CALIFORNIA STATE UNIVERSITY, NORTHRIDGE.
FORCED CONVECTION ON A ROTATING
SPHERE IN FREON 113
A project submitted in partial satisfaction of the
requirements for the degree of Master of Science in
Engineering
by
Gina Giorgi O'Shaughnessy
May 1988
The Project of Gina Giorgi O'Shaughnessy is approved
by:
Dr. E. Larson
Dr. S .~ H. Schwartz
~Chair)
California State University, Northridge
ii
DEDICATION
The author dedicates this work to her mother, father
(R.I.P.), brother and husband who always supported and
encouraged her throughout the difficult times.
iii
ACKNOWLEDGEMENT
My thanks go to Professor S. H. Schwartz who contributed
much of his time advising me during the course of this
project.
My deepest gratitude go to my mother, father (R.I.P.),
brother and husband whose love, devotion and unselfish
support helped
me
reach my goal.
iv
TABLE OF CONTENTS
Page
Item
....
Dedication
iii
Acknowledgement
iv
List of Tables
ix
List of Figures
xi
xvii
Abstract
Chapter I
A.
Introduction
1
. .
General Background
1
.
1
1.
Space Shuttle Turbopump
2.
Heat Transfer on Cryogenic Fluid
3.
B.
2
Film Boiling Correlation Needed for a
Rotating Sphere
4.
....
.
Bearings
~n
. . .. . . . .
....
Experimental Study by Rocketdyne
Theoretical Background
.....
4
5
.
6
1.
Convection With Rotation; No Boiling
6
2.
Convection Without Rotation; With Boiling
6
c.
.
Survey of Literature
1.
7
Studies of Film Boiling for Flow over a
Sphere Without Rotation
. .
.
7
2.
Subcooled Flow Film Boiling Over a Sphere
8
3.
Saturated Flow Film Boiling Over a Sphere
8
4.
Approach for this Research
. .. . .. .
10
v
TABLE OF CONTENTS (CONTINUED)
Page
Item
Chapter II
A.
Experimental Apparatus and Instrumentation
. 12
. . 15
Description of Apparatus
1.
Ball (Test Specimen)
15
2.
Rotating Device
15
3.
Ball Heating Device
16
B.
Description of Instrumentation
. 17
1.
Thermocouples in Ball Test Specimen
17
2.
Thermocouples in Freon 113 Bath and System
18
3.
Thermocouple Digital Display
19
4.
Freon 113 Cooling Circuit . . .
. 19
Chapter III Experimental and Calibration Procedures . . . 21
Static Experimental Procedures
A.
22
1.
Continuous Procedure
2.
Discontinuous Procedure (In and Out).
3.
Reheat Procedure
24
4.
Static In Air
24
B.
22
Rotational Experimental Procedures
.
.
25
1.
Rotate in Freon 113 (Discontinuous Method)
2.
Rotate In Air
. .
.
vi
23
..
.
25
26
p •
TABLE OF CONTENTS (CONTINUED)
Page
Item
c.
27
Calibration Procedures
.
27
1.
Freon 113 Purity
2.
Thennocouples in Ball
27
3.
Thennocouples in Freon Bath and System
28
4.
Rotating Device
Chapter IV
. . . . ..
. 28
....
Methods of Analysis . . . . . . . . . . . . . 29
A.
Weighted Average of Thermocouples
B.
Curve Fit . .
c.
Calculations
29
. 30
. . 31
1.
Heat Flux for this Study .
2.
Heat Flux Using Witte and Orozco's
. 31
Approach (Reference number 9) and Witte's
Approach (Reference number 10) . . . . . . 32
3.
Film Coefficient Using Witte and Orozco's
Approach (Reference number 9) and Witte's
Approach (Reference number 10) .
Graphs
D.
Chapter V
A.
. 33
33
Discussion of Results . . . . . . . . . . . . 35
Boiling Without Rotation . . . . . . . . . . . . 37
1.
Continuous Method at Different Degrees of
Subcooling
. . 37
vii
TABLE OF CONTENTS (CONTINUED)
Page
Item
2.
Continuous Method at the Saturation Temp.
3.
Ball in Air . . .
42
4.
Discont. and Reheat Methods With Subcooling
42
5.
Discontinuous Method at the Saturation Temp
45
Boiling With Rotation. . . . . . . . . . . . .
47
1.
Rotation at Different Levels of Subcooling.
47
2.
Various Rotational Speeds at the Same Freon
B.
. 39
113 Temperature . . . . . . . . .
3.
. 49
Comparison Between the Film Coef. from this
Study and Witte and Orozco (Ref. No. 9) . . . 52
4.
Rotation at the Saturation Temperature. .
55
5.
Comparison Between the Film Coefficients for
this Study and Witte (Reference number 10).
6.
Chapter VI
Ball Rotating In Air . . . . . .
55
. 58
Conclusions and Recommendations . . . . . . . 59
Nomenclature
62
References
65
Bibliography
67
Appendix A
Thermodynamic Properties for Freon 113
Appendix B
Raw Data Tables
Appendix C
Figures
Appendix D
Program Listing
.173
Appendix E
Sample Run . . .
.177
71
. 75
....
. . 88
viii
LIST OF TABLES
No.
1
Title
Specifications for Data from
the 2"
2
Page
o.
D. Steel Ball
. . . . . . . .. . .
36
..
72
Thermodynamic Properties for
Freon 113
. . . .
. .
3
Test 1. Continuous Static Run
4
Test 2. Continuous Static Run
5
Test 3. Continuous Static Run
76
6
Test 4. Discontinuous Static Run.
76
7
Test 5. Reheat.
.
76
8
Test 6. Continuous Static Run
9
Test 7. Continuous Static Run
10
Test 8. Reheat.
11
Test 9. Discontinuous Static Run.
77
12
Test 10. Continuous Static Run.
.
78
13
Test 11. Discontinuous Static Run
78
14
Test 12. Reheat
15
Test 13. Continuous Static Run.
16
Test 14. Discontinuous Static Run
17
Test 15. Reheat
79
18
Test 15a. Continuous in Air
80
19
Test 16. Rotate at 3437 RPM
20
Test 17. Continuous Static Run.
80
21
Test 18. Continuous Static Run.
. 80
22
Test 19. Continuous Static Run.
81
75
.
.
75
77
..
. ..
77
77
. . . .. . . .
.
ix
78
.
..
.
79
79
80
23
Test 20. Discontinuous Static Run.
81
24
Test 21. Discontinuous Static Run.
81
25
Test 22. Discontinuous Static Run.
82
26
Test 23. Rotate at 3437 RPM.
27
Test 24. Rotate at 3437 RPM.
28
Test 25. Rotate at 3437 RPM.
82
29
Test 26. Rotate at 3437 RPM.
83
30
Test 27. Rotate at 3437 RPM.
83
31
Test 28. Rotate at 3437 RPM.
83
32
Test 29. Rotate at 7830 RPM.
83
33
Test 30. Rotate at 7830 RPM.
84
34
Test 31. Rotate at 7830 RPM.
84
35
Test 32. Rotate at 9509 RPM.
84
36
Test 33. Rotate at 9509 RPM.
84
37
Test 34. Rotate at 9509 RPM.
85
38
Test 35. Rotate at 9509 RPM in Air .
85
39
Test 36. Rotate at 7830 RPM in Air .
85
40
Test 37. Rotate at 3437 RPM in Air
85
41
Test 38. Continuous Static Run .
.
86
42
Test 39. Discontinuous Static Run.
87
43
Test 40. Rotate at 3437 RPM.
...
87
.
82
....
X
82
LIST OF FIGURES
No.
Page
Title
1
Diagram of Experimental Arrangement .
13
2
Schematic Diagram of Test Section . .
14
3
Boiling Curves for Static Continuous Cases
at Various Subcooling Levels
4
38
Comparison of the Boiling Curves for Static
Cont., Discont. and Reheat Tests, Tl=89.6 F
5
40
Boiling Curves for Static Continuous and
Discontinuous Tests Compared to Yilmaz,
at the Liquid's Saturation Temperature
41
.
....
6
Boiling Curves for Static Discontinuous Tests
44
7
Boiling Curves for Static Reheat Tests
46
8
Boiling Curves with Rotation at 3437
Various Liquid Temperatures
9
48
Boiling Curves at Various Rotational Speeds
.
. .
. . .
50
Boiling Curves at Various Rotational Speeds
and Continuous Static, Tl
11
at
............
and Continuous Static, Tl = 69.8 F
10
RPM
=
109.4 F . . . .
51
Experimental and Witte and Orozco (Reference
No. 9) Film Coefficients for Various Rotational
Speeds and Tl =69.8 F . . . . . .
12
53
Experimental and Witte and Orozco (Reference
No. 9) Film Coefficients for Various
Speeds and Tl = 109.4 F . .
13
54
Boiling Curves for The Ball Rotating at Various
Rotational Speeds and Tl = 114.8 F
xi
56
14
Experimental and Witte (Reference
No. 10) Film Coefficients at Various
Rotational Speeds and Tl = 114.8 F
.....
57
15
Boiling Data for Saturated Refrigerant 113.
74
16
Test 1, Tfreon=73.2 F
. '.
89
17
Test 2, Tfreon=72.0 F
18
Tests 3C,3S,3R=0.5, Tfreon=72.0 F
91
19
Test 4, Tfreon=86.4 F
92
20
Test 5, Tfreon=84.2 F
21
Test 6, Tfreon=70.0 F
94
22
Test 7, Tfreon=70.0 F
95
23
Test 8, Tfreon=70.0 F
24
Test 9, Tfreon=70.0 F
97
25
Test 10, Tfreon=80.6 F.
98
26
Test 11, Tfreon=80.6 F.
99
27
Test 12, Tfreon=82.4 F.
28
Test 13, Tfreon=89.6 F.
29
Test 14, Tfreon=89.6 F.
102
30
Test 15, Tfreon=89.6 F.
31
Test 15A, Tamb=80.6 F
.
. 103
. 104
32
Test 16, Tfreon=69.8 F.
105
33
Test 17, Tfreon=100.4 F
34
Test 18, Tfreon=109.4 F
107
35
Test 19, Tfreon=114. 8 F
108
36
Test 20, Tfreon=114. 8 F
109
37
Test 21, Tfreon=109.4 F
.
90
.
93
.
96
..
.
.
...
101
.
.
xii
100
106
110
111
38
Test 22, Tfreon=l00.4 F.
39
Test 23, Tfreon=l00.4 F.
40
Test 24, Tfreon=l00.4 F.
41
Test 25, Tfreon=69.8 F
42
Test 26, Tfreon=69.8 F
115
43
Test 27, Tfreon=l09.4 F.
116
44
Test 28, Tfreon=ll4. 8 F.
117
45
Test 29, Tfreon=l09.4 F.
46
Test 30, Tfreon=ll4. 8 F.
119
47
Test 31, Tfreon=69.8 F
120
48
Test 32, Tfreon=ll4. 8 F.
121
49
Test 33, Tfreon=l09.4 F.
50
Test 34, Tfreon=69.8 F
123
51
Test 35, Tamb=75.2 F
.
124
52
Test 36, Tamb=75.2 F
53
Test 37, Tamb=75.2 F
54
Test 38, Tfreon=l00.4 F.
55
Test 39, Tfreon=l00.4 F.
56
Test 40, Tfreon=100.4 F.
57
Heat Flux vs. Delta Temp.
....
.
113
.......
.
.
122
125
.
....
128
129
......
130
Heat Flux vs. Delta Temp.
.
.
.
131
.
.. .
132
Test 4, Discont. Static Run, TR113=86.4 F.
. . . .
133
Heat Flux vs. De 1ta Temp.
Tests
3S,3C,3R=.5~
TR113=77,81,84 F
60
126
127
Test 2, Cont. Static Run, TR113=72. 0 F
59
114
118
Test 1, Cont. Static Run, TR113=73.2 F
58
112
Cont. Static Run,
.
. . ....
Heat Flux vs. Delta Temp.
xiii
61
Heat Flux vs. Delta Temp.
....
134
. . . . ..
135
. . . . .
136
Test 5, Reheat Static Run, TR113=84. 2 F.
62
Heat Flux vs. Delta Temp.
Test 6, Cont. Static Run, TR113=70.0 F
63
Heat Flux vs. Delta Temp.
Test 7, Cont. Static Run, TR113=70. 0 F
64
Heat Flux vs. Delta Temp.
.....
137
. . . .
138
.
....
139
Test 11, Discont. Static Run, TR113=80.6 F
. . .
140
Test 8, Reheat Static Run, TR113=70.0 F.
65
Heat Flux vs. Delta Temp.
Test 9, Discont. Static Run, TR113=70.0 F.
66
Heat Flux vs. Delta Temp.
Test 10, Cont. Static Run, TR113=80. 6 F.
67
68
Heat Flux vs. Delta Temp.
Heat Flux vs. Delta Temp.
Test 12, Reheat Static Run, TR113=82. 4 F
69
141
. . . . .
142
. . . .
143
Heat Flux vs. Delta Temp.
Test 13, Cont. Static Run, TR113=89. 6 F
70
. ..
Heat Flux vs. Delta Temp.
Test 14, Discont. Static Run, TR113=89. 6 F
71
Heat Flux vs. Delta Temp.
Test 15, Reheat Static Run, TR113=89.6 F.
72
144
.
.
145
0
0
. .
Heat Flux vs. Delta Temp.
Test 17, Cont. Static Run, TR113=100. 4 F.
74
...
Heat Flux vs. Delta Temp.
Test 16, Reheat Static Run, TR113=89. 6 F.
73
.
..
0
146
Heat Flux vs. Delta Temp.
Test 18, Cont. Static Run, TR113=109. 4 F.
xiv
.
..
147
75
Heat Flux vs. Delta Temp.
Test 19, Cont. Static Run, TR113=114. 8 F.
76
. . . .
148
. .
149
. .
150
Heat Flux vs. Delta Temp.
Test 20, Discont. Static Run, TR113=114. 8 F
77
Heat Flux vs. Delta Temp.
Test 21, Discont. Static Run, TR113=109.4 F
78
Heat Flux vs. Delta Temp.
Test 22, Discont. Static Run, TR113=100.4
79
154
. .. . ..
155
....
156
. . ... . ..
157
. . .
158
.
159
.........
160
........
161
. .
Heat Flux vs. Delta Temp.
. .
.
Heat Flux vs. Delta Temp.
.
.
Heat Flux vs. Delta Temp.
Test 31, 7830 RPM, TR113=69.8 F
88
. .
Heat Flux vs. Delta Temp.
Test 30, 7830 RPM, TR113=114 .8 F.
87
. . .
Heat Flux vs. Delta Temp.
Test 29, 7830 RPM, TR113=109. 4 F .
86
153
.
Test 28, 3437 RPM, TR113=114.8 F.
85
........
. . .
Test 27, 3437 RPM, TR113=109 .4 F .
84
152
Heat Flux vs. Delta Temp.
Test 26, 3437 RPM, TR113=69. 8 F
83
.......
Heat Flux vs. Delta Temp.
Test 25, 3437 RPM, TR113=69.8 F
82
151
Heat Flux vs. Delta Temp.
Test 24, 3437 RPM, TR113=100. 4 F.
81
. .
Heat Flux vs. Delta Temp.
Test 23, 3437 RPM, TR113=100. 4 F.
80
F.
Heat Flux vs. Delta Temp.
Test 32, 9509 RPM, TR113=114. 8 F.
XV
89
Heat Flux vs. Delta Temp.
..
162
.........
163
Test 33, 9509 RPM, TR113=109 .4 F.
90
. .
Heat Flux vs. Delta Temp.
Test 34, 9509 RPM, TR113=69. 8 F
91
. .
Heat Flux vs. Delta Temp.
Test 38, Cont. Static Run, TR113=100. 4 F.
92
. . .
Heat Flux vs. Delta Temp.
...
165
. . . .
166
. ... . . .
167
. ......
168
.........
169
.........
170
Test 39, Discont. Static Run, TR113=100.4 F
93
Heat Flux vs. Delta Temp.
Test 40, 3437 RPM, TR113=100. 4
94
164
.. .
F
Film coefficient vs. Delta Temp.
Witte and Orozco (Reference No. 8)
Test 27; 3437 RPM, TR113=109 F
95
Film Coefficient vs. Delta Temp.
Witte and Orozco (Reference No. 8)
Test 29; 7830 RPM, TR113=109 F
96
Film Coefficient vs. Delta Temp.
Witte (Reference No. 9)
Test 30; 7830 RPM, TR113=115 F
97
Film Coefficient vs. Delta Temp.
Witte (Reference No. 9)
Test 32; 9509 RPM, TR113=115 F
98
Film Coefficient vs. Delta Temp.
Witte and Orozco (Reference No. 8)
99
. . .
171
. . . . .
172
. .
Test 33; 9509 RPM, TR113=109 F
Film Coefficient vs. Delta Temp.
Witte and Orozco (Reference No. 8)
Test 34; 9509 RPM, TR113=70 F
xvi
.
ABSTRACT
FORCED CONVECTION ON A ROTATING SPHERE
IN FREON 113
by
Gina Giorgi O'Shaughnessy
Master of Science in Engineering
This study is designed to obtain the boiling curves for
Freon 113 using a rotating spherical surface at different
rotational speeds .
This is very important because this
kind of heat transfer is encountered specifically in
turbopump bearings for engines designed by the space
industry.
For this purpose, a two inch diameter ball was used as the
test specimen to simulate a ball bearing.
xvi.i
Three
thermocouples were soldered inside the ball to record the
temperature at three different locations.
The temperature
of the ball was increased by an electric heat gun and then
monitored while it decreased in the Freon 113 pool.
The
test prototype was held static as well as rotated at high
speeds during the heat transfer process.
The heat transfer results from this study were ultimately
compared to two empirical formulas found in the
literature.
One for a cryogenic fluid at the subcooled
temperatures and the other for a cryogenic fluid at the
saturation temperature.
The comparison between the two
approaches for cryogenic fluids and this study's in Freon
113 showed an agreement between the film coefficient from
this study and the one obtained from the two empirical
formulas.
xviii
Chapter I
INTRODUCTION
A.
General Background
1.
Space Shuttle Turbopump
A unique
example
of
mankind's
desire to conquer space
materialized with the advent of the Space
awesome
vehicle
Shuttle.
is not only a means of transportation to
outer space, but it can also be utilized as a
Its
incredible
This
capabilities
can
laboratory.
only be rivaled by the
complexity of its hardware.
One of the many systems in the Space Shuttle is the
Shuttle
Main Engine (SSME).
Its design includes two high
pressure turbopumps, one for the
and
one
for
the
liquid
Space
oxygen
liquid
hydrogen
(oxidizer).
The high
pressure oxygen turbopump (HPOTP), as well as other
1
(fuel)
parts
in
the
SSME,
are
high
performance components that are
supposed to be reusable, even at
rotational
31,000 revolutions per minute (RPM).
speeds
near
Notwithstanding, the
high speeds create a demanding environment
for
the
ball
bearings in the HPOTP.
Rocketdyne,
a
division
of
Rockwell
International
Corporation, has been improving their product
since
1983.
(the
SSME)
In essence, they have embarked on an effort
to re-examine the Space Shuttle Main
Engine
hardware
in
order to reduce the wear found in its parts after repeated
use.
This scrutiny is well founded,
turbopumps,
since
during a flight.
periodic
especially
for
the
the action here is extreme and intense
One
of
replacement
the
system's
are
the
parts
bearings
requiring
inside
the
turbopumps.
2.
Heat Transfer on Cryogenic Fluid in Bearings
Concentrating on the oxidizer turbopump, the balls
the
bearings
friction
races.
appear to experience heat generation due to
forces
encountered
while
traveling
in
their
A complete description of this frictional effect
is complicated by the fact that the
the
inside
shaft
as
well
as
their
2
own
balls
axes.
rotate
around
To add to the
of
intricacy
lubricated
the
and
system,
cooled
the
turbopump
are
by liquid oxygen (LOX) which is a
cryogenic liquid with a low saturation
performance
bearings
temperature.
The
of the ball bearings can be life limited as a
consequence of these and possible other factors which
are
not under investigation in this study.
The
study
of
the
different
regimes
involved
in
the
conversion of liquid into vapor has been the focus of much
exploration
by
engineers
in
the multidisciplines.
The
boiling regime is basically divided into four stages: free
convection,
nucleate
boiling,
partial
transition boiling and film boiling.
film
boiling or
Transition
boiling
and film boiling are the main regions of interest for this
investigation.
In the HPOTP, film boiling is believed to
in
the
is
generated
the
high
pressure
oxygen
turbopump.
as the balls rotate between the shaft
and the outer race .
believed
encountered
cooling/lubricating liquid oxygen surrounding the
bearing's balls of the
Heat
be
As
a consequence, the temperature
is
to increase causing the liquid oxygen to boil on
ball's
surrounding
surface.
each
ball
This
creates
a
film
of
vapor
that may hinder the heat transfer
process.
3
3.
FiJ~
Boiling Correlation Needed for a Rotating Sphere
Even though much engineering effort has
the
been
to
understanding of boiling regimes, no particular study
was found in the literature on film
spheres.
boiling
a
on
rotating
Therefore, it was necessary to infer an approach
to quantitatively determine the phenomenon
on
devoted
rotating
ball.
of
convection
The experimental approach to study
the effect of rotation on
boiling
was
felt
to
have
a
better chance of success than an analytical approach.
On the other hand, the HPOTP presents a thorny problem for
researchers
trying
ocurrence
in
the
to
understand
SSME
because
inaccessibility, thus making the
difficult.
This
the ball
by
of
film
the
study
ball
boiling
ball
temperature
experimental
rotational aspects of the HPOTP
complicated
the
bearing
measurement
focuses
bearing.
on
the
This
is
possible randomness of the orientation of
coordinate
system
while
rotating
around
the
shaft.
The
main
objective of this investigation was directed at
obtaining the experimental heat transfer-wall
temperature
relationships by quenching a heated rotating ball in Freon
113.
with
Here, the research was performed on a ball
a
fixed
rotational
vector.
experimental investigation simulates
4
In
a
rotating
addition,
uniformly
this
heated
ball.
The
immersion
of
a
heated
rotating
stagnant fluid at different speeds provides
studying
the
effect
addition,
by
varying
of
rotation
the
on
liquid's
a
ball in a
method
of
film boiling.
In
temperature
from
subcooled to saturated, a fuller view of the heat transfer
process,
and
thus
more
complete
information
can
be
obtained.
4.
Experimental Study by Rocketdyne
Rocketdyne
conducted
on a rotating sphere.
from
this
first
a preliminary study of film boiling
With the
observations
step the Rocketdyne engineers expect to
establish guidelines to quantize the heat
rotating ball.
(LN2).
transfer
on
a
In their early investigation thermocouples
were not used to
heated,
ascertained
rotating
record
ball
the
was
ball's
quenched
temperatures
as
a
in liquid nitrogen
Instead, the total cool down time was measured and
an approximate, overall film coefficient was obtained.
5
B.
Theoretical Background
1.
Convection With Rotating; No Boiling
The
forced
convection encountered when a ball bearing is
rotating about the shaft produces transfer of heat to
the
surrounding
the
fluid.
This
energy
is
generated
frictional forces from the rotational movement.
as
by
long
As
the fluid's temperature does not exceed the saturation
temperature, boiling does not occur.
2.
Convection Without Rotation; With Boiling
Natural
convection
differences
is
encountered
caused
by
the
inducing
when
a
a
transfer
displacement of the fluid.
phenomena can occur during this transfer of
instance,
temperature
between a surface and a fluid create a change
in the fluid's density; thereby
energy
when
of
Other
energy.
For
liquid comes in contact with a surface
whose temperature is higher than the
liquid's
temperature,
A layer of vapor is
vaporization
occurs.
theorized to cover the surface preventing
between the ball and the liquid.
6
saturation
direct
contact
c.
Suryey of Literature
1.
Studies of Film Boiling for Flow Over a
Sphere Without Rotation
While
surveying
the
literature,
several
studies
located for flow film boiling over static spheres.
were
Two of
these studies were performed by Aziz and Hewitt (Reference
number 1) and Dhir and Purohit (Reference number 2).
Aziz and Hewitt
forced
studied
convection
film
the
heat
boiling
transfer
on spheres.
goal was to obtain heat transfer rates
copper
spheres
mounted
on
for
in
Their main
nickel-plated
a platform moving vertically
downwards into a pool of water.
developed
regimes
With this intention, they
various tests aimeo at obtaining spherical data
at different water temperatures and platform velocities.
The work by Dhir and
film
Purohit
concentrated
boiling heat transfer from spheres.
on
subcooled
In their study,
they used steel, copper and silver spheres held statically
while
a
container
filled
with
water and attached to a
pneumatic cylinder provided the upward motion.
7
2.
Subcooled Flow Film Boiling over a Sphere
The literature search did not reveal any particular
study
on the topic of subcooled film boiling on a rotating ball.
However, a study by Witte and Orozco (Reference No. 9) was
found concerning flow film boiling over a static sphere in
subcooled Freon 11.
hollow
heated
They designed an
sphere
exposed
closed to the atmosphere.
Witte
and
Orozco
experiment
with
a
to Freon 11 inside a loop
With the data from
this
study
developed an expression to predict the
heat flux for subcooled flow film boiling over
a
sphere.
Their empirical expression is presented below.
fv
~v 5/8 Cpl(Ts-Tb)Prl
fl
~l
(--)(--)
Nuv
= 18.73
5/8
[-------------]
Rev
hfg'
5/8
----------------------------------Cpy (Tw - Ts) 3/2
[-------------]
hfg' Prv
3.
Saturated Flow Film Boiling Over a Sphere
During
the
literature search, two studies were uncovered
on saturated flow
studies
were
film
performed
boiling
over
a
sphere.
These
by Epstein and Hauser (Reference
number 7) and Witte (Reference number 10).
Epstein and
Hauser
(Reference
8
number
7)
performed
an
analytical
study on flow over a sphere and they developed
a correlation for forced
convection
film
boiling.
The
correlation follows:
fl 1/4
o.s Rev1/2 (--)
Nuv
=
fv
Cpv (Tw- Ts) 114
[------------]
Prv hfg'
research conducted by Witte (Reference number 10) was
The
on film boiling from
developed
a
a
sphere.
In
research,
he
theoretical model for calculating the forced
convection film boiling over a sphere.
this approach follows.
Nuv
this
=
CPv (Tw - Ts) 1/2
[-------------]
Prv hfg'
9
The
formula
from
4.
Approach for this Research
For
this
research,
a uniformly heated spherical surface
was rotated in subcooled and
spherical
saturated
Freon
113.
The
data obtained from the thermocouples inside the
ball at the three different radii were used
its distributed temperature.
to
determine
Then, the heat transfer-wall
temperature difference curves were plotted for this
data.
Results were also compared with the forced convection film
boiling equation replacing the free stream
the
rotational
speed,
R x
w.
The
velocity
with
formulas for this
approach are presented below.
The weighted average
from
the
three
thermocouples
calculated by:
T Wt
Avg
0.016 x Tc + 0.406 x TR=O.S + 0.578
The formula for the rotational speed follows;
2 X n X R X W
Vt
= --------------60
fv
X
Vt X D
Rev = ----------1-lv
10
X
Tsurf
was
The expression to calculate the film coefficient follows:
m x CPv x.AT
Q
= -------------At
Q
h =
A
X
(Tw -Ts)
11
Chapter II
EXPERIMENTAL APPARATUS AND INSTRUMENTATION
In
order
to achieve the objectives of this study a basic
system capable of inunersing a heated ball into a
temperature
bath
also needed to
(pool)
rotate
was
the
required.
ball
at
constant
This system was
various
speeds and measure the ball's temperature as
rotational
function of
~
time.
The system consisted of a motor,
the
liquid,
pump,
power
pulleys,
supply,
container
thermocouple
digital
display and a version of the "French guillotine" to
and
raise the ball to or from the container.
of the system is shown in Figure 1.
close-up
Figure
for
lower
The diagram
2
gives
view of the major parts for the test section.
description of
each
apparatus
follows.
12
used
in
the
a
A
experiment
MOTOR
iJ
COOLING
COIL
Figure 1.
y
Diagram of Experimental Arrangement.
13
CONNECTORS
MOTOR.
BEARINGS--<!
COLAR---
PULLEYS
PUMP
I
CONTAINER
•
,~
",, "•
II
I
I.J
... "
y
BALL AND
THERMOCOUPLES
Figure 2.
Schematic Diagram of Test Section.
14
A.
Rescription of Apparatus
1.
Ball (Test Specimen)
The test specimen that was used to simulate a ball bearing
was a 2 inch diameter ball made of 1018 steel.
of the ball was 1.2 lbm.
three
places
thermocouples.
to
permit
Two
0.040
inches.
The test specimen was drilled at
the
installation
of
three
of the perforations were oriented at
120 degrees to each other.
was
The weight
The size of
each
hole
bored
The third hole was drill€d and tapped
to accomodate the 3/8 inch shaft.
2.
Rotating Device
The rotating mechanism included a shaft supported
places
by bearings.
at
two
The shaft was driven by a pulley and
belt system connected to an electric motor. Details of the
aforementioned components are as follows:
15
A one
of
quarter horsepower motor was used at a fixed speed
1740
RPM.
Appliance
motor
Corporation,
utilized
speeds.
The
in
order
to
was
model
develop
manufactured
No.
the
L711F.
Motor
Pulleys were
various
rotational
The four pulleys used in the experiment were made
of cast iron with outside diameters of 2, 3.95,
10.93
by
inches.
The
7.93
shaft and the ball assembly included
two bearings, a collar and a 2 inch diameter pulley.
bearings
were
high
and
speed
double
The
seal bearings and the
collar was made of stainless steel. Finally, the shaft was
made
of
stainless
steel with an outside diameter of 3/8
inch, an inside diameter of 1/8 inch and a shaft length of
19 inches.
3.
Ball Heating Device
The
ball
was heated to various temperatures with the use
of an electric heat gun.
heat
gun
A 120 Volts McMaster
model number 3149k84 was used.
Its temperature
range was 750 through 1000 rlegrees Fahrenheit.
16
adjustable
B.
Qescription of Instrumentation
1.
Thermocouples in Ball Test Specimen
The temperature distribution inside the ball was
with
three
thermocouples.
The
three
chramel-alumel (type K), were soldered to
the ball with a 10% silver solder.
measured
thermocouples,
the
inside
of
The thermocouples were
insulated with magnesium oxide and protected by an inconel
sheath.
The diameter of each thermocouple wire was 0.0035
inches and the
total
0.020
The thermocouple wires were
inches.
the ambient
humidity
diameter
by
including
sealing
sheathing
was
p~otected
from
them with
epoxy
and
heating them in an oven at 302 degrees Fahrenheit for four
consecutive hours.
The same treatment
was
performed
on
three chrarnel alurnel extensions for the thermocouples.
The
thermocouples
inside
the
different radial locations.
located
at
the
center
of
ball were placed at three
One of the thermocouples
the
ball.
A second one was
affixed one half inch from the center and finally a
thermocouple was placed at the surface of the ball.
17
was
third
were
thermocouples
The
joined
to
connectors that in turn were connected
digital
display.
used in this
were
speeds.
for
to
disconnect
a
temperature
different kinds of connectors were
Two
experiment.
utilized
quick
First,
three
mini-connectors
the static and the two law rotational
Secondly, one six pin
connector
encased
in
an
aluminum cylinder was used for the high rotational speed.
The
six
pin
connector
thermocouples
was
used
to
protect
the
from the high rotational forces encountered
at this speed.
2.
Thermocouples in Freon 113 Bath and System
The temperature of the Freon 113 and the system was
monitored
with
the
iron-constantine (type
measured
the
temperature,
aid
J)
of
thermocouples.
thermocouples
were
trichlotrifluoroethane's
the
second
measured
the
also
Three
used.
One
(Freon
113)
ambient
room
temperature and the third measured the shaft's temperature
near the collar.
The glass insulated
thermocouples
were
made by twisting their ends together and spot welding. The
diameter of each thermocouple equaled
thermocouple
inches.
The
measuring the temperature of the Refrigerant
113 was placed at a
ball's
0.170
equator
when
height
equivalent
submerged
18
in
the
to
that
of
the
container.
The
radial distance between the
surface
and
the
thermocouple
thermocouple
for
at
the
the
ball's
Freon 113 was 2
inches and 3 inches between the thermocouple for the Freon
113 and the container's wall.
3.
Thermocouple Digital Display
Two
Omega
digital temperature displays were used to read
the thermocouple temperatures. The model number
displays
was
400-L
with
one
unit
set
up
for
for Type K
thermocouples (ball) and the other unit for Type J
113
and
system).
both
(Freon
The Reference point for both displays
was the ambient temperature.
4.
Freon 113 Cooling Circuit
The purpose of
maintain
down.
a
constant
Freon
pool
active cooling.
Refrigerant
113
pool
The heat rejected
subcooled
the
the
by
cooling
temperature
the
ball
circuit
was
to
during ball cool
would
raise
the
temperature to unaceptable levels without
The cooling was accomplished
by
pumping
113 through a copper coil heat exchanger
19
submerged in an ice bath.
model
No.
1020-614-14
Harrison Direct
Packard
Current
An
was
(DC)
Industrial
used
Diaphragm
pump
in this experiment.
power
supply
by
was utilized to power the diaphragm pump.
A
Hewlett
At the
beginning of each test series, 4 gallons of Freon 113 were
placed
inside a 5 gallon polymethylmethacrylate tank. The
intake for the pump was placed at the
fluid's
the outlet was placed at the bottom of the tank.
20
level
and
CHAPTER III
EXPERIMENTAL AND CALIBRATION PROCEDURES
Familiarization with
the
various procedures utilized in
this study is essential for an accurate interpretation
the
data.
For
this
of
reason, procedures are exclusively
discussed here without being influenced by
the
resulting
data or conclusions drawn.
Generally,
slip
rings
are
required to make temperature
measurements on a rotating body.
device
The high cost of such
precluded its use in this study.
alternative method had
procedures
to
be
a
Consequently, an
developed
here.
Various
for measuring the temperature of the ball were
experimentally performed in the static position
in
order
to determine the reliability level for each method. Taking
into account economic constraints, the method that
most
reliable
in
the static tests was also used for the
rotational experiments.
continuous,
proved
Three procedures
discontinuous
and
reheat.
were
followed:
An
in-air
calibration was also developed for both conditions: static
and rotational.
21
Since
this
section
deals
with
procedures
only,
validity of the individual techniques is tackled later
the
in
Chapter 5.
A.
Static Experimental Procedures
1.
Continuous Procedure
The
continuous method consisted of taking measurements of
the ball's temperature with
attached
the
thermocouples
remaining
to the recording device as the ball cooled down.
Prior to quenching, the
steel
ball
was
heated
to
305
degrees Fahrenheit with the temperature monitored by using
the three thermocouples inside the ball.
allowed
to
elapse
for
the
303.1 degrees Fahrenheit.
the
Freon
connected.
various
113
with
Enough time
was
temperature to stabilize to
Then, the ball was lowered into
all
the
thermocouple
extensions
The static temperature readings were taken
at
time intervals to quantify the drop in the ball's
temperature (see Appendix B
22
for
exact
time
intervals).
After
every
four runs the ball as well as the shaft were
polished with 800 grit
emery
cloth,
and
scrubbed
with
Freon 113 to eliminate any decomposition products.
2.
Discontinuous Procedure (In and Out)
The
discontinuous
method
involved
spherical surface from the Freon
temperature
measurement.
113
the
removal
bath
of the
before
every
The test specimen was heated to
305 degrees Fahrenheit and the temperature from the
thrmocouples
was
monitored
closely until it stabilized.
Subsequently, the spherical surface was submerged
Refrigerant
113
pool.
three
in
the
Then, fifteen seconds elapsed and
the ball was removed from the pool in order
to
record
a
temperature reading from each of the
thermocouples inside
the ball (see Appendix B for
time).
after
the
recording,
the pool again.
removed
from
measurement.
spherical
actual
Immediately
the test specimen was submerged in
Fifteen seconds elapsed and the ball
the
These
was
Freon 113 bath for another temperature
steps
were
continued
until
the
surface's temperature approached the saturation
temperature of the Freon 113.
23
3.
Reheat Procedure
The reheat method involves the heating of the ball to
temperature after every time interval.
original
was heated
to
degrees
305
in
and
Fahrenheit
continuous
the
stabilize,
as
procedures.
The test specimen was then
Refrigerant
113
and
was
then
The ball
allowed
in
time
period
heated
back
to
be
taken.
twice
that
of
The
305 degrees Fahrenheit,
for
the preceeding step (see
Appendix B for actual time). The test prototype was
removed
the
for a predetermined time period and then
stabilized and then re-immersed in the Freon 113 bath
a
to
discontinuous
immersed
removed for a temperature measurement to
ball
the
again
from the Freon 113 for a temperature measurement.
These steps were repeated until the ball was close to
liquid's,
Refrigerant
the
113, temperature at the end of the
last time step.
4.
Static In Air
The test specimen was quenched in
air
heat
during
loss
encountered
from
it
to
determine
the removal and
recording for the discontinuous and
reheat
ball
Fahrenheit
was
heated
to
305
degrees
24
the
methods.
The
as in the
continuous procedure.
Subsequently, the ball was
to
the
cool
down
temperature
in
measurements
ambient
at
each
air
while
allowed
recording
with
interval
the
thermocouples attached over the entire period.
B.
Rotational Exgerimental Procedures
1.
Rotate in Freon 113 (Discontinuous Method)
The
sphere
was quenched in Freon 113 while rotating on a
fixed axis at different speeds.
compiled,
the
discontinuous
measuring the rotational
this
Once the static data were
method was
temperature.
The
selected
for
reasons
for
choice are dealt with in the results section of this
paper.
In order to take
rotating
out.
an
on
a
temperature
measurements
of
the
shaft the following procedure was carried
The ball was heated to 305 degrees Fahrenheit
electric
ball
heat
gun.
The
25
using
temperature was allowed to
stabilize to 303.1 degrees Fahrenheit.
Consequently,
the
thermocouple connectors were disconnected from the ball in
order for the ball to be free to spin.
The motor was then
started and the ball was lowered into the pool tank.
The
timer
was started at the moment the ball touched the
Freon 113.
liquid
The ball was spun
(see
Appendix
B for
for
five
exact
removed from the Refrigerant 113. The
once
the
seconds
time).
timer
in
the
It was then
was
stopped
ball was outside the fluid. The ball rotated in
air only a half second before stopping.
Subsequently, the thermocouple extensions
and
were
connected
the temperature was displayed on the digital display.
The thermocouple's extensions were disconnected before the
motor
was again started and the ball was lowered into the
container.
The above steps were repeated until the ball's
temperature was near that of the liquid.
After every four
runs the ball as well as the shaft were polished with
800
grit emery cloth, and scrubbed with Freon 113 to eliminate
any decomposition products.
2.
Rotate In Air
The test specimen was rotated in ambient air to
26
determine
the
heat
loss to air at the different rotational speeds.
The
ball
was
readings
quenched
in
the
air
while
temperature
were taken every two seconds (see Appendix B for
exact time).
c. Calibration Procedures
1.
Freon 113 Purity
The purity of the Freon 113 was checked by determining its
boiling
point.
The
Refrigerant
113
covered Erlenmeyer flask until the first
was
heated
drops
of
113 vapor were condensated in a water heat exchanger.
in a
Freon
The
temperature recorded was 114.8 degrees Fahrenheit.
2.
Thermocouples in Ball
The three chromel-alumel thermocouples
the
inside
the
ball,
three mini-connectors and the three type K extensions
27
I
were calibrated daily before
testing
using
the
boiling
point of water and Freon 113 as well as the freezing point
of water.
The calibration showed an average agreement
in
the measurements of ± 0.1 degrees Fahrenheit.
For
the
calibration
of the single six pin connector the
average result changed to ± 0.2 degree F.
3.
Thermocouples in Freon Bath and System
The three type J thermocouples used to measure
113,
shaft
and
the
Freon
room temperatures were calibrated weekly
using the boiling point of water, and Freon 113 as well as
the freezing point of water. The average agreement between
the measurements was ± 0.2 degrees Fahrenheit.
4.
Rotating Device
The rotational speeds were calibrated with the
strobe tachometer.
28
aid
of
a
•
CHAPTER IV
METHODS OF ANALYSIS
The
data
obtained from the different tests were analyzed
in steps.
First, the weighted average of the
at
different
the
calculated.
the
cubic
ball
thermocouple
locations
Consequently, the data were curve
spline
technique.
fit
was
using
Finally, the heat flux and
film coefficient were calculated.
exposed
temperature
Tests
with
the
ball
to the ambient air temperature were performed and
referred to as calibration curves.
A.
Weighted Average of Thermocouples
The
weighted
calculated
to
average
in
the
three
thermocouples
was
obtain the ball's temperature distribution
at each time interval.
nodes
of
The ball was
divided
into
which the thermocouples were located.
29
three
Then, an
equation was derived by taking
independently,
each
thermocouple
region
as a proportion of the total volume of the
ball (refer to Nomenclature for weighted average formula).
B.
Curve Fit
A computer code was developed using the cubic spline curve
fit
algorithm
in
order
temperature values between data
eleven
continuously
points.
estimate
Originally,
an
coefficient polynomial program utilizing the least
squares technique was employed.
versus
to
time
curve
fits
The resulting temperature
deviated
from
the actual data
points enough to introduce significant error in subsequent
calculations.
As
then implemented.
for
a consequence, the cubic spline fit was
With this approach, a cubic fit is used
each interval between data points, with the condition
that the slope and the curvature agree at the joint point.
This
has
the
advantage of the resulting curve fit going
through each and every data point.
This technique proved to be more accurate for this study's
data than the polynomial curve fit for two reasons. First,
it retained smoothness when the data called for it.
Second, it fitted local irregularities without
30
the
least
squares
fit
misbehavior
usually
encountered
by
the
polynomial method.
On the other hand, the specific heat used
needed
this
study
to be used as a function of temperature because of
its variability.
eleven
in
The specific heat was curve
coefficient
polynomial.
The
fit
by
an
reason behind this
selection was that the shape of the curve was known to
be
fitted well by this technique.
c.
Calculations
A computer
code
was created to handle all the necessary
calculations and graphs for this investigation.
1.
Heat Flux for this Study
The heat flux for all the tests conducted for
this
study
was calculated by using a distributed temperature model of
the three thermocouples.
time
as
knowns,
the
With
heat
31
the
flux
temperature
was
and
obtained
the
from
essentially the change in ball's internal energy over
change
in
time.
See
the
the
Nomenclature section for the
appropriate formulas.
2.
Heat Flux Using Witte and Orozco's Approach
(Reference number 9) and Witte's Approach (Reference
number 10)
The heat flux was
using
the
calculated
empirical
for
the
formulas
rotational
by Witte
and
tests
Orozco
(Reference number 9) and Witte (Reference number 10).
this
purpose,
two
For
thermal regions were considered which
are subcooled and saturated.
For the subcooled region the
approach by Witte and Orozco (Reference number 9) was used
while for the saturated region the approach by Witte found
in Reference number 10 was utilized.
See the Nomenclature
section for the appropriate formulas.
These equations are
only
their
valid
for
film
boiling
and
use
transition region is at best an approximation.
also
be
It
in
the
should
noted that most of the cooling period was in the
transition region with actual film boiling
onJy
ocurring
at the early part of the cool down period.
When
performing
the
heat transfer calculations for film
boiling on a rotating sphere
assumed
that
the
tangential
32
for
this
project,
it
was
velocity vector is greater
than the forced convection counterpart resulting from
inflow
from
the
heat
exchanger.
number
for
this
study
was
Thus,
based
on
the
the Reynold's
the
tangential
velocity.
3.
Film Coefficient Using Witte and Orozco's Approach
(Reference number 9) and Witte's Approach (Reference
number 10)
For
the
film
coefficient
using the heat flux was
a straightforward calculation
required.
The
formula
can
be
found in the Nomenclature section.
D.
Graphs
There are three types of computer generated graphs used to
display the work of this
time,
the
heat
flux
study;
versus
the
temperature
versus
the temperature difference
(Tw- Ts) and the film coefficient versus (Tw- Ts)·
The temperature versus time
the
weighted
average
cubic spline curve fit.
graphs
were
the
result
of
of the three thermocouples and the
A curve that passes
33
through
the
real
data points was assumed to be continuous and treated
as such throughout the calculations.
The heat flux
boiling
versus
curves
Ts)
(Tw
for
each
test
graphs
condition
represent
the
(static
and
rotating).
The film coefficient versus temperature difference
were
displayed
for
each
Freon
113
thermal region and
rotational speed using the results from this study,
and
Orozco
(Reference
number
m.unber 10).
34
9)
and
graphs
Witte
Witte (Reference
CHAPTER V
DISCUSSION OF RESULTS
In
this
study
tests
were
of
boiling
on
phenomenon
without rotation.
a
at
defining
the
spherical surface with and
tests
The
These
temperatures.
directed
targeted
temperatures
different
fluid
were divided into two
regions: subcooled and saturated for each case of
boiling
with and without rotation.
From
the
static
tests
(no
rotation),
towards the discontinuous method as
measure
the
ball's
the
temperature.
results pointed
best
choice
This decision involved
the careful examination of the accuracy, the time and
available
to
the
resources involved (the discontinues method was
inexpensive
in
comparison
acquisition
hardware).
to
From
telemetry
the
temperature
rotational tests, the
results demonstrated that it is possible to obtain a
fair
agreement between the film coefficient from this study and
the film coefficient correlation
from
Witte
and
Orozco
(Reference number 9) and Witte (Reference number 10).
Table
1 is a summary of the test history showing relevant
information applicable to each test.
35
TABLE 1
SPECIFICATIONS FOR DATA FROM THE 2" 0. D. STEEL BALL
TEST #
1
2
3S
3C
3R=.5
4
5
6
7
8
9
10
11
12
13
STATIC
R-113
CONT.
CONT.
CONT.
CONT.
CONT.
DISCONT.
REHEATED
CONT.
CONT.
REHEATED
DISCONT.
CONT.
DISCONT.
REHEATED
CONT.
DISCONT.
REHEATED
RarATION
R-113
RPM
R-113 STATIC
TEMP. IN AIR
F
73.2
72.0
77.0
81.0
84.0
86.4
84.2
70.0
70.0
70.0
70.0
80.6
80.6
82.4
89.6
89.6
89.6
CONT.
69.8
100.4
109.4
114.8
114.8
109.4
100.4
100.4
100.4
69.8
69.8
109.4
114.8
109.4
114.8
69.8
114.8
109.4
69.8
RarATE AMB. COOLING
IN AIR TEMP SYSTEM
F ON/OFF
RPM
OFF
OFF
OFF
OFF
OFF
OFF
OFF
OFF
OFF
OFF
OFF
OFF
OFF
OFF
OFF
OFF
OFF
OFF
80.6
ON
OFF
OFF
OFF
OFF
OFF
OFF
ON
ON
ON
ON
ON
ON
ON
ON
ON
ON
ON
ON
9509 75.2
OFF
7830 75.2
OFF
3437 75.2
OFF
OFF
OFF
ON
14
15
15A
3437
16
17
CONT.
18
CONT.
19
CONT.
DISCONT.
20
21
DISCONT.
DISCONT.
22
23
3437
24
3437
3437
25
26
3437
27
3437
28
3437
29
7830
30
7830
31
7830
32-DC
9509
9509
33-DC
34-DC
9509
35-DC
36-DC
37-DC
100.4
38-DC CONT.
100.4
39-DC DISCONT.
40-DC
3437
100.4
DC - DIFFERENT CONNECTOR
CONT. - CONTINUOUS READ
DISCONT. - DISCONTINUOUS READ
C - CENTER THERMOCOUPLE
R=.S - RADIUS=.S THERMOCOUPLE
S - SURFACE THERMOCOUPLE
A - AIR (AMBIENT TEMPERATURE)
36
A.
Boiling Without Rotation
The cooling of a 2 inch diameter ball was monitored
in
the
static
position
and
submerged
observe the effect of boiling.
levels
and
evaluation
the
of
saturation
the
Five
point
various
while
in Freon 113 to
different
subcooled
were targeted for the
methods
of
temperature
acquisition.
1.
Continuous Method at Different Degrees of Subcooling
The
continuous temperature acquisition method was used as
the
baseline
ball
methods
to
evaluate
rated
in
how well
their
the
other
static
performance to depict the
temperature of the test specimen at
different
levels
of
subcooled Freon 113.
Boiling
curves
for three c0ntinnous tests (7, 13 and 18)
at different degrees of subcooling are shown in Figure
3.
Observing Figure 3 in detail, note that as the temperature
of the fluid increases, the peak
for
decreases.
reduction
This
indicates
transfer rate.
37
a
maximum
in
heat
flux
the
heat
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10L+----~--r-~~~~----~--~~~~rM
10'
10Z
10~
Tw- T•. DEG F
Figure 3
Boiling Curves for Static Continuous Cases
at Various Subcooling Levels
38
The heat flux curves for three tests (13, 14 and 15) using
the
continuous, discontinuous and reheat methods with the
Freon 113 at 89.6 degrees Fahrenheit are graphed in Figure
4.
In
this
Figure, it is noticed that the maximum heat
flux peak for the reheat test
other
two
methods.
is
higher
than
from
the
This is believed to be caused by the
greater amount of heat added to the pool by reheating
the
ball following this procedure in comparison with the other
two methods.
On
the
other
hand,
the
continuous
and
discontinuous methods follow each other closely.
2.
Continuous Method at the Saturation Temperature
Observing
the
Refrigerant
continuous
quenching
113
and
aids
the
effects
in
the
of a ball in saturated
comparison
discontinuous
methods
between
in
the
order to
determine the best temperature acquisition system.
The boiling curves obtained from the
discontinuous
methods
at
from
same graph
Yilmaz
for
discontinuous
(Reference
comparison.
boiling
and
the
the saturation temperature are
shown in Figure 5 (tests 19 and 20).
curve
continuous
curves
the
boiling
number 8) is shown in the
Here,
the
continuous
and
agree reasonably well with
Yilmaz's (Reference number 8) curve.
39
Also,
Although the
10-r----~~~~~~----~----~.-.-..~.
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10 2
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Tw- T•, DEG F
Figure 4
Comparison of the Boiling Curves for
Static Continuous, Discontinuous and
Reheat Tests, Tl = 89.6 F.
40
. . . . . . . ·:· ...
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101.
Tw- T•, DEG F
Figure 5
Boiling Curves for Static Continuous and
Discontinuous Tests Compared to Yilmaz
(Reference number 8) at the Liquid's
Saturation Temperature.
41
temperature difference at the peak heat flux is shifted by
forty degrees Fahrenheit (40 F).
3.
Ball in Air
The
tests with the ball rotating in air were conducted to
determine the heat losses when the ball is in ambient air.
An
average
loss
of
0.90
degrees
interval ocurred for the
static
Figure
C).
31
in
Appendix
F over
ball
This
in
was
a 15 second
the
air
(See
assumed to be a
negligible affect.
4.
Discontinuous and Reheat Method with Subcooling
The
discontinuous
circumstance
where
fluid
each
media
required.
and
reheat
methods
addressed
the sphere is removed from the active
time
a
Investigating
temperature
the
measurement
discontinuous
techniques under static conditions was the
way
of
establishing
rotational tests.
the
static
the
and
only
continuous readings.
reheat
possible
their validity for later use in the
However, it should be noted
cases
is
can
actually
be
42
only
checked against the
Hence, the validity of the
case can only be inferred.
that
rotating
The
discontinuous
procedure
reheat procedure due to
First,
heat
loss
to
the
rated
following
best against the
various
factors.
the air while measuring the ball's
temperature was negligible.
for
is
Second, the total time needed
a discontinuous test run was less than the total time
required for the reheat method.
transfered
into
the
Third,
Refrigerant
less
113
energy
pool
for
was
the
discontinuous method in contrast with the
reheat
see
released to the
Figure
4.
The
extra
energy
was
method,
surrounding Freon 113 medium as a consequence of reheating
the
ball
to
measurement.
caused
its
original
This increase in the Freon
significant
adverse
experimental control.
required
temperature
less
113
each
temperature
changes in the heat transfer
Fourth,
manual
after
the
discontinuous
method
labor than its reheat contemporary
since there was no reheating involved for
each
recording
of temperature.
The
22
boiling
are
curves for the discontinuous tests 9, 21 and
shown
subcooling.
compared
in
Figure
The
with
(continuous).
6
boiling
at
different
curves
the
boiling
The
comparison
from
curves
levels
Figure
from
6 can be
Figure
the
continuous
case,
the
discontinuous case shows that the peak
flux
decreases
with
an
temperature.
43
3
shows that the graph from
Figure 6 emulates closely the one from Figure 3.
in
of
increase
trend
for
in
Also
as
for
the
maximum
heat
the
fluid's
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. .. ·:... :. . ...
'
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~
10•
10 1
Tw- Ts. DEG F
Figure 6
Boiling Curves for Static Discontinuous Tests
44
The reheat procedure to
acquire
the
ball's
temperature
involved the heating of the test prototype to the original
temperature every time it was removed from the
bath at temperatures below saturation.
Freon
113
The boiling curves
for the reheat tests 8, 12 and 15 are shown in Figure 7 at
different levels of subcooling.
The
reheat boiling curves from Figure 7 were compared for
similarity to the continuous boiling curves from Figure 3.
The
comparison
shows
that
the
reheat
data provides a
broader boiling curve for a Refrigerant 113 temperature of
89.6
degrees Fahrenheit, as well as a higher heat flux by
about
10,000
observed
Btu/(hr-ft2).
for
a
Freon
113
Basically,
temperature
the
of
same
70
is
degrees
Fahrenheit, but the effect is not as pronounced as for the
liquid's temperature of 89.6 degrees Faherenheit mentioned
before.
The difference between the reheat graphs and
continuous
graphs
is
attributed
the
to the increase in the
fluid's temperature during a reheat run.
5.
Discontinuous Method at the Saturation Temperature
The discontinuous temperature acquisition method was
on
the
test
temperature.
specimen
at
the
liquid's
used
saturation
A comparison of the boiling curves for the
45
10~------------~--------~--~--~~~
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10~-----r--~~--~~~----~~~~~~~
10 2
10'
10~
Tw- Ts, DEG F
Figure 7
Boiling Curves for Static Reheat Tests
46
continuous
and
discontinuous
(Reference
number
8)
is
methods,
presented
and
in
for
Figure
Yilmaz
5.
By
observing the Figure, it is evident that the discontinuous
curve
follows the continuous one very closely.
continuous and discontinuous
curves
Both, the
emulate
the
Yilmaz
curve.
B.
The
Boiling with Rotation
temperature
Refrigerant
discontinuous
113
recording
was
procedure
of
achieved
used
in
a
by
ball
rotating
employing
the static tests.
in
the
The
reasons behind the selection of this method were stated in
the discontinuous discussion addressed before.
1.
Rotation at Different Levels of Subcooling
Several
levels of subcooling were studied in the rotating
experiments.
the
ball
Figure 8 represents the boiling
curves
for
rotating at 3437 RPM with three different Freon
113 temperatures below saturation (tests 24, 26
and
28).
These curves demonstrated that the heat transfer for the
47
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10~-------------------------------.-.-.--~
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10&
Figure 8
1QZ
Tw- T•. DEG F
Boiling Curves with Rotation at 3437 RPM at
Various Liquid Temperatures
48
rotational
cases
subcooling level.
increased
with
This observation
an
increase
in
the
holds
for
the
also
other rotational speeds.
2.
Various Rotational Speeds at the Same Freon 113
Temperature
The
ball
single
was
liquid
effect.
spun
different rotational speeds at a
temperature
Figures
this situation,
at
9
and
to
isolate
the
rotational
and 10 depict the boiling curves for
the
ball
in
the
static
position
( 0 RPM).
Figures
9
and 10 provide good evidence showing the trend
that as the rotational speed increases, the heat
transfer
increases.
In other words, the peak of the boiling curves
is higher.
Also, Figure 10 shows a more complete view
the
of
film boiling regime including the point were the heat
flux is a minimum.
This point of minimum heat flux
to
with
also
increase
an
increase
in
seems
the rotational
velocity.
Another observation that can be drawn from Figures
10 is that the heat flux increases with rotation.
shown by comparing the static
both Figures.
and
rotational
9
and
This is
curves
in
It is also noticed that with an increase in
49
10-·~---------------.--.-.-.-.--------------.-.--.-.~.
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10 1
Tw-
Figure 9
T•. DEG
F
Boiling Curves at Various Rotational Speeds
and Continuous Static, T! = 69.8 F
50
10~----------.-.~.-.~.~
..~--~.~~~~.~.-.~.~
.
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10'
Figure 10
1QZ
Tw- Ta, DE:G F
10~
Boiling Curves at Various Rotational Speeds
and Continuous Static, Tl = 109.4 F
51
the
fluid's
temperature
the
heat
flux
decreases.
should also be noted that data were obtained at 9509
These
data
are
It
RPM.
not shown in the main text as there were
problems with the thermocouple connections at
this
speed
which make all data at this speed questionable.
3.
Comparison Between the Film Coefficients from this
Study and Witte and Orozco (Reference number 9)
The
film
coefficients for the different rotational tests
were calculated using the weighted average
thermocouples
(this
study)
of
the
three
and the correlation by Witte
and Orozco (Reference number 9).
Figures 11 and
12
show
the film coefficient versus the temperature difference for
two
different
temperature
was
while different
observed
trend
speeds.
Here,
the
Refrigerant
113
maintained constant at a subcooled level
rotational
shows
speeds
that
as
were
the
depicted.
rotational
The
speed
increases so does the film coefficient.
The film coefficient
Figures
11
curves
(exponential
in
shape)
in
and 12 show a difference between this study's
approach and Witte and Orozco's.
The
curves
using
the
correlation by Witte and Orozco lag more than this study's
curves by a constant factor.
52
This is believed to be
2500~----------------------------------------~
THIS $TUDY
2000
.............................. .
t+-----78 30 RPM
~ 1500 ....
I
~
1000
•
••
~--7830
0
0'
•
.
..
•••••••••
0
0
•••••
3437 RPM
........ <·. ............... ·:·. ......... .
..
..
...
...
WITTE AND OROZCO
•
'
: • ••••...•••• 0.
0.
~PM
...
......................
0
••••••••
0
0
3437 RPM
o~~~~~~~~rrrr~~~~~~~~~~~
0
Figure 11
so
120
Tw- T•. DEG F
180
240
Film Coefficients for this Study and Witte and
Orozco (Reference number 9) for Various
Rotational Speeds, and Tl = 69.8 F
53
2500--------------------~------~---------.
....... THI~. STUD~ .. · .. ·;.· .. ·· .......... : .. ·· .. ····· .. ···
3437 RPM
~
1500 ......... . .... .;..... 7.8 3.0 .. EP.~................. ;. ............... .
.
.
.
.
:
...
...
.
...
...
...
I
~
Ia
~
1000 ..
O
0
0
WITTE:AND
OROZCO
O
0
..
...
...
.
...
.
0:
0
0
o
0
o
o
0
t
0
o
o
0
o
o
0
:
...
...
..
...
..
.
..
o:
..
...
...
..
..
.
0
o
I
0
0
o
0
0
o
0
o
0
o
0
o
o
~----3437 RPM
...............................
'. ..
5()()
..
o~~~~~~~~~~~~~
0
Figure 12
so
120
Tw- Ts. DEG F
180
240
Film Coefficients for this Study and Witte and
Orozco (Reference number 9) for Various
Speeds, and Tl = 109.4 F
54
caused by the formula's sensitivity to the combination
natural
and
forced convection.
of
The correlation by Witte
and Orozco was developed for forced convection.
4.
Rotation at the Saturation Temperature
The test specimen was rotated at different speeds
Freon
113
saturation
temperature.
at
Figure 13 shows the
boiling curves for the two different speeds (tests 28
30).
Looking
at
these
curves
This
and
it is observed that the
maximum heat flux peak is lowest at the lowest
speed.
the
rotational
is consistent with the fact that the static
case (0 RPM) boiling curve is lower than the boiling curve
for the lowest speed.
5.
Comparison Between the Film Coefficients for this
Study and Witte (Reference number 10)
The
film
coefficient
from
this
study and the one from
Witte (Reference number 10) were calculated, and
against
each
other.
compared
Here, the film coefficient from two
different rotational speeds at saturation are graphed
55
.
10~------------.-.-.-.-.-.-----.---.--.--.-.-.-.~
•
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o
•
o
'•'
0
•
o,o
0
•
0
•
'•',
•
o
0
I
•
o,o,o
,
\.
I
o
1
••
0
•
•
o
o
o
•
•
•,
0
0
•
•
•
o
•
I
•
o
•
•0
o
o
0
0
I
0
o
o
I
0
0
0
o
0
0
0
0
0
I
0
•
• •
0
•
••
0
0
•
•,
•
""'
''•'
•
'•
. .
..
. . . . . . . ·:· ... ·:· .. . ...: .. ..:. ·:...... .:. :·. ....... .:. . . .. .:. .. ·:... . ....
: . ·: . . :· .
. .. . ... .. . . ... .. . . . . . . . .. . . . . .. . . .... . .. . ....
. ..... .... .
.
.
.
.
...
. . . . . . . . . . , ........... ' ... .' .
.
.
. . .. . . .?:Cl
~PM.~;.
..................
. }.R.
. .....
.
.
.
.
.
. . . . . . . ' ...............
' ... '.
. . . . .. . . .. . ...........
. . ......... .
\w:.t~.
- 3;4
3 7 RE'M : :
......
: .. ·. . . .. •, . ..· .
.. .. .. .. ..
.. .. .. .. ..
. : . . .. : .. ·: . . : . ·: . .:· : .
.. .. .. .. ..
.. .. .. .. .. ..
.. .....
...
: .... .. ·: .... . ' ... ' .
~
~
~
~
\
~
~
~
~
10'
10 1
Tw- T•, DEG F
Figure 13
Boiling Curves for The Ball Rotating at Various
Rotational Speeds and Continuous Static,
Tl = 114.8 F
56
2500~----------------------------------------~
............ f:~.I.$ .. $f:"QPY .....................................
2000
•••••••••••
.
.
...
..
.
...
..
..
•••
•••••••••••••••
.
..
..
...
.
...
..
.
:
•••••••••••••
0
.
••
500
3437
WITTE
o~~~~~~~~~~~~~~~~~~~~~~~~
0
Figure 14
80
120
Tw- Ts. DEG F
180
240
Film Coefficients for this Study and Witte
(Reference No. 10) at Various Rotational
Speeds, and Tl = 114.8 F
57
together with the
formula
that
film
coefficient
by Witte, Figure 14.
the
film
coefficient
from
the
empirical
The exponential curves show
increases
faster
for
this
study's calculations than for the one's by Witte.
6.
Ball Rotating in Air
The
ball
in this
was rotated in air to monitor the heat transfer
medium.
temperature
It
was
determined
that
the
drop of the ball was± 7.2 degrees F for 9509
RPM (6 pin connector), ± 3.6 degrees Fahrenheit
RPM,
and
±
1.8
degrees
an
actual
in
7830
Appendix
C).
But
rotation test run, the ball rotated in
air for half a second only.
encountered
for
F for 3437 RPM for a 15 second
interval (see Figures 51, 52 and 53 in
during
average
Thus, the heat loss is mainly
the static position (0.9 degrees F per 15
seconds interval).
Therefore, the heat loss
assumed to be negligible.
58
in
air
was
I
CHAPTER VI
CONCLUSIONS AND RECOMMENDATIONS
The
research
of
a static and rotating spherical surface
submerged in Freon 113 provided good
transfer
evaluation
on
a
ball
version of the conclusions reached
data
bearing.
by
the
for
the
heat
A condensed
end
of
this
experiment are summarized below:
1. The discontinuous data acquisition method is an
acceptable
system to obtain data when economics are an
obstacle.
2. The reheat data acquisition method is inadequate since
it significantly changes the temperature of
due
to
the
fluid
the transfering of heat every time the ball is
heated to the original temperature.
Also, it
involves
a large time expenditure.
3. The boiling curves for the static and rotational tests
59
•
show
a
decrease in the heat transfer between the ball
and the fluid with a decrease in the subcooling level.
4. The maximum heat flux increases with an increase in the
rotational speed.
5. The minimum heat flux seems to increase with an
increase in the rotational speed.
6. Fairly good agreement is found between the shape of the
static boiling curves developed from this
data
experiment's
and the pool boiling data for saturated Freon 113
from Yilmaz study (Reference number 8).
7. Fair agreement is found between the
coefficient
from
coefficient
this
rotational film
investigation
correlation
from
and
Witte
the
and
film
Orozco
(Reference number 9).
8. Fair agreement is found between the rotational film
coefficient
obtained
curves
from
for
this
saturated
investigation
forced
and
convection
from
Witte's
empirical formula (Reference number 10).
9. The magnitude of the film coefficient (rotation) for
this study is greater than the magnitude
coefficient
from
the
of
the
film
empirical formulas by Witte and
Orozco (Reference number 9) and Witte (Reference number
10).
60
A follow-up
of
this
investigation
broaden the amount of information
transfer
on a rotating ball.
can be performed to
obtained
on
the
heat
A set of recommendations to
improve a follow up experiment are as follow:
1. If economically feasible use a
drive
motor
instead
of
variable
speed
direct
pulleys to reach the desired
rotational speed.
2. Increase the wire lead size of the ball's
thermocouple
to at least 0.1 inches outside diameter.
3. Use a continuous recording data acquisition system
during the rotational tests.
4. Lower and raise the Freon 113 container instead of the
entire ball rotational system.
5. Use solder that can withstand higher temperatures in
order
to be able to reproduce more completely the pool
boiling data.
6. Start testing with the Freon 113 at the saturation
temperature because the heat transfer
time.
This
facilitates
is
slower with
an easier observation of the
phenomenon.
7. Use different ball diameters to monitor the
relationship between the size of the
surface
and
the
heat transfer.
8. Use different density fluids.
9.
Change
the
test
specimen
from
solid
to hollow to
determine what changes ocurred by changing mass.
61
NOMENCLATURE
Ball radius
R
=
d
= Ball diameter
CPv
=
Specific heat of vapor
Cpl
=
Specific heat of liquid
hfg'
= hfg + 0.5 CPv Delta Tw
Kv
= Thermal conductivity for vapor
Nuv
= Nusselt number, vapor, (h x d)/ Kv
Pr1
= Prandtl number for liquid
Prv
= Prandtl number for vapor
fl
= Density of the liquid
fv
=
Rev
= Reynolds number for vapor
Tb
= Bulk temperature
Tf
= Film temperature
Ts
= Saturation temperature
Tw
= Wall temperature
Density of the vapor
Vt
= Tw - Ts
= Tangential velocity
w
= Rotational speed
m
= Mass of the ball
t
=Time
6t
= tfin~l - tinitial
A
=
..6.Tw
Area of ball
T Wt Avg = Temperature weighted average
Tc
= Temperature
TR=O.S
= Temperature at R=O.S thermocouple
= Temperature at surface thermocouple
Tsurf
at center thermocouple
62
The weighted average
from
the
three
thermocouples
was
calculated by:
T Wt Avg: 0.016 x Tc + 0.406 x TR=0.5 + 0.578
The
film
coefficient
assuming a
lumped
for
mass
this
sphere
X
Tsurf
study was calculated by
in
a
quasi-equilibrium
state, therefore:
m
·Q =
X
CPv x AT
m x CPv
Q:
x~T
-------------6t
Q
h =
A x (Tw -Ts)
From
Kays and Bjorklund (Reference No. 3) the approximate
equation for the Nusselt's number for forced single
phase
flow past a rotating sphere is:
Nuv
= 0.1545 x Rerot2/3 x Prl/3
From
the
literature
search
an
expression was found to
determine the Nusselt's number for forced convection
63
from
Witte
and
Orozco (Reference No. 9).
They studied forced
convection subcooled boiling on a sphere using
Freon
11.
Their equation to obtain the forced film coefficient for a
sphere in a subcooled environment is:
2
X Tt X
R
X W
Vt
= --------------60
Rev
= -----------
fv
Nuv
=
X Vt X D
18.73
fv ~v 5/8 Cpl(Ts-Tb)Prl
(--)(--)
[-------------]
fl ~l
hfg'
5/8
5/8
Rev
CPv (Tw- Ts) 3/2
[-------------]
hfg' Prv
From the literature search an expression was found for
saturated forced convection for flow over a sphere.
The
following approach was provided by Witte (Reference No. 10):
Nuv
=
2.98 Rev1/2
CPv (Tw- Ts) 1/2
[-------------]
Prv hfg'
Epstein and Hauser (Reference number 7) developed a
correlation for forced convection film boiling.
correlation follows:
fl
o.5 Rev1/2 (--)
Nuv
=
1/4
!v
Cpv (Tw- Ts) 1/4
[------------]
Prv hfg'
64
The
REFERENCES
1. Aziz S. and G. F. Hewitt: Heat Transfer Regimes in
Forced
Convection
International
Film
Boiling
Developments
presented at
the
1986
in
on
Heat
Spheres.
Transfer, paper
International
Heat
Transfer
Conference.
2. Dhir,
v.
K. and G. P. Purohit: "Subcooled Film Boiling
Heat Transfer From Spheres."
Design.
Vol. 47, 1978.
Nuclear Engineering
and
PP. 49-66.
3. Kays, W. M. and Bjorklund, I. S.: "Heat Transfer
From
a Rotating Cylinder With an Without.Cross-flow."
Transactions of the Asme.
Vol. 80, 1958.
PP. 70-78.
4. Park, E. L. Jr., Colver, C. P. and Sliepcevich,
C. M.: "Nucleate and Film
Nitrogen
and
Boiling
Heat
Vol. 70, 1960.
Rotating
s.
to
Methane at Elevated Pressures and Large
Temperature Differences." Transactions
5. Schwartz,
Transfer
of
the
Asme.
PP. 516-528.
H.: Heat Transfer Coefficient Between a
Ball
Moving
Through
Rocketdyne Internal Letter, Canoga
ATU-87-5016, 26 January 1987.
65
a
Cryogenic
Park,
Fluid.
California,
s.
6. Schwartz,
Rocketdyne
H.: Comparison Between the SRS and a
Approach
for
Calculating
Coefficient for a Rotating Ball.
Letter,
the
Rocketdyne
Film
Internal
Canoga Park, California, ATU-87-5131, 19 June
1987.
7. Schwartz,
s. H.: Experimental Program to Study
Boiling on a
Letter,
Rotating
Canoga
Sphere.
Park,
Rocketdyne
California
Internal
ATU-86-5154,
10
December 1986.
8. Yilmaz, Salim and J.
Velocity on
Heat
w.
Westwater: "Effect of
Transfer
to
Boiling
Freon
Transactions of the A$ME. Vol. 102, 1980.
9. Witte, L.
PP. 26-31.
c. and J. A. Orozco: "Flow Film Boiling From
a Sphere to Subcooled Freon 113. "
~.
113."
Vol. 108, 1986.
Transactions of the
PP. 934-938.
10. Witte, L. C.: "Film Boiling From a Sphere."
Fundamentals.
Vol. 7, 1968.
66
PP. 517-518.
I and EC
BIBLIOGRAPHY
1.
s.
Aziz
Forced
and G. F. Hewitt: "Heat Transfer Regimes in
Convection
International
Film
Developments
presented at
the
1986
Boiling
on
in
Transfer, paper
Heat
International
Spheres."
Heat
Transfer
Conference.
2. Chapman, Alan J.: "Heat Transfer."
Macmillan
Publishing Co., Inc., New York, New York, 1974.
3. Dhir,
v.
K. and G. P. Purohit: "Subcooled Film
Boiling
Heat
Transfer
Engineering and Pesign.
from
Spheres."
Vol. 47, 1978.
Nuclear
PP. 49-66.
4. Kays, W. M. and Bjorklund, I. S.: "Heat Transfer
From a Rotating Cylinder With an Without
Transactions of the Asme.
Cross-flow."
Vol. 80, 1958.
PP. 70-78.
5. Gould: "Temperature Measurement With Thermocouples."
Gould Inc., Cleveland, Ohio, 1985.
6.
Hendricks,
Comparison
Reduced
Robert
of
Theory
Gravity.
Aeronautics
and
C.: Film Boiling From Spheres.
and
Lewis
Space
Ohio, 129-01, 17 May 1971.
67
Data
Research
at
Standard
Center,
Administration,
A
and
National
Cleveland,
7. Kreith, Frank: "Principles of Heat Transfer."
International
Textbook
Company,
Scranton,
Pennsylvania, 1961.
8. Kuethe, Arnold
Aerodynamics . "
and
Chuen-Yen
John Wiley
Chow:
and
"Foundation
of
Sons, New York, New
York, 1976.
9. Kutateladge, Samson Semenovich: Fundamentals
Academic
Transfer.
Press
of
Heat
Inc., New York, New York,
1963.
10. Park, E.
C.
M.:
L.
Jr.,
"Nucleate
Colver,
and
C.
P.
and
Sliepcevich,
Film Boiling Heat Transfer to
Nitrogen and Methane at Elevated Pressures
Temperature
Differences."
Vol. 70, 1960.
Transactions
Large
of The A5me.
PP. 516-528.
11. Rohsenow, Warren M. and Harry
M9mentum
and
Transfer.
Choi:
Prentice-Hall,
~H:::.:e~a~t"",_...,Ma~s~s:__~a~n-d
Inc.,
Englewood
Cliffs, New Jersey, 1961.
12. Schwartz, S. H.: Heat Transfer Coefficient
Rotating
Ball
Moving
Through
Rocketdyne Internal Letter, Canoga
ATU-87-5016, 26 January 1987.
68
a
Between
Cryogenic
Park,
a
Fluid.
California,
s.
13. Schwartz,
H.: Experimental Program to Study
Cryogenic
Boiling Heat to Obtain Correlation Equation
for
Convection
the
Rocketdyne
Internal
Transfer
Heat
Coefficient.
Letter, Canoga Park, California,
ATU-87-5066, 14 February 1987.
s.
14. Schwartz,
Rocketdyne
H. : Comparison Between the SRS and a
Approach
Coefficient
Internal
for
for
Rotating
a
Letter,
the
Calculating
Canoga
Film
Rocketdyne
Ball.
Park,
California,
ATU-87-5131, 19 June 1987.
15. Schwartz,
s.
H.: Prelyminary Estimates of the
Flow
Subcooled
Coefficients
Internal
Film
for
a
Boiling
Rotating
Letter,
Canoga
Heat
Transfer
Ball.
Park,
Rocketdyne
California,
ATU-87-5139, 19 June 1987.
16. Schwartz, S. H.: Experimental Program to Study
Boiling on a
Letter,
Rotating
Canoga
Sphere.
Park,
Rocketdyne
California,
Internal
ATU-86-5154,
10
December 1986.
17. Yilmaz, Salim and J.
Velocity on
Heat
w.
Westwater: "Effect of
Transfer
. .,T=-r.. ,a'""'n""s.. ,a""'c....t""'i""oAln.:=s'----""o""f'--"""'t~h:.::.e"--.o!:.-'A~S::.,ME~ .
26-31.
69
to
Boiling
Vo 1 .
10 2 ,
Freon
19 80 .
113."
PP.
18. Ungar, E. K. and R. Eichhorn: "Local Surface Boiling
Heat Transfer From a
Societies.
Quenched
Sphere."
Engineering
April 1982.
19. Witte, L. C. and J. A. Orozco: "Flow Film Boiling
From
a
of ASME·
Sphere
to Subcooled Freon 113." Transactions
Vol. 108, 1986.
70
PP. 934-938.
APPENDIX A
THERMODYNAMIC PROPERTIES FOR FREON 113
71
TABLE 2.
TEMP
c
PRESSURE
~1PA
0
0.003894
0.005232
0.006936
0.009083
0.010083
0.011174
0.012361
0. 013650
0.015048
0.016562
0.018199
0.019967
0.021872
0.023923
0.026127
0.028494
0.031032
0.033750
0.036657
0.039761
0.043074
0.046604
0.050362
0.054357
0.058602
0.063105
0.067878
0.072932
0.078278
0.083929
0.089895
0.096188
0. 101325
0.10282
0.10981
0.1:!889
0.15045
0.17468
0.20181
0.23204
0.26559
0.30270
0.34358
0.38848
0.43764
0.49129
llO
0.54969
0.61310
115
0.68177
120
0.75598
125
130
0.83600
0.92212
135
140
1.0146
145
1.1139
150
1.2201
155
1.3337
160
1. 4550
165
1. 5845
170
1.7224
175
1. 8693
180
2.0256
2.1918
185
2.3685
190
2.5564
195
2.7562
200
2.9692
205
210
3.1968
*214.4 3. 4110
*CRITICAL POINT
-30
-25
-20
-15
-10
8
- 6
4
- 2
0
2
4
6
8
10
12
14
16
18
20
22
24
26
28
30
32
34
36
38
40
42
44
46
47.56
48
50
55
60
65
70
75
80
85
90
95
100
105
-
THERMODYNAMIC PROPERTIES FOR FREON 113.
VOLUME
VAPOR
m3/k~
3.761
2.8148
2.1351
1. 6401
1. 27 48
1.1562
1.0505
0.95598
0. 87144
0.79563
0.72756
0.66631
0.61113
0.56132
0.51630
0.47554
0.43859
0.40503
0.37452
0.34673
0.32140
0.29827
0.27712
0.25776
0.:4001
0.22373
0.20877
0.19501
0.18233
0.17064
0.15986
0.14989
0.14067
0.13397
0.13214
0.12423
0.10684
0.09235
0.08018
0.06992
0.06123
0.05381
0.04747
0.04201
0.03730
0.03321
0.02964
0.02653
0.02379
0.02138
0.01925
0.01736
0.01568
0.01418
0.01283
0.01162
0.01053
0.009539
0.008640
0.007819
0.007066
0.006373
0.005729
0.005127
0.004556
0.004006
0.003456
0.002857
0.001750
DENSITY
LI9UID
k~ m3
1 85.7
1674.7
1663.7
1652.6
1641. 5
1637.0
16J 2. 5
1628.0
1623.5
1619.0
1614.5
1609.9
1605.4
1600.8
1596.2
1591.6
1587.0
1582.4
1577.8
1573.1
1568.5
1563.8
1559.1
1554.4
1549.6
1544.9
1540.1
1535.3
1530.5
1525.7
1520.9
1516.0
1511.2
1507.3
1506.3
1501.3
1489.0
1476.4
1463.7
1450.8
1437.8
1424.6
1411.1
1397.4
1383.5
1369.3
1354.9
1340. 1
1325.0
1309.5
1293.5
1277.2
1260.3
1242.8
1224.7
1205.9
1186.3
1165.7
1144.0
1121.0
1096.4
1069.9
1040.9
1008.8
972.43
929.65
876.30
800.26
570.00
ENTHALPY
VAPOR
LI9UID
kJ/k~ K
kJ k~
339. 2
17 3. 0
178.14
342.46
182.43
345.53
348.62
186.76
351.72
191.13
192.89
352.97
194.66
354.22
196.43
355.47
198.21
356.72
357.97
200.00
359.23
201.79
203.59
360.49
205.40
361.75
207.21
363.01
209.03
364.28
210.86
365.54
212.69
366.81
214.53
368.08
216.37
369.35
218.22
370.62
220.08
3 71. 89
373. 16
221.94
374.43
223.81
375.71
225.69
227.57
376.98
229.45
378.25
379.53
231.34
380.80
233.24
382.08
235.14
237.05
383.35
238.97
384.62
240.89
385.90
242.81
387.17
388.16
244.31
388.44
244.74
389.72
246.68
392.89
251.53
256.43
396.07
399.23
261.35
266.30
402.39
271.27
405.54
276.28
408.67
411.80
281.32
286.38
414.90
291.47
417.99
296.59
421. 07
301.73
424.12
306.91
427.14
312.12
430.14
317.36
433.11
322.64
436.05
327.96
438.95
333.32
441.81
444.61
338.13
447.37
344.1·9
349.71
450.06
355.30
452.68
360.97
455.21
457.65
366.73
372.60
459.97
378.59
462.15
464.17
384.75
465.97
391.10
397.71
467.49
404.65
468.65
112.08
469.26
420.31
469.00
~30.26
466.91
453.60
453.60
72
ENTROPY
VAPOR
LI9UID
kJ kh K
kJ/k~ K
1. 57 6
0.89885
1. 5783
0.91613
1.5775
0.93324
1.5772
0.95017
1. 5772
0.96694
1.5773
0. 97360
1.5775
0.98024
1.5777
0.98685
1.5780
0.99344
1.5783
1. 0000
1. 57 87
1.0065
1.5792
1.0131
1.5796
1. 0195
1. 5 802
1. 0260
1. 5807
1. 0325
1. 5813
1. 0389
1.5820
1. 045 3
1. 582 7
1. 0516
1. 5834
1.0580
1. 5842
1. 0643
1. 0706
1. 5850
1. 5858
1. 0769
1. 5 867
1. 083 2
1.5876
1. 0894
1.0956
1.5885
1.1018
1. 5894
1.1080
1.5904
1.5914
1. 1141
1.5925
1.1203
1.1264
1.5935
1.5946
1.1324
1.5957
1. 1385
1. 5969
1.1445
1. 5978
1.1492
1. 5980
1. 1505
1.1565
1.5992
1. 6022
1.1714
1.1862
1. 6053
1. 2008
1.6086
1.6119
1. 215 3
1. 6152
1. 2296
1.6187
1. 2438
1. 2579
1. 6222
1.2719
1.6258
1.2857
1. 6294
1. 2994
1.6330
1.3130
1. 6366
1.6403
1. 3265
1. 6439
1. 3399
1.3532
1. 64 76
1.3664
1. 6512
1. 3795
1.6548
1. 3925
1. 6583
1. 6618
1.4055
1.4184
1. 6652
1.4314
1. 6685
1. 6717
1. 4443
1.6748
1.4572
1.6776
1.4701
1. 4832
1. 6803
1. 6828
1. 4963
1.5096
1. 6849
1.5232
1. 6866
1.5371
1.6878
1.6883
1.5515
1.6876
1.5668
1.5834
1. 6852
1.6789
1. 6031
1.6470
1. 64 70
'
TABLE 2.
VISCOSITY, Pa
TEMP
SAT.
LIQUID
K
1790
240
1475
250
1232
260
270
1038
280
885
763
290
664
300
586
310
320
520
320.7a
516
330
465
340
419
379
350
344
360
370
315
380
289
267
390
400
246
410
228
420
210
430
193
440
175
450
158
460
133
470
107
480
77.3
487.5b
29.8
490
500
520
540
560
580
600
a NORHAL BOILING
s
SAT.
VAPOR
8.71
9.27
9.80
10.29
10.74
10.77
11.15
11.49
11.78
12.04
12.28
12.51
12.75
13.02
13.38
13.85
14.43
15. 12
15.92
16.84
18.02
19.84
29.8
POINT
(CONTINUED) THERMODYNAHIC PROPERTIES FOR FREON 113.
THERHAL CONDUCTIVITY
mW/m K
GAS
SAT
SAT
( 1 Atm.) LIQUID LIQUID
87.0
83.7
83.0
80.9
78.7
76.8
74.7
72.6
70.7
10.77
70.5
8.66
68.7
11.00
66.4
11.24
11.47
64.5
11.69
62.4
11.90
60.4
12.11
58.3
12.32
56.4
12.53
54.3
12.73
52. 1
12.93
49.8
13.14
47.4
13.35
44.8
13.56
41.8
13.78
38.6
14.00
34.6
14.22
30+
(21+)
14.38
14.43
14.64
b CRITICAL POINT
73
SPECIFIC HEATS Cp
kJ/kg K
SAT.
GAS
SAT.
( 1 Atm.) LIQUID VAPOR
0.845
0.584
0.877
0 .• 594
0.895
0.604
0.916
0.614
0.933
0.624
0.946
0.634
0.958
0.644
0.971
0.654
0.983
0.664
8.66
0.984
0.665
9.11
0.992
0.675
9.58
1.000
0.686
10.07
0.697
1.013
10.56
0.709
1. 029
11.05
1. 042
o. 722
11.54
0.737
1.059
12.04
0.753
1.084
12.54
1.109
o. 770
13.05
1.138
0.796
13.59
0.841
1.176
14.19
0.902
1. 218
14.83
1. 268
15.51
1. 318
16.23
1 .381
16.99
1. 452
17.79
1. 54
( 1. 6)
18.42
18.64
19.54
21.53
23.54
25.55
27.56
GAS
(0 Atm.)
0.583
0.591
0.599
0.607
0.615
0.623
0.632
0.641
0.650
0.651
0.659
0.668
0.678
0.688
0.697
0.706
0.715
0.724
o. 733
0.742
0.750
0.758
0. 766
0. 774
0.782
0.790
0.798
0.705
0.719
.
200 J.4------ Zuber's Predicted tAaximum
N
~
~
100
/Hesse's Boiling Curve
~
t:- 70
-~
Cl)
-
o50
30
20
Bromley's Equation
130
Figure 15.
Boiling Data for Saturated Refrigerant 113.
Yilmaz (Reference number 8)
74
APPENDIX B
RAW DATA
TABLE 3. TEST 1 CONTINUOUS STATIC RUN.
TEMPERATURE IN DEG F, TIME IN SEC.
FREON
TIME
SURFACE CENTER
R=0.5
73.2
0
302
302
302
73.2
123.44
121.28
130.1
30
74.6
45
109.04
109.22
104.36
76
60
100.4
101.12
99.68
77.4
75
97.16
97.52
96.26
78.8
90
94.46
94.1
93.92
78.8
105
91.76
92.12
91.94
78.8
120
90.68
89.6
90.5
78.8
135
89.06
89.42
87.8
78.8
150
87.8
87.98
87.98
78.8
165
86.72
86.9
86.54
78.8
180
85.64
85.64
85.64
78.8
195
84.2
84.56
84.56
78.8
210
83.48
83.84
83.84
78.8
225
83.12
83.12
83.12
78.8
240
82.4
82.76
82.76
78.8
255
82.04
82.4
82.4
78.8
270
81.68
81.86
82.04
TABLE 4 . TEST 2 CONTINUOUS STATIC RUN ..
TEMPERATURE IN DEG F, TIME IN SEC.
FREON
TIME
SURFACE CENTER
R=0.5
72
0
305.6
310.1
310.64
73
15
248.36
268.52
244.4
74.1
30
141.8
176
156.2
75.1
45
122
133.34
125.6
76.1
60
113.36
117.68
114.62
76.2
75
107.96
109.94
108.5
76.4
90
104.36
105.98
104.9
76.5
105
101.48
102.56
102.2
76.7
120
99.14
99.86
99.68
76.8
135
97.16
98.06
97.88
76.9
150
95.54
96.26
96.08
165
93.92
94.46
94.46
76.9
77
180
92.48
93.38
93.2
195
91.4
91.94
91.94
77
77
210
90.14
90.86
90.86
77
225
89.24
89.78
89.96
77
240
88.52
89.06
89.06
77
255
87.62
88.16
88.34
77
270
86.9
87.44
87.44
75
WT. AVG
302
126.1094
107.1428
100.1192
96.80036
94.235
91.83884
90.58964
88.5542
87.87596
86.6498
85.64
84.35192
83.63192
83.12
82.55192
82.19192
81.82904
WT. AVG
307.7182
247.0748
148.1936
123.6430
113.9406
108.2109
104.6051
101.7896
99.37076
97.46672
95.77076
94.14788
92.78672
91.62788
90.44384
89.54096
88.74788
87.92096
87.12788
TABLE 5. TESTS 3C, 3S, 3R=0.5, THREE CONT. STATIC
SEPARATE TESTS . TEMPERATURE IN DEG F, TIME IN SEC.
TIME SURFACE FREON CENTER
FREON
R=O . 5
FREON
0
303.08
77
304.34
81
305.06
84
296.6
77.4
303.44
81.4
303.44
84.3
15
30
285.8
77.8
302.54
81.8
298.76
84.5
45
276.8
78.2
297.68
82.2
295.52
84.8
60
266
78.6
289.4
82.6
291.74
85.1
75
258.8
79
282.92
82.9
284.9
85.3
90
246.2
79.4
273.02
83.3
277.34
85.6
105
221
79.8
266
83.7
269.6
85.9
120
206.6
80.2
254.3
84.1
259.52
86.1
135
158
80.6
244.94
84.5
244.58
86.4
150
145.4
81
225.32
84.5
234.5
86.4
165
145.4
81
209.12
84.5
210.74
86.4
180
145.4
81
178.34
84.5
198.5
86.4
195
145.4
81
166.84
84.5
183.4
86.4
TABLE 6. TEST 4 DISCONTINUOUS
TEMPERATURE IN DEG F, TIME IN
TIME
SURFACE CENTER
0
303.08
305.24
15
280.4
291.2
45
233.6
240.8
75
132.8
147.2
105
118.4
123.8
STATIC RUN.
SEC.
R=0.5
FREON WT. AVG
305.6
86.4 304.1376
282.2
87 281.3036
217.4
87.5 227.138
145.4
88. 1 138. 146
123.8
88.6 120.6788
TABLE 7. TEST 5 REHEAT STATIC RUN.
TEMPERATURE IN DEG F, TIME IN SEC.
TIME
SURFACE CENTER
R=0.5
0
303.08
303.8
303.62
15
276.8
284
282.2
30
233.6
239
239
45
143.6
181.4
161.6
60
129.2
143.6
154.4
76
FREON
83.9
84.2
86.4
87.8
88.5
WT. AVG
303.3107
279.1076
235.8788
151.5128
139.6616
TABLE 8. TEST 6 CONTINUOUS STATIC RUN.
TEMPERATURE IN DEG F, TIME IN SEC.
TIME
SURFACE
FREON
0
302
70
15
249.8
70.8
30
141.8
71.6
45
125.6
72.4
60
112.28
73.2
TABLE 9. TEST 7 CONTINUOUS STATIC RUN.
TEMPERATURE IN DEG F, TIME IN SEC.
FREON
TIME
SURFACE CENTER
R=0.5
0
302.72
303.8
305.6
70
70.7
15
260.6
262.4
266
30
143.6
177.8
156.2
71.3
45
129.2
150.8
141.8
72
72.6
60
116.6
123.8
120.2
75
107.6
111.2
111.2
73.2
73.7
90
104
105.8
105.8
105
100.4
102.2
102.2
74.1
74.4
120
96.8
98.6
98.6
TABLE 10. TEST 8 REHEAT STATIC RUN.
TEMPERATURE IN DEG F, TIME IN SEC.
TIME
SURFACE CENTER
R=0.5
0
303.08
305.6
303.8
15
251.6
271.4
246.2
30
161.6
179.6
170.6
45
123.8
143.6
136.4
60
111.2
114.8
113
75
107.6
109.4
109.4
FREON
70
70.6
71.2
71.5
71. 8
72
WT. AVG
303.9065
262.8212
149.2628
134.6612
118.1768
109.1192
104.7596
101.1596
97.5596
WT. AVG
303.4126
249.7244
165.542
129.2324
111. 9884
108.3596
TABLE 11. TEST 9 DISCONTINUOUS STATIC RUN.
TEMPERATURE IN DEG F, TIME IN SEC.
TIME
SURFACE CENTER
R=0.5
FREON WT. AVG
0
303.08
303.8
303.8
70 303.3838
15
244.4
255.2
249.8
70.6 246.7652
30
141.8
174.2
154.4
71.2 147.434
45
120.2
134.6
1~27. 4
71.9 123.3536
60
111.2
116.6
72.5 112.0172
113
75
104
107.6
105.8
73.1 104.7884
90
98.6
100.4
100.4
73.8 99.3596
77
TABLE 12. TEST 10 CONTINUOUS STATIC RUN.
TEMPERATURE IN DEG F, TIME IN SEC.
FREON WT. AVG
TIME
SURFACE CENTER
R=0.5
0
303.08
305.24
305.96
80.6 304.2838
15
266
284
282.2
83.3 272.8652
30
147.2
195.8
190.4
86 165.5168
45
125.6
138.2
136.4
87.8 130.1864
60
114.8
120.2
118.4
87.8 116.348
75
107.6
113
111.2
87.8 109.148
90
104
107.6
107.6
87.8 105.5192
105
102.2
104
104
87.8 102.9596
120
98.6
100.4
100.4
87.8 99.3596
TABLE 13. TEST 11 DISCONTINUOUS STATIC RUN.
TEMPERATURE IN DEG F, TIME IN SEC.
TIME
SURFACE CENTER
R=0.5
FREON
0
303.08
305.6
305.6
80.6
15
260.6
282.2
278.6
81.5
30
150.8
206.6
190.4
82.4
45
123.8
140
134.6
83.3
60
113
120.2
118.4
84. 2
75
107.6
111.2
111.2
85.1
90
102.2
109.4
109.4
86
105
100.4
104
104
86.9
120
98.6
100.4
100.4
87.8
TABLE 14. TEST 12 REHEAT STATIC RUN.
TEMPERATURE IN DEG F, TIME IN SEC.
TIME
SURFACE CENTER
R=0.5
0
303.08
305.6
303.8
15
264.2
284
280.4
30
152.6
201.2
190.4
45
125.6
138.2
134.6
60
116.6
122
120.2
75
109.4
114.8
111.2
90
104
107.6
107.6
105
100.4
102.2
102.2
78
FREON
80.6
81.1
81.7
82.4
83.4
85.1
86.5
87.8
WT. AVG
304.1434
268.2536
167.7704
128.444
115. 307 6
109.1192
105.2384
101.9192
99.3596
WT. AVG
303.4126
271.094
168.7244
129.4556
118.148
110.2172
105.5192
101.1596
TABLE 15. TEST 13 CONTINUOUS STATIC RUN.
TEMPERATURE IN DEG F, TIME IN SEC.
FREON WT. AVG
TIME
SURFACE CENTER
R=0.5
0
303.08
305.6
305.6
89.6 304.1434
15
282.2
291.2
289.4
90.3 285.2672
30
242.6
253.4
251.6
91 246.4268
45
136.4
159.8
158
91.8 145.544
60
122
131
129.2
92.5 125.0672
75
114.8
118.4
118.4
93.2 116.3192
90
111.2
113
113
93.7 111.9596
105
107.6
109.4
109.4
94.3 108.3596
120
105.8
107.6
107.6
95 106.5596
TABLE 16. TEST 14 DISCONTINUOUS STATIC RUN.
TEMPERATURE IN DEG F, TIME IN SEC.
TIME
SURFACE CENTER
R=0.5
FREON
0
303.08
305.6
305.6
89.6
15
284
293
291.2
90.3
30
233.6
244.4
242.6
91.2
45
131
149
147.2
91.9
60
120.2
127.4
125.6
92.7
75
111.2
114.8
114.8
93.4
90
104
105.8
105.8
94.3
105
96.8
102.2
102.2
95
TABLE 17. TEST 15 REHEAT STATIC RUN.
TEMPERATURE IN DEG F, TIME IN SEC.
TIME
SURFACE CENTER
R=O. 5
0
303.08
305.6
305.6
15
280.4
289.4
293
30
239
257
251.6
45
131
136.4
134.6
60
125.6
131
129.2
75
118.4
122
122
90
111.2
113
113
79
FREON
89.6
90.9
91.9
93.2
94.5
95.5
96.8
WT. AVG
304.1434
287.0672
237.4268
137.8652
122.5076
112.7192
104.7596
99.0788
WT. AVG
304.1434
285.6596
244.4036
132.548
127.148
119.9192
111.9596
p •
TABLE 18. TEST 15A CONT. STATIC RUN IN AIR.
TEMPERATURE IN DEG, TIME IN SEC .
TIME
SURFACE
AIR
0
276.6
80.6
15
275.5
80.6
30
273.2
80.6
45
272.3
80.6
60
271
80.6
75
269.6
80.6
90
268.2
80.6
105
266.7
80.6
120
265.3
80.6
TABLE 19. TEST 16 DISCONT. RUN, BALL RarATING AT
3437 RPM. TEMPERATURE IN DEG F, TIME IN SEC.
TIME
SURFACE CENI'ER
R=. 5
FREON
WT. AVG
0
303.8
305.6
305.6
69.8 304.5596
23
108.86
113
110.84
73.4 109.7301
TABLE 20. TEST 17 CONI'INUOUS STATIC RUN.
TEMPERATURE IN DEG F, TIME IN SEC.
TIME
SURFACE CENTER
R=O. 5
FREON WT. AVG
0
303.08
305.6
303.8
100.4 -303.4126
15
271.4
282.2
276.8
100.9 273.7652
30
244.4
253.4
251.6
101.5 24 7. 4672
45
145.4
156.2
154.4
102 149.2268
60
129.2
132.8
131
102.4 129.9884
75
122
127.4
125.6
102.9 123.548
90
120.2
122
122
103.5 120.9596
105
118.4
118.4
118.4
104
118.4
120
116.6
118.4
116.6
104 116.6288
TABLE 21. TEST 18 CONTINUOUS STATIC RUN.
TEMPERATURE IN DEG F, TIME IN SEC.
TIME
SURFACE CENTER
R=0.5
FREON WT. AVG
0
303.08
305.6
303.8
109.4 303.4126
15
275
284
278.6
109.6 276.6056
30
255.2
264.2
251.6
109.9 253.8824
45
150.8
204.8
170.6
110.1 159.7028
60
134.6
147.2
138.2
110.3 136.2632
75
127.4
131
129.2
110.5 128.1884
90
123.8
125.6
123.8
110.8 123.8288
105
122
122
122
111
122
120
120.2
122
120.2
111.2 120.2288
80
TABLE 22. TEST 19 CONTINUOUS STATIC RUN.
TEMPERATURE IN DEG F, TIME IN SEC.
FREON WT. AVG
TIME
SURFACE CENTER
R=0.5
114.8 303.4126
0
303.08
305.6
303.8
15
278.6
285.8
282.2
115 280.1768
30
246.2
273.2
258.8
115.2 251.7476
45
163.4
208.4
174.2
115.5 168.5048
60
132.8
143.6
138.2
115.7 135.1652
75
125.6
131
129.2
115.9 127.148
116.1 124.5596
90
123.8
125.6
125.6
105
122
123.8
122
116.3 122.0288
120
122
122
122
116.5
122
116.6
120.2
135
120.2
120.2
120.2
TABLE 23. TEST 20 DISCONTINUOUS STATIC RUN.
TEMPERATURE IN DEG F, TIME IN SEC.
TIME
SURFACE CENTER
R=0.5
FREON
0
303.08
305.6
303.8
114.8
15
273.2
284
276.8
115
30
253.4
266
258.8
115.3
45
158
204.8
177.8
115.5
60
134.6
147.2
140
115.7
75
125.6
129.2
127.4
115.9
90
122
125.6
123.8
116.1
105
120.2
122
120.2
116.3
120
118.4
118.4
118.4
116.6
WT. AVG
303.4126
274.8344
255.794
166.7876
136.994
126.3884
122.7884
120.2288
118.4
TABLE 24. TEST 21 DISCONTINUOUS STATIC RUN.
TEMPERATURE IN DEG F, TIME IN SEC.
TIME
SURFACE CENTER
R=0.5
FREON
0
303.08
305.6
303.8
109.4
15
269.6
280.4
275
109.8
30
244.4
251.6
248
110.1
161.6
194
177.8
45
110.7
60
129.2
141.8
134.6
111
75
123.8
129.2
127.4
111.4
90
122
125.6
123.8
111.7
105
120.2
123.8
118.4
112. 3
120
116.6
118.4
118.4
112.6
135
114.8
116.6
116.6
113
WT. AVG
303.4126
271.9652
245.9768
168.6956
131.594
125.348
122.7884
119.5268
117.3596
115.5596
81
TABLE 25. TEST 22 DISCONTINUOUS STATIC RUN.
TEMPERATURE IN DEG F, TIME IN SEC.
FREON
TIME
SURFACE CENTER
R=O. 5
100.4
0
303.08
305.6
305.6
15
260.6
267.8
264.2
101.5
30
226.4
239
237.2
102.4
45
140
168.8
152.6
103.5
60
127.4
134.6
131
105.4
106.5
75
122
123.8
122
90
118.4
120.2
118.4
107.6
107.6
105
116.6
116.6
116.6
WT. AVG
304.1434
262 .1768
230.9864
145.5764
128.9768
122.0288
118.4288
116.6
TABLE 26. TEST 23 DISCONT. RUN, BALL RarATING AT
3437 RPM. TEMPERATURE IN DEG F, TIME IN SEC.
TIME
SURFACE CENI'ER
R=. 5
FREON
WT. AVG
0
303.08
305.6
305.6
100.4 304.1434
15
154.04
154.4
154.4
101.3 154.1919
30
102.2
104
104
102.2 102.9596
TABLE 27. TEST 24 DISCONT. RUN, BALL ROTATING AT
3437 RPM. TEMPERATURE IN DEG F, TIME IN SEC.
TIME
SURFACE CENI'ER
R=.S
FREON
WT. AVG
0
303.08
305.6
305.6
100.4 304.1434
17
154.4
159.8
156.2
101.3 155.2172
32
110.84
111.2
111.2
102.2 110.9919
TABLE 28. TEST 25 DISCONT. RUN, BALL ROTATING AT
3437 RPM. TEMPERATURE IN DEG F, TIME IN SEC.
TIME
SURFACE CENTER
R=. 5
FREON
WT. AVG
0
303.08
305.6
305.6
69.8 304.1434
6
195.8
201.2
197.6
70.52 196.6172
11
126.32
127.04
127.04
71.24 126.6238
17
96.26
96.8
96.8
71.96 96.48788
22
84.56
84.74
84.56
72.68 84.56288
27
77.36
77.18
77.36
73.4 77.35712
82
TABLE 29. TEST 26 DISCONT. RUN, BALL ROTATING AT
3437 RPM. TEMPERATURE IN DEG F, TIME IN SEC.
TIME
SURFACE CENTER
R=. 5
FREON
WT. AVG
0
303.08
305.6
305.6
69.8 304.1434
7
183.74
188.42
185
70.7 184.3264
14
118.04
118.4
118.4
71.6 118.1919
21
89.96
89.96
90.14
72.5 90.03308
28
78.08
77.9
78.26
73.4 78.1502
TABLE 30. TEST 27 DISCONT. RUN, BALL ROTATING AT
3437 RPM. TEMPERATURE IN DEG F, TIME IN SEC.
TIME
SURFACE CENTER
R=. 5
FREON
WT. AVG
0
303.08
305.6
305.6
109.4 304.1434
7
283.46
286.16
284.18
109.4 283.7955
14.4
239.72
242.6
239.54
109.4 239.693
21.4
173.84
174.74
174.92
109.4 174.2928
27.9
133.16
133.7
133.52
109.4 133.3148
34.1
114.62
115.34
115.7
109.4
115.07
TABLE 31. TEST 28 DISCONT. RUN, BALL ROTATING AT
3437 RPM. TEMPERATURE IN DEG F, TIME IN SEC.
TIME
SURFACE CENTER
R=. 5
FREON
wr. AVG
0
303.08
305.6
305.6
114.8 304.1434
6.8
288.14
293
293.72
114.8 290.4832
13
260.96
265.82
259.52
114.8 260.4531
19.5
204.98
208.04
205.52
114.8 205.2482
25.5
155.12
155.84
155.48
114.8 155.2776
31.5
127.22
128.12
128.3
114.8 127.6728
37.5
116.78
116.96
116.78
114.8 116.7828-
TABLE 32 . TEST 29 DISCONT. RUN, BALL ROTATING AT
7830 RPM. TEMPERATURE IN DEG F, TIME IN SEC.
TIME
SURFACE CENTER
R=. 5
FREON
WT. AVG
0
303.08
305.6
305.6
109.4 304.1434
7
268.88
272.12
272.3
109.04 270.3203
14
232.52
234.86
234.86
108.68 233.5074
21
160.34
161.78
161.24
108.32 160.7284
28
123.98
124.16
124.16
107.96 124.0559
35
109.94
110.12
109.94
107.6 109.9428
83
TABLE 33. TEST 30 DISCONTI. RUN, BALL ROTATING AT
7830 RPM. TEMPERATURE IN DEG F, TIME IN SEC.
TIME
SURFACE CENTER
R= . 5
FREON
WT. AVG
0
303.08
305.6
305.6
114.8 304.1434
7.5
277.88
282.92
282.92
114.26 280.0068
15.3
250.52
253.58
254.12
113.54 252.0305
22.3
208.58
210.74
209.84
113 209.1261
29.3
152.78
153.14
153.14
112.46 152.9319
35.8
120.2
122.54
122.36
111.74 121.1144
42.8
114.8
116.24
115.88
111.2 115.2615
TABLE 34. TEST 31 DISCONT. RUN, BALL ROTATING AT
7830 RPM. TEMPERATURE IN DEG F, TIME IN SEC.
TIME
SURFACE CENTER
R=. 5
FREON
WT. AVG
0
303.08
305.6
305.6
69.8 304.1434
6
157.46
162.68
162.14
70.7 159.4436
12.5
99.68
102.02
101.84
71.6 100.5944
19.5
78.62
79.34
79.52
72.5 78.99692
26.5
70.88
70.88
70.88
73.4
70.88
TABLE 35. TEST 32 DISCONT. RUN, BALL ROTATING AT
9509 RPM. TEMPERATURE IN DEG F, TIME IN SEC.
TIME
SURFACE CENTER
R=. 5
FREON
WT. AVG
0
303.08
305.6
305.6
114.8 304.1434
4.5
266.36
271.22
271.22
114.26 268.4109
8.5
241.52
246.02
246.02
113.54 243.419
13
211.82
212.9
212.9
113 212.2757
17.5
164.3
163.58
163.58
112.46 163.9961
21.5
131.18
131.72
131.72
111.74 131.4078
25.5
124.16
124.7
124.88
111.2 124.4609
29.5
118.58
118.94
119.12
110.66 118.805
33.5
115.16
115.34
115.34
109.94 115.2359
37.5
111.02
110.48
110.48
109.4 110.7921
TABLE 36. TEST 33 DISCONT. RUN, BALL ROI'ATING AT
9509 RPM. TEMPERATURE IN DEG F, TIME IN SEC.
TIME
SURFACE CENTER
R=. 5
FREON
WT. AVG
0
303.08
305.6
305.6
109.4 304.1434
4.5
288.86
290.3
290.66
108.5 289.6138
8.5
263.48
264.02
266
107.6 264.5117
13.5
190.4
190.94
190.94
106.7 190.6278
18
136.04
136.04
136.04
105.8
136.04
22.5
114.62
114.62
114.62
104.9
114.62
26.5
104
104.18
104.18
104 104.0759
31
102.56
102.56
102.56
103.1
102.56
35
102.2
102.2
102.2
102.2
102.2
84
TABLE 37. TEST 34 DISCONT. RUN, BALL ROTATING
9509 RPM. TEMPERATURE IN DEG F, TIME IN SEC.
TIME
SURFACE CENTER
R=.5
FREON
WT. AVG
0
303.08
305.6
305.6
69.8 304.1434
5
183.74
185.72
185.72
70.34 184.5755
9
132.44
132.26
132.26
71.06 132.3640
13.5
102.02
102.02
102.02
71.6
102.02
18
85.64
85.82
85.82
72.14 85.71596
22
77.36
77.54
77.54
72.86 77.43596
26
75.38
75.38
75.38
73.4
75.38
TABLE 38. TEST 35 DISCONT. RUN, BALL ROTATING
IN AIR AT 9509 RPM. TEMP. IN DEG F, TIME IN SEC.
TIME
SURFACE AMB.
0
300.2
75.2
2
292.1
75.2
4
286.7
75.2
6
281.3
75.2
8
275.72
75.2
10
269.78
75.2
12
265.64
75.2
14
259.16
75.2
TABLE 39. TEST 36 DISCONT. RUN, BALL ROTATING
IN AIR AT 7830 RPM. TEMP. IN DEG F, TIME IN. SEC.
TIME
SURFACE AMB.
0
303.08
75.2
2
294.98
75.2
4
290.12
75.2
6
285.08
75.2
8
280.58
75.2
10
277.34
75.2
12
274.64
75.2
14
270.5
75.2
TABLE 40. TEST 37 DISCO~IT. RUN, BALL ROTATING
IN AIR AT 3437 RPM. TEMP. IN DEG F, TIME IN SEC.
TIME
SURFACE AMB.
0
303.08
75.2
2
295.16
75.2
4
292.1
75.2
6
287.78
75.2
8
285.26
75.2
10
282.02
75.2
12
278.78
75.2
14
277.16
75.2
85
TABLE 41. TEST 38 CONTINUOUS STATIC RUN.
TEMPERATURE IN DEG F, TIME IN SEC.
TIME
SURFACE
FREON
0
300.92
100.4
2
298.4
100.9
4
296.24
101.3
6
294.26
101.8
8
292.1
102.4
10
289.4
102.9
12
287.06
103.3
14
285.62
103.8
16
282.38
104.4
18
279.68
104.9
20
275
105.3
22
272.3
105.8
24
271.04
105.8
26
268.9
105.8
28
266.9
105.8
30
265.1
105.8
32
262.4
105.8
34
256.5
105.8
36
246
105.8
38
228.2
105.8
40
212
105.8
42
199.4
105.8
44
185
105.8
46
174.2
105.8
48
167
105.8
50
159.8
105.8
52
154.4
105.8
54
149
105.8
56
145.4
105.8
58
141.8
105.8
60
140
105.8
62
136.4
105.8
64
135.5
105.8
66
132.8
105.8
68
131
105.8
70
129.2
105.8
72
127.4
105.8
74
127.4
105.8
76
126.7
105.8
78
126
105.8
80
124.9
105.8
82
124
105.8
84
123.4
105.8
86
122.9
105.8
88
122.2
105.8
86
TABLE 42. TEST 39 DISCONTINUOUS STATIC RUN.
TEMPERATURE IN DEG F, TIME IN SEC.
TIME
SURFACE
FREON
0
303.08
100.4
15
280.4
100.9
30
264.2
101.3
45
183.2
101.8
60
141.8
102.2
75
127.4
102.7
90
120.2
103.1
105
114.8
103.6
120
109.4
104
135
106.7
104.5
150
105.8
104.9
TABLE 43. TEST 40 DISCONT. RUN, BALL ROI'ATING
AT 3437 RPM. TEMPERATURE IN DEG F, TIME IN SEC.
TIME
SURFACE FREON
0
303.08
100.4
5
244.4
100.94
10
212
101.66
15
149
102.2
87
APPENDIX C
LIST OF FIGURES
Note: The experimental data obtained at the rotational
speed of 9509 RPM with the six pin connector was distorted
by some heating during testing. A shift in the
thermocouple's reference point is believed to be caused by
the difference in material in the six pin connector, thus
any temperature change in the connector during testing was
not accounted for. The distortion in the ouput signal can
not be compensated for because it depends on the
temperature of the shaft instead of the temperature of the
ambient. No calibration curve can be determined since the
friction created by the bearings on the shaft while the
ball was rotating relies on time, the ball's temperature
and the rate of heat traveling up the shaft from the
bearing.
88
350.-------~--------~----------------~
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Test 2, Tfreon=72.0 F
90
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Figure 18.
40
TIME <S.c>
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Tests 3C,3S,3R=0.5, Tfreon=72.0 F
91
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Test 4, Tfreon=86.4 F
92
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40
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94
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40
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95
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96
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Figure 24.
Test 9, Tfreon=70.0 F
97
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Figure 25.
40
TIME <Sec>
so
Test 10, Tfreon=80.6 F
98
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40
TIME <Sec:>
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99
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Test 12, Tfreon=82.4 F
100
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Figure 28.
40
TIME <Sec>
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Test 13, Tfreon=89.6 F
101
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40
TIME <Sec:>
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Test 14, Tfreon=89.6 F
102
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Figure 30.
40
TIME CSec>
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Test 15, Tfreon=89.6 F
103
eo
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Figure 31.
40
TIM£ CSec>
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Test 15A, Tamb=80.6 F
104
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Figure 32.
40
TIME (Sec>
80
Test 16, Tfreon=69.8 F
105
80
350~--------------------------------------~
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TIME <Sec>
Figure 33.
Test 17, Tfreon=100.4 F
106
eo
350~--------------------------------------~
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Figure 34.
40
TIME <Sec:>
so
Test 18, Tfreon=109.4 F
107
eo
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Figure 35.
Test 19, Tfreon=114.8 F
108
~
350~------------------~------~--------~
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Figure 36.
40
TIME CSec>
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Test 20, Tfreon=ll4.8 F
109
eo
350------------------------------~---------.
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Figure 37.
40
TIME <Sec>
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110
eo
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Figure 38.
40
TIME CSec>
so
Test 22, Tfreon=l00.4 F
111
eo
350~----------------------------------------~
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TIME CS•cl
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Test 23, Tfreon=100.4 F
112
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Figure 40.
40
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60
Test 24, Tfreon=100.4 F
113
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Figure 41.
40
TIME CSec>
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Test 25, Tfreon=69.8 F
114
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Figure 42.
Test 26, Tfreon=69.8 F
115
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Figure 43.
Test 27, Tfreon=109.4 F
116
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Figure 44.
40
TIME CSec>
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117
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40
TIME <Sec>
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Test 29, Tfreon=l09.4 F
118
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Test 30, Tfreon=ll4.8 F
119
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Figure 47.
Test 31, Tfreon=69.8 F
120
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Figure 48.
40
TIME <Sec>
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121
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40
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122
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Figure 50.
40
TIME <Sec>
so
Test 34, Tfreon=69.8 F
123
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40
TIME CSec:>
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124
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TIME <Sec>
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126
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127
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128
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Figure 56.
Test 40, Tfreon=100.4 F
129
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Figure 57. Heat Flux vs. Delta Temp.
Test 1, Cont. Static Run, TR113=7 3. 2 F
130
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Figure 58. Heat Flux vs. Delta Temp.
Test 2, Cont. Static Run, TR113=72. 0 F
131
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Figure 59. Heat Flux vs. Delta Temp.
Tests 3S,3C,3R=.5, Cont. Static Run,
TR113=77 ,81,84 F
132
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Figure 60. Heat Flux vs. Delta Temp.
Test 4, Discont. Static Run, TR113=86.4 F
133
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Figure 61. Heat Flux vs. Delta Temp.
Test 5, Reheat Static Run, TR113=84. 2 F
134
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Figure 62. Heat Flux vs. Delta Temp.
Test 6, Cont. Static Run, TR113=70. 0 F
135
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Figure 63. Heat Flux vs. Delta Temp.
Test 7, Cont. Static Run, TR113=70. 0 F
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Figure 64. Heat Flux vs. Delta Temp.
Test 8, Reheat Static Run, 'rR113=70. 0 F
137
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Figure 65. Heat Flux vs. Delta Temp.
Test 9, Discont. Static Run, TR113=70.0 F
138
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Figure 66. Heat Flux vs. Delta Temp.
Test 10, Cont. Static Run, TR113=80. 6 F
139
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Figure 67. Heat Flux vs. Delta Temp.
Test 11, Discont. Static Run, TR113=80.6
140
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Figure 68. Heat Flux vs. Delta Temp.
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Figure 69. Heat Flux vs. Delta Temp.
Test 13, Cont. Static Run, TR113=89. 6 F
142
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Figure 70. Heat Flux vs. Delta Temp.
Test 14, Discont. Static Run, TR113=89.6 F
143
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Figure 71. Heat Flux vs. Delta Temp.
Test 15, Reheat Static Run, TR113=89.6 F
144
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Figure 72. Heat Flux vs. Delta Temp.
Test 16, Reheat Static Run, TR113=89.6 F
145
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Figure 73. Heat Flux vs. Delta Temp.
Test 17, Cont. Static Run, TR113=100.4 F
146
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Figure 74. Heat Flux vs. Delta Temp.
Test 18, Cont. Static Run, TR113=109.4 F
147
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Figure 75. Heat Flux vs. Delta Temp.
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Figure 76. Heat Flux vs. Delta Temp.
Test 20, Discont. Static Run, TR113=114.8 F
149
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Figure 77. Heat Flux vs. Delta Temp.
Test 21, Discont. Static Run, TR113=109.4 F
150
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Figure 78. Heat Flux vs. Delta Temp.
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151
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Figure 79. Heat Flux vs. Delta Temp.
Test 23, 3437 RPM, TR113=100.4 F
152
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Figure 80. Heat Flux vs. Delta Temp.
Test 24, 3437 RPM, TR113=100.4 F
153
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Figure 81. Heat Flux vs. Delta Temp.
Test 25, 3437 RPM, TR113=69.8 F
154
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Figure 82. Heat Flux vs. Delta Temp.
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155
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Figure 83. Heat Flux vs. Delta Temp.
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156
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Figure 84. Heat Flux vs. Delta Temp.
Test 28, 3437 RPM, TR113=114.8 F
157
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Figure 85. Heat Flux vs. Delta Temp.
Test 29, 7830 RPM, TR113=109.4 F
158
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Figure 86. Heat Flux vs. Delta Temp.
Test 30, 7830 RPM, TR113=114.8 F
159
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Figure 87. Heat Flux vs. Delta Temp.
Test 31, 7830 RPM, TR113=69.8 F
160
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Figure 88. Heat Flux vs. Delta Temp.
Test 32, 9509 RPM, TR113=114.8 F
] h1
101~------------.-.-.-.-.-.----------------••
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Figure 89. Heat Flux vs. Delta Temp.
Test 33, 9509 RPM, TR113=109.4 F
Jfi2
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Tw- T•, DEG F
Figure 90. Heat Flux vs. Delta Temp.
Test 34, 9509 RPM, TR113=69.8 F
1()\
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Figure 91. Heat Flux vs. Delta Temp.
Test 38, Cont. Static Run, TR113=100 .4 F
164
10'T----------------------------------~
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Tw- Ts, DEG F
Figure 92. Heat Flux vs. Delta Temp.
Test 39, Discont. Static Run, TR113=100.4 F
165
10~--------------------~--~~~~~
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Tw- T•. DEG F
Figure 93. Heat Flux vs. Delta Temp.
Test 40, 3437 RPM, TR113=100.4 F
166
5~----------------------------------~
3
.
2
.(
o+.-r~~~~~~~~~~~~
0
20
40
60
II)
100
120
140
160
111)
200
r... - Tt, D19 F
D lfXP
+ hll£0
Figure 94.
Film Coefficient vs. Delta Temp.
Witte and Orozco (Reference No. 8)
Test 27; 3437 RPM, TR113=109 F
167
5~-----------------------------------
4
J
.
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0
~
~
60
D
100
I~
I~
160
I~
Tw- Ts, Dig F
tOP
+ hll£0
Figure 95.
Film Coefficient vs. Delta'Temp.
Witte and Orozco (Reference No. 9)
Test 29; 7830 RPM, TR113=109 F
168
26
24
22
20
rI
18
16
t~
Ic
14
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12
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vl
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6
4
2
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10
50
10
90
110
Ill
150
110
190
Tw- T1, [119 F
D
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+
Figure 96.
hll£0
Film Coefficient vs. Delta Temp.
Witte (Reference No. 9)
Test 30; 7830 RPM, TR113=115 F
169
26
24
22
20
rI
t1I c
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vl
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16
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40
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120
140
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ft -Ta, Dig F
I£XP
+ hll£0
Figure 97.
Film Coefficient vs. Delta Temp.
Witte (Reference No. 10)
Test 32; 9509 RPM, TR113=115 F
170
!
.
0
20
40
fJ
II)
100
120
140
lfJ
Ill)
200
Tw- l•, Dig F
D
lOP
+ hn£0
Figure 98.
Film Coefficient vs. Delta Temp.
Witte and Orozco (Reference No. 9)
Test 33; 9509 RPM, TR113=109 F
171
5~==~-------------------------------
4
.
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40
60
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120
140
160
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Tw- Tt, Dig F
D lOP
+ hll£0
Figure 99.
Film Coefficient vs. Delta Temp.
Witte and Orozco (Reference No. 9)
Test 34; 9509 RPM, TR113=70 F
17'1
APPENDIX D
PROGRAM LISTING
10 'SPLINE CURVE-FIT COMPUTER PROGRAM
20 '
30 'WRITTEN BY GINA GIORGI-O'SHAUGHNESSY
DATED 11/23/87
40 'BASIC COMPUTER LANGUAGE
50 '
60 '
70 DIM X(lOO),Y(100),S(100),A(100,4)
80 PRINT "
CURVE-FIT USING SPLINE TECHNIQUE"
90 PRINT
100 PRINT
110 ,
120 '
130 ' DATA INPUT
140 ,
150 ,
160 INPUT "PLEASE INPUT THE FILE NAME
DATA" ;F$
170 PRINT
180 PRINT
190 INPUT "PLEASE INPUT THE FILE NAME
200 PRINT
210 PRINT
220 OPEN F$ FOR INPUT AS #1
230 OPEN G$ FOR OUTPUT AS #2
240 N=O
250 N=N+1
260 INPUT #1,X(N),Y(N)
270 IF EOF(1) THEN GOTO 280 ELSE GOTO
280 ' N= # OF POINTS IN DATA
290 PRINT "X", "Y"
300 FOR I=1 TO N
310 PRINT X(I),Y(I)
320 NEXT I
330 ,
340 '
350 PRINT
360 PRINT
370 PRINT "INPUT THE FOLLOWING OUTPUT
AXIS"
380 PRINT
390 INPUT "
START=" ;START
400 INPUT "
STOP=";STOPP
410 INPUT "INCREMENT="; INCREMENT
420 IF START< X(1) THEN GOTO 790
430 IF STOPP > X(N) THEN GOTO 790
440 PRINT
450 PRINT
460 PRINT "1 LINEAR ENDS"
4 70 PRINT "2 PARABOLIC ENDS"
480 PRINT "3 CUBIC ENDS"
490 PRINT
173
WHICH CONTAINS THE
TO PRINT RESULTS" ;G$
250
PARAMETERS FOR THE X
p '
500 INPUT "INPUT NUMBER OF DESIRED END-FIT"; lEND
510 PRINT
520 PRINT
530 ,
540 ,
550 GOSUB 860 'SUBROUTINE WHICH FINDS SPLINE COEFICIENTS
560 ,
570 ,
580 FOR X=START TO STOPP STEP INCREMENT
590 JJ=1
600 JJ=JJ+1
610 IF JJ > N THEN GOTO 810
620 IF X <= X(JJ) THEN GOTO 640
630 GOTO 600
640 S1=S(JJ-1)
650 S2=S(JJ)
660 X1=X(JJ-1)
670 X2=X(JJ)
680 FX1=Y(JJ-1)
690 FX2=Y(JJ)
700 A=(S2-Sl)/(6*(X2-X1))
710 B=S1/2
720 C=(FX2-FX1)/(X2-X1)-(2*(X2-X1)*S1+(X2-X1)*S2)/6
730 D=FX1
740 FX=A*(X-X1)A3+B*(X-X1)A2+C*(X-X1)+D
750 PRINT X,FX
760 PRINT #2,X,FX
770 NEXT X
780 GOTO 830
790 PRINT "ERROR IN SELECTING OUTPUT PARAMETERS"
800 GOTO 830
810 PRINT "ERROR IN DETERMINING SPLINE"
820 GOTO 830
830 END
840 ,
850 ,
860 'SUBROUTINE WHICH FINDS SPLINE COEFICIENTS
870 ,
880 ,
890 NM2=N-2
900 NM1=N-1
910 DX1=X(2)-X(1)
920 DY1=(Y(2)-Y(1))/DX1*6
930 ,
940 ,
950 FOR I=l TO NM2
960 DX2=X(I+2)-X(I+l)
970 DY2=(Y(I+2)-Y(I+1))/DX2*6
980 A(I,1)=DX1
990 A(I,2)=2*(DX1+DX2)
1000 A(I,3)=DX2
1010 A(I,4)=DY2-DY1
1020 DX1=DX2
1030 DY1=DY2
1040 NEXT I
174
1050
1060
1070
1080
1090
1100
1110
1120
1130
1140
1150
1160
1170
1180
1190
1200
1210
1220
1230
1240
1250
1260
1270
1280
1290
1300
1.310
1320
1330
1340
1350
1360
1370
1380
1390
1400
1410
1420
1430
1440
1450
1460
1470
1480
1490
1500
1510
1520
1530
1540
1550
1560
1570
1580
1590
,
,
IF IEND = 1 THEN G0T0 1110
IF IEND = 2 THEN GOTO 1130
IF IEND = 3 THEN GOTO 1180
,
GOTO 1290
,
A(1,2)=A(1,2)+X(2)-X(1)
A(NM2,2)=A(NM2,2)+X(N)-X(NM1)
GOTO 1290
,
,
DX1=X(2)-X(1)
DX2=X(3)-X(2)
A(1,2)=(DX1+DX2)*(DX1+2*DX2)/DX2
A(1,3)=(DX2*DX2-DX1*DX1)/DX2
DXN2=X(NM1)-X(NM2)
DXN1=X(N)-X(NM1)
A(NM2,1)=(DXN2*DXN2-DXN1*DXN1)/DXN2
A(NM2,2)=(DXN1+DXN2)*(DXN1+2*DXN2)/DXN2
GOTO 1290
,
,
FOR I=2 TO NM2
A(I,2)=A(I,2)-A(I,1)/A(I-1,2)*A(I-1,3)
A(I,4)=A(I,4)-A(I,1)/A(I-1,2)*A(I-1,4)
NEXT I
.
,
,
A(NM2,4)=A(NM2,4)/A(NM2,2)
,
,
FOR I=2 TO NM2
J=NM1-I
A(J,4)=(A(J,4)-A(J,3)*A(J+1,4))/A(J,2)
NEXT I
,
,
FOR I=1 TO NM2
S(I+1)=A(I,4)
NEXT I
,
,
IF IEND = 1 THEN GOTO 1540
IF lEND = 2 THEN GOTO 1590
IF lEND = 3 THEN GOTO 1640
,
,
5(1)=0
S(N)=O
RETURN
,
,
S(1)=S(2)
175
1600
1610
1620
1630
1640
1650
1660
1670
S(N)=S(N-1)
RETURN
'
'
S(1)=((DX1+DX2)*S(2)+DX1*S(3))/DX2
S(N)=((DXN2+DXN1)S(NM1)-DXN1*S(NM2))/DXN2
RETURN
END
176
APPENDIX E
SAMPLE RUN
TEST 27
DISCONTINUOUS RUN, BALL ROTATING AT 3437 RPM.
TIME SURFACE CENTER
R=. 5
(SEC)
TEMPERATURE (DEGREES
0
303.08
305.6
305.6
7
283.46
286.16
284.18
14.4 239.72
242.6
239.54
21.4 173.84
174.74
174.92
27.9 133.16
133.7
133.52
34.1 114.62
115.34
115.7
AMB. TEMP & SHAFT TEMP BEFORE=
SHAFT TEMP AFTER = 94 . 1 F
TIME
0
1
2
3
4
5
6
7
8
9
10
11
12
13
14
15
16
17
18
19
20
21
22
23
24
25
26
27
28
29
30
31
32
33
TEMP
304.1434
301.7376
299.2691
296.6754
293.8938
290.8617
287.5165
283.7955
279.6391
274.9996
269.8323
264.0925
257.7355
250.7166
242.9911
234.5235
225.4179
215.8854
206.1399
196.3954
186.8658
177.7651
169.2988
161.5472
154.4943
148.1215
142.4102
137.3419
132.898
129.0423
125.6864
122.7324
120.0823
117.638
0/A
24887.67
25303.00
26348.98
28005.98
30251.86
33065.57
36427.04
40285.34
44507.54
49052.76
53911.88
59077.70
64544.19
70305.16
76269.37
81182.77
84135.55
85167.02
84334.48
81695.30
77305.43
71291.90
64747.73
58478.54
52487.92
46758.67
41274.00
36020.02
31125.36
26995.94
23691.12
21197.69
19505.48
18604.96
h
FREON
WEIGHTED AVG
FAHRENHEIT)
109.4
304.1434
109.4
283.7955
109.4
239.693
109.4
174.2928
109.4
133.3148
109.4
115.07
87.8 F
131.5810
135.5003
142.9918
154.1539
169.1051
188.0203
211.1510
238.6636
270.3340
306.5805
348.1953
396.2486
452.1944
518.0292
595.8959
679.2201
761.9739
844.1957
925.3300
1003.684
1075.691
1135.852
1192.433
1256.327
1328.999
1411.731
1505.790
1612.218
1739.041
1922.473
2216.941
2741.411
3837.923
7052.677
177
CPyT
0.206223
0.204338
0.202514
0.200709
0.198893
0.197045
0.195153
0.193215
0.191238
0.189239
0.187240
0.185260
0.183316
0.181414
0.179556
0.177732
0.175948
0.174212
0.172527
0.170897
0.169335
0.167864
0.166512
0.165287
0.164187
0.163207
0.162340
0.161581
0.160924
0.160362
0.159877
0.159455
0.159079
0.158735
98.32
0.523
0.000457
MtN=
0.000006
0.161
CpV=
0.218
CpL=
NtN=
0.000012
KV=
0.005
KL=
0.038
63.33
HFG=
9.44
PrL=
0.87
PrV=
3437
ROT SPEED
RHOL=
RHOV=
MUL=
77 F
117.6 F
89 F
89 F
140 F
77 F
112 F
112 F
77F
115 F
RHOV/RHOL0.140345
MUV/MUL= 0.071557
VEL TANG 29.99355
REv=
389053.2
THEQREI:ICAL CALCUIAIIQNS
I Wsll
304.1434
301.7376
299.2691
296.6754
293.8938
290.8617
287.5165
283.7955
279.6391
274.9996
269.8323
264.0925
257.7355
250.7166
242.9911
234.5235
225.4179
215.8854
206.1399
196.3954
186.8658
177.7651
169.2988
161.5472
154.4943
148.1215
142.4102
137.3419
132.898
129.0423
125.6864
122.7324
120.0823
117.638
115.3015
Tw-T§
I RU;3
109.4 189.1434
109.4 186.7376
109.4 184.2691
109.4 181.6754
109.4 178.8938
109.4 175.8617
109.4 172.5165
109.4 168.7955
109.4 164.6391
109.4 159.9996
109.4 154.8323
109.4 149.0925
109.4 142.7355
109.4 135.7166
109.4 127.9911
109.4 119.5235
109.4 110.4179
109.4 100.8854
109.4
91.1399
109.4
81.3954
109.4
71.8658
109.4
62.7651
109.4
54.2988
109.4
46.5472
109.4
39.4943
109.4
33.1215
109.4
27.4102
109.4
22.3419
109.4
17.898
109.4
14.0423
109.4
10.6864
109.4
7.7324
109.4
5.0823
109.4
2.638
109.4
0.3015
Tb-Ts
Hfg'
5.6 78.55604
5.6 78.36237
5.6 78.16366
5.6 77.95486
5.6 77.73095
5.6 77.48686
5.6 77.21757
5.6 76.91803
5.6 76.58344
5.6 76.20996
5.6 75.79400
5.6 75.33194
5.6 74.82020
5.6 74.25518
5.6 73.63328
5.6 72.95164
5.6 72.21864
5.6 71.45127
5.6 70.66676
5.6 69.88232
5.6 69.11519
5.6 68.38259
5.6 67.70105
5.6 67.07704
5.6 66.50929
5.6 65.99628
5.6 65.53652
5.6 65.12852
5.6 64.77078
5.6 64.46040
5.6 64.19025
5.6 63.95245
5.6 63.73912
5.6 63.54235
5.6 63.35427
178
NUv
594.0114
604.2211
615.0351
626.7842
639.8471
654.6619
671.7460
691.7239
715.3490
743.5007
777.2980
818.2246
868.2963
930.3276
1008.369
1108.345
1237.252
1403.510
1618.825
1899.420
2267.477
2752.323
3390.666
4237.515
5381.704
6960.075
9188.700
12418.49
17236.51
24698.66
37067.02
60027.88
112321.8
299548.8
7732543.
ll
17.82034
18.12663
18.45105
18.80352
19.19541
19.63985
20.15238
20.75171
21.46047
22.30502
23.31894
24.54673
26.04889
27.90982
30.25108
33.25036
37.11757
42.10531
48.56475
56.98261
68.02431
82.56970
101.7199
127.1254
161.4511
208.8022
275.6610
372.5549
517.0954
740.9599
1112.010
1800.836
3369.656
8986.465
231976.3