Presented at the 16th International Cryocooler Conference, held May 17-20, 2008 in Atlanta, Georgia.High efficiency pulse tube coolers driven by linear compressors usually operate between 30 Hz and 60 Hz. This article presents the performance of a high efficiency in-line PTC with an operating frequency of 100 Hz. The theoretical model of a PTC is based on thermoacoustic theory. Analytical results indicate that the PTC operating at 100 Hz could obtain a high efficiency with appropriate parameters. To couple the PTC, the parameters of linear compressor are optimized using compressor governing equations. Experimental results show that a no-load temperature of 31.8 K and a cooling power of 12.4 W at 77 K are obtained with an input electric power of 185.2 W

Dai, Wei

Hu, Jianying

Luo, Ercang

Wang, Xiaotao

Zhou, Yuan

Scholarly Materials And Research @ Georgia Tech

157Performance of a Stirling-Type Pulse TubeCooler for High Efficiency Operationat 100HzXiaotao Wang1, 2, Wei Dai1, Jianying Hu1, Ercang Luo1, Yuan Zhou11Technical Institute of Physics and Chemistry of CAS, Beijing 100190, China2 Graduate University of Chinese Academy of Sciences, Beijing 100049, ChinaABSTRACTHigh efficiency pulse tube coolers driven by linear compressors usually operate between 30 Hzand 60 Hz. This article presents the performance of a high efficiency in-line PTC with an operatingfrequency of 100 Hz. The theoretical model of a PTC is based on thermoacoustic theory. Analyticalresults indicate that the PTC operating at 100 Hz could obtain a high efficiency with appropriateparameters. To couple the PTC, the parameters of linear compressor are optimized using compres-sor governing equations. Experimental results show that a no-load temperature of 31.8 K and acooling power of 12.4 W at 77 K are obtained with an input electric power of 185.2 W.INTRODUCTIONIn comparison to Stirling or Gifford-McMahon (G-M) coolers, the pulse tube cooler (PTC)eliminates moving parts in the cold region, and brings the advantages of low cost, long life and lowmechanical vibration. The Stirling pulse tube coolers driven by linear compressors usually operatebetween 30 Hz and 60 Hz and have been developed for decades.1 The coolers operating at thesefrequencies have already reached a high level of efficiency.2, 3, 4  Higher frequency operation willlead to a reduction in the size and mass of the compressor with the same acoustic power and,therein, provide a more compact system. In 2007, NIST setup an in-line Stirling PTC operating at120 Hz, which provide a cooling power of 3.44 W at 80 K5. In 2008, NGST reported their coaxialpulse tube cooler operating at about 100 Hz and a cooling power of 1.3 W at 80 K was achievedwith an input electric power of 49 W.6The research of 100 Hz PTC at our laboratory has been carried out for years. By using theCFIC 2S102W compressor in our lab, a miniature pulse tube cooler was designed in 2008.7 In theearly experiments, a cooling power of 0.8 W at 80 K was achieved. Through a series of improve-ments, the cooling power at 80 K was raised to 2.6 W in 2009. Because this compressor is originallydesigned at 40-60 Hz, the compressor can only reach 44% of its design power even though theresonance frequency has been adjusted to 100 Hz. In 2009, a bigger PTC designed to provide 10 Wcooling powers at 77 K is designed and fabricated.  To couple with this cooler, a moving magnetlinear compressor was designed and manufactured by Lihan Technology Inc. The cooler design andexperimental system are introduced in the next sections. The main experimental results and furtherplan are also presented.Figure 1. Cooling power at 77 K Vs Input acoustic power, different regenerator hydraulic diametervalues are used in simulation.PULSE TUBE COOLER DESIGNThe principal design goal of this cooler is to provide 10 W of cooling power at 77 K within 120 Wof acoustic power. A numerical model8 based on thermoacoustic theory9, 10 is used for the optimiza-tion. A large number of calculations have been carried out to optimize the different componentssuch as the regenerator, the pulse tube and the inertance tube. The key parameters of these compo-nents are chosen appropriately. The modeling was successful because the simulation results arevery close to the experimental results.Figure 1 shows the PTC cooling power at 77 K with different levels of input acoustic power.  Theregenerator is the key component of PTC and regenerator material will directly affect the cooler perfor-mance. Since the high frequency operation decreases the thermal penetration depth, the required hydrau-lic diameter in the regenerator is much smaller than that under conditions of 30 Hz to 60 Hz. Theinfluence of the different regenerator hydraulic diameters is investigated, as shown in Figure 1. Theperformance is degraded when the hydraulic diameter is too large, but the difference is not great whenthe value of hydraulic diameter ranges from 26 to 34 μm. The cooler can provide 12.3 W of coolingpowers with 125 W of input acoustic power.  Too small a value for the hydralic diameter is not suitablebecause the pressure drop become bigger as the hydraulic diameter decreases.The analytical results also indicate that an appropriate phase at the hot end of the pulse tube canbe easily obtained at a high frequency with an inertance tube plus and a reservoir as the phase shifter.The other goal of the simulation is to compute the acoustic impedance (Ζ) of the PTC, which isused to optimize the compressor parameters using the compressor governing equations. The com-pressor is a single-piston configuration.  A spring-mass oscillator with a resonance frequency of100 Hz is installed at the back of the compressor to reduce the vibration.EXPERIMENT SYSTEM AND MEASUREMENTFigure 2 shows the schematic of the experiment system with a in-line PTC configuration cho-sen. The input electric power is calculated by measuring the compressor's driving voltage and cur-rent. With the assumption of an adiabatic compression in the backside space of the compressor, thepiston velocity is computed through the dynamic pressure measured in the backside space. Thedynamic pressure and the mean pressure in the compression space and reservoir are also measured.The acoustic power (PV power) can be calculated approximately using the dynamic pressure in thecompression space and piston velocity.158 MEDIUM-CAPACITY 50-80 K SINGLE-STAGE CRYOCOOLERS Figure 2. A schematic drawing of Stirling-type pulse-tube cooler driven by linear compressorFigure 3. Cooldown curve of the cold head, with mean pressure 3.55 MPa and 3.0 MPa, respectivelySpringMoving MagnetPistonCold HeadRegeneratorPulse TubeHot ExchangerBacksideSpaceCoilCompressor SpaceAfter CoolerReservoirInertance TubeThe ambient heat exchangers are kept at room temperature with chilling water at 288 K . Thetemperature of the cold-head was measured by a calibrated PT100 sensor. The cooling power of thePTC is measured via a resistor with the external DC power supply.EXPERIMENT RESULTS AND DISCUSSIONFigure 3 shows the typical cool down curve of the cold-head with a driving voltage of 114 Vrms.The cold-head is made from copper with a mass of 53 g. The cool-down time to 77 K is 4.76 minutesfrom 297 K at a mean pressure of 3.55 MPa and it takes 4.33 minutes from 291 K to 77 K at 3.0 MPa.The input electric power becomes larger as the cold-head temperature decreases. The input electricpower is about 183.2 W when cold-head reaches at the lowest temperature. The lowest cold-head159STIRLING-TYPE PT COOLER FOR OPERATION AT 100 HZFigure 4. No load temperature of the cold head & compressor efficiency vs input electric power.Figure 5. Cooling power at 77 K and relative Carnot efficiency vs input electric power. The wholesystem means the relative Carnot efficiency using input electric power, while the cold part means therelative Carnot efficiency using estimated acoustic powertemperature of 31.8 K at 3.55 MPa is acquired and the difference of the lowest temperatures be-tween two mean pressures is very slight.Figure 4 shows no load cold-head temperature at different input electric power at the meanpressure of 3.55 MPa.  The cold-head temperature can be maintained at 52 K with 42 W inputelectric power and the acoustic power is about 28 W. This figure also shows the compressor effi-ciency. It can be seen that compressor efficiency decreases as the input electric power increases.With 183.2 W input power, the approximately calculated acoustic power using the dynamic pres-sures at both sides of the piston is 111.4 W with an compressor efficiency of 61 %, which is a littlelower than our design goal.The cooling power at 77 K with different input electric power is presented in Figure 5. Themean pressure usedi s 3.55 MPa. A cooling power of 12.4 W at 77 K is required with an inputelectric power of 185.2 W. The corresponding calculated acoustic power is 113.6 W. The whole160 MEDIUM-CAPACITY 50-80 K SINGLE-STAGE CRYOCOOLERSFigure 6. Cooling power at 77 K vs cold-head temperature.system-relative Carnot efficiency is also shown in Figure 5 and it reaches 18.4 % at 185.2 W. Inorder to evaluate the performance of the cooler, the relative Carnot efficiency of the cold-head isalso calculated using an approximation of the acoustic power and is presented in Figure 5. As thisfigure shows, the maximum Carnot efficiency of cold-head can reach approximately 30 %. Figure6 shows the cooling power at different cold-head temperatures when the input electric power ismaintained around 185 W. The cooling powers are a little lower at a lower mean pressure, althoughthe lowest temperatures are almost the same.Compared with the design goal, the compressor efficiency is not satisfied. In the next step, thedesign parameters of compressor will be optimized. The single piston configuration will be re-placed by a dual-piston configuration because of lower vibration and easiness to adjust frequency.An air-cooled co-axial PTC will also be developed.CONCLUSIONSIn this paper, the performance of a high efficiency in-line PTC with an operating frequency of100 Hz is presented. The PTC is designed using a theoretical model based on thermoacoustic theory.In the experiments, a no-load temperature of 31.8 K and a cooling power of 12.4 W at 77 K isobtained with 185.2 W of input electric power. The corresponding relative Carnot efficiency of thewhole system including compressor reaches 18.4 %. The PTC cool-down time is 4.76 minute from297 K to 77 K. The simulation results agree well with the experimental results.ACKNOWLEDGMENTThe authors would like to thank Haibin Li and Lin Jiang for their technical support. This workis financially supported by the National Natural Science Foundation of China under contract num-ber of [50625620], [10874190] and [50890181].REFERENCES1. R. Radebaugh and A. O’Gallagher, “Regenerator operation at very high frequencies formicrocryocoolers,” Adv. in Cryogenic Engineering, Vol. 51, Amer. Institute of Physics, Melville, NY(2006), pp.1919-1928.2. Tward E, Chan C K, Colbert R, et al. “High efficiency cryocooler,” Adv. in Cryogenic Engineering,Vol. 51, Amer. Institute of Physics, Melville, NY (2006), pp. 1077-1084.161STIRLING-TYPE PT COOLER FOR OPERATION AT 100 HZ3. Zia. J H. “A pulse tube cryocooler with 300 W refrigeration at 80 K and an operating efficiency of 19%Carnot,” Cryocoolers 14, ICC Press, Boulder, CO (2007), pp. 141-147.4. Hu, JianYing, Wang Xiaotao, Dai Wei, Luo Ercang, “High efficiency linear compressor driven pulsetube cryo-cooler operating in liquid nitrogen temperature,” Chinese Science Bulletin,Vol.54(2009), pp.4428-4431.5. Vanapalli, S., Lewis, M., Gan, Z.,Radebaugh, R.,  “120 Hz pulse tube cryocooler for fast cooldown to50 K,”  Appl. Phys. Letters,Vol. 90 (2007), 072504.6. Petach, M., Waterman, M., Pruitt, G., and Tward, E., “High Frequency Coaxial Pulse Tube Micro-cooler,” Cryocoolers 15, ICC Press, Boulder, CO (2009), pp. 97-103.7. Wang, X., Dai, W., Luo, E.C., et al., “Characterization of a 100 Hz miniature pulse tube cooler drivenby a linear compressor,” Adv. in Cryogenic Engineering, Vol. 55A, Amer. Institute of Physics, Melville,NY (2010), pp. 183-190.8. Dai, W., Luo, E. C., Zhang, Y., et al, “Detailed Study of a Traveling Wave Thermoacoustic RefrigeratorDriven by a Traveling Wave Thermoacoustic Engine,” J. Acoust. Soc. Am., Vol. 119, pp. 2686-2692.9. G. Swift, Thermoacoustics: A unifying perspective for some engines and refrigerator, Sewickley,  2002pp. 99 - 102, 136 - 139, respectively.10. Xiao, J.H., "Thermoacoustic effects and thermoacoustic theory for regenerative cryocoolers (heat en-gines)," Ph.D Dissertation, Institute of Physics, Chinese Academy of Sciences (1990) (in Chinese).11. Ward, B., Clark, J., and Swift,G., “Design Environment for Low-amplitude Thermoacoustic EnergyConversion, DeltaEC, Version 6.2, Users Guide,” Los Alamos National Laboratory, 2008.162 MEDIUM-CAPACITY 50-80 K SINGLE-STAGE CRYOCOOLERS

Performance of a Stirling-Type Pulse Tube Cooler for High Efficiency Operation at 100 Hz.

https://smartech.gatech.edu/bitstream/1853/38769/1/021.pdf

Performance of a Stirling-Type Pulse Tube Cooler for High Efficiency Operation at 100 Hz.

Abstract

Similar works

Full text

Available Versions

Scholarly Materials And Research @ Georgia Tech