NBSIR 73-339

PRELIMINARY HYDROGEN FREEZING STUDIES

D. E. Daney

W. G. Steward

R. 0. Voth

Cryogenics Division

Institute for Basic Standards

National Bureau of Standards

Boulder, Colorado 80302

October 1973

Final Report

Prepared for

NASA Headquarters

Washington, D. C.

NBSIR 73-339

PRELIMINARY HYDROGEN FREEZING STUDIES

D. E. Daney

W. G. Steward

R. 0. Voth

Cryogenics Division

Institute for Basic Standards

National Bureau of Standards

Boulder, Colorado 80302

October 1973

Final Report

Prepared for

NASA Headquarters

Washington, D. C.

U.S. DEPARTMENT OF COMMERCE, Frederick B. Dent, Secretary

NATIONAL BUREAU OF STANDARDS. Richard W Roberts Director

CONTENTS

Page

1. Introduction [

2. Freezing Calculations 2

2. 1 Introduction 2

2.2 Thermal Conductivity of Solid Hydrogen 3

2. 3 Analytical 7

3. Experimental Program 19

3. 1 Introduction 19

3. 1. 1 Hydrogen System 19

3. 1.2 Helium Refrigerant System 20

3. 1. 3 Hydrogen -to-Helium Gas Heat Exchange

System 20

3.2 Preliminary Experiment 20

3.2.1 Procedure 20

3. 3 Results 22

3.4 Conclusions and Recommendations 26

4. References 31

5. Nomenclature 32

Appendix A. Cylinder Freezing from the Outside 34

Appendix B. Cylinder Freezing from the Inside 83

Appendix C. Sphere Freezing from the Outside 148

Appendix D. Linear Freezing 197

iii
LIST OF FIGURES

Page

Figure 2.1. Thermal Conductivity of Solid Hydrogen 14

Figure 2.2. Schematic Temperature Distribution during

One -Dimensional Freezing 15

Figure 2.3. Cylinder, Freezing from Outside 16

Figure 2.4. Cylinder, Freezing from Outside 17

Figure 2.5. Cylinder, Freezing from Outside 18

Figure 3. 1. Hydrogen Freezing Apparatus 29

Figure 3.2. Instrumentation Schematic 30

iv
Preliminary Hydrogen Freezing Studies

D. E. Daney, W. G. Steward, and R. O. Voth

The study summarized in this report is aimed at

developing the technology required to fill space vehicle

propellant tanks with solid hydrogen by in-place freezing.

Planned continuation of this work was terminated with the

loss of NERVA funding by the NASA. Therefore, progress

to-date is summarized but substantial experimental results

have not yet been obtained.

The program was to have been carried out in two

phases: a mathematical analysis and experimental verification of the analysis. Freezing times and heat flux have

been calculated for four geometrical shapes, and a range

of sizes, refrigerant temperatures, ortho-para concentrations, and heat transfer coefficients. The results of

these calculations are presented in generalized graphical

form, in a total of 240 graphs.

The freezing experimental apparatus has been built

and a preliminary test performed which generally demonstrates the validity of the analytical and experimental

approaches. With only minor modifications the apparatus

is ready for a full test program of hydrogen freezing and

melting techniques.

1. 0 Introduction

This study is aimed at developing the technology required to fill

space vehicle propellant tanks with solid hydrogen by in-place freezing.

The specific goals of this phase of the study are, first, to calculate the

freezing and melting rates of hydrogen for various geometries, refrigerant temperatures, and refrigerant heat transfer coefficients, secondly,

to measure hydrogen freezing and melting rates for a simple geometry

such as a cylinder, and finally and most important, to develop techniques

which yield a uniform and high density solid.
At this time, only the freezing rate calculations and the experimental apparatus have been completed. One preliminary hydrogen

freezing experiment has been performed which generally demonstrates

the validity of both the analytical and experimental approaches. With

only minor modifications, the apparatus is ready for a full test program

to study hydrogen freezing and melting techniques.

Termination of funding has temporarily halted this program, so

this report is a summary of our progress rather than a final report of

the completed study.

2. 0 Freezing Calculations

2. 1 Introduction

The choice of a mathematical model for the freezing of solid

hydrogen was governed by several considerations which indicated the

desirability of a relatively simple model of modest accuracy. First,

we are interested in a large number of combinations of geometry,

heat transfer coefficient, refrigerant temperature, and ortho-para

composition. Second, we are interested more in approximate answers

which might indicate the feasibility of a scheme, rather than precise

answers for a specific geometry and set of conditions. Third, even

detailed approximate solutions of the freezing problem are extremely

complex, and finally, the accuracy of the thermal conductivity data

for solid hydrogen is so poor that high accuracy in the mathematical

formulation is not justified at this time.

In general, the problem of calculating freezing rates is a

difficult one. The boundary conditions are non-linear, and only a few

exact solutions exist for one -dimensional problems with constant thermal

properties [Carslaw and Jaeger, 1959]. Numerical methods, or

approximate methods such as the integral technique, are generally

required for the solution of the freezing problem, and even then, the

calculations are usually complex. When we consider the calculation of
hydrogen freezing rates, the situation is complicated even further by the

strong variation of the solid thermal conductivity with temperature and

ortho-para composition. As indicated in figure 2. 1, this variation ex- ceeds two orders of magnitude over the range of 4K to 14K.

What effect does this temperature dependence of the thermal

conductivity have on freezing rates? The freezing rate is proportional to

f

Tw

J kdT where k is the thermal conductivity of the solid, T is the

freezing-point temperature, and T is the temperature of the refrigerated w

wall. For substances with constant k the freezing rate is then proportional to the temperature difference T - T . For hydrogen, however,

f w

a relatively small change in the temperature difference (T. - T ) can

f w

cause a large change in the value of the integral. For example, if T

w

is lowered from 6. 8K to 4. 8K (T is 13. 8K), AT increases by 28 percent

/if

kdT increases by over 300 percent for parahydrogen.

T

TJw

Thus, relatively small reductions in the refrigerant temperature can

result in substantially reduced freezing times.

2. 2 Thermal Conductivity of Solid Hydrogen

Because the accuracy of the freezing calculations can be no

better than the accuracy of the thermal conductivity data, a discussion

of the thermal conductivity of solid hydrogen is in order. The two

salient features of the thermal conductivity curves (figure 21) are the

strong dependence of the thermal conductivity on the temperature and on

the ortho-para composition.

The temperature dependence of the thermal conductivity is typical

of dielectric solids (see, for example, Rosenberg, 1963). At the high

temperature end of the curve, the thermal resistance (l/k) is dominated

by Umklapp (U) processes (phonon-phonon scattering). For T £ 0/10 but

T greater than where the conductivity is maximum, U processes require

3
k ~ exp (9/gT) where 9 is the Debye temperature (9 = 116K for

[Rosenberg, 1963]) and g is a numerical factor whose value is about 2. Thus at sufficiently low T the conductivity should undergo an exponential rise with decreasing temperature. At higher temperatures

T 2" 9 , U processes require k ~ l/T, and in the range in between 9 and

9/10, one would expect a gradual change from a l/T behavior to an exp

(9/gT) behavior in k.

The complete disapearance of the thermal resistance as the

temperature is decreased is prevented by other phonon scattering

_3

processes, such as grain boundary scattering (1/k ~ T ), which increase with decreasing temperature. The characteristic humped thermal conductivity curve is thus a result of the interplay of these different phonon scattering mechanisms.

The dependence of the thermal conductivity of solid hydrogen on

the ortho-para composition, is believed to arise from a process not

generally encountered with dielectric solids. We quote from Hill and

Schneidmesser [1958] who first measured the thermal conductivity of

solid hydrogen. "A process which may also contribute appreciably to

thermal resistance arises when molecules can make transitions between

states of different energy. In the simple case when the molecules can

exist in two states separated by an energy E, transitions can be excited

between these states by the absorption or emission of phonons of energy

sufficiently close to E. Since this scattering process is effective in

only a small part of the phonon spectrum, the contribution to the total

thermal resistance will be small; comparatively little importance has

therefore been attached to it. However, in a substance whose molecules can make transitions corresponding to a wide range of values of

E, an important contribution to the thermal resistance is possible at

suitable temperatures. Solid hydrogen is believed to be a substance of

this type. "
In figure 2. 1 the dashed lines represent extrapolations of the

data beyond the range of measurements. The extrapolated curves are

anchored to the thermal conductivity for solid deuterium measured by

Daney [1971} rather than the measurements of Dwyer, Cook, and

Berwaldt [1966] for solid parahydrogen. There are several reasons

for this choice. The measurements of Dwyer, Cook, and Berwaldt were

at elevated pressure (88-201 atm), and the relatively high compressibility of solid hydrogen [Lander, et al. , 1966] might give rise to a strong pressure dependence in the thermal conductivity similar to that

observed by Webb, Wilkinson, and Wilks [l952] in solid helium. In

addition, the measurements appear to be of rather low accuracy, since

measurements on liquid H made in the same apparatus [Dwyer, et al. , 1966] are about 200% higher than recent measurements reported by Roder

and Diller [l970]. All of the curves should converge at high temperature

since the ortho-para phonon scattering disappears at higher temperatures

[Daney, 1971; Hill and Schneidmesser, 1958]. A curious set of high temperature curves results if the Hill and Schneidmesser curves are extrapolated to the Dwyer, Cook, and Berwaldt points.

Hill and Schneidmesser [l95 6] note that their conductivity curve

for normal deuterium (33% para) was very similar to the corresponding

curve of hydrogen (33% ortho). On the basis of this information, we

chose the deuterium measurements of Daney [l97l] as the anchor for the

higher temperature curves. A smooth and natural appearing extension

of the thermal conductivity curves results.

5
Contreras and Lee [l972] have recently reported values for the

thermal conductivity of solid hydrogen based on a transient measurement

scheme. At higher temperatures near the triple point their measurements

fall considerably below the values selected here, but at lower temperatures their measurements and our selected values are in much better

agreement. They attribute this discrepancy primarily to hairline cracks

which were observed in their solid. Although cracks would cause an

additional thermal resistance, this resistance should remain approximately constant over a range of temperatures. Because thermal resistances are additive, the thermal conductivity curve for cracked solid

hydrogen should deviate from the uncracked curve most where the conductivity is the highest. A much flatter conductivity curve would result.

This predicted behavior is opposite to the behavior of the Contreras and Lee

data. Excessive radiation heat leak into their solid sample seems a more likely explanation for this discrepancy.

The uncertainty in the Hill and Schneidmes ser data is estimated

to be no greater than 10 percent, with less uncertainty for the higher

conductivities. The uncertainty in the deuterium measurements is

estimated to be less than 5 percent. The uncertainty in the extrapolation

is no more than an educated guess, but we estimate it to be on the order

of 20 percent. The agreement between the Hill and Schneidmesser data

and the Bohn and Mate data is excellent along the right hand portion of

the curves before the bend over to the conductivity maximum occurs.

The maximums of the curves, however, differ by a factor of 3 for nearly

the same composition. This discrepancy is probably due to different

impurity levels or sample preparation techniques, and it should be

considered as a variation that may be encountered in practice. It should

be noted that for hydrogen with an ortho content less than 1 percent, this

variation in the thermal conductivity will only become significant below

6K.

6
2. 3 Analytical

Only one -dimensional or radially symmetric cases arc treated

because of the considerations discussed previously. Those cases

chosen were: freezing a one -dimensional slab, freezing an infinitely

long cylinder from the outside, freezing an infinitely long cylinder from

the inside, and freezing a sphere from the outside. Expressions are

presented for both freezing with constant wall temperature, and freezing

with constant refrigerant temperature and heat transfer coefficient.

Calculations were performed for only the latter case, since in practice

it is almost impossible to freeze with constant wall temperature; however,

as the heat transfer coefficient increases, the solution to the constant

heat transfer coefficient problem approaches that of the constant wall

temperature problem.

The physical model assumed for the constant heat transfer

coefficient calculations is shown in figure 2. 2. Heat is removed from

the freezing hydrogen by a stream of cold helium gas with a constant

temperature, T , and a constant heat transfer coefficient, h. The

wall temperature, T , is allowed to float at whatever value is required w

by the process. The heat capacity of the solid is neglected and the

liquid temperature is fixed at the melting point.

The error introduced into the calculations by neglecting the heat

Tf - Tw capacity is approximately equal to C where C is the specific

p 21 p ^ heat of the solid hydrogen. For hydrogen, this error should never exceed

10 percent, and the resulting simplification of the calculations is enormous.

The overall accuracy of the calculations is estimated to be about 20 percent,

when the accuracy of the thermal property data is considered also. For

refrigerant temperatures below 5 K or ortho contents above one percent,

the disagreement with experiment could be larger than 20 percent due to

the variability from sample to sample in the thermal conductivity of solid

hydrogen in this region.

7
To illustrate the method, we will derive the expression

for one -dimensional linear freezing with constant heat transfer coefficient.

The results for the other cases will then be summarized.

Case I. Linear one -dimensional freezing with constant heat transfer

coefficient and constant refrigerant temperature . Refer to figure 2„ 2 for the physical model. The heat transferred

in the various zones is

dT Q = -kA "

(1) dx

in the solid, >

dX

Q = -P^A— (2)

at the liquid-solid interface, and

Q = -hA (T - T ) (3) w o

at the helium side of the wall. The upper case X refers to the position

of the liquid- solid interface, whereas the lower case x refers to any

position in the solid.

Equating (1) and (2) we obtain

dX kdT = pi — dx. (4)

If we now integrate (4) from the wall to the liquid-solid interface, we

obtain

T,

f X

/ kdT f pi ^rr dx, or * J dt T o w

A. pi X dX

dt = — • (5)

t/

f kdT

w

8
Since T varies with time or position of the interface, f kdT

W rj. w

also varies and equation (5) cannot be integrated.

In order to evaluate / kdT, we must find T . Equating

Tw

1) and (3) we obtain

h(T - T ) = k ~- „ (6;

w o dx

Integrating (6) from the wall to the liquid-solid interface yields

X T

f h (T - T ) dx = f kdT, J wo J

© T

w

or solving for T , w

T

T = T + t^t f

f kdT. (7:

w o hX J

w

In equation (7) T is obtained as a function of the liquid-solid interface

position, X, and not as an explicit function of time.

Equations (2), (3), (5), and (7) can now be used to numerically

obtain the time history of the liquid- solid interface, and the time history

of the heat transfer rate Q. The procedure is as

follows:

1. Divide the length to be frozen into a number of even intervals

(100 in this work).

2. Obtain the initial heat transfer rate from (3) by assuming the

wall to be at the freezing temperature, i. e. ,

(Q/A)

1 = h (T

f

- T

q

)

(values of h are assumed).

3. Calculate the initial value of (At/AX) from equation (2)

9
4. Obtain the wall temperature, T , at the remaining w

positions by iteration from equation (7).

5. Calculate (At/ AX) for the remaining positions using

equation (5) and T obtained in step 4.

w

6. Calculate the heat transfer rate at each position using

equation (3).

7. Obtain the total elapsed time at any position by integrating

the values of At / AX calculated from steps 2 and 5.

Case II. Freezing an infinite cylinder from the outside with constant

heat transfer coefficient and constant refrigerant temperature.

A derivation in cylindrical coordinates analogous to that of

case I yields:

dt 9l R

R

R

m r

Tf kdT

w

R R

R R

o o

T = T

w o hR In

R

o R

o T

kdT

w

7a)

T- = 2tt h R (T - T ) L o w o

3a)

_ , ^ „ „ dR Q/L = -2tt pl.R —dt

2a)

Case III. Freezing an infinite cylinder from the inside with constant

heat transfer coefficient and constant refrigerant temperature.

2

T R R

(5b)

dt pi R

(R \ T ~) T^*

f kdT

o w

R , R

R~ ln R~

o o J

10
T

T =T + /* f kdT (7b) w o , _ , R ^ /

h R In ~— TJ

s o R w

o

Q/L = -2nR h (T - T ) (3b) o w o dR Q/L = -2tt pi R — (2b)

Case IV. Freezing a spherey from the outside with constant heat transfer coefficient and constant refrigerant temperature.

An analogous derivation in spherical coordinates yields:

2

z T

5c)

T = T + =- — I kdT (7c) w o

- 'I'X - ']

J'

w

•~ = 4tt R h (T - T )

( 3c) R o w ov

' o^ 2 dR Q = -4tt pi R (2c)

The following three cases are for constant wall temperature, T . w

When T is held constant, equation (5) (or the corresponding equation for

w

cylindrical or spherical coordinates) can be integrated analytically, because I kd T is also constant. The resulting expression for the time,

w

t, required to freeze a thickness of solid, X, is as follows:

11
Case V. Linear one -dimensional freezing with constant wall

temperature.

t = (5d)

2 /

f kdT

T

w

Case VI. Freezing on infinitely long cylinder with constant wall temperature from the inside or outside.

t = cl *°

( t Iz^Mn » + - II «,l I > (5e

Tf f kdT

w

Case VII. Freezing in sphere from the outside with constant wall

temperature.

2 3 2

Dl R

t = —2 ^ Tf f kdT

w

The results of a typical set of calculations are shown in

figures 2. 3, 2. 4, and 2. 5. Because of the choice of parameters, the

results are independent of size and may thus be applied to any size

cylinder, sphere, or flat plate. Figures 2.3 and 2.4 are

self explanatory; they merely give the dimensionless

position of the liquid solid interface and the heat transfer rate as a function of the time parameter for various heat transfer coefficient

parameters.

Figure 2. 5 requires some explanation. When consideration is

given to sizing a refrigerator for a particular solid hydrogen freezing

application, one observes that the refrigeration requirements are

initially very high. Rather than sizing a refrigerator to these high

12
initial requirements, a more reasonable approach would be to size the

refrigerator as small as is consistent with freezing the hydrogen in the

required time. The curves in figure 2. 5 show the time required for

complete freezing of a cylinder if the maximum refrigeration available

is limited to QM. The nearly vertical portions of the curves are a region where large reductions in refrigeration capacity may be achieved

with insignificant increases in the freezing time. A refrigeration

capacity lying in this region would be oversize. The common asymptote

is a refrigeration limited region, i. e, , the freezing time depends only

on the refrigeration rate and not on the heat transfer coefficient.

The complete set of calculated freezing curves for the various

combinations of geometry, ortho-para composition, and refrigerant

temperature are given in the appendices. It should be noted, that if the

wall of the vessel has a significant thermal resistance, then the overall

heat transfer coefficient, U, should be used in place of the film or surface heat transfer coefficient h.

13
B
Figure 2. 2 Schematic Temperature Distribution during One -Dimensional

Freezing.

15
i i

i i

i t » > » I ^

o c:> o> <lz> * >

H/H = Cd/d

16
(VI.o

01

1 c

£

o

cr

O

CLO

CO

O

o

CO

o

or

UJ

a

Lack: o

•rH

'I/O

17
TV D= UO/fl "|/WC

18
3. 0 Experimental Program

3. 1 Introduction

The experimental apparatus for freezing of hydrogen has been

completed and tested. The assembly drawing ( figure 3. 1) and description of the apparatus are presented here. All the basic features

are shown in figure 3. 1 with the exception of the liquid nitrogen shield

dewar and external instrumentation. The instrumentation and piping

are shown schematically in figure 3.2. In section 3. 1. 1 the numbers

in parentheses refer to the legend of figure 3. 1.

3. 1. 1 Hydrogen System

1. A hydrogen freezing chamber (27) has walls made

of 0. 127 mm (0. 005 inch) plastic (polyethylene terephthalate

film) to minimize thermal resistance while allowing a clear

view of the freezing hydrogen.

2. A standpipe (18) is located above (and connected to)

the freezing chamber, to serve as a liquid hydrogen reservoir

during freezing. The fall in liquid level, as indicated by the

capacitance level gage, provides an indication of the reduction

in volume of the hydrogen in the freezing chamber. From this

liquid level reading, the mass of hydrogen solidified and the

rate of freezing at a given time can be determined. The freezing

rate provides one indication of the heat flux. A heater (21) on

the standpipe prevents solid hydrogen blockage of the passageway

leading into the freezing chamber.

3. A hydrogen chamber (3) at the upper end of the apparatus acts as a radiation shield and source of precooling refrigerant.

19
3. 1. 2 Helium Refrigerant System

1. The liquid helium bath (7) provides the refrigeration

for freezing the hydrogen.

2„ The variable speed blower (4) circulates helium heat

exchange gas by variable paths as indicated by the arrows in

figure 3. 1.

3. A rotary valve (16) at the blower discharge allows a choice or combination of two possible paths for the helium gas,

thus controlling the helium gas temperature and the freezing

rate: For maximum refrigeration, all of the flow may be

diverted through the ribbon packed heat exchanger (13) communicating with the liquid helium bath. For minimum refrigeration,

the flow may be routed through the inner passage which is insulated from the liquid helium bath. This passage is also provided with a heater (9) to enable thawing the hydrogen. Intermediate degrees of refrigeration may be obtained by splitting

the helium gas stream in any proportions desired.

3. 1. 3 Hydrogen-to -Helium Gas Heat Exchange System

Cold helium gas is routed around the outside of the pyrex

baffle (24), then upward next to the freezing chamber. Refrigeration

is restricted, as far as possible, to the vertical walls of the freezing

chamber by means of the foam insulating blocks (23) and vacuum jackets

surrounding the liquid and gaseous hydrogen containers.

3. 2 Preliminary Experiment

3. 2. 1 Procedure

A preliminary experiment was performed to test the

apparatus, instrumentation, and operating procedure. The procedure

was as follows:

20
1. The freezing cylinder was purged, first with helium,

then with hydrogen gas. The helium system was purged with

helium gas.

2. Hydrogen gas for condensation into the freezing

chamber was supplied by evaporation from liquid to ensure the

composition being nearly equilibrium para-hydrogen. The

freezing chamber was pressurized to 9 psig.

3„ The pre-cooling chamber above the blower housing

was temporarily filled with liquid nitrogen. (Liquid hydrogen

would normally be used for pre-cooling). The liquid nitrogen

shield dewar surrounding the liquid helium dewar was filled,

and the system was allowed to pre-cool to 76K with the blower

operating at low speed. The pre-cooling chamber was then

purged and pressurized with helium gas.

4. The vacuum space in the hydrogen standpipe was

pressurized with helium gas to provide heat transfer from the

hydrogen gas entering the freezing chamber.

5. The liquid helium dewar was filled to the top of the

heat exchanger, the blower speed was increased, and the

freezing chamber and standpipe were condensed full of liquid

hydrogen. (Unintentionally, some freezing occurred simultaneously with condensation).

6. The standpipe vacuum space was evacuated to prevent further heat transfer in the area of the capacitance liquid

level sensor.

7. The temperature of the helium gas refrigerant was

lowered and the remainder of the hydrogen was frozen.

21
8. Thawing was initiated at the top of the cylinder bymeans of the standpipe heater. After a liquid pool had formed,

the helium gas temperature was raised above the thawing point.

A problem connected with this thawing procedure is discussed in

Section 3. 3.2.

3. 3 Results

The primary purpose of this experiment was to test the apparatus, instrumentation and operating procedure, and to assess the need

for changes. Additional recording equipment and refinements of the

procedure will be required in order to obtain accurate and complete data;

however, the following preliminary data were obtained:

3

(1) Helium gas flow rates ranging from 0 to I960 cm Is

were measured.

(2) Helium gas temperatures down to 6. 2K were obtained.

This was achieved with a pump speed of only 5, 500 RPM (rated

speed is 10, 700 RPM). Thus, even lower temperatures can

easily be attained by increasing the pump speed. Control of

the temperature through any desired range for condensing,

freezing, or thawing was possible through variation of the liquid

helium level, pump speed (gas flow rate), helium gas flow

splitter valve position, heater current, or combination of these

factors.

During this test we experimented with variation of all

the control factors in order to gain experience with the operating characterisitic s and capabilities of the apparatus. As

a result, the conditions were unsteady and heat transfer calculations are only estimates based on averages. Further, we

found that helium gas temperature was quite sensitive to the

liquid helium bath level; therefore, in future tests it will be

necessary to maintain a constant bath level through continuous

22
replenishing rather than periodic replenishing of the bath.

Because of temperature fluctuation, some undesirable freezing

and thawing took place during condensation. The formation of

solid hydrogen during condensation interferes with the intended

use of the standpipe liquid level sensor as an indicator of the

fraction of volume solidified. The freezing must begin onlyafter the entire freezing chamber and standpipe volume have

been filled with liquid in order to approach a radial progression

of the solid-liquid boundary. This pattern would allow comparison with freezing calculations for cylinders. Therefore,

maintenance of a constant coolant temperature during condensation just above the hydrogen freezing point (13. 8K) will be an

objective in future tests.

(3) An average heat transfer rate during condensation was

calculated from the rate of condensation and this was compared

with a prediction based on a correlation for the outside convection coefficient. (Verification of heat transfer correlations will

be essential to the design of large scale equipment for solidification of hydrogen. )

(a) 14. 7 grams of hydrogen were condensed in 1620

seconds from initially room temperature gas. Approximately 60% was solidified simultaneously. The resulting

average heat transfer rate was approximately,

Q = 37. 4 W.

(b) A heat transfer coefficient was calculated from

forced convection correlation for double pipe heat exchangers with heat transferred through the inner wall

only (Grober, Erk, Grigull, (1961), p. 263).

23
1 Nu = 0. 021 (Re)

0" 8

(Pr)

3

(§*) " ""(2>) " (3. 1)

1 ^W

3 For an average helium flow rate of V = 704 cm Is,

hydraulic diameter D = D - D. = 0. 2 cm, flow area

2 e o i A = 2. 67 cm , and helium bulk temperature T =

f bHe

10. 8K, the heat transfer coefficient resulting from

equation (3. 1) is

W

0. 45 . 0. 14

h = 0.024

cm K

W

Temperature T was measured on the inner wall of the

w

plastic (polyethylene terephthalate film) cylinder. Allowing for temperature drop through the wall, we obtain,

Q = A

h -

ATI>H«>

. S 1 5

1 +h —

K w

Heat transfer surface area A was assumed to be the

s area of the unfilled portion of the cylinder.

Average T during condensation = 20K • w

^ A (cylinder empty) = 398 cm . so

5 thickness of cylinder wall = 0. 005 in = 0. 0127 cm . k thermal conductivity of the wall material = 0. 001

w cm* K

Then

Q = 67. 1 W (cylinder empty)

o

= 22. 4 W(at the end of measurement period).

Due to the dependence of q on A

g

, the time averaged Q

is: Q - Q,

Q = ° - = 40. 7 W

(as compared to 37. 4 watts calculated from condensation

rate).

24
(4) Comparison of experimental radial freezing rate with

prediction:

The rate at which the solid-liquid boundary progressed

inward was observed at one axial location in the cylinder.

The time required for the boundary to move from the wall to

the center was

At = 15 min or 900 seconds

R (radius of the cylinder) = 4. 13 cm . o During the freezing period h as calculated from eq. (3.1) was

W

h = 0. 028 2"

cm K

hR = 0. 116 . o From Appendix A for a cylinder freezing from the outside with

a refrigerant at 10K, 1 percent ortho -hydrogen and hR = 0. 116

o we find

At — = 41,

R

D

from which

At^ = 699 s or 11. 6 min.

(as compared to 15 min observed).

(5) The thawing procedure as outlined above resulted in a broken plastic test cylinder. Even though thawing was initiated

from the top by means of an electrical resistance heater and a pool of liquid had formed, the cylinder cracked when the helium

gas temperature was raised above the thawing point. Since

the warmer gas passed upward over the cylinder, thawing began at the bottom where no path was open for the expanding

liquid to discharge.

25
As a possible remedy for this problem an electrical resistance

heater could be installed along the cylinder axis. The heater

would extend into the standpipe reservoir so that melting

would begin along a line leading into the discharge tube and

progress outward from that line.

3.4 Conclusions and Recommendations

A preliminary test indicates that the hydrogen apparatus may

be used to obtain heat transfer and phase transition data which will pertain to the design of large scale solidification equipment. Control of

the amount of refrigeration or heating over a wide range was possible

through variation of the helium heat exchange gas flow rate, or by

routing the gas through or away from a liquid helium heat exchanger.

Therefore, data could be obtained for a wide range of conditions.

For one set of conditions approximate calculations indicate

that a standard heat transfer correlation adequately predicts the heat

transfer coefficient between the freezing chamber and the refrigerant

gas. (Conditions were not sufficiently steady during this preliminary

test to obtain accurate heat transfer data, however. ) The rate of

freezing as calculated from one of the graphs discussed in the preceding

section predicted a freezing time within 25% of the observed time.

These tentative results indicate the freezing rate calculations will be

applicable to the design of hydrogen solidification equipment.

The results of the preliminary test have led to the following

proposed changes to be made in the apparatus and operating procedure

for future tests:

26
(1) Liquid helium should be replenished continuously in

order to provide constant rate of heat transfer. This will

enable refrigerant conditions to be held steady and controlled

more precisely to prevent freezing and thawing during condens ation.

(2) Data acquisition should be automated this will permit

the operator's attention to be focused on controlling the apparatus.

(3) An electrical resistance heater should be installed

along the axis of the freezing cylinder extending into the discharge tube. A broken test cylinder resulted from attempts

to thaw from the outside wall. The central heater would create

a path through which the expanding liquid could escape through

the discharge tube.

27
Legend for Figure 3. 1

1. Helium Blower Motor.

2. Helium Blower Shaft.

3. Liquid Hydrogen Radiation Shield.

4, Helium Blower Impeller.

5, Internal Gear.

6. Helium Flow Control Valve.

7. Liquid Helium Bath.

8. Direction of Helium Gas Flow.

9. Heater.

10. 6-InchI.D. Pyrex Dewar.

11. Flow Meter (Venturi in Final Design).

12. Dewar Vacuum Space.

13. Heat Exchanger (4-1/8 O. D. x 0. 095 inch wall copper tube with

3/8 inch fins at 1 / 4 inch spacing outside, ribbon packing inside).

14. Fill Line Heater.

15. Co- Axial Capacitor Leads.

16. Vacuum or He Transfer Gas.

17. Fill Line.

18. Standpipe with Concentric Tube Capacitor for Liquid Level Meas.

19. Vacuum.

20. Liquid Hydrogen.

21. Heater.

22. 4-Inch Pyrex Dewar With Stainless Steel-to-Pyrex Joint.

23. Foam.

24. Pyrex Baffle.

25. Germanium Thermometer.

26. Gold Iron vs. Copper Differential Thermocouple (Typical).

27. freezing Hydrogen.

28. 82 mm O. D. x 0. 005 Inch Plastic (polyethylene terephthalate film)

Cylinder.

28
8- -
30
4. References

1. Bohn, R. G., and Mate, C. F. , Phys. Rev. B2, 2121 (1970).

2. Carslaw, H. S. , and Jaeger, J. C, Conduction of heat in solids,

2nd Edn. , 283 (Oxford University Press, London, 1959).

3. Contreras, W. , and Lee, M. , Melting characteristics and bulk

thermophysical properties, Technical Report AFRPL-TR72-48, Grumman Aerospace Corp. (1972).

4. Daney, D. E. , Cryogenics, 11_, 290 (1971).

5. Dwyer, R. F. , Cook, G. A. , and Berwaldt, O. E. , J. Chem.

Eng. Data, 1L, 351 (1966).

6. Grober, H. , Erk, S, , and Grigull, U. , Fundamentals of heat transfer, 3rd Edn. , McGraw-Hill Book Co. , Inc. , New York, N. Y. , (1961).

7. Hill, R. W. , and Schneidmes ser, B. , Bull. IIF, Annexe 2, 115

(1956).

8. Hill, R. W. , and Schneidmes ser , B. Z. , Physik. Chem. Neue

Folge, 16, 17 (1958).

9. Lander, H. R. , Dwyer, R. F. , and Cook, G. A. , Advances in Cryogenic

Engineering, U_, 261 (Plenum Press , New York, N. Y. , 1966).

10. Roder, H. M. , and Diller, D. E. , J. Chem. Phys., 52_, 5928

(1970).

11. Rosenberg, H. M. , Low temperature solid state physics (Oxford

University Press, London, 1963).

12. Webb, F. J. Wilkinson, K. R. , and Wilk s, J., Proc. Roy. Soc. , A214, 546:63 (1952).

31
NOMENCLATURE

Text Figure

Symbol Symbol

area, cm

A fluid flow cross sectional area, cm

A surface area, cm s C specific heat, j/g

p

D hydraulic diameter = D - D.. cm e

3 o 1' D. inner diameter of annulus, cm 1 D outer diameter of annulus. cm o E energy, j

g numerical factor

2 h h convective heat transfer coefficient, W/cm *K

k thermal conductivity, W/cm-K

I latent heat of fusion, j/g

L L cylinder length, cm

N Nusselt number = hD /k,

u e b

P_ Prandtl number = C u/k, r p b

Q Q heat transfer rate, W

QM QM maximum heat transfer rate, W

r radius, cm

R R radial position of the liquid -solid interface, cm

Re Reynolds number = pVD/p.

RI radius of refrigerated wall for cylinder freezing

from inside, outward, cm

R radius of refrigerated wall, cm o

6

RO radius of refrigerated wall for cylinder freezing

from outside, inward, cm

t T time , s T temperature, K

32
NOMENCLATURE (continued)

melting-point temperature , K

refrigerant temperature, K

T wall temperature , K w c

2 U overall heat transfer coefficient, W/cm *K

v fluid velocity, cm/s

• 3 / V volume flow rate, cm /s

x distance from wall, cm

X distance of liquid-solid interface from wall, cm

6 wall thickness, cm

[L viscosity, g/cm-s

9 Debye temperature, K

p density, g/cm^

SUBSCRIPTS

b bulk fluid property

w fluid property at wall or property of the wall

material

33
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FORM Nbi-i 14A (1-71) U.S. dept. of comm. 1. PUBLICATION OR REPORT NO. 2. Gov't Accession

BIBLIOGRAPHIC DATA NBSIR 73-339 N°*

3. Recipient's Accession No.

4. TITLE AND SUBTITLE

PRELIMINARY HYDROGEN FREEZING STUDIES

5. Publication Date October 1973

6. Performing Organization Code

7. AUTHOR(S) o TP TtonAir Tsr r* cj.„,T ,-, j . j _ ^ jjaney, w. vj. oteward, and.

R. O. Voth 1

ft Pprformin o Organization

9. PERFORMING ORGANIZATION NAME AND ADDRESS

NATIONAL BUREAU OF STANDARDS, Boulder Labs.

DEPARTMENT OF COMMERCE

10. Project/Taslc/Work Unit No. 2750550

11. Contract/Grant No. NASA W13, 300

12. Sponsoring Organization Name and Address

NASA Headquarters, Washington, D. C.

13. Type of Report & Period

Covered

Final

14. Sponsoring Agency Code

IS. SUPPLEMENTARY NOTES

ABSTRACT (A 200-word or less factual summary of most significant information. If document includes a significant

bibliography or literature survey, mention it here.) The study summarized in this report is aimed at developing the technology

required to fill space vehicle propellant tanks with solid hydrogen by in -place

freezing. Planned continuation of this work was terminated with the loss of

NERVA funding by the NASA. Therefore, progress to-date is summarized but

substantial experimental results have not yet been obtained.

The program was to have been carried out in two phases: a mathematical

analysis and experimental verification of the analysis. Freezing times and heat

flux have been calculated for four geometrical shapes, and a range of sizes,

refrigerant temperatures, ortho-para concentrations, and heat transfer coefficients

The results of these calculations are presented in generalized graphical form, in a total of 240 graphs.

The freezing experimental apparatus has been built and a preliminary test

performed which generally demonstrates the validity of the analytical and experimental appraoches. With only minor modifications the apparatus is ready for a

full test program of hydrogen freezing and melting techniques.

17. KEY WORDS (Alphabetical order, separated by semicolons)

Freezing rates; solid hydrogen; thawing; thermal conductivity

18. AVAILABILITY STATEMENT

FH UNLIMITED.

FOR OFFICIAL DISTRIBUTION. DO NOT RELEASE

TO NTIS.

19. SECURITY CLASS

(THIS REPORT)

UNCL ASSIFIED

21. NO. OF PAGES

20. SECURITY CLASS

(THIS PAGE)

UNCLASSIFIED

22. Price

USCOMM-DC 66244. P71



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