Simulation on alternating oscillation flow in microchannel pulse tube coupled with active piston using non-equilibrium molecular dynamics

doi:10.1016/j.cplett.2020.137965

Chemical Physics Letters

Volume 759, 16 November 2020, 137965

https://doi.org/10.1016/j.cplett.2020.137965 Get rights and content

Highlights

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The non-equilibrium MD method is used to simulate the alternating oscillation flow.
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The microcosmic mechanism of flow in micro-channel pulse tube is studied.
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A model includes tube, compression piston and phase shifter piston is established.
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The instantaneous and time-averaged value of physical parameters are counted.
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The parameters of phase difference, stroke ratio, period are adjusted as the variable.

Abstract

The molecular dynamics method was used to calculate the alternating oscillating flow in the micro-channel pulse tube. A thermodynamics corresponding process of the pulse tube coupled with an active piston was simulated. The simulation results show that the pressure amplitude at middle of tube was smaller than the two ends of the tube, but the main temperature gradient was distributed among them and the temperature at cold end further decreased with the motion of active piston at hot end. The optimal field distribution was obtained when the displacement phase angle for the compression piston and the active piston was 108°.

Graphical abstract

Introduction

The pulse tube refrigerator has high reliability because it has no moving parts at the cold end, and uses nitrogen or helium as the refrigerant, but its cooling efficiency is still far behind that of traditional Oxford and Stirling refrigerators. In recent years, many researchers have studied the components of the refrigerator through numerical simulation and experimental methods. The researches to improve the performance of the refrigerator mainly focuses on the phase shift mechanism such as orifice type, double-inlet valve type, multi-bypass type, and inertance tube type, etc. These methods were widely used to improve the efficiency of the refrigeration. McKinley [1] reported on the latest development of the pulse tube refrigerator about driving frequency, thermodynamic characteristic parameters, and heat rejection temperature. The Darcy coefficient in the hydrodynamics equation was determined according to the Ergun equation.

Ashjaee [2] had performed a numerical study on natural convection heat transfer of a horizontal iso-thermal cylinder located underneath an adiabatic ceiling. Eslam [3] and Jafarpur analyzed the laminar natural convective heat transfer process of isolated objects. The results showed that the heat transfer gradually decreased as the angle increased from horizontal to vertical, besides, the natural convection intensity was related to the shape of the object. The natural convection and forced convection in the reciprocating fluid in the tube and the establishment of the temperature gradient in the tube was not only related to the period but also related to the ratio of length-diameter and the shape of the tube [4]. Ashwin [5] conducted the CFD simulation non-equilibrium alternating flow in high-frequency pulse tube with inertance tube. It carried out that the phase shift of pressure; temperature and massflow were significant either. A proper ratio of length to the diameter of the tube could balance the relationship between the axial heat conduction loss and the empty volume loss, causing a decrease of temperature at the cold end, which affected the working condition of the compressor.

In order to further improve the efficiency of the refrigerator, Japanese researches Matsubata [6] proposed for the first time to place an active piston at the hot end of the pulse tube, which adjusted the phase shift at the cold end. The active piston caused excessive mass flow that made the heat conduction loss and failure loss of the regenerator the main loss [7], but the ability of phase shifter was superior to the inertance tube and orifice. When the displacement angle between the active piston and compression piston was adjusted, the phase angle between pressure wave and massflow could be regulated to any angle. This broke the limitation that the inertance tube had the given capability of phase shifter [8]. For the multi-temperature and multi-state coupling type, the stepped warm displacer at hot end recovered the expansion power, which improved on 40% of Carnot efficiency under 20 K temperature [9], [10]. Compared with the linear arrangement, the coaxial multi-state coupling structure combined with an active piston at the hot end let the phase shifter closer to the cold end. The structure was more compact and the cooling power was higher [11], [12]. Afterward, Masuyama [13] further replaced the free piston to an active piston as a phase shifter and the gas storage structure was omitted, besides the pressure wave led the mass flow wave by 76° at the hot end. By the way, the optimal pressure amplitude ratio of APC (Active phase controller) and PWG (Pressure wave generator) outlet was given. In addition, the effects of the charge pressure, operating frequency, input power and other parameters on no-load temperature, cooling power, and cooling efficiency were also been discussed gradually [13], [14]. The active piston directly connected to the pulse tube as a phase shifter, and the acoustic power flow of the active piston and compression piston intersected in the tube, which changed the phase distribution in the tube between pressure wave and massflow. However, the mechanism of the formation process of the temperature fields which influence by the piston stroke of compression piston and active phase shifter was not clear.

In this paper, a phase modulation structure was added to the basic pulse tube at the hot end which led to a larger temperature gradient in the tube based on the previous work [15]. The effect of ratio of piston stroke and position phase angle between compression piston and active piston on the alternating oscillation flow and the temperature, pressure, velocity and massflow are affected by these parameters. Therefore, the establishment process and capability of phase shifter based on natural convection and forced convection in a known geometry of pulse tube were predicted and evaluated. In the model, the cold end connected to the compression cavity, the compression piston provided the pressure wave. The hot end connected to an expansion cavity with an active piston as a phase shifter and a moving reflect-wall was set to be the piston to adjust the phase. This work helps to clarify the separation process of cold and hot gas in the tube, and the space–time distribution of temperature, pressure, velocity, density. The effect of the combined action of the compression piston and the phase-shifting piston on the alternating oscillating flow in the tube was clarified. The influence mechanism of the phase angle at the cold end on the gas piston in the pulse tube was explored to deepen the understanding of the refrigeration mechanism.

Section snippets

Analysis of pulse tube refrigeration mechanism

According to the phase theory [16], [17], the time-averaged enthalpy flow expressed as: $p_{i} = p_{0} + Δ p_{t} s i n 2 π t f$ $〈 \dot{H} 〉 = \frac{c_{p} m T}{τ} = \frac{C_{p} A_{g}}{R τ} \int_{0}^{τ} u p d t = \frac{C_{p} A_{g}}{R τ} \int_{0}^{τ} p_{0} u_{0} s i n ω t s i n (ω t - φ) d t$ $〈 \dot{H} 〉 \propto \frac{1}{2} p_{d} u_{0} c o s φ$

$p_{0}$ is amplitude of pressure oscillation, $u_{0}$ is amplitude of speed oscillation. $Φ$ is the phase difference between pressure wave and velocity wave. A maximum enthalpy flow could be obtained when $φ = 0^{°}$ . Adding an active piston at the hot end could adjust the phase difference distribution of the pressure wave and velocity wave at

Molecular dynamics model building and simulation method

The total energy of the molecule are the sum of the total potential energy U and total kinetic energy E_k. The total potential energy U include Vander-waals force and internal potential energy of the molecule. A Van-der-waals force between molecules was usually described by the force field. In this paper, Lennard-Jone potential energy is used between He atoms. This force field equation includes the exclusive term of the power of 12 and the attraction term of the power of 6 as follows [18]: $U_{ij} = 4 ε [(σ)]$

Instantaneous parameter changes in pulse tube

Figs. 3 and 4 show the variation curve of in basic pulse tube and combined with an active piston at the hot end. The red line and blue line are the instantaneous pressure at the hot end and cold end, the dotted line is the displacement of compression piston changes with the times. The pressure oscillation curve in the figure intercepts the state when the system reaches a steady-state. The pressure oscillation curves at the hot end and cold end are both similar to the sinusoidal curve, besides

The influence on the phase angle in the pulse tube

Fig. 10a, Fig. 10b, Fig. 10c, Fig. 10d shows the curve of pressure wave and velocity wave changes with time about two types of the pulse tube. The ordinary least squares method was used to fit the nine-order multinomial of curves in the figure. The starting point of the curve is the time when the temperature is stable. The velocity waves at the cold end approach to sinusoidal function and have a fixed phase difference between velocity and pressure. The phase difference between pressure and

Influence of displacement stroke ratio (Ds)

Fig. 15 shows that the maximum value of the pressure wave in a cycle at cold end increases accordingly and the minimum value does not change when the Ds increases from 0.25 to 0.6. As a result, the pressure ratio increases and the effective acoustic power increases. As shown in Figs. 16 and 17, the axial temperature gradient in the tube is the largest and the temperature at the cold end is the lowest under Ds is 0.6. Therefore, there is an optimal dimensionless ratio of Ds.

Comprehensive consideration of Ds and displacement phase angle

The largest axial

Conclusion

In this paper, the molecular dynamics simulation method is used to simulate the cold and hot separation process under high-frequency alternating oscillation in a micro pulse tube coupled with an active piston. The effects of displacement stroke ratio of the active piston to compression piston and displacement phase angle on the axial temperature gradient. The process of establishing the axial temperature gradient in the micro pulse tube closely related to the pressure wave at each position and

CRediT authorship contribution statement

Yanjin Che: Conceptualization, Methodology, Software, Investigation, Writing - original draft. Yingxia Qi: Conceptualization, Methodology, Writing - review & editing. Shizhe Niu: Software, Formal analysis. Yali Liu: Visualization, Investigation. Hua Zhang: Conceptualization, Methodology.

Declaration of Competing Interest

The authors declare that they have no known competing financial interests or personal relationships that could have appeared to influence the work reported in this paper.

Acknowledgement

The project was supported by the Shanghai Key Laboratory of Multiphase Flow and Heat Transfer in Power Engineering (13DZ2260900).

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Citation Excerpt :
Their simulation results showed that the energy flow density of acoustic waves was high when the forced oscillation time was lower than the natural oscillation time. After that, the research of [84] used MDS to effectively simulate the thermodynamic process of the coupling between the microchannel pulse tube and the active piston. Their simulation results presented that when the piston was located in the middle of the tube, the pressure amplitude was smaller than that at both ends of the tube.
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Research paperSimulation on alternating oscillation flow in microchannel pulse tube coupled with active piston using non-equilibrium molecular dynamics

Highlights

Abstract

Graphical abstract

Introduction

Section snippets

Analysis of pulse tube refrigeration mechanism

Molecular dynamics model building and simulation method

Instantaneous parameter changes in pulse tube

The influence on the phase angle in the pulse tube

Influence of displacement stroke ratio (Ds)

Comprehensive consideration of Ds and displacement phase angle

Conclusion

CRediT authorship contribution statement

Declaration of Competing Interest

Acknowledgement

Appl. Therm. Eng.

Cryogenics

Cryogenics

Int. J. Refrig.

Int. J. Refrig.

Cryogenics

Int. J. Refrig.

Int. J. Therm. Sci.

Int. J. Refrig.

Int. J. Refrig.

Energy

Characterization testing of Lockheed Martin high-power micro pulse tube cryocooler

IOP Conf. Ser.: Mater. Sci. Eng.

A numerical study on natural convention heat transfer from a horizontal isothermal cylinder located underneath an adiabatic ceiling

Heat Transfer Eng.

Research paper
Simulation on alternating oscillation flow in microchannel pulse tube coupled with active piston using non-equilibrium molecular dynamics