- Email: [email protected]
Cryogenic refrigeration using a low temperature heat source
A non mechanical gas sorption refrigeration system which could be powered by a low temperature heat source was designed and analysed. The system involved no sealing, no mechanical moving parts and no active control The system was analysed using a 1 W cooling load at 74 K as an example. It was found that the new system was competitive with a passive radiator and superior to a solid cryogen system.
Cryogenic refrigeration using a low temperature heat source C. K. Chan
Nomenclature
p
density
A
area
A
difference
C
concentration
Subscript
Cp h
heat capacity enthalpy
1, 2, 3, thermodynamical states illustrated in Fig. 1 4, 5 or zeolite states illustrated in Fig. l
m
mass
c
cold
m
mass flow rate
h
hot
P
pressure
H
high
Q
heat transfer rate
L
low
t
time
s
container
T
temperature
st
isoteric
Au
heat of desorption or adsorption
z
zeolite
X
mass ratio
Superscript
o
stress, Stefan Boltzman constant
*
source
The demand for higher resolution and sensitivity of various detectors used in space missions has aroused interest in developing more sophisticated cooling systems for the detectors. 1 The cooling capacity requirement of these detectors varies from 1 mW to 10 W, while the temperature requirement varies from 1 K to 230 K. Because of the unique environment of space vehicles, the cooling system has to be designed taking into consideration: weight, size, input power, packaging restrictions, operating life, maintenance intervals, life cycle and temperature environment. A deep space vehicle usually has an ample supply of waste heat from a radioisotope thermal electric generator (RTG) and has near zero degree Kelvin heat sink. In the past, passive radiator coolers have been used extensively for cooling temperatures above 90 K. 2 As the cooling temperature gets lower, the weight of the radiator becomes a problem. Other avenues of cooling have to be explored.
eratures below 90 K. However, the weight of the cryogen may be a problem in a long duration space mission. The reliability and maintenance interval or mechanical refrigeration in long-term, unmanned missions is a concern to many space vehicle designers. The use of magnetic refrigeration for low temperature instrument cooling has been considered but substantial development work is still required, s In space missions, besides the basic requirements of temperatures and heat load, the size and the weight of the cooling device should be acceptable to space vehicle designers. Its operating life and reliability should be acceptable to space vehicle designers. Its operating life and reliability should meet the mission duration of one to nine years. The power supply to operate such a device will preferably come from the sun or the waste heat of an RTG. A good candidate to meet these stringent requirements is a non-mechanical gas compressor together with an appropriate refrigeration cycle.6
Cooling involving phase changes of solid or liquid cryogen3 or mechanical refrigeration4 can be used for cooling temp-
It is known that non-mechanical gas compression can be accomplished by using a thermally cycled adsorber such as zeolite, charcoal or silica gel, to adsorb and desorb various gases. 7 The two features which make the non-mechanical gas compressor attractive are the absence of moving parts, and its ability to utilize heat, rather than electric power,
The author is a member of Technical Staff, Apphed Mechanics Technology, Jet Propulsion Laboratory, California Institute of Technology, Pasadena, CA 91103, USA. Paper received 30 December 1980.
0011-2275/81/007391-09 $02.00 © 1981 IPC B.siness Press Ltd CRYOGENICS. JULY 1981
391
as the energy input. It is anticipated that such a concept could be extended for earth application where low quality heat such as solar or industrial waste heat could be used. This paper involves material investigations of various adsorbents with various gases, and performance evaluations of a novel refrigeration system design. The material investigations stressed a review of adsorbing materials and their adsorption characteristics which would be suitable for the non-mechanical gas compressor, By adsorbing and ejecting heat, a compression and decompression cycle in the adsorbent chamber without the use of moving pistons, displacers or motors could be generated. A conceptional design using a Joule-Thompson (J-T) valve for cooling, check valves for gas control, and louvre for heat control was examined. An analytical technique was developed to evaluate gas flow requirements and other refrigeration system performance. The methodology was illustrated with a numerical example of a cooling load of 1 W at 74 K. The compressor design involved the determination of adsorbent mass, temperature variation, container volume and power requirements. The objective of these analyses was to determine the feasibility of using gas adsorption compressors for cryogenic cooling.
Physical adsorption The gas adsorption compressor depends on the adsorption characteristics of the gas by the adsorbents at different temperatures. When the gas is brought into contact with the adsorbent, some of the molecules striking the solid surface will be retained for a finite period of time, resulting in a significantly higher molecular concentration at the surface than in the gas phase. The forces holding the molecules to the solid are due to molecular interactions. This process is known as physical adorption and has been studied, both at ambient and cryogenic temperatures. A comprehensive review of the subject at cryogenic temperatures has been carried out by Kidnay and Hiza. 7 The adsorptivity of the gas by the adsorbent is usually expressed in the form of isotherms as exemplified by the nitrogen-zeolite system shown in Fig. 1. These isotherms are extracted from the experimental data of Harper8 and Woltman. 9 It is observed, that the amount of gas being adsorbed increases as temp10
01
:~
_
~
0.01
0
u
~ ooo1!/
i
Q1
J
i I 10
I
i
,
, I 10
I
I
i
L I 100
Pressure, Qtm Fig. 1 Isotherms of nitrogen with zeolite and compression and suction cycle
392
erature decreases and as pressure increases. The isotherms are usually obtained by two different methods: volumetric and gravimetric. Flapper and Gijsman ~° used a gravimetric method to measure adsorption of nitrogen on the zeolites 13X, 5A and 3A at 77 K, and of helium on 13X and 5A at 20 K. Daunt and Rosen H used a volumetric method to measure adsorption of He, N2 and Ar on zeolites at 78 K and of 3 He and 4He on zeolite in the temperature range 4 K to 20 K, as well as their isoteric heats of adsorption. A survey was made of the experimental data for adsorption of various cryogenic gases by such adsorbents as charcoal, zeolite and silica gel. Table 1 lists the cryogenic gases in the ascending order of their triple points. It is observed that in most instances, experimental values for the adsorption isotherms are available in the low pressure range. This is due to the fact that the main application of gas adsorption has been related to low-pressure gas removal processes. More data on isotherms at higher pressures are needed for a workable compressor. Another parameter that is important in the design of the compressor is the heat of adsorption, ie the heat that has to be removed from the gas upon the adsorption of a unit mass or mole of the gas. When the adsorbent surface is free of gas molecules, the heat of adsorption is termed the isoteric heat of adsorption, Qst. At a coverage of one monolayer, the heat of adsorption decreases in value. This value decreases further with more layers of gas molecules. The heat of adsorption for several systems are tabulated in Table 2.
Gas adsorption refrigeration design A bed of adsorbent can be used as a compressor and a suction pump based on the following principles as explained with the aid of Fig. 1. The high-pressure portions of the isotherms in Fig. 1 are obtained by extrapolation from the low pressure experimental data. Consider a bed of zeolite where heat can be added or removed and where gas can enter or leave the bed at two regulated pressure levels. Starting from state point 1 in Fig. 1, where the zeolite is at temperature T~, pressure P~, and concentration of nitrogen C~, further removal of heat coupled with gas flow from the outside at constant pressure would cause the temperature to drop but the concentration to rise. The state point 2 represents the equilibrium state point when the heat removal process is stopped. When the zeolite bed is heated with no outflow of the nitrogen gas (process 2-3), both the temperature and the pressure would increase with little change of concentration. At state point 3, when the gas pressure is high enough for its escape, the concentration drops with further increase of temperature and release of gas at constant pressure. At state point 4, when the heat flow reverses direction, but no gas is permitted to flow into or out of the bed, both the pressure and the temperature will decrease. Hence the bed acts as a compressor in processes 2-3 and 3-4 while it acts as a suction pump in processes 1-2 and 4-1. Taking advantage of high-pressure compression during desorption and low-pressure suction during adsorption of an adsorption bed, a cryogenic refrigeration system could be designed. Two ways to achieve refrigeration were considered: 2~ one, by causing the working gas to do external work; or two, by making use of the JouleThompson (J-T) effect, or internal work of expansion.
CRYOGENICS. JULY 1981
Table 1.
Adsorption data of cryogenic gases by common adsorbents
Gas
Triple point
Critical point
Inversion temperature
Helium He
2.17 K 0.05 a t m
5.19 K 2.26 atm
40 K
A d s o r p t i o n data
Zeolite
: 4 . 2 - 20 K; 0.01 - 2 a t m 11 76K;1-9atm 12 20 K; 10 -5 - 1 a t m 1° 1 7 3 - 2 7 3 K ; 0 . 1 - 1 a t m 11
Hydrogen H2
Neon Ne
13.89 K 0.071 a t m
19.01 K 0.426 arm
33.24 K 12.8 a t m
44.4 K 26.84 atm
202 K
250 K
Fluorine FI
53.54 K 0.0022 atm
119.17 K 55 a t m
600 K
Nitrogen N2
63.33 K 0.1237 atm
126.2 K 33.54 atm
622 K
Carbon monoxide CO
66.11 K 0.1 a t m
Argon Ar
83.78 K 0.68 atm
132.91 K 34.53 atm
150.72 K 48 atm
660 K
722 K
Carbon
: 76 K; 1 - 9 a t m 12
Silica Gel
: None
Zeolite
: 2 0 . 4 K; 10 -7 - 0.1 a t m 13 76 K; 1 - 95 a t m 12 77 K; 10 -5 - 1 a t m 1°
Carbon
: 76 K; 1 - 9 5 a t m 12
Silica Gel
: None
Zeolite
: 2 0 . 4 K; 10 -7 - 0.1 a t m 13
Carbon
: None
Silica Gel
: None None
Zeolite
: 1 9 5 - - 3 0 3 K; 0.1 - 1 a t m 8 77 K; 10 - 7 - 1 a t m 1° 80 - 3 5 0 K; 1 a t m 2° 173 - 2 7 3 K ; 0 . 1 - 1 a t m 9
Carbon
: 8 9 - 172 K; 2.5 x 10 -3 - 0 . 8 2 a t m 14
Silica Gel
: 4 7 3 - 7 5 3 K; 10 -9 - 10 -6 a t m 15
Zeolite
: 193-323K;0.1-
Carbon
: None
Zeolite
:77-323K;0.1 -latm 78 K; 10 - 3 - 1 a t m 11
latm 8
8
173 - 2 1 8 K; 0.1 - 1 a t m 9
Methane CH 4
Ammonia NH 3
Sulphur dioxide SO2
Carbon dioxide CO2
CRYOGENICS.
88,7 K 0.1 a t m
195.56 K 0.06 atm
197.68 K 0.00165 atm
216 K 5.11 a t m
J U L Y 1981
190.7 K 45.8 atm
406 K 111.5 a t m
430.7 K 77.8 atm
304.2 K 72.9 a t m
1000 K
2000 K
2150 K
1500 K
Carbon
: None
Silica Gel
: None
Zeolite
:95-320K;0.1-1atm
Carbon
: 89 - 172 K; 10 - 3 - 0 . 1 4 a t m
Silica Gel
: None
Zeolite
: 273-
Carbon
: None
Silica Gel
: None
Zeolite
: None
Carbon
: None
Silica Gel
: None
Zeolite Carbon
: 1 5 5 - 3 2 0 K; 0.01 - 1 a t m 8 2 0 0 - 6 0 0 K; 1 a t m 2° : None
Silica Gel
: None
8 TM
563 K;0.01 - 1 atm 9
393
A possible system design using the J-T effect is shown in Fig. 2a and the thermodynamic path of the process is shown in Fig. 2b. Upon heat addition to the adsorbent bed in chamber A, the temperature increases and the amount of gas being adsorbed decreases. The liberation of gas from the adsorbent causes the gas pressure inside the chamber to rise. At one point the pressure is high enough to push open the check valves 1 and 4 and close valves 2 and 3. At the same time, the removal of heat from chamber B will cause the temperature to drop and more gas can be adsorbed. The compression action of chamber A and the suction action of chamber B cause the flow of the high-pressure gas through the pre-cooler and the counterflow heat exchanger where it is cooled to a lower temperature before it expands through a J-T valve. Upon expansion, the gas enters the refrigeration chamber in the form of a two-phase mist. The refrigeration load causes the vaporization of the liquid. Hence, the outlet of the refrigeration chamber is at state point 4 (Fig. 2b). Upon passage through the counteflow heat exchanger, the gas is heated, thereby cooling the incoming gas. For a perfect heat exchanger, the outlet temperature of the gas at state point 5 is the same as the inlet temperature (state point 1). The low pressure in the refrigeration chamber is maintained by the suction process in chamber B where gas is being adsorbed.
Heat add
Heat rem ova I Chamber A
Check | valve 1-I ' 1
JCheck
I _l valve 2 #t~ll~ Check I I valve 3 I._1 _~"
1 I
t
I
.
J'"
Chamber B
Precooler
.-
Heat removal
.(~)l m
4
'I'
.
I
I Heat iadd
flow heat exchanger
J - T valve
_
®1
• ~'/
@
®
Refrigeration chamber
When the gas inventory in chamber A has been depleted, the heat flow of both chambers reverses direction. Chamber B functions as the role of the compressor while chamber A functions as the suction pump.
I efrigerat ion load
Refrigeration cycles analyses From the total energy balance, the refrigeration load Q is related to the mass flow as: Q = m(hs--hi)
(1)
where m is the mass flow rate through the J-T valve, hs is the enthalpy of the outlet at the low-pressure side of the counterflow heat exchanger, and hi is the enthalpy of the inlet gas after the precooler. For a given refrigeration temperature, 7"3 is fixed and this determined the low-pressure isobar P3, P4 and Ps in Fig. 2b. For example, if the refrigeration temperature is 74.22 K, the saturation pressure of nitrogen at that temperature is 10 psi (0.68 arm). Hence, the low pressure isobar is 10 psi. From a designer's point of view there are two adjustable parameters; one, the gas temperature, T1 after the precooler, and two, the pressure P1 upstream of the J-T valve. Fig. 3 shows the effect of precooling temperature and pressure ratio (Px [P2)on the mass flow per unit watt of refrigeration load for the case of the refrigeration temperature being 74 K and P3 = 10 psia (0.68 atm). The mass flow requirement is strongly affected by the pressure ratio and the precooler temperature. As the pressure ratio increases, the mass flow decreases. As TI decreases for a given pressure ratio, the mass flow also decreases. The mass flow rate corresponds directly to the zeolite mass in the compressor. In calculating the mass flow as shown in Fig. 3, the heat exchanger is assumed to be perfect, ie, Ts = T~. A perfect heat exchanger requires infinite heat transfer area; from a practical point of view, no heat exchanger is perfect. The effect of counterflow heat exchanger efficiency on the mass flow required for the pressure ratio ofP~/P3 = 10 is shown in Fig. 4. For a given precooler temperature there
394
J /
.J ®\
Fig. 2 a -- Gas adsorption refrigeration designwith J-T valve; b - T-S diagram for the heat exchangerand J-T valve process is an upper limit for the inefficiency of the heat exchanger. There is a minimum value of Ts beyond which the principle of J-T refrigeration breaks down. For example, at T1 = 278 K, the maximum value of the temperature difference (T1 -- Ts) beyond which the J-T principle does not work is 2 K or the minimum value of T5 is 276 K. As the precooling temperature is decreased, the temperature difference is increased, ie, there is more tolerance for the inefficiency of the heat exchanger. A practical value of the temperature difference is about 5 K. Then, the precooling temperature has to be in the neighbourhood of 111 K in order to keep the mass flow at a reasonable level.
C R Y O G E N I C S . J U L Y 1981
Table 2. systems
C =/1 (T, P) exp(aT) that fits the isotherms data of Fig. 1 is found to be
Heat of adsorption for several gas/adsorbent
C = 22.59/°1°"1674 exp(°~0548T) l exp(--0.03638T) Ost
E2
Ost
Monolayer,
Two
j mole-1
j mole-1
j mole-1
4 H e + Z e o l i t e 11
1580
1030
480
3 He + Zeolite 11
1420
-
-
4He
+ C h a r c o a l 16
1750
-
-
G r a p h i t e 17
1700
-
-
A r + C a r b o n 18,19
11 0 1 6
-
-
N 2 + Carbon 18,19
11 9 0 0
-
-
N 2 + Z e o l i t e 19
20 082
-
-
3He+
(3)
layer,
for 173 K < T < 273 K and 1 < P < 200 cm Hg It should be cautioned that (3) was derived from lowpressure data. Because of the unavailability of the highpressure data, the extrapolation of (3) for high-pressure application in the present analysis should be viewed as a first order approximation. The term (OC/~T)p represents the concentration variation with temperature at constant pressure. Basically, it is a function of the adsorbent temperature T and the compressor pressure P.
The precooling temperature and the temperature difference (T~ -- Ts) define the inlet temperature of the hot stream and the outlet temperature of the cold stream of the counterflow heat exchanger. A heat exchanger analysis was performed for the case of TI = 111 K and Ts = 106 K. In this case, the mass flow for 1 W cooling is 0.272 g s-~ (6 × 10-4 lb s-1 ) (see Fig. 4). The temperatures 7"2 and T4 correspond to the saturation temperatures of the high and low pressures respectively. For the case ofP~ = 6.8 atm (100 psia) andP4 = 0.68 atm (10 psia), T~ = 98 K and /'4 = 74 K. With these specifications, the length requirement of a 0.3175 cm (1/8 in) single tube with wall thickness of 0.10 cm (0.04 in) in the counterflow heat exchanger is 118 cm (3.87 ft). The weight of two of these aluminium tubes is 63.5 g (0.14 lb).
Equation (2) shows that the mass of the zeolite is proportional to the mass flow rn, inversely proportional to (aC/~T)p and inversely proportional to the rate of temperature rise dT/dt. The temperature rise rate in the zeolite is governed by the heat transfer mechanism into or out of the adsorbent material. It is difficult to estimate the temp-
1°2f
Gas a d s o r p t i o n c o m p r e s s o r design
All refrigeration processes which inctude isentropic, isenthalpic and free expansions, involve depressurization of highly pressurized gas. Hence, in the refrigeration cycle, a compressor is needed to provide the required gas flow at the desired pressure and temperature. It has been shown in previous sections how one can specify mass flow and pressures of the gas from the compressors based on the refrigeration requirement. It will be shown in tb_is section how one can specify the parameters for the gas adsorption compressor such as the zeolite mass, the container mass, the energy required to power the compression, the surface areas for adsorbing and rejecting heat and the temperature swing of the zeolite for the compression and decompression cycle.
"T cO th 10- 3 m
X
Zeolite mas~ When the adsorbent is heated at constant pressure (Process 3-4 in Fig. 1), the mass flow required for refrigeration comes from the liberation of the adsorbed gas. The mass flow rate m is related to the temperature rise rate (dT/dt) as 11b = 4 5 3 6 g
mz
~
p at
(2)
where C is the concentration which is the ratio of gas being adsorbed over the adsorbent mass. For zeolite-nitrogen combination, the relation between C and pressure P and temperature T are expressed in the form of the isotherms, shown in Fig. 1. An analytical expression of the form
CRYOGENICS.
JULY
1981
10 -4
I 15
I 2
I 2.5
I 3
I 4
I 5
I 6
I 7
P2/P3
I 8
I 9 10
Fig. 3 Effect of pressure ratio on mass f l o w rate for v a r i o u s p r e c o o l i n g t e m p e r a t u r e s f o r 1 W of refrigeration
395
T a b l e 3.
V a l u e s o f A C and ( A T ) m a x f o r various values o f
P H , (AT)swing and T 2
T2 = 1 7 3 K PH = (AT)swing
(AC)
1.36 atm
6.8 atm
13.6 atm
(AT)ma x
(AT)ca x
(AT)max
20
0.028
30.64
52.36
85.28
40
0.0582
48.95
93.26
114.35
60
0.0823
77.39
120.37
-
80
0.0947
96.5
-
-
100
0.1055
123.19
-
-
The mechanism to dissipate the heat from the compressor to outer space during the depressurization phase is also by thermal radiation. A louvre system that can accommodate the cyclic heat in and heat out of the compressor is shown in Fig. 5. During the compression phase, the louvres facing the heat source are open, but the louvres facing the heat sink are closed, so heat is transferred to the compressor. During the depressurization phase, the louvres facing the heat source are closed but the louvres facing the heat sink are open, so heat is transferred out of the compressor. In determining the heat required to produce unit mass flow, it is assumed that all the heat adsorbed by the compressor surface is instantly transferred to the zeolite. This heat causes the temperature rise of the zeolite and the container as well as the liberation of the nitrogen gas. Hence, neglecting the heating up of the gas
T2=195 K
Qh = mzCpz dT
PH =
1.36 atm
6.8 atm
13.6 atm
(AC)
(AT)max
(AT)ma x
(AT)max
20
0.0313
230
269.88
94.52
40
0.0545
253.75
295.79
-
60
0.0658
271.18
-
-
80
0.076
297.44
-
-
0.0806
-
-
-
,,u
+ msCps \ d t ]
Qh/Tn = ((()~--) p AU+ Cpz-I-XCps)/(~T)p (AT)swing
100
(6)
The heat Qn required is computed for different compressor pressures and temperatures, and the results are shown in Fig. 6. It is seen that compressor pressure has a minor effect on the heat required but temperature plays an important role.
erature rise rate without a detailed compressor design and heat transfer analysis of the zeolite medium. Hence, for the present analysis, dT/dt is assumed to be of a certain value for the estimation of the zeolite mass. Conversely, for a specified value of zeolite mass, (2) could be used to specify the value of dT/dt which would serve an objective goal in designing the heat transfer enhancement mechanism inside the compressor. Following the example where m = 6 x 10 -4 lb s-1 (0.272 g s-t ), compressor pressure = 6.8 atm and temperature = 250 K, then (aC/aT)p = 3.5 x 10 -3 K -1 , and if dT/dt = 0.03 K s -t , then the mass of zeolite required, mz = 5.7 lb (2.6 kg).
If the heat is obtained by radiation from a heat source of T* and if the compressor temperature is Th, if the heat transfer area An is black and the exchange view factor is unity, then Ah is related to Qh by
1 I
10 -1
I
2 II
3 I
( T1 - T5 ) K 4 5 t I I
6 t
7 I
8 I
Container mass. In estimating the container mass, a cylindrical container completely filled with zeolite is assumed. By relating the Hooke stress o of the cylindrical wall resulting from internal pressurization P, the mass ratio of the cylindrical container to the zeolite can be expressed
as
X
=
ms - 2PsP mz pzO
"T ¢-,
-E"
(4) 10-~
If the material is stainless steel the density Ps = 7.86 g cm -3 and the maximum stress = 9000 psi, for P = 100 psi then ms/mz ---0.16, ie the mass of the container is roughly 20% of the mass of the zeolite. 11b = 4 5 3 . 6 g
Power required. In determining the power required by the compressor, it is anticipated that the compressor is used in a spacecraft where adequate waste heat is available from the spacecraft electrical power generator. The mechanism to transfer this waste heat from the RTG to the compressor during the compression phase is by means of thermal radiation.
396
10"
0
Fig. 4
different
1
2
3 4 5 6 7 8 9 10 11 12 Tempereture difference ( T~ - T5) °R
13 14 15
E f f e c t o f heat exchanger efficiency on mass f l o w rate precooling t e m p e r a t u r e ; P1/P3 = 10
for
CRYOGENICS. JULY 1981
sorptivity of zeolite increases with increasing (A T)swing but also with decreasing T2. It appears that 7"2 should be as low as possible from the mass flow point of view. However, from heat transfer area considerations, T2 should be high.
Heat source
I
Compressor
I
Heet transfer area A c Closed louvers
Heat sink Fig. 5
Qh
(AT)max. Cycle time. The cycle time At for the zeolite to adsorb
Louvre system for gas adsorption compressor
=
AhO( T*4 -- ~h)
The parameter that characterizes the power required for the entire cycle is the maximum temperature difference (AT)max = (T4 - T2). The values of (AT)ma x as functions of (A T)swing for various temperatures 7"2 and pressures PH are shown in Table 3. For the same (A T)swing higher pressures PH and temperatures T2 would yield a higher
(7)
the gas is approximated by
mz
At = ~ - AC A h _ m
+Cpz +XCps] [o(T.4 -- T4)]
[(aC/OT)p A u (i)C/aT)p
(8)
The A t calculated by (10) represents approximately 1/4 of the total cycle time.
It is found that the area is quite independent of pressure but is strongly affected by zeolite temperature. As temperature is reduced, the irradiation heat is reduced, hence more of the heat can go to the zeolite. This temperature Th changes as the zeolite is heated from state point 2 to state point 4 in Fig. 1. For simplicity, Th being equal to T4 is used for area calculation. This would give a conservative (largest) estimate OfAh.
Design procedures For a given refrigeration load and temperature, one fflust first decide on the refrigeration system and the gas-adsorbent combination in the compressor. The choice of the gas depends on the refrigeration system. For example, for the J-T process, the gas should have a critical point above the refrigeration temperature but a triple point below that temperature of that gas. The critical point, the triple point and the inversion temperature for various gases are listed in Table 1.
A similar procedure can be applied to calculate the heat that has to be taken out of the compressor to adsorb a unit mass of nitrogen during the process 1-2. Equation (6) and Fig. 6 can be used to calculate the heat loss rate Qc To calculate the heat transfer area for dissipating heat, the compressor is assumed to radiate directly to a 0 K environment. Hence, Ac
7n -
[(aC/aT)p Au + Cpz + XCp~]
(~ C/O T)r o T~
(9)
The value of Ac/m is plotted in Fig. 7 for various zeolite temperatures at a pressure of 51 cm Hg. The value of Ah/m for high pressure of 517 cm Hg is shown in the same figure for comparison. It is observed that the heat transfer area for heat rejection reaches a minimum temperature of around 250 K, and the area required for heat rejection is one order of magnitude greater than that for heat adsorption.
Temperature cycle. After obtaining the basic design parameters of the compressor, the next step is the determination of the operation parameters, ie, the state points 1, 2, 3 and 4 in Fig. 1. As previously stated, the lower pressure is fixed by the refrigeration temperature. For a refrigeration temperature of 74 K in the J-T system, the lower pressure is 0.68 atm. Referring to Fig. 1, this pressure defines the left vertical line of the rectangular cycle. As shown in Fig. 3, the higher pressure, the less mass flow is needed. However, as the pressure increases so does T4 resulting in a greater heat transfer area. For a given/'2 (see Fig. 1), (AT)swing = T1 -- 7"2 represents the temperature difference through which the zeolite must swing in order to absorb an amount of nitrogen gas, AC, from the refrigeration system. By symmetry, this will be the amount of gas evolved during heating in the process 3-4. From the calculation, it was observed that the ad-
CRYOGENICS. JULY 1981
(10)
Dl
To illustrate the procedures, take a refrigeration load (Q) of 1 W and a refrigeration temperature (T) of 74 K. From Table 1, nitrogen appears to be the appropriate gas for a J-T system. The pressure in the refrigeration chamber corresponds to the saturation pressure of nitrogen at 74 K. In this case, the low pressure PL is 0.68 atm and the choice of the high pressure upstream of the J-T valve needs some optimization consideration. At present, ifPH is equal to ten times PL (6.8 atm), with a perfect heat exchanger and precooling temperature of 111 K (200 R), the mass flow required is 0.1 g s -1 (2.2 x 10 -4 lb s-l). Suppose the heat exchanger has an effectiveness of 0.65 (T1 -- Ts = 5.6 K). Then, the mass flow required is 0.27 g s -I (6 x 10 -4 lb s -1 ). Based on the 0.27 g s -1 flow rate, the 6.8 atm high pressure, 10 4
T: 275 K
~
I
10 2
I 10
I
I
I I Ltll
I
I
i
i ~ itl[
10 2
i
i
i
i i ii
10 3
10 4
Pressure, cm Hg Fig. 6 Effect of compressor temperature and pressure on heat required
397
Table 4. Weight estimation of the gas adsorption refigeration system for I W cooling
106
Power receiver panel 1 ft 2 at 10 Ib ft -2 10.0 Ib (4.55 kg) Heat rejection panel 47 f t 2 at 1 Ib ft -2 47.0 Ib (21.36 kg) Compressor (4 units) Zeolite = 5 . 7 1 b x 4 Container = 1.14 Ib x 4
22.8 Ib (10.36 kg) 4.6 Ib (2.09 kg)
Heat exchanger Total
5.0 Ib (2.27 kg) 89.4 Ib (40.63 kg)
Solid cryogen
Weight
= 2000 Ib (910 kg) for a period of one year for 1 W cooling
.; 105 £3
From (I0), the total cycle time for mz = 2.6 kg, m = 0.27 g s -1 and AC= 0.0582 is 37 min. In estimating the weight for the entire system, as shown in Table 4, it is assumed that four compressors each of which has a cycle behaviour are needed to provide a continuous refrigeration function. The weight of the heat exchanger and plumbing is estimated to be 5 lb. 21 Hence the total weight of the system is 89.4 lb (40.6 kg). This value is lower than that of the solid cryogen which is estimated to be 2000 lb (910 kg) for a period of one year and 1 W cooling. It is competitive with passive radiator at 74 K which requires 50 ft 2 (4.64 m 2) heat transfer area and weighs 65 lb (30 kg) for 1 W cooling, 22 in spite of its thermal inefficiency. The main reason is because in the gas adsorption cycle, heat is radiated at a much higher temperature level. Conclusions
The use of gas adsorption and desorption processes as a compressor to drive a cryogenic refrigeration system for long-term sensor cooling has been examined. Among varous designs, the J-T expansion process has high potential to meet the unmanned deep space vehicle environment. The J-T system requires no sealing, no mechanical moving parts and no active control system. However, it has the disadvantage of low efficiency and hence requires more gas flow from the compressor than other cycles such as the Gifford-McMahon cycle) l The present analysis represents a first step in the explora-
398
p~¢3'~c~~~7
% ,E \ b
Passive radiator for 1 W cooling at 75 K Weight = 65 Ib (30 kg) Heat transfer area = 50 ft 2 (4.64 m 2)
and the 0.68 atm low pressure, a nitrogen-zeolite compressor could then be designed. The two pressure levels define the two vertical isobars in Fig. 1. Choosing a minimum temperature/'2 of the compression cycle to be 172 K, for a (AT)swing = 40 K, then from Table 3 (AT)max = 93 K and AC = 0.0582. The maximum temperature/'4 in the cycle is 266 K, TI is 213 K and T3 is 207 K. The temperature differences T1 - / ' 2 , 7'3 - 7'2,/'4 - T3 and 7'4 - Tz are 40, 37, 56 and 53 K respectively. The heat addition rate at 266 K and 6.8 atm is 351 W (Fig. 6). The heat removal rate at 173 K and 0.68 arm is 216 W (Fig. 6). The heat transfer areas at those temperatures and pressures are 47 ft 2 (4.37 m 2) and 10 ft 2 (0.93 m 2) for heat rejection and adsorption respectively (Fig. 7).
•
104
10 3 170
l 175
l 200
l 225
I 250
TH or Tc K
I 275
I 300
I 325
Fig. 7 Effect of compressor t e m p e r a t u r e on heat transfer area of b o t h h o t and c o l d sides
tion of using direct heat to perform cryogenic refrigeration in an unmanned spacecraft. The methodology is intended to be simple. Because some of the calculations were based on extrapolation of the low-pressure isotherms, the numerical results should be used with extreme care. Nevertheless, these results provide an order of magnitude estimation of the gas adsorption refrigeration performance. The weight of a refrigeration system is an important aspect, but not the only aspect, in spacecraft design. The versatility of the system and the interaction of the system with the other spacecraft components should be considered in the merit evaluation of the design. From the present study, certain conclusions can be made: It is feasible from a thermodynamic point of view to design a gas adsorption refrigeration system to be powered by heat energy. The weight of such a system does not seem to be unmanageable in future spacecraft environment. By choosing the appropriate gas adsorbent combination, the system can be applied to other cryogenic temperatures rather than the 74 K exemplified in the present study. This leads to its application in temperature range where radiator or solid cryogen could not be used effectively. In addition, there is no restriction on the refrigeration load of the gas adsorption system. The system offers potentials of compactness and versatility to meet spacecraft and mission constraints. References
1 2
Sherman,A. Astronautics and Aeronautics 16 (Nov 1978) 39 Annable,R.V.Applied Optics 9 1 (1970) 185
CRYOGENICS . JULY 1981
3 4 5 6 7 8 9 10 11 12
Caren, R., Coston, R. Advances in CryogenicEngineering 13 (1976) 450 Kroebig, H.L. AFFDL-TR-78-760, (1978) Steyett, W.A.JApplPhys49(1978) 1227 Lehffeld, D., Boser, O. AFFDL-TR-74-21, AF Flight Dynamics Laboratory, Wright-Patterson AFB (1974) Kidnay, A.J., Hiza, M.J. Cryogenics 10, (1970) 271 Harper, F.J., Stifel, G.R., Anderson, R.B. Canadian J Chem 47 (1969) 466 Woltman, A.W. Ph.D. Thesis, University of Texas, (1978) Flapper, G.L.B.F., Gijsman, H.M. Cryogenics 14 (1974) 150 Daunt, J.G., Rosen, C.Z. Low TemperaturePhysics 3 (1970) 89 Kidnay, A.J., Hiza, M.J. Advances in CryogenicEngineering 12 (1966) 730
CRYOGENICS
. JULY
1981
13 14 15 16 17 18 19 20 21 22
Bewilogua, L., Binnebetg, A., Jackel, M, Cryogenics 15 (1975) 238 Kxatz, W.C. Paper presented at Cryogenic Engineering Conference, Madison, WI, (1979) Beher, J.T.Advances in CryogenicEng 2 (1957) 182 Itterbeek, A.V., Dingensen,W.V.,Physica 5 (1938) 529 Hellemans, R., Ittetbeek, A.V. Physica 34 (1967) 429 Ross, S.,Winkler, W.JColloidSci 10 (1955) 319 Lexner, E., Darun, J.G., JofLow TemperaturePhysics 10 (1973) 299 Haxtwig, W.H. Forty-Seventh Monthly Progress Report, December 1 - December 31, (1978) University of Texas at Austin Chart, C.K. JPL report 715-58 (1980) Haskin, W.L., Dexter, P.F. Paper 79-0179, 17th Aerospace Sciences Meeting, New Orleans, LA, (Jan 15-17, 1979)
399
Cryogenic refrigeration using a low temperature heat source C. K. Chan
Nomenclature
p
density
A
area
A
difference
C
concentration
Subscript
Cp h
heat capacity enthalpy
1, 2, 3, thermodynamical states illustrated in Fig. 1 4, 5 or zeolite states illustrated in Fig. l
m
mass
c
cold
m
mass flow rate
h
hot
P
pressure
H
high
Q
heat transfer rate
L
low
t
time
s
container
T
temperature
st
isoteric
Au
heat of desorption or adsorption
z
zeolite
X
mass ratio
Superscript
o
stress, Stefan Boltzman constant
*
source
The demand for higher resolution and sensitivity of various detectors used in space missions has aroused interest in developing more sophisticated cooling systems for the detectors. 1 The cooling capacity requirement of these detectors varies from 1 mW to 10 W, while the temperature requirement varies from 1 K to 230 K. Because of the unique environment of space vehicles, the cooling system has to be designed taking into consideration: weight, size, input power, packaging restrictions, operating life, maintenance intervals, life cycle and temperature environment. A deep space vehicle usually has an ample supply of waste heat from a radioisotope thermal electric generator (RTG) and has near zero degree Kelvin heat sink. In the past, passive radiator coolers have been used extensively for cooling temperatures above 90 K. 2 As the cooling temperature gets lower, the weight of the radiator becomes a problem. Other avenues of cooling have to be explored.
eratures below 90 K. However, the weight of the cryogen may be a problem in a long duration space mission. The reliability and maintenance interval or mechanical refrigeration in long-term, unmanned missions is a concern to many space vehicle designers. The use of magnetic refrigeration for low temperature instrument cooling has been considered but substantial development work is still required, s In space missions, besides the basic requirements of temperatures and heat load, the size and the weight of the cooling device should be acceptable to space vehicle designers. Its operating life and reliability should be acceptable to space vehicle designers. Its operating life and reliability should meet the mission duration of one to nine years. The power supply to operate such a device will preferably come from the sun or the waste heat of an RTG. A good candidate to meet these stringent requirements is a non-mechanical gas compressor together with an appropriate refrigeration cycle.6
Cooling involving phase changes of solid or liquid cryogen3 or mechanical refrigeration4 can be used for cooling temp-
It is known that non-mechanical gas compression can be accomplished by using a thermally cycled adsorber such as zeolite, charcoal or silica gel, to adsorb and desorb various gases. 7 The two features which make the non-mechanical gas compressor attractive are the absence of moving parts, and its ability to utilize heat, rather than electric power,
The author is a member of Technical Staff, Apphed Mechanics Technology, Jet Propulsion Laboratory, California Institute of Technology, Pasadena, CA 91103, USA. Paper received 30 December 1980.
0011-2275/81/007391-09 $02.00 © 1981 IPC B.siness Press Ltd CRYOGENICS. JULY 1981
391
as the energy input. It is anticipated that such a concept could be extended for earth application where low quality heat such as solar or industrial waste heat could be used. This paper involves material investigations of various adsorbents with various gases, and performance evaluations of a novel refrigeration system design. The material investigations stressed a review of adsorbing materials and their adsorption characteristics which would be suitable for the non-mechanical gas compressor, By adsorbing and ejecting heat, a compression and decompression cycle in the adsorbent chamber without the use of moving pistons, displacers or motors could be generated. A conceptional design using a Joule-Thompson (J-T) valve for cooling, check valves for gas control, and louvre for heat control was examined. An analytical technique was developed to evaluate gas flow requirements and other refrigeration system performance. The methodology was illustrated with a numerical example of a cooling load of 1 W at 74 K. The compressor design involved the determination of adsorbent mass, temperature variation, container volume and power requirements. The objective of these analyses was to determine the feasibility of using gas adsorption compressors for cryogenic cooling.
Physical adsorption The gas adsorption compressor depends on the adsorption characteristics of the gas by the adsorbents at different temperatures. When the gas is brought into contact with the adsorbent, some of the molecules striking the solid surface will be retained for a finite period of time, resulting in a significantly higher molecular concentration at the surface than in the gas phase. The forces holding the molecules to the solid are due to molecular interactions. This process is known as physical adorption and has been studied, both at ambient and cryogenic temperatures. A comprehensive review of the subject at cryogenic temperatures has been carried out by Kidnay and Hiza. 7 The adsorptivity of the gas by the adsorbent is usually expressed in the form of isotherms as exemplified by the nitrogen-zeolite system shown in Fig. 1. These isotherms are extracted from the experimental data of Harper8 and Woltman. 9 It is observed, that the amount of gas being adsorbed increases as temp10
01
:~
_
~
0.01
0
u
~ ooo1!/
i
Q1
J
i I 10
I
i
,
, I 10
I
I
i
L I 100
Pressure, Qtm Fig. 1 Isotherms of nitrogen with zeolite and compression and suction cycle
392
erature decreases and as pressure increases. The isotherms are usually obtained by two different methods: volumetric and gravimetric. Flapper and Gijsman ~° used a gravimetric method to measure adsorption of nitrogen on the zeolites 13X, 5A and 3A at 77 K, and of helium on 13X and 5A at 20 K. Daunt and Rosen H used a volumetric method to measure adsorption of He, N2 and Ar on zeolites at 78 K and of 3 He and 4He on zeolite in the temperature range 4 K to 20 K, as well as their isoteric heats of adsorption. A survey was made of the experimental data for adsorption of various cryogenic gases by such adsorbents as charcoal, zeolite and silica gel. Table 1 lists the cryogenic gases in the ascending order of their triple points. It is observed that in most instances, experimental values for the adsorption isotherms are available in the low pressure range. This is due to the fact that the main application of gas adsorption has been related to low-pressure gas removal processes. More data on isotherms at higher pressures are needed for a workable compressor. Another parameter that is important in the design of the compressor is the heat of adsorption, ie the heat that has to be removed from the gas upon the adsorption of a unit mass or mole of the gas. When the adsorbent surface is free of gas molecules, the heat of adsorption is termed the isoteric heat of adsorption, Qst. At a coverage of one monolayer, the heat of adsorption decreases in value. This value decreases further with more layers of gas molecules. The heat of adsorption for several systems are tabulated in Table 2.
Gas adsorption refrigeration design A bed of adsorbent can be used as a compressor and a suction pump based on the following principles as explained with the aid of Fig. 1. The high-pressure portions of the isotherms in Fig. 1 are obtained by extrapolation from the low pressure experimental data. Consider a bed of zeolite where heat can be added or removed and where gas can enter or leave the bed at two regulated pressure levels. Starting from state point 1 in Fig. 1, where the zeolite is at temperature T~, pressure P~, and concentration of nitrogen C~, further removal of heat coupled with gas flow from the outside at constant pressure would cause the temperature to drop but the concentration to rise. The state point 2 represents the equilibrium state point when the heat removal process is stopped. When the zeolite bed is heated with no outflow of the nitrogen gas (process 2-3), both the temperature and the pressure would increase with little change of concentration. At state point 3, when the gas pressure is high enough for its escape, the concentration drops with further increase of temperature and release of gas at constant pressure. At state point 4, when the heat flow reverses direction, but no gas is permitted to flow into or out of the bed, both the pressure and the temperature will decrease. Hence the bed acts as a compressor in processes 2-3 and 3-4 while it acts as a suction pump in processes 1-2 and 4-1. Taking advantage of high-pressure compression during desorption and low-pressure suction during adsorption of an adsorption bed, a cryogenic refrigeration system could be designed. Two ways to achieve refrigeration were considered: 2~ one, by causing the working gas to do external work; or two, by making use of the JouleThompson (J-T) effect, or internal work of expansion.
CRYOGENICS. JULY 1981
Table 1.
Adsorption data of cryogenic gases by common adsorbents
Gas
Triple point
Critical point
Inversion temperature
Helium He
2.17 K 0.05 a t m
5.19 K 2.26 atm
40 K
A d s o r p t i o n data
Zeolite
: 4 . 2 - 20 K; 0.01 - 2 a t m 11 76K;1-9atm 12 20 K; 10 -5 - 1 a t m 1° 1 7 3 - 2 7 3 K ; 0 . 1 - 1 a t m 11
Hydrogen H2
Neon Ne
13.89 K 0.071 a t m
19.01 K 0.426 arm
33.24 K 12.8 a t m
44.4 K 26.84 atm
202 K
250 K
Fluorine FI
53.54 K 0.0022 atm
119.17 K 55 a t m
600 K
Nitrogen N2
63.33 K 0.1237 atm
126.2 K 33.54 atm
622 K
Carbon monoxide CO
66.11 K 0.1 a t m
Argon Ar
83.78 K 0.68 atm
132.91 K 34.53 atm
150.72 K 48 atm
660 K
722 K
Carbon
: 76 K; 1 - 9 a t m 12
Silica Gel
: None
Zeolite
: 2 0 . 4 K; 10 -7 - 0.1 a t m 13 76 K; 1 - 95 a t m 12 77 K; 10 -5 - 1 a t m 1°
Carbon
: 76 K; 1 - 9 5 a t m 12
Silica Gel
: None
Zeolite
: 2 0 . 4 K; 10 -7 - 0.1 a t m 13
Carbon
: None
Silica Gel
: None None
Zeolite
: 1 9 5 - - 3 0 3 K; 0.1 - 1 a t m 8 77 K; 10 - 7 - 1 a t m 1° 80 - 3 5 0 K; 1 a t m 2° 173 - 2 7 3 K ; 0 . 1 - 1 a t m 9
Carbon
: 8 9 - 172 K; 2.5 x 10 -3 - 0 . 8 2 a t m 14
Silica Gel
: 4 7 3 - 7 5 3 K; 10 -9 - 10 -6 a t m 15
Zeolite
: 193-323K;0.1-
Carbon
: None
Zeolite
:77-323K;0.1 -latm 78 K; 10 - 3 - 1 a t m 11
latm 8
8
173 - 2 1 8 K; 0.1 - 1 a t m 9
Methane CH 4
Ammonia NH 3
Sulphur dioxide SO2
Carbon dioxide CO2
CRYOGENICS.
88,7 K 0.1 a t m
195.56 K 0.06 atm
197.68 K 0.00165 atm
216 K 5.11 a t m
J U L Y 1981
190.7 K 45.8 atm
406 K 111.5 a t m
430.7 K 77.8 atm
304.2 K 72.9 a t m
1000 K
2000 K
2150 K
1500 K
Carbon
: None
Silica Gel
: None
Zeolite
:95-320K;0.1-1atm
Carbon
: 89 - 172 K; 10 - 3 - 0 . 1 4 a t m
Silica Gel
: None
Zeolite
: 273-
Carbon
: None
Silica Gel
: None
Zeolite
: None
Carbon
: None
Silica Gel
: None
Zeolite Carbon
: 1 5 5 - 3 2 0 K; 0.01 - 1 a t m 8 2 0 0 - 6 0 0 K; 1 a t m 2° : None
Silica Gel
: None
8 TM
563 K;0.01 - 1 atm 9
393
A possible system design using the J-T effect is shown in Fig. 2a and the thermodynamic path of the process is shown in Fig. 2b. Upon heat addition to the adsorbent bed in chamber A, the temperature increases and the amount of gas being adsorbed decreases. The liberation of gas from the adsorbent causes the gas pressure inside the chamber to rise. At one point the pressure is high enough to push open the check valves 1 and 4 and close valves 2 and 3. At the same time, the removal of heat from chamber B will cause the temperature to drop and more gas can be adsorbed. The compression action of chamber A and the suction action of chamber B cause the flow of the high-pressure gas through the pre-cooler and the counterflow heat exchanger where it is cooled to a lower temperature before it expands through a J-T valve. Upon expansion, the gas enters the refrigeration chamber in the form of a two-phase mist. The refrigeration load causes the vaporization of the liquid. Hence, the outlet of the refrigeration chamber is at state point 4 (Fig. 2b). Upon passage through the counteflow heat exchanger, the gas is heated, thereby cooling the incoming gas. For a perfect heat exchanger, the outlet temperature of the gas at state point 5 is the same as the inlet temperature (state point 1). The low pressure in the refrigeration chamber is maintained by the suction process in chamber B where gas is being adsorbed.
Heat add
Heat rem ova I Chamber A
Check | valve 1-I ' 1
JCheck
I _l valve 2 #t~ll~ Check I I valve 3 I._1 _~"
1 I
t
I
.
J'"
Chamber B
Precooler
.-
Heat removal
.(~)l m
4
'I'
.
I
I Heat iadd
flow heat exchanger
J - T valve
_
®1
• ~'/
@
®
Refrigeration chamber
When the gas inventory in chamber A has been depleted, the heat flow of both chambers reverses direction. Chamber B functions as the role of the compressor while chamber A functions as the suction pump.
I efrigerat ion load
Refrigeration cycles analyses From the total energy balance, the refrigeration load Q is related to the mass flow as: Q = m(hs--hi)
(1)
where m is the mass flow rate through the J-T valve, hs is the enthalpy of the outlet at the low-pressure side of the counterflow heat exchanger, and hi is the enthalpy of the inlet gas after the precooler. For a given refrigeration temperature, 7"3 is fixed and this determined the low-pressure isobar P3, P4 and Ps in Fig. 2b. For example, if the refrigeration temperature is 74.22 K, the saturation pressure of nitrogen at that temperature is 10 psi (0.68 arm). Hence, the low pressure isobar is 10 psi. From a designer's point of view there are two adjustable parameters; one, the gas temperature, T1 after the precooler, and two, the pressure P1 upstream of the J-T valve. Fig. 3 shows the effect of precooling temperature and pressure ratio (Px [P2)on the mass flow per unit watt of refrigeration load for the case of the refrigeration temperature being 74 K and P3 = 10 psia (0.68 atm). The mass flow requirement is strongly affected by the pressure ratio and the precooler temperature. As the pressure ratio increases, the mass flow decreases. As TI decreases for a given pressure ratio, the mass flow also decreases. The mass flow rate corresponds directly to the zeolite mass in the compressor. In calculating the mass flow as shown in Fig. 3, the heat exchanger is assumed to be perfect, ie, Ts = T~. A perfect heat exchanger requires infinite heat transfer area; from a practical point of view, no heat exchanger is perfect. The effect of counterflow heat exchanger efficiency on the mass flow required for the pressure ratio ofP~/P3 = 10 is shown in Fig. 4. For a given precooler temperature there
394
J /
.J ®\
Fig. 2 a -- Gas adsorption refrigeration designwith J-T valve; b - T-S diagram for the heat exchangerand J-T valve process is an upper limit for the inefficiency of the heat exchanger. There is a minimum value of Ts beyond which the principle of J-T refrigeration breaks down. For example, at T1 = 278 K, the maximum value of the temperature difference (T1 -- Ts) beyond which the J-T principle does not work is 2 K or the minimum value of T5 is 276 K. As the precooling temperature is decreased, the temperature difference is increased, ie, there is more tolerance for the inefficiency of the heat exchanger. A practical value of the temperature difference is about 5 K. Then, the precooling temperature has to be in the neighbourhood of 111 K in order to keep the mass flow at a reasonable level.
C R Y O G E N I C S . J U L Y 1981
Table 2. systems
C =/1 (T, P) exp(aT) that fits the isotherms data of Fig. 1 is found to be
Heat of adsorption for several gas/adsorbent
C = 22.59/°1°"1674 exp(°~0548T) l exp(--0.03638T) Ost
E2
Ost
Monolayer,
Two
j mole-1
j mole-1
j mole-1
4 H e + Z e o l i t e 11
1580
1030
480
3 He + Zeolite 11
1420
-
-
4He
+ C h a r c o a l 16
1750
-
-
G r a p h i t e 17
1700
-
-
A r + C a r b o n 18,19
11 0 1 6
-
-
N 2 + Carbon 18,19
11 9 0 0
-
-
N 2 + Z e o l i t e 19
20 082
-
-
3He+
(3)
layer,
for 173 K < T < 273 K and 1 < P < 200 cm Hg It should be cautioned that (3) was derived from lowpressure data. Because of the unavailability of the highpressure data, the extrapolation of (3) for high-pressure application in the present analysis should be viewed as a first order approximation. The term (OC/~T)p represents the concentration variation with temperature at constant pressure. Basically, it is a function of the adsorbent temperature T and the compressor pressure P.
The precooling temperature and the temperature difference (T~ -- Ts) define the inlet temperature of the hot stream and the outlet temperature of the cold stream of the counterflow heat exchanger. A heat exchanger analysis was performed for the case of TI = 111 K and Ts = 106 K. In this case, the mass flow for 1 W cooling is 0.272 g s-~ (6 × 10-4 lb s-1 ) (see Fig. 4). The temperatures 7"2 and T4 correspond to the saturation temperatures of the high and low pressures respectively. For the case ofP~ = 6.8 atm (100 psia) andP4 = 0.68 atm (10 psia), T~ = 98 K and /'4 = 74 K. With these specifications, the length requirement of a 0.3175 cm (1/8 in) single tube with wall thickness of 0.10 cm (0.04 in) in the counterflow heat exchanger is 118 cm (3.87 ft). The weight of two of these aluminium tubes is 63.5 g (0.14 lb).
Equation (2) shows that the mass of the zeolite is proportional to the mass flow rn, inversely proportional to (aC/~T)p and inversely proportional to the rate of temperature rise dT/dt. The temperature rise rate in the zeolite is governed by the heat transfer mechanism into or out of the adsorbent material. It is difficult to estimate the temp-
1°2f
Gas a d s o r p t i o n c o m p r e s s o r design
All refrigeration processes which inctude isentropic, isenthalpic and free expansions, involve depressurization of highly pressurized gas. Hence, in the refrigeration cycle, a compressor is needed to provide the required gas flow at the desired pressure and temperature. It has been shown in previous sections how one can specify mass flow and pressures of the gas from the compressors based on the refrigeration requirement. It will be shown in tb_is section how one can specify the parameters for the gas adsorption compressor such as the zeolite mass, the container mass, the energy required to power the compression, the surface areas for adsorbing and rejecting heat and the temperature swing of the zeolite for the compression and decompression cycle.
"T cO th 10- 3 m
X
Zeolite mas~ When the adsorbent is heated at constant pressure (Process 3-4 in Fig. 1), the mass flow required for refrigeration comes from the liberation of the adsorbed gas. The mass flow rate m is related to the temperature rise rate (dT/dt) as 11b = 4 5 3 6 g
mz
~
p at
(2)
where C is the concentration which is the ratio of gas being adsorbed over the adsorbent mass. For zeolite-nitrogen combination, the relation between C and pressure P and temperature T are expressed in the form of the isotherms, shown in Fig. 1. An analytical expression of the form
CRYOGENICS.
JULY
1981
10 -4
I 15
I 2
I 2.5
I 3
I 4
I 5
I 6
I 7
P2/P3
I 8
I 9 10
Fig. 3 Effect of pressure ratio on mass f l o w rate for v a r i o u s p r e c o o l i n g t e m p e r a t u r e s f o r 1 W of refrigeration
395
T a b l e 3.
V a l u e s o f A C and ( A T ) m a x f o r various values o f
P H , (AT)swing and T 2
T2 = 1 7 3 K PH = (AT)swing
(AC)
1.36 atm
6.8 atm
13.6 atm
(AT)ma x
(AT)ca x
(AT)max
20
0.028
30.64
52.36
85.28
40
0.0582
48.95
93.26
114.35
60
0.0823
77.39
120.37
-
80
0.0947
96.5
-
-
100
0.1055
123.19
-
-
The mechanism to dissipate the heat from the compressor to outer space during the depressurization phase is also by thermal radiation. A louvre system that can accommodate the cyclic heat in and heat out of the compressor is shown in Fig. 5. During the compression phase, the louvres facing the heat source are open, but the louvres facing the heat sink are closed, so heat is transferred to the compressor. During the depressurization phase, the louvres facing the heat source are closed but the louvres facing the heat sink are open, so heat is transferred out of the compressor. In determining the heat required to produce unit mass flow, it is assumed that all the heat adsorbed by the compressor surface is instantly transferred to the zeolite. This heat causes the temperature rise of the zeolite and the container as well as the liberation of the nitrogen gas. Hence, neglecting the heating up of the gas
T2=195 K
Qh = mzCpz dT
PH =
1.36 atm
6.8 atm
13.6 atm
(AC)
(AT)max
(AT)ma x
(AT)max
20
0.0313
230
269.88
94.52
40
0.0545
253.75
295.79
-
60
0.0658
271.18
-
-
80
0.076
297.44
-
-
0.0806
-
-
-
,,u
+ msCps \ d t ]
Qh/Tn = ((()~--) p AU+ Cpz-I-XCps)/(~T)p (AT)swing
100
(6)
The heat Qn required is computed for different compressor pressures and temperatures, and the results are shown in Fig. 6. It is seen that compressor pressure has a minor effect on the heat required but temperature plays an important role.
erature rise rate without a detailed compressor design and heat transfer analysis of the zeolite medium. Hence, for the present analysis, dT/dt is assumed to be of a certain value for the estimation of the zeolite mass. Conversely, for a specified value of zeolite mass, (2) could be used to specify the value of dT/dt which would serve an objective goal in designing the heat transfer enhancement mechanism inside the compressor. Following the example where m = 6 x 10 -4 lb s-1 (0.272 g s-t ), compressor pressure = 6.8 atm and temperature = 250 K, then (aC/aT)p = 3.5 x 10 -3 K -1 , and if dT/dt = 0.03 K s -t , then the mass of zeolite required, mz = 5.7 lb (2.6 kg).
If the heat is obtained by radiation from a heat source of T* and if the compressor temperature is Th, if the heat transfer area An is black and the exchange view factor is unity, then Ah is related to Qh by
1 I
10 -1
I
2 II
3 I
( T1 - T5 ) K 4 5 t I I
6 t
7 I
8 I
Container mass. In estimating the container mass, a cylindrical container completely filled with zeolite is assumed. By relating the Hooke stress o of the cylindrical wall resulting from internal pressurization P, the mass ratio of the cylindrical container to the zeolite can be expressed
as
X
=
ms - 2PsP mz pzO
"T ¢-,
-E"
(4) 10-~
If the material is stainless steel the density Ps = 7.86 g cm -3 and the maximum stress = 9000 psi, for P = 100 psi then ms/mz ---0.16, ie the mass of the container is roughly 20% of the mass of the zeolite. 11b = 4 5 3 . 6 g
Power required. In determining the power required by the compressor, it is anticipated that the compressor is used in a spacecraft where adequate waste heat is available from the spacecraft electrical power generator. The mechanism to transfer this waste heat from the RTG to the compressor during the compression phase is by means of thermal radiation.
396
10"
0
Fig. 4
different
1
2
3 4 5 6 7 8 9 10 11 12 Tempereture difference ( T~ - T5) °R
13 14 15
E f f e c t o f heat exchanger efficiency on mass f l o w rate precooling t e m p e r a t u r e ; P1/P3 = 10
for
CRYOGENICS. JULY 1981
sorptivity of zeolite increases with increasing (A T)swing but also with decreasing T2. It appears that 7"2 should be as low as possible from the mass flow point of view. However, from heat transfer area considerations, T2 should be high.
Heat source
I
Compressor
I
Heet transfer area A c Closed louvers
Heat sink Fig. 5
Qh
(AT)max. Cycle time. The cycle time At for the zeolite to adsorb
Louvre system for gas adsorption compressor
=
AhO( T*4 -- ~h)
The parameter that characterizes the power required for the entire cycle is the maximum temperature difference (AT)max = (T4 - T2). The values of (AT)ma x as functions of (A T)swing for various temperatures 7"2 and pressures PH are shown in Table 3. For the same (A T)swing higher pressures PH and temperatures T2 would yield a higher
(7)
the gas is approximated by
mz
At = ~ - AC A h _ m
+Cpz +XCps] [o(T.4 -- T4)]
[(aC/OT)p A u (i)C/aT)p
(8)
The A t calculated by (10) represents approximately 1/4 of the total cycle time.
It is found that the area is quite independent of pressure but is strongly affected by zeolite temperature. As temperature is reduced, the irradiation heat is reduced, hence more of the heat can go to the zeolite. This temperature Th changes as the zeolite is heated from state point 2 to state point 4 in Fig. 1. For simplicity, Th being equal to T4 is used for area calculation. This would give a conservative (largest) estimate OfAh.
Design procedures For a given refrigeration load and temperature, one fflust first decide on the refrigeration system and the gas-adsorbent combination in the compressor. The choice of the gas depends on the refrigeration system. For example, for the J-T process, the gas should have a critical point above the refrigeration temperature but a triple point below that temperature of that gas. The critical point, the triple point and the inversion temperature for various gases are listed in Table 1.
A similar procedure can be applied to calculate the heat that has to be taken out of the compressor to adsorb a unit mass of nitrogen during the process 1-2. Equation (6) and Fig. 6 can be used to calculate the heat loss rate Qc To calculate the heat transfer area for dissipating heat, the compressor is assumed to radiate directly to a 0 K environment. Hence, Ac
7n -
[(aC/aT)p Au + Cpz + XCp~]
(~ C/O T)r o T~
(9)
The value of Ac/m is plotted in Fig. 7 for various zeolite temperatures at a pressure of 51 cm Hg. The value of Ah/m for high pressure of 517 cm Hg is shown in the same figure for comparison. It is observed that the heat transfer area for heat rejection reaches a minimum temperature of around 250 K, and the area required for heat rejection is one order of magnitude greater than that for heat adsorption.
Temperature cycle. After obtaining the basic design parameters of the compressor, the next step is the determination of the operation parameters, ie, the state points 1, 2, 3 and 4 in Fig. 1. As previously stated, the lower pressure is fixed by the refrigeration temperature. For a refrigeration temperature of 74 K in the J-T system, the lower pressure is 0.68 atm. Referring to Fig. 1, this pressure defines the left vertical line of the rectangular cycle. As shown in Fig. 3, the higher pressure, the less mass flow is needed. However, as the pressure increases so does T4 resulting in a greater heat transfer area. For a given/'2 (see Fig. 1), (AT)swing = T1 -- 7"2 represents the temperature difference through which the zeolite must swing in order to absorb an amount of nitrogen gas, AC, from the refrigeration system. By symmetry, this will be the amount of gas evolved during heating in the process 3-4. From the calculation, it was observed that the ad-
CRYOGENICS. JULY 1981
(10)
Dl
To illustrate the procedures, take a refrigeration load (Q) of 1 W and a refrigeration temperature (T) of 74 K. From Table 1, nitrogen appears to be the appropriate gas for a J-T system. The pressure in the refrigeration chamber corresponds to the saturation pressure of nitrogen at 74 K. In this case, the low pressure PL is 0.68 atm and the choice of the high pressure upstream of the J-T valve needs some optimization consideration. At present, ifPH is equal to ten times PL (6.8 atm), with a perfect heat exchanger and precooling temperature of 111 K (200 R), the mass flow required is 0.1 g s -1 (2.2 x 10 -4 lb s-l). Suppose the heat exchanger has an effectiveness of 0.65 (T1 -- Ts = 5.6 K). Then, the mass flow required is 0.27 g s -I (6 x 10 -4 lb s -1 ). Based on the 0.27 g s -1 flow rate, the 6.8 atm high pressure, 10 4
T: 275 K
~
I
10 2
I 10
I
I
I I Ltll
I
I
i
i ~ itl[
10 2
i
i
i
i i ii
10 3
10 4
Pressure, cm Hg Fig. 6 Effect of compressor temperature and pressure on heat required
397
Table 4. Weight estimation of the gas adsorption refigeration system for I W cooling
106
Power receiver panel 1 ft 2 at 10 Ib ft -2 10.0 Ib (4.55 kg) Heat rejection panel 47 f t 2 at 1 Ib ft -2 47.0 Ib (21.36 kg) Compressor (4 units) Zeolite = 5 . 7 1 b x 4 Container = 1.14 Ib x 4
22.8 Ib (10.36 kg) 4.6 Ib (2.09 kg)
Heat exchanger Total
5.0 Ib (2.27 kg) 89.4 Ib (40.63 kg)
Solid cryogen
Weight
= 2000 Ib (910 kg) for a period of one year for 1 W cooling
.; 105 £3
From (I0), the total cycle time for mz = 2.6 kg, m = 0.27 g s -1 and AC= 0.0582 is 37 min. In estimating the weight for the entire system, as shown in Table 4, it is assumed that four compressors each of which has a cycle behaviour are needed to provide a continuous refrigeration function. The weight of the heat exchanger and plumbing is estimated to be 5 lb. 21 Hence the total weight of the system is 89.4 lb (40.6 kg). This value is lower than that of the solid cryogen which is estimated to be 2000 lb (910 kg) for a period of one year and 1 W cooling. It is competitive with passive radiator at 74 K which requires 50 ft 2 (4.64 m 2) heat transfer area and weighs 65 lb (30 kg) for 1 W cooling, 22 in spite of its thermal inefficiency. The main reason is because in the gas adsorption cycle, heat is radiated at a much higher temperature level. Conclusions
The use of gas adsorption and desorption processes as a compressor to drive a cryogenic refrigeration system for long-term sensor cooling has been examined. Among varous designs, the J-T expansion process has high potential to meet the unmanned deep space vehicle environment. The J-T system requires no sealing, no mechanical moving parts and no active control system. However, it has the disadvantage of low efficiency and hence requires more gas flow from the compressor than other cycles such as the Gifford-McMahon cycle) l The present analysis represents a first step in the explora-
398
p~¢3'~c~~~7
% ,E \ b
Passive radiator for 1 W cooling at 75 K Weight = 65 Ib (30 kg) Heat transfer area = 50 ft 2 (4.64 m 2)
and the 0.68 atm low pressure, a nitrogen-zeolite compressor could then be designed. The two pressure levels define the two vertical isobars in Fig. 1. Choosing a minimum temperature/'2 of the compression cycle to be 172 K, for a (AT)swing = 40 K, then from Table 3 (AT)max = 93 K and AC = 0.0582. The maximum temperature/'4 in the cycle is 266 K, TI is 213 K and T3 is 207 K. The temperature differences T1 - / ' 2 , 7'3 - 7'2,/'4 - T3 and 7'4 - Tz are 40, 37, 56 and 53 K respectively. The heat addition rate at 266 K and 6.8 atm is 351 W (Fig. 6). The heat removal rate at 173 K and 0.68 arm is 216 W (Fig. 6). The heat transfer areas at those temperatures and pressures are 47 ft 2 (4.37 m 2) and 10 ft 2 (0.93 m 2) for heat rejection and adsorption respectively (Fig. 7).
•
104
10 3 170
l 175
l 200
l 225
I 250
TH or Tc K
I 275
I 300
I 325
Fig. 7 Effect of compressor t e m p e r a t u r e on heat transfer area of b o t h h o t and c o l d sides
tion of using direct heat to perform cryogenic refrigeration in an unmanned spacecraft. The methodology is intended to be simple. Because some of the calculations were based on extrapolation of the low-pressure isotherms, the numerical results should be used with extreme care. Nevertheless, these results provide an order of magnitude estimation of the gas adsorption refrigeration performance. The weight of a refrigeration system is an important aspect, but not the only aspect, in spacecraft design. The versatility of the system and the interaction of the system with the other spacecraft components should be considered in the merit evaluation of the design. From the present study, certain conclusions can be made: It is feasible from a thermodynamic point of view to design a gas adsorption refrigeration system to be powered by heat energy. The weight of such a system does not seem to be unmanageable in future spacecraft environment. By choosing the appropriate gas adsorbent combination, the system can be applied to other cryogenic temperatures rather than the 74 K exemplified in the present study. This leads to its application in temperature range where radiator or solid cryogen could not be used effectively. In addition, there is no restriction on the refrigeration load of the gas adsorption system. The system offers potentials of compactness and versatility to meet spacecraft and mission constraints. References
1 2
Sherman,A. Astronautics and Aeronautics 16 (Nov 1978) 39 Annable,R.V.Applied Optics 9 1 (1970) 185
CRYOGENICS . JULY 1981
3 4 5 6 7 8 9 10 11 12
Caren, R., Coston, R. Advances in CryogenicEngineering 13 (1976) 450 Kroebig, H.L. AFFDL-TR-78-760, (1978) Steyett, W.A.JApplPhys49(1978) 1227 Lehffeld, D., Boser, O. AFFDL-TR-74-21, AF Flight Dynamics Laboratory, Wright-Patterson AFB (1974) Kidnay, A.J., Hiza, M.J. Cryogenics 10, (1970) 271 Harper, F.J., Stifel, G.R., Anderson, R.B. Canadian J Chem 47 (1969) 466 Woltman, A.W. Ph.D. Thesis, University of Texas, (1978) Flapper, G.L.B.F., Gijsman, H.M. Cryogenics 14 (1974) 150 Daunt, J.G., Rosen, C.Z. Low TemperaturePhysics 3 (1970) 89 Kidnay, A.J., Hiza, M.J. Advances in CryogenicEngineering 12 (1966) 730
CRYOGENICS
. JULY
1981
13 14 15 16 17 18 19 20 21 22
Bewilogua, L., Binnebetg, A., Jackel, M, Cryogenics 15 (1975) 238 Kxatz, W.C. Paper presented at Cryogenic Engineering Conference, Madison, WI, (1979) Beher, J.T.Advances in CryogenicEng 2 (1957) 182 Itterbeek, A.V., Dingensen,W.V.,Physica 5 (1938) 529 Hellemans, R., Ittetbeek, A.V. Physica 34 (1967) 429 Ross, S.,Winkler, W.JColloidSci 10 (1955) 319 Lexner, E., Darun, J.G., JofLow TemperaturePhysics 10 (1973) 299 Haxtwig, W.H. Forty-Seventh Monthly Progress Report, December 1 - December 31, (1978) University of Texas at Austin Chart, C.K. JPL report 715-58 (1980) Haskin, W.L., Dexter, P.F. Paper 79-0179, 17th Aerospace Sciences Meeting, New Orleans, LA, (Jan 15-17, 1979)
399