A large amount of electricity is used in the liquefaction of gases, however, during regasification the liquid is warmed using ambient heat without recovering this electricity. Our goal is to develop a Stirling engine that operates between ambient and cryogenic temperatures to recover part of the electricity for small-scale end-user sites (3–10 kW). In this presentation, the thermodynamic analysis of this system is discussed.
A linearized first-harmonic phasor model based on isothermal assumptions is developed and implemented. The working gas is treated as ideal, and each working, compression, heater, regenerator, cooler, and expansion space, is assumed isothermal at its respective temperature, with the regenerator described by a logarithmic mean temperature. Instantaneous pressure is derived from the effective volume, and the sensitivity of pressure to piston and displacer displacement is obtained analytically. The full set of volume, pressure, and mass-flow phasors are calculated and drawn, providing visualization of phase relationships between thermodynamic quantities and energy quantities such as heat and acoustic power.
For the baseline design (Ambient temperature 300 K, Cold temperature 77 K, operating pressure 23 bar, and frequency 50 Hz), the model yields a net electrical output of approximately 1 kW. Assuming a 25 percent second law efficiency, the cold side absorbs approximately 3.7 kW of heat, corresponding to a liquid nitrogen evaporation rate that produces approximately ~54 Nm³/h of nitrogen gas at standard conditions.

This work is part of the CryoHarvest project, supported by TKI HTSM.
 

Keywords
Stirling engine|Regasification|phasor model|Electricity recovery|cryogenic fluid