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.     

A two-stage Stirling-type pulse tube cryocooler with a cold inertance tube

A thermally coupled two-stage Stirling-type pulse tube cryocooler (PTC) with inertance tubes as phase shifters has been designed, manufactured and tested. In order to obtain a larger phase shift at the low acoustic power of about 2.0 W, a cold inertance tube as well as a cold reservoir for the second stage, precooled by the cold end of the first stage, was introduced into the system. The transmission line model was used to calculate the phase shift produced by the cold inertance tube. Effect of regenerator material, geometry and charging pressure on the performance of the second stage of the two-stage PTC was investigated based on the well known regenerator model REGEN. Experimental results of the two-stage PTC were carried out with an emphasis on the performance of the second stage. A lowest cooling temperature of 23.7 K and 0.50 W at 33.9 K were obtained with an input electric power of 150.0 W and an operating frequency of 40 Hz.     

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.     

40 K single-stage coaxial pulse tube cryocoolers

Several 40 K single-stage coaxial high frequency pulse tube cryocoolers (PTCs) have been developed to provide reliable and low-noise cooling for GaAs/AlGaAs Quantum-Well infrared photodetectors (QWIPs). The inertance tubes together with the gas reservoir become the only phase shifter to guarantee the required long-term stability. The mixed regenerator consisting of three segments has been developed to enhance the overall regenerator performance. At present, the cooler prototype has achieved a no-load temperature of 29.7 K and can typically provide 860 mW cooling at 40 K with 200 W electric input power rejecting at 300 K. The performance characteristics such as the temperature stability and ambient temperature adaptability are also presented.     

Condensation stage of a pulse tube pre-cooled dilution refrigerator

In our article, experiments with a pulse tube (PTR) pre-cooled dilution refrigerator (DR) are presented, where an upgraded ³He condensation stage has been tested. The DR had a ³He flow rate of up to 1.1 mmol/s. The ³He gas entering the refrigerator was first pre-cooled to a temperature of ～50 K at the first stage of the PTR. In the next cooling step, the ³He was run through a recently installed heat exchanger, which was attached to the regenerator of the second stage of the pulse tube cryocooler; at the outlet of this heat exchanger the temperature of the ³He was as low as ～4 K. Due to the non-ideality of the helium gas, the second regenerator of a two stage PTR has excess cooling power which can be made use of without affecting the base temperature of this stage, and it is this effect which was put to work, here. Finally, the ³He was further cooled in a heat exchanger, mounted at the second stage of the PTR, before it entered the dilution unit of the cryostat.The installation of a heat exchanger at the regenerator of the second stage of the PTR is especially important for the construction of DRs with high refrigeration capacities; in addition, it allows for a plain design of the subsequent Joule–Thomson (JT) stage, and herewith facilitates considerably the construction of “dry” DRs. The condensation rate of the ^3,4He mash prior to an experiment was increased. The pressure during condensation could be kept near 1 bar, and thus a compressor was no longer necessary with the modified apparatus.     

Experimental study of the influence of cold heat exchanger geometry on the performance of a co-axial pulse tube cooler

Improving the performance of the pulse tube cooler is one of the important objectives of the current studies. Besides the phase shifters and regenerators, heat exchangers also play an important role in determining the system efficiency and cooling capacity. A series of experiments on a 10 W @ 77 K class co-axial type pulse tube cooler with different cold heat exchanger geometries are presented in this paper. The cold heat exchangers are made from a copper block with radial slots, cut through using electrical discharge machining. Different slot widths varying from 0.12 mm to 0.4 mm and different slot numbers varying from around 20–60 are investigated, while the length of cold heat exchangers are kept the same. The cold heat exchanger geometry is classified into three groups, namely, constant heat transfer area, constant porosity and constant slot width. The study reveals that a large channel width of 0.4 mm (about ten times the thermal penetration depth of helium gas at 77 K, 100 Hz and 3.5 MPa) shows poor performance, the other results show complicated interaction effects between slot width and slot number. These systematic comparison experiments provide a useful reference for selecting a cold heat exchanger geometry in a practical cooler.     

Study on a 10 W/90 K in-line pulse tube cryocooler

A Stirling-type in-line pulse tube cryocooler (PTC) has been designed, built and tested at Shanghai Institute of Technical Physics (SITP), Chinese Academy of Sciences. This PTC prototype can obtain a low-noise cooling capacity of more than 10 W at around 90 K cold head temperature and is used for cooling a space-borne infrared photo detector. In order to achieve a highly efficient PTC, a simplified numerical simulation model has been established for design and optimization. The simulation results of the regenerator, pulse tube and inertance tube are analyzed in detail. Besides, some key parameters of the PTC are listed in the paper. The PTC’s performances are tested at different operating frequencies from 42 Hz to 55 Hz and its reject temperature dependence is observed in the range of 290 K to 320 K. Furthermore, the map of the PTC’s performance characteristics is presented.     

Method for estimating off-axis pulse tube losses

Some Stirling-type pulse tube cryocoolers (PTCs) exhibit sensitivity to gravitational orientation and often exhibit significant cooling performance losses unless situated with the cold end pointing downward. Prior investigations have indicated that some coolers exhibit sensitivity while others do not; however, a reliable method of predicting the level of sensitivity during the design process has not been developed. In this study, we present a relationship that estimates an upper limit to gravitationally induced losses as a function of the dimensionless pulse tube convection number (N_PTC) that can be used to ensure that a PTC would remain functional at adverse static tilt conditions. The empirical relationship is based on experimental data as well as experimentally validated 3-D computational fluid dynamics simulations that examine the effects of frequency, mass flow rate, pressure ratio, mass-pressure phase difference, hot and cold end temperatures, and static tilt angle. The validation of the computational model is based on experimental data collected from six commercial pulse tube cryocoolers. The simulation results are obtained from component-level models of the pulse tube and heat exchangers. Parameter ranges covered in component level simulations are 0–180° for tilt angle, 4–8 for length to diameter ratios, 4–80 K cold tip temperatures, −30° to +30° for mass flow to pressure phase angles, and 25–60 Hz operating frequencies. Simulation results and experimental data are aggregated to yield the relationship between inclined PTC performance and pulse tube convection numbers. The results indicate that the pulse tube convection number can be used as an order of magnitude indicator of the orientation sensitivity, but CFD simulations should be used to calculate the change in energy flow more accurately.     

Second law based modeling to optimum design of high capacity pulse tube refrigerators

The optimum design of a high capacity double inlet pulse tube refrigerator based on second law of thermodynamics has been presented in this paper. Second law is applied to calculate the work loss in the regenerator and to optimize the cryocooler performance. To investigate the behavior of the pulse tube refrigerator, mass and energy balance equations are applied to several control volumes of the cryocooler cycle. A complete system of conservation equations is employed to solve the regenerator analytically. The proposed model reports the cooling capacity of 110 W at 80 K cold end temperature at frequency of 50 Hz, orifice conductance of 0.4 and double inlet coefficient of 0.6, with 2.4 kW net power delivered to the gas. In this case, the entropy generation in the gas phase is dominant which is contributing more than 85% of the total lost work in the regenerator. The optimum thermal efficiency of 99.1% was achieved at a proper mesh number. However, the second law efficiency is reported to have an inverse behavior at this mesh number.     

3He/4He dilution refrigerator with high cooling capacity and direct pulse tube pre-cooling

In the article, a ³He/⁴He dilution refrigerator (DR) is described which is pre-cooled by a commercial two-stage pulse tube refrigerator (PTR); cryo-liquids are not necessary with this type of milli-kelvin refrigerator. The simple design of the condensation stage of this so-called dry DR is novel and explained in detail. In most dry DRs the circulating ³He gas is cooled by a two-stage PTR to a temperature of about 4 K. In the next cooling step, the ³He flow is cooled and partially liquefied in a Joule–Thomson circuit, before it is run to the dilution refrigeration unit. The counterflow heat exchanger of the Joule–Thomson circuit is cooled by the cold ³He gas pumped from the still of the DR. In the DR described here, the heat exchanger of the Joule–Thomson stage was omitted entirely; in the present design, the ³He gas is cooled by the PTR in three different heat exchangers, with the first one mounted on the first stage of the PTR, the second one on the regenerator of the second stage, and the third one on the cold end of the second stage. The heat load caused by the ³He flow is mostly absorbed by the first two heat exchangers. Thus the ³He flow presents only a small heat load to the second stage of the PTR, which therefore operates close to its base temperature of 2.5 K at all times. A pre-cooling temperature of 2.5 K of the ³He flow is sufficiently low to run a DR without further pre-cooling. The simplified condensation system allows for a shorter, compacter and more economical design of the DR. Additionally, the pumping speed of the turbo pump is no longer obstructed by the counterflow heat exchanger of the Joule Thomson stage as in our earlier DR design.     

Investigation on phase shifting for a 4 K Stirling pulse tube cryocooler with He-3 as working fluid

He-3 is generally recognized for its ability to provide more excellent thermophysical performance than He-4, especially in the 4 K temperature range. However, this was not always the case in our preliminary experiments on a three-stage Stirling-type pulse tube cryocooler (SPTC). Our ongoing studies, as reported in this paper, demonstrate that the different working fluids also affect the performance through their phase shifting capability. This feature has been passed over in large part by researchers considering refrigerant substitution. Unlike previous theoretical analyses that focus primarily on regenerator losses, this report investigates the effects of the working fluid on the phase angle at the cold end in order to quantitatively reveal the relationship between the lowest attainable temperature and the cooling capacity. The analysis agrees well with our experimental results on a three-stage SPTC. While running with the operating parameters optimized for He-3, the lowest temperature of the SPTC decreased from 5.4 K down to 4.03 K. This is the lowest refrigeration temperature ever achieved with a three-stage SPTC.     

CFD modeling and experimental verification of a single-stage coaxial Stirling-type pulse tube cryocooler without either double-inlet or multi-bypass operating at 30–35 K using mixed stainless steel mesh regenerator matrices

This paper presents the CFD modeling and experimental verifications of a single-stage inertance tube coaxial Stirling-type pulse tube cryocooler operating at 30–35 K using mixed stainless steel mesh regenerator matrices without either double-inlet or multi-bypass. A two-dimensional axis-symmetric CFD model with the thermal non-equilibrium mode is developed to simulate the internal process, and the underlying mechanism of significantly reducing the regenerator losses with mixed matrices is discussed in detail based on the given six cases. The modeling also indicates that the combination of the given different mesh segments can be optimized to achieve the highest cooling efficiency or the largest exergy ratio, and then the verification experiments are conducted in which the satisfactory agreements between simulated and tested results are observed. The experiments achieve a no-load temperature of 27.2 K and the cooling power of 0.78 W at 35 K, or 0.29 W at 30 K, with an input electric power of 220 W and a reject temperature of 300 K.     

A modified two-stage pulse tube cryocooler utilizing double-inlet and multi-mesh regenerator

In this paper a thermally coupled Stirling-type two-stage pulse tube cryocoolers (TSPTC) is studied using a one-dimensional (1-D) CFD code. After validating the results of the simulations, effects of synchronous utilization of multi-mesh regenerator and double-inlet on the performance of the TSPTC are investigated. Results of simulations show that non-oscillating friction factors do not possess sufficient accuracy for calculation of oscillating friction losses in non-porous media. Whereas, using oscillating friction factor of non-porous media leads to sufficient accurate results. According to the results, using multi-mesh regenerator and double-inlet increases the COP and decreases the minimum attainable temperature of the system. It is observed that a minimum temperature of 18.2 K is attainable using optimum multi-mesh regenerator and double-inlet; whereas, for a simple TSPTC with a uniform mesh regenerator, a minimum temperature of 26.4 K is concluded.     

Investigation on a thermal-coupled two-stage Stirling-type pulse tube cryocooler

Multi-stage Stirling-type pulse tube cryocoolers with high frequency (30–60 Hz) are one important direction in recent years. A two-stage Stirling-type pulse tube cryocooler with thermally coupled stages has been designed and established two years ago and some results have been published. In order to study the effect of first stage precooling temperature, related characteristics on performance are experimentally investigated. It shows that at high input power, when the precooling temperature is lower than 110 K, its effect on second stage temperature is quite small. There is also the evident effect of precooling temperature on pulse tube temperature distribution; this is for the first time that author notice the phenomenon. The mean working pressure is investigated and the 12.8 K lowest temperature with 500 W input power and 1.22 MPa average pressure have been gained, this is the lowest reported temperature for high frequency two-stage PTCS. Simulation has reflected upper mentioned typical features in experiments.     

A closed-cycle 1 K refrigeration cryostat

A 1 K closed-cycle cryostat has been developed to provide continuous cooling to a photon detector below 2 K. A two-stage 4 K pulse tube cryocooler is used to liquefy evacuated vapor from a 1 K pumping port to form a closed-cycle refrigeration loop. A 1 K instrumentation chamber, attached to the 1 K cooling station, is designed to operate with helium inside and provide more uniform cooling. The design of the cryostat has no direct mechanical contact between the pulse tube cryocooler heat exchangers and the 1 K cooling station resulting in almost no vibration transfer to instrumentation chamber. The cryostat can reach a no-load temperature of 1.62 K and provide 250 mW cooling power at 1.84 K.     

High-capacity 60 K single-stage coaxial pulse tube cryocoolers

A high-capacity single-stage coaxial pulse tube cryocooler operating at around 60 K has been developed to provide the appropriate cooling for the next-generation very-large-scale long wave infrared focal plane arrays under development. The application background and cooler design process are described, and the performance characteristics are presented. At present, the cooler typically provides 4.06 W at 60 K with the input power of 180 W at 300 K reject temperature. 4.72 W can also be achieved when the input power increases to 200 W, and over 9.4% of Carnot efficiency at 60 K has been realized. The larger pulse tube diameter of 14.2 mm is used and the evident orientation sensitivity is observed in the range of 55–65 Hz. The experiments also observe the obvious reject temperature dependence.     

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.     

An approach for estimating acoustic power in a pulse tube cryocooler

Acoustic power at the cold end of regenerator is the measure of gross cooling capacity for a pulse tube cryocooler (PTC), which cannot be measured directly. Conventionally, the acoustic power can only be derived from the measurement of velocity, pressure and their phase angle, which is still a challenge for an oscillating flow at cryogenic temperatures. A new method is proposed for estimating the acoustic power, which takes use of the easily measurable parameters, such as the pressure and temperature, instead of the velocity and phase angle between the pressure and velocity at cryogenic temperatures. The ratio of acoustic powers at the both ends of isothermal components, like regenerator, heat exchangers, can be conveniently evaluated by using the ratio of pressure amplitudes and the local temperatures. The ratio of acoustic powers at the both ends of adiabatic components, like transfer line and pulse tube, is obtained by using the ratio of pressure amplitudes. Accuracy of the approach for evaluating the acoustic power for the regenerator is analyzed by comparing the results with those from REGEN 3.3 and references. For the cold end temperature range of 40–80 K, the deviation is less than 5% if the phase angle at the cold end of regenerator is around −30°. The simple method benefits estimating the acoustic power and optimizing the PTC performance without interfering the cryogenic flow field.     

Numerical investigation on a 300 Hz pulse tube cryocooler driven by a three-stage traveling-wave thermoacoustic heat engine

A 300 Hz pulse tube cryocooler (PTC) driven by a three-stage traveling-wave thermoacoustic heat engine (TSTHE) has been proposed and studied in this paper. In the configuration, three identical thermoacoustic heat engine units are evenly incorporated in a closed traveling-wave loop, in which three pulse tube cryocoolers are connected to the branch of each thermoacoustic heat engine. Compared with the conventional thermoacoustic heat engine which involves a traveling-wave loop and a long resonator, it has advantages of compact size and potentially high thermal efficiency. A TSTHE–PTC system was designed, optimized and studied in detail based on the thermoacoustic theory. Firstly, numerical simulation was conducted to design the system thus the optimum structure parameters of the system were obtained. With the operating condition of 4 MPa mean pressure and high working frequency, a cooling power of 7.75 W at 77 K and an overall relative Carnot efficiency of 11.78% were achieved. In order to better understand the energy conversion characteristics of the system, distributions of key parameters such as acoustic work, phase difference, dynamic pressure, volume flow rate and exergy loss were presented and discussed. Then, the coupling mechanism of the system was investigated. In addition, influence of coupling position on the system performance was further studied.     

两级同轴型脉管制冷机回热器与脉管壁换热影响的模拟与实验

针对同轴型结构的两级脉管制冷机,采用热力学方法分析了回热器与脉管壁间换热作用对制冷机性能的影响。发现当脉管内热量通过壁面传向回热器时,脉管冷端焓流将增大,进而提升脉管冷指的制冷量。对设计的一台两级同轴型高频脉管冷指进行了数值模拟。模拟结果表明相同结构参数及输入下,引入回热器与脉管壁间的径向换热作用,低温级制冷量由原先的0.55 W@30 K提升至1.39 W@30 K,而对高温级的影响却小到可以忽略。