Library, B.». Bldg

MAR 1 1 1965

Unical ^lote 9fe. 227

THE JOULE-THOMSON PROCESS IN CRYOGENIC

REFRIGERATION SYSTEMS

J. W. Dean and D. B. Mann

U. S. DEPARTMENT OF COMMERCE

IATIONAL BUREAU OF STANDARDS
THE NATIONAL BUREAU OF STANDARDS

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NATIONAL BUREAU OF STANDARDS

technical <7i©te 227

Issued February 14, 1965

THE JOULE THOMSON PROCESS IN CRYOGENIC

REFRIGERATION SYSTEMS

J. W. Dean and D. B. Mann

Cryogenics Division

National Bureau of Standards

Boulder, Colorado

NBS Technical Notes are designed to supplement the Bureau's regular publications program. They provide a means for making available scientific data that are of transient or limited interest. Technical Notes may be

listed or referred to in the open literature.

For sale by the Superintendent of Documents, U.S. Government Printing Office Washington D.C. 20402

Price: 30 cents

CONTENTS

PAGE

ABSTRACT 1

1. INTRODUCTION 1

2. NOMENCLATURE 2

3. PROPERTIES OF FLUIDS 3

4. JOULE-THOMSON EXPANSION PROCESS 8

5. PROCESS DISCUSSION 10

6. METHOD OF PERFORMANCE RATING 13

7. CALCULATIONS 15

8. DISCUSSION 21

9. REFERENCES 38

LIST OF FIGURES

FIGURE PAGE

1. Helium Inversion Curve 4

2. Para-Hydrogen Inversion Curve 5

3. Nitrogen Inversion Curve 6

4. Joule- Thomson Expansion Process 9

5. Schematic of Refrigeration System 11

6. Heat Exchanger Cooling Curve - General Case 18

7. Generalized Performance Surface for a Joule-Thomson

Refrigeration System 22

m
8.

20.

LIST OF FIGURES (CONTINUED) PAGE

Refrigerator Performance - Helium Gas -(T -T ) = 0. 0°K ... 25

1 5

9. Refrigerator Performance - Helium Gas-(T -T ) = 0. 25°K . . 26

1 5

10. Refrigerator Performance - Helium Gas-(T.-T) = 0. 50°K . . 27

1 5

IT. Refrigerator Performance - Helium Gas-(T -T ) = 0. 75°K . . 28

1 5

12. Refrigerator Performance - Helium Gas-(T -T ) = 1. 0°K ... 29

1 5

13. Refrigerator Performance - Para-Hydrogen-(T -T ) = 0. 0°K . 30

1 5

14. Refrigerator Performance - Para-Hydrogen-(T -T ) = 1. 0°K . 31

1 5

15. Refrigerator Performance - Para-Hydrogen-(T -T ) = 2. 0°K .32

1 5

16. Refrigerator Performance - Para-Hydrogen-(T -T ) = 3. 0°K . 33

1 5

17. Refrigerator Performance - Nitrogen Gas-(T -T)

1 5 — 0. K • • 34

18. Refrigerator Performance - Nitrogen Gas-(T -T ) = 2. 0°K . . 35

J- 5

19. Refrigerator Performance - Nitrogen Gas-(T -T ) = 5. 0°K . . 36

Refrigerator Performance - Nitrogen Gas-(T -T ) = 10. 0°K . .37

IV
The Joule -Thorn son Process in Cryogenic Refrigeration Systems

J. W. Dean and D. B. Mann

A comprehensive analysis of the Joule-Thomson process as

applied to cryogenic refrigeration systems is presented. The

descriptions of the process already in the literature are usually

for specific applications. In contrast, performance characteristics

are presented here for helium, para-hydrogen, and nitrogen operations

over a large range of process parameters.

1. INTRODUCTION

The objective of this report is to present a comprehensive analysis

of the Joule-Thomson process as applied to cryogenic refrigeration

systems. The descriptions of this process already in the literature [ l]

,

[ 2] are usually for specific applications. In contrast, performance

characteristics are presented here for helium, para-hydrogen, and

nitrogen operation over a large range of process parameters.

Energy and flow rate requirements are given for the Joule -Thomson

refrigeration process operating in a system consisting of a heat exchanger,

an expansion valve, and an evaporator. These components are often

found in the lowest temperature portion of a refrigeration system with

precooling provided by a liquid bath or an expansion engine. Therefore,

the information contained in this report may be combined with performance

characteristics of other components to find the overall energy requirements of a more complex refrigeration system. For example, liquid

nitrogen use rate and cost information may be combined with data from

this work to obtain the overall energy requirement for a nitrogen precooled

hydrogen refrigerator. In addition, by using the charts which follow, a

complete refrigeration system can be constructed by cascading the
Joule-Thomson process. It is expected that the graphs and tables of this

report will be helpful to the engineer in optimizing his design or evaluating

an existing design.

The data presented in this report represent the results of manyprocess calculations that were made possible by the use of an electronic

digital computer.

2. NOMENCLATURE

P - pressure - atm.

p

- density - gm/liter

T - temperature - °K

H - enthalpy - joule s/gm

m - mass flow rate - gm/sec

Q - refrigeration - watts

v - specific volume - liters/gm

WC - rate of compressor work -watts

R - universal gas constant - 8. 3147 j/°K-mole

SCFM - standard cubic feet per minute defined at 760 mm. Hg and

0°C

M - gram molecular weight

-n - isothermal compression efficiency

'c

[x - Joule-Thomson coefficient - °K/atm.

C - specific heat - j/gm-°K

P

Numerical subscripts refer to the state of the gas as shown on the temperature - entropy diagram of figure 5. amb. - refers to the ambient temperature of the compressor, taken as

300°K.
3. PROPERTIES OF FLUIDS

The refrigerants used for this analysis are helium, para-hydrogen,

and nitrogen. Isothermal refrigeration is made available by the

evaporation of these fluids from the liquid state at their respective normal

boiling point temperatures of 4. 2l°K, 20. 268°K, and 77. 36°K.

Thermodynamic properties of these fluids have been generated

by the National Bureau of Standards-Cryogenics Division in order to

obtain thermodynamically consistent data of high accuracy and are now

available in the literature [3, 4, 5], The thermodynamic data tabulated

at 1°K increments for integer values of pressure were put on magnetic

tape for high speed input to the computer. These data have been generated

by the manipulation of the state equations given in the above referenced

works. Functional relationships, derived for the generation of properties,

were used in the refrigeration analysis, when data at non-integer values

of pressure were required, and are:

P=f(p, T), p=f(P, T), H=£(p, T), (8P/8p) and (8P/8T) . 1 P

Data for normal hydrogen [ 6] had been generated, but were not

used in the refrigeration analysis. If a constant ortho-para fraction is

established in the hydrogen refrigerant throughout the process, the

analysis is such that the actual ortho-para fraction does not effect the

results. Para-hydrogen was used because of the greater range of

available data.

Since the Joule-Thomson refrigeration process exploits the cooling

effect obtained by expansion of gases under certain conditions, it is

necessary to establish the conditions where cooling occurs. The inversion

curve for each of the gases is shown in figures 1, 2, and 3. These curves

were obtained by calculation from the state equations [3, 4, 5] in order to

be consistent with the refrigeration process data presented in this report.
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Calculations of the pressure and temperature locus for the

inversion curves were performed by satisfying the condition that the slopes

of the isenthalps be zero. These slopes are given by the Joule-Thomson

coefficient, [i = (8T/8P) , and may be defined in terms of the physical

properties by the expression [ 7]

u = C

P

T<-|£>p-v

In order to satisfy the condition that the Joule-Thomson coefficient be

zero, it is necessary and sufficient that

9v_\ _ v_ . . 8T JP " T

* 1 '

Equation (1) was modified to be consistent with the state equations and

their derivatives resulted in the following form:

*- - f = o. (2)

8P

The locus of points satisfying (2) was found for temperatures

ranging from near the critical to the maximum inversion temperature.

Inversion pressures were found to a precision of 0. 1 atmospheres. Values

of pressure and temperature for the inversion curves obtained from the

state equations were found to be in good agreement with inversion curve

data of the literature [7, 8, 9» lOj . Dashed portions of the inversion

curves indicate regions of extrapolation.
4. JOULE -THOMSON EXPANSION PROCESS

Regions of heating and cooling are clearly shown when the inversion

curve is plotted on temperature pressure coordinates. A Joule -Thomson

expansion process which has initial and end states within the inversion

curve envelope (figure 4) will lower the temperature of the fluid while

such a process occurring outside the envelope will raise the temperature

of the fluid. Expansion from a temperature above the maximum inversion

temperature will always result in heating. If the fluid is expanded from

state A to state B, the temperature of the fluid will rise. Further ex- pansion to state C results in cooling to the original temperature and an

end state of D will lower the temperature below the initial temperature.

Since the same net temperature drop is obtained by expanding the gas from

either states C or A to state D, there is no reason for expending the energy

required to compress the fluid to any pressure higher than the pressure

at C.

Lowering the initial temperature results in operation in the portion

of the temperature-pressure plane where the slopes of the isenthalps are

greater and eventually where the isenthalps intersect the vapor pressure

curve. This intersection is the extension of the isenthalps into the two

phase liquid-vapor region and means that a fraction of the gas expanded

into this region is liquefied.

i State D is the intersection of the isenthalp with the two phase liquid

vapor region and E' is the intersection of the isenthalp with the final

pressure isobar. The choice of the final pressure corresponding to E'

establishes the temperature of the liquid following the expansion process.

i The pressures at D and E' should be as low as possible if maximum

temperature drop is desired.
T

c ^sj? ISENTHAi o A

COOLING ^s. HEATING

r CRITICAL POINT ^/

( B' ^0*^*^ —^A*

f^VAPOR PRESSURE CURVE

Figure 4. Joule -Thomson Expansion Process
5. PROCESS DISCUSSION

The Joule -Thomson refrigeration system is defined as a counterflow regenerative heat exchanger connected in series with an expansion

valve and an evaporator as shown schematically in figure 5. The compressor for the system operates at ambient temperature while the heat

exchanger of figure 5 operates generally in the cryogenic temperature

range. Intermediate heat exchangers and expansion engines are not

considered as part of the thermodynamic system.

The system may be considered to be at a uniform temperature

before starting. This may be the case when a liquid precoolant bath is

in contact with, but outside of the system. Under this condition, gas

expansion at the valve acts as discussed previously under the expansion

process. Thus, appropriate precooling temperature and operating

pressure choices must be made for each refrigerant considered. Starting

the refrigeration process consists of providing a quantity of compressed

gas to point 1. The refrigeration made available by the expansion process

is used to cool the mass of metal of the evaporator and the return stream

side of the heat exchanger. The external heat load is withheld in order to

expedite cooling. Cooling the heat exchanger return stream side, between

points 4 and 5, results in cooling the inlet gas stream between points 1 and

2. For the ideal heat exchanger considered here, points 1 and 5 remain

at the initial temperature while the temperature of points 2, 3 and 4

are depressed. As the temperature of point 2 is depressed, the temperature of points 3 and 4 also become colder due to the Joule-Thomson effect.

Thus the refrigeration process is self-perpetuating until an equilibrium

condition is reached.

10
T

HEAT

EXCHANGER

EXPANSION

VALVE

EVAPORATOR

Figure 5. Schematic of Refrigeration System

11
A possible equilibrium condition is shown by points 1, 2, 3, 4, and

5 on the temperature- entropy surface of figure 5. An external heat load

has been applied to the evaporator between points 3 and 4 and is just equal

to the refrigeration available. No refrigeration is available to further cool

the heat exchanger. No condensation of liquid occurs; under this condition

the term "evaporator" is a misnomer as refrigeration is obtained nonisothermally from the sensible heat of the gas. This condition is difficult

to maintain because of the low thermal capacitance of the gas in the

evaporator. Small variations in the heat load will rapidly change the

system temperature.

The stable equilibrium condition at which the Joule -Thomson

refrigeration process is normally operated is shown by points 1, 2', 3',

4

1 and 5 on the temperature-entropy surface of figure 5. Temperature

depression at the expansion valve continues until liquid is condensed into

the evaporator. Refrigeration is obtained isothermally by the evaporation

of the liquid. A prerequisite for this type of operation is that the return

stream pressure be less than critical pressure since the temperature at

which the evaporator will operate is fixed by this pressure as defined by

the vapor pressure curve of the refrigerant. Operation with a one atmosphere return stream pressure will result in evaporator temperatures

as given under the normal boiling temperatures in the section on data.

This type of operation tends to be stable in temperature due to the

presence of liquid and the magnitude of the heat of vaporization. Mass

flow through the evaporator must be matched to the heat load for continuous

stable operation as an excessive heat load will result in reducing the

quantity of liquid rather than changing the system temperature. If corrective action is not taken, such as increasing the compressor flow

rate, the evaporator will eventually go dry forcing the evaporator

temperature to increase into the non- isothermal operating region. In

12
contrast, insufficient heat load will result in flooding of any type of

evaporator. Thus, the refrigeration process must be controlled in either

mode, but the case of isothermal operation is easier to control.

6. METHOD OF PERFORMANCE RATING

If the coefficient of performance method of rating refrigerators is

applied to cryogenic systems, the results are performance figures less

than unity. Here the performance has been rated by the reciprocal of

the coefficient of performance and is defined as the compression power

requirement divided by the refrigeration absorbed. Actual calculations

of refrigeration and power were performed in the metric system using

joules and seconds as energy and time units; however, the performance

rating is a dimensionless number always greater than unity and may be

considered as the ratio of the watts of electrical power provided to the

compressor motor at ambient temperature to watts of refrigeration

available at cryogenic temperature.

The power required for the compressor was assumed to be equal

to the power required to compress an ideal gas isothermally between the

same states:

R T

WC =-m M

amb IMP^Pg) . (3)

To obtain realistic refrigeration power requirements, the power term as

calculated by (3) must be divided by the isothermal compression efficiency-

a figure of 60 to 70 percent is common for reciprocating compressors using

piston rings. The useful refrigeration, Q, absorbed at cryogenic temperature was calculated from first law energy balance considerations. Performance is rated by the ratio WC/Q, a dimensionless figure of merit. In

order to put the calculations on a common basis, division by the isothermal

13
efficiency has not been performed and is left to the reader who must consider the merits of his compressor. When a refrigeration system is

considered that utilizes other energy sources, such as an auxiliary refrigerator, that power term must be added to the numerator to obtain an

overall performance figure.

Refrigeration performance may also be stated in terms of theoretical

work as found by the Carnot principle. The Carnot work may be expressed

as a dimensionless number by the ratio of the work input to the quantity of

heat received at the lowest temperature. The expression for the Carnot

work per unit of refrigeration available is

T -T' ^ *. „r amb 3 Carnot Work = —

T

3

and gives the limit to the performance of a refrigerator between the

stated temperatures.

A method of rating cryogenic refrigerators now in some use is to

compare the ratio of the Carnot work to the measured or calculated work

considering the irreversabilities. Thus, a process efficiency is stated in

terms of percent Carnot as

T -T' amb 3

T

3

Percent Carnot = — x 100. . (4) w c

ti Q 'c A result of 25 percent Carnot, meaning that the calculated or measured

work is four times theoretical, is a possible result. If care is not taken,

this method leads to some difficulty when non -isothermal refrigeration

occurs. Under this condition, the Carnot work must be defined by the

more general expression [ 1 1J

:

14
Tambu C"

n0t W° rk

(T

4

- T

3

)/ln (T

4

/T

3

) -

J • < 5 >

The percent Carnot expression for non-isothermal refrigeration then

becomes:

amb

( T

4

- T

3

)/ln(T

4 / T

3

)

1 Percent Carnot = —

x 100. . (6) WC

x] Q 'c

Difficulty arises with the percent Carnot method of performance

rating when the distinction is not made between equations (4) and (6).

When superheating occurs, a portion of the evaporator is isothermal

while the remainder is not. To use the percent Carnot performance

rating method under this condition requires the combination of equations

(4) and (6). To avoid the ambiguity of the percent Carnot approach, this

, work uses the performance rating of WC/Q.

7. CALCULATIONS

Application of the first law of thermodynamics to the refrigeration

system of figure 5 where frictibnal losses due to velocity effects are

negligible yields the following energy balance:

Q =rfi (H

g

- Hj) . (7)

The externally useful refrigeration is equal to the difference in the total

enthalpy of the refrigerant entering and leaving the system at the top of

the heat exchanger -points 1 and 5. The temperature at which the useful

refrigeration is available is not explicitly defined by (7) and may range

15
from near the boiling temperature of the refrigerant to near the precooling

temperature. Equation (7) is valid for the isothermal and non-isothermal

mode of refrigerator operation and will yield identical results for the same

state of the refrigerant at points 1 and 5. Under these conditions the work

of compression is also the same. The performance rating, WC/Q, is

therefore independent of the mode of refrigerator operation and depends

only on the state of the refrigerant at points 1 and 5.

The above statement seems to be incongruous in view of the Carnot

principle; the compressor is operated at ambient temperature while the

evaporator temperature level is varied, yet at the same time the WC/Q

remains unchanged. Compressor power requirements are based on the

conditions of (7), and these conditions are independent of the evaporator

operating temperature. Therefore, the figure of merit, WC/Q,is insensitive to changes in the evaporator temperature once states 5 and 1 have

been found. Operation in the non-isothermal mode of refrigeration does

not allow the refrigeration system to achieve its low temperature

capability; therefore, non-isothermal operation of the Joule-Thomson

refrigeration system is normally not desired. The WC/Q figure of this

work, although valid for the non- isothermal operating mode, should be

considered for isothermal refrigeration.

Calculations were made on the 'digital computer satisfying equations

(3) and (7) for a wide range of parameters consisting of the heat exchanger

operating pressures, precooling temperature, and temperature difference

at the top of the heat exchanger. The majority of the calculations were

made with a return stream pressure of one atmosphere allowing isothermal

refrigeration at the normal boiling point temperature. Inlet stream

pressure and precooling temperature were varied from near the critical

to near the maximum inversion pressure and temperature. The temperature difference at the top of the heat exchanger was varied by reducing the

16
temperature at point 5. The figure of merit and the flow rate in gram

moles per second required to produce one watt of useful refrigeration

was calculated for each set of parameters.

Temperature differences between heat exchanger refrigerant

streams introduce irreversabilities, but they are necessary to effect

heat transfer. Consider the equations which describe the heat transfer

between the two gas streams of the heat exchanger : a b

heat exchanger load = m \ Cp dT= m \ Cp dT, (8)

1 5

where a and b are intermediate temperatures of the high and low pressure

gas streams (see figure 6). The temperature and pressure dependency

of the specific heat allows the possibility that b > a for small values of

T, - T . Since b represents the temperature of the available refrigeration

1 5

of the low pressure stream, the condition b > a is not consistant with the

second law concept of heat energy flow and is therefore indicative of an

invalid choice of operating parameters. Either T - T must be increased

or other operating pressures and precooling temperatures must be chosen.

Increasing T - T without changing the precoolant temperature will always

increase WC/Q because of the temperature dependency of the term

(H - H ) in (7). The designer should investigate the temperature distribution within the heat exchanger for both gas streams from (8). Even

though a minimal temperature difference occurs within or at the cold

end (T - T ) of the exchanger, the temperature difference T - T may

be used as a parameter to indicate heat exchanger energy losses. Once

this temperature difference is fixed, then the internal temperature differences become a function of the properties of the gas.

17
HEAT EXCHANGER LOAD, Q

Figure 6. Heat Exchanger Cooling Curve - General Case

18
It is desirable to determine the combination of parameters that

give both the maximum obtainable refrigeration for a given compressor

size and the most economical operation. However, no practical single

set of parameters satisfies both requirements.

An examination of figure 4 has shown that the maximum refrigeration is obtained by an expansion process when the inital state of the gas

before expansion is on the inversion curve. The effect of inserting an

evaporator and a heat exchanger in the system is not so easily seen. Consider equation (7). The pressure, temperature, and mass flow rate

at point 5 and the temperature and flow rate at point 1 may be considered

constant for an equilibrium condition. Thus, the only variable is H = f(P),

and the condition for maximum refrigeration becomes ( \ = 0.

\ /

Using an elementary relationship for partial derivities, this condition

may be restated as

/

8H 1\ /8T\

or

Cp . [i=0. (9)

The Joule-Thomson coefficient must be zero in order to satisfy

(9) as Cp is never zero through the operating range of the Joule-Thomson

process. Thus, to obtain maximum refrigeration for a fixed mass flow

rate and precooling temperature, the inlet stream pressure must lie on

the inversion curve.

Note that the above statement does not define the temperature of the

expansion valve. In the case where T and P are chosen to lie on the

lower portion of the inversion curve, the expansion valve temperature will

be in the region of heating of figure 4 because of the temperature

19
depressing effect of the heat exchanger. Of course, no heating will occur

during the expansion as the Joule-Thomson process is undefined except

for the end states which lie inside the cooling region of figure 4.

The minimal value of the figure of merit, WC/Q, for a fixed precooling temperature, temperature difference at the top of the heat

exchanger, and return stream pressure indicates the most economic

inlet stream pressure for refrigeration system operation. This inlet

stream pressure may be found by plotting the results of calculations with

equations (3) and (7). The resulting curves do not give clear minimum

points. Therefore, an explicit expression was developed to determine

these points.

The minimum figure of merit for the conditions described above

is determined by

8 , Q

WC \

9P,

1 J T

= , (10)

1

substituting equations (3) and (7) into (10) and differentiating, yields

' -^S-) 1 Hs

- H i p

i / 8H

l - + *n _! ( ' = . (11)

ap i p p ap,

1 J T 1 5 ^ 1 'T

The computer was programmed to solve equation (11) in an iterative

manner for sets of precooling temperatures, return stream pressures,

and heat exchanger temperature differences. The partial derivative was

determined for trial P and a new P chosen to reduce the derivative

toward zero. The optimum operating pressure was determined to a precision of 0. 1 atmospheres.

20
8. DISCUSSION

Figure 7 is an unsealed representation of the performance surface

for a Joule-Thomson refrigeration system giving the figure of merit and

flow rate as a function of inlet pressure for values of T 15- T with P =

5

one atmosphere. Continuous curves of WC/Q are shown for each precool

temperature (T.) from near the normal boiling temperature to near the

maximum inversion temperature. The locus of the minimum WC/Q

shown as calculated by (11) is marked "optimum, " indicating the best

operating pressures from the standpoint of power requirement. The

inversion curve has been superimposed on the performance curve to

indicate the states where maximum refrigeration is achieved as a function

of mass flow.

Flow rate information , ^, , , included with the performance curves QM

by dashed lines, gives the flow in gram moles per second required to

produce one watt of refrigeration. Since this is a flow rate divided by an

energy rate, the time units cancel causing the flow information to have

units of gm-mole/j. Multiplying these values by 47. 5 converts to cubic

feet per minute (standard of 1 atm and 0°C) per watt of refrigeration-

convenient units when dealing with American compressor manufacturers.

Results of (8) are given by a line marked "second law violation, "

indicating a limit to the range of possible operating parameters. Calculations of heat exchanger operation on or below this line result in T > T

for isothermal refrigeration. Attempts to operate in this region result in

T, - T becoming larger than the designer anticipates with a corresponding reduction of performance- -possibly to a point where no useful refrigeration is obtainable. One exception to this statement may be made if the

refrigeration system is modified by inserting another heat exchanger

and expansion valve in series as discussed in the literature [ 12, 13j .

21
t

56

QC

hi

O

INLET PRESSURE (P.),atm.

Figure 7. Generalized Performance Surface for a Joule-Thomson

Refrigeration System

22
If an expansion valve was located in the high pressure stream at

the location marked 1 in figure 6 and expansion allowed to take place to a pressure near, but slightly higher than the return stream pressure,

then the temperature inversion at point 2 - or second law violation - might be avoided. The shape of the intermediate pressure cooling curve

would become nearly that of the low pressure cooling curve. With care,

the proper pressure might be found such that a > b.

Pressure drop within the heat exchanger cannot reduce the available

refrigeration as it is a function of the gas state at points 1 and 5. However,

heat exchanger pressure drop will effect the temperature at which the

refrigeration takes place, since the pressure at 4 controls the isothermal

refrigeration temperature as defined by the vapor pressure curve.

Pressure changes at 5 within a region where the gas is nearly ideal -- H ^ f(P )--will have little effect on the refrigeration but will effect the

5 5

power requirement. WC/Q will decrease as the pressure at 5 is increased

while the refrigeration temperature will increase as predicted by the

relationship for Carnot work. An approximate correction to WC/Q values

for a change in P may be made by multiplying WC/Q by (In P' /P)/

(In P /P ) where P' is a value other than one atmosphere.

5 15

The general problem of pressure drop must be considered in a practical system irrespective of the foregoing discussion. Performance

of the heat exchanger is based on the assumed temperature difference

between points 1 and 5. Unless pressure drop is held to a minimum in

both the high and low pressure streams, the temperature profile within

the heat exchanger will be changed in such a way as to make the initially

assumed temperatures unattainable.

Figures 8 through 2 show the performance surface for helium,

para-hydrogen, and nitrogen refrigerants. Enough plots with different

T - T values are given so that five percent accuracy may be achieved

23
for WC/Q and flow values when linearly interpolating between plots in the

lower half of these graphs. Interpolating at high precooling temperatures

(T.) should be conducted using a three point routine or crossplotting to

enhance accuracy.

Optimum and inversion curves closely parallel each other and would

appear as double valued functions if the performance data extended

through a greater temperature range. Each gas having different characteristics allows different portions of the optimum and inversion curves to

appear on the performance plot. The effect of increasing the value of

T, - T is to increase WC/Q and to shift the optimum curve to the right

1 5

or to higher pressures. The helium gas case with T - T = 1°K shows

an effect where the optimum and inversion curves lie on the performance

surface at very low WC/Q values and at low pressures. Performance

curves for T = 6 and 8°K show a positive slop indicative that these curves

lie above the optimum pressure. This region of the graph represents a

folded surface causing loss of clarity in data presentation with the

complication of the possible crossing of the inversion and optimum curves.

24
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37
9. REFERENCES

[ l] P. K. Lashmet and J. M. Geist "A Closed-Cycle Cascade Helium

Refrigerator", Advances in Cryogenic Engineering, Vol. 8,

K. D. Timmerhaus (ed), Plenum Press, New York (1963). p. 199.

[ 2] D. B. Chelton, J. W. Dean, and B. W. Birmingham, "Closed

Circuit Liquid Hydrogen Refrigeration System", Review of Scientific

Instruments, Vol. 31, No. 7, 712-716, (July, i960).

[3] D. B. Mann, "The Thermodynamic Properties of Helium from

3 to 300°K Between 0. 5 and 100 Atmospheres", NBS, TN 154,

(Jan. 1962).

[4] H. M. Roder and R. D. Goodwin, "Provisional Thermodynamic

Functions for Para-Hydrogen", NBS, TN 130, (Dec. 1961).

[ 5] T. R. Strobridge, "The Thermodynamic Properties of Nitrogen

from 64 to 300°K Between 0. 1 and 200 Atmospheres", NBS, TN-129,

(Jan. 1962).

[ 6] J. W. Dean, "A Tabulation of the Thermodynamic Properties of

Normal Hydrogen from Low Temperatures to 300°K and from 1 to 100 Atmospheres", TN-120,(Nov. 1961).

[ 7] M. W. Zemansky, Heat and Thermodynamics, McGraw Hill Book

Co. , New York, N. Y. (4th ed), (1957).

[8] R. W. Hill and O. V. Lounasmaa, "The Thermodynamic Properties

of Fluid Helium" , Phil. Trans. Royal Soc. (London), 252A, p. 357-

359 (March, i960).

[9] J. R. Roebuck and H. Osterberg "The Joule- Thomson Effect in

Nitrogen", Physical Review, Vol. 48, p. 450-457, (Sept. 1935).

[10] A. Michels, W. DeGraaff and G. J. Wolkers, "Thermodynamic

Properties of Hydrogen and Deterium at Temperatures between

-175°C and 150° C and at Densities up to 840 Amagat", Physica

Vol. 25, p. 1097-1124, (1959).

[ ll] R. B. Jacobs, "The Efficiency of an Ideal Refrigerator",

Advances in Cryogenic Engineering, Vol. 7, K. D. Timmerhaus

(ed), Plenum Press, New York ( 1962), p. 567.

38
[12] D. B Chelton, J. W. Dean, T. R. Strobridge, B. W. Birmingham

and D„ B. Mann, "Helium Refrigeration and Liquefaction Using

a Liquid Hydrogen Refrigerator for Precooling", TN 39, p. H,

(Jan. I960).

[13] D. B. Mann, W. R. Bjorklund, J. Macinko, and M. J. Hiza,

"Design, Construction and Performance of a Laboratory Size

Helium Liquefier", Advances in Cryogenic Engineering, Vol. 5,

K. D. Timmerhaus (ed), Plenum Press, New York, (i960),

p. 346.

39

GPO 847 . 242