Numerical investigation of displacer pulse tube refrigerators based on thermoacoustic theory

The displacer pulse tube refrigerator (DPTR) is a work-recovery pulse tube refrigerator, which provides phase shifting and also enables the recovery and reuse of acoustic power that would otherwise be dissipated. The strong coupling among displacer parameters complicates practical design, while a systematic framework for comprehensively characterizing their coupled effects is still lacking. This study developed a unified thermoacoustic numerical model that enables systematic investigation of the DPTR operating mechanism and performance under different displacer configurations, operating conditions, and system control strategies. For the passive system, when the rod diameter ratio is fixed, the displacer with lower mass combined with a spring of low stiffness can satisfy the miniaturization requirement of the DPTR without compromising cooling performance. Introducing an appropriate active motor force can improve the cooling performance of the passive system, but the motor force amplitude and phase required to enhance cooling power are generally different from those required to improve power recovery efficiency. Under the given operating parameters, the maximum achievable cooling power of the system is nearly independent of the rod diameter ratio. However, increasing the rod diameter ratio leads to a pronounced decline in the achievable power recovery efficiency. Therefore, prioritizing cooling power enhancement at low rod diameter ratios and power recovery efficiency improvement at high rod diameter ratios can provide greater performance gains. The proposed model and the resulting findings provide an effective approach and theoretical guidance for the rapid design and optimization of the DPTR.