Contents lists available at ScienceDirect Cryogenics journal homepage: www.elsevier.com/locate/cryogenics Research paper The thermodynamic characteristics of a Stirling/pulse tube hybrid cryocooler Yongxiang Guo a,b , Yijun Chao a,b , Bo Wang a,b, ⁎ , Haiying Li d , Sizhuo Li a,b , John M. Pfotenhauer c , Zhihua Gan a,b, ⁎ a Institute of Refrigeration and Cryogenics, Zhejiang University, Hangzhou 310027, China b Key Laboratory of Refrigeration and Cryogenic Technology of Zhejian Province, Hangzhou 310027, China c Department of Mechanical Engineering, University of Wisconsin-Madison, Madison 53706, USA d Kunming Institute of Physics, Kunming 650223, China ARTICLE INFO Keywords: Stirling/pulse tube hybrid cryocooler Stirling cryocooler Idealized model Thermodynamic characteristic ABSTRACT A Stirling/pulse tube hybrid cryocooler (SPC), comprised of a Stirling cryocooler as the first stage and a pulse tube cryocooler as the second stage, features the ability of shifting cooling capacity between stages by adjusting the movement of the displacer in the first stage. Such an ability allows an SPC to accommodate itself to time- varying heat loads at different temperatures, which makes it a competitive candidate in space applications. However, due to the gas coupling, there exists a significant mutual effect between stages which endows an SPC with special thermodynamic characteristics and has a significant effect on the SPC’s capability of shifting cooling capacity between stages. With the phasor analysis and the thermodynamic analysis, this paper establishes an idealized model of an SPC. The model is then used to study the effect of the second stage on the first stage and reveal the condition that an SPC is able to shift cooling capacity between stages. Also, the model is compared with a Sage numerical model and the two models are consistent on the overall trend. Though it is unable to reflect reality precisely, the idealized model can interpret the mechanism and highlight some of the essential nature of an SPC, which will eventually benefit the appropriate design of an SPC. 1. Introduction A low temperature environment is necessary for space detectors in order to provide high sensitivity and resolution. For example, an arsenic doped silicon focal plane provides an advantage for Long Wave Infrared astronomy and it demands cryogenic temperatures below 12 K for proper operation [1]. In the past, stored-cryogen systems have been adopted to provide time-varying cooling capacity at different cryogenic temperatures to cool different types of space detectors, but their life- time is limited by the finite storage of the cryogen. Closed cycle cryo- coolers, which are lighter in weight and longer in lifetime, provide another option for space cryogenic cooling [2], but the application of traditional cryocoolers is limited by their inability to provide time- varying cooling capacity simultaneously at different temperatures. A Stirling/pulse tube hybrid cryocooler (SPC) can overcome the shortage of traditional cryocoolers mentioned above while maintaining the advantages of traditional cryocoolers. An SPC, first proposed by K. D. Price etc. in 1999 [3], is comprised of a Stirling cryocooler as the first stage and a pulse tube cryocooler as the second stage and the two stages are gas-coupled. By adjusting the movement of the displacer in the first stage, the cooling capacity can be shifted between stages. Therefore, an SPC is able to provide time-varying cooling capacity simultaneously at different temperatures. Moreover, eliminating the moving parts in the second stage endows an SPC with a higher reliability than a multi-stage Stirling cryocooler; adjusting the mass flow and pressure with the dis- placer in the first stage allows an SPC to achieve a higher efficiency than a multi-stage pulse tube cryocooler. The SPC has presented itself as a competitive candidate for cooling space detectors. Since the SPC was first proposed in 1999, a series of SPCs have been designed, fabricated and tested, such as the LT-RSP2(55 K/10 K) for low temperature, the HC-RSP2(85 K/35 K) for high cooling capacity and the MC-RSP2(110 K/58 K) for medium cooling capacity [1]. In 2003, a report on the RSP2 verified the SPCs’ ability of shifting cooling capacity between stages by experiment [4]. Thereafter, an ambient temperature phase shifter[5] and a low temperature inertance tube [6] were adopted one after the other to improve the SPCs’ efficiency. A report on the HC- RSP2 in 2009 claims to have a cooling capacity of 2.6 W@35 K and 16.2 W@85 K with an input power of 513 W, implying an FOM of https://doi.org/10.1016/j.cryogenics.2018.10.011 Received 18 April 2018; Received in revised form 20 September 2018; Accepted 19 October 2018 ⁎ Corresponding authors at: Institute of Refrigeration and Cryogenics, Zhejiang University, Hangzhou 310027, China. E-mail addresses: wang_bo@zju.edu.cn (B. Wang), gan_zhihua@zju.edu.cn (Z. Gan). Cryogenics 96 (2018) 133–143 Available online 01 November 2018 0011-2275/ © 2018 Elsevier Ltd. All rights reserved. T