Design and analysis of compact work-recovery phase shifter for pulse tube refrigerator

This paper proposes and describes a compact work-recovery phase shifter of a pulse tube refrigerator. Most pulse tube refrigerators recently developed utilize a long inertance tube and a reservoir for phase control between dynamic pressure and mass flow rate at the cold-end of pulse tube refrigerators. An inertance tube-type phase shifter (long inertance tube and reservoir), however, sometimes creates a problem of compact packaging in cryocooler applications and dissipates the work transferred from a compressor as heat. To overcome this disadvantage, an inertance tube-type phase shifter is replaced with a compact work-recovery phase shifter composed of a mass–spring–damper system and a linear generator in a pulse tube refrigerator. This process is achieved by using analogy of the inertance tube-type phase shifter and the mass–spring–damper system. This paper describes a specific configuration of the designed compact work-recovery phase shifter. Using the simulation code, the performance of the pulse tube refrigerator with the compact work-recovery phase shifter is estimated. As a result, the pulse tube refrigerator with the compact work-recovery phase shifter has the comparable cooling capacity with the pulse tube refrigerator with the inertance tube-type phase shifter. If the recovery work is properly utilized, it can also achieve higher efficiency than that of the pulse tube refrigerator with a typical inertance tube-type phase shifter. In this paper, the parametric study of the mass, the spring and damper coefficients of the compact work-recovery phase shifter has been done and their effects are specifically evaluated.     

Wave-shaping of pulse tube cryocooler components for improved performance

The method of wave-shaping acoustic resonators is applied to an inertance type cryogenic pulse tube refrigerator (IPTR) to improve its performance. A detailed time-dependent axisymmetric experimentally validated computational fluid dynamic (CFD) model of the PTR is used to predict its performance. The continuity, momentum and energy equations are solved for both the refrigerant gas (helium) and the porous media regions (the regenerator and the three heat-exchangers) in the PTR. An improved representation of heat transfer in the porous media is achieved by employing a thermal non-equilibrium model to couple the gas and solid (porous media) energy equations. The wave-shaped regenerator and pulse tube studied have cone geometries and the effects of different cone angles and the orientation (nozzle v/s diffuser mode) on the system performance are investigated. The resultant spatio-temporal pressure, temperature and velocity fields in the regenerator and pulse tube components are evaluated. The performance of these wave-shaped PTRs is compared to the performance of a non wave-shaped system with cylindrical components. Better cooling is predicted for the cryocooler using wave-shaped components oriented in the diffuser mode.     

A numerical method of regenerator

A numerical method for regenerators is introduced in this paper. It is not only suitable for the regenerators in cryocoolers and Stirling engines, but also suitable for the stacks in acoustic engines and the pulse tubes in pulse tube refrigerators. The numerical model is one dimensional periodic unsteady flow model. The numerical method is based on the control volume concept with the implicitly solve method. The iteration acceleration method, which considers the one-dimensional periodic unsteady problem as the steady two-dimensional problem, is used for decreasing the calculation time. By this method, the regenerator in an inertance tube pulse tube refrigerator was simulated. The result is useful for understanding how the inefficiency of the regenerator changes with the inertance effect.     

斯特林型脉管制冷机中惯性管的优化设计

介绍了斯特林型脉管制冷机中惯性管调相的原理和惯性管的传输线理论模型,给出了惯性管尺寸的优化计算方法.采用该方法对现有的脉管制冷机中惯性管的调相能力进行了模拟计算,研究了PV功、压比和气库容积等参数对最佳惯性管尺寸的影响,并与实验结果进行了对比,计算结果与实验结果符合较好.     

Comparison of two different ways of using inertance tube in a pulse tube cooler

It is well known that the pressure wave should lead the volume flow rate at the ambient end of the pulse tube for a high-efficiency operation of a pulse tube cooler. Inertance tube can provide such a phase relationship without DC flow problem. However, inertance tube is always connected with a reservoir in previous literatures. Through theoretical calculation here, inertance tube without a reservoir can also provide a rather large phase-leading effect. Thus phasor diagram is used to analyze the relationship between phase-leading requirement and the pulse tube geometry. Roughly speaking, a larger void volume of pulse tube would require a larger phase-leading effect. Comparison experiments are also done on a thermoacoustically-driven pulse tube cooler. With i.d.2 mm tube as inertance tube, the tube without reservoir yields close results in terms of lowest temperature to that of the tube with reservoir and both give much better performance than that of an orifice with reservoir. Finally, the advantages of using inertance tube without reservoir are given.     

Numerical analysis of stirling type pulse tube cryocoolers

A one-dimensional finite volume discretization method is proposed and is implemented as a computer program for the modeling of a family of stirling type Pulse Tube Cryocoolers (PTC). The set of unsteady, one-dimensional, viscous compressible flow equations are written in a general form such that all, porous and non-porous, sections of the PTC can be modeled with these governing equations. In present work, temperature dependency of thermo-physical properties are taken into account as well as the heat transfer between the working fluid and the solid parts, and heat conductions of the gas and solid. The simulation tool can be used to model both the inertance tube type and the orifice type cryocoolers equipped with regenerators made up of different matrix constructions. The PTC might have an arbitrary orientation with respect to the gravitational field. By using the computer program, an orifice type and an inertance tube type pulse tube cryocooler are simulated. Diameter of the orifice and length of the inertance tube are optimized in order to maximize the coefficient of performance. Furthermore, the cooling power of the two types is obtained as a function of the cooling temperature. The behavior of thermodynamic parameters of the inertance tube PTC is investigated. Mean cyclic values of the parameters are presented.     

Enthalpy flow rate of a pulse tube in pulse tube refrigerator

An integration formula of enthalpy flow rate along a pulse tube in pulse tube refrigerators is described on the assumption of sinusoidal mass flow rate and sinusoidal pressure fluctuation. For ideal double inlet and ideal orifice pulse tube with helium as working medium, it is simplified to a polynomial formula. Polynomial formulas for roughly evaluating the volume of the pulse tube in ideal double inlet and ideal orifice pulse tube refrigerators are also given.     

Performance characteristics of pulse tube refrigerators

In the present study experiments were carried out to investigate the performance characteristics of pulse tube refrigerators. It was found that the cool-down time t_c during the transient or start-up period is dominated by the time constant of the pulse tube wall τ_pt and that the dynamics of a basic pulse tube (BPT) refrigerator approaches that of a first-order system. For steady state operation, the cold-end temperature T_L was found to vary with τ_pt, and the cooling load Q_L increases monotonically with increasing τ_pt. This indicates that heat pumped by the gas from the cold to the hot end increases with decreasing h_pt (i.e. less energy exchange between the gas and wall). The process of heat storage or release of the pulse tube wall is thus shown to have a negative effect on the performance of a BPT refrigerator. It was thus found experimentally that the gas compression/expansion process inside the pulse tube, which is similar to a Brayton cycle but lies between isothermal and adiabatic, can explain the performance of BPT refrigerators. The present experiment also shows that the performance of a pulse tube refrigerator at transient and steady states is mainly dominated by the time constant of the pulse tube wall τ_pt.     

Performance of the inertance pulse tube

The rate of refrigeration of the inertance pulse tube (IPTR) is found as a function of the relevant parameters. In the simplified case of infinite volume of the reservoir and zero dead volume of the regenerator, these parameters are the dimensions of the inertance tube, the volume of the pulse tube, the conductance of the regenerator, the driving pressure, and the frequency. The effective conductance of the inertance tube is determined using a simple turbulent flow model. It is found that the performance of the IPTR is superior to that of the orifice pulse tube refrigerator (OPTR) over a limited range of frequencies. The improvement is explained in terms of the pressure amplitude in the pulse tube, the flow rate between the regenerator and the pulse tube, and the phase angle between these parameters. The analysis is extended to the case of finite reservoir and regenerator volumes. It is indicated how the results obtained can be useful in experimental work.     

Leakage effect analysis on the performance of a cylindrical adjustable inertance tube

The inertance tube plays a significant role in improving the performance of the Stirling type pulse tube cryocooler by providing the desired phase angle between the mass flow and pressure wave. The phase angle is highly depended on the inertance tube geometry, such as diameter and length. A cylindrical threaded root device with variable thread depth on the outer screw and inner screw creates an adjustable inertance tube whose diameter and length can be adjusted in the real time. However, due to its geometry imperfectness, the performance of this threaded inertance tube is reduced by the leaks through the roots between the two screws. Its phase angle shift ability is decreased by 30% with the leakage clearance thickness of 15.5 μm according to both the theoretical prediction and the experimental verification.     

A review of pulse tube refrigeration

The pulse tube belongs to the class of miniature cryogenic refrigerators usually referred to as cryocoolers. In common with Stirling and Gifford-McMahon machines, operation depends on a regenerative gas expansion cycle but unlike these coolers the pulse tube has no moving parts at low temperature and hence offers the potential for high reliability. Although comparisons may be drawn between the operation of a pulse tube and that of a Stirling cooler, the exact nature of the working cycle is far from clear and the device continues to intrigue. We provide here an introduction to the device and attempt to explain it's operation as a conventional second law system.     

Analysis on the stirling-type pulse tube refrigerator in consideration of dynamics of linear compressor

This paper describes the performance analysis of Stirling-type pulse tube refrigerator (PTR) in conjunction with the dynamics of the accompanied linear compressor. The dynamic behavior of the piston in the linear compressor is directly influenced by the load condition of the PTR. In this paper, the dynamic equation of the piston is simultaneously solved with the thermo-hydraulic governing equations of the PTR using linear analysis model and the performance of the PTR is predicted with the accompanied thermal losses. The developed analysis code is verified with the experimental results. The effect of the inertance tube length which plays an important role in the PTR is also specifically investigated from the experimental and simulation results. It clearly shows the effect of the flow impedance of the inertance tube on the dynamic response of the piston as well as the cooling performance of the PTR.     

300 Hz脉冲管制冷机特性研究

从实验和数值计算两个方面研究了1台工作频率为300 Hz的单级脉冲管制冷机的制冷特性.实验方面,验证了平均压力、入口压比、惯性管长度以及均流化元件对其制冷性能的影响,该制冷机在平均压力为3.96 MPa、入口压比为1.21时获得了79.6 K的最低制冷温度;数值计算方面,基于线性热声理论的模拟结果与实验结果进行了比较,以验证程序的有效性.     

Influence of the connecting tube at the cold end in a U-shaped pulse tube cryocooler

In some special applications, the pulse tube cryocooler must be designed as U-shape; however, the connecting tube at the cold end will influence the cooling performance. Although lots of U-shape pulse tubes have been developed, the mechanism of the influence of the connecting tube on the performance has not been well demonstrated. Based on thermoacoustic theory, this paper discusses the influence of the length and diameter of the connecting tube, transition structure, flow straightener, impedance of the inertance tube, etc. on the cooling performance. Primary experiments were carried out in two in-line shape pulse tube cryocoolers to verify the analysis. The two cryocoolers shared the same regenerator, heat exchangers, inertance tube and straightener, and the pulse tube, so the influence of these components could be eliminated. With the same electric power, the pulse tube cryocooler without connecting parts obtained 31 W cooling power at 77 K; meanwhile, the other pulse tube cryocooler with the connecting parts only obtained 27 W, so the connecting tube induced more than a 12.9% decrease on the cooling performance, which agrees with the calculation quite well.     

CFD analysis of thermodynamic cycles in a pulse tube refrigerator

The objectives of this paper are to study the thermodynamic cycles in an inertance tube pulse tube refrigerator (ITPTR) by means of CFD method. The simulation results show that gas parcels working in different parts of ITPTR undergo different thermodynamic cycles. The net effects of those thermodynamic cycles are pumping heat from the low temperature part to the high temperature part of the system. The simulation results also show that under different frequencies of piston movement, the gas parcels working in the same part of the system will undergo the same type of thermodynamic cycles. The simulated thermal cycles are compared with those thermodynamic analysis results from a reference. Comparisons show that both CFD simulations and theoretical analysis predict the same type of thermal cycles at the same location. However, only CFD simulation can give the quantitative results, while the thermodynamic analysis is still remaining in quality.     

Experimental study of a thermoacoustically-driven traveling wave thermoacoustic refrigerator

New configurations of traveling wave thermoacoustic refrigerators driven by a traveling wave thermoacoustic engine were introduced and tested in this paper. First, the performance of the refrigerator with different-diameter inertance tubes was investigated experimentally. Then, investigation of substituting a flexible membrane attached to inertial mass for inertance tube was tested. The experimental results show that the substitution could improve the efficiency of the system and lead to a larger cooling power. So far, using helium gas as the working gas, the system could provide 340 W cooling power at the temperature of −20 °C with working frequency of 57 Hz and average pressure of 3.0 MPa. The total COP, i.e., cooling power divided by heating power, is 0.16.     

脉冲管制冷机交变流动动态特性数值研究：第一部分;基本方程和数值方法

针对脉冲管制冷机的特点建立了数值模拟模型，采用改进的数值模拟方法对脉冲管制冷机的内部交变流动，换热以及制冷过程进行了详尽的数值研究，得到了脉冲管制冷机内部各参数的动态变化，并分析了各动态参数变化对制冷机整机性能的影响。数值模拟分析与实验结果符合良好。该模拟方法从基本流动换热微分方程出发，尽可能多地考虑实际制冷机工作过程中的各种不可逆因素，包括实际气体的物性变化，各部件的流动阻力和传热损失。     

基于CFD的惯性管流动特性研究

湍流和近壁处理对惯性管计算结果有重要影响,这是造成基于一维、小压比的惯性管模型存在较大偏差的根本原因.借助商用计算流体动力学(CFD)软件F1uent,采用Reynolds时均方程对惯性管内气体流动进行数值模拟.构建包括惯性管和气库的二维轴对称数学模型.研究4种不同湍流模型对计算结果的影响.模拟结果表明:以调相角为标准...     

主动调相型脉管制冷机数值模拟与实验研究

设计了一台主动调相型斯特林脉管制冷机,采用线性压缩机作为脉管制冷机主动调相控制器(APC),连接于冷指热端出口。通过控制调相压缩机与驱动压缩机(PWG)间的位移相位角实现主动调相,从而调节质量流和压力波之间的相位关系,优化制冷性能。利用模拟软件进行数值模拟并进行实验研究。研究结果表明,定输入功下APC与PWG位移相位角为-110°及扫气容积比(PWG扫气容积/APC扫气容积)2.98时,无负载制冷温度最低,同时比卡诺效率最高,能够达到原惯性管型脉管制冷机同样的效率。     

Computational fluid dynamics simulations of an orifice type pulse tube refrigerator: Effects of operating frequency

A numerical study is reported here for the investigation of the fundamental flow and heat transfer processes found in an orifice type pulse tube refrigerator (OPTR). The OPTR is driven by a cyclically moving piston at one end of the system with helium as the working fluid. The regenerator and the various heat exchangers are modeled as porous media and a thermal non-equilibrium model is applied in these regions. The system is studied for different operating frequencies of the driver piston. The simulations reveal interesting steady-periodic flow patterns that develop in the pulse tube due to the fluctuations caused by the piston and the presence of the inertance tube. The predicted secondary-flow recirculation patterns in the pulse tube are found to affect the OPTR performance. When the secondary-flow patterns are well-developed, they help isolate the cold and hot ends of the pulse tube and create a thermal buffer zone at the center of the pulse tube, enhancing the performance of the OPTR.