1. Indian Institute of Technology Bombay
Performance improvement in a Stirling cooler with Methane as a condensable component in Helium-Methane mixture as working fluid for refrigeration temperature about 130 K
Prof. S. L. Bapat
Indian Institute of Technology Bombay
Powai, Mumbai –

2. Actual system and schematic of β Configuration Stirling Liquefier
Performance improvement in a Stirling cooler with Methane as a condensable component in Helium-Methane mixture as working fluid for refrigeration temperature about 130 K
Actual system and schematic of β Configuration Stirling Liquefier

3. Use of condensable working fluid component:
Performance improvement in a Stirling cooler with Methane as a condensable component in Helium-Methane mixture as working fluid for refrigeration temperature about 130 K
Use of condensable working fluid component:
It is expected that the condensable component (Methane) will condense inside the regenerator; at the cold temperature end.
The condensate will be drawn in to the expansion space along with the gaseous fluid (He) and will work as carrier fluid for the condensate.
Some quantity of condensable fluid will expand isentropically to the lowest pressure level in the system; during expansion stroke of the displacer.
Heat load on the condenser head causes it to evaporate in the atmosphere of carrier gas (He).
The condensable component will evaporate only till the expansion space becomes saturated with the vapour.

4. Use of condensable working fluid component (Contd.)
Performance improvement in a Stirling cooler with Methane as a condensable component in Helium-Methane mixture as working fluid for refrigeration temperature about 130 K
Use of condensable working fluid component (Contd.)
The isentropic expansion process will provide work output which will reduce the net work input for the system.
During the return stroke of the displacer, the condensable fluid vapours will be pushed back in to the regenerator and will re-condense at the cold end of the regenerator.
Due to presence of the condensable fluid vapours, the mass of carrier fluid (He) in the system reduces.
This results in the reduction in contribution from expansion of gaseous fluid towards the cooling effect against the normal Stirling cycle.

5. Table 1. Geometric and operating parameters of the cooler
Performance improvement in a Stirling cooler with Methane as a condensable component in Helium-Methane mixture as working fluid for refrigeration temperature about 130 K
Table 1. Geometric and operating parameters of the cooler
Piston diameter
8.0 mm
Piston stroke
± 4.5 mm
Displacer diameter
7.5 mm
Displacer stroke
± 2 mm
Phase difference between displacer and piston motion
45o
Mean pressure
≅ 20.5 bar
Connecting tube length between compressor and displacer
50 mm
Frequency
55 Hz
Regenerator length
Ambient temperature
300 K

6. Saturation Pressure (bar) 1.01325 3.6805 6.4223 10.414 15.939
Performance improvement in a Stirling cooler with Methane as a condensable component in Helium-Methane mixture as working fluid for refrigeration temperature about 130 K
Temperature (K)
(NBP)
130.0
140.0
150.0
160.0
Saturation Pressure (bar)
3.6805
6.4223
10.414
15.939
Liquid Enthalpy (kJ/kg)
-222.1
Vapour Enthalpy (kJ/kg)
250.57
261.19
268.05
269.92
Latent Heat (kJ/kg)
510.3
472.67
445.38
412.42
371.81
Cp of vapour (kJ/kg.K)
2.3994
2.5801
2.8589
3.3292
Cv of vapour (kJ/kg.K)
1.6600
1.7000
1.7488
1.8101
Cp of liquid (kJ/kg.K)
3.6582
3.8253
4.0764
4.4870
Thermal Conductivity (W/m.K)
Viscosity (μPa.s)
5.2498
5.7225
6.2482
6.8623
Gamma, γ
1.4454
1.5177
1.6347
1.8393
Molecular Weight
16.043

7. Temperature at the cooler cold tip, K 130 140 150 160 Cooling capacity
Performance improvement in a Stirling cooler with Methane as a condensable component in Helium-Methane mixture as working fluid for refrigeration temperature about 130 K
Temperature at the cooler cold tip, K
130
140
150
160
Cooling capacity
with Helium, W
with Helium-Methane Mixture, W
increase with respect to Helium
176 %
245 %
318 %
388 %
Net power
6.4847
- 1.6 %
- 1.9 % %
+ 5.1 %
Coefficient of Performance
with Helium
with Helium-Methane Mixture
180 %
251 %
321 %
364 %
Methane Molar Concentration
0.1571
0.272
0.4345
0.647

8. Figure 1. Variation in refrigerating capacity
Performance improvement in a Stirling cooler with Methane as a condensable component in Helium-Methane mixture as working fluid for refrigeration temperature about 130 K
Helium
Helium-Methane
Mixture
Frequency = 55 Hz
Mean pressure = 20.5 bar
Figure 1. Variation in refrigerating capacity

9. Performance improvement in a Stirling cooler with Methane as a condensable component in Helium-Methane mixture as working fluid for refrigeration temperature about 130 K
Figure 2. Variation of the power requirement at different refrigeration temperatures

10. requirement as a function of refrigeration temperature required
Performance improvement in a Stirling cooler with Methane as a condensable component in Helium-Methane mixture as working fluid for refrigeration temperature about 130 K
Figure 3. The simultaneous effect of the variations in the cooling capacity and power
requirement as a function of refrigeration temperature required

11. Performance improvement in a Stirling cooler with Methane as a condensable component in Helium-Methane mixture as working fluid for refrigeration temperature about 130 K
Figure 4. The simultaneous variation of coefficient of performance (C.O.P) and
Methane molar composition with respect to the refrigeration temperature

12. Performance improvement in a Stirling cooler with Methane as a condensable component in Helium-Methane mixture as working fluid for refrigeration temperature about 130 K
Figure 5. The variation of Methane molar concentration versus refrigeration
temperature

13. When the in-situ re-condensation of Methane is considered, one of
Performance improvement in a Stirling cooler with Methane as a condensable component in Helium-Methane mixture as working fluid for refrigeration temperature about 130 K
Conclusions
When the in-situ re-condensation of Methane is considered, one of
the main options is to use the closed cycle Stirling cycle cryo-cooler.
With reference to C.O.P. with Helium as the working fluid, the use of
Methane-Helium mixture as the working fluid in the same cooler,
without absolutely any change in hardware shows an increase in
refrigeration capacity of around 180% at 130 K further increasing to
more than 350% at higher refrigeration temperature of 160 K.
The use of condensable fluid in a Stirling cryo-cooler for Methane or
natural gas re-condensation shows great promise and that too
without any hardware modifications.

14. Thank You!

15. Comparison of Carnot Cycle and Stirling Cycle
Performance improvement in a Stirling cooler with Methane as a condensable component in Helium-Methane mixture as working fluid for refrigeration temperature about 130 K
Comparison of Carnot Cycle and Stirling Cycle
on P-V and T-S Charts
Comparison is for the same maximum and minimum temperature and same maximum and minimum pressure condition corresponding to state points 3 and 1. For same maximum and minimum volume, output of Stirling cycle is much more compared to Carnot cycle.

16. Schematic representation of state points in ideal Stirling engine,
Performance improvement in a Stirling cooler with Methane as a condensable component in Helium-Methane mixture as working fluid for refrigeration temperature about 130 K
Schematic representation of state points in ideal Stirling engine,
Time-displacement diagram of ideal
Stirling engine