The degradation of regenerator effectiveness below 10K is due to the imbalance of the heat capacity of the regenerator material and helium gas as a working fluid. One of the attractive methods to increase this efficiency could be realized by a gap regenerator system regarding helium gas property. This paper describes an experiment using pressurized helium gas as a regenerator material. A two stage G-M cycle refrigerator has been used for precooling the gap regenerator system. With this method, minimum temperature below 5K has been obtained when the precooling temperature maintained at 10K

Matsubara, Y.

Yasukochi, K.

English

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AN APPLICATION OF GAP REGENERATOR/EXPANDER
PRECOOLED BY TWO STAGE G-M REFRIGERATOR
Y. Matsubara and K. Yasukochi
Atomic Energy Research Institute
College of Science and Technology
Nihon University
ABSTRACT
The degradation of regenerator effectiveness below 1OK is due to the
imbalance of the heat capacity of the regenerator material and helium gas
as a working fluid. One of the attractive methods to increase this
efficiency could be realized by a gap regenerator system regarding helium
gas property.
This paper describes an experiment using pressurized helium gas as a
regenerator material. A two stage G-M cycle refrigerator has been used for
precooling the gap regenerator system. With this method, minimum
temperature below 5K has been obtained when the precooling temperature
maintained at 10K.
INTRODUCTION
In order to obtain the liquid helium temperature effectively by a
regenerative cycle cryocooler, such as Stirling cycle or Gifford-McMahon
cycle, we need to know the thermal behavior of regenerator material and
property of helium gas as a working fluid. One of the solutions to
obtaining the liquid helium temperature is to use the gap regenerator
method with plastic cylinder and displacer which has been successfully
developed by Zimmerman, et al.(1).
This paper describes the experimental results of a gap regenerator
/expander which is made of plastic piston and stainless steel cylinder with
helium gas annulus, precooled by two stage Gifford-McMahon refrigerator.
REGENERATOR CONFIGURATION
One of the features of a gap regenerator, when compared to lead shot
type regenerator, is that the contents of working gas in the regenerator
can be kept to minimum. This effect is particularly noticeable at a
temperature level below 10K where the volumetric specific heat of the
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helium gas increases, as pointed out by Radebaugh(2)and Daney (3).
On the other hand, the heat transfer area of a gap regenerator is
limited to the finite displacer length and its cylinder surface, therefore,
the regenerator heat capacity of wall materials becomesvery small at a
temperature level below 10K. For this reason, it then becomesnecessary to
balance the heat capacity ratio of the regenerator material and working
gas.
Figure 1 shows the volumetric specific heat of helium gas below 15K,
as comparedto those of lead and G-10, explaining this fact very well.
This also indicates that the high operating pressure maynot be applicable
due to the imbalance of the heat capacity ratio when lead or G-10 is used
as a regenerator material.
To change the view point, high pressure helium gas seemsto be a good
regenerator material below 10K, if the thermal diffusion coefficient is
maintained at a level high enough to create a reasonable operating cycle
speed. This is because the low thermal diffusion coefficient would
necessitate the cycle speed to be lowered to an unacceptable value for the
regenerative cycle. Performance as a regenerator material when the
operating speed is constant can be explained as follows:
Considering the sinusoidal temperature fluctuation on the surface of
semi-infinite solid, the quantity of heat accumulated by the regenerative
material during the half cycle is expressed as (4)
Q=AT.A/XC p2
/ p _0 '
where AT is the amplitude of temperature oscillation on the surface of
the solid, A is the surface area, t0 is the period of oscillation,
is the thermal conductivity, Cp is the specific heat and p is the
density. Therefore, the value of _pp represents the effectiveness of
the material as a regenerator.
Fig. 2 shows this effectiveness of the helium gas compared to that of
G-10, and it shows the pressurized helium gas ranging between 0.4-1.0 MPa
becomes a regenerative material superior to G-IO in the temperature range
below 8K.
EXPERIMENTAL APPARATUS
Fig. 3 shows the schematics of our experimental apparatus. The
purpose of this study is related to the effectiveness of the regenerator
operating below 10K. Therefore, we used two stage Gifford-McMahon cycle
refrigerator as a precooler for the test section, which gives the warm heat
station of 50K and cold heat station of 10K. With this arrangement, gap
158
regenerator/expander system as a test section can be madewith a pair of
single cylinder and displacer. This precooler was also constructed in our
laboratory, which has a pneumatically controlled displacer, electronically
controlled valves, copper mesh regenerator for warm stage and lead-shot
regenerator for cold stage.
Details of the test section are shownon Fig. 4. Cylinder of the test
section is madeof stainless steel having an outer diameter of 13 mmand a
thickness of 0.5 mm. Displacer is madeof cotton-cloth reinforced phenolic
resin, which has a diameter of 11.9 mmand a total length of 65 cm.
Betweenthe cold heat station and the cold end of the test section, the
cylinder is covered with another stainless steel tube which has an outer
diameter of 15 mm,a thickness of 0.4 mm,and a length of 24.5 cm.
Helium gas as a regenerator material is introduced from the capillary
tube to this annular space where the carbon fiber was packed for the
purpose of preventing convection. In this experiment, a small amount of
lead-shots were also used as a regenerative material around 10K. Lead-
shots of 0.3 mmdiameter immersedin the epoxy resin were coated on the
surface of the lower part of the displacer with its diameter rearranged to
11.9 mmby lathe.
A stepping motor was used to drive the displacer. The timing of the
intake and exhaust valves were controlled by meansof a computer using an
input signal of the diaplacer position. Pressure changewas measuredby
the strain guagebonded on the cold end cap.
RESULTS AND DISCUSSIONS
Fig. 5 shows the P-V diagrams obtained at the cold end volume with the
displacer stroke of 8 mm and intake and exhaust pressure of 0.6 and 0.12
MPa, respectively. The reason of decreased pressure ratio of (b)-(e)
compared to (a) is explained as follows:
This test section basically forms a G-M cycle which has a maximum
refrigeration work per one cycle when it has a rectangular P-V diagram.
This condition will result if the intake valve is opened when the expansion
volume is at its minimum, and exhaust valve is opened when the expansion
volume is at its maximum. However this condition increases the regenerator
load due to the effect of the incomplete expansion of the excessive intaked
mass of the helium gas. In the example of Fig. 5 to reduce this effect,
early cut-off of the intake valve was executed.
When the expansion volume is maintained at room temperature, P-V
diagram shows a rectangular shape, even when the early cut-off has been
excuted. However, if the temperature of the expansion volume decreases,
area of P-V diagram decreases due to the condensation of the gas at the
expansion volume. The turning corner at upper right position on the P-V
diagram is a point at which the exhaust valve is opened.
159
Mass velocity of the helium gas passing through the gap regenerator
can be controlled by changing the valve timing with the appropriate
displacer position. The difference between (c) and (d) is caused by this
timing change.
Fig. 6 shows the minimum temperature, Tmi n, obtained at the cold end
of the test section with an operating pressure of 0.6MPa-0.12MPa and
constant temperature of the cold heat station at 10K. Fig. 6 (a) shows the
effect of helium gas pressure inside of the annulas, Preg , with a fixed
cycle speed at 17rpm. This result indicates that the hellum gas in the
annulus acts as a regenerative material. The cold end temperature below 6K
did not obtained without helium gas in this annulus space. Fig. 6 (b)
shows the effect of cycle speed with a fixed Preg •
As expected, optimum cycle speed is very low and we obtained minimum
cold end temperature of 4.8K at 12rpm. Below this speed, cold end
temperature increases again. The expander work calculated from the P-V
diagram of Fig. 5 (e) is about 22mwatts. At this condition, a heat input
of 8mwatts was added to the cold end. Cold end minimum temperature
increased to 5.8K and expander work also increased to 24mwatts , therefore,
thermal efficiency of the test section will be about 35% and main losses
will be caused by shuttle loss, insufficient heat transfer area, and excess
enthalpy flow into the expansion volume due to the non-ideality of helium
gas.
CONCLUSION
While our data were not complete enough, our experimental results
indicate that in the gap regenerator/expander system it is very effective
to use pressurized helium gas as a regenerator material at a temperature
level below 10K. We found a refrigeration temperature below 5K can be
obtained under this method with the precooling temperature of 10K.
Although, under the regenerator design as shown in Fig. 4, optimum cycle
speed was as low as around 12 rpm, the highest possible cycle speed is
desirable as regenerative cycle, as far as the pressure loss permits. We
thus propose as follows:
The highest possible cycle speed should be obtained through the
regenerator fabricated by putting the pressurized helium gas into fin- or
wool-state of materials ( such as copper, lead or other pure metal ) which
are high in its thermal conductivity, while low in its specific heat, in
the temperature range below 1OK. In our experiments, in order to know the
optimum P-V diagram we employed such G-M cycle which can change the valve
timing and we also used a different type refrigerator in the precooling
system to avoid the effect on the upper stage to be caused by change in
temperature.
Our experimental results suggest that we would be able to obtain the
helium temperature from the room temperature by employing this system at
the final stage of multistage Stirling cycle, without using the different
160
type precooling system.
Wewish to thank S.Uosaki and T.Munekata for technical assistance.
REFERENCES
i. J.E.Zimmerman and D.B.Sullivan,"A Study of Design Principles for Power
Cryoelectronic Devices", NBS Technical Note 1049 (1982)
2. R.Radebaugh,"Prospects for Small Cryocoolers", Proceeings of the 9th
Int'l Cryog. Eng. Conf.,P.761,(1982).
3. D.E.Daney,"cooling Capacity of Stirling Cryocoolers the split cycle and
nonideal gas effects", Cryogenics 22, 531 (1982)
4. S.Kutateladze,"Fundamentals of Heat Transfer", p.134, Academic Press.
(1963)
DISCUSSION
Question by C. Winter, Simon Fraser University: Please descrive the
mounting of the strain gage pressure transducer on the cold end cap. What
was its sensitivity to pressure changes?
Answer by author: A foil strain gage is glued on the membrance of the
cold end cap. Effective diameter and the thickness o_ the membrance is 8mm
and 0.5mm respectively. This gauge ( as shown in Fig. 7) consists of four
different gauges which give signals proportional to a radial and a
tangential strain of the membrance. Calibrated sensitivity of this
pressure transducer was (3.48±0.02)KPa/Volt below IMPa, using strain
amplifier with the voltage gain of 350.
161
1"21
0
0
G-IO
4 6 8 i0 12 14
Figure i.
T (K)
Volumetric heat capacity of helium, lead and G-IO.
162
0.006
0
0.004
O.
-<
12 M_a
0 ' I I I I 1 l
0 2 4 6 8 lO 12
Fig.2
T(K)
Performance of helium gas as a regenerative material.
163
G-M CYCLE
I_FRI _I_.TOR
He gas
SUPPLY
DISPLACER
DRIVE MOTOR
I ....... --
/ GAP _GENERATOR/
EXPANDER
50K
BRAIDED COPPER
WIRES
SCHIELD
10K
•2-4.8K
Figure 3. Schematic of experimental arrangement.
164
INTAKE
VALVE
EXHAUST
VALVE
DISPLACE R
WARM
HEAT
STATION
THE RMOCOUPLE
TYPE-E
COLD
HEAT
STATION
CARBCN-GLASS
THERMOMETER
TUBE
FOR HELIUM GAS
SUPPLY
CARBGNFIBER
GERMANIUM THEATER
THERMO_TER PRESSURE
TRANSDUCER
Figure 4. Gap regenerator/expander with pressurized
helium gas annulus.
165
PPh
Ph=0.6 MPa
PI=0.12 MPa
Vmax=0.9 cm 3
N=I7 rpm (a-c)
=12 rpm (d-e)
P1
) V
0 Vmax
(a) T=290 K
(b) T=-7.0 K (d) T=6.1 K
(c) T=6.3 K
Figure 5.
(e) T=5.0 K
P-V diagrams of the expander.
166
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167
Figure 7. Strain gaugepressure transducer.
168


An application of gap regenerator/expander precooled by two stage G-M refrigerator

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