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.     

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.     

80K脉管制冷机惯性管调相机理及优化研究

液氮温区脉冲管制冷机在高温超导等领域的应用越来越广泛。基于热声理论,本文采用Delta EC软件对纯惯性管及惯性管加气库的调相能力进行模拟研究,建立了80 K温区制冷机整机数值模型,分析了不同惯性管及气库组合方式对制冷机性能的影响。结果表明:纯惯性管结构和单段惯性管加气库两种方式可以达到较为接近的调相能力,采用双段惯性管接气库方式可以提高制冷机性能,最低温度可以达到48.8 K。最后搭建制冷机整机性能测试实验台对模拟结果进行了验证。     

Multi-dimensional flow effects in pulse tube refrigerators

Pulse tube cryocoolers are often modeled as one-dimensional flow fields. We examine the adequacy of this assumption in this study. Two entire inertance tube pulse tube refrigerator (ITPTR) systems operating under a variety of thermal boundary conditions are modeled using a computational fluid dynamics (CFD) code. Each simulated ITPTRs includes a compressor, an after cooler, a regenerator, a pulse tube, cold and hot heat exchangers, an inertance tube, and a reservoir, and the simulations represent fully coupled systems operating in steady-periodic mode. The objectives are to ascertain the suitability of CFD methods for ITPTRs, and examine the extent of multi-dimensional flow effects in various ITPTR components. The results confirm that CFD simulations are capable of elucidating complex periodic processes in ITPTRs. The results also show that one-dimensional modeling is appropriate only when all the components in the system have large length-to-diameter (L/D) ratios. Significant multi-dimensional flow effects occur at the vicinity of component-to-component junctions, and secondary-flow recirculation patterns develop when one or more components have relatively small L/D ratios. Parameters in need of experimental measurement are discussed.     

内调相型脉管制冷机的理论分析

对内调相型脉管制冷机进行热力学理论分析.内调相型脉管制冷机的特点是两个冷头在脉管热端通过针阀串联,两边脉管内的压力和流量耦合,通过调节各自的输入压力相位来主动调节脉管冷端流量与压力的相位差,输入压力相位由一个具有双出口的旋转阀来实现.分析表明,该调相方法可使脉管冷端流量与压力同相,从而使制冷量最大,而且相比于传统的小孔加气库型和双向进气型脉管制冷机,其制冷效率大大提高.该结构省却了体积较大的气库,结构更加紧凑.     

An innovative configuration for thermoacoustically-driven pulse tube coolers

Obtainable lowest temperature of a thermoacoustically-driven pulse tube cooler is generally limited by the pressure ratio provided by the thermoacoustic engine with helium as working gas. It is also known that a thermoacoustic engine filled with nitrogen can generally provide much larger pressure ratio and lower frequency than the same engine filled with helium. Here we introduce an innovative system configuration which uses an elastic membrane as the interface between the thermoacoustic engine subsystem and the pulse tube cooler subsystem. The membrane can transport acoustic work from the engine to the cooler, and meanwhile separate the working gases used in respective subsystems. Through this way, it is possible for the engine to operate with nitrogen to provide larger pressure ratio and more suitable frequency for the pulse tube cooler which can still use helium as the working gas. To test this idea, a thermoacoustically-driven pulse tube cooler was built. With the innovative configuration, the pulse tube cooler reached a lowest temperature of 139 K. On the other hand, without the membrane, the PTC only achieved a lowest temperature of 186 K when using nitrogen and 145 K with helium for both the PTC and the engine.     

Effects of reservoir volume on performance of pulse tube cooler

A pulse tube cooler has the advantages of long-life and low-vibration over conventional cryocoolers such as G-M and Stirling coolers because of the absence of moving parts at low temperature. On the other hand, the combination of a reservoir and orifice is indispensable to optimize the performance of pulse tube coolers. In order to make the pulse tube cooler compact for practical applications, the volume of reservoir should be minimized. This paper analyzes the effects of the reservoir volume on the thermodynamic performance of various components in a simple orifice and a double-inlet pulse tube cooler by combining a linearized model with a thermodynamic analysis. Expressions of entropy production for those components are presented. The results show that the reservoir volume has a significant influence on the entropy production in the various components when the reservoir to pulse tube volume ratio is smaller than about 5. The ratio is important to determine the minimum reservoir volume for a pulse tube cooler. Optimum settings for a double-inlet pulse tube cooler are also discussed.     

Numerical method of inertance tube pulse tube refrigerator

A nodal analysis method for simulating inertance tube pulse tube refrigerators is introduced. The energy equation, continuity equation, momentum equation of gas, energy equation of solid are included in this model. Boundary condition can be easily changed to enable the numerical program calculate thermal acoustic engines, inertance tube pulse tube refrigerators, double inlet pulse tube refrigerators, and others. Implicit control volume method is used to solve these equations. In order to increase the calculation speed, the continuity equation is changed to pressure equation with ideal gas assumption, and merged with momentum equation. Then the algebraic equation group from continuity and momentum equation becomes one group. With this numerical method, an example calculation of a large scale inertance tube pulse tube refrigerator is shown.     

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.     

Innovative phase shifter for pulse tube operating below 10 K

Stirling type pulse tubes are classically based on the use of an inertance phase shifter to optimize their cooling power. The limitations of the phase shifting capabilities of these inertances have been pointed out in various studies. These limitations are particularly critical for low temperature operation, typically below about 50 K. An innovative phase shifter using an inertance tube filled with liquid, or fluid with high density or low viscosity, and separated by a sealed metallic diaphragm has been conceived and tested. This device has been characterized and validated on a dedicated test bench. Operation on a 50–80 K pulse tube cooler and on a low temperature (below 8 K) pulse tube cooler have been demonstrated and have validated the device in operation. These developments open the door for efficient and compact low temperature Stirling type pulse tube coolers. The possibility of long life operation has been experimentally verified and a design for space applications is proposed.     

A novel coupled VM-PT cryocooler operating at liquid helium temperature

This paper presents experimental results on a novel two-stage gas-coupled VM-PT cryocooler, which is a one-stage VM cooler coupled a pulse tube cooler. In order to reach temperatures below the critical point of helium-4, a one-stage coaxial pulse tube cryocooler was gas-coupled on the cold end of the former VM cryocooler. The low temperature inertance tube and room temperature gas reservoir were used as phase shifters. The influence of room temperature double-inlet was first investigated, and the results showed that it added excessive heat loss. Then the inertance tube, regenerator and the length of the pulse tube were researched experimentally. Especially, the DC flow, whose function is similar to the double-orifice, was experimentally studied, and shown to contribute about 0.2 K for the no-load temperature. The minimum no-load temperature of 4.4 K was obtained with a pressure ratio near 1.5, working frequency of 2.2 Hz, and average pressure of 1.73 MPa.     

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.     

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.     

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。     

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...     

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.     

Design and prototyping of a large capacity high frequency pulse tube

This document describes the design and the prototyping performed at CEA/SBT in partnership with AIR LIQUIDE of a high frequency large cooling power pulse tube. Driven at 58 Hz by a 7.5 kW flexure bearing pressure wave generator, this system provides a net heat lift of 210 W at 65 K. The phase shift is obtained by an inertance and a buffer volume. This type of cryogenic cooler can be used for on site gas liquefaction or drilling site and for high temperature superconductivity power device cooling (transmission lines, large generators, fault current limiters).In this paper, we focus on two essential points, the regenerator and the flow straightener. The regenerator is a key component for good performance of the pulse tube cooler. It must have a large thermal inertia, a low dead volume, a good heat transfer gas/matrix and at the same time, small pressure drop. In the present case and unlike typical moderate cooling power pulse tubes, the regenerator is very compact. However, the resulting conductive losses remain negligible compared to the cooling power targeted. The goal of the flow straightener is to avoid as much as possible any jet stream effect and to guarantee the uniformity of the velocity field at both ends of the pulse tube. Indeed multi-dimensional flow effects can significantly impact the performances of the machine.     

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.     

Characteristics of the double inlet pulse tube

The performance of the double inlet pulse tube (DIPT) is analyzed using a linearized model that takes account of the void volume of the regenerator. The maximum rate of refrigeration obtainable with the regenerator is determined as a function of frequency and void volume. This rate can be achieved by a DIPT with infinitely large reservoir volume. Corrections resulting from a finite reservoir volume are important only at low frequency. The coefficient of performance of a DIPT with optimized rate of refrigeration is less than half of the thermodynamic maximum. The results obtained for the DIPT are compared with corresponding results for the optimized orifice pulse tube refrigerator (OPTR). The large improvements in performance obtained with the DIPT over the OPTR are due primarily to an increase in the pulse tube pressure. The maximum rate of refrigeration decreases as the temperature at the cold side decreases. This is caused primarily from the resulting decrease in cold side flow rate. At given temperature ratio, addition of the second inlet reduces the flow rate through the regenerator over a range of intermediate frequencies.     

An electrical circuit analogy model for analyses and optimizations of the Stirling-type pulse tube cryocooler

The existing electrical circuit analogy (ECA) models are mainly used to optimize the inertance tube and to analyze the crude phase of the dynamic pressure and the volume flow rate. The specific analyses and optimizations of other components or the whole Stirling-type pulse tube cryocooler (SPTC) with the ECA model have not been carried out. In this paper, a new ECA model including the main components of the SPTC such as regenerator, pulse tube, phase shifter and reservoir has been developed. To improve the practicability of the ECA model, based on the basic governing equations, calculation expressions of the above components are worked out, and their equivalent analogical electrical elements are defined according to the analogy theory. Through the developed ECA model, the specific pressure and volume flow rate at any position can be acquired. Further optimizations on the SPTC based on the ECA model show that, with the same pressure and PV power at the warm end of the regenerator, there exists an optimal phase angle between the pressure and the volume flow rate for the SPTC to achieve the highest gross cooling capacity. In addition, with the same ratio of the pressure to the volume flow rate and the same phase angle between them at the warm end of the regenerator, when the regenerator ineffectiveness loss is neglected, the SPTC efficiency keeps constant with variations of the PV power, however, the efficiency will increase with the increase of the PV power if the loss is considered.