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A Critical Review of Real Gas Effects on the Regenerative Refrigerators

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Abstract

The regenerative refrigeration is an important reverse work-heat conversion cycle with a theoretical coefficient of performance (COP) identical to the Carnot efficiency. Practical regenerative refrigerators are capable of working down to 4 K and largely fulfill the refrigeration requirement of modern technologies in many fields, especially for space applications. However, the enthalpy flow associated with the pressure dependence, abbreviated as pressure-induced enthalpy flow, brought about by real gas effects degrades the theoretical COP of the refrigerator to below about 30% of the Carnot efficiency at the temperatures of below the critical point. This paper reviews the long history of exploring the real gas effects which dates back to the 1970s and continues to now. Important explorations of uncovering the loss mechanism and reducing such losses are summarized. The theories that are in accordance with experimental results and simulation results are expounded. We further carry out analyses on the expansion components, including the pulse tube and the clearance gap. Several inferences are made in order to explore the long-lasting puzzles about real gas effects. It is emphasized that the underlying cause of the loss in the regenerator is an indirect effect of the real gas properties. Further study about carrying out a direct verification of the theory is proposed.

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Abbreviations

AC:

alternative-current flow

COP:

coefficient of performance

c p :

specific heat capacity/J·kg−1 ·K−1

DC:

direct-current flow

\(\left\langle {{{\dot H}_p}} \right\rangle \) :

time-averaged pressure-induced enthalpy flow/W

\(\left\langle {{{\dot H}_T}} \right\rangle \) :

time-averaged heat-associated enthalpy flow/W

k T :

coefficient between \(\left\langle {{{\dot H}_T}} \right\rangle \) and temperature gradient

\(\dot m\) :

mass flux/kg·s−1

P r :

pressure ratio

PTR:

pulse tube refrigerator

p :

pressure/MPa

\(\left\langle {p\dot V} \right\rangle \) :

PV power/acoustic power/W

\(\left\langle {\dot Q} \right\rangle \) :

heat flow or refrigeration power/W

\(\left\langle {{{\dot Q}_{{\rm{loss}}}}} \right\rangle \) :

heat loss in the pulse tube/W

rCOP:

relative Carnot COP

\(\left\langle {\dot S} \right\rangle\) :

time-averaged entropy flow/W·K−1

T :

temperature/K

t :

time/s

U :

internal energy/W

v :

specific volume/m3·kg−1

x :

position/mm

Z :

compressibility factor

β :

volume expansivity/K−1

ε :

attenuation coefficient of heat load

0:

mean (pressure)

c:

cold end

cond:

conduction

DC:

direct-current flow

ex:

exit flow

g:

gas

gen:

(entropy) generation

gross:

gross (refrigeration power)

h:

hot end

i :

index

in:

inflow

max:

maximum

min:

minimum

n:

number of grid

net:

net (refrigeration power)

prec:

precooling

PT:

pulse tube

R:

regenerator

r:

reduced

T :

temperature related

tot:

total amount

x :

unfixed position

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Acknowledgement

This work is supported by National Natural Science Foundation of China (No. 51506152 and No. 51777141) and the Fundamental Research Funds for the Central Universities (inter-disciplinary program) under the contract No. kx0080020173427. The revision of this manuscript by Prof. D. Roundy (emeritus) from Tongji University, and now an adjunct professor with BYU Hawaii, is acknowledged.

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Authors and Affiliations

  1. Institute of Refrigeration and Cryogenics, School of Mechanical Engineering, Tongji University, Shanghai, 201804, China

    Qiang Cao, Mingkai Luan, Peng Li & Yan Wu

  2. Shanghai Key Laboratory of Vehicle Aerodynamics and Vehicle Thermal Management Systems, Tongji University, Shanghai, 201804, China

    Qiang Cao

  3. Department of Electrical Engineering, School of Electronics and Information Engineering, Tongji University, Shanghai, 201804, China

    Li Wei

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  1. Qiang Cao
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  2. Mingkai Luan
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Correspondence to Yan Wu.

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Cao, Q., Luan, M., Li, P. et al. A Critical Review of Real Gas Effects on the Regenerative Refrigerators. J. Therm. Sci. 30, 782–806 (2021). https://doi.org/10.1007/s11630-020-1381-4

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