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Frontiers in Energy

ISSN 2095-1701

ISSN 2095-1698(Online)

CN 11-6017/TK

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Front. Energy    2019, Vol. 13 Issue (3) : 450-463    https://doi.org/10.1007/s11708-018-0569-8
RESEARCH ARTICLE
Theoretical modeling and experimental verifications of the single-compressor-driven three-stage Stirling-type pulse tube cryocooler
Haizheng DANG1(), Dingli BAO2, Zhiqian GAO3, Tao ZHANG2, Jun TAN1, Rui ZHA2, Jiaqi LI2, Ning LI1, Yongjiang ZHAO2, Bangjian ZHAO2
1. State Key Laboratory of Infrared Physics, Shanghai Institute of Technical Physics, Chinese Academy of Sciences, Shanghai 200083, China
2. State Key Laboratory of Infrared Physics, Shanghai Institute of Technical Physics, Chinese Academy of Sciences, Shanghai 200083, China; University of Chinese Academy of Sciences, Beijing 100049, China
3. Institute of Fundamental and Frontier Technology, Midea Refrigerator Co., Ltd., Hefei 230601, China
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Abstract

This paper establishes a theoretical model of the single-compressor-driven (SCD) three-stage Stirling-type pulse tube cryocooler (SPTC) and conducts experimental verifications. The main differences between the SCD type and the multi-compressor-driven (MCD) crycooler are analyzed, such as the distribution of the input acoustic power in each stage and the optimization of the operating parameters, in which both advantages and difficulties of the former are stressed. The effects of the dynamic temperatures are considered to improve the accuracy of the simulation at very low temperatures, and a specific simulation example aiming at 10 K is given in which quantitative analyses are provided. A SCD three-stage SPTC is developed based on the theoretical analyses and with a total input acoustic power of 371.58 W, which reaches a no-load temperature of 8.82 K and can simultaneously achieve the cooling capacities of 2.4 W at 70 K, 0.17 W at 25 K, and 0.05 W at 10 K. The performance of the SCD three-stage SPTC is slightly poorer than that of its MCD counterpart developed in the same laboratory, but the advantages of lightweight and compactness make the former more attractive to practical applications.
Keywords single-compressor-driven      three-stage      Stirling-type pulse tube cryocooler      theoretical modeling      experimental verification     
Corresponding Author(s): Haizheng DANG   
Just Accepted Date: 14 May 2018   Online First Date: 17 July 2018    Issue Date: 04 September 2019
 Cite this article:   
Haizheng DANG,Dingli BAO,Zhiqian GAO, et al. Theoretical modeling and experimental verifications of the single-compressor-driven three-stage Stirling-type pulse tube cryocooler[J]. Front. Energy, 2019, 13(3): 450-463.
 URL:  
https://academic.hep.com.cn/fie/EN/10.1007/s11708-018-0569-8
https://academic.hep.com.cn/fie/EN/Y2019/V13/I3/450
Fig.1  Schematic of the SCD three-stage SPTC
The first stage The second stage The third stage
Regenerator Diameter F30.3 mm × 0.2 mm F24.8 mm × 0.2 mm F19.5 mm × 0.2 mm
Length 55.0 mm 76.4 mm 98.2 mm
Matrix #400 SS 40% #400 SS
+ 60% Lead		 45% #400 SS+ 25% Lead+ 30% Er3Ni
Hot heat exchanger Diameter 30.3 mm 24.8 mm 19.5 mm
Length 15.2 mm 13.2 mm 10.8 mm
Cold heat exchanger Diameter 30.3 mm 24.8 mm 19.5 mm
Length 7.3 mm 6.7 mm 5.1 mm
Tab.1  Main geometrical parameters of the SCD three-stage SPTC
Fig.2  Influence of Tg on |pd| and |U?| in the third regenerator
Fig.3  Distributions of |Tg|, |Ts|, qg, and qs in the first regenerator
Fig.4  Distributions of (a) |Tg| and (b) |Ts|, and qg and qs in the second regenerator
Fig.5  Distributions of (a) |Tg| and (b) |Ts|, and qg and qs in the third regenerator
The first stage The second stage The third stage Total
|U?i|/( × 10-4 m3/s) 11.26 7.37 5.27 23.61
qui/(°) 9.76 23.16 31.28 18.63
|pdi|/kPa 273 273 273 273
qpi/(°) 0 0 0 0
Dqi/(°) -9.76 -23.16 -31.28 -18.63
W/W 219.57 91.37 60.64 371.58
Tab.2  Dynamic pressure and volume flow rate at the inlet of each stage
Fig.6  Temperature profiles between 10 K and 25 K in the third regenerator with different matrices
Fig.7  Influences of different matrices on (a) |Tg| and (b) |Ts| between 10 K and 25 K in the third regenerator
Fig.8  Influences of different matrices on (a) <S?a> , (b) <S?p> , (c) <S?c> , and (d) <S?g> between 10 K and 25 K in the third regenerator
Fig.9  Effects of charge pressure on Qg1, Qg2, and Qg3, respectively
Fig.10  Effects of pressure ratio on Qg1, Qg2, and Qg3, respectively
Fig.11  Effects of operating frequency on Qg1, Qg2, and Qg3, respectively
Fig.12  Cold fingers of the developed SCD SPTC
Fig.13  Experimental setup
Fig.14  Comparisons of simulated and experimental results
Fig.15  Comparisons of experimental results between SCD and MCD SPTCs
A Area/m2
c Specific heat/(J?kg?1?K?1)
Cf Compressibility factor
E Ratio of dynamic temperature between gas and matrix
f Frequency/Hz
F New defined parameter (kg/m?s2)
g Variation coefficient for volume flow rate caused by temperature gradient/m?1
hgs Convective heat transfer coefficient between gas and solid/(W?m?2?K?1)
H Enthalpy flow/J
p Pressure/Pa
pd Dynamic pressure/Pa
ps Charge pressure/Pa
Q Heat/W
Qc Cooling capacity/W
Qg Gross cooling capacity/W
Qp Precooling capacity/W
Qt Total cooling capacity/W
rg Flow resistance per unit length/(kg?m?5?s?1)
rh Hydraulic radius/m
R Ideal gas constant/(J? kg?1?K?1)
Rv Viscous resistance/(kg?s?4?s?1)
S Entropy/(J?K?1)
Sg Entropy generation/(J?K?1)
t Time/s
T Temperature/K
u Gas velocity/(m?s?1)
U? Volume flow rate/(m3?s?1)
W Acoustic power/W
Greek symbols
β Specific surface area/m?1
γ Specific heat ratio
dv Viscous penetration depth/m
η Heat conduction efficiency
θ Angle/rad
λ Thermal conductivity/(W?m?1?K?1)
m Viscosity/(Pa?s)
Porosity
Perimeter/m
r Density/(kg?m?3)
ω angular frequency/(rad?s?1)
Subscripts
c Cold end of the regenerator
g Gas
h Hot end of the regenerator
i Inner part
m Mean value
s Solid
w Wall
  
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