Efficient cross-sectional area ratio of step displacer in two-stage Stirling cooler

Abstract The impact of the cross-sectional area ratio of the step displacer in two-stage Stirling cooler is investigated. To achieve cooling temperature of 100 K at the first stage and 50 K with 10 W of cooling power at the second stage, two-stage Stirling coolers are designed according to the cross-sectional area ratio of the displacer. The results show that the optimal phase condition of the mass flow at the cold end of the regenerator cannot be satisfied in both stages simultaneously. When the area ratio of displacer is small, the phase angle of mass flow at the cold end of first stage regenerator is far from the optimum phase. As the area ratio of displacer increases, the phase angle of mass flow rate at the cold end of the first stage regenerator becomes closer to the optimum value while maintaining that of the second stage regenerator optimum value. The results suggest that the area ratio of displacer greater than 5 is recommended for cooling temperature of 100 K and 50 K, which corresponds to cooling power ratio larger than 6 between the first and the second stages.