Cryogenics notes

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Module I
INTRODUCTION TO CRYOGENIC SYSTEMS
1.1. Introduction
The word cryogenics means, literally, the production of icy cold; however,
the term is used today as a synonym for low temperatures. The point on the
temperature scale at which refrigeration in the ordinary sense of the term ends and
cryogenics begins is not sharply defined. The workers at the National Bureau of
Standards at Boulder, Colorado, have chosen to consider the field of cryogenics as
that involving temperatures below 150°C (123 K) or 240°F (2200
R). This is a
logical dividing line, because the normal boiling points of the socalled permanent
gases, such as helium, hydrogen, neon, nitrogen, oxygen, and air, lie below 150°C,
while the Freon refrigerants, hydrogen sulfide, ammonia, and other conventional
refrigerants all boil at temperatures above 150°C. The position and range of the field
of cryogenics are illustrated on a logarithmic thermometer scale in Fig. 1.1.
In the field of cryogenic engineering, one is concerned with developing and
improving lowtemperature techniques, processes, and equipment. As contrasted to
lowtemperature physics, cryogenic engineering primarily involves the practical
utilization of lowtemperature phenomena, rather than basic research, although the
dividing line between the two fields is not always clearcut. The engineer should be
familiar with physical phenomena in order to know How to utilize them effectively;
the physicist should be familiar with engineering principles in order to design
experiments and apparatus.
A system may be defined as a collection of components united by definite
interactions or interdependencies to perform a definite function. Examples of
common engineering systems include the automobile, a petroleum refinery, and an
electric generating power plant. In many cases the distinction between a system and a
component depends upon one's point of view. For example, consider the
transportation system of a country. An automobile is a system also; however, it
would be only one part or subsystem of the entire transportation system. Going even
further, one could speak of the power system, braking system, steering system, etc.,

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of the automobile. In general, we shall use the term cryogenic system to refer to an
interacting group of components involving low temperatures. Air liquefaction plants,
helium refrigerators, and storage vessels with the associated controls are some
examples of cryogenic systems.
Fig. 1.1. The cryogenic temperature range.
1.2. Historical background
In 1726 Jonathan Swift wrote in Gulliver's account of his trip to the
mythical Academy of Lagado:
He (the universal artist) told us he had been thirty years employing his
thoughts for the improvement of human life. He had two large rooms full of
wonderful curiosities, and fifty men at work. Some were condensing air into a dry
tangible substance, by extracting the nitre, and letting the aqueous or fluid particles
percolate.

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At the time Gulliver's Travels was written, air was considered to be a
"permanent gas." Thus Swift envisioned the liquefaction of air some 150 years
before the feat was actually accomplished.
In the 1840s, in an attempt to relieve the suffering of malaria patients, Dr.
John Gorrie, a Florida physician, developed an expansion engine for the production
of ice. Although Dr. Gorrie’s engine was used only to cool air for air conditioning of
sickrooms and was not part of a cryogenic system, most largescale air liquefaction
systems today use the same principle of expanding air through a workproducing
device, such as an expansion engine or expansion turbine, in order to extract energy
from the air so that the air can be liquefied.
It was not until the end of 1877 that a socalled permanent gas was first
liquefied. In this year Louis Paul Cailletet, a French mining engineer, produced a fog
of liquidoxygen droplets by precooling a container filled with oxygen gas at
approximately 300 atm and allowing the gas to expand suddenly by opening a valve
on the apparatus. About the same time Raoul Pictet, a Swiss physicist, succeeded in
producing liquid oxygen by a cascade process.
In the early 1880s one of the first lowtemperature physics laboratories, the
Cracow University Laboratory in Poland, was established by Szygmunt von
Wroblewski and K. Olszewski. They obtained liquid oxygen "boiling quietly in a test
tube" in sufficient quantity to study properties in April 1883. A few days later, they
also liquefied nitrogen. Having succeeded in obtaining oxygen and nitrogen as true
liquids (not just a fog of liquid droplets), Wroblewski and Olszewski, now working
separately at Cracow, attempted to liquefy hydrogen by Cailletet's expansion
technique. By first cooling hydrogen in a capillary tube to liquidoxygen
temperatures and expanding suddenly from 100 atm to I atm, Wroblewski obtained a
fog of liquidhydrogen droplets in 1884, but he was not able to obtain hydrogen in
the completely liquid form.
The Polish scientists at the Cracow University Laboratory were primarily
interested in determining the physical properties of liquefied gases. The everpresent
problem of heat transfer from ambient plagued these early investigators because the

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cryogenic fluids could be retained only for a short time before the liquids boiled
away. To improve this situation, an ingenious experimental technique was developed
at Cracow. The experimental test tube containing a cryogenic fluid was surrounded
by a series of concentric tubes, closed at one end. The cold vapor arising from the
liquid flowed through the annular spaces between the tubes and intercepted some of
the heat traveling toward the cold test tube. This concept of vapor shielding is used
today in conjunction with highperformance insulations for the longterm storage of
liquid helium in bulk quantities.
A giant step forward in preserving cryogenic liquids was made in 1892
when James Dewar, a chemistry professor at the Royal Institution in London,
developed the vacuumjacketed vessel for cryogenicfluid storage. Dewar found that
using a doublewalled glass vessel having the inner surfaces silvered (similar to
presentday thermos bottles) resulted in a reduction of the evaporation rate of the
stored fluid by a factor of 30 over that of an uninsulated container. This simple
container played a significant role in the liquefaction of hydrogen and helium in bulk
quantities. In May 1898 Dewar produced 20 cm) of liquid hydrogen boiling quietly
in a vacuuminsulated tube, instead of a mist.
In 1895 two significant events in cryogenic technology occurred. Carl von
Linde, who had established the Linde Eismaschinen AG in 1879, was granted a basic
patent on air liquefaction in Germany. Although Linde was not the first to liquefy air,
he was one of the first to recognize the industrial implications of gas liquefaction and
to put these ideas into practice. Today the Linde Company is one of the leaders in
cryogenic engineering.
After more than 10 years of lowtemperature study, Heike Kamerlingh
Onnes established the Physical Laboratory at the University of Lei den in Holland in
1895. Onnes' first liquefaction of helium in 1908 was a tribute both to his
experimental skill and to his careful planning. He had only 360 liters of gaseous
helium obtained by heating monazite sand from India. More than 60 cm3
of liquid
helium was produced by Onnes in his first attempt. Onnes was able to attain a
temperature of 1.04 K in an unsuccessful attempt to solidify helium by lowering the
pressure above a container of liquid helium in 1910.

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The physicists at the Leiden laboratory were interested in investigating the
properties of materials at low temperatures and in checking natural principles known
to be valid at ambient temperatures, at cryogenic temperatures. It was in 1911, while
he was checking the various theories of electrical resistance of solids at liquidhelium
temperatures, that Onnes discovered that the electrical resistance of the mercury wire
on which he was experimenting suddenly decreased to zero. This event marked the
first observation of the phenomenon of superconductivitythe basis for many novel
devices used today.
In 1902 Georges Claude, a French engineer, developed a practical system
for air liquefaction in which a large portion of the cooling effect of the system was
obtained through the use of an expansion engine. Claude's first engines were
reciprocating engines using leather seals (actually, the engines were simply modified
steam engines). During the same year, Claude established l'Air Liquide to develop
and produce his systems.
Although cryogenic engineering is considered a relatively new field in the
U.S., it must be remembered that the use of liquefied gases in U.S. industry began in
the early 1900s. Linde installed the first airliquefaction plant in the United States in
1907, and the first Americanmade airliquefaction plant was completed in 1912. The
first commercial argonproduction was put into operation in 1916 by the Linde
company in Cleveland, Ohio. In 1917 three experimental plants were built by the
Bureau of Mines, with the cooperation of the Linde Company, Air Reduction
Company, and the JefferiesNorton Corporation, to extract helium from natural gas
of Clay County,' Texas. The helium was intended for use in airships for World War I.
Commercial production of neon began in the United States in 1922, although Claude
had produced neon in quantity in France since 1907.
On 16 March 1926, Dr. Robert H. Goddard conducted the world's first
successful flight of a rocket powered by liquidoxygengasoline propellant on a farm
near Auhurn, Massachusetts. This first flight lasted only 2½ seconds, and the rocket
reached a maximum speed of only 22 m/s (50 mph). Dr. Goddard continued his work
during the 1930s and by 1941 he had brought his cryogenic rockets to a fairly high

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degree of perfection. In fact, many of the devices used in Dr. Goddard's rocket
systems were used later in the German V2 weapons system.
During that same year (1926), William Francis Giauque and Peter Debye
independently suggested the adiabatic demagnetization method for obtaining
ultralow temperatures (less than 0.1 K). It was not until 1933 that Giauque and
MacDougall at Berkeley and De Haas, Wiersma, and Kramers at Leiden made use of
the technique to reach temperatures from 0.3 K (Giauque and MacDougall) to 0.09 K
(De Haas et al.).
As early as 1898 Sir James Dewar made measurements on heat transfer
through evacuated powders. In 1910 Smoluchowski demonstrated the significant
improvement in insulating quality that could be achieved by using evacuated
powders in comparison with unevacuated insulations. In 1937 evacuatedpowder
insulations were first used in the United States in bulk storage of cryogenic liquids.
Two years later, the first vacuum powderinsulated railway tank car was built for the
transport of liquid oxygen.
The world became aware of some of the military implications of cryogenic
technology in 1942 when the German V 2 weapon system was successfully test
fired at Peenemunde under the direction of Dr. Walter Dornberger. The V2 weapon
system was the first large, practical liquid propellant rocket. This vehicle was
powered by liquid oxygen and a mixture of 75 percent ethyl alcohol and 25 percent
water.
Around 1947 Dr. Samuel C. Collins of the department of mechanical
engineering at Massachusetts Institute of Technology developed an efficient liquid
helium laboratory facility. This event marked the beginning of the period in which
liquidhelium temperatures became feasible and fairly economical. The Collins
helium cryostat, marketed by Arthur D. Little, Inc., was a complete system for the
safe, economical liquefaction of helium and could be used also to maintain
temperatures at any level between ambient temperature and approximately 2 K.
The first buildings for the National Bureau of Standards Cryogenic
Engineering Laboratory were completed in 1952. This laboratory was established to

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provide engineering data on materials of construction, to produce large quantities of
liquid hydrogen for the Atomic Energy Commission, and to develop improved
processes and equipment for the fast growing cryogenic field. Annual conferences in
cryogenic engineering have been sponsored by the National Bureau of Standards
(sometimes sponsored jointly with various universities) from 1954 (with the
exception of 1955) to 1973. At the 1972 conference at Georgia Tech in Atlanta, the
Conference Board voted to change to a biennial schedule alternating with the
Applied Superconductivity Conference. This schedule has been followed with
meetings in Kingston, Ontario in 1975, Boulder in 1977, Madison, Wisconsin in
1979, San Diego, California in 1981, and Colorado Springs in 1983.
Early in 1956 work with liquid hydrogen was greatly accelerated when Pratt
and Whitney Aircraft was awarded a contract to develop a liquid hydrogenfueled
rocket engine for the United States space program. The following year the Atlas
ICBM was successfully testfired. The Atlas was powered by a liquidoxygenRPl
propellant combination and had a sea level thrust of I. 7 MN (380,000 Ibf). At the
Cape Kennedy Space Center on 27 October 1961, the first flight test of the Saturn
launch vehicle was conducted. The Saturn V was the first space vehicle to use the
liquid hydrogenliquidoxygen propellant combination.
In 1966, Hall, Ford, and Thompson at Manchester, and Neganov, Borisov,
and Liburg at Moscow independently succeeded in achieving continuous
refrigeration below 0.1 K using a He3
He4
dilution refrigerator. This new
refrigeration technique had been proposed in 1951 by H. London. The dilution
refrigerator had certain advantages over the magnetic refrigerator, which relied on
the adiabatic demagnetization principle to achieve temperatures in the 0.01 K to 0.10
K range. Thus considerable research effort has been devoted to the study and
improvement of the dilution refrigerator. .
In 1969 a 3250hp, 20Drpm superconducting motor (Fawley motor) was
constructed by the International Research and Development Co., Ltd., in England. In
1972 IRD installed a superconducting motor in a ship to drive the electrical
propulsion system.

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This chronology of cryogenic technology is summarized in Table 1.1.
We see that cryogenics has grown from an interesting curiosity in the times
of Linde and Claude to a diversified, vital field of engineering.
1.3. Present areas involving cryogenic engineering
Presentday applications of cryogenic technology are widely varied, both in
scope and in magnitude. Some of the areas involving cryogenic engineering include:
1. Rocket propulsion systems. All the large United States launch vehicles use
liquid oxygen as the oxidizer. The Space Shuttle propulsion system uses both
cryogenic fluids, liquid oxygen, and liquid hydrogen.
2. Studies in highenergy physics. The hydrogen bubble chamber uses liquid
hydrogen in the detection and study of highenergy particles produced in large
particle accelerators.
3. Electronics. Sensitive microwave amplifiers, called masers, are cooled to
liquidnitrogen or liquidhelium· temperatures so that thermal vibrations of the
atoms of the amplifier element do not seriously interfere with absorption and
emission of microwave energy. CryogenicaIly cooled masers have been used in
missile detectors, in radio astronomy to listen to faraway galaxies, and in space
communication systems.
Table 1.1. Chronology of cryogenic technology
Year Event
1877 Cailletet and Pictet liquefied oxygen (Pictet 1892).
1879 Linde founded the Linde Eismaschinen AG.
1883 Wroblewski and Olszewski completely liquefied nitrogen and oxygen at the
Cracow University Laboratory (Olszewski 1895).
1884 Wroblewski produced a mist of liquid hydrogen.
1892 Dewar developed a vacuuminsulated vessel for cryogenicfluid storage
(Dewar 1927).
1895 Onnes established the Leiden Laboratory. Linde was granted a basic patent on
air liquefaction in Germany.
1898 Dewar produced liquid hydrogen in bulk at the Royal Institute of London.

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1902 Claude established l'Air Liquide and developed an airliquefaction system
using an expansion engine.
1907 Linde installed the first airliquefaction plant in America. Claude produced
neon as a byproduct of an air plant.
1908 Onnes liquefied helium (Onnes 1908).
1910 Linde developed the doublecolumn airseparation system.
1911 Onnes discovered superconductivity (Onnes 1913).
1912 First Americanmade airliquefaction plant completed.
1916 First commercial production of argon in the United States.
1917 First naturalgas liquefaction plant to produce helium.
1922 First commercial production of neon in the United States.
1926 Goddard testfired the first cryogenically propelled rocket. Cooling by
adiabatic demagnetization independently suggested by Giauque and Debye.
1933 Magnetic cooling used to attain temperatures below I K.
1934 Kapitza designed and built the first expansion engine for helium. Evacuated
powder insulation first used on a commercial scale in cryogenicfluid storage
vessels.
1939 First vacuuminsulated railway tank car built for transport of liquid oxygen.
1942 The V2 weapon system was testfired (Dornberger 1954). The Collins
cryostat developed.
1948 First 140 ton/day oxygen system built in America.
1949 First 300 ton/day onsite oxygen plant for chemical industry completed.
1952 National Bureau of Standards Cryogenic Engineering Laboratory established
(Brickwedde 1960).
1957 LOXRPI propelled Atlas ICBM testfired. Fundamental theory (BCS
theory) of superconductivity presented.
1958 Highefficiency multilayer cryogenic insulation developed (Black 1960).
1959 Large NASA liquidhydrogen plant at Torrance, California, completed.
1960 Largescale liquidhydrogen plant completed at West Palm Beach, Rorida.
1961 Saturn launch vehicle testfired.
1963 60 ton/day liquidhydrogen plant completed by Linde Co. at Sacramento,
California.
1964 Two liquidmethane tanker ships designed by Conch Methane Services. Ltd.,
entered service.

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1966 Dilution refrigerator using HeJHe' mixtures developed (Hall 1966; Neganov
1966).
1969 3250hp de superconducting motor constructed (Appleton 1971).
1970 Liquid oxygen plants with capacities between 60,000 mJ/h and 70,000 mJ/h
developed.
1975 Record high superconducting transition temperature (23 K) achieved.
Tiny superconducting electronic elements, called SQUIDs (superconducting
quantum interference devices) have been used as extremely sensitive digital
magnetometers and voltmeters. These devices are based on a superconducting
phenomenon, called the Josephson effect, which involves quantum mechanical
tunneling of electrons from one superconductor to another through an insulating
barrier.
In addition to SQUIDs, other electronic devices that utilize superconductivity
in their operation include superconducting amplifiers, rectifiers, transformers, and
magnets. Superconducting magnets have been used to produce the high magnetic
fields required in MHD systems, linear accelerators, and tokamaks. Superconducting
magnets have been used to levitate highspeed trains at speeds up to 500 km/h.
4. Mechanical design. By utilizing the Meissner effect associated with
superconductivity, practically zerofriction bearings have been constructed that
use a magnetic field as the lubricant instead of oil or air. Superconducting
motors have been constructed with practically zero electrical losses for such
applications as ship propulsion systems. Superconducting gyroscopes with
extremely small drift have been developed.
5. Space simulation and highvacuum technology. To produce a vacuum that
approaches that of outer space (from 1012
torr to 1014
torr), one of the more
effective methods involves low temperatures. Cryopumping or freezing out the
residual gases, is used to provide the ultrahigh vacuum required in space
simulation chambers and in test chambers for space propulsion systems. The
cold of free space is simulated by cooling a shroud within the environmental
chamber by means of liquid nitrogen. Dense gaseous helium at less than 20 K

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or liquid helium is used to cool the cryopanels that freeze out the residual
gases.
6. Biological and medical applications. The use of cryogenics in biology, or
cryobiology, has aroused much interest. Liquidnitrogencooled containers are
used to preserve whole blood, tissue, bone marrow, and animal semen for long
periods of time. Cryogenic surgery (cryosurgery) has been used for the
treatment of Parkinson's disease, eye surgery, and treatment of various lesions.
This surgical procedure has many advantages over conventional surgery in
several applications.
7. Food processing. Freezing as a means of preserving food was used as far back
as 1840. Today frozen foods are prepared by placing cartons on a conveyor belt
and moving the belt through a liquidnitrogen bath or gaseousnitrogencooled
tunnel. Initial contact with liquid nitrogen freezes all exposed surfaces and
seals in flavor and aroma. The cryogenic process requires about 7 minutes
compared with 30 to 48 minutes required by conventional methods. Liquid
nitrogen has also been used as the refrigerant in frozenfood transport trucks
and railway cars.
8. Manufacturing processes. Oxygen is used to perform several important
functions in the steel manufacturing process. Cryogenic systems are used in
making ammonia. Pressure vessels have been formed by placing a preformed
cylinder in a die cooled to liquidnitrogen temperatures. Highpressure nitrogen
gas is admitted into the vessel until the container stretches about 15 percent,
and the vessel is removed from the die and allowed to warm to room
temperature. Through the use of this method, the yield strength of the material
has been increased 400 to 500 percent.
9. Recycling of materials. One of the more difficult items to recycle is the
automobile or truck tire. By freezing the tire in liquid nitrogen, tire rubber is
made brittle and can be crushed into small particles. The tire cord and metal
components in the original tire can be separated easily from the rubber, and the

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rubber particles can be used again for other items. At present the cryogenic
technique is the only effective one to recover the rubber from steel radial tires.
These are a few of the areas involving cryogenic engineeringa field in
which new developments are continually being made.

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MODULE II
LOWTEMPERATURE PROPERTIES OF
ENGINEERING MATERIALS
Familiarity with the properties and behavior of materials used in any system
is essential to the design engineer. At first thought, one might suppose that by
observing the variation of material properties at room temperature he could
extrapolate this information down through the relatively small temperature range
involved in cryogenics (some 300°C) with fair confidence. In some cases, such as for
the elastic constants, this may be done with acceptable accuracy. On the other hand,
there are several significant effects that appear only at very low temperatures. Some
examples of these effects include the vanishing of specific heats, superconductivity,
and ductilebrittle transitions in carbon steel. None of these phenomena can be
inferred from property measurements made at nearambient temperatures.
In this chapter, we shall investigate the physical properties of some
engineering materials commonly used in cryogenic engineering. The primary
purpose of the chapter is to examine the effect of variation of temperature on
material properties in the cryogenic temperature range and to become familiar with
the properties and behavior of materials at low temperatures.
MECHANICAL PROPERTIES
2.1. Ultimate and yield strength
For many materials, there is a definite value of stress at which the strain of
the material in a simple tensile test begins to increase quite rapidly with increase in
stress. This value of stress is defined as the yield strength Sy of the material. For
other materials that do not exhibit a sharp change in the slope of the stressstrain
curve, the yield strength is defined as the stress required to permanently deform the
material in a simple tensile test by 0.2 percent (sometimes 0.1 percent is used). The
ultimate strength Su of a material is defined as the maximum nominal stress attained
during a simple tensile test. The temperature variation of the ultimate and yield
strengths of several engineering materials is shown in Figs. 2.1 and 2.2.

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Fig.2.1. Ultimate strength for several engineering materials: (I) 2024T4 aluminum;
(2) beryllium copper; (3) K Monel; (4) titanium; (5) 304 stainless steel; (6) CI020
carbon steel; (7) 9 percent Ni steel; (8) Teflon; (9) Invar36 (Durham et al. 1962).
Many engineering materials are alloys, in which alloying materials with
atoms of different size from those of the basic material are added to the basic
material; for example, carbon is added to iron to produce carbon steel. If the
alloyingelement atoms are smaller than the atoms of the basic material, the smaller
atoms tend to migrate to regions around dislocations in the metal. The presence of
the smaller atoms around the dislocation tends to "pin" the dislocation in place or
make dislocation motion more difficult (Wigley 1971). The yielding process in
alloys takes place when a stress large enough to pull many dislocations away from
their "atmosphere" of alloying atoms is applied. Plastic deformation or yielding
occurs because of the gross motion of these dislocations through the material.
As the temperature is lowered, the atoms of the material vibrate less
vigorously. Because of the decreased thermal agitation of the atoms, a larger applied
stress is required to tear dislocations from their atmosphere of alloying atoms. From

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this line of reasoning, we should expect that the yield strength for alloys would
increase as the temperature is decreased. This has been found to be true for most
engineering materials.

Fig. 2.2. Yield strength for several engineering materials: (1) 2024 T4 aluminum:
(2) beryllium copper; (3) K Monel; (4) titanium; (5) 304 stainless steel; (6) CI020
carbon steel; (7) 9 percent Ni steel; (8) Teflon; (9) Invar36 (Durham et al. 1962).
2.2. Fatigue strength
There are several ways to express the resistance of a material to stresses that
vary with time, but the most common method is a simple reversed bending test The
stress required for failure after a given number of cycles is called the fatigue strength
Sf. Some materials, such as carbon steels and aluminummagnesium alloys, have the
property that the fatigue failure will not occur if the stress is maintained below a
certain value, called the endurance limit Se, no matter how many cycles have elapsed.

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The temperature variation of the fatigue strength at 106
cycles for several materials is
shown in Fig. 2.3.
Because of the time involved to complete a test, fatigue data at cryogenic
temperatures are not as extensive as ultimatestrength and yield strength data;
however, for the materials that have been tested, it has been found that the fatigue
strength increases as the temperature is decreased.
Fig. 2.3. Fatigue strength at 1()6 cycles: (I) 2024 T4 aluminum; (2) beryllium
copper; (3) K Monel; (4) titanium; (5) 304 stainless steel; (6) CI020 carbon steel
(Durham et al. 1962).
Fatigue failure generally occurs in three stages for the case of more than
about 10) cycles: microcrack initiation, slow crack growth until a critical crack size
is achieved, and the final rapid failure either by ductile rupture or by cleavage.
Microcrack initiation usually occurs at the surface of the specimen as a result of
inhomogeneous shear deformation or at small flaws near the surface. The growth of
the microcracks occurs as the material fails at the highstress region around the tip of

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the crack. As the temperature of a material is decreased, a larger stress is required to
extend the crack; therefore, we should expect to observe that the fatigue strength
increases as the temperature is decreased.
For aluminum alloys, it has been found (De Money and Wolfer 1961) that
the ratio of fatigue strength to ultimate strength remains fairly constant as the
temperature is lowered. This fact may be used in estimating the fatigue strength for
nonferrous materials at cryogenic temperatures if no fatigue data are available at the
low temperatures.
2.3. Impact strength
The Charpy and the Izod impact tests give a measure of the resistance of a
material to impact loading. These tests indicate the energy absorbed by the material
when it is fractured by a suddenly applied force. Charpy impact strength of several
materials is shown in Fig. 2.4.
Fig. 2.4. Charpy impact strength at low temperatures: (I) 2024·T4 aluminum; (2)
beryl· lium copper; (3) K Monel; (4) titanium; (5) 304 stainless steel; (6) CI020
carbon steel; (7) 9 percent Ni steel (Durham et al. 1962).

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A ductilebrittle transition occurs in some materials, such as carbon steel, at
temperatures ranging from room temperature down to 78 K, which results in a
severely reduced impact strength at low temperatures. The impact behavior of a
metal is largely determined by its lattice structure. The facecenteredcubic (FCC)
lattice has more slip planes available for plastic deformation than does the body
centeredcubic (BCC) lattice. In addition, interstitial impurity atoms interact only
with edge dislocations to retard slipping in the FCC structure; whereas, both edge
and screw dislocations can become pinned in the BCC structure. The metals with a
FCC lattice or hexagonal lattice tend to fail by plastic deformation in the impact test
(thereby absorbing a relatively large amount of energy before breaking) and retain
their resistance to impact as the temperature is lowered. The metals with a BCC
lattice tend to reach a temperature at which it is more energetically favorable to
fracture by cleaving (thereby absorbing a relatively small amount of energy). Thus
these materials become brittle at low temperatures.
Most plastics and rubber materials become brittle upon cooling below a
transition temperature also. Two notable exceptions are Teflon and KelF.
2.4. Hardness and ductility
The ductility of materials is usually indicated by the percentage elongation
to failure or the reduction in crosssectional area of a specimen in a simple tensile
test. The accepted dividing line between a brittle material and 'a ductile one is 5
percent elongation or a strain of 0.05 cm/cm at failure. Materials that elongate more
than this value before failure are called ductile; those with less than 5 percent
elongation are called brittle. The ductility of several materials as a function of
temperature is shown in Fig. 2.5.
For materials that do not exhibit a ductiletobrittle transition at low
temperatures, the ductility usually increases somewhat as the temperature is lowered.
For the carbon steels, which do have a lowtemperature transition, the elongation at
failure drops from 25 to 30 percent for the softer steels down to 2 or 3 percent during
the transition. Obviously, these materials should not be used at low temperatures in
any applications in which ductility is important.

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Hardness of metals is measured by the indention made in the surface of the
material by a standard indenter. Common hardness tests include (1) Brinell (ball
indenter), (2) Vickers (diamond pyramid indenter), and (3, Rockwell (ball or
diamond indenter with various loads). In general, the hardness of metals as measured
by any of these means is directly proportional to the ultimate strength of the material;
therefore, the hardness increases as the temperature is decreased. This proportionality
is to be expected because a penetration test is essentially a miniature tensile test.
Fig. 2.5. Percent elongation for various materials: (I) 2024T4 aluminum; (2)
beryllium copper; (3) K Monel; (4) titanium; (5) 304 stainless steel; (6) C1020
2.5. Elastic moduli
There are three commonly used elastic moduli: (1) Young's modulus E. the
rate of change of tensile stress with respect to strain at constant temperature in the
elastic region; (2) shear modulus G. the rate of change of shear stress with respect to
shear strain at constant temperature in the elastic region; and (3) bulk modulus B, the
rate of change of pressure (corresponding to a uniform threedimensional stress) with
respect to volumetric strain (change in volume per unit volume) at constant
temperature. If the material is isotropic (many polycrystalline materials can be

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considered isotropic for engineering purposes), these three moduli are related
through Poisson's ratio v, the ratio of strain in one direction due to a stress applied
perpendicular to that direction to the strain parallel to the applied stress:
E
B
3(1 2)

  (2.1)
E
G
2(1 )

  (2.2)
Fig. 2.6. Young's modulus at low temperatures: (I) 2024 T 4 aluminum; (2)
beryllium copper; (3) K Monel; (4) titanium; (5) 304 stainless steel; (6) ClO20
The variation of Young's modulus with temperature for several materials is
given in Fig. 2.6.
As the temperature is decreased, interatomic and intermolecular forces tend
to increase because of the decrease in the disturbing influence of atomic and
molecular vibrations. Because elastic reaction is due to the action of these
intermolecular and interatomic forces, one would expect the elastic moduli to

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increase as the temperature is decreased. In addition, it has been found
experimentally that Poisson's ratio for isotropic materials do not change appreciably
with change in temperature in the cryogenic range; therefore, all three of the
previously mentioned elastic moduli vary in the same manner with temperature.
THERMAL PROPERTIES
2.6. Thermal conductivity
The thermal conductivity kt of a material is defined as the heattransfer rate
per unit area divided by the temperature gradient causing the heat transfer. The
variation of thermal conductivity of several solids is shown in Fig. 2.7. Values of the
thermal conductivity of cryogenic liquids and gases are given in Appendixes B
through E.
Fig. 2.7. Thermal conductivity of materials at low temperatures: (ll 2024T4
aluminum: (3) beryllium copper; (3) K Monel; (4) titanium; (5) 304 stainless steel;
(6) C1020 carbon steel; (7) pure copper; (8) Teflon (Stewart and Johnson 1961).

24
To understand the variation of thermal conductivity at low temperatures,
one must be aware of the different mechanisms for transport of energy through
materials. There are three basic mechanisms responsible for conduction of heat
through materials: (l) electron motion, as in metallic conductors; (2) lattice
vibrational energy transport, or phonon motion, as in all solids; and (3) molecular
motion, as in organic solids and gases. In liquids, the primary mechanism for
conduction heat transfer is the transfer of molecular vibrational energy; whereas in
gases, heat is conducted primarily by transfer of translational energy (for monatomic
gases) and translational and rotational energy (for diatomic gases).
U sing principles of kinetic theory of gases (Eucken 1913), we may obtain a
theoretical expression relating the thermal conductivity to other properties of the
material:
tk 1 8(9 5) C    
where = specific heat ratio
= density of material
Cv = specific heat at constant volume
v = average particle velocity
A = mean free path of particles, or average distance a particle travels before
it is deflected
For all gases the thermal conductivity decreases as the temperature is
lowered. Because the product of density and mean free path for a gas is practically
constant, and the specific heat is not a strong function of temperature, the thermal
conductivity of a gas should vary with temperature in the same manner as the mean
molecular speed u, as indicated by eqn. (2.3). From kinetic theory of gases (Present
1958), the mean molecular speed is given by
1 2
c8g RT 
    

25
where gc is the conversion factor in Newton's law (gc = 1 kgm/Ns2
in the SI system
of units; gc = 32.174 Ibmft/lbrsec2
in the British system of units), R is the specific gas
constant for the particular gas (R = Ru/M, where Ru is the universal gas constant,
8.31434 J/molK or 1545 ftlbf/lbmoleo
R, and M is the molecular weight of the gas),
and T is the absolute temperature of the gas. A decrease in temperature results in a
decrease in the mean molecular speed and, consequently, a decrease in the gas
thermal conductivity.
All cryogenic liquids except hydrogen and helium have thermal
conductivities that increase as the temperature is decreased. Liquid hydrogen and
helium behave in a manner opposite to that of other liquids in the cryogenic
temperature range.
For heat conduction in solids, the thermal conductivity is related to other
properties by an expression similar to that for gases,
1
t 3k C   (2.5)
Energy is transported in metals by both electronic motion and phonon
motion; however, in most pure electric conductors, the electronic contribution to
energy transport is by far the larger for temperatures above liquidnitrogen
temperatures. The electronic specific heat is directly proportional to absolute
temperature (see Sec. 2.7), and the electron mean free path in this temperature range
is inversely proportional to absolute temperature. Because the density and mean
electron speed are only weak functions of temperature, the thermal conductivity of
electric conductors above liquidnitrogen temperatures is almost constant with
temperature, as would be predicted by eqn. (2.5). As the absolute temperature is
lowered below liquidnitrogen temperatures, the phonon contribution to the energy
transport becomes significant. In this temperature range, the thermal conductivity
becomes approximately proportional to T2
for pure metals. The thermal conductivity
increases to a very high maximum as the temperature is lowered, until the mean free
path of the energy carriers becomes on the order of the dimensions of the material
sample. When this condition is reached, the boundary of the material begins to
introduce a resistance to the motion of the carriers, and the carrier mean free path

26
becomes constant (approximately equal to the material thickness). Because the
specific heat decreases to zero as the absolute temperature approaches zero, from
eqn. (2.5) we see that the thermal conductivity would also decrease with a decrease
in temperature in this very low temperature region.
In disordered alloys and impure metals, the electronic contribution and tire.
phonon contribution to energy transport are of the same order of magnitude. There is
an additional scattering of the energy carriers due to the presence of impurity atoms
in impure metals. This scattering effect is directly proportional to absolute
temperature. Dislocations in the material provide a scattering that is proportional to
T2
, and grain boundaries introduce a scattering that is proportional to T3
at
temperatures much lower than the Debye temperature. All these effects combine to
cause the thermal conductivity of allays and impure metals to decrease as the
temperature is decreased, and the high maximum in thermal conductivity is
eliminated in alloys.
2.7. Specific heats of solids
The specific heat of a substance is defined as the energy required to change
the temperature of the substance by one degree while the pressure is held constant
(c ) or while the volume is held constant (cv). For solids and liquids at ordinary
pressures, the difference between the two specific heats is small, while there is
considerable difference for gases. The variation of the specific heats with
temperature gives an indication of the way in which energy is being distributed
among the various modes of energy of the substance on a microscopic level.
Specific heat is a physical property that can be predicted fairly accurately by
mathematical models through statistical mechanics and quantum theory. For solids
the Debye model gives a satisfactory representation of the variation of the specific
heat with temperature. In this model, Debye assumed that the solid could be treated
as a continuous medium, except that the number of vibrational waves representing
internal energy must be limited to the total number of vibrational degrees of freedom
of the atoms making up the mediumthat is, three times the total number of atoms.
The expression for the specific heat of a monatomic crystalline solid as obtained
through the Debye theory is

27
D/T
3 4 x
3 x 20
D DD
9RT x e dx T T
C 3R D
(e 1)


   
     
      

(2.6) where
8D is called the Debye characteristic temperature and is a property of the material,
and D(T/ D) is called the Debye function. A plot of the specific heat as given by eqn.
(2.6) is shown in Fig. 2.8, and the Debye specificheat function is tabulated in Table
2.1. Values of D for several substances are given in Table 2.2.
Fig. 2.8. The Debye specific heat function.

28
Table 2.1. Debye specific heat function
T/ D Cv/R T/ D Cv/R T/ D Cv/R
0.08
0.09
0.10
0.12
0.14
0.16
0.18
0.20
0.25
0.30
0.35
0.40
0.1191
0.1682
0.2275
0.3733
0.5464
0.7334
0.9228
1.1059
1.5092
1.8231
2.0597
2.2376
0.45
0.50
0.60
0.70
0.80
0.90
1.00
1.10
1.20
1.30
1.40
1.50
2.3725
2.4762
2.6214
2.7149
2.7781
2.8227
2.8552
2.8796
2.8984
2.9131
2.9248
2.9344
1.60
1.70
1.80
1.90
2.00
2.20
2.40
2.60
2.80
3.00
4.00
5.00
2.9422
2.9487
2.9542
2.9589
2.9628
2.9692
2.9741
2.9779
2.9810
2.9834
2.9844
2.9900
The theoretical expression for the Debye temperature is given by
1
3
a
D
h 3N
k 4 V
  
   
  (2.7)
where h = Planck’s constant
va = speed of sound in the solid
k = Boltzmann’s constant
N/V = number of atoms per unit volume for the solid.
2.8 Specific Heat of Liquids and Gases
In general, the specific heat Cv of cryogenic liquids decreases in the same
way that the specific heat of crystalline solids decreases as the temperature is
lowered. At low pressures the specific heat cp decreases with a decrease in
temperature also. At high pressures in the neighborhood of the critical point, humps
in the specificheat curve are observed for all cryogenic fluids (and in fact for all
fluids). From thermodynamic reasoning we know that the difference in specific heats
for a pure substance is given by

29
P
P
p
C C T
T T


    
     
     (2.10)
In the vicinity of the critical point, the coefficient of thermal expansion
P
1
T
 
   
  
becomes quite large; therefore, one would expect large increases of the specific heat
cp in the vicinity of the critical point also.
The specific heat of liquid helium behaves in a peculiar wayit shows a high,
sharp peak in the neighborhood of 2.17 K (3.91o
R). The behavior of liquid helium is
so different from that of other liquids that we shall devote a separate section to a
discussion of its properties.
Gases at pressures low compared with their critical pressure approach the
idealgas state, for which the specific heat Cu is independent of pressure. According
to the classical equipartition theorem, the specific heat of a material is given by
Cv = ½Rf (2.11)
where f is the number of degrees of freedom of a molecule making up the material.
For monatomic gases, the only significant mode of energy is translational kinetic
energy of the molecules, which involves three degrees of freedom. From eqn. (2.11)
the specific heat Cv for such monatomic gases as neon and argon in the idealgas state
is Cv = 3
/2R. In diatomic gases, other modes are possible. For example, if we consider
a "rigiddumbbell" model of a diatomic molecule such as nitrogen (i.e., we neglect
vibration of the molecule), there are three translational degrees of freedom plus two
rotational degrees of freedom. We consider only two rotational degrees of freedom
because the moment of inertia of the molecule about an axis through the centers of
the two atoms making up the molecule is negligibly small compared with the
momel1t of inertia about an axis perpendicular to the interatomic axis. From eqn.
(2.11) the specific heat Cv for the rigiddumbbell model of an ideal diatomic gas
would be Cv = 5
/2R. This is true for most diatomic gases at ambient temperatures, at
which the gases obey classical statistics. Because the molecules in a diatomic gas are
not truly rigid dumbbells, we should also expect to have vibrational modes present,

30
in which the two molecules vibrate around an equilibrium position within the
molecule under the influence of the interatomic forces holding the molecule together.
In this case, two more degrees of freedom due to the vibrational mode would be
present, so the specific heat for a vibratingdumbbell molecule would be Cv = ~R
according to the classical theory.
In the actual case, the rotational and vibrational modes are quantized, so
they are not excited if the temperature is low enough. The variation of the specific
heat of diatomic hydrogen gas with temperature is illustrated in Fig. 2.9. At very low
temperatures, only the translational modes are excited, so the specific heat Cv takes
on the value 3
/2R, the same as that of a monatomic gas. To determine whether the
rotational modes will be excited, one must compare the temperature of the gas with a
characteristic rotation temperature r, defined by
2
r 2
h
8 Ik
 
 (2.12)
where h = Planck's constant
I = moment of inertia of the molecule about an axis perpendicular to the
interatomic axis
k = Boltzmann's constant
If the temperature is less than about 1
/3 r the rotational mode is not appreciably
excited; if the temperature is greater than about 3 r, the rotational mode is practically
completely excited. Most diatomic gases become liquids at temperatures higher than
3 r; however, H2, D2, and HD are exceptions to this statement. Because of the small
moment of inertia of the hydrogen molecule, the characteristic rotation temperature
is quite a bit above the liquefaction temperature for hydrogen ( r = 85.4 K or
153.7o
R for hydrogen, so 3 , = 256.2 K or 461.1o
R). The specific heat Cv of
hydrogen gas rises from 3
/2R at temperatures below about 30 K (54°R) to 5
/2R at
temperatures above 255 K (459°R).

31
The vibrational modes for a diatomic gas are also quantized and become
excited at temperatures on the order of a characteristic vibration temperature v
defined by
h
k

 
f
(2.13)
Fig. 2.9. Variation of the specific heat c, for hydrogen gas.
where fv is the vibrational frequency of the molecule. The characteristic vibration
temperature for gases is much higher than cryogenic temperatures, so the vibrational
mode is not excited for gases at cryogenic temperatures ( v = 6100 K or 1O,980o
R
for hydrogen gas).
The change in the specific heat of hydrogen between 30 K and 255 K is
important for hydrogen liquefiers and hydrogencooled helium liquefiers because it
affects the effectiveness of the heat exchangers, as we shall see in Chap. 3.
At pressures higher than near ambient, the specific heats of gases vary in a
more complicated manner with temperature and pressure. A complete coverage of
this effect is beyond the scope of our present discussion.
2.9. Coefficient of thermal expansion
The volumetric coefficient of thermal expansion is defined as the
fractional change in volume per unit change in temperature while the pressure on the

32
material remains constant. The linear coefficient of thermal expansion t is defined
as the fractional change in length (or any linear dimension) per unit change in
temperature while the stress on the material remains constant. For isotropic materials,
= 3 t. The temperature variation of the linear coefficient of thermal expansion
for several materials is shown in Fig. 2.10.
The temperature variation of the coefficient of thermal expansion may be
explained through a consideration of the intermolecular forces of a material. The
intermolecular potentialenergy curve, as shown in Fig. 2.11, is not symmetrical.
Therefore, as the molecule acquires more energy (or as its temperature is increased),
its mean position relative to its neighbors becomes larger; that is, the material
expands. The rate at which the mean spacing of the atoms increases with temperature
increases as the energy or temperature of the material increases; thus, the coefficient
of thermal expansion increases as temperature is increased.
Fig. 2.10. Linear coefficient of thermal expansion for several materials at low
temperature: (I) 2024T4 aluminum; (2) beryllium copper; (3) K Monel; (4) titanium;
(5) 304 stainless steel; (6) C1020 carbon steel (NBS Monograph 29, Thermal
Expansion of Solids at Low Temperatures).

33
Since both the specific heat and the coefficient of thermal expansion are
associated with intermolecular energy, one might expect to find a relationship
between the two properties. For crystalline solids, the Gruneisen relation expresses
this interdependence:
GC
B
 
 
(2.14)
where is the density of the material, B is the bulk modulus, and G is the
Gruneisen constant, which is independent of temperature as a first approximation.
Values of the Gruneisen constant for some materials are presented in Table 2.4.
Table 2.4. Values of the Gruneisen constant for selected solids
Material G
Aluminum 2.17
Copper 1.96
Gold 2.40
Iron 1.60
Lead 2.73
Nickel 1.88
Platinum 2.54
Silver 2.40
Tantalum 1.75
Tungsten 1.62
We have seen previously that the bulk modulus B is not strongly dependent
upon temperature for solids (it increases somewhat as the temperature is decreased);
therefore, the coefficient of thermal expansion for solids should vary with
temperature in the same way that the Debye specific heat varies with temperature.
This general variation has been found true experimentally. At very low temperatures
(T < D/12), the coefficient of thermal expansion is proportional to T3
•
ELECTRIC AND MAGNETIC PROPERTIES
2.10. Electrical conductivity
The electrical conductivity k, of a material is defined as the electric current
per unit crosssectional area divided by the voltage gradient in the direction of
current flow. The electrical resistivity re is the reciprocal of the electrical

34
conductivity. The variation with temperature of the electrical resistivity of several
materials is shown in Fig. 2.12.
Fig.2.11. Variation of the intermolecular potential energy for a pair of molecules. At
absolute zero, the molecular spacing would be r0.
When an external electric field is applied to an electric conductor, free
electrons in the conductor are forced to move in the direction of the applied field.
This motion is opposed by the positive ions of the metal lattice and impurity atoms
present in the material. Decreasing the temperature of the conductor decreases the
vibrational energy of the ions, which in turn results in a smaller interference with
electron motion. Therefore, the electrical conductivity increases as the temperature is
lowered for metallic conductors.
One of the first theories of electric resistance was developed by Drude
(Kittel 1956), who treated the free electrons as an "electron gas." He obtained the
following expression for the electrical conductivity:

35
2
e
e
(N / V)e
k
m


 (2.15)
where N/V = number of free electrons per unit volume
e = charge of an electron
= electron mean free path
me = mass of an electron
 = average speed of an electron
Equation (2.15) gives the correct order of magnitude for the electrical
conductivity of a metal such as silver at room temperature if we assume that N/V is
on the order of the number of valence electrons per unit volume, is on the order of
the interatomic spacing, and the mean electron kinetic energy is given by
2
3
e 2½m kT  , according to classical theory. In order to obtain the correct
temperature dependence for the electrical conductivity from eqn. (2.15), however, we
must assume that the electron mean free path is inversely proportional to T ½
because
the electrical conductivity is approximately inversely proportional to absolute
temperature.
An application of quantum mechanics and band theory to the problem of
prediction of the electrical conductivity does not result in an equation different from
eqn. (2.15); however, it does allow us to predict the correct relationships for the
electron velocity and mean free path. According to the quantummechanical picture,
the velocity appearing in eqn. (2.15) is the average velocity of the electrons near the
socalled Fermi surface of the metal. For ordinary temperatures this velocity is
practically constant:
1
3n
F
e e
h 3 N
2 m 2 m
 
         (2.16)

36
Fig. 2.12. Electrical resistivity ratio for several materials at low temperatures:
(1)copper; (2) silver; (3) iron; (4) aluminum (Stewart and Johnson 1961).
2.11. Superconductivity
One of the properties of certain materials that appears only at very low
temperatures is superconductivity the simultaneous disappearance of all electric
resistance and the appearance of perfect diamagnetism. In the absence of a magnetic
field, many elements, alloys, and compounds become superconducting at a fairly
welldefined temperature, called the transition temperature in zero field T0.
Superconductivity can be destroyed by increasing the magnetic field around the
material to a large enough value. The magnetic field strength required to destroy
superconductivity is called the critical field HC. For Type I superconductors, there is
a single value of the critical field at which the transition from superconducting to
normal behavior is abrupt. For Type II superconductors (socalled "hard"
superconductors), there is a lower critical field HC1, at which the transition begins,

37
and an upper critical field HC2 at which the transition is complete. Table 2.5 lists the
critical field at absolute zero H0 and the transition temperature for several materials.
Note that some alloys are superconductors even though the pure elements making up
the alloys are not superconductors.
For Type I specimens in the shape of a long cylinder or wire placed parallel
10 the applied magnetic field, the critical field is well defined at every temperature
and is a function of temperature. The critical field may be related approximately to
the absolute temperature by
2
C 0 0H H [1 (T / T ) ]  (2.24)
Although the parabolic relationship is not exactly true, it is adequate for
many purposes.
The phenomenon of superconductivity was discovered by Kamerlingh
Onnes in 1911 while investigating the electric resistance of mercury wire. After its
discovery, this new state of matter became the object of investigation by several
theoretical and experimental physicists to determine the properties of
superconductors and to try to explain the basic mechanism of the phenomenon. The
early attempts to develop a thermodynamic theory were unsuccessful because it was
assumed that any magnetic field present within the material in the normal state
remained frozenin when the substance became superconducting.
Gorter (1933) applied the principles of reversible thermodynamics to the
superconducting phenomenon and obtained results that were in excellent agreement
with experimental measurements. This caused quite a bit of discussion because many
investigators thought that the transition was not thermodynamically reversible. In the
same year, this matter was cleared up somewhat by an experiment by Meissner and
Ochsenfeld (1933). They cooled a monocrystal of tin in a magnetic field until it
became superconducting and found that the magnetic field was expelled from within
the material when the sample became superconducting, as shown in Fig. 2.13. The
results of the MeissnerOchsenfeld experiment indicated that the magnetic flux
density within a bulk superconducting material (Type I) was always zero, no matter
what value of magnetic flux density existed within the material before the transition.

38
Superconductivity was shown to be a case not only of zero electric resistance but
also of perfect magnetic insulation. The Meissner effect as the expulsion of the
magnetic field when a material becomes superconducting is called, forms the basis
for the frictionless bearing and superconducting motor.
Fig. 2.13. The Meissner effect. When a material is normal, the magnetic flux lines
can penetrate the material. When the material becomes superconducting, the
magnetic field is expelled from thin the material.
Shortly after the discovery of the Meissner effect, two "phenomenological
theories" of superconductivity were proposed. Gorter and Casimir (1934) proposed a
twofluid model, in which two types of electrons took part in the electric currentthe
normal or "uncondensed" ones and the superconducting or "condensed" ones. This
model was used to predict thermodynamic properties of superconductors with good
success. Fritz and Heinz London (1935) proposed an electromagnetic theory that, in
conjunction with the classical Maxwell equations of electromagnetism, predicted
many of the electric and magnetic properties of superconductors. The results of the
calculations made by the Londons showed that the magnetic field actually did
penetrate the surface of a superconductor for a very small distance (on the order of
0.1 m) called the penetration depth. The results also predicted that extremely thin
superconductors should have much higher critical fields than thick ones. Kropschot
and Arp (1961) suggested that this property of thin superconducting films could be
used in highfield, thinfilm superconducting magnets.
Both the theory of the Londons and the theory of GorterCasimir predicted
many of the properties of superconductors, but the theories did not explain the "why"

39
of the phenomenon. It was not until 1950 that an acceptable fundamental theory of
superconductivity was suggested. Frolich (1950) and Bardeen (1950) independently
proposed a mechanism involving the interaction of electrons in the superconductor.
Their ideas were developed into the BCS theory in 1957 by Bardeen, Cooper, and
Schrietfer (1957). They applied the quantum theory to pairs of electrons produced by
a special electronlattice interaction. This process may be visualized as one in which
the first electron moving through the lattice causes a slight displacement of the ions,
which results in a positive screening charge slightly greater than the charge of the
electron. The second electron is then attracted toward the net positive charge region.
A correlation exists between all the pairs of electrons in the superconductor, and a
finite amount of energy is required to break up the pair, corresponding to the so
called energy gap for the superconductor. As the temperature is increased above the
threshold value, enough energy is available to uncouple the electron pair, and the
material becomes normal.
Ginzburg and Landau (1950) developed a phenomenological theory that
explained the difference between the Type I and Type II superconductors in terms of
a parameter k, which was related to the surface energy of the material. Those
materials for which k is less than 1/ 2 have a positive surface energy and are Type
I superconductors. On the other hand, those materials for which k is greater than
1/ 2 have a negative surface energy and are Type II superconductors. This theory
of superconductivity is now known as the GLAG theory after the four Russian
contributors: Ginzburg, Landau, Abrikosov, and Gor’kov. Based on the concepts of
the theory, relationships between the parameter K and the upper and lower critical
fields were established.
C
C1
H (0.081 ln k)
H
k 2

(2.26)
and
C2 CH 2 kH
From a practical standpoint, eqn. (2.27) indicates that materials with a large
value of K will have a high value of the upper critical field HC2.

40
For materials which have a relative permeability of approximately unity, the
magnetic induction and the magnetization M are related by
= 0(H+M) (2.28)
For Type I superconductors, the magnetic induction is zero, and H = –M.
At. The behavior of Type II superconductors is similar, for fields less than the lower
critical field HC1. For higher magnetic fields, the field begins to penetrate the
material, and the behavior of the material is shown in Fig. 2.14.
There are several properties that change either abruptly or gradually when a
material makes the transition from the normal to the superconducting state. Some of
these properties include:
1. Specific heat. The specific heat increases abruptly when a material becomes
superconducting.
2. Thermoelectric effects. All the thermoelectric effects (Peltier, Thomson,
and Seebeck effects) vanish when a material becomes superconducting. A
superconducting thermocouple would not work at all.
3. Thermal conductivity. In the presence of a magnetic field, the thermal
conductivity of a pure metal decreases abruptly when the metal becomes
superconducting, although for some alloys (for example, PbBi in a limited
range of compositions) the opposite is true. In the absence of a magnetic
field, there is no discontinuous change in the thermal conductivity, but the
slope change is sharp on the conductivitytemperature curve.
4. Electric resistance. For Type I superconductors the decrease of resistance
to zero is quite abrupt; however, for Type II superconductors the change is
sometimes spread over a temperature range as large as 1 K.
5. Magnetic permeability. The magnetic permeability suddenly decreases to
zero for Type I superconductors (the Meissner effect); however, for Type II
superconductors the Meissner effect is incomplete for magnetic fields
greater than the lower critical field.

41
Fig. 2.14. Variation of the magnetization with applied magnetic field intensity for
Type I and Type II superconductors.
Over the years considerable experimental effort has been expended in the
study of superconducting alloys and compounds in order to develop materials that
would remain superconducting at high values of magnetic field and at temperatures
nearer to liquidhydrogen temperature (about 20 K). The materials most used for
superconducting magnets have been either the bodycenteredcubic alloys of niobium
and titanium or the cubic betatungstentype (Al5) compounds, such as Nb3Sn.
The bodycenteredcubic alloys have been used in construction of magnets
with field strengths up to 10 tesla, while the niobiumtitanium alloys can reach 12
tesla. In order to achieve thermal and magnetic stability, the niobiumtitanium wires
used in superconducting magnets are usually clad with highconductivity copper.
Although the compound niobiumtin has superconducting properties somewhat
superior to niobiumtitanium, Nb3Sn is extremely brittle, and special fabrication
methods are required for its use.
PROPERTIES OF CRYOGENIC FLUIDS
2.12. Fluids other than hydrogen and helium
A summary of some of the thermodynamic and transport properties of fluids
commonly used in cryogenic engineering is shown in Table 2.6. Further data on fluid
properties are contained in the appendix.

42
Liquid nitrogen is a dear, colorless fluid that resembles water in appearance.
At standard atmospheric pressure (101.3 kPa) liquid nitrogen beils at 77.36 K
(139.3°R) and freezes at 63.2 K (113.8°R). Saturated liquid nitrogen at 1 atm has a
density of 807 kg/m3
(50.4 lbm/ft3
) in comparison with water at 15.6o
C (60°F), which
has a density of 999 kg/m3
(62.3 lbm/ft). One of the significant differences between
the properties of liquid nitrogen and water (apart from the difference in normal
boiling points) is that the heat of vaporization of nitrogen is more than an order of
magnitude smaller than that of water. At the normal boiling point, liquid nitrogen has
a heat of vaporization of 199.3 kJ/kg (85.7 Btu/lbm), while water has a heat of
vaporization of 2257 kJ/kg (970.3 Btu/lbm).
Nitrogen with an atomic number of 14 has two stable isotopes with mass
numbers 14 and 15. The relative abundance of these two isotopes is 10,000:38. They
are relatively difficult to separate.
Because nitrogen is the major constituent of air (n.08 percent by volume or
75.45 percent by weight), it is produced commercially by distillation of liquid air.
Liquid oxygen has a characteristic blue color caused by the presence of the
polymer or longchain molecule O4. At 1 atm pressure liquid oxygen boils at 90.18 K
(162.3°R) and freezes at 54.4 K (98.00
R). Saturated liquid oxygen at 1 atm is more
dense than water at 15o
C (liquidoxygen density = 1141 kg/m3
= 71.2 lbm/ft3
). Oxygen
is slightly magnetic (paramagnetic) in contrast to the other cryogenic fluids, which
are nonmagnetic. By measuring the magnetic susceptibility, small amounts of
oxygen may be detected in mixtures of other gases. Because of its chemical activity,
oxygen presents a safety problem in handling. Serious explosions have resulted from
the combination of oxygen and hydrocarbon lubricants.
Oxygen with an atomic number of 16 has three stable isotopes of mass
numbers 16, 17, and 18. The relative abundance of these three isotopes is
10,000:4:20.
Oxygen is manufactured in large quantities by distillation of liquid air
because it is the second most abundant substance in air (20.95 percent by volume or
23.2 percent by weight).

43
Liquid argon is a clear, colorless fluid with properties similar to those of
liquid nitrogen. It is inert and nontoxic. At 1 atm pressure liquid argon boils at 87.3
K (157.1o
R) and freezes at 83.8 K (150.8°R). Saturated liquid argon at 1 atm is more
dense than oxygen, as one would expect, because argon has a larger molecular
weight than oxygen (argon density = 1394 kg/m3
= 87.0 Ibm/ft3
for saturated liquid at
1 atm). The difference between the normal boiling point and the freezing point for
argon is only 3.5 K (6.3°R).
Argon has three stable isotopes of mass numbers 36, 38, and 40 that occur in
a relative abundance in the atmosphere in the ratios 338:63:100,000.
Argon is present in atmospheric air in a concentration of 0.934 percent by
volume or 1.25 percent by weight. Because the boiling point of argon lies between
that of liquid oxygen and that of liquid nitrogen (slightly closer to that of liquid
oxygen), a crude grade of argon (90 to 95 percent pure) can be obtained by adding a
small auxiliary argonrecovery column in an airseparation plant.
Neon is another gas that can be produced as a byproduct of an air
separation plant. Liquid neon is a clear, colorless liquid that boils at 1 atm at 27.09 K
(48.8°R) and freezes at 24.54 K (44.3°R). The boiling point of neon is somewhat
above that of liquid hydrogen. But the fact that neon is inert, has a larger heat of
vaporization per unit volume, and has a higher density makes it an attractive
refrigerant when compared with hydrogen.
Neon (atomic weight = 20.183) has three stable isotopes of mass numbers
20, 21, and 22 that occur in a relative abundance in atmospheric air in the ratios
10,000:28:971.
Liquid fluorine is a light yellow liquid having a normal boiling point of
85.24 K (153.4°R). At 53.5 K (96.4°R) and 101.3 kPa, liquid fluorine freezes as a
yellow solid, but upon subcooling to 45.6 K (82°R) it transforms to a white solid.
Liquid fluorine is one of the most dense cryogenic liquids (density at normal boiling
point = 1507 kg/m3
= 94.1 Ibm/ft3
).
Fluorine is characterized chemically by its extreme reactivity, as indicated
by the emf of its electrochemical half cell (E = –2.85 volts). Fluorine will react with

44
almost all inorganic substances. If fluorine comes in contact with hydrocarbons, it
will react hypergolically with a high heat of reaction, which is sometimes sufficiently
high that the metal container for the fluorine is ignited. Such metals as lowcarbon
stainless steel and Monel, which are used in fluorine systems, develop a protective
surface film when brought in contact with fluorine gas. This surface film prevents the
propagation of the fluorinemetal reaction into the bulk metal.
Fluorine is highly toxic. The fatal concentration range for animals is 200
ppmhr (Cassutt et al. 1960). That is, for an exposure time of I hour, 200 ppm of
fluorine is fatal; for an exposure time of 15 minutes, 800 ppm is fatal; and for an
exposure time of 4 hours, 50 ppm is fatal. The maximum allowable concentration for
human exposure is usually considered to be approximately 1 ppmhr. The presence
of fluorine in air may be detected by its sharp, pungent odor for concentrations as
low as I to 3 ppm. Because of its high toxicity, liquid fluorine is not utilized on a
large scale.
Methane is the principal component of natural gas. It is a clear, colorless
liquid that boils at 1 atm at 111.7 K (201.1o
R) and freezes at 88.7 K (159.7°R).
Liquid methane has a density approximately onehalf of that for liquid nitrogen
(methane. density = 424.1 kg/m3
= 26.5 lbm/ft3
). Methane forms explosive mixtures
with air in concentrations ranging from 5.8 to 13.3 percent by volume. Liquid
methane has been shipped in large quantities by tanker vessels. The Methane Pioneer
made her maiden voyage on January 28, 1959 with 5000 m3
of LNG (liquid natural
gas). Since that time, several vessels have been commissioned for LNG transport.
2.13. Hydrogen
Liquid hydrogen has a normal boiling point of 20.3 K (36.5o
R) and a density
at the normal boiling point of only 70.79 kg/m3
(4.42 Lbm/ft3
). The density of liquid
hydrogen is about onefourteenth that of water; thus, liquid hydrogen is one of the
lightest of all liquids. Liquid hydrogen is an odorless, colorless liquid that alone will
not support combustion. In combination with oxygen or air, however, hydrogen is
quite flammable. Experimental work (Cassutt et al. 1960) has shown that hydrogen
air mixtures are explosive in an unconfined space in the range from 18 to 59 percent
hydrogen by volume.

45
Natural hydrogen is a mixture of two isotopes: ordinary hydrogen (atomic
mass = 1) and deuterium (atomic mass = 2). Hydrogen gas is diatomic and is made
up of molecules of H2 and HD (hydrogen deuteride) in the ratio of 3200:1. A third
unstable isotope of hydrogen exists, called tritium; however, it is quite rare in nature
because it is radioactive with a short half life.
One of the properties of hydrogen that sets it apart from other substances is
that it can exist in two different molecular forms: orthohydrogen and para
hydrogen. The mixture of these two forms at high temperatures is called normal
hydrogen which is a mixture of 75 percent orthohydrogen and 25 percent para
hydrogen by volume. The equilibrium (catalyzed) mixture of oH2 and pH2 at any
given temperature is called equilibriumhydrogen (eH2). The equilibrium
concentration of pH2 in eH2 as a function of temperature is given in Table 2.7. At
the normal boiling point of hydrogen (20.3 K or 36.5o
R), equilibrium hydrogen has a
composition of 0.20 percent oH2 and 99.80 percent pH2. One could say that it is
practically all parahydrogen .
The distinction between the two forms of hydrogen is the relative spin of the
particles that make up the hydrogen molecule. The hydrogen molecule consists of
two protons and two electrons. The two protons possess spin, which gives rise to
angular momentum of the nucleus, as indicated in Fig. 2.15. When the nuclear spins
are in the same direction, the angular momentum vectors for the two protons are in
the same direction. This form of hydrogen is called orthohydrogen. When the
nuclear spins are in opposite directions, the angularmomentum vectors point in
opposite directions. This form of hydrogen is called parahydrogen.
Table 2.7. Equilibrium concentration of parahydrogen in equilibriumhydrogen
Temperature
(K)
Mole fraction
ParaHydrogen
20.27 0.9980
30 0.9702
40 0.8873
50 0.7796
60 0.6681
70 0.5588
80 0.4988
90 0.4403

46
100 0.3947
120 0.3296
140 0.2980
160 0.2796
180 0.2676
200 0.2597
250 0.2526
300 0.2507
Deuterium can also exist in both ortho and para forms. The nucleus of the
deuterium atom consists of one proton and one neutron, so that the hightemperature
composition (composition of normal deuterium) is twothirds orthodeuterium and
onethird paradeuterium. In the case of deuterium, pD2 converts to oD2 as the
temperature is decreased, in contrast to hydrogen, in which oH2 converts to pH2
upon decrease of temperature. The hydrogen deuteride molecule does not have the
symmetry that hydrogen and deuterium possess; therefore, HD exists in only one
form.
As one can see from Table 2.7, if hydrogen gas at room temperature is
cooled to the normal boiling point of hydrogen, the oH2 concentration decreases
from 75 to 0.2 percent; that is, there is a conversion of oH2 to pH2 as the
temperature is decreased. This changeover is not instantaneous but takes place over a
definite period of time because the change is made through energy exchanges by
molecular magnetic interactions. During the transition, the original oH2 molecules
drop to a lower molecularenergy level. Thus the changeover involves the release of
a quantity of energy called the heat of conversion. The heat of conversion is related
to the change of momentum of the hydrogen nucleus when it changes direction of
spin. This energy released in the exothermic reaction is greater than the heat of
vaporization of liquid hydrogen, as one can see from the tabulated values of the heat
of conversion and heat of vaporization shown in Appendix D.2.

47
Fig. 2.15. Orthohydrogen and parahydrogen.
When hydrogen is liquefied, the liquid has practically the roomtemperature
composition unless some means is used to speed up the conversion process. If the
unconverted normal hydrogen is placed in a storage vessel, the heat of conversion
will be released within the container, and the boiloff of the stored liquid will be
considerably larger than one would determine from the ordinary heat in leak through
the vessel insulation. Note that the heat of conversion at the normal boiling point of
hydrogen is 703.3 kJ/kg (302.4 Btu/lbm) and the latent heat of vaporization is 443 kJ
/kg (190.5 Btu/lbm). The conversion process evolves enough energy to boil away
approximately 1 percent of the stored liquid per hour, so the reaction would
eventually result in much of the stored liquid being boiled away. For this reason, a
catalyst is used to speed up the conversion so that the energy may be removed during
the liquefaction process before the liquid is placed in the storage vessel.
In the absence of a catalyst, the orthopara transformation is a second order
reaction (Scott et al. 1934); that is, the rate of change of the oH2 mole fraction is
given by
20
2 0
dx
C x
dt
 
(2.29)
where C2 is the reactionrate constant, 0.0114 hr–1
for hydrogen at the normal boiling
point, and x0 = 1 – xp is the mole fraction of oH2 present at any time t. If eqn. (2.29)
is integrated from the initial time when the aH2 composition is that in normal
hydrogen (0.750), the mole fraction of oH2 at any time is given by
o
2
0.75
x
1 0.75C t

 (2.30)

48
for liquid hydrogen at the normal boiling point. In the presence of a catalyst that is
well mixed with the hydrogen, the reaction approaches a first order reaction for the
gas phase (Chapin et al. 1960), for which
20
1 0
dx
C x
dt
 
(2.31)
where C1 is the reactionrate constant, which depends upon the catalyst used, the
temperature, and the pressure of the gas. If the catalyst is added to the liquid phase,
the reaction is a zeroorder one (Cunningham et al. 1960), for which
0
0
dx
C
dt
 
(2.32)
where C0 is the reactionrate constant for the zeroorder reaction, which also depends
upon the catalyst, the fluid temperature, and the pressure.
Fig. 2.16. Specific heat c. for pH2• nH2• and oH2 (by permission from Fowler and
Guggenheim 1949).

49
These two forms of hydrogen have different specific heats because of the
different weighting of the energy levels of the two forms, as indicated in Fig. 2.16.
Because of this difference in specific heats, other thermal and transport properties are
also affected. For example, parahydrogen gas has a higher thermal conductivity than
orthohydrogen gas because of the higher specific heat of pH2.
2.14. Helium 4
Helium has two stable isotopes: He4
, the most common one, and He3
.
Ordinary helium gas contains about 1.3 × 10–4
percent He3
, so when we speak of
helium or liquid helium, we shall be referring to He4
, unless otherwise stated. Liquid
He4
has a normal boiling point of 4.214 K (7.58°R) and a density at the normal
boiling point of 124.8 kg/m3
(7.79 lbm/ft3
), or about oneeighth that of water. Liquid
helium has no freezing point at a pressure of 101.3 kPa (1 atm). In fact, liquid helium
does not freeze under its own vapor pressure even if the temperature is reduced to
absolute zero. At absolute zero, liquid helium 4 must be compressed to a pressure of
2529.8 kPa (24.97 atm or 366.9 psia) before it will freeze, as indicated in Fig. 2.17.
Liquid He4
is odorless and colorless and has an index of refraction near that of
gaseous He4
(nr = 1.02 for liquid He4
). The heat of vaporization of liquid He4
at the
normal boiling point is 20.90 kJ/kg (8.98 Btu/lbm), which is only 1
/110 that of water.
Although helium is classified as a rare gas, and it is one of the most difficult
gases to liquefy, its unusual properties have excited so much interest that helium has
been the object of more experimental and theoretical research than any of the other
cryogenic fluids.

50
Fig. 2.17. Phase diagram for helium 4.
We notice from Fig. 2.17 that the phase diagram of He4
differs in form from
that of any other substance. As mentioned previously, liquid He4
does not freeze
under its own vapor pressure; therefore, there is no triple point for the solidliquid
vapor region of helium as there is for other substances. There are two different liquid
phases: Liquid helium I, the normal liquid; and liquid helium II, the superliquid. The
phase transition curve separating the two liquid phases is called the lambda line, and
the point at which the lambda line intersects the vaporpressure curve is called the
lambda point, which occurs at a temperature of 2.171 K (3.9lo
R) and a pressure of
5.073 kPa (0.050 atm or 0.736 psia).
In Fig. 2.18, we see that the specific heat of liquid helium varies with
temperature in an unusual manner for liquids. At the lambda point, the liquid specific
heat increases to a large value as the temperature is decreased through this point.
With a little imagination, one could say that the form of the specificheat curve looks
somewhat like the small Greek letter lambda; hence, the name lambda point. It was
first believed that the transition form helium I to helium II was a secondorder
transition; however, later work has shown that the transition is more complicated.

51
Because the specific heat of liquid helium has such a different behavior
from that of other liquids, we should expect that the other thermal and transport
properties could also differ in behavior. Strangely enough, the thermal conductivity
of helium I decreases with a decrease in temperature, which is similar to the behavior
of the thermal conductivity of a gas.
Heat transfer in the other form, helium II, is even more spectacular. When a
container of liquid helium I is pumped upon to reduce the pressure above the liquid,
the fluid boils vigorously (depending upon the rate of pumping) as the pressure of the
liquid decreases. During the pumping operation, the temperature of the liquid
decreases as the pressure is decreased and liquid is boiled away. When the
temperature reaches the lambda point and the fluid becomes liquid helium II, all
ebullition suddenly stops. The liquid becomes clear and quiet, although it is
vaporizing quite rapidly at the surface. The thermal conductivity of liquid helium II
is so large that vapor bubbles do not have time to form within the body of the fluid
before the heat is quickly conducted to the surface of the liquid. Liquid helium I has
a thermal conductivity of approximately 24 mW/mK (0.014 Btu/hrfto
F) at 3.3 K
(6°R), whereas liquid helium II can have an apparent thermal conductivity as large as
85 kW/mK (49,000 Btu/hrft°F) – much higher than that of pure copper at room
temperature! There is some question about defining a thermal conductivity for liquid
helium II because the thermal conductivity defined in the ordinary manner depends
not only on temperature, but also on the temperature gradient and the size of the
container (Keesom et al. 1940). The reason for this behavior will illustrate the nature
of this unique liquid.
One of the unusual properties of liquid helium II is that it exhibits
superliquidity; under certain conditions, it acts as if it had zero viscosity. In
explaining the behavior of1iquid helium II, it has been proposed (Landau 1941) that
the liquid be imagined to be made up of two different fluids: the ordinary fluid and
the superfluid, which possess zero entropy and can move past other fluids and solid
boundaries with zero friction. Using this model, liquid helium II has a composition of
normal and superfluid that varies with temperature, as shown in Table 2.8. At

52
absolute zero, the liquid composition is 100 percent superfluid; at the lambda point,
the liquid composition is 100 percent normal fluid.
Fig. 2.18. Specific heat of saturated liquid helium 4.
The addition of heat to liquid helium II raises the local temperature of the
liquid around the point where heat is being added, which raises the concentration of
normal molecules and lowers the concentration of superfluid ones. The superfluid
then moves to equalize the superfluid concentration throughout the body of the
liquid. Because the superfluid is frictionless, it can move rapidly; therefore, we see
that the high apparent thermal conductivity of helium II is really due to a fast
convection process rather than simply to conduction.
This type of transfer mechanism also explains the socalled "fountain effect"
that is observed in liquid helium II (Allen and Jones 1938; Keller 1969). When heat
is added to the powder in the apparatus shown in Fig. 2.19, the increase in
temperature tends to raise the concentration of normal fluid, and the superfluid
rushes in to equalize the concentration. Normal fluid, because of its viscosity, cannot
leave through the small openings between the fine powder particles very rapidly. The
amount of helium quickly builds up within the tube as a result of this inflow of

53
superfluid, and finally liquid squirts out the open end of the capillary tube. Fountains
as high as 25 cm to 30 cm (10 in. to 12 in.) have been observed.
Table 2.8. Variation of the mass fraction (pn/p) of normal fluid in liquid helium II
according to the twofluid model
Temperature (K) Mass Fraction of Superfluid Mass Fraction of Normal Fluid
0
0.6
0.7
0.8
0.9
1.0
1.1
1.2
1.3
1.4
1.5
1.6
1.7
1.8
1.9
2.0
2.1
2.171
0.000
0.427×10–4
2.52
9.66
0.00295
0.00752
0.0156
0.0292
0.0478
0.0754
0.11
0.17
0.24
0.32
0.43
0.56
0.74
1.00
1.000
0.999957
0.999748
0.999034
0.99705
0.99248
0.9844
0.9708
0.9522
0.9246
0.890
0.83
0.76
0.68
0.57
0.44
0.26
0.00

54
Fig. 2.19. The fountain effect in liquid helium II.
Fig. 2.20. The creeping film in liquid helium II.
Another phenomenon associated with superfluid liquid helium is the Rollin
film, as illustrated in Fig. 2.20. If a beaker is filled with liquid helium II from a larger
container, and the beaker is lifted above the surface of the helium II in the larger
container, a thin film (about 30 nm or 10–6
in. thick) creeps up the inner wall of the

55
beaker, over the side, and falls back into the liquid in the larger container. If the
beaker is emptied and placed, say, halfway into the liquid in the large container, the
film of liquid creeps up the outside of the beaker until the beaker is filled to a level
identical with that of the liquid in the larger container. The velocity of the Rollin film
is dependent upon the film temperature and somewhat on the condition of the surface
over which the film flows.
Second sound is another phenomenon that occurs in liquid helium II. Second
sound is similar to ordinary sound in that it possesses a definite velocity (which is
different from first or ordinary sound velocity), standing waves may be set up, and
the second sound waves may be reflected. Second sound is different from ordinary
sound in that it consists of temperature waves or local oscillations in temperature,
rather than pressure waves or local oscillations in pressure. Second sound was
predicted theoretically by Tisza in 1939, some 7 years before it was measured
experimentally by Peshkov. The velocity of second sound varies from zero at the
lambda point to 239 m/s (783 ft/sec) near absolute zero.
2.15. Helium 3
Liquid He) is a clear, colorless fluid having a normal boiling point of 3.19 K
(5.75°R) and a density at the normal boiling point of 58.9 kgfm) (3.68 lbm/ft3). The
heat of vaporization of liquid He) at the normal boiling point is only 8.49 kl/kg (3.65
Btu/lbm)so small that there was some doubt in the minds of early investigators that
He3
could be liquefied at atmospheric pressure. As in the case of liquid He4
, liquid
He3
remains in the liquid state under its own vapor pressure all the way down to
absolute zero. He) must be compressed to 2930.3 kPa (29.3 atm) at 0.32 K
(0.576°R), whi.ch is the minimum point on the freezing curve shown in Fig. 2.21,
before it will solidify.

56
Fig. 2.21. Phase diagram for helium 3.
The properties of liquid He3
differ considerably from those of liquid He4
at
low temperatures because of quantum effects arising from the difference in mass and
the fact that He3
has an odd number of particles in its nucleus, whereas He4
has an
even number of nuclear particles. Liquid He3
undergoes a different type of superfluid
transition at approximately 3.5 mK (0.006°R).
Mixtures of liquid He3
and liquid He4
also display some peculiar properties.
At temperatures below 0.827 K (1.49°R), He) and He4
mixtures spontaneously
separate into two phasesone that is superfluid (and rich in He4
) and the other that is
normal (and rich in He3
). This phase separation phenomena forms the basis for the
helium dilution refrigerator used to achieve temperatures below 1 K.

57
MODULE III
GASLIQUEFACTION SYSTEMS
After the introduction to the behavior of materials at low temperatures, we
are now ready to study some of the systems that can produce low temperatures
required for liquefaction. The liquefaction of air in the production of oxygen was the
first engineering application of cryogenics. Even today, the production and sale of
liquefied gases is an important area in cryogenic engineering.
In this chapter, we shall discuss several of the systems used to liquefy the
cryogenic fluids. We shall be concerned with the performance of the various
systems, where performance is specified by ·the system performance parameters or
payoff functions. The critical components of liquefaction systems will be examined
to complete this study.
INTRODUCTION
3.1. System performance parameters
There are three payoff functions we might use to indicate the performance
of a liquefaction system:
1. Work required per unit mass of gas compressed, W/m.
2. Work required per unit mass of gas liquefied, W/mf
3. Fraction of the total flow of gas that is liquefied, y = mf/m.
The last two payoff functions are related to the first one by
(–W/m) = (–W/mf)y (3.1)
In any liquefaction system, we should want to minimize the work
requirements and maximize the fraction of gas that is liquefied.
These payoff functions are different for different gases; therefore, we should
also need another performance parameter that would allow the comparison of the
same system using different fluids. The figure of merit (FOM) for a liquefaction
system is such a parameter. It is defined as the theoretical minimum work
requirement divided by the actual work requirement for the system:

58
FOM =
i i f
f
W W / m
W W / m


(3.2)
The figure of merit is a number between 0 and 1. It gives a measure of how
closely the actual system approaches the ideal system performance.
There are several performance parameters that apply to the components of
real systems. These include:
1. Compressor and expander adiabatic efficiencies.
2. Compressor and expander mechanical efficiencies.
3. Heatexchanger effectiveness.
4. Pressure drops through piping, heat exchangers, and so on.
5. Heat transfer to the system from ambient surroundings.
In our initial discussions of system performance, we shall not consider these
component factors but shall return to them when we discuss the major components of
the systems. Thus, we shall first assume that all efficiencies and effectivenesses are
100 percent and that irreversible pressure drops (losses) and heat inleaks are zero.
3.2. The thermodynamically ideal system
In order to have a means of comparison of liquefaction systems through the
figure of merit, we shall first analyze the thermodynamically ideal liquefaction
system. This system is ideal in the thermodynamic sense, but it is not ideal as far as a
practical system is concerned, as we shall see later. The perfect cycle in
thermodynamics is the Carnot cycle. Liquefaction is essentially an opensystem
process; therefore, for the ideal liquefaction system, we shall choose the first two
processes in the Carnot cycle: a reversible isothermal compression followed by a
reversible isentropic expansion. The ideal cycle is shown on the temperatureentropy
plane in Fig. 3:1 along with a schematic of the system.
The gas to be liquefied is compressed reversibly and isothermally from
ambient conditions (point 1) to some high pressure (point 2). This high pressure is
selected so that the gas will become saturated liquid upon reversible isentropic

59
expansion through the expander (point}). The final condition at point f is taken at the
same pressure as the initial pressure at point 1.
The pressure attained at the end of the isothermal compression is extremely
highon the order of 10 GPa or 80 GPa (107
psia) for nitrogen. It is highly impractical
to attain this pressure in a liquefaction system, which is the reason it is not an ideal
process for a practical system.
Fig. 3.1. The thermodynamically ideal liquefaction system
In the analysis of each of the liquefaction systems, we shall apply the First
Law of Thermodynamics for steady flow, which may be written in general as
2 2
net net
c c c coutlets inlets
gz gz
Q W m h m h
2g g 2g g
    
            
   
 
(3.3)
where Qnet is the net heat transfer to or from the system (heat transferred to the
system is considered positive), Wnet is the net work done on or by the system (work
done by the system is considered positive), and the summation signs imply that we
add the enthalpy terms (h), kineticenergy terms ( 2
/2gc where is the fluid velocity
and gc is the conversion factor in Newton's Second Law, gc = 1.00 kgm/Ns2
or
32.174 lbmft/lbfsec2
), and potentialenergy terms (gz/gc, where z is the fluid
elevation above a datum plane and g is the local acceleration due to gravity, 9.806
m/s2
or 32.174 ft/sec2
at sea level) for all inlets and outlets of the system. A system

60
might consist of several different streams, which would result in more than one inlet
and one outlet. In all our system analysis, we shall assume that the kinetic and
potentialenergy changes are much smaller than the enthalpy changes (not a bad
assumption), and these energy terms may be neglected. Thus, in our special case, the
First Law for steady flow may be written.
net net
outlets inlets
Q W mh mh   
(3.4)
Applying the First Law to the system shown in Fig. 3.1,
QR – Wi = m(hf – h1) = m(h1 – hf) (3.5)
The heat transfer process is reversible and isothermal in the Carnot cycle.
Thus, from the Second Law of Thermodynamics,
QR = mT1(s2 – s1) = –m T1(s2 – s1) (3.6)
because the process from point 2 to point f is isentropic, s2 = sf, where s is the entropy
of the fluid. Substituting QR from eqn. (3.6) into eqn. (3.5) we may determine the
work requirement for the ideal system:
i i
1 1 2 1 f
f
W W
T (s s ) (h h )
m m
    
(3.7)
In the ideal system, 100 percent of the gas compressed is liquefied, or m=mf,
so that y = 1. Notice that a liquefaction system is a workabsorbing system;
therefore, the net work requirement is negative (work done on the system), and the
term Wi/m is a positive number.
Equation (3.7) gives the minimum work requirement to liquefy a gas, so this
is the value which we should try to approach in any practical system. Because we
have set the final pressure at point f equal to the initial pressure at point 1, and point f
is on the saturatedliquid curve, the ideal work requirement depends only on the
pressure and temperature at point I and the type of gas liquefied. Ordinarily, we take
point I at ambient conditions. Table 3.1 lists idealwork requirements for some
common gases, with point I taken at 10 1.3 kPa (14.7 psia) and 300 K (80°F).

61
Example 3.1. Determine the idealwork requirement for the liquefaction of
nitrogen, beginning at 101.3 kPa (14.7 psia) and 300 K (80°F). From the Ts diagram
in Appendix F, we find the following property values:
hi = 462 J/g at 101.3 kPa (1 atm) and 300 K
hf = 29 J/g at 101.3 kPa (1 atm) and saturated liquid
Table 3.1. Idealwork requirements for liquefaction of gases beginning at 300 K
(80o
F) and 101.3 kPa (14.7 psia)
Normal Boiling Point
Ideal Work of Liquefaction,
–Wi/mf
Gas K o
R kJ/kg Btu/lbm
Helium3 3.19 5.74 8.178 3.516
Helium4 4.21 7.58 6.819 2.931
Hydrogen, H2 20.27 36.5 12.019 5.167
Neon, Ne 27.09 48.8 1.335 574
Nitrogen, N2 77.36 139.2 768.1 330.2
Air 78.8 142 738.9 317.7
Carbon monoxide, CO 81.6 146.9 768.6 330.4
Argon, A 87.28 157.1 478.6 205.7
Oxygen, O2 90.18 162.3 635.6 273.3
Methane, CH4 111.7 201.1 1.091 469
Ethane, C2H6 184.5 332.1 353.1 151.8
Propane, C3H6 231.1 416.0 140.4 60.4
Ammonia, NH3 239.8 431.6 359.1 154.4
s1 = 4.42 J/gK at 101.3 kPa (I atm) and 300 K
sf = 0.42 J/gK at 101.3 kPa (I atm) and saturated liquid

62
Substituting these values in eqn. (3.7) results in
iW / m ̇ ̇= (300) (4.42 – 0.42) – (462 – 29) = 767 J/g (330 Btu/Ibm)
PRODUCTION OF LOW TEMPERATURES
3.3. Joule Thomson effect
Most of the practical liquefaction systems utilize an expansion valve or
JouleThomson valve to produce low temperatures. If we apply the First Law for
steady flow to the expansion valve, for zero heat transfer (insulated valve) and zero
work transfer and for negligible kinetic and potentialenergy changes, we find that
h1 = h2. Although the flow within the valve is irreversible and is not an isenthalpic
process, the inlet and outlet states do lie on the same enthalpy curve. We could plot a
series of points of outlet conditions for given inlet conditions and obtain lines of
constant enthalpy. For a real gas, such a plot is shown in Fig. 3.2. We note that there
is a region in which an expansion through the valve (decrease in pressure) produces
an increase in temperature, while in another region the expansion results in a
decrease in temperature. Obviously, we should want to operate the expansion valve
in a liquefaction system in the region where a net decrease in temperature results.
The curve that separates these two regions is called the inversion curve.
The effect of change in temperature for an isenthalpic change in pressure is
represented by the Joule Thomson coefficient JT, defined by
JT = h
T
p
 
 
  (3.8)
where the derivative is interpreted as the change in temperature due to a
change in pressure at constant enthalpy. Note that the JouleThomson coefficient is
the slope of the isenthalpic lines in Fig. 3.2. The JouleThomson coefficient is zero
along the inversion curve because a point on the inversion curve is one at which the
slope of the isenthalpic line is zero. For a temperature increase during expansion, the
JouleThomson coefficient is negative; for a temperature decrease, the Joule
Thomson coefficient is positive.
From calculus, it can be shown that

63
JT = ph T
T T h
p h p
      
     
       (3.9)
Fig. 3.2. Isenthalpic expansion of a real gas.
From basic thermodynamics (Van Wylen and Sonntag 1976), it can be
shown that
p
p pT
h h
dh dT dp c dT T dp
T p T
       
         
          (3.10)
where is the specific volume of the material. By comparison of the
coefficients of dT and dp in eqn. (3.10), we see that
p
p
h
c
T
 
  
  and pT
h
T
p T
   
    
    (3.11)
By combining eqns. (3.9) and (3.11) the JouleThomson coefficient may be
expressed in terms of other thermodynamic properties as
JT
p p
1
T
c T
  
     
    (3.12)
For an ideal gas, = RT/p, and

64
p
R
T p T
  
  
 
Therefore, from eqn. (3.12), for an ideal gas
JT
p
1
T 0
c T
   
      
  
An ideal gas would not experience a temperature change upon expansion
through an expansion valve. To the gratification of cryogenic engineers, gases are
imperfect at low enough temperatures and high enough pressures.
We have seen that an ideal gas always has a zero JouleThomson
coefficient; therefore, a positive or negative JouleThomson coefficient must arise
from the departure of real gases from the idealgas behavior. Enthalpy is defined as
h = u + p (3.13)
where u is the internal energy of the substance. Making this wbstitution in
eqn. (3.9),
 
JT
p T T
p1 u
c p p
     
      
       (3.14)
The first term in eqn. (3.14) represents a departure from Joule's law, which
states that the internal energy of an ideal gas is a function of temperature alone. If
u = u(T) = c T, for example, then this term is zero. This term is always negative for
real gases; thus, it contributes to the production of a temperature decrease (positive
JT). As molecules are moved farther apart in reducing the pressure during the
expansion process, their microscopic potential energy is increased. No external work
or heat is added; therefore, this increase in microscopic potential energy must be
offset by a decrease in microscopic kinetic energy. Temperature is one measure of
microscopic kinetic energy, and any decrease in microscopic kinetic energy results in
a decrease in temperature.
On the other hand, the second term in eqn. (3.14) may be either positive,
negative, or zero. The second term represents a departure from Boyle's law, which

65
states that the product of pressure and volume for an ideal gas is a function of
temperature alone. If p = f(T) = RT, for example, then this term is always zero. A
sketch of p as a function of pressure is shown in Fig. 3.3. At low pressures and
temperatures near the saturatedvapor condition, gases are more compressible than
Boyle's law predicts because attractive forces are in action that try to condense the
gas. This means that the second term in eqn. (3.14) is negative and contributes to the
production ofa temperature decrease. This is the case for gases at room temperature,
with the exception of hydrogen, helium, and neon. At high pressures, the molecules
are squeezed close together and repulsive forces are brought into action; thus, the gas
is less compressible in this region than Boyle's law predicts. This behavior makes the
second term in eqn. (3.14) positive, which contributes to the production of a
temperature increase upon expansion. Whether the JouleThomson coefficient is
positive, negative, or zero for a real gas depends upon the relative magnitude of the
two terms we have been discussing.
Fig. 3.3. Variation of the product pI' with pressure and temperature for a real
gas. For an ideal gas, each isothermal curve would be a horizontal straight line.
One equation of state for gases that illustrates the behavior of real gases is
the van der Waals equation of state,
 2
a
p b RT
 
   
  (3.15)
where a is a measure of the intermolecular force and b is a measure of the
finite size of the molecules. For an ideal gas, a = b = 0 because an ideal gas has no

66
intermolecular forces, and the molecules are considered to be mass point with no
volume. A van der Waals gas has molecules that are considered to be weakly
attracting rigid spheres.
3.4. Adiabatic expansion
The second method of producing low temperatures is the adiabatic
expansion of the gas through a workproducing device, such as an expansion engine.
In the ideal case, the expansion would be reversible and adiabatic, and therefore
isentropic. In this case, we can define the isentropic expansion coefficient IL" which
expresses the temperature change due to a pressure change at constant entropy:
s
s
T
p
 
   
  (3.18)
The isentropic expansion coefficient can be related to other properties of a
gas in a manner similar to the ones we used with the JouleThomson coefficient:
s
pp ps T
T T s T
p s p c T
         
           
          (3.19)
The second factor in eqn. (3.19) is the volumetric coefficient of thermal
expansion multiplied by the specific volume, or , so s is positive (a temperature
decrease results from a pressure decrease) when the volumetric coefficient of
expansion is positive. This is the case for all gases (although some substances, such
as liquid water between 0o
C and 4°C, have negative coefficients of expansion). For
an ideal gas,  p
/ T R / p / T    
, so
s p/ c   for an ideal gas (3.20)
For a van der Waals gas, one can show that
 
  
s 2
p
1 b /
c 1 2a / RT 1 b /
  
 
    
  , van der Waals gas (3.21)
which is positive because > b.
We can make the observation that, for a gas, an isentropic expansion
through an expander always results in a temperature decrease, whereas an expansion
through an expansion valve mayor may not result in a temperature decrease. During

67
the isentropic process, energy is removed from the gas as external work; this method
of lowtemperature production is sometimes called the externalwork method.
Expansion through an expansion valve does not remove energy from the gas but
moves the molecules farther apart under the influence of intermolecular forces. This
method is called the internalwork method.
Table 3.2. Maximum inversion temperature
Maximum Inversion Temperature
Gas K o
R
Helium4 45 81
Hydrogen 205. 369 I
Ncon 250 450
Nitrogen 621 1118
Air 603 1085
Carbon monoxide 652 1174
Argon 794 1429
Oxygen 761 1370
Methane 939 1690
Carbon dioxide 1500 2700
Ammonia 1994 3590
It appears that expanding the gas through an expander would always be the
most effective means of lowering the temperature of a gas. This is the case as far as
the thermodynamics of the two processes is concerned. Between any two given
pressures, an isentropic expansion will always result in a lower final temperature
than will an isenthalpic expansion from the same temperature. The practical
problems associated with the expansion of a two phase mixture (liquid and vapor) in
an expander make the use of an expansion valve necessary in all liquefaction
systems.

68
LIQUEFACTION SYSTEMS FOR. GASES OTHER THAN NEON,
HYDROGEN, AND HELIUM
3.5. Simple LindeHampson system
Historically, the LindeHampson system was the second used to liquefy
gases (the cascade system was the first), although it is the simplest of all the
liquefaction systems. A schematic of the LindeHampson system is shown in Fig.
3.4, and the cycle is shown on the Ts plane in Fig. 3.5.
Fig3.4:Lindehampson liquefaction system
In order to analyze the performance of the system, let us assume ideal
conditions: no irreversible pressure drops (except for the expansion valve), no heat
inleaks from ambient, and 100 percent effective heat exchanger. The gas is first
compressed from ambient conditions at point I reversibly and isothermally to point 2.
In a real system, process 1 to 2 would actually be two processes: an irreversible
adiabatic or polytropic compression followed by an after cooling to lower the gas
temperature back to within a few degrees of ambient temperature. The gas next
passes through a constantpressure heat exchanger (ideally) in which it exchanges
energy with the outgoing lowpressure stream to point 3. From point 3 to point 4, the
gas expands through an expansion valve to p4 = p1. At point 4, some of the gas stream
is in the liquid state and is withdrawn at condition g (saturatedliquid condition), and
the rest of the gas leaves the liquid receiver at condition g (saturatedvapor
condition). This cold gas is finally warmed to the initial temperature by absorbing
energy at constant pressure (ideally) from the incoming highpressure stream.

69
Fig. 3.5. The LindeHampson cycle. The statepoints refer to the numbered points in
Fig. 3.4.
Applying Law for steady flow to the combined heat exchanger, expansion
valve, and liquid receiver, we obtain
 f 1 f f 20 m m h m h mh   ̇ ̇ ̇ ̇
because there is no work or heat transfer to or from the surroundings for
these components. Solving for the fraction of the gas flow that is liquefied,
f 1 2
1 f
m h h
y
m h h

 

̇
̇ (3.22)
The fraction of gas liquefied (the liquid yield) thus depends upon (1) the
pressure and temperature at ambient conditions (point I), which fix h1 and hf and (2)
the pressure after the isothermal compression, which determines h2 because the
temperature at state point 2 is specified by the temperature at point I.

70
We do not have much freedom in choosing or varying ambient conditions;
therefore, points I and f are practically prescribed. We are at liberty to vary the
performance of the system by varying the pressure at point 2 only. What would be
the best pressure to pick for p2 from a thermodynamic viewpoint? In order to
maximize the liquid yield, the best or optimum pressure at point 2 would be the one
that minimizes h2 according to eqn. (3.22). Mathematically, for minimum h2 we must
have
1T T
h
0
p 
 
 
  (3.23)
Referring to eqns. (3.9) and (3.11), we see that this is equivalent to saying
  1
1
JFT p T T
T T
h
0 c
p 

 
   
  (3.24)
or that the pressure which minimizes h2 is the pressure for which JT = 0 for a
temperature T1. For optimum performance (maximum liquid yield y) of the Linde
Hampson system, state 2 should lie on the inversion curve. For air at 300 K (80°F),
the corresponding pressure is approximately 40 MPa (5880 psia); however, actual
systems commonly utilize pressures on the order of 20 MPa.
The simple LindeHampson system shown in Fig. 3.5 would not work for
gases such as neon, hydrogen, and helium for two reasons. First, the system would
never get started because the maximum inversion temperature for these gases is
below room temperature. Referring to the Ts diagram for helium, for example, we
see that in first starting the system, there would be no heat exchange and points 2 and
3 would coincide. Expansion through the expansion valve at ambient temperature
from point 3 to point 4 would result in an increase in temperature so that as the
operation progressed, the gas entering the heat exchanger would be continually
warmed rather than cooled. Therefore, we could never produce low temperatures.
This is illustrated in Fig. 3.6.
In the second place, from eqn. (3.22) we see that y is negative as long as h,
is smaller than h2, which is the case for helium, hydrogen, and neon at room

71
temperature. This means that, even if we could attain low temperatures with the
LindeHampson system, the expansion through the expansion valve at low
temperatures would pass completely into the vapor region, and no gas would be
liquefied. Beginning at ambient conditions, not enough energy can be exchanged in
the heat exchanger to lower the gas temperature to the point at which liquid could be
obtained after expansion. This is illustrated in Fig. 3.7. We see now why we have
divided the liquefaction systems into two categories.
The work requirement for the LindeHampson system may be determined
by applying the First Law for steady flow to the isothermal compressor shown in Fig.
3.4:
 R 2 1Q W m h h  ̇ ̇ ̇ (3.25)
Fig. 3.6. Startup ofa LindeHampson system (no precooling) using helium or
hydrogen as the working fluid. The fluid expands through the expansion valve from
2 to 3 and increases in temperature, since this condition is to the right of the
inversion curve.

72
Fig. 3.7. Even if we could get the simple LindeHampson system using helium or
hydrogen started in the right direction, it is still physically impossible to transfer
enough energy in the heat exchanger to produce liquid.
Substituting for the reversible isothermal heat transfer from eqn. (3.6),
   1 1 2 1 2W / m T s s h h    ̇ ̇ (3.26)
The work requirement per unit mass liquefied is
   1 f
1 1 2 1 2
f y 1 2
h hW W
T s s h h
m m h h
  
        
̇ ̇
̇ ̇ (3.27)
Performance figures for various gases are shown in Table 3.3.
3.6. Precooled LindeHampson system
A plot of liquid yield y as a function of the temperature at the entrance of
the heat exchanger (point 2) for the simple LindeHampson system is shown in Fig.
3.8. It is apparent that the performance of a LindeHampson system could be

73
improved if it were modified so that the gas entered the heat exchanger at a
temperature lower than ambient temperature. Such a modified system is shown in
Fig. 3.9, and the cycle is shown on the T s plane in Fig. 3.10. A separate
refrigeration system using a fluid such as carbon dioxide, ammonia, or a Freon
compound is used to cool the main gas stream. The critical temperature of the
auxiliary refrigerant must be above ambient temperature in order that the refrigerant
can be condensed by exchanging heat with the atmosphere or with cooling water at
ambient temperature.
Table 3.3. Performance of the LindeHampson system using different fluids,
p1 = 101.3, kPa (14.7 psia); p2 = 20.265 MPa (200 atm); T1 = T2 = 300 K (80o
F); heat
–exchanger effectiveness = 100 percent; compressor overall efficiency = 100 percent.
Fluid
Normal Boiling Point Liquid
Yield y =
fm / ṁ ̇
Work per Unit Mass
Compressed
Work per Unit Mass
Liquefied
Figure of
Merit FOM
=
iW / Ẇ ̇K o
R kJ/kg Btu/Ibm kJ/kg Btu/Ibm
N2 77.36 139.3 0.0708 472.5 203.2 6673 2869 0.1151
Air 78.8 142 0.0808 454.1 195.2 5621 2416 0.1313
CO 81.6 146.9 0.0871 468.9 201.6 5381 2313 0.1428
A 87.28 157.1 0.1183 325.3 139.8 2750 1182 0.1741
O2 90.18 162.3 0.1065 405.0 174.1 3804 1636 0.1671
CH4 111.7 201.1 0.1977 782.4 336.4 3957 1701 0.2758
C2H6 184.5 332.1 0.5257 320.9 138.0 611 262 0.5882
C3H8 231.1 416.0 0.6769 159.0 68.4 235.0 101.0 0.5976
NH3 239.8 431.6 0.8079 363.1 156.1 449.4 193.2 0.7991

74
Fig. 3.8 Liquid yield versus compressor temperature for a LindeHampson system
using nitrogen as the working fluid. The heat exchange are 100 percent effective.
Fig. 3.9 Precooled LindeHampson system.

75
Fig. 3.10 Precooled LindeHampson cycle. The statepoints refer to the numbered
points in Fig. 3.9.
For a 100 percent effective heat exchanger, the temperature at points 3 and 6
(see Fig. 3.10) are the same. From a consideration of the Second Law of
Thermodynamics, T) and T6 cannot be lower than the boiling point of the auxiliary
refrigerant at point d; otherwise, we would be transferring heat "uphill"from a low to
a high temperaturewithout expending any work. These factors place restrictions on
the performance of the precooled LindeHampson system.
Applying the First Law for steady flow to the combined threechannel heat
exchanger, primarygas heat exchanger, liquid receiver and expansion valve, and
auxiliary refrigerant expansion valve, for no work or heat transfers from the
surroundings to these components,
 f 1 r a f f 2 r d0 m m h m h m h mh m h     ̇ ̇ ̇ ̇ ̇ ̇ (3.28)
If we define the refrigerant mass flowrate ratio r as
rm
r
m

̇
̇ (3.29)

76
where rṁ, is the mass flow rate of the auxiliary refrigerant, then eqn. (3.28) may be
written as follows, solving for the liquid yield fy m / m ̇ ̇:
a c1 2
i f 1 f
h hh h
y r
h h h h

 
  (3.30)
The first term on the righthand side of eqn. (3.30) represents the liquid
yield for the simple LindeHampson system operating under the same conditions as
the precooled system, given by eqn. (3.22). The second term represents the
improvement in liquid yield that is obtained through the use of precooling. As
mentioned before, the temperature of the auxiliary refrigerant does limit the liquid
yield. Otherwise, with a suitable value of the refrigerant flowrate ratio r, eqn. (3.30)
could yield a value of 100 percent for the liquid yield y. The maximum liquid yield
for the precooled system is
6 3
max
6 f
h h
y
h h


 (3.31 )
where h3 and h6 are taken at the temperature of the boiling refrigerant at point d.
Another limiting factor is that if the refrigerant flowrate ratio were too arge,
the liquid at point d would not be completely vaporized, and liquid would enter the
refrigerant compressornot a very desirable situation. The variation of the liquid yield
and the limiting liquid yield is shown in Fig. 3.11 for nitrogen gas as the working
fluid and Freon12 as the refrigerant, operating from 101.3 kPa (1 atm) and 21°C
(70°F) to 585 kPa (5.77 atm).

77
Fig. 3.11. Liquid yield versus refrigerant flowrate ratio for the precooled Linde
Hampson system using nitrogen as the working fluid. The curves terminate at the
value of r that would result in liquid entering the auxiliary compressor.
If the main compressor is reversible and isothermal and the auxiliary
compressor is reversible and adiabatic, the work requirement per unit mass of
primary gas compressed is
     1 1 2 1 2 b aW / m T s s h h r h h      ̇ ̇ (3.32)
The last term represents the additional work requirement for the auxiliary
compressor; therefore, the total work requirement for the precooled LindeHampson
system is greater than that for the simple system. The last term is usually on the order
of 10 percent of the total work. The increase in liquid yield more than offsets the
additional work requirement, however, so that the work requirement per unit mass of
gas liquefied is actually less for the precooled system than for the simple system, as
indicated in Fig. 3.12.

78
Fig. 3.12. Work required to liquefy a unit mass of nitrogen in a precooled Linde
Hampson system. The dashed curve is the locus of limiting values of r to ensure that
nQ liquid enters the auxiliary compressor.
Example 3.2. Determine the liquid yield, the work per unit mass
compressed, and the work per unit mass liquefied for the simple LindeHampson
system and for the precooled LindeHampson system using nitrogen as the working
fluid and FreonI 2 as the refrigerant. The nitrogen portion of the system operates
between 101.3 kPa (14.7 psi a) and 300 K (80°F) and 20.3 MPa (200 atm or 2940
psia) at point 2. The state points for the refrigerant portion of the system are as
follows:
ha = 207.94 kl/kg (89.40 Btu/Ibm) at 101.3 kPa (14.7 psia) and 300 K
hb = 250.20 kl/kg (107.57 Btu/Ibm) at 681.7 kPa (98.9 psia) and 99.7°C
hc = 61.23 kl/kg (26.37 Btu/Ibm) at 300 K (80°F) and saturated liquid

79
Point d is at 101.3 kPa (14.7 psia) and –29.8°C (–21.6°F) in the twophase
region. The refrigerant flowrate ratio is r = 0.10
Simple LindeHampson system. From the Ts diagram for nitrogen. we find
the following property values:
h1 = 462 J/g at 101.3 kPa (1 atm) and 300 K
h2 = 432 J/g at 20.3 MPa (200 atm) and 300 K
hf = 29 J/g at 101.3 kPa (: atm) and saturated liquid
s2 = 2.74 J/gK at 20.3 MPa (200 atm) and 300 K
sf = 0.42 J/gK at 101.3 kPa (I atm) and saturated liquid
The liquid yield, according to eqn. (3.22), is
1 2
1 f
h h 462 432
y 0.0693
h h 462 29
 
  
 
The work requirement per unit mass compressed is, from eqn. (3.26),
   1 1 2 1 2W / m T s s h h    ̇ ̇
    W / m 300 4.42 2.74 462 432    ̇ ̇
= 504 – 30 = 474 J/g (204 Btu/Ibm)
The work per unit mass liquefied is
 m
f
W W / m 474
6840 J / g 2940 Btu / Ib
m y 0.0693
 
  
̇ ̇ ̇
̇
From Example 3.1, the ideal work requirement was 767 J/g; therefore, the
figure of merit for this system is
i f
f
W / m 767
FOM 0.1121
W / m 6840
  
̇ ̇
̇ ̇
Precooled LindeHampson system. By using the previously detem1ined
property values, from eqn. (3.30) the liquid yield for the precooled system is

80
 
462 432 207.94 61.23
y 0.10
462 29 462 29
  
   
  
= 0.0693 + 0.0339 = 0.1032
By the addition of precooling, there is an improvement of the liquid yield of
almost 50 percent. The total work requirement is, from eqn. (3.32),
W / m ̇ ̇ = (300) (4.42 – 2.74) – (462 – 432) + (0.10) (250.20 – 207.94)
= 504 – 30 + 4.2 = 470 J/g (202 Btu/Ibm)
The work requirement per unit mass liquefied is
 m
f
W 470
4554 J / g 1958 Btu / Ib
m 0.1032

 
̇
̇
For the precooled LindeHampson system, the figure of merit is
767
FOM 0.1684
4554
 
This value is about 50 percent better than the value for the simple Linde
Hampson system previously worked out.
3.7. Linde dualpressure system
The simple LindeHampson system can be modified in another way to
reduce the total work required, although this modification reduces the liquid yield
somewhat. Because only a small portion of the gas that is compressed is liquefied in
the simple system, we could modify it so that not all the gas is expanded to the
lowest pressure but some is expanded to an intermediate pressure. The work
requirement for an ideal isothermal compressor and an ideal gas would be RT1 ln
(p2/p1), so a reduction in the compression pressure ratio would decrease the work
requirement. This is accomplished in the Lindedualpressure system shown
schematically in Fig. 3.13. The cycle is shown on the Ts plane in Fig. 3.14.

81
Fig. 3.13. Linde dualpressure system.
Fig. 3.14. Linde dualpressure cycle. The statepoints refer to the numbered points in
Fig. 3.13.

82
The gas is first compressed to an intermediate pressure and then to the high
pressure of the cycle after a return system has been added. The high pressure gas is
passed through a threechannel heat exchanger and expanded to the intermediate
pressure at point 5, where some of the gas is liquefied. The saturated liquid and vapor
are separated in a liquid receiver, and the vapor is returned to the second compressor
through the threechannel heat exchanger while the liquid is expanded further to the
low pressure of the cycle.
Applying the First Law for steady flow to the heat exchanger, the two liquid
receivers, and the two expansion valves, we can determine the liquid yield for the
Linde dualpressure system:
1 3 1 2
1 f 1 f
h h h h
y i
h h h h
 
 
  (3.33)
where i is the intermediatepressurestream flowrate ratio,
ii m / m ̇ ̇ (3.34)
The quantity iṁ is the mass flow rate of the intermediate pressure stream at
point 8, and ṁ is the total mass flow rate through the highpressure compressor. The
second term represents the reduction in the liquid yield below that of the simple
system because of splitting the flow at the intermediatepressureliquid receiver.
Applying the First Law for steady flow to the two compressors, we find that
the work requirement per unit mass of gas compressed in the high pressure
compressor is
   1 1 3 1 3W / m T s s h h      
̇ ̇
   1 1 2 1 2i T s s h h      (3.35)
From eqn. (3.35) we see that the work requirement is reduced below that of
the simple system by the amount given by the second bracketed term. Practical
liquefaction systems usually operate with i on the order of 0.7 to 0.8, so that the
reduction in work requirement more than offsets the reduction in liquid yield;
therefore, as for the precooled system, the work requirement to produce a unit mass

83
of liquid is less for the dual pressure system than for the simple system. Work
requirements for air are illustrated in Fig. 3.15.
Example 3.3. Determine the liquid yield, work requirement per unit mass
compressed in the highpressure compressor, and work requirement per unit mass
liquefied for a Linde dualpressure system operating with nitrogen as the working
fluid between 101.3 kPa (I atm) and 300 K (80°F) and 20.3 MPa (200 atm). The
intermediate pressure is 5.07 MPa (50 atm), and the intermediatepressure flowrate
ratio is 0.80. From the Ts diagram for nitrogen, we find the following property
values:
h1 = 462 Jig at 101.3 kPa (I atm) and 300 K (80°F)
h2 = 452 Jig at 5.07 MPa (50 atm) and 300 K
hf = 29 Jig at 101.2 kPa (I atm) and saturated liquid
From eqn. (3.33), we find the liquid yield
 
462 432 462 452
y 0.80
462 29 462 29
  
   
  
y = 0.0693 – 0.0185 = 0.0508
This value may be compared with the liquid yield of 0.0693 obtained for the
simple system in Example 3.2. The work requirement per unit mass compressed is
found from eqn. (3.35),
W / m ̇ ̇ = [(300) (4.42 – 274) – (462 – 432)]
– (0.80) [(300) (4.42 – 3.23) – (462 – 452)]
= 474 – 277.6 = 196.4 J/g (84.4 Btu/Ibm)
The work required to liquefy a. unit mass of gas is

84
f
W 196.4
m 0.0508


̇
̇ = 3866 J/g (1662 Btu/Ibm)
Fig. 3.15. Work required to liquefy a unit mass of air in the Linde dualpressure
system.
The figure of merit for the Linde dualpressure system is:
767
FOM 0.1984
3866
 
3.8. Cascade system
The cascade system is an extension of the precooled system, in which the
precooled system is precooled by other refrigeration systems. The cascade system
was the first liquefaction system used to produce liquid air. A cascade system
suggested by Keesom (1933) is shown in Fig. 3.16. This system uses ammonia to
liquefy ethylene at 1925 kPa (19 atm), which is used in turn to liquefy methane at
2530 kPa (25 atm). The methane is used finally to liquefy nitrogen gas at 1885 kPa
(18.6 atm). Another possible cascade combination is the Freon compounds F22, F
13, and F14 used to liquefy nitrogen, air, or oxygen. Ball (1954) has also described a
partial cascade system that uses only two Freon compounds.

85
Fig 3.16:The cascade system
From a thermodynamic point of view, the cascade system is very desirable
for liquefaction because it approaches the ideal reversible system more closely than
any other discussed thus far. As one can see from the complexity of the system
shown in Fig. 3.16, nothing is gained by trying to write down a general equation for
the liquid yield as we have done for the other systems. The fact that the irreversible
expansions through the expansion valves occur across smaller pressure ranges than in
the other systems would lead us to believe, however, that the cascade system would
have improved performance over the other systems mentioned. The lower pressure
requirements are another point in favor of this system. On the other hand, the cascade
system does have a serious practical disadvantage. Each loop of the system must be
completely leak proof in order to prevent the fluids from getting into the wrong

86
place. This imposes a maintenance hardship to make sure that leaks do not occur and
introduces a safety hazard when leaks do occur.
3.9. Claude system
The expansion through an expansion valve is an irreversible process,
thermodynamically speaking. Thus if we wish to approach closer to the ideal
performance, we must seek a better process to produce low temperatures. In the
Claude system, shown in Fig. 3.17, energy is removed from the gas stream by
allowing it to do some work in an expansion engine or expander. The Claude cycle is
shown on the T s plane in Fig. 3.18. If the expansion engine is reversible and
adiabatic (which we shall assume to be true for this analysis), the expansion process
is isentropic, and a much lower temperature is attained than for an isenthalpic
expansion, as we saw in Sec. 3.4.
In the Claude system, the gas is first compressed to pressures on the order of
4 MPa (40 atm or 590 psia) and then passed through the first heat exchanger.
Between 60 and 80 percent of the gas is then diverted from the mainstream,
expanded through an expander, and reunited with the return stream below the second
heat exchanger. The stream to be liquefied continues through the second and third
heat exchangers and is finally expanded through an expansion valve to the liquid
receiver. The cold vapor from the liquid receiver is returned through the heat
exchangers to cool the incoming gas.
Fig 3.17: the claude system

87
Fig. 3.18. The Claude cycle. Statepoints refer to the numbered points in Fig. 3.17.
The heat exchangers are 100 percent effective, and the expander has 100 percent
adiabatic efficiency.
An expansion valve is still necessary in the Claude system because much
liquid cannot be tolerated in the expander in an actual system. The liquid has a much
lower compressibility than the gas; therefore, if liquid were formed in the cy m
expansion engine positive displacement type), high momentary stresses would result.
Some rotary turbine expanders (axialflow type) have been developed that can
tolerate as much as 15 percent liquid by weight without damage to the turbine blades.
In some Claude systems, the energy output of the expander is used to help
compress the gas to be liquefied. In most smallscale systems, the energy is
dissipated in a brake or in an external air blower. Whether the energy is wasted or not
does not affect the liquid yield; however, it does increase the compression work
requirement when the expander work is not used.
Applying the First Law for steady flow to the heat exchangers, the
expansion valve, and the liquid receiver as a unit, for no external heat transfer,
 f 1 f f e e 2 e 30 m m h m h m h mh m h     ̇ ̇ ̇ ̇ ̇ ̇ (3.36)

88
If we define the fraction of the total flow that passes through the expander as
x, or
ex m / m ̇ ̇ (3.37)
then the liquid yield may be obtained from eqn. (3.36) as
3 ef 1 2
1 f 1 f
h hm h h
y x
m h h h h

  
 
̇
̇ (3.38)
Again, we see that the second term represents the improvement in
performance over the simple LindeHampson system. Of course, x + y must be less
than unity in eqn. (3.38).
The work requirement per unit mass compressed is exactly the same as that
for the LindeHampson system if the expander work is not utilized to help in the
compression. This value is given by eqn. (3.26). On the other hand, if the expander
work is used to aid in compression, then the net work requirement is given by
c cW / m W / m W / m   ̇ ̇ ̇̇ ̇ ̇
Applying the First Law for steady flow to the expander, we obtain the
expander work expression,
 e e 3 eW m h h ̇ ̇ (3.39)
If the expander work is utilized to aid in compression, the net work is given
by
     1 1 2 1 2 3 eW / m T s s h h x h h        
̇ ̇
(3.40)
The last term in eqn. (3.40) is the reduction in energy requirements due to
the utilization of the expander work output.
For each value of high pressure (p2 or p3) and each value of expansion
engine flowrate ratio x, one can find by a series of calculations using the
thermodynamic charts for the fluid used in the system that there is a finite
temperature at point 3 (the condition at the inlet of the expander) that will yield the
smallest work requirement per unit mass liquefied. Energy requirements under this

89
condition of astutely chosen TJ are shown in Fig. 3.19. We see that, for a given
pressure level, there is also a value of x that makes the work requirement a minimum.
As the high pressure is increased, the minimum work requirement per unit mass
liquefied decreases.
Example 3.4. Determine the liquid yield, the total work per unit mass of gas
compressed, and the work to liquefy a unit mass of gas for the Claude system using
nitrogen as the working fluid. The system operates between 101.3 kPa (I atm) and
300 K (80°F) and 5.066 MPa (50 atm or 735 psia). The expander flow rate ratio is
0.60, and the expander work is utilized to aid in compression of the gas. The
condition of the gas at the inlet of the expander is 270 K (26°F) and 5.066 MPa (50
atm).
From the Ts diagram for nitrogen, we find the following property values:
h1 = 462 Jig at 101.3 kPa (I atm) and 300 K (80°F)
h3 = 418 Jig at 5.066 MPa (50 atm) and 270 K (26°F)
he = 238 Jig at 101.3 kPa (I atm) and se = s3(Te = 86.1 K = 305°F)
hf = 29 Jig at 101.3 kPa and saturated liquid
s3 = 5, = 3.11 J/gK at 5.066 MPa (50 atm) and 270 K (26°F)

90
Fig. 3.19. Work required to liquefy a unit mass of air in the Claude system
(Lenz 1929).
From eqn. (3.38), we can determine the liquid yield:
 
462 452 418 238
y 0.60
462 29 462 29
  
   
  
= 0.0231 + 0.2494 = 0.2725
Since 0.40 kg/kg compressed was passed into the liquid receiver, we see that
almost 70 percent of this flow was liquefied. The total work requirement is, from
eqn.(3.40),
W / m ̇ ̇ = (300) (4.42 – 3.23) – (462 – 452) – (0.60) (418 – 238)
= 347 – 108 = 239 J/g compressed (102.8 Btu/Ibm)
The work required to liquefy a unit mass of gas is
f
W 239
m 0.2725


̇
̇ = 877 J/g liquefied (377 Btu/Ibm)
For the Claude system operating under the conditions given In this problem,
the figure of merit is quite high:

91
i f
f
W / m 767
FOM 0.897
W / m 877

  

̇ ̇
̇ ̇
Of course, in an actual system, irreversibilities in the heat exchangers,
expander, and compressor would reduce this figure considerably, as illustrated in
Sec. 3.25. In any event, we see that the Claude system is a very effective liquefaction
system.
3.10. Kapitza system
Kapitza (1939) modified the basic Claude system by eliminating the third or
lowtemperature heat exchanger, as shown in Fig. 3.20. Several notable practical
modifications were also introduced in this system. A rotary expansion engine was
used instead of a reciprocating expander. The first or hightemperature heat
exchanger in the Kapitza system was actually a set of valved regenerators, which
combined the cooling process with the purification process. The incoming warm gas
was cooled in one unit and impurities were deposited there, while the outgoing
stream warmed up in the other unit and flushed out the frozen impurities deposited in
it. After a few minutes, a valve was operated to cause the high and lowpressure
Fig. 3.20. The Kapitza system. The warm heat exchanger is actually a switching
regenerator. This system was one of the first to use rotary expanders streams to

92
switch from one unit to the other. The Kapitza system usually operated at relatively
low pressureson the order of 700 kPa (7 atm or 100 psia).
3.11. Heylandt system
Helandt (Davies 1949) noted that for a high pressure of approximately 20
MPa (200 atm) and an expansionengine flowrate ratio of approximately 0.60, the
optimum value of temperature before expansion through the expander was near
ambient temperature. Thus, one could eliminate the first heat exchanger in the
Claude system by compressing the gas to 20 MPa. Such a modified Claude system is
called the Heylandt system, after its originator, and is used extensively in high
pressure liquefaction plants for air. The system is shown schematically in Fig. 3.21.
The advantage of the Heylandt system is that the lubrication problems in the
expander are not difficult to overcome. In the airliquefaction system, the gas enters
the expander at ambient temperature and leaves the expander at approximately 150 K
(190°F) so that light lubricants can be used. In the Heylandt system, the expander
and the expansion valve contribute nearly equally in producing low temperatures,
whereas in the ordinary Claude system, the expander makes by far the largest
contribution, as one will note from Example 3.4.
3.12. Other liquefaction systems using expanders
There are many modifications that one could use to improve the
performance of the basic Claude system. In Fig. 3.22 is shown a dualpressure Caude
system, similar in principle to the Linde dualpressure system. In this system, only
the gas that is passed through the expansion valve is compressed to the high pressure.
The gas that is circulated through the expander is compressed to some intermediate
pressure; therefore, the work requirement per unit mass of gas liquefied is reduced.
Optimum performance for nitrogen gas compressed from 101.3 kPa (1 atm) to 3.5
MPa (35 atm or 514 psia) is attained for this system when approximately 75 percent
of the total flow is diverted through the expander.

93
Fig 3.21: heylandt system
Fig. 3.22. Dualpressure Claude system.

94
3.13. Liquefaction systems for LNG
Several LNG plants operate on a modification of the cascade system called
the mixed refrigerant cascade (MRC) system, as shown in Fig. 3.23. This system has
also been designated as the autorefrigerated cascade (ARC) system (Linnett and
Smith 1970). The operation of this system is made possible by the fact that natural
gas is made up of several components that condense at different temperature levels.
These various components may be used to cool the feed stream in the MRC system
without using separate cooling circuits for the refrigerants by carefully controlling
the composition of the refrigeration cycle gas composition. This allows the use of a
single compressor for the recirculating gases instead of a separate compressor for
each of the different streams, as in the case of the ordinary cascade system.
Fig. 3.23. Mixed refrigerant cascade system used for liquefaction of natural gas.
The natural gas feed stream generally enters the MRC system at 3.9 MPa
(565 psia) to 5.3 MPa (765 psia). If the natural gas feed stream pressure is
sufficiently high, the booster compressor would not be needed. The refrigerant cycle

95
gas mixture is compressed and partially condensed in the compressor aftercooler.
The stream is passed to a phase separator from which the propanerich liquid phase is
expanded through a valve and mixed with the return gas stream to furnish cooling in
the first threefluid heat exchanger. The vapor from the phase separator is partially
liquefied in the threefluid heat exchanger and passed to a second phase separator,
from which the ethanerich liquid is expanded through a valve and passed into the
second threefluid heat exchanger.
The vapor from the second phase separator and the natural gas stream are
partially condensed in the final threefluid heat exchanger. At this point, the
refrigeration cycle stream is primarily methane, so the stream is expanded through an
expansion valve and recirculated to provide cooling for the feed stream in the three
fluid heat exchanger. The LNG is expanded down to the storage pressure in the
liquid receiver.
The liquefaction of natural gas for such applications as peakshaving
involves several factors not encountered in other cryogenic liquefaction systems,
such as air liquefaction plants. In the case of air liquefaction, there are only two
components (nitrogen and oxygen) that are present in amounts larger than I percent,
whereas natural gas involves three or more components in amounts larger than I
percent, including methane, ethane, propane, and nitrogen. These components
condense over a wide temperature range. This fact makes the MRC system well
suited for LNG plants; however, the system is not applicable for liquefaction of pure
gases or mixtures such as air.
3.14. Comparison of liquefaction systems
The performance parameters of the systems discussed are given in Table 3.4
for air as the working fluid. The systems are assumed to operate between 101.3 kPa
(1 atm) and 20°C (68°F) and the conditions stated. Some measured performance
figures are given for comparison with the calculated values.

96
LIQUEFACTION SYSTEMS FOR NEON, HYDROGEN, AND HELIUM
3.15. Precooled LindeHampson system for neon and hydrogen
Because of its simplicity, the LindeHampson system is quite desirable for
smallscale liquefaction plants. We have seen, however, that the basic Linde
Hampson system with no precooling would not work for neon, hydrogen, or helium
because the maximum inversion temperature for these gases is below ambient
temperature. With the precooled system, the temperature of the gas entering the basic
LindeHampson part of the liquefier can be lowered below ambient temperature by
choosing the correct fluid to precool the system.
In principle, any fluid that has a triplepoint temperature below that of the
maximum inversion temperature of neon orhydro2en could be used as a precoolant.
Checking Table 2.6, we see that such fluids would include fluorine, oxygen, air,
methane, argon, and nitrogen. The first four can be ruled out from a practical
consideration because of their explosion hazard. Argon would be a possibility;
however, it is generally more expensive than liquid nitrogen. This leaves liquid
nitrogen as the choice for the precoolant for hydrogen and neonliquefaction
systems.
A liquidnitrogenprecooled LindeHampson system is shown schematically
in Fig. 3.24. For small laboratory liquefiers, the nitrogenliquefaction subsystem
would be replaced by a small storage vessel from which liquid nitrogen could be
withdrawn and passed through the precooling bath, and the vapor discharged through
the threechannel heat exchanger to the atmosphere. For largescale systems, an
economic study should be made to determine whether a separate nitrogen
liquefaction plant should be used or not.

97
Fig 3.24: liquidnitrogen precooled linde –hampson system for neon or nitrogen
Because the part of the hydrogen system below the nitrogen precooling bath
is an ordinary LindeHampson system, from eqn. (3.22) the liquid yield is given by
7 4
7 f
h h
y
h h


 (3.41)
Another parameter of interest for this system is the liquidnitrogen
requirements. Applying the First Law for steady flow to the two heat exchangers in
the hydrogen or neon subsystem, the liquidnitrogen bath, the liquidhydrogen or
neon receiver and expansion valve, for no heat inleaks,
 2 2N c f 1 f f N a 20 m h m m h m h m h mh     ̇ ̇ ̇ ̇ ̇ ̇
(3.42)
where 2Nṁ
is the mass flow rate of liquid nitrogen boiled away to precool the
incoming hydrogen or neon, ṁ is the mass flow rate of hydrogen or neon through
the compressor, and fṁ is the mass flow rate of hydrogen or neon which is
liquefied. If we define the nitrogen boiloff rate per unit mass of hydrogen or neon
compressed as

98
z = 2Nm / ṁ ̇
(3.43)
Then, solving for z from eqn. (3.42),
2 1 1 f
c a c a
h h h h
z y
h h h h
 
 
  (3.44)
The amount of nitrogen boiled away per unit mass of hydrogen or neon
liquefied would be
2 2N N
f f
m m / m z
m m / m y
 
̇ ̇ ̇
̇ ̇ ̇ (3.45)
From our discussion in Sec. 3.6, we observed that the liquid yield for the
precooled LindeHampson system could be improved by lowering the temperature at
the entrance to the cold heat exchanger (point 4 in Fig. 3.24). This can be
accomplished easily in the hydrogen or neonliquefaction system by lowering the
pressure in the liquidnitrogen bath. Because the liquid nitrogen boils in the
precoolant bath, a reduction in pressure lowers the boilingpoint temperature or the
bath temperature. There is a practical limit to this process of lowering the bath
temperature, however. At 63.2 K (113.7"R) liquid nitrogen solidifies under its own
vapor pressure (this is the triple point to nitrogen), and further reduction in pressure
results in solid nitrogen in the bath instead of liquid. Good thermal contact is difficult
to achieve between solid nitrogen and the heatexchanger walls because a layer of
vapor forms between the solid and the exchanger walls. This phenomenon limits the
precoolant bath temperature to values above 63.2 K. The precoolant boiloff
parameter z/y is shown in Fig. 3.25 as a function of temperature of the precoolant
bath, assuming a reversible system.

99
Fig. 3.25. Nitrogen boiloff per unit mass of hydrogen produced for the liquid
nitrogen precooled LindeHampson system as a function of the liquidnitrogen bath
temperature.
3.16 Claude system for hydrogen or neon
The Calude system does not depend primarily on the expansion valve to
produce low temperatures. Therefore, the system discussed in Sec. 3.9 may be used
for hydrogen or neon without modification. The performance is improved, however,
if a liquidnitrogen precooling bath is used with the Claude system, as shown in Fig.
3.26. With the liquidnitrogen precooling, the Claude system for hydrogen
production has a figure of merit 50 to 75 percent higher than that of the precooled
LindeHampson system.

100
Fig. 3.26. Precooled Claude system for hydrogen or neon.
3.17. Heliumrefrigerated hydrogenliquefaction system
An auxiliary heliumgas refrigerator can be used to condense hydrogen or
neon, as shown in Fig. 3.27. In this system, hydrogen or neon is compressed,
precooled by a liquidnitrogen bath to reduce the heliumrefrigerator work
requirement, and finally condensed by heat exchange with cold helium gas. The
helium refrigerator is a modified Claude system in which the gas is not liquefied but
is still colder than liquid hydrogen. The helium is compressed, precooled in the
liquidnitrogen bath, and expanded in an expander to produce the low temperatures.

101
Fig. 3.27. Heliumgasrefrigerated hydrogenliquefaction system.
An advantage of the heliumrefrigerated system is that relatively low
pressures can be used. The compressor size can be reduced (although two
compressors are required) and the pipe thickness can be reduced, in comparison with
that required for higher pressures. The hydrogen or neon need be compressed only to
a pressure high enough to overcome the irreversible pressure drops through the heat
exchangers and piping in an actual system. Pressure from 300 kPa (3 atm) to 800
kPa (8 atm) is usually adequate for the hydrogen loop. The system is relatively
insensitive to the pressure level of the helium refrigerator. For a heliumgas pressure
of I MPa (10 atm), work requirements of approximately 11,000 kl/kg liquefied
(26,000 Btu/Ibm) can be realized for a practical system, or a figure of merit of 0.11,
which includes the work required to produce the liquid nitrogen.
3.18. Orthoparahydrogen conversion in the liquefier

102
We saw in Sec. 2.13 that hydrogen can exist in two different forms
parahydrogen and orthohydrogen. The orthopara concentration in equilibrium
hydrogen depends upon the temperature of the hydrogen. Near room temperature, the
composition is practically 75 percent orthohydrogen and 25 percent parahydrogen,
whereas at the normal boiling point of hydrogen, the equilibrium composition is
almost all parahydrogen. When hydrogen gas is passed through a liquefaction
system, the gas does not remain in the heat exchangers long enough for the
equilibrium composition to be established at a particular temperature. The result is
that the fresh liquid has practically the roomtemperature orthopara composition and
will, if left alone in the liquid receiver, undergo the exothermic reaction there. The
changeover from ortho to parahydrogen involves a heat of conversion that is
greater than the heat of vaporization of parahydrogen; therefore, serious boiloff
losses will result unless measures are taken to prevent it. This is a problem peculiar
to hydrogenliquefaction systems that must be solved in any efficient system.
A catalyst may be used to speed up the conversion process, while the heat of
conversion is absorbed in the liquefaction system before the liquid is stored in the
liquid receiver. Because the heat of conversion results in an increase in liquid
evaporated, it is advantageous to carry out as much of the conversion in the liquid
nitrogen bath as possible. The nitrogen is much less costly to produce than the liquid
hydrogen. Note from Table 2.7 that the equilibrium composition at temperature near
70 K (126°R), corresponding to liquid nitrogen boiling under vacuum, is
approximately 55 to 60 percent parahydrogen. Thus if the conversion is complete at
this temperature, the energy released in the• liquid receiver is reduced by almost one
half.
Two possible arrangements for orthopara conversion are shown in Fig.
3.28. In the first arrangement, the hydrogen' is passed through the catalyst in the
liquidnitrogen bath, expanded through the expansion valve into the liquid receiver,
and drawn through a catalyst bed before passing into a storage vessel. The hydrogen
that is evaporated due to the heat of conversion flows back through the heat
exchanger and furnishes additional refrigeration to the incoming stream. The second
arrangement is similar to the first one, except that the highpressure stream is divided

103
into two parts before the expansion valve. One part is expanded through an
expansion valve and flows through a catalyst bed immersed in a liquidhydrogen
bath; the converted hydrogen is passed to a storage vessel.
Fig. 3.28. Orthoparahydrogen conversion arngements.
The other part of the highpressure stream is expanded through another
expansion valve into the liquid receiver to furnish refrigeration for the catalyst bed;
the vapor is passed back through the heat exchanger to cool down the incoming gas.
The second arrangement allows approximately 20 percent higher liquidhydrogen
yields compared with the first arrangement.
Some of the catalysts that have proved effective are (1) hydrous ferric oxide,
(2) chromic oxide on alumina particles, (3) charcoal and silica gel, and (4) nickel
based catalyst. Of these, hydrous ferric oxide is the most active; that is, a relatively
small volume of catalyst is required to produce practically complete conversion to
the equilibrium composition. The conversion process is speeded up for any of the
catalysts if they are ground into fine pellets, which offer a larger surface area per unit
volume than do large chunks of material.

104
Certain impurities will "poison" the catalysts or severely reduce their
effectiveness (Scott et al. 1964). Methane, carbon monoxide, and ethylene act as
temporary poisons, whereas chlorine, hydrogen chloride, and hydrogen sulfide
permanently decrease the catalyst activity. It is important to remove these materials
from the hydrogen feed stream before they enter the liquefier.
3.19. Collins heliumliquefaction system
As for the case of hydrogen and neon, the precooled LindeHampson system
may be used to liquefy helium by using liquid hydrogen as the precoolant. This type
of precooled system was used in several of the earlier helium liquefiers (Mann et al.
1960).
One of the milestones in cryogenic engineering was the design and
development of a helium liquefier by Samuel C. Collins at the Massachusetts
Institute of Technology. This liquefier is an extension of the Claude system, as
shown in Fig. 3.29. Depending upon the helium inlet pressure, from two to five
expansion engines are used in this system.
Applying the First Law for steady flow to the system consisting of all
components except the helium compressor and the expansion engines, we find that
the liquid yield fy m / m ̇ ̇ is
2eei1 2
1 2
1 f 1 f 1 f
hhh h
y x x
h h h h h h

  
   (3.46)
where 11 ex m / m ̇ ̇
22 ex m / m ̇ ̇
1eh = enthalpy change of fluid passing through expander 1
2eh = enthalpy change of fluid passing through expander 2
1 2e , em ṁ ̇
= mass flow rates of fluid through expanders 1 and 2,
respectively.
For more than two engines, an additional term similar to the second term for
each expander would be added to eqn. (3.46).

105
The cooldown time for the Collins liquefier may be reduced from about 4
hours to 2 hours by the use of a liquidnitrogen precooling bath. In addition, the use
of the precooling bath increases the liquefaction performance of the system (the
liquid yield can be almost tripled); however, the precoolant bath is not required
because the system does not depend solely upon the JouleThompson effect for the
production of low temperatures.
3.20. Simon heliumliquefaction system
One of the methods used to liquefy small quantities of helium is the Simon
liquefaction system (Pickard and Simon 1948). This system does
Unless the mass released from the vessel is measured, the calculation
procedure is an iterative one because m6 must be known to find y. However, the
mass at point 6 can be determined only after the liquid yield is known.
Cailletet observed a thick mist when oxygen gas at 32°C ( 26°F) and high
pressure was suddently expanded in an apparatus similar to the Simon liquefier;
however, in general, the Simon liquefier does not work so well for gases other than
helium. There are two reasons for this fact: (1) The ration g/ f is smaller for
helium than any other gas at the normal boiling point ( g/ f = 7.5 for helium; 53.3
for hydrogen; and 175 for nitrogen), which means that for a given liquid yield y, the
volume ratio Vf/V is larger for helium than for other gases. (2) The specific heat of
metals is extremely small at helium temperatures, so only a small amount of cooling
capacity is lost into the walls of the vessel for helium liquefaction.
The Simon system is primarily a laboratory liquefier because it can produce
helium only in relatively small quantities. It is especially well suited for experiments
involving magnetic fields in which a small space is available between the poles of a
magnet. The liquid in the heavywalled container could serve as the refrigerant to
cool a paramagnetic material, for example, on which experiments would be carried
out.

106
MODULE IV
CRYOGENIC REFRIGERATION SYSTEMS
Systems that utilize cryogenic temperatures in their operation, such as
advanced electronic systems, superconducting magnets and motors, all depend upon
an effective refrigeration system to maintain the low temperatures required. Many
refrigeration systems have the same components and thermodynamic cycles as the
corresponding liquefaction systems. The difference between the refrigeration system
and the liquefaction system is that the liquid produced is evaporated in a refrigeration
system instead of being utilized in some other way external to the system, as in the
liquefaction system. In this chapter, we shall examine these refrigeration systems that
are similar to Liquefaction systems, and in addition we shall consider some unique
refrigerators based on entirely different conceptsthe Philips refrigerator, based on
the old Stirling cycle, and the GiffordMcMahon refrigerator. We shall also examine
methods of obtaining and maintaining temperatures below 2 K (3.6°R), such as
magnetic refrigeration and the dilution refrigerator.
IDEAL REFRIGERATION SYSTEMS
4.1. The thermodynamically ideal isothermalsource system
As in the preceding chapters, we shall first investigate the
thermodynamically ideal system in order to have a basis for comparison of the
various practical refrigeration systems. In the case of refrigerators, however, there are
two types of lowtemperature source that may be used. If we evaporate a liquid to
furnish the cooling, energy is added to the refrigerant in an isothermal manner, asfar
as the evaporator of the refrigerator is concerned. On the other hand, we may use a
cold gas such as helium (which gets quite cold before it Liquefies), and energy is
added at constant pressure (for the refrigerant) without liquefying the gas. Therefore,
we must differentiate between an isothermalsource refrigerator and an isobaric
source refrigerator. The sink into which energy is rejected is usually the atmosphere;
thus, we shall have an isothermal sink in both cases. We use the term "source" to
mean the source of heat for the refrigeratorthat is, the space to be cooled. The term
"sink" refers to the region into which heat is rejected from the refrigerator.

107
Fig. 4.1 Carnot refrigerator. (a) Reversible isothermal compression; (b) reversible
adiabatic expansion; (c) reversible isothermal expansion with heat adsorption from
the low temperature source; (d) reversible adiabatic compression.
The thermodynamically ideal isothermalsource refrigerator is the Carnot
refrigerator, shown schematically in Fig. 5.1. The processes involved in the Carnot
refrigerator are as follows.
Process 12. The working medium is compressed while energy is rejected to
the ~ink to maintain the refrigerant temperature constant.
Process 23 The working medium is expanded reversibly and adiabatically
from the sink temperature Th to the source temperature Tc.
Process 34. Energy is transferred from the source (the region to be cooled)
to the refrigeration medium, while work is done by the medium to maintain the
refrigerant at constant temperature.
Process 41. The refrigerantis then compressed reversibly and adiabatically
(isentropic process) from the source temperature to the sink temperature.

108
The Carnot cycle thus consists of two reversible adiabatic processes and two
reversible isothermal processes as shown in Fig. 5.2.
A measure of the performance of a refrigerator is the coefficient of
performance (COP), defined as the energy removed from the source divided by the
work required to remove this amount of energy:
   a net a netCOP Q / W Q / m / W / m    (4.1 )
where Qa/m is the refrigeration effect or the energy absorbed by the
refrigeration medium per unit mass of refrigerant, and Wnet/m is the net work
expended per unit mass of refrigerant. Notice that Qa is a positive quantity (heat
added to the system is considered positive), while the net work expended is a
negative quantity (work done on the system is considered negative; work done by the
system is considered positive). For this reason, we have included the negative sign in
eqn. (4.1) so that the coefficient of performance will be a positive number.
To compare the performance of practical systems, we shall use the figure of
merit for the refrigerator, defined by
FOM = COP/COPi (4.2)
where COP is the coefficient of performance of the actual system and COP, is the
coefficient of performance of the thermodynamically ideal system. As in the case of
liquefaction systems and separation systems, the figure of merit is a number between
zero and unity. A FOM near unity implies a very "good" refrigerator, and a small
FOM implies a "poor" refrigerator compared with the ideal refrigerator.

109
Fig 4.2: carnot cycle
As a consequence of the First Law of Thermodynamics, the net work in a
cycle is equal to the net heat transferred because the initial and final states in a cycle
are identical. In the Carnot cycle, all processes are reversible; therefore, the net heat
transfer is given by
   net h 2 1 c 4 3Q mT s s 0 mT s s 0      or
  net h c 1 2 netQ / m T T s s W / m     (4.3)
where s is the entropy and the subscripts refer to the numbered points in Fig. 5.2. The
energy added to the system from the source at constant temperature is given by
   a c 4 3 c 1 2Q / m T s s T s s    (4.4)
Using the expressions for the net work and the heat absorbed from the
source, we find the coefficient of performance for the Carnot refrigerator to be
c
i
h c
T
COP
T T

 (4.5)

110
where the temperatures are absolute temperatures (K or OR).
From eqn. (4.5) we see that the coefficient of performance for the Carnot
system is independent of the refrigerant. That is, between the same temperature
limits, the COP would be the same if helium gas or liquid nitrogen or liquid argon
were used as the refrigerant. This was not the case for liquefaction systems.
One of the corollaries of the Second Law of Thermodynamics is that no
refrigeration system can have a COP larger than that of a Carnot refrigerator
operating between the same two temperature limits; otherwise, a perpetualmotion
machine of the second kind could be formed. All practical refrigerators require more
work for a given refrigeration effect than that required by a Carnot refrigerator. For
an ambient or sink temperature of 300 K (5400R or 80°F), the coefficient of
performance for various source temperatures is shown in Table 4. 1. We note from
Table 4.1 that the work requirement for a given refrigeration effect increases as the
source temperature is lowered. Even for the thermodynamically ideal refrigerator,
large expenditures of work are required to maintain very low temperatures. The
cryogenics engineer must pay dearly to maintain a low temperature, and the
"dearness" increases as the temperature is lowered.
4.2. The thermodynamically ideal isobaricsource system
In coldgas refrigerators or refrigeration systems in which the working
medium is not condensed, energy is absorbed at a varying temperature instead of a
constant temperature as in the Carnot refrigerator (Jacobs 1962). In this case, it
would be unfair to compare the actual system with the Camot system because the
source temperature for the real system is not constant. The thermodynamically ideal
isobaricsource refrigeration cycle is shown on the temperatureentropy plane in Fig.
4.3. This is the ideal cycle that must be used in comparing real systems that absorb
heat at constant pressure.

111
Table 4.1. Coefficient of performance for a Carnot refrigerator operating between 300
K (5400R) and a low temperature Tc
Source Temperature
No K o
R COPi = –Qa/Wnet –Wnet,Qa
1 111.7 201.1 0.5932 1.686
2 77.4 139.3 0.3477 2.876
3 20.3 36.5 0.07258 13.778
4 4.2 7.56 0.01420 70.43
5 1.0 1.8 0.003344 299.0
6 0.1 0.18 0.0003334 2,999.0
7 0.01 0.018 0.0000 333 29,999.0
Suppose we let the sink temperature (usually ambient temperature) be T0,
the lowest source temperature be T1, and the highest source temperature be T2.
Energy is added reversibly to the refrigerant at constant pressure between the
temperatures T1 and T2. The energyrejection process is a reversible isothermal
process; therefore, the energy rejected from the system is given by
   r 0 4 3 0 2 1Q mT s s mT s s     (4.6)

112
Fig 4.3: Reversible isobaricsource refrigeration cycle
Because the heatabsorption process is a constantpressure process, the total
energy absorbed from the source is given by
   
2 2
a 2 1
1 1
Q mT ds m dh dp m h h      
(4.7)
From the First Law of Thermodynamics applied to the entire cycle, we find
that the net work transfer is equal to the net heat transfer:
   net net r a 0 2 1 2 1W Q Q Q m T s s h h          (4.8)
Using the definition of the coefficient of performance, eqn. (4.1), we find
the following expression for the COP for an ideal isobaricsource refrigerator:
   
a 2 1
i
net 0 2 1 2 1
Q h h
COP
W T s s h h
 
 
   (4.9)
Equation (4.9) is valid for any working substance. However, for many cold
gas refrigerators, the pressures are sufficiently low that the working fluid may be

113
assumed to behave approximately as an ideal gas. For an ideal gas, the enthalpy
change is given by
 2 1 p 2 1h h c T T  
For an ideal gas in a constantpressure process, the entropy change is given
by
     2 1 p 2 1 2 1 p 2 1s s c ln T / T R ln p / p c ln T / T   
If we make these substitutions into eqn. (4.9), we obtain the following
expression that is valid for an ideal gas with constant specific heats:
   
2 1
i
0 2 1 2 1
T T
COP
T ln T / T T T


  (4.10)
This expression may be written in terms of the temperature ratios T2/T1, and
T0/T1, as follows:
 
     
2 1
i
0 1 2 1 2 1
T / T 1
COP
T / T ln T / T T / T 1


  (4. 11)
From eqn. (4.11) we see that the COP is independent of the ideal gas used as
the refrigerant. The COPi depends only upon the ratios of the highest Source
temperature to the lowest Source temperature and the sink temperature to the lowest
source temperature. Equation 4.11) is plotted in Fig. 4.4. It can be shown that if T2/T1
approaches unity, eqn. (4.11) reduces to the expression for the COPi of a Carnot
refrigerator.
Example 4.1. Determine the ideal COP for an isobaric Source refrigerator
operating reversibly between a sink temperature of 300 K (80°F) and a minimum
source temperature of 110 K (198°R) and a maximum source temperature of 180 K
(324°R). The working fluid is gaseous nitrogen, and the source pressure is 1.013
MPa (10 atm).

114
Fig. 4.4. Coefficient of performance for an ideal isobatic source refrigerator. To is
the sink temperature: T1 and T2 are the minimum and maximum source temperatures,
respectively.
From the temperatureentropy diagram for nitrogen, we find the following
property values:
h1 = 248 J/g at 110 K and 1.013 MPa
s1 = 2.59 J/gK f
h2 = 332 Jig at 180 K and 1.013 MPa
s2 = 3.18 J/gK .
The ideal COP may be determined from eqn. (4.9):
 
    i
332 248
COP 0.903
300 3.18 2.59 332 248

 
  
In this pressure and temperature range, nitrogen is not quite an ideal gas.
Thus we should expect to get a slightly different answer if the idealgas expression,
eqn. (4.10), is used:

115
 
     i
180 110
COP 0.900
300 ln 180/110 180 110

 
 
This value differs by only about 0.3 percent from the answer obtained
previously.
We may compare the ideal COP obtained in this problem with the COP for a
Carnot refrigerator operating between 300 K (5400R) and 110 K (198°R). Using eqn.
(4.5),
i
110
COP 0.579
300 110
 

In this case, there is considerable difference between the COP, of the Camot
refrigerator and that of the isobaricsource refrigerator.
REFRIGERATORS FOR TEMPERATURES ABOVE 2 K
4.3. Joule Thomson refrigeration systems
Any of the liquefaction systems that do not use an expansion engine may be
classed as JouleThomson refrigerators because they depend upon the Joule
Thomson effect to produce low temperatures. Instead of withdrawing the liquid
formed in a refrigerator, heat is absorbed from the low temperature Source to
evaporate this liquid. A, simple LindeHampson refrigerator is shown in Fig. 4.5, and
its cycle is shown on the temperatureentropy plane in Fig. 4.6 .
. As mentioned in Chap. 3, the compression from point I to point 2 in Fig,
4.6 would be isothermal in the Ideal case. In practice, the gas enters the compressor
at point I' and there is a small temperature difference because the effectiveness of the
heat exchanger is less than unity. The compressed gas is passed through the heat
exchanger, cooled to low temperatures by heat exchange with the cold outgoing gas
stream, and expanded through a JouleThomson valve into an evaporator. In the
evaporator (which corresponds to the liquid receiver in the liquefaction system), the
liquid formed after the expansion process is evaporated (at constant temperature) by
absorbing heat from the space to be refrigerated. The vapor then returns through I
•the heat exchanger to the compressor.

116
Fig. 4.5. LindeHampson refrigerator.
Fig. 4.6. Thermodynamic cycle for the LindeHampson refrigerator.
If we apply the First Law of Thermodynamics to the system consisting of
the heat exchanger, expansion valve, and evaporator and assume no heat inleaks
from ambient as well as negligible kineticenergy and potentialenergy changes of
the working fluid, we obtain

117
 a 1 2Q m h h ̇ ̇ (4.12)
where 1h is the actual enthalpy of the fluid leaving the heat exchanger at the
warm end. The heat exchanger effectiveness is defined by
1 g
1 g
h h
h h
 

 (4.13)
Using eqn. (4.13) to eliminate the enthalpy h~, the refrigeration effect may
be written in terms of the fluid properties and the heat exchanger effectiveness:
    a 1 2 1 gQ / m h h 1 h h    ̇ ̇
(4.14)
where hi is the enthalpy of the fluid at the exit of the heat exchanger under
ideal conditionsthat is, at the same temperature as at point 2.
We may make two observations from eqn. (4.14). First, we see that the
JouleThomson refrigerator cannot be used with neon, hydrogen, or helium as the
working medium, unless these gases are first precooled below their maximum
inversion temperatures. Because the heat absorbed by the refrigerator must be a
positive quantity (considering the refrigerator as the thermodynamic system), h1 must
be larger than h2 for an ideal heat exchanger in order to have a positive refrigeration
effect  aQ / ṁ ̇
. This condition is not met if the working fluid enters the heat
exchanger at the warm end at a temperature above the maximum inversion
temperature for the fluid.
Second, we see that there is a value of the heat exchanger effectiveness
below which the refrigerator will not work. This limiting effectiveness may be
determined by setting the refrigeration effect equal to zero in eqn. (4.14).
The work requirement for the system is given by
   
0
2 1 2 1 2
a
T s s h hW
m
  


̇
̇ (4.15)

118
where 0a is the overall efficiency of the compressor. From the definition of
the coefficient of performance, eqn. (4.1), we find the COP for the LindeHampson
refrigerator to be
    
   
c, 0 1 2 1 ga
2 1 2 1 2
h h 1 h hQ
COP
W T s s h h
        
  
̇
̇
(4.16)
The liquid in the evaporator boils at constant temperature; thus this
refrigerator is of the isothermalsource type. Liquid nitrogen is a suitable refrigerant
for maintaining temperatures in the region between about 65 K (117o
R) and 115 K
(207o
R). The temperature in the evaporator can be regulated by controlling the
pressure in the evaporator by means of the expansionvalve setting. At 65 K the
evaporator pressure would be 17.4 kPa (2.53 psia), and at 115 K the evaporator
pressure would be 1.939 MPa (281 psia), using nitrogen as the working fluid. The
temperature range for the refrigerator is limited on the lower end by the triple point
of the working fluid and also by the difficulty in maintaining low vacuum pressure
with large mass flow rates. If the pressure were lowered below triplepoint pressure,
nitrogen snow would form in the evaporator and clogging of the expansion valve
could result. In addition, there would be poor heat transfer in the evaporator between
the evaporator wall and the porous solid cryogen. The temperature is limited on the
high end by the critical point. As the critical point is approached, the heat of
vaporization of the liquid approaches zero. If we are not concerned with having an
isothermal source, the temperature range of the LindeHampson refrigerator can be
extended up to ambient temperatures. However, when we get into the temperature
region above about 200 K (3600R), other refrigerants such as the Freon compounds
become more attractive as refrigeration media.
Stephens (1970) and Buller (1971) have described miniature JouleThomson
refrigerators that utilize thermostatically operated expansion valves. The self
regulating JouleThomson refrigerator has the advantage of rapid cooldown because
the initial gas flow rate is much larger than that for a fixedorifice refrigerator. In
addition, the problem of solid contaminants in the gas stream is significantly

119
reduced. Reliable operation at pressures from 34.5 MPa (5000 psi) to 69 MPa
(10,000 psi) are made possible with the use of the selfregulating orifice.
Chan et al. (1981) described a miniature JouleThomson refrigerator using
an adsorption compressor. Large quantities of gas are adsorbed in an adsorbent, then
the adsorbent is heated in a closed system to produce a high pressure gas. The gas
passes through a JouleThomson system and is adsorbed in a second adsorbent
chamber, which is cooled. A minimum COP of 0.22 was reported for nitrogen gas as
the working fluid absorbing energy at 77 K (139°R). The cold compressor
temperature was 150 K (2700R), and the hot compressor temperature was 470 K
(846°R or 386°F).
Example 4.2. Determine the refrigeration effect, COP, and figure of merit
for a simple LindeHampson refrigerator operating from 300 K (80°F) and 101.3 kPa
(I atm) to 10.13 MPa (100 atm). The overall efficiency of the compressor is 75
percent, and the heat exchanger effectiveness is 0.960. The working fluid for the
refrigerator is nitrogen.
From the temperatureentropy diagram for nitrogen, we find the following
property values:
hi = 462 J/g at 300 K and 101.3 kPa (I atm) $, = 4.42 J/gK
h2 = 444 J/g at 300 K and 10.13 MPa (100 atm)
s2 = 3.00 J/gK i
hg = 229 J/g at 101.3 kPa (77.36 K) and saturated vapor conditions
hr = 29 J/g at 101.3 kPa (I atm) and saturated liquid conditions.
The work requirement per unit mass for the refrigerator is
   2 1 2 1 2 c,0W / m T s s h h / n      
̇ ̇
= [(300) (4.42 – 3.00) – (462 – 444)] / (0.750)
= (408)/(0.750) = 544 J/g (234 Btu/Ibm)
  a 1 2 1 gQ / m h h 1 h h     
 
̇ ̇

120
= (462 – 444) – (1 – 0.960) (462 – 229)
= 8.68 J/g (3.73 Btu/Ibm
)
The coefficient of performance for the refrigerator is:
aCOP Q / W 8.68/544 0.01596   ̇ ̇
The COP, for a Carnot refrigerator operating between Th = 300 K and
Tc = 77.36 K is given by
     i c h cCOP T / T T 77.36 / 300 77.36    = 0.3475
The figure of merit for the system is
FOM = COP/COPi = 0.01596/0.3475 = 0.0459
4.4. Refrigerator optimization
In the design of a JouleThomson refrigerator, the designer may determine
the heat exchanger effectiveness at the design stage by selection of the heat
exchanger surface area. If an effectiveness near unity is selected, the heat exchanger
surface area is quite large and corresponding high heat exchanger costs results. On
the other hand, if an effectiveness near the lower limiting value is chosen, the mass
flow rate for a given heat absorption rate is quite large and a corresponding high
compressor cost results. It is apparent that there is an intermediate value of the heat
exchanger effectiveness (optimum value) that will minimize the total annual cost of
the refrigerator. This problem has been examined by Gifford (1960) for the case of a
balanced heat exchanger.
The primary components of cost of the refrigeration system are the
compressor costs, which includes both operating costs (energy costs) and capital
costs, and the heat exchanger costs. As an initial approximation, the compressor,
costs are proportional to the power requirement of the compressor,
 c 1 c 1 cC C W C W / m m ̇ ̇ ̇ ̇
(4.17)
where C1 is the compressor cost per unit power requirement, including both operating
and capital costs. Similarly, the heat exchanger costs are proportional to the surface
area of the heat exchanger, as an initial approximation:

121
CE = C2A (4.18)
Ordinarily, such items as piping, valves, insulation and so on have costs that
are not dependent upon the heat exchanger effectiveness. Therefore, let us consider
the total system cost as the sum of the compressor and heat exchanger costs:
CT = Cc + CE
The optimum condition may be found by setting the derivative of the total
cost equal to zero, or
cT
1 2
WdC dm dA
0 C C
di m di di
 
   
 
̇ ̇
̇ (4.19)
where i = 1 –  t = heat exchanger ineffectiveness.
The required mass flow rate through the system may be determined from
eqn. (4.14):
      
a a
1 2 1 g 1 g
Q Q
m
h h i h h h h H i
 
    
̇ ̇
̇
(4.20)
where
   1 2 1 g maxH h h / h h i    (4.21)
The quantity H is the upper limiting ineffectiveness above which the
refrigerator will not work at all. From eqn. (4.20), we find
  
a
2
1 g
Qdm
di h h H i

 
̇̇
(4.22)
Because most heat exchangers used in cryogenic systems are counter flow
exchangers, the surface area may be found from eqn. (3.88):
 
 
c R R
R
mc / U 1 C C i
A ln
1 C i
  
  
  
̇
(4.23)
where CR = Cc/Ch = capacity rate ratio
Cc = mean specific heat of the cold stream

122
Ch = mean specific heat of the warm stream
The term  cmc / U̇ is generally a weak function of the mass flow rate
because the overall heat transfer coefficient is proportional to the mass flow rate
raised to a power near unity; therefore, this ratio may be considered as a constant as a
first approximation. The area derivative may be found from eqn. (4.23):
 
 
c
R R
mc / UdA
di i 1 C C i
 
 
̇
(4.24)
For convenience, let us define the parameter as follows:
  
 
2 1 g c
1 c a
C h h mc / U
C W / m Q

 
̇
̇̇ ̇ (4.25)
Making the substitutions from eqns. (4.22), (4.24), and (4.25) into eqn.
(4.19), we obtain
   2 2
R RC i 2 H 1 C i H 0         (4.26)
For the case in which is not equal to CR, we may define the following
dimensionless parameters:
 
R
1
R
2 H 1 C
B
2 C
  

  (4.27)
2
2
R
H
B
C


  (4.28)
We may write eqn. (5.26) in the simple form,
2
1 2i 2B i B 0   (4.29)
Two values of the optimum ineffectiveness result from the solution of eqn.
(5.29); however, only one solution yields an ineffectiveness value less than imax = H.
The optimum ineffectiveness for RC  is given by
 
1/ 2
2
opt opt 1 1 2i 1 B B B    
(4.30)

123
If by chance, RC  , the optimum ineffectiveness may be determined
directly from eqn. (4.26):
2
R
opt
R R
C H
i
2C H 1 C

  (4.31)
Note that if we are given the heat exchanger "free"; that is, if C2 = O. we
find that = a and B2 = O. From eqn. (4.30), we find that the optimum
ineffectiveness would be iopt = 0, which is the result that we would anticipate for a
free heat exchanger.
4.5 Cascade or precooled JouleThomson refrigerators
For temperatures lower than those obtainable with liquid nitrogen, the only
available working fluids are neon, hydrogen, and helium. For these fluids,
precooling must be used in any system that has no expansion engine. A typical
precooled liquidneon or liquidhydrogen refrigerator (Geist and Lashmet 1961) is
shown schematically in Fig. 4.7. The cycle for the system is shown in the
temperatureentropy plane in Fig. 4.8.
Fig 4.7: Precooled LindeHampson refrigerator

124
Fig 4.8: Thermodynamic cycle for the Precooled LindeHampson refrigerator
If we apply the First Law of Thermodynamics to all components of the
system shown in Fig. 4.7 except the compressors, neglect heat inleaks from ambient,
and neglect kineticenergy and potentialenergy changes of the fluids, we obtain
   a 1 2 p a bQ m h h m h h    ̇ ̇ ̇ (4.32)
where ṁ
is the mass flow rate of the main refrigerant, pṁis the mass flow rate of
the precoolant, and the subscripts on the enthalpy terms correspond to the points in
Fig. 4.8. If we define the precoolant massflowrate ratio as
z = pm / ṁ ̇
then eqn. (4.32) may be written
   a 1 2 a bQ / m h h z h h    ̇ ̇ (4.33)
We may introduce the heat exchanger effectiveness for the main heat
exchanger E and for the precoolant heat exchanger p , defined by
1 g
1 g
h h
h h
 

 (4.34a)

125
a e
p
a e
h h
h h
 
 
 (4.34b)
Making these substitutions into eqn. (4.33), we find
    a 1 2 1 gQ / m h h 1 h h    ̇ ̇
    a b p a ez h h 1 h h     
  (4.35)
where h1 is the enthalpy of the main refrigerant at the temperature T2, and h.
is the enthalpy of the precoolant at the temperature Tb.
Applying the First Law to the cold exchanger and the evaporator, we obtain
a 1 4Q / m h h ̇ ̇ (4.36)
Introducing the effectiveness of the cold exchanger,
1 g
c
7 g
h h
h h
 
 
 (4.37)
the refrigeration effect may be written as follows:
    a 7 4 c 7 gQ / m h h 1 h h    ̇ ̇
(4.38)
The required precoolant massflowrate ratio may be determined by equating eqns.
(4.35) and (4.38), if we assume that the temperature at point 4 is practically equal to
the precoolant bath temperature so that h. and 117 are known quantities.
Lower temperatures may be attained by using a threestage cascade
refrigerator with nitrogen (or argon), hydrogen (or neon), and helium as the working
fluids. An example of this type of refrigerator is shown in Fig. 4.9.

126
Fig 4.9 : Three stages Joule Thomson liquid helium refrigerator
The Claude liquefaction system or the Collins liquefaction system could be
used as a refrigeration system. A schematic of a Claude refrigerator is shown in Fig.
4.10. If we apply the First Law to the three heat exchangers, the expansion valve, and
the evaporator as a unit, neglecting heat inleaks from ambient and kineticenergy and
potentialenergy changes, we obtain the following for the heat absorbed by the
refrigerant:
   a 1 2 3 eQ / m h h x h h    ̇ ̇ (4.39)

127
where ex m / m ̇ ̇ = expander massflowrate ratio, eṁ = mass flow rate
through the expander, ṁ = mass flow rate through the compressor, and the
subscripts refer to the points given in Fig. 4.11. If we let he = enthalpy at the end of
an isentropic expansion from point 3 to the pressure at point e, then the expression
for the refrigeration effect may be written in terms of the expander adiabatic
efficiency as follows:
   a 1 2 ad 3 eQ / m h h x h h    ̇ ̇ (4.40)
The net work requirement, assuming that the expander work is utilized to
help in the compression of the gas, is given by
     net 2 1 2 1 2 c,0 e,m ad 3 eW / m T s s h h / x h h           
̇ ̇
(4.41)
Fig. 4.10. Claude refrigerator.

128
Fig. 4.11. Thermodynamic cycle for the Claude refrigerator.
where c,0 is the overall efficiency of the compressor and e,m is the
mechanical efficiency of the expander.
Meier and Currie (1968) described the performance of a Claude refrigerator
used to maintain a low temperature of 4 K (7.2°R) while providing I watt of
refrigeration. Whitter (1966) described the design of a refrigerator utilizing two
expansion engines, similar to the Collins liquefier.
Two significant modifications of the basic Claude system are the use of a
"wet" expander or expander operating in the twophase region to replace the
expansion valve (Johnson et al. 1971), and the use of a low temperature compressor
(Minta and Smith 1982). A schematic of this system is shown in Fig. 4.12, and the
cycle is shown on the temperature entropy plane in Fig. 4.13. The twophase
expander is used primarily for systems involving helium as the working fluid
because the thermal capacity of the compressed gas is generally larger than the latent
heat of the liquid phase. Unlike an air or nitrogen expansion engine in which the
engine efficiency is seriously affected by the presence of liquid in the engine,

129
operation of the helium expander in the twophase region does not result in a serious
deterioration of the engine performance. The thermodynamic performance of the
system is improved by the use of the saturatedvapor compressor. In addition, the
required heat exchanger surface is less than that required for the conventional Claude
system because of heattransfer coefficients are higher when the cold gas stream
pressure is increased.
Fig. 4.12. Claude refrigerator with a wet expander and a saturatedvapor compressor.
Fig 4.13: Thermodynamic cycle for the system shown in fig 4.12
4.7. Philips refrigerator
The Philips refrigerator operates on the Stirling cycle, which was in vented
in 1816 by a Scottish minister, Robert Stirling, for use in a hotair engine. As early as

130
1834, John Herschel (Kohler 1960) suggested that this engine could be used as a
refrigerator. The first Stirling cycle refrigerator was constructed by Alexander Kirk
(Kirk 1874) around 1864. A schematic of the sequence of operations of the Philips
refrigerator is shown in Fig. 4.14, and the cycle is shown on the temperatureentropy
plane in Fig. 4.15.
The Philips refrigerator consists of a cylinder enclosing a piston, a displacer,
and a regenerator. The piston compresses the gas, while the displacer simply moves
the gas from one chamber to another without changing the gas volume, in the ideal
case. The heat exchange during the constantvolume process is carried out in the
regenerator.
Fig 4.14 Philips refrigerator schematic
The sequence of operations for the system is as follows.

131
Process 12. The gas is compressed isothermally while rejecting heat to the
hightemperature sink (surroundings).
Process 23. The gas is forced through the regenerator by the motion of the
displacer. The gas is cooled at constant volume during this process. The energy
removed from the gas is not transferred to the surroundings but is stored in the
regenerator matrix.
Process 34. The gas is expanded isothermally while absorbing heat from
the lowtemperature source.
Process 41. The cold gas is forced through the regenerator by the motion of
the displacer; the gas is heated during this process. The energy stored during process
23 is transferred back to the gas. In the ideal case (no heat inleaks), heat is
transferred to the refrigerator only during process 34, and heat is rejected from the
refrigerator only during process 12.
If we assume that the heat transfers to and from the refrigerator are
reversible, the heat transferred may be determined by the Second Law of
Thermodynamics.
Heat rejected = Qr = mT1(S2 – s1)
Heat absorbed = Qa = mT3 (s4 – s3)
where m is the mass of gas it' the refrigerator cylinder. By the First Law,
Wnet = Qr + Qa for a cycle, so the coefficient of performance of the ideal Philips
refrigerator is
   
a 3
net 1 1 2 4 3 3
Q T
COP
W T s s / s s T

 
   (4.42)
If the working fluid behaves as an ideal gas. we may write
   1 2 1 2 1 2s s c ln T / T R ln /    
   1 2 4 3R ln / R ln /      = s4 – s3

132
because 1 2T T and 3 4T T , 1 4   and 2 3   , where is the gas specific
volume. The coefficient of performance of an ideal Philips refrigerator with an ideal
gas as the refrigerant is
3
1 3
T
COP
T T

 (4.43)
This is the same expression as that for the COP, of a Carnot refrigerator;
therefore. the ideal Philips refrigerator would have a figure of merit of unity.
Frictional energy dissipation, pressure drops through the regenerator, finite
temperature differences during heat rejection and heat absorption. and finite
temperature differences between the regenerator and the working fluid all tend to
lower the figure of merit in the actual refrigerator.
The first analysis of the details of operation of the Stirling system was
presented by Schmidt (1871). An excellent summary of Schmidt's analysis was given
by Walker (1983). The Schmidt analysis did not include the effects of nonisothermal
compression and expansion and regenerator Ineffectiveness. A more exact analysis
was presented by Finkelstein (1975); however, the application of this analysis
requires the use of a rather involved computer program.
Fig. 4.15. Thermodynamic cycle for the ideal Philips refrigerator.

133
The Philips refrigerator is constructed by the Philips Company of
Eindhoven, Netherlands. It has been used successfully in the liquefaction of air at a
rate of 5.5 liter/hr (11.6 Ibm/hr), in gas separation systems, and in miniature cooling
systems for electronic components. The figure of merit for the actual system as
contrasted to the ideal Philips refrigerator is about 0.30 when the source temperature
is that of liquid air (79 K or 142°R).
5.9. Vuilleumier refrigerator
The Vuilleumier refrigerator, first patented by Rudolph Vuilleumier in
1918, is similar to the Stirling refrigerator, except the VM refrigerator uses a
"thermal" compressor instead of a mechanical compressor. A variation of the VM
device was also invented by Vannevar Bush (1938), and another version was
patented by K. W. Taconis (1951). A schematic of the VM refrigerator is shown in
Fig. 4.16, and the ideal VM cycle is shown on the temperatureentropy plane in Fig.
4.17.
In the ideal VM cycle, heat is added from a hightemperature source to the
gas in the "hot" cylinder, and the displacer moves downward to maintain the
temperature of the gas constant at Th (process 12). At the same time, nearambient
temperature gas flows from the intermediate volume through the regenerator to the
hot volume (process 41). The displacer then moves upward and gas is displaced
from the hot volume to the intermediate volume (process 23). Heat is rejected from
the intermediate volume to maintain the temperature of the gas in the volume
constant at T. (process 34). As the cold displacer is moved to the left, heat is
absorbed by the gas in the cold volume from the lowtemperature source to maintain
the gas temperature constant at T, (process 56). At the same time, gas from the
intermediate volume flows through the cold regenerator to the cold volume (process
45). The cold displacer then moves back to the right, and gas is displaced from the
cold volume through the cold regenerator to the intermediate volume (process 63).
Assuming that all processes are thermodynamically ideal and that the
working fluid may be treated as an ideal gas, the heattransfer terms may be
determined as follows. The heat added from the high temperature source is

134
   h h h 2 1 h h 2 1Q m T s s m RT ln /     (4.47)
The heat added from the lowtemperature source is

135
   c c c 6 5 c c 6 5Q m T s s m RT ln /     (4.48)
where mh and mc are the mass finally within the hot and cold volumes,
respectively. and R is the specific gas constant. Finally, the heat rejected to the
intermediatetemperature sink is given by
       a h c a 4 3 h c a 3 4Q m m T s s m m RT ln /        (4.49)
From the temperatureentropy diagram for the cycle, we see that 2 = 3 =
6 and 1 = 4 = U5.
Because the net heat transfer for the system is zero (there is no external
work done on or by the gas, for the ideal system), Qh + Qc + Qa = 0, and
       h h 2 1 c c 2 1 h c a 2 1m RT ln / m RT ln / m m RT ln / 0         
or
   c h h a a cm / m T T / T T  
Because this system is driven by a heat transfer from a hightemperature
source, instead of by mechanical work, the coefficient of performance must be
defined a little differently. In this case, the COP is
c h c c h hCOP Q / Q m T / m T 
Making the substitution for the mass ratio, we find
 
 
c h a
h a c
T T T
COP
T T T


 (4.50)
This analysis of the performance of the Vuilleumier refrigerator is quite
simplified because the effects of harmonic motion of the displacers, regenerator
ineffectiveness, and other thermodynamic losses are not considered. A more
complete (and more complicated) analysis of the VM refrigerator has been presented
by Rule and Qvale (1969) and by White (1976). In general, the COP of the VM
refrigerator is less than that for a Slirling or Philips refrigerator because a fraction of
the heat added from the high temperature source in the VM refrigerator must be
rejected, according to the Second Law of Thermodynamics; whereas all of the

136
mechanical work input can be utilized in the Philips refrigerator, in the ideal case.
Using eqn. (4.50) with temperatures of Th = 800 K (14400R), Ta = 360 K (648°R),
and Tc = 78 K (140AOR), the COP of the ideal VM refrigerator is 0.1521. For a
Philips refrigerator operating between Th = 360 K and Tc = 78 K, the COP is 0.2766,
which is about 82 percent larger than the COP of the VM refrigerator.
One of the advantages of the Vuilleumier refrigerator is that the thermal
input may be provided by solar energy or isotope energy, which makes the VM
refrigerator attractive for cryogenic cooling in longduration space exploration and in
applications where mechanical vibration of a drive engine must be avoided (Sherman
1982).
5.10. Solvay refrigerator
The Solvay refrigerator was invented in Germany about 1887 (Solvay
1887), and was the first system planned for air liquefaction using an expansion
engine (Collins and Canaday 1958). Solvay's prototype apparatus was able to achieve
a low temperature of only 178 K (3200R or 140°F), so the system was not
considered for cryogenic refrigeration until the late 1950s when Gifford and
McMahon (1960) of A. D. Little, Inc., described the use of the refrigerator in a
miniature infrared cooler.
The Solvay refrigerator is shown schematically in Fig. 4.18. If we were to
consider a unit mass of gas as it flows through the system, if would trace out the path
on the temperatureentropy plane as shown in Fig. 4.19. The sequence. of operations
for the Solvay refrigerator is as follows.
Process 12. With the piston at the bottom of its stroke, the inlet valve is
opened. The highpressure gas flows into the regenerator, in which the gas is cooled,
and the system pressure is increased from a low pressure PI to a higher pressure P2'
Process 23. With the inlet valve still open, the piston is raised to draw a
volume of gas into the cylinder. The gas has been cooled during its flow through the
regenerator.
Process 34. The inlet valve is closed, and the gas within the cylinder is
expanded (isentropically in the ideal case) to the initial pressure Pi As the gas

137
expands, it does work on the piston, and energy is removed from the gas as work.
The temperature of the gas therefore decreases.
Process 45. The exhaust valve is opened, and the piston is lowered to force
the cold gas out of the cylinder. During this process, the cold gas passes through a
heat exchanger to remove heat from the cooled.
Fig. 4.18. Solvay refrigerator schematic.
Process 51. The gas finally passes out through the regenerator, in which the
cold gas is warmed back to room temperature.
Assuming that the work output during the expansion process is utilized in
the compression process, the net work requirement for this system is given by
     net 2 1 2 1 2 c,0 e, m ad 3 4W / m T s s h h / h h            (4.51)
where the first term represents the compressor work and the second term represents
the work output during the expansion process. The enthalpy h4 is the value that
would be achieved at the end of an isentropic expansion from point 3 to the pressure
P, at point 4. The energy removed from the lowtemperature Source is given by

138
  a 5 4 5 4 ad 3 4Q / m h h h h 1 h h        (4.52)
Fig. 4.19. Path traced out by a unit mass of gas on the Ts plane for the Solvay
refrigerator.
The expansion piston in this system is similar to t'1e Heylandt piston shown
in Fig. 4.45. The piston is constructed of a poor heat conductor, such as micarta, so
that it may be sealed at the warm end, which helps to avoid the problem of a low
temperature moving seal.
The miniature Solvay refrigerator described by Gifford and McMahon
(1960) was capable of attaining 55 K (99°R) in a single stage. The cylinder had a
diameter of 5.6 mm (0.22 in.) and a length of 51 mm (2.0 in.). The working fluid was
helium gas, which varied in pressure between 345 kPa (50 psig) and 1725 kPa (250
psig).
4.11. GiffordMcMahon refrigerator
A schematic of the GiffordMcMahon refrigerator (McMahon and Gifford
1960) is shown in Fig. 4.20. The path of a unit mass of the working fluid on the
temperatureentropy plane is shown in Fig. 4.21. This system consists of a

139
compressor, a cylinder closed at both ends, a displacer within the cylinder, and a
regenerator. This system differs from the Solvay refrigerator in that no work is
transferred from the system during the: expansion process. The displacer serves the
purpose of moving the gas from one expansion space to another and would do zero
net work in the ideal case of zero pressure drop in the regenerator.
The sequence of operations for the GiffordMcMahon refrigerator is as
follows.
Process 12. With the displacer at the bottom of the cylinder, the inlet valve
is opened and the pressure within the upper expansion space is increased from a low
pressure PI to a higher pressure p1. The volume OJ the lower expansion space is
practically zero during this process because the displacer is at its lowest position.
Position 23. With the inlet valve still open and the exhaust valve closed, the
displacer is moved to the top of the cylinder. This action moves the gas that was
originally in the upper expansion space down through the regenerator to the lower
expansion space. Because the gas is cooled as it passes through the regenerator, it
will decrease in volume so that gas will be drawn in through the inlet valve during
this process to maintain a constant pressure within the system.
Fig. 4.20. GiffordMcMahon refrigerator schematic.

140
Fig. 4.21. Path traced out by a unit mass of gas on the Ts plane for the Gifford
McMahon refrigerator.
Process 34. With the displacer at the top of the cylinder, the inlet valve is
closed and the exhaust valve is opened, thus allowing the gas within the lower
expansion space to expand to the initial pressure Pi The gas that is finally within the
lower expansion space does work to push out the gas that leaves during this process;
therefore, energy is removed as work from the gas finally left in the lower expansion
space. This causes the gas in the lower expansion space to drop to a low temperature.
This process is similar to the expansion process in the Simon liquefier (see Sec.
3.20).
Process 45. The lowtemperature gas is forced out of the lower expansion
space by moving the displacer downward to the bottom of the cylinder. This cold gas
flows through a heat exchanger in which heat is transferred to the gas from the low
temperature source.
Process 51. The gas flows from the heat exchanger through the regenerator,
in which the gas is warmed back to near ambient temperature.
The net work requirement for this system is given by
   1 1 2 1 2 c, 0W / m T s s h h / n       (4.53)
The energy removed from the lowtemperature source is given by
     a e 5 4 ad c 5 4Q / m m / m h h m / m h h     (5.54)

141
where me, is the mass of gas within the lower expansion space at the end of
the expansion process 34, and m is the total mass of gas compressed. Because the
volume of the expansion space remains constant during the expansion process. the
mass ratio me/m may be written in terms of the density ratio:
e 4 3m / m p / p (4.55)
There arc several factors that contribute to a loss in performance of the
GiffordMcMahon refrigerator (Ackermann and Gifford 1971), including the
regenerator ineffectiveness, thermal conduction down the displacer and Its housing,
"shuttle" heat transfer, and the finite volume within the regenerator. Measurements of
the performance of a small infrared cooler operatll1g on the GiffordMcMahon cycle
showed that the actual refrigeration effect was approximately 59 percent of the ideal
refngcratiui1 effect.
In both the Solvay and the GiffordMcMahon refrigerators, the regenerator
is a critical component, as in the case of the Philips refrigerator. For an efficient
refrigerator, the regenerator effectiveness should be 98 percent or better. Punched
copper or brass screens were used as the regenerator packing material, as shown in
Fig. 4.22. To reduce the heat conduction along the length of the regenerator, the
punched screens were separated by a coil of stainlesssteel wire. For very low
temperature regenerators, lead may be used instead of copper because lead has a
'higher specific heat at low temperature due to its lower Debye temperature.
The Solvay and GiffordMcMahon refrigerators have several advantages in
common. The engine valves and displacer piston seals are at room temperature;
therefore, lowtemperature sealing problems are eliminated. Through the use of a
regenerator instead of an ordinary heat exchanger, high effectiveness of the heat
exchange component can be attained, and the system can operate with slightly
impure gas as the refrigeration medium. Because of the backandforth motion of the
gas through the regenerator, the impurities are deposited in the regenerator during the
intake process and are swept back out during the exhaust process. Regenerators are
generally less expensive, for a given surface area, than heat exchangers, also.

142
The Solvay system has two advantages over the GiffordMcMahon system:
(I) The coefficient of performance of the Solvay system is inherently higher than that
of the GiffordMcMahon system because more energy is removed from the working
fluid by the externalworkproducing process. (2) In the GiffordMcMahon system, a
small motor is required to move the displacer back and forth while the expanding gas
moves the piston in the Solvay system. On the other hand, the GiffordMcMahon
system has some advantages over the Solvay system: (I) There is practically no
leakage past the displacer in the GiffordMcMahon system because of the small
pressure difference across the displacer seals. (2) The displacer and crank arm in the
GiffordMcMahon system need not be designed to support a large force; therefore,
the motion transmission system can be quite simple and subject to fewer problems
with vibration.
Fig. 4.22_ Regenerator schematic. The stainlesssteel wire spacer is used to reduce
the longitudinal conduction heat transfer within the matrix
One of the major attractive features of the GiffordMcMahon system is the
ease with which it can be adapted to multi staging. A threestage refrigerator is
shown in Fig. 5.23. By using helium gas as the working fluid, refrigeration may be
achieved at three different temperature levels with only a slight increase in the
complexity of the overall system. All the valves in the multistage system operate at

143
room temperature, and the 'three displacers are operated by a single actuator. By
multistaging, temperatures near 15 K (27o
R) can .be attained with less work than by
using a singlestage system.
Example 5.6. A GiffordMcMahon refrigerator operates between the
pressure limits of 101.3 kPa (1 atm) and 1.013 MPa (10 atm) using helium as the
working fluid. The maximum temperature of the space to be cooled is 70 K (126o
R)
and the temperature of the gas leaving the compressor is 300 K (540o
R). Assume that
the regenerator is 100 percent effective, and the compressor overall efficiency is 60
percent. The expansion efficiency is 90 percent. Determine the COP for the system.
From the temperatureentropy diagram for helium, we find the following
property values:
h1 = 629 J/mol = 1572.7 J/g at 101.3 kPa (1 atm) and 300 K (540o
R)
s1 = 125.7 J/molK = 31.41 J/g
h2 = 6308 J/mol = 1575.8 J/g at 1.013 MPa (10 atm) and 300 K
Fig. 4.23. Threestage GiffordMcMahon refrigerator. All three displacers are moved
by the same actuator. Three different levels of refrigeration are possible with this
refrigerator.

144
s2 = 106.6 J/molK = 26.63 J/gK
h3 = 1518 J/mol = 379.2 J/g at 1.013 MPa (10 atm) and 70 K (I 26°R)
p3 = 1.71 mol/L = 6.85 g/L
h4 = 636 J/mol = 158.8 J/g at 101.3 kPa (I atm) and s4 = s3 = 19.05 J/gK
h5 = 1514 J/mol = 378.2 J/g at 101.3 kPa and 70K
The work requirement per unit mass for the compressor is
   2 1 2 1 2 c, 0W / m T s s h h /       
W / m  [(300)(31.41 26.63) (1572.7 1575.8)J/(0.60)
–W/m = 1437.1/0.60 = 2395.2J/g(1030Btu/Ibm)
The actual enthalpy at the end of the expansion process may be determined
from
  4 4 ad 3 4h h 1 h h     
4h = 158.8 + (I 0.90)(379.2 – 158.8) = 180.8 J/g = 724 J/mol
At a pressure of 101.3 kPa (I atm) and 4h = 724 J/mol, we find the actual
density at the end of expansion to be
4h = 0.38 mol/L = 1.52 g/L
The mass ratio is
e 4 3m / m p / p 1.52/ 6.85 0.2219  
The refrigeration effect is
  a e 5 4Q / m m / m h h 
  aQ / m 0.2219 378.2 180.8  = 43.80 J/g (18.83
Btu/Ibm)
The COP for the refrigerator is

145
COP = –Qa/W = 43.80/2395.2 = 0.01829
The temperature limits for the system are: sink temperature, 300 K (540o
R);
maximum Source temperature, 70 K (l26°R); and minimum source temperature (at
point 4), 32.1 K (57.8o
R). Assuming that the helium gas is nearly an ideal gas, we
may calculate the ideal COP, for an isobaric Source refrigerator using eqn. (4.9):
     
70 32.1
COP 0.1934
300 ln 70/32.1 70 32.1

 
 
The figure of merit for this system is
FOM = COP/COPi = 0.10829/0.1934 = 0.0946
REFRIGERATORS FOR TEMPERATURES BELOW 2 K
4.13. Magnetic cooling
In the systems discussed previously, either a liquid or a gas was used as the
working substance. For these systems, we are limited to the regions of temperature
above about 0.6 K. To produce this low temperature, we can use only liquid He4
or
liquid He3
boiling under reduced pressure because all other materials are solid at 0.6
K. The low temperature we can attain with boiling helium is determined by the
pressure above the liquid. At I K (1.8°R) the vapor pressure of liquid He4 is 16 Pa
(0.12 torr), while the vapor pressure of liquid He4 at 0.6 K is only 37.5 mPa (2.81 X
104 torr). Liquid He3 can be used to reach 0.6 K with a little less effort because the
vapor pressure of liquid He) at 0.6 K is 72.6 Pa (0.545 torr). About 0.4 K (O.7"R) is
the limit we can attain in a practical system because of the difficulties in maintaining
such low pressures with even moderate flow rates. It would be a sad situation for
lowtemperature physicists, though, if this were the lowest temperature that could be
reached.
Giauque (1927) and Debye (1926) independently suggested a way to break
this "temperature barrier." They pointed out that a paramagnetic substance could be
used instead of a gas or liquid and that a magnetic field could be used instead of the
expansion of a fluid to attain the low temperatures. If we were to compress a gas at
constant temperature, we should increase the order (or decrease the entropy) of the
system because we move the molecules closer together without increasing their

146
random velocities. Then, if we were to expand the gas reversibly and adiabatically,
we should not change the degree of order (because the entropy remains constant) of
the system. We should move the gas molecules farther apart, however, so that the
random molecular velocities (and therefore the gas temperature) must decrease in
order to maintain the same degree of order (or entropy). When we get a gas to very
low temperatures, there is not much room left for any more ordering of the system
because it is almost as ordered as it can be.
A paramagnetic substance, however, has another way of ordering itself. In
the absence of an external magnetic field, the dipoles of the paramagnetic material
are more or less randomly arranged, even at low temperatures. If we apply a
magnetic field at constant temperature (analogous to compressing a gas
isothermally), we shall tend to align the magnetic moments of the atoms of the
paramagnetic material, thereby introducing order or decreasing the entropy of the
material. If the magnetic field is removed reversibly and adiabatically (corresponding
to a reversible adiabatic expansion of a gas), the entropy remains constant but the
alignment of the dipole moments is not as great as before. To preserve the degree of
order (or maintain the entropy constant), the temperature of the paramagnetic
material must decrease. This process is called adiabatic demagnetization and it is the
process that allows us to enter the temperature region below 0.6 K.
A schematic of an apparatus to carry out the adiabatic demagnetization
process is shown in Fig. 4.24. A paramagnetic salt pellet is suspended in a chamber
by silk or nylon threads. This chamber is initially filled with gaseous helium, and the
chamber is then immersed in a liquidhelium bath. The liquid helium is boiling under
reduced pressure, so its temperature and the temperature of the paramagnetic salt are
about I K. The helium bath is surrounded by a liquidhydrogen or liquidnitrogen
shield to reduce the heat transfer from ambient to the helium bath. This entire
assembly is placed between the poles of a powerful electromagnet, which is shaped
so that the field of the magnet is concentrated around the salt pellet. The magnetic
field is turned on and maintained for about an hour to allow the heat of magnetization
(similar to the heat of compression for a gas) to be conducted to the helium bath by
the gaseous helium in the small chamber, thereby maintaining the salt at its original

147
temperature. When thermal equilibrium is attained, the gaseous helium (which is
called an exchange gas) is pumped away to thermally isolate the paramagnetic salt.
The magnetic field is then removed, and the temperature of the salt drops to a very
low value. Temperatures as low as 0.0014 K or 1.4 mK (0.0025"R) have been
attained by this method, according to de Klerk, Steen land, and Gorter (1950). A
detailed summary of the adiabatic demagnetization process is given by White (1979).
Fig. 4.24. Apparatus for carrying out an adiabatic demagnetization process.
This process of adiabatic demagnetization will work only for very low
temperatures because of the magnitude of the lattice thermal effects at temperatures
much above 2 K or 3 K. The lattice entropy must be much smaller than the entropy
associated with the magnetic dipoles of the paramagnetic material if a significant
temperature change is to be achieved. At very low temperatures, the lattice entropy is
given by
s (lattice) = 77.9 R(T/ p)3
(4.79)
As we shall see later, the maximum dipole entropy for a simple spin
sys¬tem (S = ½) is given by
s(dipole, H = 0) = R In 2 (4.80)

148
To ensure the success of the adiabatic demagnetization process, we should
want the lattice, entropy to be 1 percent or so of the dipole entropy. The temperature
for this condition to be true can he found from eqn.
   
3
p77.9R T / 0.01 R ln 2 
or, solving for the upper limiting temperature T0,
 
1/3
0 p pT ln 2 / 7790 0.0446      (4.81 )
This result indicates that a materia1 with a high Debye temperature p
would be advantageous for magnetic cooling.
4.14. Thermodynamics of magnetic cooling
The magnetic process may be analyzed thermodynamically if, in order to
simplify the situation, we consider pressure and volume changes sm.1I enough to be
neglected. In this case, we may write
T ds = du – 0H dI (4.82)
where 0 = 4 × 10–7
T –m/A = permeability of free space in SI units, H is
the magnetic field intensity, A/m, and J is the magnetic moment per unit mass, A
m2
/kg The quantity – 0H dI represents the magnetic work per unit mass
corresponding to the volumechange work + p dv for a pure substance.
For pure substance, it can be shown from thermodynamic reasoning (van
Wylen and Sonntag 1976) that
p
p
Tds dh dp c dT T dp
T
 
      
  (4.83)
The analgoues expression for a paramagentic substance can be obtained by
replacing the specific volume by the magnetic moment per unit mass I and by
replacing the pressure p by the quantity – 0H:
H 0
H
I
Tds c dT T
T
 
    
  (4.84)
where cH is the specific heat at constant magnetic field intensity (analogous
to cp for a pure substance)

149
For the adiabatic demagnetization process, the entropy of the paramagnetic
material remains constant; therefore, ds = 0. Making this substitution into eqn.
(4.84), we may solve for the differential temperature change due to a differential
change in the magnetic field intensity while entropy remains constant.
0
M
H H
TT I
H c T
    
      
     (4.85)
The magnetic moment may be determined from eqn. (4.89)
J = ½ ng B B( )
J = (½)( 1.6147)(1024
)(1.992)(0.9273)( 10–23
)(5.9684)
J = 89.01 A–m2
/kg
We can compare this value with the one obtained by using the Curie law
(which does not hold, in this case, as we shall see). The Curie constant for
gadolinium sulfate may be found in Table 4.4:
C = 263.3 × 10–6
Km3
/kg
Using the Curie law to determine the magnetic moment, we obtain
J = CH/T = (263.3)(10–6
)(320)(103
)/(0.50)
J = 168.5 Am2
/kg
We see that the correct magnetic moment differs from the one obtained from
the Curie law by
(168.5 89.01)(100)/(89.01) = 89 percent which is not negligible.
4.16 Magnetic refrigeration systems
With this, background on the thermodynamic and magnetic properties of
paramagnetic materials, we can now look into the application of adiabatic
demagnetization in maintaining temperatures below 1.0 K (1.8o
R). Such a
refrigeration system has been developed by Daunt et al. (1954) at Ohio State
University. A schematic of this refrigerator is shown in Fig. 4.26, and its ideal cycle
is shown on 'he tempecatureentropy plane in Fig 4.27. Because the working medium
is a paramagnetic material (iron ammonium a/urn), lines of constant magnetic field

150
intensity appear on the temperatureentropy diagram instead of lines of constant
pressure. In the ideal case, the refrigerator cycle is a Carnot cycle. However,
irreversibility’s due to beat transfer from ambient and the finite time rate of change
of the magnetic field introduce entropy increases during the adiabatic processes and
temperature increases during the ideal isothermal processes. Modifications on the
basic refrigerator have been made by Zimmerman et al. (1962), who used
superconducting magnets instead of ordinary magnets.
Fig. 4.26. Magnetic refrigerator schematic.

151
Fig. 4.27. Thermodynamic cycle for the magnetic refrigerator.
The sequence of operations for the magnetic refrigerator is as follows.
Process 12. The magnetic field is applied to the working salt while the
upper thermal valve is open and the lower thermal valve is closed. When the upper
thermal valve is open, heat may be transferred from the working salt to the liquid
helium bath, thereby maintaining the salt temperature fairly constant. The thermal
valve between the working salt and the reservoir salt is closed so that heat will not
flow back into the lowtemperature reservoir during this process.
Process 23. Both thermal valves are closed, and the magnetic field around
the working salt is reduced adiabatically to some intermediate value. During this
process, tee temperature of the working salt decreases.
Process 34. The thermal valve between the working salt and the reservoir
salt is opened, and the field around the working salt is reduced to zero while heat is
absorbed isothermally by the working salt from the reservoir salt.
Process 41. Both thermal valves are closed, and the magnetic field around
the working salt is adiabatically increased to its original value.

152
The energy absorbed as heat from the reservoir salt in the ideal case is given
by
Qa = mT3(s4 – s3) (4.100)
because the process 34 is reversible and isothermal ideally. The entropy values may
be determined from the Brillouin expression, eqn. (4.98). The quantity m is the mass
of the working salt, and the subscripts refer to the numbered points in Fig. 4.28. In
the ideal case, the energy rejected as heat from the working salt is given by
   r 1 2 1 2 4 3Q mT s s mT s s     (4.101)
Applying the First Law to the entire cycle, we find the work requirement for
one cycle:
  net a r 1 3 4 3W Q Q m T T s s      (4.102)
From eqn. (4.100) and (4.102), we see that the coefficient of performance
for the ideal magnetic refrigerator is the same as that for a Carnot refrigerator.
Because of the irreversibility’s involved, the ideal performance of the
refrigerator is not attained in practice. The actual performance of the magnetic
refrigerator constructed by Daunt et al. is compared with the ideal performance in
Fig. 4.28. The mass of the working salt is 15 g, and the helium bath is maintained at
a temperature of 1.11 K. The sequence of processes is carried out so that one cycle
requires about 2 minutes to complete.

153
Fig. 4.28. Actual and ideal performance of the magnetic refrigerator.
The working salt used in the magnetic refrigerator by Daunt et al. was an
iron ammonium alum salt, and the reservoir salt (which was used as a "thermal
flywheel" to smooth out temperature fluctuations in the space to be cooled) was
chromium potassium alum. These salts have low thermal conductivities; therefore,
heat transfer to and from the salts poses quite a problem. Copper fins and 3mm (1/8
in.) lengths of fine copper wire (0.05mm to 0.08mm diameter) were embedded in
the salt pellets to improve the heattransfer situation. About I g of copper wire and I g
of silicone vacuum grease were mixed with the IS g of paramagnetic salt, and the
pellet was formed by pressing under a pressure of 20 MPa (3000 psi). The vacuum
grease acted as a binder and improved the mechanical stability of the salt pellet.
One of the advantages of the magnetic refrigerator is that it can operate
effectively in zero gravity. Because of this characteristic, magnetic refrigerators have
been used to cool infrared bolometers in space systems by NASA (Sherman 1982).
4.17. Thermal valves
One of the critical components of the magnetic refrigeration system is the
thermal valves. In the DauntHeer refrigerator, thin lead strips were used as the
thermal valves. It was observed that the thermal conductivity of lead was different in
the superconducting state compared with the normal state, as shown in Fig. 4.29.

154
When the material is below the transition temperature in zero field (and therefore in
the superconducting state), many of the electrons that would ordinarily take part in
the heattransport process are restricted from doing so because of the quantum
considerations of the superconducting state. The thermal conductivity is not zero in
the superconducting state because there is still energy transport by the lattice
(phonon energy transfer).
When a magnetic field is applied to the lead strips, the lead is driven into the
normal state if the applied field is above the transition value, and the electrons are
once again free to take part in the heattransport process. The difference between the
normal thermal conductivity and the superconducting thermal conductivity can be as
much as two orders of magnitude. The valve is thus in the "open" position (heat flow
can take place) when it is driven normal by the valve magnet, and the valve is in the
"closed" position (heat flow is restricted but there is some leakage) when the valve
magnet field is removed.
There are other thermal valves that might be used, but they are usually not
as effective as the superconducting valve. Collins and Zimmerman (1953) used a
mechanical contact switch in a magnetic refrigerator. This type of valve has the
advantage that there is zero thermal leakage when the contact is broken. The serious
disadvantage is that there is energy dissipated when the contact is made or broken,
and this energy is too large to be tolerated in the region below 1.0 K. It is difficult for
the refrigerator to remove energies on the order of 40 W (1.4 X 104
Btu/hr) without
having to remove the energy dissipation in the valves, too.
4.18. Dilution refrigerators
The idea that cooling could be achieved by means of dilution of He3
by
super fluid He4
was first suggested by H. London (1951). Phase separation in
He3
–He4
mixtures had not been discovered at that time, so there was little interest
expressed in developing a practical dilution refrigerator. After Walters and Fairbank
discovered the phase separation phenomenon in 1956, London presented a practical
technique for the dilution refrigerator (London et al. 1962). Hall et al. (1966) and
Neganov et al. (1966) constructed and operated dilution refrigerators that reached
0.065 K (0.11o
R) and 0.025 K (0.045°R), respectively. Commercial dilution

155
refrigerators are now available that operate at 0.005 K (0.009°R), such as shown in
Fig. 4.30.
Fig. 4.29. Thermal conductivity of lead in the normal and superconducting states.
A schematic of a He3
He4
dilution refrigerator is shown in Fig. 4.31. The gas
(which is practically pure He) is "compressed" in a vacuum pump from about 4 Pa
(0.03 torr) to a pressure on the order of 4 kPa (30 torr), then cooled in a
heatexchanger and a liquid helium bath at 4.2 K. The gas is next condensed in a bath
of liquid helium boiling at about 1.2 K. The liquid He3
expands through a
constriction (capillary tube) and is cooled further in the still, which operates at about
0.6 K. The liquid is again cooled in another heat exchanger before entering the
mixing chamber, where the He3
is mixed with He4
at temperatures between 0.005 K
and 0.050 K.
In the mixing chamber, the liquid separates into two phasesa less dense
concentrated He3
mixture and a more dense dilute He3
mixture. The temperature
composition diagram for He3
He4
mixtures is shown in Fig. 4.32. Numerical values

156
are tabulated in Table 4.7. The He) molecules "expand" from the concentrated phase
into the dilute phase (actually, diffuse through the dilute phase), and the mixture
temperature would tend to decrease; however, heat is added to the mixing chamber
from the low temperature region to maintain a constant temperature. This process is
analogous to the isothermal expansion of a gas, except no external work is done by
the He) in the mixing chamber.
The dilute mixture returns through the heat exchanger to the still, where heat
is added to evaporate the He3
from the mixture. The concentration of He3
in the liquid
phase in the still is approximately 1.0 percent, and the composition of the vapor is
around 95 to 98 percent He) 3

The refrigeration effect of the dilution refrigerator may be determined by
application of the First Law to the mixing chamber:
 a 3 m iQ n h h ̇ ̇ (4.103)
where n3 is the molar flow rate of He3
, hm is the molar enthalpy of the He3
in
the dilute phase leaving the mixing chamber, and h, is the molar enthalpy of the
practically pure He) entering the mixing chamber. Radebaugh (1967) noted that, for
temperatures below about 0.04 K, the enthalpies could be approximated by'
2
m 1 mh C T , where C1 = 94 J/molK2
(4.104)

2
i 2 ih C T , where C2 = 12 J/molK2
(4.105)

157

Fig. 4.30. He3
–He4
dilution refrigerator unit.  The system
allows samples with up to eight electrical contacts to be
toploaded into the working refrigerator. Samples can be
cooled from room temperature to below 10 mK
(0.018o
R) in 2 hours (courtesy of Oxford Instruments,
Osney Mead, Oxford, England).
Table 4.7:  Phase separation temperature curve for liquid He3
– He4
mixtures
(Radebaugh 1967)
Mole fraction He3
Temperature Mole fraction He3
Temperature
x (K) x (K)
0.0640 0.0 0.12 0.2902
0.0641 0.01486 0.13 0.3166
0.0642 0.0208 0.14 0.3412
0.0643 0.0253 0.15 0.3644
0.0645 0.0323 0.16 0.3863
0.0647 0.0377 0.17 004072
0.065 0.0445 0.18 004272
0.066 0.0606 0.20 0.4647
0.067 0.0721 0.25 0.5460
0.068 0.0817 0.30 0.6097
0.070 0.0970 0.35 0.6558
0.072 0.1102 0040 0.6843
0.074 0.1223 0.847 0.60

158
0.076 0.1335 0.876 0.55
0.078 0.1436 0.904 0.50
0.080 0.1528 0.928 0.45
0.085 0.1747 0.949 0.40
0.090 0.1946 0.968 0.35
0.095 0.2129 0.982 0.30
0.10 0.2301 0.9965 0.20
0.11 0.2616 1.000 0.10
where Tm is the temperature of the dilute phase leaving the mixing chamber, and T, is
the temperature of the practically pure He) entering the mixing chamber.
A typical He) flow rate for dilution refrigerators is about 1.0 × 10–4
mol/so.
For an ideal heat exchanger (Ti = Tm) and a mixing chamber temperature of 0.040 K,
the maximum refrigeration effect should be
   24 6
aQ 10 94 12 0.040 13.1 10 W 13.1 W 
     ̇
One of the more critical aspects in the design of a dilution refrigerator is the
design of the heat exchanger between the mixing chamber and the still. From eqn.
(4.103), we note that the temperature ratio for zero heat addition is Ti/T m = (94/12)½
=
2.80. For Tm = 0.04 K, the largest value of T, for finite heat addition is 0.112 K, or
the maximum temperature difference at the cold end of the exchanger is (Ti Tm) =
0.072 K. Large surface areas per unit volume have been achieved for heat exchangers
using sintered metal elements within the flow passages.

159
MODULE V
CRYOGENICFLUID STORAGE AND TRANSFER SYSTEMS
After a cryogenic fluid has been liquefied and purified to the desired level, it
must then be stored and transported. Cryogenicfluid storagevessel and transferline
design has progressed rapidly as a result of the growing use of cryogenic liquids in
many areas of engineering and science. Cryogenic fluid storage vessels range in size
from small Iliter flasks used in laboratory work up to 106 ml (28,000 gal U.S.) and
larger vessels used to store liquid nitrogen, liquid oxygen, and liquid hydrogen for
industrial use and in spacevehicle ground support systems. Storage vessels range in
type from lowperformance containers, insulated by rigid foam or fibrous insulation
so that the liquid in the container boils away in a few hours, up to highperformance
vessels, insulated by multilayer evacuated insulations so that less than 0.1 percent of
the vessel contents is lost per day.
Because the storage and transfer system is considered to be one of the
critical parts of any cryogenic system, many examples of cryogenicfluid storage
vessel design have appeared in the literature (Hallett et al. 1960; Wilson 1960;
Eichstaedt 1960; Canty and Gabarro 1960; Zenner 1960). In this chapter, we shall
consider the basic design approach for conventional storage vessels and transfer
lines, along with the auxiliary components used in storage and transfer of cryogenic
fluids.
CRYOGENICFLUID STORAGE VESSELS
5.1. Basic storage vessels
In 1892 Sir James Dewar developed the vacuuminsulated doublewalled vessel that
bears his name today (Dewar 1898). The development of the dewar vessel (which is
the same type of container as the ordinary Thermos bottle used to store coffee, iced
tea, etc.) represented such an improvement in cryogenicfluid storage vessels that it
could be classed as a "breakthrough" in container design. The highperformance
storage vessels in use today are based on the concept of the dewar design principlea
doublewalled container with the space between the two vessels filled with an
insulation and the gas evacuated from the space. Improvements have been made in

160
the insulation used between the two walls, but the dewar vessel is still the starting
point for highperformance cryogenic fluid vessel design.
Fig. 5.1. Elements of a dewar vessel.
The essential elements of a dewar vessel are shown in Fig. 5.1. The storage
vessel consists of an inner vessel called the product container, which encloses the
cryogenic fluid to be stored. The inner vessel is enclosed by an outer vessel or
vacuum jacket, which contains the high vacuum necessary for the effectiveness of
the insulation and serves as a vapor barrier to prevent migration of water vapor or air
(in the case of liquid hydrogen and liquid helium storage vessels) to the cold product
container.
The space between the two vessels is filled with an insulation, and the gas in
this space may be evacuated. In small laboratory dewars, the "insulation" consists of
the silvered walls and high vacuum alone; however, insulations such as powders,
fibrous materials, or multilayer insulations 'are used in larger vessels. Since the
performance of the vessel depends to a great extent upon the effectiveness of the
insulation, we shall devote a section to the discussion of insulations used in
cryogenicfluid storage and transfer systems.
There is no need for fill and drain lines for small laboratory containers (the
fluid is simply poured in or out through the open end of the container); however, a

161
fill and drain line (which may be two separate lines or a single line) is necessary for
larger vessels. A vapor vent line must be provided to allow the vapor formed as a
result of heat inleak to escape. In addition, some method must be provided to remove
the liquid from the container. Liquid removal may be accomplished either by
pressurization of the inner container or by a liquid pump. If pressurization of the
inner vessel is used, a vapor diffuser must be incorporated in the vent line in order
that that warm presurrization gas be distributed within the ullage space (vapor space
above the liquid) and in order that the warm gas be directed away from the surface of
the cold liquid to reduce recondensation of the pressurization gas. Antislosh baffles
are employed in transportable vessels to damp motion of the liquid while the
container is being moved. A suspension system must be used to support the product
container within the vacuum jacket.
The design capacity and design pressure for a storage vessel is usually
established by the storage requirement of the user. When large storage vessels first
came into use, most were customtailored for the specific use. However, most
cryogenicvessel manufacturers have reached the point that a set of standardsize
vessels is available. These standard units are generally more economical than
specially made vessels.
Cryogenicfluid storage vessels are not designed to be completely filled for
several reasons. First, heat inleak to the product container is always present;
therefore, the vessel pressure would rise quite rapidly because of vaporization of the
liquid if no vapor space were allowed. Second, inadequate cooldown of the inner
vessel during a rapid filling operation would result in additional boiloff, and the
liquid would be percolated through the vent tube if no ullage spa~ were provided. A
10 percent ullage volume is commonly used for large storage vessels. This means
that a nominal 106 m) (28,000 gal U.S.) dewar actually has an internal volume of
116.6 m) (30,800 gal U.S.).
Cryogenicfluid storage vessels may be constructed in almost any shape one
desirescylindrical, spherical, conical, or any combination of these shapes. Generally,
one of the most economical configurations is the cylindrical vessel with either
dished, elliptical, or hemispherical heads or end closures. Spherical vessels have the

162
most effective configuration as far as heat inleak is concerned, and they are often
used for largevolume storage in which the vessel is constructed on the site.
A cylindrical vessel with a lengthtodiameter ratio of unity has only 21
percent greater surface area than a sphere of the same volume, so the heatinleak
penalty is not excessive for a cylindrical vessel compared with a spherical vessel.
Cylindrical vessels are usually required for transportable trailers and railway cars
because the outside diameter of the vessel cannot exceed about 2.44 m (8 ft) for
normal highway transportation. For shopfabricated stationary vessels that are
shipped to the site by rail, the maximum diameter depends upon the route taken, but
generally not more than 3.05 m (10 ft) to 3.66 m (12 ft) can be accommodated.
5.2. Innervessel design
The details of conventional cryogenicfluid storage vessel design are
covered in such standards as the ASME Boiler and Pressure Vessel Code, Section
VIII (1983), and the British Standards Institution Standard 1500 or 1515. Most users
require that the vessels be designed, fabricated, and tested according to the Code for
sizes larger than about 250 dm3
(66 gal U.S.) because of the proved safety of Code
design.
The product container must withstand the design internal pressure, the
weight of the fluid within the vessel, and the bending stresses as a result of beam
bending action. The inner vessel must be constructed of a material compatible with
the cryogenic fluid; therefore, stainless steel, aluminum, Monel, and in some cases
copper are commonly used for the inner shell. These materials are much more
expensive than ordinary carbon steel, so the designer would like to make the inner
vessel wall as thin as practical in order to hold the cost within reason. In addition, a
thick walled vessel requires a longer time to cool down, wastes more liquid in cool
down, and introduces the possibility of thermal stresses in the vessel wall during
cooldown. For these reasons, the inner vessel is designed to withstand only the
internal pressure and bending forces, and stiffening rings are used to support the
weight of the fluid within the lower vessel.
5.3. Outervessel design

163
Because the outer shell of a dewar vessel has only atmospheric pressure
acting on it, one could erroneously think that the shell thickness could be made quite
small. Indeed, if were used to determine the shell thickness, ridiculously small
thickness values would be obtained. Actually, the outer shell would not fail because
of excessive stress, but it would fail from the standpoint of elastic instability
(collapsing or buckling). A thin cylindrical shell will collapse under an externally
applied pressure at stress values much lower than the yield strength for the material.
Table 5.1. Typical mechanical properties of metals
Density Youngs modulus
Metal kg/m3
Ibm/in3
GPa psi Poisson's
Ratio
Carbon steel 7720 0.279 200 29 × 106
0.27
Lowalloy
steel
7830 0.283 200 29 × 106
0.27
Stainless
steel
7920 0.286 207 30 × 106
0.28
Aluminum 2700 0.098 69 10 × 106
0.33
Copper 8940 0.323 117 17 × 106
0.33
Monel 8830 0.319 179 26 × let 0.32
5.4. Suspension system design
One of the critical factors in the design of an effective cryogenicfluid
storage vessel is the method used to suspend the inner vessel within the outer vessel.
A poor suspension system can nullify the effect of using a high performance
insulation. Some commonly used suspension systems are: (I) tension rods of high
strength stainless steel, (2) saddle bands of metal or plastic, (3) plastic (Micarta, for
example) compression blocks, (4) multiplecontact supports (stacked discs), (5)
compression tubes, and (6) wire cables or chains.
The innervessel suspension system is subjected to the weight of the inner
vessel and its contents plus dynamic loads that arise in transporting the vessel,
earthquakes, and so on. Even if the storage vessel is a stationary vessel, it must

164
withstand dynamic loads when empty during shipment if the vessel is not constructed
on site. Seismic loads are possible for a vessel constructed on site.
Fig. 5.2. Typical methods of supporting the inner vessel within the outer
vessel in a dewar.
Some typical acceleration loadings that have been specified in design are
given in Table 5.2. These loadings are given in multiples of the local acceleration
due to gravity, so that a container subject to a 2g acceleration load has a force
equivalent to twice the container weight acting on the suspension system.
Table 5.2. Acceleration loads specified in suspension system desi.gn for
cryogenicfluid storage vessels
Vertical Vertical Transverse, longitudinal
Type of unit Up,g Down, g g g
Stationary storage vessels:
Empty 0.5 3 0.5 5
Full 0.5 1.5 0.5 0.5
Full with blast loading 3 5 4 4
Transport trailers:
Small (below 4 m' or 1060 2 5 4 8
gal U.S.)
Large (above 4 m') 4 2 4

165
Let us analyze the suspension system loads for the case of highstrength
tension rods. The suspension rods are arranged such that the rods support tensile
loads only. The forces for verticaldown loading, verticalup loading, and transverse
loading (two cases) are shown in Fig
Fig. 5.3. Dynamic loading conditions for support system If we apply a force balance
for the case of the verticaldown loading, we obtain
2F – W – Ng W = 0
Or, the force in one set of vertical rods is
F – (1 + Ng) W/2
where Ng = acceleration load
W = weight of the inner vessel and its contents
By applying a similar force balance and moment balance (for the transverse
loading), the forces in the suspension system can be obtained for the other cases. The
results are summarized in Table
If the angle between the longitudinal rods and the vessel wall is denoted by
, then the acceleration load for the longitudinal rods is

166
1 gF N W / cos 
Two sets of longitudinal rods must be usedone set for forward loading and
another set for rearward loading.
For safety reasons, generally two or more rods are used at each support
point. The support rods are attached at the main support rings on the outer vessel and
at one of the innervessel stiffening rings. Resistance to heat transfer down the rods
may be achieved by using springs or washers at either end or both ends of the
support members. Spherical washers may be used to reduce misalignment of the rods
resulting from thermal contraction of the inner vessel. A typical support bracket is
shown in Fig.
5.5. Piping
Piping necessary to remove liquid from the container, vent vapor from the
vessel, and so on, introduces a source of heat in leak to the product container. With a
properly designed piping system, the heat transfer down the piping is due to
conduction along the pipe wall only. For this reason, the piping runs should be made
as long as possible, and thin walled pipe should be used. Schedule 5 pipe (the
thinnest piping available in 304 stainless steel) or schedule 10 pipe is typically used
in many larger cryogenicfluid storage vessels. The thermal contraction of the piping
runs must be considered in the piping system design also.
Fig. 5.4. Cryogenicfluid storagevessel piping arrangements
Four piping arrangements are shown in Fig. 5.10. Arrangement 1 is
commonly used for multilayerinsulated vessels. A long length of pipe is obtained
between the warm outer vessel and the cold inner vessel by extending the vacuum

167
space around the pipe back into the inner vessel. Arrangement 2 is one of the "don'ts"
in cryogenic vessel designa poor arrangement. Condensation of vapor will take
place along the top of the horizontal portion of the line exposed to fluid within the
inner vessel. This liquid will flow along the horizontal section of the line to the
warmer portion of the pipe, at which point the liquid will evaporate. Heat will be
transferred to the inner container by the quite efficient boilingcondensation
convection process, and a large heattransfer rate will result. In addition, no provision
is made for thermal contraction of the line; therefore, high thermal stresses will be
produced in the pipe. In arrangement 3, a vertical rise in the vacuum space is used to
prevent the convection problem present in arrangement 2, and an expansion bellows
is introduced to allow for thermal contraction. Arrangement 3 presents a serious
problem in reliability of the container, however, and this arrangement should not be
used if possible. If a leak into the vacuum space should occur, it would most likely
occur in the bellows because of fatigue loading of the bellows during repeated cool
down. With the bellows located as in arrangement 3, the leak would be quite difficult
and costly to repair. The best piping arrangement is shown in arrangement 4, in
which the expansion bellows is located in the stand off, where the bellows is easily
accessible for repair. A vertical rise is also incorporated in arrangement 4 to prevent
percolation of the liquid within the line.
The minimum wall thickness for piping subjected to internal pressure is
determined according to the ASA Code for Pressure Piping by the of lowing
expression:
0
a
pD
t
2s 0.8p


where p = design pressure
D0 = outside diameter of pipe
sa = allowable stress of pipe material
5.6. Comparison of insulations

168
A comparison of the advantages and disadvantages of the insulations used in
cryogenic systems is given in the following summary.
Advantages Disadvantages
1 Expanded foams Low cost.
No need for rigid vacuum jacket.
Good mechanical strength.
High thermal contraction.
Conductivity may change with time.
2 Gasfilled powders and liberous
materials Low cost.
Easily applied 10 irregular shapes.
Not flammable.
Vapor barrier is required.
Powder can pack and conductivity is
increased.
3 Vacuum alone
Complicated shapes may be easily
insulated.
Small cooldown loss.
Low heat flux for small thickness
between inner and outer vessel.
A permanent high vacuum is
required. Lowemi£sivity boundary
surfaces needed.
4 Evacuated powders and fibrous
materials Vacuum level less
stringent than for multilayer
insulations.
insulated.
Relatively easy to evacuate.
May pack under vibratory loads and
thermal cycling.
Vacuum filters are required. Must be
protected when exposed to moist air
(retains moisture).
5 Opacified powders
Better performance than straight
evacuated powders.
insulated.
Vacuum requirement is not as
stringent as for multilayer
insulations and vacuum alone.
Higher cost than evacuated powders.
Explosion hazards with aluminum in
an oxygen atmosphere.
Problems of settling of metallic
flakes.
6 Multilayer insulations
Best performance of all insulations.
Low weight.
Lower cooldown loss compared
with powders.
Better stability than powders.
High cost per unit volume. Difficult
to apply to complicated shapes.
Problems with lateral conduction.
More stringent vacuum requirements
than powders.
5.7. Vaporshielded vessels
Another method of reducing the heat inleak to a cryogenicfluid storage
vessel is to ~se the cold vent gas to refrigerate an intermediate shield, as shown in
Fig. 7.17. T e escaping vent gas intercepts some of the heat that would otherwise d its

169
way to the product liquid. The effectiveness of this method' reducing the heat inleak
depends upon the ratio of sensible heat abs ed by the vent gas to the latent heat of the
fluid, as indicated in the following analysis.
The heattransfer rate from ambient to the vapor shield through all paths
may be written
     2 s 2 2 s 2 2 1 s 1Q U T T U T T T T        
̇
where the coefficient U2 may be determined from
     2 t t tins sup piping
U k A / x k A / x k A / x     
where kt is the thermal
conductivity for the insulation, supports, or piping; A is the heattransfer area for
each of these components; and x is the length of conduction path (thickness for the
insulation, support length for vessel supports, an~ piping length for piping). The
heattransfer rate between the shield and the product container may be written in a
similar manner:
 s 1 1 s 1 g fgQ U T T m h   ̇ ̇
where gṁ is the mass flow rate of boiloff vapor and hfg is the heat of vaporization of
the fluid. Assuming that the vent gas is warmed up to the shield temperature within
the shield flow passages, the sensible heat absorbed by the vent vapor is
 g g p s 1Q m c T T ̇ ̇
From an energy balance applied to the shield, we find
2 s s 1 gQ Q Q  ̇ ̇ ̇
U2[(T2 – T1) – (Ts – T1)] = U1(Ts – T1) + U1cp(Ts – T1)2
/hfg
Let us introduce the following dimensionless parameters:
 1 p 2 1 fgc T T / h  
2 1 2U / U 
   s 1 2 1T T / T T   
Making these substitutions, we obtain the following expression for the
dimensionless temperature of the shield:

170
 2
1 2 2 1 1 0        
or
 
½
2 1 2
2
1 2 2
1 4
1 1
2 1
      
     
       
Fig. 5.5. Vaporshielded cryogenicfluid storage vessel.

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