The behaviour of the various gas elements which enter the tube of a pulse tube refrigerator from its cold end has been analysed using the method of characteristics. It is found that, in an orifice pulse tube refrigerator, the gas elements can be divided into three parts. The specific cooling capacity produced by the second part of the gas elements is the largest. If the total mass is fixed, in order to improve the overall cooling capacity of an orifice pulse tube refrigerator, the ratio of the gas elements in the second part should be increased, while those in the first part and the third part should be decreased.

In order to improve the performance of a one-stage pulse tube cryocooler, gas mixtures are used for comparison, which have been used in other cryocoolers. A mixture of hydrogen and helium was investigated in this study. When the structure of the pulse tube is the same as mentioned in [C. Wang, P.Y. Wu, Zh.Q. Chen, Numerical modeling of an ori

Abstract The effect of the tube wall heat conduction on the natural convection in a tilted long cylindrical envelope with constant, but different temperature of the two ends and an adiabatic outer surface was numerically investigated. The envelope is supposed to be a simplified model for the pulse tube in a pulse tube refrigerator when the pulse tube is positioned at different orientations. It is found that the cylindrical envelope lateralwall heat conduction can enhance the heat transfer fromthe hot end to the cold end, not only because of the increase in pure heat conduction in the wall, but more importantly, also the intensification of the natural convection within the enclosure. This enhancement is resulted fromthe big temperature difference between the tubewall and the adjacent fluid near the hot and cold ends. Adoption of low thermal conductivity tube can effectively reduce such additional heat transfers fromhot to cold end, thus reducing the loss of cooling capacity for the pulse tube refrigerator.

Numerical simulations were conducted to reveal the inherent relation between the filed synergy principle and the three existing mechanisms for enhancing single phase convective heat transfer. It is found that the three mechanisms, i.e., the decreasing of thermal boundary layer, the increasing of flow interruption and the increasing of velocity gradient near a solid wall, all lead to the reduction of intersection angle between velocity and temperature gradient. It is also revealed that at low flow speed, the fin attached a tube not only increases heat transfer surface but also greatly improves the synergy between the velocity and the temperature gradient.

本文建立了分置式微型斯特林制冷机的理论分析模型，给出了其内部各种参数（热力参数、流动参数、传热参数）的动态变化规律；并进行了主要结构参数的优化分析；同时还给出了各组成部件变质量、非稳定流动系统的（火用）损失计算式。可推荐给工程买际应用。

The natural convection heat transfer and fluid flow in a vertical cylindrical envelope with constant but different temperatures of the two end surfaces and an adiabatic lateral wall was numerically investigated. Apart from some other applications, it serves as a simplified model of the pulse tube of a pulse tube refrigerator. The simulation was conductedfor two end wall temperature differences: DTw ¼ 10 and 220 K. For the cases of DTw ¼ 10 K, it is found that the variation patterns of NuL vs. RaL within the range of L=D ¼ 3-10 are in good consistency with the experimental and theoretical results provided by Catton and Edward for L=D ¼ 0-2:5. The C-E chart is thus extended from L=D ¼ 2:5to 10. Within the range of RaL ¼ 1:1×105 to 4 • 107 the fluid isothermals in both longitudinal and cross-sections exhibit some laminated character, and the convective heat transfer rate is in the same order or one-order larger than that of pure heat conduction. For the case of large temperature difference (DTw ¼ 220 K) the natural convection in the enclosure is quite strong in that the convective heat transfer rate is about two-orders larger than that of pure heat conduction which occurs when the cold end is placed down. To reduce the loss of cooling capacity of the pulse tube refrigerator, the pulse tube should be positioned with cold end down. Numerical simulation also revealed that the ratio of the axial length, L, to the diameter, D, has effect on the average heat transfer rate of the envelope under the same other conditions. Within the range of L=D ¼ 1-9, the increase in L=D leads to the decrease in heat transfer rate.

In engineering fields there are such energy transport and or conversion processes in which the resulting quantity is expressed by the dot production of two vectors. For such processes, the reduction of the intersection angle (or phase angle shift) between the two vectors is the most fundamental way for enhancing the processes (field synergy principle). For a pulse tube refrigerator (PTR) its cooling capacity at the hot end is shown to be proportional to the dot production of velocity vector and pressure vector. Detailed numerical analyses are conducted for the PTR to reveal the variation of its cooling capacity with the phase angle shift between the velocity wave and pressure wave. Numerical results clearly reveal the size effect of the orifice and double inlet valve of the PTR on the phase angle shift, and hence, on the PTR cooling capacity. The field synergy principle is further used to determine the optimum length to diameter ratio of the pulse tube and the optimal molar percentage of helium for a PTR using hydrogen/helium mixture as a working medium. Simulation results definitely show that the field synergy principle is a powerful guide to enhance energy conversion and transport processes.

In this paper, two models were introduced with the governing equations to simulate two kinds of tapered pulse tube cryocoolers. The simulation results were in good agreement with the results of respective experiments. It was also found that there was an optimum cone angle for tapered pulse tube cryocooler. When the cryogenic refrigerator works with this optimum cone angle, the performance could be improved a lot, which means decreasing the lowest cooling temperature and or increasing the cooling power.

本文建立了分置式微型斯特林制冷机的理论分析模型，给出了其内部各种参数（热力参数、流动参数、传热参数）的动态变化规律；并进行了主要结构参数的优化分析；同时还给出了各组成部件变质量、非稳定流动系统的粗（火用）损失计算式。可推荐给工程实际应用。

The natural convection heat transfer and fluid flow in a vertical cylindrical envelope with constant but different temperatures of the two end surfaces and an adiabatic lateral wall was numerically investigated. Apart from some other applications, it serves as a simplified model of the pulse tube of a pulse tube refrigerator. The simulation was conducted for two end wall temperature differences: △Tw=10 and 220K. For the cases of △Tw =10K, it is found that the variation patterns of NuL vs. RaL within the range of L/D=3-10 are in good consistency with the experimental andtheoretical results provided by Catton and Edward for L/D=0-2.5. The C-E chart is thus extended from L/D=2.5 to 10. Within the range of RaL=1.1×105 to 4×107 the fluid isothermals in both longitudinal and cross-sections exhibit some laminated character, and the convective heat transfer rate is in the same order or one-order larger than that of pure heat conduction. For the case of large temperature difference (△Tw=220K) the natural convection in the enclosure is quite strong in that the convective heat transfer rate is about two-orders larger than that of pure heat conduction which occurs when the cold end is placed down. To reduce the loss of cooling capacity of the pulse tube refrigerator, the pulse tube should be positioned with cold end down. Numerical simulation also revealed that the ratio of the axial length, L, to the diameter, D, has effect on the average heat transfer rate of the envelope under the same other conditions. Within the range of L/D=1-9, the increase in L/D leads to the decrease in heat transfer rate.