PEAK PRESSURES DUE TO STEAM BUBBLE
COLLAPSE-INDUCED WATER HAMMER
by
GARRY WAYNE PERKINS
/
SUBMITTED IN PARTIAL FULFILLMENT
OF THE REQUIREMENTS FOR THE
DEGREE OF
BACHELOR OF SCIENCE
at the
MASSACHUSETTS INSTITUTE OF TECHNOLOGY
MAY 1979
Signature of Author,
ne r
e*a.E
De;pArment of
Certified by
...---.
.
echanwla1 Engineering, 5-11-79
.OM
'"
" '
"
s s
0
Thesis Supervisor
Accepted by
7
D
Cw
h
w,
SChairman,
D
ARCHIVES
MASSACHUSETTS INSTiTUTZ
OF TEC HENOI.OGY
JUN 26 19t9
LIBRARIES
. "zm
en
..
6
Committee
on Thesis
mental
-2-
PEAK PRESSURES DUE TO STEAM BUBBLE
COLLAPSE-INDUCED WATER HAMMER
by
GARRY WAYNE PERKINS
Submitted to the Department of Mechanical Engineering
on May 11, 1979 in partial fulfillment of the requirements
for the Degree of Bachelor of Science.
ABSTRACT
Experiments were conducted, trying various methods
of producing inertia and heat transfer controlled steam
bubble collapse in a straight pipe geometry of 0.62 inches
I.D. A maximum pressure value of 500 psig was observed. It
was concluded that, in general, induced water hammer pressure decreases as the water temperature increases to that
of saturated vapor. It was also concluded than an inertia
controlled, or low water temperature collapse contributed to greater hammer pressures while heat transfer controlled
decreased the water hammer effect.
Peter Griffith, Professor of Mechanical Engineering
-3I.
Abstract - -
- - -
- -
TABLE OF CONTENTS
-
-
-
- - - -
- -
Pag,
- - -
2
List of Figures - - - - - - - - - - - - - - - - - - - - -4
Introduction - - - - - - - - - - - - - - - - - - - - - - 5
Theoretical Analysis
A. Water Hammer (General Equations) - - - - - - - - - 6
B. Inertia & Heat Transfer Controlled Water Hammer - -7
Experimental Procedure
A. Experimental "Banger" - - - - - - -- - - -- - -9
B. Measuring Water Temperature & Hammer Pressure - - -9
C. Testing Modes - - - - - - - - - - - - - - - - - - 11
Results and Discussion
A.
Pressure Trace Variation (one temperature) - - -12
B.
C.
D.
E.
Pressure Traces & Varying Time Sweeps - - - - - - 17
Pressures Comparing Initial Water Height - -17
Peak Pressure versus Temperature - - - - - - --20
Discussion of Errors - - - - - - --- - - - - -27
Conclusions and Recommendations - - - - - - - - - - - - 28
Acknowledgements - - - - - - - - - - - - - - - - - - - -31
References - - - - - - - - - - - - - - - - - - - - - - -31
Appendix
As Transducer Operating Specifications
B: Thermocouple Calibration Plot - - Ct Sample Data Points for Figure H - Ds Sample Data Points for Figure G - E: Sample Data Points for Figure F - -
-
-
-
-
-
-
-
32
33
34
37
38
-r4II. LIST OF FIGURES
Page
Figure 1: Generation of Water Hammer Pressure
Increase - - - - - - - - - - - - - - - - - - - 6
Figure 2: Inertia and Heat Transfer Controlled
Water Hammer - - - - - - - - - - - - - - - - - 7
Figure 3: Schematic of Experimental "Banger" - - - - - -11
Figures 4-7, Mode I, Low Temperature Scope Traces
Figures 8&9: Mode I,
Figure 10s Mode II,
--
13-14
Varying Time Sweep Traces - - - - -19
Varying Time Sweep Trace - - - - - -20
Figures 11-14s Mode II, Peak Pressure vs. Temperature
Traces - - - - - - - - - - - - - - - - - 21-22
Figure
Experimental "Banger" - - - - - - - - - - - - 10
Figure
Plot of Mode I, Low Temperature Data - -
Figure
Plot of Mode I, Room Temperature Data - - - - 16
Figure
Plots of Mode II, Pressure as a Function
of Water Height in Reservoir - - - - - - - - -18
-15
Figure Es Plots of Mode I, Low Temperature & Room
Temperature Peak Pressures - - - - - - - - - -23
Figure
Mode I,
Figure
Mode II, Pressure vs. Temperature - - - - - - 25
Figure
Mode II,
Pressure vs. Temperature - - - - - - -24
Pressure vs. Temperature - - - - - - 26
-5III. INTRODUCTION
During certain operating transients, such as a main
feedwater pump trip, the feedwater sparger in a steam
generator can lose its normal liquid cover. Cold auxiliary feedwater continues to be supplied at low flow rates to
the steam generator through the sparger. A liquid/steam
interface can then exist in the sparger feedpipe, creating
the potential for a water hammer in the pipe if a steam
bubble becomes trapped by the liquid. Steam discharges
into Boiling Water Nuclear Reactor (BWR) pressure suppression pools involve similar phenomena. During the routine
actuation of safety relief valves, steam is discharged
into a water pool through a load-mitigation device. The
violent collapse of the steam bubbles can produce water
hammer type loads on the pool boundaries that can cause
damage to containment walls. Similar problems would be
encountered during a Loss of Coolant Accident (LOCA) in a
BWR when steam discharges through the downcomer pipes.*
The aim of this experimental investigation is to
study the evolution of a water hammer pressure "signature"
as a bubble-collapse source signal is transmitted through
a piping system of known geometry and properties. Variation of a single parameter in the system will yield peak
pressures as a function of the input temperature of the
steam-condensing water. The results should be of use as
*Taken from P. Huber's, "Proposal on Thermal Hydraulic Aspects of Reactor/Plant Eng. & Safety Analysis,"(MIT,1978,p.2).
-6a baseline reference for further investigation involving
the variance and measurement of multiple parameters.
IV. THEORETICAL ANALYSIS
A. Water Hammer(General Equatinons)
Water hammer is a series
A
of shocks, sounding like ham1
mer blows, produced by sud-
B
denly reducing the flow of
a fluid in a pipe. Hammer
occurs when a wall of water
C
in a pipe must pass through
a constriction such as a
D
partially open valve or
when it
is brought to a
complete stop by a fully-
FIG. 1-Generation of Water
Hammer Pressure Increase
closed valve.
Figure 1 represents a vertical section of steel piping. Section A-B of the diagram contains a continuous column of moving water with an initial velocity, u
initial
Section C-D contains a stationary volume of water. Upon
impact with the stationary water, the moving column will
generate a water hammer pressure rise at C given by the
following equations
AP =-p c Au
(1)
where /o= mass density of water
Au = for the water in A-B, velocity at impact less
- u
initial velocity(u
final
)
initial
-7c = speed of sound in water.
The value of 4860 feet/second is used when the pipe or
tubing containing the water is assumed to be inelastic.
When the ratio of the wall thickness to internal diameter
is much less than one, the value of c must be modified
to account for the elastic stretching of the wall:
c* =
where B =
/O=
E =
DODi=
B
(2)
Bulk modulus of water
mass density of water
Elastic modulus of steel
outside diameter of pipe
inside pipe diameter
The time, t, for a pressure wave, produced by the water
hammer effect, to travel the length of pipe L and return
is given bys
t = (2L)/ o
(3)
B. Inertia and Heat Transfer-Controlled Water Hammer
•seam
Dubl±e
collapse ou-
curs when superheated water
is trapped within subcooled
c
water. Consider a volume of
steam in a pipe between a
moving column of water and a
G
stationary column of water.
Figure 2 illustrates this
phenomenon. A volume of steam
is injected at F above a
FIG. 2-Inertia & Heat Transfer Controlled Water Hammer
-8stationary column of water at G. A moving column of water
contacts the steam at E. The steam can affect the velocity
of the fluid slug sufficiently to reduce the pressure increase that will occur when the water is stopped at G.
Vapor bubble collapse can be classified into three
categoriess (I) liquid inertia controlled, (ii)
heat trans-
fer controlled, and (iii) the intermediate case where both
effects are of importance.
If
collapse is caused by a
coupling of heat transfer and inertia effects, collapse
rate analysis becomes complex. A dimensionless quantity
can be defineds
B
where/
0
j2
AT
[ L
k
Ro
,
/
P
(4)
=O density of liquid
= equilibrium vapor density
= reference volume of latent heat
c = specific heat of liquid
T = saturation temperature at final system pressure
less system temperature
k = thermal conductivity of liquid
R = initial vapor bubble radius
= final system pressure less initial equilibrium
vapor pressure
When B is sufficiently small, the vapor pressure becomes
nearly equal to the system pressure. This is the situation
where heat transfer controls the collapse. The collapse
rates are relatively slow and decrease as the collapse proceeds. When B is large enough, the vapor pressure will remain close to its initial value and the collapse will be
essentially controlled by liquid inertia effects. The collapse rates are high and continue to increase as the col-
-9lapse proceeds. The values, B=0.30 and B=0.036, are values
representing inertia dominated and heat transfer dominated
collapse, respectively. The value, B=0.10, illustrates
what might be termed an intermediate case where neither
the heat transfer nor the liquid inertia effect is dominant;
both effects play a comparable role.
V. EXPERIMENTAL PROCEDURE
A. Experimental "Banger"
Figure A is the design drawing of the "banger" used
to obtain data. It is essentially a two and a half gallon steel reservoir supported by three legs in the manner of a tripod. Extending directly beneath it is a five
foot length of half inch steel pipe. The floor of the reservoir (attached to the first four inches of pipe is designed to be removable and can be replaced by a drain orifice of another diameter if desired. The two longest pipe
sections are joined by a specially-made cross. It allowed
a pressure transducer to be placed in a 1-3/4" plug and positioned the transducer within a half inch of the pipe's stationary internal column of water. A steam inlet to the
reservoir assists in controlling the bubble-collapsing
water temperature.
B. Meas-uringWater Temperature and Hammer Pressure
A Kristal series 6606 piezoelectric pressure transducer was inserted into the banger's special cross, locating it 1-9/16" below the surface of the stationary wa-
-lo-
p-4__-i
-
srI
3
------- .kr____~~.~_ ~..._..._
------ 4·
a~"
_~k .~~__._....
._.....
..~_~~__
-------.---
l..ri
t i,.
za
~
a
.4,
Dbd
·.
?N
/SB
22V
I
i
i
i \
\ i
\\
i '
/'
-11ter column. Transducer specifications are included in Appendix A.
A copper/constantan thermocouple was positioned near
the drain at the bottom of the reservoir. An ice bath was
used as a reference junction. The use of a thermocouple
allowed easy temperature measurement of the reservoir water. A characteristic voltage/temperature calibration curve
for the thermocouple was established and is reproduced in
Appendix B. A schematic of the set-up is shown in Figure 3.
E
ch
cJ
amp
_j
drain
FIG. 3-Schematic of Experimental Set-up
C. Testing_Modes
Experimental data was collected and recorded from two
-12methods or modes. The following descriptions refer to Figure
3.
1. MODE Is
This procedure has water contained from B to F. Low
pressure steam is blown in at A. Valves B and D are then
closed and C is opened. E is filled with water of a desired
temperature. A and C are then closed, D is opened and a pressure trace is obtained on an oscilloscope.
2. MODE II:
Tn this mode, all valves are closed except D. E is
again filled with water of a desired temperature and valve
A is opened for approximately four seconds, then closed.
Again, a pressure trace is obtained.
VI.
BESULTS AND DISCUSSION
A. Pressure Trace Variation for One Temperature Condition
To obtain low-temperature traces,
a mixture of ice and
water was prepared in the banger reservoir. At first glance,
the traces in Figures 4 through 7 exhibit similar characteristics. They are nearly all of the same magnitude, positive pressure rise indicated downward. All four traces are
outlined by rough, erratic oscillations.
This is particu-
larly noticeable at the peak of Figure 5. The only significant pattern discernable is that all four traces are more
sharply erratic on their initial pressure rise side. All
of the traces have secondary reflections. Their outlines are
less rough and jagged.
-13-
FIG. 4-MODE I,
Low Temp. Trace
Temp=2-8 0 C
Scope scale:
horz=2ms/div
vert=0.1V/div
FIG. 5-MODE I,
Temp. Trace
Temp=2-80C
scope scale:
horz=2ms/div
vert=0. 1V/div
Low
-14-
FIG. 6-MODE I,
Low Temp. Trace
Temp=2-80C
Scope scale:
horz=2ms/div
vert=0. 1V/div
FIG. 7-MODE I,
Temp. Trace
Temp=2-80 C
scope scale:
horz=2ms/div
vert=0.1V/div
Low
-15FIGURE B-Mode I,
Low Temperature
0C)
(2-8
7¼±
-T-
500
-
~1
400 -
Average:
356psi
-·- · -- ---·- -------
200 -
00 -
0r
Consecutive B uns
2
3!
5
.
6
7
8
91n 10
I IM
10
11
12
13
14
3?
-16-
450
FIGURE C-Mode I,
Room Temperature
(25-30 0c)
400--
350-
Ui
-- 300
oo--
)
250
-1-
i
A4
~1
200
i-
11--
150
i
Av
_1
1
I
'Ki
i
100
i
t
r
50
I
i
0
2 314 5 6
i
Consecutive Runsi
8 90 12
17 /
1515
3 192j2
i 22
erage i
193psi
-17-
Figure 6 represents the largest peak pressure obtained during any of the recorded runs for any temperature
in either experimental mode. Using the following pressure/
voltage conversion factor;
1 psig =
1 millivolt
the value of that pressure is
,
(5)
500 psi. Figures B and C
illustrate the variation in peak oressure for consecutive
runs for Mode I low-temperature(2-80 C) and room temperature(25-300C) data.
B. Pressure Traces With VaryinS Time Sweeps
Figures 8, 9, and 10 are illustrative of the detail obtainable by varying the oscilloscope time sweep speed.
Figure 10 allows reasonable detail in secondary reflection
traces(not detectable in Figures 4-7). However, increasing
the sweep speed can overlap enough traces to become confusing. Figure 9 reduces this overlap problem, and two secondary reflections are detectable. But once again, decreasing the sweep speed can entirely wipe out detail as in
Figure 8.
C. PRESSURE VARIATION VS. INITIAL RESERVOIR WATER HEIGHT
Figure D seems to indicate that there is a variation in
peak pressure resulting from initial water height in the
banger reservoir(at least at room temperature). In Mode II
operation, a reservoir water height of 7*" generated a
majority of pressure values above 150 psi. With an initial
height of 2", the pressure generated was, generally, less
-18-
5
FIGURE D-Mode II,
Pressure variation
as a function of
water hgt in reservoir.
Room Temperature.
4.
i
2__
L½z~4ii
1-
0
J
51-100
0-50
-
~_III
01
151-200
1-150
201-250
Peak Pressure (psi)
4,
F
714
1
o
1-
C-5~L--~--1---
0-50
~
--
1 51-100 I 101-150
-
IL~DI
S151-200
Peak Pressure (psi)
..............
I
I 201-250 I
-19 -
C
FIG. 8-MODE I,
Pressure Traces
of Varying Time
Sweeps
Room Temp
scope scales
horz=0. lsec/div
vert=O. 1V/di-
FIG.
9-MODE I,
Pressure Traces
of Varying Time
Sweeps
Room Temp
scope scale:
horz=20ms/div
vert=0.1V/div
-20-
FIG. 10-MODE II,
Pressure Traces
of Varying Time
Sweeps
Room Temp
scope scales
horz=O, lms/div
vert=0.1V/div
than 150 psi.
D. Peak Pressure VS.
Temperature
Figures 11 through 14 illustrate the decreasing peak
pressure with increasing temperature. This is shown graphically in Figure E as well. Two other characteristics are
also noticeable:
1) Secondary reflections die out and become non-existent
at higher temperatures.
2) The jagged pressure-trace outlines become more rounded
and blunt. This phenomenon begins to occur around 60 0 C.
In both experimental modes, it was observed that the time
between the water hammer bang and initial reservoir water contact with the steam became longer and longer at
higher temperatures.
-21-
FIG- 11-MODE II,
temp=22 0 C
FIG. 12-MODE II,
temp=310oC
Peak Pressure vs Temp
Scale: horz=2ms/div
vert=0.1V/div
Peak Pressure vs Temp
Scale: horz=2ms/div
vert=0. 1V/div
-22-
FIG. 13-MODE II,
temp=360 C
Peak Pressure vs Temp
horz=2ms/div
Scale
vert=0.1V/div
FIG. 14-MODE II, Peak Pressure vs Temp
Scales horz=5ms/div
temp=72 C
vert=O. 1V/div
-23FIGURE E-Mode I
Low Temperature (2-8
5
4.
ri
I_
K--"1
i
i
r
0
C)
!1
2
11
0
0
1 51
1011 151
201
2517 301
3 51
K401 4511r"
-50 -100 -150 -200 -250 -300 -350 -400 -450 -500
Peak Pressure (psi)
re
re
2
-50 -100
Peak Pressure (psi)
40Q,
FIGURE F-Mode I Pressure versus Temperature. Refer to Appendix E for data.
* = two points at the
same location
3 50.
'7*
300-
0-%
XX
P4
P4
150-"
\
10 O-
I>,
50-
~c~i~c
-
--
0t
Temperature (oC)
8b
-25400.
FIGURE G-Mode II Pressure versus Temperature.
Refer to Appendix D f'or
data ,
* = two points at the
350-
same location
2*
300--
CO
q4
IoC)
P4
100 --
X--
XX -.
5o0
\
I
3o0
I/
II
o
J
I
6
Temperature (oCO
•
'
10o
400 _
FIGURE H-Mode II Pressure
versus Temperature.
Refer to Appendix for data
350 .n
300 -
0
I
IJ
m
)*
50 -100
3
\\
50
J
o
1\
I
JI \
L
0
_
______
"
7a
10
•
-
•
lo
Temperature (oC)
Intervals of 4 0 C
II
80
I1
100
-27Figures F and G are Pressure vs. Temperature plots for
Modes I and II. The corresponding scatter in pressure values
is
indicated. Figure H is a representation of over 300 Mode II
data points. To assemble them in a meaningful manner, the
data has been plotted at intervals of 4 degrees Celsius.
The bars indicate the two most extreme values for that particular interval. The dots are the arithmetic means of the
data contained in the interval.
E. Discussion of Errors
1. Thermocouple readings:
The scope values could only be read to 0.05 divisions on a
2mV/div scale, thus making possible an error of + 0.lmV.
This corresponds to a + 20 C conversion. Adding on the possibility of error from determining the thermocouple calibration slope and ice bath temperature variation;
temperature error = + 30 C
2. Peak pressure values:
Temperature transients in the pressure transducer acted to
trace over the start-up points of the peak pressures. This
can contribute to an uncertainty of + 0.2 div on a scale of
0.1V/div. This, in turn, implies that peak pressure values
can be off by + 20 psi.
3. Mode errorst
In Mode I,
several errors can arise. Referring back to Figure
3, while blowing steam from A to C(with all other valves
closed), the four inch section above D heated up more rapidly
-28than did the water at E. The thermocouple measurements did
not account for this four inch column of water. More importantly, this volume of water was what the steam first
encountered when D was opened. Therefore, Mode I temperatures
recorded are probably about 100C higher. Also, the line
pressure of the steam inlet at A was 14 psig. Since the
maximum static pressure head at D used in the reservoir was
less than 14 psig, the steam pressure had to be reduced by
closing C after A. The time delay in closing C varied during Mode I runs. In Mode II, better data was obtained if
valve A was held open longer.
VII.
CONCLUSIONS AND RECOMMENDATIONS
In equation (4),
it can be shown that as the differ-
ence between the steam temperature and reservoir temperature becomes less and less, the value of B decreases.
This,
in turn, signifies that heat transfer-controlled
steam bubble collapse is the dominating mechanism. Since
collapse rates for this mechanism are relatively slow
and decrease as collapse proceeds, the value of u in equation (1),
or water velocity, must decrease. This gives rise
to a smaller generation of water hammer peak pressures.
This corollates extremely well with observations and the
results plotted in Figure H. When the temperature difference between steam and reservoir water increases, B is
large (signifying inertia controlled collapse). The collapse rates are high and continue to increase as collapse
-29proceeds. A larger u will be generated, leading to larger water hammer pressures. This agrees with Figure H also.
Evidence was found in both Mode I and II that indicate peak pressure to be a function of initial reservoir
height. Comparisons of Figures F and H to Figure G show
that all three graphs are similar above 600 C (with Figure
F shifted to the right slightly to account for temperature
errors previously discussed). Only at lower temperatures are
the pressures of Figures F and H much higher than Figure G
(which contains only 2 * height of water in reservoir).
This does not seem peculiar when one considers that at the
lower temperatures, inertia collapse dominates. More mass
produces more inertia.
The values obtained from both methods indicated fairly good reproducability. Aside from low start-up values in
Figures B and C (probably due to trapped air bubbles), the
scatter variation was reasonable.
Using equation (3),
one is able to determine the dura-
tion of a positive pressure state. Referring to the largest
pressure obtained, Figure 6,
the maximum width of the large
trace is approximately 1.8 divisions or 3.6 milliseconds. If
the drain valve at the bottom of the vertical pipe is shut,
it can be modeled as a "closed end." The reservoir can be
considered an "open end." Recalling that the pressure resulting in a wave reflection from an open end is opposite
in sign and reflection from a closed end retains its sign,
-30one can follow the history of the pressure trace. The
length of pipe below the transducer is 23 inches and the
length above it is approximately 35 inches. The steam bubble-collapsing water impacts above the transducer and as the
wave travels downward, there is a
large
rise in pressure
seen at the transducer. This wave rebounds off the closed
end, encounters the transducer again and increases the pressure to 500 psi. The wave hits at the open end and reflects
a -500 psi pressure wave. This reduces the pressure at the
transducer to zero. If the preceeding history is valid, then
the wave travels a distance of 2 x (23" + 35*) or 116 inches.
Plugging into equation (3) yieldes
L = (3.6 ms)(1/1000) 58320in/sec = 104 inches.
2
This value is reasonably close to the correct value. Also,
since the distance from the transducer to the closed end is
shorter than the distance to the open end, the slope of the
trace on the increasing pressure side should be steeper
because of the smaller amount of time required. Figures 4
through 7 all exhibit this asymmetry. For 3.6 milliseconds,
the piping system was under an induced hammer pressure.
If the piping system were even longer, as in an actual nuclear piping system configuration, the piping would have to
be designed to sustain high pressures during even longer
periods of loading time. Also, the secondary reflected peaks
ranged from j to * of the value of the initial hammer peaks.
In larger systems, this can be a significant loading.
-31Suggestions for future investigations are as follows:
1) Reduce the length of the four inch pipe section beneath
the reservoir. Also, construct a reservoir with enough height
capacity to generate a higher pressure at the quick-acting
reservoir valve than the steamline pressure for Mode I runs.
2) Remove valve and unnecessary pipeline obstructions for
Node II runs.
3) Collect data at the extreme temperature points (i.e.
00 C and 10000C).
VIII.
ACKNOWLEDGEMENTS
I wish to express my thanks and appreciation to the
following people for their time and assistance:
Fred Johnson
Bob Gruel
Prof. P. Griffith
IX. REFERENCES
1. Florschuetz, L, Chao, B., "On the Mechanics of Vapor
Bubble Collapse," ASME 64-HT-35, 1964.
2. Gwinn, J., Wender, P., "Start-up Hammer in Service
Water Systems," ASME 74-WA/Pwr-8, 1974.
3. Parmakian, John, Waterhammer Analysis, Dover Publications,
Inc., New York, 1963.
4. Tong, L.S., Boiling Heat Transfer and Two-phase Flow,
R. Krieger Publishing Co., New York, 1975.
-32APPENDIX A
Kristal's series 6606 low impedance quartz pressure transducer with integral electronics- - - - - - - - - - - - - -
88
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APPENDIX B
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APPENDIX C
Mode II Pressure vs. Temperature Datas
Scope scales
2mV/div
0.
Thermocouple
Transducer
Voltage
Voltae_
- -16
0.8
o0.45
0.55
0.75
0.9
1.1
1,2
1.35
1.55
1.7
1.9
1.9
1.85
1.95
1.95
- - -
V/div
1.8
2.05
0.7
2
2.1
2
1.8
1.9
1.9
1.5
1
1.3
-
plotted on Fig H
2mV/div
0.1V/div
Thermocouple
Transducer
Voltage_
Voltage
0.75
210
1.9
1.9
0.65
2
2
2
0.4
0.5
0.8
1
1.2
1.3
1.5
1.65
1.7
1*95
1.9
1.8
1.6
1.8
1.4
1.1
1.2
1.2
1
1.8
1.9
0.8
0.9
0.7
1*95
0.6
2
2.05
0.6
0.3
0.4
0.8
0.4
1.8
2
2.1
2.1
2.1
0.4
0.2
0.5
1
0.45
0.6
0.65
1.3
0.65
0.75
1.7
2.1
1.3
0*75
0.8
0.9
2
0.95
1.7
1.1
1.8
1.2
1.8
1.25
1.25
1.3
2
1.2
1.35
1.8
1.4
1.5
1.45
1.5
1.2
1.8
1.6
1.2
1.4
1.8
0.9
0.8
1.85
0.8
1.9
1.95
2
0.6
1.95
0.6
2
2.05
0.3
0.6
2.1
0.85
0.85
0.9
12
1.4
1.5
1.55
1.65
1.75
2.1
0.7
0.4
0.3
1.6
2
2.1
2.2
1.1
1.15
1.3
1.6
1.7
1.75
1.85
2.05
2.1
1.4
1.6
1.7
1.6
1.5
1.8
2
1.7
1.8
0.9
0.8
1.1
0.7
0.5
0.5
0.4
0.5
-35APPENDIX C (con't)
Mode II Pressure vs. Temperature Data:
Scope scale:
2mV/div
Thermocouple
Volta~
0.55
0.65
0.7
0.8
0.9
1.1
1.15
1.25
1.35
1.45
1.55
1.65
1.7
1.8
1.9
2
2
2
0.4
0.5
0.65
0.75
0.85
0.95
1.1
1.2
1.25
1.4
1.5
1.55
1.65
1.7
1.8
1.9
2
0.55
0.65
0.75
0.85
0.95
0.1V/div
Transducer
Voltage
2.3
2
2.2
2.2
1.4
1.9
1.6
2.9
1.9
1.9
1.6
1.5
1.5
1.2
0.9
1
0.9
0.6
0.9
plotted on Fig H
2mV/div
Thermocouple
Voltage0.5
0.6
0.65
0.75
0.85
1.05
1.1
1.2
1.3
1.4
O.1V/div
Transducer
Voltags
2.1
2.4
2.2
1.6
1.8
1.9
2.9
1.8
1.9
1.6
1.7
1.7
0.9
1.85
1.1
1.2
1.2
0.8
1.5
1.65
1.75
1.95
2
2
0.3
0.8
1.5
0.45
2.5
2.1
2.6
2
2.2
2
2
1.8
1.9
1.4
1.7
1.5
1.2
1.1
0.7
0.7
0.6
0.7
2.5
1.6
2
0.7
3
1.9
3
1.8
0.8
0.9
1
1.15
1.25
1.3
1.45
1.5
1.6
1.7
1.75
1.85
1.95
0.5
0.6
0.8
0.9
1
2
2
2
2
2
1.9
1.9
1.6
1.2
1.4
0.9
0.9
0.9
o.6
2.7
1.4
1.9
1.8
3.2
1.6
-
-36APPENDIX C (con't)
Mode II
plotted on Fig H
Pressure vs. Temperature Data:
Scope seal e:
2mV/div
0.1V/div
2mV/div
0.1V/div
Thermocoup)le
Voltage
Transducer
Voltag
2
Thermocouple
Transducer
1.05
1.15
3
1.2
1.3
1.2
1.35
1.45
1.55
1.25
2
1.3
1.4
1.5
2.4
1.6
1.6
1.4
1.2
1,65
0.9
1.7
1.8
1.8
1.9
2.
2.05
2.1
0.4
0.45
0.55
1.5
1.15
1.2
1.25
1.3
1.35
1.4
1.45
0.8
0.5
0.5
0.4
2
0.5
0.6
0.65
0.7
0.8
0.85
1.8
1.6
1.1
1.9
1.4
1.4
0.6
0.4
1.3
2
1.6
2
2
1.85
0o.45
0.9
1.2
2
1
1.9
1.7
1.1
0.95
1.1
1.3
1.35
1.4
1.4
1.45
0.8
1.2
1.1
0.8
1.05
1,1
1.15
1.2
1.25
1.5
1.75
1
0.6
1.9
2
0.8
1.9
1.55
1.6
1.7
1.85
0.9
0.9
0.9
0.7
2,1
2.1
2.1
1.8
1
0.8
0.8
1.3
1.5
1.7
1.2
1.6
1.4
1.6
1.3
1
1.9
1.95
0.4
1.5
2
1,05
1.1
Voltage
0.5
1
0.8
1
1.65
1.7
-
1.75
1.6
0.95
1.55
_
1.1
1.1
0.65
0.7
0.7
0.85
Voltage._
1.1
0.2
1.6
1.65
1.7
1.8
1.8
2.05
0.7
1.2
2
1
1.3
1.2
1.1
1.3
1
1.2
2
0.8
0.9
1
0.9
0.8
0.6
0.6
0.2
0.3
.
-37APPENDIX D
Mode II
Pressure vs. Temperature Datas
plotted on Fig G
Scope scales
2mV/div
0.1V/div
2mV/div
0.1V/div
Thermocouple
Transducer
Thermocouple
Transducer
Voltaxe
Voltage
1.8
1
0.8
0.35
0.55
0.8
0.85
1.4
1.5
1.6
1.7
1.75
0.7
1.8
1.65
1.75
1.75
1.8
1.9
2.05
2.15
0.9
1.4
1.25
1.45
1.55
0.8
1.1
1.1
1.3
1
0.8
1.5
1.2
1.4
0.9
1.8
1.4
1
0.6
1.5
2.2
2
0.95
0.5
0.7
Voltagge
0.8
0.9
1.1
0.7
1.05
1.2
1.3
0.8
0.8
1.8
0.7
0.2
2
2.1
0.1
1.85
2.15
0.7
0.6
0.4
0.2
0.1
_
-38APPENDIX E
Temperature Datat
Mode I Pressure vs.
plotted on Fig F
Scope scale,
2mV/div
0.1V/div
2mV/div
0.1V/div
Thermocouple
Transducer
Thermocoup)le
Transducer
Voltage
Voltag~
Voltag e
1
3.8
0.8
1.8
2.1
3.3
0.7
1.7
2.1
0.9
0.7
1.9
1.1
1.9
3.1
3.4
0.1
2.4
2.2
0.7
1.4
1.8
SVoltage
0.7
1.4
1.5
3.3
2.1
0.7
1.6
1.3
1.9
2.1
2.4
3.1
0.6
1.3
2.2
1.95
3.25
3.1
1.05
3.3
3.6
1
3.4
0.5
0.1
3.8
0.1
0.6
1.2
1.6
1.8
2.1
2.4
2.55
2.5
0.6
2.5
2.5
2.8
1.1
2.7
0.8
0.9
3
0.1
3.5
3
3.4
3.6
1
1.3
1.5
0.8
4.1
1.7
2
2.2
0.1
3.2
1
1.6
0.8
1.4
0.6
1.5
1.7
3.7
1.6
0.9
0.8
0.9
0.1