Research paperTheoretical and experimental investigations on the three-stage Stirling-type pulse tube cryocooler using cryogenic phase-shifting approach and mixed regenerator matrices
Introduction
The pulse tube cryocooler (PTC) is acknowledged as a significant technological innovation in regenerative cooling technology since it eliminates the moving component at the cold end. The Stirling-type PTC (SPTC) driven by a linear compressor with clearance seal and flexure springs further realizes the long life of the driver at the warm end, and thus, has appeal to a variety of applications such as in space [1], [2], [3], [4]. Cooling at 10 K and below has played a key role in the fields of security defense, deep space exploration, and low-Tc superconducting. In practice, for a SPTC, three stages are usually needed to meet the cooling requirements [5], [6], [7], [8], [9], [10], [11], [12], [13].
Normally, the third stage of a three-stage SPTC is the focus because it achieves the target temperature. To pursue lower no-load temperature, some researchers employ external precooling approaches for the former stages, such as additional cryocoolers or cryogens. However, for most practical applications, the external precooling is not feasible because it makes the system much more complicated, and furthermore, external precooling is not always available. Therefore, our design excludes any external precooling approaches and only depends on the three-stage SPTC itself.
The cryogenic phase-shifting approach refers to the third-stage inertance tube and reservoir placed at cryogenic temperatures rather than in the ambient environment. This approach can significantly reduce the heat load at the warm end of pulse tube and decrease the temperature gradient in pulse tube to improve the third-stage performance. The impedance amplitude of the inertance tubes with different temperatures and lengths is analyzed, and the phase relationship, the dynamic pressure and the mass flow rate of the third stage with the optimal inertance tubes is proposed when the phase-shifters are at 40 K, 50 K and 293 K, respectively.
Regenerator irreversible losses usually account for most of the system losses. Mixed regenerator matrices were proposed and used to develop single-stage and two-stage SPTCs with minimized the regenerator losses [14], [15], [16], [17]. The principle was to minimize the flow resistances while keeping the necessary thermal penetration depths of the regenerator matrix along the whole regenerator. Third-stage regenerators have a larger temperature gradient making the successful implementation of rare-earth mixed matrices with the high heat specific capacity at 10 K and below including Er0.6Pr0.4, Er3Ni and HoCu2 more challenging. Regenerator performance with these rare-earth matrices is analyzed quantitatively using the entropy analysis method [11]. The different ratios and combinations of the mixed matrices are analyzed, compared and summarized.
The improved electrical circuit analogy (ECA) model developed for single- and two-stage SPTCs [4], [18], [17] is employed to build the third-stage model. The fourth-order Runge-Kutta method, which has been used successfully in the analysis of the single-stage SPTCs [16], is used to solve the equations.
Section snippets
Theoretical model and analyses
The three-stage SPTC schematic in Fig. 1 shows the first two stages driven by one linear compressor while the third stage by another. The third stage is precooled by the first two stages via Thermal link I and Thermal link II.
The first two stages adopt the coaxial arrangement, and their inertance tubes and reservoirs are at ambient temperature. The third stage adopts the linear arrangement, and its inertance tubes and reservoir are in the Dewar and work at the cryogenic temperature. The main
Experimental set-up
The photo of the actual cold fingers is shown in Fig. 12. The experimental dimensions of the three-stage SPTC are the same as the ones used in model, as shown in Table 1. Both compressors are dual-opposed moving-coil linear compressors developed in the same laboratory with a maximum swept volume of 13 cc. The Thermal links consist of 30 pieces of sleet copper with ends which are welded together. As shown in Fig. 12, one end of the third-stage inertance tube is connected to Warm HX II and the
Conclusions
This paper conducts theoretical analyses and experimental verifications for a three-stage SPTC expected to operate at 5–12 K, in which the cryogenic phase-shifting approach and the mixed regenerator matrices are employed to improve the performance at the third stage.
An improved ECA model for the third stage is built, and the fourth-order Runge-Kutta method employed to solve equations. Several important factors are considered including the real gas effect of helium, the thermal properties of the
Acknowledgements
The work is financially supported by The Aeronautical Science Foundation of China (No. 20162490005) and The Science and Technology Commission of Shanghai Municipality (No. 18511110100).
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