The conceptual design selected for detailed system analysis and optimization is the reciprocating gadolinium core in a regenerative fluid column within the bore of a superconducting magnet. The thermodynamic properties of gadolinium are given. A computerized literature search for relevant papers was conducted and is being analyzed. Contact was made with suppliers of superconducting magnets and accessories, magnetic materials, and various types of hardware. A description of the model for the thermal analysis of the core and regenerator fluids is included

Hartley, J. G.

Larson, A. V.

Shelton, S. V.

Smith, M. M.

English

NASA Technical Reports Server

FEASIBILITY ANALYSIS OF RECIPROCATING 
HAGNElXC HKCLT PUNPS 
Semiannual Status Report 
for the Period 7/3/85 to 1/2/86 
A. V. Larson 
J. G. Hartley 
S. V. Shelton 
H. H. Smith 
NASA Mearch G r a n t  NAG 3-600 
Georgia Institute of Technology 
Atlanta, Georgia 
qn-9- 
JV-)-)L 
https://ntrs.nasa.gov/search.jsp?R=19870010214 2020-03-20T11:12:23+00:00Z
Semiannual Report 
Feasibility Analysis of Reciprocating Magnetic Heat Pumps 
Obi ective: 
The goal of the project is to study the commercial feasibility of magnetic 
heat pumps and refrigerators operating near room temperature. An analytical 
Phase Zero study is being to quantify the expected performance and 
economics of commercial magnetic thermodynamic devices and to recommend 
whether a Phase One program should be started to include experimental R and D. 
conducted 
Background: 
Until recently, interest in magnetic heat pumps and refrigerators was 
limited to temperatures under 20K. In 1976, Brown [ 1,2] at NASA/Lewis 
suggested the possibility of practical magnetic devices operating near room 
temperature. Noting that all heating/cooling effects in magnetic materials 
are greatest near the Curie point, he considered available materials, e.g. 
gadolinium, with Curie points near room temperature. Several thermodynamic 
cycles were considered. From those, the magnetic Stirling cycle with 
regeneration was selected for further study. A reciprocating, porous 
gadolinium core in a column of regenerative fluid inside the bore of a 
superconducting magnet was envisioned. A proof-of-concept laboratory device 
was successfully demonstrated. 
Status : 
The conceptual design selected f o r  detailed system analysis and 
optimization is the reciprocating gadolinium core in a regenerative fluid 
ine ir'nermo6ynamic 
properties of gadolinium are giver? by Griffel, et al. [ 31 , Brow. [4], axd 
Benford and Brown [5]. The general thermodynamic relations for magnetic 
materials are given by Hatsopoulos and Keenan [ 6 ]  and Booker [ 7 ] .  The 
relation between the applied fields (no magnetic material present) and the 
internal fields in the gadolinium in place is taken to be that of an ellipsoid 
of gadolinium [8,9]. Initially, it is assumed that the gadolinium does not 
perturb the sources of the applied field. The forces are calculated on the 
basis of the approximation of a small dipole in a field gradient [8]. 
m. -*l..-- -.-.LL.:- LL- .I----- -c 
W A L l I A I L  Lut: UULC VI a i i i i p e r s O d u C t i t i g  magriei. 
A computerized literature search for relevant papers has been conducted 
and is being analyzed. Contact has been made with suppliers of 
superconducting magnets and accessories, magnetic materials, and various types 
of hardware. model for the thermal analysis of the core 
and regenerator fluids is included in the following section. 
A description of the 
Thermal Analysis of Regenerator Coluum: 
The thermal analysis of the regenerator fluid and gadolinium core is 
presently based upon a one-dimensional, transient model. This model will be 
used to identify important design performance parameters and to identify 
areas which require further investigation. 
and 
-2- 
The assumptions listed for the model in the previous status report [ l o ]  
have been altered: 
1. Viscous forces are neglected. 
2. Thermal equilibrium has been assumed between the gadolinium and the 
fluid at any cross section in the regenerator column. A one- 
temperature model follows in which the heat transfer coefficient is 
not required. 
To facilitate the computation, the coordinate systems have been changed. 
Now two coordinate system are used. The first (x,y) is fixed to one end of the 
regenerator column. The second (x , y ) is fixed at the magnet center. 
The energy equation based on the assumption of local thermal equilibrium 
is : 
where 
- 
Pf 
C constant pressure specific heat of the fluid 
porosity 
intensity of the magnetic field 
density of the Gd (fluid) 
entropy of Gd 
temperature 
time 
velocity of the plug relative to the regenerator column 
specific volume of Gd 
column fixed coordinate along the regenerator axis. 
-3- 
is the total change in the field intensity observed at the magnetic material. 
The first term appears because the field appears to be time varying relative 
to the column due to the column motion. This term can be referenced to the 
magnet fixed coordinates which removes the time varying component. Then 
] = [ 'abs] >t * [ a(vii) + v a(vii) 
ax X,Y ax" XI Y a t  
where 'abs = 'col -k vplug/col 
If E = 1 we are outside the Gd and the equation is 
aT aLT 
at Pf 'pf - = kf -2 ax 
As expected, the energy equation reduces to conduction in the fluid. 
Boundary Conditions: 
1. Initially adiabatic at the regenerator column ends: 
At the plug ends: 
- 
plug - Tfluid 2. T 
3.  aT 
[ks (1-E) + kf&1 I = kf a x  Ifluid Plug 
These conditions represent the continuity of temperature and heat flux. 
The energy equation was implemented on the computer using a finite difference 
scheme. Non-dimensionalizing the equation was attempted. This proves to be 
very'difficult due to non-constant coefficients and the lack of global 
geometric scales that can be for references. A dimensional approach was 
adopted for the present. 
used 
Problems in implementation: 
(1) Node Types. 
The nodes are picked to be fixed relative to the regenerator column. As 
the plug moves along the column the character of the nodes changes. Also,  
the plug-fluid boundary is in general not at a node location. The 
numerical scheme must recognize different node types and use various 
schemes to calculate new temperatures. This leads to bookkeeping problems 
with the nodes. 
-4- 
(2) Stability and Convergence. 
This is the usual problem with the ratio of step sizes. The space 
increment At is computed to keep the coefficients in the numerical scheme 
positive. The increment At is also checked so that the plug advances by 
fractions of a space step. 
aT The convective terms (those with - 
wind difference to improve stabid&. As V, the relative velocity between 
column and plug changes sign, the - terms change relative to the upwind 
directions. Higher order difference was also tried but did not improve 
stability. 
( 3 )  Convective Terms. 
had to be treated as one-sided up- 
ax 
Results: 
Some initial predictions from the model are given in Figures 1-3. 
The regenerator column has a length of lm, the gadolinium plug, 0.2m. The 
fluid is half water, half methyl alcohol by volume. The porosity of the 
gadolinium (open area/section area) is 80%. The cylinder and ends of the 
regenerator are adiabatic. The vacuum field of the superconducting magnet is 
assumed constant in time and given by American Magnetics for their 8 Tesla 
unit operating at 6T maximum. 
At the start of the first the fluid and gadolinium are uniform in 
temperature at 295K. The end of the regenerator nearest to the magnet is lm 
from magnet center and the gadolinium is at the near end. After a half-cycle, 
the gadolinium and magnet are concentric, the gadolinium is at the other 
end of the regenerator. 
Figure 1 shows the temperature profile within the regenerator after 14.5 
and 15 cycles. The cycle period is 37 seconds with no pauses and with 
velocities given by appropriate step functions. During this computer run, the 
minimum separation between the gadolinium and regenerator end was 5cm at each 
end. The column position, 0.00, marks the near end of the column at the start 
of a cycle. The drop in temperature at the other end between the two profiles 
by repositioning the column to complete the cycle). At present the model 
includes thermal conduction in the column, but excludes mixing. The gradients 
at the column ends reveal that axial conduction has a minor effect. 
Figure 2 shows the maximum and maximum temperatures in the column after 
each half-cycle. The nearly isothermal sections again reveal the minor effect 
of axial conduction. The curvatures suggest that asymptotes will be 
approached, but the AT is already close to the value found in the experiment 
by Brown and Pappel. 
Figure 3 gives the results of a run in which there is no dead space 
between the gadolinium and the ends of the regenerator. The temperatures at 
the column ends are now changing with each cycle. 
cycle, 
and 
chnw_c C-C~~ZO 0 nffnrrt ------ cf r = ~ e y i ~ g  the g & c l i n i * z  from magnet (fslloued 
current Plans: 
Next we plan to incorporate mixing into the model and also the transfer of 
energy between load and sink. 
- 
-5- 
1. G. V. Brown, "Magnetic Heat Pumping Near Room Temperature," J.  Appl. 
Phys., 47, 3673-3680, (1976). 
2. G. V. Brown, "Basic Principles and Possible Configurations of Magnetic 
Heat Pumps," ASHRAE Transactions, 87, pt. 2, 1981. 
3. M. Griffel, et al., "The Heat Capacity of Gadolinium from 15 to 355"K, 
Phys. Rev., 93, 657-661, (1954). 
4. G. V. Brown, "Magnetic Stirling Cycles--A New Application for Magnetic 
Materials," IEEE Trans. Magnetics, MAG-13, No. S . ,  1146-1148, Sept. 1977. 
5. S. M. Benford and G. V. Brown, "T-S Diagram for Gadolinium near the Curie 
Temperature," J. Appl. Phys., 52, 2110-2112, March 1981. 
6. G. N. Hatsopoulos and J. H. Keenan, Principles of General Thermodynamics, 
Wiley, New York, 1965, 
7. H. G. Booker, Energy in Electromagnetism, the Institute of Electrical 
Engineers, London and New York, Peter Peregrinus Ltd., New York, 1982. 
8. P. Moon, Magneto-Solid Mechanics, Wiley, New York, 1984. 
9. C. W. Chen, Magnetism and Metallurgy of Soft Magnetic Materials, North 
Holland, Amsterdam and New York, 1977. 
10. A. V. Larson, J. G. Hartley, S. V. Shelton, Feasibility Analysis of 
Reciprocating Magnetic Heat Pumps, Semiannual Status Report, NASA Grant 
NAG 3-600, Georgia Tech, July 1985. 
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Feasibility analysis of reciprocating magnetic heat pumps

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