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NBS SPECIAL PUBLICATION 698

U.S. DEPARTMENT OF COMMERCE/National Bureau of Standards

QC

100

• U57

No. 698

1985

C. ?

Proceedings

of the Third

Cryocooler

Conference

National Bureau of Standards

Boulder, Colorado

September 17-18, 1984
he National Bureau of Standards' was established by an act of Congress on March 3, 1901. The

m

Jf Bureau's overall goal is to strengthen and advance the nation's science and technology and facilitate their effective application for public benefit. To this end, the Bureau conducts research and provides: (1) a

basis for the nation's physical measurement system, (2) scientific and technological services for industry and

government, (3) a technical basis for equity in trade, and (4) technical services to promote public safety.

The Bureau's technical work is performed by the National Measurement Laboratory, the National

Engineering Laboratory, the Institute for Computer Sciences and Technology, and the Center for Materials

Science.

The National Measurement Laboratory

Provides the national system of physical and chemical measurement;

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furnishes essential services leading to accurate and uniform physical and

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produces, and distributes Standard Reference Materials; and provides

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• Basic Standards2 • Radiation Research

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Provides technology and technical services to the public and private sectors to address national needs and to solve national problems; conducts research in engineering and applied science in support of these efforts; builds and maintains competence in the necessary disciplines required to carry out this research and technical service; develops engineering data and measurement

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Gaithersburg, MD 20899.

2Some divisions within the center are located at Boulder, CO 80303.

3 Located at Boulder, CO, with some elements at Gaithersburg, MD.
Proceedings of the Third

Cryocooler Conference

National Bureau of Standards

Boulder, Colorado

September 17-18, 1984

Edited by:

Ray Radebaugh, Beverly Louie, and Sandy McCarthy

Natbnal Bureau of Standards

Boulder, Colorado 80303

Sponsored by:

Cryogenic Engineering Conference

International Institute of Refrigeration -Commission A 1/2

NASA/Goddard Space Flight Center

National Bureau of Standards

Naval Research Laboratory

Office of Naval Research

Q

z

U.S. DEPARTMENT OF COMMERCE, Malcolm Baldrige, Secretary

NATIONAL BUREAU OF STANDARDS, Ernest Ambler, Director

Issued May 1985
Library of Congress Catalog Card Number: 85-600544

Natbnal Bureau of Standards Special Publication 698

Natl. Bur. Stand. (U.S.), Spec. Publ. 698, 279 pages (May 1985)

CODEN: XNBSAV

U.S. GOVERNMENT PRINTING OFFICE

WASHINGTON: 1985

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

This document contains the proceedings of the Third

Cryocooler Conference, held at the National Bureau of

Standards, Boulder, Colorado, on September 17-18, 1984. About

140 people from 10 countries attended the conference and represented industry, government, and academia. A total of 26

papers were presented orally at the conference and all appear

in written form in this document. The emphasis in this conference was on small cryocoolers in the temperature range of 4 - 80 K. Mechanical and nonmechanical types were discussed in the

various papers. Applications of these small cryocoolers

include the cooling of infrared detectors, cryopumps, small

superconducting devices and magnets, and electronic devices.

Key words: conference; cryocoolers; cryogenics, cryopumps;

helium; infrared detectors; refrigeration; superconductors.

DISCLAIMER

Except where attributed to NBS authors, the content of individual sections of this

volume has not been reviewed or edited by the National Bureau of Standards. NBS therefore

accepts no responsibility for quality of copy, comments, or recommendations therein. The

mention of trade names in this volume is in no sense an endorsement or recommendation by

the National Bureau of Standards.

i i i
DEDICATION TO THE MEMORY OF PROFESSOR WILLIAM E. GIFFORD

The 3rd Cryocooler Conference on Refrigeration for Cryogenic Sensors and Electronic

Systems is dedicated to our late colleague, Professor William E. Gifford of Syracuse

University, for his valuable contributions to the field of cryoref rigeration. He was

one of our pioneers, an inventor of practical systems, a dedicated teacher who

inspired his students, and founder of an organization to carry on the development and

manufacturing of cryoref rigeration machinery.

SPONSORS

National Bureau of Standards

Office of Naval Research

Naval Research Laboratory

International Institute of Refrigeration - Commission Al/2

Cryogenic Engineering Conference

NASA/Goddard Space Flight Center

CHAIRMAN

Ray Radebaugh - National Bureau of Standards

ADMINISTRATOR

Sandy McCarthy - National Bureau of Standards

ADVISORY COMMITTEE

Edgar A. Edelsack - Office of Naval Research

Max Gasser - NASA/Goddard

Peter J. Kerney - CTI Cryogenics

Paul Lindquist - Wright-Patterson AFB Ralph Longsworth - Air Products and Chemicals

Martin Nisenoff - Naval Research Laboratory

Allan Sherman - NASA/Goddard

Klaus D. Timmerhaus - University of Colorado

Graham Walker - General Pneumatics Corp.

James E. Zimmerman - National Bureau of Standards

LOCAL COMMITTEE

Beverly Louie - National Bureau of Standards

Ray Radebaugh - National Bureau of Standards

James E. Zimmerman - National Bureau of Standards

iv
CONTENTS

Page

1. INTRODUCTION AND SUMMARY 1

2. "DESIGN OF CRYOCOOLERS FOR MICROWATT SUPERCONDUCTING DEVICES,"

by J. E. Zimmerman 2

3. "RECENT CRYOCOOLER PROGRESS IN JAPAN,"

by Yoichi Matsubara 10

4. "MAGNETIC REFRIGERATION FOR LOW-TEMPERATURE APPLICATIONS,"

by John A. Barclay 20

5. "RECIPROCATING MAGNETIC REFRIGERATOR,"

by Dean L. Johnson 33

6. "IMPROVED HEAT SWITCH FOR GAS SORPTION COMPRESSOR,"

by Chung K. Chan 42

7. "HYDRIDE ABSORPTION REFRIGERATOR SYSTEM FOR TEN KELVIN AND BELOW,"

by Jack A. Jones 53

8. "CLASSIFICATION OF CRYOCOOLERS,"

by G. Walker 65

9. "AN EXPERIMENTAL STUDY FOR A MINIATURE STIRLING REFRIGERATOR,"

by Shimo Li, Chen Guobang, Cuangji Cui , and Jiazhang Li 71

10. "PARAMETRIC TESTING OF A LINEARLY DRIVEN STIRLING CRYOGENIC REFRIGERATOR,"

by F. R. Stolfi and A. Daniels 80

11. "DESIGN OF A FLIGHT QUALIFIED LONG-LIFE CRYOCOOLER,"

by L. Knox, P. Patt, and R. Maresca 99

12. "SIMPLE CONSTRUCTION AND PERFORMANCE OF A CONICAL PLASTIC CRYOCOOLER,"

by N. Lambert 119

13. "EFFECT OF LEAKAGE THROUGH CLEARANCE SEALS ON THE PERFORMANCE OF A 10 K STIRLING-CYCLE REFRIGERATOR,"

by C. S. Keung and E. Lindale 127

14. "AN EXPERIMENTAL RECIPROCATING EXPANDER FOR CRYOCOOLER APPLICATION,"

by Moses Minta and Joseph L. Smith, Jr 135

15. "EXPERIMENTS WITH A FULLY INSTRUMENTED SPLIT STIRLING CRYOCOOLER,"

by Alain Faure, Serge Reale, and Philippe Bernhein 147

16. "LOW FREQUENCY SPLIT CYCLE CRYOCOOLER,"

by S. X. Bian, Y. D. Zhang, W. W. Wan, L. Wang, and Q. C. Hu 156

17. "PASSIVE MOTION CONTROL OF PNEUMATICALLY DRIVEN DISPLACERS IN CRYOGENIC COOLERS,"

by N. Pundak and S. Shtrikman 161

18. "A NONPROPRIETARY, NONSECRET PROGRAM FOR CALCULATING STIRLING CRYOCOOLERS,"

by William R. Martini 168

19. "A SIMPLE, FIRST STEP TO THE OPTIMIZATION OF REGENERATOR GEOMETRY,"

by Ray Radebaugh and Beverly Louie 177

v
20. "A COMPUTATIONAL MODEL FOR A REGENERATOR,"

by John Gary, David E. Daney, and Ray Radebaugh 199

21. "CRITERIA FOR SCALING HEAT EXCHANGERS TO MINIATURE SIZE,"

by Philipp B. Rudolf von Rohr and Joseph L. Smith, Jr 212

22. "A CLOSED CYCLE CASCADE JOULE THOMSON REFRIGERATOR FOR COOLING JOSEPHSON

JUNCTION DEVICES,"

by Emanuel Tward and Raymond Sarwinski 220

23. "A SMALL HELIUM LIQUIFIER WHICH PROVIDES CONTINUOUS COOLING BASED ON CYCLED ISENTROPIC EXPANSION,"

by Calvin Winter, Suso Gygax, Ken Myrtle, and Russel Barton 226

24. "VUILLEUMIER CYCLE CRY0C00LER OPERATING BELOW 8 K,"

by Yoichi Matsubara and Mitsuhiro Kaneko 234

25. "4 K REFRIGERATORS WITH A NEW COMPACT HEAT EXCHANGER,"

by R. C. Longsworth and W. A. Steyert 240

26. "THE DESIGN OF A SMALL LINEAR-RESONANT, SPLIT STIRLING CRYOGENIC

REFRIGERATOR COMPRESSOR,"

by R. A. Ackerman 250

27. "JOULE-THOMSON VALVES FOR LONG TERM SERVICE IN SPACE CRYOCOOLERS,"

by James M. Lester and Becky Benedict 257

ATTENDANCE LIST 267

vi
INTRODUCTION AND SUMMARY

This document contains the proceedings of the Third Cryocooler Conference, which was held at the National Bureau of Standards, Boulder, Colorado, on September 17-18, 1984.

This series of conferences began in 1977 when about 40 invited speakers and participants

assembled at the National Bureau of Standards in Boulder to discuss cryocoolers for small superconducting devices. Proceedings of that meeting are available from the Superintendent of

Documents, U. S. Government Printing Office, Washington, D. C. as NBS Special Publication 508,

entitled "Applications of Closed-Cycle Cryocoolers to Small Superconducting Devices". Since it was open only to invited participants, it may be considered conference number zero.

Because the scientific and engineering community showed great interest in a conference on cryocoolers, the first open conference, consisting mostly of contributed papers, was held in 1980

at the National Bureau of Standards, Boulder, with about 115 in attendance. The emphasis in that

First Cryocooler Conference still was on the temperature range below 20 K. Proceedings of that

conference are available from the U. S. Government Printing Office as NBS Special Publication 607,

entitled "Refrigeration for Cryogenic Sensors and Electronic Systems". In response to a questionnaire, participants favored holding such a conference every two years and that trend has

been followed.

The Second Cryocooler Conference was held in 1982 at NASA Goddard Space Flight Center,

Greenbelt, Maryland. At that time the scope of the conference was expanded by considering

temperatures up to 80 K, but it still emphasized small cryocoolers. The broadened scope brought

in more participants and it was found that many concepts and techniques used at 80 K were common

to lower temperature coolers as well. It was here that the scope of these series of conferences

seemed to jel 1

.

The scope of this Third Cryocooler Conference was the same as the second - small cryocoolers

of about 10 W or less and temperatures below 80 K. However, any studies on devices or concepts

outside this range that would have applications within the range were still considered. About 140

participants from 10 countries attended the conference. The two-year interval for the Cryocooler

Conferences has meshed well with the Cryogenic Engineering Conference held on the alternate years.

Sessions on small cryocoolers at the Cryogenic Engineering Conference are attended by the general

cryogenic engineering community. The Cryocooler Conferences attended by specialists allow for a more in depth focus on cryocoolers.

Twenty-six papers were presented at the Third Cryocooler Conference and the written versions

of all appear in this document. Three invited review papers were given on areas of widespread

interest. A survey of the papers presented here as well as those in past conferences shows

considerable progress in this area of high reliability as indicated by the papers on the Stirling

cryocooler with magnetic bearings. The split Stirling cryocooler is well represented and shows

advances in the area of a more reproducible drive for the displacer. Interest and progress in non-mechanical refrigeration techniques, such as magnetic refrigeration and absorption compressors

for Joule-Thomson coolers, are evident from the number of papers in that session. Significant

advances were made in the modeling of cryocoolers and in the understanding of regenerator

behavior. Considerable work on cryocoolers is now being done in China and we are pleased to have

had for the first time at these Cryocooler Conferences two papers from Chinese authors.

Applications of cryogenics depend intimately on the development of efficient, reliable, and

inexpensive cryocoolers. We feel that the cryocooler progress represented by the papers that

follow will have a significant impact on the development of cryogenics.

The Editors

1
DESIGN OF CRYOCOOLERS FOR MICROWATT SUPERCONDUCTING DEVICES

J. E. Zimmerman

National Bureau of Standards

Electromagnetic Technology Division

Boulder, CO 80303

The primary applications of the cryocoolers considered here are for

cooling various Josephson devices such as SQUID magnetometers and

amplifiers, voltage standards, and microwave mixers and detectors. The common feature of these devices is their extremely low inherent bias

power requirement, of the order of 10" W (or sometimes much less) per

junction. This provides the possibility, not yet fully exploited, of

designing compact, low-power cryocoolers for these applications, the

design criteria being totally different from those of any cryocoolers

presently available. Several concepts have been explored and a number

of laboratory model cryocoolers have been built. These include lowpower non-magnetic regenerative machines of the Stirling or GiffordMcMahon type, three- or four-stage Joule-Thomson machines, liquid-helium

dewars with integral small cryocoolers to reduce the evaporation rate,

and liquid-helium dewars with integral continuously or intermittently

operated small helium liquefiers to permit operation of cryogenic

devices for indefinite time periods.

Key words: Cryocooler; cryogenics; refrigeration; superconducting

devices; SQUID.

1. Introduction

A workshop on "Applications of Closed-Cycle Cryocoolers to Small Superconducting Devices"[l]

was held at the National Bureau of Standards Boulder Laboratories in October 1977, out of which

came the present series of conferences, more broadly conceived, on refrigeration for cryogenic

sensors and electronic systems. The intent of this paper is to return to the narrower theme of

the first workshop, to emphasize again the nature of the problem and to give at least the

rudiments of a design philosophy which is appropriate to the needs of Josephson and other very

low-power superconducting devices. This paper is presented in the conviction that the practical

potential of superconducting devices, primarily SQUIDs and other Josephson devices, is largely

unrealized precisely because of the lack of a compatible, low-cost cryocooler. The commercial

viability of systems consisting of these devices and integral cryocoolers can hardly be judged

from the market for the devices themselves, currently estimated to be of the order of a hundred

per year, since the cost and inconvenience of the present cryogenic support systems greatly

inhibits their use.

2. Small Superconducting Devices

For the past 20 years most cryoelectronic systems- have been built around superconducting

tunnel junctions or microbridges exhibiting the Josephson effect, commonly known as Josephson

junctions. Bias power is typically in the range of a few microwatts (the order of 1 mA at 1 mV)

down to a few picowatts per junction. Arrays of up to 1000 Josephson junctions should have bias

power requirements of a milliwatt or less. While most Josephson devices are specifically designed

for operation in the neighborhood of 4 K (that is, in liquid helium at atmospheric pressure or below), research and development continues on higher-temperature materials. Many niobium devices

have been made which operate at temperatures of 8 to 9 K, and a double-junction Nb-Al-Ge SQUID

2
(the SQUID, or superconducting quantum interference device, used primarily as an ultra-sensitive

magnetic sensor but also as memory element, counter, and for other purposes, consists of a lowinductance superconducting loop with one or two Josephson junctions appropriately biased for the

application) has been demonstrated to operate at a temperature above 20 K [2].

Room-temperature transistors when used at low temperatures typically require much greater

bias power than Josephson junctions. GaAs FETs which have been used as low-noise preamplifiers

for SQUIDs require 20 to 50 mW, so that an array of these could require a considerable

refrigeration capacity. However, these are not cryogenic devices, and their noise performance

does not improve below 50 K or so, at which temperature refrigeration is at least 12 times

cheaper, so to speak, than at 4 K. It has been suggested that a true cryogenic transistor is one

of the prime requirements, along with reliable and convenient miniature cryocoolers, for the

widespread acceptance of cryogenic instrumentation in general. A number of cryogenic transistors

have been suggested [3,4].

There is considerable interest in arrays of cooled infrared sensors both for astronomical

studies, and more extensively, for military applications. Both the scale of the arrays and the

requirement of an infrared window to the outside world may impose relatively large heat loads on the cooling mechanism. In any case, this application will not be considered in this paper,

although some of the design principles discussed may be applicable.

3. Refrigeration Requirements

Since Josephson devices require virtually no bias power, the essential function of a cryocooler reduces to that of intercepting radiation and conduction heat leaks along electrical

connections and mechanical supports from the room-temperature environment. Elementary arguments

show that it is much more efficient, and also easier, to provide for these heat leaks by some optimum distribution of cooling capacity at several discrete temperatures, or by a continuous

distribution of refrigeration, than by simply providing a large cooling capacity at the lowtemperature end. This principle is well-known, and yet it is common practice to specify the

cold-end cooling capacity of cryocoolers and to mention the refrigeration at higher temperatures

almost as an afterthought, if at all, rather than the other way around. Lending weight to the

argument is the fact that heat conduction in all the commonly used materials, both metallic alloys

and non-metals, but excluding copper and other pure metals, increases monotonical ly with

temperature (see figure 1) [5]. The fourth-power law of radiation is a more dramatic example of

the same tendency.

Some typical magnitudes of low-temperature heat leaks are instructive. Radiant energy from a low-emi ssivity (0.1) surface of a radiation shield at 20 K is about 0.9 mW/m . As an example of

heat leaks through support structures, it can be shown that a mass of 1 kg at a temperature of 10

K can be kinematical ly supported at 10 G loading inside a radiation shield at 20 K by cords or wires 10 cm long with heat leaks of 9 yW for nylon or 60 yW for stainless steel (these heat leaks were calculated using thermal conductivities from figure 1 and tensile strengths of 900 MPa for

nylon and 1800 MPa for stainless steel). Thus, the heat leaks would still be small for shorter

and thicker support structures, and most cryoelectronic devices have much less than 1 kg mass. The case of electrical leads is slightly more complicated. For bias power in the range of

milliwatts or less, negligible heat leak can be achieved by the use of fine wires of lowconductivity alloy. Signal lines, on the other hand, may have to have low electrical resistance,

and relatively high thermal conductance, to avoid degrading the signal-to-noise ratio. Nominally

pure copper is widely used for this purpose, but since its conductivity may be 1000 times that of

most alloys at low temperatures, it may introduce unnecessarily large heat leaks to the cryogenic

device to which the signal lines are connected. We will return to the subject of signal lines

after a discussion of refrigeration mechanisms.

4. Liquid Helium As a Refrigeration Mechanism

A liquid-helium bath provides a relatively small cooling capacity at the boiling point (the

heat of vaporization, 83 J/mol at 4.2 K). The cold vapor provides additional cooling capacity,

the specific heat at constant pressure, which is nearly uniformly distributed in temperature above

8 or 10 K (^ 21 J/mol. K). The total cooling capacity of the vapor, % 6000 J/mol, is more than 70

times the heat of vaporization. In general, liquid helium does not provide an ideal distribution

of refrigeration. As shown below and elsewhere, ideal cryogenic refrigeration systems for small

superconducting devices will usually require monotonical ly increasing cooling capacity vs temperature, and only in rather special applications (perhaps to absorb the ohmic heat generated

in high-current leads to a superconducting magnet) would the temperature-independent cooling

capacity of helium provide an efficient refrigeration mechanism. This may be the essential reason

for using liquid nitrogen or some other mechanism (see example below), along with liquid helium as

a low-temperature cryogen, to provide additional cooling capacity at higher temperature.

3

5. Cryocoolers

Two types of cryocooler are under development for small superconducting devices,

Joule-Thomson (J-T) and regenerative (Stirling, Gif ford-McMahon , Vui 1 1 eumier) . Joule-Thomson

cryocoolers are highly attractive for very low-power applications because of their simplicity of

construction and, more importantly, for having no solid moving parts in the cryogenic part of the

system, so they generate essentially no magnetic interference or vibration (there may be highfrequency noise or hiss due to turbulent flow of the working flu-id). Let us see how their

qualitative features compare with the those of the heat leaks through various materials as noted

above, and of thermal radiation. The following table gives the gross cooling capacities of a hypothetical four-stage Joule-Thomson cryocooler, with gas flow rates of 10 mL/s (standard

temperature and pressure) per stage:

Working Fluid CF

4

N 2 H

? H p Temperature (K) 160 84 23 4.2

Low/high Pressures (MPa) 0.2/10 0.2/10 0.2/10 0.1/2

Gross Cooling Capacity (W) 3.3 1.1 0.13 0.012

The gross cooling capacities for a multi-stage reversible machine (Stirling, Carnot, etc.)

with the same gas flows per stage are similar to the Joule-Thomson case. Here the cooling

capacity, in the perfect-gas approximation, is of the form PV(T2/Tl)ln(Pl/P2) , where the

pressure-volume product PV is at standard temperature and pressure, P1/P2 is the compression

ratio, and T2/T1 is the ratio of temperature of the stage to ambient temperature. Thus for P = 0.1 MPa (atmospheric pressure), V = 10 cm /s (per stage), Tl = 300 K, 1 n ( P1/P2 ) = 1.0, the gross

cooling capacities for a hypothetical four-stage machine are:

Temperature (K) 150 50 15 5 Gross cooling capacity (W) 0.5 0.17 0.05 0.017

Using ordinary helium as the working fluid, the cooling capacity of the bottom stage may be

considerably less than 0.017 W, since the perfect-gas approximation is quite inadequate at 5 K. These cooling capacities are roughly comparable to those of the Joule-Thomson example with the same flow rates, but note that Stirling and similar regenerative machines typically operate at much lower pressures and compression ratios than Joule-Thomson machines.

The point to be noted here is that in an intuitively "balanced" design (that is, comparable

gas flows in all stages), the refrigeration capacities of the successive stages increase with

increasing temperature, qualitatively matching the heat leaks that are expected from the lowconductivity materials commonly used in cryogenic design.

6. Electrical Connections

Copper, the most widely used material for electrical connections , may be a poor choice from

the point of view of cryocooler design and thermal (Nyquist) noise generated in the lead

resistance. The thermal conductivity of copper peaks at a temperature in the neighborhood of 20 K before dropping off linearly to zero at 0 K. Thus, the use of copper leads may result in large

heat leaks just in the low-temperature region where cooling capacity is inherently small. The

electrical resistivity of pure copper is small at low temperatures, so that the high-temperature

portion of the leads will dominate the total lead resistance, and also the Nyquist noise. For most alloys, on the other hand, the thermal conductivity decreases more or less linearly below

room temperature. It is easy to show that wires of practically any alloy such as brass,

copper-nickel, or beryllium-copper, of the appropriate diameter for a specified total lead

resistance, will reduce the heat leak at the low-temperature end by a factor of 100 or more, relative to copper, with only a moderate increase in the heat leak at the high-temperature end.

The use of such alloys should provide a much better match to a "balanced" cryocooler design (as

defined above) than pure copper. In addition, Nyquist noise generated in the leads will be lower

in the alloy than in copper, since a relatively larger part of the electrical resistance will be

at low temperature. The spectral density of total Nyquist noise power is proportional to the

integral over the length of the wire of the product of Boltzmann's constant, the temperature, and

the differential resistance, that is, the integral of k^TdR(T).

High-frequency and microwave leads can give large heat leaks if not specifically designed for

cryogenic use. The above principles still apply, but since high-frequency currents flow only in a thin surface layer (less than 1 ym at 10 GHz in copper at room temperature), electrical losses and

5
heat leaks can both be reduced by using thin layers of low-resistivity metal on high-resistivity

or insulating substrates, rather than using thick self-supporting conductors of low-resistivity

metal. Furthermore, waveguides for very high frequency radiation can incorporate vacuum gaps to eliminate heat conduction entirely.

In a previous paper [6], we derived the optimum (minimum input power) distribution of

refrigeration for cooling an electrical lead or a mechanical support of constant cross section,

extending from ambient temperature T . to a low temperature T , whose thermal conductivity K could be expressed as a power of the temperature T: K=K T

n

. The analysis was based on the

Wiedemann-Franz Law for the relationship between thermal conductivity K and electrical resistivity

p, that is, Kp/T ^ 2.4 x 10 W-Q/K . Applying this analysis to the case of

temperature-independent conductivity gives an optimum temperature distribution (see Appendix for a summary of the mathematical analysis)

T = T

o exp(az), where a = 1n ( Tamb/ T0

)

>

and z is the reduced distance measured from the cold end. For the case where the conductivity is proportional to temperature (K = K^T), the optimum temperature distribution is

T- «1">T„1/2

It turns out that in all cases the optimum distribution of refrigeration has the same z-dependence

as the temperature. In the earlier paper we gave, as an example, the ideal minimum input power

required to refrigerate an electrical lead (or set of leads) with temperature-independent thermal

conductivity and net electrical resistance of .023 ft. The result was 315 mW for the distributed

refrigeration plus 93 mW for the heat flow remaining at the cold end of the leads, a total of 408

mW of mechanical power to produce the required refrigeration. In the case of thermal conductivity

proportional to temperature (and the same electrical resistance), the ideal minimum input power

works out to be 280 mW for the distributed refrigeration and only 19 mW for the cold end, a total

of 299 mW. Although the difference in total power for the two cases is hardly significant, the

factor of five difference in the cold end term could be very significant for cryocoolers where the

performance at the cold end is limited by regenerator losses and non-ideal gas properties. This

numerical example provides some quantitative support for the qualitative arguments given above for

choosing the right kind of materials for electrical connections.

The optimum temperature distribution of refrigeration is the quantity of interest in

designing a cryocooler. The optimum distribution is temperature-independent for the case of

constant conductivity and proportional to T ' for the case of conductivity proportional to temperature. Thus, liquid helium would provide essentially ideal refrigeration for the improbable

example where it is necessary to use only materials of constant conductivity (probably no such

materials exist) and constant cross section. An additional degree of freedom available to the

designer is to vary the cross section of the electrical wires or wave guides in some optimum way

as a function of position within the cryocooler. In fact, deviations from the Wiedemann-Franz Law

(see above) are such as to be favorable to the use of copper or other pure metals such as silver

and unfavorable to the use of high-resistivity alloys such as stainless steel, provided the

cross-section is varied in some more-or-less optimum way. Materials of moderate electrical

resistivity such as brass obey the Wiedemann-Franz Law more closely. Consideration of all the

options can make the optimum design a difficult analytical problem, but it can be asserted with

some confidence (based partly on experience) that the casual use of pure copper for electrical

leads in the low-temperature end of low-power cryoelectronic systems can be disastrous.

7. Examples

One notable example of the use of a cryocooler with small superconducting devices is the

hybrid cryostat recently reported by Archer [7]. He incorporated a two-stage commercial

cryocooler with a 4.5-liter helium reservoir to achieve better than a five-day operating time for

a pair of 100-120 GHz receivers at 2.5 K. The receivers consist of superconducting (tunnel

junction) mixers at 2.5 K and GaAs FET IF preamplifiers at 20 K. Estimated heat leaks (actual

heat leaks were slightly greater) to the 2.5 K helium bath include radiation (M.5 mW) and

conduction (^12 mW) through fill tube, dc leads, IF coaxial lines, 3-mm waveguides, four

mechanical tuning rods, and massive solid supports for the helium reservoir and the receivers.

Direct-current and microwave-bias-power levels were not mentioned in the paper and can be assumed

to be negligible. Heat leaks at higher temperatures are intercepted by the cryocooler, which

provides heat sinks and radiation shields at 20 K and at 65 K. Heat conduction through electrical

connections was minimized by using design principles and materials already described (see above):

unplated stainless steel waveguides for local-oscillator power, vacuum gaps in the low-loss signal

waveguides, copper-beryllium alloy for the coaxial lines, and brass wire for dc connections.

6
This example demonstrates the small magnitude of total heat leak that can be achieved by

careful design in a rather difficult application. It should be noted that this impressive

performance was obtained without taking advantage of two mechanisms which, in principle, might

further reduce the 13.5 mW heat leak by a considerable factor. First, by thermally linking the

evaporating helium vapor to the various conducting members listed above, most of the heat leak

from 20 K could be intercepted before reaching the 2.5 K bath. Second, if optimally loaded

support members in tension were substituted for the massive supports, much of the heat conduction

could be eliminated, although this substitution might be inconvenient to put into practice. It is curious to note that with this system as described (or any similar system), the cryocooler can easily provide all of the refrigeration required at higher temperatures, so that only about 1% of

the total cooling capacity of the liquid helium, namely the heat of vaporization at 2.5 K, is actually essential to the operation of the system. One percent is not as bad as it seems, however, since one must apply the Carnot factor in calculating the work necessary to perform this

refrigeration. Needless to say, any mechanism which leads to reducing the required mass and size

of the cold components (the helium reservoir, for example) has a synergistic effect of reducing

heat leak through reduction or elimination of support structure and surface area. This might be

significant if the helium reservoir were eliminated in favor of a microminiature Joule-Thomson or Stirling stage, perhaps usina helium-3 as the working fluid, to provide continuous cooling at 2.5

K.

There are other examples of small superconducting devices being operated in hybrid cryostats

or in cryocoolers, but few which illustrate so nicely the variety of design problems that may be

encountered. One problem not encountered in this example is that of magnetic interference, which

is of overriding concern in designing cryocoolers for SQU IDs and certain other Josephson devices.

The problem of scaling Joule-Thomson refrigeration systems down to "microminiature" size, as needed for Josephson and similar devices, has been addressed by Little in previous conferences of

this series. His work has resulted in the commercial production of a remarkable series of tiny

J-T cryocoolers whose gas-flow channels are etched into the surface of glass plates which are then

bonded to cover plates, giving milliwatt cooling capacities at 80 K when supplied with nitrogen at

10 or 20 MPa [8]. Multi-stage units capable of maintaining cryogenic temperatures required for

superconducting devices have not yet been demonstrated, but such a development would be extremely

interesting because of the possibility of integrating the superconducting circuits on the same substrate.

A four-stage J-T cryocooler using more conventional materials and techniques, and

specifically intended for a SQUID biomedical gradiometer, is under development by Tward. It is

described in another paper in these proceedings [9]. J-T systems are highly attractive for

low-level magnetic-measurement devices because there are no solid moving parts in the cryogenic

system itself, and so magnetic interference is inherently low or non-existent. Simple Stirling or Gifford-McMahon cryocoolers with gap regenerators, for temperatures in the range of 7 to 9 K, have

been under development for several years in the author's laboratory and elsewhere [10 to 15].

These typically have four or five discrete stages or else a tapered displacer to provide a continuous distribution of refrigeration as anticipated by the discussion above. In either case,

the available refrigeration capacity is very small by the usual standards, but sufficient for the

purpose of cooling microwatt superconducting devices and their associated electrical connections

and support structure, as anticipated by the discussion above. The problem of compressor

contamination is inherently less serious with these machines than with Joule-Thomson machines, but

nevertheless there is a similar need for extremely clean compressors or pressure-wave generators

with the appropriate pressures and compression ratios. Temperatures as low as 4 K have not been

achieved with regenerative machines operating at the same pressure throughout. However, the

possibility of maintaining temperatures below 4 K has been demonstrated using a separate cold-end

stage operating at sub-atmospheric pressure [16]. A J-T stage operating at the same peak pressure

as the regenerative machine with which it is incorporated, so that only one compressor is required, has also been reported [17].

Perhaps the greatest challenge facing the designer of a practical miniature J-T cryocooler is to build a set of almost perfectly clean compressors to provide the necessary high pressures and

high compression ratios for the different stages. Both Tward and Little (private communication),

and others, are currently working on solutions to the problem. Metal bellows or diaphragms are attractive in principle, but not easy in practice, since the slightest plastic deformation of the

metal (at the valve ports, for example) will cause almost immediate failure. Gas-lubricated or magnetically suspended clearance seals between piston and cylinder, and unlubricated sliding seals

of glass or graphite-filled teflon on hardened metal, and "hard-on-hard" clearance seals where

both piston and cylinder are made of hard materials like ceramic or metal carbides and nitrides

have all been demonstrated, in various applications, with varying degrees of success and

reliability. Yet another approach is to demand less in the way of cleanliness of the compressor

and to effectively purify the gases after compression (see paper by Tward in these proceedings).

7
8. Discussion

Several laboratory cryocoolers for microwatt superconducting devices, based more or less on the refrigeration mechanisms and design principles summarized above, have been developed during

the last few years. These have demonstrated significant advances in construction methods, use of

materials, computer analysis, miniaturization, interference reduction, and efficiency. Although a completely satisfactory machine has not yet been produced, it is likely that this goal will be

realized during the next year or two. Work in the immediate future will surely concentrate on the

design of miniature., ultra-clean compressors. One or more of the current experimental cryocoolers

will be used with SQUID magnetometers and gradiometers to determine levels of vibration and

magnetic interference. Further miniaturization of Joule-Thomson systems and new concepts for

integrating these with superconducting microcircuits will certainly inspire active interest.

9. References

[I] Zimmerman, J. E., and Flynn, T. M. , eds . "Appl ications of Closed-Cycle Cryocoolers to Small

Superconducting Devices, NBS Special Publication 508, April 1978.

[2] Rogalla, H., University of Giessen, private communication.

[3] Van Zeghbroeck, B. J., "Superconducting Current Injection Transistor", Appl. Phys. Lett. 42,

April 15, 1983, p. 736.

[4] Frank, D. J., Brady, M. J., and Davidson, A., "A New Superconducting-Base Transister", 1984

Applied Superconductivity Conference, Sept. 9-13, 1984, San Diego, CA.

[5] Goodall, D. H., Cryogenic Data. A. P. T. Division, Culham Laboratory, March 1970.

[6] Sullivan, D. B., Daney, D., Radebaugh, R., and Zimmerman, J. E., "An Approach to Optimization

of Low-Power Stirling Cryocoolers", in Refrigeration for Cryogenic Sensors, Max Gasser,

ed., NASA Conference Publication 2287, December 1983, p. 107. We regret that a page of text was omitted from the published version of this paper. The missing page should follow

page 109 of the proceedings. Also the references were missing. There should be a plus sign

(+) between the two terms of equation 7, not minus (-), and the words "Bottom and top radii

for the displacer and" should be deleted from the captions of figures 4 to 7. A corrected

copy of this paper is available from the authors.

[7] Archer, J. W. , "A High-Performance 2.5 K Cryostat Incorporating a 100-120 GHz Dual

Polarization Receiver", Rev. Sci. Inst. To be published, 1985.

[8] Little, W. , Microminiature Refrigeration, Rev. Sci. Instr. 55, 1984, p. 61.

[9] Tward, E., these proceedings.

[10] Chen Guobang, Zhejiang University, private communication.

[II] Heiden, C. University of Giessen, private communication.

[12] Lambert, N. these proceedings.

[13] Matsubara, Y., and Yasukochi, K. , "An Application of Gap Regenerator/Expander Precooled by

Two Stage G-M Refrigerator", in Refrigeration for Cryogenic Sensors, Max Gasser, ed., NASA

Conference Publication 2287, December 1983, p. 157.

[14] Myrtle, K. , Gygax, S., Plateel, C, and Winter, C, "Regeneration Efficiency, Shuttle Heat

Loss and Thermal Conductivity in Epoxy-composite Annular Gap Regenerators From 4 K to 80

K" , in Refrigeration for Cryogenic Sensors, Max Gasser, ed., NASA Conference Publication

2287, December 1983, p. 131.

[15] Sager, R. E., and Paulson, D. N., "Regeneration Experiments below 10 K in a Regenerative-cycle Cryocooler", in Refrigeration for Cryogenic Sensors, Max Gasser, ed.,

NASA Conference Publication 2287, December 1983, p. 81.

[16] Sullivan, D.B., and Zimmerman, J. E., "Very Low-Power Cryocoolers Using Plastic and

Composite Materials", Int. J. Refrigeration, 1979, p. 211.

[17] Zimmerman, J. E., "Recent Developments in Self-contained Cryocoolers for SQUIDs and Other

Low-power Cryoelectronic Devices", Proc. ICEC10 (Helsinki), Collan, H., Berglund, P., and

Krusius, M., eds. Butterworth, 1984, p. 13.

8
10. Appendix

Following are the results (from the analysis of reference 6) of the optimization of the

refrigeration distribution along a cryogenic member (a wire or support post), of constant cross section A and length a, with one end at ambient temperature T , and the other end at a low

temperature T , whose thermal conductivity can be expressed as a power of the temperature, K = K T . Here z°is the fractional distance measured from the cold end, Q(z) is the heat flow rate,

dQ/dz and dQ/dT are the optimum distributions of refrigeration in z and in T, respectively,

required to achieve the minimum ideal mechanical input power W expended on the working fluid, and

T(z) is the corresponding temperature distribution:

CASE 1: K = constant, (n = 0)

T(z) = T e zln(T

amb/T

o

}

dQ/dz = (KA/a)Tln

2 (Tamb

/T

o

)

dQ/dT = (KA/a)ln(T

amfc) /T0

)

W = (KA/a)T

o ln

2 (Tamb

/T

o

;

CASE 2: K = K T

n

, (n f 0)

n

T(z) . (I/' 2 0z)

2'" where a . T^2

- T^2

dQ/dz = 2a

2 (2 + n)K AT/an2 n

dQ/dT = o(2 + n)K AT

n/2 /an

n

W = 4K

n Aa2Tamb/

an2

9
RECENT CRYOCOOLER PROGRESS IN JAPAN

Yoichi Matsubara

Atomic Energy Research Institute

Ninon University

Tokyo 101, Japan

This paper reviews the recent progress of cryocoolers and its

related devices in Japan. Part of the research and development of

cryogenic technology including small scale cryocoolers is supported by

a number of national projects. The Japanese National Railways has been

developing the light weight 4 K on-board refrigerators since 1977 as part of the MAGLEV train program. An investigation of superconducting

and cryogenic fundamental technology has been conducted by the Science

and Technology Agency since 1982, including high performance cryocooler

(related to Stirling cycle), magnetic refrigerator and superfluid

refrigeration. A study of space cryogenics such as the cooling systems

of IR-detectors was started by the Ministry of International Trade and

Industry in 1984. In addition to these national projects, several

companies also have done their own activities on cryocooler investigation,

for special applications such as cryopump, NMR-CT and JJ devices. Compact

heat exchangers, high performance regenerators and reliable compressors

are also being investigated as a critical component technology.

Keywords: Cryocoolers; heat exchangers; helium; low temperature;

refrigerators; regenerators.

1. Introduction

The research and development scheme of cryocoolers can be classified into two categories.

The first one is related to the investigation of reliability, compactness and cutting costs of the

well known cryocooler systems. Stirling or Gifford-McMahon cryocoolers with a JT loop and small

scale Claude cycle also belong in this category. The second one is a fundamental approach to the

novel refrigeration systems such as a magnetic refrigerator or regenerative cryocoolers which can

be cooled down to liquid helium temperature without a JT loop. As a critical component, compact

heat exchangers, high performance regenerators and reliable compressors are also important. With

this in mind, the recent progress of the relatively small cryocoolers, operated at liquid helium

temperature are reviewed.

2. Claude Cycle Cryocooler

The Claude cycle has been used for rather high capacity helium liquefiers, however, two on- board Claude cycle cryocoolers with a capacity of 30 watts at 4.4 K and 5 watts at 4.5 K have been

fabricated for the MAGLEV project of JNR since 1978 [1, 21. In this particular case, the

following considerations were taken:

(1) The automatic inlet and exhaust valves of the expanders and cylindrical cam for the

piston were employed for the compactness of the crosshead.

(2) A direct coupling system of the high speed flywheel was employed as an energy absorber

of the expander. This energy absorber system makes the expander unit compact and light

weight

.

(3) The laminated metal heat exchangers made of aluminum perforated plates and plastic

separators were employed for the 5 watt systems.

10
In the field of industrial electronics, the need for cryocoolers to cool superconducting

magnets in such systems as magnetic resonance imaging or the control of the single crystal

drawing furnaces has gradually increased. To meet these requirements, the Toshiba Co. developed 4.4 K 5 watt Claude cycle cryocooler, as shown in figure 1. Figure 2 shows the

available energy balance of this system. It is reported that the JT valve loss is limited,

although the losses due to the heat exchangers and expanders could be decreased.

The research activity for developing smaller Claude cyqle cryocoolers has been

continuing, however, there are almost no reports about the long term operation to date, and

it has remained as a problem for the future.

3. G-M Cycle Cryocooler with JT Loop

The G-M cycle or modified Solvay cycle has been developed mainly as a 20 K cryocooler for the

cryopump applications. Recently, several companies have been investigating the relatively high

power G-M cycle cryocooler as a precooler for the JT loop for the recondensor of liquid helium.

Most of the cooling systems for superconducting magnets require simultaneous cooling of the

radiation shield and liquid helium bath. Figure 3 shows the flow diagram of a 4.5 K cryocooler

with 77 K additional cooling loop developed by Hitachi Ltd.. This work has been supported by MITI since 1982. The typical cooling power of the G-M cooler is 18 watts at 20 K and 60 watts at 80 K,

respectively. The expander efficiency is reported as 44% at first stage and 38% at second stage.

The details are shown in figure 4. The layered heat exchangers with perforated aluminum plates

are used for the JT loop. It has a scroll type cross section as shown in figure 5. Figure 6 shows the cooling power at 4.5 K and 77 K where the JT flow rate was maintained at 10 Nm /hr.

Indications shows that this system can be applied to both the large cryostat with low heat load at 4.5 K (such as superconducting NMR-CT) and the small cryostat with high heat load at 4.5 K (such

as J-J devices).

The Mitsubishi Electric Co. investigated the 4.3 K 5 watt system, where a G-M cooler was used

as a precooler developed by Osaka Oxygen Industries in 1981. They reported the effect of the

different ambient temperature on the cooling power of the system. Figure 7 shows that the cooling

capacities of G-M cooler decreased about 30% when the ambient temperature was increased to 40 C and the inlet helium gas temperature was increased to 50 C, (line B in figure 7), compared to the

capacities operating at 20 C (line A). Figure 8 shows the cooling capacities for the 4.3 K J-T

stage. It should be noted that the degradation of cooling capacities, 5.8 to 4.9 watts, is only

about 16%. They also studied the effect of the ambient magnetic field on the valve motor up to 1 kGauss

.

Sumitomo Heavy Industries Ltd. investigated 4.3 K 3 watts (max. 3.65 watts) cryocooler. The

typical cooling capacity of their G-M cooler is 8 watts at 20 K and 20 watts at 77 K. One of

their interests is related to the development of a reliable compressor. Three rotary compressors

were used at the operating pressure of 1-20 atm for the JT loop (9 Nm /hr.) and 7-20 atm for the

G-M cycle as shown in figure 9. The total input power is about 7 kW. The amount of lubrication

oil for each compressor is successfully controlled by the overflow at a constant level which feeds

it back to the intake port of the lower pressure stage. The dew point of the working helium gas

is initially controlled below -70°C, although the pressure drop within the first heat exchanger

increased 0.6 -0.84 Kg/cm during 1660 hr. operations.

4. Fundamental Approach to the Novel Refrigeration Systems

Most of the cryocoolers being commercially used at liquid helium temperature have a JT loop

as a final stage of the cooling system. However, a couple of attractive methods are now being

investigated. An investigation of superconducting and cryogenic technology was conducted by the

Science and Technology Agency in 1982. In this program, studies of high performance cryocoolers

(related to Stirling cycle) and magnetic refrigerators were included.

4.1 Stirling Cycle

In the development of the Stirling cycle, there are some similarities between the prime mover

and cryocooler. Figure 10 is presented by Ishizaki (ECTI). As a prime mover, he developed the

miscellaneous Stirling engines of output power below 50 kW ((a) of figure 10), the cold energy

application system of LNG (b), and a hybrid system using L0X and liquid hydrogen (c) [3, 4], As for the cryocooler, the most popular two stage cycle (d) were used for several applications where

the cooling temperature was above 10 K. He also investigated a cryocooler operating at the liquid

phase of helium (e).

11
According to the program of the Science and Technology Agency, the R & D of high performance

Stirling cryocooler is now in progress at JNR, in cooperation with the Aisin Seiki Co. and ECTI. Figure 11 shows the single stage Stirling cycle operating below 15 K. The hot end temperature of

the regenerator was maintained at a constant, using the evaporating gas from the liquid helium.

The relation between the hot and cold end temperature is shown in figure 12. These figures

indicate that the rare earth compounds (Gd-Er-Rh) when used as regenerator material improve the

regenerator efficiency when it works below 15 K. The lowest temperature achieved in this

experiment on the rare earth compounds was 3.74 K at the lower limit of temperature oscillation,

when the mean operating pressure was about 0.7 atm and the hot end temperature was' about 8K. They

also confirmed that the cooling system can obtain near 4 K by using the two stage Stirling cycle

when the hot end temperature maintained near 30 K.

4.2 Magnetic Refrigerator

The study of the magnetic refrigerator according to the Science and Technology Agency program

is divided into three groups, a fundamental study of working materials (Institute of Metallic

Material), a fundamental study of the refrigeration cycle (Tokyo Institute of Technology) and

magnetic refrigeration systems (Toshiba Co.).

Figure 13 shows a schematic of the reciprocating magnetic refrigerator developed by the

Toshiba Co. through this program. It consists of two sets of superconducting DC magnets and

pistons with working materials (GGG). A two stage G-M cycle cryocooler (Air Products and

Chemicals), USA) was used for the precooler of the working materials. The distance between the

maximum and zero magnetic field is about 100 mm, which corresponds to the piston displacement, and

is realized using field correcting magnets. All of the magnets are connected in series and

operated at a permanent current mode after the initial excitation using detachable current leads.

The experimental results of the test run are shown in figure 14 at the excitation current of 80 A and the maximum field of the working material of 4 Tesla. It indicates the increasing liquid

helium level within the refrigeration space at each heat absorption process.

Hitachi Ltd. is also investigating a magnetic refrigerator which is operating between 20 K and 4 K, using a G-M cycle precooler and rotary moving method. Details may be obtained at the end

of this year.

4.3 Component Technology

A study of regenerators below 20 K is now in progress at Nihon University and is supported by

the program of the Science and Technology Agency. Thermal properties of regenerative materials

which have a high specific heat below 20 K such as GdRh have been measured. To evaluate the

effectiveness of the regenerator, a simple Vuilleumier cycle cryocooler was used. The minimum

temperature of 5.4 - 6.5 K was obtained with this VM cooler. The details of these results will be

given later in this proceedings.

Most of the compact heat exchangers, which can be used for a small Claude cycle cryocooler or JT loop precooled by a regenerative cryocooler, have been made by the perforated aluminum plates

and plastic separators, however, Hitachi Ltd. recently developed a new heat exchanger made by a diffusion bonding method using perforated cooper plate and SUS304 separators, which has a similar

cross section shown in figure 5. They reported that the axial conduction loss of this heat

exchanger is greater th an that of epoxy bonding type, although the total heat transfer

effectiveness is not decreased significantly when it is used at high Re number.

Showa Seiki Industries, in cooperation with Tohoku University and ECTI, developed a small oil

free compressor, constructed by three stage reciprocal pistons and swash plate mechanism with a diaphragm for separating oil. Input power is 750 watts and the helium gas pressure at the inlet

and outlet are 0.1 and 2.0 MPa with the flow rate of 2 Nm /hr. This compressor can be applied to the JT loop of the small cryocooler system for SQUID or other JJ devices.

5. Summary

Most of the cryocooler activities in Japan, at this time, seems to be aimed at the

development of a compact and reliable cryocooler having several watts at liquid helium

temperature. It will depend on the progress of the small superconducting magnet applications such

as super LSI pattern printing devices, the single crystal drawing controller and the

superconducting NMR-CT. Due to the improvement of the superconducting materials, the allowable

cooling temperature is nearly 10 K, however, in considering the cooling temperature stability, the

latent heat of the liquid helium is still attractive.

12
Miniature cryocoolers for the IR-detector , SQUID or other JJ devices are not being

investigated in Japan, except for some fundamental research. However, a conceptual study of the sensor technology for unexplored spectrum has been started by the Ministry of International Trade

and Industry this year, which includes the study of IR-detector cooling system for space

application. Research will be conducted next year at the Electrotechnical Laboratory.

I wish to acknowledge to Y. Ishizaki, T. Koisumi, T. Horigami, N. Matsuda, A. Obara, K. Sawada and H. Wada for their useful information.

6. References

[1] Ohtsuka, T. and Iguchi, M., Proceedings of the Second International Seminar on Superconductive Magnetic Levitated Train, (Nov. 1982).

[2] Fujita, T. et al. Japanese Activities in Refrigeration Technology (Refrigeration for Cryogenic

Sensors, NASA CP-2287, 33-46, (Dec. 1982).

[3] Ishizaki, Y., Stirling Engine Technology in Japan, ( Intersociety Energy Conversion

Engineering Conference), Boston (1979).

[4] Oshima, K. et al, The Utilization of LH

2 and LNG Cold for Generation of Electric Power by a Cryogenic-type Stirling Engine, ICEC 7, 310-317, London (1978).

13
16atm

313 K

Comp.(20Nm*hr)

— latrn

H.Ex.

No.1

120K

No. 2

No.3

22.5K

No.

5

Exp.

^Engine

No.1

82.4 K

No. 2

13.5 K

KXh-^/VWV\H

J-T Valve

fl 5w

Fig. 1 Flow diagram of 4.5 K 5 watt

Claude cycle Fig. 2 Energy balance of the Claude cycle

4.2 atm

First

Compressor

1j05 atm

308 K@

A \7 Secor

ZA V Compi

Nal Heat Exchanger

54.1 K©

Na2 Heat Exchanger

14.5K®

No.3 Heat Exchanger

1.2 atm, 4.5K

mj

Second

Compressor

16 atm ©313K

IDE

Qs

(D64.1K ©

©58DK

2

©20.8K

(6)15.1 K

Expander

K/////// 77///// 77777771

15 atm D6^© I® ©"

Qs

•LN5 Shield

Fig. 3 4.5 K 6.5 watt cryocooler with JT loop

precooled by G-M cycle

V777* Pressure drop loss

E?77<i p-V diagram loss

i i Heat conductance loss

Shuttle heat transfer loss

Net Refrigeration Capacity

H

O

ft <-N 5 s

% £ 55 H

O

C ft

ti d W °

W r—i O rf i—I <D

> "O H n

© o K !->

100

80

60-

40-

20

1st Stage 2nd Stage

Fig. 4 Expander loss analysis

of G-M cycle

14
Spacer

Low pressure He

High pressure He

Heat transfer plate

Fig. 5 Cross section of scroll type

heat exchanger

6 -

-r 2

o

JT flow = 10 Nm 3 /hr

0 20 40 60

Cooling Power at 77 K (W)

Fia.6 Cooling power dependency

of 4.5 K and 77 K

_ A (21° C)

*

*

*> * B (50°C:)

2 nd Stage Temp ( K I

| st stage Temp ( « |

Fig. 7 Ambient temperature effect of the G-M cooler performance

45 50 55 60 65 70 75 80

7

6

5

4

3

2

20°C

< i^40°C

10 13 14

Flow Rate (Nm 3 /nr)

Fig. 8 Performance of 4.5 K cooler with JT loop precooled by G-M cycle

15
16
1000

Y. Ishizaki

ENTROPY

Fig. 10 Schematic T-S diagrams of the Stirling cycle machines

17
Fig. 11 Single stage Stirling cycle

operating below 15 K

[

/

3 1 1 1 1 5 10 T

n !5 ( K ) 20

Temperature at the hot end

of the regenerator

Fig. 12 Test result of the Stirling cycle

18
Fig. 13 Schematic of the reciprocating magnetic refrigerator
MAGNETIC REFRIGERATION FOR LOW-TEMPERATURE APPLICATIONS

J. A. Barclay

Gp. P-10, MS-K764

Los Alamos National Laboratory

Los Alamos, New Mexico 87545

An increasing number of applications require refrigeration at low

temperatures ranging from production of liquid helium for medical imaging

systems to cooling of infrared sensors on surveillance satellites. Cooling

below about 15 K with regenerative refrigerators is difficult because of the

decreasing thermal mass of the regenerator compared to that of the working

material. In order to overcome this difficulty with helium gas as the working

material, a heat exchanger plus a Joule-Thomson or other expander is used.

Regenerative magnetic refrigerators with magnetic solids as the working

material have the same regenerator problem as gas refrigerators. This problem

provides motivation for the development of non-regenerative magnetic

refrigerators that span ~4 K to -20 K. Several laboratories around the

world have magnetic-refrigeration programs underway; some are working on

4 - 20 K refrigerators. In the development efforts, particular emphasis has

been placed on high reliability and high efficiency. Detailed calculations

indicate considerable promise in this area, but several key problems have been

identified in each of several possible devices. The principles, the potential,

the problems, and the progress towards development of successful 4 - 20 K magnetic refrigerators are discussed.

Key words: Carnot cycle; low temperature; magnetic; non-regenerative;

refrigerator; review.

I. INTRODUCTION

Magnetic resonance tomography and magnetic-field-gradient ore separation are two examples of

developing commercial applications of superconducting magnets . [1 ,2] Many other potential users

for superconducting magnet systems exist. [3] All of the superconducting magnet systems will

require liquid helium or closed-cycle refrigeration near 4 K. Long wavelength infrared (LWIR) sensors need to be cooled to 8 - 10 K to obtain an adequate signal-to-noise ratio for high

sensititivity. [4] Small helium liquefiers and some LWIR systems require approximately 1 W of

cooling power. At this size, the efficiency of conventional refrigeration systems is typically a few percent of Carnot efficiency for heat rejection near room temprature. [5] Mean periods between

failures or major maintenance are several thousand hours.

Regenerative gas refrigerators typically cease operation near 15 K because of decreasing

thermal mass of the regenerator material. Hence both regenerative and recuperative gas

refrigerators have a recuperative low-temperature stage plus an expander, such as a Joule-Thomson

(J-T) device. [6] The efficiency of the bottom heat exchanger and J-T expander operating from

15 - 20 K down to -4 K is 50-60% of Carnot if carefully designed. [7] The J-T loop suffers from

poor reliability and requires a high-pressure compressor for operation.

If a simple, non-regenerative, non-recuperative 20 - 4 K refrigerator with high reliability

and high efficiency (greater than 60% of Carnot) could be developed, it would offer significant

improvements to existing refrigerator systems by eliminating the J-T loop and its associated

problems. Refrigerators based on the magnetocaloric effect that execute a magnetic Carnot cycle

between -15 - 20 K and -4 K can potentially satisfy these requirements. This conceptual

20
review paper will try to illustrate the development of magnetic refrigerators for the 20 - 4 K temperature region. The reference list is not complete but is representative.

II. PRINCIPLES

A. Materials

All refrigeration processes require an entropy change to absorb heat from a cold thermal source and deliver it to a higher temperature sink. Therefore, the entropy-temperature (S-T)

diagrams for the working magnetic materials are essential to understanding the operation of

magnetic refrigerators. In the 4 - 20 K region several types of magnetic materials can be used;

the most obvious ones are paramagnets. There are many criteria for selection of suitable

refrigerants including low lattice specific heat and a large magnetic moment. A survey of

existing and potential paramagnetic materials has been published. [8] This and other work

[9,10,11,12] have shown that gadoliunium gallium garnet (GGG) is an excellent initial choice for

4- 20 K magnetic refrigerator design. Figure 1 shows the S-T curves for GGG as a function of

aplied magnetic field.

T(K)

Figure 1: The entropy of gadolinium gallium garnet as a function of temperature and magnetic

field.

It is also possible to consider composites of paramagnets such as DyVO/j-GGG as suggested

by the Grenoble group. [13] Physical mixing of materials allows some freedom in shaping the

entropy-temperature diagrams which, in turn, allows cycles other than the Carnot cycle to be

considered. Figure 2, taken from reference 13, shows the S-T curves for a 50-50% composition of

the materials. As will be explained in the next section, this composite would be unsuitable for a magnetic Carnot cycle but is well suited to a magnetic Ericsson cycle, as was suggested in

reference 13. The entropy change at 20 K in the composite is comparable to that in GGG alone, but

the parallel nature of the S-T curves is essential for effective regeneration if a good

regenerator material is used.

Finally, ferromagnetic materials can also be considered as working materials in this

temperature range. An example is EuS whose calculated S-T curves [14] are shown in Fig. 3. Other

ferromagnets such as GdRh [15] could be used although rhodium is extremely expensive. GdRh has a Curie temperature near 20 K but lower Curie temperature materials are available. For example, the

ErRh-GdRh series has Curie temperatures ranging from ~6 K to -20 K. [16]

B. Cycles

The only non-regenerative, non-recuperative cycle that exists for use in the 4-20 K range is

the magnetic Carnot cycle. This consists of two isothermal stages and two adiabatic stages while

magnetizing or or demagnetizing. Characteristics of this cycle are that the magnetic field is

21
continously changing and excellent heat transfer is required during the isothermal parts of the

cycle. Because the lattice entropy of many paramagnets becomes comparable to the field-induced

entropy change near 20 K, the upper operational limit of the Carnot cycle is near 20 K, depending

upon the magnetic field strength and the magnitude of the lattice entropy.

24

22

20

ie

16

14

T(K) 12

10

8

6

4

2

0 I I I I l I i 1 0 4 8 12 16 20 24 28 32

S(J/moleK)

Figure 2: The entropy of 50% gadolinium gallium garnet and 50% Dyprosium Vanadate as a function

of temperature and magnetic field.

Other cycles besides the Carnot cycle have possibilities if regeneration or recuperation can

be effectively added. The magnetic Stirling cycle (two isomagnetization stages and two

isothermals) ; magnetic Ericsson cycle (two isofield stages and two isothermals) and the magnetic

Brayton cycle (two isofield stages and two isentropes are all possible in the 4-20 K range. These

cycles are illustrated in Fig. 4 using the entropy temperature diagram of a paramagnetic

material. Each cycle has different field-temperature changes required at different parts of the

cycle. These requirements will be reflected in the designs of actual refrigerators. The magnetic

Stirling cycle using a paramagnet such as GGG is probably a good choice because the amount of

regeneration is minimal, as is shown in Fig. 4.

B^OT

50% Gd,Ga,0„

50% Dy V04 (EXPERIMENTAL)

TAKEN FROM B DAUDIN et al CRYOG 22, 439 (1982)

22
Figure 3: The calculated entropy of europium sulfide as a function of temperature and

magnetic field.

Figure 4 also shows that the Brayton and Ericsson cycles are not feasible with a single

paramagnetic material because the regenerative heat flows will be completely unbalanced.

Composites or ferromagnets will be required for successful implementation of these cycles.

The entropy changes in the various cycles can be obtained from

«-«"(»•

Knowledge of Cg and M as a function of B and T allows calculation of the heat and work flows

during the idealized cycles. Real cycles, of course, are polytropic and require detailed

knowledge of many additional sources of irreversible entropy and heat capacities of thermal

addenda in order to be correctly modelled.

III. Potential

A. Designs

A series of ~2 - 4 K magnetic refrigerators have already been built and tested with varying

degrees of success. [17, 18, 19, 10] The Grenoble group has reported efficiencies as high as 79% of

23
Carnot [17] for a 2 - 4 K reciprocating design using GGG. In the 4 - 20 K range there is a large

variety of magnetic refrigerator design possibilities. Table I presents an attempt at classification of the possibilities and includes location of groups working on devices of the

various types.

S S

s s

Figure 4: The magnetic cycles illustrated on the entropy-temperature diagram of a paramagnetic

material

.

Table I. Possible 4 - 20 K Magnetic Refrigerator Designs

Non-Regenerative

Non-Recuperative Regenerative Recuperative Hybrid

Rotational *LANL, **HAC Grenoble

Reciprocating ***J.P.L., Tokyo LANL (LANL)

Other ****Tokyo HIT (MIT)

*LANL - Los Alamos

**HAC - Hughes Aircraft Co. ***J.P.L. - Jet Propulsion Laboratory

****Tokyo - Japanese groups at Tokyo Institute of Technology, Hatachi-Research Laboratories, and

other interacting laboratories.

24
The majority of devices underdevelopment appear to be non-regenerative, non-recuperative. Both

rotating and reciprocating designs have been chosen. The details on most of these devices are not fully known because the various groups have not yet published reports. There are pros and cons to each design. Some of these design choices will become apparent in the discussion of the problems

in the next major section.

B. Second-law analysis ^! 1

The efficiency of a refrigerator executing a thermodynamic cycle between hot and cold

temperature, Th and Jq, respectively, can be written as

where Qq is the reversible cooling power and W^0 tal i s net work flow into the refrigerator.

This total work rate includes the pump power, magnet supply power, etc., in addition to the work

rate from the refrigerator itself. The refrigerator work rate can be calculated from the Second

Law according to

/dT ~Ji~T /dT

where w^ is the power added externally that the refrigerator must remove, e.g., friction, qj

is the power introduced through heat conduction from the surroundings; and a'Sjrr is the rate

of irreversible entropy production from different mechanisms. Once a specific design is chosen, a detailed analysis of the device can be done and a projected efficiency obtained. For example, in

a Carnot-cycle rotational device designed at Los Alamos, the work rates from each mechanism were

calculated and are presented in Table II.

Assuming good heat exchangers, pump efficiencies of 50%, and drive motor efficiency of

90%, the overall projected efficiency for the wheel device was 65% when rotating at 0.2 Hz through

a 6-T field to pump 0.67 W from 4.3 K to 15 K. This is an excellent efficiency but only slightly

greater than a very well designed J-T loop. However, the low rotational frequency suggests it may

have a long lifetime and good reliability.

Table II. WORK RATES FROM VARIOUS MECHANISMS FOR A CARNOT-CYCLE

WHEEL REFRIGERATOR

Item W (watts)

W reversible 1 .64

«h

conduction 0.046

"h

heat transfer 0.012

W

H pressure drop 0.011

.c conduction 0.016

c heat transfer 0.012

W

c pressure drop 0.0001

W 4-15 K conduction 0.18 w friction 0.10 w parasitic heat leak 0.10

%

heat exchanger 0.060

W

c heat exchanger 0.060

25
IV. Problems

A. Isothermal Stages

The importance of the need for "isothermal" stages in efficient low-temperature cycles was realized by Jacob [22] some years ago for a Brayton cycle. The isothermal stages are essential

for all efficient low temperature cycles for the following reasons. In order to^ transfer heat to and from magnetic material to a single-phase heat-transfer gas, a temperature difference between

the cold magnetic material and the gas (ATC

) and hot magnetic material and gas (AT^) must

exist. The direct effect of ATC and AT^ on efficiency can be calculated from Eqs (2) and

(3) by integrating from Tc - ATC to T c at the cold stage and T^ to T + AT^ at the

hot stage. The total expression is complex, but for only the reversible cooling power component

to the efficiency, we obtain

n =

For example, between 4 and 20 K, if ATC ~ 0.3 K and AT^ ~ 1 K, the efficiency drops

from 100% (reversible) to 92.5% from this effect alone. This clearly indicates that magnetic

Brayton cycles in the 4-20 K range will be less efficient than the other cycles.

While this effect is probably obvious, it is important to remember for operation at very low

temperatures

.

B. Addenda

The major effect of additional thermal mass from various sources is to reduce the cooling

power of a magnetic refrigerator. This is particularly important in non-regenerative designs

using the magnetic Carnot cycle because many of the addenda items have temperature-dependent

thermal masses that tend to contribute more entropy near 20 K than near 4 K. There are several

ways to account for the effects of addenda on the refrigerator, but the total entropy approach is one of the more useful ways. In this approach, the entropy of each item in the refrigerator and

that of the magnetic materials are totaled. The change in total entropy caused by the magnetic

field is easily obtained.

Some of the addenda items common to many 4 -20 K designs are containers, forms, supports, etc. which must be present to support or contain the paramagnetic material. Because excellent heat

transfer between the working material and heat-transfer gas is required, a porous

magnetic-material of some geometry along with convected helium gas are used. The porosity of the

material can lead to entrained helium gas, which causes an internal thermal load and gas movement

during the cycle. The housing around the moving working material doesn't contribute to the

addenda once thermal equilibrium is attained, but thermal conduction from hot to cold sections

adds a thermal load equivalent to thermal addenda. Figure 5 shows the relative magnitudes of the

entropy of the addenda for a particular design. These effects are a severe problem in non-regenerative designs.

26
24

22

20

18

16

14

T(K) 12

0

8

6

4

2

0

0 4 8 12 16 20 24 28 32

S'(J/K)

Figure 5: The total entropy of a particular design that shows the effects of various contributions

of thermal addenda.

C. Flow Control

and

In any 4 -20 K refrigerator that uses convective heat transfer between helium gas-the magnetic

solid, there will be a flow-control problem. The problem is caused in part by the temperature

differences in the refrigerator and in part by the motion of the working material. In a rotating

design, either crossflow or counterflow gas motion in sections of the wheel is possible and heat

transfer occurs continously. The hot and cold section must be separated by some sealing

mechanism, such as clearance or labyrinth seals. Rubbing seals of various designs are possible,

but careful attention must be paid to clogging due to small particles from abrasion. Because of

the close tolerances in highly effective porous beds, performance could degrade rapidly with

clogging. Friction must also be kept to a minimum, especially when it occurs at the cold part of

the refrigerator.

Reciprocating designs need flow during the motion of the piston of working material in order

to achieve an isothermal stage in a cycle. Clever designs are needed to establish flow through

the piston in some fashion and at the same time have isolated hot and cold sections in the

refrigerator cylinder.

Pumps are essential to flow control. The pumping power must be fairly small compared to the

cooling power in order to attain high efficiency. Efficient, reliable, long-lifetime pumps

27
operating at low temperatures are a real problem area. The small pressure differences and modest

volume flow rates are different requirements from most previous low-temperature pump work [23]

D. External Heat Exchangers

High performance heat exchangers are very important for high efficiency because the

temperature differences allowed on each end of the refrigerator must be relatively small according

to Eq. 4. The heat exchanger heat-transfer irreversibility for single-coil heat exchangers in a pot of boiling or condensing cryogen, such as liquid hydrogen or helium, can be shown to be given

by [24]

where Sirr is the entropy generation rate, Cp is the fluid thermal mass flow rate, J] n is

the gas inlet temperature, T0is the cryogen bath temperature, and N^ u is the number of heat

transfer units characterizing the heat exchanger. For N^ u greater than about 10, Eq. (5)

reduces to

S IRR £ mC n f 1 » (6)

where AT is defined by T^ n = T0 + AT. Equation (6) clearly shows that a small AT is

important for efficient heat exchangers if the N^ u is reasonably high. Exchangers with

Nj-u > 10 are readily achieveable. [25]

E. Magnetic Field

1 . Forces

The forces between the magnetic material and the magnet can be substantial if high fields and

large volumes of material are combined. For example, in a simple axial case where dB/dz might be

70 T/m, 100 cm^ of saturated GGG in a cylindrical piston will experience a force of -5400 N (1200 1 bsf) .Clearly, forces of this magnitude must be carefully considered in any design.

Reciprocating devices have the possibility of partially cancelling the forces by using two

opposing pistons, but these designs must have supports for the large compressive stress between

magnetic pistons. Rotating devices have natural cancellation of forces but have a large load on the drive shaft bearing because the entire wheel is attracted into the magnet.

2. Profile

Reciprocating devices use solenoidal magnets which are rather straight forward but do require

some field shaping depending upon the desired cycle. Non-regenerative Carnot cycles require

approximately linear field profiles which are readily approximated. Rotating devices allow

several possible ways for production of the magnetic field such, as Helmholtz pairs, racetrack

coils, and solenoids or bent solenoids. The first two allow axial drive while the latter requires

rim drive. The difficulty in all these cases in that the ratio of field at the magnetic material

to the field in the magnet windings is large, i.e., 1: 1.2-1,4. This restricts the maxiumum

field easily obtainable at the magnetic material when the colls are wound with NbTi

superconducting wire. [26] If Nb3Sn is used to wind the magnets, higher fields are possible but

only at higher costs.

28
V. PROGRESS

There are several magnetic-refrigeration development projects around the world. The comments here

are restricted to those with immediate interests in ~4 to -20 K prototypes.

A. Hughes Aircraft Corporation

As indicated in Table I, HAC has started a magnetic refrigerator development program on low-temperature devices for applications as spacecraft coolers. [27]

B. Jet Propulsion Laboratory

The deep-space communications network uses a series of antennaes with cooled maser

amplifiers. The present Gif f ord-McMahon plus J-T loop coolers have worked for many years, but

there is a desire to see if the J-T loop could be replaced by a magnetic stage that would increase

efficiency and improve reliability. A report on this project is included in another session of

this conference. [28]

C. Massachusetts Institute of Technology

This is a fairly new program working on a magnetic regenerative concept and on hybrid

gas-magnetic devices. [29]

D. Grenoble Group

Following the outstanding success of their 2-4 K reciprocating magnetic refrigerator, the

French group have started work on a 4-20 K rotational magnetic refrigerator. [30]

E. Tokyo Group

The Japanese group represents several industrial research laboratories in collaboration with

Professor Hashimoto's group in the Department of Applied Physics at Tokoyo Insititute of

Technology. Their general interest is in low-temperature refrigerators for cryogen liquefaction.

They have reported several results on their use of GGG to liquefy helium [31] with a charge/discharge magnet cycle. We understand that they are now modifying their apparatus to operate in a reciprocating mode between ~4 and 20 K.

F. Los Alamos National Laboratory

The 4-20 K rotational refrigerator under development at Los Alamos is part of a broad magnetic

refrigeration program. The objectives include basic research to provide a data base for design

and prototype development to prove the potential of this technology by constructing and testing

working devices. The 4-20 K device is described below in more detail.

1. Description. The rotational concept has several desirable features, such as balanced

magnetic forces and continuous refrigeration. The Carnot cycle is also the easiest of the cycles

to execute, although the entrained fluid problem must be carefully handled. A magnetic wheel

designed to execute a Carnot cycle is shown in Fig. 6. The GGG used in this design is contained

in small rectangular compartments on the rim of the wheel. The GGG is in the form of

approximately spherical chunks. The wheel is made from stainless steel, and stainless steel screen is used to enclose the inside and outside of each compartment.

The wheel rotates inside a stationary housing that has two duct regions such that helium gas

can pass radially through the GGG. The ducts are located at positions where the GGG reaches 20 K as it is magnetized and where the GGG reaches > 4.2 K as it is demagnetized. The external heat

exchangers are connected to the ducts and form part of a hermetic system around the wheel that

contains the helium gas. Two pumps circulate the helium gas through the wheel and external heat

exchangers. The wheel can be driven inside the housing by a magnetic coupling to avoid any cold

seals to a rotating shaft. The fabrication tolerances on the wheel and the housing need to be

very close, so that clearance seals are formed between the moving wheel and the fixed housing.

Because the entire housing contains helium gas, there should be very little movement of helium

past these clearance seals.

29
PUMP EXCHANGER

Figure 6: A schematic diagram of a Carnot-cycle, wheel-type magnetic refrigerator for operation

between 4.5 and 20 K.

The magnet consists of a pair of solenoids wound on iron cores and supported by an iron yoke

for flux return. The resultant c-shaped magnet is designed for a maximum field of ~ 6T in the

gap of 2 cm. The leads can be removable so that after the magnet is charged and put in persistent

mode, the power supply can be turned down and the leads removed. The magnet is kept at ~ 4.2 K by liquid helium in the dewar surrounding the magnet. Because the whole magnetic refrigerator

operates in a vacuum chamber, the liquid helium dewar need only be single-walled and have no superinsulation directly on it.

2. Results

The magnet works well in persistent-mode and produces 6T in the gap where wheel is located.

The flow of helium through the wheel is about as expected with respect to the pressure drops, but

there is significantly more leakage from duct to duct than expected. There is substantial loading

on the central shaft bushing and early versions of the wheel jammed when the field was increased

from zero. As an example of the performance. Fig. 7 shows an early curve of the cooling power as

a function of temperature span.

30
Qc (mW)

90

80 Q

Q^* = 005Hz

70 "

60 *

50 ^_^v = 0.10 Hz

40

GGG Wheel 30 B=4T

TMIN

= 5K

20

^MIN

"

10

0 11 I 1

i i i ' i i i i i 01 23456789 10 II 12 AVE. TEMP SPAN (K)

Figure 7: The cooling power as a function of average temperature span for the Carnot-cycle

rotational refrigerator.

So far the results indicate that gas movement is the dominant problem, as might have been

expected. The efficiency of the overall refrigerator, including drive motor, gear reducers,

friction, etc., is low, typically 1% of Carnot but the efficiency of the refrigerator excluding

these contributions is ~20% of Carnot. Obviously much more work needs to be done to achieve the

design goals but these early results are very encouraging, and we expect they are the beginning of

a series of successful devices from the several existing programs.

Acknowlegements

This work was performed under the auspices of the U.S. Department of Energy. Funding support

from DOE (BES), DARPA, and NASA (KSC) are gratefully acknowledged.

References

1. Manatt, S. L., Some Potential Application of Nuclear Magnetic Resonance, NASA Jet Propulsion

Laboratory, Report D-902, June 1983.

2. Selvaggi, J., 5 Tesla, Iron Clad, Fast Field, Superconducting HGMS, paper to be presented at ASME winter meeting, Dec. 10-14, 1984, New Orleans, LA

3. See, for example, the proceedings of any applied Superconductivity Conference or Cryogenic

Engineering Conference, such as Adv. in Cryog. Eng. 29_, 29-255 (1984).

4. Haskin, W. L., Cryogenics in Space Systems; Presented at the meeting of the IRIS Speciality

Group on Infrared Detectors, Boulder, CO., Aug. 2-4, 1983.

5. Strobridge, T. R., Cryogenic Refrigerators - an Updated Survey, NBS-TN-655 (1974).

6. Barron, R. F., Liquefaction cycles for Cryogens, Adv. in Cryog. Eng. V7, 20 (1972).

7. Dean, J. W. and Mann, D. B., The Joule-Thomson Process in Cryogenic Refrigeration Systems,

NBS-TN-227 (1965).

8. Barclay, J. A. and Steyert, W. A., Materials for Magnetic Refrigeration Between 2 K and 20 K,

Cryogenics 22, 73 (1082).

9. Daudin, B., Lagnier, R. and Salce, B., Thermodynamic Properties of the Gadolinium Gallium

Garnet, Gd3Gas0i2 Between 0.5 and 25 K, J. Mag, and Mag. Mat. 27., 315(1982).

10. Numazawa, T., Watanabe, Y., Hashimoto, T., Sato, A., Nakagome, H. , Horigami, 0., Takayama,

S. and Watanabe, M., The Magnetic Refrigeration Characteristics of Several Magnetic

Refrigerants below 20 K, II:Thermal Properties, Proc. Int'l Cryog. Eng. Conf., Kobe, Japan,

May, 1982.

11. Hakuraku, Y. , Kapitza conductance of the gadolinium gallium garnet, Gd3GasOi2 between

1.4 K and 2.1 K.

31
12. Hornung, E. W., Fisher, R. A., Brodale, G. E., and Giauque, W. F. Magnetothermodynamics of

Gadolinium Gallium Garnet. II. Heat Capacity, Entropy, Magnetic Moment from 0.5 to 4.2 K,

with Fields of 90 kG, Along the [111] axis, J. Phys. Chem. 61_, 282(1974). See also J. Chem

Phys. 59, 4652 (1973).

13. Daudin, B., Lacaze, A. A., and Salce, B., DyV04-Gd3Ga50]2: A Composite material

to Achieve Magnetic Refrigeration Using a Cycle with Internal Heat Transfer, Cryogenics 22,

439 (1982).

14. Hashimoto, T., Numazawa, T., Shino, M. , and Okada, T., Magnetic Refrigeration in the

Temperature Range from 10 K to Room Temperature: the Ferromagnetic Refrigerants, Cryog. 2]_, 647 (1981).

15. Azhar, A. A., Mitescu, C. D., Johanson, W. R. , Zimm, C. B., and Barclay, J. A., Specific

Heat of GdRh, paper accepted to be presented at the 30th Annual Conf. on Magnetism and

Magnetic Materials, San Diego, Nov. 1984.

16. Buschow, K. H. J., Olyhock, J. F., and Miedema, A. R., Extremely Large Heat Capacities

between 4 and 10 K, Cryogenics 15, 261(1975).

17. Lacaze, A. F., Beranger, R., Bon Mardion, G, Claudet, G., and Lacaze, A. A. Double Acting

Reciprcating Magnetic Refrigerator: Recent Improvements, Adv. Cryog. Eng. 29, 573 (1984).

18. Hashimoto, T., Numazawa, T., and Maro, T., The Carnot type Magnetic Refrigeration below

4.2 K: Computer Simulation, Adv. Cryog. Eng. 29, 589 (1984).

19. Pratt, W. P., Jr., Rosenblum, S. S., Steyert, W. A., and Barclay, J. A., A Continuous

Demagnetization Refrigerator Operating near 2 K and a Study of Magnetic Refrigerants, Cryo.

17, 689 (1977).

20. Barclay, J. A., Moze, 0., and Paterson, I.., A Reciprocating Magnetic Refrigerator from 2-4K

Operation: Initial Results, J. Appl . Phys. 50, 5870 (1979).

21. Tolman, R. C, and Fine, P. C, On the Irreversible Production of Entropy, Rev. Mod. Phys.

20, 51 (1948).

22. Jacobs, R. B., The Efficiency of an Ideal Refrigerator, Adv. in Cryog. Eng. 7, 567 (1962).

23. McConnell, P. M., Liquid Helium Pumps, NBSIR 73-316 (AFAPL-TR-73-72) June, 1973.

24. Bejan, A., Second Law Analysis in Heat Transfer and Thermal Design, in Adv. in Heat

Transfer, 15, 1 (1982)

25. Kadi, F. J., and Longsworth, R. C, An Assessment and Study of Existing Concepts and Methods

of Cryogenic Refrigeration for Superconducting Transmission Cables, Air Pdts. and Chem.

Inc. Report COO-0255206.

26. See, for example, the critical current vs field curves from I.G.C. 1875 Thomston Ave.,

Waterbury, CT. 06704.

27. Private Communication - 0. Weinstein, Hughes Aircraft Corporation

28. Private Communication - D. Johnson, Jet Propulsion Laboratory

29. Private Communication - J. L. Smith Jr., M.I.T.

30. Private Communication - A. Lacaze, Grenoble

31. Nakagome, H., Tanji, N., Horigami, 0., Ogivara, H., Numazawa, T., Watanabe, Y., and

Hashimoto, T., The Helium Refrigerator I.: Development and Experimental Results, Adv. Cryog.

Eng. 29, 581 (1984).

32
RECIPROCATING MAGNETIC REFRIGERATOR

Dean L. Johnson

Jet Propulsion Laboratory,

California Institute of Technology,

Pasadena, CA, USA

The Jet Propulsion Laboratory is developing a 4-15 K magnetic

refrigerator to test as an alternative to the Joule-Thomson circuit as the low

temperature stage of a 4-300 K closed-cycle refrigerator. The reciprocating

magnetic refrigerator consists of two matrices of gadolinium gallium garnet

spheres located in tandem on a single piston which alternately moves each

matrix into a 7 tesla magnetic field. A separate helium gas circuit is used as the heat exchange mechanism for the low and the high temperature extremes of

the magnetic refrigerator. Details of the design and results of the initial

refrigerator component tests are presented.

Key words: Closed cycle refrigerators; expansion engine; gadolinium gallium

garnet; gas pumps; magnetic refrigeration.

1. Introduction

In the past few years a lot of interest has been generated towards designing and developing a continuously operating 4 K magnetic refrigeration stage for a closed cycle refrigerator (CCR)

[1-4]. Its potential for high efficiency performance makes magnetic refrigeration a likely

alternative to the passively operating, but highly inefficient Joule-Thomson circuit. The success

of the magnetic refrigerator for this temperature range will depend on the development of suitable

design approaches to answer questions of heat transfer effectiveness, helium gas movement, wear

rates of materials and expected life cycles of the refrigerator components.

The Jet Propulsion Laboratory (JPL) has initiated the development of a 4-15 K magnetic

refrigerator to assess its potential as a replacement to the Joule-Thomson circuit of a closed

cycle refrigerator [5]. JPL has been using 1 Watt at 4.5 K closed cycle refrigerators since 1965

for cooling the low-noise maser amplifiers required to receive very weak signals from spacecraft

in deep space. Up to 30 CCRs are in near continuous operation in the Deep Space Communications

Network that JPL operates for the National Aeronautics and Space Administration. These CCRs log

approximately one quarter of a million hours annually. The successful development of a magnetic

refrigerator would reduce the overall life-cycle costs of the CCR by reducing the electrical power

consumption of the CCR and by insuring a longer MTBF for the operating refrigerator.

The design of the engineering model 4-15 K magnetic refrigerator under development at JPL

addresses the basic requirements of refrigeration power, DC field stability, reliability and

efficiency. It is the objective of this paper to describe the design of the magnetic

refrigerator, discuss the component test results, and provide a status of the development effort.

33
2. Experimental design

Choice of the magnetic refrigerator design must depend ultimately on the device it is to cool, in this case the maser, an ultrasensitive microwave signal amplifier whose performance

depends critically on a stable DC magnetic field, and on a low operating temperature having

mi 1 1 i Kel vi n stability. The refrigerator package for the maser must be orientation -independent

since it is located in the feedcone of a large tracking antenna which points anywhere from horizon

to zenith. The design requirements for the magnetic refrigeration system is therefore quite

stringent. The design of the engineering model presently under development addresses only the

basic requirements of refrigeration capacity, DC field stability, reliability and efficiency. The

reciprocating design has been selected for its relative 1 simpler fabrication requirements and the

greater ease with which the experimental results could be verified theoretically.

The schematic of the magnetic refrigerator design is shown in figure 1. All components have

been fabricated at JPL. The major components are shown in figure 2. The CTI Model 1020 expansion

engine provides the high temperature heat sink for the magnetic refrigerator and is capable of

producing better than 9 W of refrigeration at 15 K. This refrigeration capacity is a major

determining factor in the final 4 K cooling power of the magnetic refrigerator. The hydrogen heat

switch is used during initial cooldowns to precool the helium dewar and magnet assembly to 20 K before liquid helium is transferred into the dewar. This experimental design presently calls for

the external transfer of liquid helium to cool the magnet; future designs will require the

magnetic refrigerator stage to provide the parasitic refrigeration requirements of the magnet.

The 7 T magnetic field is supplied by a 10.2 cm NbTi solenoid having a 6.3 cm bore. The

magnet is operated in persistent mode. When the magnet is fully charged, the current leads will

be detached at the magnet to minimize heat leak into the liquid helium bath. Quench protection of

the magnet is provided by a short length of stainless tubing attached across the magnet leads and

immersed in the liquid helium bath. The magnet is encased with a magnetically soft material,

Hiperco (Carpenter Technology Corp., Reading, PA), having a saturation induction of 2.4 T. The

Hiperco is used to entrap much of the magnetic flux exiting from the bore of the magnet.

The piston is driven with a 185 W (1/4 H-P) speed-controllable gearmotor. This rotational

motion is converted to reciprocating motion by means of a "ball reverser" (Norco, Inc.,

Georgetown, CT) , a nut with ball bearings that run in a cross-hatched track cut into the drive

shaft. The track has a set stroke length of 9.2 cm and provides a displacement of

3.175 cm/2 it rad. A 10 rad/s rotation rate for the gearmotor translates to a 5.1 cm/s linear speed

for the GGG piston and to a cycle frequency of 0.28 Hz. A turn-around in the ends of the track

automatically reverse the direction of travel of the nut to provide smooth reciprocating motion

without reversing the direction of rotation of the drive motor. A rotary ferrofluidic feedthrough

(Ferrofluidics Corp., Nashua, NH) couples the gearmotor to the ball reverser, which is housed in the helium gas of the magnetic piston circuit. This eliminates the requirement for reciprocating vacuum seals on the piston drive shaft.

The key components of the 4-15 K magnetic refrigerator are the cylinder assembly and the

piston containing the paramagnetic material. The cylinder assembly is made of thin-wall stainless

steel and provides the ducts through which the heat exchange fluid flows (Fig. 2). The ducts are made from thin-wall rectangular waveguide to minimize the annular gap between the piston and the

magnet. The phenolic piston is machined in three parts — two thin-wall cups to contain the porous

Gd3Ga50i2 (GGG) matrices and a solid center section to separate the matrices (Fig. 2). Threads were cut into each piece to facilitate both the assembly of the piston and the modifications to the matrices. Each compartment is 33 mm long and 38 mm in diameter and is filled with 160 gm of

1.1 mm diameter GGG spheres for a fill factor of about 60%. Stainless screens are inserted in each end of the compartment to prevent the GGG from migrating out the holes in the piston.

The use of the two matrices doubles the heat removal capacity per cycle of the piston and

provides a more continuous transfer of heat to help reduce temperature fluctuations. The 4.2 K cooling power of the magnetic stage operating ideally in a Carnot cycle can be given as

Qc

= "TcvASti

34
where n is the number of moles of Gd3+ in the matrices, Tq is the refrigeration temperature, v is the frequency of operation and AS is the change in entropy during the isothermal demagnetization,

and r) is the fraction of Carnot efficiency at which the magnetic refrigeration stage operates. In this design there is 0.948 moles of Gd3+, and if the matrix cycles between 0.5 T and 6.5 T over the temperature span of 4 K and 16 K we can assume AS is 0.3R (which takes into account the

entropy change of the GGG minus the entropy change of the entrained helium gas), then the

refrigeration power at 4.2 K is

6c = 9.9vti W.

Some of the factors effecting the efficiency are the thermal heat leaks along the cylinder wall

and the drive shaft, the heat capacities of the piston and cylinder, and the heat transfer between

the gas and the GGG matrices. These factors ccontri buti ng to the loss of cooling power of the

refrigerator will be identified and minimized during refrigerator testing. No attempt will be

made to calculate these effects here. To minimize the internal heat load due to the entrained

helium, the helium gas pressure will need to be kept below about 0.1 MPa.

Helium gas provides the heat transfer between either matrix and the low-temperature source

and the high-temperature sink. When the GGG matrix is positioned adjacent to a gas duct in the

cylinder, helium gas is forced through the holes on one end of the matrix compartment, through the

porous matrix, and out the set of holes on the other end of the compartment (fig. 3). The ridge in the center prevents gas leakage along the outside of the piston. The indents in the outer surface

of the piston allow the gas to flow through the matrices while the displacer is still in motion so that gas flow need not be limited to the time the piston is positioned at the ends of the stroke.

The placement of the gas ports in the cylinder and the geometry of the piston eliminate the need

for mechanical valves at these low temperatures. During this portion of the cycle the refrigerator

operates in an isothermal fashion. As the piston is then moved from one end of the stroke to the

other, the outer ridges of the piston act as close tolerance seals to prevent the gas from either

circuit from passing along the cylinder wall and thermally short-circuiting the matrices. The

low-friction fiberglass-impregnated teflon seals further insure that the gas leakage is minimized.

This allows the matrices to magnetize or demagnetize in an adiabatic fashion. Thus the cycle of

the piston should approximate the Carnot cycle.

Heat exchangers filled with phosphor-bronze screens are used to transfer heat between the

helium gas in the circuits and the heat source or the heat sink. Fluid flow through the gas circuits is produced by separate linear-induction, positive-displacement pumps in both the

low- and high-temperature gas circuits. The two gas pumps are driven back and forth in phase

relation to the motion of the GGG piston. The pumps easily develop the low pressure head required

to overcome the pressure drop through the GGG matrices and the heat exchangers. These pumps have

been operated successfully at low temperatures but their long-term performance has not yet been

determined.

3. Component Test Results

The use of the Hiperco surrounding the magnet provides a more rapid transition between the

high field and low field regions enabling a shortened stroke length for the GGG piston. Figure 4 compares the measured axial magnetic field profile of the solenoid with and without the Hiperco

and shows the position of the piston at the end of the stroke. At either end of the stroke, the

axial field at the position of the center of the two GGG matrices is 0.5 T and 6.5 T, with a maximum ±7% change in the measured axial field over the length of the GGG matrix in both the

high-field and the low-field regions.

The magnetic field pulls both GGG matrices towards the center of the magnet. The magnitude of

this attractive force depends on both the magnitude and gradient of the magnetic field which, for

cylindrical symmetry, may be approximated by F z = (3Bz/9z), where F , m , and B

z are the axial

components of the force, the GGG magnetization and the magnetic field, respectively. The use of

the Hiperco to shape the 7 T field has generated a magnetic field gradient of 105 T/m which

produces a force as high as 1550 N on each of the 160 gm GGG matrices at 4.2 K. This large force

dictates the need for careful positioning of the matrices to provide adequate force balancing.

From the force equation the first choice made was to position the matrices so as to coincide with

35
the distance between the maxima in the field gradient. Figure 5 shows the measured force required

to move the 4.2 K piston through the magnetic field, with the maximum.net force being measured as 630 N. This force could be reduced by decreasing the separation distance between the two matrices.

This reduction in force is desirable to reduce the power needed to drive the piston. However the

matrices then move through a different portion of the magnetic field profile which will have an unknown effect on the refrigerator performance. These effects will be examined during testing of

the magnetic refrigerator. Additional force compensation, if needed, may be provided by imbedding

small slugs of GGG in the center section of the piston so as to be thermally isolated and not a part of the refrigeration process.

4. Conclusion

The high reliability of the individual components should result in a high reliability for the

magnetic refrigerator as well. The gearmotor has been overdesigned to handle the anticipated

large loads for smooth operation at slow speeds. Operation at these slow speeds will minimize the wear rate on the low-temperature sliding seals. The magnetic refrigerator has been designed to minimize the problems associated with gas contamination. The magnetic refrigerator stage is a closed gas loop system; the gas circuit is sealed after the initial charge of helium gas. The

internal gas displacers eliminate the need for an external compressor to provide the gas flow.

The external and internal portions of the piston drive train are coupled together with a rotary

seal to prevent gas contamination entering the circuit along the drive shaft. The magnetic

refrigerator also requires no small orifices as with the Joule-Thomson valve, further minimizing

the problems associated with gas contamination. Elimination of the Joule-Thomson circuit can reduce the input power requirements for the compressor by about a third.

The design of the reciprocating magnetic refrigerator to pump heat from 4 K to 15 K has been

presented. Initial tests to examine the field shaping ability of the Hiperco and to measure the

resulting magnetic forces on the GGG piston have been made in an open-cycle dewar. Further testing

to reduce the magnetic force through field shaping will be made in the assembled refrigerator so that the refrigerator performance may be measured as well. The magnetic refrigerator is currently

being assembled.

The research described in this paper was performed by the Jet Propulsion Laboratory,

California Institute of Technology, under contract with the National Aeronautics and

Space Administration.

5. References

[1] Van Geuns, J.R., A study of a new magnetic refrigerating cycle. Philips Res. Rep. Suppl .6:1

(1966).

[2] Nakagome, H., Tanji, N., Horigami, 0., Numazawa, T., Watanabe, Y., and Hashimoto, T., The

helium magnetic refrigerator I: Development and experimental results. Advances in Cryogenic Engineering Vol. 29, Plenum Press, New York (1984).

[3] Barclay, J. A., Overton, Jr., W.C., Stewart, W.F. and Steyert, W.A., Magnetic refrigeration

for 4-20 K applications'. Technical Report AFWAL-TR-83-3120 (Dec. 1983).

[4] Lacaze, A.F., Claudet, G., Lacaze, A. A., and Seyfert, P., Prospects in Magnetic Refrigeration

Proceedings of the ICEC10: Paper Al-2, Helsinki (1984).

[5] Deardorff, D.D. and Johnson, D.L., Magnetic refrigeration development. The Telecommunications

and Data Aquisition, Progress Report 42-78, pp 49-58, Jet Propulsion Laboratory,

Pasadena, CA (July 84).

36
gearmotor((0

rotary seal

BALLREVERSER

HELIUM

DEWAR

HIPERCO

SUPERCONDUCTING

MAGNET

H„ HEAT

SWITCH

VACUUM HOUSING

P I STON

70K

RADIATION

SHIELD

CYLINDER

HEAT

RESERVOIR

IrS"—-^GAS PUMPS

15K STAGE

OF CTI 1020

Fig. 1 Schematic of the magnetic refrigerator.

37
PISTON CYLINDER GAS PUMP

Fig. 2 Magnetic refrigerator components.

38
-PERIOD OF HEAT EXCHANGE

-PERIOD OF HEAT EXCHANGE

CYLINDER TIME

Fig. 3 Schematic showing the time during one cycle of the piston when the indents

align with the gas ducts to allow the heat exchange gas to flow through

the GGG matrices.

39
E

i—

O

E

• U-h

tea?

I I

[1] 013ldOll3NOVW

Fig. 4 Comparison of the measured axial magnetic field profiles with and without

the Hiperco material. The extreme positions of the piston are shown with

respect to the field profiles.

40
Fig. 5 a) The measured net force required to move the piston through the magnetic

field, b) The magnitude of the axial field gradient for the magnet/Hiperco

assembly. The extreme positions of the piston are shown with respect to these curves.

41
IMPROVED HEAT SWITCH FOR GAS SORPTION COMPRESSOR

Chung K. Chan

Jet Propulsion Laboratory

California Institute of Technology

4800 Oak Grove Drive

Pasadena, California 91109

Thermal conductivities of the charcoal bed and the copper matrix for the gas adsorption compressor were measured by the concentric-cylinder method. The pre- sence of the copper matrix in the charcoal bed enhanced the bed conductance by at least an order of magnitude. Thermal capacities of the adsorbent cell as well as the heat leaks of two compressor designs were measured by the transient method.

The new gas adsorption compressor had a heat switch that could transfer eight

times more heat than the previous one. Because of this, the cycle time for the new prototype compressor was also improved by a factor of eight to within the

minute range.

Key words: Charcoal bed; copper foam; gas adsorption; gas heat switch; heat

capacitance; refrigerator; switch ratio; thermal conductance.

1 . Introduction

In the gas sorption refrigeration cycle, whether it is the gas adsorption system [1,2] or the

gas absorption system [3,4], the sorption (adsorbent or absorbent) bed must be cycled between the

temperature of the heat source and the temperature of the reservoir to which heat is being rejected.

Thus, making and breaking thermal contacts of the sorption bed with the reservoirs are essential

operations. A similar situation exists for the salt bed of the magnetic refrigerator. Heat

switches based upon different physical mechanisms have been developed. Mechanically actuated heat

switches [5] have been proved unreliable at cryogenic temperatures, and require large contact force.

Magnetoresisti ve heat switches [6] are, except at very low temperatures, of very low efficiency and

require a magnetic field. Gaseous thermal switches [7,8] which are probably the oldest idea, depend

on the switching action resulting from the presence or absence of the gas. Efficient gaseous

switches require a small gas gap but large heat transfer areas which are sometimes hard to achieve.

Since the primary goal of the sorption refrigerators is one of lifetime and reliability, it was decided to use a reliable gas heat switch for the adsorption compressor [9].

Since the switching function in the gaseous heat switch is accomplished by the presence and

absence of the gas between two surfaces, gas supply and a suction pump are required. These functions are provided by an adsorption pump connected to the switch. In our earlier gas adsorption

compressor (GAR-I) [9] the heat switch in each compressor unit was controlled by a miniature pump.

In our current modular design ( GAR- II), each compressor unit has one heat switch but four heat

switches are controlled by one pump [10].

42
One major difficulty in the gas adsorption or desorption process is to transport heat into and out of the porous media rapidly. In the GAR-I design, because of this limitation, the cycle time of

the gas sorption refrigerator was in the range of six to fifteen minutes. This time was too long

for a practical refrigerator. As an ongoing development effort of nonmechani cal (gas adsorption or absorption) refrigerators for spaceborne instruments, research has been performed to study the heat

transfer characteristics of the porous charcoal medium, the porous medium enhanced by a metal matrix, and the gas heat switch. This paper presents the results of these research efforts that lead

to the construction of the rapidly cycled compressor [10].

2. Thermal conductance and gas adsorption compressor designs

The thermal properties of charcoal beds with heat transfer enhancement element are essential

data for compressor design and performance analyses. The thermal conductivity of a bed of charcoal

was measured in the temperature range between 20C and 475C, using a conventional steady-state

method, the so-called concentric-cylinder method, with the inner cylinder being a heater. The charcoal particles (200 ym - 400 ym in size) were filled into the space between the heater and an outer

stainless steel cylinder. The heat flow was radial as the length of the cylinder (L) was large

(5.1 cm) compared to the distance between the cylindrical shells (0.85 cm). The temperature gradient due to the radial heat flow was measured by two thermocouples located at radii r-j and r0 , close to the mid-point of the cylinder,

the following relation:

The thermal conductance k of the bed was calculated from

where k = Q

= V

Qln(r

o /r.)

thermal conductance (W/cmK)

power of the central heater (Watt)

(1)

o temperatures measured at radii r. , r , respectively

With r- = 0.31 cm and rQ

= 1.17 cm, the results for the thermal conductivities k of the charcoal

bed are listed in Table 1. Thermal conductivities between 1.17 x 10" 3 W/cmK and 1.26 x 10" 3 W/cmK

are found. These values are in the same order of magnitude as those of the zeolite bed reported in

the literature [11].

VC)

Table 1. Thermal conductance of charcoal bed

T.(C) I Q(W) | u i k (cmK)

229

295

365

420

475

59

78

90

104

116

4.45

6.24

8.19

9.49

11.12

1.17 x 10"

1.17 x 10"

1.22 x 10"

1.23 x 10

1 .26 x 10

-3

-3

The thermal conductivity of a copper foam [3% by volume) was determined by the similar method

and the value was listed in Table 2. It was observed that the copper foam had thermal conductivity

an order of magnitude better than the charcoal bed. Hence, when the charcoal was packed into the

copper foam matrix, the thermal conductance of the bed would be increased by an order of magnitude.

Because of this heat enhancement, in our earlier adsorption compressor (GAR-I), as shown in Fig. 1,

7.38 gm of charcoal which was confined within a stainless steel cylinder of volume 14.35 cm 3

, was packed into the open foam copper matrix. The temperature of the adsorbent cell was controlled by a 40 W heater and a gas heat switch gap to a 77 K heat sink. The presence and absence of the gas in the gap are controlled by a miniature adsorption pump containing a small amount of charcoal. A schematic of the adsorbent bed, the heat switch and the miniature pump is shown in Fig. 1.

43
Table 2. Thermal conductance of copper foam

VC) Q(W) k (cmk)

46 44 2.15 0 . 040

76 69 4.66 0.026

144 130 11 .28 0.033

195 170 16.7 0.027

274 227 28.1 0.024

The heat path from the adsorbent bed to the 77 K heat sink passes through the porous bed and

the stainless steel wall and is interrupted by the 0.18 mm annular gap between the inner stainless

steel cylinder and the outer brass cylinder before it reaches the 77 K heat sink. The gap may be vacuum or filled with hydrogen gas through the stainless-steel capillary tube C, depending on the

temperature of the miniature adsorption pump. The pump is maintained in weak thermal contact with

the heat sink through an appropriately sized wire. A heater and a silicon diode were attached to the pump chamber.

The pump chamber was leak tested, vacuum outgassed and backfilled with hydrogen at 77 K and

200 torr. At that temperature all the gas was adsorbed onto the charcoal and there was no gas in

the heat switch gap, i.e., the heat switch was off. When the pump was heated to about 110 K, the

gas was released and the pressure built up. Hydrogen began to flow from the pump to the gas gap, i.e., the switch was on. Hydrogen was chosen because of its relative high thermal conductivity.

The test results are presented in the next session.

The new refrigerator design (GAR- II) of 250 mW at 20 K consists of banks of individual com- pressor modules. A schematic of a modular design is shown in Fig. 2. This design involves four

banks (A, B, C and D) containing sixteen compressor modules in total. Each compressor module is a double walled cylindrical unit as shown in Fig. 3. The charcoal, confined within the stainless

steel inner pressure vessel, is packed into an open copper matrix foam. The gap between the inner

and the outer cylinders is the gas heat switch. The heat switches of four compressors are con- trolled by one miniature adsorption pump of charcoal which when heated supplies gas to the switch,

turning it on and when cooled, removing gas from the switch, turning it off. Each bank has one such

miniature adsorption pump, so all the compressors in each bank are cooled at the same time.

3. Transient experimental measurements and results

Transient thermal tests were performed for the GAR-I compressor (Fig. 1) and the GAR-II com- pressor module (Fig. 3) to determine the heat capacity of the adsorbent bed, the heat leak, and the

switching capacity of the heat switch.

In the tests involving the heat capacity, both the adsorbent cell and the heat switch pump were evacuated. The adsorbent cell was then heated, and the transient temperature was recorded.

As the first iteration, the heat leak was ignored and the heat capacity of the adsorbent cell

(mc ) which included the charcoal, the stainless steel vessel and the copper foam was determined by mc ) n = — (2) p'cel 1 / dT v

v ; (£)

a_ = transient temperature gradient of the cell

where Q = heat input

dT

dt

The heat leak K c

from the cell was determined by recording the temperature during the cool

down of the eel 1

:

44
"%'cell .„

tf -t, (3)

where , are temperatures at times t^ and t

f

T" s is the heat sink temperature

With the knowledge of the heat leak, as a second iteration the heat capacity was recalculated by

Q

(mc v ) n n p'cell

K (T - T ) u a s' (4)

where T is the adsorbent cell temperature,

a The heat capacities of the GAR-I adsorbent cell calculated by equations (2) and (4) are shown in Fig. 4. A theoretical curve based on the properties of carbon, stainless steel and copper is also

shown in the same figure for comparison. It was observed that the experimental data were about 30%

higher than the theoretical prediction. Fig. 5 shows the response of the switch to the heating of

the charcoal pump. Within 50 seconds the switch is conducting. The value of the conductance K can

be determined from the temperature transient by an energy balance of the adsorbent cell:

dT

[(mC ) + (mC ) + (nriC L ) 1 -rr^ = -K(T - T ) p'a v p's.s. v p'c J dt v a s (5)

where m is the mass

0^ is the heat capacity

the subscripts a, s.s. and c represent the adsorbent, the stainless steel vessel and the

copper foam, respectively

^a is the gradient of the temperature transient

dt

T is the heat sink temperature

The thermal conductance K was plotted as a function of the mean temperature, i.e., (T + T )/2) in Fig. 6. The theoretical K was calculated by knowing the heat switch area A, the gap size 5 and

the thermal conductivity k of the gas as

Thus, with hydrogen as the working gas, the switch of GAR-I has a conductance of 0.8W/K when the

switch is on and a conductance of 0.14W/K when the switch was off, giving a switch ratio of 5.7.

Similar tests were performed for the GAR- II compressor, and the results are shown in Figs. 7, 8 and 9. The thermal conductance of this new heat switch design was found to be 8 times better

than the previous design. The switch of GAR-II has a conductance of 5W/K when the switch was on and a conductance of 0.37W/K when the switch was off, giving a switch ratio of 14.

4. Conclusions

The thermal properties of the adsorbent bed and the heat switch were determined by steady state

and transient experiments. Results of these heat transfer studies led to the design and the con- struction of a new gas sorption compressor which had a heat switch that could transfer 5 W/K of

heat from a 6 cm (H) x 2.54 cm (D) cylindrical modular compressor. Because of this, the cycle time

for the new prototype compressor was about one minute. Since the system weight is almost inversely

proportional to the cycle time, this improvement will no doubt reduce the refrigerator weight in spaceborne missions.

45
The research described in this paper was carried out by the Jet Propulsion Laboratory,

California Institute of Technology, through contract with the National Aeronautics and Space

Administration.

5. References

[I] Chan, C. K. , Cryogenic refrigeration using a low temperature heat source, Cryogenics 21_, 391-399 (1981).

[2] Chan, C. K. , Tward, E. and Elleman, D. D., Miniature J-T refrigerators using adsorption

compressor, Advances in Cryogenic Eng. 27, 735-743 (1 981 )

.

[3] Lehrfeld, D. and Boser, 0., Absorption-desorption compressor for spaceborne/ai rborne cryogenic refrigerators, AFFDL-TR-74-221 , AF Flight Dynamics Laboratory, Wright-Patterson AFB

[4] Jones, J., LaNi^ hydride cryogenic refrigerator test hardware results, Refrigerator for

Cryogenic Sensors, NASA Conference Publication 2287, 357-373 (1982).

[5] Siegwarth, J. D., A high conductance helium temperature heat switch, Cryogenics j_6, No. 2,

73-76 (1976).

[6] Radebaugh, R., Electrical and thermal magnetoconductiviti es of single-crystal beryllium at low temperatures and its use as a heat switch, J. of Low Temperature Physics 2_7, 91-105

(1977).

[7] Torre, J. P. and Chanin, G., Heat switch for liquid helium temperatures, Rev. Sci . Instrum.

55, 213-215 (1984).

[8] Tward, E., Gas heat switches, NBS Special Publication 607, Boulder, CO, 178-187 (1981).

[9] Chan, C. K., Tward, E., and Elleman, D. D., Kinetics of gas adsorption compressor, Advances

in Cryogenic Engineering 29, 533-542, (1983).

[10] Chan, C. K., Performance of rapid cycled gas adsorption compressor, paper presented at the

10th International Cryogenic Conference, Helsinki, Finland, July 31-August 3, 1984.

[II] Vol kl , J., Heat conduction in zeolite beds, Heat Transfer 1982, 2, C018, 105-108.

46
/— HIGH PRESSURE / GAS LINE

r— VACUUM

/ CHAMBER

[H] HEATER

0 THERMAL SENSOR

Fig. 1. GAR - I COMPRESSOR

47
48
49
CD

CO

I

CD

LU

<c

Q_

>/r 113:>

( d

Dw)

50
220

190

£. 160

it! <

Si%

£ 130

100

70

i 1 1 1

ADSORBENT CELL

1

HEAT SWITCH PUMP

A

/

> - /

/

/

/ -/

/

!

1 1 1 1 1 250 500 750 1000 1250 1500

TIME (sec)

Fig. 5. TRANSIENT TEMPERATURE OF ADSORPTION CELL AND HEAT SWITCH PUMP OF GAR- I

1.2

\ 1.0

EXPERIMENTAL DATA

THEORETICAL PREDICTION

1 I 1 1

70 80 90

Fig. 6.

100 110 120 130 140

AVERAGE TEMPERATURE (K)

HEAT SWITCH THERMAL CONDUCTANCE OF GAR - I

150 160

51
170

160

150

140

£ 130

LU

!< 120

_£

UJQ-_ no

h100

90

80

70

—, . _____———,

1

1

1 ADSORBENT CELL —i—i—

i

' i ~

HEAT SWITCH PUMP /

\ / \/ \

\ /

v v

\ / \

/-

/ - / -

/ i

- / 1

/ 1

~ / I

/ \ V

;

i i i i i i i 100 300

Fig.

6 "

200

TIME (sec)

7. TRANSIENT TEMPERATURES OF ADSORBENT CELL AND HEAT SWITCH PUMP OF GAR - II.

400

V r

Z

<

i—u

D

Q

Z

o

u

0£

LLi X

I—X

u

<UJX

T T

2 -

EXPERIMENTAL DATA

THEORETICAL PREDICTION

70 80

FIG. 8.

90 100 110

AVERAGE TEMPERATURE (K)

HEAT SWITCH CONDUCTANCE OF GAR - II

52

120 130
HYDRIDE ABSORPTION REFRIGERATOR SYSTEM FOR TEN KELVIN AND BELOW

Jack A. Jones

Applied Mechanics Division

Jet Propulsion Laboratory

California Institute of Technology

Pasadena, California 91109

Recent work at J PL has shown that a very long-life, lightweight and

efficient hydride absorption refrigerator system can be built to operate at

ten Kelvin and below. The system consists of four basic stages of

refrigeration. The first stage can be accomplished by means of an active

refrigeration system such as a long-life Gifford-McMahon expander or a charcoal -sorption refrigerator, or even by a passive space radiator operating

below 120 K. The second stage is operated by a hydride absorption system,

wherein a heated hydride powder drives off high pressure hydrogen through a Joule-Thomson/heat exchanger expansion loop such that the hydrogen is

partially liquefied (20 K at 1 atmosphere pressure). In the third stage, the

vapor pressure over the collected liquid hydrogen is lowered by means of

absorbing the hydrogen vapor onto a different low pressure, warm hydride.

With a 1.7 torr partial pressure of hydrogen gas in the hydride, liquid

hydrogen is solidified and sublimes at 10 K. Long-life adiabatic

demagnetization refrigerators, helium desorption, or helium diaphragm

compressors may possibly be used to cool to 4 K or below.

Preliminary analysis shows that the hydride concepts provide an extremely

efficient means of refrigeration to 10 K, and that an entire sorption

refrigeration process can be accomplished solely by using low grade heat

energy at about 150oc. Furthermore, an entire sorption refrigerator system

has no moving parts, other than long-life valves, which have been life- tested

at JPL to an accelerated life of 500 years. Preliminary tests and analyses of

the sorption refrigerators indicates an expected lifetime of at least ten years. Present lightweight Gifford-McMahon expanders have lifetimes greater

than 2.3 years, although this can likely be increased by means of redesign

and/or redundancy.

Key words: absorption; adiabatic demagnetization; adsorption; cryogenic;

Gifford-McMahon; hydride; hydrogen; refrigerator; sublimation.

1. Introduction

There are a number of mechanical cryogenic refrigerator systems that are capable of

producing temperatures as low as ten Kelvin and below. These systems, which include various

Stirling cycles, Brayton cycles and Vuilleumier cycles, all require the use of wear-related

moving parts and/or very complicated electrical equipment. Although much progress has been made

in recent years, none of these systems has, to-date, demonstrated extremely long life (five years

or greater), primarily because of mechanical failure problems. It was precisely for this reason

that the Jet Propulsion Laboratory decided in 1979 [1] to explore the possibility of using

non-mechanical sorption refrigeration systems for sensor cooling systems that would eventually

explore the outer planets. These missions require lifetimes of ten years and more. With

sorption refrigeration systems, there are no wear- related moving parts, and the controlling

electronics can consist entirely of simple, long-life, solid state timers.

Recent work at JPL has demonstrated the feasibility of extremely long life (at least ten

years) for hydride absorption coolers in the twenty Kelvin range [2, 3], and analyses has proven

53
that this temperature range can be lowered to ten Kelvin by means of using an additional,

non-mechanical solid hydrogen sublimation stage. This extremely efficient stage then opens the

door to even lower temperature, long-life systems when used as a preliminary stage for helium

sorption systems or for adiabatic demagnetization refrigeraters, both of which will be described

later in this paper.

2. Principle of Operation

2.1 20 K Refrigeration

The basic principle of operation for the 20 K hydride refrigerator is that a continuous flow

of high pressure hydrogen gas is generated by means of non-mechanical hydride compressors. The

high pressure gas is pumped through a series of heat exchangers and a Joule-Thomson (J-T) valve

such that the net cooling effect due to expansion of the gas at the J-T valve lowers the hydrogen

temperature to its liquefaction point, 20 K at one atmosphere pressure (Figure 1).

The principle of the compressor operation is based on the fact that the intermetallic

hydrides such as LaNi'5, absorb about six atoms of hydrogen per unit formula with an equilibrium

pressure of a few atmospheres at room temperature. The density of the absorbed hydrogen at room temperature is almost twice the density of free liquid hydrogen at cryogenic temperatures.

The equilibrium pressure of the absorbed hydrogen is a very strong function of temperature,

and thus the hydrogen static pressure can be increased from 4 atmospheres at 40oc (313 K) to about 60 atmospheres at 120oc (393 K). Cycling can also be achieved with the use of other

metallic hydrides, whose temperature-pressure characterises are different than LaNis. By

alternately heating and cooling a series of hydride containers, a continuous flow of high

pressure gas is thus supplied to the Joule-Thomson (J-T) expansion valve in Figure 1. The

expansion of the gas causes partial liquefaction which can then absorb heat at liquid hydrogen

temperatures.

The basic advantages of this type of system are that it provides considerably lower

temperatures (20 K or lower) than those from passive radiator systems (approximately 80 K), and

yet it still has no mechanical moving parts, other than self-operating check valves, which have

been life-tested at JPL for an accelerated life of 500 years. It is much simpler, and has a much

longer life expectancy than present orbiting mechanical refrigeration systems, and it can be

operated using low temperature waste heat or direct solar heat.

In order to provide heating and cooling of the hydride compressors, a simple gas-gap thermal

switch can be used (Figure 2). For spacecraft application, heating could be obtained by means of

a flat plate solar collector (or possibly a radioactive thermal energy source), and the heat

could be transferred to the hydride by injecting a gas into the gold-plated gap between the solar

plate collar and the hydride. To cool the compressor, the solar plate thermal switch gap would

be evacuated, and gas would be injected into the gap between the compressor and the cooler

radiator heat pipe. Low pressure hydrogen, e.g. 1 torr, gas could be used as the thermal switch

actuator gas, and this could be stored in a cooled hydride material for very long-life and lightweight storage.

2.2 10 K Refrigeration

In order to produce temperatures as low as 10 K, the vapor pressure over collected liquid

hydrogen is lowered by means of absorbing the hydrogen vapor onto a very low pressure, warm

hydride. With a 1.7 torr partial pressure of hydrogen (corresponding to a hydride temperature of

about OOC), the hydrogen is solidified and sublimes at 10 K (Figure 3). A cryogenic sensor can

be continuously maintained at 10 K by means of providing two dewars of hydrogen. While one is

being liquified, the other is sublimated. The cryogenic sensor can be attached to both dewars by means of a thermal switch, thus being continuously maintained at 10 K.

Another design for the 10 K stage involves liquefying hydrogen at 20 K by means of a hydride

liquifier stage, and then expanding the liquid directly to a low pressure 10 K solid hydrogen

"snow". Blockage of the J-T valve could be prevented by means of using a porous copper trap,

wherein sensor heat is readily transmitted to the J-T valve itself.

54
3. Overall Cycle Possibilities

3.1 Multi Stage Sorption Refrigeration System

In order to produce an entire spacecraft refrigeration system, a number of possibilities

exist in terms of refrigerator staging. Although some spacecraft applications (such as sun-synchronous polar orbits, geosynchronous orbits, and interplanetary missions) adapt

themselves well for very low temperature passive radiator stages in the 80 K to 120 K region,

most low earth orbit applications cannot readily achieve radiator temperatures below about

150 K. Since this results in relatively high specific power requirements for the hydride system,

a number of alternate colder upper stage refrigeration systems have been studied.

For one type of system, solar heat could be collected at 425 K, and used to power four

sorption stages (Figure 4), while a small amount of electrical power is used for a thermoelectric

cooler (TEC) stage. For the charcoal /methane and charcoal /nitrogen sorption stages, large

quantities of gas are absorbed onto charcoal at low pressure and 225 K. The gas is then released

at high pressure when the charcoal is heated to 425 K. The process is similar to the hydride

system, except that the gases are physically adsorbed onto the surface of the charcoal, while the

hydrogen is chemically bonded to tne metal hydride powder. The charcoal sorption stages and the

TEC are cooled by a ZZb K radiator, a temperature which is readily obtainable for radiators

facing away from earth, with or without solar light, in low earth orbit. The TEC provides

cooling to 175 K, which liquifies methane at high pressure (26.5 atm). When the liquid methane

is expanded to 1.8 atm, it cools to 120 K. This 120 K stage is then used to liquefy nitrogen at

24.8 atmospheres. When the nitrogen expands to 1.4 atm, it cools to 80 K, which is then staged

to a rare earth, misch metal hydride compressor to reach 18 K for liquid hydrogen. The

refrigerator system then cools to 10 K for the solid hydrogen sublimation stage.

A sorption system design to obtain one watt of cooling at 10 K requires a total estimated

power of only 600 watts, most of which is supplied directly as solar heat. This is therefore the

most efficient 10 K refrigeration system presently possible, primarily because it does not

require the use of a very inefficient helium refrigeration cycle. Prior to the hydride

sublimation stage design, it simply had not been possible to achieve such low hydrogen pressures

for extended periods in a closed-cycle operation. It should also be mentioned that the entire

refrigeration system uses absolutely no wear-related moving parts, other than extremely

long-life, room-temperature valves. All calculations are based on actual empirical

absorption/adsorption data for the respective gases.

A charcoal /hel i urn sorption refrigeration stage, similar to the methane and nitrogen stages,

may be possible to obtain temperatures of about 4K, but preliminary calculations have shown that

is likely to take many kilowatts of charcoal sorption heating to produce enough helium flow to generate one watt of liquid helium J-T cooling. A likely alternative to a charcoal /helium

sorption compressor, however, is an oil-free helium diaphragm compressor, although much

development work is necessary in order to obtain a contamination-free life of ten years. Another

lower stage alternative is to desorb helium from a saturated 10 K charcoal bed. The heat of

desorption is relatively high compared to the very low charcoal specific heat at this

temperature, and substantial cooling can result. Although temperatures below 4 K have been

obtained with this method [4], much development is still needed in this area also.

3.2 Gifford-McMahon Pre-Cooling

Another extremely efficient means to achieve first stage cooling for the hydride system is

to use a Gifford-McMahon (G-M) refrigeration cycle [5], which is powered by compressed hydrogen

from a hydride system. In the G-M cycle, gas is compressed in a cylinder to a high pressure and

the heat of compression is rejected at some temperature, typically room temperature. The gas is

then forced through a piston- type cold regenerator that has a low cycle rate and low pressure

drop seals. The gas is then allowed to expand to a very low pressure while flowing back through

the regenerator and into the low pressure end of the compressor. The isentropic expansion of the

gas precools the regenerator for the next cycle. Although not as efficient as some other

refrigeration cycles, one of the big advantages of this system is that the primary frictionrelated part is a piston seal, which has a low cycle rate and a very low pressure drop across

it. In fact, present Cryogenic Technology Incorporated (CTI) Gifford-McMahon refrigerators have

expansion cooler mean-time-between- failure (MTBF) lifetimes in excess of 20,000 hours [6].

Since present CTI expansion coolers are run at about 72 RPM, if lower speeds or stronger,

multiple seals are used, even greater MTBFs can be expected. Also, since a 9 kg expander can provide about 15 watts of cooling at 70 K, multiple expanders could be used and valved off, if

the low pressure drop expansion seal begins to show signs of degraded life.

55
At present, the major problem with G-M upper stage refrigerators is that oil -lubricated

compressors are used. Although elaborate oil cleaning systems have been devised, eventually the

oil will freeze out and contaminate the cryogenic portions of the system. This requires periodic

maintenance every 2000 to 5000 hours. With a hydride compressor, however, there is absolutely no

oil present, and the entire system can operate free of contamination, essentially forever.

A sketch of a G-M upper stage expander and a lower stage adiabatic demagnetization

refrigerator, discussed in the next section, appears in Figure 5. Pre-cooling of the hydrogen

gas at about 70 K can be accomplished with the G-M expander. The overall specific power, i.e.

power required per cooling watt, of this system is relatively good, and in-fact, approaches

approximately 300 for 20 K cooling, and is about 400 for 10 K when combined with a hydride

sublimation cooler. This compares with about 1000 or higher for most other mechanical systems at 10 K.

3.3 Adiabatic Demagnetization Lower Stage

An adiabatic demagnetization (ADM) stage, which purportedly achieves 80% of carnot

efficiency [7, 8] can be used to reach temperatures of 4 K or lower. For ADM, a wheel of

paramagnetic material is rotated partly inside an extremely high superconducting magnetic field,

typically about 7 Tesla. The application of the magnetic field causes heat to be generated in

the paramagnetic material. This heat can then be removed at some elevated temperature, e.g.

10 K. When the wheel is rotated away from the 10 K heat sink, it rotates out of the high

magnetic field, and its temperature is lowered a tremendous amount, typically to 4 K or below.

The entire cycle can be designed to use no moving parts, other then a slowly rotating wheel and

possibly some low pressure drop helium circulators to enhance heat transfer into and out of the

paramagnetic material.

The 10 K or 14 K hydride stage can be of great advantage for the ADM refrigerator, since ADM

requires extremely strong super conducting magnets in order to operate. Since 14 K is just

within the superconducting magnet temperature region, the system may be able to "bootstrap"

itself from 14 K to lower temperatures by progressively increasing superconductive magnetic field

strength with decreasing temperature.

4. Experimental Results

4.1 Charcoal Sorption Refrigeration

Recent work at JPL has confirmed the use of charcoal sorption to produce a continuous flow

of high pressure nitrogen. By alternately heating and cooling from cannisters of charcoal

between 250 K and 400 K, a continuous flow of 50 atmospheres (750 psi) nitrogen has been

produced. By flowing the gas through a J-T/heat exchanger assembly, a total cooling power of

approximately 1/2 watt has been generated.

Although the total average power required for this proof-of-principle test was approximately

200 watts, much lower LN2 specific powers are predicted with methane-staged sorption

refrigeration, as previously described and shown in Figure 4.

4.2 Liquid Hydrogen Refrigeration

Most of the experimental results regarding liquid hydrogen hydride refrigeration life

testing are available in [3, 9], and are summarized for convenience below:

In particular, a complete heated hydride compressor system has been thus far successfully

tested at ERGENICS Corporation to 6000 hours of continuous operation, and the JPL cryogenic J-T

system has accumulated over 1,000 hours of successful operation between 14 K and 29 K, without

any evidence of wear. It should be noted that the ERGENICS compressor that operated for 6000

hours weighed only about 10 kg and yet delivered a hydrogen flow which would have been equivalent

to about 3 watts of cooling at 25 K if a J-T/heat exchanger loop were used. With a lower cycle

speed, it can be said that it survived at least 18000 hours of 1 watt equivalent cooling and yet

still performed close to original specifications. Preliminary third-stage experiments have

confirmed the sublimation of hydrogen at 13.8 K, although a reduced pressure drop heat exchanger

system is required to reach lower temperatures. Furthermore, the only moving parts in the

system, room- temperature check valves, have been life-tested at JPL to an accelerated life of 500

years [10].

56
Life tests on hydride particle size have confirmed that the hydride particles break down

after repeated cycling, but the average particle size reaches a final spherical equivalent

diameter of about 1 micron after about 5000 cycles. Although some binary hydride alloys, such as

LaNi'5, have shown a significant loss of capacity when subjected to many cycles at elevated

temperatures [11], small additions of aluminum to rare earth, nickel -type alloys make the alloy

greatly resistant to disproportionate. [12]. ERGENICS Corporation has estimated effective

hydride disproportionate as approximately 1% per year, based on aluminized misch-metal hydride

alloys. For expansion cooling, Joule-Thomson (J-T) valves have long proven their inherent

reliability, as evidenced by well over one million hours of accumulated life for the J PL Deep

Space Network Maser receivers [13]. Although simple decontamination thaws are recommended every

six to twelve months for the JPL maser fixed-orfice, J-T valves, it is likely that no thaws would

ever be needed for the new JPL design of non-clogging, spring-loaded, J-T valves [3].

Furthermore, the hydride system has absolutely no oil -contaminated vapors, as are present on the

JPL mechanical refrigeration Maser compressors and thus overall contamination can be

substantially reduced if proper initial decontamination steps are taken.

4.3 Solid Hydrogen Sublimation

There has been considerable work done on solid hydrogen sublimation by Lockheed Corporation

[14]. Although hydrogen solidifies at about 14 K and 1 psi pressure, its temperature has been

readily lowered to as low as 7 K by means of evacuating the vapor space above the hydrogen,

thereby causing it to sublimate directly from the solid phase to the gaseous phase. Since the

transition heat from gas to liquid is very high (190 BTU/lbm) and the solid latent heat is

relatively low (25 BTU/lbm), the amount of cooling energy required to go from liquid to solid is

quite low, although the heat of sublimation, which is approximately 190 + 25 = 215 BTU/lbm, is

very high.

That is to say, once liquid hydrogen has been made, it takes very little extra power to produce solid hydrogen. This in fact, has been confirmed by analysis using a specialized JPL

sorption computer program [15], using LaNi*5 to produce liquid hydrogen and a low pressure

hydride to further reduce the vapor pressure, and thus its temperature.

5. Summary and Conclusions

Recent work at JPL has shown the possibility of achieving extremely long-life (10 years or greater), efficient, and relatively simple refrigeration systems for obtaining 10 K temperatures

and below. The various possible stages are described below:

1. The first stages of refrigeration can be obtained by either passive radiation (80 K to 120 K for high orbits or interplanetary missions), charcoal /methane sorption (120 K)

combined with charcoal /nitrogen sorption (80 K), or by a Gifford-McMahon refrigeration

system (40 K minimum) powered by a hydride compressor.

2. The next stage of refrigeration to 20 K can be accomplished by a standard hydride J/T

compressor system, such as the compressor unit recently life tested for 6000 hours [3].

3. The ten Kelvin temperature stage is obtained by low pressure hydride sublimation

evacuation of the vapor space above hydrogen to 1.7 torr pressure. This can be

accomplished by batch processing the liquid hydrogen and then reducing the hydrogen

pressure by absorption onto the hydride or by direct expansion of liquid hydrogen

through a J/T valve to produce solid hydrogen "snow".

4. Temperatures of 4 K or below may possibly be obtained by adiabatic demagnetization

refrigeration, helium desorption, or by an oil -less diaphragm helium compressor.

All of the sorption refrigeration stages have life expectancies of at least ten years, since

their only moving parts are room- temperature valves that have been life tested to an accelerated

equivalent life of 500 years. Although present CTI Gifford-McMahon expanders have a guaranteed

life expectancy of 20,000 hours, their extremely light weight allows for multiple unit redundancy

and/or stronger seals and lower cycle frequency to achieve 10 year life (88,000 hours). It is

quite likely that longer life seal materials can be made, since the G-M expander seal sees only a very low pressure drop which is at low temperatures. Present G-M refrigerators are life-limited

primarily due to oil -contamination from mechanical compressors, a problem which is totally absent

with hydride compressor systems.

57
The overall specific power efficiency to reach 10 K by sorption staging is estimated to be

about 600 watts per cooling watt at 10 K, while the specific power with G-M staging is about 400

watts per cooling watt. Most of the power for both systems is in the form of low temperature

heat, such as 425 K solar heat or RTG waste heat. This compares with values generally greater

than 1000 for every other known 10 K helium cycle refrigeration system.

When compared with all other closed-cycle spacecraft mechanical refrigeration systems,

sorption refrigeration, and in particular the 10 K hydrogen sublimation hydride sorption system,

appears to be the simplest, most efficient, lightest and least interfering (vibrations and

magnetics) and to have the longest potential life of any other existing system.

The help of Dr. Dave Elliott of JPL is gratefully appreciated for his suggestion of

combining a Gifford McMahon expander as a first stage to a hydride Joule-Thomson hydrogen

liquefier system, and the help of Dr. Steven Bard, also of JPL, is appreciated for the design and

testing of the charcoal /nitrogen sorption refrigeration system. Furthermore, the original idea

of hydrogen sublimation to obtain 10 K cooling is acknowledged and appreciated from Dr. Al Johnson of Aerospace Corporation.

The research described in this paper was carried out by the Jet Propulsion

Laboratory/California Institute of Technology under a contract with the National Aeronautics and

Space Administration.

REFERENCES

[1] JPL White Paper: "The Status of Cooler Technology in Relation to Future JPL Space Instrument

Cooler Requirements," by the Cooler Technology Study Committee (R. Beer, W. Petrick, D. Pidek, J. Plamondon, M. Saffren and J. Wellman), March 22, 1979.

[2] Jack A. Jones, "LaNi's Hydride Cryogenic Refrigerator Test Results," Second Biennial

Conference on Refrigeration for Cryogenic Sensors and Electronic Systems, GSFC, Greenbelt,

Maryland, December 7 and 8, 1982.

[3] Jack A. Jones and P. M. Golben, "Life Test Results of Hydride Compressors for Cryogenic

Refrigerators," AIAA Paper No. 84-0058, AIAA 22nd Aerospace Sciences Meeting, January 9-12,

1984, Reno, Nevada. Publication pending in Cryogenics Magazine.

[4] J. C. Daunt and C. Z. Rosen, "Desorption Cooling below 12 K using He^ desorbed from

synethetic zeolite," Cryogenics , June, 1972.

[5] W. E. Gifford, "The Gifford McMahon Cycle," Advances in Cryogenic Engineering , Vol. 11, 1966.

[6] Franz Eberth Fred Chellis, "Comparing Closed Cycle Cryocoolers," CTI Cryogenics Publication,

Waltham, Massachusetts, 1979.

[7] W. A. Steyart, "Rotating Carnot-Cycle Magnetic Refrigerators for use near 2 K," Journal of

Applied Physics 49(3), March 1978,

[8] Dean L. Johnson, "Reciprocating Magnetic Refrigerator", 3rd Cryocooler Conference on Refrigeration for Cryogenic Sensors and Electronic Systems", National Bureau of Standards,

Boulder, Colorado, September 17-18, 1984.

[9] Jack A. Jones, "Cryogenic Hydride Refrigeration," 29 Minute Video Presentation, World

Hydrogen Conference, Toronto, Canada, July 15-20, 1984.

[10] Emanuel Tward, Jet Propulsion Lab, Low Temperature Physics Group Supervisor, Private

Communication, October, 1983.

58
REFERENCES (CONTINUED)

[11] J. J. Reilly, A. Holtz, and R. H. Wiswall, Jr., "A New Laboratory Pump for Intermediate

Pressures," Review of Scientific Instruments, 42 (10), 1485, 1971.

[12] Doug Goodell, "Stability of Rechargeable Hydriding Alloys during Extended Cycling,"

Publication pending in Journal of Less Common Metals .

[13] W. H. Higa and E. Wiebe, "One Million Hours at 4.5 Kelvin", National Bureau of Standards

Cryocooler Applications Conference, Boulder, Colorado, October 1977.

[14] T. C. Nast and D. 0. Murray, "Orbital Cryogenic Cooling of Sensor Systems," Systems Design

Driven by Sensors AIAA Technical Specialist Conference, Pasadena, California Oct. 19-20,

1976.

[15] Katherine B. Sigurdson, "A General Computer Model for Predicting the Performance of Gas

Sorption Refrigerators," Second Biennial Conference on Refrigeration for Cryogenic Sensors

and Electronic Systems, GSFC, Greenbelt, Maryland, December 7-8, 1982.

59
Q Q Q Q Q Q

OUT IN OUT IN OUT IN

LaNi, LaNi, LaNi, COMPRESSOR

ASSEMBLY

rO^On r<X<h pO^O-j CHECK VALVE

U 1A „ ASSEMBLY

AIR NATURAL

CONVECTION

LN

2

IN

LN

2

OUT

LOAD

HEATER

SIMULATED HIGH

TEMPERATURE RADIATOR

HIGH

TEMPERATURE

HEAT EXCHANGER

SIMULATED LOW

TEMPERATURE RADIATOR

LOW

TEMPERATURE

HEAT EXCHANGER

Figure 1 Hydride Refrigerator Operational Schematic

60
CO<I O

CO o

CO

«0I

0) o

1/1 £io

en

61
LOW PRESSURE

HYDROGEN

ABSORBENT

Figure 3 Ten Kelvin Hydrogen Sublimation Refrigerator

62
Figure 4 Four Stage Sorption Refrigerator System

63
Figure 5 Hydride Refrigerator With G-M Upper Stage and ADM Lower Stage

64
CLASSIFICATION OF CRYOCOOLERS

G . Walker

General Pneumatics Corporation

Western Research Center

7662 East Gray Rd.

Scottsdale, Arizona 8525^

A great diversity of methods and mechanisms have been devised to effect cryogenic refrigeration.

This paper reviews some of the basic parameters and considerations affecting the selection of a particular system.

A classification scheme for mechanical cryocoolers is presented. An important distinguishing feature is the incorporation

or not of a regenerative heat exchanger, of valves, and of the

method for achieving a pressure variation.

Key words: Cryocoolers; mechanical refrigerators, regenerative

heat exchanger.

1. Introduction

A cryocooler is a refrigerating system capable of achieving temperatures in

the cryogenic range, generally reckoned to be less than 120K. The word cryogenic

is derived from the Greek "icy cold".

Cryocoolers are often rated by their available refrigeration capacity

measured in watts. To be meaningful however it is necessary to specify not only

the refrigeration capacity but also the temperature at which the refrigeration is

available. A cryocooler having a capacity of 1 watt at 4K (liquid helium temperature) is very much different to the cryocooler having a capacity of 1 watt at

80K (liquid nitrogen temperature).

Another important parameter is the power input or work required to achieve

refrigeration.

The coefficient of performance of a refrigerator is defined as the ratio:

COP = Refrigeration Capacity/Power Input or Heat Lifted/Work Done

The ideal coefficient of performance is the Carnot value:

COP (Carnot) = T /(T - T ) 11 C E where T = minimum cycle temperature (usually the refrigeration temperature)

T^ = maximum cycle temperature (generally the atmosphere temperature)

The ratio of the actual coefficient of performance to the Carnot coefficient

of performance is sometimes called the efficiency . It is a useful measure of the

way an actual machine measures up to the thermodynamic ideal machine. Thus:

Efficiency = Actual COP/Carnot COP

= Refrig Cap/Power Input X (T

c - Tg)/Tg

The efficiency of presently available cryocoolers ranges from a minimum of less

65
than 1 percent to a maximum of near 50 percent. Strobridge (197*0 presented

"experience" charts for 1^10 different cryocoolers with the above efficiency variations . The small machines used for electronic applications have the lowest efficiencies. This is because nearly all the refrigeration generated is consumed in

cooling, and maintaining cold, the low temperature region of the machine itself.

The surplus or useful refrigeration available from these units is very small; only

fractions of a watt are required. Applications requiring a larger useful refrigeration load use systems bigger in size and tending to be more efficient. The

highest efficiencies are found in large machines used for liquefiers and range

from 20 to 50 percent of the Carnot value.

Other significant parameters for cryocoolers include the total mass and volume

of the system and the mass and volume of the cold region. This latter is of

particular importance in infra red (I-R) missile guidance or night vision systems

with cooled detectors and associated optical/electronic systems mounted in swivelling gimbals. A low mass and volume is necessary to facilitate a fast response

with low inerita.

Cooldown time , the period necessary for the machine to achieve stable operation at the design condition following startup is important in some applications

of miniature systems, usually weapons related. The combination of a quick cooldown and a slow warmup is a particularly challenging requirement involving mutually

opposed high and low 'thermal masses'. Cooldown is sometimes accelerated by

operating at a high pressure or speed on startup and later switching to the normal

operating mode.

Mechanical vibration and electro-magnetic emissions in the cold region are often important characteristics of cryocoolers. Some applications require the

total elimination of any mechanical or electro-magnetic noise. This is best approached by

a) physical separation of the cold region and the compressor unit where large

power input and heat transfers take place

b) elimination of moving parts in the cold region

c) the use of plastic, ceramic or other non-magnetic parts in the cold

region

.

Operating life is another important characteristic often quoted as the mean

time before failure (m.t.b.f.) or the mean time before maintenance (m.t.b.m.).

This is generally taken to mean the average time of operation before failure (or

maintenance) of a number of identical cryocoolers operating under similar conditions. Reliable data for m.t.b.f. and m.t.b.m. based on the accumulated experience

of users is very hard to come by. There appears to be no properly organized

system for data collection, reduction, rationalization and distribution. Operating life is

affected to a large extent by the nature of the system used: Moving parts, sliding seals,

bearings, piston rings, etc. wear and generate detritus with deleterious effects on valves, and

small passages. Sometimes questions of lubricated versus unlubricated parts involve the balancing

in increased wear against the possibilities of contamination of lubricant. Re 1 i a b i 1 ity can often

be improved by incorporating excess capacity so that operation is intermittent or by the provision

of redundant systems.

The shelf life of a cryocooler is frequently important. This is the interval

a unit may be required to maintain the capability for operation while standing un- used or in occasional intermittent use. Many systems involve mechanical units

containing high pressure helium and equipped with a variety of sealed flanges,

66
shaft seals, screwed fittings etc. Hermetic sealing by seal welding is the best

approach to ensure a long shelf life but this of course is not possible for a mechanical unit with dynamic seals.

In split systems where the cold region is separated from the power input unit

the nature of the leads connecting the two elements is important. Some systems

have flexible leads, others are inflexible. Sometimes they are cold, sometimes at

ambient temperature, sometimes a single lead with a cyclic fluctuating pressure,

sometimes twin leads with a high pressure feed line and a low pressure return.

All these affect the insulation required, the forces and bending moments imposed on gimballed units, the transmission of mechanical, vibration, thermal conduction and

pressure attenuation or phasing effects.

Cost , of course, is always important, more so in some cases than others.

Separate consideration of capital cost and operating cost including scheduled maintenance and unscheduled maintenance or replacement is necessary. Sometimes the

lack of opportunity or possibility for maintenance (space systems) justify increase

in the capital cost by the provision of redundant systems or the use of a large,

lightly loaded, slow running unit.

The power supplied to drive the cryocooler is eventually degraded to heat and

must be rejected from the system. Thus the cooling system to carry the waste heat

is an important feature of the cryocooler. Liquid cooling is more efficacious

than air or gas cooling because of high heat transfer coefficients and heat

capacities achieved with liquids. Air cooling is attractive on grounds of simplicity to almost everyone concerned except those actually responsible for the cooling

system. Frequently miniature machines are air cooled but are then located in a pod along with other heat emitting power equipment so the environmental temperature

is increased. This complicates the cooling problem. The range of environmental

temperature over which the equipment is required to operate ranges from -40°C

to as much as 60°C. This in itself presents problems which are compounded in many

cases by the further requirement that the refrigeration temperature is a precise

value having a tolerance as slight as + or - 0.1°C.

System cooling and heat rejection presents special problems in space applications. All the heat must ultimately be rejected by radiation. The well-known

equat ion

:

Q = EAST4

where Q = radiation heat flux

E = surface emissivity

A = area of emitter

S = Stefan - Boltzman constant

T = temperature of emitter

clearly dictates a high temperature. However the coefficient of performance

equations

COP = T

E/(T

C

- T

E

)

dictate the lowest possible maximum cycle temperature, T

p

, (corresponding to T in

the above radiation equation)

.

Continuing with the special requirements for aerospace cryocoolers important

characteristics are the ability to withstand the high acceleration and vibration

spectrum of a rocket launch, the ability to operate in any orientation and in a zero or low gravity regimen. Reliability and long-life assume an importance not

found elsewhere.

2. Classification of cryocoolers

There are many military, civil, medical, and scientific applications for

cryocoolers in electronic, space, and defense-related systems. These needs, with

the multifarous and diverse requirements enumerated above, have, over the past HO

67
years, attracted the attention of ingenious and resourceful engineers and scientists. The result is an enormous literature and a wide range of different systems

and solutions. Walker (1983) has recently summarized the situation and provided

an extensive bibliography and a guided introduction to the field.

The ultimate refrigerator has not yet been invented. This would produce whatever refrigeration was required at the appropriate temperature

, ^would be compact,

lightweight and run forever with no maintenance on a pennyworth of* kerosene without vibration, noise, or smell. All practical machines are essential compromises

of conflicting requirements with particular features emphasized as specified by

the client for their application.

The classification chart shown in Figure 1 represents one attempt to clarify

a confusing situation. The chart is limited to mechanical cryocoolers producing

cryogenic refrigeration by compression and expansion of gases including liquefaction of gases at low temperature. It does not include any of the solid state

refrigerators or those customarily confined to temperatures below 3K.

2.1 Regenerative heat exchanger

With the above sweeping limitation in mind the first question to ask when

confronted with an unknown cryocooler is

:

"Does it have a regenerative heat exchanger".

All types of heat exchangers may be broadly classified into regenerative or recuperative heat exchangers. Recuperative exchangers are equipped with separate

flow passages for the two or more fluids involved. The passages are usually con- tained in conduits with solid walls and the fluids flow continuously. Most heat

exchangers are the recuperative type. Regenerative exchangers contain a porous

matrix of finely divided material, granules, balls, wires, etc. The fluids flow

through the matrix in cyclic succession so the cold blow follows the hot blow,

etc. The matrix acts as a thermodynamic sponge alternately releasing heat to the

cold fluid and receiving heat from the hot fluid.

The unknown cryocooler will almost invariably include one or more recuperative

heat exchangers but if there is no regenerative exchanger it will belong to the

group of cryocoolers shown in the upper right-hand box of Figure 1. Claude,

Linde-Hampson, Joule-Thomson or Joule-Brayton . These are the names of the originators of the thermodynamic cycles on which these various systems work. They all

operate with compression of the working fluid at high temperature, expansion at

low temperature, and incorporate counter flow, recuperative heat exchangers.

Expansion engines are included in the Claude and Joule-Brayton systems.

2.2 Valves

If the specimen cryocooler does include a regenerative exchanger the next

question is:

"Does it have any valves to regulate the flow of the working fluid".

If the unit does include valves as well as a regenerator it will be an Ericsson engine of the type shown in the mid-left box, Solvay, Postle and GiffordMcMahon. The distinction between Solvay and Postle machines is that the Solvay

unit includes a work-producing low temperature expansion machine. The Postle

unit operates with a displacer only. Gifford and McMahon invented the machines

carrying their names in the late 1950 's but both their inventions were actually

reinventions of the Postle and Solvay engines of the previous century.

2 . 3 Compressor

If the specimen cryocooler contains a regenerative heat exchanger but no valves the next step in classification is the type of device used to achieve a pressure variation.

68
Stirling engines incorporate a mechanical compressor so the total enclosed

volume of the working space varies cyclically usually as the result of the

motion of a piston in a cylinder.

In Vuilleumier engines there is no piston but simply a displacer moving working fluid from a hot space to a cold space and vice versa. The machine Is said

to have a thermal compressor and is sometimes called a thermocompressor . The

variation in temperature at constant volume causes a change in pressure, (high

when the fluid is in the hot space, low when it is in the cold space). The change

in pressure is utilized in a separate but connected cylinder also containing a displaoer to achieve refrigeration. The machine was devised by Rudolph Vuilleumier

in 1918.

There are innumerable variations of Stirling engines some of which are set

out in Figure 1. They involve displacer-piston and two piston versions and multiple piston arrangements and variations.

Vuilleumier engines are also found in a range of variations broadly classified

as split systems or integral systems. In both the Stirling and Vuilleumier units

a split system has the cold expansion space located in a separate cylinder remote

from the hot compression cylinder and coupled to it by a single small-bore lead

up to 2 m long.

3. Conclusion

Multiple applications for cryogenic cooling systems have resulted in the

development of many different cryocoolers with different characteristics and attributes .Some of the important requirements and the different types of unit are briefly

reviewed

.

4. References

[1] Strobridge, T.R., Cryogenic refrigerators - an updated survey, National Bureau

of Standards Technical Note 655, (Sup. Docs. U.S. Govt. Printing Office),

12 pp, (197*0 •

[2] Walker, G . , Cryocoolers, (2 volumes), The International Cryogenics Monographs

Series, Plenum Publishing Corporation, New York, (1983)

•

69
REGENERATIVE

HEAT EXCHANGER

YES

CLAUDE/LINDE-HAMPSON

JOULE-THOMSON

JOULE-BRAYTON

SOLVAY

POSTLE

GIFFORD-MCMAHON

SPLIT-STIRLING

TANDEM OPPOSED

PISTON

TANDEM

CYLINDER

ORTHOGONAL

CYLINDER

FIGURE 1. CLASSIFICATION OF CRYOCOOLERS

70
AM EXPERIMENTAL STUDY FOR A MINIATURE

STIRLING REFRIGERATOR

Shimo Li and Chen Guobang

Zhixiu Huang Fagao Zhang

Cryogenic Engineering Laboratory

Zhejiang University, China

Cuangji Cui and Jiazhang Li

Low Temperature Physics Laboratory

Beijing University, China

In this paper, experimental results of a miniature two-stage

Stirling cryocooler are introduced. The influence of filling gas

pressure and refrigeration temperature on the refrigerating capacity

along with the relationship between parameters has been measured. The

valley pressure corresponding to the lowest refrigeration temperature

and the cooldown time versus operating pressure have been discussed.

The coefficient of performance and thermodynamic efficiency of the

cryocooler have been calculated based on experimental data.

Key words: Cryocooler; cryogenics for infra-red detectors; miniature

Stirling refrigerators; refrigeration.

1. Introduction

In recent years, we have studied the thermodynamic characteristics of both types 3Ly-08/194

which is a small single stage refrigerator [1] and A3040 Stirling cycle refrigerator which is a miniature two-stage refrigerator. Measurements have been made of refrigeration temperature,

operation pressure, cooling capacity, cooldown time along with the relationship between them. In addition, the influence of surrounding conditions and contamination of the regenerator on the

performance of the refrigerator is also considered. In the following, the experimental study on

the miniature two-stage Stirling refrigerator will be discussed.

2. Structural Features of the Cryocooler

This miniature two-stage Stirling refrigerator was built in Beijing University in 1972. Its major specifications are listed in Table 1. The device was designed for refrigerating infra-red

detectors requiring a refrigeration temperature of about 25-30 K [2]. Most components of the

refrigerator are made of stainless steel. The cylinder and displacer define two low temperature

expansion spaces. There are two co-axially located regenerators in the displacer. Stacks of

stainless steel screen are used as regenerative packing material. A copper shield is installed on the first cold head and there are several layers of Al-coated Mylar outside £he shield to reduce

radiation loss. During the experiment the insulation space is about 5 x 10" mmHg dynamic vacuum.

The second stage cold head and the cylinder made of oxygen-free copper, are connected together for

better thermal stability. The machine was operated at 1400 rpm. Helium gas is used for working

medium. The compressive heat of helium gas is carried away by cooling water.

71
Table 1. Major specifications of A3040 Refrigerator

Component

Compressor-cyl i nder

diameter/stroke/ volume

Primary cylinder

diameter/stroke/ volume

Secondary cylinder

diameter/stroke/ volume

Length/diameter of the

primary regenerator

Length/diameter of the

secondary regenerator

Structure angle e

Volumetric phase angle <|>

Pressure phase angle 6

Pressure parameter 6

Pressure ratio o

Filling gas pressure

1st and 2nd stage

temperature Tm

/T

& 1st and 2nd stage regenerators

packing material

1st and 2nd theoretical

refrigerating capacity Qm

/Q

e Weight of the refrigerator

(exclude the motor)

Unit

mm/mm/ cm

3

mm/mm/cm3

mm/mm/cm3

mm/ mm

mm/mm

degree

degree

degree

dimensionless

dimensionless

bar

K/K

mesh

watts/watts

Ka

Value

60/15/42.4

23.9/13/3.53

15/13/2.3

40/19

26/14.3

60

67

38

0.45

2.67

6.5

95/30

250/300

39.4/25.7

17

For refrigeration power measurement, 6 m of 0.2 mm constantan wire is coiled on the copper

cylinder of the secondary cold head. The electric resistance of the wire is about 50 ohm at room temperature. Power is supplied by an adjustable D.C. supply. The heating power is less than 12

W.

Temperature is measured at three points: T is measured with a Ni-Cr-Au-Fe thermocouple at the secondary cold head, while T and T are measured with Cu-constantan thermocouples at the hot

ends of the secondary and the primary cylinder, respectively, (see Fig. 1).

72
T

e Expansion space

Regenerator 1

Primary expansion

space

Regenerator 2

Heat exchanger

Compression space

Piston

Figure 1. Arrangement for temperature measurement.

Type UJ-26 electric potential meters (with a precision of 0.1 yV) and PZ26b direct digital voltage

meters are used in measuring. Good thermal contact of the thermometer with cold head is provided.

The relationship of the lowest refrigeration temperature, cooldown time and filling gas

pressure have been measured. The experiment was made under bad conditions, e. g. the outdoor

temperature was about 35 C. The temperature of the cooling water was 30 C, and the room temperature was not lower than 30 C.

Under a condition of no heat load, a minimum is found in the lowest refrigeration temperature

as a function of filling pressure. The relationship between them is shown in figure 2. The

refrigeration temperature will increase when the pressure is either higher or lower than the

optimum pressure (in the measurement on 3LY-08/194 refrigerator, two optimum pressures have been

observed [1]).

The time required for the temperatures T and T of first and second stage cold heads to decrease from room temperature to the lowest equilibrium temperature under a given operating

pressure is called the cooldown time. Figure 3 shows these temperature-time curves under a filling gas pressure of 7.5 bar. It seems that the cooldown time of the machine on the order of

15 minutes is somewhat longer than that of a normal one under normal operating pressure. Probably

this is because of the larger heat capacity of the secondary cold head and the copper block of the

2nd cylinder. The cooling curve takes a similar shape with that of reference [3]. As filling gas pressure increases the unloaded cooldown time is shortened (see Fig. 4). When the filling gas pressure decreases from 7.5 bar to 3.5 bar, the cooldown time almost doubles (from 15 minutes to 34 minutes).

3. Experimental Results

3.1 The Lowest Refrigeration Temperature

3.2 Cooldown Time

73
59

30 \ 1 1 l 1 1 1 1 5 4 5 6 7 8 9 10 P,bar

Figure 2. Lowest refrigeration temperature versus operation pressure.

t ,min

Figure 3. Cooldown curve of miniature two-stage Stirling refrigerator.

74
Experimental results show that the cooling curves of T and T are similar to each other.

The temperature of the hot end of the 1st cylinder quickly Reached a steady state. At the initial

stage, the decreasing rate of T is greater than that of T . Then two cooling curves of T and T

p intersect each other. At last, Tm

and T

g curves almost re^ch their equilibrium temperature

simul taneously.

3.3 Cooling Capacity

The refrigeration temperature T varies approximately linearly with cooling capacity Q

g when

the filling pressure is under 9 bar fsee Fig. 5). At a given refrigeration temperature T , the

cooling capacity Q increases at the pressure increases. The critical heating power under which

the machine is at the full-loaded state is about 9.5 - 10 W when filling gas pressures are 6.5 bar

and 7.5 bar (see Fig. 5). While the heating power is increased continually temperatures of the

1st and 2nd stage are reversed, i.e., T <T . Since only a few watts and a temperature just below

40 K are required for practical applications, the cooling capacity required cannot be

supercritical. Figure 5 also shows that the variation extent of T versus cooling capacity is not great. While the 2nd stage cooling capacity is increased from zero

1 to the critical value, the

corresponding difference of the 1st stage temperature is approximately 10 K.

T

1 1 1 r

I 1 i i i L /4 Id 12 Zb 50 J4

t ,min

Figure 4. Filling gas pressure versus cooldown time.

Figure 5. Cooling capacity versus refrigeration temperature.

75
3.4 Thermodynamic Efficiency

Coefficient of performance e and thermodynamic efficiency n are defined as follows

£ = Vn

where Qe

= actual cooling capacity, W

N

= actual input power, W

e. = coefficient of performance for Carnot cycle

T

1 = ambient temperature, K

According to thermodynamic principle, the input power increases while the temperature T of

the expansion space decreases due to the reduction in heat displacement of unit working medium.

Thus both of the coefficient of performance and thermodynamic efficiency will be reduced. Figure

6 shows results calculated- from experimental data.

Figure 6 shows an optimize-region for the cycle efficiency of the refrigerator correlated to the thermodynamic efficiency n of the Carnot cycle, i.e. the efficiency of the machine is highest

when operating at corresponding temperatures in this region. However, the coefficient, e, which

depends only upon the temperature ratio, increases almost linearly with the refrigeration

temperature. On the other hand, it is also learned from studying the effect of dead expansion

space S . on n

c and e, that a temperature increase and a reduction in efficiency n take place as

S . increases while e continues to increase. In fact, this shows that it is unreasonable to evaluate cycle efficiency at different refrigeration temperature by using £ only.

- e

(1)

(2)

76
0.10 10 10.0 1000.0 Specific Weightdbw"* 1

)

10,0 100,0 1000,0 10,000,0

Specific Power (WW ) Figure 7. Characteristics of miniature Stirling refrigerator.

Figure 7 shows power and weight characteristics of Stirling refrigerators [4]. Calculated

data of our experimental machine are also plotted in the figure (plotted by "*" and numbered 03).

From figure 7 it can be seen that specific weight and specific power of our cryocooler are in the

middle of the wide band.

4. Discussion

Using experimental data of temperatures and refrigeration powers measured, the different cold

losses of the refrigerator are evaluated according to reference [5]. Calculated net cooling

capacities are essentially consistent with measured ones. Now the discussion will be made in the

following two problems.

4.1 An Optimum Pressure in Figure 2.

A number of experiments on two refrigerators proved that the working pressure has a strong

effect on refrigeration temperature and that there is an optimum pressure on pressure versus refrigeration temperature diagram (Fig. 2). It could be explained as follows.

77
Major cold losses of a refrigerator include shuttle loss, pumping loss, heat conduction loss

of the displacer and the cylinder wall, and regenerator inefficiency loss, etc. There are over 30

parameters in all equations which are applied to calculate cold losses. Most of those parameters

are structure ones, and only one fourth. of those are physical parameters of working medium and

operation parameters. Under our operating condition of the machine, the specific heat and thermal

conductivity of the working medium undergoes a small change when the pressure changes. The

shuttle loss and heat conduction loss are mainly functions of the temperature gradient in the axis

direction, but independent of working pressure [6]. The operating temperature of this machine is

far away from the critical temperature of the working medium He, so that the enthalpy flow loss

caused by the nonideal property of the working as is negligible. Thus the major -cold losses which

have apparent relations with the pressure are the following three terms:

Pumping loss

Qpu =

(3)

1.5ZH 1 -V6 (^a) 1 ' 6

6

2 = ^ (^max~^min)

Friction heat loss in regenerator

(W+pmin) 3v cmN3fLr 2(ZRT e )3gcA2 eg/0

2DeJ (4)

= B C^max+^min^

3

Heat load due to limiting value of film coefficient in regenerator

( ^max^min^ VcmN

2RT eZ • (5) Qrh = (1-7r )C

p

(T w

-T e

)-

= C (Piaax+^min^

The total pressure dependent loss is

Qt = ACP.mtW 1-6

* B ( pmax+pmin) 3+ C ( pmax+I>min) < 6 >

Experimental results and theoretical calculations show [5-7] that these terms account for a major portion of the total loss (over 60% normally) and affect cooling capacity or temperature

significantly.

On the o ther hand the theoretical cooling capacity is proportional to the average operating

pressure P = /Pmax . Pmin to the first approximation, i.e., it is a linear function of the

pressure. But it is known from eq. (6) that the changing rate of the cold loss Q. increases with

the pressure. Therefore, if the changing rate of the cold loss versus pressure is lower than that

of theoretical cooling capacity, the net cooling capacity would have increased with pressure, i.e.

the limiting refrigeration temperature of the machine could have decreased with pressure. On the

contrary, the net cooling capacity should decrease while the pressure increases, i.e. the limiting

refrigeration temperature will increase with the pressure. So there must exist an optimum

pressure for the refrigerator. Reference [7] discussed the influence of the working pressure of

refrigerators on the cooling capacity. As for the case when a possible low refrigeration

temperature is required in small power consumption refrigeration, the machine has better operation

near the optimum pressure. The advantage of low pressure operation is particularly apparent when

the increment in pressure causes a rapid increase in regenerative heat loss.

78
Incidentally, if the working medium is instead of He, the corresponding highest pressure

Pmax reaches the critical pressure of when filling gas pressure is greater than 4.5 bar. The

lowest refrigeration temperature of the refrigerator cannot be lower than the critical temperature

(33 K) of HL even though the pressure is increased continuously. Mean while the enthalpy flow

loss reaches a considerable large value due to non-ideal property of the working medium.

4.2 Comment

Most of the structure parameters and operation conditions of the refrigerator, such as the

gas distribution proportion in the 1st and 2nd stage cold chambers (20% and 80%, respectively) and

the relative volume of dead spaces of the 1st and 2nd stage cold chambers corresponding to the

largest displacement volume etc. are approaching normal values of practical refrigerators. But why is the refrigeration temperature still higher? First, the length and construction of the

secondary regenerator is imperfect, e.g. the dead space of the regenerator is less than 1.5 times

the largest volume of the cold space (normal values are 1.5 - 3.5 times). Second, the copper

cylinder connected with the cold head of 2nd stage is so close to the 1st stage cold head (about

15 mm) that temperature distribution is unreasonable. The temperature difference AT = T - T is relatively small. Thirdly, the specific heat of the stainless steel packing material in m

the

secondary regenerator will rapidly decrease and working medium He will increase, when the

temperature is further reduced. This phenomenon leads to "thermal saturation" in a regenerator

and reduces its efficiency. Besides, the experimental conditions were rather difficult, the

temperature of the cooling water which was put into the compressor was too high, and therefore the

hot end temperature of the primary regenerator was even higher than 40 C. Therefore, the

structure of the 2nd stage regenerator has to be improved and the packing material has to be

changed as wel 1

.

5. References

[1] Li, S. M., et al. Single Stirling Cycle Refrigerator, to be published. (1984).

[2] Cui, G. J., et al. Development Introduction of A3040 Miniature Stirlino Refrigerator,

(1972).

[3] Daniels, A. and du Pre, F. K. , Advances in Cryogenic Engineering 16, 178-184, (1971).

[4] Wolfe, W. L. and Zissis, G. J., The Infrared Handbook, Office of Naval Research,

Department of the Navy, Arlington, VA, 15-31, (1978).

[5] AD-A 027055 (1976).

[6] Radebaugh, R., XV International Congress of Refrigeration, Al/2-16, Venice, Italy,

(September, 1979).

[7] Walker, G., Cryocoolers, Plenum, (1983).

79
PARAMETRIC TESTING OF A

LINEARLY DRIVEN STIRLING CRYOGENIC REFRIGERATOR

F. R. Stolfi and A. Daniels

PHILIPS LABORATORIES

A Division of North American Philips Corporation

Briarcliff Manor, New York 10510

This paper describes the parametric testing of a novel Stirling cycle

cryogenic refrigerator which incorporates electro-magnetic bearings,

clearance (i.e., non- contacting) seals and electronically controlled

linear motion. The last feature, which involves the use of two linear motors,

position transducers and a highly accurate electronic feedback network,

produces the system capability which forms the basis for the tests. The test

results provide designers with an understanding of the basic operation of the

Stirling cycle and give potential users some indication of the capabilities

of this refrigerator under off design conditions.

Key Words: Control system performance; cryogenic; linear motors; magnetic

bearings; refrigerator; Stirling cycle; test results.

1 . Introduction

Philips Laboratories designed, fabricated, and tested a unique Stirling refrigerator which can operate for many years without the need for periodic maintenance and without performance

degradation, and which is therefore compatible with spaceborne applications. This was accomplished by suspending the internal moving parts of the refrigerator electro-magnetically, to eliminate contact and the associated wear. The electro-magnetic suspension was further enhanced

by the use of a direct (linear) drive and by clearance (rather than contacting) seals.

The testing of the refrigerator went through four phases: subassembly tests of the major

components in dedicated test fixtures, performance tests at the design point (5 W at 65°K),

parametric tests of the performance sensitivity to changes in various operating parameters and a life test. The first two phases of testing were discussed extensively at a previous conference

(1); the third is the subject of this paper. The life test is currently in progress, with over

11,000 hours of maintenance- free and degradation- free operation attained to date. The life test

will be discussed briefly at the end of this paper.

Since the purpose of a cryogenic refrigerator is to produce cold at very low temperatures

with high efficiency, its performance criteria can be readily defined. Input power, cold

production (output power) and operating temperature are obviously very important characteristics.

The magnitude of these quantities (e.g., the input required to produce a certain amount of cold)

depends on the refrigerator geometry (e.g., the size of the components) and on the operating

parameters. Therefore, a measure of any cryogenic refrigerator's capabilities is the way in which

the performance criteria - input power, cold production and temperature - vary with the various

geometric and operational parameters.

To assess its operational capabilities, a parametric study was performed on the refrigerator

system at this stage of its development. Specifically, the study was meant to:

Establish the optimum operating conditions required to produce the

nominal cooling (5 W at 65°K) level.

80
• Provide potential users with information on how the refrigerator performs

under off-design conditions.

• Measure the tolerances of the various predicted design quantities as a step

toward initiation of the next design.

The parameters of interest are either characteristic variables of the basic refrigeration

cycle or those which will determine the capabilities of the refrigerator for potential users. These parametric tests are considered the first logical step in the design of the next generation

of this refrigerator, a design which has already been initiated.

2 . The Cycle

The Stirling cycle is based on the linear, reciprocating motion of two elements: the piston

and the displacer. The reduction to practice, that is, the mechanization of the piston and

displacer motions, has proven to be a difficult task. Three approaches deserve mention: crank

drives, free-displacer drives and linearly driven piston and displacer drives.

A crank drive, which converts rotary to reciprocating motion is a complex mechanism. It has

a crankshaft, connecting rods (drive linkages) and numerous bearings and pressure seals.

The free-displacer drive, which makes use of the gas compressed by the piston to reciprocate

the displacer, requires careful attention to the mass of the displacer and to the magnitude of the

gas flow; it also requires adjustment of various parameters once the refrigerator is built.

The linearly driven piston and displacer concept, incorporated into the refrigerator design

presented in this paper, is an elegant approach to the mechanization of the Stirling cycle, even though its realization requires the construction of two special-purpose linear motors and an electronic position control system.

Although its mechanization is difficult, such designs are chosen because the Stirling cycle

is inherently thermodynamically efficient and is very attractive for applications requiring

temperatures in the 8°K - 100°K (-450°F 280°F) range.

In the refrigerator design presented in this paper, the reciprocation of the piston and

displacer is sinusoidal, with the displacer position leading that of the piston by about 70° . The

p-v (pressure vs. volume) diagram for an ideal (isothermal) cycle is shown in figure 1b, the

approximate position of the piston and displacer at the transitions being noted in figure 1a. The

variations in the volume of the expansion space (Ve ) and the volume of the compression space

(Vc ) due to the motions of the piston and displacer are shown in figure 1c.

For the ideal cycle, the cold production Q (Watts) is given by,

Q = to ^ p dVe

* - a) x y Pm Aa sin <)>dr ( 1 )

where, oj = operating frequency (rad/sec)

p

= pressure (N/m ) x = amplitude of displacer (m) y = amplitude of piston (m)

2 = mean pressure in refrigerator (N/m ) A^ = surface area of displacer (m ) ^dr = phase angle between piston and displacer positions (°),

Similarly, the mechanical power which must be provided to the cycle (Watts) is,

W = co y p dVc

« - oj x y Pm A

p sin <|>dr (2)

o where, Ap = surface area of piston (m )

.

For the ideal Stirling cycle, the thermodynamic efficiency is,

Q T

* = w

= T-hr (3) c e

81
COMPRESSION

SPACE

PISTON

COLD END HEAT EXCHANGER

65°K

AMBIENT HEAT EXCHANGER 300°K

OUT,

til

{REGENERATION)

Tm

o IN

(REGENERATION)

Tl

PRESSURE

VOLUME OF COMPRESSION

SPACE

VOLUME OF

EXPANSION SPACE

VOLUME V-

(b) p-v Diagram.

(a) Phases.

TIME

(c) Volume Variations.

Figure 1. Phases, p-v diagram and volume variations for ideal Stirling cycle.

82
where, Te = temperature of expansion space (cold finger) (°K) Tc = temperature compression space (ambient heat exchanger) (°K)

which equals that of the Carnot cycle, meaning that the ideal Stirling cycle is completely

reversible.

The actual efficiency of the refrigerator is less than the ideal because losses in the cycle

cause the input power to increase and the cold production to decrease. Factors which directly

effect the input power include mechanical loss (friction) in the drive, flow losses, and adiabatic

losses (i.e., where the process differs from the isothermal ideal). Factors which reduce the cold

production include flow, insulation and conduction losses, as well as losses due to the non- ideal

nature of the regenerator and heat exchanger. The regenerator, often called the heart of a Stirling refrigerator, stores thermal energy in one half cycle to release it in the other half and

thereby increase efficiency. In an ideal regenerator (perfect heat transfer), a temperature

gradient is established along the regenerator in the direction of flow, which allows the gas to be

cooled down and heated reversibly. Also, the pressure drop across an ideal regenerator is zero. In an ideal heat exchanger, the temperature of the gas is constant, exactly equal to the

temperature of the heat exchanger walls, regardless of the amount of heat in the gas. All real

regenerators and heat exchangers differ from the ideal to some extent.

From the above discussion, it can be seen that the displacer amplitude (x) , piston

amplitude (y) , operating frequency (to), mean pressure (Pm ) , and piston/displacer phase ( <t>dr) are important parameters which characterize the operation of a Stirling refrigerator.

3 . Description of the Refrigerator

The useful life of a conventional Stirling refrigerator is limited by two major factors: wear and outgassing. Wear is present in most mechanical devices which have moving parts.

Bearings and pressure seals wear out; mechanical rubbing and the associated friction generate

potentially harmful particles. The other problem is the outgassing products (impurities) of

organic materials in the refrigerator working spaces such as lubricants and seals. These

impurities are "gettered" (attracted) by the low temperature regions in the machine and eventually

clog critical passages. Since both surface wear and the presence of impurities result in thermal

degradation, the simplest and perhaps the only road to longevity is to eliminate both.

The Philips refrigerator was designed to produce 5 Watts of refrigeration at 65 °K for 5 years or longer (2). Four major features of the unit led to the long life attained: a purely

rectilinear drive (with linear motors and with an electronic axial-control system),

electro-magnetic bearings, clearance seals, and an all metal/ceramic working-gas envelope. The

synergistic combination of these four features has completely eliminated wear and impurities.

A cross sectional view of the rectilinear drive and of the linear motors is shown in figure

2. The drive produces the required linear piston and displacer motions directly, i.e., without

the use of a crankshaft or linkages. The motors are of the moving-magnet type, which have the

PISTON IRON MOTOR COILS

PERMANENT MAGNETS

Figure 2. Cross-sectional view of rectilinear drive

showing displacer and piston motors.

83
advantage that no flexing power leads are required. The directly coupled drive eliminates the

mechanical drive losses associated with conventional refrigeration devices. Direct coupling

requires an axial control system to maintain the proper piston and displacer amplitudes and the

phase relationship dictated by the Stirling cycle. The capabilities and versatility of this

control are important aspects of this novel refrigerator design and form the system basis which

makes the type of testing, described in this paper, possible. The control system is discussed in more detail in section 5. \

The electro-magnetic bearings consist of a set of electromagnetic actuators, radial position

sensors and an electronic control system. The actuators are small electromagnets, consisting of a coil of wire and iron pole pieces. The radial position sensors are eddy-current type, indicating

the radial position by the amount of change in eddy current loss that a radial position change

produces in a pick off coil. The radial displacement of the shaft is detected by the sensor which

signals the control system to adjust the current in the actuators, thereby suspending and

maintaining the reciprocating shaft in the center of its bore. This method permits both the

piston and displacer in the refrigerator to be supported without contact and without any bearing

friction losses.

The clearance seals are long, narrow, annular passages around the piston and the displacer.

Pressure sealing is attained by the flow restriction these passages provide to the oscillating

working gas. This method of sealing requires that the piston and displacer reciprocate in close

proximity to the adjoining walls. This is made possible by the highly accurate operation of the

electro-magnetic bearings.

Since the electro-magnetic suspension, linear drive, and pressure sealing are accomplished

without mechanical contact, it was possible to fabricate the working space envelope of the

refrigerator (i.e., those internal areas in contact with the working gas) from metal and ceramic

only. There are, as a result, no organic compounds of any kind exposed to the working gas. The

organic materials required in the construction, such as the insulation of the motor wire or various potting compounds are hermetically sealed in thin-walled envelopes.

A photograph and a cross section of the refrigerator are shown in figure 3. The expander

subassembly which houses the displacer is at the left; cold is produced at the far left tip (cold

finger). The refrigerator is a single-stage expansion Stirling design (i.e., only one cryogenic

temperature, 65°K, is produced) and thus has a single diameter for the displacer bore. The

compressor subassembly (in the center of the photograph and right side of cross section) houses

the piston and associated parts. The refrigerator has a passive counterbalance, a spring-mass

system which significantly reduces the axial vibration of the unit. It is shown at the far right

of the photograph and discussed in reference 1.

The moving displacer contains the regenerator, a moving-magnet linear motor, and a non-contacting element for the axial position transducer. The regenerator is fabricated from a phosphor bronze wire mesh which has a high thermal capacity and which remains relatively porous to the reciprocating flow of the helium gas with which the refrigerator is charged. The

electro-magnetic bearings which support the displacer (along with the radial position sensors)

also form the clearance seals, forcing the gas through the regenerator and through the ambient

heat exchanger. The heat exchanger is maintained at ambient temperature by a water jacket; its

surface also permits the attachment of a heat pipe instead of the jacket. A vacuum Dewar

(partially shown in the cross section and absent in the photograph) lined with super insulation

(multi-layers of foil and mesh) thermally isolates the cold finger.

The piston in the compressor subassembly is coupled to its moving-magnet linear motor and to

a non-contacting element for its axial position transducer. The electro-magnetic bearing near the

compression space forms a clearance seal to the compression pressure; the bearing at the rear of

the piston is used for support but forms no seal. All electrical connections are hermetic, using

nickel and ceramic f eedthroughs.

In the following section, the general procedure for the parametric tests is discussed. Each

test involved varying one operating parameter and noting its effect on refrigerator performance

(change in the output variables). Section 5 describes the axial control system to provide some understanding of how the parameters can be varied during operation. Finally, section 6, presents

test results. It should be noted that all plots and data presented in these sections and section

7 (life testing) represent actual measurements taken on the refrigerator.

84
( a ) Photograph

.

DISPLACER/REGENERATOR

DEWAR (PARTIAL)

COMPRESSION

SPACE

AXIAL POSITION SENSOR

65°K

EXPANSION SPACE

(b) Cross Section.

Figure 3. Photograph and cross section of refrigerator.

85
4. Overview of the Parametric Testing

The parameters of interest are either characteristic variables of the Stirling cycle (Eqs. 1 and 2) or those which will determine the capabilities of the refrigerator for potential users. Parameters which fall into the first category are piston and displacer amplitudes, operating

frequency, mean pressure, and piston/displacer phase. Tests which fall into the second category

are output temperature versus cold production and variations in heat-rejection' temperature. For

simplicity, only one parameter was varied in each test while the others were held constant. The

effect of the one parameter on the output variables can then be easily observed. The values at which the other parameters were held constant differ between tests and were chosen so that the

parameter which was varied could have a wide excursion. Given this limited scope of the testing,

some care must be exercised in the interpretation of results. Even though "optimal" performance

was sometimes achieved with only one variable changing, it is possible that a better operating

condition exists. The operating parameters are not independent in general and the selection of

the operating conditions for performance other than the nominal 5 W at 65 °K often involves

adjusting several parameters. This also means that if two parameters are varied, the net result

on performance may not be the sum of the results of varying each one independently.

A schematic representation of the refrigerator test setup is shown in figure 4. Three pieces

of laboratory equipment are required for normal operation: two water coolers and a vacuum

station. The water cooler for the ambient heat exchanger removes the heat of compression

(thermodynamic cycle) and the ohmic loss of the displacer motor. The water cooler for the piston

housing removes only the ohmic loss from the piston motor. (Since this motor is 70% efficient,

the power loss is small.) The vacuum station produces the thermally insulating vacuum in the

Dewar. The refrigerator was instrumented with transducers to measure temperature, pressure,

radial and axial position, coolant flow, and case acceleration (3).

The approach for each test followed a similar procedure. The temperature of the cold tip was first reduced to the nominal 65°K with no heat load applied. This required supporting the piston

and displacer with their electro-magnetic bearings, engaging the safety interlock system, and

reciprocating the piston and the displacer. The nominal peak displacements for the piston and

displacer are 7 mm and 3 mm, respectively, with a nominal phase relationship of 67° (1.17 rad)

.

Once the desired cold temperature (65°K) was reached, a resistive heater (load) on the cold

tip was turned on, a given parameter was varied and its effect on the other system parameters was measured. The signals measured were either slow-varying dc (e.g., cold temperature) or primarily

single-frequency ac (at the operating frequency) with a large amount of noise and higher harmonics

(e.g., piston motor current). To measure the former, a dc voltmeter was employed, and the

RESISTIVE HEATiWQ ELEMENT REDUNDANT SILICON DIODE SENSORS

REDUNDANT TFD'S

AXIAL POSITION SENSOR

VACUUM STATION

WATER COOLER

1 ACCELEROMETER

WATER COOLER OUT

TFD TEMPERATURE SENSORS ALONG

HOUSING

Figure 4. Schematic representation of refrigerator under test.

86
measured quantity was considered stable when no notable change was observed for about 5 min. The

latter was measured with instruments employing one of three standard signal processing techniques:

heterodyning with the input reference oscillator used for locking, rms averaging of spectra

obtained from a Fast Fourier Transform routine, or time averaging of signals obtained from a high-speed data acquisition system. In this paper, db is defined as 20 log (quantity) , the normal

mode for the equipment employed. Measured data points are noted; curves are computer-generated

using either a linear or polynomial least-squares routine.

5 . Axial Control System

As an aid to understanding how parameters can be varied during refrigerator use, the

operation and accuracy of the axial control system will be discussed next. A block diagram of the

control system is shown in figure 5. The piston amplitude, displacer amplitude, frequency, and

piston/displacer phase angle are set with dc voltages which are adjusted at the control panel.

The frequency and phase control electronics employ local feedback loops to maintain the accuracy

of the reference signals for the displacer and piston closed loop position servomechanisms in

spite of component drifts. The reference signals are amplitude-controlled sinusoids with less

than 0.1% harmonic distortion. The reference signal to the piston lags the signal to the

displacer, producing the desired piston/displacer phase angle. The two closed loop position

servomechanisms then control the motions of the piston and displacer with a high degree of

accuracy and low harmonic content.

Although the closed-loop position servomechanisms for the piston and displacer look similar

in figure 5, they are considerably different because of the extreme dissimilarities in the

frequency response of their motor and system dynamics. The displacer, as the measured dynamics of

figure 6 indicates, is nearly a pure inertial load. (The additional rolloff which begins at 200

Hz is from filtering the axial position sensor). Principally, the force produced by the motor

serves only to accelerate and decelerate the mass. Since the motion is sinusoidal, with the

displacer returning to its axial center position after each half cycle, there is no net

displacement and no work is done. The mechanical output power is reactive (power factor of 0),

SET POINTS

( D C. VOLTAGES)

PISTON AMPLITUDE

<V>

REFERENCE

SIGNALS ERROR

SIGNALS

DISPLACER AMPLITUDE

OPERATING FREQUENCY

(w)

PHASE BETWEEN

PISTON AND

DISPLACER MOTIONS

! j DRIVE* _

PISTON MOTOR

CURRENT

FREOUENCY

AND PHASE CONTROL

ELECTRONICS

ycos (wt- $ DR , VE ) PISTON PISTON MOTOR

DRIVER COMPENSATOR

ELECTRONICS

PISTON SERVOMECHAMSM

PISTON MOTOR

AND SYSTEM

DYNAMICS

PISTON

AXIAL POSITION TRANSDUCER

x cos (wt)

DISPLACER MOTOR

CURRENT Or

DISPLACER COMPENSATOR

ELECTRONICS

DISPLACER MOTOR

DRIVER

DISPLACER SERVOMECHANJSM

DISPLACER

AXIAL POSITION « TRANSDUCER

DISPLAOER MOTOR

AND SYSTEM

DYNAMICS

OUTPUT

SIGNALS

PISTON

POSITION

DISPLACER

POSITION

Figure 5. Block diagram of axial control system.

87
and therefore, the electrical input power to the motor is only the ohmic loss dissipated in having

to produce the required force. Ignoring the inductive reactance, therefore,

Pd = Id

2 % = w4 x2 Rd/Kd

2 (4)

where Pd = average electrical input power to displacer motor (W)

Id = current in displacer motor (A)

Rd = motor armature resistance (ft) Kd = motor force constant (N/A) (i.e., Force = Kdld)

The piston, on the other hand, is designed to resonate on the gas spring of compression (the

effective "spring" of gas being compressed in a closed cylinder) which leads to highly efficient

electromechanical operation. Its motor and system dynamics, as shown in the measured dynamics in

figure 6, has a spring-mass resonance characteristic (along with the position sensor filtering).

The reactive inertial force is balanced by the reactive gas spring force, and the motor only

produces a real (as opposed to reactive) force term which supplies the required mechanical input

power to the thermodynamics (power factor of 1). The electrical input power to this motor can thus be separated into two terms s one resulting from supplying the real mechanical input power to the thermodynamics (Equation 2 above) and one relating to the balanced reactive inertial power and

gas spring power. For normal operation, the piston is in resonance and the net reactive power is

zero; however, for the parametric tests discussed here, the piston does come out of resonance

slightly.

FREQUENCY (Hz)

Figure 6. Frequency responses - displacer and

piston motor and system dynamics.

The dynamics of a gas spring are different from those of a mechanical spring in two important

respects. First, the damping in a gas spring is generally higher than in a mechanical spring.

Thus, power is dissipated at resonance which must be supplied by the linear motor, and the quality

factor (Q) of the system is low. Second, because of flow losses and leakage past the compression

seal, the stiffness of the gas spring is a function of frequency and is slightly nonlinear (i.e.,

it has some higher harmonic components). These disadvantages of the gas spring are outweighed by

the advantage of having a spring for resonance with no mechanical contact, no danger of fatigue

failure and no possibility of fracture.

88
The harmonic operation of the displacer axial control system is illustrated in figure 7a.

The system applies current to produce the displacement at the operating frequency (26 Hz) shown in

the figure. Power at higher harmonics of the operating frequency is also applied to reduce the

harmonic content of the displacement. The amount of rejection of these higher frequencies is

determined by the gain of the control system. As discussed in Reference 2, the bandwidth of the

displacer control system is 105 Hz, which implies that there is some control system gain at the

third harmonic (about 78 Hz). Note in the figure that the second harmonic is 31 dB below the

fundamental.

Similarly, the harmonic operation of the piston axial control system is illustrated in figure

7b. The control system bandwidth is 65 Hz, which implies that there is no control system gain and

thus no rejection of the third harmonic (the third harmonic content of the displacement is small,

however, because of dynamic characteristic of the gas spring) . It should be noted that the piston

operates at its resonant point with high accuracy (small error in the control loop) because of the

high open-loop gain at that frequency (see Ref. 2).

-7 0*

2 24mm RMS

(3.2mm PEAK)

13 9*

4 95mm RMS

(7 Omm PEAK)

— -18.5*

1 18mm RMS

10 20 30 40 50 60 70 80 FREQUENCY (Hz) FREQUENCY (Hz)

(a) Displacer. (b) Piston.

Figure 7. Frequency spectrum - displacer and piston displacement.

The low harmonic content of the displacements in the figure means that the assumption of

sinusoidal volume variations discussed above is valid. For the most part, the variations in input

and output power for different operational parameters are therefore approximated well by Equations

1 and 2.

6. Parametric Test Results

6. 1 Heat Load

The variations of output (cold) temperature and of electrical input power to the motors with

changes in the load power (ie. the power in the resistive heater mounted on the cold finger) are shown in figure 8. The parameter values that were held constant for this test and for all those

that follow are listed in appendix A. As expected, as the applied load power increases, so does

the cold temperature. It should also be realized that "no applied load" is not the same as zero power output since there are always parasitic loads on the cold finger. Even with the resistive

heater off, heat is being radiated from the inner surface of the vacuum Dewar which encloses the

cold finger and is being conducted down the wires which connect the temperature sensors and the

resistive heating element, as well as down the body of the cold finger itself. These parasitic

loads account for the non-linearity of the temperature line at low applied power.

The electrical input power to the linear motors drops as the applied load power increases.

This can be explained by referring to Equation 3 above (n = Te/(TC- Te ) ) and by examining

89
several losses. The thermodynamic efficiency of the refrigerator increases as the temperature of

the cold finger (Te ) increases. Thus, although the applied load on the cold finger is higher,

the refrigerator can cool this load using less electrical input power because of the increased

efficiency of the cycle. (The overall measured efficiency — applied load power/electrical input

power to the piston and displacer motors — is shown versus applied load power in figure 9.) Also,

the radiation and conduction losses decrease as the temperature of the -cold finger increases

(since there is less of a temperature difference between the cold finger and ambient). Finally,

the flow losses decrease because the gas density decreases with the increase in average

temperature of the refrigerator (flow friction for turbulent flow is a function of density). This

last effect is very small.

Figure 8. Cold temperature and electric Figure 9. Overall measured efficiency

input power to motors vs. applied ( % of Carnot ) vs. applied load power,

load power.

It should be noted that the operating parameters of the refrigerator (strokes, frequency,

phase, etc.) were not varied for this test. It is possible to produce the off-design cold outputs

(i.e., other than 5 W at 65°K) with less electrical input power than given in figure 8 by

optimizing these parameters appropriately. Such multi-parameter tests were beyond the scope of

this paper. It should also be noted that this test and the heat rejection temperature test which

follows are the only ones in which the cold temperature was allowed to vary. In all others, the

applied load from the resistive heating element was adjusted to maintain a constant 65°K

temperature on the cold finger.

6.2 Operating Frequency

Figure 10 shows the variation of applied load power (cold production) and electrical input

power to the motors with changes in the operating frequency. Several effects contribute to the

shape of these curves. First, it can be seen from Equations 1 and 2 that both the ideal cold

production and the ideal mechanical input power to the Stirling cycle vary linearly with operating

frequency ( since both are proportional to the number of times that the p-v curve is traversed per

unit time) . Secondly, many losses such as those due to flow and to imperfect regeneration are functions of gas velocity and therefore of operating frequency. Some losses, such as that caused

by the fluid friction of the flowing gas or that resulting from the temperature oscillation of

local sections of the regenerator package over a cycle ( since the transfer rate between the gas

and the regenerator is finite), increase with increasing frequency. Others, such as the clearance

seal leakage decrease with increasing frequency. Finally, as discussed, the nature of the

displacer and piston motor and system dynamics means that the magnitude and phase of the input

power for each are functions of the operating frequency.

90
For the small range of frequencies considered, the motor and system dynamics produce by far

the most significant effect. The displacer motor input power increases as the fourth power of the

operating frequency, as noted in Equation 4 and the piston power has a resonant mass-spring

characteristic (with some nonlinear effects produced by the gas spring) . The sum of these two

effects determine the shape of input power variations noted in figure 10. The variation of piston

and displacer motor force with operating frequency is shown in figure 11. The displacer motor

force varies approximately as the square of the operating frequency as would be true of the purely

inertial system, and the piston motor force exhibits the spring-mass characteristic (minimum force

at resonance) . From this, it is also apparent that the system dynamics dominate the response and

any change in the losses is not significant.

OPERATING FREQUENCY (Hz) OPERATING FREQUENCY (Hz)

Figure 10. Applied load power and electrical Figure 11. Displacer motor force and

input power to motors vs. operating frequency. piston motor force vs. operating frequency.

Again, some caution should be exercised in interpreting this data. Since this is a test in

which only one parameter is varied, conclusions can not be drawn about what is the best frequency

at which to operate the refrigerator. Both the mean charge pressure and the piston/displacer

phase affect the resonant frequency of the gas spring to some degree. The "optimum" operating

frequency must take all such effects into account.

6.3 Piston/Displacer Phase

Figure 12 shows the variations of applied load power and electrical input power to the piston

and displacer motors as a function of the piston/displacer phase. For the ideal cycle, the load

power and electrical input power should vary as the sine of the phase (see Eqs. 1 and 2). This is

the approximate shape of the curves in figure 12. The piston/displacer phase also influences flow

losses and the piston gas spring resonance to a lesser degree. These effects are more easily

observed in the variations in the piston and displacer motor force shown in figure 13. The

z

tro

o

PISTON / DISPLACER PHASE (DEGREES) PISTON/DISPLACER PHASE (DEGREES)

Figure 12. Applied load power and electrical input Figure 13. Displacer motor force and piston

power to motors vs. piston/displacer phase. motor force vs. piston/displacer phase.

91
displacer motor force shows the effects of the flow losses; the piston force shows the change in resonance. From the figure, it should be noted that the variations in force are less than + 10%.

6.4 Displacer Amplitude

The variations of applied load power (cold production) and electrical input power to the

piston and displacer motors with displacer amplitude are shown in Figure 14. For the ideal cycle,

the applied load power is proportional to displacer amplitude (Eq. 1). Several losses, however, are functions of displacer amplitude; the most notable is one associated with the regenerator,

referred to as shuttle loss. As the displacer moves, the regenerator passes over different

portions of the housing. As a result, there is a mismatch between the temperature gradient along

the housing wall and the temperature gradient along the regenerator, and the mismatch increases

for increasing amplitudes of oscillation. This mismatch results in heat transfer between the

displacer and the housing walls and thus a loss.

Another important effect in this test and in the one which follows relates to the variation

in refrigerator dead volume. The designation 'dead volume' is given to those regions in the

working space of the refrigerator which do not change in volume as the displacer and piston move

(i.e., do not participate in the thermodynamic cycle (Fig. 15)). Dead volume includes the heat

exchanger space, connecting passages, and the unfilled space in the regenerator. Relevant to this

test, dead volume also includes those regions in the expansion and compression space which are not

swept by the peak amplitude of the displacer motion.

J APPLIED LOAD POWER / • ELECTRICAL M=UT POWER /

Z

H250 Q.H °E

, or in

ui a. ?S

z> a.

Cl hi z o I - <

_l -I < 0- o <2 &8

Figure 14. Applied load power and electrical

input power to motors vs. displacer amplitude.

1.5 2 0 2.5 3 0 3.5 4 0 DISPLACER AMPLITUDE (mm)

COMPRESSION

SPACE k PEAK OF PISTON DEAD VOLUME AMPLITUDE

DISPLACER AMPLITUDE

CONNECTING

DUCT

EXPANSION SPACE

DEAD VOLUME

REGENERATOR

DEAD VOLUME HEAT EXCHANGER

ACTIVE COMPRESSION

SPACE

Figure 15. Schematic of dead volume (shaded).

(Clearances are out of proportion for clarity)

.

92
A discussion of dead volume is given in Appendix B of Reference 2. For this paper, several

comments will suffice. In general, dead volume reduces the cold production of a refrigerator.

Often, it also reduces the required mechanical input power so that the refrigerator efficiency

remains roughly constant. The magnitude of the effect of a given region of dead volume on the

cold production or mechanical input power depends on the absolute temperature of that region. The

colder the region, the greater the effect.

The electrical input power to the piston motor versus displacer amplitude is shown in figure

16. Since the displacer amplitude has little effect upon the gas spring resonance, the electrical

input power to the piston motor is only that which is required to do the thermodynamic work. For

the ideal cycle (Eq. 2), the mechanical input power required by the thermodynamics is proportional

to displacer amplitude. The piston must also supply the work required to overcome the shuttle

loss. Further, from the above discussions about dead volume, the mechanical input power should

also be inversely proportional to the displacer amplitude (i.e., the mechanical input power

required from the piston should decrease as the displacer amplitude increases because the dead

volume decreases and this effect is independent of Eq. 2). In figure 16, the electrical input

power to the piston motor varies approximately as the square of displacer amplitude.

Figure 16. Electrical input power to Figure 17. Displacer motor force and

displacer motor and to piston motor vs. piston motor force vs. displacer amplitude

displacer amplitude.

Consider now the electrical input power to the displacer motor versus displacer amplitude in

figure 16. Since the displacer is an inertial load, the electrical input power is expected to vary as the square of the displacer amplitude (Eq. 4), as observed. Figure 17 which shows the

variation of displacer motor force with displacer amplitude, also varies 'linearly, as expected for

an inertial load.

6.5 Piston Amplitude

The change in applied load power and in electrical input power to the piston and displacer

motors with piston amplitude is shown in figure 18. For the ideal cycle (Eqs. 1 and 2), the

applied load power and electrical input power are proportional to piston amplitude. This

characteristic was indeed observed. Flow losses and the effects of dead volume both change with

piston amplitude tending to cancel. The flow losses increase with increasing amplitude because

the peak oscillating pressure and volumetric flow rate increase as more volume is displaced by the

piston. The dead volume decreases by the amount above the piston in the compression space as the

piston amplitude increases (Fig. 15 above). As discussed, this dead volume effect is minimized

because the volume is at the temperature of the ambient heat exchanger (warm).

93
An elegant characteristic for potential users of this refrigerator is illustrated by the

linearity shown in Figure 18. If, for any reason, it is desirable to hold the cold temperature

constant as the load varies, then piston amplitude provides a very effective means. A control

system can be designed to measure cold temperature and adjust piston amplitude to hold the

temperature constant (leaving all other operating parameters - displacer stroke, frequency, phase,

etc. - fixed). Since the characteristic in Figure 18 is linear over a wide range, such a control

system would be trivial to construct.

Figure 19 shows the variations in the force produced by the piston and displacer motors with

piston amplitude. It is apparent from the linear nature of the piston force curve that the piston

amplitude minimally affects the resonance of the gas spring.

4 5 6 7 8

PISTON AMPLITUDE (mm)

Figure 19. Displacer motor force and piston motor

force vs. piston amplitude.

94
6.6 Mean Pressure

A pressurized bottle of helium was connected to the refrigerator via a pressure regulator and

pressure gauge. For the following test, the mean pressure in the refrigerator was varied by

adjusting the pressure regulator, while all other operational parameters were held constant

(Appendix A) . The mean pressure was measured with the pressure gauge, and sufficient time was allowed for the pressure in the refrigerator to stabilize for each measurement data point. The

variations of applied load power and electrical input power to the piston and displacer motors

with mean pressure are shown in figure 20. For the ideal cycle (Eqs. 1 and 2), these variations

are expected to be proportional to mean pressure and, for this small change in pressure (± 1 0%),

this was observed.

Flow losses and regenerator losses are functions of pressure. Flow losses increase with

pressure (density) because the flow is turbulent. This effect is small as shown by the small

change in displacer motor force with mean pressure in figure 21 . The regenerator becomes less

efficient as the heat capacity of the gas increases with pressure (density) but this effect is

also small for the small range of pressure variations used in the test and the relatively high

cold temperature of this refrigerator (on an absolute scale). The mean charge pressure also

Figure 20. Applied load power and electrical input power to motors

vs. mean pressure.

Figure 21. Displacer motor force and piston motor force vs. mean pressure.

95
determines the resonance of the gas spring and thus affects the electrical input power to the

piston motor. The required motor force changes linearly with the mean pressure, again making the

effect small for this range of variations tested.

6 . 7 Heat Exchanger Temperature

As discussed in Section 4 above, the temperature of the ambient heat exchanger is controlled

with a closed-cycle water cooler. The water is circulated through a water jacket which surrounds

the heat exchanger and returned to the reservoir of the cooler. The cooler has heating and

refrigeration capabilities; the temperature of the water in the reservoir is determined by the

set point of the thermostat on the water cooler. For the following test, the set point of the

water cooler thermostat was varied, and all other operational parameters were held constant. The

temperature of the water at the inlet of the water jacket was measured with a thin-film detector

(TFD). Since the heat exchanger is not perfect, the temperature of the gas in the heat exchanger

was considerably higher than the temperature of the water at the inlet. The gas temperature was not measured directly; however, it has been estimated to be about 15°C higher than the

temperature of the water.

The variations in cold temperature and electrical input power to the piston and displacer

motors with heat exchanger temperature are shown in figure 22. The cold temperature is

proportional to the heat exchanger temperature, with a 3

0 K [3°C] change in heat exchanger

temperature producing an approximate 1 °K change in cold temperature.

235

HEAT EXCHANGER TEMPERATURE (°C)

Figure 22. Cold temperature and electrical input

power to motors vs. heat exchanger temperature.

The small change in electrical input power to the piston and displacer motors for changes in

heat exchanger temperature is to be expected since there is only a negligible change in the

efficiency of the refrigerator. Considering the ideal efficiency (Eq. 3), although the numerator

increases because the cold temperature (Te ) increases, the denominator (Tc

- Te ) also

increases because of the difference between the cold temperature and heat exchanger temperature

increases. There is also some net cancellation in the losses. Insulation losses and conduction

losses between the room ambient and the cold finger (such as along the electrical leads to the

temperature sensor and to the resistive heating element) decrease because the temperature of the

cold finger increases. At the same time, conduction losses between the cold finger and the heat

exchanger (i.e., along regenerator and cold finger housing) increase because the temperature

difference increases. Also, there is a small decrease in flow losses because the gas density

decreases as the average temperature of the refrigerator increases (the flow is turbulent, making

the loss a function of density)

.

96
7. Life Testing

On August 30, 1984, the refrigerator exceeded 11,000 hours of operation at the nominal

operating point of 65 "K with a cold production of 5 Watts and continues to operate without

problems. During this time, the refrigerator was stopped and restarted over 300 times. The cold

temperature (along with several other operational parameters) is being measured with a digital

data acquisition system. Measurements are taken every 30 minutes using a sampling frequency of 1 kHz. The samples are averaged over 2 seconds to reduce noise. As of this date, no temperature

degradation has been observed to the accuracy of the silicon diode sensors (0.1°K). With the

constant cold production, the cold temperature is also measured to be stable within + 0.2 e K (i.e.,

temperature fluctuations including noise induced by the silicon diode thermometer are also about

0.1°K). During this period, the refrigerator has never had to be disassembled for maintenance or inspection.

The electro-magnetic bearings along with their radial position sensors are left on continually even if the refrigerator is not operating or is undergoing tests. As of August 30,

1984, the bearings have logged over 21,000 hours of operation.

A small helium leak (approximately 1 psi per day) due to a manufacturing error has developed

in one of the housing flanges. A technique to weld the flanges shut, which is proposed for the

final version of the refrigerator and which was successfully demonstrated in a test fixture, was

not used in this refrigerator. The helium loss is presently being compensated from a helium

bottle.

The electronics which control and drive the refrigerator use only commercial parts (instead

of space qualified parts) and no redundancy was attempted. Twice during the life test, a commercial electronic part failed. In both cases, the safety interlock system responded correctly

and safely shut down the machine. The failed part was replaced and the life test continued. The

final version of this refrigerator for actual spaceborne deployment will use space qualified,

redundant electronics.

8 . Conclusions

A novel feature of this refrigerator, namely full electronic control of the motion of its

moving parts, was utilized to characterize its capabilities under parametric changes. The

characterization is useful both for designers of the next generation of the refrigerator and for

potential users. Designers have both an indication of the accuracy of their "optimal" design

point and a determination of the tolerance of the design point to changes in operational

parameters. Potential users have an indication of the operation of the refrigerator under

off-design conditions which will broaden the range of potential applications.

Some care must be taken in the interpretation of results. In each test only one parameter

was varied and its effect was measured. The data shows the quantitative influence of the

parameter on the operation of the refrigerator. In general, however, the effect of each parameter

is not independent, and thus the combination of two test results will not show the combined effect

of varying the two parameters. This also means that more "optimal" off-design operating points

than those shown in this paper generally exist, These off-design points are achieved by varying

more than one parameter, depending on the operating point desired.

In spite of the limited scope of this work, the versatility of this refrigerator must be

appreciated both as a tool for understanding the Stirling cycle and as a general instrument for a wide variety of cryogenic applications. The capability of having parameters electronically

controlled and able to be changed in operation, which made this study possible, sets this design

apart from refrigerators built in the past.

This work was supported by the NASA Goddard Space Flight Center (Contract No. NAS5-25172).

97
Appendix A

The following table lists the values for the refrigerator operating parameters which were held constant during each test. As mentioned above, these values were chosen so that the

parameter which was varied could have the largest possible excursion.

Tests

6.1 6.2 6.3 6.4 6.5 6.6 6.7

Disp. Pist. Mean Re j

.

Parameters Load Freq

.

Ampl

.

Ampl

.

Pres

.

Temp

.

Cold Temperature (°K) var 65 65 65 65 65 var

Load Power (W) var var var var var var 5 Operating Frequency (Hz) 25 var 25 25.5 25.5 25 25.5

Piston/Displ Phase (°) 67 67 var 67 67 67 66

Piston Amplitude (mm) 7.3 7.1 7.3 7.0 var 7.2 7.0

Displacer Amplitude (mm) 3.0 3.0 3.0 var 3.0 3.0 3.0

Mean Pressure (psig) 220 241 220 253 245 var 248

Ambient Heat Exchanger

Inlet Temperature (°C) 10.9 9.3 10.9 10.6 10.7 10.0 var

Piston Case Water Jacket

Inlet Temperature (°C) 20.3 17 19.1 16 16 15 16

References

[1] A Magnetically Suspended Linearly Driven Cryogenic Refrigerator, by F. Stolfi, M. Goldowsky,

J. Ricciardelli and P. Shapiro, Proceedings of the Second Biennial Conference on Refrigeration for Cryogenic Sensors and Electronic Systems, Greenbelt, Md, December 1982.

[2] Philips Laboratories, Division of North American Philips Corp., Design and Fabrication of a Long-Life Stirling Cycle Cooler for Space Applications, Phase I and II - Engineering Model,

Final Report: Sept. 1978 - Dec. 1982, by F. Stolfi, M. Goldowsky, C. Keung, L. Knox, E. Lindale, R. Maresca, J. Ricciardelli, P. Shapiro, NASA contract NAS5-25172, Briarcliff

Manor, N.Y., March 1983.

[3] Philips Laboratories, Division of North American Philips Corp., Final Report for Parametric

Testing of Engineering Model Refrigerator, by F. Stolfi, NASA contract NAS5-26688,

Briarcliff Manor, N.Y. , February, 1984.

98
DESIGN OF A FLIGHT QUALIFIED

LONG-LIFE CRYOCOOLER

L. Knox, P. Patt, R. Maresca

Philips Laboratories

A Division of North American Philips Corporation

Briarcliff Manor, NY 10510

This paper describes a second generation Stirling cycle cryogenic

refrigerator with a linear drive, magnetic bearings, and clearance seals,

designed to produce 5 watts of cooling at 65 Kelvin and to meet Space Shuttle

mission requirements. The first generation refrigerator (Engineering Model)

met all performance specifications, and has operated with no failure for over 12,000 hours. It was not, however, intended to meet launch requirements.

Meeting those requirements necessitated improvements in the electromagnetic

bearings, the radial position sensors, and in the structural design of the

moving elements. As in the first generation refrigerator, organic

contamination has been eliminated by the use of all metal and ceramic

construction. Reductions in system input power have also been attained by an integral magnetic spring/motor for the displacer and by more efficient linear

motors and drive electronics. At the design point, the refrigerator consumes

140 watts, delivered by the system electronics.

Ferrite variable reluctance position sensors reduce the temperature

drift of the magnetic bearing system. Additional bearing improvements are realized through increases in gas film damping, ac/dc force capabilities, and

structural resonant frequencies. All clearance seal surfaces are specially

treated to eliminate potential damage due to contact during launch and system

failures. Transmitted vibrations are minimized by a six-degree-of-freedom

spring mount.

The work summarized in the paper is being supported by the NASA-Goddard

Space Flight Center. (Contract Number NAS5-26688)

Key words: Clearance seal; cryogenics; ferrite sensors; gas film damping;

launch vibrations; linear motor; magnetic bearings; magnetic spring; Stirling

cycle.

1. Introduction

A long-life refrigerator capable of providing 5 watts of cooling at 65 Kelvin has been

successfully designed, fabricated, and tested by Philips Laboratories. [1] Long life was achieved

by eliminating wear and working gas contamination. Wear was prevented by use of magnetic bearings

and clearance seals. The working gas volume is hermetically sealed from all organic materials

used in the construction which prevents degradation due to outgassing. The details of this

refrigerator are described in earlier papers; parametric and life test results are presented in a companion paper[2],

A refrigerator of this type is expected to be part of a complete satellite structure which

will be launched into space on the Space Shuttle. However, the ability to survive launch

99
vibrations was not considered in the first generation 'proof of concept' design. Analysis of the

expected launch vibrations indicated that the first generation magnetic suspension system could

not be modified to accommodate those produced by the shuttle. The second generation design

considers these vibrations and is capable of suspending all moving elements during launch and

normal operation.

This paper describes the vibration analyses performed and the design revisions which were made to accommodate the vibrations. Several cooler component improvements are "also described in this paper.

2. System description

The second generation refrigerator, the Flight Prototype described here, is a single stage,

moving regenerator Stirling refrigerator. The piston and displacer/regenerator are linearly

reciprocated within a cylindrical housing and radially supported with active magnetic bearings. A brief overview of system construction and operation is presented in this section. A detailed

description of the theory of operation of this cooler is available in earlier reports.

The cooler is comprised of a compressor and an expander section (fig. 1). The expander

section contains the moving displacer/regenerator and the cold and warm side heat exchangers. The

compressor section contains the compressor piston, piston linear motor and gas buffer volume. The

piston and displacer are supported by the magnetic bearings, three of which also form clearance

seals. Two seals direct the gas flow in the expander section during the cycle; the third seals

the compression volume above the piston.

Gas at the cold end expands (i.e. cools) as the piston retracts and increases the total gas

working volume. The expanding gas cools the aluminum slit cold end heat exchanger. The heat load

is cooled by a thermally conductive cable (not shown) attached to the cold end heat exchanger.

The cable minimizes the transmitted mechanical vibrations. The heat exchanger is stationary and

supported with a long thin walled tube, or cold finger. In the next phase of the cycle, the

displacer moves toward the cold end. The clearance seal forces the gas through the regenerator

where it is warmed. As the piston moves toward the cold end, the heat of compression is rejected

through another slit heat exchanger in the expander section housing. Finally, the displacer moves toward the compressor end cooling the gas as it flows through the regenerator thus completing the

cycle. These discrete motions are approximated by continuous sinusoids, where a phase angle

describes the relative timing between the displacer and compressor motion.

The piston (compressor) is reciprocated with a moving magnet linear motor, similar to that

used in the Engineering Model. The current to the motor, and therefore the piston motion, is controlled with a low frequency, high efficiency pulse-width-modulated current driver system. The

displacer is reciprocated with a novel integrated magnetic spring/linear motor. The phasing is controlled via the system electronics. The displacer spring/motor and the pulse-width-modulated

piston motor drive system is described in more detail in a latter section of this paper.

Primary design parameters (such as piston and displacer diameter, strokes, frequency, and

radial clearance to the stationary walls) were determined by considering the overall system

dynamics. Trade-offs result among system dynamics, thermodynamic losses (primarily conduction),

and difficulty of construction (such as clearance seal machining tolerances). The Philips

Stirling cycle model was used to develop an optimal design meeting all the design criteria.

Since launch conditions are the primary new considerations in this second generation design,

a description of the various vibration analyses is provided in the next section. Other component

level improvements such as new reluctance radial position sensors with excellent temperature

stability, and an integrally formed aluminum/titanium cold end heat exchanger are described

following the vibration section. Finally, primary system design parameters and predicted

performance levels are presented in the last section.

3. Vibration considerations

The Engineering Model refrigerator demonstrated the concept of using magnetic bearings and

linear drive methods to obtain long-life operation. The Prototype refrigerator described in this

paper will demonstrate these concepts in actual space-qualified hardware. As part of this effort,

the refrigerator dynamics were modelled to determine the effect of launch vibrations and the

design was tailored to achieve an acceptable system response.

100
I I STATIONARY HARDWARE (TITANIUM)

|Y : j MOVING HARDWARE (TITANIUM) SOFT MAGNETIC MATERIAL f~~l HARD MAGNETIC MATERIAL

ffi MAGNETIC BEARINGS Q RADIAL POSITION SENSORS

E><] MOTOR DRIVE COILS

\-t 4/\ REGENERATOR

HELIUM GAS

PASSAGE

WARM END

HEAT EXCHANGER

COLD END SLIT HEAT EXCHANGER

ALUMINUM

COLD FINGER

VACUUM DEWAR J BEARING COIL WELDABLE FLANGE

7m

FEEDTHRU

b.

Figure 1. Refrigerator sectional lay-outs

a. Expander (displacer) section

b. Compressor (piston) section

101
3.1 Refrigerator dynamics

The contiguous surfaces in the clearance seals are the area most susceptible to vibrational

damage. If the ultra-clean titanium surfaces of the clearance seals come in contact, potentially

catastrophic failure in the form of galling is possible. Magnetic bearings accurately center the

shafts within the bores thus maintaining the non-contact operation of the clearance seals. The

vibration analyses are focused on determining the bearing performance required to maintain

non-contact support during launch. The launch vibrations are described by three independent specifications; random, acoustic, and quasi-static. The analyses for each of these excitations

fol low.

The bearing performance requirements can be determined from the solid-body vibration amplitudes of the refrigerator. For this purpose, simple first and second order models are sufficient.

Forces are transmitted to the refrigerator through the isolation mount (fig. 2) and by acoustic

coupling directly to the housing. The vibration amplitudes are calculated assuming a lumped

spring-mass system model (fig. 3).

Figure 2. Refrigerator isolation spring mount design

The random vibration specification is a power spectral density (PSD) function describing the

random vibrations of the shuttle mount surface. PSD is a statistical method of describing the

frequency content of random signals. The vibration amplitude PSD is determined via the given

acceleration PSD and the calculated inertial transfer function. The random vibration

specifications and the resulting refrigerator vibration PSD function are shown in figure 4. The

mounting surface vibrations are effectively filtered by the 7.0 Hz isolation spring mount. The

resulting solid-body RMS vibration amplitude is 17 urn with most of the vibration energy contained

below 45 Hz.

Acoustic sound energy also induces vibrations in the refrigerator. The pressure difference

across the refrigerator produces a net force on the housing. In general, the force on a cylinder

perpendicular to a 2-D pressure field is

2tt F = A / P(e) cos(e) de (1)

o

102
MODEL

REFRIGERATOR

MASS

VIBRATION

ISOLATION

MOUNT

a REFRIGERATOR MOTION

* (POWER SPECTRAL DENSITY)

////// I A SHUTTLE VIBRATIONS

(POWER SPECTRAL DENSITY)

VIBRATION TRANSMISSION

1.0

Figure 3. Random vibration lumped spring-mass system model

where A is the cylinder radius and P(e) is the pressure distribution over the cylinder surface.

Assuming a sinusoidal plane wave, the peak force is

F

=

(2:

where P 0

is the peak pressure, w is the angular frequency of the pressure wave, c is the speed

of sound in air and E is defined to be

E =1 { J Q

2 (ka) + J22 (ka) + Y Q2 (ka) + Y

2

2 (ka) - JQ

(ka)J

2 (ka) - YQ

(ka) Y

2 (ka) } (3)

where k = 2tt/x

respectively.

and J and Y represent the Bessel functions of the first and second kind

The acoustic coupling is maximum when the housing diameter is 40% of the sound wavelength.

The coupling decreases monotonical ly at higher and lower acoustic frequencies. Using this model

and the acoustic sound pressure specifications shown in figure 5, the refrigerator RMS vibration

amplitudes are determined to be less than 2.0 ym. The vibration energy is centered at 40 Hz and

is negligible above 100 Hz.

NASA utilizes a third specification to include the effects of shock loads, mount

amplification, and launch uncertainty. This specification is termed "Quasi-Static Loading" and is by far the most severe of the three specifications on the refrigerator design. This data was compiled from previous flights and represents the maximum acceleration levels measured on devices

with similar isolation mounts.

103
.015

2<

DC

_l

UJQ

O<

-30

SHUTTLE VIBRATIONS

REFRIGERATOR VIBRATIONS

-50 db/dec

20 120 450 2,000

FREQUENCY (Hz)

VIBRATION LEVELS

ACCELERATIONS .014 g's rms (20-45 Hz)* DISPLACEMENTS 1 7.0 jum's rms (20-30 Hz)*

* Note: Bandwidth containing 85% of energy

Figure 4. Space shuttle random launch vibrations:

specifications and refrigerator vibrations

i

5 1.0 E11

SOUND PRESSURE LEVEL DURING LAUNCH

_i 1—iiiii

100 1000 FREQUENCY (Hz)

Figure 5. Sound pressure level during launch

104
The specification describes the vibrations during the three launch phases: lift-off,

transonic/maximum aerodynamic pressure, and ascent. Each phase has an ac and dc acceleration

component which is applied to the refrigerator simultaneously in three orthogonal axis for a specified duration. The isolation mount frequency determines the ac acceleration specifications;

the design frequency of 7.0 Hz yields the specifications presented in table 1.

Table 1. Quasi-static launch vibrations

D.C. A.C. Vibration

Occurrence Acceleration Acceleration Duration

(g's) at 7.0 Hz (g's) (seconds)

Lift-off 1.5 5.4 20.

Transonic/Maximum 3.0 2.7 10.

Aerodynamic Pressure

Ascent 3.2 0. 100.

Meeting these specifications requires either improvements in the magnetic suspension system

to totally prevent contact or changes to the titanium surfaces to permit limited contact during

launch. The following design changes improve the suspension system performance. In addition,

surface treatments will improve the clearance seals to permit limited contact during launch.

3.2 Design changes

The Engineering Model magnetic bearing stiffness must be improved 60-70 d B to avoid

contact during launch. The magnetic bearings are controlled by a closed-loop control system which

monitors the shaft position and excites the appropriate electromagnets to center the shaft. The

achievable open-loop gain of the control system, which determines the apparent bearing stiffness,

is limited by the shaft dynamics. The 70 dB gain improvement was demonstrated in a test fixture

with a solid (rigid) shaft. Thus, if the shaft dynamics can be improved sufficiently, the

refrigerator will withstand the launch vibrations.

The design changes made to improve the shaft dynamics are presented in table 2. The goal is to increase any resonant frequencies beyond the desired control bandwidth and to increase the

system damping. The increase in diameters, shorter lengths, and decreased suspended mass all increase the resonant frequencies. The system damping is improved by decreasing the radial

clearance in the clearance seal. This cylindrical annulus is filled with the working gas and acts

as a viscous dashpot as the shaft moves radially. Decreasing the clearance 25% will double the

damping forces. These changes result in the dynamics presented in table 3. These improvements

are sufficient to achieve the required bearing stiffness.

Table 2. Design changes to improve shaft dynamics

Engi neering

Model Prototype

• Increase stiffness

Displacer diameter (cm) 2.0 3.16

Piston diameter (cm) 3.68 4.45

Cold finger diameter (cm) 2.15 3.31

Piston wall thickness (cm) 0.26 0.57

• Increase damping

Clearance seal gap (um) 25. 17. Clearance seal length (cm)

Piston 4.0 8.0

Displacer 2.5 5.0

• Minimize cold finger suspended mass

Heat exchanger material Copper Aluminum

105
Table 3. Improved shaft dynamics

Engineering

Model Prototype

Squeeze film damping breakpoint (kHz)

Piston 2.5 50-85

Displacer 0.7 45-155

First bending resonances (Hz)

Piston 400 900

Displacer 840 1800

The clearance seal surfaces will be treated with titanium nitride to improve the wear properties. This provides additional protection to the clearance seals and minimizes the chance

of catastrophic failure should the surfaces come in contact during launch. Various surface

treatments were investigated. Clearance seal samples were coated and subjected to the launch

vibrations. The surfaces were analysed microscopically. The samples were subjected to increased

vibration amplitudes until excessive wear occurred. The treatments tested and the relative

performance data are presented in table 4.

Table 4. Surface treatment evaluation results

Shaft Surface Acceleration

Number Treatment level (g's) Results

A.C. D.C.

0 none 3 5 Severe fretting & abrasion

1 TiN plated 3 5 No degradation

1 TiN plated 10 25 Fretting

2 Sn-N implanted 3 5 Minor fretting

2 Sn-N implanted 6 10 Extensive fretting

3 Ag--N vs C implanting 3 5 Light fretting

4 Ti-N plated 3 5 Light abrasion

4 Ti-N plated 6 10 Light abrasion

4 Ti-N plated 9 15 Severe abrasion

5 C implanted 3 5 Moderate fretting

6 C implanted 3 5 Moderate fretting

4. Component improvements

In addition to the work discussed above, several key system components have been improved

vis-a-vis the Engineering Model design. Improvements in long term temperature stability and

reliability of the bearing control system result from replacing the eddy current sensors in the

Engineering Model with ferrite reluctance position sensors. An aluminum slit heat exchanger is used to reduce the cantilevered mass at the end of the cold finger. System efficiency is improved

with a magnetic spring integrated in the displacer linear motor and by using a novel low frequency

switching driver for the piston motor. Although the thermodynamic efficiency is reduced from the

Engineering Model, the overall efficiency (the ratio of cooling to electric input power) has

increased as a result of the improved drive systems. Detailed descriptions of each of these

improvements follow.

4.1 Aluminum cold end heat exchanger

The Engineering Model refrigerator has a copper annulus cold end heat

exchanger. The Flight Prototype uses a slit aluminum heat exchanger. The slits provide an equivalent heat transfer surface area with a shorter heat exchanger length. A reduction in weight

results from the reduced material density. The fabrication of the aluminum heat exchanger is outlined in figure 6 [3],

106
<*/////////,

REGION TO BE

- DEVELOPED INTO HARDWARE

COMPONENTS

CAST ALUMINUM

TITANIUM

HE AT EXCHANGER

SLI'I S

Al UMINUM

TITANIUM

ALUMINUM

Kb AC HON ZOUl

a. b. c.

Figure 6. a. Aluminum-titanium heat exchanger fabrication

b. Heat exchanger photograph

c. SEM photographs of bond interface

A 5 Al-2.5 Sn titanium cup and a mating commercially pure aluminum piece are cleaned and degassed. The assembly is heated in a high vacuum furnace. As the aluminum melts, it wets and adheres to the titanium surface forming a metallurgical joint. The bonded structure is then hipped

to remove any voids and improve the structural properties. The center of the aluminum material is removed to form a thick walled composite structure. The heat exchanger slits are electro-discharged-machined (EDM) in the aluminum walls. The outer titanium wall provides the needed

strength for pressure vessel containment and is subsequently welded to the cold finger.

A heat exchanger sample has been temperature cycled 1000 times from room temperature to 77 Kelvin and 10 times to 4.2 Kelvin. Metallographic and scanning electron microscopy of the tested

sample show good metallurgical bonding. Tensile tests of a cast sample showed that the bond

strength exceeds the strength of the aluminum. Figure 6c is a photograph of the aluminum/titanium

joint indicative of a superior bond. A heat exchanger sample pressurized to four times the design

pressure is currently being cycled from room temperature to 77 Kelvin. To date, 1,000 cycles have

been accumulated with no indication of failure.

During operation, the displacer shuttles gas between the cold and warm ends. The displacer

reciprocates at a specified frequency, stroke, and phase relative to the piston motion. The displacer construction includes the regenerator mesh, bearing armature and radial position 'target'

material, structural walls, and linear motor. For designs of this type, the fluid damping forces

acting on the displacer are small in comparison to inertial forces during operation. Ideally, for

compact cooler design, the machine should operate at the highest frequency allowed by the regenerator heat capacity and fluid viscous losses. In addition to the size and weight reduction, the

linear compressor motor size decreases with higher speeds, since the output force decreases.

However, the displacer motor power loss is proportional to the fourth power of frequency while the

cooling capacity is only linearly proportional to frequency. The significance of the displacer

motor power has resulted in larger, lower frequency cooler designs.

Due to the large ratio of inertial to damping forces, a resonant displ acer/spring system

would greatly reduce the required motor power. In fact, 'free displacer' coolers have been made

which have no displacer motors. These coolers use the operating pressure wave to drive a resonant

displ acer/mechanical spring system.

Long life mechanical springs can be designed provided the operating stress levels are sufficiently low. The damping forces for a well mounted mechanical spring are also quite low. However, experience with mechanical spring balancers has shown that small particles are generated

during operation. These particles would be catastrophic to the clearance seals. Thus, mechanical

4.2 Integral magnetic spring/linear motor

107
springs could not be used in the design. Gas springs have no wear problems, but do have limited

linearity, higher damping than mechanical springs, and do require an additional clearance seal.

For these reasons, the gas spring was also not used in this design. Magnetic springs, on the

other hand, do not need clearance seals and have no life-limiting properties. As a result of the

advances made in permanent magnet material, new, high strength magnets with minimal long term

aging and good temperature stability are now available. These improvements have made magnetic

springs feasible and the Flight Prototype incorporates one in the displacer design.

One advantage of the Engineering Model's linear motor drive system is the freedom to adjust

the displacer and piston strokes independently as well as the phase. In a free displacer design,

control and flexibility is lost though fewer components are needed. Thus an adjustable spring or

a spring and motor is desirable to maintain operating flexibility.

The Flight Prototype incorporates such an integrated magnetic spring/motor. The motor

provides control of the displacer motion. A schematic of the integral spring/motor with the displacer at full stroke is shown in figure 7. The moving magnets act as springs and interact with

the stationary coil to produce a force which is proportional to the current in the coils.

The construction of the motor is very similar to the displacer linear motor of the Engineering Model. Radially magnetized magnets are added to the stator at both ends of the coils to provide a self-centering magnetic spring. Good linearity is achieved over the design stroke

through proper positioning of the concentric magnets. Another advantage in this design is the

single diameter construction. No dead space or void volumes are introduced which would have

existed with a conventional face-to-face repulsion magnet spring. The springs reduce the peak

force requirements of the motor. Table 5 compares the power requirements of the integral

spring/motor design to a conventional linear motor design with equivalent size envelopes. In both cases SmC05 magnets are used because of their very rigid magnetization and excellent thermal and

long term aging stability.

INTEGRAL MAGNETIC SPRING / LINEAR MOTOR

TYPICAL FLUX PATH HH PERMANENT MAGNET

Figure 7. Schematic of integral displacer magnetic spring/linear motor

108
Table 5. Power comparison: Integral spring/motor vs. linear motor

Spring/motor Conven. linear motor

Peak motor force (N) 12 46

Magnet moving mass (Kg) .033 .035

Total electric power (W) 5 20

Eddy current damping generated in this magnetic spring is difficult to accurately predict.

These eddy currents dissipate stored energy and lower the spring quality factor (Q). Another

problem with a magnetic spring of this design is the radial instability and resulting side loads.

These side loaas occur not only from magnetic eccentricities resulting from mechanical

construction, but also from magnet non-uniformity. These side loads have static as well as dynamic components. Because of the difficulty in estimating these effects, tests were performed

with a dedicated test fixture.

4.2.1 Static spring test results

Axial springs of this design have a radial instability stiffness which is less than or equal to negative one half the axial stiff ness[4,5] . The sign is critical since a 10 N/m axial

stiffness PM spring has a radial stiffness ranging from negative 5 N/m to negative infinity. For designs involving no soft magnetic material the inequality qualifier can be removed.

The stiffness of a simple magnet pair (no soft magnetic material) was tested and compared to

a finite element analysis of the same geometry (fig. 8). The characteristic geometry of the

magnet rings is very close to the spring/motor design. Side load tests were performed by

displacing the inner ring toward the outer ring and measuring the radial force. The radial

stiffness was measured to be negative one half the axial stiffness. The side loads for zero mechanical eccentricity of various magnet pairs were measured to determine the magnet

non-uniformity. Table 6 summarizes the test results. These results indicate that matched magnet

segments must be used to produce acceptable performance.

STATIC SINGLE SPRING TEST RESULTS

55 r

a. b.

Figure 8. Static test of single magnet pair vs.

a. Test set-up

b. Axial test results

analysi s

109
Table 6. Static side load test results

Radial instability of single magnetic spring pair

Axial stiffness at mid position

Radial instability stiffness

11,000 N/m

Theoretical analysis

Finite element analysis

Measured 5,000 -

5,500 N/m

5,500 N/m

7,000 N/m

Magnet non-uniformity

Magnet pair number 1 2 3 4

Peak radial side force (N) 2.0

(in concentric position)

1.1 2.6 0.25

Equivalent geometric (cm)

eccentricity

0.047 0.005

4.2.2 Dynamic test results

Following these static tests, two sets of springs were mounted to an active radial magnetic

bearing test fixture which exhibits no friction and extremely low damping in the axial direction.

Figure 9a is a schematic of the test fixture. The integral magnetic spring/motor was in effect

split and placed at either end of the bearing test fixture. Figure 9b is a scope trace of the

position of the moving mass vs. time resulting from an initial step displacement. The resulting

Q of about 70 indicates that there is very little eddy current damping in the magnets. The

quality factor, Q, does get lower as additional magnets or magnetic material is placed near the

spring indicating that eddy current damping is not negligible.

The test set-up was further modified to test the integral motor/spring concept. An additional small magnet ring was attached to each inner magnet ring as in figure 9c. A coil is placed around each inner magnet ring. This test was performed to verify the analytic procedure

used to determine the force constant of the displacer motor. Both dc and ac tests were performed

using the motor to excite the moving mass. The dc force constant of the motor agrees well with

the predictions. The displacer is driven off-resonance (as it will be in operation) and open-loop

and the resulting frequency spectrum of the displacement is recorded. Figure 9d( 1 ) is a force

displacement curve of the spring for positive and negative displacements. At low amplitudes, the curves match well, indicating that there should not be any even harmonics in the displacement

spectrum. At larger strokes, the curves vary indicating that even harmonics will be present. The

resulting frequency spectrum measurement of the displacement is shown in figure 9d(2). These

harmonics produce insignificant adverse effects on the thermodynamics.

Through the introduction of bonded high energy product magnets, the

damping can be further reduced because of their very high resistivity. In a free displacer

design, the motor can be eliminated and axially magnetized springs can be used thus simplifying

the fabrication.

The accuracy of the radial position sensors in a magnetic bearing system determines the limit

of the achievable accuracy of that system. The Engineering Model cooler which employed magnetic

bearings, used eddy current sensors as the means of measuring radial position. These sensors, however, are not without drawbacks: they must be isolated from the helium working gas by a ceramic window and titanium pressure wall, and their extreme temperature drift precludes the use

of these sensors in the single-ended mode. Thus, each axis requires two matched sensors, two window assemblies which tend to trap particulates, and high frequency differential electronics to acquire a single position signal (fig. 10).

4.3 Radial position sensors

110
DYNAMIC SPRING TEST EXPERIMENT

ACTIVE RADIAL PASSIVE ELECTROMAGNETIC

AXIAL SPRING BEARINGS

BEARING J TEST DISPLACER

^ V2 KT

$ V2 DS

-I.

^ ^

7 1 ^

V2 KT

1

' 2 DS

"INSTABILITY

2

LU

"js LUU

<

-JaQ

X

_J

0. 1 7cm

200ms

TIME

a. b.

DYNAMIC SPRING TEST - ONE SIDE

PERMENDUR

STATOR

PERMENDUR

ARMATURE

TYPICAL FLUX PATH

TO BEARING TEST

FIXTURE HOUSING

— MAGNET

ADDED FOR INTEGRAL MOTOR TESTING

TO BEARING TEST

FIXTURE DISPLACER

c.

Figure 9. Dynamic test results

a. Dynamic test schematic

b. Damping with permendur backing (Q = 70)

c. Dynamic test fixture with coil and additional

magnets

d. Motor test results - displacement spectrum

(see next page)

111
STATIC MOTOR TESTS

(NO CURRENT)

0.00 0.05 0.10 0.15 0 20 0.25 0 30 0.35 DISTANCE (CM)

.05 -

.005

.0005

_1_ _1_ 10 20 26 30 40 52 60 70 78 FREQUENCY (Hz)

90 100

d(l) pull to left and right d(2) large stroke

PROBE (COIL RESONATED AT 1MHz)

WINDOW MOUNT (5AI, 2.5Sn, TITANIUM ALLOY)

CERAMIC WINDOW

CASE

SHAFT (5AI, 2.5Sn, TITANIUM ALLOY)

25jum RADIAL AIR GAP

MAGNITUDE OF EDDY CURRENTS

INDUCED IN THE SHAFT CHANGES

WITH THE POSITION OF THE SHAFT

IN THE AIR GAP

HIGH FREQ. DIFFERENTIAL ELECTRONICS

POSITION SIGNAL

(1 VOLT/MIL)

Figure 10. Differential eddy-current sensors

112
In an effort to simplify both the mechanical and electrical aspects of the radial position

sensing, a number of alternative sensing schemes were considered. The major features desired for

the new radial position sensor are summarized below:

- Single-ended (to allow redundancy)

- High bandwidth

- Negligible temperature drift

- High signal-to-noise ratio

- Simple electronics (reliability)

- Repeatable, stable, easily cleaned, mechanical assembly

The most promising method, with regard to simplicity of electronics, was that of variable

reluctance sensing. Furthermore, with the application of ferrite to a reluctance sensor, eddy

currents are eliminated; and thus, high bandwidth is achieved. With appropriate magnetic and

electronic design, a reluctance sensor also offers a reasonably linear response with negligible

temperature drift in a single-ended configuration. Finally, the reluctance sensor greatly

improves the mechanical design if the ferrite sensor itself can penetrate the titanium wall, be

ground flush with the wall, and serve as a hermetic barrier. This mechanical design required a hermetic ferrite/ceramic/titanium joint which was the subject of a major effort in materials

technology. A functionally representative schematic of the ferrite sensor is shown in figure 11.

FERRITE

TITANIUM

Figure 11. Ferrite radial position sensor

Extensive testing of the ferrite sensor was performed to measure the position sensitivity and

the temperature drift in the single-ended mode. Inductance measurements were taken at constant

temperature over the range of 0 - 4 mils (fig. 12). The data shows that the inductance, L, is

L(jiH)

700

600

500

4O0

300

200

A L

A L _ 10OpH A X

~ ml

^AX

1.0 2.0 3.0 4.0 X(mils)

Figure 12. Inductance L vs. position x

113
inversely proportional to the gap size, x, with a sensitivity, dL/dx, of approximately 100 uH per mil. This represents a change in impedance of 20% per mil of displacement for the ferrite sensor

as compared to roughly a 1% change in impedance for existing eddy current sensors.

The relatively high sensitivity to position was one major step towards the minimization of

temperature drift; the next criterion to consider was the sensitivity of inductance to temperature. \

The temperature sensitivity is measured using a specially designed test fixture which

maintains a fixed gap between sensor and target. The fixture is placed in a temperature

controlled oven which is cycled from 20 °C to 80 °C repeatedly. The inductance of the sensor is continuously monitored and recorded to quantify any drift in inductance due to a change in temperature.

Figure 13 is a plot of inductance vs. temperature for a fixed 3 mil gap over the range of 20

- 80 °C. The data shows an increase in inductance with temperature from 390 uH at 20 °C to 395 pH at 80 °C. This 5 uH change in inductance translates to a position error of approximately 50

u-inches which represents only 5% of the 1 mil radial clearance between the piston and cylinder.

Previously, the acceptance criterion for matching eddy current probes was expressed in terms

of a maximum position error of 200 y-inches or 20% of the 1 mil radial clearance with the probes

used in the differential mode. Thus, the ferrite radial position sensor offers much improved

temperature stability with the added advantage of operating in the single-ended mode.

Having achieved adequate temperature stability through appropriate choice of materials and

geometrical design, the linearity and sensitivity of the electronics was tested. The output

voltage as a function of gap size is plotted in figure 14 along with a line describing the ideal

linear output.

The close fit of data points to the ideal curve shows a fairly linear relationship between output

voltage and position, and a sensitivity of about 10 volts per mil.

In summary, the ferrite radial position sensor has exhibited excellent performance over a wide temperature range. It has demonstrated adequate linearity, good sensitivity, and exceptional

temperature stability, while obviating the need for differential sensing and facilitating the

incorporation of redundant sensing techniques. Furthermore, it has greatly simplified the

electronics design which leads to a lower parts count and, hence, increased reliability. And

finally, the mechanical assembly provides a flush bore which is hermetic and can be easily

cleaned.

U»H)

7 00

400

X= CONSTANT

to

20°C < T < 80°C

20 30 40 50 60 70 80 T(°C)

39S - 394

393 - 392 - 391 390

"T AL 5>lH => 50>l-in

20 30 40 SO 60 70 80 (T°C)

Figure 13. Inductance vs. temperature

114
V4 (VOLTS)

Figure 14. Output voltage (V4) vs. position (x)

4.4 Synchronous linear motor controller

In the Engineering Model cooler, moving magnet linear motors are used in axial control loops

to prescribe the reciprocating motions (i.e. amplitude, phase, speed & center position) of the

piston and displacer. The axial control is performed with position servo loops employing LVDTs to measure position and linear amplifiers to drive the motors. The linear amplifiers exhibit

excellent reliability and high bandwidth, and in general meet all the performance requirements of

the original design specifications. However, the poor (-40%) efficiency of the linear drivers

precludes their use in a spaceborne system. Therefore, alternative driving methods were investigated, specifically, switching drivers which would provide an axial control system with

high reliability and maximum efficiency.

High frequency (100 kHz) switching amplifiers have been used for this application and have

achieved efficiencies on the order of 75% with a bandwidth of 1 kHz. Using this type of

amplifier, one could directly replace the linear amplifier and use the same control system.

However, for high current applications, viz. the piston driver, the high frequency switcher

becomes complex and less reliable due to parasitic oscillations associated with the paralleling of

power MOSFET transistors and the finite reverse recovery times associated with high current

diodes.

A significantly different approach to the axial control provides an alternative driving

scheme. Using a nonlinear control system which employs phase lock loop techniques and takes

advantage of the electro-mechanical filtering properties of the linear motors. The amplifier used

in this system produces a switching waveform at the same frequency as the refrigerator operating

frequency. The ac component, the dc component, and the phase of the waveform are controlled by

three separate inputs to the amplifier as shown in figure 15.

The amplitude of the fundamental component of the switching waveform is varied by a common mode modulation of the positive and negative pulse widths. The dc component of the waveform is varied by a differential modulation of the positive and negative pulse widths; and the phase and

frequency of the switching waveform are prescribed by an ac signal at the third input to the

amplifier. These three control lines are used in three distinct control loops to accurately

prescribe the amplitude, center position, and phase of a piston or displacer motor (fig. 16).

In the first control loop, a low-pass averaging circuit is used to feedback the dc position

of the motor and compare it to a reference signal; the resultant error signal is then compensated

and used to adjust the dc component of V ou t to achieve the desired dc position. A second

control loop is realized by using a peak to peak detector to determine the stroke of the

reciprocating motor. The stroke amplitude is compared to a reference signal, and the resultant

error signal is compensated and used to adjust the ac component of V ou t to achieve the desired

stroke of the motor. Finally, a third control loop is formed to control the phase of the motor.

115
LARGE VCM SMALL VCM TO Wi

NEGATIVE VDM POSITIVE VDM 1W1

VCM - CONTROLS AMPLITUDE OF FUNDAMENTAL COMPONENT BY A COMMON

MODE MODULATION OF THE POSITIVE AND NEGATIVE PULSE WIDTH

VDM - CONTROLS THE LEVEL OF THE D.C. COMPONENT BY A DIFFERENTIAL MODULATION OF THE POSITIVE AND NEGATIVE PULSE WIDTHS

V0

- A.C. SIGNAL (REFRIGERATOR OPERATING FREQUENCY) WHICH

PRESCRIBES THE PHASE OF V0

Figure 15. Open loop amplifier

ACflEF D.C^O

VOLTAGE CONTROLLED

PHASE

SHIFTER

LINEAR MOTOR

+ GAS SPRING DYNAMICS

PHASE DETECTOR

DC POSITION AVERAGING

CIRCUIT

A.C. AMPLITUDE PEAK DETECTOR

Figure 16. Control scheme showing 3 distinct control loops

A clock signal provides the frequency and phase reference onto which the motor phase is locked via

phase locked loop techniques.

A prototype system which can deliver 500 watts of real power to the piston motor with an amplifier efficiency of 95% was designed and fabricated. The system exhibits excellent control of

critical operating parameters with negligible distortion of the desired sinusoidal motion (fig.

17) and a surprising tolerance to noise and non-ideal sensor performance.

116
MOTOR

VOLTAGE

t MOTOR

CURRENT

MOTOR

POSITION

Figure 17. Characteristic waveforms: Voltage, Current, and Position

Since the switching frequency of the amplifier is very low, i.e. the same as the operating

frequency of the refrigerator (15 - 25 Hz), the design of the amplifier is greatly simplified,

resulting in a lower parts count and hence higher reliability. Furthermore, at these frequencies,

switching losses are negligible, and transistors are easily paralleled to achieve very high

efficiencies.

In summary, the synchronous motor controller, although exhibiting a slower transient

response, provides better efficiency, potentially greater reliability, and better control of

steady-state operating parameters than is possible with either a linear amplifier or a high

frequency switching amplifier used in a classical position servo loop.

5. System performance

Table 7 is a summary of the key design parameters of the Flight Prototype model. System

performance is summarized in Table 8. The thermodynamic efficiency of the design is comparable to the Engineering Model. Overall reduction in system power results from higher efficiency driver

systems and the inclusion of the magnetic spring in the displacer motor. The counterbalance

design (including power requirements) have not yet been addressed.

Table 7. Flight prototype design parameters

Piston design stroke (mm) 7.4

Piston diameter (cm) 4.45

Displacer design stroke (mm) 2.3

Displacer diameter (cm) 3.155

Operating speed (Hz) 18.9

Charge pressure (N/m 2

) (mm)

1.69 E6

Regenerator wall thickness 0.5

Cold finger wall thickness (mm) 0.5

Displacer moving mass (Kg) 0.9

Piston moving mass (Kg) 3.95

Clearance seal gap (ym) 17

117
Table 7. Flight prototype design parameters (cont.)

Regenerator:

Materi al Cross sectional area (cm2

) Length (cm)

Wire diameter (pm)

Fill factor

7.31

6.0

53.

0.36

phosphor bronze

Piston motor:

Motor type

Yoke material

Magnet material

Peak motor force (N)

Mechanical output power (W)

Efficiency (%)

I 2 R Loss (W)

moving magnet linear motor

4% SiFe

SmCo5, BH max = 23 MGOe

220

100

7530

Table 8. Flight prototype system performance

Design cold production (W)

Cold end temperature (K)

Warm end temperature (K)

Thermodynamic shaft input power (W)

Piston motor input power (W)

Displacer motor input power (W)

Total input power to motors (W)

5. 140.

65.

300.

100.

135.

5.

6. Summary

A second generation magnetically suspended, linear Stirling cycle cryogenic refrigerator has

been designed to meet the space shuttle launch requirements. The design changes are primarily

focused on improving the refrigerator dynamics and thus its capability to withstand the launch

vibrations. These include; increased structural resonant frequencies, increased ac/dc bearing

force capability, and increased gas film damping. Other improvements, which increase system

reliability and efficiency, include an integral displacer magnetic spring/motor, ferrite variable

reluctance position sensors, surface treated clearance seals, and an aluminum/titanium cold-end

heat exchanger. The work summarized in this paper is being supported by the NASA-Goddard Space

Flight Center. (Contract Number NAS5-26688).

[1] Philips Laboratories, division of North American Philips Corp., Design and Fabrication of a Long-Life Stirling Cycle Cooler for Space Applications, Phase I and II - Engineering Model, Final

Report: Sept. 1978 - Dec. 1982, F. Stolfi, et al , NASA Contract NAS5-25172, Briarcliff Manor, NY,

March 1983.

[2] Philips Laboratories, division of North American Philips Corp., Parametric Testing of a Linearly Driven Stirling Cryogenic Refrigerator, F. Stolfi and A. Daniels, 3rd Cryocooler

Conference on Refrigeration for Cryogenic Sensors and Electronic Systems; Boulder, CO, Sept. 1984.

[3] Novel Titanium-Aluminum Joints for Cryogenic Cold Finger Structures, H.M. Meehand and R.C.

Sweet, Advances in Cryogenic Engineering, Vol 27, Plenum Press, New York, 1981.

[4] Directivity and Stability of Coaxial Permanent Magnet Systems, Th. Gast, A. Mirahmadi and F.E. Wagner, Paper no. V-2 at 5th International Workshop on Rare Earth-Cobalt Permanent Magnets

and Their Applications; Roanoke, VA, June 1981. (Book by University of Dayton, KL-365, Dayton,

Ohio 45469, USA).

[5] Permanent Magnet Bearings and Couplings, Jean-Paul Yonnet, IEEE Transactions on Magnetics,

Vol. MAG-17, No. 1, January 1981, pp 1169-1173.

References

118
SIMPLE CONSTRUCTION AND PERFORMANCE OF A CONICAL PLASTIC CRYOCOOLER

N. Lambert

Department of Applied Physics

Delft University of Technology

2628 CJ Delft, The Netherlands

Low power cryocoolers with conical displacers offer several advantages

over stepped displacers. The described fabrication process allows quick and

reproducible manufacturing of plastic conical displacer units. This could be

of commercial interest, but it also makes systematic optimization feasible by

constructing a number of different models. The process allows for a wide range

of displacer profiles. Low temperature performance as dominated by regenerator

losses, as well as several related effects are discussed. In addition a simple

device is described which controls gas flow during expansion.

Key words: Composites; conical displacer; cryocooler; flow controller;

low power refrigeration; low temperature; plastic; refrigeration;

regenerative cooler; Stirling cycle.

1. Introduction

The widespread use of low temperature devices by non-specialists depends heavily on the

availability of suitable coolers. Practical solutions to this problem will stimulate research

along lines that are presently unattractive. Zimmerman [1] pioneered the development of plastic

Stirling coolers with gap regeneration to cool a SQUID device directly. The emphasis is on very

low magnetic interference levels (dictating the use of plastics) and very low cooling power. A cooler's performance, as can be shown from elementary principles, improves significantly at low

temperatures if multiple stages are used. If one ignores the increase in void volume, adding

additional stages is always advantageous. However, all individual stages need separate machining

and careful assembly. An attractive alternative is a tapered displacer, which can be considered as consisting of an infinite number of stages. Du Pr£ and Daniels [2] experimented with such a conical displacer in 1971 and Myrtle et al. [3] successfully built a plastic version suitable for

SQUID applications. These units still require a lot of careful machining. In addition,

constructing a viable machine from a bare unit is time consuming. We felt the need for a different

manufacturing scheme that - is simple,

- has inherently better reproducibility,

- allowes more design flexibility, and

- reduces the time spent in completing the unit.

2. Conical displacer

In Stirling coolers all losses are distributed along the length of the displacer-regenerator,

except for the discrete radiation shields. From the thermodynamic point of view therefore,

distributed cooling represents the main advantage of Stirling coolers with a conical displacer

compared to their stepped counterparts. The shape of the cone determines the distribution of the

cooling power.

There are several more subtle effects however. Cool -down is slightly faster because of the

lower mass of the displacer. The gas is expanded within an annular gap, whereby thermal contact

during expansion is improved and (the more favourable) isothermal expansion can be achieved even at

low temperatures. Several effects depend on the width of the annular gap. At low temperatures the

regenerative losses are dominant. Although this loss is mainly due to the plastic, it is still

important to keep the thermal resistance of the gas gap low by means of a narrow gap. At higher

temperatures shuttle heat transfer losses are more important and a wider gap with corresponding

higher thermal resistance becomes attractive. The annular gap of a conical displacer depends on the angle of the taper and varies during a stroke.

119
A more important issue is the void volume. Zimmerman [1] found that his nylon displacers

contracted 1% more than the glass fibre reinforced epoxy cylinder during cool-down. In cylindrical

stages it is easy to compensate for axial contraction. However the radial contraction causes an appreciable void volume. At a typical stage length of 150 mm, the annular void volume associated

with this 1% differential contraction corresponds to about 3 mm dead stroke - compared to a typical

6 mm active stroke. Since regenerator losses are proportional to the total mass flow squared C4],

this effect roughly doubles regenerator losses. Conical displacers have different properties: The

gas gap widens during the upgoing stroke and no additional static gap is needed for the gas flow.

Axial correction can compensate for radial contraction of a linear cone. However, when either the

taper is nonlinear or the contraction is inhomogeneous (temperature gradient) this is impossible

and may result in significant void volumes. Therefore in a conical design the sleeve should

contract slightly more than the displacer. In that case the void volumes are in the gaps at higher temperatures, where they are less important or even favourable (higher thermal resistance).

The only void volume at low temperature is located at the narrow tip, which can be easily filled.

Probably the most important advantage of conical displacers is in construction. When

difficult machining can be avoided, this shape clearly favours simple, single step manufacturing

processes.

3. Manufacturing

It is not feasible to machine both tapered displacer and sleeve from plastic rods with

sufficient accuracy to get a reasonable fit. The obvious solution is to use one of these as a mould for the other; a perfect fit is guaranteed. Myrtle et al. C3] machined the displacer from

rods and wrapped glass fabric with epoxy resin around it to obtain the sleeve. However, machining

a long narrow displacer from glass fibre epoxy is tedious to say the least. It has to be done by

sections, which adds critical aligning steps to the process. We wrapped the sleeve around a brass

cone, and tried to cast the displacer in this sleeve afterwards. Uneven distribution of the glass

fibres within the epoxy resin made the displacer warp seriously at cryogenic temperatures. This

suggested the use of glass powder instead of fibres, but small irregularities in the inner surface

of the sleeve prevented a reliable release. Therefore we prepared a special mould from the brass

cone. A professional casting rubber contracted about 0.5% (elastically ), rendering the mould

useless. We obtained good results with unfilled casting wax saturated with fine sand to eliminate

contraction (causing cracks) during congealing.

The entire manufacturing scheme is illustrated in figure 1. The critical properties of the cone are sufficient roundness and a straight axis, rather than the precise diameters. The brass cone was machined in about one day on an ordinary lathe, and can be used many times. This

garantuees reproducibility.

After coating the brass cone with a parting agent, a layer of glass fibre ribbon is wrapped

around it using Stycast 1266 epoxy resin (Emerson & Cuming). Next, a helium diffusion barrier of

5 vm manganin foil and the aluminum tip are secured with a second wrapping. Electrical leads and

thermocouples are thermally anchored and protected by the third and final layer. Supports for

radiation shields can be built up from glass fibre ribbon or aluminum. Black Stycast 2850 FT (with

catalyst 24LV, Emerson & Cuming) is cast in the flange mould attached to the brass cone (fig. 1a).

Threaded holes are formed in the plastic by embedding nuts. The entire sleeve is cured at room temperature. Then the brass is released by force, and the supports for radiation shields are machined to the right size.

Figure 1b shows the manufacturing of the displacer mould. The melted wax/sand mixture is cast

around the preheated brass cone. After insulating with glass wool, water cooling causes congealing

to start from below. An anchor at the bottom prevents an upward shift of the wax during

contraction. In this way the contraction can actually be used to force a perfect fit. The brass cone is pulled free at room temperature.

Fiqure 1c shows casting of the displacer in the wax mould. We use a mixture of fused silica

(-200 mesh) and Stycast 1266 epoxy. The ratio of the powder and resin components is 180 powder: 100

component A : 28 component B in parts by weight. Immediately after preparation, the mixture is vacuum treated to remove air bubbles and then injected into the mould. After cure at room temperature the wax is melted. Small surface irregularities are corrected with sandpaper and the

displacer is machined to the right length. The glass powder/epoxy mixture is very homogeneous and we found no warp at cryogenic temperatures. However, should the need arise, the displacer can be

made flexible by segmenting it and interconnecting the pieces with wire (a single nylon fibre in the casting can be pulled out easily after cure, leaving a convenient channel). With another

trivial extension of the moulding process the displacer could be made hollow to decrease thermal

conductivity and thermal mass.

120
fa IE*

EQ

-AT

(a)

Fig. 1. Manufacturing: (a) The glass fibre epoxy sleeve (ES) is wrapped around the brass cone

(BC), with an aluminum tip (AT). An epoxy flange (EF) is cast in a covered (MC) flange

mould (FM). Screws (S) may be used to form threaded holes. Supports for radiation

shields (RS) are built up and machined after cure, (b) A wax/sand mixture (WS) is cast

around the brass cone (BC) within an aluminum tube (AT), and insulated with glass wool

(GW). Water cooling (WC) through an insulating flange (PF) determines the direction of

congealing. Brass anchors (BA) hold the wax down, (c) Glass powder/epoxy mixture (EQ) is injected into the wax mould.

The photograph (fig. 8) shows the different components. Except for a lathe, no special tools

are needed. At the moment the entire process takes about 40 man hours in the laboratory. The main

part is consumed by preparation. For a small series a significant gain is possible. A more

detailed description of the process can be obtained from the author on request.

4. Results

We compared the dimensions of the plastic displacer and brass cone at room temperature and

found the displacer to be about 0.05 mm smaller in diameter along the entire length. The tip of

the displacer was shortened until it fitted the sleeve exactly, and this length corresponded to the

length of the brass cone within 0.1 mm. Then the tip was lengthened by a 1 mm piece of aluminum.

The displacer was now completely free to move in the sleeve. The top of the fully inserted

displacer shifted less than 0.1 mm after warming up to room temperature, indicating negligible

difference between contraction of sleeve and displacer. At cryogenic temperatures the displacer

was still free to move and rotate in the sleeve, indicating negligible warp.

121
SERVO DRIVE

LOW PRESSURE BUFFER

CONTINUOUSLY PUMPED

DOUBLE

O-RING SEAL

VACUUM

PUMP

te si 'COMPRESSOR

HIGH PRESSURE BUFFER

VACUUM CAN

Fig. 2. Experimental setup. The cold space inside the vacuum can is surrounded by radiation

shields and superinsulation

.

Figure 2 shows a diagram of the experimental setup. The displacer unit with radiation shields

and superinsulation is mounted in a continuously pumped vacuum can. For experimental purposes the

displacer is driven by a servo motor (electronically controlled) through a vacuum pumped double

0-ring seal to avoid contamination of the helium. A small, standard, rubber membrane air

compressor is used to compress the helium in a closed circuit. Solenoid valves control compression

and expansion in the displacer unit.

-300

temperature

(K)

•200

100

0 0 100 200 300 400 500

distance from top (mm)

Fig. 3. Diameter (solid line) and temperature (dots) along the length of the cone. Tip

temperature measured with germanium resistor, others with thermocouples. Positions of the

two radiation shield supports are indicated at horizontal axis.

The first experimental results are promising: At a 1 second period, a 6 mm stroke and a 0.42

to 0.10 MPa (absolute) pressure cycle it cooled down to 10.1 K in 18 hours. Temperature

distribution and dimensions of the cone are indicated in figure 3. The temperature at the tip

rises 0.4 K with a 1 mW heat load. At present the lowest temperature is limited by the performance

of the compressor, and we intend to improve the system in the near future. Although the manganin

shield inside the plastic sleeve wall of this unit was damaged during manufacturing, it took about

5 hours before the tip temperature started to rise noticeably due to helium diffusion if pumping

was discontinued.

diameter

(mm) >

122
5. Gas pressure and displacement

Several parameters are important in optimizing the operation of a cooler. The gas pressure

and displacement waves are of general importance for any regenerative system. At temperatures

below about 20 K the regenerator losses are dominant. The gas flows in an axial temperature

gradient qT/dz and the heat load on the regenerator is proportional to the thermal capacity of the

gas flow mC and the thermal gradient. Heat exchange with the plastic is not perfect. This can be

expressed as a thermal impedance lj. The temperature difference 6T between gas and plastic

(reference) is given by

6T = ZfnC jjl

The net regenerator loss Qreg

is a time averaged product

Qreg

= «iC6TV <(mC)

2

Z T

>t g

In many textbooks a basic distinction is made between Stirling (piston), Gifford-McMahon

(continuous compressor with valves) and Vuilleumier (regenerative thermal compressor) cycle.

Indeed the room temperature arrangements and their inherent limitations (high drive forces and

sealing, lower efficiency, high temperature construction and low compression ratio, respectively)

are quite different, but at the low temperature end the cycles are very similar. The lower

regenerator heat load of a constant density cycle (the theoretical Stirling cycle) can in fact be

achieved by moving stacked displacer segments down (or up) one by one (analogous to the ripple that

passes through a queue of cars waiting at the fast food drive-in). The conventional single

displacer system, however, leads to the 5/3 times higher heat load of a pressure controlled system.

displacer position (mm)

Fig. 4. Pressure - displacement oscilloscope trace. Compression valve opens at CO and closes at

CC. Expansion valve opens at E0 and closes at EC.

There are still some possibilities left to reduce the regenerator heat loss significantly by

manipulating the pressure and displacement cycle. As was pointed out above, it is very important

to keep the low temperature void volume low compared to the swept volume. This reduces the

unnecessary part of the mass flow. Figure 4 shows the pressure - displacement oscilloscope trace

of the actual cycle employed in our machine. The refrigeration power is directly proportional to the area enclosed in the pressure - displacement diagram. The total mass flow corresponds to the

difference between maximum and minimum of the product of pressure and displacement (at E0 and CO).

In a regenerator loss dominated machine like ours, it is important to truncate the rectangular

cycle of a typical Gifford-McMahon machine as shown (CC to E0 and EC to CO) by timing the valves

properly. In this way a small amount of the available refrigeration power is sacrificed, but the

regenerator losses are reduced significantly by the decrease in mass flow. Typical numbers are 10%

reduction of refrigeration and an improvement of about a factor two in regenerator loss. The ideal case would be truncation along a line of constant amount of gas (hyperbole), i.e. zero mass flow.

Unfortunately the unavoidable room temperature volume at the top of the displacer limits the

pressure drop between CC and E0.

Another possible improvement involves the time dependence of the mass flow. In the case of a purely resistive thermal impedance (e.g. a narrow gas gap) a square wave is optimal. A sine wave

123
is only a factor n

2 /8 worse, but peaked functions are clearly less desirable. As indicated by

Radebaugh [4] the thermal penetration depth in the plastic will usually dominate at low

temperatures. In that case the thermal impedance has an imaginary part. This introduces a 45

degree phase shift and corresponding 1 /V(f requency ) dependence in all Fourier components [5].

The phase shift introduces a extra factor of 1/^ for a sine wave. In this case, determining the

optimum wave form involves some mathematics. The optimal solution results in an improvement of

only about 20% compared to the sine wave.

time

Fig. 5. Displacer movement. C: Compression valve open. E: Expansion valve open.

However, in practical valve operated coolers the mass flow cycle is highly asymmetric and

peaked. The performance can be improved significantly by smoothing the gas flow. Our experimental

setup allows full electronic control of the displacer movement. Figure 5 shows a typical

oscilloscope trace of the non-sinusoidal movement employed in our machine. Most of downward gas

transport occurs during the upward displacer movement at high pressure. Most of the upward gas

transport occurs during expansion when the displacer is at top position. Therefore more time is spent in raising the displacer and near the top position.

Fig. 6. Gas flow controlling device. Gas flows through needle valve at the left to the outlet

port B. The nylon piston at the right stabilizes the pressure difference over the needle

valve by closing the inlet port A.

Smoothing of the pressure cycle during expansion and compression is usually achieved by means

of a needle valve. The mass flow through such a constriction generally depends on both the

pressure difference and the average pressure at inlet and outlet port. This gives rise to a long

tail in the pressure decrease as a function of time (a hyperbolic cotangent for laminar flow). The

time derivative of the pressure, which represents the mass flow when the displacer is stationary,

is highly peaked. A simple solution would be to use a spring-loaded needle valve which opens when

the pressure difference over the constriction drops. It is difficult, however, to adjust the flow

characteristics of such a device while in operation. Figure 6 shows a more sophisticated device,

which essentially consists of a pressure regulator and needle valve in series. Expansion to the

low pressure outlet is controlled by the needle valve. The pressure difference over the needle

valve is stabilized by a spring-loaded nylon piston which closes the high pressure inlet when

necessary. The flow through the device now depends on pressure at the outlet only. In figure 7

124
the oscilloscope traces of expansion through this device and through an ordinary needle valve can

be compared. The lowest temperature in our cooler improved about 0.8 K with this modification, and

the effect should be even more important at lower temperatures. Several versions are possible,

e.g. a membrane instead of a piston, a stem or needle instead of a poppet valve, an adjustable

spring, etc. We suppose that this device can be used in other fields as well. A similar device

could be designed for compression, but this is a less critical part .of the cycle. Regenerator heat

load during compression is low because the displacer is near the bottom position, and compression

is inherently more linear than expansion.

4 absolute

pressure

0 H *

time

Fig. 7. Expansion through ordinary needle valve (a) and through flow controlling device (b). Note that the time derivative, representing the mass flow, is highly peaked in (a) but almost

perfectly constant in (b).

6. Future work

Besides improving the current performance by operating at somewhat higher pressures, we intend

to build several different units in the near future. An obvious improvement would be a hollow

displacer. This is only relevant at the high temperature section. A significant improvement is expected in low temperature performance by incorporating a higher heat capacitance, e.g. lead

particles or He on charcoal, in the plastic. Because the loss from static conduction is negligible at low temperature, regenerator losses can also be reduced by using materials with a higher thermal conductivity. We hope to perform a rather detailed computer analysis including all

relevant details, in order to optimize low temperature performance. Another simple extension would

be a small, low pressure Joule-Thomson stage using the gas from the regenerative cycle to prevent

impurity build up. The gas lines can be embedded in the plastic sleeve. A similar experiment on a stepped cooler [6] indicated that this approach is feasible.

7. Summary

Multiple stage plastic cryocoolers require accurate machining of all separate stages and

careful assembly to achieve a close fit of the displacer within the cylinder. Conical displacers

are thermodynamically attractive, but were thus far more difficult to make than multiple staged

designs. This paper describes a simple process to make both the cold finger and the displacer from

a single conical mould. Vacuum flange, cold tip and supports for radiation shields are included.

Thermocouples and electric wiring are embedded in the plastic. The first experimental results in low temperature performance are promising. In a laboratory the entire process takes about 40 manhours, which seems a reasonable starting point for small scale production. The reproducibility of

the product allows for systematic performance optimization by constructing a number of different

models. The flow controlling device for expansion, and several other improvements concerning

regenerator loss may be useful for other projects as well.

This work was initiated during a stay at NBS Boulder Laboratories and carried out at Delft

University. We thank Dr J. E. Zimmerman for instructive discussions and advice. The work is sponsored by the Delfts Hogeschoolfonds. We cordially acknowledge the additional support by

Prof. H. Postma and Prof. J. E. Mooij, which made the visit to NBS Boulder possible.

125
8. References

[1 ] Zimmerman, J. E. and Sullivan, D. B., A Study of Design Principles for Refrigerators for Low- Power Cryoelectronic Devices, 1982, National Bureau of Standards Technical Note 1049

(National Technical Information Service, Springfield, VA 22161).

[2] Du Pre\ F. K. and Daniels, A., Gap-regeneration method for Stirling =and similar cycles

(Proc. XIII Int. Congr. of Refr., Washington D.C., 1971), in Progr. in Refrigeration Science

and Technology 1_, 137-141 (AVI Publishing Company, Inc. Westport, Connecticut, 1973).

[3] Myrtle, K., Winter, C, and Gygax, S., A 9 K conical Stirling-cycle cryocooler, Cryogenics 22,

139-141 (1982). —

[4] Radebaugh, R., Analysis of regenerator inefficiency for Stirling-cycle refrigerators with

plastic displacers, XV Intern. Congress of Refrigeration, Venice, Italy, September 1979).

[5] Carslaw, H. S. and Jeager, J. C, Conduction of heat in solids, 64-70

(Oxford at the Clarendon Press, 1959).

[6] Zimmerman, J. E., Recent developments in self-contained cryocoolers for SQUIDs and other lowpower cryoelectronic devices (to be published in the

Proceedings of the 10th International Cryogenic Engineering Conference, Helsinki, 1984).

Fig. 8. From left to right: Superinsulation packs and radiation shields, glass fibre epoxy

sleeve, brass cone with flange mould and cover, 30 cm scale, wax/sand mould with flange,

glass powder/epoxy displacer.

126
EFFECTS OF LEAKAGE THROUGH CLEARANCE SEALS ON THE PERFORMANCE

OF A 10 K STIRLING-CYCLE REFRIGERATOR

C. S. Keung and E. Lindale

Philips Laboratories

A Division of North American Philips Corporation

Briarcliff Manor, NY 10510

The use of clearance seals is essential to achieve long-life, wear-free

operation of Stirling-cycle cryogenic refrigerators. This paper describes an experiment which determined the effect of leakage through clearance seals on the performance of such a refrigerator operating at temperatures ranging from

20 K down to 10 K.

The ability of a Stirling-cycle refrigerator to achieve 10 K with clearance

seals was successfully demonstrated. Results indicate that the leakage flow

undergoes gap regeneration before reaching the cold expansion volume. A simple model of gap regeneration was used to estimate the regeneration loss

due to the leakage flow. This regeneration process minimizes the loss in

refrigerator performance caused by the clearance-seal leakage. As a result,

clearance seals remain effective down to a refrigeration temperature of 10 K.

Key words: clearance seal; cryogenic refrigerator; cryogenics; heat transfer;

regenerator; Stirling cycle.

1. Introduction

One of the life-limiting mechanisms in a typical cryogenic refrigerator is the wear of its

seal surfaces. Wear of the seal surface not only increases leakage but also generates

contaminants. In order to achieve long-life, wear-free operation of cryogenic refrigerators, the

use of clearance seal is essential.

A clearance seal is a long, narrow annular gap established between the outside surface of a reciprocating cylinder and the internal surface of a mating cylindrical housing. Sealing is attained by the flow resistance provided by the long narrow gap. Clearance seals were first

implemented successfully on a long-life, Stirling-cycle refrigerator operating down to 38 K [1] . In this study, a triple-expansion, Stirling-cycle refrigerator was tested to study the

effectiveness of clearance seals to attain temperatures below 20 K. This paper describes the

experiment with the three-stage refrigerator and a first order analytical model of the effects of

the clearance seal on cold production.

2. Description of refrigerator

The first successful operation of the triple-expansion, Stirling-cycle cryogenic refrigerator

used in this study was reported by Daniels and duPre

- [2] in 1971. In this earlier study, this

refrigerator originally reached a temperature of 9 K with a third-stage (coldest) regenerator

filled with lead spheres. The refrigerator configuration is typical of conventional

Stirling-cycle machines driven by a simple crank-type mechanism (fig. 1). The compression heat is rejected to water through a cooling jacket. The crankshaft is driven externally by a variable-speed motor.

127
Figure 1. Motor drive and triple expansion refrigerator

The displacer is stepped to three diameters (figs. 2 and 3), with each section containing a regenerator matrix. The first (i.e., warmest) and second stage matrices are made of layers of

phosphor-bronze mesh.

Figure 2. Three stage displacer Figure 3. Schematic of triple

expansion refrigerator

The original lead spheres were replaced by lead mesh. Lead mesh is made by expanding

lead-calcium-tin alloy sheets (fig. 4). Lead mesh was used as a test for its potential as an alternative to lead spheres.

Each of the three displacer stages has a Rulon-band seal (see fig. 3) which is epoxied to the

lower section, and was machined to fit their respective bores in the cold finger. The seals also

act as bearings guiding the reciprocating motion of the displacer.

The temperature of the coldest stage was monitored with a helium gas thermometer. The 1st

and 2nd stage temperatures were monitored with copper-constantan thermocouples mounted on the

flanges of the cold finger. An electric resistance heater was mounted to the third stage to measure the cold production.

128
Figure 4. Magnified view of lead mesh

The refrigerator was first run with all contacting seals and a temperature of 9.4 K was reached. Table 1 summarizes the major dimensions and operating conditions of the refrigerator.

Table 1. Major refrigerator dimensions and operating conditions

1st stage 2nd stage 3rd stage

Displacer diameters, mm 39.9 20.0 15.1

Regenerator:

length, mm 39.4 29.4 24.5

mesh material phosphor-bronze phosphor-bronze lead

mesh fill -factor 0.4 0.4 0.4

Piston diameter, mm 63.5

Displacer stroke, mm 12 Piston stroke, mm 32

Displ acer-piston phase angle 60

Charge pressure, psia 89.6

Speed, cps 640

Piston swept volume c.c. 100.8

3. Tests with clearance seal

After a temperature below 10 K was achieved with all contacting seals, the diameter of the

third stage seal was reduced to provide a radial clearance seal. The seals/bearings on the second

and third stage were responsible for guiding the displacer. The total indicated runout of the

clearance seal was less than 0.0002". The refrigerator was re-run with a third-stage clearance

seal of 0.0015" radial clearance. The test was then repeated with a 0.002" radial clearance seal.

4. Simplified model of gap regeneration

Working fluid leaking through the clearance seal flows past a long, narrow annular gap before

reaching the expansion space (fig. 5). The leakage flow undergoes gap regeneration by exchanging

heat with the two concentric walls surrounding the annulus. The loss in cold production due to clearance-seal leakage is a result of imperfect gap regeneration experienced by the leakage flow.

129
SECOND-STAGE

EXPANSION VOLUME

THIRD-STAGE EXPANSION VOLUME

LEAD-MESH REGENERATOR

PHOSPHOR-BRONZE

REGENERATOR

Figure 5. Schematic of leakage flow passing through the

clearance seal and regeneration gap with dimension of the clearances exaggerated

A model was developed to estimate the regeneration loss of the leakage flow.

In order to treat the involved regeneration theory analytically, the following

simplifications are made.

1. The temperature and pressure of the fluid in the regeneration gap vary spacially with axial

position, z, only.

2. The time-averaged wall temperature varies linearly with z.

3. The thermal properties of both fluid and wall are constant.

4. The regeneration losses are the sum of the losses from two independent cases. In case 1. the

regenerator has finite heat transfer rate but infinite wall heat capacity. In case 2, the

regenerator has finite wall heat capacity but infinite heat transfer rate, and the fluid

pressure fluctuates with time.

Case 1. Finite heat transfer

The leakage with an average mass flow rate of m0

, flows through an annular regeneration gap with average diameter D and gap width s. If heat transfers between the fluid and wall through a coefficient h, the energy equation is:

where Tg = fluid temperature

T w

= wall temperature

Cp = specific heat of fluid

The heat transfer coefficient for flow through an annulus with equal linear temperatures on both

walls is given by [3]

k

h = 8.23 , where k = thermal conductivity of fluid.

130
With a linear wall temperature, eq. (1) can be integrated over the entire seal length L to yield

T

g (L) =TC+ I^ (l-e

A

) , (2)

where Tn

= temperature at the warm end of the regeneration gap,

T c

= temperature at the cold end of the regeneration gap,

• . 2-rrdLh and A = -m c

o p

For laminar flow in the gap. the average mass flow rate in the gap can be expressed as

• _ irpDd

3 AP ,

. 12/2 ui

where p = fluid density,

y = fluid viscosity,

d = clearance seal width.

i = clearance seal length,

and

AP = pressure drop along the entire seal length.

The regeneration loss due to finite heat transfer, qn is then given by

^h o p g c

or using eq. (2),

'n op q

= m c Th " C (l-e"

A

M ) . (4)

n o d A

\. j > \

i

Case 2. Finite heat capacity and fluid pressure fluctuation

The wall heat capacity available for regeneration is limited by the thermal penetration

depth. 6. of the wall material. Since heat transfer in or out of the wall over half of the cycle,

6 is given as

a 1/2

where aw

= thermal diffusivity of the wall

oj = angular frequency of the refrigeration cycle

Thus the wall heat capacity per unit length available for regeneration is 2p wcw

ttD6, where

p w

and cw

are density and specific heat of the wall material respectively.

131
Since the effects of finite heat capacity and fluid pressure fluctuation are time-varying,

the transient energy equation must be used to analyze the effects. Applying the energy equation

on a volume of fluid contained in a length of dz of the regeneration gap, one has [4]

*

9 T DT nn

o ^

6 w _ g DP " 2p

w

cw s "ST- ~ p lnr

- " ur ' (5)

where P is fluid pressure. If flow resistance is neglected and the assumption of infinite heat

transfer (i.e., Tw

= Tg) is used, eq. (5) can be written as

3T , 2D • C 3T

g 1 3P m p g

, fi» m

where c = pcd + 2p, c - . m P w w s

The time-varying pressure and mass flow rate can be expressed as

P = P - P cos at (7)

o

m = m cos (ut - e) (8)

m = / 2

' m

o

The fluctuation of pressure and mass flow in the regeneration gap are modeled as being in phase with the fluctuation in the main working volume.

Using eqs. (7) and (8), one can integrate eq. (6) to obtain

T_=P ^ !&!!is1n(«t- e) . (9)

g c ttUsw c

"37 m m

The regenerator loss due to finite heat capacity and pressure fluctuation, qc

, is given by

the rate of flow of enthalpy, which is

or

f> mc T dt x ?tt p g

, -

r i m cos e . (10) m

The total loss due to clearance seal leakage is given by the sum of q n and qc

,

132
5. Results and Discussion

Cold production of the triple-expansion refrigerator at temperatures ranging from 10 K to 20 K were measured. In figure 6, the top curve shows the performance of the refrigerator with

line-to-line contacting seal, and the lower two curves represent the 0.0015" and 0.002" clearance

seals. The differences between the top curve and the lower two are the losses in cold production

due to the leakage of the clearance seals. These measured losses are plotted in figure 7 together

with the losses predicted by eqs. (4) and (10).

CO

ti-<

zo

I-o

O

o

a.

Q.o

o

0.5 -

to

t-<

LU

DC=5CO

co

LU

LT

CLO

o

co

coO

—i

9 10 11 12 13 14 15 16 17 18 19 20 TEMPERATURE ( K)

o CALCULATED

A MEASURED

0.7 o

0.6 o

0.002" CLEARANCE SEAL

0.5 A o

0.4 A A A A

0.3

A

o

0.2 A A

A A A A

0.1 o O O o

O o O

0.0015" CLEARANCE SEAL

0 I I I I I

I I i i i i 10 11 12 13 14 15 16 17 18 19 20 TEMPERATURE ( K)

Figure 6. Cold production at the

coldest stage

Figure 7. Loss in cold production due

to clearance seal leakage

The discrepancy between the measured and calculated results is most likely due to the

simplification made in the theoretical model for gap regeneration. Furthermore, friction heating

by the contacting seal and slight eccentricity of the annular clearance seals were not accounted

for in the model. But the comparisons show that eqs. (4) and (10) give good first order

estimation of the loss due to the use of clearance seals in Stirling-cycle refrigerators.

This experiment shows that the clearance seal losses produce a warm-up of 1.6 K and 3.5 K with clearances of 0.0015" and 0.002". respectively. This is an acceptable penalty in the design

of a refrigerator with long-life as the leading priority. Furthermore, the loss due to clearance

seals can be significantly reduced by using seals with smaller clearances. At the present,

refrigerator with clearance of 0.001" is in operation [1], and the design of refrigerator with

clearances of 0.00075" is in progress [5].

6. Conclusions

Measurements from a triple-expansion Stirling refrigerator show that the loss caused by

clearance seals is low and is an acceptable penalty in the design of a long-life cryogenic

refrigerator. The losses due to clearance-seal leakage can be modeled as imperfect gap regeneration. A simple gap regeneration model gives good first order estimation of these losses.

This study is partially funded by the Satellite Systems Division, Rockwell International

133
7. References

Stolfi, F., Goldowsky, M., Keung, C, Knox, L., Lindale. E., Maresca. R.. Ricciardelli, J.,

and Shapiro, P., Design and Fabrication of a Long-Life Stirling Cycle Cooler for Space

Application, Philips Laboratories. Briarcliff Manor. N.Y., NASA Contract NAS5-25172, March

1983.

Daniels. A. and duPr§. F. K., Triple Expansion Stirling Cycle Refrigerator, Advances In Cryogenic Engineering , Vol. 16, pp. 178-184 (1971).

Kays, W. M. and Crawford. M. T., Convective Heat and Mass Transfer , pp. 100 (McGraw-Hill Book

Co., Inc, New York, N.Y., 1980).

Schlichting, H., Boundary-Layer Theory , Seventh Edition, pp. 265-268. McGraw-Hill Book Co..

Inc., New York. N.Y., 1979.

Knox, L.. Patt, P.. Maresca, R.. Design of a Flight Qualified Long-Life Cryocooler, presented

at the 3rd Cryocooler conference on Refrigeration for Cryogenic Sensors and Electronic

Systems, NBS, Boulder. Colorado, September 17-18, 1984,

134
AN EXPERIMENTAL RECIPROCATING EXPANDER FOR CRYOCOOLER APPLICATION

Moses Minta and Joseph L. Smith, Jr.

Cryogenic Engineering Laboratory

Massachusetts Institute of Technology

Cambridge, MA 02139

An experimental reciprocating expander has been designed with features

appropriate for cryocooler cycles. The expander has a displacer piston, simple

valves, and a hydraulic/pneumatic stroking mechanism. The expander has a valve

in head configuration with the valves extending out the bottom of the vacuum enclosure while the piston extends out the top. The expander has been tested

using a CTI 1400 liquefier to supply gas at about 13 atm in the temperature

range 4.2 to 12 K. Expander efficiency has been measured in the range 84 to 93% while operating the apparatus as a supercritical wet expander and in the

range 91 to 93% as a single phase expander. The apparatus can also be modified

to operate as a compressor for saturated helium vapor.

Key words: Cryogenic expander; two-phase expander; experimental expander;

reciprocating expander; expander valve actuator; expander efficiency.

1. Introduction

Small cryogenic refrigerators have been extensively and successfully used to meet the low

power refrigeration requirements of cryopumps, cryogenic sensors and electronic systems at temperatures above 20 K in the past decade. Most of these cryocoolers have been based on the

Gif ford-McMahon , Modified Solvay, Stirling, or Vuilleumier cycle. The modification required to meet low power refrigeration needs below 6 K result in considerable increase in cost, power and

complexity. This makes cryocoolers based on work-extraction devices attractive, particularly

because of increased efficiency.

Large capacity helium liquefiers invariably use the Collins two-expander cycle. These units

use reciprocating expanders or turbo-expanders which appear unattractive for scaling down to low

capacity helium liquefaction. In the case of turbo-expanders, this is because of an efficiency

penalty since the losses scale down disproportionately with geometric size. By contrast, the

principal losses associated with the reciprocating machine are heat transfer losses which may be

minimized by proper design. These losses may be grouped, generally, into those affecting the power

and those directly manifesting themselves as heat leaks to the working fluid.

The power losses are due to valve flow, leakage, mechanical friction, blow down, blow in, and

cyclic heat transfer. The cyclic heat transfer loss is the result of periodic heating and cooling

of the working gas by the cylinder walls. The incoming gas is warmer than the cylinder walls and

is therefore cooled while the cold gas after the expansion process is warmed by the cylinder walls.

The net effect is that the expander processes more gas without a corresponding increase in expander

work per stroke. The heat input losses consist of static heat leak, shuttle heat transfer and

cylinder-piston gap pumping loss.

135
Figure 1. Cross section of expansion engine

136
Recent advances, especially in heat transfer analysis and experimentation have enhanced our understanding of the losses associated with the expander, and analytical models of varying

1-3 sophistication and adequacy are now available for the losses . This has made it possible to design an efficient reciprocating expander. However, noise vibration and size considerations of

the work-absorbing assembly associated with the conventional reciprocating expanders still limit

the practicality of scaling down these units. This paper describes an experimental reciprocating

H expander which has been designed for high efficiency and uses a hydraulic-pneumatic drive

mechanism and a pneumatic valve actuator in place of the flywheel, brake motor, mechanical camactuator assembly used in conventional large capacity liquefiers. The device can therefore be

scaled down for cryocooler applications.

2. Description of expander

The reciprocating expansion engine, Fig. 1, consists of a long displacer closely fitted inside

a long cylinder which hangs from a base plate, which is the top plate of a vacuum chamber. Above

the base plate is an adjustable hydraulic-pneumatic system for piston motion and valve control.

The valves for the engine extend down from the cylinder head. Surge chambers are located at the

inlet and exhaust of the expansion engine to convert the pulsatile flow to a relatively smooth and

continuous flow. Detailed description of these components follow.

The cylinder is made of 304 stainless steel because of its high strength to thermal

conductivity ratio, low specific heat capacity and lack of brittleness at low temperatures. The

thin wall of the cylinder coupled with low thermal conductivity of the material minimizes the

conduction loss. Stiffening rings spaced 1.5 in apart around the outside diameter keep the tubing

round. The thin wall tubing is TIG welded to the valve block (cylinder head containing the valve

ports) at one end and a thick wall tube at the warm end used for mounting the engine. A solid

phenolic micarta rod is used for the displacer because of its good wear characteristics. Also the

thermal contraction characteristics closely match those of the stainless steel. The diametral

clearance between the piston and cylinder is 0.006 in and is chosen by consideration of the shuttle

heat transfer loss, the possibility of seizure due to small solid impurities and the possibility of

displacer-cylinder contact.

The engine uses a single buna 0-ring seal M at the warm end of the displacer-cylinder

assembly. An oily felt washer L provides continuous lubrication for the 0-ring. Thus there is

minimal wear which reduces the possibility of wear material contamination. Also the small

frictional heat generated is dumped into the atmosphere and does not detract from the cooling power

of the engine.

Since the radial clearance on the 33-in-long displacer N is 0.003 in, only a small

misalignment will cause the displacer-cylinder assembly to bind. The vertical alignment of the

engine avoids gravity side loads and associated rubbing. The displacer is rigidly threaded to the

piston rod D of a tandem cylinder assembly A. The tandem cylinder has four rod seals and two piston seals. Therefore the integral unit consisting of the tandem piston rod and the engine

displacer ride on a total of seven supports of close tolerances. By proper initial positioning,

the unit can be maintained reasonably well aligned in the vertical. The axes of the engine

cylinder and the tandem cylinder are aligned by piece C, which fits inside the engine cylinder E and outside the bushing B at the end of the tandem cylinder. The cylinder is rigidly supported at the warm end on top plate H and extends into the vacuum chamber. The warm end of the cylinder E is

attached to the plate by a split ring, groove and clamp flange, G and F.

Since throttling in the valves degrades the performance, the valve ports are located in the

cylinder head to allow for reasonably large ports with minimum throttling. This port location also

helps to reduce the clearance volume. The ports are 1/4-in holes drilled through the valve

block/cylinder head 0 which is TIG welded to the cylinder J. Tubular valve sheaths S of 304

stainless steel are also welded to the valve block and extend from the bottom of the engine. These

tubular sheaths enclose the valve pull-rods Q. The valve face, P, is a teflon disk mounted on the

cold end of the phenolic micarta pull-rod with a screw and locked in place with a belleville

washer. The valve is held closed by the spring in the miniature air cylinder which actuates the

valve. A buna 0-ring serves as the warm end seal on the valve rod which fits closely in the

sheath. Because of the rather short travel of the pull-rods, no lubricant reservoir is provided

for the 0-ring. The pull rod is adequately guided by the sheath since the clearance in the sheath

is only 0.003 in.

137
3. Hydraulic-pneumatic piston-motion control system

The overall layout for the control system is shown in Fig. 2. Air limit switches send

position signals to the air controller. The controller sends direction and speed signals to the

control valves to control piston direction and speed. The hydraulic controller absorbs the

expander work, and sets three different speeds during the exhaust stroke, the intake stroke and the

expansion stroke. The expander work is dissipated in flow control valves in the hydraulic circuit.

The principal components of the hydraulic controller are three adjustable flow* control valves G1,

G2, G3 and a three-way hydraulic valve H (Fig. 2). The three-way valve is a two-position, singleair-piloted, spring-return valve. The oil flow through this valve is through valve G3 when there

is air pressure at the pilot, or through line GM when there is no air pressure. The adjustable

flow control valve is a throttle and check valve combination which allows throttled flow in one direction and full flow in the other. Valves G2 and G3 restrict flow during the power stroke,

while valve G1 restricts flow during the exhaust stroke. Therefore the setting on valve G1 determines the engine speed during the exhaust stroke. Valve G3 is by-passed during this stroke.

During the intake stroke, air pressure at the three-way valve H switches the oil flow to valve G3

which meters the flow together with valve G2. The valve settings on these two valves therefore

determine the piston speed during the intake process. At cut off, air pressure is released on the

three-way valve and the spring returns the oil flow to line G4. Valve G2 is now by-passed. There

is full flow in valve G1 and metered flow in valve G2 which sets the piston speed during the

expansion process. A bleed line L is provided for the hydraulic circuit. Also an air-pressurized

oil reservoir is provided to maintain the oil under pressure and eliminate air leaks into the

hydraulic circuit. With air in the oil the piston velocity cannot be controlled.

The heart of the air limit switch system is a miniature double-plunger two-position fully

ported four-way spool valve F, Fig. 2. The valve is supported by threaded rods attached to the

tandem-cylinder assembly. A yoke, BB, F1, and F2 is attached to the free end of the piston rod.

At maximum volume, surface F1 actuates the plunger and at minimum volume surface F2 actuates the

plunger of the spool valve. The stroke of the machine is adjusted by adjusting the vertical

position of the four-way valve and the distance between F1 and F2. Threaded rods and nuts

facilitate these adjustments.

The cut-off switch E sends a position signal to the pneumatic control at the end of the intake

process. Switch E is a heavy duty miniature air limit switch. It is a two-position, plungeractuated normally-closed valve. A cam, E1, attached to the piston rod actuates the cut-off switch.

The output signal from switch E1 is used to actuate the expander inlet valve and the three-way

hydraulic valve in the hydraulic controller. The cut-off switch is attached to the tandem cylinder

with threaded rods for position adjustment. The expander cut-off point is adjusted by changing the

position of this switch.

The two principal components of the pneumatic controller are a directional valve C and a NOT

element B, which is described in the next paragraph. The directional valve is a heavy-duty, twoposition, double-air-piloted, fully-ported, four-way spool valve. The pilot signals to operate the

valve are supplied by the limit switches. The four way directional valve switches pressure and

exhaust to the double acting pneumatic cylinder, thus providing pneumatic power for both the up

(expansion) and down (exhaust) strokes. Thus the pneumatic driver can drive the piston even when

no helium is being processed by the expander. This feature allows a later adaptation of the

expander as a compressor.

The purpose of the NOT element is to provide the signals to open the engine inlet valve only

at the end of the exhaust stroke, after the exhaust valve has been closed and to close the inlet

valve at the cut-off point of the power stroke. The two input signals to this element are a signal

from the cut-off switch to input port 1 and another signal from the end-of-stroke limit switch F to input port 2. The output of the NOT element is pressure at port 3 if there is pressure. at input 1 and if there is no pressure at input 2. During the intake stroke the switch E is depressed sending

pressure to port 1 of the not element B. There is no pressure at port 2 of B so pressure at 1 passes to 3. This pressure holds the inlet valve open and switches valve H causing hydraulic valve

G3 to be active. At cut off, E switches which exhausts the pressure a\ 1. With no pressure at 1, the NOT element switches which exhausts the pressure at 3. closes the inlet valve, and allows valve

H to spring return. At the end of the expansion stroke, valve F switches sending no pressure to E and pressure to port 2 which also opens the the discharge valve. Switch E has no pressure and no influence as it is depressed during the discharge stroke. At the end of the discharge stroke

valve, F switches pressure through E to port 1. Only after the pressure in the discharge valve

actuator has dropped, does the NOT element B see no pressure at 2 and switch pressure from 1 to 3 which the opens the inlet valve.

138
VALVE

ACTUATORS AIR CONTROLER

Figure 2. Hydraulic-pneumatic control system

Debugging the pneumatic circuit

The hydraulic and pneumatic system was assembled from standard catalogue item components.

Since these were not optimum components and their internal design and port sizes were not readily

available, an experimental rather than an analytical approach was used to tune and adjust the

system. The pneumatic circuit was instrumented with several pressure transducers. The engine was instrumented for cylinder pressure and piston position. Data from these instruments were observed

and recorded with a digital oscilloscope and subsequently transferred to a VAX computer for

analysis. This data was sufficient to tune the system for satisfactory operation. Typical curves

showing the phase relationships are shown in Fig. 3-

5. Time sequence in the expander

Fig. 3 shows piston position, inlet valve actuator pressure, exhaust actuator pressure, and

expander cylinder pressure on the same time base for a typical cycle. Starting at TDC (minimum

volume) with the inlet pressurized (open) and the exhaust closed (depressurized) , the piston moves

up at low velocity until the cutoff point (CO) is reached. The inlet valve closes and the

hydraulic three-way valve switches to a low flow resistance (G4 of Fig. 2). The cylinder pressure

falls rapidly and the piston velocity increases. When the piston reaches BDC (maximum volume) the

exhaust pressurizes (opens) and the piston reverses direction. The piston moves rapidly to TDC

(minimum volume). Subsequently the piston switches direction, the exhaust depressurizes (closes),

and the three-way hydraulic valve switches to high flow resistance G3. The inlet then pressurizes

(opens), to repeat the cycle. The cut off switch resets on the exhaust stroke, but has no action

since it has no pressure supply.

139
CO BDC TDC

TIME

Figure 3. Expander cycle

Fig. 3 also shows that the times required to pressurize and depressurize the valve actuators

are significant. The inlet valve actuator takes about 0. 14 s to 0.16 s to pressurize up to full

pressure (80 psig). However it takes about 0.06 to 0.085 s to reach the level high enough to switch the valve. On the other hand, depressurization takes about 0.20 to 0.24 s. Again the valve

closes after about 0.16 s. Similarly, pressur ization of the exhaust valve actuator takes between

0.10 and 0.12 s and depressurization about 0.14 s. The quicker response of the exhaust actuator

results from its being connected directly to the limit switch whereas the inlet actuator is

connected to the limit switch through a NOT element with a smaller port size than the air limit

switch (Fig. 2). There is always a residual pressure at one of the actuators whenever there is

pressure in the other. The residual pressure is about 6 psig for the inlet valve actuator and 12 psig at the exhaust valve actuator. There is no pressure in either actuator only during the

expansion process (and also briefly at the end of the exhaust stroke before the inlet valve opens).

There is also evidence of pressure signals propagating between components through the air pressure

source because of the source impedance.

140
190 T

INTAKE

-10

:utoff

CUTOFF RATIO = 29%

0.0 0.5 1.0 1.5 2.0 DISPLACEMENT (in.)

2.5 3.0

Figure 4. Pressure-displacement diagram for single-phase operation

CUTOFF RATIO = 17%

0.0 0.5 1.0 1.5 2.0 DISPLACEMENT (in.)

2.5 3.0

Figure 5. Pressure-displacement diagram for single-phase operation

141
6. Expander diagrams

Figures 4, 5, and 6 show typical pressure-displacement diagrams for the expander. The

diagrams show a significant drop in pressure during the intake process. A surge chamber of

approximately ten times the expander displacement was provided at the inlet and the piston speed

during intake was kept minimal. The cause of the pressure drop in spite of these precautions is

the high flow resistance in the J-T stage of the Model 1400 liquefier that supplied the inlet gas.

A fairly constant, inlet pressure was obtained in Fig. 4 for operation in the single phase region

with a slow intake process. Table I summarizes time and speed distribution for a typical cycle.

Table 1. Typical time distribution for expander cycle

process piston speed time

(in/s) (s)

intake 0.21 1.87

expansion 9.14 0.28

exhaust 7.76 0.38

dwell at TDC 0. 10 dwell at BDC 0.04

total 2.76

The cycle of Fig. 4 has a blow down loss, while, in contrast, the cycle in Fig. 5 shows

complete expansion. It was possible to adjust the cut-off point to ensure negligible blow down

loss at the expense of expander capacity. The two cycles just described in Figs. 4 and 5 were obtained for single phase operation of the expander. The cut-off ratio is about 20%, which is

defined as cylinder volume at the closing of the inlet valve divided by the maximum cylinder volume

at the end of the stroke. The diagram of Fig. 6 was obtained for a comparable cut-off ratio and

for operation in a two-phase expander mode. The diagram indicates an overexpansion followed by a small recompression.

7. Evaluation of engine performance

The reciprocating expander was tested as a supercritical wet expander and as a single phase

expander using a CTI model 1400 liquefier to supply gas at about 13 atm in the temperature range of

4.2 to 12 K. The efficiency of the wet expander is defined with reference to Fig. 7 as

efficiency = W / W ( 1

)

act rev where

actual work = W . = m(h. - h_) + Q . act 1 3 act reversible work = W = m(h - h_) + Q rev 1 3 rev mass flow rate = m

actual refrigeration = Q . act reversible heat input = Q = m T t (s - s ) rev sat 3 1 inlet enthalpy = h

saturated vapor enthalpy = h^

The actual work is also given by the difference between the indicated work and the heat leak.

This gives an alternative method for evaluating the efficiency. The measurements required to evaluate the performance are therefore: 1. The state (temperature and pressure) of the working

fluid at the inlet and at the exhaust. 2. The actual refrigeration effect. 3- The indicated work

from a P-V trace. 4. Heat leak by static conduction 5. Heat leak due to piston motion.

The experimental setup for obtaining these measurements is shown in Fig. 8. The states of the

helium were measured in the inlet and in the heater tanks. The pressure was measured with a warm pressure gage connected with capillary tubing. The temperature was measured using helium vapor

pressure thermometers.

142
4 1r CTI MODEL 1400 HELIUM LIQUIFIER

J-T VALVE

ENGINE

INLET SURGE

CHAMBER

EXHAUST

SURGE

CHAMBER

MASS FLOW

METER

TEMPERATURE SENSOR

LIQUID LEVEL SENSOR

HEATER

HEATER TANK

Figure 8. Expander test setup

Actual refrigeration capacity was measured as the power to the heating element. The heater

power supplied was adjusted to be just sufficient to evaporate the liquid resulting from the

expansion process so that the leaving stream was saturated vapor. The helium vapor pressure

thermometer was provided to monitor that the gas was not overheated. It was also found necessary

to use a liquid level gauge to maintain a steady liquid level in the heater tank.

The indicated Work was calculated from measurements of the pressure inside the expander

working space and the piston position. The pressure was measured using a high-impedance

piezoelectric miniature pressure transducer operating at expander temperature. The charge output

of the sensing element, a quartz crystal, was fed to a signal conditioning module and converted

into a proportional voltage signal. The transducer was threaded into a mounting adaptor which was connected to the cylinder through a short capillary tube.

The static heat leak to the expander was measured with the engine valves propped open. The

expander and the peripheral apparatus were then cooled down to the operating temperature by

operating the liquefier on the J-T valve. The two-phase flow from the J-T valve was gradually

reduced until a small temperature rise was detected across the expander. The temperatures were recorded from vapor pressure thermometers. To measure the mass flow rate, the cold return gas from

the engine was warmed up external to the liquefier and then passed through a calibrated mass flow

transducer

.

Piston motion heat transfer loss was measured with the setup shown schematically in Fig. 8. The engine was first cooled down to the operating temperature. Both valves were propped open and

the refrigeration capacity of the liquefier operating with the J-T valve was determined by

measurement of heater power required to achieve saturated vapor at the heater tank discharge. With

the valves still propped open, the piston was shuttled by means of the piston motion control

system. Because of the heat loss through this piston motion, the heater supply power to boil away

the liquid (indicating the refrigeration capacity) was reduced. The difference between the two measured capacities gave the loss due to the piston motion.

143

8. Results

Typical state point measurements are summarized in Table II. For the data of the Table, the

single phase expander efficiency is 93 percent. For other tests the single phase expander

efficiency ranged between 91 and and 93 percent.

Table 2. Expander performance data

single phase two phase

operation operation

Inlet pressure (atm) 13.21 13.24

Inlet temperature (K) 11.51 6.55

exhaust pressure (atm) 1.2 1.2

exhaust temperature (K) 4.72 4.42

The performance of the expander operating in the two-phase region was evaluated. Typical data

are

:

Refrigeration effect = Q = 33.4 W act Mass flow rate = m = 2.18 g/s

(from displacement and inlet state)

Reversible work = W = 21.8 W

rev Actual work = W t

= 20.4 W

act Expander efficiency = 94%

The wet expander efficiency was also calculated from the indicated work and the measured heat

leak losses. Typical data are:

Indicated work = W. = 21.4 W

ind

Piston motion loss = 1.3 W

Static heat conduction loss = 1.6 W

Actual work = W t = 18.5 W

act Expander efficiency = 84.5%

The two methods always gave values which differed by less than 10 percent. A major source of

inaccuracy in the result is calculating the mass flow rate from the expander inlet temperature

9. Conclusion

The hydraulic-pneumatic mechanism for piston motion and valve control enabled fairly good

control over the cycle events in the expansion engine. The high efficiencies measured demonstrate

the potential for scaling down reciprocating expanders for cryocooler applications.

The expander was run only long enough to obtain performance data. No endurance data was taken

because the system was assembled from inexpensive catalogue items which were not designed for long

life. Most of the experimental difficulties were the result of the compromises required to use standard items for the hydraulic-pneumatic control system.

The research plan is to modify the apparatus for testing as a vapor compressor operating at 4.2 K. This test will require modification of the connections to the helium liquefier and a modification of the valve control sequence. These modifications are rather simple since the

apparatus was designed for the compressor tests. If the compressor tests are as successful as the

expander tests, the plan is to demonstrate the full potential of the saturated vapor helium

liquefaction cycle. This will require the design an expander and compressor module to match the

model 1400 liquefier, and the replacement of the J-T heat exchanger in the liquefier.

145
10. References

[1] Rios, P. A., An approximate Solution to the Shuttle Heat Transfer Losses in a Reciprocating

Machine, Journal of Engineering for Power , (April 1971 ).

[2] Radebaugh, R. and Zimmerman, J. E. , Shuttle Heat Transfer in Plastic Displacers at Low

Speeds, NBS Special Publication 508.

[3] Lee, K. , Smith, J. L. Jr., and Faulkner, H. B., Performance Loss due to Transient Heat Transfer in the Cylinders of Stirling Engines, 15th Intersociety Energy Conversion

Engineering Conference Proceedings , Vol 2, (1980).

[4] Minta, M., Analytical and Experimental Studies of a Helium Liquefaction Cycle, ScD Thesis,

Department of Mechanical Engineering, MIT, (Feb. 1 984 )

.

146
EXPERIMENTS WITH A FULLY INSTRUMENTED SPLIT STIRLING CRYOCOOLER

Alain FAURE, Serge REALE, Philippe BERNHEIN

L'Air Liquide

Advanced Technology Division

Sassenage 38360 FRANCE

A development program is being undertaken by L'Air Liquide in order

to establish a practical model that can be used to accurately size and

optimise split Stirling cryocoolers.

For any given application the performance of this type of refrigerator must be carefully optimised and, in addition, the specifications for one application may vary greatly from those needed for another (eg. operating temperature, cold power, cold finger volume, size and dead volume

in the interconnecting line etc.). The final optimised design for any

particular application requires time consuming and expensive testing as no system exists for precisely calculating the design from the operating

parameters.

It was necessary to develop a practical model that could be used to extrapolate existing designs to meet different specifications. However in

order to do this detailed knowledge of the dynamic operating parameters

of this type of cryocooler was required.

The first stage of the program has been to fully instrument a refrigerator so that various dynamic parameters could be measured.

The second stage of the program will involve the application of these

measurements to the design and optimisation of a range of coolers.

Key words : cryogenic refrigerator, cryocoolers split Stirling coolers,

refrigeration cycle calculation model, displacer, regenerator, pneumatic

displacer drive.

1 - Introduction

L'Air Liquide has been developing and producing miniature cryocoolers for the last ten

years. Most of this work has been aimed at products mainly intended for military applications.

In addition to the range of open cycle coolers and flash coolers (ambient to 80 K in about

one second), there is an increasing demand for coolers which can operate virtually continuously,

and it was to meet this demand that L'Air Liquide undertook the developnent of split Stirling

cryocoolers.

147
As a result of this work an optimised split Stirling cryocooler has been

designed and built . This machine is shown figure. 1.

RfFRIGERATEUR

SPLIT STIRLING

A major development program was necessary in order to optimise : - the reliability of the cooler and

- the efficiency of the refrigeration cycle.

In order to improve reliability, considerable effort has been devoted

to the development and selection of technologies to minimise

- leaks

- wear due to friction

- pollution caused by the compressor lubricants.

The estimated without maintenance operating time, has been progressively

increased from 500 h to 2000 h (actual test results range from 3000 h to 6000

h) .

In parallel, the efficiency of the refrigeration cycle has been optimised

for given and fixed values of various system parameters. These parameters

include : - thermal mass to be cooled,

- physical size of the dewar,

- thermal losses in the dewar and

- distance between the dewar and the compressor

148
Some of the resulting operating characteristics are shown figure 2.

It is evident that for other applications these parameters, and to some extent the specifications (environment temperatures, cooldown time...), may

vary significantly. Considerable effort would be required to extrapolate and

optimise the existing design for other applications. Consequently a new development program was undertaken, concentrating on the development of a design

model which would permit a range of cryocoolers to be optimised to meet specific requirements.

Figure 2. L'AL RH 820 split Stirling cryocooler caracteristics

Nominal data

base temperature ' 76 K (-197°C)

operating temperature range - 40 °C + 70°C

cooling capacity at 76 K ' 150 - 1000 mW at 20 °C

! 150 - 800 mW at 70 °C Cooldown time ! 4 rn i n power supply ! 20 - 30 V dc

power absorbed ! 60 W at maximum cooling

! 25 W with a 200 mW heat

capacity

load . system reliability ! 2000 operational hours

(without any maintenance or gas purging)

2 - Initial design criteria

2.1. Method selection

Various starting points were considered, as there already exist different

theoritical and practical operating models for the Split Stirling cycle. Such

models vary from the extremely simple where, for instance the cycle is assumed

to be isothermal, to the vastly complex, where each part of the cycle is modeled in detail.

The first type of model is not sufficiently accurate to optimise a practical machine and the second requires the use of complex calculations and calculating methods, access to which is not always easily available.

Moreover, in order to verify any of the existing models it is necessary to

compare the peformance they forecast with the performance and results obtained

from real machine, specifically in the case of the split Stirling cycle, where

the phase shift between pressure and displacement of the piston, and conse- quently the performance, depend greatly on technological problems (friction,

leaks etc...). The corresponding parameters can only be determined by experiment.

In order to do this one must have a system which can be used to measure

all the relevant cycle parameters during the operation. Two experimental

aproaches can be considered

- either build specific test facilities and measure the different parameters (pressure drop, leaks, friction loads, efficiency) under static

conditions « - or equip a real machine with different instruments and use it to measure

the same or equivalent parameters under actual working conditions i.e.

under variable cyclic pressure, temperature, volume etc...

149
The first method is the simplest way to handle the measurement problems.

However, it requires the construction of several specific test assemblies

and the extrapolation of experimental results to actual cryocooler performance

needs elaborate calculation. It will also include approximations resulting from

discrepancies between test conditions and operating conditions. This method

seems well adapted to the development of a rather multi-purpose model for the

prediction of performance for a wide range of machines.

The second method, i.e. measurement of internal parameters on an operating

machine, presents technological difficulties due to the small size of the cryocooler subassemblies and to the high rate of change of the parameters concerned. Provided the associated problems can be solved, this method enables the

definition of a rather simpler model which is well adapted to the sizing of similar machines.

In view of our specific requirements, this second method has been selected. Our efforts were concentrated on the selection and development of the mea- surement methods and the measuring equipment.

2.2. Operating procedure

Generaly speaking the starting point for cryocooler sizing is the power re- quirement at the end of the cold finger. This nett cooling power results from

the difference between. *

- the cold power generated during each cycle by the gas expansion or JPdV

where P is the pressure at the cold tip and dV the variation of the cold

volume and

- the thermal losses (heat conduction, shuttle losses...).

PV diagram recording and simultaneous measurement of the nett cooling power

enable approximation of the total losses and the verification of the corresponding values calculated from the model.

In the same way, instantaneous measurements of pressure, temperature and

volume at both, cold and warm ends of the cold finger can be used to calculate

regenerator efficiency, pressure drop, etc. ..and to establish the correlation

between the thermodynamic gas cycles at both ends of the finger.

Identical measurements in the compressor cylinder(s), the compressor crank

case and the pneumatic spring volume of the cold finger give information which

can be used to determine the total pneumatic power absorbed by the gas and the

different losses due to

- the gas leak from the compressor cylinder to the crankcase

- the gas leak in the pneumatic spring

- the pressure drop in the connecting line

A power balance in the compressor (friction losses, motor efficiency', power

supply and electronic efficiency) gives the required electrical power.

In parallel the force balance in the pneumatic spring allows a comparison

between the forecast and actual displacement of the piston to be made thus

determining the sizing of pneumatic drive .

With this step by step method, based on the previous experimental optimisation of a particular cryocooler for specific operating conditions, cryocoolers can be designed for differents conditions corresponding to other specifications .

150
However, in order to do this the following parameters must be measured and

recorded : - the pressure and the temperature at both cold and warm ends of

the cold finger

- the pressure in the compressor cylinder(s), the pneumatic spring and the compressor crankcase.

- the position of the regenerator-displacer piston and of the compressor

piston( s)

- the gas flow in the connecting line

This adds up to a total of 10 operating parameters.

3 - Experimental arrangement :

3.1 - Test bed :

A RH 800 cryocooler has been used, which is the first development version

of the present standard RH 820 unit. The RH 800 has the following differences

in comparison with the present machine

- single cylinder compressor (The R H 820 is a flat twin compressor to

reduce vibration)

- No temperature control, (the RH 820 model is equipped with a cold end temperature controller to monitor rotational speed and thus cold power with

respect to actual dewar heat losses when operating over the required - - 40°C to 70°C temperature range).

The rotational speed can be adjusted from 800 to 1500 RPM. Apart from rotational speed other operating parameters can be adjusted : - the mean pressure (from 9 to 25 bar)

- the connecting rod diameter of the pneumatic displacer spring

- the cold end temperature

A heater in the test Dewar allowed the temperature to be set at the desired

level

.

3.2. Operating method :

The refrigerator was equipped with the measuring instruments mentioned

above which had to be adapted to cope with the small size and to special operating requirements, such as

- no increase of dead volume (pressure)

- no increase in heat loss (temperature)

- no perturbation of dynamic balance (displacement)

- high frequency response (cycle can last 50 ms and less)

- small dimensions

3.2.1. Pressure measurement :

The pressure sensor must meet the following requirements : - minute size (sensor diameter 1,5 mm ) - no dead volume (less than a few mm3

)

- frequency response 10 kHz

high offset : small pressure variations at a high mean pressure (in

crank case and pneumatic spring)

- low temperature operation (down to 50 K at cold end)

The two last requirements become increasingly difficult when the first

ones are met (problems of the differential pressure, sensor output variations

due to large temperature differences).

151
3.2.2. Temperature measurement : Whilst wall temperature measurements at the warm end present no specific

problems this is not the case for the gas temperature measurements, specifically in the cold expension volume. Thermal inertia requirements leads to the

choice of resistance wire of 1 to 5J+m.

The compromise between power input and temperature resolution at cold end

has been difficult to reach.

3.2.3. Displacement measurement

The small volume available, both on the cold finger and on the compressor,

as well as the problem of not disturbing the equilibrium of the system, have

limited the choice to optical and Eddy current sensors. Availibity problems

with these measuring sensors have delayed the optical measurements.

The Eddy current sensors have been installed perpendicular to the axis of

the piston movements and measure the displacement/distance by means of an inclined groove in the piston, which is machined between the piston rings.

3.2.4. Flow measurement : Though difficult, a hot wire flow meter was installed in a 1 mm diameter

tube, allowing the flow measurements to be made.

3.2.5. Data recording

The rapidly changing parameters required the use of a high performance,

real time data logger to achieve high resolution (better than 1 %) at a rate of more than 100 samples per cycle for 10 measurements, some of which are low level.

3.2.6. Power measurement

A calori metric bench was developped to measure the power balance in the

compresor module. The compressor module was immersed in a boiling Freon bath . The freon vapor from the bath was condensed and weighed in order to measure the

heat input to the bath.

Comparison with electrical input and PV measurements in the compressor cylinder

gives an estimate of

- motor inefficiency (joule losses, eddy current losses)

- friction losses

- non isentropic compression

4 - First experimental results

A considerable amount of development work was required due to problems

encountered with these type of measurement.

Solutions have been found and several hundred sets of parameters have been

tested, each set consisting of : - mean pressure

- compressor motor revolution speed

- connecting rod diameter for displacer

- regenerator diameter in the displacer

- cold end temperature

Some exemples of the recorded data are shown in figure 3.

152
The diagrams 3a and 3b represent an optimal situation. The PV diagram is virtually rectangular. The displacer moves exactly at the maximum and

minimum pressures.

The diagrams 3c and 3d respresent a non-optimised situation

A shape coefficient has been defined in order to measure the level

of optimization .

The variations of the shape coefficient as a function of the parameters

listed above and the influence of the connecting rod diameter of the displacer

in connection with the other parameters are shown in figure 4.

This figure emphasizes the importance of pneumatic drive sizing in order

to have the proper phase shift and thus the maximum cold power.

In addition it illustrates the difficulty in optimising a cryocooler for a wide operating range. A cryocoler can be optimised for the highest frequency

and the maximum pressure and hence have the proper phasing at maximum cold po- wer output resulting in the shortest cool down time and, non-optimised perfor- mance under nominal conditions or vice versa.

For instance a cool down time of less than 2 minutes has been obtained

with a particular design, at the cost of lower specific performance under steady

state conditions.

5 - Conclusion

The first steps in experimental modelisation of the split Stirling cycle

have been made. Having solved the delicate measurement problems a large amount

of experimental data has become available and now awaits processing. The experiments described above give a better insight into the cycle and a better

understanding of the various parameters involved with the dimensioning of

cryoloolers

.

153
FIG. 3 PV DIAGRAM AT THE COLD END

3 a. 3b OPTIMISED CONFIGURATION

Sc.id NON OPTIMISED CONFIGURATION

154
FK3.4 VARIATIONS OF THE PV DIAGRAM AREA

155
LOW FREQUENCY SPLIT CYCLE CRYOCOOLER

S. X. Bian, Y. D. Zhang, W. W. Wan, L. Wang, and Q. C. Hu

Department of Power Machinery Engineering

Xian Jiaotong University

Xian, China

A split cycle Stirling cryocooler with two different drive motors and

operating at a low drive frequency can have high thermodynamic efficiency.

The temperature of the cold end of the cryocooler varies with drive frequency,

voltage of the input electrical power and initial charge pressure values. The

cryocooler operating at 8 Hz can provide 7 watts of refrigeration at 77 K for

230 watts of electrical input power.

Key Words: High efficiency; low power; Stirling cryocooler.

1. Introduction

Cryocoolers for infrared detectors must have high efficiency, small size and weight, low

vibrational levels, high reliability, rapid cool-down and simple operation. If they are to be

used in satellites, long unattended lifetime is also of great importance [1]. These requirements,

generally speaking, can be satisfied by the Stirling cycle, and improvements in the operation of

Stirling coolers have been reported in recent years [21. In the case of direct crankshaft drive,

it is not always possible to obtain ideal dynamic balance and the resulting vibrations may effect

the performance of the infrared elements. For this reason, the split cycle was developed.

However, the net refrigeration of the split cycle, either driven pneumatically or by a linear

motor, is small. In order to get more refrigeration without sacrificing efficiency, we have

tested a low frequency split cycle cryocooler which give 7 watts of refrigeration at 77 K for an input power of 230 watts.

2. Description

The prototype cryocooler consisted of two parts, a compressor unit and a displacer unit,

which are connected by a small diameter tube 30 cm long. Figure 1 shows a sketch of the

cryocooler. The compressor unit is a modified Stirling refrigerator driven by a small DC motor so that its speed can be easily controlled. The displacer unit is driven by a separate DC linear

motor. The cold displacer is made of stainless steel. The case of the displacer is made of epoxy

glass fibre in which a stainless steel net matrix is embedded. The phase angle between the

compressor piston and the displacer is controlled by an electronic system. The consumption of

power for the DC linear motor is less than 10 watts. Using two DC motors with respective voltage,

control devices and the electronic system, it is possible to conveniently and individually control

and adjust the speed of the compressor, the stroke of the displacer and the phase angle between

the compressor piston and the displacer.

3. Results

It is well known that the performance of the cryocooler is dependent on the charge pressure,

the speed of the motor, displacer stroke and compressor stroke, when the diameters of the

compressor and displacer are given. Because the compressor and displacer are separated and driven

by different DC motors, the speed of the compressor and the displacer stroke can be individually

adjusted and controlled [3]. Hence there is an extra parameter - input voltage - added to the

performance of the cryocooler [4].

156
3.1 Influence of Input Voltage to Linear Motor

During operation when the input voltage to the linear motor is varied, the stroke of the

displacer is changed, and the performance of the cryocooler is varied. Figure 2 shows the

variation in the performance of the cryocooler. As the input voltage increases, the stroke of the

displacer increases rapidly. For input voltages greater than 18 V, the stroke is almost constant

(curve Z). The temperature of the cold end is almost constant until the input voltage is over 27

V, when the temperature of the cold end slightly increases (curve T - V,). The curve N. shows

variation of input power of the linear motor with V^.

3.2 Influence of the Speed of the Cryocooler

It is well known that the performance of the cryocooler is dependent on speed for a constant

charge pressure. Figure 3 shows the variation of the temperature of the cold end and of the

stroke of the displacer with the speed of the cryocooler. The T . of the cold end is obtained at

a speed of 480 RPM. The stroke of the displacer also varies witR speed. The curve illustrates

that if the operation of the cryocooler deviates from optimum, the losses increase rapidly.

3.3 Influence of Charge Pressure

The cryocooler was operated with charge pressures ranging from 3.92 bar to 7.84 bar. Figure

4 shows that the temperature of the cold end varied with charge pressure which can be explained by

the change in the stroke of the displacer as the charge pressure is varied.

3.4 Exergy Efficiency

This cryocooler has been tested at about 8 Hz. With the input voltage to the linear motor of

18 V and charge pressure is 7.84 bar, the minimum temperature of cold end is about 34 K. The

cooling time from ambient temperature to T . is about 20 minutes. The exergy efficiency of the

cryocooler n is computed as follows [5]:

T - - ambient temperature (K),

and T - - temperature of cold end (K).

It is rather satisfactory that a small cryocooler showed an exergy efficiency of 8.8%. Table 1 shows the exergy efficiency of different Stirling cycte cryocoolers.

Table 1. Exergy Efficiency of Different Stirling Cryocooler

Type

Refrigeration

(Watt)

Consumed

Power

(Watt)

Exergy

Ef f iciency

(%)

Rhombic driven 0.3 (64 K - 70 K)

1.5 (135 K - 150 K)

30 3.68 - 3.28%

6.11 - 5.0%

Pneumatically driven 0.87 (73 K) 48 5.6%

Entirely electromagnetical ly driven[6] 0.5 (80 K) 30 4.6%

Prototype 7 (77 K) 230 8.8%

where Q - - net refrigeration (W),

N.

t

- - total consumed power (W)

4. Conclusions

The prototype cryocooler showed that a single stage Stirling cooler with a two drive system

and phase angle control can be operated with satisfactory results. It is possible to develop this

drive system for larger systems and to minimize size and height.

157
5. Acknowledgment

The authors would like to thank Professor Z. Y. Zhang for his encouragement and advice.

6. References

Leffel , C, S., and Wingate, C. A., "The Stirling cycle cooler: approaching one year of

maintenance-free life", Advances in Cryogenic Engineering, Vol. 23, 1977, p. 411.

Horn, S. B., Lumpkin, M. E., and Walters, B. T., "Pneumatically driven split-cycle cryogenic

refrigerator", Advances in Cryogenic Engineering, Vol. 19, 1973, p. 216.

Polman, J., de Jonge, A. K. , and Castelijns, A., "Free piston electrodynamic gas compressor"

Proceeding of the 1980 Purdue Compressor Technology Conference", pp. 241-245.

Pollak, Eytan, Soedel , W. , Friedlaender , F. J., and Cohen, R. "Mathematical model of an electrodynamic oscillating refrigeration compressor", Proceedings of the 1980 Purdue'

Compressor Technology Conference", pp. 246-259.

Bian, S. X., Gao, Y. Y., and Wan, W. W., "Small Cryocoolers" , Book, written in Chinese,

Machine-building Industry Press, Beijing, 1983, pp. 39-40.

Davey, G. , The Oxford University Miniature Cryogenic Refrigerator, University of Oxford, UK,

1983.

Compressor Unit Displacer Unit

Figure 1. Sketch of the cryocooler.

158
159
2 4 8 8 10

Pav (kg/cm2

)

Figure 4. Temperature of the cold end T and stroke

of the displacer Z as function of charge c pressure

P av

(n = 540 rpm, V

rf = 27 V).

160
PASSIVE MOTION CONTROL OF PNEUMATICALLY DRIVEN DISPLACERS IN CRYOGENIC COOLERS

N. Pundak; Ricor Ltd., En-Harod Ihud, Israel

and

S. Shtrikman, The Samuel Sebba Professor of Applied Physics

Department of Electronics

Weizmann Institute of Science

Rehovot, Israel

The split cryogenic cooler with a remote cold finger offers many advantages

for use in cooling of infra-red systems. A pneumatic drive for the displacer

in such coolers has since been adopted in many cryocooler designs. This concept

can be significantly improved by causing the displacer to move sinusoidally

rather than in an essentially square wave, as in most of the present models.

The way this motion has been achieved passively is described in detail and its

advantages outlined. Data of minicoolers using the above mentioned concept is presented.

Key Words: Cryocooler; displacer; eddy current; magnetic damper; phase delay;

split Stirling; Stirling cycle.

1. Introduction

One of the major advantages of the Stirling type cooler is its simplicity - being a valveless

system. The gross cooling power Q of thermodynamic cycles in general and the Stirling cycle in particular, can be expressed by th^ equation:

Q

c = d> PdV < 0 . (1)

Note that negative Q means cooling. In steady state, both P and V are the periodical

pressure and volume in th^ expansion chamber at a constant chamber temperature T. To a first

approximation, both P and V vary sinusoidally with time, and as shown directly from eq. (1), the

volume change has to lag behind the pressure change to get cooling. For a given stroke and

pressure pulse, the maximum gross cooling is obtained for a 90 phase delay of volume with respect

to pressure. The optimal selection and the control of the phase angle between the pressure change

and the expansion volume change has a great importance in determining the potential cooling power.

In the integral Stirling cooler the phase angle is maintained and kept constant by a crank

mechanism. The Split Stirling version which gives significant advantage in some applications, for

example to the electro-optic system designer, forces the designer to look for alternative

solutions for the expansion volume cyclic change, and for the creation of the desired phase angle.

A few mechanisms were developed and presented during the last decade; most of them are based on pneumatic drive of the expansion volume cyclic change and on a dry friction, viscous flow or electrical timing as a phase angle control mechanisms [1, 2, 3].

The major problem of the Split-type Stirling coolers is their relatively poor reliability.

The primary factor affecting the reliability of this type of coolers is the dynamic seal wear in the compressor piston seal and the displacer seal of the expander unit. This statement is

specially true in the case where the expander dynamic seal friction controls the motion of the

displacer. Additional factors affecting reliability are solid or gaseous contaminants accumulated

in the regenerator or around the displacer assembly, affecting its motion and degrading its

efficiency. The "conventional" problems, such as external leaks, motor and bearing failure, can

be considered a secondary mode of failure and are not part of this discussion.

161
2. Design Considerations

The basic approach of our new design concept is the elimination of the seal wear and

contaminants modes of failure. The expander is based on a pneumatic drive. In order to allow

high temperature vacuum baking, it is constructed of metal and of 3 Viton static 0-rings only.

The metal displacer has a screen type regenerator. The displacer and driving piston clearance

type seals are constructed of metal (PH 5-15 Stainless Steel) and are located'on the same plunger as shown in fig. 1. The all metal clearance type seals are characterized by their

negligible wear rate and by their very low friction force.

The displacer motion phase delay control is governed by an independent passive mechanism

located in the expander drive compartment. This mechanism consists of magnetic damper and helical

suspension springs. By proper design of the damper mechanism, a near sinusoidal displacer motion

- utilizing practically the full stroke available - with a prescribed phase delay relative to the

pressure wave, can be achieved.

Assuming a sinusoidal pressure wave, the displacer driving force can be expressed by:

F drive

= A A P C0S wt ' (2)

where A is the driving piston cross section area, aP = the difference between the maximum pressure

and the mean pressure (equivalent to the pneumatic volume pressure) and to is the angular frequency

of the displacer. If the desired displacer motion is sinusoidal with, for example, a 90° phase

delay to the pressure wave, it can be expressed by the following quotation:

X = Xo SIN art, (3)

where Xo symbolizes half the maximum stroke possible. The sum of the forces affecting the

displacer motion (neglecting the low value of the dry friction created by the clearance type seal) can be expressed by the following differential equation:

F drive

+ NX + CX + KX = 0 , (4a)

AAP COS oit + Mu>2 Xo SIN art + CXow COS ait + KX SIN art = 0 , (4b)

where C is the damping coefficient, M is the sum of all the expander moving masses and K is the

spring coefficient. As is shown clearly in these equations, the necessary conditions for balance

are:

AAP = CXou) , (5)

M / = K. (5)

Equation 5 shows that the peak damping force must be equal to the peak driving force and eq.

(6) shows that the inertial forces must be balanced by the proper selection of the springs. In addition, the springs determine the average position of the displacer stroke, which is important

in order to obtain symmetrical displacer motion around midstroke. It is important to emphasize

that the damping forces used in these equations are the sum of the drag created by the viscous

flow in the regenerator and the force created by the additional damper. The generator viscous

flow drag is a parasitic by-produce of the regenerator operation. The use of this drag as a sole

damping mechanism to control the proper phase angle (as applied in one of the alternative designs)

(2), enforces a compromise in the regenerator design between the thermodynamic and the viscous

drag requirements.

The magnetic damper, as used in our design, is shown in fig. 2. This device is basically a miniature eddy current generator in which an inverted cup-shaped copper body is reciprocated in radial magnetic field - created by rare earth permanent magnet rings. The copper cup shape is

162
bolted to the end of the displacer driving piston and therefore, both move simultaneously. The

eddy currents generated by the copper cup moving in the magnetic field create a mechanical drag

force proportional to the displacer linear velocity. Proper selection of the magnetic damper

design parameters, taking into consideration the regenerator viscous flow drag, will result in smooth full stroke sinusoidal displacer motion and in the desired phase angle. The amount of

damping forces related to the linear velocity and to the operational frequency, can affect the

displacer stroke as shown in fig. 3. The damper design point must be selected to balance the

driving force with the expander at its cold, steady state, condition.

By using the dry friction phase delay mechanism, almost rectangular in shape, indicator

diagrams can be achieved. This results in maximum cooling power achievable in the given pressure

and volume change made. The sinusoidal displacer motion, however, results in elliptical shape

diagrams with an area about 20% smaller. This reduction is compensated by the lower dynamic

thermal losses which depend on the working gas mass flow rate. These rates are much higher in the

square type diagram than in the smooth elliptical shape diagram. The smooth non-contacting

sinusoidal displacer motion is a very desirable characteristic from the acoustical and mechanical

noise level point of view.

3. Conclusion

1/4 W Split Stirling coolers based on the eddy current damper and clearance seal design

concepts are in production by RICOR LTD. in Israel since 1982. Several hundreds of coolers have

been delivered and are accumulating laboratory and field experience. A 1/4 W Split Stirling

cooler of this concept is shown in fig. 4. Several reliability demonstration tests of the

expander units were performed as part of qualification programs and a proven MTBF higher than 1500

hours was demonstrated. Actually, the expander reliability is limited by contamination originated

in the compressor, and accumulating on the cold surfaces inside the regenerator, around the

displacer tube and in the clearance seals. The combination of our next generation

contamination-free compressors and the present magnetic damper/clearance seal type expanders, will

result in reliability greater than 2500 hours.

4. References

[1] Horn, S. B., Lumpkin, M. E., and Walters, B. T. , "Pneumatically Driven Split Cycle Cryogenic

Refrigeration", Advances in Engineering, 19. P216, 1973.

[2] De Junge, A. K. , "Small Free Piston Stirling Refrigerator", 14th Intersociety Energy

Conversation Engineering Conference, Paper 799245, PI 13 , (1979).

[3] Ackerman, K. A., Bhate, S. K. , Bryne, D. V., "Split Stirling Cycle Displacer Linear Electric

Drive", Refrigeration for Cryogenic Sensors - NASA conference publication 2287, P231

(1983).

163
DRIVING PISTON

PNEUMATIC VOLUME

SEA «- REGION

CLEARANCE TYPE

SEAL ASSEMBLY

OISPLACER

SEAL REGION

ALL METAL DI3PLACER

SCREEN TYPE REGENERATOR

Figure 1. Expander clearance type dynamic seals.

164
Figure 2. Magnetic damper - Conceptional scheme.

165
ure 3. Displacer motion at different damping levels at constant frequency.

166
Figure 4. Ricor Mode K413H 1/4 split Stirling cooler - general view.

167
A NONPROPRIETARY, NONSECRET PROGRAM

FOR CALCULATING STIRLING CRYOCOOLERS

William R. Martini

Martini Engineering

2303 Harris

Richland, WA 99352, USA

(509) 375-0115

Using entirely nonproprietary and nonsecret sources of information, a design program for an integrated Stirling cycle cryocooler has been written on an IBM-PC computer. The program is easy to use and shows the trends and

itemizes the losses. The calculated results have been compared with some measured performance values. In its present form the program predicts somewhat

optimistic performance. The program needs to be calibrated more with experimental measurements. As has been done before, adding a multiplier to the

friction factor can bring the calculated results in line with the limited test results so far available. The program is offered as a good framework on which

to build a truly useful design program for all types of cryocoolers.

Key words: Analysis; computer program; cryocooler; integral cooler; second

order; Stirling cycle.

1. Introduction

When I received a request from a client to produce a cryocooler design program for the

IBM-PC, which both they and I had available, I assumed that such a program would be readily

available from a government agency with an interest in this technology. It would simply

be a matter of adapting it to the client's

computer. We found, however, that access to all these programs is restricted, usually, to

U. S. companies who already have a contract

with a government agency to make cryocoolers.

It is perfectly legitimate to have such re- strictions. However, there needs also to be

available a program that can be used in schools

and by companies who do not have an official

need to know.

Since I had written two design manuals for

Stirling engines, and since many of the equations that were used in these manuals came from

earlier publications showing how to design

cryocoolers, I have undertaken the process of

producing a cryocooler design program analogous

to my numerous Stirling engine design programs.

The previous literature will be cited.

The method of analysis will be explained in

general. The specific arrangement of a Stirling cycle cryocooler for which the program was written is given. A full list of input values

i's presented with typical input values. A sample of the full calculated output is given

and explained. Limited test results are compared with calculated performance and discussed. Application areas for this type of

design program are suggested. Finally, conclusions are drawn about the utility of this type

of design program.

2. Literature Review

A full literature review on cryocooler

analysis is not attempted. Only those antecedent publications that have a bearing on the

computer program described in this paper will

be given. In 1968 the author lead a group of

engineers at the Donald W. Douglas Laboratories, in Richland WA in developing a Stirling

engine for an artificial heart. We developed

our own design method. Gradually we became aware of other methods of analysis. We had

simple methods and very complicated and time

consuming methods. Later the author now at the

Joint Center for Graduate Study, University of

Washington and sponsored by NASA-Lewis, wrote

two design manuals for Stirling engines [1,2].

Also a long IECEC paper outlined in detail this

design method [3]. As a result of these publications this method of design has been used

widely among those who had no access to proprietary information.

There were a number of prior publications

which were discovered in a literature search

which had an important bearing in selecting the

equations that were recommended in the design

168
program which was presented. Crouthamel and

Shelpuk [4] gave all the design equations for a VM cycle cooler. Zimmerman and Longsworth [5]

contributed to our understanding of shuttle

heat loss as did Rios [6]. Leo [7] supplied

the equation for appendix loss. Gorring [8]

supplied the equation for matrix conduction.

Note that many of these publications are in the

cryocooler literature.

Since the design manuals have been written

the author has continued to evaluate and perfect the isothermal analysis. A 1980 IECEC

paper showed that up to that time the isothermal analysis was as good as any other available

[9]. A further extension of this isothermal

program for large machines was done in which

the effect of adiabatic hot and cold gas spaces

was included for both heat engines and heat

pumps. This effect is particularly serious for

engines or heat pumps that operate over a small

temperature ratio. The 1983 IECEC paper showed

that the improved isothermal analysis agreed

with some engine test data over almost the full

operating range for both power output and efficiency to within plus or minus 10 percent with

absolutely no adjustments [10]. Finally the

isothermal analysis has been extended to predict the operation of free-piston machines and

search for an optimum design [11].

3. Method of Analysis

In the literature of Stirling engine design, methods are classified as first, second,

and third order. First order methods use variations of the Beale equation [12] to predict

what the power can be, given the displacement,

speed, pressure and temperatures. This method

has been extended to large cryogenic refrigerators by Walker [13], It does not apply to miniature cryocoolers. The method suggested in

this paper is second order. It will be defined

in more detail later. Second order methods are

the simplest methods that take into account all

the dimensions that influence performance.

Third order methods use nodal analysis to simulate the physical process very closely. They

are expensive to run because they use a large

amount of time on the very largest and fastest

computers. They are useful for special studies, but are not practical to be used in

search routines to find the best design.

The basic assumption of the isothermal,

second order analysis is that at each point in

the cycle the pressure throughout the working

gas volume is the same for each instant in

time. In reality there are pressure differences between the different parts of the working

gas due to flow friction. In a well designed

machine these differences are small in comparision to the pressure changes due to expansion

and compression. Neglecting the pressure differences at this stage greatly simplifies and

speeds the calculation with little loss in

accuracy.

It is also assumed that an effective gas

temperature can be identified for each part of

the working gas volume which holds for the full

cycle. This assumption is easy to defend in

the regenerator where gas is in close thermal

contact with the solid. It is not true and

requires corrections [10] for the hot and cold

spaces of large machines. Careful measurements

of the pressure and total gas volume during one cycle in a Stirling engine for artificial heart

power showed that on this scale the isothermal

assumption was better than the adiabatic as- sumption. The artificial heart engine is on

the same order of size as the miniature cryocoolers .

Using the two above assumptions, it is a simple matter to calculate the pressure during

the cycle usually using the perfect gas law.

If the pressure of the working gas is plotted

against the volume of gas in the cold space, a closed curve is produced. The area inside this curve is equal to the heat absorbed by the

working gas in one cycle. When multiplied by

the frequency we call this the thermodynamic

heat input. If the pressure of the working gas

is plotted against the total working gas volume, a closed curve is also produced. The area

inside this curve is equal to the work required

to be applied in a perfect machine during one

cycle. When multiplied by the frequency, we

call this the thermodynamic power input.

These basic thermodynamic values must be

modified by the many losses that occur in a real cryocooler. To the basic thermodynamic

power must be added the flow losses of the

working gas, chiefly in the regenerator matrix.

Also the seal friction, the mechanical friction, and the electric motor losses must be

added to obtain an estimate of the power re- quired.

From the basic thermodynamic cooling effect must be deducted all the thermal conduction and radiation heat losses. Also the flow

losses in the cold part are converted to heat

which must also be deducted. The matrix heat

transfer is not perfect. Therefore, the gas

returning back to the cold space is at a higher

temperature than when it left and must be re- cooled. Finally, there is a loss involving the

gap between the displacer and the cold finger

cylinder. Heat is transferred by this shuttle

loss only when the displacer oscillates.

Each one of these losses mentioned above

is calculated by an equation. In the second

order method there is assumed to be no interaction between the various loss mechanisms. In a miniature cryocooler accurate estimation of

these loss mechanisms is especially important.

We find that in most cases the mechanical and

electrical losses are more important than the

gas flow losses and the thermodynamic power in

determining the electric power requirement. On

the cooling side, we find that the thermal

169
losses consume most of the thermodynamic cooling effect. Therefore the net cooling effect

is subject to relatively large errors because

it is the small difference between large numbers .

In a miniature cryocooler there is so much

heat transfer area for so little volume that one would be tempted to assume that the heat

transfer is nearly perfect. If tests show that

this is so, calculation of the performance

would be speeded and simplified. We did not

make this assumption. We calculated a heat

transfer coefficient for the hot space and the

cold space and also decided on a heat transfer

area. By trial and error we found an effective

cold gas temperature lower than the specified

cold metal temperature such that the heat that can be transferred based upon the calculated

area and heat transfer coefficient is equal to the heat that needs to be transferred. At the same time by trial and error we found an effective warm space temperature that is higher than

the specified warm metal temperature such that

the heat that can be removed from the warm

space is equal to the heat that must be re- moved. When the fractional error in the heat

balance at both ends is less than the conver- gence criteria for two trials in a row, the

calculation ends and the results are printed

out.

4. Cooler Geometry

Although this program can be adapted to any type of Stirling cryocooler, it is particularly set up for an integral cryocooler shown

schematically in figure 1. An hermetically

sealed electric motor operates two cranks. One

crank operates the displacer in the normal

manner. The other crank operates the displacer

piston in the inverted manner. The cold finger

containing the displacer is in the same plane

as the compressor piston. The two cranks are offset 90 degrees to provide the proper phase

relationship. The program takes into account

the slightly non-sinusiodal nature of the piston and displacer motion due to the crank geometry.

Figure 1. Schematic of Cooler Geometry

-Cold tip

-Cold Space

Cold Finger Regenerator Matrix

Electric Drive Motor

Sealed Crankcase

5. Input Values

The program stores all the input data on a disk file. The user has the option of starting

with the set of input data which was used last

which is on this disk file, or using base case

input data which is written into the program.

The operator makes this decision to start the

program. Then the main menu is displayed on

the screen (table 1). The operator can start

calculating the next case by keying in a 1 or look at one of seven submenus by keying in 2 thru 8.

Table 1. Main menu for input.

WIN MENU

1 — Start calculating next case. 2 — Pros ran control paraneters. 3 — Engine operating conditions. k — Pistons and connect ins rods and crank case. 5 — Hare flow passages. 6 — Regenerator properties. 7 — Cold flew passages. 8 — Heat cond.t seal, and notor. Your choice is — (Key number and enter) —6

Program control parameters. Table 2 shows

the menu for all the program control parameters. On the left hand side is the menu number. In the middle is the definition. On the

right hand side is the current value. Note

that at the bottom of the table a menu number

is called for. The operator puts in an integer

between 1 and 8 (No decimal point.). If a real

number with a decimal point, or an integer

outside of the specified range is entered the

program displays the appropriate error message

and asks for the menu number again. If 1 is

entered the program displays the master menu

again.

Table 2. Submenu for Program Control Paramenters

Program control parameters:

1 — Return to wain Menu. 2 — Convergence criteria. .W1B

3 — Case number defined by operator. 31 4 — Graphic option — 0=no» l=yes 1 5 — Printing option -- 8=no. l=yes 0 5 — Number of time steps per cycle. 24 7 — Pressure drop option 3 0 = Calculate fro* pressure drop correlation.

1 = Calculate from pressure drop test. 8 — Reheat loss option 0

0 = Calculate from heat transfer correlation.

1 = Calculate from pressure drop test using Reynolds analogy. 9 — MultiPl ier for friction factor ).f® Menu number'' 1

If 2 is entered, the program then asks

that a real number be entered with a decimal

point. This convergence criteria is compared

Compressor Crank Displacer Crank 170
witH the fractional change from one trial to the next of the thermodynamic power input and

the thermodynamic heat input. This criteria

must be a small positive real number. The

program checks to see if the number input is

between 0.0 and 0.1. If it is, the convergence

criteria is changed to the new value, and the menu is displayed again with the new value in

place. If the number that is input is not

within the specified range, an error message is

displayed, and the menu is redisplayed without

change.

If 3 is entered, the program asks for an

integer. If this case number is negative, the

program rejects it and asks for another.

Otherwise the case number can be set to any

number desired. The case number is automatically indexed without operator attention.

If 4 is entered, the graphic option can be

changed. Some IBM-PC's have the ability to draw graphs on the screen. Others do not. The

program can be used either way. If the computer does not have the ability to do graphics

and the graphics option is set at 1, the computer will probably hang up. The program will

have to be restarted.

If 5 is entered, the printing option can

be changed. Since some computers are equipped

with printers and others are not, the program

can be used either way. If a printer is called

for but is not connected, the program will

stop.

If 6 is entered, the number of time steps

per cycle can be changed. More time steps

leads to higher accuracy at the expense of

speed of computation. Twenty-four has been

found to be a good compromise. A formula has

been developed to compensate for a small number

of time steps [1]. However, is has not been

used in this particular program.

If 7 is entered, the option on the way

flow losses are calculated can be changed. For

the 0 option, the flow loss is determined based

upon a correlation by Kays and London as simplified by Martini [2]. For the 1 option, the

flow resistance test used to qualify the displacer for use is employed instead. Other

options can be added as needed.

If 8 is entered, the option on the way the

heat transfer coefficient for the regenerator

is calculated can be changed. For the 0 option, a simplified Kays and London correlation

is used [2]. For the 1 option, the heat transfer coefficient is derived from the flow friction test using Reynolds analogy. Other options can be added as needed.

If 9 is entered, a multiplier on the friction factor can be changed. If. the Kays and

London correlation is used, this factor is

multiplied by the calculated friction factor to

give the friction factor used to calculate flow

loss. If the pressure drop test data is used,

the computed pressure drop is multiplied by

this factor.

Engine operating conditions. Table 3 shows the menu for the engine operating conditions. The menu is shown twice to illustrate

how it is changed. The inputs are self explanatory. The program adjusts the working gas

inventory for the first 4 cycles to make the

time averaged working gas pressure equal to the

input value. After that leakage continues to operate between and crank case and the working

gas. An effort has been made to ask for the

input values in customary units. They are then

converted to a consistent set of units in the

program.

Table 3. Submenu for Engine Operating Conditions

En9ine operating conditions!

1 — Return to main menu. 2 — Average working gas pressure! psis iifflM 3 ~ Motor speed, rpm 12(30.88 4 -- Metal temperature in cold space, K I^M

5 — Metal temperature in war* space, F R8.0P

Menu number 7 4 Value? (with decimal Point)E0. Engine operating conditions:

1 -- Return to main menu. 2 -- Overage working gas pressure, psis 3 — fiotor speed, rpm 12W.W

k — Metal temperature in cold space. K 80,60 5 — Metal temperature in warn space, F Btt.SP

Menu number?

Pistons -- connecting rods -- crankcase

Table 4 shows the menu which allows values

connected with the mechanical motion to be

changed. The same organization is used as with

previous tables. There is enough space to clearly define each input value and give the

units. At present the volume of the crank case

space is not known very well and is not used in

the calculation. Strictly, however, it should

be used in leakage calculations and in kinetic

simulations of the cooler.

Table 4. Submenu to change inputs related to pistons, connecting rods and crankcase

Pistons and connecting rods and crank case.

1 — Return to main menu. 2 — Crank angle, degrees 96. UP 3 — Diameter of conpressor Piston, inch .5520

4 — Seal diameter at dispiacer, inch . i875 5 — Radius of compressor Piston crank, inch . P580

E — Radius of dispiacer drive crank, inch . .K5P

7 -- Length of compressor Piston conn, rod, inch .4180 S — Length of dispiacer drive conn, rod, inch 1.2!$? S — Volume of crank case space, cu. inches 2.BJM

Menu number'' 1

171
Warm flow passages Table 5 shows the

submenu which allows values connected with the warm flow passages to be changed. Most of the

entries are self explanatory by reference to figure 1. The warm displacer duct is the hole

thru the seal and bearing part of the displacer

to allow gas to pass from the connecting tube

to the warm end of the regenerator matrix. The

number of velocity heads are used to account

for the flow resistances of entrances, exits

and bends in the gas flow passages. Standard

handbook values were used [13]. The dead volume is an estimate of the dead volume in the warm space in addition to that in the piston

end clearance, connecting tube, and the warm

displacer duct.

Table 5. Submenu for Warm Flow Passage Values

Ham flow passages:

1 — Return to twin menu. 2 — Diameter of connecting tubei inch 3 — Diameter of warm displacer ducti inch 4 — Effective compressor Piston clearance* inch 5 — Length of connecting tube* inch 6 — Length of warm displacer duct, inch

._ 2

0520 0835

2940

2.26

2.24 7 — Nuniber of velocity heads in connecting tube —

S — Number of velocity heads in displacer duct 9 — Dead volume at warm end of displacer. cu. inch Menu number? 1

Regenerator properties Table 6 shows the

submenu which allows values connected with the

regenerator to be changed. The length of the

regenerator matrix includes space for the two coarse screens on each end. The porosity of

the matrix is computed from the total volume of

the fine matrix, the weight of the fine screens, and the density of stainless steel

(7.817 g/cc)

Table 6. Submenu for Regenerator Properties

Regenerator properties!

1 — Return to main menu. 2 — Inside diameter of displacer cylinder, inch 3 — Diameter of regenerator matrix, inch 4 — Hire diameter in regenerator matrix, inch 5 — Square mesh of screens in res. matrix, wires/in._ 6 — Number of fine screens in res. uatrix. 7 — Length of regenerator Matrix, inch 8 — Height of fine regenerator screens, grams 9 — Number of coarse end screens in matrix

10 - Thickness of each coarse end screen, inch

11 - Test flow rate of N2 thru disPl., std cc/min. —

12 - Pressure drop at test flow rate, psi Menu number? 1

.1840

.1250

.0009 500.00

909 2.2580

1.3180

4 .8140 710.00

10.00

Table 7. Submenu for Cold Flow Passages

Cold flow passages:

1 — Return to main menu. 2 — Diameter of cold orifice inch .0780 3 — Effective displacer clearance at cold end, inch_ .0050 4 — Length of cold orifice, inch .0400 5 — Number of velocity heads in cold orifice 1.50

Menu number? 1

Heat conduction, seal, and motor properties Table 8 shows the submenu which allows

values connected with heat conduction, seal,

and motor properties to be changed. All the

input values in this list, except for the inch

dimensions are difficult to determine. The

emmissivities can vary over a wide range depending upon the exact properties of the surfaces.

However the heat loss thru the vacuum insulation is small in any case, so these errors are unimportant. The efficiency of the drive motor

and the seal and mechanical fricition are very

important. They must be measured by separate

tests. In this case the efficiency of the

motor was estimated from the motor specifications. The seal and mechanical friction was determined by adjusting it so that the electric

power demand at the very beginning of a cool

down test was about right. The speed of the

motor during this test was not recorded and had

to be estimated. In reality the seal and mechanical friction should depend upon engine speed

and working gas pressure. More realistic friction can be added when the information is

available.

Table 8. Submenu for Heat Conduction,

Motor Values.

Seal and

Heat conduction, seal, and motor values:

1 — Return to main menu. 2 — Diameter of vacuum insulation chamber, 3 — Efficiency of drive motor, % 4 — Emissivity of cold finger 5 — Emissivity of vacuum insulation chamber 6 — Combined seal leakage, cu. inch/sec/psi 7 — Seal and mechanical friction, watts 8 — Thickness of cold finger wall, inch

inch 60.00

0450 0380

8801

9 — Gap between cold finser wall and displacer, inch

Menu number? 1

0868

6. Calculated Outputs

Cold flow passages Table 7 shows the

submenu which allows values connected with the

cold flow passages to be changed. In this case

there is a single orifice which squirts gas

into the cold space. The correlation by Hauser

[16] was used to calculate the heat transfer

coefficient in the cold space.

During solution two outputs are possible.

If the graphic option is on, a display is shown

on the screen like that shown in figure 2. This display is very useful to show at a glance

whether the solution is converging and where

some of the problems in design are. The ellipses at the right show the gas pressure plotted

against the total volume. The first cycle is on

172
top. The other 6 cycle are below as the gas

pressure is adjusted. The ellipses at the left are the cold gas volume plotted against the

working gas pressure. The sine curve at the

top is the displacer motion for one cycle. The

sine curve at the bottom is the compressor

motion for one cycle. The nearly horizontal

line at the top left records the trials of the

effective warm space temperature. Full vertical

scale is 0-400 K. Note that most of the

adjustment is made after the first cycle. The

nearly horizontal line at the bottom left re- cords the trials for the effective cold space

temperature. Note that there was little

change.

Figure 2. Graphical Display during Solution

If the graphic option is off, Table 9 is

displayed on the screen. The numbers in the

first two columns are the numbers that are compared with the convergence criteria which is

shown in the top line of Table 9. These fractional changes for cycle 6 and 7 were all under

0.001. Note that the work in and the heat out

are now only changing in the fourth significant

figure. The last column, the gas inventory,

has unusual units. It is the gas inventory in

gram moles multiplied by the universal gas

constant, 8.314 J/(gmol*K).

Table 9. Progress to convergence table

Conversence criteria is> .00110 for Run • 31 Cycle Chans? Chans* Wort Cool ins End Tine Gas Nu*. Potter In Cool In In In Pressure Step Invent.

Frac. Frac. Joules Joules MPi Msec. J/K

1 1.001868 .999676 .185957 .064755 2.E003 1.5015 .0132520

2 .173488 .195875 .172291 .052871 2.6343 1.5015 .0128819

3 .852747 .823358 .163204 .030855 2.6295 1.5015 .0128738

4 .804126 .888079 .162530 .058851 2.6286 1.5015 .8128912

5 .808381 .801417 .162690 .050923 2.6286 1.5015 .8128933

6 .088338 .800137 .162743 .050930 2.6275 1.5015 .8128877

7 .088388 .800443 . 162681 .058907 2.62E5 1.5015 .0128823

Speed of Solution On the IBM-PC equipped

with the 8087 coprocessor, and running Microsoft FORTRAN- 77 , the solution time for the

above same case with 7 iterations is 6 seconds

without graphics and 20 seconds with graphics.

This does not include the time for printing out

or displaying the solution. The display of the

output to the screen takes 2.4 seconds additional. The printout takes much longer and

depends upon the type of printer that is being

used. With some type of spooler, printing can

lag behind. Meanwhile the operator may investigate new possibilities using the information

available at the monitor.

Calculated Performance At the end of the

solution, the table of calculated performance

is displayed on the monitor and is printed out

as well, if the print option is on. Table 10

is the calculated performance for the input

values given in Tables 2 to 8. The first thing

to notice is that some losses are very impor- tant and some are negligible. However, it is

dangerous to neglect the negligible losses in

the design calculation. If you do your search

for a better design will lead you into an area where these negligible losses are no longer

negligible

.

Table 10. Calculated Performance

Martini Ens. Analysis of Stirling Cycle Cryocooter

Integral Geonetry. **CflLCULATED PERFORMANCE**

POWER REQUIREMENT. WATTS

Thernodynati. Power 4.5144

Cld. Orfc. F.L._ .0001

Res. Flow Loss _ 1.2366

Disp. Duct.F.L- .0367

Conn. Tube F.L._ .0027

Hech. Friction _ 7.8080

Elect. Htr. Loss. 9.0603

Elect. Pwr.In 22.6588

Eff.Cld.Sp.TenP..K- 78.1260

Eff.WrH.Sp.TettPo.K.324.3140

COOLING EFFECT, WATTS The r. Dm. Coo I ins Eff. 1.4127

Cld. Orfc. Fric. Heat .0001 Resen. Fric. Heat .6183 Shuttle Heat Loss .1257 Reheat Loss .1190 Appendix Loss .0380

TeitP. Swins Loss .0005

Cld. Finser Wall Cnd. .1206

Dsp. Wall Cond. .0123

Res. Mtx. Cond. .0077

Vac. Irani. Heat Loss .0011 NET COOLING EFFECT .3695

On the power requirement side, note the

mechanical friction and the electrical motor

losses are the two big ones accounting together

for 74.4 7. of the power requirement. The flow

loss thru the regenerator accounts for 5.5 7. of

the power requirement. All the other flow

losses account for only 0.2 7., leaving 19.9 7. for the necessary thermodynamic power. Obviously the place to start with improvements is to find some way to reduce the mechanical and

electrical losses.

On the cooling effect side, it appears

that only 26.2 7. of the thermodynamic cooling

effect survives the gauntlet of losses to be- come net cooling effect. In this analysis it

is assumed that all the cold orifice flow loss

and half the regenerator flow loss must be

173
deducted as heat loss from the thermodynamic

cooling effect.

The shuttle heat loss and the appendix

loss must be considered together, because as one increases the other decreases. Shuttle

heat loss occurs by radial conduction across

the gap between the cold finger cylinder and

the displacer. Because of the longitudinal

temperature gradient along the cold finger

cylinder and along the displacer, when the

displacer is at the warm end of its stroke it

is colder than the cold finger cylinder all the

way along, so it heats up. When the displacer

is at the cold end of its stroke, it is warmer

than the cold finger cylinder, so it cools

down. Each cycle this process moves the heat

that has been transferred one stroke length

toward the cold end. This important heat loss can be minimized by using low conductivity

cylinder walls such as plastic or glass or ceramic. The loss can be minimized by increasing the gap and increasing the length of the

regenerator.

Appendix loss occurs as the gas is packed

into and unpocked from the appendix gap between

the displacer and the cold finger wall. This

gap is closed off at the warm end with a sliding seal and is open at the cold end to the

cold space. As the pressure increases cold gas

is packed into this space. As the pressure

decreases not so cold gas flows back into the

cold space. Increasing the thickness of the

gap reduces shuttle loss but increases the

appendix loss.

A number of equations have been published

for shuttle heat loss and for appendix heat

loss. As far as is known there has been no experimental confirmation published of any of

these equations.

The reheat loss should, for a cryocooler,

be called the recool loss. Both due to pres- sure changes and flow, a large amount of heat

must be transferred each cycle in the regenerator. No matter how good the heat transfer, the

gas always re-enters the cold space warmer than

when it left. The reheat loss can be made

small at the expense of making the flow heating

or the heat conduction loss or both too large. A careful balancing of dimensions is needed.

The temperature swing loss is a correction

to the reheat loss to compensate for the heat

capacity of the regenerator being less than

infinite. In this case it is negligible, but

it can be important.

The last 4 losses are heat conduction or radiation losses that go on whether the displacer moves or not. By far the largest is the

cold finger wall since this must be thick and

metal to hold back the pressure and contain the

helium. The displacer wall conduction is much

less because this is made of plastic. The displacer matrix conduction is even smaller because the metal screens are divided and make

contact only in a few spots. Vacuum insulation

loss is negligible.

Record keeping The operator can continue

to experiment with the computer program to see how different inputs affect the output. He can

do this without waiting for1 the printer on line

at all. However with a spooler of some sort,

the printer can keep track of all the inputs

and all the outputs for further study. It may

be running many cases behind what the operator

is considering. After the output of table 10,

the full input values are printed out. These

values are printed out in the same order as they are shown in tables 2 to 8.

7. Results and Discussion

Figure 3 shows how the computed perfor- mance without any adjustmentof the calculation

proceedure with test results. The net cooling

effect is plotted against the cold finger tem- perature. Note that if the flow resistance

data is used for both the flow loss and the

reheat that the net cooling is too optimistic

by 0.2 to 0.3 watts. If the Kays and London

correlations are used, the net cooling is

optimistic by 0.12 watts. From the data that

so far has been obtained, it appears that when

the cryocooler motor speed was not measured

that it was running at 1600 to 1700 rpm. Fig- ure 3 shows that the calculated and measured

performance shows the same trend.

For the flow rate that results in a 10

psi pressure drop thru the displacer, the Kays

and London correlation calculated 18.4 psi.

Also a number of investigators have found that

the flow resistance calculated for steady flow

must be multiplied by a factor to make the

measurements and the predictions for engines

agree more closely. At one time the author used

a factor of 2.9 to make the calculated output

agree with measurements for both helium and

hydrogen [17]. Tew [18] used a factor of 4 for

hydrogen and 3 for helium to make his calculations agree with test results. A recent test reported by Taylor and Aghili [14] showed that

oscillating flow in tubes increased the friction factor by a factor of about 3. Possibly

finding the right multiplier between reversing

flow and steady flow resistance and the right

way to apply this multiplier could bring the

experimental and test results into agreement.

Figure 4 shows the first attempt at adjusting the program to fit the current experimental data. When the flow resistance test data are used, a mutiplier on the computed pressure

drop of 3.3 to 3.6 is needed to bring the

computed results in line with the measurements.

The measurements are consistant in that they

show a trend with very little scatter. The

computed results derived from flow resistance

test data do not show quite the same trend.

174
When the Kays and London flow correlation

is used, the multiplier only has to be 1.25.

Also the trends in the data and the adjusted

calculation are the same. The correlation

shows a transition from pressure drop proportional to flow rate to pressure drop proportional to the square the the flow rate in a smooth manner over a factor of about 10 in flow

rate. Possibly the pressure drop is not directly proportional to the flow rate.

These exercises in adjustment have been

successful in showing that adjustments can be

made. However, when we have more information,

particularly the motor speed, for each point, our conclusions may be quite different than

they are now. However, the isothermal method

has an important advantage in that it itemizes

the losses and therefore gives guidance about

where to make improvements.

8. Application Areas

Although the specific cryocooler design

program described in this paper is for an integral Stirling cryocooler, The same programing

concept can be applied to split Stirling and

free-piston Stirling machines. A free-piston

engine has been calculated using this type of

analysis [11]. The speed for calculating each

case is fast enough so that once the design

method is calibrated, an optimization search

can be programed to search for the best design

automatically. A thorough optimization search

is already programed [11].

9. Conclusions

Using only open sources of information, a cryocooler design program has been written

which gives reasonable results. It requires

inputs of cooler dimensions, measured flow

losses, mechanical friction, and electric motor

losses. Since the current error between calculated and measured performance is not large,

and since the calculated performance shows the same trend as the measured performance, we expect that this computer program can be adjusted to model a real cryocooler quite exactly.

The program needs to be adapted and customized

for each user since there are so many ways to build a cryocooler. Also skill is needed in

making the proper adjustments so that the program will be accurate over a wide range of

design options. In itemizing the losses the

program shows clearly where the greatest improvements in design can be made.

10. References

[1] Martini, W. R., Stirling engine design

manual, DOE/NASA/3152-78/1

NASA CR-135382 (April 1978)

[2] Martini, W. R., Stirling engine design

manual, second edition, DOE/NASA/3194-1

NASA CR-168088 (Jan. 1983)

[3] Martini, W. R., A simple method of calcula

ting Stirling engines for engine design

optimization, 1978 IECEC Record 1753-1752.

[4] Crouthamel, M. S., and Shelpuk, B., Regenerative gas cycle air conditioning using

solar energy, Advanced Technology

Laboratories ATL-CR-75-10 (Aug. 1975)

[5] Zimmerman, F. J., and Longsworth, R. C,

Shuttle heat transfer, Advances in Cryogenic

Engineering, Vol. 16, 342-351, Plenum

Press (1971)

[6] Rios, P. A., An approximate solution to the

shuttle heat- transfer losses in a reciprocating machine, Journal of Engineering for

Power, 177-182, (April 1971)

[7] Leo, B., Designer's handbook for spaceborne

two-stage Vuilleumier cryogenic refrigerators, Air Force Flight Dynamics Laboratory,

Report No. AFFDL-TR-70-54 , (June 1971)

[8] Gorring, R. L. , and Churchill, S. W. , Thermal

conductivity of hetrogeneous materials,

Chemical Engineering Progress, 53-59

(July 1961)

[9] Martini, W. R., Validation of published

Stirling engine design methods using engine

characteristics from the literature, 1980

IECEC Record, 2245-2250

[10] Martini, W. R., A revised isothermal

analysis program for Stirling engines, 1983

IECEC Record, 743-748

[11] Martini, W. R., Development of free-piston

Stirling engine performance and optimization codes based on Martini simulation

technique (May 1984) To be published by

NASA-Lewis.

[12] Stirling Engine Newsletter, p. 5 (May 1982)

Martini Engineering

[13] Walker, G., Design guidelines for large

Stirling cryocoolers, University of

Calgary, Mechanical Engineering Dept.

(1982)

[14] Taylor, D. R., and Aghili, H., An investigation of oscillating flow in tubes, 1984

IECEC Record, 2033-2036 (Aug. 1984)

[15] Perry, J. H., (editor) Chemical engineers'

handbook, Third Edition, McGraw-Hill

388 (1950)

[16] Hauser, S. G., Experimental measurements

of transient heat transfer to gas inside a closed space, Masters thesis, University

of Washington (1979)

175
[17] Martini, W. R., A simple, non-proprietary

code for Stirling engine design, Presented

at DOE Highway Vehicle Systems Contractors'

Coordination Meeting, 16-20 Oct. 1978.

[18] Tew, R. C, Thieme, L. G., and Miao, D. , Initial comparison of single cylinder

Stirling engine computer model predictions

with test results., DOE/NASA/1040-78/30

NASA TM-79044, Presented at International

Congress and Exposition SAE, Detroit, MI Feb. 26 - Mar. 4, 1979

Figure 3 Comparison of calculated cooling

effect without adjustments with measurements.

Figure 4. Comparison of calculated cooling

effect with adjustments with measurements

Ctlcultted NmiwM

- 0.6

Symbol SpeedRPH sat, - 0.5 0

A

1665

1665 166S

Tilt

Tltt

Corr.

3. JO 3.60

1.25

A

•

1665?

16*57 1200

1300

1425 1665 - 0.« "FFM" Friction Factor m1t1p]1«r •

T

Cold Tip Temperature , K

176
A SIMPLE, FIRST STEP TO THE OPTIMIZATION OF REGENERATOR GEOMETRY

Ray Radebaugh and Beverly Louie

Chemical Engineering Science Division

National Bureau of Standards

Boulder, Colorado 80303

This paper presents a simplified set of equations

for calculating and optimizing regenerator geometries.

A number of competing parameters must be accounted for

in the design of a regenerator. To obtain high values

of effectiveness, there is need for a large surface

area for heat transfer and high heat capacity. The void

volume should be small to maintain the pressure ratio in

the entire system. Moreover, the pressure drop should

be small compared to the absolute pressure. With the

assumptions made here, the calculations can be done with

a hand calculator.

The equations show that the optimum regenerator length,

hydraulic radius, and porosity are independent of mass flow

rate and the gas cross-sectional area is proportional to the mass flow rate. It is shown that using gas gaps

between parallel plates produces a significantly better

regenerator than is possible with packed spheres or screens, particularly at temperatures below approximately 50 K. The improvement is due to enhanced heat transfer and the

flexibility in using a lower porosity in the gap configuration.

Keywords: Cryocoolers, cryogenics, gaps, geometry,

heat exchangers, optimization, packed spheres, regenerators.

1. Introduction

The regenerator is often one of the major loss sources in regenerative-cycle refrigerators.

It contributes loss terms due to its limited heat transfer units, limited matrix specific heat,

pressure drop, dead volume, and axial thermal conduction. An optimum design of these re- generators would significantly improve the performance of the overall refrigerator.

The calculation of regenerator performance with various assumptions has been discussed extensively in the literature. First order calculations assume the void volume in the regenerator is zero. Such calculations were first done by Lambertson [1] and Hausen [2] with graphs and tables

presented in the books by Kays and London [3] and Schmidt and Willmott [4]. Second order calculations take into account the regenerator void volume but neglect any pressure oscillation in the

void volume gas. These calculations have been done by Heggs and Carpenter [5], by Daney and

Radebaugh [6], and by others cited in these two works. A third order calculation considers void

volume in the regenerator and a pressure oscillation as seen by regenerators in regenerativecycle refrigerators. Gary, et al. [7] discuss such a third order calculation where very few as- sumptions are made.

*Work partially funded by the David Taylor Naval Ship R&D Center and the Office of Naval

Research.

177
All of the cited calculations require the regenerator geometry as the input parameter and

compute the regenerator effectiveness. The problem facing the designer is how to determine the

optimum geometry without resorting to trial and error through such performance calculations.

Such an approach can be very costly and time consuming, especially for third order calculations

where considerable computer time is required for each case. In this paper we discuss a simple

technique for determining the optimum geometry associated with a desired value of regenerator

effectiveness. The technique reverses the "normal" first order calculations and computes the

various geometrical parameters that give the minimum regenerator void volume. If the void volume

is not negligible a second iteration should be done with reversed second or third order calculations.

2. Basis for optimization

In any optimization scheme it is important to determine the proper parameter to be optimized. Most often the input power is minimized for a refrigerator with a specified net refrigeration power. (In some applications, such as cooling SQUID's, the net refrigeration power is zero

and the gross refrigeration is used entirely for loss terms. Nevertheless, the input power is

still the quantity to be minimized in SQUID cryocoolers. ) It would appear that a general system

requirement would preclude a simple optimization of a single component like a regenerator, especially when the regenerator may consist of several stages. Any exact analysis must consider the

entire system as a coupled system and various loss terms will necessarily be dependent on each

other. However, Smith and coworkers [8-11] have found that a decoupled approach to the loss terms

has resulted in relatively good approximations to the overall system performance. In the decoupled approximation the gross refrigeration power, Q , is absorbed by several independent terms: Q=Q+Q^ y

+ Q+ Q +Q+Q. + , (1)

r y net Vad x

x reg

y

s xh ' v J

where Q ne

^. is the net refrigeration power, Q

racj is the radiation loss, Q

c is the conduction loss,

Q is the loss due to regenerator ineffectiveness, Q is the shuttle heat loss due to the oscil- reg a ' x

s lating displacer, and is the loss caused by an excess enthalpy flow through the regenerator

during the hot blow for certain conditions with a non-ideal gas. Another possible term would be one due to the pressure drop, AP, in the system. That term would be used whenever Q

r is

calculated from the pressure amplitude at the compressor. If Q

r is calculated from the pressure

amplitude at the expansion space, then no such term would be used, but the pressure drop would

indicate the required pressure amplitude at the compressor.

In the decoupled approximation of eq. (1) the entire system is optimized by minimizing Q

r for

a fixed value of Q .. For an ideal gas = 0. For the second and third stages Q

racj is often

negligible. The other terms, Q

c

, Q reg, and Q

s

, are then usually of comparable values when a minimum is found. Likewise, the percentage loss due to a pressure drop, AP/P, will be comparable

to the percentage loss of these other three terms. The simplest approximation for Q

r assumes an isothermal expansion. If an adiabatic expansion is considered, is reduced by approximately a factor of two [12].

178
In dimensionless form eq.(l) is given as

Q +/Q + Q a/Q + Q /Q + x Q /Q + 6 /Q + 6. /Q + =1 (2) net y

r

v rad H

r xc yr x reg y

r y

s yr yh Hr

For any particular refrigerator an experienced designer can then make reasonable estimates of

such terms as Q

c /Q

r and Q reg

/Q

r and AP/P. For example, with an ideal gas in a cryocooler where

Q net/Q

r is to be small, the aforementioned terms may be approximately 0.1-0.2. Good estimates of

these terms are the first and most important step in the optimization of a regenerator. The performance of the overall system is also affected by the void volume of the regenerator, V . A normalized void volume would be V

rg/V

g

, where V

g is the expansion space volume. The four terms

^reg^r' ^c^r' Af> / p > and V rg^

V

e are 1 nterre ^ ated; a decrease of one must cause an increase of

another.

The basis for the optimization procedure described herein is to use Q reg/Q r > Q(/Q r

> ancJ AP/P

as known input parameters and then find the geometry which gives a minimum v

rg/ve

- At an early,

intermediate point, the regenerator ineffectiveness assoicated with Q reg/Q r 1S calculated. If V

rg/V

g << 1, then the input parameters could be decreased to the point where Vrg/Ve becomes

significant. If V

rg/V

g >> 1> then the three input parameters must be increased. If the values

are as large as they can be, the process probably is not feasible with the conditions chosen,

unless an abnormally large compressor is used. The optimization done here is not fully rigorous

since estimates are used for the input parameters and the effects of AP/P and V

r g/Vg on the

system are not fully quantified.

The geometry of a regenerator can be divided into two components: (a) the configuration of

the packing, such as packed spheres, plates, tubes, etc. and (b) the macroscopic geometry, such

as cross-sectional area, porosity, length, and hydraulic radius. The optimization procedure

discussed here treats both components. The best configuration is the one which has the highest

heat transfer rate for a fixed pressure drop. However, any configuration may be chosen and the

optimization procedure then gives the best geometrical parameters. Pressure drop and heat

transfer correlations often incorporate the friction factor, f, and the Stanton number

N st = h/(m/A )c , (3)

where h is the heat transfer coefficient, m is the mass flow rate, is the gas cross-sectional

area, and c

p is the specific heat of the gas at constant pressure.

2/3 Figure 1 shows a plot of N .N and f as a function of the Reynolds number, N , for one

st pr

particular configuration, an infinitely long and wide gap. The two curves of N st

N pr are for the

case of constant heat flow and for constant temperature. Kays and London [3] provide the

correlations for gaps and several other configurations. The Prandtl number Npr

is included to make the correlations valid for a wide range of fluids. For helium gas N = 0.666 under ideal

2/3 P r conditions. Note that both N^N

r and f have nearly the same dependence on N^. For regenerators the curve of interest is that of constant heat flow. The practical difficulty in

179
achieving a uniform hydraulic radius, however, suggests the lower, constant temperature curve may

be more realistic.

We define the ratio: a = N + N 2/3

/f

st pr

(4)

A high value of a is desired since it gives a high heat transfer for a given pressure drop. (A more quantitative argument is given later.) Figure 2 shows a as a function of the Reynolds num- ber for several packing configurations and for a constant temperature heat transfer. The data are from Kays and London [3]. The two important points to note from these curves are (a) they

are nearly independent of Reynolds number, and (b) a gap configuration has the highest a - significantly higher than that of a packed bed of spheres. Because a is nearly independent of

Reynolds number, it becomes a useful parameter to use in calculations since there is no need to specify the flow rate.

10" 10^

l I I I u I J I I I I I 1 1

1

10J 10*

0.02

0.010.2 j I '''I'

0.5

_! I I I I I I I10 20

Figure 1. Heat transfer and friction factor

curves as a function of Reynolds number for

gas flow in a gap.

10~ 3 N r Figure 2. Ratio of Heat transfer and friction

factor curves as a function of Reynolds number

for several configurations.

3. Optimization procedure

The equations which are developed in the following sections describe the procedure to calculate the actual dimensions of an optimum regenerator geometry. The development begins by relating

Q

c /Qr to a regenerator ineffectiveness. By using published performance curves for regenerators,

a set of values for the number of heat transfer units per half cycle, N

t(j

, and the ratio of matrix

heat capacity to the heat capacity of the fluid that passes through the regenerator, C r/C

f

, can

be found that yields the correct ineffectiveness. Because an infinite set of values will yield

the same ineffectiveness, the goal is to find the set of N tu and C r/C

f values that gives the minimum V

rg/V

e

- Expressions for the geometrical parameters of cross-sectional area, length,

porosity, and hydraulic radius are developed in terms of the optimized N tu and C

r/Cf and the

input parameters Q

c/Qr and AP/P. The conf igurational parameter a is used in the equations to make them valid for all N and to show how a maximum a produces a minimum V /V . v i y 6 180
0.001 J I 10

J I I I I 1 1

1

100

I'll 1000

o

uj o.oi Cvoid /C| - 1

J I !

I I I I ll10 J Ill

Figure 3. Calculated regenerator ineffectiveness for zero void volume.

Figure 4. Calculated regenerator ineffectiveness for a finite void volume but with no pressure wave.

3.1 Performance curves

The effectiveness, e, of a regenerator is defined as the ratio of heat actually transferred

to the maximum possible heat transfer. The first optimization step utilizes the performance

curves as shown in figures 3 and 4. Figure 3 shows the ineffectiveness, 1 - e , as a function of

N. and C

r/Cf

. The plot assumes zero void volume, zero thermal conductivity in the axial

direction, infinite thermal conductivity in the radial direction, gas and matrix thermal

properties independent of temperature, constant inlet temperatures, constant flow rate, and

constant heat transfer coefficient. The curves in figure 3 are plotted from data in Kays and

London [3] modified by the appropriate change for our definition of N. . Figure 4 is for the case of a finite void volume without a pressure wave [5,6]. All other assumptions are the same

as for figure 3. Other curves could be generated using fewer assumptions. Since the thermal

conductivity in the axial direction is taken into account separately via a decoupled loss term,

it should always be neglected in the performance curves. For a predetermined value of Q

reg/Q r a value of 1 - e can be calculated for a regenerator

operating between some upper temperature T.. and a lower temperature T. . By definition

1 - £ = Qreg/^u " H

L

} ' (5)

where H is the enthalpy per unit mass. Since refrigeration in a regenerative-cycle cryocooler

occurs only during one half-cycle, the refrigeration rate is given as

Q

r =mq

r/2, (6)

181
where q is the heat absorbed per unit mass during the expansion process. Combining eqs. (5) and

(6) gives

1 - e = (Q reg

/Q

r )q/2(H

U

- H

L

). (7)

As shown in figure 3, a given ineffectiveness is satisfied by a wide range of and C^/C^

values. The optimum combination will become evident later, but we proceed with the optimization

procedure assuming that the best N t and C^/C^ have already been determined.

3.2 Gas cross-sectional area, A

9

A high in a heat exchanger is achieved by using a high surface area, but the high

surface area will also lead to a large pressure drop unless the cross-sectional area is sufficiently large. The pressure drop in the core of the regenerator is given by

AP = f(m/A

g

) 2 L/2pr

h

, (8)

where f is the friction factor, L is the regenerator length, p is the gas density, and r^ is the

hydraulic radius. Equation (8) does not consider the entrance and exit pressure changes associated with acceleration and deceleration, but these terms are generally negligible in a well designed regenerator. By using the term a from eq. (4) the pressure drop in eq. (8) can be related

to the heat transfer by

AP = N stN^3 (m/A

g

) 2 L/2apr

h

. (9)

By using the definition for U ^ in eq. (3) and the following definitions

N tu = hA/mc

p (10)

r

h = LA

g/A, (11)

where A is the total heat transfer area, we can express in terms of N gt

as

N tu = Nst

L/V (12)

182
Rearranging eq. (12) and substituting into eq. (9) for N ^ allows us to write for the gas

cross-sectional area

A

g /m = [N^r^apAP] 2

. (13)

Equation (13) is one of the most important equations in the design of a heat exchanger, whether

it is regenerative or recuperative. It gives the gas cross-sectional area needed to achieve a given N^

u for a fixed value of AP across the exchanger. Equation (13) also shows that A

g should

be linearly proportional to m and that a large a means a small A . The term a is nearly constant

for a given heat exchanger packing and is taken from figure 2. An average value of p must be

used when large temperature differences occur from one end to the other. In dealing with a mass flow rate that is not constant, e.g. sinusoidal flow, the average m should be used to determine

Ag. Likewise the AP then corresponds to the average m and not the peak.

3.3 Regenerator length, L

Equation (13) shows that V could be made as small as desired by using a short regenerator.

However conduction in the regenerator would then become large. We now calculate the length

assoicated with the given value of Q /Q . By definition

(14)

where A^ is the regenerator solid or matrix cross-sectional area and k is its thermal conductivity. The term A is related to A through the porosity n by

n g = V(A

m

+ V" (15)

Equations (15) and (6) are substituted into eq. (14) to yield

2(A/m)(l - n) JkdT

L = 3 9 . (16)

n q (Q /Q ) g

M

r vxc xr

For some packing configurations n is fixed, such as packed spheres or stacked screens. In those

cases, L can then be calculated from the known input parameter Q

c /Qr

- For other configurations,

such as gaps, the porosity is entirely flexible and L cannot be calculated until the porosity is

first calculated. Note that eq. (16) also applies to either recuperative or regenerative heat

exchangers, since the C /C, term has not been used.

183
3.4 Porosity, n g

In configurations where the porosity is flexible, additional matrix heat capacity can be

obtained by adding more matrix material and still keeping A

g constant. However, at some poinl

conduction effects become important. The regenerator matrix heat capacity is given by

C

r = VmV W

where p is the matrix density, c is the matrix specific heat, and V is the matrix volume

m m

r m mm

Equation (15) is used to express Vm

in terms of A

g by

V = A L(l - n )/n . (19)

m g g g

Substitution of eq. (19) into eq. (17) gives

C = p c A L(l - n )/n . (20)

r Km m g g g

The heat capacity of the fluid that passes through the regenerator is

C. = mc t/2 = mc /2v, (21)

f p p

where t is the period of one cycle and v is the frequency of operation for the regenerative cryo- cooler. The use of eq. (21) now restricts subsequent results to regenerative heat exchangers.

When eq. (20) is divided by eq. (21) and rearranged the result is

n g /(l - n g

) = 2v(p

m

c m )(A

g /m)L/cp

(C

r/C

f

). (22)

For simplicity in subsequent calculations we define X as

184
X = n /(1-n ) g g (23)

or

n g = X/(l + X) (24)

The length in eq. (16) is substituted into eq. (22) to yield

X = 2(A /m)

v(pVK c UkdT

m nr

J

c q (C /C-)(Q /Q ) p^r v r f v

c xr

(25)

In calculating n^ the ratio C^/C^ is assumed to be known from the performance curves in figure 3,

although any combination of and C^/C^ can be used. The optimum combination is yet to be

determined. Equations (24) and (25) show that the porosity is independent of the refrigerator

capacity since (A /m) and the other terms are independent of mass flow rate. Likewise the length

in eq. (16) is independent of mass flow rate or refrigerator capacity. Also, the porosity

equation applies to the case of variable porosity. The proper technique for dealing with a fixed

porosity is discussed in section 5.

3.5 Regenerator gas volume, V

rg

With A and L already determined, V is easily calculated. However the ratio V /V needs to be

g

y ' rg 3 rg e calculated to determine what effect V will have on the system. The volume of gas in the

regenerator void space can be given by

V = XV . rg m (26)

The matrix volume can be expressed as

V = C /p c , m r K m m (27)

which means eq. (26) becomes

V = XC /p c . rg r

K m m (28)

185
The expansion space volume is given by

V

e = Cf/pe

c (29)

where p

g is the density of gas in the expansion space. The term p

g should be evaluated at the

temperature and pressure of the expansion space at the time of flow reversal. For a first approximation the lower temperature T^ and the average pressure are used. From eqs. (28) and (29) the

volume ratio becomes

V /V

rg e X(Cv /C-)p c /(p c ) r f Ke p

Vf m m

y (30)

This simple expression for V

rg/Ve

is useful when X has already been calculated. However, since

the optimum N^

u and C^/C^ have not been selected, we now develop an expression, for v

rg/ve in

terms of N. and C /Z f . We substitute eq. (25) for X into eq. (30), and at the same time eq. tu r (13) is used for A^/m in the expression for X. The resultant volume ratio becomes

V /V = p rg e

K

e

2N

tu (C /C-)N 2/3

vc J"kdT

r f pr p

J

apAPq (Q /Q )(p c ) (31)

It now becomes clear how V

rg/V

g depends on the various input and material parameters and the

packing configuration. The volume ratio is minimized when the conf igurational parameter a is

largest. Figure 2 shows that gaps offer the largest a for the configurations compared. The

authors are unaware of other configurations with a higher a. Of course, the equations derived

here are valid if one chooses to use a configuration with a smaller a. In regard to matrix

material parameters, the ratio [JkdT/(p

m

cm

)]

2 should be minimized. The input parameters AP/P and

Q

c /Qr should be made large to reduce Vrg/V

e but they cannot be made larger than about 0.1-0.2.

A minimum value for V /V is obtained when the product N. (C /C,) is a minimum. Figure 5 rg e

K tu r f

shows curves of N. (C /C £ ) vs. (C /C £ ) for various values of ineffectiveness. We see from figure

tu v r f v r f 3

5 that C /C, = 1.8 qives a minimum in N. (C /C,) for all values of 1 - e shown. The curves of

r f y tu v r f

y figure 5 are subject to some uncertainty since they were derived from the graph in figure 3 rather

than using numerical calculations. Fortunately the minimum in N tu(C

r/Cp 15 fairly broad so some uncertainty can be tolerated. The calculation of (A

g/m), L, n g

, and v rg

/ v e

is now done using the

optimum N^

u and Cy/Cf combination from figure 5.

For an ideal gas and isothermal expansion we have

p = P/RT (32)

186
100 L 10 c r /c f

Figure 5. The \u (C

r /Cr

) product for several values of regenerator ineffectiveness

from the case of zero void volume.

pK = P/RT

e e (33)

q = RT £n(P./P„),

r e

v h $," (34)

where R is the gas constant, P is the average pressure, P^ is the high pressure, P^ is the low

pressure, and T

g is the expansion space temperature. (Usually Tg = T^). Then eq. (31) becomes

2N. (C /C.)N 2/3c TvfkdT

tu v r f

J pr p

J V rg /V

6 = —RT

° T a(p c )(Q /Q )(AP/P)ln(P./PJ

for an ideal gas and isothermal expansion.

(35)

Equation (35) shows that the volume ratio is independent of pressure and

will increase as the temperature T

g is lowered. For the optimum (C^/C^.) = 1.8, the

ineffectiveness is approximately

1 - e = 2. IN -0.9

tu (36)

187
for N. > 50. The term is then proportional to (1 - e) ' * and using eq. (7) for (1 - e)

shows N

t(j is proportional to (Q

re g/Q r

) *

" The denominator inside the brackets of eqs. (31) and

(35) subsequently contains the three input parameters in the form of (Q

reg/Q r )* (Q

c/Or)(AP/P).

Such an expression would suggest that (Q reg/Q r

) should be larger than the other terms for minimizing v rg/v

e

.

There may be instances where the total regenerator volume is to be minimized. This possibil

ity may occur when there are external packaging constraints or in cases where no pressure wave

exists. For instance, regenerators used in magnetic refrigerators operate at constant pressure.

Here, the void volume is often of little concern. Of more importance is the total regenerator

volume, since it may need to fit inside a magnetic field region. The total regenerator volume,

V . , can be expressed in reduced units by

V ./V = V /V n . (37)

rt e rg e g

v '

The use of eqs. (24), (25), and (30) leads to

V ./V =

rt e

PK (C /C,)c

e

v r f p

(Pvt c ) m nr

2N. (C /C.)N2/3vc fkdT

orpAPq (6 /Q )(p c ) (38)

The first term on the right hand side of eq. (38) is the reduced matrix volume and the second

term is V /V of eq. (31). PQ 6 It is now apparent that the minimum in V

r^/V

g occurs at a smaller

value of (C /C f

) than the 1.8 used for V /V , and the N. will be higher than for that case.

3.6 Hydraulic radius

Here we derive the hydraulic radius and other characteristic dimensions of the regenerator

packing that must be used to give the desired N. in a regenerator with a length and

cross-sectional area as previously calculated. When both sides of eq. (12) are multiplied by

2/3

N prand rearranged, the result is

N .N 2/3

= N. N2/3

r. /L. st pr tu pr h (39)

The Reynolds number is defined as

N

r = 4rh/u(A /m), (40)

188
where p is the gas viscosity.

For every geometry of interest there is some function g where

N stNpr^

= 9<V- (41 >

2/3 Equations (39-41) represent three equations in the three unknowns, r^, N^, and N st

N

p ^ that must

be solved numerically in the general case. When g is in graphical form, the solution is easily

2/3 found by trial and error. For a chosen value of r h , eq. (39) is used to find N.N. The same

2/3 ^ r value of r. gives N from eq. (40) which in turn gives a value of N .N from the graph of eq.

n r

^ /o st pr

(41). If the two values of N.N do not agree, another value of r. is chosen until the two

yj-i st pr n N ,N values agree,

st pr M

For laminar flow , eq. (41) is

N stNp

2/3 = a/N

r» (42)

where a is a constant depending on geometry. For infinitely wide and long gaps with constant

temperature heat transfer, a = 8.5. For infinitely long tubes, a = 4.2. Equations (39), (40),

and (41) are solved then by

r

h = aLp(A

g

/m)

4N. N 2/3

tu pr

(43)

In the high-performance heat exchangers discussed here, the flow is usually laminar. The value

of a in figure 2 can be refined with N^ if necessary. Since a is only a weak function of N^,

further iterations may not be necessary.

The characteristic dimension of a heat exchanger may be expressed in terms of the hydraulic

radius. They are given for various geometries as follows:

t = 2r

h gap thickness (44)

d = 4r

h tube diameter (45)

189
d = 6r

h/X sphere diameter (46)

d = 4r^/X wire diameter. , (47)

For a gap configuration the thickness of the plates that comprise the matrix is

t = t /X. (48)

m g

For all of the preceding calculations to be valid, the thermal penetration depth A. must be

large enough to penetrate throughout the matrix. For a semi-infinite plate the thermal penetration depth for sinusoidal heat flow is

A. = [k/(p

|n c|n )nw]!s

. (49)

For a set of stacked plates with gas on both sides we require

t < 2k. (50)

3.7 Equation summary

As an aid to computations for regenerators, the significant steps and equations are summarized in

the order necessary for a regenerator with flexible porosity.

1. Determine largest input parameters Q

re g/Q r > Q(/Q r

' AP/P the overall system can tolerate.

2. Evaluate system and material parameters v, Ty , T^, m, P, q^, p, p

g , Cp, Np^, p, (Pm

cm

)» and JkdT.

3. Ineffectiveness: 1 - e = (Q reg/Q

r )qr/2(HU

- H^)

.

4. From figure 3 or 5 determine: N. at C /C^ = 1.8.

5. Determine packing parameters a from figure 2 and laminar coefficient a in eq. (42).

2/3 h

6. Gas cross-sectional area: A /m = [N. N /2apAP] . g

L tu pr

7. Porosity: n = X/(l + X),

9

X = 2(A

g /m)

v(pVK c )JkdT

m m' J

c q (C /C.)(Q Q ) PT r f /VM

c xr

190
(in original parameters) X = 2 2apAPc q

r (Cr/Cf )(Q

c /Qr

)

8. Regenerator M gas 9 volume: V /V = X(C /C.)c p /(p c ). rg e

v r f

y p

H

e

VHm nr

(in original parameters) V /V = p rg e K <

2N. (C /C,)N2/3

vc jkdT

tu v r f pr p

J

apAPq (Q /Q )(p /c )

9. Regenerator length: L = 2(A

g /m)JkdT/Xq

r (Q

c /Q

r

)

.

(in original parameters) L =

c (C

r /Cf )JkdT

v(pM c )q (Q /Q ) m nr T

vy

c x r'

10. Hydraulic radius: r

h =

al_u(A /m)

*£_ 4N. N 2/3

tu pr

, laminar flow.

(in original parameters) r

h = (ap)'

c (C

r/Cf )JkdT

2apAPN. N 2/3

M v(p c )q (Q /Q ) tu pr

VKm m

yH

r vvc xr

y

11. Reynolds number: = 4rj

i /p(Ag/m)

Recalculate r^ if flow not laminar.

12. Reevaluate a. If necessary, repeat from step 6.

13. For gaps: tg = 2r

h> tm

= t

g /X

14. Thermal penetration depth in plates: A. = [k/(p

m

cm

)nw] , sinusoidal flow .

15. Check to see if: t < 2A. m

If not, increase v to decrease t . • m

16. Error check: (a) AP = f L/2pr

h (A

g /m) 2

, with f from figure 1 or similar curve. Calculated value should equal input value.

(t>)V rg/V

e = 2(A

g/m)Lvp

e

, should be same as from step 8.

4. Example solutions

(51)

(52)

(53)

The solution to the design equations can best be illustrated through some examples. In the

design of a cryocooler for a SQUID, nonmagnetic and nonmetallic parts need to be used in the cold

parts to prevent magnetic noise. The regenerator material chosen for this illustration is G-10

fiberglass epoxy. Even though its volumetric heat capacity is small compared with lead and other

regenerator materials, its very low thermal conductivity gives it a desirably small value of

k/pm

cm

, the important material parameter which appears in eq. (31). In fact G-10 may have a lower k/p c than Pb-5% Sb although k for the latter has not been measured,

^m m

3

191
The parameters chosen for the example solution are given in table 1.

Table 1. Input parameters for example solutions

1 - e = 0.01 (Q reg

/Q

r = 0.22) Ty = 4T^

Q

c/Q

r =0.1 a = 0.35 (gap)

AP/P = 0.05 regenerator material: G-10

P = 0.5 MPa fluid: ideal helium gas

P

h /P£ =2.0 isothermal expansion

The temperature T^ is allowed to vary from 4 K to 100 K to evaluate the temperature dependence of

the optimum geometry. The upper temperature Ty of the regenerator is assumed to be 4T^, which is typical for cryocoolers. Such a dependence of 1^ on T^ means that eq. (7) may be written as

1 - e = (Q /Q )q /6c T. (54)

reg r r p L

for the case of an ideal gas. Also, for an ideal gas q^ from eq. (34) can be substituted into

eq. (54), and for the normal case of T

g = T^, we obtain

1 - e = (Q reg

/Q

r )R£n(Ph /P£ )/6c

p

. (55)

For the input parameters in table 1, (Q reg/Q r

) = 0-22 from eq. (55).

The material parameters needed in the calculations are (p c ) and JkdT. Figure 6 shows

(Pm

c m

) for G-10 f iberglass-epoxy, Pb [13], and GdRh [14]. The alloy Pb + 5% Sb is commonly used

as a regenerator material and GdRh is a potential regenerator material because of its high specific heat (Pm

c m

) at low temperatures. The thermal conductivity of G-10 is the average of the paral

lei and perpendicular heat flow directions from the work of Kasen, et al . [15]. Table 2 gives

representative values of (pm

c m

), k, and JkdT used in our calculations.

For the ideal helium gas we use c p = 5.19 J/g-K, R = 2.077 J/g-K, N pr

= 0.666. The viscosity

values from McCarty [16] are nearly independent of pressure over the range we have considered and are approximated by u = 5. 0 x 10 ^ + 4. 6 x 10 ^T " ^ g/cm. s over the range of 10-300 K.

Figure 7 shows (A^/m) and the length of the regenerator as a function of T^ for three different frequencies. The term (A /m) is independent of frequency. The porosity, n , and the volume

9 9 ratio, V

rg/Vg

, are shown in figure 8.

Note that the optimum porosity is on the order of 0.01 for T

L = 5K. Such a low porosity

allows a large volume of regenerator material to be used to obtain a reasonably high total heat

capacity. The volume ratio V

rg/Ve

1S insignificant at higher temperatures and remains smaller

192
5

1

I I

/

COE y /

J/CI d 0.1

0.01

0.05

Pb/ /

/ / I

/G-10

/Fiberglass Epoxy

I

-

1 10 100 500

TEMPERATURE, K

Figure 6. The volumetric heat capacity of candidate regenerator materials.

Table 2. Thermal properties of G-10 fiperglass epoxy

(K) (J/cm3 -K) (W/cm-K) (W/cm)

5 0 0058 0 815xl0" 3

2. OOxlO

-3

10 0 0255 1 24 xlO"

3

7. 23xl0" 3

20 0 078 1 73 xl0~

3 22. 3 xlO"3

50 0. 245 2. 66 xlO" 389. 1 xlO"

3

100 0. 520 3. 76 xlO"

3 251. xl0~3

200 1. 10 5. 53 xlO

-3

718. xlO"

3

300 1. 64 7. 17 xlO"

3 1355. xlO"3

than 1.0 even at T^ = 5K. For the case of v = 1 Hz the volume ratio is small enough that the

assumption of zero void volume in the performance curve of figure 3 may hold. For higher frequencies, a more realistic performance curve probably should be used for the lowest temperatures.

The small values of V

rg/Ve also imply that the entire process for refrigeration at 4-5 K is feasible with an ideal gas. (Calculations for a real gas are easily done but are not shown here.)

Figure 9 shows the gap and matrix thicknesses as a function of T^. Shown for comparison

with the matrix thickness, tm

, is the thermal penetration depth, 2\. For all cases except at 1 Hz and the lowest temperature t << 2A. When t = 2\, there will be a slight degredation in re- generator performance because the term C will be reduced. The gap thickness has a slight depenr -3

dence on temperature and is in the range of 10 cm. An extremely small t could present some practical problems in the construction of the regenerator. The Reynolds number also is very

small - in the range of 10-200 - with higher values occurring at lower temperatures and lower

frequencies.

193
Tu, K

10 20 50 100 200

~| i

1 1—I I l I l |

1 1

1

I I I l I I I |

1 1 1—i i | i i _

TL

, K

Figure 7. The calculated gas cross-sectional Figure 8. The calculated porosity and the re- area per unit mass flow, and the regenerator duced regenerator gas volume for the conditions

length for the conditions in table 1. in table 1.

Tu. K

10 20 50 100 200

1

1 1 1

1 I I I I | I l ~

10° i

1—|1—| | | I |

1 1 1—I

I I I I

)-4 l I I i I I i i I I I I 1—I—l_LJ_

2 5 10 20 50 100

TL

, K

Figure 9. The calculated gap thickness, matrix thickness and thermal penetration depth i

regenerator with conditions in table 1.

194
5. Comparison of gap and packed sphere configurations

Packed spheres are commonly used for regenerator packings since such regenerators are simple

to make. However a is significantly lower for packed spheres than for gaps. Also, the porosity

of packed spheres is fixed at about 0.38, which is much higher than optimum for temperatures below about 50 K according to figure 8. In this section we show how much inferior a packed sphere

bed is in comparison with the gap configuration. Of course, the packed sphere bed still has the

advantage of simplicity. For a fixed n , eq. (51) is solved for the ratio N^/CC^/C^). The

optimum values for N^

u and C^/C-f are found by simultaneous solution with the (Cr/C^) curves of

figure 5. This approach maintains (Q

c /Qr

) at the fixed input of value. Included in the

assumptions is that JkdT for spheres is the same as for the bulk material. After N. and C

r/C^

are determined, the parameters A^/m, L, V

rg/Ve

> and r^ are calculated from the appropriate

equations.

Figure 10. The reduced regenerator gas volume for gaps and for' packed spheres. See test for

details of packed-sphere curves.

195
Figure 10 shows v

rg/ve f° r both packed spheres of G-10 and gaps between plates of G-10. At

higher temperatures the difference between the two sets of curves is mainly due to the higher a for gaps. At lower temperatures the much smaller V

rg/Vg f° r gaps is due to both the higher a and

the lower porosity. Also shown in figure 10 for packed spheres is the curve labeled = 378,

which is the value used for the gaps. At higher temperatures this curve gives a lower V /V

because Q

c /Qr is greater than 0.1. At lower temperatures the reverse is true, and Qc /Q

r is less

than 0.1. Wherever the packed-sphere curves are below the N^

u = 378 curve, the Nt(j is greater

than 378. In fact, for te.mperatures less than 15 K the N

t|j

is rapidly approaching numbers as high as 10^, a practical impossibility. Even an N^

u of 378 may be difficult to achieve in practice without extreme care in making all flow channels the same size. If a smaller JkdT is used

in the calculations of the packed powder, an even higher N

t(j is needed for the optimum condition.

However, the reduction in V

rg/Ve is insignificant at temperatures below about 15 K. The Nt(j = 378 curve should be considered a lower practical limit for the V

r g/V

g of the packed spheres.

6. Conclusions

A simple scheme for optimizing regenerators in cryocoolers has been developed which uses the

system loss terms, Q reg/Q r » Q

c /Q

r

» anc' AP/P as input parameters. Any set of regenerator perfor- mance curves can be used, although the examples discussed here use the simplest one of zero void

volume. A set of equations were developed to determine the regenerator geometry that yields the

minimum void volume. In comparison with other packing configurations It is shown that gaps between parallel plates is the best, producing regenerator dead volumes one to two orders of magnitude smaller for temperatures in the range of 5-10 K. It is shown that G-10 f iberglass-epoxy is

a favorable material for a multiple gap regenerator because of its relatively low k/pm

cmratio.

The authors are grateful to David Daney and James Zimmerman, both of NBS, for some valuable discussions. Debra Schlender is acknowledged for careful preparation of the manuscript.

7. References

[1] Lambertson, T. J. , Performance factors of a periodic-flow heat exchanger, Trans. ASME 80,

586-592 (1958).

[2] Hausen, H. , in Warmeiibertragung im Gegenstrom, Gleichstrom und Kreuzstrom (Springer-Verlag,

Berlin, 1950).

[3] Kays, W. M. , and London, A. L. , in Compact Heat Exchangers , 2nd ed. (McGraw-Hill Book Co.,

New York, 1964).

[4] Schmidt, F. W. , and Willmott, A. J., in Thermal Energy Storage and Regeneration , 114 (McGrawHill Book Co., New York, 1981).

[5] Heggs, P. J. and Carpenter, K. J., The effect of fluid hold-up on the effectiveness of contraflow regenerators, Trans. Instn. Chem. Engrs. 54, 232-238 (1976).

196
[6] Daney, D. E. , and Radebaugh, R. , Non-ideal regenerator performance - the effect of void volume fluid heat capacity, Cryogenics 24, 499-501, (1984).

[7] Gary, J. M. , Radebaugh, R. , and Daney, D. E. , A numerical model for a regenerator, Proc. 3rd

Cryocooler Conf. (this publication, 1985).

[8] Qvale, E. G. , and Smith, J. L. , Jr., Trans. ASME, J. Eng. for Power, 91A, 109 (1969).

[9] Rios, P. A., Smith, J. L. , Jr., Qvale, E. G. , An analysis of the Stirling-cycle refrigerator, in Advances in Cryogenic Engineering , Vol. 14, 332-342 (Plenum Press, New York, 1969).

[10] Rios, P. A., and Smith, J. L. , Jr., An analytical and experimental evaluation of the pressuredrop losses in the Stirling cycle, ASME paper no. 69-WA/Ener-8, ASME, New York (1969).

[11] Harris, W. S. , Rios, P. A., and Smith, J. L. , Jr., The design of thermal regenerators for

Stirling-type refrigerators, in Advances in Cryogenic Engineering , Vol. 16, 312-322 (Plenum

Press, New York, 1971).

[12] Walker, G. , in Cryocoolers , part 1: Fundamentals, 126-127 (Plenum Press, New York, 1983).

[13] Johnson, V. J. , A compendium of the properties of materials at low temperatures (phase I),

part II. Properties of Solids, Wright Air Development Division Technical Report 60-56 (1960).

[14] Buschow, K. H. J., Olijhoek, J. F. , and Miedema, A. R. , Extremely large heat capacities bet- ween 4 and 10 K, Cryogenics 15, 261-264 (1975).

[15] Kasen, M. B. , MacDonald, G. R. , Beekman, D. H. , Jr., and Schramm, R. E. , Mechanical, electrical, and thermal characterization of G-10CR and G-11CR glasscloth/epoxy laminates between

room temperature and 4K, in Advances in Cryogenic Engineering , Vol. 26, 235-244 (Plenum

Press, New York, 1980).

[16] McCarty, R. D. , Thermophysical properties of helium-4 from 2 to 1500 K with pressures to 1000 atmospheres, NBS Technical Note 631 (1972).

8. Nomenclature

English letter symbols

A regenerator total heat transfer area

A gas cross-sectional area

9 A matrix cross-sectional area

m

a geometrical constant for laminar flow

C

f heat capacity of fluid passed through regenerator

C^ heat capacity of regenerator matrix

C • heat capacity of gas in regenerator void volume

c specific heat of matrix

m

c specific heat at constant pressure of gas

Pd tube, sphere, or wire diameter

f friction factor

Hjj, specific enthalpies at T^ and T^

h heat transfer coefficient

k thermal conductivity of matrix

L length of regenerator

m mass flow rate of gas through regenerator

SI units

m

2

2 m

2

J/K

J/K

J/K

J/kg-K

J/kg-K

J/kg

W/m2 -K W/m-K

mkg/s

197
N Prandtl number, a fluid properties modulus

Reynolds number, a flow modulus

Stanton number, a heat transfer modulus

N^

u Number of heat transfer units per half cycle

n porosity of regenerator = A /(A + A ) g g g nr

P average pressure Pa

P

n

> high ancl l°w pressures Pa AP pressure drop in regenerator Pa

Q conduction heat loss W

;c enthalpy deficit loss W

Q net net refrigeration power W

Q gross refrigeration power W

^rad radiation heat loss W

Q regenerator loss W

;reg

Q

s shuttle heat loss W

q

r heat absorbed per unit mass during expansion J/kg

R gas constant J/kg-K

r^ hydraulic radius (LA^/A) m

T

g expansion space temperature K

Tjj, upper and lower temperatures of regenerator K t gap thickness m

9 t thickness of plates in gap regenerator m

3 V maximum expansion space volume m

e

3 V matrix volume m m

2 V regenerator void volume m

3 rg V^^ regenerator total volume m

X porosity parameter [n /(1-n )] 9 9

Greek letter symbols

2/3

a ratio of heat transfer and friction terms (N .N /f)

st pr

e regenerator effectiveness

1-s regenerator ineffectiveness

\ thermal penetration depth in matrix m

p gas viscosity kg/m*s

v cycle frequency Hz

3 p gas density in regenerator kg/m

3 p gas density in expansion space kg/m

e 3 Pm matrix density kg/m

i period of one cycle s

198
A COMPUTATIONAL MODEL FOR A REGENERATOR

John Gary

Scientific Computing Division

David E. Daney

Ray Radebaugh

Chemical Engineering Science Division

National Bureau of Standards

Boulder, Colorado 80303

This paper concerns a numerical model of a regenerator running at very low

temperatures. The model consists of the usual three equations for a compressible fluid with an additional equation for a "matrix temperature." The

main difficulty with the model is the very low Mach number (approximately

l.E-3). The divergence of the velocity is not small, the pressure divergence is

small, and the pressure fluctuation in time is not small. An asymptotic

expansion based on the "bounded derivative" method of Kreiss is used to give a "reduced" model which eliminates acoustic waves. The velocity is then

determined by a two-point boundary value problem which does not contain a time

derivative. The solution obtained from the reduced system is compared with the

numerical solution of the original system.

Key words: bounded derivative; compressible flow; cryocoolers; heat transfer;

implicit scheme; numerical model; regenerator; stiff equations.

1. The differential equations

The oscillating flow takes place in a cylinder filled with small metal spheres [1]. The

compressible flow equations are used to describe the flow around the spheres. A "resistance" term

involving the resistance factor F is used to account for the porous media effects. The "matrix" of

spheres has a heat capacity and heat can be transferred between the matrix and the gas. This

conductance is determined by the coefficient h. The temperature of the matrix is given by Tm

* The

variables are listed in the appendix. The partial differential equations for these variables are

the following.

3p

at

3T 3T 3u 4h 1 2F — = - u Gr

T — + - (Tm

- T) + | u | 3 (2)

3t 3x 3x CvDh p Cv

Dh

3p 3u 4Grh

2 + (Tm

-T) +

3x 3x °h

2Gr F

Dh P|"l (1)

199
3u 9u 1 3P 2F

9t 3x p 3x Dh

(3)

3T„ 4h<j>

3t (l-<j>) pm

Cm

Dh

(Tm

-T) +

3*T„

(4)

The domain is 0 < x < L. We will discuss the boundary and initial conditions in the next section.

Their determination is crucial to the success of the numerical approximation.

To set up the numerical approximation we need to write these equations in dimensionless form.

For this purpose we assume an ideal gas described by the following relations.

P P

p = —- pc

2 = - Rc = 2.03 E+3 J/kg'K y = 0.6 RCT Y

The scaling factors for the basic variables are the constants (p, u, T). The time is scaled by the

period (t) of the imposed oscillation in the mass flow. This is the same as the period of the

piston oscillation. The x coordinate is scaled by the length L. We use (p, u, T, Tm

) for the

scaled variables (p/p, u/u, T/ AT, Tm

/ AT)

.

3p -3p il - 3u a/- A 3 lPF - _ = _ TlU p — + aih ^Tm

- Tj + |u| 3 3t 3x Y 3x

3T — = - T2 3t 3x 3x

(5)

~3T - 3u h/» -\ u G

r

i 2T — + a2-lTm

- tI + g2F|u| 3 (6) -w „ *

'

3u -3u 1 T 3p 1 01 — = - t 2u - — + |u|u (7)

3t 3x e p 3x e Gr

x

1

3Tn

at

= - d3h

(Tm

" T

)

(8)

200
Typical values of these dimensionless parameters are:

Tl = 0.92 t 2 = 14 cq = 70 a2 = 709

a3 =64 B X = 5.8E-4 32 = 8.7E-3 e = 1.4E-5

This Is based on the values

t » 0.5 s U = 0.12 m/s L = 0.057 m Rc = 2.03E+3 J/kg'K

Gr = 0.65 Cv

= 3.1E+3 j/kg*K h = 8.7E+3 W/m2 *K

T = 15 K Dh = 1.2E-4 7=2

Clearly the term with the dominant coefficient is the one containing the factor e~ . The

pressure must be very nearly constant in order to balance the terms in these equations. In order to avoid high velocity sound waves we must carefully set the initial and boundary conditions. The

"bounded derivative" method of Kreiss is used to set the initial conditions. We chose the Initial

conditions so that the first two derivatives of the basic variables with respect to time are 0(1)

rather than 0(e~*). The work of Kreiss indicates that we can expect the time derivatives to remain

bounded during the time integration of the partial differential equations. This implies that the

fast sound waves do not appear, since their presence would require derivatives which are 0(e

-

*).

2. The bounded derivative expansion

This method was developed by Kreiss [4]. Gustafsson has shown that, in certain cases, the

results of Kreiss can be obtained by an asymptotic expansion [3], Gustafsson has given a good

expository treatment of the method [2]. If we assume an expansion of the basic variables in the form

p(x,t) = pQ (x,t) + epi(x,t) +

•••

then we obtain a new system of equations for the functions (p^, T^, u^, Tm:£), i = 0, 1, ... by

equating like powers of e in the usual way. Thus, we obtain from the velocity eq (7)

3PC = 0.

The first term in the pressure expansion is therefore independent of x. Using this fact, eq (1) can

be differentiated with respect to x to obtain an equation for the velocity (hereafter we drop the

subscript "o" and the "* M modifier for the asymptotic expansion).

If the functions T and p are known and u is known at the boundary, then this equation can be solved

for u(x) in the interior. Equation (9) implies that the right side of the pressure eq (1) is

independent of x. Therefore eq (1) can be regarded as an ordinary differential equation for p(t).

201
Equation (2) can be regarded as a hyperbolic partial differential equation for T(t,x) and

eq (4) is an ordinary differential equation for Tm

(t,x). Note that these equations do not require

any boundary conditions for the pressure p or the temperature Tm. If we regard the equation for the

gas temperature as a hyperbolic equation, then we must specify T at an inflow boundary and leave it

unspecified at an outflow boundary. We want to specify constant temperatures T(t,o) = Tt and

T(t,L) = Tr at the boundary. However, when the flow reverses this would cause a discontinuity in

the temperature at the boundary. Therefore we impose a fast exponential decay in time from the

temperature at the time of reversal to the desired temperature or Tr«

The velocity boundary values are chosen so that the mass flow is sinusoidal, that is

p(t,o)u(t,o) = CQ sin(ut)

p(t,L)u(t,L) = CL sin(wt+9)

These conditions insure that mass is conserved over a cycle.

3. The numerical scheme for the asymptotic expansion

A finite difference mesh (t n ,x^) is used where tn

= nAt, and x^ = iL/N for 0<i<N. The spatial

derivatives are approximated by centered second order differences, for example

dT Ti+i-T^! — (t nt x ±

) = dX 2Ax

n where T^ is the approximation for T(t n

,Xj_). An implicit type of predictor corrector is used which

is similar to a Crank-Nicolson scheme. We will not write out the complete scheme for the full

equations; instead we describe the scheme for the following simple equation

du du

dt dx

n *o n+1

Given the values at the nth time level, U^, and an approximation for , then compute a

"1 corrected approximation from

Ui-lJi

ho nWA

l n * 1 n \ yjj +UjJ yJi+l+Ui-H-Ui-l-Uj-lj

At 2 4Ax

This is a tridiagonal linear system for the unknown vector U^. A correction is made for the

variables p,T, and Tra in that order; then an updated value of the velocity is obtained by solving a

n finite difference version of eq (9) for U^. If the heat transfer cofficient, h, is constant, then

this is another tridiagonal linear system. If h = h(u) depends on the velocity, then the resulting

nonlinear equation is solved by a Newton iteration. The boundary conditions are described in the

previous section. Generally, from two to five iterations (or corrections) were used. On the first

"o n iteration = u^.

202
4. A fully implicit scheme for the original equations

We have a second computer code which is based on the original eqs (1) through (4) rather than

2 the asymptotic expansion. Since MQ

= e is small we expect this sytem to be very stiff. Therefore, we expect that an implicit scheme is required. However, we use a CN (Crank-Nicolson) scheme rather

than a BDF (backward-dif f erence-f ormula) . We choose the initial conditions to avoid the fast moving

acoustic waves; therefore we do not need the BDF scheme to damp out the fast waves. We can choose

arbitrary initial values for T(x,o); however p(x,o) is required to be constant and u(x,o) must

satisfy (9). This is the bounded derivative principle of Kreiss. The initial conditions are chosen

so that the first two time deriatives of the solution (p, T, u, Tm) at t = 0 are bounded independent

of e.

The finite difference scheme uses three-point centered approximations for the spatial

derivatives except at outflow boundaries, where a one-sided first order approximation is used. A Crank-Nicolson approximation is used in time. The difference scheme for each of the four variables

is thus similar to (1) for the asymptotic approximation. However, the four equations are now

coupled. Therefore, each time step requires the solution of a linear block-tridiagonal system with

4x4 blocks. We do not use a Newton iteration to deal with the nonlinearity . Instead, we use an iteration and evaluate the coefficients of the derivative terms at the previous iteration.

The boundary approximation for the temperature T(x,t) is the same as for the asymptotic

equations. The boundary conditions for u(x,t) are specified at all times using the same values as in eq (6). There is no boundary condition for the p equation; instead one-sided differences are used to approximate derivatives at the boundary. No boundary condition is needed for the Tm

equation since this equation contains no spatial derivatives.

5. Computational results

In this section we give some results obtained from the two numerical methods described in the

previous sections. Unless otherwise stated, the results were obtained using the bounded derivative

(i.e. asymptotic expansion) model. Within SI, many units choices exist for most quantities! In all

of these runs the heat transfer coefficient between the gas and matrix was given by the term

h(m) = 40 exp(-1.6m) + 220( l-exp(-l . 6m) )m

where

m = p | u | .

The exponential factor is included to avoid a discontinuous derivative of h(|pu|) with respect to to

u at u=0.

The formula used to bring the boundary temperature of the gas back to its constant inflow value

when the velocity reverses is

T(t) = TT (

Trev

" TL)exp^t rev-t^/T)

Here T^ is the constant inflow temperature (15 K for most of our runs) and Trev is the temperature

direction. The time of reversal is t rev and t is

is the period of the mass flow oscillation.

The mass flow at the boundary is given by

at the left boundary and 10 K at the right boundary

of the gas at the time when the velocity reverses

an input parameter, whose value was 0.05P where P

pu = C sin(2Tift+0)

203
where f is the frequency and 0 is the phase. At the left boundary 0=0, at the right values in the

range -45°<0<O° were used.

All runs assumed an ideal gas with equation of state

p = Rc pT.

The specific heat of the gas at constant volume was

Cv

= 3120. J/kg-K

The thermal conductivity of the matrix was 0.3 W/m'K and of the gas was 0.13 W/m*K. The regenerator

length was 0.0572 m.

5.1 The temperature and pressure wave forms

The temperature as a function of time at the left and right boundaries is given in figures 1 and 2. In this case, which we refer to as case I, the inflow temperatures at these boundaries were

15 K and 10 K; the mass flow amplitude was 77.9 kg/m^s; the starting pressure was 3.3 Mpa; the heat

capacity of the matrix was 2.64E+5; the hydraulic diameter was 1.21E-4; and the frequency was 5 Hz. The time interval shown is 12<t<13, that is, the system has been run for 60 cycles before these curves are drawn. The matrix temperature is shown as a dashed line; the gas temperature is a solid

line. In this case, the two temperatures were almost identical. The temperature at a point 4/5 of

the distance across the regenerator (x=0.8) is shown in figure 3.

The temperature as a function of position x across the regenerator at certain times in the

cycle is shown in figure 4. The pressure oscillation is shown in figure 5.

15.0

S 14.6

D

<

m

Q. 14.2

13.8

T

J L 12.0 12.2 12.4 12.6

TIME, s

1 2.8 13.0

Figure 1. Temperature (K) vs. time (a) at x = 0 for case I.

204
11.2

111 £E 10.8

I-<

LU

Q. 10.4

in

n r n

1

1 1 1 r

10.0

12.0

1

12.2 12.4 12.6

TIME, S

12.8 13.0

Figure 2. Temperature vs. time at x = 1.0 for case I.

13.0

9

i

1 1 r 1 —i1 1 r

J I I L J I I L 2.0 12.2 12.4 12.6

TIME, S

12.8 13.0

Figure 3. Temperature vs. time at x = 0.8 for case I.

205
Figure 4. Temperature vs. x at the given t for case I.

206
12.0 12.2 12.4 12.6 12.8 13.0

TIME, S

Figure 5. Pressure vs. time for case I.

5.2 The effect of the hydraulic diameter and matrix heat capacity

In figure 6 the temperature wave at the right boundary is shown. All parameters are the same

as in case I above, except the hydraulic diameter has been increased by a factor of four. There is

Figure 6. Temperature vs. time at x = 1.0 with (hydraulic diameter) = 4.84E-4 m.

207
11.0

10.3-

now some separation of the matrix and gas temperature. A greater separation is seen in figure 7. Here the heat capacity of the matrix has been increased by a factor of 20 over case I.

Our definition of the ineffectiveness is given by the following integral which is taken over

the outflow portion of the cycle,

/p|u| (T(L,t)-TL

)dt / /p|u| (TQ -TL )dt.

Here TQ and denote the fixed gas temperature and T(L,t) denotes the gas temperature o outflow.

The ineffectiveness as a function of hydraulic diameter, D^, is shown in figure 8 for the conditions

of case I. In figure 9 the variation with matrix heat capacity, pm

Cm , is shown.

In table 1, we compare our computed ineffectiveness with that obtained by Daney using a model

which assumes no pressure variation. Our results are higher, which is probably explained by our non-zero pressure swing during the cycle. The table shows that ineffectiveness increases with the

pressure swing.

5.3 The accuracy and consistency of the model

In table 2 the value of the ineffectiveness is shown as a function of the numerical resolution.

These results are for case I where the frequency is 5 Hz. Note that with At = 0.001 s and Ax = 0.1 we have 10 mesh intervals across the regenerator and 200 time steps per cycle. The last run with At

= 0.004 s did not yield valid results. The need for a small time step may be explained by the rapid

change in the temperature at the boundary. When the flaw changes from outflow to inflow the

temperature is raised to the boundary value in about 0.01 seconds in this case. Therefore we might

expect some trouble with the larger time step.

208
CO

CO

LU

z

LU

>

o

111 LL

LL

LU

0.25

0.15

HYDRAULIC DIAMETER, m

Figure 8. Ineffectiveness vs. hydraulic diameter.

1.0

0.01 1 I

I 1.E+4 1.E + 5 1.E + 6

MATRIX HEAT CAPACITY, J/m3-K

Figure 9. Ineffectiveness vs. matrix heat capacity.

209
Table 1. Comparison with Constant Pressure Model.

1 1U UCl Tnof JLllCl fictLlvcUcob opf ~i uonoc c Temperature Swing Pressure Swing

Clr a

constant pressure (Daney) 0.015

phase = 0.0 0.027 10.0 - 10.50 2.9 - 3.3

phase = -14° 0.079 10.0 - 10.62 2.8 - 3.8

phase = -29° 0.122 10.0 - 10.79 2.6 - 4.5

Table 2. Accuracy.

Resolution Ineffectiveness

At""- o'.'ooi'

s"

'

Ax = 0.1

0.207

At = 0.001 s

Ax = 0.05

0.202

At = 0.0005 s

Ax = 0.025

0.201

At = 0.004 s

Ax = 0.05

0.23*

Did not reach a steady state - mass loss 1% per cycle.

In table 3 we compare the results for case I obtained from the two models. The full equation

solution shows a small oscillation in the velocity field which is not present in the solution using

the reduced equations. The CPU time is on a CDC Cyber 750. The results for the two models seem to be in good agreement.

5.4 Achieving a quasi-steady state

The results described above were obtained by running the model for 66 cycles. At this point

there is very little change of average or maximum values from one cycle to the next. For example,

in case I the maximum gas temperature at the cold end is changing at a rate of 10-

^ K per cycle.

This is a very small change; however, this rate appears to be virtually constant over the last 10 or 20 cycles. Therefore, we don't know how close we are to a steady oscillation. At this rate 1000

cycles would be required to effect a 10 percent change in this maximum temperature. We need to find

a method to accelerate convergence.

Table 3. Comparison of Reduced and Full Equations Models.

Temperature Pressure CPU

Swing Swing Time/Cycle

Model Ineffectiveness K MPa s

Reduced 0.202 10.0 - 11.2 2.7 - 4.3 6.8

Full 0.186 10.0 - 11.1 2.8 - 4.3 23

21Q
6. References

[1] Daney, D. and Radebaugh, R. , Nonideal Regenerator Performance - the Effect of Void Volume Fluid

Heat Capacity, Cryogenics 24_, 499-501 (1984).

[2] Gustafsson, B. , Numerical Solution of Hyperbolic Systems with Different Time Scales Using

Asymptotic Expansions, Jour. Comp. Phys. 36, 209-235 (1980).

[3] Gustafsson B. Asymptotic Expansions for Hyperbolic Problems with Different Time-Scales, 17 , 623-634 (1980).

[4] Kreiss, H. , Problems with Different Time Scales for Partial Differential Equations, Comm. Pure. App. Math, XXXIII, 399-439 (1980).

Notation SI Units

P - pressure MPa

p - gas density Kg/m

p m

- matrix density kg/nr^

c - acoustic velocity m/s

u - velocity m/s

Gr - Grueneisen parameter

h - heat transfer coefficient W/mz *K

D^ - hydraulic diameter m

T - gas temperature k

Tm

- matrix temperature k

F - friction factor

Cv

- gas heat capacity J/kg*K

cm

- matrix heat capacity J/kg*K

<(> - porosity

Rc - gas constant J/kg*K

Y - ratio of specific heats

L - length of regenerator m

a(t) - left endpoint (piston position) m

b(t) - right endpoint m

211
CRITERIA FOR SCALING HEAT EXCHANGERS TO MINIATURE SIZE

Philipp B. Rudolf von Rohr and Joseph L. Smith, Jr. Massachusetts Institute of Technology

Cryogenic Engineering Laboratory

Cambridge, MA 02139

ABSTRACT

The purpose of this work is to highlight the particular aspects of

miniature heat exchangers performance and to determine an appropriate

design approach. A thermodynamic analysis is performed to express the

generated entropy as a function of material and geometric

characteristics of the heat exchangers. This expression is then used to

size miniature heat exchangers.

Key words: Miniature heat exchanger design; laminar flow heat

exchanger optimization; second law analysis.

1 . Introduction

In recent years a large number of applications have been developed for small

superconducting devices being cooled around 4.2 K . Their viability will depend on the

availability of closed cycle, efficient refrigerators. An extended survey CO has

shown that small scale refrigerators, for loads around 1 watt, are not commercially

avai I ab I e.

Different approaches have been undertaken to build reliable and efficient closedcycle refrigerators. In particular, Vuillemier, Gi f ford-McMahon and Stirling cycles

were investigated. These cycles are efficient at temperatures greater than 10 K. The

main problems in these pressure-cycling refrigerators for liquid helium temperatures

are rooted in the poor heat capacity of regenerators materials at low temperatures.

Preliminary studies L2D show that for small loads Collins cycle refrigerators are advantageous.

As part of a program to develop an efficient, closed cycle Collins type

refrigerator for 1 watt at 4.2 K, we investigate the performance of miniature helium

plate heat exchangers (Fig. 1). Due to the mass flows Involved, these heat exchangers

operate in laminar flow conditions.

We will show that the axial conduction in the solid wall has a considerable impact

on the performance of low temperature miniature heat exchangers.

212
F igure 1 : PI ate heat

exchanger

2. Thermodynamic analysis

The three major contributions to irreversibilities in heat exchangers are:

2.1. Entropy generation due to friction, S 2.2. Entropy generation due to temperature^d i f f erence

between the heat exchanger streams, ST

2.3. Entropy generation due to heat conduction in the

sol id wal I , Sc Their sum will furnish the generated entropy for the isolated heat exchanger:

S = S + ST

+ S • ( 1 ) p T c

2.1. Entropy generation due to friction

Assuming that helium behaves as a perfect gas, we find that the entropy generation

due to flow friction is given by:

S

p = mR[( Ap

L /pL

) + <ApH/p

H

)] f (2)

where: m = mass flow

R = gas constant

p. = low pressure

p = high pressure ,

Since the high pressure stream friction loss is negligible, S

p is given by:

S = mR( tp. /p. ) , (3)

213
A p, = Cm /( D )](f/2Re)(L/D)

f/4Re= friction factor |_3j

Re = Reynolds number

= density

B,D,L= geometric parameters (Fig. 1).

Substituting Ap^ into eq. (3), we find:

S = (m

2R/p )(f/2Re)LL/(B

2D

2 )], (4)

It may be immediately seen from eq. (4) that entropy generation by friction will

increase with increasing heat exchanger length L and decreasing breadth B and wall-towall d i stance D.

2.2. Entropy generation due to finite temperature difference

The generated entropy due to finite temperature difference is:

ST

= m

2c

2L(2D/(k,Nu) + t/k )£(T -T )/(T T )]( 1 /(BL ) ) , (5)

I p t w 12 12

where: c = specific heat at constant pressure of the fluid

k? = fluid thermal conductivity

k = wall thermal conductivity

w Nu = Nusselt number.

The derivation of eq. (5) is summarized in the Appendix.

It may be seen from eq. (5) that the entropy generation will decrease with

decreasing wall-to-wall distance D and wall thickness t and increasing plate breadth B and heat exchanger length L.

2.3. Entropy generation due to heat conduction in the solid wall

The temperature gradient in the heat exchanger walls is linear and the heat

conductivity k and the crossectional area A are constant; then the entropy generation

S c associated with the heat transfer by conduction, is:

Sc

= O

c

(T rT

2

)/( Tl T

2

) , (6)

where:

Q = (T,-T„)k A /L . (7) c 1 2 w s

It may be seen from eqs. (6) and (7) that the entropy generation by axial wall

conduction will increase with increasing crossectional area A =3Bt and decreasing heat

exchanger length L.

2.4. Overal I entropy generation

The generated entropy in a laminar counterflow heat exchanger, assuming helium

behaves as perfect gas and with constant material properties, is derived from eqs.

(1 ), (3), (4), (5) and (6):

214
S = m

3 R[f/(2^Rep

L )][L/(B2D

3 )] +

m

2c

p

2[(2D/k

f Nu) + t/k

w )X(T

1 -T

2 )/(T

1 T

2 )Xl/(BL)D + (8)

k w L(T

1 -T

2

) 2 /(T

1 T

2 )](Bt/L) .

It will be useful, for the purposes of simplifying the expression of S and to recognize familiar dimension less parameters, to obtain a dimensionless form for eq.

(8). This is achieved by dividing eq. (8) by L(k,/u)m], that is constant at pressures

below 20 atm L4J. Equation (8) then becomes:

S/[(k

f /u)mJ = L(k

w/k

f )(t/L)(1 •5/Re)(T

1 -T

2

) 2 /(T

1 T

2 ))J +

(9)

[( (Tj-Tjr/CTjT^) )(Pr Re/Nu)(D/U] +

L(k

f /kw

) (t/L ) (RePr 2 /2) ( (T, -J ) 2 /(T

) T

2

) )] +

C(R/c )(PrRe)(f 2 /(8p

L

P L

) ) (L/D

3

)] .

This is the entropy S generated in a counterflow laminar heat exchanger, valid for

ideal gases in the laminar flow range with Re larger than 100 L33.

3. Heat exchanger sizing

The geometrical parameters chosen are the wal I thickness t, the breadth B, the

wall-to-wall distance D and the heat exchanger length L. Material properties are defined by k .

' w Results will show that the entropy generation decreases with decreasing t and

increasinga L and B, with k ww= k (B) and D = D(L)=

3.1 General methodology for miniature heat exchanger sizing

Equation (9) shows that the wal I thickness t needs to be smal I for minimum entropy

generation. Consequently its value will be determined by structural requirements.

The first derivative of S with respect to k is set to zero:

w

k w

= 0.82RePrk

f

. (10)

Equation (10) has a form that is similar to the optimized wall thermal

conductivity for a concentric tube heat exchanger u5H. For B considerably larger than D, the Reynolds number may be expressed as:

Re = 2m/(Bu ) . (11)

Substituting eq. (10) into eq. (9), we find:

S/[(k

f A) )m] = 1 .22Pr((T

1 -T

2

) 2 /(T

1 T

2 ))(t/L) +

(Pr

2Re/Nu)(T

l -T

2

) 2 /(T

1 T

2 )(D/L) + (12)

(PrRe)(R/c ) ( f

u

2 /(8p

L

) ) (L/D3

) .

215
The minimum of the entropy generation with respect to the wall-to-wall distance D

is then determined similarly:

D = C((R/c )(f u2/(2p,p

|_))(Nu/Pr))/((T1 -T2

) 2 /(T

1 T

2 ))T25

LL3'

5

. (13)

Equation (13) is substituted into eq. (12); S is then expressed as a function of I and Re, where Re is defined by eq .(11 )

:

S/[(k^ )m] = c^t/L) + c

2Re(L)"*

5

, (14)

where:

Cl = 1 .22Pr((T

1 -T

2

) 2 /(T

l T

2

))

1 75 75 2 75 25 2 25 c_ = 1 .05(Pr

* 'VNu * )((T.-T„) 7(T.TJ)' (R/c ) (fo /(p,p, )) I 1 2 i 2 p L L

The function S is monotonic decreasing with increasing L and decreasing Re. The

remaining parameters B and L may be evaluated by considering space limitation, heat

leak to the surrounding and manufacturing costs.

3.2. Applications for helium heat exchangers

We take into consideration a laminar counter f I owp I ate heat exchanger for a twoexpander-saturated-vapor-pressure cycle refrigerator L6] with a cooling load of 1 watt

at 4.2 K. With a reasonable expander efficiency, the mass flow in the balanced heat

exchanger between 300 K and 60 K is 0.1 g/s, while the mass flow in the heat exchanger

between 30 K and 14 K is 0.085 g/s.

The generated entropy as a function of the length L, using the Reynolds number as

a parameter, is shown in Figures 2 and 3 for the two heat exchangers.

The heat exchangers breadth B is computed from eq. (10) for two Reynolds numbers : Figure 2: for Re = 100, B = 0.171 m and for Re = 300, B = 0.057 m Figure 3: for Re = 150, B = 0.294 m and for Re = 300, B = 0.147 m.

The optimized wall-to-wall distance D is computed from eq. (13):

Figure 2: for 0.1m< L < 1.0m 0.26mm < D < 0.82mm

Figure 3: for 0.1m< L < 1 .0m 0.06mm < D < 0.19mm .

Figures 2 and 3 also show the entropy generation due to axial wall conduction. Its contribution to the total entropy generation is particularly significant for the cold

miniature heat exchanger and, in general, for low Reynolds numbers.

216
1.6

1.4

1.2

1.0

0.8

0.6

0.4

0.2

0.0

.0 0.2 0.4 0.6 0.8 1.0 heat exchanger length L [m]

Figure 2: Entropy generation rate vs. length of heat exchanger

for two Reynolds numbers

(T = 300 K, T = 60 K, p =2 bar, p = 20 bar)

(m'= 0.1 g/s, t = 0.2 mm) L H

0.0

0.0 0.2 0.4 0.6 0.8 1.0 heat exchanger length L [m]

Figure 3: Entropy generation rate vs. length of heat exchanger

parameter: Reynolds number Re

(T. = 30 K, T = 14 K, p =2 bar, p = 20 bar)

(m = 0.085 g/s, t = 0.2 mm)

H

217
4. Conclusions

The thermodynamic analysis performed in this work consists of:

- expressing the entropy generation contributions due to the axial wall conduction, due

to the pressure loss and due to the finite temperature d i f f erence, as a function of four

geometrical parameters and one material characteristic.

- minimizing the generated entropy and thereby reducing the set of independent

parameters.

In miniature heat exchangers, axial conduction in the wall may become an important

phenomenon

.

It is shown that the miniature heat exchanger design may not be performed by

simply scaling down standard heat exchangers because of the short heat exchanger length

and the laminar flow.

Acknow ledgments

Ph. B. Rudolf von Rohr was supported by the "Schwei zer i scher National fonds".

Append ix

The temperature difference AT between the streams compared to the axial

temperature difference (T-T ) is assumed to be small, then the heat transfer rate

through the heat exchanger surface A is:

0 = mc (T-T„) = h ATA . (A1 ) p 1 2

Assuming the same convective heat transfer coefficients h for the high and low

pressure streams, we find:

h = (NukJ/D (A2) co f

Thus the overall heat transfer coefficient h is:

1/h = 2/h + t/k . (A3)

CO w

Considering the fluid heat conductivity k independent of the pressure, eq. (A2)

shows that the wall-to-wall distance D is equal for both channels.

The finite temperature difference is derived from eqs. (A2),(A3) and (A1):

AT = (mcpi/ /A)(T 1 -T„)[(20/(k,Nu)) + (t/k )] . (A4)

t w

The entropy generation due to the finite temperature difference AT is:

ST

= mc (A T(T,-T_)/(T.T0

) • (A5) T p 12 12

By substituting eq. (A4) into eq. (A5), the entropy generation Sj becomes:

ST

= m

2

c 2[(2D/(k<Nu)) + (t/k >X (T. -T„

)

2

/ (T. T. /(BL )] (A6)

T p f w 1 2 1 l

218
Nomenclature

" area Re Reynolds number

B plate width S entropy

c

1 constant in eq. (14) t plate thickness

T temperature

c

2 constant in eq. (14) A difterence

v viscosity

0^ specific heat of gas p density

D plate spacing Subscripts

f friction factor

h heat transfer coefficient 1 warm end of exchanger

h co convective heat transfer coefficient 2 cold end of exchanger

c wal I conduction

k thermal conductivity f fluid

L heat exchanger length H high pressure passage

m mass L low pressure passage

Nu Nusselt number p frictional pressure drop

p pressure s cross section

Pr Prandtl number T gas heat transfer

0 heat transfer rate w wal

I

R gas constant

References

CO Smith, Jr., J.L., Robinson, Jr., G.Y. and Iwasa Y., Survey of the

state of the art of miniature cryocoolers for superconductive

devices. Cryog. Eng. Lab. of MIT (Jan. 1984).

C23 Pirtle, F.W. et al., Thermodynamic aspects of small 4.2 K cryocoolers, Adv. in Cryog. Engng. 27, (1982), pp. 595/602.

C3] Kakac, S., Shah, R.K. and London A.L., Low Reynolds number heat

exchangers, Hemisphere Publ. Corp., Washington, New York, London

(1983).

[4] VDI-Lehrgang, Kryotechnik (1981), VD I Bildungswerk Duesseldorf.

C5] Chowdhury, K. and Sarangi, S., A second law analysis of -the

concentric tube heat exchanger: optimization of wall conductivity,

J. Heat Mass Transfer, Vol 26., (1983), pp. 783-786.

Q63 Minta, M. and Smith, Jr., J.L., Helium liquefier cycles with

saturated vapor compression, Adv. in Cryog. Engng. 27, (1982),

pp. 603/610.

219
A CLOSED CYCLE CASCADE JOULE THOMSON REFRIGERATOR

FOR

COOLING JOSEPHSON JUNCTION DEVICES

Emanuel Tward

Jet Propulsion Laboratory

California Institute of Technology

Pasadena, California 91109

and

Raymond Sarwinski

R. G. Hansen and Associates

San Diego, California 92121

A closed cycle cascade Joule Thomson refrigerator designed to cool Josephson Junction magnetometers to liquid helium temperatures is being developed.

The refrigerator incorporates 4 stages of cooling using the working fluids CF»,

N^, Hp and He. The high pressure gases are provided by a small compressor designed for this purpose. The upper three stages have been operated and performance will be described.

Key words: Cascade Joule Thomson refrigerator; cryocooler.

1. Introduction

The problem of cooling of Josephson junction devices to liquid helium temperatures is becoming

increasingly important as systems incorporating such devices are becoming more widespread. Traditionally, experimentalists have preferred the use of liquid helium dewars since, in a laboratory

setting where liquid helium is readily available, they are convenient to use. Devices can be

cooled and warmed quickly and tests can be made with little attention to the cooler other than re- plenishment of the liquid helium cryogen. However, once devices are integrated into a system and

are to be used for extended periods of time, the use of liquid helium dewars often becomes inconvenient, especially if the system is to be operated remotely from a readily available liquid helium

supply or if the system is inaccessible by service personnel.

Under these circumstances, it would be preferable to use a cryocooler. The ideal cryocooler

would be one that is convenient to operate (i.e., flick the switch to turn on the power) and it

does the job. In addition, the cooler should be efficient, occupy a small volume, be adaptable to cool a wide range of instruments, and have minimal interaction with the instrument (other than

cooling it). This latter requirement is especially important for the cooling of Josephson junction

magnetometers which are very sensitive to electromagnetic interference (EMI) and to vibration.

Because of this constraint almost all magnetometers are cooled in liquid helium dewars. All

commercially available cryocoolers use expansion engines and hence act as sources of both EMI and

vibration. Therefore, all such coolers are generally unsuitable for the most demanding applications, unless the instrument is contained in a liquid helium dewar and is being continuously cooled

220
by a remotely sited refrigerator. Such a refrigerator could be coupled to the instrument, for ex- ample, through a continuously flowing liquid helium transfer line. It is often the case that the

cooling power required is much less than one watt. The smallest commercially available coolers

have cooling powers greater than one watt. In this sense they are also ove-designed for the small

cooling power applications.

Attempts have been made to build low cooling power Stirling cycle cryocoolers [1] . These

machines incorporate plastic materials in order to reduce EMI from moving conducting materials and

require mechanical balancing in order to reduce vibration. In our view, a far better approach is to construct a refrigerator with no cold moving parts. This has been implemented through the use of the cascade Joule Thomson process [2], Since Joule Thomson refrigerators require a source of

very pure high pressure gas, suitable low flow rate large compression ratio compressors are re- quired. We have taken two approaches to this problem. For very long life refrigerators, chiefly

for space applications in which no servicing is possible, we have developed non-mechanical adsorption compressors which are thermally driven and incorporate no moving parts [3]. In the second

approach we have designed and built a small mechanical compressor which provides very clean high

pressure gas to the refrigerator. The compressor can be remotely sited from the refrigerator and

connected to it only through long capillaries through which the high pressure room temperature

gases are brought to the JT refrigerators and the low pressure room temperature return gases are returned to be recompressed . In this way, EMI is reduced by distance and vibration is greatly

reduced because of the weak mechanical coupling to the cold (business) end of the refrigerator.

2. Cascade Joule Thomson refrigerators

The Joule Thomson process is in wide use for cryogenic coolers. For small cooling powers its

major application is in the cooling of IR sensors typically to liquid nitrogen temperatures and

above. For small cooling powers the JT refrigerators (heat exchanger plus expansion valve) can be

implemented in a variety of ways [4, 5]. In our case we have used parallel metal tube heat ex- changers with a constricted tube as the expansion valve.

The Joule Thomson process is conceptually simple. High pressure gas of enthalpy enters the

inlet of heat exchanger, expands and cools at the JT orifice and returns through the low pressure

side of the heat exchanger in order to precool the incoming pressure gas. At the outlet of the

heat exchanger the low pressure gas has an enthalpy H. . The cooling power of the device is given

by

Q - m(H

L

- H

h

) , where m is the mass flow rate. The JT process produces cooling (rather than heating) only if

Hj_ > for the particular gas at the inlet temperature of the heat exchanger. The temperature

aDOve which H, is always less than is called the inversion temperature. Therefore, in order

to reach liquid helium temperatures a minimum of three different gases in three cooling loops are required. In the cascade process an upper temperature refrigerator precool s the inlet gas to a lower stage refrigerator to a temperature below the inversion temperature of the gas in the lower

stage

.

In our system we have implemented each JT loop in similar fashion. A schematic of the upper

stage loop and the components incorporated is shown in figure 1. The loop incorporates both warm

and cold filters as a precaution against contamination resulting in clogging of the refrigerator.

The cascaded JT refrigerator which we are reporting on has been implemented with four stages using

the working fluids CF^, N^, J^, He. The four stages (rather than three) were used because of increased thermodynamic efficiency and because lower pressures are required from the compressor for

the upper stages. The four independent fluid loops are configured as shown in figure 2.

Because of the low gas flows, the eight gas lines to the refrigerator (2 per stage) can be

long enough for the compressor to be far from the refrigerator (we have used 3.2 meter lengths) and

can be of small diameter (smallest diameter 0.16 cm 0D). This provides a very flexible interface

to the sensor cryogenics. The refrigerator operates in any orientation which should make the device much easier to use than sensors using liquid helium dewars. The prototype refrigerator shown

in figure 3 was specifically designed to cool a SHE biomagnetic probe [6] with a 2nd order gradiometer input coil. A schematic of the cryostat is shown in figure 4. To date, only three of the

four stages have been operated. Figures 5 and 6 show cool down curves for the various stages. The

221
longer than necessary cool down times are due to the fact that these measurements were taken with

a leak in one of the loops which resulted in excessive heat leak through the inadequately maintained dewar vacuum. The temperature reached at each stage is determined by the pressure at the

liquid reservoir which is in turn determined by the impedance of the J-T orifice, the pressure

drop in the low side heat exchanger and the inlet pressure to the compressor. In the experiments

to date, gas flows through each of the loops have been in the range of 50 STP cc/sec and are chiefly determined by the impedance of the J-T orifice. With lower gas flows We expect smaller

pressure drop in the low side heat exchangers, smaller compressor inlet pressures and hence lower

operating temperatures at each stage. The design goal was for flow rates of 15 STP cc/sec in each

loop. Once all four stages are operating we intend to reduce the flow rates (and cooling powers)

to each stage so that the lowest possible temperatures can be achieved.

3. Conclusions

Closed cycle Joule Thomson coolers appear to be an attractive solution to the problem of

cooling low power devices to low temperatures. Their small size, orientation independent performance, and absence of cold moving parts make them particularly useful for application where EMI and

vibration are a problem.

The assistance of John Watkins, John Gatewood and James Peterson has contributed greatly to this effort. Support for this research was provided by the Office of Naval Research and the Air

Force Medical Research Laboratories.

4. References

[1 ] Zimmerman, J. E., Davey, D. E. and Sullivan, D. B. In M. Gasser (Ed.), Refrigeration for

Cryogenic Sensors, NASA Conference Publication 2287, 95-105.

[2] Tward, E. and Steyert, W. A., In M. Gasser (Ed.), Refrigeration for Cryogenic Sensors, NASA

Conference Publication 2287, 419-425.

[3] Chan, C. K. , Tward, E. and Elleman, D. D. Proceedings of Cryogenic Engineering Conference,

1983, in press.

[4] Walker, G. Cryocoolers, Plenum Press, New York, 1983.

[5] Little, W. A. Microminiature refrigeration, Rev. Sci . Instrum. 55_ (5) 661-680 (1984).

[6] SHE Corporation, San Diego, California.

222
Cf,

MECHANICAL COMPRESSOR

CONTAMINANT

FILTER

LONG CAPILLARY

[ CF. COLD PLATE

HEAT EXCHANGER

f* M; COL n n a f •<

"

CONTAMINANT

FILTER

PARTICULATE

FILTER

1 H 2 COLD PLATE

RESERVOIR

| He COLD PLATE

"

Fig. 1. Schematic of a single stage J-T cooler. Fig. 2. Schematic of a cascaded four stage J-T

cooler.

Fig. 3. Four stage cascaded J-T cooler designed to cool biomagnetic probe.

223
SQUID ELECTRICAL

CONNECTOR

TRIM TAB

ADJUST . (1 OF 3)

24"

PICKUP^

COIL

2.4"

GAS INPUT AND

OUTPUT (2 OF 8)

ELECTRICAL

CONNECTOR

VACUUM

165K PLATE

(CF4 JT COOLER)

84K PLATE

(N 2 JT COOLER)

22K PLATE

(H 2 JT COOLER)

4.5K PLATE

(He JT COOLER)

SQUID

LIQUID HELIUM

RESERVOIR

84K THERMAL SHIELD

(G10)

22K THERMAL SHIELD

(G10)

4.5K THERMAL SHIELD

(G10)

SUPERINSULATION

Fig. 4. Schematic of single sensor neuromagnetometer incorporating closed J-T cooler

224
- Fig. 5. Cooldown of upper two stages of refrigerator. The H2 stage is being cooled by con- duction. The curve labelled, CF.X indicates the outlet temperature of the heat exchanger.

The low temperature after cooldown is due to excess cooling power.

250

230 CH4 210

190 2 170

liJ !| 150

1-<N2 £ 130

Q_| 110 —

90

\

\ 70

50

\

\

\

V H2

30 1 1 i -i 1 0 4 8 12 16 20 24 TIME (HRS)

Fig. 6. H„ stage cool down. Note temperature stability. The rapid cool down below 70 K is due

to increased gas flow and cooling power as the impedance of the refrigerator drops with

temperature

.

225
A SMALL HELIUM LIQUIFIEE WHICH PROVIDES CONTINUOUS

COOLING BASED ON CYCLED ISENTROPIC EXPANSION

Calvin Winter, Suso Gygax *, Ken Myrtle and Russel Barton

Quantum Technology Corp.

6237 - 148 ST. Surrey, B.C., CANADA V3S 3C3

* Simon Fraser University

Department of Physics

Burnaby, B.C., CANADA V5A 1S6

This simple cryocooler provides a small reservoir of liquid helium at a stable temperature of 4.2K. It uses a novel adaptation of the Simon expansion

cryocooler to provide continuous cooling. Operation is in a four stage cycle:

(1) A closed vessel of helium under high pressure is cooled to 12K using a conventional Giff ord-McMahon closed-cycle cryocooler. (2) The pressure is

released adiabatically providing cooling to 4.2K. (3) Liquid helium is

collected in a second, well insulated, vessel. (4) The first vessel is re- pressurized. The cycle time is 15-30 minutes. In this manner, a pool of liquid

helium is continuously maintained in the second vessel, with a temperature

stability of 0.03 degrees. The continuous cooling power available is 3mW.

This design provides simplicity and reliability through the absence of any

orifices or moving parts at cryogenic temperatures except for the conventional

Gif f ord-McMahon cryocooler.

Key words: Cryocoolers; small; liquifiers; helium liquifiers; liquid helium;

helium; isentropic expansion; Simon; Gif f ord-McMahon; refrigerators.

1. Introduction

Historically, the development of low temperature physics and its applications have rapidly

followed the development of cryogenic refrigerators, or "cryocoolers". There is now a host of

applications of low temperatures, especially those using superconductors, which are not economical,

given the high cost of most commercial helium liquifiers. Those applications which are economical

generally rely on the presence of a large helium liquifier in their vicinity. Driven by this need

for inexpensive helium liquifiers our group has developed a number of different cryocoolers. This

paper describes one of our cryocoolers. For a more complete review of our work and that of others

in this field the reader is referred to several recent reviews of progress in the field of

inexpensive helium liquifiers [1,2,3],

We have built a simple and inexpensive helium liquifier using a commercial two stage

Gifford-McMahon cycle cryocooler (of the type used in cryopumps) for the initial stages of cooling.

The novelty of our cryocooler is that it is able to provide continuous cooling at liquid helium

temperature, by recycling an adiabatic expander. The liquifier is useful for many applications

with modest cooling power requirements, i.e. the operation of small superconducting devices,

infra-red detectors, laboratory measurements of material properties at low temperatures and neutron

diffraction measurements.

2. Principles of operation

2.1 Adiabatic Expansion

Helium is liquified in our cryocooler by adiabatic (isentropic) expansion of previously

cooled, high pressure helium gas. This technique was exploited by Simon [4] in 1932 using liquid

hydrogen to precool the compressed gas. In our cryocooler, an expansion volume of 10 ml is cooled

226
to 12K, by the two stage Giff ord- McMahon cryocooler, while filling with helium at. a pressure of 6.2

MPa (62 bars). Once cooled, the mass or supercritical gas in the expansion volume will be 1.6 g [5]. When an exhaust valve is opened to allow this gas to escape (to the atmosphere) to a pressure of 0.1 MPa cooling is produced in the expansion volume. This process is very nearly

adiabatic because at these low temperatures the specific heat of the metal vessel is negligible

compared to the specific heat of helium gas. At the O.lMPa pressure, the expansion volume will

contain 1.7 ml of liquid helium with the remainder gaseous for a total of 0.35 g.

2.2 Principle of cycled adiabatic expansion

The liquefaction process described above is of a one-shot nature. After the liquid

generated has been boiled off, the temperature rises. In order to recycle the expansion volume

it must be filled with compressed helium gas. Since the refill gas comes from outside the

apparatus it is initially warm. In addition, the process of compressing the gas adiabatially

produces heating. The expansion volume must be cooled to 12K again by the two stage

Gif f ord-McMahon cryocooler before the next expansion and liquefaction cycle may commence. In this manner the adiabatic expansion may be cycled, but the temperature of the expansion volume will

oscillate between 4.2K and 20K.

In order to achieve a constant temperature liquid helium bath, a separate, well insulated,

container is attached to the bottom of the expansion volume to act as a liquid helium

reservoir. This reservoir is replenished with liquid helium at each expansion phase of the

cycle. During the compression phase, however, the liquid in this reservoir may be boiled to provide a continuous 4.2K temperature bath.

2.3 Principle of thermal diode

Proper operation of the liquid helium reservoir requires that it be in good thermal contact

with the expansion volume during the expansion phase, but that it be thermally isolated during

the compression phase. The natural tendency of cold helium to flow to the bottom of a container

is used to provide this switching action in our cryocooler. The liquid reservoir is located

directly below the expansion vessel. During the expansion phase a slight overpressure in the

reservoir allows helium to condense on its cold top surface. This liquid then flows to the bottom

of the reservoir. During the compression phase the expansion volume heats up to approximately 20K.

This also heats the gas in the upper part of the insulation tube. However, due to the low

thermal conductivity of helium and due to the natural stratification of the gas with the warm gas

on top, little heat is conducted down to the liquid reservoir.

The function of the long insulation tube at the top of the liquid reservior is analogous to an electrical diode. When the top end is cold it conducts heat, either by natural convection currents

or by liquefaction and boiling of helium. When the top end is hot it becomes a thermal insulator.

The helium eas stratifies and convection currents cease.

2.4 Operating cycle

The operating cycle is shown in figure 1. There are four phases to the cycle. At (a), helium gas

at a pressure of 6.2MPa (62 bars) is cooled to 12K using a conventional two-stage Gif f ord-McHahon

closed cycle refrigerator. At (b), a valve at room temperature is opened allowing the gas to expand. The expansion is essentially adiabatic, since at 12K the specific heat of the stainless

steel and copper high pressure expansion vessel is negligible compared to the heat of its gaseous

helium contents. The cooling provided by the expansion results in the vessel remaining

approximately one-sixth full of liquid helium. At (c), helium gas at a slight overpressure is

piped through counterflow heat exchangers and enters the liquid reservoir. Good thermal contact

with the bottom of the expansion vessel causes condensation of the incoming helium and evaporation

of liquid helium in the expansion vessel. The cold helium produced by evaporation is piped through

the counterflow heat exchangers and is vented to the atmosphere. In effect, liquid helium from the

expansion vessel is "transferred" to the liquid reservoir, although there is no plumbing connection

joining the two vessels. The final step in the cycle, (d), is that high pressure helium gas is

forced back into the expansion vessel, figure 1(d). This compression raises the temperature of the

expansion vessel to about 20K. At this stage of the cycle, gravity causes stratification to the

helium gas - thermally insulating the liquid helium (4.2K) at the bottom of the liquid reservoir,

from the relatively hot (20K) expansion vessel.

227
i KV//A

62 bar

-> 1.0 bar

12 K

1.0 bar

4.2 K

1 bar

4.2 K

1.0 bar

4.2 K

.2 bar

4.4 K

4.2 K

62 ba r

1.0 ba

20 K

4.2 K

(b)

> ADIABATIC > EXPANSION

12K TO 4.2K

(c)

'TRANSFER' > LIQUID HELIUM

TO RESERVOIR

(d) (a)

REPRESSURIZE > COOL -—

>

EXPANSION VESSEL EXPANSION

HEATING IT TO 20K VESSEL TO 12K

1 MINUTE 4 MINUTES 2 MINUTES 8 MINUTES

Figure 1 - Cycle of operation

1. 12K Cold finger of Gif ford-McMahon cryocooler.

2. High pressure expansion volume.

3. Sintered copper heat exchanger.

4. Low pressure liquid reservoir.

228
Figure 2 - Schematic diagram of cryocooler

1. 2-Stage, closed-cycle Gif f ord-McMahon cryocooler.

2. Expansion volume (high pressure).

3. Insulation tube.

4. Liquid helium reservoir (low pressure).

5. Vacuum vessel with heat shields (not shown).

R Pressure regulator valves.

V Electronically driven solenoid valves.

H To helium recovery.

E Heat exchangers.

2.5 Temperature stability in the liquid reservoir

The temperature in the pool of liquid helium in the reservoir is held stable at the boiling

point of liquid helium (4.2K). In order to allow helium to condense the pressure in the reservoir

is increased to about 0.12MPa (1.2 atmospheres) during the expansion phase. Condensation causes heating of the top layer of liquid helium to its boiling point at this new increased pressure

(4.4K). However, the liquid lower down in the reservoir is not heated by condensation. The liquid

helium stratifies with a thin warm layer on top. Heating of the liquid at the bottom of the

reservoir is by thermal conduction through the liquid and by adiabatic compression of the liquid.

The adiabatic compression term is only approximately 20 millidegrees . The thermal conduction term

can be much larger. However, the high specific beat of liquid helium and its low thermal

conductivity make thermal conduction through the liquid a very slow process. The variation in

temperature 6T at a depth x due to an abrupt change in temperature of AT at the surface is

229
given by,

where

erf ( u ) = -L

6T

is Gauss's error integral[6]. The specific heat of liquid helium per unit volume, at constant

pressure is pCp. The thermal conductivity of liquid helium is K and t is the time elapsed

since the temperature change on the surface.

For example, consider the 0.2 degree change in temperature at the surface of the liquid. The

time required for that to cause a temperature change of 0.020 degree is one minute for a liquid

helium depth of 0.3cm but is one hour for a depth of only 2.5cm.

In our cryocooler, the liquid reservoir is at a pressure above atmospheric for only 5 minutes

during each cycle. Temperature fluctations due to warming of the liquid during this period are therefore substantially dampened once the liquid reservoir starts to accumulate a certain depth of

liquid helium.

A schematic of the four-stage cryocooler is shown in figure 2. The first two stages of

cooling, nominally 70K and 12K, are provided by a conventional laboratory Gif f ord-McMahon cycle

crycooler. The third and fourth stage system is thermally connected to the two-stage crycooler.

Helium gas lines go from room temperature to the third stage expansion vessel and to the fourth

stage liquid helium reservoir. The two gas lines are not interconnected and their helium supplies

are independent. Operation of the crycooler is achieved by cycling the pressures at the room temperature ends of the expansion vessel line and the liquid reservoir line.

For simplicity and ease of construction, the pressures are cycled by means of opening and

closing electric solenoid valves. The gas lines are alternately charged from compressed gas

cylinders and vented to a helium recovery system at one atmosphere pressure. Maximium pressures

are set by regulator valves on the gas cylinders. They are set at 6.2MPa (62 bars) for the

expansion vessel and 0.12MPa (0.02MPa above atmospheric) for the liquid helium reservoir line. The

solenoid valves are controlled by an electronic cycle timing circuit. The rates of charging and

venting are quite critical, they are set by manual valves.

The cycle timing is mainly determined by how long it takes the two-stage croycooler to cool

the expansion vessel to a threshold temperature of approximately 12K. If the threshold is set too low then it takes a very long time to cool down and the cycle time becomes too long. If the

threshold is set too high then very little, or no, liquid helium will be produced during the

expansion phase. Typical cycle times are shown in figure 3.

The critical parameter in the design is the length of the time required to complete one cycle.

If it takes too long then all the liquid in the reservoir will boil away before the next expansion

(cooling) phase commences. During each cycle almost all of the helium gas in the expansion vessel

is taken to room remperature then returned to below 12K. The minimum cycle time is mainly

determined by how long it takes the two-stage crycooler to cool this mass of helium gas from 300K

to 12K. This time is substantially reduced by using effective regenerators to utilize the cooling

power of the escaping gasses of one cycle to cool the incoming gasses of the next cycle. The

dimensions and masses of the heat exchanger-regenerators are given in table 1. Note that,

effective regeneration is assured between 300K and 70K by 500 grams of stainless steel in exchanger

El. Regeneration below 70K is acheived by 350 g of lead shot in exchanger E3. These massive

components lengthen the initial cooldown of the crycooler (by about 20 hours) but speed up the

operating cycle rate. We have also tested a Simon expander without these regenerators. As expected, its minimum cycle time was too long (over one hour) to maintain a bath of liquid helium.

Another feature worthy of note is the use of the counterflow heat exchanger number E4

(12K-4.2K). This is essential in order for the liquid helium 'transfer', phase (c), to take place.

Helium gas entering the liquid reservoir must be cooled to just above its boiling point before

passing through the copper powder heat exchanger number E5. If this is not done the cooling power

of the boiling liquid in the expansion vessel will be wasted in irreversible heat transfer to hot

helium gas and no liquid will be collected in the reservoir.

3. Cryocooler design

230
Figure 3 - Cryocooler cycle with no heat load

I) Pressure at the room temperature end of the expansion volume gas line.

II) Pressure at the room temperature end of the liquid reservoir gas line.

Ill) Measured temperature at the bottom of the expansion volume.

IV) Estimated volume of liquid helium in the expansion volume.

V) Measured temperature at the bottom of the liquid reservoir.

VI) Estimated volume of liquid helium in the liquid reservoir.

VII) Phases of the operating cycle (see also fig. 1).

231
4. Experimental performance

Figure 3 shows measured cyclic temperature variations at the bottom of the expansion vessel

and at the bottom of the liquid reservoir. For convenience, estimated pressure and liquid helium

level variations are also shown. The cryocooler provides a good degree of inherent temperature

stability. The observed temperature fluctuations at the bottom of the liquid reservoir were only

30 millidegrees , in spite of the 16 degree variation in the temperature of the expansion vessel.

This stability is achieved without any electronic temperature regulation.

It was not possible to directly measure the amount of liquid helium in each of the vessels

with our apparatus. We have estimated the amount of liquid produced by measuring the time required

to boil it off by means of electric heaters. In a series of single expansion experiments we observed that approximately 2 ml of liquid is produced in the expansion vessel. After a similar

expansion followed by a 'transfer' phase approximately 1 ml of liquid had collected in the

reservoir. The expansion vessel itself acts as a thermal diode and can retain its charge of liquid

for 28 minutes in spite of the fact that its upper surface stays near 12K. That heat leak

corresponds to 3 mW which agrees with the value calculated from the thermal conductivity through

its thick steel walls. A low thermal conductivity between the top and bottom of the expansion

vessel is important so that a pool of liquid may remain at the bottom for long enough to be

'transferred' to the reservoir.

The startup of the cryocooler requires 24 hours of operation of the two stage Gif f ord -McMahon

cycle cryocooler in order to reach 12K. This is due to the massive regenerators which must be

cooled. The startup time could be reduced somewhat by providing heat switches to improve the

thermal contact to the regenerators. Once the 12K threshold has been reached full operation starts

quickly with liquid helium remaining in the reservoir after a couple of cycles. The temperature

stability in the reservoir improves dramatically after several additional cycles due to the

accumulation of a sufficient depth of liquid helium.

The success of our cryocooler depends on the excellent thermal isolation provided by the thin

wall stainless steel insulation tube which separates the expansion vessel from the liquid

reservoir. The dimensions of this tube are given in table 1. With one end of the tube at 20K and

the other end at 4.2K the theoretical heat leak by conduction through the steel is 0.4 mW and by

conduction through the helium is 0.06mW. The liquid reservoir was observed to retain a charge of

liquid for over two hours without replenishment. The liquid charge was approximately 2 ml, so this corresponds to a total heat leak of only 0.6 mW.

The cryocooler has been operated with a continuous heat load of 3 mW and it maintains a pool

of liquid helium at all times. This power setting agrees with that expected* from the latent heat

of boiling of 1 ml of liquid every 15 minutes. Naturally, the heat load increases the temperature

variation at the liquid reservoir. The maximum temperature variation is nevertheless limited by

the boiling point of helium at the pressure applied. Additional temperature regulation could also

be incorporated by controlling the pressures in the two gas lines.

The consumption of helium gas from the supply cylinder is such that the cryocooler can be

operated for approximately 250 cycles from a laboratory 6 standard cubic meter compressed gas

cylinder. With 15 minute cycles this corresponds to 60 hours of continuous operation. If the

maximum cooling power is not needed the cycle time may be increased to 30 minutes to extend this

period. Another advantage of this design is that cycling can be stopped in the primed state, phase

(a), such that liquid helium may be produced at the touch of a button when needed.

5. Conclusions

A cycled adiabatic expansion crycooler which provides continuous cooling at liquid helium

temperature has been demonstrated. Temperature stability of the liquid reservoir is very good

because it is controlled by the boiling point of liquid helium. Unlike Joule-Thompson cryocoolers,

this design does not have any small orifices prone to plugging. It also has no moving parts in the

third or fourth stages. These features allow this crycooler to operate even with contaminated

helium and make it highly reliable.

The cycled adiabatic cryocooler does not provide as much cooling power at liquid helium

temperature as the Quantum Technology Corp. Joule-Thompson cryocoolers using the same two-stage

Gif f ord-McMahon cryocooler. However, it does have its own domain of application where the inherent

temperature stability and reliability of the cycled adiabatic cryocooler make it more advantageous.

232
6. Acknowledgements

The authors thank the Science Council of British Columbia and the National Sciences and

Engineering Research Council for their support of this research.

7. References

[1] Winter, C, New approaches to small scale cryogenic facilities, to be published in the Proc. of the 5th World Conference on Biomagnetism, Vancouver, Canada, 1984 Aug. 27; Plenum,

[2] Gygax, S., Cheap helium liquifiers, to be published in LT-17, proceedings of the International

Low Temperature Conference-17, Karlsruhe, W. Germany, 1984 August 14.

[3] Zimmerman, J.E., Recent developments in self-contained cryocoolers for SQUIDS and other lowpower cryoelectronic devices, to be published in ICEC-10, (Proc. of ICEC-10, Helsinki,

Finland, 1984 July 31-August 3).

[4] Simon, F. , Phys. Z., 34, 232 (1932).

[5] McCarty, R.D., Thermophysical properties of He-4 from 2 to 1500K with Pressures to 1000

atmospheres, NBS Technical Note 631, (NBS, Boulder, Colorado, 1972).

[6] Jakob, M. , Heat Transfer, v. 1, (Wiley, New York, 1962).

Table 1 - Helium liquifier dimensions

STAGE TEMP.

RANGE

K

(A) EXPANSION VOLUME HIGH PRESSURE TUBING

E1 300-70 0.48 0.09 500 SS 500

E2 70 0.95 0.15 23 Cu 90

E2 70 copper shot inside copper tube 30

E3 70-12 0.48 0.05 210 SS 130

E3 70-12 lead shot regenerator inside SS tube Pb 75

E3 70-12 lead shot regenerator outside SS tube Pb 775

E^ 12-4 0.32 0.05 50 SS 20

Expansion volume 4.2 1.6 0.17 8 SS 65

(B) LIQUID RESERVOIR LOW PRESSURE TUBING

E1 300-70 0.16 0.02 500 SS 50

E3 70-12 1.27 0.09 210 SS 550

E4 12-4.2 0.16 0.02 50 SS 4

E5 4.2 1 0.5 Pressed Cu powder 20

Insulation tube 4.2 0.64 0.02 14 SS 5 Liquid reservoir 4.2 2 ml volume Cu 10

NOTES: - Expansion chamber volume = 10 ml.

- Low pressure and high pressure tubes are concentric heat

exchangers at stages E1, E3 and E4.

233

TUBE TUBE TUBE MATERIAL MASS

DIAMETER WALL LENGTH

cm 00 cm cm gr
VUILLEUMI ER CYCLE CRYOCOOLER OPERATING BELOW 8 K

Yoichi Matsubara

Atomic Energy Research Institute

Ninon University

Tokyo 101, Japan

and

Mitsuhiro Kaneko

Cryogenic Department, Suzuki Shokan Co., Ltd.

Saitama 362, Japan

This paper describes the design and development of a Vuilleumier cycle

cryocooler (VM cooler) operating below 8 K, for the application of small

superconducting devices. Liquid nitrogen has been used as a heat sink of

the hot displacer. The annular gap between the phenolic displacer and SUS

304 stainless cylinder has been used as a gap regenerator. In order to obtain the cooling temperature below 8 K, we designed a single stage VM cooler which is precooled to 10 K by another two stage VM cooler.

The effect of the mean operating pressure, cycle speed and phase difference

between the hot and cold displacer of each VM cooler will be also discussed,

including the experimental results.

Key words: Cryocoolers; heat exchangers; helium; low temperature;

refrigerators; regenerators; Vuilleumier cycle.

1. Introduction

The requirement of low-power cryocooler investigation for several electronic devices, such as infrared detectors or superconducting devices, has recently increased. This kind of cooler will

be used for long term operation with no maintenance. Closed-cycle cryocoolers using

gap-regenerators are suitable for these requirements. Zimmerman and Radebaugh have developed a four-stage split-Stirling cryocooler operating at the temperature of about 8.5 K as a SQUID cooler

[1]. Myrtle, et al have also demonstrated operation of a split-Stirling cryocooler at 9 K using a single hollow conical displacer [2]. Sager and Paulson have constructed a four stage

Gifford-McMahon cycle which achieved an ultimate temperature of 7.1 K [3].

It seems to be difficult to obtain the temperature of below 5 K with these methods, however,

Zimmerman and Sullivan have demonstrated the feasibility of operation at the temperature below 4 K using a Stirling cycle cryocooler with the hot end temperature of near 10 K [4]. In our previous

work, a Gifford-McMahon cycle cooler anchoring at 10 K also achieved 4.8 K [5]. These results

indicate the choice of a cryogenic cycle and the optimized design of regenerators are important in order to achieve the temperature below 8 K. In this paper, we describe the experimental results

of two different types of VM cryocooler.

2. Three Stage Vuilleumier Cryocooler

We have built the three stage Vuilleumier cryocooler as a test apparatus. To decrease the

mechanical complexity we used liquid nitrogen as a heat rejection stage. A schematic of the VM cooler is shown in figure 1. The expansion and the compression displacers have been driven in sinusoidal motion using a stepping motor with an adjustable eccentric shaft cam. The annular gap

between the stainless steel cylinder and the cotton reinforced phenolic displacer was used as a regenerator in each stage. The hot and the three cold displacers were 60, 30, 20, and 10 mm in di'ameter and about 20 cm in length. The compression part and the expansion part have been

operated, respectively, with 15 mm and 20 mm stroke. In the final stage of this cooler, the

temperature swing was 7.7 to 8.8 K when the first stage was 33 K and the second was 13 K under the

following operating conditions: phase angle of 40 degrees, average pressure of 0.54 MPa, and the

234
frequency of 70 rpm. Figure 2 shows the cooling capacities at the cold end of this cooler. We have not controlled the quantity of liquid nitrogen flow in its minimum condition, but total LN

? consumption, including external losses, was 0.5 liter per hour at most.

In order to obtain a lower temperature while reducing the losses in the regenerator, the

pressure was decreased. The resulting operation of the cryocooler was not as effective as before.

When the phase angle was less than 40 degrees, the temperature difference between the second and

final stages increased, despite increasing the temperature of the final stage. We theorized that

the changes required an increase in the P-V quantity. To accomplish this it is possible to increase the working mass of the helium gas. However, the losses from the regenerator would

simultaneously increase. Another important factor is the second stage temperature. The second

stage expansion volume could be increased to optimize the operation when the working pressure is

reduced. The cryocooler could be made to produce the same cooling power without increasing the

frequency. Consideration of the thermal strain of the thin walled cylinder and the plastic piston

during the cool down period shows it is desirable to make the regenerator short. The temperature

difference between the warm and the cold end of such a short regenerator must be small in order to reduce the losses in the final stage.

3. The Composite VM Cryocooler

The investigation of the coldest section of the composite VM cryocooler is presented here.

Figure 3 shows the schematic diagram. This cooler is made of the two stage pre-cooler and the

single stage test cooler. These two coolers have the same driving mechanism in which a variable

speed stepping motor and two scotch yokes are used. The working space is separated from

atmospheric ambience by two small 0-ring seals. The physical dimensions are described in Table I.

Table I. Physical Dimensions of Two VM Coolers

Pre-cooler Test Cooler

Cyl inder

Displacer

Displacer

Compression

48

46.8

136

1st Stage

Expansion

20

18.8

180

2nd Stage

Expansion

1412.8

180

Compression

48

46.8

136

Expansion.

1211.4 * 235 *

All values in millimeters

* - Below pre-cooler 2nd stage (test section)

The test cooler was pre-cooled through a 4 cm width copper band. The radial clearance of the

displacer sections were about 0.1 mm. A cotton reinforced phenolic resin rod was used for the

displacer. Lead tape 1 mm in width and 0.2 mm thick was wound spirally around the pre-cooler

second stage. We used GdRh powder (45 vol. %) with epoxy resin as a regenerative material for the test cooler final stage. The displacer was coated with its material in the thickness of about 0.2

mm.

The pre-cooler was operated without the load of the test cooler. Figure 4 shows its

performance under the conditions of 62 degrees in phase angle, 48 rpm and a minimum pressure of

0.25 MPa. The ultimate temperature was 13.4 K. We also obtained about 14 K with the phase angle

at about 50 degrees and 65 rpm. Figure 5 shows the test cooler performance with pre-cooler. The

minimum pressure of the test cooler was 0.65 MPa and the phase angle was increased by increasing

the operating speed until the temperature reached approximately 7 K. This figure shows that the

temperature difference of test section is about 11 K under these optimized conditions. It is required to decrease the temperature of pre-cooler 2nd stage in order to obtain the temperature of

below 5 K. Table II shows the operating conditions and the results. The temperature swing of the

final stage of the test cooler was 5.4 K to 6.5 K without the external heat load. The second

stage temperature of the pre-cooler was about 16.1 K with the phase angle of 50 degrees and the

minimum pressure of 0.4 MPa. In any other conditions, the temperature of below 16 K was not obtained.

235
Table II. Test Results of the Composite VM Cooler

I. Pre-cooler

Phase angle: 50 degrees

Pressure swing: 0.4 MPa to 0.96 MPa Operating speed: 60 rpm

Stroke of the compression displacer: 18 mm * Stroke of the expansion displacer: 10 mm Temperature of the compression part at cold stage: 81 K Temperature of the expansion part at 1st stage: 34.4 K Temperature of the expansion part at 2nd stage: 16:1 K

II. Test Cooler

Phase angle: 53 degrees

Pressure swing: 0.155 MPa to 0.34 MPa Operating speed: 39 rpm

Stroke of the compression displacer: 18 mm Stroke of the expansion displacer: 5 mm Temperature of the expansion part at cold stage: 81.4 K Temperature of the expansion part at point 1: 41.2 K Temperature of the expansion part at point 2: 16.1 K Temperature of the expansion part at cold end: 5.4 to 6.5 K

In order to determine the cooling power which the cooler was producing, we measured

simultaneously the warm end pressure and the movement of the displacer with the time axis using a pressure transducer and a linear displacement converter. The P-V diagrams are shown in figures 6 and 7. The pre-cooler produced the cooling power of about 250 mW at the second stage. The test cooler produced the cooling power of about 27 mW at the final stage. The effect of the backlash

of a scotch yoke appeared at the top and the bottom end in the figures. We estimate that most of

the cooling power produced by the pre-cooler was consumed by the regenerator loss. The amount of

heat rejection from the test cooler is estimated to be less than 50 mW.

4. Conclusion

We obtained the ultimate temperature of 5.4 K and about 10 mW at 7 K by using the composite

VM cryocooler when the temperature of the pre-cooler was about 16 K. However, there remain many

problems to be solved such as the regenerator loss analysis including the effect of dead volume

and a specific heat of the regenerative materials, phase angle optimization, and the effect of the

non-ideality of the helium properties.

The authors would like to thank Professor K. Sekizawa for providing the GdRh powder. Part of

this work has been supported by the Science and Technology Agency.

5. References

[1] Zimmerman, J. E. , Radebaugh, R. , NBS SP-508, Page 59 (1978).

[2] Myrtle, K. , Winter, C. , and Gygax, S., Cryogenics, 22, Page 139 (1982).

[3] Sager, R. E. , Paulson, D. M. , NASA CP-2287, Page 81 (1983).

[4] Zimmerman, J. E. , Sullivan, D. B., Cryogenics, 19, Page 170-171 (1979).

[5] Matsubara, Y., Yasukochi, K. , NASA CP-2287, Page 157 (1983).

236
THERMAL COMPRESSOR

Fig. I. Schematic diagram of threestage VM cooler

40 1 ' ' 1 1

' r

Fig. 2.

temperature swing TEMPERATURE (K)

237
TEST COOLER PRE -COOLER

Fig. 3. Schematic diagram of the composit

VM cooler

POINT 2 2nd STAGE

F INAL STAGE

40

~ 30 E

cco

O

O

20

Fig. 4. Pre-cooler cooling capacity of the

2nd stage temperature

13 14 15 TEMPERATURE (K)

238
30

82 rpm 39 rpm

7 8 9 10 11 12 TEMPERATURE (K)

Fig. 5 Test cooler cooling capacity vs temperature

( T^: Temperature of the precooler 2nd stage)

1.18 .

00

00

en

a.

0.4

WORKING VOLUME (cc)

Fig. 6. P-V diagram of the 2nd stage

of the pre-cooler

0.39

Q.

0000

0.155

WORKING VOLUME (cc]

Fig. 7. P-V diagram of the final stage

of the test cooler

239
4K REFRIGERATORS WITH A NEW COMPACT HEAT EXCHANGER

R. C. Longsworth

W. A. Steyert

Air Products and Chemicals

Allentown, PA 18105

ABSTRACT

Two refrigerators have been developed which have nominal capacities of 0.25W and

0.5W at 4.2K. These use standard two stage DisplexR expanders and compressors

combined with a new compact heat exchanger which is concentric with the expander

cyl inder.

These refrigerators can be used to cool superconducting electronic devices by

direct attachment to the 4K heat station, or they can be plugged into the neck of a liquid helium superconducting magnet cryostat where they can cool the radiation

shields and reliquefy helium.

Key Words: Compact heat exchanger; cryogenic refrigerator; helium recondenser;

superconducting electronics; superconducting magnet

1. Introduction

The use of superconducting magnets for Magnetic Resonance Imaging (MRI)

represents the first major commercial application of superconductivity. The magnets

presently in use utilize liquid cryogens, helium and nitrogen; however, a number of

options for cooling magnets using small refrigerators or liquefiers have been studied

[1]. The approach to cooling a superconducting magnet which is the size of an MRI magnet that appears most promising to the authors is to have a multistage refrigerator

mounted integrally into the magnet cryostat. This refrigerator will fit into the neck

of the cryostat, cool one or two radiation shields, and recondense the helium. This

approach has the advantage that heat is removed from the system very close to the

point where it enters the system, thus avoiding additional thermal losses associated

with transferring refrigeration from a remote liquefier and minimizing temperature

drops between the cryostat and refrigerator. The Japanese National Railway in

evaluating refrigerators for their magnetically levitated train program recently

concluded that multiple Stirling plus J-T cycle coolers are less efficient than one central Claude cycle refrigerator, but the losses in the cryogenic transfer system add

so much to the refrigeration requirement of the Claude cycle system that it consumes

more power than multiple Stirling plus J-T coolers. They have thus decided to use individual Stirling plus J-T cycle refrigerators mounted in each magnet cyrostat [2].

240
The most widely used small 4K refrigerators today consist of a two-stage

Gifford McMahon type expander with a J-T exchanger [3,4]. These units utilize

rather long and bulky finned tube or corrugated tube heat exchangers for the J-T loop,

making them difficult to install in the neck of a helium cryostat. These systems

would also have thermal losses due to convective heat transfer between the heat

exchangers, the expander, and the neck tube.

Recognizing the potential need for a heat exchanger which would fit compactly in

the annular space around a two-stage GM type expander cylinder and which would match

the temperature gradient in the cylinder, a program was initiated to study heat

exchanger designs that would be suitable for this application. This led to an experimental program to test the newly designed heat exchangers by utilizing them in a nominal 0.25 W and a 0.5 W 4K refrigerator. The experimental program also included

studies of heat station design, interaction of the refrigerator with magnetic fields,

servicing the refrigerator and control of contaminants. This paper describes the

results of this work.

2. Design Description

The two units which have been built and tested are designated as a CS302 and a CS304 with nominal capacities at 4K of 0.25 W and 0.5 W, respectively; they consist

of standard DisplexR refrigerators having 20K capacities of 2 W and 6 W,

respectively. A J-T heat exchanger and a second slightly modified standard compressor

for the J-T return flow are added to provide the 4K refrigeration.

After studying many heat exchanger designs and experimenting with different

fabrication techniques, we elected to utilize a heat exchanger design which consists

of multiple high and low pressure tubes in a close contact, coiled configuration. The

heat exchanger is continuous from 4K to 300K and is coiled around the expander

cylinder in such a way that the temperature in the heat exchanger matches the

temperature in the adjacent cylinder. It is thermally bonded to the cylinder at the

two heat stations. Adsorbers are installed at the inlet to the heat exchanger and

just upstream of the J-T orifice.

Figure 1 shows the essential features of the 0.5 W expander which is designed to fit into the neck of a helium cryostat. A plug at the 20K heat station is designed to fit snugly into a mating receptacle in the neck tube to cool a radiation shield. For

cryostats which use liquid nitrogen to cool a shield at 77K, a heat station on the

first stage of the refrigerator is unnecessary. The 4K heat station consists of a finned tube which serves to recondense helium boil -off.

The 0.25 W unit which we built is designed to be operated in a vacuum. It has a warm heat station to which a radiation shield can be attached and a 4K

heat station for conductively cooling a device and/or instrumentation. This unit has

a very small pneumatically actuated J-T valve which permits high J-T flow rates to be

maintained during cool down and adjustment of the operating temperature with maximum

capacity when cold.

The adjustable J-T valve is convenient for a research worker who can set it

manually but is difficult to automate. A fixed J-T orifice is used in the 0.5W unit.

The flow rate is quite low when the helium is warm so cool -down of the 4K heat station

is prolonged when the unit is run in a vacuum. This does not matter when the unit is

plugged into a cryostat with helium in it because some venting helium cools it

quickly. Temperature is set by means of a pressure regulator which controls J-T

return pressure. Flow through the fixed orifice is constant so for any pressure above

the minimum design pressure, the regulator bypasses the excess flow in the low

pressure compressor.

241
The CS304 unit shown in Figure 1 incorporates several features that facilitate

installing and removing it from the neck of a helium cryostat. Guide sleeves are mounted on the valve motor housing which slide over rods that keep the refrigerator

centered as it is raised or lowered. A radial "0" ring seal on a short skirt at the warm end allows for axial contraction while maintaining good thermal contact at the

20K heat station. The warm end skirt is also used to tie on an elastomer sleeve which

prevents air from getting into the neck tube when the refrigerator is removed to be

serviced.

3. Experimental Program

3.1 Refrigeration Capacity

Both size expanders were built with pressure taps just upstream of the orifice in

order to monitor contaminant freeze out in the heat exchanger, and temperature sensors

on each stage of the refrigerator. Heaters were added as required for specific

tests. The capacity of each refrigerator was measured by mounting it in a vacuum pot

and wrapping it with six to ten layers of aluminized mylar.

Figure 2 shows the relationship between temperature and heat load applied to the

4K heat station for different settings of the J-T valve in the CS302. This test was

run with no heat loads applied to the upper two stages; however, the second stage can carry about 0.5W and the first stage, about 5W without seriously reducing the

refrigeration available at the third (4K) stage. Radiation and instrument lead

conduction are estimated to impose an additional lOOmW heat load on the third stage. A radiation shield attached to the first stage would thus make more refrigeration

available at 4K.

Temperature at the 4K heat station is set primarily by the pressure at which the

helium leaving the J-T valve is evaporating. Closing the J-T valve reduces the helium

flow rate and the compressor return pressure drops. The slight increase in

temperature with load is due to an increase in heat transfer between the surface

of the heat station and the evaporating liquid as the heat load is increased. At

sufficiently high heatloads all of the liquid produced is evaporated and the gas

stream itself is heated. A J-T unit has the characteristic that the refrigeration

produced drops rapidly when the maximum capacity is exceeded because the flow rate drops as the temperature of the gas flowing through the J-T valve increases.

Figure 3 shows the interrelationship between the refrigeration available at the

three heat stations for the CS304 unit. This data was obtained by setting heat loads

on the first and second stages and increasing the heat load on the third stage until

the unit warmed up. An example of how to interpret Figure 3 is that a load of 15W on the first stage, 3 watts on the second stage and from 0 to 0.5 W on the third stage

results in temperatures of 80K and 16K on the first and second stages respectively.

The third stage capacity is available over a temperature range of about 3.9 to 4.5K

depending on the setting of the pressure regulator.

3.2 Heat Exchanger Performance

Heat exchanger efficiency was measured by adding differential thermocouples (iron

doped gold vs. chromel ) to the warm ends of each section of the heat exchanger.

Figure 4 plots the data in dimensionless heat transfer and pumping energy after Kays

and London Fig. 24 [5]. It is seen that the heat exchanger has higher heat transfer

efficiency for a given pumping energy than typical plate fin heat exchangers.

242
3.3 Magnetic Effects

Studies were made of the effect of operating in magnetic fields in terms of the

effect of the fields on the refrigerator expander and the effect of the expander on the homogeneity of the field. It was found that the valve motor can only operate

satisfactorily in fields of 0.08T and that the 1 Kg of iron in the valve motor

contributes the only significant amount of inhomogenity to the field [6].

3.4 Test Cryostat

A double-walled cryostat was built for the CS304 which simulates the neck tube of

a large liquid helium cryostat and has room to accumulate IL of liquid. It has an 89mm (3.5") bore and a second stage receptacle to mate with the tapered plug on the

second stage of the refrigerator. It has no first stage neat station. This cryostat

was used to measure heat transfer characteristics of the second stage thermal

coupling, temperature stability, serviceability and long-term operation.

3.5 Cool Down

Figure 5 shows the cool down data collected and plotted on an HP34S7/HPS7 data

acquisition/computer system for the CS304 in the double-walled cryostat. The

temperature scale is folded at 30K so the second and third stage temperatures snovi scale changes at 30K. The first and second stages cool down relatively fast, but the

third stage takes a long time because of the thermal mass of the test pot, the cooling

of the 11 volume of helium (which is maintained at 1,1 atsa pressure), and the low flow

rate of helium in the J-T loop during most of the cool down. When operating in a vacuum with no applied heat loads or extra -ass a-tached botn refriAerators reach 4.21 in 4 hours.

3.6 lemperature Stability

Despite the lack of a precooling heat exchangers on the CS3C4 first ana second

stages the unit condenses 1L of helium overnight. After accumulating liquid in tne

pot, the feed valve is closed and pressure in the cryostat monitored. Over a period

of a week the cryostat pressure is typically maintained in the pressure range of 700

to 720 Torr. Most of the variation is due to changes in barometric pressure which is

normally 760 Torr.

3.7 Thermal Coupling

Studies of the heat transfer characteristics of the thermal coupling showed that

heat is transferred primarily by gas conduction in the gap and metal -to-metal contact

contributes only a small amount. The weight of the refrigerator is sufficient to maintain good contact. A temperature of 1.1K was measured for a-heat load of 3H at 16K.

3.8 Serviceability

The refrigerator is designed to be easily serviced. During tne testing phases,

the refrigerator was removed from the cryostat and reinstalled a number of times to demonstrate tnat this procedure could be accomplished with no undo proolems (sucn as air inclusion, ice, etc.), as well as to establish service instruction data. On one occasion, for example, the refrigerator was removed using the flexible sleeve to preclude air in-leakage, and warmed to room temperature, a different size J-i orifice

was installed, the J-T heat exchanger was purged, and reinstalled in tne cryostat in

45 minutes. The unit cooled back to 20K before the last of the IL liquid helium

e , a:: -a.a:

.

243
3.9 Reliability

In order to assure long-term reliability, a considerable effort was. expended to determine the most efficient means to clean up the system initially and keep it clean,

in order to avoid accumulating contaminants in the gas stream which could have the

potential to block the J-T heat exchanger. After initial experimentation, the last

9,000 hours of cumulative operation on several CS304 units, most of it at

subatmospheric pressure, have resulted in no indications of contaminant freeze out in

these systems.

4. Summary

Compact 4K refrigerators have been developed and tested, primarily to be utilized

in superconducting magnet and electronic applications. A simple compact J-T heat

exchanger, has been developed which can be mounted on a two-stage G-M type

refrigerator, providing a small, efficient, three-stage machine. Extensive testing

has been completed on initial prototype and preproduction machines, which has included

in-house performance and life testing. Field testing has included the successful

cooling of the cold radiation shield and recondensing the helium in an MRI magnet and

cooling of a small superconducting electronic device.

References

[1] R. C. Longsworth, "Interfacing Small Closed-Cycle Refrigerators to Liquid Helium

Cryostats," Cryogenics , 24, (1984), pg. 175.

[2] T. Ohtsuka, and Y. Kyotani , "Recent Progress on Superconducting Magnetic

Levitation in Japan," Plenary Talk at ICEC 10, Helsinki, August 3, 1984.

[3] W. H. Higa and E. Wiebe, "One Million Hours at 4.5 Kelvin," NBS Special

Publication 508 V., 1978, pg. 99.

[4] R. C. Longsworth, "Serviceable Refrigerator System for Small Superconducting

Devices," NBS Special Publication , 607 V., 1981, pg. 82.

[5] W. M. Kays, and A. L. London, "Compact Heat Exchangers, " Second Ed.,

McGraw-Hill, New York, 1964, p. 4.

[6] R. C. Longsworth, and W. A. Steyert, "The Use of Small Cryogenic Refrigerators

Near High Homogeneity Magnets, " Cryogenics 24 , No. 5, (1984), p. 243.

244
JT GAS

IN/OUT

DE204 SL EXPANDER

REMOVAL GUIDE

EXPANDER GAS

IN/OUT

REMOVAL/RETAINER

ROD

SEAL TO NECK TUBE

JT HEAT EXCHANGER

FIRST STAGE

SECOND STAGE

HEAT STATION

66 mm (2.6") COLD ADSORBER

JT RESTRICTOR

HELIUM RECONDENSER

Figure 1. CS304 Refrigerator, Two Stage Expander

with Concentric Spiral J-T Heat Exchanger

245
246
0 .2 .4 .6 .8 1.0 1.2

CAPACITY @ 4.2K — WATTS

Figure 3. CS304 Maximum Refrigeration Capacity (? 4.2 K vs. First and Second Stage Heat Loads

247
Figure 4. Heat Transfer Coefficient, h, vs. Flow Friction

Energy Loss Per Unit Area for APCI Coiled Tube

J-T Heat Exchanger and Typical Plate F in Surfaces

248
visd — aunssaud (d) 'x — aaruvaadiAiai (i)

Figure 5. Cool down of CS304 .5 W 4 K Refrigerator

with Experimental Heat Exchanger in Helium Filled Cryostat

249
THE DESIGN OF A SMALL LINEAR-RESONANT, SPLIT

STIRLING CRYOGENIC REFRIGERATOR COMPRESSOR

R.A. Ackermann

MECHANICAL TECHNOLOGY INCORPORATED

968 Albany-Shaker Road

Latham, New York 12110

For the past two years, Mechanical Technology Incorporated (MTI) has been

engaged in the development of a small linear-resonant compressor for use in a 1/4-watt, 78K, split Stirling cryogenic refrigerator. The compressor contains

the following special features: 1) a permanent-magnet linear motor; 2) resonant

dynamics; 3) dynamic balancing; and, 4) a close-clearance seal between the com- pressor piston and cylinder. This paper describes the design of the compressor,

and presents component test data and system test data for the compressor driving

a 1/4-watt expander.

Key words: close-clearance seal; compressor; cryogenic refrigerator; dynamic

balancing; linear-resonant compressor; permanent-magnet linear motor; resonant

dynamics; split Stirling; 1/4-watt expander

1. INTRODUCTION

The objective for this program was to design, fabricate, and test a linear compressor that could

be used in the military's 1/4-watt split Stirling cooler. The compressor was designed to demonstrate

that it could ultimately meet the existing specifications for size, weight, and input power when

driving an existing expander. The important requirements designed for in the compressor are:

1) high reliability, and MTBF's greater than 3000 hours;

2) the elimination of all lubricants;

3) low mechanical vibration; and,

4) the elimination of contacting seals.

Items 1 and 2 were achieved by using a linear drive system that eliminated mechanical linkages

and the need for lubricants. Item 3 was achieved by incorporating into the compressor a balancing

technique previously developed and patented by MTI, and Item 4 was achieved by using a close-clearance piston/cylinder seal.

2. COMPRESSOR DESCRIPTION

The prototype linear cooler developed is shown in Figure 1, and the design of the compressor is

shown in Figure 2. Beginning at the left end, the compressor consists of the piston/cylinder, with

the piston connected to the motor plunger through a flexible rod. The plunger, which is made up of

radially energized Sm Co 5 permanent magnets and a back iron, is supported on either end by teflon

bearing pads that position the plunger inside the motor stator. The stator contains the electric

coils and the end caps rigidly fastened to the stator on either end form the compression cylinder and

bearing assemblies described above. On the right end of the compressor is the counterbalance weight,

which is connected to the plunger through a mechanical spring and attached to the outer case, along

with the stator, through a flexible support configuration. Mechanical springs between the plunger

and end caps provide the resonant characteristics. The outer pressure case, gas transfer tube, and

displacement sensor located in the center of the plunger complete the design.

250
is.

Figure 1 MTI Linear 1/4-Watt Split Stirling Breadboard Cooler

Helium Transfer Tube

Support

Stator Coils Plunger SmCo5 Magnet

Motor Back Iron

1.83 Dia

Support

Bearing Pad

/ Housing

Coil Spring

Figure 2 Compressor Layout (Dimensions in inches]

251
The specifications for the compressor were:

Frequency 22 Hz Mean Pressure 600 psia

Pressure Differential 400 psia*

input Power >30 watts

Weight >2.5 lb

In the design, it turned out that the critical design trade-off parameters were:

• bore-to-stroke ratio;

• resonant frequency;

• mechanical spring design;

• weight of the motor plunger; and,

• pressure differential.

The bore-to-stroke ratio was important in establishing the size of the motor, the

compression-space spring component, the stress in the mechanical springs, and the piston leakage and

frictional losses. A trade-off analysis of these parameters with the bore-to-stroke ratio showed

(Figure 3) that an upper limit on stroke of 0.6 inch was set by the stress in the mechanical springs,

and a lower limit of 0.3 inch was set by the outside diameter of the motor and the amount of gas

spring developed in the compression space. The mechanical springs were limited to a stress of 60,000

psi, the gas spring was limited by a maximum plunger weight of 0.5 lb, and the motor size was limited

by the maximum diameter specification of 1.750 inch. As for the bore-to-stroke ratio, the other four

items also relate to the dynamic operation of the compressor. For this design, the operating frequency of the compressor was specified as 22 Hz. Achieving resonant operation in a high-pressure

differential, low-stroke compressor at this low frequency is difficult because of the large spring

component derived from the compression space. Balancing this spring with the inertia component of

the moving assembly required a large plunger weight. To minimize this weight, a maximum stroke of

0.6 inch was selected.

0.5

_ 0.4 d

a>| 0.3 b

co

CO 0.2

0.1

Operating Specifications:

Frequency = 22 Hz Mean Pressure = 600 psia Pressure Diff. = 400 psia

0.1 0.2 0.3 0.4 Piston Stroke (in.

0.5 0.6 0.7

Figure 3 Compressor Bore-Stroke Relationship

When connected to a 1/4-watt split Stirling cooler expander or equivalent volume.

252
The final design criteria for the compressor were:

Frequency

Swept Volume

Stroke

Bore

Motor Diameter

Plunger Weight

22 Hz 0.82 cm 3 15.24 mm

7.9 mm

44.45 mm

0.25 kg

2.1. Motor Characteristics

The linear motor used is one of a family of permanent-magnet (Sm C05) linear motors developed at MTI. Figure 4 schematically shows a section of the motor with the plunger in the center position.

The motor consists of stationary outer electrical coils wound on a steel bobbin, and an inner permanent-magnet plunger. The magnets are radially magnetized, with alternate magnets having north polarity on the outside diameter and south polarity on the inside diameter. The design characteristics

for the motor are:

Frequency

Stroke

Static Force

Electrical Input Power

Voltage

Weight

22 Hz

15 mm

35.6 nt @ 2.0 amp D.C. <30.0 watts

17.5 V.A.C.

< 1.0 Kg

Stator Bobbin

2ul Linear

Motion

Sm C05

Magnets

Plunger

Figure 4 Permanent-Magnet Motor

2.2. Vibration Isolation

Vibration isolation is achieved by employing a counterweight system with the isolation characteristics described in Figure 5. For this isolation technique, the counterweight is attached to the

stator through a mechanical spring, and both the stator and counterweight are supported from the

housing by mechanical springs. Through the proper design of this spring mass system, the counterweight (M^ is tuned so that the transmitted force to the case through the two springs (K3 and K4 ) may be designed to cancel one another, producing zero transmissibi 1 ity. The advantages of this sys253
tem are that the counterweight mass and amplitude are kept small, and good force isolation can be obtained over a broad operating range of frequencies (u) equal to or near u>0

. The characteristics of

the isolation system are:

Kl = 343 nt/m

K2 = 820 nt/m

K3 = 491 nt/m

Mm

= 0.09 kg

<«k = 18 Hz

0)o

= 22 Hz

Type of Isolator: Dynamic Two-Degree-of-Freedom

Force Transmissibility Ratio (T,)

Notes:

f = Fsiniot = dynamic exciting force T( i Xs = dynamic displacement of isolated machine (M3 ) XS F~ 0 as tu ~* °° T( = 0 when u> = o> 0 Good force isolation can be obtained at (or close to) Xs = 0 when w = <o n w = w0 regardless of the magnitude of Xs

Figure 5 Dynamic Force Transmissibility Characteristics —Vibration Isolation Technique

2.3. Test Results

Testing of the compressor was performed using both a 1/4-watt split Stirling cooler expander and

a simulated test volume that matches the expander and transfer tube volumes at the design operating

point of 80°K. Tests conducted on the compressor showed that the compressor performed better at 30 Hz than at 22 Hz. Rather than change the plunger mass to reduce the operating resonant frequency, it was felt that at this point in the development, testing at the higher frequency should continue, and

the ineff iciences from the mismatch between the compressor and expander should be accepted.

During the initial checkout tests of the compressor, it took significantly more than 30 watts to develop the required pressure differential of 400 psi. The problem was diagnosed as too large a clearance between the compressor piston and cylinder. By inspecting the hardware, it was found that

instead of a radial clearance of .0002 to .0004 inch, the actual clearance was .0006 inch. After re- furbishing this hardware and achieving a .0003-inch radial clearance, the machine performed much

better. The pressure difference generated by the machine is given in Figure 6. As shown, at the design specification of 400-psi pressure difference, the input power was less than 30 watts.

The cooling capacity of the compressor driving the 1/4-watt expander (shown in Figure 1) is given

in Figure 7. The results of these tests showed that the lowest temperature achieved was 35°K; at 77°K, the machine produced 0.35 watts of refrigeration for an input power of 34.5 watts. The

cool-down time to 80°K was four minutes.

254
0 I i i i i i i i i i i i i i i i i 30 35 40 45 50 55 60 65 70

Temperature (K)

Figure 7 1/4-Watt Cryocooler Cooling Capacity

255
Another interesting test result was that the number of electrical coils in the stator could be

reduced without affecting compressor performance. In the fabrication of this machine, the five

coils were wound individually, and separate power leads were brought out of the machine, enabling the

coils to be disconnected and the effect studied. The result (shown in Figure 8) was that the two

outer coils could be eliminated without a reduction in the pressure differential (the right-hand or- dinate), or an increase in input power (the left-hand ordinate). The implication of this is that the

motor length can be reduced by two coil segments (1.44 inches), and the overall length of the com- pressor can be reduced from 7.00 inches (Figure 1) to less than 5.5 inches.

3. CONCLUSION

The concept of using a linear drive for the military 1/4-watt split Stirling cooler compressor is

practical, as demonstrated by the program; in particular, the program showed the following:

1. It is difficult to design for a low frequency of 22 Hz and a large pressure difference because of

the large spring force produced by the compression space and the large moving weight required to

balance the spring component. Increasing the frequency will eliminate this problem.

2. A linear compressor can be developed for the 1/4-watt split Stirling cooler that will meet all of

the present cooler specifications.

3. Effective vibration isolation can be incorporated and still meet the design specified envelope.

i i i i i i i i i 0 1.0 2.0 3.0 4.0

Current (rms), amps

Figure 8 Effect of Eliminating Coils

256
JOULE-THOMSON VALVES FOR LONG TERM SERVICE

IN SPACE CRYOCOOLERS

James M. Lester and Becky Benedict

Cryogenics, Space Systems

Ball Aerospace Systems Division

Boulder, CO 80306

Joule-Thomson valves for small cryocoolers have throttling passages on the

order of 0.1 millimeter in diameter. Consequently, they can become plugged easily

and stop the operation of the cooler. Plugging can be caused by solid particles,

liquids or gases. Plugging is usually caused by the freezing of contaminant gases

from the process stream. In small open loop coolers and in closed loop coolers

where periodic maintenance is allowed, the problem is overcome by using careful

assembly techniques, pure process gases, warm filters and cold adsorbers. A more thorough approach is required for closed loop cryocoolers which must operate

unattended for long periods. This paper presents the results of an effort to solve this problem. The causes of plugging are examined, and various ways to eliminate plugging are discussed. Finally, the development of a "J-T defroster"

is explained. We conclude that a combination of preventive measures and a defroster will reduce the chance of cooler failure by plugging to such a degree

that J-T coolers can be used for long term space missions.

Key words: J-T cryocooler, J-T defroster, J-T valve, long life mechanical

refrigerator, space cryocooler

1 . Introduction

Typical space cooling applications now being considered are for instruments costing upwards of one hundred million dollars. The required operating lifetime of these instruments is 5 to 10 years

without maintenance. One watt of cooling at less than 1 0K is a typical goal. There is a desire to start these missions in less than 5 years; but, to develop a reasonable chance that such missions can

be accomplished, a great deal of successful cooler testing must be done. Ideally, we would like to have many of the coolers operating for longer than ten years before risking huge sums of money on entire instrument systems. Temperatures less than 10K for sufficiently high cooling power have not even been demonstrated for space cooler configurations, much less in any statistically significant

way. Realistically, we will not have the luxury of completing statistically significant life testing

before a large risk is taken.

In view of this situation, a good design approach is to use the hardware concepts which best

avoid the need for extensive life testing and will still do the job. In cryocoolers, machines which

do the best job of avoiding the uncertainties of wear, fatigue, critical materials and contamination

are favorable at this time. The passive Joule-Thomson (J-T) cold section does this very well except

for the plugging problem due to contamination. Test time limitations make it difficult to guarantee

that a J-T cooler will not freeze up in 10 years even if traditional purification techniques are applied to the fullest extent possible. This leaves us with an unacceptable risk which must be overcome by some other means.

Fortunately, we can employ a strong countermeasure - namely a defroster, to clean out the J-T

valve. Many short duration tests can then be run under severe contaminating conditions in an attempt

to show that this cleaning process will always renew the cooler. Then, in flight, under less severe contaminating conditions, the cooler can be "defrosted" on a preset schedule more frequently than the

statistically proven safe operating interval. Confidence in the cooler will then be developed on a cycle basis rather than on a total time basis, thus allowing greatly accelerated testing.

We concluded that the plugging problem should be solved prior to refining other components in

the J-T system because it is the key to determining if J-T's are usable for long term missions. We

are currently developing a J-T valve and defroster with encouraging initial results. This paper describes that work.

257
2. The plugging problem in J-T coolers

This paper is primarily concerned with small cryocoolers for use in space instruments. Table 1 gives approximate design values which relate to the plugging problem for a 1 watt Helium J-T stage

operating between 18 and 1.6 atmospheres.

Table 1 - Approximate cooler characteristics (Example)

Helium Flow rate 1 Standard 2,/sec

Helium Quantity Required

to charge the stage

Cryocooler area which outgasses into the Helium

Volume of a plug in the

J-T valve (Assumes 0.1 mmDia-byO. 1mm long plug)

Volume of a plug in the small

heat exchanger tubing upstream

of the J-T valve (Assumes

2mmDia-by20mm long plug)

10 Standard I

3 2 10° cm

10" 6 cm

3

-1 3 10 cnT

Operating time - 10 years-approx

,

10 hours

The geometry of the J-T valve is assumed to be a short small hole, and this sets the size of its

plug. The upstream high pressure side of the heat exchanger is characterized by a single line of

small diameter tubing. Plugging by freezing of the mixture of contaminants will be spread over a considerable distance in this tube as dictated by the flow, temperature gradients and freezing points

of the various contaminants in the mixture. We suspect that the assumption of a ten diameter

freezing zone is a low estimate; but, the point to be considered is that the volume of contaminant

required to form a plug is several orders of magnitude greater in the heat exchanger than in the

valve itself. The downstream, low pressure side of the heat exchanger is much larger as dictated by

the requirement for low pressure drop in the compressor return, so there is much less concern about

plugging there.

2.1 Sources of contamination

Potential contaminants are gases, liquids or solid particles. Particles are dirt or chips left

in the cooler during construction and dust from adsorbers. Liquids are things like free water or oils, the latter possibly from an oil lubricated compressor. There are three sources of gas: outgassing from the interior surfaces of the entire cooling loop, trace contaminants in the initial charge

of Helium, and continuous vaporization of a cooler component. Plastic parts or oil in a compressor

fall into this last category. The potential for plugging the example cooler of table 1 was estimated

by calculating the sizes of these sources.

2.2 Gaseous contamination

The classical view of metal surface outgassing is given in [1] . This data shows that the

outgassing of initially "clean and dry" surfaces at room temperature decreases* from a fairly

consistent value of

3 3 STD cm STD cm

-8 — -9 —

10 2 „ after one hour in vacuum to 10 2 „ after ten hours and continues to decrease

cm Sec cm Sec

by another order of magnitude for each additional order of magnitude span of time. The outgassing of

a cooler, at least in the warm areas, will be roughly the same into a charge of pure Helium where the

partial pressures of the contaminants are very low.

258
The outgassing relates to the potential for plugging in a logarithmic manner. In the first

logarithmic time interval of outgassing, 1-10 hours, the outgassing will accumulate the equivalent of

160 plugs in the J-T valve and 1.6(0 ) plugs in the heat exchange tube upstream the J-T valve. The

density of the frozen plug is approximately 10 times greater than standard density of the gaseous

contaminant. Continuing from the second _Jjime interval, 10-100 hours, to the last, 10000-100000

hours, the total accumulation is about 8(10 ) cm of solid, or about 1 milligram. This amount could

produce 800 plugs in the J-T valve. (Note that the amount of outgassing by this theory is the same

for each time interval. Note also that the heat exchanger is relatively immune to plugging by

gaseous contaminants because of its relatively large size.)

If ultra pure grade Helium is used for the initial charge, the total quantity of contaminants is

about the same as the 10 year outgassing. Typical specifications for^ maximum contaminants in ultra

pure Helium and the resultant amounts in the initial charge of 10 standard liters include trace

amounts of 0 2 , N 2 , Ne, Ar , H 2 , C0 2 , and H 2 0 (greatest contaminant listed first). The total amount of

solid impurities is about (10 3

) cm 3 or about 1 milligram. This amount could produce 1000 valve

plugs

.

Lastly, the system may have components which vaporize continuously throughout the operating

period. Plastic^parts or compressor oils are in this category. A good oil will have a vapor

pressure of 10 torr at 300K. The amount of oil vapor (apart from free oil droplets) circulated

toward the J-T valve would be that amount which saturates the process gas at the oil vapor pressure.

If one standard liter per second of Helium flows in the system and the pressure is 1.6 atm at the oil

vapor pickup point, the total amount of oil vapor frozen into solid form would be 3(10 ) CM 3

. This

is enough to produce about 30 plugs.

A loaded adsorber can act as a continuous source of contamination if left "wet" from a previous

test, and be a large additional source. In summary, over 2000 potential J-T valve plugs can be

present in the system due to gaseous contaminants.

2.3 Liquid and solid contamination

Plugging due to free water is possible if the system has been left open to the atmosphere. Oil

mist (suspended droplets) from compressors may be present in large quantities. Dirt and chips can be

left in the cooler during manufacture. Residue from soldering operating has been known to dislodge

and stop at J-T valves. Most J-T coolers use adsorbers which consist of charcoal particles or molseive pellets. These adsorbents lose fine dust particles and these are a concern because they are

not easily filtered without creating the risk of freezing contaminant gases at the filters.

2.H The nature of plugging

In spite of the large potential for becoming plugged, J-T coolers usually work. Plugging most

often occurs during startup or after a power interruption, when the heat exchangers are warm and will

not "cold trap" the contaminant gases. If the initial cool down period is passed, the cooler will

usually continue to work. The reason is that the heat exchangers do a very good job of collecting

the contaminants before they get to the J-T valve. Then also, the contaminants which do not stick to the heat exchanger walls are mostly in the form of minute ice crystals which are simply blown through

the J-T valves. Sometimes coolers will operate at different cooling capacities on separate cooldowns

- an indication of partial plugging.

3-. Solutions to the plugging problem

Plugging of the J-T valve can be reduced or eliminated by three major techniques: reduction of

contamination sources, the use of certain valve geometries, or by methods which counteract the

contamination within the system when it is operating. While large improvements can be made with the

first two techniques, the potential for plugging still exists. Counteractive measures are necessary.

In the final analysis, renewing the valve by defrosting is the surest way to ensure long-term

operation.

3.1 Reduction of contamination sources

Initial thorough cleaning and vacuum baking is necessary to reduce massive quantities of

contaminants. It is not likely that the outgassing rate can be reduced to below

STD cm

J

-1 ? 10 2 therefore a significant potential for plugging will still exist in the system,

cm Sec

Research grade gases can be used to charge the cooler instead of ultra pure grade, reducing the

potential for plugging by a factor of 5. Careful control of the charging process is necessary to

259
maintain this improvement. All cooler components should be low vapor pressure materials. Careful

design will ensure that the gas produced by these sources is a 35}^1 fraction of the total

contamination. As a general guide, materials with vapor pressure above 10 Torr should be avoided.

Compressors should either be oil free or should have a very low output of free oil droplets in

mist form. The space in and around the J-T valve itself can be treated as a critical component and

assembled in the strictest clean room conditions. This will virtually eliminate the chance of

plugging by particles in the cooler if the valve capsule is protected by suitable filters.

3.2 Valve geometries

Most J-T valves are simple, short circular holes. Other geometries are possible, but there is

little to be gained by these designs and they may be harder to unplug. A long capillary tube could

be used as a J-T expansion device, allowing the flow passage to be larger in diameter. The flaw in

this idea is that total plugging of the valve is not the only concern. Partial plugging in a long

capillary could cause a large change in performance and is not allowable. The idea of using a porous

plug suffers from the same flaw. In addition, the very fine pores of the plug will be much more easily plugged by minute ice crystals suspended in the stream.

One attractive compromise geometry is to put a wire through a small hole. This arrangement

distributes the orifice into a ring shape which is not sensitive to plugging by a few particles left

in the cooler during assembly.

3.3 Counteractive measures

Starting from the warm high pressure end of the system, there are a number of things that can be

done to reduce the chance of plugging. In a cooler using oil lubricated compressors, virtually all

of the free droplets must be removed by coalescing filters. Fortunately, these filters can be made

very long and efficient since they are in the warm areas. Barrier film techniques are also necessary

to prevent creep of oil films down the heat exchanger tubing. The more critical problem here is to reduce the mass of free oil to a level lower than that required to saturate downstream gas adsorbers

and cause freeze up by that mechanism.

Adsorbers consisting of beds of charcoal, silica-gel, or molecular sieve materials are the most

effective way to reduce the flow of contaminants to the J-T valve. Adsorbers in the cold areas just

upstream of the J-T valve are very powerful purifiers, possibly eliminating the plugging problem

completely, but the problem is in the proof. Several imperfections inherent with adsorbers may allow

plugging to occur after a long period of operation. If the beds are made too 'tight* then they

themselves may become subject to plugging. Channeling may occur leading to variations in purification efficiency from bed to bed. Adsorbers in flow streams tend to act as chromatograph columns.

That is, concentration fronts gradually migrate to the downstream side and eventually a large release

of adsorbed contaminants will occur. This effect has been observed in helium liquifiers causing

unexpected freeze up after a long period of normal operation.

Particle filters such as screens or porous metals will be needed downstream of adsorbers to trap

released dust or particles, but care must be taken to allow sufficient area so that freeze up does

not occur in the filters. Chemical getters which combine with the more active gases are useful in

reducing those contaminants.

After all of these precautions are taken, it will still be very difficult or impossible to say

that a J-T valve will not be plugged in a long mission. Also, if power is interrupted, the entire

cooler may become filled with gaseous contaminants. These uncertainties require some sort of valve

cleaner which can remove the contamination. Mechanical devices have been used for this purpose, but

they are risky because they may not totally remove the contamination and they may become stuck. The

safest way to clear a J-T valve is to use a defroster. The design of such a device is described in

Section k.

4. Design of a J-T valve defroster

The J-T valve was arranged as shown in figure 1. Cold, high pressure gas passes through the

final adsorber where most of the remaining impurities are trapped. The gas enters the thin wall

stainless steel tube whose length is shown as % , then it passes into the relatively large diameter

entry section of the copper J-T valve. The wire passes through the throat of the valve causing this

restriction to be ring shaped which reduces the chance of a few particles forming a plug. After

expansion at the valve, the gas-liquid mixture passes through the thin wall stainless steel outlet

tube, labeled I , to the boiler and from there to the low pressure side of the heat exchanger. A resistance heater is wound around the outer throat of the valve. Figure 2 shows a test model of the

device

.

260
CHARCOAL ADSORBER HEATER

SIDE

4733

Figure 1 J-T Valve Defrosting Scheme

84-1606

Figure 2 JT-Valve Defroster

261
The purpose of the arrangement is to allow complete defrosting in a short time period with

minimal disturbance to the useful operation of the cooler. The low conductivity stainless steel

tubes act as thermal standoffs between the heated copper J-T valve and the adsorber or boiler. This

confines most of the heat to the valve where it is needed. Standoff 8, is also needed to prevent the

adsorber from warming up to a temperature where contaminants will be released. The boiler contains a reserve of liquid which maintains constant temperature cooling for the load during the defrosting

cycle. The purpose of the copper entry section of the valve is to prevent sudden replugging of the

valve after the heater is turned -off. This copper part is warmed to room temperature in a few

seconds along with the throat of the valve. If the entry section were not there, contaminants from

the warm end of the standoff tube would be immediately available to collect in the valve. As it

is, the annular gap between the copper and stainless tubes acts as a cold trap for this temporary

source. Further enhancements of this cold trapping scheme are possible but they do not seem to be

needed. The heater must be able to raise the valve temperature rapidly to minimize the total heat

input to the system and also to the reserve liquid in the boiler.

The heater must also be able to operate over a broad range of heating conditions depending on

whether the valve is completely plugged or not plugged at all. This means that the heating power

must be several times the steady state cooling power of the cooler because the effective short term

cooling power of the stream is high when working against an unplugged warm J-T valve. When the valve

is plugged, the same heating power will cause very rapid valve temperature rise because there is no cooling flow, and the heater could burn out. A closed loop heater shut down controlled by valve

temperature is needed to handle this range of conditions. Redundancy of heaters and temperature

sensors can be provided.

Standoff dimensions, boiler capacity, and heater size are a function of the application. There

are considerable differences between HK Helium valve defrosters and 77K Nitrogen valve defrosters

because of the large differences in thermal properties of the materials. To get a feel for the numbers, a 2-watt Nitrogen cooler requires about 20 watts of heating for 10 seconds resulting in a heat

input of 200 joules. This consumes about 1 gram of liquid Nitrogen from the reserve in the boiler if precise cooling temperature stability is to be maintained at the load. The heat required to vaporize

the plug is negligible and the heat required to warm the copper is only 15 joules. The total heat

leak down the standoff tubes is only about 5 joules. Most of the heat goes into the cold gas stream

at the valve.

When operated at lower power levels, the defrost heater is also a handy device to control warm

up of the system and to aid in initial bakeout. Heating by induction has been suggested as an alternate but this method complicates the power supply for space applications. Section 5 describes

the tests performed on the device shown in Figure 2.

5. Defroster testing

Preliminary testing on the J-T defroster (Fig. 2) has been completed for an open-loop Nitrogen

J-T system. The results indicate that defrosting can be done in a short time with minimal

disturbance to the cooling temperature using low heater input energy. These tests run on our preliminary J-T defroster have been beneficial both in confirming our calculations on the defroster

and in defining necessary modifications to the hardware and test methodology.

5.1 Apparatus

The test apparatus, shown in Figure 3. uses K-bottle Nitrogen (ultra high purity) as the source

gas. The outer jacket, which houses the coiled tube exchanger and its thermal shroud, is evacuated

to 10 Torr prior to testing. In the 'cold end' of the assembly, there are three thermocouples

located and labeled as follows: T

Q

-potential cooling load (on the downstream mol seive trap), T^-J-T

defroster, T^-upstream mol sieve trap. The contamination loop inlet is also located in the cold

section just upstream of the J-T valve and defroster. A flow meter, temperature scanner, contamination cylinder (H^0) , power supply, voltmeter, ammeter, and pressure controller complete the

apparatus

.

Note that the system shown in figure 3 makes provisions for the addition of a useful cooling

load where the downstream mol sieve trap is currently located. The only load that was applied during

these tests was conductive and radiative heat leak.

5.2 Test methodology

In order to develop a J-T defroster that will be able to recover from a variety of worst-case

conditions, two concepts required testing. The defroster heater design was tested in order to determine its effect on the overall cooler thermal stability. After sufficient testing and mapping

of the defroster's operating characteristics using the pure (ultra high purity) Nitrogen gas source, additional tests were done with a contaminated Nitrogen source. The pure Nitrogen tests are discussed first.

262
CONTAMINATION

SOURCE O

H 20

N2

K- BOTTLE

THERMOCOUPLE

LOCATIONS

JT-VALVE

HEATER'

r

VACUUM

COILED TUBE

HEAT EXCHANGER

COPPER

/SHROUD

OUTER

^/JACKET

FLOWMETER

o

A/N 4733

Figure 3 Defroster Test Apparatus

To assure consistency in the pure Nitrogen tests, two variables, the operating pressure (high

pressure source) and the time interval between the defrosting, were specified. During the current

tests, a source operating pressure of 450 psia provided sufficiently low temperatures at the J-T

valve to test the defroster, while still providing the cooling necessary to recover from the defrost.

The time interval between defrosting was always less than 2 hours.

When starting a test run, we used a Nitrogen operating pressure of 2000 psia to expedite the

equipment cool down by producing high pressure (and relatively high temperature) liquid Nitrogen.

Then, over a period of one and a half hours, we gradually decreased the operating pressure until the

system was stabilized at 450 psia. Under these conditions the 'cold end' of the apparatus was usually operating under partially flooded conditions. This was apparent when the temperature

gradient between the three thermocouples (Fig. 3) was 10K or less. When these conditions were met we tested the defroster.

We powered the defroster heater with a measured voltage while watching the thermocouple attached

to the valve, T. . When the high temperature limit, approximately 20°C, was reached we manually shut

off the power supply and recorded the highest temperature observed on the J-T valve. Then we recorded the system response for all thermocouples, flow and vacuum level. The temperature scanner recorded the three temperatures continuously for analysis after completion of the tests.

The contamination loop shown in Figure 3 was used to provide a water saturated Nitrogen source.

The contamination loop was used either to provide 100 percent water saturated or partially saturated

Nitrogen by using only flow through the contamination source or through the exchanger and the

contamination source. When using the contamination source, the source cylinder was heated to

263
approximately 100°C, in order to fully saturate the Nitrogen. The water was expected to freeze out

in the J-T valve in a short period of time, as indicated by a reduction in flow rate. Once the flow

slowed enough to indicate that the valve was plugged the J-T defroster testing was carried out in the same manner as described for the pure Nitrogen source tests.

5.3 Results

The results for testing done at 450 psia are shown in figure 4, for four separate defrosting

tests, case I, case II, case III, and case IV. These tests on the apparatus were 'done consecutively,

during one cool down period. For this reason, we feel that these are the most representative results

out of all the tests completed to date. The defrost in case I required 7.6 W and the cooler required

40 minutes before it had stabilized to the conditions prior to the defrost. In case IV, the defrost

required 15 W and the cooler returned to the conditions prior to defrosting in only 4 minutes. The

heater input power for case I disturbed the thermal stability of the entire cooler ten times longer

than the heater input power in case IV. Note that in case I the total energy input is 718 W«s and it

decreases to 285 W«s in case IV. The trend can be traced from case I to case IV (Fig. 4).

When the valve is heated, the mass flow is substantially reduced because of the large change in

fluid conditions there. This effect reduces the pressure downstream of the valve and results in a lower temperature in the boiler for a short time. This effect would be less noticeable in a cooler

with more open downstream plumbing as would be the case for a more refined cooler. There would still

be a substantial decrease in flow in a more refined cooler and this would tend to minimize the heat

addition due to the defrosting pulse.

The data plotted in figure 5 compare the defroster's requirements in W*s and in equivalent grams

of L-N2. This plot is particularly useful design information for the valve tested here, but is only

characteristic of this valve. Knowledge of the equivalent grams L-N2 boiled off during defrost cycle

allows for the design of a L-N2 reservoir with enough capacity to absorb the entire heat input of the

defrost cycle without allowing a change in load temperature.

Defrosting tests run using the contamination loop to simulate a wet Nitrogen source show that

the device is effective, but the tests were not entirely conclusive. The loop (Fig. 3) supplies

contaminated Nitrogen directly to the system upstream of the J-T valve. However, the valving on the

current apparatus allows wet Nitrogen to remain in the contamination tube. Consequently some recontamination would occur before we could take adequate flow measurements to prove that the valve

had been totally cleared.

5.4 Conclusions

The tests done using pure Nitrogen confirm that the J-T defroster can be operated with little

effect on the thermal stability of the cooler. The current testing equipment must be refined in

order to conduct conclusive testing of the J-T defrosting action.

One additional testing problem encountered was the need for better control on the defroster

power supply. To protect against heater burnout, the power supply must be automated to shut off the

power before the J-T valve temperature exceeds 20°C. An additional thermocouple must be added to the

heater very close to (if not toughing) the heater wire in order to more accurately measure the heater

temperature

.

6. Additional work

Further refinements of the defroster scheme will be tested in the remainder of 1984 and in 1985.

In 1985 we will operate a closed-loop 4K helium J-T cooler employing the defroster and pressurized by

a long-life oil lubricated compressor.

The authors are grateful for the ongoing expert consultation of Dr. Tom M. Flynn on various

purification concepts and thermodynamic aspects of the J-T cyrocoolers. In addition, Dr. Thomas R. Strobridge has greatly added to our understanding of J-T cyrocoolers by drawing on his 20 years

experience with helium liquifiers.

7. References

[1] Santeler, D. J., Holkeboer, D. H., Jones, D. W., Pagano, F. , Vacuum Technology and Space

Simulation, NASA SP-105 (1966).

264

CASE IV: 15. OW APPLIED FOR 19 SEC (285 (W-S)

1.0 2.0 3.0 5.0 6.0 7.0

AT

Q

: POTENTIAL COOLING LOAD LOCATION DT^S J-T DEFROSTER OJ^. UPSTREAM TRAP

Figure 4 Pulsed Heating of the J-T Cooler

800 i700

600

500

400

300

200

100

N+ CASE I

CASE II +

CASE III

I 1I I I I 1I I I I I I I I I I I I I I I I I 5.0 10.0 APPLIED DEFROSTING POWER (W)

15.0

-13.5

3.0

2.5 *

2.0 W

1.5

1.0

J _L

A/N 4733

Figure 5 Energy Requirements for Defrosting the J-T Valve (to ~20°C)

266
ATTENDANCE LIST

3rd Cryocooler Conference on Refrigeration for

Cryogenic Sensors and Electronic Systems

National Bureau of Standards

September 17 & 18, 1984

Boulder, Colorado 80303

Robert A. Ackerman

Mechanical Technology, Inc. Stirling Engine Systems Division

968 Albany-Shaker Road

Lathan, NY 12110

518-785-2255

John Barclay

Los Alamos National Lab.

Group P-10

M. S. K764

Los Alamos, NM 87544

505-667-6431

Becky Benedict

Ball Aerospace Systems Division

P. 0. Box 1062 - M. S. TT-5

Boulder, CO 80306

303-939-4000

Mel Bello

Aerospace Corporation

El Segundo, CA 90501

213-648-7277

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Birmingham Associates

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Aerospace Corporation

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Mail Stop 4906

El Segundo, CA 90245

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M. S. A24-05

Grumman Aerospace Corp.

Bethpage, NY 11714

516-575-0988

Guenther Bogner

Siemens AG Research Labs.

8520 Erlangen

West Germany

9131-731228

Thomas W. Bradshaw

Rutherford Appleton Laboratory

Bldg. R65

Chilton, Didcot, Oxon

Engl and

Abingdon 21900 ext. 6149

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Arthur D. Little, Inc. 20 Acorn Park

Cambridge, MA 02140

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Hughes Aircraft Companv

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Ford Aerospace & Communications Corp.

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Jet Propulsion Laboratory

California Institute of Technology

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Aerojet Electro Systems Company

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Bldg. 160 - Dept. 4323

Azusa, CA 91702

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Air Force Wright Aeronautical Labs.

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David E. Daney

National Bureau of Standards

Division 773.10

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303-497-3595

Ken H. Davies

U. K. Science & Engineering

Research Council

Rutherford Appleton Laboratory

Chilton, Didcot,

Enaland

0235-21900

267
Axel Dehne

Hughes Aircraft

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Riverside Research Institute

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Centre D'Etudes Nucleaires de Grenoble

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Univ. of Giessen

Institut fur Angewandte Physik

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Analytic Decisions, Inc. 1401 Wilson Blvd.

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L'Air Liquide

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France

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CTF Systems Inc. #15-1750 McLean Ave. Port Loquitlam

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Ford Aerospace Corporation

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Geoffrey Green

U. S. Navy - DTNSRDC

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Annapolis, Maryland 21402

301-267-3632

Chen Guobang

Cryogenic Engineering Lab.

Zhejiang University

Hangzhou

China

21701-2427

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Naval Weapons Center

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China Lake, CA 93555

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Jack E. Jensen

CVI Incorporated

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268
Dean L. Johnson

Jet Propulsion Laboratory

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Mark Johnson

Ball Aerospace Svstems Division

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Jack A. Jones

Applied Mechanics Division

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California Institute of Technology

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Air Products & Chemicals, Inc. 1833 Vultee Street

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Cryogenic Department

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CTI Cryogenics

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Philips Laboratories

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NASA

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AEG Telefunken

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Delft University of Technology

Department of Applied Physics

Lorentzweg 1 2645 NE Delfgauw

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Magnavox

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269
Shi mo Li Cryogenic Engineering Lab.

Zhejiang University

Hangzhou

China

21701-2427

Paul Lindquist

U. S. Air Force

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HR Textron Inc. 25200 W. Rye Canyon Road

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Italy 50013

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215-481-3708

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National Bureau of Standards

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Sperry Corp.

P. 0. Box 64525 - M. S. U1K14

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Martini Engineering

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Atomic Energy Research Institute

Nihon University

7-24-1 Narashinodai

Funabashi-Shi

Chiba-Ken

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0474-66-1111, ext. 374

Frank E. McCrea

Jet Propulsion Laboratory

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Amdahl Corp. \

P. 0. Box 3470 MS 197

Sunnyvale, CA 94088

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Philips Laboratories

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Westinghouse Electric Corporation

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Beech Aircraft Corp.

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CTI-Cryogenics

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Quantum Technology Corp.

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CVI Incorporated

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Columbus, OH 43216

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Ricor Ltd.

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National Bureau of Standards

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Laboratoires de Marcoussis-CR-CGE

Route de Noxay

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Philipp B. Rudolf von Rohr

Massachusetts Institute of Technology

Cryogenic Engineering Laboratory

Room 41-211D

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Samuel Russo

Hughes Aircraft Company

E1/C102 - P. 0. Box 902

El Segundo, CA 90245

213-616-9651

Rudy S. Saenz

Hughes Aircraft Company

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Waltham, MA 02254

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Raymond E. Sarwinski

R. G. Hansen & Associates

C/0 GWR Instruments

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Clifton Precision

I & LS Division

P. 0. Box 4508

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Centre D'Etudes Nucleaires De Grenoble

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NASA - Code 713

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Herbert Sixsmith

Creare R&D Inc.

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Joseph L. Smith, Jr. MIT Cryogenic Engineering Lab.

MIT, Room 41-204

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271
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Creare R&D Inc.

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Oxford University

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SHEET (See instructions)

PUBLICATION OR

REPORT NO. NBS/SP-698

2. Performing Organ. Report No 3. Publication Date May 1985

4. TITLE AND SUBTITLE

Proceedings of the Third Cryocooler Conference

5. AUTHOR(S)

Ray Radebaugh, Beverly Louie, and Sandy McCarthy

6. PERFORMING ORGANIZATION (If joint or other than NBS. see instructions)

National Bureau of Standards

U.S. Department of Commerce

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|] Document describes a computer program; SF-185, FlPS Software Summary, is attached.

11. ABSTRACT (A 200-word or less factual summary of most significant information. If document includes a si gnifi cant bibliography or literature survey, mention it here) This document contains the proceedings of the Third Cryocooler Conference,

held at the National Bureau of Standards, Boulder, CO, on Sept. 17-18, 1984.

About 140 people from 10 countries attended the conference and represented

industry, government, and academia. A total of 26 papers were presented orally

at the conference and all appear in written form in this document. The emphasis

in this conference was on small cryocoolers in the temperature range of 4 - 80 K, Mechanical and non-mechanical types were discussed in the various papers.

Applications of these small cryocoolers include the cooling of infrared

detectors, cryopumps, small superconducting devices and magnets, and electronic

devices

.

12. KEY WORDS (Six to twefve entries; alphabetical order; capitalize only proper names; and separate key words by semicolons)

conference; cryocoolers; cryogenics, cryopumps, helium, infrared detectors,

refrigeration ; superconductors

.

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