Passive Mechanical Device for Phase Shifting in a Pulse Tube Cryocooler

Transcription

1 C19_018 1 Passive Mechanical Device for Phase Shifting in a Pulse Tube Cryocooler D. Radchenko 1, G. Grossman Ricor Cryogenic and Vacuum Systems, Ein Harod Ihud, Israel Technion Israel Institute of Technology, Haifa 3000, Israel 1 ABSTRACT A assive mechanical device for hase shifting was develoed for a miniature Pulse Tube In- Line cryocooler develoed earlier at the Rechler Cryogenic Laboratory, Technion-Israel Institute and a mechanical analogy, and by simulations using a commercial numerical solver for ulse tube without changes. Simulation results were comared with those from the theoretical model. A ro- was due to the limitations in the recision manufacturing and assembling of the assive mechanical hase shifter. the assive iston high frequency movement (at about 100 Hz) that had to be contact-less. It was INTRODUCTION A resent worldwide trend focuses on the miniaturization of regenerative cryocoolers. It is evident that the ulse tube cryocooler is one of the best candidates for miniaturization. Downscaling the mechanical dimensions without a change in the oerating arameters becomes roblematic, as internal heat losses become dominant in the device. The method roosed to counteract these heat One of the smallest ulse tube cryocoolers constructed to-date was designed at the Rechler Cryogenic Laboratory, Technion-Israel Institute of Technology by Sobol et al. [1]. An inertance tube and a reservoir were used for hase shifting in the cryocooler. This miniature ulse tube cryocooler achieved Cryocoolers 19, edited by S.D. Miller and R.G. Ross, Jr. International Cryocooler Conference, Inc., Boulder, CO,

2 0 C19_018 limitation using the inertance tube. In miniature devices, the imedance created by the inertance tube has a large resistive comonent, which limits its ability to roduce the required hase shift. A ossible solution for increasing the hase shift in the ulse tube cryocoolers was roosed by Matsubara et al. []. The concet was to use a assive mechanical device instead of an inertance tube and a reservoir. Theoretically, any desired hase shift could be roduced by such a assive mechanical device and it could be miniaturized without deterioration of its erformance, in contrast to the inertance tube. In 01 Lewis, Bradley and Radebaugh from NIST [3] develoed and tested a miniature ulse tube with actively controlled iston installed at the hot end of the cryocooler instead of the inertance controlled iston was better than that of the same cryocooler with the inertance tube. The imrove- - length is 1 mm. The roosed design of the mechanical hase shifter is a assive iston suorted in a recise clearance ga (0 μm) between iston and cylinder. These design arameters were obtained using hasor theory and comared to the simulation of the ulse tube cryocooler with the roosed mechanism for hase shifting by commercial software Sage. Final otimization of the design arameters was erformed by Sage. the assive iston dislacement at high frequencies. For this urose, a contact-less dislacement measurement system was designed, manufactured and imlemented. THEORETICAL ANALYSIS Phasor Analysis for the Pulse Tube Cryocooler with Passive Piston Phasor analysis is a common theoretical tool for investigation of different arameters in regenerative cryocoolers. Using such analysis eliminates time deendence from the equations which are transformed from the time-deendent sace to the vector sace and only hases and amlitudes of - Figure 1 - V_ am V (1) V0 1 sint where: V is the volume of the assive iston; V 0 is the dead volume; V _ amis the swet, or stroke volume, and V _ is the amlitude of the swet volume. am PULSE TUBE ANALYSIS & EXPERIMENTAL MEASUREMENTS

3 PASSIVE MECHANICAL DEVICE FOR PHASE SHIFTING PT 03 C19_018 3 Figure 1. Schematic diagram for a Pulse Tube cryocooler equied with a Passive Piston - in Vector sace. PV _ am PV a m () RTh RTh where m P a is the mean ressure, T h is the hot temerature, V is the volumetric P Or, T PV h _ am PV a m (3) Tc RTc RTc where T c is the cold temerature. The hasor analysis indicates the following: the otimum erformance in the regenerator can sure in the regenerator. In the conventional Stirling cryocooler the same hasor arrangement would Therefore, from Figure 1, in order to obtain the otimal hase shift in the regenerator the following should hold simultaneously: ac c mac mc MECHANICAL ANALOGY The solution obtained from the hasor analysis erformed in the revious section does not include mechanical arameters that are necessary for the design of the assive iston. The roosed

4 C19_ PULSE TUBE ANALYSIS & EXPERIMENTAL MEASUREMENTS method for obtaining these design arameters is a mass-sring-damer analogy of the ulse tube cryocooler. The results from alying this method can be used together with results from the hasor analysis. The dislacement of the gas acted uon by the comressor is reresented by x c and that of the gas acted uon by the assive iston is reresented by x (which is assumed to be the same stiffness k t and negligible mass. The assive iston is reresented as a mass, M ; sring stiffness, kb c. The comressor A c and the assive iston A. The ulse tube volume is reresented as V t and the assive iston volume as V b. A schematic mass-sring-damer model of the ulse tube cryocooler with a assive iston is shown at Figure. The oscillation of gas in the ulse tube cryocooler can be described using this method by a second order ordinary differential equation (ODE): A M x cx kb kt x kt xc Ac where the ratio A Ac xk 1 t A M x cx xktot cost Ac where x 1 is the amlitude of the comressor iston dislacement. Initial conditions of the assive iston dislacement and velocity are: x (7) 00; x 00 x t A cos t B sin t (8) where xk 1 t A ktot M xk 1 t Ac A ; B Ac c ktot M Ac c ktot M m (9) g Ax where: m g is the density of the gas. Therefore, m sin cos sin (10) g t m t AA t B t A A B t in Or, m cos (11) t A A B t in Figure. Schematic mass-sring-damer model of ulse tube cryocooler with a assive iston.

5 PASSIVE MECHANICAL DEVICE FOR PHASE SHIFTING PT 05 C19_018 B in arctan A The ressure of the iston on the gas, P, can be found from the following: (1) P C D cost C ktx1 kt kt arctan ; C A ; D B D Ac A A In Figure 1 sary to shift the hase in equation (1) to be consistent with the discussion in the revious Section. Therefore, P (13) C D sin t m t A A B cos tm where, m in B C m arctan arctan A D This result can now be substituted into the results from the revious section. In conclusion, the following should hold simultaneously for the otimal erformance of the ulse tube cryocooler with assive iston: G M G M arctan arctan and H N H N M N G H M N G H (17) Pavg V P co avg Vco Vco C D G sin ; H cos Vac RT RT RT co co co T M A A B T h cos m c C D Vt Th N Vhhx Vchx A A B sin m RT c Tc GHM,,, N by Matlab software. In the following section these results would be comared with the numerical solution from Sage software that is PULSE TUBE CRYOCOOLER DESIGN IN SAGE Overview For the Stirling-based cycle cryocoolers the most commercial software for analysis is Sage, tool for cryocooler design. The software emloys theoretical models and emirical correlations in calculations of different arameters. The assembly has a modular form where each comonent of the system is organized logically inyo a hierarchical tree structure. In Figure 3 the root level editing based on the model of the earlier design develoed by Sobol et al. [1].

6 C19_ PULSE TUBE ANALYSIS & EXPERIMENTAL MEASUREMENTS Figure 3. cryocooler. Otimization Available arameters for otimization are limited because the resent design of the Passive Piston Pulse Tube cryocooler is based on the already designed and manufactured Inertance Tube Pulse Tube cryocooler [1]. Most arameters such as dimensions, frequency, comressor iston dislacement, mesh roerties, frequency and temeratures of the revious design had to remain unchanged. The arameters available for otimization are assive iston hysical arameters which otimized arameters were found. Due to the manufacturing restrictions, the values of arameters found in the otimization rocess were rounded off to accetable values. Simulation Results The results from the Sage otimization were comared to the results from the theoretical - iston mass values. also calculated and its grah was shown for the analytical solution from theoretical analysis, as well as for the Sage solution. It is necessary to discuss the difference between the grah of analytical solution and of Sage solution. Both solutions have a linear behavior. Also, it is quite simle to of these two functions is quite different. The reason for such behavior is that the analytical model neglects the comressibility and the helium gas stiffness; therefore, the calculated sring stiffness in the case of the analytical solution also contains in it the real gas stiffness. In contrast, in the Sage or otimized. Thus, the value of sring stiffness from the analytical solution is greater than the one

7 PASSIVE MECHANICAL DEVICE FOR PHASE SHIFTING PT 07 C19_018 7 Figure 4. Sring stiffness vs. iston mass. Table 1. Final arameters for Passive Piston model. Piston Mass Sring Stiffness -3 summarized Table 1. EXPERIMENTAL SETUP The arameters to be measured are the temerature, ressure and the assive iston dislace- lations were measured at the interface between the comressor and aftercooler, buffer tube and hot Piston Dislacement Measurement System without the hysical contact of any mechanical art with the oscillating iston. The values of the dislacement have to be measured at the same times as the ressure values at different cryocooler oints. Using values of the assive iston dislacement, the velocity of the assive iston can be For iston dislacement measurement an otical system was used. The oerating rincile of the system is as follows: a laser beam asses through the glass at the rear side of the cylinder which deend on the location of the laser beam imingement. A schematic concet of the iston collected by a data acquisition rogram.

8 08 C19_018 PULSE TUBE ANALYSIS & EXPERIMENTAL MEASUREMENTS 8 Passive Piston Assembly Window PSD Laser Hot Heat Exchanger Three Pressure Sensors Cold Heat Exchanger Aftercooler Figure 5. &U\RFRROHU H[FOXVLYH RI YDFXXP FKDPEHU ZLWK SDVVLYH SLVWRQ GLVSODFHPHQW PHDVXUHPHQW system. Glass Reflective Surface Piston PSD ǻ 0 -ǻ Laser Initial Position New Position Figure 6. Schematic of iston dislacement measurement. In order to eliminate the convection heat transfer at the cold end it is convenient to erform the H[SHULPHQWV ZLWK WKH FU\RFRROHU LQ D YDFXXP FKDPEHU +RZHYHU GXH WR WKH GHVLJQ UHVWULFWLRQV WKH assive iston dislacement could only be measured without the vacuum chamber. RESULTS 7KH H[SHULPHQWV ZHUH SHUIRUPHG DW WKH HQYLURQPHQWDO WHPSHUDWXUH RI. )LOO SUHVVXUH LQ WKH UHIULJHUDWRU ZDV VHW WR EDU &U\RFRROHU SHUIRUPDQFH ZDV FKHFNHG DW VHYHUDO IUHTXHQFLHV RI WKH comressor near the design oint of 100 Hz. The target ressure ratio was 1.3 (as set in the design). 7KH WHPSHUDWXUH UHFRUGHG ZDV WKH ORZHVW WHPSHUDWXUH REWDLQHG DW WKH FROG KHDW H[FKDQJHU,Q RUGHU to roduce vacuum in the vacuum chamber a Varian vacuum system was used. Passive Piston Dislacement Measurement Results As mentioned before, due to design restrictions, the assive iston dislacement measurement was erformed without the vacuum chamber. Figure 7 shows the variation of ressure, iston dis-

9 PASSIVE MECHANICAL DEVICE FOR PHASE SHIFTING PT 09 C19_018 9 Figure 7. Pressure at the inlet to the assive iston, assive iston dislacement and velocity at frequency of 10 [Hz]. lacement, and iston velocity at the inlet to the assive iston at frequency of 10 Hz. The hase shift at the boundary of the assive iston between iston velocity and ressure oscillation, which Cryocooler Performance Measurement As mentioned earlier, in order to decrease heat transfer by convection at the cold end, the measured at several frequencies around the design oint. The results are shown in Figure 8. The aftercooler inlet was measured at the same frequencies (see Figure 8). The ressure ratio at high frequencies decreased from the design oint of 1.3 to 1.. CONCLUSIONS The resent research has roved the viability of the concet of using a assive mechanical tween analytical and numerical solution by the Sage software. However, the temeratures at the in [1]. Also, the ressure ratio was lower than the design value. This was due to manufacturing and assembly inaccuracies that added arasitic friction between iston and cylinder. However, the hase shift between iston velocity and ressure oscillation that was measured at the inlet to the assive iston demonstrated the feasibility of the concet. Passive iston dislacement contactless measurement system was roosed and used in the Figure 8. Results of the exeriment in vacuum chamber.

10 10 PULSE TUBE ANALYSIS & EXPERIMENTAL MEASUREMENTS C19_ measure small dislacement values at high frequencies, due to the high accuracy of the PSD. The results of measurements heled to understand gas behavior in the ulse tube cryocooler oerating at high frequencies. ACKNOWLEDGEMENTS - REFERENCES Cryocoolers 16 Proceedings of the 5th International Cryocooler Conference Adv. in Cryogenic Engineering 4. Radebaugh, R., A Review of Pulse Tube Refrigeration, Adv. in Cryogenic Engineering Sringer US (1990),