Simulation Study on the Effects of Displacer Motion on the Performance of Pulse Tube Cryocooler

Compared to Stirling cryocooler, the theoretical efficiency of the pluse tube cryocooler with inertance tube reservoir phase shifting is relatively low. This is chiefly ascribed to the acoustic power generated at the hot end of the pulse tube, which is converted into heat within the inertance tube reservoir and not effectively utilized. In contrast, the phase shifting pulse tube cryocoolers utilizing a displacer piston can recover the expansion work from the hot end of the pulse tube, thereby offering significant advantages in improving refrigeration efficiency. A one-dimensional numerical model using Sage was employed to conduct the simulation analysis and research on a coaxial Stirling pulse tube cryocooler with a displacer piston phase-shifting mechanism, rated at 6 W @ 80 K. Firstly, the motion equation of the displacer piston and the phase relationship diagram were established. The phase relationships among the displacement, volume flow, and pressure wave in the displacer piston phase-shifting pulse tube Cryocooler were determined. Secondly, the investigation was proposed into how the displacer piston's phase and amplitude affected the phase shifting performance and refrigeration efficiency of the cryocooler. It was found that with a displacer amplitude of 3 mm and a displacer phase of 45°, the COP of the cold head reached its optimal value of 7.38%. Finally, a comparative analysis was conducted between the displacer piston phase shifting method and the dual-stage inertance tube reservoir phase shifting method, by evaluating their refrigeration performance, energy flow, and the phase relationships. It was found that under the two different phase-shifting methods, the COP of the cold heads was 7.38% and 5.71%, respectively, with phase relationships of 24.79° and −32.95° for one method, and 27.5° and −11.3° for the other. Through a comprehensive study of the overall energy flow in the system, the differences in the working principles of the two phase shifting structures were elucidated. Furthermore, it was pointed out that the displacer piston could recover the acoustic power at the hot end of the pulse tube and optimized the phase distribution.