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 – 400 076 email : slbapat@iitb.ac.in

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

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.

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.

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

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) 111.63 (NBP) 130.0 140.0 150.0 160.0 Saturation Pressure (bar) 1.01325 3.6805 6.4223 10.414 15.939 Liquid Enthalpy (kJ/kg) -222.1 -184.19 -144.37 -101.89 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) 0.014702 0.016478 0.018541 0.021082 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

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 1.93646 2.13846 2.32307 2.48832 with Helium-Methane Mixture, W 5.34821 7.37444 9.72167 12.14667 increase with respect to Helium 176 % 245 % 318 % 388 % Net power 7.20227 6.61137 6.08361 5.60862 7.08773 6.4847 6.03721 5.89467 - 1.6 % - 1.9 % - 0.76 % + 5.1 % Coefficient of Performance with Helium 0.26887 0.32345 0.38186 0.44366 with Helium-Methane Mixture 0.75457 1.13721 1.61029 2.06062 180 % 251 % 321 % 364 % Methane Molar Concentration 0.1571 0.272 0.4345 0.647

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

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

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

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

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

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.

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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.

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