Stirling Pulse Tube Cryocooler Research Articles

Numerical investigation on non-linear streaming effects in a two-stage coaxial pulse tube cryocooler

Stirling pulse tube cryocoolers (PTC) are widely used in aerospace applications for the cooling of infrared sensors and for filtering background thermal noise in the astro-imaging devices, etc. Present investigation aims to use numerical methods to demonstrate the nonlinear fluid flow, heat transfer, and vortex generation phenomena in a two-stage coaxial type inertance pulse tube cryocooler. The numerical simulation is conducted using commercially available Fluent® code for both single-stage and multi-stage configurations to show nonlinear processes with varying heat load conditions. It has been noticed that the width of the vortex produced inside the pulse tube grows with an increase in heat load capacity. This undesirable flow conditions yields an adverse effect in the cooling behavior and reduces overall performance of cryocooler with higher heat load. Additionally, streamlines, stream function, pressure and temperature variation plots are given for both stages with different heat load capacity to substantiate our results.

Effects of second-stage active phase shifter on the inter-stage refrigeration capacity of a Stirling/pulse tube cryocooler

The Stirling/pulse tube cryocooler (SPC) is one of the most promising cryocoolers for space applications due to its advantages like high efficiency and long lifetime. The second pulse tube stage is coaxial pneumatically coupled in series with the first Stirling stage. The SPC possesses a distinctive capability to dynamically adjust the inter-stage refrigeration capacity by actively controlling the Stirling displacer in the first stage. This enables the SPC to effectively cater to varying heat loads over time. Nevertheless, the investigation into the regulation mechanism of the second-stage phase shifter on inter-stage refrigeration capacity shift is hindered by the presence of the second-stage passive phase shifter. This manuscript proposes an SPC with a second-stage active phase shifter (APS), which can actively control the phase difference between the pressure wave and mass flow at the second-stage hot end of the pulse tube in real time. The effect of the APS phase and amplitude on the inter-stage refrigeration capacity shift is analyzed using the theoretical and numerical model proven by the experiment. The first experimentally reported SPC with a second-stage APS demonstrates a refrigeration capacity of 0.22 W at 20 K plus 3.11 W at 70 K, requiring a compressor electrical power of 220 W. The SPC achieves a no-load minimum temperature of 13.5 K.

Fundamental motion relation of different solid phase shifters of pulse tube cryocooler

Warm displacer type Stirling pulse tube cryocooler (SPTC) has demonstrated very promising benefits from its strong phase shifting and work recovery functions. Gas driving displacer (the passive displacer), linear motor driving displacer (the active displacer), and moving plug with orifice could be regarded as different operation modes of the general warm displacer. This work intends to fully understand the fundamental motion relation of different solid shifters for designing an effective warm displacer. Hence, starting from the basic momentum equations, the mechanism of the piston motion was studied theoretically, and the function of moving plug with orifice was mentioned in passing. It shows that the gas driving displacer can make the same optimal performance as the linear motor driving displacer does. In case of the mechanical problem of the displacer in the initial design, the gas driving displacer with orifice could be a backup to improve the performance of the SPTC. Based on the theoretical analysis and formula deduction, a simple simulation briefly displays the relationship between the displacer rod diameter ratio, displacer piston mass, and gas spring stiffness for a fixed micro SPTC. A general design method for the warm displacer was worked out eventually and could be extended to the linear compressor design.

Application of Stirling pulse tube cryocoolers in high temperature superconducting filters subsystems

The application of high temperature superconducting(HTS)filter has penetrated into various fields. In recent decades, GM-type pulse tube cryocooler and Stirling-type pulse tube cryocooler (SPTC) are two common cryocoolers. Due to the advantages of PTCs, such as no moving parts at the cold end, simple structure, small mechanical vibration and longer lifetime, pulse tube cryocoolers is gradually replacing oil-lubricated Stirling-coolers and G-M cryocoolers to cool down HTS magnets. In this paper, the development of PTC in HTS magnet cooling in the past 20 years is summarized firstly. Secondly, the development of HTS cooling system in our lab are reported. At last, the further development direction of HTS’s cooling system is discussed.

A research of micro-pulse tube cryocooler with displacer phase shifter

• The phase relationships in the whole displacer PTC system were analyzed. • Three different sizes of a displacer type micro PTCs have been designed. • A 2D CFD model was constructed and used to characterize the displacer micro PTC. • A displacer provides a good phase shifting for a small-cooling-power micro PTC. • A cooling power of 1.5 W@80 K and a COP of 20.96% is obtained by the second micro PTC. Investigations of phase shifters and power recovery mechanisms are of sustainable interest for developing Stirling pulse tube cryocoolers (SPTC) with more compact design and higher efficiency. The warm displacer type SPTC has been demonstrated with a very promising theoretical efficiency benefiting from its strong phase shifting and work recovery functions. Extending this same phase shifting approach to miniature pulse tube refrigerators may provide advantages over the other alternatives, since inertance tubes are severely limited in their phase shifting capability when the associated acoustic power decreases below 20 W. A comprehensive investigation regarding the micro-pulse tube cryocooler with a displacer phase shifter is carried out in this work, including the design of the major components of the cryocooler, theoretical analysis regarding the phase relationship in the whole displacer type cryocooler system, and 2D simulation work addressing the performance of the cryocooler systems. In the optimum phase angle conditions of the 3 mm pulse tube size cryocooler, the mass flow rate leads the pressure wave by 28.8° at the regenerator warm end, and lags the pressure wave by 27.7° at the regenerator cold end. A cooling power of 1.5 W at 80 K and a COP (Coefficient of Performance) of 20.96% is obtained with an input power of 7.4 W.

Study on micro-liquid droplets behavior at the expander of the pulse tube cryocooler under 5 K based on molecular dynamics

The alternating oscillations in the expander of the pulse tube cryocooler at liquid helium temperature level were studied by molecular dynamics method. It is found that the densely atom clusters – namely micro-liquid droplets were formed in the cold part of the pulse tube and mostly close to the wall of the tube. The size and the number of the clusters were increasing with cycle progressing. The mass proportion of the liquid droplets was up to 8.0 % in all the gas. The largest droplets contained up to 275 He atoms. The clusters moved around during the compression and expansion process of the cycles. It is known that the formation of the micro droplets had influences on the oscillating waves of the gas, resulting in the amplitudes of the density, temperature, so that pressure waves decreased greatly. The local lowest expansion temperatures were also increased over 4.2 K with the formation of the droplets. This may be one of the reasons that it is very difficult to obtain the temperature below 4 K in the Stirling pulse tube cryocoolers.

Influence of periodic side-to-side and heaving motions on the performance of a Stirling pulse tube cryocooler

Cryocoolers can experience near-periodic heaving or side-to-side motion and acceleration in some applications, in particular on moving platforms. In this work, the effect of heaving and rolling (side-to-side movement) on a Stirling pulse tube cryocooler was experimentally studied. Periodic heaving and rolling motions with various amplitudes, and frequencies in the 0.2 to 0.8 Hz range were imposed on a test section using a motion platform. The test section represented a prototypical commercial pulse tube cryocooler (PTC). The PTC was tested at two different neutral positions, vertical with the cold end pointing down (ideal orientation) and vertical with the cold end pointing up (inverted). When the PTC was at vertical position with the cold end pointing down, heaving movement had no measurable influence on its performance. Furthermore, the rolling motion caused some fluctuation but less than 2% drop in the cooling power of the tested PTC. When the PTC was at inverted, upside-down position, it showed significantly more sensitivity to periodic motions. Heaving motion and rolling motion resulted in approximately 5% and 10% maximum drops in the cooling power, respectively. Rolling motion also caused larger fluctuation in cooling power, with amplitudes about 15% of the average cooling power. Increasing the frequency and the amplitude of the motions both had notable negative effects on the performance of the PTC.

Coaxial Stirling pulse tube cryocooler with active displacer

Coaxial pulse tube cryocoolers are the configuration of choice as they allow better access to the cold head. Hence, a previously built and tested in-line pulse tube cryocooler which uses an active displacer for phase control has been modified into a coaxial configuration. The active displacer allows the mass flow and the pressure pulse at the cold end of the pulse tube to be easily adjusted for optimum performance. The displacer also allows the expansion power at the warm end of the pulse tube to be recovered in order to operate more efficiently. A numerical Sage model is used to demonstrate this by examining the work flows throughout the cryocooler and it is shown that more than 6% of the power required to drive the cryocooler comes from the warm end of the pulse tube via the displacer. When using an inertance tube or orifice, this expansion power is dissipated as heat which is why using a displacer can lead to a more efficient cryocooler. Moreover, the effect of changing the displacer phase and stroke on cryocooler performance and pressure characteristics is examined both experimentally and numerically.

Numerical investigation on non-equal section regenerators performance for pulse tube cryocooler

It is always been a research hotspot to improve the overall efficiency of Stirling pulse tube cryocoolers (SPTCs). The regenerator as the vital component directly determines the performance of SPTCs. Therefore, an approach to improve the overall efficiency is provided by improving the performance of the regenerator. The factors for the influence of the three regenerators structure on the overall efficiency are analyzed and discussed by an 8W@80K SPTC Sage model. The simulation results show the optimal overall efficiency of SPTC with three different regenerators structure varies with the compressor PV power input. Moreover, in terms of the overall efficiency, the smaller the regenerator volume is, the higher overall efficiency will be obtained. Specifically, the overall efficiency of a SPTC with the non-equal (variable and conical) section regenerators is increased by 14.7% and 50% respectively compared with the equal (constant) section regenerator, which theoretically proves the feasibility of this method.

Numerical modelling of a coaxial Stirling pulse tube cryocooler with an active displacer for space applications

A numerical model for a coaxial Stirling pulse tube cryocooler with an active displacer has been developed. An active displacer, in place of an inertance tube, has already demonstrated good efficiency in an in-line pulse tube, but incorporating this design into a coaxial configuration permits better access to the cold head. A model of the coaxial cold head was developed to include the radial flow and cooling in this region. The sub-assembly models were validated with flow testing of the physical sub-units of the cryocooler. The performance has been predicted for the cryocooler as a function of: fill pressure, operating frequency, and phase angle between the position of the linear compressor and displacer. The projected difference in performance and efficiency of the coaxial configuration was compared to the in-line design. The coaxial cryocooler numerically simulates 6 W of cooling at 80 K with an input power of 85 W, at a fill pressure of 28 bar, an operating frequency of 60 Hz, and a compressor-displacer phase angle of 41°. Overall, the coaxial cryocooler outperforms the in-line design in terms of cooling power, but not in terms of efficiency.

Minimising flow losses within the pulse tube of a Stirling pulse tube cryocooler

Successful operation of Stirling pulse tube cryocoolers relies on minimising flow mixing within the pulse tube. Hence, the pulse tube and the flow straighteners at either end must be designed with great care. In this study, the flow within the pulse tube of an existing Stirling pulse tube cryocooler is numerically analysed and alternative flow straightener designs are suggested. The numerical simulation have been carried out using CONVERGE CFD, a finite volume Navier-Stokes solver. The standard k-ε RANS turbulence model has been used to account for the effects of turbulence within the pulse tube.

Numerical analysis of miniature coaxial Stirling type pulse tube cryocooler with a modified reservoir

A Numerical model of a compact coaxial Stirling pulse tube cryocooler with a cooling capacity not less than 2W at 80K is done. The performance characteristics with varying geometrical parameters are simulated. The Inertance Pulse Tube Cryocooler (IPTC) with a modified reservoir is suggested, where the reverse fluctuation of pressure in the compressor case is used instead of the steady pressure in the reservoir to shift the phase of the flow velocity the hot end of the pulse tube. Therefore, the large reservoir volume of the cryocooler could be reduced, to make the cryocooler compact. The performance of the cryocooler was investigated and compared with the IPTC. The simulation results show that the cryocooler with modified reservoir can work as efficient as inertance type pulse tube cryocooler.

Numerical study of a gas coupled VM-PT hybrid cryocooler using 3He as the working fluid

The two-stage Vuilleumier gas-coupling pulse tube cryocooler (VM-PT) is one kind of novel low-frequency cryocoolers. In this gas-coupled form, the single stage Vuilleumier cryocooler serves as both pressure wave generator and a pre-cooler for coaxial pulse tube. Compared with the most commercialized GM and GM pulse tube cryocooler, the two-stage VM-PT cryocooler is characterized by its high stability, compact size and thermal actuation which are indispensable for space application. It has already been verified experimentally that this cryocooler can obtain 9.75mW@4.2K and the lowest no-load temperature 3.39K when 4He as the working fluid. However, such refrigerating capacity seems not enough for further application. 3He as a more potential substitution of 4He has better physical properties to improve performance, which has been studied in GM type and Stirling pulse tube cryocooler. For further optimization, a numerical study on the specific performance of two-stage VM-PT cryocooler using 3He is carried out in the present paper though Sage software. Working at the frequency of 1.0Hz and the pressure of 0.8MPa, the two-stage VM-PT cryocooler with 3He obtained 50mW@4.06K. The usage of 3He was 0.0038kg, about 30L under STP. At 4.2K, using 3He can obtain 58mW cooling power and 0.49% relative Carnot efficiency, about 1.6 times higher than using 4He.

Study on the flow nonuniformity in a high capacity Stirling pulse tube cryocooler

High capacity Stirling-type pulse tube cryocoolers (SPTC) have promising applications in high temperature superconductive motor and gas liquefaction. However, with the increase of cooling capacity, its performance deviates from well-accepted one-dimensional model simulation, such as Sage and Regen, mainly due to the strong field nonuniformity. In this study, several flow straighteners placed at both ends of the pulse tube are investigated to improve the flow distribution. A two-dimensional model of the pulse tube based on the computational fluid dynamics (CFD) method has been built to study the flow distribution of the pulse tube with different flow straighteners including copper screens, copper slots, taper transition and taper stainless slot. A SPTC set-up which has more than one hundred Watts cooling power at 80 K has been built and tested. The flow straighteners mentioned above have been applied and tested. The results show that with the best flow straightener the cooling performance of the SPTC can be significantly improved. Both CFD simulation and experiment show that the straighteners have impacts on the flow distribution and the performance of the high capacity SPTC.

Influence of minor geometric features on Stirling pulse tube cryocooler performance

Minor geometric features and imperfections are commonly introduced into the basic design of multi-component systems to simplify or reduce the manufacturing expense. In this work, the cooling performance of a Stirling type cryocooler was tested in different driving powers, cold-end temperatures and inclination angles. A series of Computational Fluid Dynamics (CFD) simulations based on a prototypical cold tip was carried out. Detailed CFD model predictions were compared with the experiment and were used to investigate the impact of such apparently minor geometric imperfections on the performance of Stirling type pulse tube cryocoolers. Predictions of cooling performance and gravity orientation sensitivity were compared with experimental results obtained with the cryocooler prototypes. The results indicate that minor geometry features in the cold tip assembly can have considerable negative effects on the gravity orientation sensitivity of a pulse tube cryocooler.

Linear adjustable inertance tubes for pulse tube cryocoolers

Inertance tube is coupled with Stirling Pulse Tube Cryocooler because its ability of varying the phase angle of pressure and mass flow thereby could potentially increase the performance of the pulse tube cryocooler. The discrepancy between the theoretically designed inertance tube and the installed one causes tons of work for the researchers to figure out the optimum dimensional parameters matching with the pulse tube cryocooler. This paper offers a substituted method to decrease the complications of determining the best match inertance tube for the specific cryocooler. A linear adjustable inertance tube is proposed to fulfill the requirement. The two section distributed component model with step transition and entrance effect resistance is built to anticipate the phase angle performance of the linear adjustable inertance tube. By a 16% length change, 12° phase angle shift is captured both from the model prediction and the experimental measurement.

Analysis and comparison of different phase shifters for Stirling pulse tube cryocooler

Investigations of phase shifters and power recovery mechanisms are of sustainable interest for developing Stirling pulse tube cryocoolers (SPTC) with higher power density, more compact design and higher efficiency. This paper investigates the phase shifting capacity and the applications of four different phase shifters, including conventional inertance tube, gas-liquid and spring-oscillator phase shifters, as well as a power recovery displacer. Distributed models based on the electro-acoustic analogy are developed to estimate the phase shifting capacity and the acoustic power dissipation of the three phase shifters without power recovery. The results show that both gas-liquid and spring-oscillator phase shifters have the distinctive capacity of phase shifting with a significant reduction in the inertial component length. Furthermore, full distributed models of SPTCs connected with different phase shifters are developed. The cooling performance of SPTCs using all four phase shifters are presented and typical phase relations are analyzed. The comparison reveals that the power recovery displacer with a more complicated configuration provides the highest efficiency. The gas-liquid and spring-oscillator phase shifters show equivalent efficiency compared with the inertance tube phase shifter. Approximately 10–20% of the acoustic power is dissipated by the phase shifters without power recovery, while 15–20% of the acoustic power can be recovered by the power recovery displacer, leading to a maximum coefficient of performance (COP) above 0.14 at 80K. A merit analysis is also done by presenting the pros and cons of different phase shifters.

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 4K 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 partby 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 5.4K down to 4.03K. This is the lowest refrigeration temperature ever achieved with a three-stage SPTC.

A three-stage Stirling pulse tube cryocooler reached 4.26 K with He-4 working fluid

Multi-stage Stirling pulse tube cryocoolers (SPTCs) working at liquid helium temperatures are attractive because of their promising potential in tactical and space applications. However, it is still a challenge for a SPTC to operate below 5K with He-4 as working fluid instead of the rare He-3. In this study, the operating characteristics of an in-house made three-stage SPTC were experimentally investigated. The mutual influence of precooling temperature, operating frequency, input power, and charge pressure on the cooling performance of the third stage was studied. A no-load temperature of 4.26K was achieved by the three-stage SPTC, which is the lowest temperature ever obtained by a multi-stage SPTC operating with He-4 as working fluid.

Impedance magnitude optimization of the regenerator in Stirling pulse tube cryocoolers working at liquid-helium temperatures

The impedance magnitude is important for the design and operation of a Stirling pulse tube cryocooler (SPTC). However, the influence of the impedance magnitude on the SPTC working at liquid-helium temperatures is still not clear due to the complexity of refrigeration mechanism at this temperature range. In this study, the influence of the impedance magnitude on the viscous and thermal losses has been investigated, which contributes to the overall refrigeration efficiency. Different from the previous study at liquid nitrogen temperatures, it has been found and verified experimentally that a higher impedance magnitude may result in a larger mass flow rate accompanied with larger losses in the warmer region, hence the refrigeration efficiency is lowered. Numerical simulation is carried out in SPTCs of different geometry dimensions and working parameters, and the experimental study is carried out in a three-stage SPTC. A minimum no-load refrigeration temperature is achieved with an appropriate impedance magnitude that is determined by the combination of frequency and precooling temperature. A lowest temperature of 4.76K is achieved at 28Hz and a precooling temperature of 22.6K, which is the lowest temperature ever achieved with He-4 for SPTCs. Impedance magnitude optimization is clearly an important consideration for the design of a 4K SPTC.