Numerical simulation of the second stage regenerator in a 4K GM cryocooler

Xu, Mingzhi; Morie, Takaaki

doi:10.1063/1.4860834

Cited by 10 publications

(14 citation statements)

References 5 publications

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“…The expansion power will be computed as

Q_{exp} = \frac{1}{τ} . \oint P_{e} d V_{e} .

The net refrigeration power will be estimated after subtracting the loss mechanisms as:

Q_{net} = Q_{exp} - Q_{losses} .

The PV work supplied by the compressor is:

W_{comp} = \frac{1}{τ} \oint \overset{m_{c}}{true} italicRT normalln \frac{P_{normalHP}}{P_{normalLP}} normaldt .

The COP of a GM cryocooler will be computed as

normalCOP = \frac{Q_{normalnet}}{W_{normalcomp}} .

The validation is shown in Figure B, and a good agreement is observed between the numerical results obtained from the experimental results (taken from the performance map of the cryocooler as a reference model in this work) and the numerical values of Xu and Morie . As suggested by Xu and Morie, here also, the cylinder diameter is taken as 8.2 cm, and its length as 19.25 cm. The swept length of expansion chamber is taken as 2.5 cm .…”

Section: Numerical Modelingmentioning

confidence: 86%

“…The numerical model used here is based on the work of Xu and Morie, on that of Panda et al for a GM cooler, and on that of Wang and Gifford for a pulse tube cooler, which was subsequently improved by considering various loss mechanisms . The governing differential equations are continuity, momentum, and energy equations for fluid domain, and energy equation for solid matrix and wall.…”

Section: Numerical Modelingmentioning

confidence: 99%

“…The mass flow rate through the HPV and LPV of the rotary valve (shown in Figure ) is given by

{\dot{m}}_{rv} = ({, \begin{matrix} {CV}_{hpv} \sqrt{P_{HP}^{2} - P_{a}^{2}} normalif P_{HP} > P_{a} \\ - {CV}_{lpv} \sqrt{P_{a}^{2} - P_{LP}^{2}} normalif P_{LP} < P_{a} \end{matrix}) .

The displacement of the displacer at the right‐hand side is given below:

x_{d} = S_{ce} + 0.5 \times S_{e} \times ({}, 1 - normalcos ([], ((), 2 π ft) - ((), θ \times \frac{true}{π}))),

where S ce is the length of dead space, S e is the stroke length of the displacer, and θ is the delay angle of the displacer motion.…”

Section: Numerical Modelingmentioning

confidence: 99%

“…A, Numerical solution algorithm of Gifford‐McMahon cryocooler; B, Validation of the developed code with Xu and Morie and experimental results…”

Section: Numerical Modelingmentioning

confidence: 99%

“…The friction factor:

C_{f} = ({, \begin{matrix} \frac{64}{Re} for laminar \\ \frac{124}{Re} + 0.0143 for turbulent \end{matrix}) .

The Nusselt number will be computed for laminar flow with isothermal BC as given by Boroujerdi et al, and turbulent flow as

italicNu = 0.023 {Re}^{0.8} {Pr}^{0.4} .

The axial‐conduction enhancement constant is

ξ = ({, \begin{matrix} 1 for laminar \\ 0.022 {Re}^{0.75} italicPr for turbulent \end{matrix}) .

More details regarding the discretization procedure may also be found in previous studies in the case of a pulse tube cooler. Furthermore, the calculation of performance parameters, such as the cooling power and COP, is similar to that proposed by Zhu and Matsubara …”

Section: Numerical Modelingmentioning

confidence: 99%

See 4 more Smart Citations

Effect of valve opening shapes on the performance of a single‐stage Gifford‐McMahon cryocooler

Panda

Satapathy

Sarangi

2019

Engineering Reports

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In this work, the effect of the triangular and Gaussian‐shaped opening of the rotary valve (ie, the valve timing diagram of high‐pressure and low‐pressure valves) on the performance of a single‐stage Gifford‐McMahon (GM) cryorefrigerator is numerically investigated. In addition, the effect of waiting time of the rotary valve on its cooling power and coefficient of performance is studied for both types of opening shapes. The governing equations representing the fluid flow and heat transfer behaviors of the refrigerator are solved by using an implicit finite‐volume discretization method. The model considers both primary and secondary loss mechanisms. The developed model is first validated with the published results on GM cryorefrigerators. A very good agreement appears among them. It is observed that no significant change can be appreciated in the cooling power between 40° to 90° of waiting time for both types of opening shapes. On the other hand, in‐between 1° to 40° of waiting time, the cooling power of the Gaussian‐shaped opening of the rotary valve is higher than the one of the triangular opening.

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“…The expansion power will be computed as