Stirling-type Pulse Tube Cryocooler Research Articles

A two-dimensional model of regenerator with mixed matrices and experimental verifications for improving the single-stage Stirling-type pulse tube cryocooler

A two-dimensional regenerator model based on Brinkman-Forchheimer equations is established to obtain a model with fast speed and acceptable accuracy. To improve the performance of the Stirling-type pulse tube cryocooler (SPTC), the different filling proportions of mixed matrices made of stainless steel (SS) screens are simulated and compared, and then the optimal proportion is suggested. The analyses are mainly focused on the cooling performance and the losses caused by the different entropy generations. The experiments are then conducted to verify the theoretical investigations based on a single-stage coaxial SPTC, in which the cooling characteristics with various frequencies and temperatures are tested and then compared with the analyses. The results show a good agreement between the simulations and the experiments. The cooling performance can be enhanced based on the optimized mixed matrix, in which for a reject temperature of 300K and an input electric power of 220W, the SPTC has experimentally achieved the cooling capacity of 0.45W at 30K and a no-load temperature of 26.7K. The performance is impressive considering that only the conventional SS matrices are employed and neither double-inlet nor multi-bypass phase-shifting approach is used.

Investigation of the effect of a bend in a transfer line that separates a pulse tube cold head and a pressure wave generator

A transfer line between a pulse tube cold head and a pressure wave generator is usually required to isolate the cold head from the vibrations of the compressor. Although it is a common practice to use a thin and narrow straight tube, a bent tube would allow design flexibility and easy mounting of the cold head, such as in a split Stirling type pulse tube cryocooler. In this paper, we report a preliminary investigation on the effect of the bending of the tube on the flow transfer characteristics. A numerical study using commercial computational fluid dynamics model is performed to gain insight into the flow characteristics in the bent tube. Oscillating flow experiments are performed with a straight and a bent tube at a filling pressure of 15 bar and an operating frequency of 40, 50 and 60 Hz. The data and the corresponding numerical simulations point to the hypothesis that the secondary flow in the bent tube causes a decrease in flow at a fixed pressure amplitude.

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 0.69W at 30K and 3.1W at 85K with an electric input power of 330W and a reject temperature of 300K. The consistency between the simulated and the experimental results is observed and the theoretical investigations are experimentally verified.

Effects of the driving voltage waveform on the performance of the Stirling-type pulse tube cryocooler driven by the moving-coil linear compressor

The effects of three typical waveforms, namely, sine, trapezoid and smeared sine, on the performance of the Stirling-type pulse tube cryocooler (SPTC) driven by the moving-coil linear compressor are analyzed and studied experimentally. The results indicate that the dynamic pressure at the inlet of the cold finger has a weak relation with the driving voltage waveform, but the latter plays an important role in affecting both the motor efficiency and the SPTC cooling performance. In the tested range, either the cooling efficiency or the motor efficiency under the smeared sine waveform is the highest, while that under the sine waveform is the lowest. Moreover, given that the input power is below 30 W, the motor efficiencies under both smeared sine and trapezoid waveforms exceed 90%, which suggests a promising approach to achieve a linear compressor with a very high motor efficiency by optimizing the voltage waveform.

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 30–35K 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 27.2K and the cooling power of 0.78W at 35K, or 0.29W at 30K, with an input electric power of 220W and a reject temperature of 300K.

Theoretical and experimental investigations on the optimal match between compressor and cold finger of the Stirling-type pulse tube cryocooler

The match between the pulse tube cold finger (PTCF) and the linear compressor of the Stirling-type pulse tube cryocooler plays a vital role in optimizing the compressor efficiency and in improving the PTCF cooling performance as well. In this paper, the interaction of them has been analyzed in a detailed way to reveal the match mechanism, and systematic investigations on the two-way matching have been conducted. The design method of the PTCF to achieve the optimal matching for the given compressor and the counterpart design method of the compressor to achieve the optimal matching for the given PTCF are put forward. Specific experiments are then carried out to verify the conducted theoretical analyses and modeling. For a given linear compressor, a new in-line PTCF which seeks to achieve the optimal match is simulated, designed and tested. And for a given coaxial PTCF, a new dual-opposed moving-coil linear compressor is also developed to match with it. The simulated and experimental results are compared, and fairly good agreements are found between them in both cases. The matched in-line cooler with the newly-designed PTCF has capacities of 4–11.84W at 80K with higher than 17% of Carnot efficiency and the mean motor efficiency of 81.5%, and the matched coaxial cooler with the new-designed compressor can provide 2–5.5W at 60K with higher than 9.6% of Carnot efficiency and the mean motor efficiency of 83%, which verify the validity of the theoretical investigations on the optimal match and the proposed design methods.

Entropy analyses of the three-stage thermally-coupled Stirling-type pulse tube cryocooler

This paper establishes a theoretical model of the three-stage thermally-coupled Stirling-type pulse tube cryocooler based on entropy analyses, in which irreversible losses in regenerators and heat exchangers including the axial conduction, pressure drop and ineffective heat convection are considered, and then the cooling performance of each stage is analyzed according to the second law of thermodynamics, respectively. The results indicate that the pressure drop is the primary loss for all stages, whereas in the third stage, the ineffective heat convection increases sharply and accounts for a much larger proportion. Losses in heat exchangers are much smaller compared with those in regenerators and can thus be ignored in many cases. Furthermore, the optimal values of several selected important operating parameters, including coupling positions, cooling temperatures, charging pressures, pressure ratios, operating frequencies and input acoustic powers for the three stages, can be obtained according to the deduced expressions. A specific example aiming at 10 K is given to provide elaborate explanations and quantitative analyses about the effects of these parameters on the cooler performance.

Dynamic and thermodynamic characteristics of the moving-coil linear compressor for the pulse tube cryocooler. Part A: Theoretical analyses and modeling

Theoretical analyses and modeling are conducted on dynamic and thermodynamic characteristics of the moving-coil linear compressor in the Stirling-type pulse tube cryocooler. Governing equations are deduced, and φ and ΔP are found to be the two key parameters connecting compressor to pulse tube cold finger. An improved ECA model is developed to investigate the cold finger characteristics and their influences on φ, ΔP. Systematic simulations based on a specific case are performed to provide elaborate explanations about the theoretical analyses with the frequency varying from 30 Hz to 100 Hz at 60 K, 80 K and 100 K, respectively. The variations of four important parameters of φ, ΔP, I and θ, and the compressor thermodynamic performances and the cryocooler cooling performances, with the frequency at above temperatures are simulated and analyzed, respectively. The effects of compressor geometrical parameters on ηmotor are also simulated. The experimental verifications will be presented in Part B.

CFD simulation of a miniature coaxial Stirling-type pulse tube cryocooler operating at 128 Hz

A two-dimensional axis-symmetric CFD model of a miniature coaxial Stirling-type pulse tube cryocooler with an overall weight of 920g operating at 128Hz is established, and systematic simulations of the performance characteristics at different temperatures are conducted. Both thermal equilibrium and non-equilibrium mechanisms for the porous matrix are considered, and the regenerator losses including the gas and solid conduction, the pressure drop and the imperfect interfacial heat transfer are calculated, respectively. The results indicate that the pressure drop loss is dominant during the first 85% and 78% of regenerator length for the thermal equilibrium and non-equilibrium models, respectively, and it decreases monotonously from warm to cold end due to the steadily decreasing Darcy and Forchheimer terms, whereas other entropy generations share similar changing tendencies, going up gradually near the warm end, increasing dramatically from about 60% of length and then decreasing sharply near the cold end. The reasons for these entropy variations are discussed.

Development of high-efficiency Stirling cryocoolers for high temperature superconducting motors

For wide spread high-temperature superconductor (HTS) devices, a cryocooler having COP of >0.1, with a compact size, light weight, high efficiency and high reliability is required. For practical use of superconductive devices, Sumitomo Heavy Industries, Ltd. (SHI) developed a high-efficiency Stirling type pulse tube cryocooler (STPC). The STPC had high reliability and low vibration. However, its efficiency was not enough to meet the demands of an HTS motor. To further improve the efficiency, we reconsidered the expander of cryocooler and developed a Stirling cryocooler (STC). Two prototype units of a compact, high-efficiency split Stirling cryocooler were designed, built and tested. With the second prototype unit, a cooling capacity of 151 W at 70 K and a minimum temperature of 33 K have been achieved with a compressor input power of 2.15 kW. Accordingly, COP of about 0.07 has been achieved. The detailed design of the prototype units and the experimental results will be reported in this paper.

Performance of an adjustable, threaded inertance tube

The performance of the Stirling type pulse tube cryocooler depends strongly on the design of the inertance tube. The phase angle produced by the inertance tube is very sensitive to its diameter and length. Recent developments are reported here regarding an adjustable inertance device that can be adjusted in real time. The inertance passage is formed by the root of a concentric cylindrical threaded device. The depth of the threads installed on the outer screw varies. In this device, the outer screw can be rotated four and half turns. At the zero turn position the length of the passage is 1.74 m and the hydraulic diameter is 7 mm. By rotating the outer screw, the inner threaded rod engages with additional, larger depth threads. Therefore, at its upper limit of rotation, the inertance passage includes both the original 1.74 m length with 7mm hydraulic diameter plus an additional 1.86 m length with a 10 mm hydraulic diameter. A phase shift change of 24° has been experimentally measured by changing the position of outer screw while operating the device at a frequency of 60 Hz. This phase angle shift is less than the theoretically predicted value due to the presence of a relatively large leak through the thread clearance. Therefore, the distributed component model of the inertance tube was modified to account for the leak path causing the data to agree with the model. Further, the application of vacuum grease to the threads causes the performance of the device to improve substantially.

Loss Analysis of High Power Stirling-Type Pulse Tube Cryocooler

For the purpose of cooling high-temperature superconductor (HTS) devices, such as superconductor motors, superconducting magnetic energy storage (SMES) and current fault limiters, cryocoolers should be compact in size, light-weight, and have high efficiency and reliability. In order to meet the demand of HTS devices world-wide, the cryocooler needs to have COP efficiency >0.1. We have developed a high power Stirling-type pulse tube cryocooler (SPTC) with an in-line expander. The experimental results were reported in June 2012[1]. The cooling capacity was 210 W at 77 K and the minimum temperature was 37 K when the compressor input power was 3.8 kW. Accordingly, the COP was about 0.055. To further improve the efficiency, the energy losses in the cryocooler were analyzed. The experimental results and the numerical calculation results are reported in this paper.

Theoretical and experimental investigations on the match between pulse tube cold fingers and linear compressors

The match between the cold finger and the linear compressor of the Stirling-type pulse tube cryocooler plays a vital role in optimizing the compressor efficiency and in improving the cold finger cooling performance. To reveal the match mechanism between the linear compressor and pulse tube cold finger (PTCF), detailed analyses have been made to understand the interactions between them. Based on the theoretical investigations, both of the design method of the PTCF to match the given linear compressor and a reverse method of the linear compressor to match the given PTCF have been proposed. In order to verify the validity of these theories and methods, actual PTCF and linear compressor are developed to match the existing linear compressor and PTCF, respectively. The experimental results show good agreements with the simulated ones.

Operating characteristics of a single-stage Stirling-type pulse tube cryocooler with high cooling power at liquid nitrogen temperatures

The operating characteristics are important for design and optimization of pulse tube cryocoolers, in particular for those with high cooling power, which up to now have been seldom extensively investigated. In this study, the dependence of cooling performance on the charge pressure and operating frequency has been investigated, both numerically and experimentally. A numerical model based on Sage software was established. Experiments were performed on a home-made single-stage high power Stirling-type pulse tube cryocooler (SPTC) working at liquid nitrogen temperatures. The results revealed that each charge pressure corresponds to an optimum frequency with respect to compressor and regenerator efficiency. A lower charge pressure results in a higher cryocooler efficiency, but the delivered maximum pV power is significantly reduced due to the stroke limit of the pistons in the linear compressor. The influence of operating characteristics on the temperature non-uniformity in the regenerator was also investigated. By optimizing the charge pressure and frequency, the minimum no-load temperature was decreased to 46.9 K at 56.5 Hz and 2.0 MPa. A cooling power of 300 W at 71.8 K was measured with an electrical input power of 8.9 kW.

Characterization of the frictional losses and heat transfer of oscillatory viscous flow through wire-mesh regenerators

In this paper, new relations for calculating heat transfer and pressure drop characteristics of oscillatory flow through wire-mesh screen regenerator such as Darcy permeability, Forchheimer’s inertial coefficient, and heat transfer area per unit volume, as a function of the wire diameter are presented. According to the derived relations, thinner wires have higher pressure drop and higher heat transfer rate. The relations are applicable for all regenerative cryocoolers. Embedding the new relations into a numerical model, three Stirling-type orifice pulse tube cryocoolers with three regenerators different in length and diameter but same volume in a variety of wire diameters, have been modeled. The results achieved by the model reveal that the local heat transfer coefficient decreases with increase of the wire diameter and the length-to-diameter ratio. In addition, it was shown that the mean absolute gas–solid wire temperature difference is a linear function of wire diameter in the range investigated. The results show that for larger length-to-diameter ratios, Forchheimer’s effect will dominate frictional losses, and the variations of the frictional losses are proportional to the inverse of the wire diameter. Wire diameter has been optimized to maximize the coefficient of performance of the cryocooler. Shorter regenerators have thinner optimum wires.

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

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

Influence of regenerator void volume on performance of a precooled 4 K Stirling type pulse tube cryocooler

Stirling type pulse tube cryocoolers (SPTC), typically operating at 30–60Hz, have the advantage of compact structure, light weight, and long life compared with Gifford–McMahon type (1–2Hz) PTC (GMPTC). The behavior of flow and heat transfer in the regenerator of a 4K SPTC deviates from that at warmer temperatures and low frequencies. In this paper the behavior of 4K regenerator at high frequencies is investigated based on a single-stage 4K SPTC precooled by a two-stage GMPTC. The 4K SPTC and the GMPTC is thermally coupled with two thermal bridges. The 4K SPTC uses a 10K cold inertance tube as phase shifter to improve phase relationship between mass flow and pressure. The regenerator void volume is an important factor that significantly influences the heat transfer between regenerator matrix and working fluid helium, pressure drop along the regenerator, and phase shift between mass flow and pressure. In this paper, influence of regenerator void volume on the performance of the 4K SPTC with different operating parameters including operating frequencies and average pressure is studied theoretically and experimentally. The first and second precooling powers provided by the GMPTC are obtained which are important parameters to evaluate the efficiency of the whole 4K system with precooling. The results of the regenerator void volume are given and discussed in normalized form for general use.

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.

Design and analysis of a high capacity stirling type pulse tube cryocooler for a helium recondensation system

This paper reports the system design and analysis of high capacity Stirling type pulse tube cryocoolers (PTC) intended to provide a cooling power of 10 W at 80 K for a small helium recondensation system. In the initial phase of the work, the regenerator and pulse tube were optimized using Sage software. The effect of the transfer line whose length is comparable to the wave length of the helium pressure wave is investigated. It is found that there is a magnification in the pressure amplitude at the expense of the PV power. Also a no load temperature of 74 K was achieved. A detailed inertance tube optimization and analysis is done and the cooler is tested with the optimized inertance. The performance improved with a no load temperature of 72 K.

Cold Inertance Tube for 4 K Stirling Type Pulse Tube Cryocoolers

The losses in the regenerator are minimized when the amplitude of the mass flow is minimized for a given acoustic power which requires that the mass flow lags the pressure by about 30° at the cold end of regenerator. The phase shift provided by an inertance tube is strongly influenced by the temperature of the inertance tube and the acoustic power at the cold end of the regenerator. For a 4K Stirling type pulse tube cryocooler, the acoustic power at the cold end of the regenerator decreases significantly with the temperature thereby it's difficult to achieve ideal phase relationship with ambient inertance tube. While cold inertance tube provide a larger phase shift in that the viscosity of the working fluid decreases and the density increases as the temperature decreases. However, use of cold inertance tube increases additional heat load to the regenerator. Therefore it's of great significance to determine when a cold inertance tube should be used. In this paper effect of temperature of inertance tube is calculated for a 4K Stirling type pulse tube cryocooler with different acoustic powers at the cold end. A comparison of ambient temperature inertance tube and cold inertance tube is made.