SELF PRESSURIZATION OF LIQUID HYDROGEN TANKAGEedge.rit.edu/edge/P07109/public/tank...
Transcript of SELF PRESSURIZATION OF LIQUID HYDROGEN TANKAGEedge.rit.edu/edge/P07109/public/tank...
/
SELF PRESSURIZATION OF LIQUID HYDROGEN TANKAGE
A Thesis
Presented to the Faculty of the Graduate School
of Corne__llU_niversity for the Degree of
Master of Science
LI AffYJ,4f'_3 !__7
LEWISLiSRARY,|':ASAby CLEVELAND,OHIO
John Charles Aydelott
, February 196'/ !
o: 'Acc'7"_'"""' ,T../__AJ'., ,coo,,(NAIA CR OR TMX OR'AD NUMBER) (CATEGORY)
i
i
1967009809
.J
BIOGRAPHICAL SKETCH
The author was born February 24, 1938 in Erie, Pennsylvania, was
graduated from Cornell University with a Bachelor of Mechanical Engi-
neering in June 1961, and spent the following year at Cornell University
as a teaching assistant and graduate student. Since July 1962, with the
exception of two months of graduate study at Cornell University during
the summer of 1964, the author has been employed by the NASA Lewis
Research Center. Mr. Aydelott was the principal author of NASA publi-
cations TM X-1006 and TM X-1052 and _.ne co-author of NASA TN D-3449.
ii
ill •
1967009809-002
nt
A CKNOWLEDGMENTS
The author gratefully acknowledges the financial support of the _......7"V
National Aeronautics and Space Administration and the technical assist-
ance of the Lewis Research Center personnel which made the preparation
of this thesis possible.
iii
i|
1967009809-003
TABLE OF CONTENTS
Page
TITLE PAGE ........................... i
BIOGRAPHICAL SKETCH ................... ii
ACKNOWLEDGEMENTS ....................... iii
TABLE OF CONTENTS ....................... iv
LIST OF TABLES .......................... v
LIST OF ILLUSTRATIONS ...................... vi
SYMBOLS ............................... ix
I. SUMMARY ........................... 1
II. INTRODUCTION ........................ 2
lII. ANALYSIS ........................... 4
IV. APPARATUS .......................... 7
V. PROCEDURE ......................... 9
VI. EXPERIMENTAL RESULTS ................. 12
VII. DISCUSSION OF EXPERIMENTAL RESULTS ........ 14
VIII. SUMMARY OF RESULTS ................... 28
APPENDIXES
A - THERMODYNAMIC CALCULATIONS ............. 29
B - HEAT TRANSFER CALCULATIONS .............. 32
C - ENERGY DISTRIBUTION CALCULATIONS ......... 36
BIBLIOGRAPHY ........................... 40
iv
i
L
1967009809-004
LIST OF TABLES
Table 1 - Summary of experimental results and heat transfer analysis
Table 2 - Results of energy distribution anaiysis
V
i
1967009809-005
LIST OF ILLUSTRATIONS
Figure 1 - Tank pressure as function of heat added for two-energy
distribution models; 1-cubic-foot tank.i
Figure 2 - Schematic drawing of liquid hydrogen experiment.
Figure 3 - Inner sphere temperature transducer locations.
Figure 4 - Test number three.
(a) Total pressure as function of time.
(b) Outer sphere and heater temperature as function of time.
(c) Upper inner sphere temperature as function of time.
(d) Lower inner sphere temperature as function of time.
Figure 5- Test number four.
(a) Total pressure as function of time.
(b) Outer sphere and heater temperature as function of time.
(c) Upper inner sphere temperature as function of time.
(d) Lower inner sphere temperature as function of time.
Figure 6 - Test number five.
(a) Total pressure as function of time.
(o) Outer sphere and heater temperature as function of time.
(c) Upper inner sphere temperature as function of time.
(d) Lower inner sphere temperature as function of time.
Figure 7 - Test num Oer ten.
(a) Total pressure as function of time.
(b) Outer sphere and heater temperature as function of time.
(c) Upper inner sphere temperature as function of time,
(d) Lower inner sphere temperature as function of time.
vi
1967009809-006
Figure 8 - Test number s',xteen.
(a) Total pressure as function of time.
(b) Outer sphere and heater temperature as function of time.
(c) Upper inner sphere temperature as function of time.
(d) Lower inner sphere temperature as function of time.
Figure 9 - Test number nineteen,
(a) Total pressure as function of time.
(b) Outer sphere and heater temperature as function of time.
(c) Upper inner sphere temperature as function of time.
(d) Lower inner sphere temperature as function of time.
Figure 10 - Test number twenty.
(a) Total pressure as function of time.
(b) Outer sphere and heater temperature as a function of time.
(c) Upper inner sphere temperature as function of time.
(d) Lower inner sphere temperature as functio; _.of time.
Figure 11 - Rate of heat input as function of time for each heat source
for typical quiescent test.
Figure 12 - Pressure as function of total heat added for two homogeneoustests.
Figure 13 - Resistance as function of temperature for typical inner
sphere temperature transducers.
Figure 14 - Pressure as function of total heat added for quiescent tests.
(a) Effect of heat transfer rate and distribution.
(b) Effect of percent filling.
Figure 15 - Inner sphere temperature as function of position for
typical quiescent test.
Figure 16 - Inner sphere temperature as function of position for three
heating configurations.
Figure 17 - Homogeneity factor as function of average heat transfer
rate.
vii
1967009809-007
Figure 18 - Inner sphere and heater emissivity as function of temper-ature.
Figure 19 - Stainless steel specific heat as function of temperature.
Figure 20 - Plastic support ring thermal conductivity as function of
temperature.
Figure 21 - Stainless steel thermal conductivity as function of temper-ature.
viii
i
1967009809-008
SYMBOLS
A surface area, sq ft
Bjl absorption factor
Cp specific heat, Btu/(Ib)(°R)
F angle factor
k thermal conductivity, Btu/(hr)(ft)(°R)
L length, ft _,,,,:
m mass, lb
P pressure, Ib/sq it,,,, abs
q heat transfer rate, Btu/hr
Q heat added, Btu
r reflectivity
T absolute temperat_ re, CR
t time, Hr "
U _otal internal energy, Btu
u specific internal energy, Btu/lb
V volume, cu ft
c emissivity
p density, lb/cu ft
a Stefan-Bo.tzmann constant, 0. 1713xi0-8 Btu/(hr)(sq ft)(°R 4)
Subs cripts:
a absorbed
ix
1967009809-009
avg. average
bulk liquid bulk
ev evaporation
f final or any intermediate state
gc gaseous conduction
i initial state
j summation variah__ E
liquid
layer liquid thermal layer -'-"
L at x=L
m mean or average value
max maximumB_
n summation variable
r radiant
s system
sat. saturation
sc solid cc,nduction
st stored
v vapor
w wall
0 at x-=0
1 irmer sphere
2 upper heater
3 lower heater
4 outer zphere
X
1967009809-010
SUMMARY ,.-
A nonventing 9-inch-diameter spherical Dewar partially filled with
liquid hydrogen was subjected to twenty-one quiescent self pressurization
tests. The Dewar was subjected to various combinations of the variables
percent filling, heat transfer rate, and either top heating only, bottom
heating only, or uniform heating. The rate of pressure rise in the Dewar
was found to be primari!y a function of the heating configuration with the
percent filling and heat transfer rate playing a secondary role. Appreci-
able energy transfer from the vapor to the liquid causing evaporation and
liquid heating occurred during both the uniform heating and top heating
only tests.
J
1967009809-011
INTRODUCTION
The space exploration program of the National Aeronautics and
Space Administration is heavily dependent on the use of liquid hydrogen
as a rocket fuel. Liquid hydrogen has many properties, in addition to a
very low boiling point, which set it apart from common liquids. Of
particular interest are the thermal transport properties of both liquid
and gaseous hydrogen which make it possible for subcooled liquid and
highly superheated vapor to coexist in the same container. This situation
occurs when a closed system containing liquid hydrogen is exposed to
energy input in the form of heat which causes an increase in the total
system pressure. The interface between the liquid and vapor phases
remai_:s at the saturation temperature corresponding to the increasing
total system pressure while the average liquid temperature increases
at a slower rate and thus the liquid becomes subcooled and the average
vapor temperature increases at a faster rate and thus the vapor becomes
superheated. As a consequence, simple thermodynamic analysis cannot
predict the rate of pressure rise in a closed system containing liquid
hydrogen.
An excellent review of the work that has been performed in this
field will be found in (ref. 1). The majority of the reported work has
been restricted to cylindrical tanks with heating only of the side walls so
1967009809-012
that natural convection theory for vertical plates could be used to predict
the heat and mass transfer within the liquid phase. In general, direct
heating of the vapor was not considered.
This thesis presents the information obtained from twenty-three
self pressurization tests of spherical tanks containing liqui:! hydrogen.
The experiment consisted of a 9-inch diameter vacuum-jacketed Dewar
partially filled with liquid hydrogen. The Dewar was surrounded by two
hemispherical radiant heaters whose temperatures could be controlled
in order to vary the distribution and rate of energy input to the hydrogen
container.
Instrumentation measured Dewar pressure, vacuum-space pressure,
surface temperatures of the Dewar, heater, and vacuum-jacket, and
temperature at seventeen locations inside the Dewar.
Twenty-one of the tests were performed with the experime,.t rigidly
bold so that the liquid hydrogen interface was quiescent. Two tests
involved violet shaking of the experiment in order to obtain a saturated
homogeneous mixture of hydrogen liquid and vapor.
The purpose of the quiescent tests was to co.npare and explain the
differences in the rate of pressure rise in a spherical hydrogen Dewar
as a function of heat transfer rate, heat flux distribution, and precent
filling of the container. The homogeneous tests were used for calibration
of the temperature transducers and error analysis.
The experimental tests were performed at the NASA Lewis Research
Center, Cleveland, Ohio during the time period from January 1965 to
April 1965.
1967009809-013
ANA LYSIS
The first law of thermodynamics is
Q = AU + P AV
For a closed, n3nexpanding system, all the heat absorbed by the system
manifests itself in a change in the total internal energy of the system
since AV = O
Q:-- AU
If the system in question is a tank containing a liquid and its vapor, a
knowledge of how the added heat affects the internal energy distribution,
and thus the temperature distribution within the tank, makes prediction
of the total system pressure possible. For a two-phase mixture, tem-
perature and pressure are dependent variables at the interface between
the liquid and the vapor.
The temperature distirbution in a cryogenic storage tank is highly
complex and is affected by many variables, the most important of which
are tank geometry, percent filling, heat flux rate, and heat flux dis-
riOution.
This thesis presents two simple models that are not intended to beP
attempts at describtng the process that actually takes place in a non-
venting Dewar but are intended to be a means of comparing one set of
experimental data with another. The position that experimental data
4
1967009809-014
5
assumes in relation to the theoretical models on a plot of Dewar pressure
against heat added is then an indication of how the energy is being dis-
tributed within the Dewar. Figure 1 is a plot of tank pressure as a
function of heat added for two energy distribution models. The plot is
for a one cubic foot container and initial fillings of 25, 50, and 75 per-
cent. The reader may approximate the energy input, as determined by
these models, that will cause a specified change in pressure for any tank
size or filling. This is possible by interpolating to determine the effect
of percent filling and by multiplying the heat added obtained by the volume
of the tank in cubic feet since the energy input IS a linear function of the
tank volume. Appendix A contains the development of the first law of
thermodynamics that makes the calculations for the theoretical models
possible. The first model assumes homogeneous conditions throughout
the Dewar and is a common calculation that is performed to compare
dam of this type. The second model assumes that all the energy absorbed
by the Dewar goes into the evaporation of liquid. The vapor-phase tem-
perature is always equal to the saturation temperature, which corre-
sponds to sphere pressure. The liquid-phase temperature remains
constant at the saturation temperature corresponding to seal-off pres-
SU re.
In order to obtain the energy input to a real tank a heat transfer
analysis must be performed. Appendix B contains the details of the
heat transfer analysis used for this experimental program. The main
source of energy input to the experiment was radiant exchange from the
heaters. Conduction along the plastic support ring, vent tube, and
instrumentation wires played a secondary role.
1967009809-015
6
Once the total energy input to the liquid hydrogen tank is known it
is of interest to know how the energy input effects the contents of the
tank; namely hcw much of the total energy input goes into heating the
vapor, evaporation of liquid, or heating the liquid. At any time during
the test the temperature distribution in the vapor and the pressure can
be determined from the instrumentation. This makes it possible for
the internal energy and mass of the vapor to be calculated at any time
and thus the energy which went into heating vapor and evaporation, mass
change times heat of vaporization, during the time interval of interest
can be determined. The energy input to the liquid during the same time
interval can then be found by subtracting the energy which went into (he
vapor and evaporization from the total input during the time period.
From knowledge of the change in the temperature of the bulk of the liquid
and the fact that the interface between the liquid and the vapor remains
at the saturation temperature the energy input to the liquid can be further
broken down into the energy that p" es into heating the bulk of the liquid
and that which heats the layer of fluid between the bulk and the liquid-
vapor interface. A detailed development of this analysis will be found
in Appendix C.
1967009809-016
APPARATUS
Figure 2 is a cross-sectional drawing of the liquid hydrogen experi-
ment that consisted of three concentric spheres; the inner sphere con-
tained the liquid hydrogen, the intermediate sphere had electric heating
coils mounted on its exterior surface, and the outer sphere served as
a vacuum jacket and had coils mounted on its exterior surface through
which liquid nitrogen was circulated during each test in order to mini-
mize the conduction heat transfer to the inner sphere. The inner sphere
and the heaters were painted black in order to increase their emissivily.
The vent tube was made of stainless steel. The inner sphere was sup-
ported by a polychlorotrifluoroethylene plastic ring that was cut out
where possible to reduce heat conduction.
A heater controller, which basically consisted of a bridge circuit
which balanced the resistance of a temperature sensor on each heater
with a corresponding reostat on _he control panel, was used to maintain
heater temperatures of 360 °, 425 °, 500° or 575 ° R.
Figure 3 shows the location of the temperature transducers on the
inner sphere and the four carbon resistor temperature rakes that were
located within the inner sphere to measure the temperature of the
hydrogen liquid and vapor. At any time prior to a test run the resistance
of any temperature transducer could be determined by the use of a digital
1967009809-017
8i
ohmmeter mounted in _he control panel. During a test the resistance of
each transducer was measured by using two bridges and amplifiers so
that temperature changes were converted to 0 to 5 volt signals which
were recorded on magnetic tape. For each transducer one bridge :_ad
a 0 to 5 volt range corresponding to anticipated changes in liquid tem-
perature and the second bridge had a 0 to 5 volt range corresponding to
the much larger anticipated changes in vapor temperature.
When a relatively high current is applied to a carbon resistor, its
temperature is quite different depending on whether the temperature
probe is in the liquid or vapor phase. This is due to self heating.
Exploitation of this fact, together with careful arrangement of the carbon
resistors, makes it possible to use the carbon resistors to determine
the liquid level in the sphere.
Temperature transducers were located on the intermediate and
outer spheres in order that the heat transfer to the inner sphere by
radiation and conduction could be calculated. A single bridge recording
system similar to the one used for the inner sphere temperature trans-
ducers was employed.
An ionization gage was used to measure the pressure in the vacuum
space. The location of the gage and two pressure transducers used to
measure the pressure in the inner sphere can be seen in figure 2. A
twenty-eight volt DC power supply was used to operate the pressure
transducers. The vacuum pressure was monitored continuously on
the control panel. During a test the 0 to 5 volt output of the inner sphere
pressure transducers was recorded on magnetic tapes.
1967009809-018
PROCEDURE
Prior to the assembly of the experiment, thermocouples were
attached to the inner sphere, heaters, and vacuum jacket. All temper-
ature transducers were calibrated at 139.5 ° R by submerging the three
spheres in a liquid nitrogen bath. The inner sphere, heaters, and vacu-
um jacket were calibrated in a carefully controlled oven at 540° R. In
addition, the heater temperature transducers were calibrated at 710 ° R
in the oven. After the experimen£ had been assembled it was filled
with liquid hydrogen and the inner sphere temperature transducers were
calibrated by violently rocking the experiment in a shaker and recording
the resistance of each transducer, which corresponds to the saturation
temperature of hydrogen at atmospheric pressure. Each bridge was
calibrated by using a decade box to obtain a voltage versus resistance
plot. Prior to each test, the pressure transducers were c_librated
with standard pressure gages. Each of the calibration curves for the
temperature and pressdre transducers and for the bridges was curve
fitted using a digital computer. The magnetic data tape from each
test could then be fed into the digital computer along with the calibration
curve fits and an automatic data reduction program returned printed
temperature and pressure data at half second intervals for every trans-
ducer.
9
t
1967009809-019
10
For each of the tests, the experiment was prepared in an identical
manner; only the actual test conditions were varied. The space between
the inner and outer spheres was evacuated by first using a mechanical
pl.mp and then a diffusion pump. The experiment was cooled by circu-
lating liquid nitrogen through the coils on the outer sphere. Then the
inner Dewar was filled with liquid hydrogen. The liquid nitrogen cooling
and the addition of 'he liquid hydrogen reduced the pressure in the space
between the inner a_d outer spheres due to cryogenic pumping. A gas
meter installed in the ve,_t line together with the carbon resistors K
described in the instrumentation section of this report, made it possible
to determine the liquid level at the beginning of the test. The resistors
accurately determine the liquid position at some time prior to the begin-
ning of the test. The gas meter records the volume of vapor which
then leaves the Dewar. Measurements of the vapor temperature, at the
g_.s meter, and the atmospheric pressure determine the density of the
vapor and the mass which leaves the Dewar before the test begins can
be calculated.
The heater controller was set to maintain the desired heater tem-
perature. All of the temperature instrumentation was checked using
the digital ohmmeter and the recording system was turned on. At -1
minute the system began recording the data on magnetic tape, at zero
time the vent valve was closed, and the experiment was allowed to self
pressurize until a pressure of slightly over one-hundred pounds per
square inch absolute was achieved. The vent valve was then opened
and the pressure was allowed to decay slowly. If a sufficieat amount
of liquid hydrogen still remained in the experiment, a similar test at a
1967009809-020
ll
lower filling wa._ run as soon as the new liquid level had been deter°
mir, ed.
For the twenty-or, e quiescent tests, the experiment was mounted in
a stand which was supported directly from the ground and was unattached
to the surrounding structure. This permitted the experiment to remain
totally undisturbed throughout the test. For the homogeneous tests, the
experiment was rocked violently in a shaker so that the contents of the
inner sphere stayed thoroughly mixed.
1967009809-021
EXPERIMENTAL RESULTS
Figures 4 through 10, pressure and temperature as a function of
time, present the data obtained from seven of the quiescent test runs.
Each of the figures i_; made up of four plots; (a) total pressure as a
function of time, (b) outer sphere and heater temperature as a function
of time, (c) upper inner sphere temperature as a fur.ction o_ time, and
(d) lower inner sphere temperature as a function of time. These seven
tests were chosen as being representative of the twenty-one qu:escent!-
tests. Figures 4, 5, and 6 show the effect of three different percent
fillings, 34. _-,, 48.97_, and 76.97o, for the uniformly heated and nearly
constant heat flux situation. Figures 8, 9, and 10 show the effect of
three different average heat fluxs, 17.1 Btu/hr-ft 2, 27.6 Btu/hr-ft 2,
and 38.2 Btu/hr-f[ 2, for an approximately half full sphere which was
heated only from the top. Figures 5, 7, and 9 show the effect of three
different heating configurations, uniform, bottom only, and top only,
for an approximately half full sphere. The bottom heating only test
(fig. 7) had the same heat transfer rate from the bottom heater as the
bottom heater of the uniform heating test (fig. 5). The top heating only
test (fig. 9) had the same heat transfer rate from the top heater as the
top heater of the uniform heating test (fig. 5). The twenty-one quiescent
12
1967009809-022
13
tests consisted of eight tests with uniform heating, six tests with bottom
heating only, and seven tests with top heating only. One of the homo-
geneous tests was uniformly heated and the other heated only from the
top. Initial percent fillings of 35, 50, and 80 percent were desired.
The high fillings proved to be the most difficult to achieve since the
boil-off was too great during the period of time required to ckeck the
experiment prior to a test. Heater temperatures of approximately
360°, 500°, 575° R were used for the uniform heating tests, 500° and
575° R for the bottom heating only tests, and 425 °, 500°, and 575° for
the top heating only tests.
m mm m nm w
1967009809-023
DISCUSSION OF EXPERIMENTAL RESULTS
A first look at the data would tend to suggest to the reader that the
rate of pressure rise would be the most important parameter to consider
when examining a group of tests which had identical heater temperatures.
However, because the hydrogen vapor does become superheated and
the top of the inner sphere does increase in temperature as a test
proceeds this approach can be quite misleading. The heating of the
_,_,_,. _nh,,,-,_ ¢-_,,_,_o a rcduction in the heat transfer to the i,yu_"r._....ve,.m
due both to the reduction in radiant exchange and the energy which is
required to increase the temperature of the container wall. Higher
heater temperatures and lower percent liquid fillings cause increasing
inner sphere temperatures so that the average heat flux to the hydrogen
is not a function only of heater temperature. As a result a better
procedure is to compare the amount of heat Ihat must be added to the
Dewar to cause a given pressure rise for a particular set of conditions.
For all the tests it was assumed that the temperature profiles
were symmeiric with respect to the vertical axis. In other words, at
any time during a test all vertical planes passing through the center
of the sphere would exhibit identical temperature patterns and the left
side of such a plane would be a mirror image of the right side. This
assumption is based on the fact that the inner sphere, heaters, vent
14
.m w
1967009809-024
15
tube, plastic support ring, instrumentation wires, and liquid-vapor
interface all have the same symmetry with respect to the vertical m
axis and consequently there is no reason to anticipate that the temper-
ature profiles would be different on opposite sides of the container.
Based upon this assumption the amount of energy reradiated by the
inner sphere can be calculated. The method of calculating the net
radiant heat transfer and the conduction heat transfer is given in
Appendix B. Heat is added to the inner sphere by radiation from the
heaters, by solid conduction through the vent tube, the plastic support
ring, and the temperature transducer wires, and by gaseous conduction.
Figure 11 is a plot of the rate of heat input as a function of time for
each of the heat sources for a typical quiescent test. The gaseous
conduction of heat was negligible for all the tests. The increasing
temperature of the inner sphere accounts for the reduction in the radi-
ant heat exchange from the upper heater, as time increases, due to the
increasing reradiation from the inner sphere. The increasing temper-
ature of the inner sphere also accounts for the decreasing and eventually
negative conduction heat transfer from the vent tube since the inner
sphere becomes hotter than the liquid nitrogen cooled outer sphere and
heat is conducted away from the top of the inner sphere
, Table I is a summary of the experimental results and the heat
transfer analysis. The initial percent filling was determined as ex-
plained in the PROCEDURE section. The pressure rise rate is an
average value obtained by dividing the difference between the pressure
at the end of the test and atmospheric pressure in psia by the total
test time. The bulk temperature was taken to be the lowest recorded
m m
1967009809-025
16
temperature, usually temperature transducers 11 or 12. Dividing the
change in the bulk temperature, during the test, by the change in the
saturation temperature during the test, gives an indication of how much
energy went into heating the liquid and thus how nearly homogeneous the
liquid is at the en¢l of the test. The maximum change in the vapor tem-
perature gives an indication of how much energy went into superheating the
the vapor. The average heat flux is determined by dividing the total
energy input to the hydrogen as determined in Appendix B by the test
time and the surface area of the inner sphere. This average is then
broken down into the heat flux through the liquid wetted walls and
through the walls exposed to vapor. Breaking the heat flux up into
parts in this manner clearly shows the effect of the increasing upper
inner sphere temperature which reduces the net radiant heat exchange.
The two homogeneous tests were run for the purpose of checking
the validity of the heat transfer analysis and to get an estimate of the
accuracy of the instrumentation. Figure 12 is a plot of sphere pressure
as a function of heat added for the two homogeneous tests. One test
was run with only the top heater installed, the other with both heaters
installed. For both tests the experiment was shaken vigorously so
that the hydrogen liquid and vapor were thoroughly mixed and at the
saturation temperature corresponding to the absolute inner sphere
pressure. Since the initial filling and pressure were known, a theo-
retical plot of homogeneous pressure versus heat added, shown as
dashed lines on figure 12, was generated using the analytical technique
presented in Appendix A. Every thirty seconds the test data was used
to perform a heat transfer analysis, as presented in Appendix B, and
1967009809-026
17
the heat added up to that point in time was plotted aginst the experi-
mentally recorded pressure. These calculated points are identified
by the symbols on figure 12. By superimposing the data obtained from
the heat transfer analysis on the theoretical homogeneous line the
combined experimental and analytical error can be seen. Ideally the
calculated points should fall on the theoretical line, but a maximum
error of two pounds per square inch or two percent of full scale was
observed.
The homogeneous tests also provided a check on the accuracy of
the inner sphere temperature transducers since saturation temperatu re
should be recorded during the entire test. As in the previous discussion
where it was impossible to separate the error associated with the pres-
sure transducer from the error in the heat transfer analysis; here it
will be impossible to separate the error associated with the pressure
transducer from the error associated with the temperature transducers.
If it is first assumed that the pressure transducer is correct, the
carbon resistor temperature transducers indicate saturated conditions
within a maximum of ,0.6 ° R with an average error of -0.3 ° R in
the range from 36 to 54° R. The platinum surface temperature trans-
ducers indicate saturated conditions within a maximum of +2.2 ° R
with an average error of ,0.9 ° R. Figure 13 is a plot of resistance as "
a function of temperature for typical inner sphere temperature trans-
ducers. This figure shows that in the temperature range of 36 to
54 ° R the carbon resistors under go approximately a seventy ohm
change in resistance while the platinum surface transducer resistance
only changes four ohms for each degree Rankine change in temperature.
IF m | m | m m mm
1967009809-027
18
Consequently, ,itthese low temperatures itwould be expected thatthe
carbon resistortemperature transducers would be more accurate. If
itisnow assumed thatthe carbon resistorsare indicatingthe true
saturationconditions,then the pressure Iransducer would have a max-
imum error of two pounds per square inch, or the same resultobtained
from the discussion associatedwith figure 12. Figure 13 is also useful
in estimatingthe accuracy of the temperature transducers at higher
temperatures. In the 200° to 300° R range the carbon resistance
transducers under go approximately a two ohm change in resistance
for each Rankine degree as compared toa seventy ohm change for each
Rankine degree atthe lower temperatures. This indicatesthatthe
resistorsare lessaccurate by a factorofthirty-fiveat the k!gher
temperatures so thaterrors as high as :L:20° R may be possible. Above
I00G R the platinum surface transducer resistance changed seven ohms
for each degree Rankine change intemperature so thatthese transducers
should be slightlymore accurate at higher temperatures than in the
liquidhydrogen temperature range. In summary, because both the
heat transferanalysis and the carbon resistorstemperature transducers
indicatedthe same error in the pressure transducers, itIs reasonable
to assume thatthe pressure data is accurate withintwo pounds per
square inch, the platinum surface temperature transducers are accurale
withintwo degrees Rankine, and the carbon resistortemperature trans-
ducers are accurate to three-tenthsof a degree Rankine atlow temp_:.r-
atures and ten degrees Rankine at lfightemperatures.
Figure 14a shows the effectof heat transferrate and distribution
on the sphere pressure as a functionoftotalheat added for the approxi-
1967009809-028
19
mately fifty percen! filled quiescent tests. The fifty percent filled
tests were chosen since they represent the least corapiicated geometr]c
situation where the liquid-vapor interface and the division between _he
upper and lower heaters are approximately in the same horizontal
plane. It is readily apparent that the heating configuration is the
primary factor affecting the slope of the pressure versus heat added
data. The heat transfer rate had the least effect on the slope of the
pressure versus heat added data for the bottom heated tests with ]n-
creasing influence on the uniformly heated and top heated tests. How-.
ever, the heat transfer rate was definitely secondary in importance _o
the heating configuration. Since the two coordinates, pressure and
heal added, are the integrals over time of pressure rise rate and
heat transfer rate, coincident test data indicates a linear relationship
between pressure rise rate and heat transfer rate; that is, doubling
the heat rransfer rate will double the pressure rise rate. For the
bottom heated tests this linear relationship was followed almost exactly,
but the uniformly heated tests, and to a greater degree, the top heating
only tests began to deviate. This indicates that the way in which energy
was distributed in the liquid was unaffected by the rate of energy input,
while the rate of energy input to the vapor greatly affected the resulting
temperature or energy distribution. Analysis based on the Rayleigh L
number indicates that the mode of heat transfer in the liquid would be
turbulent convection (ref. 2). However, a summary of liquid hydroger,
boiling studies presented in reference 3 indicates that at the heat fluxs
employed for these tests boiling is quite likely to occur. An essentially
uniform temperature liquid bulk would be anticipated for either turbulent
1967009809-029
2O
convection or boiling h_at transfer. Because a uniform temperature
liquid bulk was experimentally observed, it is reasonable to assume
that at the lower heat fluxs the heat transfer mechanism in the liquid
was dominated by turbulent convection with some boiling entering in at
the higher heat fluxs. The heat transfer processes which take place
in the vapor are r,ot clearly understood, but addilional discnssion will
be presented after the energy distribution analysis, Appendix C, is
introduced. The theoretical surface evaporation and homogeneous
lines which appear on figure 14a also help the reader to understand
how the energy distribution within the hydrogen container effects the
experimental results. It will be recalled that the surface evaporation
model is based on the concept of no heating of the hquid coupled with
a saturated vapor while the homogeneous model has both saturated liquid
and saturated vapor at all times. The top heating only tests approach
the surface evaporation model in one respect; the liquid is heated a
very slight amount, but superheating of the vapor pushes the experi-
mental data above the theoretical surface evaporation line. The bottom
heating only tests approach the homogeneous model in one respect;
the liquid is nearly saturated, but some heating of the vapor causes
superheating and the experimental data lies above the theoretical
homogeneous line. The uniformly heated tests combine some heming
of the liquid with superheating of the gas with the resulting data lying
between _he two extremes of lop and botlom h,.,ating only.
Figure 14b shows the effect of percent filling on the sphere pres-
sure as a function of heat added for three uniformly heated tests. The
data presented is for test numbers 3, 4, and 5. These three tests
m, i
1967009809-030
21
were chosen to demonstrate the effect of percent filling because the
average heat flux for the three tests was nearly the s_me. Due to the
increase in temperature of the upper part of the sphere the low filling
test had the lowest average heat flux. Based on the information obtaint.d
from figure 14a it would be expected that if the average heat flux had
been the same the experimental data would have been somewhat closer
together than that shown in figure 14b. The obvious conclusion to be
drawn from figure 14b is that the rate of pressure rise was only
slightly affected by varying the percent filling, with a trend toward
higher rates of pressure rise at higher fillings for the uniformly
heated tests. In order to understand why the rate of pressure rise is
only slightly affected by the percent filling, for the uniformly heated
tests, reference is again made to table I. The data for test numbers
3, 4, and 5 indicate _hat as the percent filling is increased ti_e liquid
becomes less subcooled and the vapor becomes less superheated.
These two effects tend to counterbalance each other. In contrast, the
bottom heating only tests exhibit decreasing rates of pressure rise with
increasing filling, a result of the increased, nearly saturated hquld
mass which is available to absorb the incoming energy. The top
heating only tests exhibit increasing rates of pressure rise with in-
creasing filling, a result of the increasing unheated liquid mass which
effectively reduces the volume of the container. Evidently the uniformly
heated tests are slightly dominated by the heating of the vapor which
causes a small increase in the rate of pressure rise with increasing
filling.
m
1967009809-031
22
In order to further explain the experimental results an analysis
was performed to determine what percentage of the incoming energy
resulted in heating of the liquid bulk, the liquid thermal layer, evap-
oration of liquid, and superheating of the vapor. The details of these
energy distribution calculations will be found in Appendix C. Figure 15
shows the inner sphere temperature as a function of position for a
typical quiescent test. The liquid-vapor interface it ".acated at a value
of height to radius of 0.8. This figure shows that the temperature of
the vapor space was only a function of the vertical coordinate since
the data for all the instrumentation, both centrally located and near
the container wall, had the same temperature profile. Consequently,
the energy distribution analysis was based on the assumption that the
vapor space could be divided up into horizontal uniform temperature
discs. These discs, or elemental volumes, were then used to perform
a summation, approximating an integration, to determine the total
mass and internal energy of the vapor space at any time during the
test. The total vapor internal energy is divided by the mass of vapor
to determine the average vapor specific internal energy which together
with the pressure defines an average vapor temperature. Knowledge
of the change in internal energy and mass of the vapor as a function
of time allows the calculation of the percentage of the energy input
which superheated the vapor and caused evaporation. The percentage
of the energy input which heated the liquid is determined by subtracting
the input to the vapor and for evaporation from the total energy input f
calculated from the heat transfer analysis The mass of the system is
a constant so the mass of the liquid can be determined at any time by
1967009809-032
f
23
subtracting the mass of the vapor from the total initial mass. The
average liquid internal energy is calculated from knowledge of the
initial conditions and the energy input to the liquid. Any average
property of the liquid can now be determined since the pressure and
average internal energy are known at any time. The average liquid
density is calculated which together with the mass of the liquid makes
it possible to determine the percent filling at any time. The ave_ :ge
percent filling is converted to an average liquid wetted area and
multiplied by the wetted area heat transfer rate to determine the energy
input to the liquid hydrogen. The energy input to the liquid was furl her
broken down into two parts; the energy which went into the bulk of the
liquid and the energy which went into heating the thermal layer between
the sat-arated liquid-vapor interface and the bulk of the liquid. Fig-
ure 16 is a plot of inner sphere temperature as a function of position
for three heating configurations. Of particular interest are the temper-
ature profiles in the liquid for the three tests. It can be seen that the
bulk temperature, or lowest recorded temperature, is representative
of a large portion of the liquid mass. For the purposes of mathematical
computation a linear temperature gradient from the bulk temperature
to the saturation temperature at the interface was assumed. It is
realized that for Jome of the tests this is a poor approximation to the
actual temperature gradient, but the analysis based on this approxi-
mation helps to further explain how energy is transported and distrib-
uted within the liquid hydrogen.
Table 2 is a summary of the results of the energy distribution
analysis. It will be noted that four tests were not included in the energy
' i
1967009809-033
24 --.-
distribution analysis. Geometric considerations were responsible for
the exclusion of these tests. The two low filling bottom heated only
test:, had some direct heating of the vapor. The two nigh filling top _-
heated only tests had some direct heating of the liquid. It is Impossible
to separate the total energy input into the quantity wi_ich heated liquid
and that which heat,_.d vapor so the te_ts were not included.
The lower heating only tests proved to be the easiest to understand
an0 th _ least interesting. The energy input to the liquid wetted walls
accounted for the heating of the bulk liquid, whicn was nearly saturated,
the energy input to a thin liquid thermal layer _nd the energy which
went into evaporation. What heating of the vapor that did occur was
due to the small energy input to the dry walls. Considering the accu-
racy of the instrumentation and the analysis, it is quite possible that
no thermal layer existed and ae experiment under the bottom beating
only condition was equivalent to heating a container of water on the
kitchen stove. The top heating only tests proved to be just the opposite;
the hardest to understand and the most interesting. As before, the
energy input to the liquid wetted walls approximately accounted for the
• heating of the liquid bulk, but the energy input to the dry walls heated
the vapor, supplied the energy for evaporation and heated the liquid
thermal layer with over fifty percent of the total energy input ending
in the liquid thermal layer. It seems reasc, nabie to assume that the Iup
energy transfer from the vapor to the liquid was intermolecular in
nature. The fact that the lines of constant temperature in the vapor
were horizontal, with increasing temperature at higher vertical posi-
tions, rules out the possibility of any convective flow. It is possible
1967009809-034
25
that an involved conduction analysis could predict both the vapor and
the liquid thermal layer gradients; however, a detailed analysis was
not undertaken. An order of magnitude type analysis using the ob-
served temperature gradients and rates of heat transfer has indicated
that conduction could be the primary mode of energy exchange. It w_
not felt that the experiment design, or the accuracy of the instrumenta-
tion and analysis, lent itself to further pursuit of this line of thought.
The results of the analysis on the uniformly heated tests were easily
identified as being the combined results of the top heating only and
bottom heating only tests. The energy input to the dry walls heated
the vapor, supplied the necessary energy for evaporation, and heated
most of the liquid thermal layer. The energy input to the liquid wetted
walls heated the liquid bulk and a portion of the liquid thermal layer.
It is quite possible that the inaccuracies in the analysis would account
for the portion of the heating of the liquid thermal layer which came
from the liquid wetted walls. These inaccuracies come from the as-
sumption of a linear temperature gradient in the liquid thermal layer, the
fact that the energy passing t_rough the liquid wetted walls near the inter-
face must add to the thermal layer, and consideration of the fact that as
the test proceeds the liquid thermal layer grows and liquid which was
previously included in the bulk now becomes part of the thermal layer.
The rate of pressure rise in the hydrogen container, for the uniformly
heated tests, is primarily a function of the energy input to the vapor
since the energy input to the iiquid wetted walls primarily heats the
liquid bulk. The nnly contribution which heating the liquid makes to the
m
1967009809-035
26
container pressure is due to the thermal expansior of the liquid.
Liquid hydrogen does have a relatively high coefficient of thermal
expansion, but this effect is secondary to the energy input to the vapor
for determining the rate of pressure rise.
To summarize the experimental results obtained from the twenty-
one quiescent tests, a simple calculation was performed. The average
liquid and vapor temperatures, obtained from the energy distributi:)n
analysis, together with the pressure at the beginning and end of e,,ch
test were used to compute the average :_quid and vapor specific
entropy. Knowledge of the mass of the liquid and vapor both at the
start and end of the test made it possible to determine the total change
in system entropy during the test. This change in system entropy was
divided by the change in entropy of the corresponding homogeneous
model and the resulting dimensionless parameter was termed the homo-
geneity factor. Figure 17 is a plot of the horaogeneity factor as a
function of average heat transfer rate for the quiescent tests.
The thermodynamic property entropy is often associated with
probability. It was with this thought in mind that the change in entropy
of a real system, as compared to a theoretical homogeneous model,
was chosen as the single parameter most suitable for summarizing
the experimental results. A homogeneity factor equal to unity would
be for a homogeneous system. In contrast, systems with low homo-
geneity factors exhibit large temperature gradients. If isolated, these
systems would decay to the uniform temperature, more probable,
situation found in a homogeneous system. The lehgth of the lines on
figure 17 is indicative of the range of heat flux that was explored for
1967009809-036
27
each percent filling and heating configuration while the thickness of
the lines represents the authors confidence limits. Nothing new or
unexpected resulted from this entropy calculation. Once again, it is
apparent that the heating configuration is the most important vamable
effecting the final state of the system. The heat transfer rate was of
significant influence only on the upper heating only tests. For the
lower heating only tests, the high fillings were more nearly homo-J
geneous since the vapor mass, which was slightly superheated, was
smaller. For the upper heating only tests the high fillings were less
homogeneous since the mass of the liquid bulk, which essentially did
not change temperature, was larger. The uniformly heated tests
showed the influence of both the top and bottom heating effects with
the top heating dominating the overall final system conditions.
1967009809-037
SUMMARY OF RESULTS
A nonventing 9-inch-diameter spherical Dewar partially filled
with liquid h'-?-'ogen was subjected to twenty-one quiescent self pres-
surization tests. The tests were terminated at a maximum pressure
of one-hundred pounds per square inch absolute. The Dewar was
subjected to various combinations of the variables percent filling,
heat transfer rate, and either top heating only, bottom heating only,
or uniform heating. The following results were obtained:
(1) The rate of pressure rise was affected most by heater config-
uration, being greatest for the top heating only tests, least for the
bottom heating only tests.
(2) The rate of pressure rise increased almost linearly with in-
creasing heat transfer rate.
(3) The rate of pressure rise was only slightly affected by varying
the percent filling.
(4) Appreciable energy transfer from the vapor to the liquid
causing evaporation and liquid heating occurred during both the uniform
heating and top heating only tests.
(5) Nearly saturated liquid temperatures were recorded throughout
the liquid for the bottom heating only tests.
28
1967009809-038
APPENDIX A
THERMODYNAMIC CALCULATIONS
One method of analyzing a system thermodynamically is to define
the conditions at the beginning and the end of a process; then the neces-
sary input to the system can be determined. For the problem of a
Dewar, which is sealed at the beginning of the test, the initial condition
is that the Dewar contains a homogeneous mixture at atmospheric pres-
sure with a known percent filling. The final condition is defined by the
model being considered. For a nonexpanding closed system, the input
is heat, and as stated by the first law of thermodynamics:
Q : _u (Al'
For the development of this analysis, the initial state will be signi-
fied by the subscript, i and the final, or any intermediate state, is
denoted by the subscript f. Equation (A1) may be written
Q :: Uf - Ui :--(m,,fu_, f + mv, fUv, f) - (m_, iu_, i + my, iUv, i) (A2)
The density and specific internal ener_--'y of each phase at state i can be
found if the system is known to be homogeneous and at the saturation
temperature corresponding to atmospheric pressure (ref. 4). The to_al
internal energy at. state i can then be delermined since
29
1967009809-039
3O
(percent filling)i V (A3)ml_,i '- Pt,i I00
[1 (percen__t filling)_mv, i = Pv, i - 100 3 V (A4)
For a closed nonexpanding system, the mass of the liquid plus the mass
of the vapor is a constant; consequently, the system density is a constant:
(percent filling)i I1 (percentl_0ofilling) i__Ps= :oo P_'i+ - :]Pv,i (AS',For the homogeneous model, state f (and thus the density and
internal energy of each phase) is defined by the fact that the system is
homogeneous and at the saturation temperature corresponding to the
system pressure. Equation (A5), written for state f, can be solved for
the percent filling at state f:
(percent filling)f = Ps - Pv, f (100) (A6"
The total internal energy at state f can then be determined since
(percent filling)f= V (AT_
mJt,f PJt,f 100
and
(percent filling)_mv, f--Pv, f - 100 .Jr (A8)
The amount of heat required to reach state f for the homogeneous model
can now be calculated by using equation (A2).
1967009809-040
31
For the surface-evaporation model, state i is the same as that
for the previous model so that the total internal energy at state i is
found by the identical procedure. The surface-evaporation model is
based on the concept that all of the energy goes into evaporating the
liquid, so that the density and internal energy of the remaining liquid
will be unaltered by the process; that is, Pt,i - P_,f and u_, i = u_ f.
The density and internal energy of the w:_por are defined by the fact
that the vapor is homogeneous and at t!:,? saturation temperature corre-
sponding to the final system pressure. Equ_.tion (A5), written for state
f, can be solved for the percent filling at state :
(percent filling)f = Ps - Pv, f 100 (A9,P_, i - Pv, f
The mass of liquid and vapor at state f can then be determined since
(percent filling)fV (A10,
m_,f = p_,i 100
and
_ (percent filling)f_my, f= Pv,f - 1-00 _ V (All?
The total internal energy at state f can now be determined, and from
equation (A2), the heat required to reach state f for the surface-
evaporation model can be calculated.
1967009809-041
APPENDIX B
HEAT T.WANSFER CALCULATIONS
The amount of energy absorbed by the contained hydrogen is equal
to the heat transferred to the sphere by radiation, solid conduction,
and gaseous conduction minus the amount of energy stored in the con-
tainer itself; that is
Qa : (qr + qsc + qgc ) At - Qs t (B1)
The amount of heat transferred by thermal radiation from the
heated intermediate sphere to thc inner sphere is de!ermined by the
method presented in reference 2. For the radiant exchange calculations
the inner sphere is assigned the number 1, the upper heater number 2.
the lower heater number 3, and the outer sphere number 4. The net
rate of radiant heat absorbed by the inner sphere when both heaters are
installed is
3
ql = _ aBjl_jAjT _ -¢;_IA1 T4 (B2)j=l
where Bjl, the absorption factor, is defined as the fraction of the total
radiant energy emission of surface j which is absor_ed by surface 1. _"
The absorption factors are determined by solution of the following
simultaneous equations:
32
i
1967009809-042
33
(FllrI - I)BII+ FI2r2B21 + FI3r3B31 1 .-.:0 tB3}
F21r1B11 -_(F22r2 - 1)B21+ F23r3B31 + F21eI _-0 (B4)
F31r1B11 + F32r2B2i + (F33r3 - 1)B31+ F31eI - 0 (BS_
This techniquetreatsalldiffuse-radiationcircumstancesand requires
onlya knowledgeofthegeometry ofthethreesurfaces,theaverage
temperatureofthesurfaces,and theemissivityofthe__urfacesas shown
infigure18. The dataforthisfigurewas rbtainedexperimentallyby
Lewis Research Centerpersonnelusinga sample surfaceidenticalto
thoseoftheexperiment.
When one ofthehemisphericalheaterswas removed inorderto
obtainonlytopor bottomheatingtheoutersphe_'e,surface4, had tobe
substitutedfortl_removed heater,surface2 or 3, inequation(B2)and
subsequentcalculations.The insideoftheouterspherewas goldplated
and an emissivity of 9.10 was assumed. Due to the variation in temper.-
ature of the inner sphere thc last term in equation (B2) was expressed
as an integral and called the inner sphere reradiated heat flux
q _ fA (_ET4dA (B6)Ireradiated I
where A I isthesurfacearea oftheinnersphere. This intpgralwas
approximatedby thesummation
n
qlreradiated _ _ _jT_ AAj (B7)j=l
As explainedintheDISCUSSION OF EXPERIMENTAL RESULTS section,
thetemperatureoftheinnerspherewas foundtobe onlya functionofthe
1967009809-043
34I
vertical coordinate so that horizontal uniform temperature sections
could be used to divide the sphere into elemental surface areas. A
, digital computer was used to curve fit the emissivity versus temperature
curve and the inner sphere temperature versus position curves for each
" time interval. An average temperature for each elemental area was
used to determine the local emissivity and the summation was performed
every thirty seconds by using a digital computer.
The energy stored in the container at any time interval was a!so
expressed as an integral
Qst = fV CppW dV (B8 _,lw
where Vlw is the volume of the container wall. This integral was
approximated by the summation
n
Qst _ _ pCpjWj AVj (B9,j=l
Assuming the same temperature distribution, a digital computer was
used to curve fit the stainless steel specific heat as a function of tem-
perature curve found in figure 19 (ref. 5) and the inner sphere temper-
ature versus position curves for each time interval. An average tem-
perature for each elemental volume was used to determine the specific
heat and the summation was performed every thirty seconds by using a
digital computer.
The differential equation and boundary conditions for one-dimensional
heat transfer by solid conduction are the following:
1967009809-044
m,
35
{:tx0TT0td 0 (B10jdx t x = L, T TL
At the very low temperatures encountered with the use of liquid hydrogen,
the thermul conductivity of most materials is highly temperature depend-
ent and can be expressed as some function of the absolute temperature.
Substituting the boundary conditions in equation (B10) and integra'tng
(ref. 2) result in
T O - TL -_(B._1'q-k
A m •_J
where
/T T h k(T) dT (B ] 2i --km _ TL 1 TO 0
Figure 20 shows the stainless stee! thermal conductivity as a function of
temperature (ref 5) and the curve fit which was used to perform the
necessary ingegration in equation (B12). Figure 21 shows the plastic
support ring thermal conductivity as a function of temperature and the
curve fit which was used to perform the necessary integration in equa-
tion (B12). The data for this figure was obtained experimentally by
Lewis Research Center personnel using a sample piece of plastic iden-
tical to that used in the experiment.
For all the tests, the heat transfer due to gaseous conduction
through the vacuum space, was negligible.
._ ........ . m •
1967009809-045
APPENDIX C
ENERGY DISTRIBUTION CALCULATIONS
As explainedin the DISCUSSION OF EXPER/MENTAL RESULTS
section, the temperature of the hydrogen vapor was found to be only a
function of the vertical coordinate so that horizontal uniform tempera-
ture sections could be used to divide the vapor space into elemental
volumes. Each elemental volume then approximated a region of constant
temperature and pressure. Since two thermodynamic properties are
known, for each elemental volume, any other ploperty can be determined.
The properties of particular interest are the density and specific internal
energy. The equations which were used to generate the hydrogen tables,
reference 4 were curve ntted using a digital computer so that the de-
sired properties were readily available once the pressure and temper-
ature were known. This mvde it possible to determine the total internal
energy and mass of the vapor at any tim,_.
mv = dmv (C
Uv =/V v Uv dm v
(C2I
These two integrals were approximated by the summations:
36
1967009809-046
37
!n
mv _ _ Pvj AVvj (C3)
n
Uv _ _ UvjOvjAVvj ,C4)
At any time thesesummations canbe evaluatedby usinga digitalcom-
puter. Itisfirstnecessaryto curvefitthevaportemperatureversus
positiondataforthetesttimes ofinterest.The computer can then
determinethenecessaryproperties,from thehydrogenpropertycurve
fits,foreach elementalvolume, and perform thenecessarymathematical
operations.The energyinputtothevaporduringany time intervalis
-- - rj
Qv = Uvf vi
The change in the mass of the vapor is:
Am v = - (C5)mvf mv i
The energy :.,put that results in evaporation is
Qev = (Amv)(heat of vaporization) (C6_
The energy input to the liquid is determined by subtracting the energy
input to the vapor and evaporation from the total energy input to the
container.
Q_ = Q1 "Qv - Qev (C7)
Inordertofurtherexploretheenergydistril:'_tionwithintheliquid
= phase it was assumed that the liquid consisted of a uniform temperature
region known as the bulk and a region of linear temperature change
between the bulk and the liquid-vapor interface known as the therm_.l
1967009809-047
3b
layer. This assumption is considerea in detail in the DISCUSSION OF
EXPERIMENTAL RESULTS section. The bulk temperature, at any
time, is determined from the instrt, mentation and the thermal layer
average temperature is:
Tbulk + Tsat' (C8)Tlayer - 2
Since the liquid-vapor interface is always at the saturation temperahJre,
the average internal energy of the liquid initially corresponds to the
saturated temperature and pressure and at any later time is:
Q_+ (c9)"1 u_ avg. = u_ i m_
where: ml_ = mi_ - Am vi
At any time the energy stored in the liquid must be equal to the sum of
the energy stored in the two regions.
+m u = mbulkUbulk + mlayer _ ,: - (C10)l_ _avg _.
The total mass of liquid is equal to the sum of the mass of liquid in the
two regions.
m_ = mbulk + ml,tyer (CII) _
Combination of equations (C10) and (Cll) yields:
mbulk = m_ (utsat + Ubulk - 2u_avg_ (C12)U_sat - Ubulk
Ad of the liquid is in':tially saturated so the energy input to the bulk is:
Qbulk = mbulkfUbulkf- m_ u_ (C13)i sat i
1967009809-048
3C
and oy suotracting the energy input to the oulk from the total energy
input to the liquid:
Qlayer " Q£ " Qbulk _C14)
The percent filling of the inner sphere at any time is
m_percent filling - × 100 (C15)
p_ Vavg
where P_avg is determined by using the computer and the values of the .-
total sphere pressure and as input.u_ avg
1967009809-049
BIBLIOGRAPHY
1. Clark, J. A. : A Review of Pressurization, Stratification_ and
Interfacial Phenomena. International Advances in Cryogenic
Engineering, Proceedings of the 1964 Cryogenic Engineering
Conference. pp. 259-283, Plenum Press, 1965.
2. Gebhart, Benjamin: Heat Transfer. McGraw-Hill Book Co., Inc.,
1961.
3. Drayer, D E. and Timmerhaus, K. D. : An Experimental Investi-
gation of the Individual Boiling and Condensing Heat-Transfer
Coefficients for Hydrogen. Advances in Cryogenic Engineering,
vol. 7, Proceedings of the 1961 Cryogenic Engineering Conference.
pp. 401-411, Plenum Press, 1962.
4. Roder, Hans M., and Goodwin, Robert D. : Extended Tables of
Provisional Thermodynamic Functions for Para Hydrogen. Rep.
7220, NBS, Jan. 3, 1962.
5. Scott, Russell B. : Cryogenic Engineering. D. Van Nostrand Co.,
Inc.. 1959.
40
1967009809-050
41
TABLE I. - SUMMARY OF EXPERIMENTAL RESULTS
AND HEAT TRANSFER ANALYSLS
'Iest Initial Pressure (Liquid} (Vapor) q/A 1 q/A 1 q/A1
number percent rise rate, ATbulk ATmax, average, wetted dryfilling psi/min oR Btu area, area,
ATsat Btu Btuhr-ft 2
hr_ft 2 hr-ft 2
Uniform heating
1 34.6 3.5 0.55 110 17.5 20.0 15.7
2 51.4 3.6 .46 I' 18,2 20.0 16.4
3 34, 9 II. 3 62 212 59, 9 80.3 45.8
4 48.9 13.5 47 200 65.0 80.7 48.9
5 76.5 17.0 32 159 72.6 80.5 54.1
6 36.8 19.3 61 258 I05.4 148.0 74.5
7 50,7 23, 6 47 245 III. 6 142.7 78.4
8 77.2 30.3 31 182 128,6 141,9 97.7
Lower heating
9 29.3 5.9 0.99 85 39.5 78.5 16,3
I0 49, 0 4.9 .99 I09 44.6 81.7 5, 1
ll 73.5 3.6 .97 73 42.6 59.5 2.9
12 31.0 II. 0 .95 87 73.3 146.6 27.3
13 47,8 8.6 .96 90 75.2 144.9 3.0
14 74.0 6.3 .92 54 75.7 I05.4 3.5
Upper heating
15 36.5 4,6 0. I0 81 15.5 1.5 25.2
16 50.5 5.8 07 85 17.1 2.2 32.2
17 80° 4 8.8 05 99 19.6 13.8 34.0
18 34.3 8.2 11 118 24° 2 2.8 38.2
19 51.2 11.2 06 123 27.6 4.6 51.7
20 47° 7 18.5 05 153 38.2 3.5 71.0
21 77, 0 30.3 04 158 53.6 42.6 77.8
........................ 1967009809-051
42
TABLE 2, - RESULTS OF ENERGY DISTRIBUTION ANALYSIS
Test Average Energy inputto Qliquid I_rapor Qevap Qbulk Qlayernumber percent liquid wetted walls
filling as percent of total As percent o._total energy inl_Jt
Uniform heating
1 35.8 46.4 77.4 8.8 13.8 32.5 44o9
2 52o9 57.2 82.9 6,7 10.3 51.7 31o2
3 36.7 54.9 76, 1 18.1 5, 8 39, 1 37° 0
4 5r 4 62, 7 79.3 15° 4 5, 2 58, 4 20. 9
5 78, 2 77, 5 91, 0 7, 7 1, 2 64, 6 26, 4
6 38.4 59.2 74.5 22.0 3.6 47.8 26.7
7 52, 2 66, 0 77, 4 18.7 3, 9 65, 5 11, 9
8 78, 7 77, 1 90, 8 8, 7 O,6 63.8 26, 9
Lower heating
10 52,8 94.4 85,4 3,5 11°1 82.6 2o8
11 79.4 98, 2 97.1 O. 9 2.1 95.6 1o5
13 50,9 98,1 84,7 3°6 11,8 80.9 3.8
14 79, 9 98, 8 96, 9 O. 9 2, 3 96, 9
Upper heating
15 36,9 4,1 70,9 9,7 19.4 5,6 65.3
16 50,7 6.6 70,8 8. _. 20,8 6.2 64,6
18 34,6 4,5 67,6 14.6 17,8 8.0 59.6
19 51,2 8,6 66,3 '2°4 21,4 5,4 60,9
20 47.7 4,4 59,3 18,9 21,8 4,8 54,5
n
1967009809-052
¢5
__ ,,ercent _ I &l 10 1 L/O l __j,i/ / ," , 1 /'= t _ ,, / / /38/ /"_' I ^
-'_ ;;_1oo i _ I 6_/ /
" • / / t/"m---+ -2 "-/ d
_- !/ /"8o i / I
I, / / /"_ k' /'/ / ,_/
- I I
17.' /'/.,-_ o }} _40& / ._/, ( A Percentfilling initially"
t/,/. P-_ I _ Homogeneous ___20I ------ Surfaceevaporation- Jt Ir lr111
n 20 60 80 100 120 140 160 180 290Heatadded, '_t_
F_gurel. - Tankpressureasfunchonofheatadoedfor two-energyd_strit,ution models;l-cubic-foottank.
F Pressuretransducerattachmentpoints
VenttubeVacuum
heater
- Plastic"- / supporlI
Lowerheater
tuidnitrogenTovacuum coolingcoilspump
InstrumentationwiringTovacuumvalve
Figure2. - Schematicdrawingofhquidhydrogenexperiment.
n
1967009809-053
4:4
Carboaresistor Distancetemperature fromwail,transducer in.
l 4._0 :3.302 2.90 Rake4
3 2.20 , 24 ,Jill resistor17 18 19 207 2.11 \_ ' ' '
9 1.18 / ", \5 I 1.o2/ \n,l: I o.oo ! \ / \1o l O.SO \ /'X
12,18 1 0,40 , \ /15.19 0 20 _
16,20 [ o,o2 I" /'
A - \
| _k,,.._ _V _;_,;_P - _ .... I Surface ]I _ /-- veto (uDe_,,/[ \ _ i _ / , Jtemperature/
, /" BT,__" I1"_... / 1" ) transducers I
XRake2-'/_ _'" / I I "'_. /._ i I " I .'
III i RakeIVenttube-:., I _ / "_
\ / ;}, ./--5,/_ 32 10
/ /3 _ Section,-A
"I-....\ ,-. JP-Ra(e2nearside/
k c=cm_-""1 Rake4far side /
_._.._., j resistors ll, 12, 15, 16
Figure3. - Inner spheretemperaturetransducerlocations.
1967009809-054
,kS
. I ._ _ I J_ I I _^ I
,_ , atcr
---_-_-" V Outer sphere at equator= l 3(_ ----J-----_- A Outer sphere at bottom
4_ t _ "-" ! I 0 Outer sphere at top
=1/" i ) _ =_ 1_ l I-_r-_-- -,.,_ --_ .- -
I i I I l i I i t i loo i I J t l J j,__L_0 100 200 )00 400 500 0 100 200 300 400 500
Time,sec Time,s_
(a) Total pressure as function of time. (b) Outer sphere and heater tempe,ature asfunction of time
Figure 4. - Test number three. Figure 4. - Continued
350 '_ 'N-Y] I
30C _ _ 0 R-4l'-IR-3
,_..,,'_"'_/'T'/ _ 0 R-2 --
" /,_;_ # _,. ,_'_ _"" "- Seefig. 3forf location of
_" _ _//" ,.CY' F --'_/r'_sdlcers -
_o-- / -- i
1.11/ 10 100 290 300 400 500
Time,sec
(c)Upperinnerspheretemperatureasfunctionoftime.
Figure 4. - Continued.
..... |
: [] R-1820O ' "2 R-IO
t'.R-20
_..___i 0 R-6
D._I I _R-Q
100 - _.....).._,-- _'_--_ A Sat. LH2" i l l Q R-IO
.- _._'(I,-' ( I See fig. ) for locationI I r of transducersl I i I 1 I i I
o I00 200 3o0 400 5O.)Time,sec
(d)Lowerinnerspheretemperatureast motionofth_e.
Figure 4. - Concluded.
1967009809-055
46
lO0 f
-- ji._ 8_ i
_ !/I 1jJ
=- j4c f
JJ
--]i L_rJ
t0 50 100 150 200 250 300 350 _:_
Time,see
(a) TotalI_ressureas functionof time.
Figure5. - Testnumberfour.
_ J ]
,,,, 400 (3 Upperheater _° I 0 Lowerheater_- _7Outersphereat equator-
i Z_ Outersphere_tbottom_ "___,300 0 Outersphereattop
200_"rv" _ v ._ "_
1000 150 100 150 ZOO 250 300 350 4CTime,see
(hiOutersphereandheatertemperatureasfunctionoftime.
Figure5. - Continued.
_="R.w. _ ........ --
1967009809-056
47
A N'30 Ii
v R-5 [ I30C 0 R-4 [ __
o R-Z -- I _..__..--_ -Q R-I i __ _Seefig. 3for location .I,_,_ _ r_
loo/L /
0 50 100 150 200 250 300 3.50 400Time,sec
(c) Upperinnerspheretemperatureasfunctionofttme.
Figure5. - Continued.
I i IO R-I/ 1A R-18O Sat LH2,_ R-19 --
R-20O R-6
65 _ _,g, 10A R-IS. 12, ll
Seefig. 'or Iocatienortranstucers ,_-
_--_ -_ __4o _ .-.- I I
0 ._ IOC 150 200 250 300 350 400,_lme,sec
(d) Lowernner spheretemlxratureasfunctionc4,Im_
Figure5. - Cnncluded.
m_
1967009809-057
48
l_ II! I Itoe --_ --i
i/ iQ" 4/ m
4o 4/ l
i0 PO 100 1.50 200 2.50 300 390
Time,sec
(_'tTotalpressureasfunctionof time.
Figure_. - Testnumberfive.
[
OU
400 ...... 0 Lowerheater%7Outersphereatequator-_A Outersphereatb_,t_om1
300 0 Outersphereattop -j
1000 50 IO0 L I_ 200 250 300 3_
Time,sec ._(b)Outersphereandheatertemperatureasfunctionortime.5"-
Figure6.- Cont;nued. ,._
1967009809-058
49
, , , _ ,
Z_N-30_R-50 R-4[]R-30 R-2
250 a R-I L.
_Seefig. 3for location___ _
oftransduceFs _ _ .---
i0 50 I00 150 200 250 300 1950
Time,sec
(c)upper, lner spheretemperatureasfunctionoftime.
Figure6. - Continued.
! I I I I I-- []Sat LH2
.59-- 0 R-I/, 18,19,20a R-l, 8,9,10,11,15
--See fig. 3for location -- _...,C.--,,., 5(]-- of transducers I"o I J I I J I,-I
_. .J ...E
/ ._..__'_39
50 I_ 150 200 250 300 350Time,sec
(d)Lowerinner spheretemperatureasfunctionof time.
Figure6. - Concluded.
1967009809-059
CO
:° I ', / I _ o I_l li^[,ij i ! , I iI / Jl ' _ '-.._i I I , I J i i-I i ,
"_ 60 1 / 400 i i I j 'O Lowe'rheater -J/ I 0 Outersphereat top
I I I _ Outersphereat equator
_ a0 // -- _ 300"---_-l }I/! A 0utersphereatbottom -i"_ j I
2o -/ _ zoo
0 200 400 (_ 800 1_ 12011 0 200 400 _ 800 1000 1200Time,sec Time,sec
(a)Totalpressureasfunction of time. (b)Outersphereandheatertemperatureasfunctionof time.
Figure7. - Testnumberten.Figure7. - Continued.
N'-30'
/,,Z_ 0 R-I 50
/ I..._. Seefig. 3for _,_'_ _ -,'"_ 90 / _ '°cati°n°f _. r--_ _ OR'17- 45 -_. _ _...?..__. transducers h ---" A R-18 I
I--- 1C /_ _.._ E 0 Sat.LH2
/ _- _ OR-6,7,8,9,1o,-__ ..-_r 35 11,12,15 ____ ______---c--- I _Seef,g.3for,_t,on3
3(ll 200 400 _ 800 1_ 1200 200 400 600 800 10110 1200Time,sec Time,sec
(c)Upperinner spheretemperatureasfunctionoftime. (d)Lowerinner sphe;etemperatureasfunction oftime.
Figure1. - Continued.Figure7. - Concluded.
\
i
1967009809-060
51
i2o I [ 1I , /
lOO I jI /
• . f ji" J t JrUpperheater
/ _ 0 Outersphereattop40 / _ _ _ a Outersphereat bottom-
0 Outersphereatequator_i• _ 20020 x j
J I0 200 400 600 800 :000 lO00 200 400 600 800 i000
Time,se; Time,sec
(a)Totalpressureasfunctionof time. (b)Outersphereandheatertemperature;.sfunctionof time.
Figure8. - Testnumbersixteen.Figure8. - Continued.
I I I I [ |- _7 R-1I
O R-18
- O Sat. I.H2 -_"-_" 0 R-19
250 i _'"_ ---'-_ r,,R-20A," _ _ "_9"_"'- O R-6
--i // .--- A R-7,8,9,10
v _ ""- lO See fig. 3 for locationo= 200/,_'_ZF .-- _ _ r..>- oftransducers f "_ =_"_" 150 "" 6o I I I_I _.;r_ _ r_-3o' _ ji _/ - E7R-5 "_
nR-3 _ / i _ ;--'_
50 ! R-1 inoperative- _ 40_i;i_Q..__ .--.-_ ___Seefig. 3 forlocation_ _
i of transducers l, , , i , _0 200 400 600 800 lO00 200 400 600 800 lO00
Time,sec =;me.sec
(c) Upperinner spheretemperatureastunc- (d)Lowerinnerspheretemperatureasfunc-tionoftime. tlonoftime•
Figure8. - Continued. Figure8. - Concluded.
mr
1967009809-061
52
1_o I i
l® i //!
/ '/ I °_ Outersphereattop _.A'- / _ Outersphereatequ,_or
40 .1_ 300 _ Outersphereatbottom-
I// _E ,< ! _>_- 200_ _,,_ -..- _20 r ! --'_ v" v
0 100 )0 500 0 100 200 300 400 500Time,sec Time,sec
(a)Totalpressureasfunctionoft_me. (b)Outersphereandheatertemperatureasfunctionoftime.
Figure9. - Testnumbernineteen.Figure9. - Continued.
/x R-18_' N-30' ' ' CI LH2 I I I
- _7R-5 _ R-I9 --I----I---I------
_ o0 R-3- 0 R-2 80 [] R-l,8,g,IO I I- C..hR-I - /I R-11,12,15I
400_Seefig.3forlocation. Seefig.3forlocation .,0",oftransducers, 70 oftransduce,"s / "-""
' I i --, -- j
200//,, 0., _ & 5O
0 lO0 200 300 400 500 0 lO0 200 300 400 500Time,sec Time,sec
(c)Upperinnerspheretemperatureasfunc- (d)Lo_erinnerspheretemperatureasfunc-tionoftime. tionoftime.
Figure9. - Continued. Figure9. - Concluded.
. i
1967009809-062
53
/1oo--_-- i /
80--- /"'
"- J_ ...... t / i
B 60: .,_
/
20/'i I ] ---_0 _0 100 150 200 250 _00 350
Time,sec
(a)Totalpressureasfunctionoftime.
Figure].0.- Testnumbertwenty.
600L---7--_--- I I _ I {I v I 3--
Upperheater0 Outersphereattop
400-- O Outersphereatequator_= Q Outersphereatbottom
t ' t
) ,SO 100 150 200 250 300 350Time,sec
(b)Outersphereandheatertemperatureasfunctionoftime.
FiguretO.- Continued.
1967009809-063
54
X_-3o'' '___- _R-5- OR-4
[i]R-)© R-2
500_ ChR-1
_Seefig,)forlocation_oftransducers _- _ _ _:
400 ill I....-.J- ""u_t_::::'" "-"I_,-IF--'T_--L=_._.__>-
N
I
ii , 10 N I00 150 ', )00 350
Time,sec
(c)Upperinnerspheretemperatureas functionot time.
Figure10. - Continued.
lzo I | -100 _
-"0 R-17 C3 Sat, LH2 Seefig. ?for
20 _ R-18 _ R-6 locationof_7 R-19 0 R-7,8,9,10 transducers0 R-20 /I R-II.12,15
0 50 IO0 150 200 250 )00 350Time, sec
(d)Lowerinnerspheretemperatureasfunctionoftime.
Figure10. - Concluded.
1967009809-064
_5
100 Lowerheater ---I J
60 .... Upperheater-
,o t tHeattransfer
20 Radlant ------- Conductive
" I "I
_ '61 1_= .4 '---Plastic suoportring
_" _ Temperaturetransducerwires_= .1 , .
-r- ".2 \
-.4 \-.6 \
•.._ Venttube
0 lo0 2O0 300 40O 5OOTime,t, sec
Figure]1. - Rateofheatinputasfunctionof timeforeachheatsourcefortypicalquiescenttest.
l I I I l I I
O Topheating(q/A)avg.
lo0 3?.9percentfilling _ Platinuml_ _ I t_surface I ---tO Uniformheating(qlA)avg-_ _ ._145.8 Btu/(hr-ft2) )3' 5000-- temperaturetransducer_ '_-J I ) l I L,,," 1
80 83.5 percentfilling O_ _ t //_
,'E_.6040 I _2_ _ = \ " I/ r [ 1
":.Theoretical _ ._, 3000
e,,G"_\ ,._ _ - homogeneous =¢ _ /_. <_ _",_C)_," 83.5percent- i
;-Carbonreslsto -----_ -- LTheoretlcal' _filling _ 2000 / _ _ I temperaturetransducer
20_ , ; homogeneous -- _ I --• 37.g percent , 10O00 to0 200 300 400 500 6001 tilling Temperature,°R
0 4 8 12 116 ' 20 28Heatadded,Btu Figure13.- Resistanceasfunctionoftemperature
fortypicalInnerspheretemperaturetransducers.Figure12.- Pressureasfunctionoftotalheataddedfortwo
homogeneoustests.
1967009809-065
4L .
56
• , , _ • -1 i i r
InitlalHeatingcon- Averagepercentfigurationheatflux,
filling Btu/lhr.fl21i
_7 47.7 Upper 38.2 ,---2-51.2 Upper 27.6
D 50.5 Upper 17.1O 50.7 Uniform 111.60 48.9 Uniform 65.0
5].4 Unlform 18.2 _--'A 47.8 Lower 75,2 J0 49.0 Lower M 6 ! I
120 _, /_ J * "' * a ,Surfaceevaporaton,# /
=_ ;, 50percenifilling
.__g, _llJl _ I,"loo-- i _e ,-"
.- _' = _P / Homogeneous,
. _ 0 __i" ,," 50,rcentf,,°g-6o_2_.- !._.,-
20 p- l
I 10 4 8 12 16 20 24 28 32
H._tadded,Btu
(a)Effectof(',eat'._ansferrateanddistribution.
Figure14.- Pressureas functionof totalheataddedforquiescenttests.
I T T I [
SurfaceevapoFation I I I I I_ Homogeneous
- filling, 1 filling,__ ---_ percent _ percent
t20 /_6.5 /. /.9 , i
' ;1_ " ''100 / .i^ I .9 =, /48.9
iv / " l
i " JIJ / <>_ ." - :_.m " J '/" I! /,_% I i - .
7 _&_ " "
= I/_o" ;" ""=" 4(] " i /I /"C_".,.':""
_ Iq#Alaw• 72,6 Biullhr-flO, 76.5Ircent filling _, 2(] ir_ ---- A (q/llav_ 65.0 Btullhr-ftli, 48.9 percentfilling
O (q/A)a_ 59.gBtu/(hr-ft2),34,9percentfillingI I l.. l I I I I l I I l l
0 4 8 12 16 20 24 28Heatadded,Btu
(b)Effectofpercentfilling.
Figure14.- Concluded.
1967009809-066
$7
z° t ic1.6
• 91
-_ 1 ' IIt. 2 - Saturation v I Ltemperature ! ._[ _ 0 [
I_ Inner sphere35percentfull•4 0 Internal resistor,centrally located
i A Internalresistor,closetewallQ Platinumtransducers,outsidesurfaceofwall
_I i I I I , I
o _ i_o i_o 2_o 2_o 28oTemperature,°R
FigureiS. - Inner sphereh,mperatureasfunctionof positionfortypi-calquiescenttest.
2.0
1.6
._c I.2 -
._=
8
I(I II I I I l --'--10, Bottomheatingonly_.-_ ,,, , , , , _.._..._H-_---_o_f_,eat,n_ "-•4__-_ -- 19,To_heat,_?,y._
,,,,_, ,j ,___!_u,, _0_ 40 50 100 150 200 250 _0
Temperature,°R
Flgure16. - Innerspheretemper_ureasfunctionof_sltlon for threeheal-ingconfigurations.
mm m
1967009809-067
58
1.0 ---_-- heating,,i ._percenti
Fimng, mIIIiiI 8oi.8 upoer-- 501 .... Filling,. __
35( uniformheating,
, ____ percent.___
- .6-35_ __== .3;_,4 .....
0 20 40 60 8() 100 120 14C
(q/Ala_, Btu/lhr-ft2)
Figure17. - Homogeneityfactorasfunctionofaverageheattransferrate,
1.o Id,,'
.8 l"/
, /.6 "/-
•- i II._ #
/ IllI I I I I I | I
J ll Ex_, imental•2 / --_ Extrapolatedto emissivityj_
l ofbasematerialat0°Rl l [ [ I I 1 I 1
0 |l 300 400 500 (O0Temperature.'_R
Figure18. - Innersphereandheateremissivityasfunctionof temperature.
1967009809-068
m,
59
,2, i Ji Jl _¸
J Io= ! o ..... .
.06 0c.=
c k!.02 0 Referenc5-I-_
l JJJJ0 100 200 300 400 500 600
Temperature,°R
Figure19 - Stainlesssteelspecificheatas functionoftemperature.
.12 I I [ I I I I ] ]_ -- O Rel.5
- _ ]""_'- I0-- -- k-0.418T-0.814xlO-4T2_ i.I0 ./ " +6.25xIO-8T3 - _I
J•- .06 _ 6 ,. --
.04-- _ 4 / --
- I_ § ".02 --L- E) Experimental _ _ /
-- k-0.0712+1.85xI0-4T E 2 / ,
i i J I I i ] I0 50 I00 150 200 N 0 I00 200 300 400 500 600
lemperature,"R Temperature,°R
Figure20. - Plasticsupportringthermal Figure21. - Stainlessstee,thermalconductivityasconductivityasfunctionoftemperature, functionoftemperature.
1967009809-069