A single stage Stifling pulse tube cryocooler was designed based on REGEN 3.2 and fabricated for testing. The experimental results show that the cooler can provide a cooling capacity of 5.0 W at 79.1 K, and produce a ...A single stage Stifling pulse tube cryocooler was designed based on REGEN 3.2 and fabricated for testing. The experimental results show that the cooler can provide a cooling capacity of 5.0 W at 79.1 K, and produce a no-load temperature of 57.0 K, operating with an average pressure of 2.50 MPa and a frequency of 60 Hz, performance results that are very close to the calculated values. The cryocooler can be cooled from room temperature to 80 K in 8.5 min. The fast cooldown time is a result of the small regenerator.展开更多
The high-frequency pulse tube cryocooler(HPTC)represents a promising miniature cryocooling technology due to its compact structure and the absence of low-temperature moving components.However,limited to the non-ideal ...The high-frequency pulse tube cryocooler(HPTC)represents a promising miniature cryocooling technology due to its compact structure and the absence of low-temperature moving components.However,limited to the non-ideal gas effect of4He,the HPTC is hard to obtain high cooling performance in the liquid helium temperature range.3He as the working fluid can effectively improve the cooling performance of the HPTC,but the high cost hinders its wide application.In consideration of both cooling performance and cost-effectiveness,this paper explores the feasibility of utilizing^(3)He-^(4)He mixtures as the working fluid for HPTCs.Firstly,the experimental results of a developed HPTC based4He are reported.With a total power consumption of 575 W,the lowest temperature of 3.26 K was observed.And the measured cooling power at 4.2 K was 20.8 mW.Then the theoretical utmost efficiency of the cryocooler was calculated in terms of the thermophysical properties of the working fluids,using ^(3)He-^(4)He mixtures with different compositions as the working fluids.The whole machine modeling of the HPTC was further carried out,and the influence of the working fluids with different components on the structural parameters such as double-inlet and inertance tube,and operating parameters such as pressure and frequency were analyzed.The calculated results show that the cooling power is expected to be increased to36 mW and 53 mW if the equimolar ^(3)He-^(4)He mixture and pure ^(3)He are used,respectively.展开更多
An inter-phasing pulse tube cooler (IPPTC) consists of two pulse tube units, which are connected to each other at hot ends of the pulse tubes through a needle valve. This paper presents the computational fluid dynamic...An inter-phasing pulse tube cooler (IPPTC) consists of two pulse tube units, which are connected to each other at hot ends of the pulse tubes through a needle valve. This paper presents the computational fluid dynamic (CFD) results of an IPPTC using a 2D axis-symmetrical model. General results such as the phase difference between pressure and velocity at cold end and hot end, the temperature profiles along the wall, the available lowest temperature as well as its oscillations and the coefficient of performance (COP) for IPPTC are presented. The formation of DC flow and its effects on the performance of the cooler are investigated and analyzed in detail. Turbulence, which is partially responsible for the poor overall performance of a single orifice pulse tube cooler (OPTC), is found to be much reduced in IPPTC and its performance is improved significantly compared with the single OPTC.展开更多
As an important component of the stirling-type pulse tube cryocooler(SPTC),an efficient phase shifter can significantly improve the cooling capacity.Compared to the common phase shifter,the active warm displacer(AWD)h...As an important component of the stirling-type pulse tube cryocooler(SPTC),an efficient phase shifter can significantly improve the cooling capacity.Compared to the common phase shifter,the active warm displacer(AWD)has a wider phase adjustment range and therefore can obtain a better phase relationship easily.Based on a two-stage thermal-coupled SPTC operating in the 20 K range,this paper studied the influence of the swept volume ratio between the compressor and displacer.The research found that the swept volume ratio changes the cooling capacity and efficiency of the cryocooler mainly by changing the phase difference between the pressure wave and the volume flow at the cold end.It was found from the results of the simulation and experiments that there is an optimal displacement of the displacer(Xd)of 2.5 mm and an optimal phase angle of 15°to obtain the highest cooling efficiency while the displacement of the compressor is constant.The cooling capacity at 20 K is 1.3 W while the input electrical power of the second stage compressor is 202 W,which indicates an overall relative Carnot efficiency(rCOP)of 0.055 in terms of input electrical power.In addition,due to the reasonable setting of precooling temperature and capacity,the swept volume ratio and phase at the maximum cooling capacity and maximum efficiency are consistent in this study.The research improves the understanding of phase shifters and has guiding significance for the optimization of the SPTC working below 20 K.展开更多
New phenomena discovered in the experimental research of the ultra-high frequency pulse tube cryocooler were presented.The cause of the new phenomena was analyzed and the third type DC flow was discovered in the pulse...New phenomena discovered in the experimental research of the ultra-high frequency pulse tube cryocooler were presented.The cause of the new phenomena was analyzed and the third type DC flow was discovered in the pulse tube cryocooler.The third type DC flow not only deteriorated cooling capacity but also led to temperature instability of the pulse tube cryocooler.From the fluid network theory and the simple regenerator model,the root of the third type DC flow was concisely investigated in theory. The asymmetric resistance of oscillating flow in pulse tube cryocooler was the key mechanism of the third type DC flow.Some suppression methods were briefly discussed.展开更多
Stirling-type pulse tube cryocoolers(SPTCs)working at liquid-helium temperatures are appealing in space applications because of their promising advantages such as high reliability,compactness,etc.Worldwide efforts hav...Stirling-type pulse tube cryocoolers(SPTCs)working at liquid-helium temperatures are appealing in space applications because of their promising advantages such as high reliability,compactness,etc.Worldwide efforts have been put in to develop SPTCs operating at liquid-helium temperatures especially with helium-4 as the working fluid.Staged structure is essential to reach such low temperatures.Generally,both the regenerator of the last section and the pulse tube together with the phase shifter are precooled by its upper stage or by external cold source to a low temperature of around 20 K.However,the precooling effects on the regenerator and the pulse tube are synthetic in previous studies,and their independent effects have not been studied clearly.In this manuscript,the precooling effects on the regenerator and on the pulse tube together with the phase shifter are tested independently on a unique-designed precooled SPTC.The tested precooling temperature is between 13.3 K and 22 K,and the no-load refrigeration temperature gets down to 3.6 K.Further analyses and numerical calculations have been carried out.It is found that the influence on the regenerator is remarkable,which is different from previous conclusions.It is also found that the precooling effects on the pulse tube are relatively weak because of the large pressure-induced enthalpy flow of a real gas working at the temperatures near to the critical point.Furthermore,the phase shifting capacity is analyzed with two cases and with both helium-4 and helium-3 as working fluids,and it keeps quite constant after optimizing the frequency and the precooling temperature for each case.The investigation on these independent effects will provide valid reference on the precooling mechanism study of SPTCs working down to liquid-helium temperatures.展开更多
A Stirling-type pulse tube cryocooler (PTC) with precooling was designed and manufactured to investigate its performance at 4 K. Numerical simulation was carried out based on the well-known regenerator model REGEN w...A Stirling-type pulse tube cryocooler (PTC) with precooling was designed and manufactured to investigate its performance at 4 K. Numerical simulation was carried out based on the well-known regenerator model REGEN with an emphasis on the performance of a 4 K stage regenerator of the Stifling-type PTC as influenced by the warm end temperature, pressure ratio, frequency and average pressure with helium-4 and helium-3 as the working fluid respectively. This study demonstrates that the use of a cold inertance tube can significantly improve the efficiency of a 4 K Stirling-type PTC. A preliminary experimental investigation was carried out with helium-4 as the working fluid and a refrigeration temperature of 4.23 K was achieved. The experimental results show that the operating frequency has a significant influence on the performance of the Stirling-type PTC and a relatively low average pressure is favorable for decreasing the loss associated with the real gas effects of a 4 K Stirling-type PTC.展开更多
Terahertz(THz) frequency region, defined from0.1 to 10 THz, is an important frequency band for radio astronomy and atmospheric science. As NbN Superconductor-Insulator-Superconductor(SIS) mixers used for terahertz det...Terahertz(THz) frequency region, defined from0.1 to 10 THz, is an important frequency band for radio astronomy and atmospheric science. As NbN Superconductor-Insulator-Superconductor(SIS) mixers used for terahertz detection, which are studied by the Purple Mountain Observatory(PMO), Chinese Academy of Sciences(CAS), work at 8–10 K, and require condition of micro vibrations, its astronomical observation in aerospace is limited by suitable refrigeration method. 4 K high frequency pulse tube cryocooler developed by Key Laboratory of Space Energy Conversion Technologies(SECT), Technical Institute of Physics and Chemistry(TIPC), CAS, offers an opportunity for the application of SIS mixers. This article introduces the progress of the two-stage high frequency pulse tube cryocooler researched by TIPC. The cryocooler has reached a no load temperature of 4.5 K which is the lowest temperature for this kind of cryocooler reported so far. The successful coupling between the THz component and the high frequency pulse tube cryocooler lays a solid foundation for space detection in the terahertz band.展开更多
The inertance tube is one of the key components of a pulse tube cryocooler. It has great influence not only on the efficiency of the pulse tube cryocooler, but also on the efficiency of the linear compressor. Meanwhil...The inertance tube is one of the key components of a pulse tube cryocooler. It has great influence not only on the efficiency of the pulse tube cryocooler, but also on the efficiency of the linear compressor. Meanwhile, it is very difficult to predict the impedance of an inertance tube because of the turbulent flow. In this paper, using a quasi-turbulent model, the inertance tube is optimized to match a linear compressor driven pulse tube cryocooler. Experimental results show that this model can predict the impedance quite well. With 127 W input electric power, the pulse tube cryocooler obtains 9.4 W cooling power at a temperature of 77 K. The relative Carnot efficiency of the whole system reaches 19.8%.展开更多
A valveless linear compressor was built up to drive a self-made two-stage pulse tube cryocooler. With a designed maximum swept volume of 60 cm3, the compressor can provide the cryocooler with a pressure volume (PV) po...A valveless linear compressor was built up to drive a self-made two-stage pulse tube cryocooler. With a designed maximum swept volume of 60 cm3, the compressor can provide the cryocooler with a pressure volume (PV) power of 400 W. Preliminary measurements of the compressor indicated that both an efficiency of 35%~55% and a pressure ratio of 1.3~1.4 could be obtained. The two-stage pulse tube cryocooler driven by this compressor achieved the lowest temperature of 14.2 K.展开更多
This paper establishes a theoretical model of the single-compressor-driven (SCD) three-stage Stirlingtype pulse tube cryocooler (SPTC) and conducts experimental verifications. The main differences between the SCD type...This paper establishes a theoretical model of the single-compressor-driven (SCD) three-stage Stirlingtype pulse tube cryocooler (SPTC) and conducts experimental verifications. The main differences between the SCD type and the multi-compressor-driven (MCD) crycooler are analyzed, such as the distribution of the input acoustic power in each stage and the optimization of the operating parameters, in which both advantages and difficulties of the former are stressed. The effects of the dynamic temperatures are considered to improve the accuracy of the simulation at very low temperatures, and a specific simulation example aiming at 10 K is given in which quantitative analyses are provided. A SCD threestage SPTC is developed based on the theoretical analyses and with a total input acoustic power of 371.58 W, which reaches a no-load temperature of 8.82 K and can simultaneously achieve the cooling capacities of 2.4 W at 70 K, 0.17 W at 25 K, and 0.05 W at 10 K. The performance of the SCD three-stage SPTC is slightly poorer than that of its MCD counterpart developed in the same laboratory, but the advantages of lightweight and compactness make the former more attractive to practical applications.展开更多
Gas-coupled Stirling-type pulse tube cryocooler(SPTC) is currently the most compact and simplest configuration among all types of cryocoolers, but it is challenging to achieve a very low temperature. This paper invest...Gas-coupled Stirling-type pulse tube cryocooler(SPTC) is currently the most compact and simplest configuration among all types of cryocoolers, but it is challenging to achieve a very low temperature. This paper investigates a gas-coupled SPTC which is capable of directly achieving a temperature of around 4 K. Theoretical analyses were performed based on SAGE to study the effects of employing one or more multi-bypass structures on apparent cooling performance, and internal working parameters. The simulation results indicate that the function of the multi-bypass is similar to that of a multi-stage gas-coupled structure, producing a pre-cooling effect on the lower-temperature section by increasing the acoustic power and the enthalpy flow in the pulse tube of the higher-temperature section. The cooperation of two multi-bypass structures can promote a higher enhancement of the cooling performance, but it is difficult to achieve the same cooling performance of a completely multi-stage gas-coupled SPTC due to weak phase-shifting capability and excessive reduction of the mass flow. Based on the model, the developed prototype has achieved a no-load temperature of 4.4 K, which shows the great potential of using a gas-coupled SPTC to obtain a cooling temperature below 4 K.展开更多
基金the National Natural Science Foundation of China (No. 50676081)the Science and Technology Department of Zhejiang Province (No. 2007C30063), China
文摘A single stage Stifling pulse tube cryocooler was designed based on REGEN 3.2 and fabricated for testing. The experimental results show that the cooler can provide a cooling capacity of 5.0 W at 79.1 K, and produce a no-load temperature of 57.0 K, operating with an average pressure of 2.50 MPa and a frequency of 60 Hz, performance results that are very close to the calculated values. The cryocooler can be cooled from room temperature to 80 K in 8.5 min. The fast cooldown time is a result of the small regenerator.
基金supported by the National Natural Science Foundation of China(No.12073058)the China National Space Administration(No.D050104,D040305)the Youth Innovation Promotion Association of the Chinese Academy of Sciences(No.2019030)。
文摘The high-frequency pulse tube cryocooler(HPTC)represents a promising miniature cryocooling technology due to its compact structure and the absence of low-temperature moving components.However,limited to the non-ideal gas effect of4He,the HPTC is hard to obtain high cooling performance in the liquid helium temperature range.3He as the working fluid can effectively improve the cooling performance of the HPTC,but the high cost hinders its wide application.In consideration of both cooling performance and cost-effectiveness,this paper explores the feasibility of utilizing^(3)He-^(4)He mixtures as the working fluid for HPTCs.Firstly,the experimental results of a developed HPTC based4He are reported.With a total power consumption of 575 W,the lowest temperature of 3.26 K was observed.And the measured cooling power at 4.2 K was 20.8 mW.Then the theoretical utmost efficiency of the cryocooler was calculated in terms of the thermophysical properties of the working fluids,using ^(3)He-^(4)He mixtures with different compositions as the working fluids.The whole machine modeling of the HPTC was further carried out,and the influence of the working fluids with different components on the structural parameters such as double-inlet and inertance tube,and operating parameters such as pressure and frequency were analyzed.The calculated results show that the cooling power is expected to be increased to36 mW and 53 mW if the equimolar ^(3)He-^(4)He mixture and pure ^(3)He are used,respectively.
基金Project supported by the National Natural Science foundation of China (No. 50706042)the Science and Technology Department of Zhejiang Province (No. 2006C24G2010027)the Natural Science Foundation of Zhejiang Province (No. Y105519), China
文摘An inter-phasing pulse tube cooler (IPPTC) consists of two pulse tube units, which are connected to each other at hot ends of the pulse tubes through a needle valve. This paper presents the computational fluid dynamic (CFD) results of an IPPTC using a 2D axis-symmetrical model. General results such as the phase difference between pressure and velocity at cold end and hot end, the temperature profiles along the wall, the available lowest temperature as well as its oscillations and the coefficient of performance (COP) for IPPTC are presented. The formation of DC flow and its effects on the performance of the cooler are investigated and analyzed in detail. Turbulence, which is partially responsible for the poor overall performance of a single orifice pulse tube cooler (OPTC), is found to be much reduced in IPPTC and its performance is improved significantly compared with the single OPTC.
基金supported by the National Natural Science Foundation of China(No.51806231)the Strategic Priority Research Program of Chinese Academy of Sciences(Grant No.XDB35000000).
文摘As an important component of the stirling-type pulse tube cryocooler(SPTC),an efficient phase shifter can significantly improve the cooling capacity.Compared to the common phase shifter,the active warm displacer(AWD)has a wider phase adjustment range and therefore can obtain a better phase relationship easily.Based on a two-stage thermal-coupled SPTC operating in the 20 K range,this paper studied the influence of the swept volume ratio between the compressor and displacer.The research found that the swept volume ratio changes the cooling capacity and efficiency of the cryocooler mainly by changing the phase difference between the pressure wave and the volume flow at the cold end.It was found from the results of the simulation and experiments that there is an optimal displacement of the displacer(Xd)of 2.5 mm and an optimal phase angle of 15°to obtain the highest cooling efficiency while the displacement of the compressor is constant.The cooling capacity at 20 K is 1.3 W while the input electrical power of the second stage compressor is 202 W,which indicates an overall relative Carnot efficiency(rCOP)of 0.055 in terms of input electrical power.In addition,due to the reasonable setting of precooling temperature and capacity,the swept volume ratio and phase at the maximum cooling capacity and maximum efficiency are consistent in this study.The research improves the understanding of phase shifters and has guiding significance for the optimization of the SPTC working below 20 K.
基金Supported by the Hundred Talents Program of the Chinese Academy of Sciences,the National Natural Science Foundation Projects(51806231)the Strategic Priority Research Program of Chinese Academy of Sciences(XDB35000000,XDB35040102)。
基金Supported by the Major Project of National Natural Science Foundation of China(Grant No.50890181)National Natural Science Foundation of China(Grant No.50676100)
文摘New phenomena discovered in the experimental research of the ultra-high frequency pulse tube cryocooler were presented.The cause of the new phenomena was analyzed and the third type DC flow was discovered in the pulse tube cryocooler.The third type DC flow not only deteriorated cooling capacity but also led to temperature instability of the pulse tube cryocooler.From the fluid network theory and the simple regenerator model,the root of the third type DC flow was concisely investigated in theory. The asymmetric resistance of oscillating flow in pulse tube cryocooler was the key mechanism of the third type DC flow.Some suppression methods were briefly discussed.
基金supported by National Natural Science Foundation of China (No.51506152)the Fundamental Research Funds for the Central Universities (inter-disciplinary program) under the contract No.kx0080020173427
文摘Stirling-type pulse tube cryocoolers(SPTCs)working at liquid-helium temperatures are appealing in space applications because of their promising advantages such as high reliability,compactness,etc.Worldwide efforts have been put in to develop SPTCs operating at liquid-helium temperatures especially with helium-4 as the working fluid.Staged structure is essential to reach such low temperatures.Generally,both the regenerator of the last section and the pulse tube together with the phase shifter are precooled by its upper stage or by external cold source to a low temperature of around 20 K.However,the precooling effects on the regenerator and the pulse tube are synthetic in previous studies,and their independent effects have not been studied clearly.In this manuscript,the precooling effects on the regenerator and on the pulse tube together with the phase shifter are tested independently on a unique-designed precooled SPTC.The tested precooling temperature is between 13.3 K and 22 K,and the no-load refrigeration temperature gets down to 3.6 K.Further analyses and numerical calculations have been carried out.It is found that the influence on the regenerator is remarkable,which is different from previous conclusions.It is also found that the precooling effects on the pulse tube are relatively weak because of the large pressure-induced enthalpy flow of a real gas working at the temperatures near to the critical point.Furthermore,the phase shifting capacity is analyzed with two cases and with both helium-4 and helium-3 as working fluids,and it keeps quite constant after optimizing the frequency and the precooling temperature for each case.The investigation on these independent effects will provide valid reference on the precooling mechanism study of SPTCs working down to liquid-helium temperatures.
基金Project (No. 50676081) supported by the National Natural Science Foundation of China
文摘A Stirling-type pulse tube cryocooler (PTC) with precooling was designed and manufactured to investigate its performance at 4 K. Numerical simulation was carried out based on the well-known regenerator model REGEN with an emphasis on the performance of a 4 K stage regenerator of the Stifling-type PTC as influenced by the warm end temperature, pressure ratio, frequency and average pressure with helium-4 and helium-3 as the working fluid respectively. This study demonstrates that the use of a cold inertance tube can significantly improve the efficiency of a 4 K Stirling-type PTC. A preliminary experimental investigation was carried out with helium-4 as the working fluid and a refrigeration temperature of 4.23 K was achieved. The experimental results show that the operating frequency has a significant influence on the performance of the Stirling-type PTC and a relatively low average pressure is favorable for decreasing the loss associated with the real gas effects of a 4 K Stirling-type PTC.
基金supported by Strategic Pioneer Program on Space Science, Chinese Academy of Sciences (XDA04074100)
文摘Terahertz(THz) frequency region, defined from0.1 to 10 THz, is an important frequency band for radio astronomy and atmospheric science. As NbN Superconductor-Insulator-Superconductor(SIS) mixers used for terahertz detection, which are studied by the Purple Mountain Observatory(PMO), Chinese Academy of Sciences(CAS), work at 8–10 K, and require condition of micro vibrations, its astronomical observation in aerospace is limited by suitable refrigeration method. 4 K high frequency pulse tube cryocooler developed by Key Laboratory of Space Energy Conversion Technologies(SECT), Technical Institute of Physics and Chemistry(TIPC), CAS, offers an opportunity for the application of SIS mixers. This article introduces the progress of the two-stage high frequency pulse tube cryocooler researched by TIPC. The cryocooler has reached a no load temperature of 4.5 K which is the lowest temperature for this kind of cryocooler reported so far. The successful coupling between the THz component and the high frequency pulse tube cryocooler lays a solid foundation for space detection in the terahertz band.
基金Supported by the National Natural Science Foundation of China (Grant No. 10874190)National Science Foundation of China for Distinguished Young Scholars (Grant No. 50625620)
文摘The inertance tube is one of the key components of a pulse tube cryocooler. It has great influence not only on the efficiency of the pulse tube cryocooler, but also on the efficiency of the linear compressor. Meanwhile, it is very difficult to predict the impedance of an inertance tube because of the turbulent flow. In this paper, using a quasi-turbulent model, the inertance tube is optimized to match a linear compressor driven pulse tube cryocooler. Experimental results show that this model can predict the impedance quite well. With 127 W input electric power, the pulse tube cryocooler obtains 9.4 W cooling power at a temperature of 77 K. The relative Carnot efficiency of the whole system reaches 19.8%.
文摘A valveless linear compressor was built up to drive a self-made two-stage pulse tube cryocooler. With a designed maximum swept volume of 60 cm3, the compressor can provide the cryocooler with a pressure volume (PV) power of 400 W. Preliminary measurements of the compressor indicated that both an efficiency of 35%~55% and a pressure ratio of 1.3~1.4 could be obtained. The two-stage pulse tube cryocooler driven by this compressor achieved the lowest temperature of 14.2 K.
基金The work was financially supported by the Aeronautical Science Foundation of China (Grant No. 20162490005)the Science and Technology Commission of Shanghai Municipality (Grant No. 18511110100).
文摘This paper establishes a theoretical model of the single-compressor-driven (SCD) three-stage Stirlingtype pulse tube cryocooler (SPTC) and conducts experimental verifications. The main differences between the SCD type and the multi-compressor-driven (MCD) crycooler are analyzed, such as the distribution of the input acoustic power in each stage and the optimization of the operating parameters, in which both advantages and difficulties of the former are stressed. The effects of the dynamic temperatures are considered to improve the accuracy of the simulation at very low temperatures, and a specific simulation example aiming at 10 K is given in which quantitative analyses are provided. A SCD threestage SPTC is developed based on the theoretical analyses and with a total input acoustic power of 371.58 W, which reaches a no-load temperature of 8.82 K and can simultaneously achieve the cooling capacities of 2.4 W at 70 K, 0.17 W at 25 K, and 0.05 W at 10 K. The performance of the SCD three-stage SPTC is slightly poorer than that of its MCD counterpart developed in the same laboratory, but the advantages of lightweight and compactness make the former more attractive to practical applications.
基金supported by the National Key R&D Program of China(Grant No.2018Y FB0504603)the National Natural Science Foundation of China(Grant No.U1831203)+2 种基金the Strategic Pilot Projects in Space Science of China(Grant No.XDA15010400)the Key Research Program of Frontier Sciences,Chinese Academy of Sciences(Grant No.QYZDY-SSW-JSC028)the Youth Innovation Promotion Association of Chinese Academy of Sciences(Grant No.2019030)。
文摘Gas-coupled Stirling-type pulse tube cryocooler(SPTC) is currently the most compact and simplest configuration among all types of cryocoolers, but it is challenging to achieve a very low temperature. This paper investigates a gas-coupled SPTC which is capable of directly achieving a temperature of around 4 K. Theoretical analyses were performed based on SAGE to study the effects of employing one or more multi-bypass structures on apparent cooling performance, and internal working parameters. The simulation results indicate that the function of the multi-bypass is similar to that of a multi-stage gas-coupled structure, producing a pre-cooling effect on the lower-temperature section by increasing the acoustic power and the enthalpy flow in the pulse tube of the higher-temperature section. The cooperation of two multi-bypass structures can promote a higher enhancement of the cooling performance, but it is difficult to achieve the same cooling performance of a completely multi-stage gas-coupled SPTC due to weak phase-shifting capability and excessive reduction of the mass flow. Based on the model, the developed prototype has achieved a no-load temperature of 4.4 K, which shows the great potential of using a gas-coupled SPTC to obtain a cooling temperature below 4 K.