

Appendix B

Appendix C

Appendix D

Appendix E

Appendix F

Both members were responsible for part design, testing, and analysis. Iman was

generally more responsible for discussing the results, while Kobtham dealt with

plotting and tabling of raw data. However, the responsibilities were not

necessarily separate, and the roles were interchangeable between the two.

fluid behaviour in microgravity - utorweb · specifically, fluids of air, kerosene, and vegetable...

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