Refrigeration and
cryogenics
Zakład Kriogeniki i Technologii Gazowych
Dr hab. inż. Maciej Chorowski, prof. PWr
Methods of lowering the
temperature



Isentropic expansion
Joule-Thomson expansion
Free expansion – gas exhaust
Gas isentropic expansion with external work
T
p1
p2
h1
1
h2
K
2'
2
S
Gas isentropic expansion with external work
Drop of the gas temperature:
Entropy is a function of pressure and temperature
S= S(p, T)
Total differential must be equal to zero:
 S 
 S 
dS    dT    dp  0
 T  p
 p T
Differential effect of isentropic expansion ms shows the change in temperature
with respect to the change of pressure:
 dT 
m s   
 dp  S
 S 
 
p T


 S 


 T  p
Gas isentropic expansion with external work
We know from thermodynamics
 S 
 v 
    
 T  p
 p T
cp
 S 
  
 T  p T
 dT 
m s   
 dp  S
 v 
T

 T  p Tb


cp
cp
We get
where: b is coefficient of cubical expansion
1   
b  
  T  p
Gas isentropic expansion with external
work
For the ideal gas:
ms 
After integration
T2  p2 
  
T 1  p1 
 1 T
 p
 1

Piston expander
3
5
2
1
p1
4
6
p2
GAZ
p1, T1, h1
GAZ
p2, T2, h2
Cryogenic turboexpander
GAZ
p1, T1, h1
GAZ
p2
T2
h2
Isenthalpic – Joule-Thomson - expansion


When gas, vapour or liquid
expands adiabatically in an
open system without doing
any external work, and
there is no increment in
velocity on the system
reference surface, the
process is referred to as
throttle expansion.
In practice, this process is
implemented by installing
in the gas stream some
hydraulic resistance such as
throttling valve, gate,
calibrated orifice, capillary,
and so on.
1
2
w1
w2
p
p1
p2
q12 


1 2
w2  w12  g z 2  z1   h2  h1  l12
2
Isenthalpic – Joule-Thomson - expansion
T
p1
p2
h
1
T1
T
T2
2
h'
K
S
Isenthalpic – Joule-Thomson - expansion
Temperature drop in Isenthalpic – Joule-Thomson - expansion
Enthalpy is a function of pressure and temperature:
h= h(p, T)
Total differential must be equal to zero:
 h 
 h 
dh    dp    dT
 t  p
 p  T
Differential throttling effect μh:
 dT 
m h   
 dp  h
 h 
 
 p  T

 h 


 T  p
Isenthalpic – Joule-Thomson - expansion
p, MPa
100,0
Ar
50,0
25,0
Ne
10,0
5,0
H2
2,5
powietrze
N2
1,0
He
0,5
3
5
10
25
50
100
250
500
1000
T, K
Isenthalpic – Joule-Thomson - expansion
Gas
Maximal inversion temperature, K
eksperyment
z równania van der Walsa
Argon
765
-----
Azot
604
837
Hel – 3
39
-----
Hel – 4
46
34,3
Neon
230
-----
Powietrze
650
895
Metan
953
-----
Tlen
771
1090
204,6
223
Wodór
Free expansion (exhaust)
V0
T0,p0
V1
pf
pf
p f V2
pf
Free expansion (exhaust)
1.
2.
3.
4.
Adiabatic process
Non equilibrium process – gas pressure and
external pressure are not the same
Constant external pressure (pf= const.)
External work against pressure pf
Free expansion (exhaust)
Final gas temperature:
I Law of Thermodynamics
u f  u0   p f (v f  v0 )
where:
u0, uf – initial and final gas internal energy
v0, vf – initial and final gas volume
Free expansion (exhaust)
For ideal gas:
u f  u 0  c v (T f  T0 )
p 0 v0  RT0
p f v f  RT f
cv  R /   1
We get:

 1  p f
T f  To 
T0 
 1

 p0

T0
k

T f 1   p f / p 0 k  1
Comparison of the processes for air
Cryogenic gas
refrigerators
Heat exchangers
Recuperative
Regenerative
Comparison of coolers
Refrigerators with recuperative heat
exchangers
Joule – Thomson refrigerators
Examples of miniature Joule-Thomson
refrigerator
Claude refrigerators
Stirling coolers
Stirling cooler
Stirling cooler
p
p max
In Stirling refrigerator a cycle consists of two
isotherms and two isobars
2
T0
1
3
p min
T0
q H2O
1
2
qH2O
T
q
4
T
R
R
R
R
3
4
q
Stirling cycle is realized in
four steps :
1.
Step 1-2: Isothermal
gas compression in
warm chamber
2.
Step 2-3: Isochoric gas
cooling in regenerator
3.
Step 3-4:Isothermal gas
expansion with
external work
4.
Step 4-1: Isochoric gas
heating in regenerator
V2
V1
V
T
qH2O
2
T0
1
V2
V1
T
3
q
4
s
Stirling split cooler
Stirling cooler with linear motor
Efficiency of Stirling cooler filled
with ideal gas
 Str
q
T


lc  le T0  T
v2
v2
dv
l c    RT o
 RT o ln
v
v1
v1
v1
dv
v1
le    RT
 RT ln
v
v2
v2
v2
q   RT ln
v1
Work of isothermal
compression
Work of isothermal
expansion
Heat of isothermal
expansion
Stirling cooler configuration:
Stirling
cooler
used for
air
liquefact
-ion
Stirling cooler used for air
liquefaction
Two stage Stirling refrigerator
Gifforda – McMahon cooler
Gifforda – McMahon cooler
Four steps of McMahon cycle:
1.
Filling .
2.
Gas displacement
3.
Free exhaust of the gas
4.
Discharge of cold chamber
Efficiency of McMahon cooler:
 GM
T  p1 / p 2  1

To p1 / p 2  T  ln  p1 / p 2 
McMahon refrigerator
Combination of McMahon and J-T
cooler, 250 mW at 2,5 K
Pulse tube – free exhaust
V0
T0,p0
V1
pf
pf
p f V2
pf
Scheme of pulse tube cooler
Development of pulse tube coolers
Gifford, 1963, rather
curiosity that efficient
cooler
Kittel, Radebaugh, 1983
orifice pulse tube
Dr. Zhu et. al., 1994, multiply
by-pass pulse tube
Comparison of Stirling and orifice
pulse tube cooler
Pulse tube cooler for 77 K
applications
Weight:2.4 kg
Dimensions (l x w x h):11.4 x 11.4 x 22 cm
Capacity:2.5W @ 65K
Ultimate low temperature:35K
Input power2kW
Pulse tube
Two stage pulse tube
Pulse tube configuration
Adiabatic demagnetization of
paramagnetic
Paramagnetic salts
Magnetic coolers
Magnetic cooler
Magnetic cooler with moving
paramagnetic
Three stage magnetic cooler with
magnetic regenerator
Ceramic magnetic regenerator
material Gd2O2S with an
average diameter of 0.35 mm
for G-M and pulse tube
cryocoolers.
Cooler efficiency at 80 K
„Family” of cryocoolers