SELF PRESSURIZATION OF LIQUID HYDROGEN TANKAGEedge.rit.edu/edge/P07109/public/tank pressurization/self pressurizati… · LIST OF ILLUSTRATIONS Figure 1 - Tank pressure as function

/

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)

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1967009809

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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.

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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.

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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

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1967009809-004

LIST OF TABLES

Table 1 - Summary of experimental results and heat transfer analysis

Table 2 - Results of energy distribution anaiysis

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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.





Figure 6 - Test number five.


(o) Outer sphere and heater temperature as function of time.



Figure 7 - Test num Oer ten.



(c) Upper inner sphere temperature as function of time,


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1967009809-006

Figure 8 - Test number s',xteen.





Figure 9 - Test number nineteen,





Figure 10 - Test number twenty.


(b) Outer sphere and heater temperature as a 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.

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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

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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

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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.

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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

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1967009809-014

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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

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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.

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1967009809-019

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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

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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

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1967009809-022

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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

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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

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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.


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.


! 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.


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

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