Study of Droplet Coalescence Criteria of a Liquid/Liquid
Interface in Micro-Gravity Conditions
Topic Area: Fluid Dynamics
DEPARTMENT OF AEROSPACE
ENGINEERING AND MECHANICS
UNIVERSITY OF MINNESOTA
107 Akerman Hall
110 Union Street SE
Minneapolis, MN 55455
Team Contact:
Nicolas G. Schellpfeffer
sche0435@umn.edu / (612) 730-2723
Supervisor:
Dr. Ellen K. Longmire
ellen@aem.umn.edu / (612) 626-7853
Team Members:
Nicolas G. Schellpfeffer, flight crew
Senior, Aerospace Engineering
sche0435@umn.edu / (612) 730-2723
Maria L. Bigwood, flight crew
Senior, Aerospace Engineering
bigw0002@tc.umn.edu / (612) 378-7886
Richard A. Johnson, flight crew
Senior, Aerospace Engineering
john3528@umn.edu / (952) 210-1826
Nathan T. Koelln, flight crew
Senior, Aerospace Engineering
koel0024@tc.umn.edu / (612) 331-4187
Matthew J. Stegmeir, alt. flight crew
Senior, Aerospace Engineering
steg0044@umn.edu / (612) 623-1129
Kimberly A. Lay, ground crew
Senior, Aerospace Engineering
layx0010@umn.edu / (612) 331-2571
Submitted on:
July 12, 2003
Table of Contents
1.0 Abstract ................................................................................................................ 3
2.0 Experiment Background .................................................................................... 4
3.0 Experiment Description...................................................................................... 6
4.0 Equipment Description ....................................................................................... 7
5.0 Structural Analysis ............................................................................................. 10
5.1 Free Body Diagram ........................................................................................... 10
5.2 Listing of Weights and Materials ....................................................................... 11
5.3 Safety Factors .................................................................................................... 13
6.0 Electrical Analysis ............................................................................................... 14
6.1 Load Tables........................................................................................................ 15
6.2 Stored Energy..................................................................................................... 16
6.3 Electrical Kill Switch ......................................................................................... 16
6.4 Loss of Electrical Power .................................................................................... 16
7.0 Experimental Procedures & Data Acquisition ................................................. 17
7.1 Equipment Shipping to Ellington Field.............................................................. 17
7.2 Ground Operations ............................................................................................ 17
7.3 Loading .............................................................................................................. 17
7.4 Pre-Flight ........................................................................................................... 18
7.5 Take-off/Landing ................................................................................................ 18
7.6 In-Flight ............................................................................................................. 18
7.7 Post-Flight ......................................................................................................... 18
7.8 Off-Loading ........................................................................................................ 18
7.8 Data Acquisition ................................................................................................ 18
8.0 Experimental Analysis ........................................................................................ 20
8.1 Ground Test Analysis ......................................................................................... 20
8.2 Flight Test Analysis............................................................................................ 22
8.3 Comparative Analysis ........................................................................................ 24
9.0 Conclusions .......................................................................................................... 27
10.0 Outreach Program ............................................................................................ 28
10.1 Science Museum of Minnesota ......................................................................... 28
1
10.2 Local Schools ................................................................................................... 28
10.3 Local Press....................................................................................................... 29
10.4 Flyer’s Hometown Press .................................................................................. 29
11.0 Bibliography ...................................................................................................... 30
Appendices ................................................................................................................. 31
2
1.0 Abstract:
Using the zero gravity environment created aboard NASA’s KC-135A aircraft, results
show the dependability of the gravitational force on the coalescence of fluids. The
analysis and results indicate that the absence of gravity favors coalescence. With the
dominant force no longer being gravity, the collisions have fewer disturbances causing an
increased stability that promotes the coalescence of the two droplets. Therefore, in a zero
gravity environment coalescence occurs over a larger region of collisions. Moreover, the
data obtained and analysis of the fluid dynamic properties during the each stage of the
collision validates the result of the experiment. The data shows obvious shifts in
transitional boundaries of coalescence between the ‘normal’ and zero gravity
environments. The shifts in transitional boundaries directly show the increased region of
coalescence. The analysis of the fluid dynamic properties of each stage of a collision also
supports the conclusions. The presence of a gravitational force creates a less stable
collision, where gravity causes the impact parameter to continually vary changing the
direction of the droplets, which causes instability during the film drainage stage of a
collision. The tests performed indicate that an environment absent of a gravitational
force promotes stable collisions, therefore favoring a wider region of coalescence.
3
2.0 Experiment Background:
The criterion for coalescence of two droplets colliding in a liquid-liquid interface is
studied in micro-gravity conditions. Previous experiments in this subject have used
droplet sizes with diameters on the order of microns to justify the assumption that
buoyancy forces were negligible. For this experiment the ability to perform the collisions
in a zero gravity environment creates a unique opportunity to analyze the criteria for
coalescence on a macroscopic scale. The zero gravity environment will establish if
coalescence can be determined directly by two dimensionless parameters, the Weber
number and impact parameter. With buoyancy forces not present, the properties of
droplet collision and coalescence are defined only by their size, relative velocity and
position at impact. Variations of these parameters will be studied to determine when
coalescence occurs.
The collision of two droplets will result in one of three possible outcomes: shattering,
bouncing, and coalescence (See Figure 2.1). Shattering occurs at high relative velocities
and will not be the focus in this experiment. As is bouncing a trivial result and will also
not the main focus when it occurs. Coalescence is a more intriguing phenomenon and
will be the emphasis of our experiment.
Figure 2.1: Time Sequence of two-drop coalescence experiments (a) Coalescence does not
occur. (b) Coalescence does occur. (Taken from Leal, L.G. – 2000)
Coalescence is the combination of two discrete fluid particles and occurs in a three-stage
process beginning with the approach of the particles toward one another. The drag on the
particles is well known due to the maintained spherical shapes. This allows the
trajectories to be easily modeled. The second stage is the ambient liquid film drainage
between the droplets as the separation distance becomes small compared to the droplet
radii. It is believed that gravity affects the drainage rate; therefore previous experiments
are done on a microscopic scale. The final stage is the rupture of the film between the
fluid droplets, which causes a combination of the two volumes. Coalescence of the
droplets will occur when a critical thickness of the film is reached; if this thickness is not
reached the droplets will bounce off one another.
4
After coalescence the droplets may remain together or separate. The outcome of
coalescence is dependant on the ratio of the inertial energy of the droplet to its surface
energy, which is quantified by the Weber number (see Figure 2.2). Separation of the
droplets can occur by stretching or reflexive separation. Stretching involves the
elongation of the new fluid particle after combination, while reflexive separation is
passing of the droplets through one another with no significant change in the original
droplet properties. If the droplets combine and remain together they will oscillate until
slowed by viscous effects. Additional effects that will not be considered in the realm of
this experiment are initial droplet oscillations from nozzle detachment and droplet wake
interactions in the collision zone.
Figure 2.2: Analytically obtained regions of coalescence, reflexive separation,
and stretching separation for two drops of same size,
together with experimental data (Taken from Ashgriz - 1990)
Previous research on droplet coalescence has been studied; however, the effects of microgravity on this phenomenon are not completely understood, and it is the intention of this
experiment to determine the manner in which the droplets will behave.
5
3.0 Experiment Description:
Coalescence of liquid drops dispersed in an immiscible liquid has a vast importance in
many industrial applications, including liquid-liquid extraction, emulsification, and
polymer blending processes. Our aim is to conduct experimentation on the effects of
droplet diameter and velocity on the probability of a droplet collision leading to
coalescence or separation. More specifically our objectives include:




Eliminating the effects of buoyancy forces on the droplets through the use of the
micro-gravity environment.
Studying how the critical film thickness is affected as droplet size is varied.
Observing how the collision outcome is affected by the relative velocity between
the two droplets.
Comparing macroscopic droplet interactions to previously obtained microscopic
droplet data.
The experiment is fully defined by seven dimensionless parameters: Weber number (We),
impact parameter (x), Reynolds number, density ratio, viscosity ratio, diameter ratio, and
a velocity ratio. However, the Weber number and impact parameter primarily influence
the outcome of droplet collision. In our experiment we intend to vary the droplet
diameter (d) and the droplet velocity (U), which are related to the Weber number through
the following equation:
We 
U 2 d

(3.1)
where ρ is density of the droplet fluid, and σ is the interfacial surface tension between the
droplet and ambient fluids. The density and surface tension will be experimentally
determined constants. The other significant dimensionless quantity in this experiment is
the impact parameter, defined by:
x
2X
d1  d 2
(3.2)
where X is the distance from the center of one drop to the relative velocity vector placed
at the center of the other drop (see Figure 4.1), multiplied by two, and divided by the sum
of the two drops diameters. The impact parameter varies between 0 and 1, where zero
corresponds to a head-on collision and tangential collisions have an impact parameter of
one.
6
Ø = d2
U2
Ur = U2 - U1
Ø = d1
U1
X
Figure 3.1: Definition of the impact parameter (Taken from Johansen, S.T. – 2002)
Our hypothesis is that collected data will validate previously determined relationships
between dimensionless parameters. It is our belief that the direction and magnitude of
the droplets’ velocities and sizes can be directly related to coalescence when the
buoyancy forces are not present. The main objective of the experiment is to find a
relationship between the impact parameter and the Weber number for which coalescence
or separation of the colliding droplets occurs.
4.0 Equipment Description:
The following are the main elements of our experimental apparatus:
Plexiglas Tank:
The tank is 18” tall x 9” wide x 9” deep, and is constructed of ½” thick Plexiglas
with a total fluid capacity of 4.43 gallons. The tank is held together using WeldOn 3, manufactured by the IPS Corporation. A quarter turn valve will be used for
filling the tank. The top of the tank will include an accumulator, which will adjust
for pressure and volume changes during flight. It is secured to the sides with bolts
and an o-ring is used to prevent possible leaks. The tank includes a deflection
plate located slightly above the fluid interface to decrease fluid mixing during
transitions. The plate is also used as a contrasting background for the top video
camera.
Nozzles:
The nozzles, fabricated from stainless steel pipe, are used to insert the waterglycerin mixture into the tank. The nozzle separation distance will be adjustable.
7
Swage lock seals around the nozzle connections to the tank allow for movement
of the nozzles while preventing the fluids from leaking.
Solenoid Valves:
Two identical solenoid valves manufactured by J. D. Gould Company, Inc., model
number M-3V, will be used to control the flow from the nozzles. The solenoid
valves are internal pilot piston operated valves. These will allow us to precisely
vary the amount of fluid contained in each set of droplets. A simple electronic
controller will be used to control the valves’ duty cycles.
Pump:
A centrifugal pump manufactured by the Little Giant Pump Company, model
number 1.5-MDI-SC, will be used to provide a constant pressure head at the
nozzles. The pump contains a leak-proof, seal-less, magnetic drive. The
advantage of using a centrifugal pump is that it is capable of continuously running
while the solenoid valves are closed. The pump is connected to a surge protector,
which functions as our main kill switch. A voltage regulation attached to the
pump allows for the variations of the pressure head.
Fluids:
Two fluids will be used in this experiment: mineral oil and a 50:50 water/glycerin
mixture (based on volume). The past two University of Minnesota Micro-Gravity
teams have used these fluids, which have been proven to provide consistent
performance under all gravity conditions encountered aboard the research plane.
The interfacial surface tension between the fluids is 14.3 mN/meter.
Fluids
Density (kg/m3)
Mineral Oil
860
Water/Glycerin
1150
Tubing:
Two types of tubing will be used to transfer the fluid from the pump to the valves.
Flexible plastic tubing is fastened onto plastic nipples using hose clamps will be
used to connect the pump to the tank and the solenoid valves. Stainless steel pipe
was used to fabricate the nozzles.
Timing Circuit:
A 555 integrated circuit timer regulates the opening and closing of the solenoid
valves. The duty cycle is controlled by a 100 kilo-ohm potentiometer. The
interval between pulses is set at approximately five seconds. A nine-volt battery
powers the circuit. Transistors are used to amplify the output signal to the 24
volts necessary to operate the solenoid valves. The timing circuit contains a kill
switch.
8
Accelerometer Circuit:
An integrated circuit accelerometer, ADXL202, connected to a digital LCD panel,
will be used to obtain g-force values while in flight. A nine-volt battery powers
the circuit. The analog output of the accelerometer is converted to a digital signal
by an A/D converter. A basic stamp controller processes the digital output and
controls the LCD.
Video Cameras:
Two digital cameras (Canon ZR40) will be positioned orthogonal to each other.
This will allow us to obtain multiple continuous video streams of the flow. These
cameras are capable of capturing images at 30 frames per second and are
equipped with a variable shutter speed. Time will be displayed in every frame to
allow us to correlate the images from both cameras. Both cameras will be
connected to the surge protector, and are mounted on the external frame.
Lights:
Four fluorescent lights with their respective casings will be used to illuminate the
testing area. The lights are connected to the frame with Velcro. Each light uses
four AA batteries.
Frame:
We will support our experiment with a frame made of Unistrut™. This material
has been used for the last two years by the University of Minnesota MicroGravity Fluids research teams. The cross section of the frame is 1 5/8 in2. The
outside dimensions of the frame are 42 in. L x 29 in. H x 19 in. W. This structure
will support our experiment. All sharp angles and edges will be rounded and
padded in accordance with the hazard checklist. Eighth inch plastic sheeting will
be attached with Velcro around the outside of the frame as a secondary leak
protection barrier.
Total Assembly:
The frame and location of the major components are shown in Figure 5.2. The assembly
will be discussed extensively in the structural load analysis section.
Component
Weight
Dimensions
Description
(lbs)
(in., LxWxH)
Camera #1
1
5.25x3x4
Aluminum Mounting Plate
Camera #2
1
5.25x3x4
Aluminum Mounting Plate
Tank and Fluids
70
9x9x18
Plexiglas and PVC box, Aluminum Mounting
Plate, Glycerin-Water, Mineral Oil
Frame
105
42x19x29
Steel
Timing Circuit
3
4x7x3
Aluminum
Accelerometer Circuit
2
2x2x1
Plastic
9
Material
Component
Weight
Dimensions
Description
(lbs)
(in., LxWxH)
Pump
7
7x3.5x4
Aluminum Mounting Plate
Nozzle (2)
5
1x1x6
Steel
Tubing, Clamps
10
N/A
Plastic, PVC, Aluminum
Solenoid Valves (2)
10
3x4x6
Brass
Lights (4)
5
1x1x8
Plastic, Fluorescent Bulbs
Secondary Plastic Covering
10
Varies
Plastic
Total
230
Material
Table 4.1: Summary of experimental hardware
5.0 Structural Analysis
5.1 Free Body Diagram
The centers of gravity (CG) of significant items are listed (Table 5.1) and diagrammed
below (Figure 5.1):
Figure 5.1: Free Body Diagram
10
Item
Frame
Tank
Pump
Shelf
All Other Items
CG
Weight (lbs)
Location (in)
105
67
6
6
41
225
x
y
z
21.0
15.0
29.5
32.0
19.2
19.4
9.8
7.0
9.5
9.5
10.6
9.1
14.5
9.8
4.0
14.7
13.8
12.7
Table 5.1: CG
5.2 Listing of Weights and Materials
Description
Weight (lb)
Symmetric Frame
95.4
4 Joints, 8 Nuts&Bolts
9.7
Tank Support #1
3.3
Tank Support #2
3.3
Top Camera Support
3.9
Shelf Support
3.9
Empty Tank, Lid, Accumulator
25.0
Mineral Oil
16.0
Water/Glycerin
20.0
Pump
6.0
Tubing, Wiring, Clamps, …
10.0
Power Strip
1.0
Solenoid #1
3.0
Solenoid #2
3.0
Electronics Box
2.0
Shelf
2.0
Outer Covering
10.0
Lighting System
5.0
Top Camera
1.0
Side Camera
1.0
Totals
224.5
11
Figure 5.2 – Experimental Setup (developed using SolidWorks)
Figure 5.3 – Tank Drawing (developed using SolidWorks)
12
Figure 5.4: Experiment Photo
5.3 Safety Factors
Safety factors derived from analysis in the NASA-RGSFOP TEDP are presented in Table
5.2:
Condition
Description
9Gs Forward 29" Columns
Handles
16" Beam
16" Beam
Straps
3Gs Aft
29" Columns
Handles
16" Beam
16" Beam
Straps
6Gs Down
29" Columns
2Gs Lateral 29" Columns
Handles
16" Beam
Straps
2Gs Up
29" Columns
16" Beam
Load
1413
172
821
945
2145
481
57
315
274
715
338
366
38
222
545
113
83
Table 5.2: Safety Factors
13
Allowed
Safety Factor
3000
2.1
11390
66.2
1690
2.1
1690
1.8
5000
2.3
3000
6.2
11390
199.8
1690
5.4
1690
6.2
5000
7.0
3000
8.9
3000
8.2
11390
299.7
1690
7.6
5000
9.2
3000
26.5
1690
20.4
6.0 Electrical Analysis
Our experiment includes six electrical circuits. These include a main 115VAC circuit,
which will be powered from a single 115 VAC outlet on the aircraft, a 24VDC circuit
powered by a power supply connected to the 115 VAC source, and 4 battery-powered
circuits. These are a 9V timing circuit, which controls the 24V solenoid circuit, a 9V
accelerometer circuit, and two digital cameras with onboard 7.4V batteries. The cameras
will normally be operated in AC mode via the included 9.6 VDC power supplies. All
exposed metal surfaces will be attached to our metal frame. The frame will be
constructed with metal surfaces flush against each other. The frame will be grounded to
the aircraft. Figure 6.1 shows a schematic of our electrical setup.
Figure 6.1 – Schematic of Major Electrical Components
14
6.1 Load Tables:
Power Source Details
Name
115 VAC from Aircraft
Output Voltage
115 VAC
Wire Gauge
14 AWG
Rated Output Current 15 Amp
Load
Pump
Power Supply
Camera1
Camera2
Total Load
Load Details
Nominal Current Draw
1.1 Amp
0.5 Amp
<100mA
<100mA
Maximum Current Draw Wire Gauge
1.1 Amp
18 AWG
1.6 Amp
18 AWG
<100mA
18 AWG
<100mA
18 AWG
2.7 Amp
The highest power electrical circuit used will be the 115 VAC circuit. This will directly
power our pump, 24V power supply, and the cameras used for data acquisition (via their
included DC supplies). A single power cord will connect the 115 VAC circuit to the
aircraft power. The power strip is equipped with a 15A circuit breaker and a switch. The
breaker will provide current limiting for the circuit and the switch will serve as the master
“kill switch” for the 115 VAC and 24 VDC circuits.
Power Source Details
Name
Valve Power Supply
Output Voltage
24VDC
Wire Gauge
18 AWG
Rated Output Current 6.25A
Load
Main Valve #1
Main Valve #2
Total Load
Load Details
Nominal Current Draw Maximum Current Draw Wire Gauge
0 Amp
1 Amp
18 AWG
0 Amp
1 Amp
18 AWG
2 Amp
The 24 VDC circuit will be powered by an Astrodyne MKS150-24 power supply. This
supply is rated to supply 6.25 A at 24 VDC. We expect to see a maximum draw of no
more than 2 A from this supply. Kill switch functionality will be provided by the power
strip, as mentioned above. The supply may also be independently switched off if desired.
This supply has the capability to self-limit current. 3A fuses will also be installed inline
with the valves to guard against short-circuit conditions. The power supply is also selfcurrent limiting.
15
Power Source Details
Name
Accelerometer Power
Output Voltage
9VDC
Wire Gauge
24 AWG
Rated Output Current 1 A
Load
Accelerometer
Total Load
Load Details
Nominal Current Draw Maximum Current Draw Wire Gauge
200 mA
200 mA
24 AWG
200 mA
The accelerometer is used to measure accelerations in flight will be powered by a
dedicated 9V battery. It will be electrically isolated from the remainder of the
experiment. A separate power switch is used to disable this circuit. The timing circuit is
also powered via an independent battery source. It also is equipped with a kill switch.
Power Source Details
Name
Control Circuit Power
Output Voltage
9VDC
Wire Gauge
24 AWG
Rated Output Current 1 A
Load
555 IC Timer Circuit
Total Load
Load Details
Nominal Current Draw Maximum Current Draw Wire Gauge
200mA
200mA
24 AWG
200 mA
6.2 Stored Energy:
We will not be using any devices to store or create large electrical charges other than
those included within our power supply.
6.3 Electrical Kill Switch:
The main experiment power is all routed through a single power switch. Turning this
switch off disables the experiment and cuts it off from all high voltage sources. Our
emergency shutdown procedure is to turn off the main power at this switch. If necessary,
we will then proceed to disable our timer and accelerometer electronics and our data
acquisition cameras using their power switches after waiting for the power indicator LED
on our power supply to go out.
6.4 Loss of Electrical Power:
Upon loss of power, the experiment will cease operation. The pump will stop, removing
the pressure head, which drives our droplet generators. The solenoid valves will remain
in their closed positions. If left on, the timing circuit and the accelerometer circuit will
continue to operate normally without affecting the rest of the experiment. If turned off
they will simply cease operating. Our experiment is designed to be in a safe state
regardless of power conditions.
16
7.0 Experiment Procedure Documentation
7.1 Equipment Shipping to Ellington Field
The experiment will be shipped directly to Ellington Field building 993. The experiment
will be enclosed in a wood crate, and shipped one day prior to our arrival (March 12,
noon). The shipping company is Independent Packing Services, Inc. Prior University of
Minnesota Micro-Gravity Teams in previous years have used this company for shipment.
7.2 Ground Operations
After unloading the experiment, small parts will be assembled into place and the fluids
will be added to the tank. Ground testing will be performed to ensure that the experiment
runs properly and that there are no leaks. We request the use of a worktable with an
available 115 V, 60Hz electrical outlet.
7.3 Loading
To load the experiment aboard the KC-135 we will require a lifting palate and a forklift.
The experiment will be strapped down to the floor using the 20-inch separation of the
floor connection points in the aircraft. The guides on the cage of our experiment will
secure the straps.
Figure 7.1: Post-Loading Group Photo aboard NASA’s KC-135A with experiment
17
7.4 Pre-Flight
Pre-flight procedures will include plugging in the electrical equipment and ensuring the
frame is properly fastened to the floor. The surge protector will remain off until proper
altitude is reached. There are no preflight requirements other than the 115V, 60Hz
electrical outlet.
7.5 Take-off/Landing
No power is required during take-off or landing and all electrical systems will remain off
during these time periods.
7.6 In-Flight
With our proposed flight conditions of three sets of ten zero gravity parabolas our in
flight procedures are as follows. During the transition between sets the nozzle separation
distance will be adjusted to the desired distance. During each individual set, droplet size
and velocity will be adjusted using the external control knobs of the duty cycle and the
pump speed for each individual parabola. The final settings of each parabola are set to
test 18 nominal settings that will focus on the transitional regions of coalescence.
7.7 Post-Flight
The first day flight team will inform the remainder of the team of difficulties experienced
in flight, if they occurred, and determine means of correction for the following flight day.
7.8 Off-Loading
The experiment will be off-loaded from the aircraft with a forklift and lifting palate. The
same shipping company, Independent Packing Services, Inc, will provide returning
shipping. The return will be arranged for the first business day after the completion of
our flights, tentatively scheduled for Monday, March 24.
7.9 Data Acquisition
The droplet collisions were recorded by two Canon ZR-10 digital cameras, one
positioned above the collision zone and the other to the side of the tank. Using two
cameras allowed us to obtain a complete three-dimensional picture of each collision.
Each camera was capable of recording data at the rate of 30 frames per second. During
each flight, roughly 70 collisions occurred in micro-gravity conditions.
As the video cameras were recording constantly during the flight, and micro-gravity
exists for only a fraction of the flight, most of the tape was not of interest. Therefore, the
raw video was edited down to contain only the collisions that occurred in micro-gravity.
Each of these bits of video was then recorded onto a CD, resulting in a total of four data
CDs from the flight (one CD for each camera per day). By using all digital media in the
editing process, it was felt that a minimum of data loss occurred.
Once the raw video had been pared down to contain only the portions of interest, it was
then possible to begin the process of making measurements of the collisions. To aid in
this process, we utilized a computer program called Videopoint 2.5. This software
allowed us to view our data frame by frame, and to make measurements of the size and
18
velocity of the droplets in a 2-D plane. By stepping through the data, it then became
possible to achieve the most accurate measurements that our video would allow. Another
strength of using digital media for our data was that it allowed us to effectively use
software like Videopoint to make these measurements.
The data from each CD was recorded in a spreadsheet, Appendix B, and consisted of
velocity data for each droplet, droplet diameter, the distance between droplet centers at
collision, and the result of the collision (bouncing or coalescence). As the cameras only
recorded 30 frames per second, often the actual collision of droplets would occur between
frames resulting in some inconsistency in making measurements at the time of collision.
In these cases, the size of the droplet was generally obtained from the frame just before
collision, while the velocity information was taken from the frame following the
collision.
After matching up the two views of each collision (horizontal and vertical), the complete
three-dimensional velocity vectors for both droplets could be obtained as well as the
three-dimensional position of each droplet throughout the collision. This information
could then be appropriately manipulated using vector algebra to obtain both the Weber
number and the impact parameter for each collision. Once these non-dimensional
parameters were obtained for each collision, it becomes possible to generate plots of
these parameters and the collision result. A series of Matlab scripts were developed to
take the data from the Excel documents, and perform all necessary needed of analysis,
which is presented in Appendix A.
Before our flight a series of ground tests and calibrations was done to determine an ideal
test procedure that would produce all possible outcomes of the collisions. It was decided
that three parameters would be varied during the experiment. These control parameters
included adjusting the needle valve setting, the nozzle separation distance and the pulse
time of the timing circuit. The first two of these parameters affect the velocity of the
droplets, and the third parameter affects the size of the droplets. The impact parameter of
the collisions was held relatively constant, due to the laterally fixed nozzle positions,
while the Weber Number varied according to the control parameter settings. Results of
ground tests indicated 18 different nominal settings, which would produce collisions in
all possible outcomes. A test procedure was designed based on the specified flight
pattern of three sets of ten parabolas. Since the flight would include more parabolas than
our nominal test settings required, it was decided to conduct multiple tests around the
transitional stages of coalescence. For analysis purposes, an official ground test was
conducted prior to flight in which the flight test procedure was followed. The results of
this ground test were compared to both previous experiments conducted in a 1-g
environment and to our flight data aboard the KC-135A zero gravity environment.
19
8.0 Experimental Analysis
8.1 Ground Test Analysis
In order to achieve data that could be compared to previous research, the droplet size and
velocity of our experiment was initially scaled to test over a region similar to this existing
data. Initial ground tests indicated that with a fixed pressure head, the viscous effects
between the nozzle and the droplet prevented the scaled droplet from achieving the
necessary velocity range. Changing our timing circuit to allow the solenoid valves to
stay open a few microseconds longer therefore increased the baseline droplet size. This
design change allowed the droplets to reach the specified velocity range, but in doing so,
increased the testing range of the Weber Number. For the ground tests, the impact
parameter varied slightly with the different nozzle distance settings as a result of the
changing velocity vector due to the presence of gravity and, therefore, buoyancy forces.
In the nominal testing environment, the absence of gravity allows the impact parameter to
remain relatively constant. The results of the official ground tests, which are shown in
Figure 8.1, illustrate the carefully calibrated testing procedure. Each of the three collision
outcomes – bouncing, coalescence, and separation – were produced under the new design
conditions.
Figure 8.1: Ground Test Collision Result
20
The experimental results can be reduced to a one-degree-of-freedom problem through the
use of the Weber number and the assumption of a relatively fixed impact parameter. The
calculated impact parameter for the ground tests varies between 0.09 and 0.84, with
uncertainties based on the effects of gravity and human error during data analysis. Figure
8.1 illustrates that distinct boundaries occur between the collision outcomes when
graphed as a function of the Weber number. The transition from bouncing to coalescence
occurs at a Weber number of approximately 100, whereas the transition from coalescence
to separation occurs at a higher value of approximately 225. Qualitatively, the ground
test results behaved as expected, following a similar pattern of previous related
experiments, such as those conducted by L. Gary Leal (see Figure 2.2). Ground tests
were conducted primarily for comparative analysis between the two gravity
environments. Given that the ground test procedure produced qualitatively expected
results – and all three modes of collision outcomes – the same procedure was defined to
be used in flight aboard NASA’s KC-135A ‘Weightless Wonder’.
21
8.2 Flight Test Analysis
Ground test data and results were used to assure that the experiment and equipment
experienced only negligible changes during the shipping process from Minneapolis to
Houston and during the flight aboard the KC-135A aircraft. By following the same
procedure throughout all of our testing, we were able to conclude that the performance of
the pump, timing circuit, and needle valve – the main mechanical components of our
experiment – was nominal throughout all data acquisition tests. Although the experiment
worked nominally in both ground tests and in-flight tests, some quantitative differences
in the data and results were expected due to changes in gravity. In-flight data predictions
included slightly lower Weber numbers due to the absence of a downward velocity
component, and a slightly smaller range of impact parameters than those calculated as a
result of ground tests. It was decided that the changes would be negligible and the
experimental procedures would not change. Therefore, the in-flight experiments should
produce comparable results, although considering possible changes due to the zero
gravity environment. The in-flight experiment results, shown in Figure 8.2, depict the two
separate flights under design conditions, aboard the KC-135A zero gravity environment.
Figure 8.2: Flight Test Collision Result
As was found in the ground tests, the results display a distinct boundary between the
bouncing and coalescence outcomes, but due to reasons that will be discussed later, the
second transition – from coalescence to separation – did not occur in flight. The impact
parameter was calculated and averaged for the two zero gravity flights and, as predicted,
fell in a smaller range than that of the ground tests. The value was found to vary between
22
0.09 and 0.78, with uncertainties due to the effects of human error during data analysis.
The transition between bouncing and coalescence occurred at a Weber number of
approximately 50, which, as predicted, was lower than in the ground tests. Qualitatively,
the results of the in-flight experiments followed a slightly different pattern as the ground
tests results, with the absence of the separation collision outcome not expected.
23
8.3 Comparative Analysis
Under the assumptions stated previously, that the experimental hardware functioned
identically during the ground and in-flight tests produced the same testing conditions and
the affects due to the absence of gravity were negligible, an identical testing procedure
verified the repeatability of our experiment. More specifically, these assumptions lead to
the conclusion that for each nominal test procedure setting, the Weber number and impact
parameter should remain constant throughout the varying gravity environments. By
making this comparison, very interesting results were produced. The comparative results
between the 1-g and zero-g environments are shown in Figure 8.3, and have two distinct
features that will be discussed in detail.
Figure 8.3: Comparative Collision Result
The first and most obvious difference between the ground and in-flight results is the
absence of the third collision outcome – separation – in the zero gravity environment. In
ground tests, under a ‘normal’ gravity environment, the transition between coalescence
and separation occurred at a Weber number of approximately 225. Although a number of
collisions were characterized by a Weber number of at least this magnitude during inflight tests, the transition to separation did not occur. Simply stated, for identical
experimental settings – meaning identical collision parameter characteristics – collision
outcome differed between the two gravity environments. Second, from this conclusion, it
24
follows that the boundary between bouncing and coalescence occurs at a lower Weber
number in the zero gravity environment than it does under normal gravity conditions.
Ground test results produced a Weber number of approximately 100 for the bouncing –
coalescence boundary, whereas in-flight data indicated a shift to a lower Weber number
of approximately 50 for this phenomenon to occur. Therefore, coalescence occurs earlier
in an environment absent of gravity.
From the previous conclusions, it can further be argued that coalescence occurs for a
wider range of the Weber number in a zero gravity environment than under ‘normal’
gravity conditions. As stated earlier, coalescence occurs upon drainage of the secondary
film between the two droplets, given that the droplet motion is directed towards one
another and a state of sufficient propinquity exists. Figures 8.4.A through 8.4.L, depict a
violent collision in the zero gravity environment aboard the KC-135A, which ends in
coalescence of the two droplets.
(A)
(B)
(C)
(D)
(E)
(F)
(G)
(H)
(I)
(J)
(K)
(L)
Figure 8.4: Time Series of Zero Gravity Coalescence
25
This same collision (i.e. identical experimental settings and therefore identical collision
characteristics) in ‘normal’ gravity conditions produced during ground tests, resulted in
separation collision outcome of the two droplets, were the two droplets first coalesced,
but their continued momentum caused the droplets to pass through each other. The series
of figures show the coalescence transient stabilization over 0.5 seconds. At the
beginning of the collision a deformation is noticeable in the droplets from the boundary
layer forces during the film drainage stage, Figure 8.4.B. Immediately after the film
drainage the droplets begin to coalescence with a transient effect. The continued
momentum of the droplets is noticeable in Figure 8.4.D, where the droplets nearly pull
through each other, but stay coalesced and continue a transient that is noticeable until the
droplet stabilizes in Figure 8.4.L.
It was determined from our analysis and discussions that the wider region of coalescence
during our zero gravity in-flight tests aboard the KC-135A was an arguably
understandable result. With the focus of the collision outcome on the time dependence of
the film drainage, the effects of gravity were analyzed during the coalescence process of
droplet approach, film drainage, and droplet coalescence.
During the approach stage in a zero gravity environment, the trajectory of the droplet is
defined and held relatively constant from the nozzle exit. The only force acting on the
droplet is the drag through the secondary fluid. The drag opposes the motion of the
droplet, causing the magnitude of its velocity to slightly decrease, but not affecting the
direction. On the other hand, under ‘normal’ gravity conditions, the approach stage is
greatly affected by the gravitational force. Due to the horizontal positioning of the
nozzles in our experiment, the gravitational force acts orthogonal to the initial trajectory
of the droplet at the nozzle exit. The force creates a new downward velocity component,
which continues to be accelerated by gravity. Approximating the coefficient of drag on
the droplet as that for a sphere, the CD is between 0.5 and 0.7. Considering the size and
density of our droplets, the more dominant force on the droplets’ velocity would be the
gravitational force. Therefore, the velocity vector direction is continually pulled
downward, away from the horizontal, as a result of the gravitational force, and the
magnitude of the velocity remains slightly larger than under a zero gravity condition.
The next stage of the collision is the drainage of the secondary fluid. This point in the
collision is determined by whether the separation distance of the two droplets is less than
the diameter of the droplets, if so the droplets are in the second stage of the collision.
The second stage sets up the outcome of the collision. This portion of the collision has a
high time dependence. For coalescence to occur all of the secondary fluid between the
droplets must drain away, while the droplets are still close and their motion is directed
towards one another. Simplified as a two-degree-of–freedom problem, the analysis is
only dependent on the film drainage and the droplets relative motion. The dominant
factor in how fast the secondary film can drain away is the interfacial surface tension
between the two fluids. This is a fixed fluid property, which is not effected by the
absence of gravity. The second criterion was that the droplet motion was still directed
towards one another. In the case of an environment with gravity, the direction of the
26
velocity vector is continually changing due to gravity, and with the addition of boundary
layer forces, as the droplets collide the motion of the droplets are less stable and more
susceptible to be forced away from each other than in an environment absent of gravity.
Additionally, the velocity magnitude of the droplets is larger in a ‘normal’ gravity
environment, therefore allowing less time for the secondary fluid to drain.
The third stage of the collision is coalescence, which was defined earlier as occurring
under a time dependence reaction with two simultaneously needed collision properties.
The analysis shows that the absence of gravity favors coalescence. The dominant force
acting on the collision is no longer gravity, allowing for a more stable drainage that
promotes coalescence. Also, the zero gravity environment aboard the KC-135 allows for
a slightly longer film drainage time than on the ground. The absence of gravity in our
data shows a more wide range of coalescence during the in-flight zero gravity
environment tests compared to the ‘normal’ gravity environment tests preformed on the
ground before our flight.
9.0 Conclusions
The data obtained aboard the KC-135A aircraft shows the dependability of the
gravitational force on coalescence. The analysis and results indicate that the absence of
gravity does favor coalescence. With the dominant force no longer being gravity, the
collisions have fewer disturbances causing an increased stability that promotes the
coalescence of the two droplets. Therefore, in a zero gravity environment coalescence
occurs over a more wide range of Weber numbers. Moreover, the data obtained and
analysis of the fluid dynamic properties during the each stage of the collision validates
the result of the experiment.
The conclusions made, like most conclusions, included certain accepted assumptions.
The primary assumption made was that the effect on the droplets trajectory due to gravity
is negligible was an adequate assumption. The zero gravity environment aboard the KC135A did in fact produce a slightly smaller range of impact parameters, but was not an
issue to the results. The Weber number was also affected due to gravity as predicted.
The zero gravity environment produced lower Weber numbers due to the absence of
gravity’s acceleration. Although the range of Weber numbers was smaller, it remained
higher than the transitional boundary between coalescence and separation for the
‘normal’ gravity ground tests. Ideally, the third collision outcome – separation - was
desired during the in-flight test for comparative reasons, but the results were still
adequate for the conclusions.
Additionally, experimentation includes uncertainty that is minimized to assure the
accuracy of results. For the analysis preformed on each collision human error and
decision were the main areas of uncertainty. The analysis process begins with data
acquisition from the fixed digital cameras aside and above the collision region. The
cameras obtained video at a rate of 30 frames a second. The collision properties were
determined using a video analysis program, Videopoint 2.5, to obtain size, position, and
velocity of the droplets at their collision to determine the Weber number and impact
parameter. Considering the rate of the collision process and the speed the camera, the
27
analysis technique using Videopoint included uncertainties due to an inadequate number
collision frames to determine the droplets properties. For more accurate analysis in later
tests the use of a high speed, 100 frames per second, camera would be a valuable
modification to the analysis process.
The data shows obvious shifts in transitional boundaries of coalescence between the
‘normal’ and zero gravity environments. In a zero gravity environment the low
transitional stage between bouncing and coalescence was decreased to a smaller Weber
number. The high transitional stage between coalescence and reflexive separation
increased past our experimental procedures causing the third collision outcome –
reflexive separation – never to occur at the higher Weber numbers of our test procedures.
The shifts in transitional boundaries directly show the increased region of coalescence.
The analysis of the fluid dynamic properties of each stage of a collision also supports the
conclusions. The presence of a gravitational force creates a less stable collision. Gravity
affects the impact parameter to vary over a larger range due to the continually changing
direction of the droplets, which causes instability during the film drainage stage of a
collision. The tests performed aboard NASA’s KC-135A aircraft indicate that an
environment absent of a gravitational force promotes stable collisions, therefore favoring
a wider region of coalescence.
10.0 Outreach Program
10.1 Science Museum of Minnesota
The semester before our team flew we had a unique opportunity to talk with Science
Museum coordinators from all across the country. After being granted special permission
from NASA to talk about our experiment before we were accepted to the Reduced
Gravity Program, we spent several hours at a conference hosted by the Science Museum
of Minnesota. We were asked to present our experiment to the group and answer
questions about it; however, the main focus of our presence was for the curators to
brainstorm and present possible ways they could incorporate a project such as ours into
their museum. With the diverse age, ethnicity, and education of the population that visit
museums, the desire was to find was to reach every person interested in learning about
the experiment. It proved to be a learning experience for us as well as for the attendees
as we were given a number of possibilities of thing we could do during our outreach.
10.2 Local Schools
The team spent an afternoon talking with 8th and 3rd graders at St. Pascal’s School in St.
Paul, Minnesota. We spent time explaining what NASA was and what they did, as well
as about the Reduced Gravity Program. We talked about the effects of weightlessness
and the necessity for our experiment to be performed under such conditions. Having the
flight footage and “B-roll” allowed us to easily explain about the Weightless Wonder: its
maneuvers, the layout of the inside, how the experiments were secured, and any other
questions the students had. Questions from the students ranged anywhere from “How did
it feel to be floating?” to the ever popular “Did you throw up?”, and even on about
becoming an astronaut. It was a great opportunity for us to explain that a person does not
necessarily have to be an engineer to work at NASA. We mentioned that many of the
28
astronauts had degrees in areas such as Biology or Physiology. We also stated that
programs such as ours that were specifically geared toward students were a great starting
point for getting to understand how NASA functions and learning if eventually working
for or with NASA was something they wanted to do. Finally, we mentioned that
although it was not always fun and games as we had to adhere to strict rules while in
Houston, it was an unbelievable experience being able to work with such professionals
and all our hard work and dedication to the experiment made it a smooth ride and allowed
us to have fun!
Our visit to the school was reported in the school newsletter, which gets sent home with
all the students, courtesy of Mrs. Christine Steigauf and Mrs. Joan Hauri, the teachers
who allowed us to speak to their classes. Pictures and a copy of the newsletter are in
Appendix C.
Similarly on May 13th Nathan, Richard, and Matt spent the entire day talking to the
Physics classes of Mr. Jack Samuell at Nathan’s former school, John Marshall High in
Rochester. They spent the day telling the classes about the Microgravity Program and
their experiences at NASA Houston. Specifically they talked about the application
process to the program, brainstorming and building our experiment, testing, and
eventually how the experiment working during flight. They also explained how the
reduced gravity environment is produced aboard the Weightless Wonder. As our team
members were talking to classes composed mainly of juniors and seniors they
emphasized the availability of programs, such as the Reduced Gravity program, that are
available for undergraduate participation and research. During the visit KTTC Channel
10 news did a follow up story on our team, specifically interviewing their hometown
“star” Nathan and shooting some footage of the guys talking to the students.
10.3 Local Press
Maria was asked by her employer at B.F. Goodrich to give a luncheon presentation about
the experiment and her experience at NASA to her fellow co-workers.
One of our local news stations, WCCO channel 4, sent reporter Bill Hudson to follow our
progress as we constructed, tested, and refined our experiments for the trip to Houston.
Unfortunately, he was unable to escort us to JSC as he was deployed overseas to follow
the war. He did send us with video cameras to record our experience and questions to
answer for a follow up story once he returned.
KTTC Channel 10 news station from came and interviewed Nathan and the rest of the
team as we were preparing to ship the experiment.
10.4 Flyer’s Hometown Press
Nic was featured on the front page of his hometown newspaper the Verona Press. He
answered a series of emails from the writer who then incorporated Nic’s responses into
his article. The complete article can be found in Appendix C.
29
11.0 Bibliography
Ashgriz N., J.Y. Poo. “Coalescence and separation in binary collisions of liquid drops.”
Journal of Fluid Mechanics 221 (1990): 183-204.
Bjelogrlic N., P. Boigenzahn, S. Salber, S. Williams, and B. Crook. “Study of Pinch-Off
of Liquid-Liquid Flows in Micro- and Macro-Gravity Conditions.” (2001).
Dhainaut M., and S.T. Johansen. “Literature Study on Observations and Experiments on
Coalescence and Breakup of Bubbles and Drops.” SINTEF Report 24 (2002): 1-64.
Leal L.G., D.J. Pine, and Y.T. Hu. "Drop deformation, breakup, and coalescence with
compatibilizer.” Physics of Fluids 12.3 (2000): 484-486.
Leal, L.G., Y.T. Hu, C. Park, and H. Yang. "The coalescence of two equal-sized drops in
a two-dimensional linear flow." Physics of Fluids 3.5 (2001): 1087-1106.
Longmire E.K., T.L. Norman, and D.L. Gefroh. "Dynamics of Pinch-off in
Liquid/Liquid Jets with Surface Tension.” International Journal of Multiphase Flow
27.10 (2001): 1735-1752.
Skelland A.H.P., and C.L. Caenepeel. “Effects of surface Active Agents on Mass
Transfer During Droplet Formation, Fall and Coalescence.” AIChE Journal 18.6 (1972):
1154-1163.
UNISTRUT Northern, “General Engineering Catalog.” North American Edition 12
(2000).
Webster D.R., and E.K. Longmire. "Jet Pinch-off and Drop Formation in Immiscible
Liquid/Liquid Systems." Experiments in Fluids 30 (2001): 47-56.
N., P. Boigenzahn, S. Salber, S. Williams, and B. Crook. “Study of Pinch-Off
30
APPENDICIES
31
Appendix A: Matlab Scripts
MAIN SCRIPT (analyze.m), which calls additional, functions for complete analysis.
%just a quick little script to call the desired functions and output pretty pictures.
if exist('figures','dir') ==0
mkdir('figures')
end
%picture function outputs nicely formatted png images to the figures directory
%using exportfig.m with preset options
figure(1)
[Weber1,impact1,status1]=dropletprops('day1vert','day1hor');
plotresults(Weber1,impact1,status1);
picture('figures\day1')
figure(2)
[Weber2,impact2,status2]=dropletprops('day2vert','day2hor');
plotresults(Weber2,impact2,status2);
picture('figures\day2')
figure(3)
[Weberg,impactg,statusg]=dropletprops('groundvert','groundhor');
[bounceg, coalesceg, reflexg]=plotresults(Weberg,impactg,statusg);
picture('figures\groundtests')
figure(4)
Weberf=[Weber1;Weber2];
impactf=[impact1;impact2];
statusf=[status1;status2];
[bouncef, coalescef, reflexf]=plotresults(Weberf,impactf,statusf);
picture('figures\flightdata')
figure(5)
compareresults(bouncef, coalescef, reflexf,bounceg, coalesceg, reflexg);
picture('figures\comparedresults')
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%function to extract colliding droplet properties from a saved data file,
%takes arguments to a vertical and horizontal camera data file, sans their extension .txt
%data file is the data fields (collision # through rsult) from spreadsheet cut and pasted into a plain
%tab delimited text file.
function [Weber,impact,status]=dropletprops(vertfile,horfile);
%set up constants here
scale = 0.000075595; %convert pixels to meters, use .3125 in/105 px
density = 1150; %kg/m^3
surfacetension = .0143; %N/m
%just text processing stuff to load the files correctly
file1=cat(2,vertfile,'.txt');
file2=cat(2,horfile,'.txt');
%load files into arrays
vertfile = load(file1);
horfile = load(file2);
%calculate the x, y and z velocites of both drops in the frame of reference of the tank
%Z is up, x is to the right on the horizontal camera, y is transverse, arranged in right-handed fashion
%with X we use averaging because we have 2 separate data sources for that axis
drop1vx=(-vertfile(:,5)+horfile(:,4))./2;
drop1vy=vertfile(:,4);
drop1vz=horfile(:,5);
drop2vx=(-vertfile(:,12)+horfile(:,11))./2;
drop2vy=vertfile(:,11);
drop2vz=horfile(:,12);
%grab the drop diameters also. in this case, both can be averaged,
32
%as the assumption is made that the droplets are reasonably 2 dimensional
%when commenting, discovered that this code was obsolete, and was never used
% drop1dia1=(vertfile(:,6)+horfile(:,6))./2;
% drop1dia2=(vertfile(:,7)+horfile(:,7))./2;
%
% drop2dia1=(vertfile(:,13)+horfile(:,13))./2;
% drop2dia2=(vertfile(:,14)+horfile(:,14))./2;
%convert position calculations to be relative to the first droplet
%so that 3 dimensional calculations can be made. Collision properties will be calculated
%relative to droplet 1. This was the most straightforward way of equating the position data on
%each camera
% y coords in tank coords
vertcamdrop2y=vertfile(:,9)-vertfile(:,2);
vertcamdrop1y=vertfile(:,2)-vertfile(:,2);
% x coords in tank coords
vertcamdrop2x=-(vertfile(:,10)-vertfile(:,3));
vertcamdrop1x=vertfile(:,3)-vertfile(:,3);
%x coords in tank coords
horcamdrop2x=horfile(:,9)-horfile(:,2);
horcamdrop1x=horfile(:,2)-horfile(:,2);
%z coords in tank coords
horcamdrop2z=horfile(:,10)-horfile(:,3);
horcamdrop1z=horfile(:,3)-horfile(:,3);
%since we have 2 sets of diameter measurements for each droplet, these will be averaged
%generation of a single "average diameter" value given 2 is left to a function, so that the calculation may be adjusted
%for alternate concepts of "diameter" of a non-spherical body may be used easily
%individual averageing is done in a function if alternate averaging needed, averaging between cameras done here
drop1diameter = (diameteraverage(vertfile(:,6),vertfile(:,7))+diameteraverage(horfile(:,6),horfile(:,7)))./2;
drop2diameter = (diameteraverage(vertfile(:,13),vertfile(:,14))+diameteraverage(horfile(:,13),horfile(:,14)))./2;
%pull in the 2 values of center to center distance
cvert = vertfile(:,8);
chor = horfile(:,8);
%put the velocity data gathered earlier into nice vector format for convenience.
%Convert from pixels to meters as well for obvious reasons like data consistency
U1 = [drop1vx, drop1vy, drop1vz].*scale;
U2 = [drop2vx, drop2vy, drop2vz].*scale;
%calculate x, y, z data, recall that the frame of reference is droplet 1 (top, left on the cams)
x1=vertcamdrop1x;
x2 = (vertcamdrop2x+horcamdrop2x)./2;
y1=vertcamdrop1y;
y2=vertcamdrop2y;
z1=horcamdrop1z;
z2=horcamdrop2z;
%average c - definately an accurate approximation to first order, and with equipment limitations that is more than good enough
c=(cvert+chor)./2;
%scale our distance measurements and put them into convenient vectors
c=c.*scale;
s1=[x1,y1,z1].*scale;
s2=[x2,y2,z2].*scale;
drop1diameter = drop1diameter.*scale;
drop2diameter = drop2diameter.*scale;
%calculate the X value and then get impact parameter from it
%valuse for this paramter agree better with past experiments than those of the Weber number
X = getbigX(c,U1,U2,s1,s2);
impact = 2.*X./(drop1diameter+drop2diameter);
33
%weber number range larger than that used in the previous experiments referenced.
%interesting
Weber = getWeber(drop1diameter,drop2diameter,density,surfacetension,U1,U2);
%generate a vector of the collision results. 0 = bounce, 1 = coalesce, 2 = reflexive separation, -1 = data acquisition error of some sort,
anything larger is ignored.
%throw in a random large number if unsure of outcome, but expected the other tape has it. Top camera always has a definative yes/no
answer, so this works fine
status = min(vertfile(:,15),horfile(:,15));
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%function to run through the intermediate outputs of dropletprops.m and generate plots of outcomes
function [bounce, coalesce, reflex]= plotresults(Weber,impact,status);
%run through entire array
numcollisions = size(Weber,1);
%initialize values to keep matlab happy
numcoalesce=0;
numbounce=0;
numreflex=0;
reflex = [0,0];
bounce = [0,0];
coalesce = [0,0];
%run through all values, cleck the value of status and place data into an output matrix accordingly
for i=1:numcollisions,
switch(status(i))
case -1
disp(sprintf('Bad Data/No Data in data row %d',i)) %let user know a set of data was unusable
case 0
numbounce = numbounce+1;
bounce(numbounce,:)=[Weber(i),impact(i)];
case 1
numcoalesce = numcoalesce+1;
coalesce(numcoalesce,:)=[Weber(i),impact(i)];
case 2
numreflex = numreflex+1;
reflex(numreflex,:)=[Weber(i),impact(i)];
otherwise
disp('Error in Data File')
break
end
end
%just pretty things up in case there are no reflexives
if reflex(1,:) ~= [0,0]
plot(bounce(:,1),bounce(:,2),'o',coalesce(:,1),coalesce(:,2),'x',reflex(:,1),reflex(:,2),'^');
legend('Bounce','Coalesce','Reflexive');
else
plot(bounce(:,1),bounce(:,2),'o',coalesce(:,1),coalesce(:,2),'x');
legend('Bounce','Coalesce');
end
xlabel('Weber Number')
ylabel('Impact Parameter x')
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
function D = diameteraverage(short,long)
%functionalize in case we use a different method to average droplet diameters
%D=min(short,long);
D = (short+long)./2;
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
function X = getbigX(c,U1,U2,s1,s2)
length = size(c,1);
34
U2(2,:);
warning off
for i=1:length
sintheta(i,1) = sin(acos(dot((U2(i,:)-U1(i,:)),(s1(i,:)-s2(i,:)))./(norm(U2(i,:)-U1(i,:)).*norm(s1(i,:)-s2(i,:)))));
end
X=c.*sintheta;
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%calculates average weber number given 2 droplet diameters, density, interfacial surface tension, and their velocities
function We = getWeber(d1,d2,rho,sigma,U1,U2);
length = size(d1);
d=(d1+d2)./2;
for i=1:length
U(i,:)=norm(U2(i,:)-U1(i,:));
end
U;
We = rho*U.*U.*d./sigma;
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
function picture(filename)
exportfig(gcf,filename,'format','png', 'width',7, 'fontmode','fixed', 'fontsize',12,'color','cmyk');
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
function compareresults(bouncef, coalescef, reflexf,bounceg, coalesceg, reflexg);
plot(bouncef(:,1),bouncef(:,2),'ob',coalescef(:,1),coalescef(:,2),'xb',bounceg(:,1),bounceg(:,2),'og',coalesceg(:,1),coalesceg(:,2),'xg',refl
exg(:,1),reflexg(:,2),'g^');
legend('Bounce(flight)','Coalesce(flight)','Bounce(ground)','Coalesce(ground)','Reflexive(ground)')
xlabel('Weber Number')
ylabel('Impact Parameter x')
35
Appendix B:
Spreadsheets containing Data from video analysis using Videopoint 2.5 software.
Ground Tests: Vertical Camera –
Raw Data Taken from videopoint - Units of pixels and pixels/s
center to center distance
Vertical camera ground test data
1=coalescence, 0 = bounce
Collision #
Top Droplet
X position
Y Position
X Velocity
distance c2c
Y Velocity
Dia Short
Bottom Droplet
Dia Long
X position
Y Position
X Velocity
Result
Y Velocity
Dia Short
Dia Long
1
793
488
15
-15
156.1
122.1
133.4
768
357
-255
510
152
133
0
2
793
503
4.286
-250.9
149
133.1
156.7
759
350
-23.59
559.3
149.2
131.2
0
3
792
478
-112.5
-585.1
146
123.5
120.8
762
361
-137
743
159
126
0
4
796
473
363.1
-1546
153
250
128.4
756
351
-236.5
994.4
161
239
0
5
797
498
285
-660
762
332
120
1260
332
120
1260
156.3
168
0
6
797
486
45
-1200
170.1
163
152.4
765
337
105
900
181
173
0
7
794
499
15
-3570
180.4
330
180.5
771
320
165
2955
166
325.3
1
8
792
520
-120
-2730
158.2
318
216.8
757
306
-255
2535
154
323
1
9
792
485
-240
-3525
177
198
136.9
769
350
15
3090
172.1
226
1
10
795
482
-114.4
-522.8
151.1
132
126.4
762
360
-206.6
577.1
148
131
0
11
792
493
-21.08
-84.7
147
135
139.7
760
357
85.05
366.7
147.3
132
0
12
792
494
66.83
-501.7
149
133
154.4
760
343
-121.5
80.42
146.1
129
0
13
799
497
81.71
-430.1
158.1
147
150.6
762
351
0.7666
309.6
153.1
145.3
0
14
801
486
420
-1080
165.1
184
148
763
343
-30
1020
169
203
0
15
797
475
230.5
-1299
186.1
158.2
126.5
760
354
-111.8
1362
178.1
180
0
16
793
495
145.7
-1760
193.1
196.1
158.3
761
340
-33.55
1235
176
199
0
17
796
499
79.69
-2004
168
309.1
166.5
762
336
-76.83
1859
176.1
354
0
18
795
476
-226.5
-2728
176
241
134.4
761
346
-129.4
2262
176.4
188.1
1
19
795
472
0
-285
149
114.2
109.6
767
366
-60
735
157.1
107.2
0
20
799
472
61.46
-540.7
144
112.1
107.9
767
369
5.714
356.3
156.1
122.1
0
21
792
472
43.24
-2736
159.1
248
128.9
765
346
115.8
2320
154.2
225
1
22
794
481
-240
-3330
157
241.1
148
760
337
-195
2730
154
237
1
23
803
455
141.6
-2696
172
187
97.95
758
368
-147.9
2333
181.8
168.2
1
24
800
505
405
-3555
166
347.1
181
762
328
-165
3570
159.1
295
2
25
792
497
0
-3855
161
311
182
765
317
105
2910
164
369
2
26
794
500
-60
-4155
166
356.1
189.8
768
312
75
3525
152
338.1
2
27
800
468
175
-429.5
156.2
105
102.5
770
370
79.58
389.9
161.3
104
0
28
796
464
-9.686
-315.1
150.5
107.2
109.2
757
362
-79.55
593.6
152.7
104
0
29
799
467
180
-975
150
108
111.3
762
362
-60
1200
161.1
106.1
0
30
796
469
-27.87
-656.8
153.1
117
113.3
765
360
73.17
1196
156.3
115.4
0
31
797
469
109.6
-3441
148
231
108.8
765
365
76.03
2906
170.2
185
1
32
799
444
142.3
-2334
140.2
212
79.71
767
371
-12.18
1871
156.1
249.1
1
33
795
490
15
-2460
157
225
146.2
760
348
-105
2670
163.2
228
0
34
797
479
159.4
-2632
165.1
247.1
138.5
762
345
-102.9
2971
166
270
1
35
795
487
195
-2310
158
266
146.5
763
344
270
2850
162
317
1
36
794
483
7.143
-3492
162.1
271
144.1
760
343
-646.4
3299
157.4
361.1
1
37
789
495
70.68
-996.3
145.2
103.2
81.32
766
417
-335.9
1607
149.4
88.09
0
38
799
526
120
-1575
115.2
143.3
157.5
766
372
-255
1275
132
135
0
39
788
491
-18.92
-1663
142
95.19
90.61
771
402
134
1779
126
104
0
40
803
532
-45
-2835
139.1
259
175.4
760
362
-45
2610
153.1
247.1
1
41
787
530
45
-3045
144.2
263
178.2
766
353
-60
2640
157
233.3
1
42
0
0
0
0
0
0
0
0
0
0
0
0
0
-1
43
785
538
8.571
-2676
162
255.1
199.3
762
340
-107.6
2695
164
241.4
2
44
789
530
-105
-3090
154.1
305
194
769
337
-30
3000
165
308
2
45
792
549
164.7
-3150
151
305
245.2
759
306
-305.5
2501
151.1
275
2
46
799
484
321.6
-1875
145
101
88.26
769
401
-4.878
1656
141.3
108.1
0
47
795
510
257.2
-2254
144
154
140.5
764
373
-480.3
2568
144.3
149.1
0
48
798
486
180
-1605
144.4
115.5
87.6
770
403
195
1755
154.3
94
0
49
793
501
7.892
-2965
150
260
132.8
766
371
236.5
2512
142.1
219
1
50
800
495
30
-2610
138.4
221.1
111.1
761
391
60
2805
140.5
305.1
1
51
798
470
210
-2985
143.3
250.1
79.85
768
396
255
2250
155.1
312
1
52
788
510
45
-3630
146
328.4
149.6
766
362
-45
2730
157.4
301
1
53
790
496
120
-3855
158
328
116.7
770
381
90
2910
165
331.1
1
54
790
572
-153.7
-3155
145.1
303.1
272.1
766
301
17.87
3150
161.1
291
1
36
Ground Tests: Horizontal Camera –
Raw Data Taken from videopoint - Units of pixels and pixels/s
center to center distance
Nozzle Dia = 0.3125" inches = 100.0 pixels
Horizontal data from Ground Test (Done by Nic)
1=coalescence, 0 = bounce
Collision #
Top Droplet
X position
Y Position
X Velocity
distance c2c
Y Velocity
Dia Short
Bottom Droplet
Dia Long
X position
Y Position
X Velocity
Result
Y Velocity
Dia Short
Dia Long
1
638
44
420
-2250
140
118
144
782
42
-300
-2850
138.1
88.02
0
2
618
96
443.8
-2542
138
104.1
160
804
108
-348.8
-2617
160.3
126
0
3
628
126
510
-2460
122
108.2
148.3
788
132
-810
-2550
134.1
98.18
0
4
630
222
1530
-2790
194.3
140.4
158
788
222
-1740
-2880
182.3
122
0
5
598
212
1350
-2490
130.8
200.2
195
830
210
-2100
-3060
168.2
134
0
6
626
210
1560
-3210
160
136.1
190
816
210
-1860
-3330
154.6
122
0
7
634
280
1770
-1950
144.1
136.2
160.1
810
280
-2610
-2070
154
148
1
8
600
302
2400
-2250
180
142
154.1
770
238
-2940
-2100
156.2
130
1
9
638
252
2400
-2460
168.2
128.1
160
798
254
-2970
-2460
164.6
134
1
10
634
38
305.1
-2514
124.1
102
156.1
790
42
-621
-3052
126
114.4
0
11
616
72
293
-1945
134
94.34
142.1
792
88
-518.9
-2113
124.1
94.34
0
12
636
34
155.1
-2044
130
94
144.3
780
44
-502.4
-2407
136.1
102
0
13
646
54
630.4
-2185
122.1
100
132
778
56
-440.3
-2447
124.1
108
0
14
638
216
1230
-2280
150.3
130
140.1
778
210
-1830
-2700
170.1
134
0
15
668
178
955
-2134
132.1
126.1
145
776
178
-564.9
-2367
148.1
130
0
16
642
216
1322
-2652
158.3
128
156.2
798
224
-1193
-2568
148.2
126
0
17
630
252
2159
-2467
172.6
136.1
164
794
252
-2348
-2477
170
138.1
0
18
598
304
1984
-2234
176.7
144.1
150
834
302
-2430
-2235
142.7
146
1
19
644
212
750
-2310
114
92.09
106.1
790
224
-800
-2610
126
104
0
20
648
120
115.3
-2704
118
102.1
128.2
776
128
-190.9
-2373
126.1
108
0
21
652
320
2360
-1805
160.2
130
144.1
796
316
-2495
-1952
148.2
128
1
22
638
324
2550
-1710
160.3
134.1
151
802
320
-2970
-1890
142.1
134.2
1
23
632
330
2820
-2220
160
158.3
174
806
330
-3720
-2160
154
148
1
24
634
340
3510
-2190
168
140
162
796
338
-3690
-2040
168
144
2
25
650
334
3750
-2040
172
134
176.2
826
342
-2640
-1380
182.1
148.3
2
26
650
350
4170
-2070
188
148.1
162.2
812
342
-4350
-2100
172.1
142.1
2
27
650
234
879.1
-2524
136.1
128
124
774
234
-1588
-2628
154.3
134
0
28
660
198
763
-2104
120.1
110.5
106.7
766
210
-971.8
-2118
134
112.1
0
29
632
260
851
-2227
136.1
128.1
114.3
806
274
-1010
-2263
144.1
116
0
30
612
344
1953
-1607
178.2
138
140.1
816
346
-2209
-1702
182
138.1
0
31
638
328
2310
-1620
162
166
159
800
324
-1950
-1830
166.1
156
1
32
640
322
2850
-2100
160
146.1
156
796
324
-2370
-1920
154
150.2
1
33
652
302
2580
-2238
168
164
132.4
784
312
-3424
-1937
140.1
148
0
34
624
336
4170
-1920
170
142.1
140.1
814
344
-4470
-1800
182
138
1
35
646
322
2490
-1860
200.2
150.7
140
786
320
-2850
-1710
210
126.1
1
36
656
312
1849
-1780
174
156.2
150.2
786
302
-2410
-2056
202
132
1
37
616
326
1650
-2040
134
114.2
120
736
328
-2520
-2370
140
112.1
0
38
614
330
1800
-2220
140
106
116
730
332
-2280
-2280
138
116
0
39
600
336
1221
-1663
124.1
118.1
114
746
342
-1487
-1730
132
124
0
40
596
382
2880
-1410
154.8
130.6
148
754
384
-3570
-1500
166.1
136.1
1
41
604
392
3671
-1430
164
122
160
772
390
-3312
-1443
184
132
1
42
0
0
0
0
0
0
0
0
0
0
0
0
0
-1
43
598
418
2490
-1380
238.7
120.1
161
774
414
-2940
-1320
242
132
2
44
634
364
2760
-1980
254.1
124.1
175
750
364
-2850
-1800
226
138.5
2
45
608
388
2400
-1290
276.2
128.1
173
762
378
-2760
-1530
246
140.1
2
46
610
354
2310
-2160
138.1
126
129
748
354
-2430
-1830
152
122
0
47
610
336
1920
-1890
148
118.3
122
718
332
-2010
-1890
148.1
118
0
48
612
348
2280
-1920
140
128.1
128.4
740
358
-2550
-1770
126
126
0
49
602
356
1920
-1800
212.2
134.1
155
742
348
-2370
-2070
190
132.2
1
50
610
408
2340
-1140
218.3
134
158
749
408
-2520
-1110
210
132.4
1
51
612
358
2198
-1890
138.4
210.2
162
740
354
-2730
-1710
242.4
122
1
52
609
397
2070
-1050
248.7
136
169
741
399
-2400
-1020
242.7
132
1
53
568
400
3330
-1410
278.5
122.3
176
796
396
-3300
-1080
280.5
136
1
54
574
398
3210
-1390
269.4
128.2
175.4
790
397
-3290
-1120
271
129
1
37
Day #1 Flight Tests: Vertical Camera –
Raw Data Taken from videopoint - Units of pixels and pixels/s
center to center distance
Vertical Data from Day 1
1=coalescence, 0 = bounce
Collision #
Top Droplet
X position
Y Position
X Velocity
distance c2c
Y Velocity
Dia Short
Dia Long
Bottom Droplet
X position
Y Position
X Velocity
Result
Y Velocity
Dia Short
Dia Long
1
735
445
472.8
-950.2
102
146
94.34
688
364
-266
1033
109.1
120
1
2
747
453
390
-465
111
142.1
74.03
703
403
240
1515
110.3
122.1
1
3
740
462
420
-1020
101
137
103.2
686
374
-60
1020
97
115
0
4
723
467
285
-1200
112
152.3
115.7
698
354
-45
1425
110
123.2
0
5
740
453
495
-1215
100
154
95.75
700
366
255
1380
115.1
112
1
6
749
417
465
-2325
105
260
64
692
388
105
1710
101.2
198.4
1
7
745
430
780
-1350
108.5
230
77.78
690
375
-90
1110
101
166
1
8
728
456
180
-1440
112.1
231.1
132.9
689
329
-300
1920
108
179
1
9
732
424
195
-2805
111
308
64.35
687
389
-345
3210
89.05
229
1
10
735
419
420
-3555
93.13
275
60
687
383
-90
2445
94
234
1
11 dead, no video
12
730
455
210
-3030
112
265.2
142.4
695
317
75
2175
104
230.1
1
13
729
438
135
-1095
104.4
133
82.73
692
364
-30
705
103
113
0
14
737
430
145.9
-557.6
107
117.5
80.71
692
363
-262.3
473.9
105.1
103.2
0
15
738
428
300
-675
99
188.2
68.68
692
377
-60
1290
90
144
1
16
737
451
525
-840
105
159
89
692
374
45
1635
117
141
1
17
721
469
-45
-1815
106
203
139
697
332
60
1620
96
156
1
18
721
453
-105
-2265
108
195
114.6
689
343
-150
1575
104
146
1
19
733
474
105
-3000
98
294
134.7
678
351
-240
2730
112
236
1
20
733
432
45
-2355
106
292
58
686
398
-315
2790
117
211
1
21
728
426
495
-2130
111
285
66.5
680
380
210
2265
110
214
1
22
727
460
105
-1470
110
237
90.82
695
375
0
1425
108
248
1
23
729
455
345
-2355
108
248
69.64
692
396
-285
2580
104
208
1
24
724
441
210
-2595
91
238
63.41
685
391
-135
1980
85
193
1
25
731
552
45
-990
124
140
131.6
687
428
-45
1485
107
200
1
26
720
451
210
-2355
97
252
76.5
687
382
-255
2175
112
201
1
27
713
475
165
-1470
105
264
141.5
674
339
-285
1170
106
189
1
28
732
471
165
-2235
101
260
120.7
687
359
-90
1410
99
204
1
29
723
471
270
-2550
107
244
100
692
377
-15
2100
105
198
1
30
726
469
180
-1365
101
186
87
692
389
60
1650
102
144
1
31
724
487
210
-900
110
153
100
687
394
-30
1380
109
124
1
32
724
476
285
-1665
105
197
128
692
352
180
2310
97
151
1
33
719
469
135
-1560
119
183
118
692
354
-165
2220
106
140
1
34
718
440
330
-1950
106
184
73.35
686
374
-255
1875
100
138
1
35
735
455
15
-1020
111
130
68.78
701
392
30
1305
99
109
1
36
724
441
135
-1005
98
127
77.6
695
369
-15
1245
98
104
1
37
717
458
-15
-810
111
145
85
698
375
180
1935
113
106
0
38
720
444
135
-1515
103
186
72.5
690
378
-360
1860
101
136
1
39
724
439
255
-1365
103
185
57.7
692
391
-105
1965
106
119
1
40
719
453
60
-1305
115
197
83.57
689
375
-60
1170
105
145
1
41
723
490
165
-1455
113
200
177
689
316
-45
2370
108
166
1
42
724
475
330
-1305
122
194.4
79.38
698
400
90
2700
110
156
1
43
724
475
165
-2400
114
277
139
687
341
-195
2505
110
223
1
44
717
453
-30
-2910
103
280
83
695
373
-135
3735
112
253
1
45
723
444
30
-2460
124
273
100
683
352
-150
2010
105
258
1
46
721
444
255
-2280
105
280
102
696
345
270
1890
94
213
1
47
721
403
-75
-2760
112
275
43
686
378
330
2145
110
241
1
48
721
455
120
-1035
113
136
92.7
689
368
45
1215
110
121
1
49
715
435
45
-1200
119
141
136
687
334
0
1365
107
122
1
50
721
425
-165
-810
105
133
48
689
389
-60
1140
108
122
1
51
726
432
135
-1425
121
177
47
690
402
45
1875
98
132
1
52
722
476
150
-1200
115
170
132.5
678
351
-525
1590
116
127
0
53
722
430
30
-1395
112
159
40.4
692
403
-120
2265
113
154
1
54
726
457
90
-2265
115
188
112.8
697
348
-75
1710
107
169
1
55
720
474
0
-2355
118
204
135
686
343
-255
2115
128
184
1
56
720
442
0
-2865
119
187
74.3
690
374
15
2175
115
177
1
57
721
448
210
-3510
115
199
90.76
692
362
150
3195
126
182
1
58
715
430
-195
-3225
112
225
54.8
701
377
30
2265
116
195.5
1
59
720
455
345
-3630
102
210
96
692
363
-270
3330
113
212
1
60
721
464
240
-2805
113
299
102.6
694
365
450
2670
113
281
1
61
721
474
-15
-3435
129
216
114.7
692
363
-195
3465
100
311
1
62
720
437
0
-1080
110
126
40.5
698
403
120
1095
108
113
1
63
720
441
60
-1695
114
136
58.14
694
389
-60
1050
110
113
1
64
735
433
360
-1350
120
143
58
696
390
-90
1500
99
101
0
65
724
462
360
-1635
116
127
111
687
357
30
780
103
103
0
66
717
483
45
-2250
117
214
133
692
352
0
2625
104
167
1
67
720
474
120
-2265
119
181
118.8
690
359
270
2190
117
152
1
68
717
428
-30
-2610
115
214
69
697
362
150
1275
102
178
1
69
724
430
255
-2745
103
190
50.8
694
389
150
3120
115
188
1
70
722
455
270
-2940
119
246
98.72
699
359
165
2805
135
241
1
71
720
464
-15
-3405
96
253
101
694
366
-180
3300
120
225
1
72
721
425
300
-3030
118
283
49.82
690
386
-15
2640
126
193
1
38
Day #1 Flight Tests: Horizontal Camera –
Raw Data Taken from videopoint - Units of pixels and pixels/s
center to center distance
Horizontal Data from Day 1
1=coalescence, 0 = bounce
Collision #
Left Droplet
X position
Y Position
X Velocity
distance c2c
Y Velocity
Dia Short
Dia Long
Right Droplet
X position
Y Position
X Velocity
Result
Y Velocity
Dia Short
Dia Long
1
576
440
1695
-285
122.1
128
114.3
689
457
-1620
-315
96.9
129.7
1
2
536
464
1560
60
112.1
176
173.2
708
484
-2820
60
116.3
144.5
1
3
570
439
1515
-330
120.1
137.5
123.6
687
479
-1200
330
108.7
131.9
0
4
541
462
1515
-60
108
160
181.5
721
485
-2190
45
112.1
161.2
0
5
589
456
2115
-270
110.2
139.3
106.4
694
473
-1965
135
103.1
123.6
1
6
575
433
2055
-465
96.42
192
95.13
668
453
-2550
-360
110.9
143.3
1
7
508
468
2055
165
90.05
267.1
247.2
755
479
-3555
45
105.2
203.5
1
8
530
468
2850
-60
93.05
246.3
241.4
771
482
-2895
-180
105.4
209.7
1
9
598
462
3375
-150
137.1
308
102.2
700
468
-4260
-510
101.4
241.3
1
10
595
463
3165
0
107
290
91.24
685
478
-3795
-45
108.2
355.3
1
11 NODATA
12
534
459
3975
-270
99
339.1
244.3
778
471
-3465
-285
90.02
278.2
1
13
591
455
1530
-30
110.7
128.6
99.46
689
472
-1425
-270
108.9
116
0
14
599
459
855
0
94.56
110.5
92.66
687
488
-855
90
105.9
107.5
0
15
586
459
645
-225
107
133.8
77.28
662
473
-2655
-135
121.2
122.8
1
16
582
463
1740
-45
131
134
95.34
675
484
-2295
225
116.5
128.3
1
17
505
462
1605
-90
98.05
250.2
261.4
766
476
-3375
-225
108.1
212.7
1
18
540
460
2190
-180
107
218.2
204.4
743
484
-2520
180
108.3
201
1
19
552
462
2265
-180
92.05
270
151.3
703
471
-3330
-285
93.19
258.4
1
20
557
452
2955
-330
90
270.1
131.2
688
460
-3225
-405
105
256.4
1
21
569
453
2595
-315
102
302
142.3
711
462
-1815
-300
104.2
270.3
1
22
531
449
2940
-285
99
299
203.5
734
463
-2400
-225
96.13
296.2
1
23
524
463
1920
0
96.05
278.4
163.7
687
478
-2820
180
102.3
259.1
1
24
464
456
3330
-405
96
339.1
305.5
769
473
-4140
-135
102.2
302.9
1
25
456
465
1740
120
143.1
154.7
169.2
624
485
-2160
45
113.3
224.5
1
26
530
459
1305
-240
95
249
142.3
672
468
-2835
-375
99.05
253.8
1
27
508
466
3090
-135
96.05
325
229.7
737
484
-2610
45
104.4
284.3
1
28
482
465
2355
-60
108.3
344
250.2
732
476
-3435
-135
108.1
336.4
1
29
531
468
1440
-120
101
299
177.3
708
479
-2670
-90
102
278.2
1
30
544
459
1770
-150
110.4
169.2
117.7
660
479
-3150
150
108.2
160.3
1
31
521
449
990
-210
131.9
143.3
152.1
666
495
-1455
300
114.8
140.9
1
32
539
436
2535
-375
107.6
215.7
166.2
704
456
-1860
-195
105.4
196.5
1
33
552
471
2430
-60
108.1
206.5
162.6
714
485
-2025
135
110.2
175.2
1
34
578
453
2010
-360
107.4
136.3
99.64
676
471
-1920
30
117.5
133
1
35
573
410
1305
-765
105.3
140.6
87.32
658
430
-1830
-465
101.4
114.8
1
36
586
459
2115
-180
116.5
125
90.24
674
479
-2145
0
105.6
116.7
1
37
568
462
1590
-135
119.3
137.6
116.7
681
491
-1920
315
111.1
119.5
0
38
576
457
1785
-225
111.5
134.5
93.77
669
469
-3000
-135
116.3
134.1
1
39
520
462
2640
-180
99
229.2
220.7
740
479
-2895
90
102.2
186.8
1
40
556
459
1800
-105
107.2
220.7
168
724
462
-2085
-465
108.2
218.1
1
41
528
456
2730
-150
107
241.3
224.9
752
476
-2400
-315
105.2
189.8
1
42
570
462
2220
0
112.3
196.2
112.3
681
479
-2610
0
108.1
161.2
1
43
505
466
2775
-180
105.1
320
259
764
469
-3105
-180
108.7
316.1
1
44
514
462
2490
-15
98.18
313.1
247.2
761
471
-3810
-165
99.98
291.3
1
45
543
459
2775
-465
113
334
223.2
766
468
-2625
-240
93.19
299.3
1
46
546
455
2880
-375
102.2
296
194.7
740
472
-3495
-45
102.4
280.3
1
47
573
457
2685
-270
105.6
267
177.2
750
466
-2280
-90
91.08
226.5
1
48
579
426
2115
-525
129.1
129.7
109.8
687
446
-2070
-210
115.3
148.1
1
49
594
462
1215
-15
97.29
128.5
81.74
675
473
-1800
-180
109.8
118.2
1
50
607
456
1905
-315
104
163.2
206.3
674
471
-1935
-60
108.4
154.4
1
51
576
463
1695
-225
108.1
195.1
221
634
481
-2310
450
93.43
189.3
1
52
531
471
2070
-150
102
183.2
198.3
729
482
-2610
45
96.05
171.9
0
53
572
456
1470
-255
110.7
113
88.28
659
471
-2250
15
97.02
110.1
1
54
515
468
2115
-165
105
230
230
745
471
-2430
-150
93.34
235.4
1
55
496
471
2520
75
93
244
241.1
737
479
-3525
-90
96.05
238.8
1
56
546
466
2835
-225
107
235
165.4
711
478
-3195
-90
98.18
220.5
1
57
572
468
3090
-150
105
197.6
133.2
705
476
-2925
-180
99.18
169.4
1
58
579
462
2775
-300
99.18
206.1
108
687
465
-3045
-285
96.33
198.2
1
59 NODATA
60
533
456
3525
-240
113.5
278.1
209.2
742
465
-3120
-195
93.19
279.3
1
61
570
462
3240
-210
98.02
223.1
117.3
687
471
-3855
-285
105
250.4
1
62
588
462
1365
-240
104.2
160.3
183.1
646
471
-1500
-195
93.19
136.4
1
63
595
465
1605
-150
91.24
113.2
56.09
650
476
-1920
-270
82.76
96.75
1
64
541
466
2295
-270
107
148.3
178.4
719
478
-2355
180
105.1
139.4
0
65
572
466
1785
-315
110.2
131.1
125.9
697
481
-1920
135
102.4
138.5
0
66
521
471
3615
-60
90
232
227
748
471
-2520
30
93.13
267.4
1
67
527
468
2670
-300
99
192.1
192.3
719
479
-3870
210
93.13
224.4
1
68
547
471
2595
-195
102
212.1
157.1
704
476
-3315
-180
90.2
197.2
1
69
569
468
2175
-210
105
162.2
116
685
471
-2265
-450
99.05
163.4
1
70
562
465
3135
-210
96.05
224.3
136.1
698
471
-2850
120
99.05
209.2
1
71
565
465
4035
-255
102
215.2
148
713
468
-3525
60
99
230
1
72
557
465
3375
-330
101
238
160
717
468
-3270
-300
96.05
223.1
1
39
Day #2 Flight Tests: Vertical Camera –
Raw Data Taken from videopoint - Units of pixels and pixels/s
center to center distance
Nozzle Dia = 0.3125" inches = 104.1 pixels
Vertical Data from Day 2 (Done by Nic)
1=coalescence, 0 = bounce
Collision #
Top Droplet
X position
Y Position
X Velocity
distance c2c
Y Velocity
Dia Short
Dia Long
Bottom Droplet
X position
Y Position
X Velocity
Result
Y Velocity
Dia Short
Dia Long
1
720
462
210
-840
108
112.1
79.4
668
402
-360
840
100
110.2
1
2
726
458
270
-930
114
142.2
79.65
676
396
0
1050
102.2
114.1
1
3
722
444
300
-1170
109.2
126
80.92
670
382
-390
930
106.2
120.1
1
4
712
462
0
-1140
110.5
106
91.76
680
376
60
1110
120.1
102.3
1
5
716
468
90
-930
106.3
97.69
93.23
680
382
0
1140
106.3
97.69
0
6
710
460
180
-1080
122.3
120
112.1
680
352
30
1050
122.1
106
1
7
706
480
0
-1260
118.1
188.1
119
672
366
-120
1080
108.7
160.2
1
8
712
490
30
-1380
106.3
194.1
151.4
672
344
-240
1860
110.2
188
1
9
722
446
270
-750
124
106
86.83
680
370
-210
630
118.3
114
1
10
716
446
90
-450
118.1
102
92.13
674
364
-60
720
112
100.1
0
11
716
430
31.46
-287.9
124.1
106
80.99
672
362
-430.2
565.1
108
94.02
0
12
718
442
150
-630
114
100
102.5
682
346
60
510
110
104
0
13
722
482
480
-1350
108
234.1
130
656
370
-660
1230
96.02
230
1
14
712
502
90
-1890
98.18
256
163.5
670
344
-330
1830
100.1
228
1
15
726
488
600
-1170
112
236
151.3
652
356
-720
1650
104.2
208.1
1
16
720
502
360
-1110
110
242.1
160.5
658
354
-570
1170
90.02
204.2
1
17
708
504
270
-1920
104.1
238.2
179.6
672
328
-120
2220
94.34
190
1
18
708
510
210
-1320
102
246
166.7
672
316
-360
1560
100
206
1
19
718
442
-60
-180
102.2
94
84.31
686
364
60
180
94.02
86
0
20
712
458
300
-2160
116
158.1
108.8
674
356
-300
1410
100
118.1
1
21
702
460
-120
-1320
110.2
134.2
105.8
674
358
-60
960
114
128.2
0
22
712
476
300
-1110
104
166
109.8
682
324
-210
1380
106
156.1
1
23
704
462
90
-1260
116.1
124
110.1
668
358
-300
1170
114.4
116
1
24
704
484
0
-2370
122
250
170.3
674
296
-90
2130
100.2
208
1
25
708
472
30
-1950
94
216.1
123.2
680
352
60
1980
96.08
190
1
26
702
460
-240
-2550
96.19
230.1
132.2
678
330
-60
2130
100.2
216
1
27
collision did not exist in file
28
712
466
0
-1770
98.33
232
115.9
682
354
-60
1950
90.8
216
1
29
710
462
30
-2310
98
238.1
135.5
690
328
150
1950
90
198
1
30
718
456
74.32
-323.4
94.19
98
91.39
682
372
-141.5
317.7
88.02
86
0
31
716
440
0
-600
94.02
90.2
75.15
684
372
-90
510
82.1
72
0
32
722
454
240
-1260
96.02
154.1
101
666
370
-270
1350
92.2
128.1
1
33
706
460
180
-1470
98.02
190
113.5
678
350
-180
1320
96.02
156
1
34
710
464
240
-1770
102
184.1
103.1
678
366
90
1620
92
156.1
1
35
716
458
90
-1410
100
168.2
112.9
672
354
-150
1530
102.1
152.1
1
36
704
464
30
-1860
106.2
140
114.6
672
354
-180
1110
106.2
112.2
1
37
718
468
210
-900
90
100
85.44
672
396
-30
990
80.02
90.09
0
38
708
462
30
-960
94.09
88
86.65
680
380
90
900
88
82
0
39
712
468
150
-930
98.08
110
86.4
676
398
-30
1020
80
88.02
0
40
710
462
60
-1080
102
114.3
80.99
682
386
30
1110
88.02
104
0
41
714
442
90
-750
94.09
90.02
82.65
672
398
-60
600
82.02
86.09
0
42
698
480
-60
-2370
112
178
136.5
672
346
-30
2160
112.2
168
1
43
706
474
60
-1710
110
176
125.3
664
356
-480
1920
108.1
156.1
1
44
702
494
-60
-3510
108
206
158.5
674
338
-150
3270
106.1
168
1
45
706
494
240
-2490
112.1
202
170.3
678
326
60
2310
100
208
1
46
706
540
120
-2490
106.2
214.1
165.4
678
320
60
2760
94.09
194
1
47
706
500
150
-3030
118.1
212.2
162.8
674
320
90
3240
102
236
1
48
706
498
330
-2970
106.2
240.1
150.6
678
350
90
3540
100.3
276
1
49
704
476
0
-1920
108
172.3
110.2
682
368
300
1620
110.5
158
1
50
698
486
-90
-3150
100.3
158
125.2
674
348
-180
3000
106.1
132.1
1
51
706
496
240
-3330
100.3
174.1
132.1
680
354
210
3360
110
162.1
1
52
706
474
210
-2340
122
182
126.6
672
352
-60
2220
124.1
186
1
40
Day #2 Flight Tests: Horizontal Camera –
Raw Data Taken from videopoint - Units of pixels and pixels/s
center to center distance
Nozzle Dia = 0.3125" inches = 104.0 pixels
Horizontal Data from Day 2 (Done by Nic for Maria)
1=coalescence, 0 = bounce
Collision #
Top Droplet
X position
Y Position
X Velocity
distance c2c
Y Velocity
Dia Short
DiaLong
Bottom Droplet
X position
Y Position
X Velocity
Result
Y Velocity
DiaShort
Dia Long
1
664
460
900
-60
98.02
156
102
822
462
-1740
-30
112
150.2
1
2
692
468
1020
-90
102.2
154.1
99.3
790
484
-2010
30
90.2
152
1
3
687
465
920
30
109.2
123
80.92
812
456
-1050
-30
106.2
120.1
1
4
677
466
1100
0
110.5
111
91.76
820
440
-1140
-60
120.1
102.3
1
5
679
467
1140
-30
106.3
98.4
93.23
820
454
-930
90
106.3
97.69
0
6
669
468
1040
-60
122.3
123
112.1
800
460
-1080
0
122.1
106
1
7
660
470
1040
90
118.1
202.1
119
798
464
-1260
30
108.7
160.2
1
8
659
461
1670
0
106.3
194.3
151.4
795
458
-1380
-30
110.2
188
1
9
678
462
650
30
124
104
86.83
814
464
-750
0
118.3
114
1
10
675
464
720
-30
116
110
92.13
812
468
-450
-90
112
100.1
0
11
673
465
570
0
124.1
98
80.99
816
462
-287.9
60
108
94.02
0
12
672
466
530
-90
114
108
102.5
821
468
-630
30
110
104
0
13
674
466
1210
60
108
230.2
130
807
462
-1350
0
96.02
230
1
14
685
469
1740
30
98.18
246
163.5
815
502
-1890
-60
100.1
228
1
15
687
461
1565
0
112
236
151.3
806
488
-1170
-60
104.2
208.1
1
16
681
459
1200
-60
110
242.1
160.5
802
502
-1110
-90
90.02
204.2
1
17
680
460
2120
-60
104.1
238.2
179.6
793
504
-1920
0
94.34
190
1
18
683
462
1720
-90
102
246
166.7
826
510
-1320
-30
100
206
1
19
666
463
210
0
102.2
94
84.31
824
442
-180
30
94.02
86
0
20
654
462
1380
-30
116
158.1
108.8
814
458
-2160
-90
100
118.1
1
21
676
461
950
30
110.2
134.2
105.8
805
460
-1320
60
114
128.2
0
22
678
462
1260
60
104
166
109.8
809
476
-1110
30
106
156.1
1
23
679
464
1200
60
116.1
134
110.1
808
462
-1260
0
114.4
116
1
24
672
464
1980
90
122
250
170.3
818
484
-2370
-60
100.2
208
1
25
690
461
1890
90
94
216.1
123.2
814
472
-1950
-60
96.08
190
1
26
690
462
2010
0
96.19
230.1
132.2
816
460
-2550
-90
100.2
216
1
27
did not analyze - so data would match
28
692
461
1950
-60
98.33
232
115.9
809
466
-1770
0
90.8
216
1
29
698
466
1920
-60
98
238.1
135.5
808
462
-2310
-90
90
198
1
30
697
467
320
90
94.19
98
91.39
818
444
-323.4
-30
88.02
86
0
31
698
468
500
-90
94.02
90.2
75.15
814
462
-600
0
82.1
72
0
32
691
467
1290
-30
96.02
154.1
101
815
468
-1260
30
92.2
128.1
1
33
677
468
1320
0
98.02
190
113.5
821
460
-1470
-30
96.02
156
1
34
685
470
1620
30
102
184.1
103.1
807
480
-1770
60
92
156.1
1
35
678
473
1590
-30
100
168.2
112.9
815
490
-1410
-60
102.1
152.1
1
36
687
469
1400
60
106.2
140
114.6
806
446
-1860
-90
106.2
112.2
1
37
694
461
900
-60
90
100
85.44
802
446
-900
30
80.02
90.09
0
38
689
465
930
-90
94.09
88
86.65
793
430
-960
60
88
82
0
39
678
465
1120
0
98.08
110
86.4
812
442
-930
-30
80
88.02
0
40
675
467
1030
0
102
114.3
80.99
813
482
-1080
-60
88.02
104
0
41
673
468
590
90
94.09
90.02
82.65
817
442
-750
90
82.02
86.09
0
42
683
462
2090
30
112
178
136.5
810
480
-2370
-30
112.2
168
1
43
681
462
1940
-30
110
176
125.3
812
474
-1710
0
108.1
156.1
1
44
680
461
3100
-60
108
206
158.5
807
494
-3510
0
106.1
168
1
45
667
464
2600
-60
112.1
202
170.3
815
494
-2490
90
100
208
1
46
689
464
2760
90
106.2
214.1
165.4
809
540
-2490
30
94.09
194
1
47
679
463
3240
90
118.1
212.2
162.8
818
500
-3030
-30
102
236
1
48
672
469
3340
-60
106.2
240.1
150.6
809
498
-2970
-60
100.3
276
1
49
678
470
1720
-60
108
172.3
110.2
802
476
-1920
-60
110.5
158
1
50
677
472
3070
-30
100.3
158
125.2
805
486
-3150
90
106.1
132.1
1
51
701
462
3240
60
100.3
174.1
132.1
813
496
-3330
90
110
162.1
1
52
671
466
2250
-30
122
182
126.6
810
474
-2340
-60
124.1
186
1
41
Appendix C: Outreach Attachments (Pictures and Articles)
42