﻿ 惯性管型脉管内气体振荡制冷机理的分子动力学模拟

# 惯性管型脉管内气体振荡制冷机理的分子动力学模拟Molecular Dynamics Simulation of Gas Oscillation Refrigeration Mechanism in Inertia Tube Pulse Tube

Abstract: In this paper, the molecular dynamics simulation method is used to study the thermodynamic mechanism of the oscillation in the inertial tube (IT). The results show that the temperature, pressure and massflow phase of the inertia tube are delayed, the phase difference between the massflow and pressure wave is reduced, and the cooling efficiency of the pulse tube is improved. At the same time, the amplitude of massflow near the hot end decreases, while that near the cold end increases. In addition, the gas temperature in the IT is reduced. The simulation results are helpful to understand the thermodynamic mechanism of the internal oscillation of the IT.

1. 简介

2. 原理

2.1. 分子动力学模拟

${F}_{i}=-{\nabla }_{i}U=-\left(i\frac{\partial }{\partial {x}_{i}}+j\frac{\partial }{\partial {y}_{i}}+k\frac{\partial }{\partial {z}_{i}}\right)U$ (1)

${a}_{i}=\frac{{F}_{i}}{{m}_{i}}=\frac{\partial {v}_{i}}{\partial t}=\frac{{\partial }^{2}{r}_{i}}{\partial {t}^{2}}$ (2)

a为原子加速度，F为所受力，m为其质量，v和r为其速度和位置。而且

${F}_{i}=\underset{j\ne i}{\sum }{F}_{ij}=-\underset{j\ne i}{\sum }{\nabla }_{ij}{U}_{ij}$ (3)

${U}_{ij}={G}_{i}\underset{i=1}{\overset{N}{\sum }}{\rho }_{h,i}+\frac{1}{2}\underset{i=1}{\overset{N}{\sum }}\underset{i\ne i}{\sum }{\varphi }_{ij}\left({r}_{ij}\right)$ (4)

${\rho }_{h,i}=\underset{j=1,j\ne i}{\overset{N}{\sum }}{\rho }_{j}\left({r}_{ij}\right)$ (5)

${\rho }_{i}\left({r}_{ij}\right)=\underset{k=1}{\overset{2}{\sum }}{A}_{k}{\left({R}_{k}-{r}_{ij}\right)}^{3}H\left({R}_{k}-{r}_{ij}\right)$ (6)

${\varphi }_{ij}\left({r}_{ij}\right)=\frac{1}{4\pi {\epsilon }_{0}}\frac{Z\left(i\right)Z\left(j\right)}{{r}_{ij}}$ (7)

U为原子对势，G为嵌入能，表示原子i嵌入其他邻近原子在该处产生的电荷密度的能量， $\rho$ 为电荷密度， $\varphi$ 为原子间相互斥能。

${U}_{ij}=4\epsilon \left[{\left(\frac{\sigma }{{r}_{ij}}\right)}^{12}-{\left(\frac{\sigma }{{r}_{ij}}\right)}^{6}\right]$ (8)

Table 1. L-J potential energy model parameters

${T}_{cal}=\frac{\underset{i=1}{\overset{N}{\sum }}{m}_{i}\left[{\left({v}_{i,x}-{v}_{ci,x}\right)}^{2}+{\left({v}_{i,y}-{v}_{ci,y}\right)}^{2}+{\left({v}_{i,z}-{v}_{ci,z}\right)}^{2}\right]}{3N{k}_{B}}$ (9)

${v}_{ci}=\frac{\underset{i=1}{\overset{N}{\sum }}{v}_{i}}{N}$ (10)

$p=\frac{NRT}{V}$ (11)

2.2. 分子动力学模型

Figure 1. (a) Basic pulse tube; (b) IT pulse tube

3. 仿真模拟结果与分析

3.1. 惯性管型脉管模拟结果及分析

Figure 2. IT pulse tube after operation

Figure 3. Temperature changes with time

Figure 4. Pressure changes with time

Figure 5. Massflow changes with time

Figure 6. Phase difference between massflow and pressure wave

3.2. 惯性管型脉管特点

Figure 7. Temperature changes with time

Figure 8. Pressure changes with time

Figure 9. Massflow changes with time

4. 结论

NOTES

*通讯作者。

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