Skip to main content
SpringerLink
Log in

Experimental Investigation and Thermoacoustic Analysis of a Single-Stage Pulse Tube Refrigerator with an Active Displacer

  • Published:
Journal of Low Temperature Physics Aims and scope Submit manuscript

Abstract

The Stirling-type pulse tube refrigerator is a widely used refrigerator that has been extensively applied in space. An optimal phase angle between the pressure wave and volume flow is essential for a pulse tube refrigerator. The active displacer installed at the hot end of a pulse tube can be used to actively control the phase angle and enable recovery of the expansion power at the warm end of the pulse tube, leading to high efficiency. The main parameters for a pulse tube refrigerator with an active displacer are the phase and displacement of the active displacer. This manuscript studies the impact of displacer phase and displacement on a 40 K single-stage pulse tube refrigerator with an active displacer by thermoacoustic analysis, which is helpful for studying the thermodynamic characteristics of such a refrigerator and provides a method for more effective design and computing. The effects on the pressure, acoustic power, and cooling capacity are investigated by analytically solving the thermoacoustic model. A pulse tube refrigerator developed in our laboratory is tested, and the experimental results are compared with the results of thermoacoustic analysis.

This is a preview of subscription content, log in via an institution to check access.

Access this article

Log in via an institution

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

Instant access to the full article PDF.

Institutional subscriptions

Fig. 1
Fig. 2
Fig. 3
Fig. 4
Fig. 5
Fig. 6
Fig. 7
Fig. 8
Fig. 9
Fig. 10
Fig. 11

Similar content being viewed by others

Abbreviations

A :

Area (\({\text{m}}^{2}\))

\({\varvec{a}}_{1}\) :

Phase constant defined in Eq. (17)

\({\varvec{a}}_{{\varvec{2}}}\) :

Phase constant defined in Eq. (18)

\({\varvec{a}}_{{\varvec{3}}}\) :

Phase constant defined in Eq. (19)

\({\varvec{a}}_{{\varvec{4}}}\) :

Phase constant defined in Eq. (20)

c :

Acoustic compliance per unit length (m2/Pa)

C :

Acoustic compliance (m/Pa)

\({\varvec{d}}_{{\varvec{1}}}\) :

Function defined in Eq. (22)

\({\varvec{d}}_{{\varvec{2}}}\) :

Function defined in Eq. (22)

\({\varvec{d}}_{{\varvec{3}}}\) :

Function defined in Eq. (22)

\({\varvec{d}}_{{\varvec{4}}}\) :

Function defined in Eq. (22)

\(d_{{\text{h}}}\) :

Hydraulic diameter (m)

\(D\) :

Diameter (m)

\(f_{M}\) :

Friction factor under turbulent flow

g :

Simplified attenuation constant for volume flow

\(i\) :

Imaginary unit

\(L\) :

Length (m)

\(l\) :

Acoustic inertance per unit length (kg/m5)

\(m\) :

Mass (kg)

n :

Polytropic index

\({\varvec{P}}\) :

Pressure phasor (Pa)

PV:

Acoustic power (W)

\(Q\) :

Cooling capacity (W)

\(R_{{\text{g}}}\) :

Specific gas constant (J/Kg K)

\(r_{\mu }\) :

Viscous resistance per unit length (m)

\(r_{{\text{h}}}\) :

Hydraulic radius (m)

\(T\) :

Temperature (K)

\({\text{t}}\) :

Time (s)

\({\varvec{U}}\) :

Volume flow phasor (m3/s)

\({\varvec{V}}\) :

Volume phasor (m3)

\(W\) :

Work (W)

\(x\) :

Position (m)

\({\varvec{\alpha}}\) :

Phase constant defined in Eq. (31)

\(\beta\) :

Fitting constant defined in Eq. (26)

\(\gamma\) :

Ratio of isobaric to isochoric specific heats

\(\delta_{k}\) :

Viscous penetration depth (m)

\(\delta_{\mu }\) :

Thermal penetration depth (m)

\(\varepsilon\) :

Equivalent roughness (m)

\({\epsilon }\) :

Coefficient of expansion

\(\theta\) :

Phase angle (°)

\(\lambda\) :

Thermal conductivity (W m−1 K−1)

\(\mu_{{\text{m}}}\) :

Dynamic viscosity (N s m−2)

\(\omega\) :

Angular frequency (°/s)

\(\rho\) :

Density (kg/m3)

\(\tau\) :

Periodic time (s)

\(\varphi\) :

Volumetric porosity

CCT:

Compressor connecting tube

cond:

Conductivity

cold:

Cold end of the pulse tube

CC:

Compression space in the main compressor

CT:

Connecting tubes

DC:

Compression space in the phase shift compressor

\({\text{DT}}\) :

Displacer tube

gas:

Working gas

H :

Ambient temperature

i:

Inner part of the regenerator

L :

Cold end temperature

net:

Net refrigeration capacity

m:

Mean value

mt:

Regenerative material

P:

Pressure wave

P_CC:

Pressure in the main compressor space

P_DC:

Pressure in the phase shift compressor space

PT:

Pulse tube

RE:

Regenerator

U :

Volume flow

w:

Wall

| |:

Magnitude of phasor

〈 〉:

Time average

References

  1. T. Nast, D. Murray, Orbital cryogenic cooling of sensor systems. Syst. Des. Driven Sens. (1976)

  2. R. Radebaugh, Development of the pulse tube refrigerator as an efficient and reliable cryocooler, in Proceedings of the Institute of Refrigeration, London (2000)

  3. E.I. Mikulin, A.A. Tarasov, M.P. Shkrebyonock, Low-temperature expansion pulse tubes, in Iop Conference Series: Material Science (1983), pp. 629–37

  4. Y.C.W. Ju, Z. Yuan, Dynamic experimental study of the multi-bypass pulse tube refrigerator with two-bypass tubes. J. Therm. Sci. 7(1), 61–66 (1998)

    Article  ADS  Google Scholar 

  5. Q. Zhou, L. Chen, X. Zhu et al., Development of a high-frequency coaxial multi-bypass pulse tube refrigerator below 14K. Cryogenics 67, 28–30 (2015)

    Article  ADS  Google Scholar 

  6. S. Zhu, P. Wu, Z. Chen, Double inlet pulse tube refrigerators: an important improvement. Cryogenics 30(6), 514–520 (1990)

    Article  Google Scholar 

  7. L.W. Yang, Y.Q. Xun, G. Thummes et al., Single-stage high frequency coaxial pulse tube cryocooler with base temperature below 30K. Cryogenics 50(5), 342–346 (2010)

    Article  ADS  Google Scholar 

  8. L. Chen, X. Wu, J. Wang et al., Study on a high frequency pulse tube cryocooler capable of achieving temperatures below 4 K by helium-4. Cryogenics 94, 103–109 (2018)

    Article  ADS  Google Scholar 

  9. R.Z.J. Radebaugh, D.R. Smith, et al., A comparison of three types of pulse tube refrigerators: new methods for reaching 60K, in IOP Conference Series: Material Science (1985), pp. 779–89

  10. E. Luo, Inertance tube models and their experimental verification, in AIP Conference Proceedings (2004), pp. 1485–1492.

  11. R. Ackerman, Dynamic analysis of a small free-piston resonant cryorefrigerator, in Refrigeration for Cryogenic Sensors and Electronic Systems: Proceedings of a Conference Held at the National Bureau of Standards (Boulder CO, 1980), pp. 57–69

  12. Y. Shi, S. Zhu, Experimental investigation of pulse tube refrigerator with displacer. Int. J. Refrig. 76, 1–6 (2017)

    Article  Google Scholar 

  13. M.A. Abolghasemi, H. Rana, R. Stone et al., Coaxial Stirling pulse tube cryocooler with active displacer. Cryogenics 111, 103143 (2020)

    Article  Google Scholar 

  14. Z. Jiang, Y. Wu, Z. Lu et al., On-orbit performance of the FY-4 GIIRS stirling cryocooler over 2 years. J. Low Temp. Phys. 203(1–2), 244–253 (2021)

    Article  ADS  Google Scholar 

  15. M.P.G. Brito, Experimental analysis of free warm expander pulse tube. Cryogenics 41(10), 757–762 (2001)

    Article  ADS  Google Scholar 

  16. M.P.G. Brito, Numerical model of free warm expander pulse tube cooler. Cryogenics 41(10), 751–755 (2001)

    Article  ADS  Google Scholar 

  17. S. Masuyama, Y.H. Kim, S.J. Park et al., Experimental research of Stirling type pulse tube refrigerator with an active phase control. Cryogenics 46(5), 385–390 (2006)

    Article  ADS  Google Scholar 

  18. S. Zhu, M. Nogawa, Pulse tube stirling machine with warm gas-driven displacer. Cryogenics 50(5), 320–330 (2010)

    Article  ADS  Google Scholar 

  19. S. Zhu, Y. Matsubara, Numerical method of inertance tube pulse tube refrigerator. Cryogenics 44(9), 649–660 (2004)

    Article  ADS  Google Scholar 

  20. S. Zhu, Step piston pulse tube refrigerator. Cryogenics 64, 63–69 (2014)

    Article  ADS  Google Scholar 

  21. K. Liang, A. Abolghasemi, C.R. Stone, et al., Numerical study on the performance sensitivity of a pulse tube cryocooler with active phase shifter, in IOP Conference Series: Materials Science and Engineering, vol. 502 (2019), p. 012018

  22. H. Rana, M.A. Abolghasemi, R. Stone et al., Numerical modelling of a coaxial Stirling pulse tube cryocooler with an active displacer for space applications. Cryogenics 106, 103048 (2020)

    Article  Google Scholar 

  23. M.A. Abolghasemi, K. Liang, R. Stone et al., Stirling pulse tube cryocooler using an active displacer. Cryogenics 96, 53–61 (2018)

    Article  ADS  Google Scholar 

  24. X. Chen, F. Ling, Y. Zeng et al., Investigation of the high efficiency pulse tube refrigerator with acoustic power recovery. Appl. Therm. Eng. 159, 113904 (2019)

    Article  Google Scholar 

  25. N. Rott, Thermoacoustics. Adv. Appl. Mech. 20, 135–175 (1980)

    Article  ADS  MATH  Google Scholar 

  26. G.W. Swift, Thermoacoustics: a unifying perspective for some engines and refrigerators second edition. Acoust. Soc. Am. ASA Press (2017)

  27. Q. Yang, E. Luo, W. Dai et al., Thermoacoustic model of a modified free piston Stirling engine with a thermal buffer tube. Appl. Energy 90(1), 266–270 (2012)

    Article  Google Scholar 

  28. K. Luo, J. Hu, E. Luo et al., Theoretical investigation on the optimal PU phase relationships of regenerative cooling systems with highest efficiency. Cryogenics 98, 5–11 (2019)

    Article  ADS  Google Scholar 

  29. B. Liu, Z. Jiang, K. Ying et al., Theoretical model of a Stirling/Pulse tube hybrid refrigerator and its verification. Appl. Therm. Eng. 189, 116587 (2021)

    Article  Google Scholar 

  30. G.W. Swift, W.C. Ward, Simple harmonic analysis of regenerators. J Thermophys. Heat Transf. 10(4), 652–662 (1996)

    Article  Google Scholar 

  31. T. Kuriyama, F. Kuriyama, M. Lewis, Thermoacoustics advances in applied mechanics. Adv. Cryog. Eng. 43, 1611–1618 (1998)

    Google Scholar 

  32. L. Yang, Shuttle loss in pulse tubes. Cryocoolers 11, 353–362 (2001)

    Google Scholar 

  33. X. Zhi, Pulse tube losses mechanism based on a two-dimension non-adiabatic model. J. Cent. South Univ. (Sci. Technol.) 43(9), 3672–3677 (2012)

    Google Scholar 

  34. Q. Cao, M. Luan, P. Li et al., A critical review of real gas effects on the regenerative refrigerators. J. Therm. Sci. 30(3), 782–806 (2020)

    Article  Google Scholar 

  35. S. Liu, X. Chen, A. Zhang et al., Investigation on phase shifter of a 10 W/70 K inertance pulse tube refrigerator. Int. J. Refrig. 74, 450–457 (2017)

    Article  Google Scholar 

  36. Z.H. Gan, G.J. Liu, Y.Z. Wu et al., Study on a 5.0 W/80 K single stage stirling type pulse tube cryocooler. J Zhejiang Univ. sci. A. 9(9), 1277–1282 (2008)

    Article  MATH  Google Scholar 

Download references

Acknowledgements

This work is supported by the Hundred Talents Program of the Chinese Academy of Sciences, the National Natural Science Foundation Projects (51806231), the Strategic Priority Research Program of Chinese Academy of Sciences (XDB35000000, XDB35040102).

Author information

Authors and Affiliations

  1. Shanghai Institute of Technical Physics, No.500 Yu Tian Rd, Shanghai, 200083, People’s Republic of China

    Kongkuai Ying, Zhenhua Jiang, Wang Yin, Jiantang Song, Shaoshuai Liu, Nanxi Li & Yinong Wu

  2. University of Chinese Academy of Sciences, No.19 Yu Quan Rd, Beijing, 100049, People’s Republic of China

    Kongkuai Ying, Zhenhua Jiang, Wang Yin, Jiantang Song & Yinong Wu

  3. Nantong Zilang Science and Technology City, Nantong, 226000, Jiangsu, People’s Republic of China

    Haifeng Zhu

Authors
  1. Kongkuai Ying
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. Zhenhua Jiang
    View author publications

    You can also search for this author in PubMed Google Scholar

  3. Wang Yin
    View author publications

    You can also search for this author in PubMed Google Scholar

  4. Jiantang Song
    View author publications

    You can also search for this author in PubMed Google Scholar

  5. Shaoshuai Liu
    View author publications

    You can also search for this author in PubMed Google Scholar

  6. Haifeng Zhu
    View author publications

    You can also search for this author in PubMed Google Scholar

  7. Nanxi Li
    View author publications

    You can also search for this author in PubMed Google Scholar

  8. Yinong Wu
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding authors

Correspondence to Zhenhua Jiang, Shaoshuai Liu or Yinong Wu.

Additional information

Publisher's Note

Springer Nature remains neutral with regard to jurisdictional claims in published maps and institutional affiliations.

Rights and permissions

Springer Nature or its licensor (e.g. a society or other partner) holds exclusive rights to this article under a publishing agreement with the author(s) or other rightsholder(s); author self-archiving of the accepted manuscript version of this article is solely governed by the terms of such publishing agreement and applicable law.

Reprints and permissions

About this article

Check for updates. Verify currency and authenticity via CrossMark

Cite this article

Ying, K., Jiang, Z., Yin, W. et al. Experimental Investigation and Thermoacoustic Analysis of a Single-Stage Pulse Tube Refrigerator with an Active Displacer. J Low Temp Phys 210, 514–535 (2023). https://doi.org/10.1007/s10909-022-02929-z

Download citation

  • Received:

  • Accepted:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1007/s10909-022-02929-z

Keywords

Search

Navigation