AERONAUTICS. AND SPACE ...... of variables, the energy equation becomes, after letting. Tf = Tm,. [ {IOS. + .... of a run in which there is no dead space between.
/x,' =3
FINAL
c,'C._
REPORT
FEASIBILITY
ANALYSIS
OF RECIPROCATING
MAGNETIC
HEAT
PUMPS
By A. V. Larson --
--J.
G. Hartley Sam V. Shelton M. M. Smith
-
--
Prepared for NATIONAL AERONAUTICS LEWIS
RESEARCH
AND
SPACE
ADMINISTRATION
CENTER A
CLEVELAND,
OHIO
44135
Under NASA
Grant
NAG-3-N)0 T
December
1989 2
GEORGIA
INSTITUTE
OF TECHNOLOGY
A Unit of the University System THE GEORGE W. WOODRUFF ATLANTA,
GEORGIA
of Georgia SCHOOL
OF MECHANICAL
ENGINEERING
30332-0405 N'_O - I S 3(,:,
-_
_ 5
(NASA-CR-186Z05) FFASI_IL ' _iY .... _.I y I'< ,l;. RECIPROCATING MAGNETIC _L.,%T PU_PS I-in_l Robert (georrzi-_ Tl_st. of Tech.) 59 p 20D G31_4 "
ii
I
Unclas u253177
J
FEASIBILITY
ANALYSIS
OF RECIPROCATING
MAGNETIC
HEAT
PUMPS
By A. V. Larson,
Co-P.I.
J. G. Hartley,
Co-P.I.
Sam V. Shelton, M. M. Smith
w
Co-P.l.
r
FINAL
REPORT
for the period
July
1985 to July
Prepared for NATIONAL AERONAUTICS LEWIS m
RESEARCH
CLEVELAND,
1986
AND
SPACE
ADMINISTRATION
CENTER
OHIO
44135
Under NASA
Grant
December
GEORGIA
NAG-3-600
1989
INSTITUTE
OF TECHNOLOGY
A Unit of the University System THE GEORGE W. WOODRUFF ATLANTA, w
w
GEORGIA
30332-0405
of Georgia SCHOOL
OF MECHANICAL
ENGINEERING
ABSTRACT
w
A reciprocating warm
Gadolinium
bore of a superconducting
refrigeration presented magnet
to
frequency
the
(1000
amount
Estimated
reciprocation
analysis
exhibits
of
in a regeneration
solenoidal
MW
of
approaches
Officer
costs
A cable
for
an
to conventional
10 Hertz. cycling
at
grant
in the
for magnetic procedure needed
ideal
in
chillers
Hertz
is Gerald
V.
is the
magnetic as the
A one-dimensional 0.027
seen in the experiments
for this
column
is considered
superconducting
comparable
a regenerator
fluid
applications.
capital
some of the features
The NASA Technical RESEARCH CENTER.
magnet
ton)
system
of this type become
of
difference
3.517
minimize
design.
refrigerator
which
in
core
finite
is presented
of G.V. Brown.
Brown,
NASA
LEWIS
ACKNOWLEDGEMENTS
The on
the
authors
wish
mechanical
manuscript; drawings.
and
to thank
system;
students,
our colleague,
Betty Steven
Holtsinger Corson
J.W. for
Brazell, typing
and Michael
for discussions and
proofing
L. Robertson
for
the the
TABLE OF CONTENTS
ABSTRACT ACKNOWLEDGEMENTS NOMENCLATURE I
II.
,
INTRODUCTION BACKGROUND Magnetic
............................. ..............................
Cooling
Reciprocating
III.
Devices
Magnetic
Pumps ...................
ESTIMATES
.........................
7
Cost Model
.........................
7
Logic
Pumps
4
ECONOMIC
.....................
6
.......................
12
........................
12
Minimum
Radius
Ratio, e
Optimum
Magnet
Dimensions .......................
14
Input Data Case
I
..........................
14
Input Data Case
II ..........................
16
Results
...............................
Operating
Costs
REGENERATOR Results
Column Column
DISCUSSION/CONCLUSION
FIGURES APPENDIX
.......
20
...................
21
...............................
B. Isothermal
REFERENCES
17
...........................
COLUMN
A. Adiabatic
VI.
2
Magnetic
Cost Minimization
Vo
.......................
Heat
Heat
2
Rotating
Capital
IV.
1
Ends, Ends,
Initial
29
Thermal
Initial
Internal
........................
............................. ............................... ..............................
Equilibrium Thermal
...... Gradients
29 30
32 34 39 51
NOMENCLATURE
r
A
Column
B
Magnetic
induction
Bo
Magnetic
induction
Bw
Magnet
C
Cost of magnet
Ca
Cost of auxiliary
Cm
Specific
cost of magnetic
metal
Cp
Specific
heat at constant
pressure
Cs
Specific
cost of superconducting
Cst
Cost of magnet
Ct
Total
CI
Cost coefficient
CV
Control
F
Form factor
f
Frequency
H
Magnetic
Hz
Hertz
H*
Enthalpy
cross-section;
induction
Ampere
at magnet
center
in central
plane
at wall
and magnetic
metal
core
of core
.
£_
equipment
structural
cable
support
cost of system defined
by eq.
(16)
E_
w
defined
by eq. (21)
of demagnetization intensity
(cycles/sec)
m
I
Volume
(cycle frequency)
E
h
Specific
enthalpy
J
Globally
averaged
Jsa
Characteristic
K
Unit
k
Thermal
L
Length
M
Magnetization
Mm
Mass
of core magnetic
Ms
Mass
of superconducting
N
Unit
of force,
Ri
Innerradius
of magnet
winding
Ro
Outer radius
of magnet
winding
P
Cost term defined
Pmi n
P at emi n
QL
Heat transfer
to column
QH
Heat transfer
from column
Refrigeration
load rate
current
current
of temperature,
density
density
in magnet
of superconducting
Kelvin
conductivity of magnet
winding
v
L_
V
w
metal cable
Newton
by Eq. (19)
_in
Thermal
input power
_out
Thermal
output
power
winding
end from
source
end to sink
alloy
Specific
refrigeration
S
Specific
entropy
T
Temperature;
t
Time
U
Internal
V
Speed of core relative
Vb
Volume
Vabs
Speed of core relative
V
Speed
qL
col
capacity
Unit of magnetic
of magnetic
field,
energy
of magnet
of column
to column
bore to magnet
relative
Speed of fluid
V
Volume
of superconducting
cable
Volume
of superconducting
alloy
Volume
of magnet
including
V
in core,
to magnet
Vf
S
Tesla
relative
to column
in cable
sa
V w
windings
V
Spec ifi c volume
W
Unit of
X
Coordinate
relative
to magnet
X
Coordinate
relative
to column
power,
Watt
spacing
metal
Greek
w
Symbol s Ratio of outer to inner radii
Ratio of length
V
to inner diameter
winding
for magnet
winding
_min
Value
of _ at emi n
6
Fraction
of winding
volume
filled
by superconducting
alloy
6s
Fraction
of winding
volume
filled
by superconducting
cable
6sa
Fraction
of cable cross-section
(
Porosity
defined
Y
Fraction
of core filled
P
Density
Pm
Density
of magnetic
Ps
Density
of superconducting
#o
Magnetic
H
high
L
low
f
fluid
m
magnetic
min
minimum
metal
filled
by superconducting
by Af/A
permeability
Subscripts
m
for magnet
by magnetic
metal
metal
(non-porous cable
of vacuum
form)
alloy
I.
INTRODUCTION
r_
Some
materials
become
hotter
(cooler)
when
magnetized
(demagnetized).
E
Refrigerators
and heat pumps
based
on the effect
In practice,
adiabatic
demagnetization
few
Kelvin.
This
can be imagined
has been
important
in principle.
in cooling
below
a
w
degrees
application The
report
of a magnetocaloric
motivation
flexibility
is
than
to are
find
considers
refrigerator
devices
found
in
of
the
feasibility
operating
greater
conventional
near
capacity,
of
room
commercial
temperature.
economy
technology
to
or
meet
design
particular
applications. In 1976,
Brown
magnetocaloric earths
such
magnets
__k w
magnetic concept
gadolinium
effect
is
and less
suggested
temperatures. the
advent
power
stronger
the possibility
The bulk availability of
higher
consumption
near
the
of practical
was
Curie
field
superconducting
intriguing
point
of rare-
(Gd
because
293K)
and
the with
field changes.
Brown
w
at normal
considerably
magnetocaloric larger
devices as
with
[1,2] at NASA/Lewis
discussed Stirling
laboratory
feasibility
several cycle
with
device
was
was thought
of the regenerator.
possible
thermodynamic
regeneration successfully
to rest on economics
These
are the factors -
I
-
for
cycles
further
demonstrated
and
selected
study. [3].
A
of
The commercial
and the thermodynamic addressed
proof
the
in this paper.
performance
Comparisons conventional gadolinium
are 1000
core
made
ton
here
on
chillers
and
the a
in a fluid regenerating
Progress
is
regenerator.
This
and irreversible
system
and
using
operating
a
costs
reciprocating
of
porous
column.
reported
on
modelling
is to eventually
processes,
capital
modelling
but hasn't
the
done
gadolinium
take
into
-
account
fluid rate
column
dependent
so yet.
v
II.
BACKGROUND
r_
W
Magnetic
Cooling
Devices
The magnetocaloric 1918.
Prior
refrigerators
to
this
effect Edison
and engines
Temperatures
was
based
first
[5]
and
observed Tesla
by Weiss
[6]
had
and
Piccard
patented
on the ferromagnetic-paramagnetic
down to I K can be obtained
to liquefy
He.
[4] in
designs
for
transition.
Debye
[7] in 1926
w
and Giauque
[8] in 1927
be produced
by the adiabatic
method
was
Adiabatic w
independently
successfully demagnetization
suggested
demagnetization tested has
in been
research.
-2
1933 used
that
lower
temperatures
of a paramagnetic by
Giauque
since
then
and in
substance. MacDougall
could The [9].
low-temperature
v
In
"one-shot"
contact
w
with
devices
a low
a
temperature
low
temperature.
An applied
the
paramagnetic
material
established field
the
is
paramagnetic
thermal
lowered
to
substance
reservoir
of
magnetic into
the
contact
to
zero.
The
placed
He and a material
field
causes
Once
reservoir
experimental
energy
broken
material
and
thermal
be studied
thermal
is
in
to
thermal
reservoir. the
is
to
flow
at from
equilibrium
is
and
the
magnetic
the
paramagnetic
L
substance
will
then
drop
Refrigerators
have
temperatures
below
to
a temperature
been
I
K
in
using
built
for
below
using
loads
that
of
paramagnetic
less
than
the
reservoir.
substances
i
mW [10,
to
11].
maintain There
is
w
substantial V
to
20
[13,
interest
K)
in
14,
superconducting
15].
There
similar
These
are
devices
devices
devices
would
basically
two
and need
to
to
to
maintain
cool
temperatures
instruments
handle
competing
low
loads
designs
in
greater in
(I
space
than
current
craft
I W. magnetic
r
refrigeration
w
magnetic
research material
moving
other
design
uses
fluid
acting
as
referred rotating
to
applications industrial
as
and
at
temperatures
with
a rotating the
the
link
a reciprocating wheel
between
reciprocating
reciprocating in
waste
space,
above
laser
magnetic
the
source
and
rotating
heat recovery
amplifier
K.
heat
in
material and
with
designs, pumps
cooling,
involves
a fluid
sink.
[13, 14, 15, 16, 17]. - 3
One
motion
of
magnetic
i
have helium
a
porous
column.
The
a counterflowing
The
two
designs
respectively. been
proposed
liquefication
are Both for and
Reciprocating
The
Magnetic
reciprocating
magnetic
material,
A typical In
cycle
the
Pumps
magnetic
heat
a fluid-filled
mechanical
material
cooled.
The
increase
in
core.
In the
is completed
for
Here,
process
temperature
be vertical
I.
cycle,
in the
cycle
pump
consists
regenerator
is shown in Fig.
magnetic
likely
Heat
by In
proper
fluid
the magnet I-2
part
control.
magnet.
of
the
2-3 the material 3-4
necessary
At
porous
magnetization
process
the
the
is on continuously.
demagnetization
practice,
of
and the external
includes
isofield
core
4-I.
column
in
steady
and an
isofield
translation
operating
is
would
conditions
_m
the fluid
in the regenerator
and has an overall
Fig. I the left to the magnet and off with
high-field
column
temperature
end is hot.
is not always the
magnetic
superconducting
is stratified
difference
The motion required.
with
respect
of TH - T L.
In the column
of the magnetic Instead,
material
inside
the
magnets
may favor
material
the magnet bore.
to temperature
with
could
However,
shown
respect
be turned the
the use of relative
in
nature
motion
on of
and a
v
constant The
field. details
of
the actual
ends
of the regenerator
column
and
these,
the
variation is
along
with
in the magnetic
achieved.
Fig.
2
energy
are not shown.
details
field,
shows
addition
of
the
and rejection
Various relative
will determine
a cycle - 4
consisting
what of
processes
methods motion
could and
at
be used,
the
type thermodynamic two
isothermal
the
spatial cycle and
two
isofield
paths
regeneration then
the
Carnot
which
is the representation
paths 2-3 and 4-I were
ideal
cycle
device.
the partial
congruent
would
have
the
(The dashed
path
could
magnetization
of
same
the cycle
considered
as suggested
coefficient
be achieved
of the core during
by the dashed
of
which
If
line,
performance
in practice
warming,
here.
as
the
by programming
is not considered
initially.) The reciprocating
magnetic
heat pump was first
proposed
by J. R. Van Geuns
m
in 1966 m
[18].
More
by G. V. Brown
recently
[i, 2, 191.
this device Brown
has been discussed
and Papell
reciprocating
magnetic
device
maximum
employed
was 7 T producing
field
80 K.
In separate
K
328
and
K.
refrigerator
fluid, issuing
but
Two
factors
depends the
from
the
on
the
gradient core
The
in
would
the
test
fluid
the
device mixing
of
a
a temperature was
region
a small
span
of
by
The
of
about
were an
241
actual
reciprocating
gradient
degraded
in the
papers
sink).
attained
performance
operation of
or
temperature
temperatures
limit
successful
and tested
(no source
a maximum
maintenance
causing
walls
and highest
which
noted.
[3] have built
adiabatic
tests the lowest
were
refrigerator
with
in several
jets
behind
in of
it.
the
fluid Also,
L_
more
surface
area was needed
Two other
reciprocating
to enhance
magnetic
heat transfer.
refrigerators
have been
tested.
Barclay
v
et
al.
[20]
temperatures noted:
built of
and
tested
2.2 K and 4.2
(i) frictional
heating
a
device
K, respectively. (mechanical 5 -
= w
which
operated These
contact),
at
source
limiting
(2) viscous
and
sink
factors
were
heating,
and
(3) mixing tested
owing
a double
device
acting
one-half
watt
Rotating
Magnetic
The
was tested
Heat
as
magnetic
rotates
through
magnetic
refrigerator The cold
and thermal
between
et al.
in
section
energy
[21]
1981.
This
is located
is rejected
from
1.8 K and 4.2 K and produced
at
each
nearly
capacity.
refrigerator in
Fig.
material.
3.
Fluid
high-field
A prototype
magnetic
C. Delpuech
Pumps
illustrated
porous
core.
and magnets.
column
of refrigeration
rotating
exchanger
cores
of the regenerator
The refrigerator
of the porous
reciprocating
has two paramagnetic
the middle end.
to the motion
is The
is
rim
pumped
and low-field
to test the rotary
arranged of
as
the
through
a
counterflow
wheel the
is
heat
composed
porous
rim
of
as
it
regions.
magnetic
heat pump
principle
was designed,
T
built was
and tested
in 1977
a forerunner
[23].
Also,
of
The
two
concentrated
heat
refrigeration
This
device
temperature
magnetic
operated
device
refrigerator
that
at room was
operating
temperature
reported between
on
about
and
in
1981
2 K and
[24].
main
problems
field
at
and controlling expected
a room
a rotating
4 K has been tested
[22].
one
with
rotary
location
on the
the flow of the fluid. transfer capacity
between of
400
a
wheel
These
the fluid W,
designs
obtaining
and a zero
problems,
and magnetic
Coefficient 6 -
are
of
field
along
a
high
elsewhere,
with
lower
material,
resulted
Performance
(COP)
than in a of
26
r
percent
of the Carnot
COP and a maximum
of 1000 W, 70 percent
and 40 K, respectively
that
might
the flow problem
would
be driven
A Different
through
Magnetic
the previous
w
T.
be alleviated
device
[26].
material
connected
operating
device
somewhat
the porous material
using
two categories,
Hashimoto
[23].
Barclay
goals
[25] has suggested
by using
by magnetic
to design
a ferrofluid
which
forces.
Heat Pump
One other current
L_
AT of 7 K as compared
is described
They to
magnetic
envision
one-way
a
heat
materials,
that does
in a 1984 patent refrigerator
pipes.
No
not fall
into
by H. Nakagome
and
composed published
of
a
accounts
magnetic of
an
have been located.
m
III.
Capital To
magnet
ECONOMIC
ESTIMATES
Cost Model obtain
economic
estimates
and a reciprocating
assumptions
were
the
magnetic
basic
porous
system
of
Fig.
core was chosen.
I with
Some
a steady
simplifying
made.
I)
The porous
2)
The
core just fills
the bore of the magnet
windings.
w
vacuum
field
of
the magnet
is
uniform
in
_÷
equal to that calculated
for the magnet -
7
-
center.
the
bore
with
a value
w
f
v
3)
Any
metallic
field
in
the
ellipsoid. 4)
The
The
6)
is
vacuum
The
same
voids
spatially
of magnetic manner
as
Demagnetization
magnet
adequate 5)
piece
averaged
the
demagnetization Eddy currents
8)
The
the
center
stacking
channels magnet
uniform
refrigeration
7)
by
for cooling at
responds
to
the
element
uniform of
a
applied
long
thin
coils
with
is negligible.
assembled
field
core
is
disk-shaped
and structural
center
current
rate
thin
members.
is calculated
using
a global
density.
proportional
to
the
frequency
of
of the core. are ignored.
coefficient
of
performance
is
the
maximum
COP:
There
are
no
irreversibilities.
The
logic that
of magnetic the
follows
material
superconducting
optimized uniform
to
provide
starts with
to satisfy cable the
is
a load
specification.
the load requirement chosen,
necessary
the
shape
field
at
of
Then
is found. the
minimum
Finally
magnet cable
the
after
solenoid
weight
is
(for
winding).
The refrigeration
rate
is (_L -- qL Mm f
where
amount
qL is the refrigeration
capacity
(1)
per unit mass
per each demagnetization,
Mm is the mass of the core magnetic -8-
metal,
and
of core magnetic
metal
a
7 V
f J
is the frequency
Therefore
of demagnetization.
the required
volume
of the magnetic
material
is
_L V
(2)
= m
where
Pm
is the density
for the porosity
qL f Pm
of the magnetic
metal
in non-porous
form.
of the core,
(3)
Vm = _ Vb where
Vb
is the volume
of the magnet
is the filling
The magnet where
Allowing
is illustrated
fraction
in more
bore,
and
of the magnetic
detail
metal
in the core.
in Fig. 4
Ro
is the outer radius
of the winding,
Ri
is the inner radius
of the winding,
L
is the length
J
is the globally
of the winding, averaged
current
density,
and
Bo = Bw = B is assumed. Defining R 0
(4)
R. l
L
(5)
# " 1
it follows
that Vb = 27r R3'] /9. -9
(6)
V
The windings
and their spacing
occupy
a volume,
given
Vw
by
(7)
Vw : (_2 _ I) V b.
The superconducting
cable has a volume
Vs
(B)
V s = 6 s Vw where
6s is the fraction
of the winding
volume
filled
with
superconducting
cable. A
typical
superconductor
superconducting necessary cable
alloy
to specify
cross-section
embedded
the cable which
cable
in
consists For
copper.
the
tiny
filaments
purposes
here,
Let 6sa be the fraction
in more detail.
is superconducting
of
alloy,
Vsa is the volume
of the superconducting
Defining
6
then
Vsa = 6Vw. Now
the
global
superconducting
average
alloy characteristic J
A complication
arises
density current
(10) (11) J
can
density,
be
related
to
sa (B)
qL = qL (B' TL) 10 -
the
known
Jsa-
= 6 Jsa
. J
of the
alloy.
in that qL and Jsa each depend
Jsa
is
(9)
_ 6sa 6s
current
it
then
Vsa = 6sa Vs where
of
(12)
on the field.
(13)
(14)
Thus
one must
equation
choose
(2),
equations
then
B, then
proceed
find the volume
to
find
the
of magnetic
optimum
material,
winding
shape
Vm, through
starting
with
(13) and (12).
Since Vm and Vsa (expected may seek to estimate
to be high cost variables)
the system cost
as a function
are coupled
by B one
of B.
Let C t be the total cost of the system
(15)
C t : Cm Mm + CsM s + Cst + Ca
.y
where
Cm
is the specific
cost of the magnetic
Cs
is the specific
cost of the superconducting
Cst
is the cost of the magnet
Ca
is the cost of the auxiliary
structure,
metal, cable,
and
equipment.
Assume Cs t + CsMs L
C1CsM s.
(16)
Define C _ CmPmVm + ClCs#sVs where
Pm
is
the
density
Ps
is the density
of
the
(17)
magnetic
material
in
non-porous
form, and
Rewrite
equation
(17) using
equations
of the superconducting
cable.
(3), (7) and (8):
C - CmPmVm
(18)
[I + P]
where IC1CsPsSsl p:[
Cm--_m?)(2_
-
L
11 -
(19) i).
L
L_
Cost Minimization
Recall
Logic
equation
(2).
_L V
=
--
m
The
application
Choose
the
Choose
B which
the
cable:
Choose
the
filling
B also
fixes
field
can
equations Cs,
B by minimizing
CI
to
Minimum
minimize
Radius
Following
CI
is
e for
Ratio,
#s,
" Jsa(B) the
that
magnetic
#m.
and
?,
6 s.
(18).
6sa-
•
cost
C of
(:2 not
metal,
TL).
(2)
fractions:
minimize
Assuming seeks
Jsa
and the
qL = qL (B,
in
Choose
Now one
f,
fixes
fixed
qL#m
QL, TL.
frequency,
Now Vm is
r
fixes
f
1)
the in
a sensitive
a given
magnet
equations
and magnetic (19)
function
and
of
material
for
given
(18).
the
design
variables,
one
B.
e
Reference
[28] for this type magnet B = J Ri F 12 -
we have
(20)
where
F is a form factor F = F (e,#)
1/2 -
°
(21)
where
#o is the magnetic
In equations relate
only
to
(20) and (21), the
shape
shape which minimizes The
latter
can
permeability
be
of
B and J have
the magnet:
e subject
recast
of vacuum. been
Ro,
R i, L.
to the constraints
in an
informative
fixed.
The parameters
One
seeks
of equations
manner.
Combine
to
e, #
find
the
(20) and
(21).
equations
(3),
(6), (12), (20) and (21) to get:
(22) F3 or, using equation
(2)
(23)
Since the parameters
on the right #-- =
have been fixed, constant.
(24)
F3
From equation One
typical
(21), #/F 3 is a function
can easily
curve
find
emi n subject
for e vs # is shown
of # associated
with
to
only
the constraint
in Fig. 5.
emin13 -
of e and #. in equation
Now let #min
stand
(24).
A
for the value
Optimum Magnet
Combine
Dimensions
equations
(3) and (6) after
inserting
the values
for emi n, #min to
get
-_
R
IvllJ 3
=
m 2_ _/ #min
(25)
R° = emi n Ri.
(26)
i
From equation
The "build"
(4)
of the winding
defined
as Ro - Ri, is
Ro - Ri " Ri (emin
From equation
E--
the inner and outer
Input Data Case
diameters
Ri.
(28)
are
Di = 2 Ri
(2g)
DO - 2 Ro
(3O)
I
For the parameters
of equation
(23),
Load Requirements:
QL " 3517 kw (1000 Tons of Refrigeration) f
(27)
(5), L = 2 #min
Of course
I).
= IHz
- 14
Geometric
Design: - .8
6 Magnetic
- .1125 (6 s = .g, 6sa - .125) Metal:
Gadolinium
Pm
= 7.9 x 103 Kg/m 3
Cm
= $200/Kg
qL
=
[.589B
- .0817 B3/2] KJ/Kg
B in Tesla, Superconducting
Ref.
m
[29].
Cable:
I part superconducting
alloy,
Ps
= 8.6 x 103 Kg/m 3
Cs
= $66/Kg,
Superconducting
Ref.
as given
= Jsa(B)
Jsa
= (5-90) 1010
- Equations
below.
(.773) B Amp/m2, 2.5T _ B _ 12T.
(18) and (19):
CmP m = 1.58 x 106 $/m 3 CsP s -
copper
Alloy:
Jsa
Formula
7 parts
[30].
for B in the range Cost
at T L = 280K
.568 x 106 $/m 3.
_ 15 _
Ref
[31].
Equation (18) becomes C = $(I.58E6) [I + Pmin] VM,
Where
Pmin is given by setting
Equation
e = emi n in equation
(31)
(19).
(19) becomes P - (.404)CI
In the above,
the cost
(emin 2
I).
(32)
of the Gd is: (33)
$(I.58E6)VM The cost of the superconducting
cable
is:
P (34) $(I.58E6)VM
The cost of the superconducting
magnet
---_1 •
is:
(35)
$(I.58E6)V M P.
Input Data Case
II
The only change
frequency
made for the second
by a factor
of 10.
- 16
evaluation
was to increase
the
Results The
cable
results
of
are given
magnet
in Tables
and the auxiliary
The magnet appropriate
cost
data.
Resonance
Imaging
length
those
the
the calculations
as
need
for
homogeneity hand,
the
withstand
cost
equipment
There
in Tables
of
large
a large
commercial
over
not so critical will
forces
uncertainty
Gadolinium
and the
for the costs
a
the
of the
same
of the lack of
for bore
are strongly
relatively
in magnetic
the
because
magnets
MRI costs
escalate as
bore
of about
The
homogeneity
the latter
estimates
warm
applications
I and 2.
internal
with
of the
[30].
have
are
and other
is probably
the costs
I and 2, along
estimates
field
for
large
heat
due to the Gadolinium
is
Magnetic
diameter
and
escalated
volume.
pumps. need
the
by
Field
On the other
of the magnet
withdrawn
from
to the
magnet. For the cost of the magnet,
Cs + Cst, we have
Cs + Cst - $(14B
This
m_
cost
shape
and
costs
of
system, quantity from
formula
size a rack
both
fits
similar of
used
production
high quantity
fairly
to those
electronics for the and
do
well
,
of the
include
manufacturing.
- 17
non-MRI
! and 2.
and a closed-loop
the
used the expression:
B in Tesla.
to marketed
of Tables
operation not
+ 19)k
simply
The
liquid
magnet.
The
significant
magnets
$19k helium costs
with
bore
represents
the
refrigeration reflect
reductions
small
expected
o
.
Table
1.
Capital
Cost
Estimates
Vs.
Applied
Field,
f
= 1 Hz.
3_TT
6T
9T
.3315
.1908
.1438
_/F 3, A6/N 3
7.036E25
4.970E23
1.093E22
emi n
1.00265
1.01384
1.04972
_min
1.4
1.4
1.45
Vm, m3
R i, cm
36.12
Ro-R i, cm L, cm Cost,
Gd $
Cost,
Cable,
.0957 101.1 524k $
Cost of Magnet,
s
Cost of Auxiliaries Cost of System,
Table
$
2.
Capital
12__!T
3.819E20 1.15458 1.5 25.24
30.04
27.02
.416 84.1
1.112 78.4
301k
.1212
3.90 75.7 192k
227k
1.1k
3.4k
9.4k
25.8k
61k
I03k
145k
187k
30k
30k
30k
30k
615k
434k
402k
409k
Cost
Estimates
vs. Applied
Field,
f - 10 Hz
3T
6T
9T
12T
.03315
.01908
.01438
.01212
_/F 3, A6/N 3
7.036E24
4.970E22
1.093E21
3.819E19
emi n
1.00572
1.02991
1.10808
_min
1.4
1.45
1.5
Vm, m3
R i, cm Ro-Ri, L, cm Cost,
cm Gd, $
Cost, Cable,
$
Cost of Magnet,
Cost of Auxiliaries, Cost of System,
$
$
1.65 ]1.34
16.76
13.77
12.39
.0959 46.9
.419" 39.9
1.339 37.2
37.4
52.4k
30.Ik
22.7k
19.2k
2.1k
6.2k
.2k $
1.3425
.7k
3.89
61k
103k
145k
187k
30k
30k
30k
30k
143k
163k
198k
236k
- 18-
L
Separately
listed
to drive
the motion
magnetic
refrigerator
and the work
operates
of 377 kN with level
vertical,
the
estimated
level
Even
the
length a peak
would
be
about
weight
of
the
37.7
with
the
steel
5 cm
(an
effect
internal 3-4
rod of
say
end
of the
each each
would
neglected
latching
(Fig.
I),
needed
to
mechanical drivers.
must
it may
be
diameter
use only
between
forces
core). a small
I and
the core
the
be
COP is 9.33,
force
would
be on
At f = 10 Hz, the
actual
added,
ideal
be 377 kJ of work
high.
the
power
possible
motion
which
would
be
increases
the
2).
would
If
f -
to
have
i) can
actuators. suffice
the rods
percentage
by
with
non-magnetic
as the
major
had
traverse
to
of the volume
However,
the major
A
be met
using
driver
the
available
some
walls
in paths
drivers
attached
kind
of
1-2 and to
the
column.
column
costs
valves
relative
requirements
The initial
(B = 3T,
and the regenerator
set of piston/cylinders, move
Since
If the
ideal
the average
twice as
electromagnetic
metal
in Tables
ends of the regenerator Another
about kN.
greatest
stainless
column,
I m, then
Gadolinium
and
fluid
the
required
about 8%.
case
on
and 310K,
system
core.
MW load at f - I Hz would
force
piston/cylinders
rod
280K
were
hydraulic
(one
is t_e mechanical
and the magnetic
between
for a 35.17
If the stroke
the order
equipment
of the regenerator
required
per cycle.
average
as auxiliary
to
here
estimated
the
are
and rods core much
(the minor
in paths smaller
for the mechanical
- 19 -
2-3 than
system
drivers) and
for
4-I. the
are [39]:
are The
major
$ 6k
two cylinders
4k
two pumps
6k
valves
4k
controller
10k TOTAL
Operating
An of
ideal
thermodynamic
irreversibilities
increase
cost
with
A serious
power
efficiency much
better
motors,
cycle
due
and other
advantage
shaft
$ 30k
Cost
Gadolinium
do
miscellaneous
to
causes
cycle
has been
core/fluid
to cylinder is about
80%
efficiencies
and valves
assessed
and will
of higher frequency
offset
observed
power.
[39].
system
higher
look_ very encouraging
- 20 -
the
[39].
The
some
in
the
irreversibilites
extent
the
in the conversion
systems
existing
pressures
currents
effects
capital
I and 2.
In conventional
However,
by using
to
quantitative eddy
yet.
in Tables
in the mechanical
rod
The
interactions,
have not been
frequency
loss occurs
assumed.
trend
and very
this
of motor
conversion
in hydraulics efficient
to
pumps,
IV.
The
conceptual
reciprocating
a dissertation treat
the
transient
design
core
superconducting
selected
for
in a regenerative
magnet
regenerator
detailed
fluid
as in Fig. I.
in progress
column
The analysis
by one of the authors
fluid
and
core
using
system
within
the bore
is the subject, [32].
a
analysis
The first
simplified
is
the
of a steady in part,
of
task was to
one-dimensional,
model.
The assumptions I.
REGENERATOR COLUMN
The core
in the model is assumed
are:
to have a porous
structure
composed
of gadolinium
w
having 2.
a uniform
Temperature of motion
gradients
equilibrium
3.
Viscous
4.
Fluid properties
5.
The magnetic
6.
in the
are negligible.
in thermal
steady
porosity.
forces
magnetic
forces
are independent intensity,
of the gadolinium
field
normal
to the direction
and gadolinium
in the
The gadolinium
H, is a known
function
of position
to be the vacuum
field
of the magnet.
is a known
and the fluid - 21 -
m
and
of temperature.
function
of temperature
intensity. is rigid
are
are ignored.
_=
7.
core
in any cross-section.
and inertial
field
and core
The fluid
in time, and is taken
The entropy
fluid
is incompressible.
and
8.
The velocity
of the core with respect to the regenerator column is
constant during core traversals 9.
There is no dwell time. motion relative
10.
Any effects
Either the core or column (or both) is in
to the magnet at all
of magnetically
The thermodynamic properties Brown [2],
The relation
and the internal ellipsoid
times.
induced eddy currents are negligible. of gadolinium are given by Griffel
and Benford and Brown [34].
for magnetic materials [36].
in the column.
The general thermodynamic relations
are given by Hatsopoulos and Keenan [35] and Booker
between the applied fields
fields
(no magnetic material
present)
in the gadolinium in place is taken to be that of an
of gadolinium [37,38] with no demagnetization effect.
To write the energy balance, fix
a reference frame (x) to the left
the column in Fig. I and assumethe Gd core is moving to the right V.
[33],
For a differential
auI
_-_
end of
with speed
control volume located at x in this frame
: Q + W + Net Enthalpy
Input
(36)
Rate
CV
au
I cv
*j aH = _
ah I m cv " PmAm Ax _ + #fAfax
ahf (37)
at
I'Tml 'Ti]m ,A,f I'T
aTf
(_=kA m
m
ax
x + Ax
ax
x + Ax
x
dM : Am r% Ax H--dt
- 22 -
ax
(38)
(39)
Net Enthalpy where
Input Rate - -
U is the internal
hx + Ax
hxlm PmAmV"
lhx +Ax"
hxlf
energy,
t is the time,
is the thermal
power,
is the rate of magnetic
work,
H* is the enthalpy,
h is the specific
enthalpy,
m, f are subscripts
for magnetic
metal,
fluid,
# is the density,
Am, f is the cross-section k is the thermal
area of metal
or fluid,
conductivity,
T is the temperature,
Po is the magnetic H is the magnetic
permeability
of free space,
intensity,
M is the magnetization, V is the metal speed,
relative
to the column,
Vf is the fluid speed
in the core,
u
23 -
relative
and
to the column.
#fAfVf
(40)
In this model the two magnetic vectors are colinear. Combining the equations, dividing
by AAx, and taking the limit,
one
obtains
Pm (I-()
E°hm 1 dt
/_oVm
dT
+ pfCpf
E°Tf l
a2Tm k (I-() _ m ax 2
where
is the porosity
Cp is the constant and use has been made
volume defined
(1-()V
a2Tf (41)
+ kf E
A is the column cross-section
vm is the specific
E a-t-
ax 2
area,
of the solid, by E _ Af/A,
pressure
specific
heat,
of the relations: dh = C dT P
d dt
a = a_
- 24 -
a + V a--_
(42)
It is convenient to change variables of Gd are available
because the thermodynamic properties
[33,34] in the form of the entropy function s - s(T,P,H)
at atmospheric pressure.
From Ref. [35], Tds = dh - _ovHdM-vdP
(43)
so that for the metal in a constant pressure process,
ds P = I dt dhm T _-_
_oVmHdM
(44)
L
which
is the factor to be transformed.
From calculus,
at constant
pressure,
_si.T[a.] dT [as I d_vH_ _4s_
T_-_
P
_
By this transformation
p,vH
dE
of variables,
+ T
_
the energy
p,T
equation
dt
becomes,
after
letting
Tf = Tm,
[
OS
Pm (l-E)
+
#mT
{I
T
+
a-T p, vH
_
#fE Cpf
#fCpf
Ot
8--_
p,vH
[
#m (I-E)
T
{osl a(vH)
8tS(vH) + V
8--x---a(vH) ]] = [kf E + km(1-E)]
p,T
The factor
a(vH) St
+V
a(vH) ax
- 25
a2Tax 2
is the total The first
change in the field
intensity
term appears because the field
the column due to the column motion.
observed at the magnetic material.
appears to be time varying relative
to
This term can be referenced to the magnet
fixed coordinate (X) which removes the time varying component. Then
a--t-_
a--x--
--
aX
(47)
Vbs
=
where
Vab s = Vco I + V.
If E = I, there
Vco I is the speed
of the column
is no Gd and the equation
relative
to the magnet.
is
aT
a2T (48)
#f as expected,
then the energy
The boundary
conditions
I.
At the regenerator
Initially
2.
Cpf_-_
change
-
kf--ax 2
is due only to conduction
in the fluid.
are: column
adibatic,
ends:
aT --:0; 8x
then
later
isothermal,
T = fixed.
At the Gd core ends:
Tcore " Tflui d
w
o
aT I
[km(1-( ) + kfE] _-_ ore -
These conditions
represent
kf
(49)
aT Ifluid _
the continuity
- 26 -
of temperature
and heat flux.
Initially,
the core and regenerator column are in thermal equilibrium
the temperature of the environment. mechanical cycle of Fig. I will
The column ends are adiabatic
cause a temperature gradient
regenerator column, the left
end being the hotter.
not a cycle
each mechanical cycle,
differs. thermal
because after
However, eventually conduction
limits
so that the
to develop in the
The thermodynamic path is the temperature
a thermodynamic cycle should result
in the fluid
at
profile
as the axial
the maximumtemperature difference
between the column ends. After the column ends have reached temperatures suitable
for refrigeration,
the column ends are to be put into appropriate thermal contact with the source and sink of the refrigeration calculations walls
included thermal reservoirs
at the column ends.
conduction in the fluid Solution finite
scheme. As a step in that direction, in contact with perfectly
Heat transfer
with
diathermal
the reservoirs
occurs via
and Gd.
of the energy equation was implemented on a computer using a
difference
scheme.
Non-dimensionalizing
This proved to be very difficult of global
the first
geometric
scales that
the equation was attempted.
due to non-constant coefficients can be used for
references.
and the lack Therefore a
dimensional approach was used initially. Someimplementation difficulties,
discussed more completely later 27 -
[32], are
categorized
(I)
as:
Node Types. The
finite
difference
regenerator the nodes node
column.
are
As the core
changes.
location.
nodes
Also,
picked
moves
to
along
the core-fluid
The numerical
scheme
be
relative
the column
boundary
must
fixed
is
recognize
to
the
the character
in general different
of
not at a node
types
w
and
use
various
bookkeeping (2)
Stability This
schemes
problems
to
with
calculate
new
temperatures.
This
leads
to
the nodes.
and Convergence.
is
the
usual
problem
with
the
ratio
of
step
sizes.
The
space
w
increment
is chosen
arbitrarily
keep the coefficients is
also
fraction (3)
checked
difference
and column
tions.
that
the
core
increment
scheme
positive.
advances
through
At
is computed
The
the
increment
column
by
a
to
At set
Terms.
The convective
core
in the numerical
time
of a space step.
Convective
upwind
so
and the
A higher
terms
[those with _-_ aT]
to improve
changes
sign,
stability.
had to be replaced As V, the relative
aT the _-_ terms
order difference
change
was also tried
28-
relative
with
a one-sided
velocity
between
to the upwind
but did not improve
direc-
stability.
Results
Adiabatic
Ao
Some
Column
initial
component
water,
The
time
and
operating
at
At
is
length
by
of by
0.80.
vacuum
given
a
the
model
Im,
are
of
American
of the
cylinder
the
given that
core,
volume.
The
field
Equilibrium
independently
alcohol
area)
adiabatic.
from
chosen
has
methyl
area/section
in
was
column half
Initial Thermal
predictions
sizing
regenerator
Ends,
in
The
porosity
and
ends
(see
Figs.
Section
O.2m.
superconducting
Magnetics
in
The of
of
Appendix)
the
III.
The is
half
core
(open
regenerator
is
for
The
fluid
the
magnet
6-8.
assumed
their
are
constant
8 Tesla
unit
6T maximum.
the
start
of
temperature
at
from
magnet
center
and
magnet
are
the
295K.
first
The
end
and the
core
cycle, of
concentric,
the
the
fluid
and
regenerator
is
near
and
the
that
nearest
end.
core
gadolinium
After
is
are
to
the
uniform
magnet
a half-cycle,
near
the
other
end
the
magnet
is
is
O.Im/s
orzero.
in
is
Im
the
core
of
the
w
regenerator. Also, period step
the
The speed
is
37
the
core
seconds
6 shows
15 cycles.
During
and regenerator near
of
with
the
column
relative
relative no
to
pauses
the
and
to magnet
with
velocities
given
O.Im/s
by
or
zero.
The
cycle
appropriate
functions. Fig.
in
of
speed
end of
the
temperature
this
computer
end was 5cm at the
column
profile
at
the
run,
each start
end. of - 29
within the
the
minimum The column
a cycle.
regenerator separation position,
The drop
in
after
14.5
and
between
the
0.00,
marks
the
at
the
temperature
core
other
end
between
gadolinium
from
the mechanical column,
w
axial
but
the
7 shows The
At present mixing.
effect
by repositioning includes
gradients
and minimum
isothermal
close
cooling
at
the
removing
column
thermal
the
of
to
complete
conduction
column
ends
the
in the
reveal
that
effect. temperatures
sections
The curvatures
but TH-T L is already
the
the model
The
the maximum nearly
shows
(followed
has a minor
conduction.
Pappel
profiles
magnet
excludes
half-cycle. axial
two
cycle).
conduction Fig.
the
suggest
to the value
again
that
in the column
reveal
the minor
asymptotes
found
will
be
in the experiment
at
each
effect
of
approached,
by
Brown
and
[3].
Fig. 8 gives the gadolinium
the results
of a run in which
and the ends of the regenerator.
ends are now changing
by a larger
B.
Ends,
Isothermal
The
Column
column
is
amount with
Initial
operated
Internal
there
is no dead
space
The temperatures
between
at the column
each cycle.
Thermal
adiabatically
Gradients
as
before
until
the
highest
w
temperature column
in the
column
below
280K.
goes
diathermally
n
to
the
by holding
core
to travel
transfers
thermal
energy
above
Then
hot
computationally is assumed
goes
and
and
reservoirs cold
the end the entire
directly
ends,
nodes
to
the at
lowest
310K
the
temperature
and
280K
respectively.
of the column
column
- 30 W
310K
length
at 310K
so at various
reservoirs.
The
are
in
coupled
This
is
and
280K.
times
heat
the
done The
the core
transfer
is
calculated increment
from
the temperature
of time.
This
gradient
is summed
into the cold end and the energy
cycle
is achieved,
and conductivity
over
a mechanical
rejected
the difference
at each
cycle
at the hot end.
in these
two quantities
end for each
to get
Once
the energy
a thermodynamic
equals
the work
into
the system. Figure cycle
versus
0.50. the
9
QH
shows
the
the number
is the heat
source.
exchange
of successive
transfer
It appears
achievement
energy
that
of thermodynamic
with
the
mechanical
at the sink asymptotic
reservoirs
cycles.
The
per mechanical
values
may
per
porosity
cycle,
occur,
mechanical
thus
is now
and QL
is at
signalling
the
cycling.
w
In Fig.
10, the values of
QL QH - QL
are plotted does
versus
not represent
been obtained.
asymptotic
the number the work
However
approach
of successive involved
mechanical
because
cycles.
a thermodynamic
The denominator cycle
has not yet
the data of Figs. 9 and 10 are not inconsistent
to
a COP
in the vicinity
of
the
ideal
COP
of
with
9.33
an
for
a
M
Carnot
refrigerator
with
reservoirs
at 310K and 280K.
L
Such of
a limit will
the Gd execute
shown
in Fig.
mechanical
not be reached
different
11 for three
in this model
thermodynamic
sections
(left
cycle. - 31 -
i
paths.
because
different
The thermodynamic
end, middle,
right
end)
sections paths
are
for the 30th
The differ same
program
by less criteria
different
core
is stopped
arbitrarily
than
I% from their
for
program
respective
cut-off
porosities.
when
was
The results
both
QH and
values
used
in
are given
QL
in the
in the
(N-1)th
calculations
Nth cycle
cycle.
starting
The with
in Fig. 12, where
QL QH - QL
is plotted
versus
core
porosity.
Any
since Figs. 9 and 10 suggest
a closer
The
may
result
Carnot
at
low
porosity
limit
of
9.33,
Clarification
of
this
because
not a
conclusions approach
be
in
be
drawn
to the asymptote
error
thermodynamic
should
even
cycle
though has
cautiously
may be needed. it
exceeds
not been
the
achieved.
w
two-temperature
was
not
Large conventional an
electric
Performance
of
because
research
has
been
started
on
a
model.
V.
$150k,
pursued
DISCUSSION/CONCLUSION
chillers operating
5.86
and
an
(1000 ton : 3.517 use
ideal
near
COP
600
of
kW,
10 when
MW) have an
a capital
actual
operating
cost near
Coefficient between
280K
of and
308K. The
estimated
system
capital
costs
for
ideal
magnetic
refrigeration
w
systems -approaches
of
the
same
capacity
10Hz, as shown
in Table
become 2. - 32
comparable
as
the
cycle
frequency
A
significant
regenerator increase
due
with
to
driven material w
Neither
the
cost
been
and considerably been
costs
(Gd in this have
made
relative
to
is
that
motion
Such
of
the the
irreversibilities fluid
irreversibilites
and
the
in
porous
have not yet been
the metal
treated
of the regenerator.
capital by
the
trend
cycle frequency.
in our modelling The
counter
for
and
magnetic
refrigeration
temperature-entropy
report)
cost
Magnetic
materials
are available
incorporate
cost
system
characteristics
and by the structure/assembly
optimized. less
the
of
costs
of slightly
which
the
to
magnetic
performance
No attempt
accompany
be
of the magnet.
less
and may be suitable.
reductions
appear
high
has
quantity
manufacturing. Future estimate
effort
toward
may not be warranted
reducing until
have been completed.
The appropriate
case,
program
an experimental
would
the
uncertainties
estimates
the
of the COP of actual
literature be necessary.
33-
in
to do so seems
magnet
cost
regenerators
scarce.
In any
Vl.
i. Brown,
G. V.,
Applied
2. Brown,
"Magnetic
Physics,
G. V.,
Materials,"
Heat
REFERENCES
Pumping
Vol. 47, 1976,
"Magnetic
Room
Temperature,"
Journal
of
pp. 3673-3680.
Stirling
IEEE Transactions
Near
Cycles
- A New Application
on Maqnetics,
Vol.
Mag
for Magnetic
13, 1977,
pp. 1146-
1148.
3. Brown,
G. V. and Papell,
Magnetic
4. Weiss,
Refrigerator
Pierre,
lorique," m
5. Edison,
w
u
6. Tesla,
Vol.
and Heat
and Piccard,
ComDtes
Sciences,
Rendus
166, 1918,
T., British
P.,
"Einige
Temperature,"
Annalen
Pump,"
Auguste,
Tests
unpublished,
of a Room Temperature 1978.
"Sur un Nouveau
Hebdomadaires
Des
Phenomene
Seances
De
Magnetoca-
L'Academie
Des
pp. 352-354.
Patent
W., U.S. Patent
7. Debye,
S. S., "Regeneration
16709,
428,057,
1887.
1890.
Bemerkungen Der Physik,
zur
Magnetisierung
Vol. 81, 1926,
bei
tiefer
pp. 1154-1160.
w
8. Giauque, A
W.
Proposed
Absolute,"
F.,
"A Thermodynamic
Method Journal
of
Treatment
Producing
of the American
of Certain
Temperatures Chemical
i1864-1870. 34 -
Magnetic
Considerably
Society,
Vol.
49,
Effects. Below
I°
1927,
pp.
w
9. Giauque,
W.
F. and MacDougall,
D. P., Letter,
Physical
Review,
Vol.
43,
1933, p. 768.
10. Heer,
C. V., Barnes,
of a Magnetic Review
C.
B., and Daunt,
Refrigerator
of Scientific
J. G.,
for Maintaining
Instruments,
"The
Design
Temperatures
and Operation
Below
I K,"
The
Vol. 25, 1954, pp. 1088-1098•
W
11 • Zimmerman m
, J .... E , McNutt,
Refrigerator
Employing
J
D
,
and
Superconducting
Bohm,
H . V.,
Solenoids,"
"A
Magnetic
.C_ZY_O_g__Cb__=, Vol.
2,
1962, pp. 153-159.
r--
JW
12. Rosenblum,
S.
Refrigeration
S.,
Sheinberg,
H.,
at i0 mK using Adiabatic
and
Steyert,
W.
A.,
Demagnetization,"
"Continuous
Gryoqenics,
Vol.
16, 1976, pp. 245-246.
13. Barclay,
J.
A.
Applications," Conference,
14. Barclay,
Genova,
J.
15. Barclay,
Steyert,
Proceedinqs
A.
Intersociety Francisco,
and
"Magnetic
California,
A.,
Refrigerators,"
of
International
on
July
13-15,
Alamos
of
Refrigeration Cryoqenlc
for
Space
Enqineer_ng
1980, pp. 213-217.
_nvironmenta!
for
Spacecraft
Systems,
ASME
Systems," preprints,
11th San
1981.
Liquefaction
National
1981. - 35 w
"Magnetic
Refrigeration
"An Analysis Los
A.,
Italy, June 3-6,
Conference
J.
W.
of
Laboratory,
Helium Report
Using
Magnetic
LA-8991,
Dec.
16. Johnson, D. L., "Magnetic Refrigeration Te]ecQmmunications Propulsion
17. Mills,
Laboratory,
J.
Cycles
for
18. Van
19. Brown, Heat
J.
R.,
Research
Pumps,"
20. Barclay,
Heat
Haaften,
Vol.
42-67,
Nov.-Dec.
D. H.,
Recovery,"
Study
of
a
Supplements,
Principles
3,
19th San
N82
1981,
Th____e
20119,
Jet
pp. 29-38.
"Magnetic
Heat
Intersociety
Francisco,
Pump
Enerqy
California,
0.,
and
Magnetic
Refrigerating
No. 6, 1966,
pp. 1-105.
and Possible
Transactions,
Moze,
New
Configurations
Cycle,"
of Magnetic
Vol. 87, Pt. 2, 1981, pp. 783-793.
Paterson,
for 2-4 K Operation:
Vol.
21. Delpuech,
"A
"Basic
A.,
Refrigerator
California,
Conference,
Reports
ASHRAE
J.
Report
Cooling,"
1984, pp. 1369-1374.
G. V.,
Physics,
Waste
Enqineerinq
Geuns,
Acquisition
L. D., and Van
Industrial
19-24,
Phillips
Data
Pasadena,
I., Kirol,
Conversion August
and
for Maser Amplifier
L.,
Initial
"A
Reciprocating
Results,"
Journal
Magnetic of
Applied
50, 1979, pp. 5870-5877.
C., Beranger,
R., Bon Mardion,
G., Claudet,
G., and Lacaze,
A.
i
A.,
"Double
Experiments,"
22. Rosenblum, Magnetic National
Acting
Reciprocating
Cryoqenics,
Vol. 21, 1981,
S . S. , Steyert, Refrigerator Laboratory,
Magnetic
W . A . , and
Operating Report
Near
LA-6581, - 36 -
u
w
Refrigerator:
First
pp. 579-584.
Pratt, Room
May 1977.
W.
P., Jr . , "A
Temperature,"
Continuous Los
Alamos
23. Barclay,
J. A. and Steyert,
Electric April
W. A.,
"Magnetic Refrigerator
Power Research Institute,
Development,"
Final Report EL-1757, Project
7867-I,
1981.
24. Pratt,
W. P., Jr.,
Rosenblum, S. S., Steyert,
"A Continuous Demagnetization Refrigerator of Magnetic Refrig'erants,"
25. Barclay,
J.
Magnetic
A.,
"Use
_,
of
Refrigerator,"
a
W. A., and Barclay, J. A.,
Operating near 2 K and a Study
Vol. 17, 1977, pp. 689-693.
Ferrofluid
Journal
of
as
the
Heat-exchange
Fluid
in
Applied
Physics,
Vol.
53,
1982,
Patent
4,464,903,
Aug.
14, 1984.
a
pp.
2887-2984.
m
26. Nakogome,
H. and Hashimoto,
27. Larbalestier,
D.,
Fisk,
G.,
field Superconductivity,"
28. Wilson,
M.,
T., U.S.
Montgomery,
Physics
Superconductinq
Today,
Maqnets,
B.,
and
Hawksworth,
Vol. 39, 1986,
Oxford
University
D.,
"High-
pp. 24-33.
Press,
New
York,
1983.
29. An approximation calculations
using As data
for Fig. 5 of Ref.
30. Conversations
with
31. Wilson,
ibid.,
densities
M.,
(qL = TAs)
various
Fig.
computer
[34].
commercial
12-17,
for niobium-tin." - 37
w
from Brown's
suppliers.
"The
best
recorded
critical-current
32.Smith,
M. M. Ph.D., dissertation
33. Griffel, Physical
M.,
et al.,
in progress,
"The Heat Capacity
Revie.______w, Vol. 93, 1954,
34. Benford,
S.M.
and
Brown,
Curie Temperature,"
G.
Journal
Georgia
Tech.
of Gadolinium
from
15 to 355OK, "
pp. 657-661.
V.,
"T-S
of Applied
Diagram
for
Gadolinium
Physics,
Vol.
J.
Principles
52,
Near
1981,
the
pp. 2110-
2112.
35. Hatsopoulos,
G.
ThermodYnamics,
36. Booker,
H.
Engineers,
G.
N.,
Wiley,
Keenan,
New York,
Enerqv
London
and
in
Peter
37. Moon,
F., Maqneto-Solid
Mechanics,
38. Chen,
C. W., Maqnetism
and Metallurqy
Holland,
39.
Amsterdam
Conversations Georgia
and New York,
with
Institute
J.
W.
Of
General
1965.
Electromaqnetism,
and New York,
H.,
the
Peregrinus
Wiley,
Institute Ltd.,
New York,
of
Electrical
New York,
1982.
1984.
of Soft
MaQnetic
Instructor
in
Materials,
North
1977.
Brazell,
of Technology.
m
38-
Mechanical
Design,
Regenerator THigh_
Magnet
Column I TLow
_Core
Fluid-J_
2
w
3
4
u
Fig.
1.
Cycle Magnetic
Motion Heat
of
a Reciprocating Pump,
Tc
F
_
u
E
Zero
Total
Fig.
2.
A Theoretical of the Magnetic
Field
Entropy
Reversible Material
Thermodynamic in the Core
- 4C
-
Cycle
High Field Region
f
() ---
_h
KTL J
Low
Region
m
L--
Fluid
Field
Fig.
3.
Schematic Magnetic
of Heat
a
w
__m
-41 w
-
Rotating Pump
Pump
L
"i
\ \
\
I !
Ro
\ \
Ri
I Bo l
I
=
I
!
\ \
i !
/ 7
=
Bw
/ /
/
Fig. 4. w
,wT...-
Schematic
of
the
Magnet
Winding
2.5
q
2.0
m
;9 F3
(_min
°_,,_
[]
0
0 C_
0 _:_ 0 o
ck_
d
[]
I o
I 0
I
I
I
t
I
I
I
0 o
I
o
o
o
o
o
o
0
o
o
0
o_
o6
e-
_5
u6
#
o"J.
od
,_
o
I-....4
cto_s
_.I_.IFOad
1_
w
I
50
_b -
o_
--
APPENDIX The magnetic below.
The
arbitrarily
field
profile
_
--
--
--
--
--
--
for
multiplied Distance
profile an
by 3/4.
for the modelling
8T
magnet
The values
from center,m
supplied
of the regenerator by
American
Tesla
0.0000
6.000
0.0127
5.966
0.0254
5.850
0.0381
5.700
0.0508
5.275
0.0635
4.669
0.0762
3.776
0.0889
2.729
0.1016
1.829
0.1143
1.210
0.1270
0.818
0.1397
0.572
0.1524
0.413
0.1651
0.308
0.1778
0.236
0.1905
0.184
0.2032
0.147
0.2159
0.119
0.2286
0.098
0.2413
0.082
0.2540
0.0691
0.2667
0.059
0.2794
0.051
0.2921
0.045
0.3048
0.038 - 51 -
Magnetics
are for the axis locations. Field,
is given was