Projected performance requirements for cryogenic spacecraft sensor cooling systems which demand higher reliability and longer lifetimes are outlined. The gas/solid sorption refrigerator is viewed as a potential solution to cryogenic cooling needs. A software model of an entire gas sorption refrigerator system was developed. The numerical model, evaluates almost any combination and order of refrigerator components and any sorbent-sorbate pair or which the sorption isotherm data are available. Parametric curves for predicting system performance were generated for two types of refrigerators, a LaNi5-H2 absorption cooler and a Charcoal-N2 adsorption cooler. It is found that precooling temperature and heat exchanger effectiveness affect the refrigerator performance. It is indicated that gas sorption refrigerators are feasible for a number of space applications

Sigurdson, K. B.

English

NASA Technical Reports Server

A GENERALCOMPUTERMODELFORPREDICTINGTHE
PERFORMANCEOFGASSORPTIONREFRIGERATORS*
Katherine B. Sigurdson
Jet Propulsion Laboratory
California Institute of Technology
ABSTRACT
Projected performance requirements for cryogenic spacecraft sensor cooling
systems demand higher reliability and longer lifetimes than the
state-of-the-art provides. The gas/solid sorption refrigerator is viewed as a
potential solution to these cryogenic cooling needs. A generalized analytical
software model of an entire gas sorption refrigerator system has been
developed. The numerical model, generated from a systems point of view, is
flexible enough to evaluate almost any combination and order of refrigerator
components and any sorbent-sorbate pair for which the sorption isotherm data
are available. Parametric curves for predicting system performance were
generated for two types of refrigerators, a LaNi5-H 2 absorption cooler and
a Charcoal-N 2 adsorption cooler. It was found that precooling temperature
and heat exchanger effectiveness affect the refrigerator performance
significantly. Examination of the results indicates that gas sorption
refrigerators are feasible for a number of space applications.
INTRODUCTION
Projected performance requirements for cryogenic sensor cooling systems
demand higher reliability and longer lifetimes than the state-of-the-art can
provide. A Joule-Thomson cryostat driven by a gas/solid sorption compressor,
the "gas sorption refrigerator", is a potential solution. In support of the
sorption refrigerator research program at JPL, a software analytical model of
a general gas sorption refrigerator system has been developed. The numerical
model was used to examine the relationships between heat exchanger
effectiveness, cycle times, precooling temperature, total cooling power,
system mass, and input power requirements. Two cases, a 30 K LaNi5-H 2
absorption cooler and a 91K Charcoal-N 2 adsorption cooler, with maximum
compressor pressures of 40 and 60 bar, respectively, are presented here.
*The research described in this paper was carried out by the Jet
Propulsion Laboratory, California Institute of Technology under contract with
the National Aeronautics and Space Administration.
343
https://ntrs.nasa.gov/search.jsp?R=19840007281 2020-03-22T08:11:38+00:00Z
NOMENCLATURE
C
COP
Cp
Cpc
Cpm
_Ps
dJT
fo
fmicro
fsolid
h
hco
hhi
Ho
k
K
L
m
m e
mg
m m
m s
M
NTU
P
Pho
Pr
9ij
?L
Qheat
R
Re
tij
Atsorp
Tci
Tco
Thi
V
X
n
Pg
Ps
Oy
gas to sorbent concentration ratio
coefficient of performance
specific heat
specific heat, compressor case
specific heat, metal foam
specific heat, sorbent
inside diameter of compressor
J-T valve diameter
sorbent packing factor
volume fraction of solid sorbent per particle
volume fraction of micropores per particle
heat transfer coefficient
enthalpy, heat exchanger cold side outlet
gas enthalpy, heat exchanger hot side inlet
isosteric heat of adsorption/absorption
thermal conductivity
ratio of gas specific heats
length
gas mass flow rate
mass
mass, compressor case
mass, gas
mass, metal foam
mass, sorbent
gas molecular weight
number of transfer units, heat exchanger
maximum pressure in compressor
pressure, heat exchanger hot side outlet
Prandtl Number
heat input from point i to j in compressor
cooling power
time averaged input power, total compressor
universal gas constant
Reynolds Number
time from point i to j in compressor cycle
desorption time in compressor cycle
temperature, heat exchanger cold side inlet
temperature, heat exchanger cold side outlet
temperature, heat exchanger hot side inlet
volume
volume percent of metal foam in compressor
heat exchanger effectiveness
mass density of gas
mass density of sorbent
maximum yield strength of compressor metal
344
GAS SORPTION REFRIGERATOR SYSTEMS
The basic components of a gas sorption refrigerator are the gas sorption
compressor, a precooling radiator, a counterflow heat exchanger, and a J-T
expansion valve. A typical block diagram is shown in Figure i. The gas
sorption compressor is a non-mechanical compressor which utilizes the
phenomenon of gas absorption or adsorption to pressurize the gas. The sorbent
material in the compressor absorbs/adsorbs the gas in large quantities when
cooled at low pressure and desorbs the gas at higher temperatures and
pressures when heated. The flow through the compressor is controlled with
self-operating check valves. The high pressure gas from the compressor is
precooled below the inversion temperature upon passing through the radiator
and is further cooled in the counter-flow heat exchanger in the J-T cryostat
before being isenthalpically expanded through the J-T valve. The heat load is
absorbed upon evaporation of the condensate.
NUMERICAL MODEL APPROACH
A previous numerical model (ref. I) evaluated one refrigerator system
design with a LaNi5-H 2 absorption compressor. The current, modified
version has the capability to evaluate a wide range of combinations and orders
of refrigerator components and any sorbent-sorbate pair, for which the data
are available, in the compressor. Generated from a systems point of view, the
model is a steady-state program that evaluates the characteristics of each
refrigerator component from the state properties of the working fluid at the
corresponding nodes. The program evaluates the component masses and pressure
drops; the required fluid mass flow rate; the required J-T valve diameter; and
the gas to sorbent concentration ratios, temperatures, and pressures in the
compressor based upon the input refrigerator performance requirements and
constraints. The program starts by evaluating the J-T cryostat and then
proceeds to evaluate the remaining components in an order opposite to the gas
flow. The LaNi5-H 2 cooler schematic, Figure I, illustrates the node
numbering scheme and component order. The Charcoal-N 2 cooler is similar but
with only one radiator and no intermediate heat exchanger. All the
temperatures and pressures throughout the system are found and any required
gas properties such as enthalpy and thermal conductivity are evaluated through
a gas properties look-up code (ref. 2). Currently the capability of the model
is restricted to one fluid loop with one J-T cryostat and only data for
Charcoal-N 2 adsorption (ref. 3) and LaNi5-H 2 absorption (ref. 4) have
been entered into the program.
J-T CRYOSTAT
The J-T cryostat is a combination of a counterflow heat exchanger, a J-T
345
expansion valve, and an evaporator. The required fluid massflow rate through
the system is found from the given cooling heat load and the change in
enthalpy through the J-T cryostat. The change in enthalpy is a function of
the precooling temperature, Thi , and the heat exchanger effectiveness, _.
The heat exchanger cold side outlet temperature is found from the precooling
temperature, the cooling temperature, and the effectiveness
T = (Thi-Tci)n + T (i)co ci
= QL/ (hco-hhi) (2)
The maximum JT valve diameter is found as a function of the mass flow rate
and the gas properties, assuming choked isentropic expansion:
. FThoR(K+I ] (K+I_
djT = 2 [-_ho] 5 L_,-_--, _K--Z-_j]. 25
(3)
The mass of the J-T cryostat is assumed to be the mass of the counter-flow
heat exchanger because the mass of the J-T valve is negligible in comparison.
The masses of the refrigerator components tend to increase linearly with fluid
mass flow rate, therefore the system mass increases nearly linearly with the
cooling load. Consequently, minimizing the fluid mass flow rate will tend to
optimize the coefficient of performance, COP, and minimize the system mass.
COUNTERFLOW HEAT EXCHANGER
The hot and cold inlet temperatures of the heat exchanger are determined
by the adjacent components in the system. The hot and cold outlet
temperatures are determined from the heat exchanger effectiveness and an
energy balance across the heat exchanger. The required length of the heat
exchanger is determined as a function of the number of transfer units, NTU,
and the heat transfer coefficient, h,
L =NTU _ Cp (4)
_dh
The mass of the exchanger is determined from the passage size, the
required wall thickness, and the required length. As the effectiveness
increases, the change in enthalpy through the cryostat increases, decreasing
the fluid mass flow rate. As the masses of the system components are all
dependent upon this mass flow rate, the total system mass is reduced as the
heat exchanger effectiveness increases, as shown in Figure 2. Also the COP is
346
improved as the effectiveness is increased due to the reduce massof the
compressor.
SPACERADIATOR
The compressor heat rejection componentand the gas precooling component
are both passive space radiators. Assuminga constant heat load, an estimate
of the radiator masseswasmadeby based on the equations developed for JPL's
advaced radiator (ref. 5,6). The COPis shownas a function of the precooling
temperature in Figure 3 for a 30 K LaNi5-H2 system and a 91K C-N2
system. Reducing the precooling temperature increases the change in enthalpy
across the JT valve thus reducing the required fluid mass flow rate to heat
load ratio and improving the COP. As the massof the entire system is nearly
linearly dependent upon the fluid mass flow rate, the refrigerator system mass
also decreases with the precooling temperature, Figure 4.
SORPTIONCOMPRESSOR
The gas sorption compressor is madeup of a set of compressor sub-units
cycled sequentially to supply an essentially continuous stream of high
pressure gas to the J-T valve. The inlet and outlet pressures and
temperatures are determined by the adjacent componentsin the refrigerator.
The compressor cycle consists of a heating phase and a cooling phase. Each
phase is assumedto be madeup of a constant gas concentration pressure change
and an isobaric gas concentration change, thus there are four states in the
idealized compressor cycle. Consequently, the pressures, temperatures and
concentration ratios can be found at all points in the idealized cycle from
the sorption isotherms and the compressor inlet and outlet conditions. The
required mass of sorbent is directly related to the fluid mass flow rate, the
desorption time, the gas concentration change in the compressor, and the void
volume in the lines
m = (_/Ac)gt (5)
s sorp
The void volume, or dead volume, increases the required sorbent massas
additional sorbent is required to pressurize this volume as well as the gas
that is being passed through the compressor. At higher pressures and
temperatures, this effect becomespredominant and the refrigerator efficiency
degrades.
The heat transfer within each compressor unit is enhancedwith a copper
foam. Thus the componentsof the compressor unit are the sorbent, the metal
347
foam, and the pressure case. The total volume is a function of the sorbent
packing factor, the volume percent of metal foam, and the case thickness. The
heat input between any two points i and j in the compressor cycle is the
sensible heat transfer to the sorbent, metal foam, compressor case, and gas,
and the isosteric heat of adsorption/absorption
Qij = (mCp)(Tj-Ti) + m (cj-ci)H° + mg(hj-hi)s g (6)
mCp= CPmmm + CPcmc + CPsms (7)
The coefficient of performance is determined from the calculated total
heat rejection requirement and the cooling heat load
COP= QL/Qheat (8)
The coefficient of performance is a strong function of precooling
temperature, as shownin Figure 3. This is expected as the massof the
compressor decreases nearly linearly with fluid mass flow rate which is
reduced by lowering the precooling temperature. It was found that by staging
the compressor for the Charcoal-N2 system, illustrated in Figure 5, the COP
can be improved somewhatat intermediate to high precooling temperatures,
Figure 3. However, at low precooling temperatures a cross-over occurs and the
single stage C-N2 system becomessuperior to the two-stage C-N2 system,
Figure 4.
The system massesshowninclude the estimate massesof the supports,
insulation, and the compressor heat addition-rejection component. Using Table
I, the massesof each system without these extras can be deduced.
CONCLUSIONS
A numerical model has been developed and is available to size and evaluate
gas sorption refrigeration systems for spacecraft applications. Two
refrigerator types, LaNi5-H 2 and Charcoal-N2, have been studied to
demonstrate the versatility of the model. It was found that the heat
exchanger effectiveness and the precooling temperature have significant
effects on the predicted refrigerator performance. It was also determined
that staging the compressor with an intermediate radiator improves the
performance of the Charcoal-N 2 adsorption refrigerator at higher precooling
temperatures. Further studies need to be completed with different adsorption
systems in order to characterize the effect of staging the compressor.
348
Although the COP's of the systems presented here are somewhatnon-competitive
with conventional mechanical refrigerators, the non-mechanical aspect of the
sorption refrigerator makesthe sorption refrigerator more attractive for
long-life applications whenexcess waste heat is available.
Table 1
Component Mass Fraction (in percent) at Constant Precooling Temperature
i Watt Heat Load
Component
Precooling Temperature
80 K i00 K 120 K
LaNi5-H 2 Refrigerator:
Compressor
Compressor heat add/rej
component
High temperature radiator
Heat exchanger
Precooling radiator
JT cryostat
Support, plumbing, insulation, etc.*
3.9 5.7 6.5
41.0 60.2 68.4
2.2 3.3 3.8
1.0 3.3 5.2
42.1 19.5 9.0
O.1 0.I 0.5
I0.0 I0.0 I0.0
C-N 2 Refrigerator (2-Stage Compressor):
Compressors
Intermediate radiator
Compressor heat add/rej component
Precooling radiator
JT Cryostat
Support, plumbing, insulation, etc.*
150 K 200 K 250 K
O.2 O.8 2.8
5.8 3.1 0.9
78.5 83.7 86.3
6.5 3.3 0.9
I0.0 I0.0 i0.0
* assumed constant mass fraction of 0.i
349
Jll I
IIi
I
I "
,ot
I
,1
I
COMPONENT
TYPE 2
7t 1
RAp. ]1 I
_J -_
[
COMPONENT
TYPE 4
1
I J COMPRESSORII
__ .I
L._____ 13
_}9 14r- ---1
I EXCHANGER I TYPE 3
I J8 __115
rh
[....... I
EXCHANGER J
J JT COMPONENT
J VALVE TYPE 1
I , I
l J
Figure i. LaNi5-H 2 System Block Diagram
350
40
30
A
_O
20-
10
Figure 2.
95
LaNi_-H2 30 K SYSTEM
SS
I
COP
QL" !.OW
PH/PL- 4018bar/bar
tCYC LE" 270 $
TpRECOOL"80 K
- 8OO
- 700
-600
5OO
4OO
3OO
I 200
97 99
HEAT EXCHANGER EFFECTIVENESS,nHX
System Mass and COP versus Heat Exchanger Effectiveness
351
1400
1200
1000
800
600
400
200
100
I I I
n = 0.99
HX
30 K LaNis-H2 SYSTEM
1 STAGE
2 STAGE
K C-N2 SYSTEM
C-N 2" 150
I
LaNi5- H 2" 80
175 200 225 250
1 1 I I
90 I00 II0 120
PRECOOLING TEMPERATURE (K)
Figure 3. COP versus Precooling Temperature
352
=E
=E
>-
70
60
50
4O
I
"rIHx = 0. 99
91K C-N2 SYSTEM
I STAGE
C-N2 2 STAGE
C-N2
10
C-N2:
LaNi5 - H2:80
I I I
150 175 200 225 250
I I I I I
90 100 110 120
PRECOOLING TEMPERATURE (K)
Figure 4. System Mass versus Precooling Temperature
353
00
m_
m_
0
a.
0
m m i m m
X
mmIX_
>
W
354
o
o
4-J
0
E
0
_.J
0
U
4J
ilJ
REFERENCES
1. Klein, G. A., Jones, J. A.: Molecular Absorption Cryogenic Cooler for
Liquid Hydrogen Propulsion Systems. Paper # AIAA-82-0830, AIAA/ASME
3rd Joint Thermophysics, Fluids, Plasma and Heat Transfer Conference,
June 7-11, 1982, St. Louis, Missouri.
. McCarty, R.: Interactive Fortran For Computer Programs for the
Thermodynamic and Transport Properties of Selected Cryogens. NBS
Technical Note 1025, 1980.
Be Yang, L. C., Yo, T. D., Burris, H. H.: Nitrogen Adsorption Isotherms
in Zeolite and Activated Carbon. Cryogenics, Vol. 22, No. 12,
December 1982, pp 625-634.
. Jones, J. A.: LaNi 5 Hydride Cryogenic Refrigerator Test Results.
Second Biennial Conference on Refrigeration for Cryogenic Sensors and
Electronic Systems, NASA CP - , 19 . (Paper of this
compilation.)
. Bard, S.: Development of an Advanced Passive Radiator for Cryogenic
Cooling of Spaceborne Instruments. AIAA Journal of Spacecraft and
Rockets, in press, 1983.
. Bard, S., Stein, J., Petrick, S. W.: Advanced Radiative Cooler with
Angled Shields. Spacecraft Radiative Transfer and Temperature
Control, Vol. 83, Progress in Astronautics and Aeronautics, 1982.
355


A general computer model for predicting the performance of gas sorption refrigerators

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