Theoretical and experimental investigations on the cooling capacity distributions at the stages in the thermally-coupled two-stage Stirling-type pulse tube cryocooler without external precooling

The two-stage Stirling-type pulse tube cryocooler (SPTC) has advantages in simultaneously providing the cooling powers at two different temperatures, and the capacity in distributing these cooling capacities between the stages is significant to its practical applications. In this paper, a theoretical model of the thermally-coupled two-stage SPTC without external precooling is established based on the electric circuit analogy with considering real gas effects, and the simulations of both the cooling performances and PV power distribution between stages are conducted. The results indicate that the PV power is inversely proportional to the acoustic impedance of each stage, and the cooling capacity distribution is determined by the cold finger cooling efficiency and the PV power into each stage together. The design methods of the cold fingers to achieve both the desired PV power and the cooling capacity distribution between the stages are summarized. The two-stage SPTC is developed and tested based on the above theoretical investigations, and the experimental results show that it can simultaneously achieve 0.69 W at 30 K and 3.1 W at 85 K with an electric input power of 330 W and a reject temperature of 300 K. The consistency between the simulated and the experimental results is observed and the theoretical investigations are experimentally verified.     

Investigation on a three-cold-finger pulse tube cryocooler

This paper introduces a new type of pulse tube cryocooler, three-cold-finger pulse tube cryocooler (TCFPTC), which consists of one linear compressor and three cold fingers, i.e., CFA, CFB and CFC. Those three cold fingers are driven by the linear compressor simultaneously. This paper investigates two aspects. First, it studies the mass flow distribution among the three cold fingers by varying the input electrical power. The cooling powers of the three cold fingers at constant cooling temperatures and the cooling temperatures of the three cold fingers at constant cooling powers with various input electrical powers are investigated. Secondly, the interaction among the three cold fingers is investigated by varying the heating power of any one cold finger. Generally, if the heating power applied on one cold finger increases, with its cold head temperature rising up, the cold head temperatures of the others will decrease. But, when the cooling power of CFC has been 4 W, the cold head temperature of whichever cold finger increases, the cold head temperature of CFA or CFB will seldom change if its heating power keeps constant.     

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.     

Vibration reduction of pulse tube cryocooler driven by single piston compressor

The development of pulse tube coolers has progressed significantly during the past two decades. A single piston linear compressor is used to in order to reduce the size and mass of a high frequency pulse tube cryocooler. The pulse tube achieved a no-load temperature of 61 K and a cooling power of 1 W@80 K with an operating frequency of 80 Hz and an electrical input power of 50 W. By itself, the single piston compressor generates a large vibration, so a set of leaf springs with an additional mass is used to reduce the vibration. The equation relating the mass, the elasticity coefficient of leaf spring and the working frequency is obtained through an empirical fit of the experimental data. The vibration amplitude is reduced from 55 mm/s to lower than 5 mm/s by using a proper leaf spring. This paper demonstrates that a single piston compressor with vibration reduction provides a good choice for a PTC.     

Study on cold head structure of a 300 Hz thermoacoustically driven pulse tube cryocooler

High reliability, compact size and potentially high thermal efficiency make the high frequency thermoacoustically-driven pulse tube cryocooler quite promising for space use. With continuous efforts, the lowest temperature and the thermal efficiency of the coupled system have been greatly improved. So far, a cold head temperature below 60 K has been achieved on such kind of cryocooler with the operation frequency of around 300 Hz. To further improve the thermal efficiency and expedite its practical application, this work focuses on studying the influence of cold head structure on the system performance. Substantial numerical simulations were firstly carried out, which revealed that the cold head structure would greatly influence the cooling power and the thermal efficiency. To validate the predictions, a lot of experiments have been done. The experiments and calculations are in reasonable agreement. With 500 W heating power input into the engine, a no-load temperature of 63 K and a cooling power of 1.16 W at 80 K have been obtained with parallel-plate cold head, indicating encouraging improvement of the thermal efficiency.     

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.     

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 experimental investigation of the high efficiency 1.5 W/4.2 K pneumatic-drive G-M cryocooler

The development of a high cooling power and high efficiency 4.2 K two stage G-M cryocooler is critically important given its broad applications in low temperature superconductors, MRI, infrared detector and cryogenic electronics. A high efficiency 1.5 W/4.2 K pneumatic-drive G-M cryocooler has recently been designed and developed by ARS. The effect of expansion volume rate and operation conditions on the cooling performance has been experimentally investigated. A typical cooling performance of 1.5 W/4.2 K has been achieved, and the minimum temperature of the second stage is 2.46 K. The steady input power of the compressor at 60 Hz is 6.8 kW, while the operation speed of the rotary valve is 30 rpm. A maximum cooling power of 1.75 W/4.2 K has been obtained in test runs.     

Development of high performance moving-coil linear compressors for space Stirling-type pulse tube cryocoolers

This paper presents a review of the recent development of moving-coil linear compressors for space Stirling-type pulse tube cryocoolers in National Laboratory for Infrared Physics, Shanghai Institute of Technical Physics, Chinese Academy of Sciences. The design, manufacture and assembly methods are described with special emphases laid on linear motor, clearance seal, flexure springs, dual-opposed configuration and flexible design. Several key components are focused on and studied in a detailed way in terms of material selection, geometry design, configuration optimization, manufacture approaches and optimal assembly to achieve high efficiency, easy producibility, high reliability and long life. Experiences from the forerunners and the state-of-the-art approaches are reviewed and used for useful references, while our own successful experiences are emphasized and discussed in more detail together with some lessons learned. A series of compressors for space applications have been worked out with high confidence of reliability and long life expectation, which achieve input capacities of 0–500 W with motor efficiencies of 74.2–83.6%. Single-stage pulse tube cryocoolers driven by these compressors have already covered the temperature range of 25–200 K with cooling capacities varying from milliwatt levels to over 30 W. The commonly-used compressor types and purposes, performance characteristics and their applications in typical space cryocooler projects are also presented.     

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.     

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.     

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.     

10 W/90 K single-stage pulse tube cryocoolers

A single-stage 10 W/90 K coaxial pulse tube cryocooler has been developed for space-borne optics cooling. The design considerations are described, and the optimizations on the double-segmented inertance tubes are presented. The preliminary engineering model (EM) of the cooler has been worked out, which typically provides the cooling of 10 W at 90 K with the input power of 175.6 W at 310 K reject temperature, and achieves around 14% of Carnot efficiency at 90 K. The reject temperature dependence experiments on the EM show a smaller slope of 10.2 W/10 K and indicate a good adaptability to the reject temperature range from 290 K to 333 K.     

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.     

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.     

Stirling-type pulse tube refrigerator (PTR) with cold compression: Cold compressor,colder expander

This research paper focuses on the performance prediction and its validation via experimental investigation of a Stirling-type pulse tube refrigerator (PTR) equipped with a cold linear compressor. When the working gas is compressed at cryogenic temperature, the acoustic power (PV power) can be directly transmitted through the regenerator to the pulsating tube without experiencing unnecessary precooling process. The required PV power generated by the linear compressor, furthermore, can be significantly diminished due to the relatively small specific volume of the working gas at low temperature. The PTR can reach lower temperature efficiently with higher heat lift at the corresponding temperature than other typical single-stage Stirling-type PTRs. Utilizing a cryogenic reservoir as a warm end and regulating the entire operating temperature range of the PTR will enable a PTR to operate efficiently under space environment.In this research, the experimental validation as a proof of concept was carried out to demonstrate the capability of PTR operating between 80 K and 40 K. The linear compressor was submerged in a liquid nitrogen bath and the lowest temperature was measured as 38.5 K. The test results were analyzed to identify loss mechanisms with the simple numerical computation (linear model) which considers the dynamic characteristics of the cold linear compressor with thermo-hydraulic governing equations for each of sub components of the PTR. All the mass flows and pressure waves were assumed to be sinusoidal.     

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.     

Intermediate cooling from pulse tube and regenerator in a 4 K pulse tube cryocooler

This paper introduces intermediate cooling by thermally attaching heat exchangers on the second stage pulse tube and regenerator in a commercial 4 K pulse tube cryocooler. Due to the large enthalpy flow in the 2nd stage pulse tube and regenerator, both intermediate heat exchangers on the pulse tube and regenerator can provide cooling capacities in the temperature range of 5–15 K without or with minor effect on the performance of the 4 K stage. Extracting cooling capacity from the pulse tube or regenerator reduces the 1st stage cooling performance in the present study. The joint intermediate heat exchanger on the pulse tube and regenerator has demonstrated promising results for applications.     

Opposed piston linear compressor driven two-stage Stirling Cryocooler for cooling of IR sensors in space application

A two-stage Stirling Cryocooler has been developed and tested for cooling IR sensors in space application. The concept uses an opposed piston linear compressor to drive the two-stage Stirling expander. The configuration used a moving coil linear motor for the compressor as well as for the expander unit. Electrical phase difference of 80 degrees was maintained between the voltage waveforms supplied to the compressor motor and expander motor. The piston and displacer surface were coated with Rulon an anti-friction material to ensure oil less operation of the unit. The present article discusses analysis results, features of the cryocooler and experimental tests conducted on the developed unit. The two-stages of Cryo-cylinder and the expander units were manufactured from a single piece to ensure precise alignment between the two-stages. Flexure bearings were used to suspend the piston and displacer about its mean position. The objective of the work was to develop a two-stage Stirling cryocooler with 2 W at 120 K and 0.5 W at 60 K cooling capacity for the two-stages and input power of less than 120 W. The Cryocooler achieved a minimum temperature of 40.7 K at stage 2.     

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.