This article presented a hybrid cryocooler which combines the room temperature displacers and the pulse tube in one system. Compared with a traditional pulse tube cryocooler, the system uses the rod-less ambient displacer to recover the expansion work from the pulse tube cold end to improve the efficiency while still keeps the advantage of the pulse tube cryocooler with no moving parts at the cold region. In the meantime, dual-opposed configurations for both the compression pistons and displacers reduce the cooler vibration to a very low level. In the experiments, a lowest no-load temperature of 38.5 K has been obtained and the cooling power at 80K was 26.4 W with an input electric power of 290 W. This leads to an efficiency of 24.2% of Carnot, marginally higher than that of an ordinary pulse tube cryocooler. The hybrid configuration herein provides a very competitive option when a high efficiency, high-reliability and robust cryocooler is desired.

Small scale cryocoolers play important role in many applications, such as cooling infrared sensors for much improved resolutions or cooling superconducting electronics for advanced digital filters. Figure 1 illustrates several configurations including the hybrid one to be studied here. Among them, Stirling cryocooler has long been used, which has a high efficiency and compact structure. The most recent two decades have seen the rapid development of pulse tube cryocoolers as the new generation of cryocooler.1 By removing the cryogenic displacer, the pulse tube cooler offers the advantage of low vibration at the cold head, easy manufacturing and robustness (especially in handling transverse mechanical load on the cold finger). However, the intrinsic mechanism of the pulse tube cooler determines that its theoretical efficiency is marginally lower than that of the Stirling cryocooler. The later uses displacer to recover the expansion work (namely the gross cooling power). While at the hot end of the pulse tube, expansion work comes down from the cold end of the pulse tube and gets dissipated in the so-called phase shifters such as orifice and inertance tube with reservoir.2,3 Due to this, in practice, Stirling cryocoolers offers a much better efficiency than the pulse tube cryocooler, which is one of the important factors that impede the wide acceptance of pulse tube cryocoolers in many applications. Meanwhile, the dissipated heat at the hot end of the pulse tube sometimes also needs extra heat transfer means to emit into the environment, especially for those with relatively large cooling power at temperatures, say, higher than 60 K. How to overcome these disadvantages is one of the research topics in the pulse tube cryocooler research field.

FIG. 1.

Schematic of three different configurations of cryocooler based on Stirling cycle: 1. Driving piston; 2.Ambient heat exchanger; 3. Regenerator; 4. Cold-head; 5. Displacer; 6. Displacer rod; 7. Spring; 8. Pulse tube; 9.Secondary ambient heat exchanger; 10. Inertance tube; 11. Reservoir ;a) .Free piston Stirling cryocooler; b) .Pulse tube cryocooler; c). Hybrid pulse tube cryocooler; The black arrow denotes the direction of acoustic work flow as well as the positive direction of x axis.

FIG. 1.

Schematic of three different configurations of cryocooler based on Stirling cycle: 1. Driving piston; 2.Ambient heat exchanger; 3. Regenerator; 4. Cold-head; 5. Displacer; 6. Displacer rod; 7. Spring; 8. Pulse tube; 9.Secondary ambient heat exchanger; 10. Inertance tube; 11. Reservoir ;a) .Free piston Stirling cryocooler; b) .Pulse tube cryocooler; c). Hybrid pulse tube cryocooler; The black arrow denotes the direction of acoustic work flow as well as the positive direction of x axis.

Close modal

In 2010, Zhu et al. proposed the ambient displacer structure to improve the efficiency of the Stirling type pulse tube cryocooler4 and did some theoretical analyses. Namely, the configuration inserts inside the typical Stirling cryocooler a hollow pulse tube in between the cold end heat exchanger and the displacer. Through carefully tuning the displacer mass, rod area and spring stiffness, the expansion power could be recovered in this hybrid configuration. For the displacer configuration, a net area difference on both sides of the displacer and associated net force provides the main driving force for the displacer movement. This rod displacer configuration generally needs two sliding seals, either dry lubrication or clearance seal, which is sometimes cumbersome. For this reason, here we further proposes rod-less configuration to simplify the structure (Fig. 1(c)). From the thermoacoustic viewpoint, rod and rod-less configuration has different requirements on the displacer physical parameters. With the help of phasor diagram, the following will show mechanisms underlying the difference.

In the cryocooler systems discussed here, the thermal function is realized through oscillating flow where the pressure wave and gas velocity oscillates sinusoidally. Similar to the methodology used in acoustics and alternating circuits, complex values and phasor diagrams are used to illustrate the relationship between different physical quantities. Most often used are the complex pressure wave phasor p ˆ and complex volume flow rate phasor U ˆ (gas velocity multiplied by the void cross-sectional area), in analogous to the alternating voltage and current in electric circuits, respectively. Cycle-averaged product of these two physical parameters, namely the acoustic work, is important and can be presented as:

W = 1 2 p ˆ U ˆ cos θ = 1 2 r e a l ( p ˆ U ˆ * )
(1)

Where ‖ means taking the amplitude, θ is the phase angle between the two phasors, real means taking real part, * means taking conjugate.

At the surface of the compressor piston, the acoustic work is equal to the mechanical compression work. At the upper side of the displacer the acoustic work is equal to the expansion work, which is the gross cooling power of the cryocooler. To have the acoustic work flow in the right direction as shown in Fig 1, basic requirement is that cosθ should be positive. In fact, for a high efficiency operation, a more specific requirement is that p ˆ and U ˆ are in phase somewhere in the middle of the regenerator to ensure that the same amount of work goes with minimal velocity to minimize the gas flow dissipation loss therein. For this reason, a typical Stirling type cryocooler has a p ˆ leading U ˆ by a certain degree (typically 30° ∼ 50°) at the cold end and a p ˆ lagging U ˆ by a similar degree at the regenerator ambient end. To realize this phase relationship, there is a delicate difference for the configurations with rod and without rod.

With figure 2, we look at and compare the phasors for both the displacer with rod and without rod. p ˆ com , p ˆ exp are the dynamic pressures at the compression space and expansion space respectively. The former one is used as the reference phasor along the real axis. Ad, Arod are the area of displacer and rod respectively; k is the spring stiffness; m is the displacer mass; Rm is the displacer mechanical damping coefficient; U ˆ c , U ˆ d are the volume flowrate at the regenerator cold end and the volume flowrate swept by the displacer respectively ω is the angular frequency; Cpt is the equivalent acoustic capacitance caused by the void volume in the pulse tube. For the displacer with rod, the dynamics equation is:

P ˆ exp A d P ˆ com ( A d A rod ) = ( i ω m + k i ω + R m ) U ˆ d A d
(2)
FIG. 2.

Phasor diagrams illustrating the working mechanism for both the a) rod and b) rod-less displacer.

FIG. 2.

Phasor diagrams illustrating the working mechanism for both the a) rod and b) rod-less displacer.

Close modal

When Arod is zero, the equation reduces to the one for the rod-less configuration.

For the displacer with a rod (Fig. 2(a)), net force on the displacer (i.e. vector F ˆ 1 ) has a small acute angle ϕ1 with p ˆ exp . As said, to ensure an efficient operation of the cryocooler, the displacer velocity must lag the p ˆ exp by a certain acute angle (β1 in Fig. 2(a)) to transfer the expansion acoustic power to the compression space. Since F ˆ 1 already lags p ˆ exp by an acute angle of ϕ1, a small angle provided by iωm + k/ + Rm would suffice to meet the phase requirement. Due to the relatively small value of Rm, a slight tuning of moving mass or spring constant around the resonant value, or, tuning the cryocooler operating frequency slightly away from the resonance frequency could realize the target. All in all, this leads to an operating frequency close to the displacer resonance frequency. Then, considering the void volume effect of both the pulse tube and the regenerator, we have the volume flowrate phasor lying on both sides of the pressure phasors, which is required by the high efficiency operation of the cryocooler, as explained before.

However, in case of rod-less configuration, without the net area difference, the corresponding net force phasor F ˆ 2 on the displacer forms an obtuse angle ϕ2 with p ˆ exp . As addressed above, we need a displacer velocity forming an acute angle with the p ˆ exp . According to Eq. (1), we need to have a powerful complex value to tune the final U ˆ d to an angle of an acute value (β2 in Fig. 2(a)). This could be realized by setting a much larger spring stiffness and thus tuning the resonance far off the cryocooler operation frequency. After this, the same discussion holds for this rod-less configuration as well as that for the rod configuration.

After the qualitative analyses, we resort to numeric model for quantitative analyses and optimizations5,6 for the hybrid Stirling-pulse tube cryocooler with rod-less configuration. To ensure an easy cancellation of the vibration, we adopted dual-opposed configuration for the hybrid system. The layout drawing of the experimental configuration is shown in Figure 3. It is composed of dual-opposed pistons, dual-opposed room temperature displacers, the ambient heat exchanger, regenerator, cold-head and the pulse tube. The dual opposed flexure-bearing supported displacers are placed between the compression space and the hot end of the pulse tube. The configuration leads to an easy cancellation of the vibration caused by the moving mass. Placing the rod-less displacers at ambient temperature also brings manufacturing advantages.

FIG. 3.

Schematic diagram of the hybrid system used in experiment, arrows denote the direction of acoustic work flow as well as the positive direction of x axis and the values represent the calculated acoustic work flow inside the system and the angle between pressure wave and volume flowrate, in correspondence to the best experimental data point.

FIG. 3.

Schematic diagram of the hybrid system used in experiment, arrows denote the direction of acoustic work flow as well as the positive direction of x axis and the values represent the calculated acoustic work flow inside the system and the angle between pressure wave and volume flowrate, in correspondence to the best experimental data point.

Close modal

The optimized parameters are as follows. The pistons have a diameter of 38 mm to provide a swept volume of 16 cm3. The regenerator is of coaxial structure with the pulse tube placed in the center. The regenerator annular area is equivalent to that of a circle with i.d. 27 mm and has a length of 50 mm, filled with 400 mesh stainless steel screens. The heat exchangers at both ends of the regenerator are made of copper with axial slots cut through EDM technology. The ambient heat exchanger is chilled by the water with a temperature of 20 °C. The pulse tube has an i.d of 16 mm and a length of 60 mm. One end of the pulse tube is set close to the cold–head and the other end connects with the expansion space through a tube with an i.d of 4 mm. Each ambient displacer is supported by two flexure springs with a mass of 24 grams and a total stiffness of 15 kN/m. The natural resonance frequency is 125.8 Hz. The displacer has an i.d of 25 mm and a sealing length of 5 mm.

In figure 3, part of the simulation results according to the optimum experimental data point is shown. An acoustic work of 232 W is provided by the compressor pistons. Then, together with the feedback of 54.6 W acoustic work through the displacer, a total acoustic work of 286.6 W enters the ambient heat exchanger. At the cold end, an expansion work of 58 W is transferred to the displacer, which reduces to the feedback value of 54.6 W due to mechanical dissipation.

Figure 4 shows simulation results about how the operating frequency affects the system performance. The pressure ratio at the compression space is kept at 1.31 and the relative Carnot efficiency is calculated with input acoustic power as the reference. As the results show, the system acquires a highest cooling power at 40 Hz and a highest efficiency at around 35 Hz, much lower than the natural resonance frequency of the displacer.

FIG. 4.

Simulated performance of the cryocooler at different operating frequency.

FIG. 4.

Simulated performance of the cryocooler at different operating frequency.

Close modal

Figure 5 show some experimental results. Limited by the capability of the motors driving the pistons, the system only works at frequencies higher than 45 Hz. In all the experiments, the compressor electric to acoustic efficiency changes a little around 80%. Corresponding to the right side of the curves in figure 4, we can see in the experiments that the cooling power and the efficiency also decreases as the frequency increases. At the operating condition of a mean pressure of 3.5 MPa and a frequency of 45 Hz, this hybrid cryocooler reached a lowest no-load temperature of 38.5 K and the cooling power at 80K was 26.4 W with an input electric power of 290 W, which means an efficiency of 24.2% of Carnot, marginally higher than a normal Stirling type pulse tube cryocooler. With more optimization work on the way, this compact hybrid cryocooler provides a very competitive option for many applications when efficiency, size and robustness are very important.

FIG. 5.

Experimental performance of the cryocooler at different operating frequencies.

FIG. 5.

Experimental performance of the cryocooler at different operating frequencies.

Close modal

This work is financially supported by the National Natural Science Foundation of China (Contract number 51206177, 51376187) and National High Technology Research and Development Program of China (Contract number 2013AA032703).

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