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High-frequency pulse tube cryocooler (HPTC) has advantages of compact structure, low vibration, high reliability and long operation time. In this study, Theoretical analysis and experimental tests have been conducted in four aspects based on a developed 4 K HPTC. Firstly, a compressor with larger power output capability was employed and the impedance match between the cold head and the compressor was discussed. Secondly, simply using inertance tube configuration to replace the traditional inertance tube-gas reservoir structure. Then, the type and the size of the regenerator materials working at 4–20 K have been experimentally optimized. Finally, the performance of double-inlet working at as low as 20 K has also been tested for the first time for the HPTC. The present prototype achieved a no-load temperature of 3.6 K, which is the lowest temperature record ever reported for HPTC using helium-4 as working gas. A cooling power of 6 mW/4.2 K was also obtained with 250 W input power and a precooling power of 12.1 W/77 K.

The heat transfer and pressure drop under oscillatory condition in helical rectangular channel heat exchangers are numerically investigated by using uniform design method. The correlations of three models with different ratios of height to width are obtained. The results show that the channel with the largest ratio of length to width has a larger heat transfer rate and a lower friction factor. Then, the field synergy principle is used to analyze heat transfer enhancement of helical rectangular channel heat exchanger. Besides, the Performance Evaluation Criteria (PEC) method has been used to compare the thermal-hydraulic performances of helical rectangular channel heat exchanger with helically coiled tube heat exchanger. The results show that the helical rectangular channel heat exchanger has a better performance operating at high frequency and high velocity. So it is more suitable for the Stirling type machines. Finally, a helical rectangular channel heat exchanger was experimentally used in our thermal-compressor system to verify the present numerical result.

The work presents the first wide-range equation of state (EOS) for 3He–4He mixtures based on the reduced Helmholtz free energy multi-fluid approximation model. It covers the temperature range from 2.17 to 300 K and the pressure from the vapor pressure up to 3 MPa for any given mixture 3He mole fraction. In this model, the 4He and 3He reduced Helmholtz free energy equations and departure functions from the literature are employed and only five unknown mixture parameters are needed for each given departure function. The parameters and the best model for the concerned binary mixture were determined by the Levenberg–Marquardt optimization method. With the best developed model, the liquid, gaseous, and saturated thermophysical properties of the mixture can be mostly described with an accuracy better than 5%. Furthermore, a database for the thermophysical properties of 3He–4He mixtures is generated and provided for interpolation in temperature, pressure, and 3He mole fraction. The current EOS and database can be applied to the design and optimization of ultra-low temperature refrigerators.

VM type pulse tube cryocooler is a new type pulse tube cryocooler driven by the thermal-compressor. This paper presented the recent experimental results on a novel single-stage VM type pulse tube cryocooler with multi-bypass. The low temperature double-inlet, orifice and gas reservoir, and multi-bypass were used as phase shifters. With the optimal operating frequency of 1.6 Hz and optimal average pressure of 1.4 MPa, a no-load temperature of 4.9 K has been obtained and 30 mW@5.6 K cooling power has been achieved. It was the first time for the single-stage VM-PTC obtaining liquid helium temperature reported so far. Moreover, it was also the first time for the multi-bypass being used in the low-frequency Stirling type pulse tube cryocooler.

Thermal compressor, different from the linear compressor, is one kind of compressor utilizing heat power directly to generate a pressure wave. Combining with the pulse tube cryocooler, it could become a new type high efficiency 4 K cryocooler. In present work, a numerical method based on finite volume method was carried out to study the characteristics of thermal compressor. The simulation results were verified by experiments at first. Then the no-load performance of thermal compressor was studied and the results showed that the waves in the thermal compressor no longer obeyed the linear thermoacoustics theory. And then, the RC load method was used to study the output thermoacoustics characteristics of thermal compressor. With a RC load, the wave mode in the thermal compressor would convert into the traveling wave from standing wave. The results showed that thermal compressor was preferable to drive the capacitive load and the best impedance of orifice valve was about 5 × 10 9 Pa s/m 3 . According to the optimum load impedance optimized above, we can design a suitable PTC for the TCP.

A cryogen-free cryostat cooled using a 4 K commercial GM or pulse tube cryocooler (PTC) displays temperature oscillations caused by the intrinsic working principle of the regenerative cryocooler. To dampen such oscillations usually requires either a large heat capacity or a large thermal resistance. To understand this phenomenon better and suppress it more effectively, both the step response characteristic and the intrinsic oscillation characteristic of cryostat have been used to obtain the complete transfer functions of a simulation model. The latter is used to test and optimize traditional PID feedback control. The results showed this approach has almost no effect on the temperature oscillation amplitude. Based on this simulation model, a novel active method was proposed and tested numerically. Simulation results predict the method should suppress the amplitude of the original temperature oscillation by a factor of two., Comment: 16 pages, 10 figures

The SPRIGT team in TIPC has achieved the most stable long-term pressure in the world in the range from 30 to 90 kPa. The pressure instability is less than 0.1 ppm (0.0032 Pa at 30 kPa, 0.009 Pa at 90 kPa), which can build the foundation for the success of SPRIGT.

International audience; The Vuilleumier (VM) type pulse tube cryocooler (VPTC) is a new kind of 4 K cryocooler which had been experimentally verified. This paper presents the recent advances on a 4 K VPTC in our laboratory. First, the mechanism of multi-bypass was numerically studied using Sage software. The results showed that the function of the multi-bypass is not only similar to a double-inlet, but also to an orifice, which makes the VPTC work like a two-stage cryocooler. Based on the simulation results, the performance of VPTC was experimentally studied. Under its optimal operating conditions, a no-load temperature of 3.7 K has been obtained, which is the first demonstration of a single-stage VPTC obtaining temperatures below 4 K. It can supply about 14mW cooling power at 4.2 K and about 100 mW cooling power at 35 K simultaneously, which has potential application as the pre-cooler for an adiabatic demagnetization refrigerator (ADR). Finally, based on this VPTC, a new mK cooling chain for HUBS (Hot Universe Baryon Surveyor) satellite is proposed and its prospect has also been theoretically analyzed.

Vuilleumier coupling pulse tube (VM-PT) cryocooler is a novel kind of cryocooler capable of attaining liquid helium temperature which had been experimentally verified. Depending on different coupling modes and phase shifters, VM-PT cryocooler can be designed in several configurations. This paper presents a numerical investigation on three typical types of VM-PT cryocoolers, which are gas-coupling mode with room temperature phase shifter (GCRP), gas-coupling mode with cold phase shifter (GCCP) and thermal-coupling mode with cold phase shifter (TCCP). Firstly, three configurations are optimized on operating parameters to attain lower no-load temperature. Then, based on the simulation results, distributions of acoustic power, enthalpy flow, pressure wave, and volume flow rate are presented and discussed to better understand the energy flow characteristics and coupling mechanism. Meanwhile, analyses of phase relationship and exergy loss are also performed. Furthermore, a GCCP experimental system with optimal comprehensive performance among three configurations was built and tested. Experimental results showed good consistency with the simulations. Finally, a no-load temperature of 3.39 K and cooling power of 9.75 mW at 4.2 K were obtained with a pressure ratio of 1.7, operating frequency of 1.22 Hz and mean pressure of 1.5 MPa.

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.

A numerical method for simulating cryocooler below 10K, especially for VM cryocooler, is carried out based on the finite volume method. Compressibility, real gas effect, temperature dependence of properties and porous heat transfer are considered simultaneously in this model. The under-relaxation method is used to increase the stability of simulation. By comparison of the simulation results and experimental results, the simulated and tested no-load temperatures and cooling powers agree with each other very well. By using a computer program written, the lowest temperature, the pressure in three cavities, the real gas effect and the losses of cold displacer are comprehensively analyzed. Furthermore, the phase angle, the cold regenerator and the hot end temperature are optimized.

We describe measurements of thermodynamic temperature in the range 5 K to 24.5561 K (the triple point of neon) using single-pressure refractive-index gas thermometry (SPRIGT) with 4He. In the wake of the May 2019 re-definition of the kelvin and its associated mise en pratique, the main purpose of the work is to provide values of T–T 90, the discrepancy between thermodynamic temperature and that of the International Temperature Scale of 1990 (ITS-90). The link to ITS-90 is made via calibrated rhodium-iron resistance thermometers. Innovations required to reach the level of accuracy required for meaningful measurements (uncertainty in T–T 90 less than the expected deviation) include the suppression of temperature oscillations in a cryogen-free cryostat, a pressure stabilization scheme based on a non-rotating piston balance, modelling of the hydrostatic head correction and refinements of the measurement of microwave resonances in a quasi-spherical copper resonator. The accuracy of measurements varies from 0.05 mK to 0.17 mK and is competitive with that of all previous ones in this temperature range using other techniques. The improvement stems partly from the new techniques used for the new definition of the kelvin as well as ab initio calculations of the thermophysical properties ofgaseous 4He. In addition to confirming the validity of SPRIGT as an accurate, easier-to-implement alternative to other low-temperature primary thermometry techniques (e.g. acoustic gas thermometry) yet with scope for improvement, the results should provide important input data for any future revision of ITS-90.

To achieve an uncertainty of 0.25 mK in single-pressure refractive-index gas thermometry (SPRIGT), the relative pressure variation of He-4 gas in the range 30 kPa to 120 kPa, should not exceed 4 ppm (k = 1). To this end, a novel pressure control system has been developed. It consists of two main parts: a piston gauge to control the pressure, and a home-made gas compensation system to supplement the micro-leak of the piston gauge. In addition, to maintain the piston at constant height, a servo loop is used that automatically determines in real time the amount of extra gas required. At room temperature, the standard deviations of the stabilized pressure are 3.0 mPa at 30 kPa, 4.5 mPa at 60 kPa and 2 mPa at 90 kPa. For the temperature region 5 K–25 K used for SPRIGT in the present work, the relative pressure stability is better than 0.16 ppm i.e. 25 times better than required. Moreover, the same pressure stabilization system is readily transposable to other primary gas thermometers.

A cryogen-free cryostat cooled by a closed cycle cryocooler is compact, can provide uninterrupted long-term operation (up to ten thousand hours) and is suited to temperatures from 3 K to 300 K. Its intrinsic temperature oscillation, however, limits its application in experiments requiring high thermal stability at low temperature (below 77 K). Passive suppression methods are effective but all suffer from drawbacks. We describe a novel, active suppression scheme more efficient than traditional proportional-integral (PI) control. The experimental results show that it can reduce the standard deviation of the temperature oscillation by a further 30% compared with PI feedback. To the best of our knowledge, this is the first time such active suppression of temperature oscillations has been implemented with the cryogen-free cryostat. The results also show, however, that an unwanted lower frequency thermal noise will be generated, which appears to be the limit of the method. Nevertheless, the approach could be used to improve the temperature stability in all cryogen-free cryostats.

Vuilleumier cycle was first patented in 1918. It was usually regard as the thermal-driven Stirling refrigeration cycle, which combined the low-frequency working pattern like Giffod-Mcmahon (GM) cryocooler and the compactness of Stirling-type cryocooler. With the continuous development in the past 100 years, the Vuilleumier-type (VM-type) cryocoolers have to been proved to generate cooling power from ambient temperature to liquid nitrogen temperature and even to liquid helium temperature. In recent decades, some efforts were made on traditional displacer-type VM cryocooler, Vuilleumier hybrid pulse tube cryocooler (VM-HPTC) and the VM-type pulse tube cryocooler (VM-type PTC) to obtain the liquid helium temperature. Successfully, not only the 4 K was obtained, but also the limit temperature of oscillating cryocooler by He4 was hit. This paper presents the progress of the 4 K-class VM-type cryocooler and analyzed the possible applications of 4 K class VM-type cryocooler.

A novel single pressure refractive index gas thermometry(SPRIGT) allows the determination of thermodynamic temperature of helium gas filled in quasi-spherical microwave cavity resonator(QMCR) by combination of microwave measurements, temperature and pressure control. A long-term temperature stability better than O.2mK is demanded for the QMCR from 5K to 24.5561 K. The uncertainty below 4ppm for pressure needs to precisely control the oscillation of temperature along the gas line. Microwave resonance frequency measurement in QMCR should be better than 2ppb. To meet these requirements, SPRIGT has been built in China and the first run experimental data was analysis in this paper.

Quasi-spherical microwave cavity resonators are widely used in primary thermometry. To realize high-accuracy microwave resonant frequency measurement, it is essential to close the two quasi-hemispheres correctly. We show how to do this using microwave resonance signals to monitor shape and sealing as torques to equatorial bolts are increased. The present resonator was closed with torques up to 105 cNm. The method should be useful to monitor the closing of other quasi-spherical cavities.

The Vuilleumier (VM) refrigerator, known as heat driven refrigerator, is one kind of closed-cycle Stirling type regenerative refrigerator. The VM refrigerator with power being supplied by liquid nitrogen was proposed by Hogen and developed by Zhou, which shows great potential for development below 10 K. This paper describes the experimental development of a VM cryocooler operating below 8 K, which was achieved by using liquid nitrogen as a heat sink of middle cavity. The regenerator was optimized by using a part of metallic magnetic regenerator material Er3Ni to replace the lead sphere and a no-load temperature of 7.8 K was obtained. Then all the lead spheres were replaced by Er0.6Pr0.4 material and a no-load temperature of 7.35 K was obtained, which is the lowest temperature for this kind of refrigerator reported so far. The cooling power at 10 K is about 500 mW with a pressure ratio near 1.6 and a charge pressure of 1.8 MPa. Especially, the magnetic material Er0.6Pr0.4 was found to be a potential substitution for the conventional lead.

The VM refrigerator with power being supplied by liquid nitrogen shows great potential for application below 10K. The 2D axisymmetric model refers to actual geometry under oscillating flow conditions is carried out using FLUENT software. The lowest temperature, the pressure in three cavities, the temperature profile along the regenerator is presented. The simulation results show good agreement with available data. Then the regenerator between cold and middle cavity is optimized to obtain the lowest temperature, it is filled with stainless steel screens and lead shot. It is found that there exists an optimal ratio of stainless steel screens and lead in the same length regenerator.

This paper will introduce our recent experimental results of cryogenic regenerator materials employed in Stirling-type one-stage pulse-tube refrigerator for the use at liquid hydrogen temperature. Thermal diffusion coefficient, according to which we choose the suitable regenerator materials, will prove to be a useful reference. We will also discuss the impact of resistance of sphere regenerator materials on the performance of the refrigerator and the method to improve it. Take an overall consideration, suitable-size Er 3 Ni will be applied as the regenerator materials at the cold head and we achieve a remarkable 14.7 K no-load temperature.

The VM refrigerator, known as heat driven refrigerator, is one kind of closed-cycle regenerative refrigerator. There are some losses in VM refrigerator, but the losses in regenerator are the main loss when the refrigeration temperature is below 100 K. This paper present one method to calculate the pressure drop loss in the regenerator, which is one main part loss in the regenerator. The pressure drop loss in the regenerator will decrease the refrigeration capacity in two aspects. On the one hand, due to the friction pressure drop in the regenerator will be converted into heat that causes reduced the refrigeration capacity. On the other hand, the pressure drop in the regenerator will decrease the pressure ratio in cold end. From a practical standpoint, this calculation method was used for analysis one VM refrigerator proposed by Zhou in 1984. The results showed that the results by using this method are very close to the experimental results in three temperature points.

Single-pressure refractive-index gas thermometry (SPRIGT) is a new type primary thermometry jointly developed by TIPC of CAS in China and LNE-Cnam in France. To realize a competitive uncertainty of 0.25 mK for the thermodynamic temperature measurement, a cryogen-free cryostat with high-stability better than 0.2 mK should be designed. This paper presented the first experimental results of temperature control for this cryostat. To realize this objective, multi-layer radiation shields combined with a thermal-resistance method were used to isolate the thermal-noise from surroundings. Besides, a new temperature control method based on a gas-type heat switch and proportional-integral-derivative control method was proposed, which was applicable to different temperature ranges by changing the working modes of the heat switch. After optimizing, the ultra-high precision temperature control in the range of 5-25 K has been fully realized, which was the temperature instability (with standard deviation) of 0.021 mK at 5.0 K, 0.05 mK at 5.7 K, 0.042 mK at 7.4 K, 0.029 mK at 14.3 K, and 0.022 mK at 25 K with the sampling time of 0.8 s. This was almost the best reporting result in the world and showed its great potential in SPRIGT.

The Stirling-type cryocooler with its compact size and high efficiency is always expected to obtain its temperature limit of below 3 K. However, the pressure drop losses caused by high-frequency oscillation create large obstacles for this objective. This paper reports a novel thermal-driven Stirling-type cryocooler to obtain the lowest temperature of a Stirling-type cryocooler. The advantages of a thermal-driven cryocooler (Vuilleumier cryocooler) and pulse tube cryocooler are combined with a new type of cryocooler, called the Vuilleumier gas-coupling pulse tube hybrid cryocooler (VM-PT). A prototype of the VM-PT was recently developed and optimized in our laboratory. By using helium-4 as the working gas and magnetic regenerative materials (HoCu2 and Er3Ni), the lowest temperature of 2.5 K was obtained, which can be regarded as an important breakthrough for the Stirling-type cryocooler to achieve its limit temperature of below 3 K. It can supply >30 mW cooling power at 4.2 K and >500 mW cooling power at 20 K simultaneously. Theoretically, it is feasible to use this VM-PT for cooling the superconducting devices in space applications.The Stirling-type cryocooler with its compact size and high efficiency is always expected to obtain its temperature limit of below 3 K. However, the pressure drop losses caused by high-frequency oscillation create large obstacles for this objective. This paper reports a novel thermal-driven Stirling-type cryocooler to obtain the lowest temperature of a Stirling-type cryocooler. The advantages of a thermal-driven cryocooler (Vuilleumier cryocooler) and pulse tube cryocooler are combined with a new type of cryocooler, called the Vuilleumier gas-coupling pulse tube hybrid cryocooler (VM-PT). A prototype of the VM-PT was recently developed and optimized in our laboratory. By using helium-4 as the working gas and magnetic regenerative materials (HoCu2 and Er3Ni), the lowest temperature of 2.5 K was obtained, which can be regarded as an important breakthrough for the Stirling-type cryocooler to achieve its limit temperature of below 3 K. It can supply >30 mW cooling power at 4.2 K and >500 mW cooling power at 2...

Sub-kelvin refrigerator has many applications in space detector and manned space station, such as for the transition-edge superconducting (TES) bolometers operated in the 50 mK range. In order to meet the requirement of space applications, the high efficient, vibration free and high stability refrigerator need to be designed. VM/PT hybrid cryocooler is a new type cryocooler capable of attaining temperature below 4K. As a low frequency Stirling type cryocooler, it has the advantages of high stability and high efficiency. Combined with the vibration free sorption cooler and ADR refrigerator, a novel sub-kelvin cooling chain can be designed for the TES bolometer. This paper presents the recent experimental progress of the 4K VM/PT hybrid cryocooler in our laboratory. By optimizing of regenerators, phase shifters and heat exchangers, a lowest temperature of 2.6K was attained. Based on this cryocooler, a preliminary sorption cooler could be designed.

This paper introduces our recent experimental results of pulse tube refrigerator driven by linear compressor. The working frequency is 23-30 Hz, which is much higher than the G-M type cooler (the developed cryocooler will be called high frequency pulse tube refrigerator in this paper). To achieve a temperature below 10 K, two types of two-stage configuration, gas coupled and thermal coupled, have been designed, built and tested. At present, both types can achieve a no-load temperature below 10 K by using only one compressor. As to gas-coupled HPTR, the second stage can achieve a cooling power of 16 mW/10K when the first stage applied a 400 mW heat load at 60 K with a total input power of 400 W. As to thermal-coupled HPTR, the designed cooling power of the first stage is 10W/80K, and then the temperature of the second stage can get a temperature below 10 K with a total input power of 300 W. In the current preliminary experiment, liquid nitrogen is used to replace the first coaxial configuration as the precooling stage, and a no-load temperature 9.6 K can be achieved with a stainless steel mesh regenerator. Using Er3Ni sphere with a diameter about 50-60 micron, the simulation results show it is possible to achieve a temperature below 8 K. The configuration, the phase shifters and the regenerative materials of the developed two types of two-stage high frequency pulse tube refrigerator will be discussed, and some typical experimental results and considerations for achieving a better performance will also be presented in this paper.

Single-pressure refractive index gas thermometry (SPRIGT) is a new type of primary thermometry, which needs an extremely stable working pressure (stability

We used absolute primary acoustic gas thermometry (AGT) to calibrate a Pt–Co resistance thermometer on the thermodynamic temperature scale by measuring the speed of sound in helium at a temperature T* chosen to be near the temperature of the triple point of neon, T Ne. Prior to the present AGT, the Pt–Co thermometer was used with a neon triple-point cell as part of an interlaboratory comparison. Taken together, the results of the interlaboratory comparison and the present AGT redetermined the thermodynamic temperature T Ne = (24.555 15 ± 0.000 24) K. This new value of T Ne is consistent with other recent determinations obtained with various primary methods. After completing the AGT thermodynamic calibration, we used the Pt–Co thermometer to link T* to the temperature ratios measured by single-pressure refractive-index gas thermometry (SPRIGT) in a different laboratory. (Gao et al 2020 Metrologia 57 065006) Now, the T*-linked SPRIGT system can calibrate other thermometers on the thermodynamic temperature scale T in the range 5 K ⩽ T ⩽ T Ne without using the international temperature scale ITS-90. At most temperatures in this range, the uncertainties of the T*-linked SPRIGT system are smaller than those of the ITS-90 systems used by National Metrology Institutes to calibrate resistance thermometers.