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Citation: Zhou Y, Gu C, Cai H K. The third type DC flow in pulse tube cryocooler. Sci China Ser E-Tech Sci, 2009, 52(12): 3491―3496, doi: 10.1007/s11431-009-0287-x

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The third type DC flow in pulse tube cryocooler

ZHOU Yuan1†, GU Chao1,2 & CAI HuiKun1,2 1 Key Laboratory of Cryogenics, Technical Institute of Physics and Chemistry, Chinese Academy of Sciences, Beijing 100190, China; 2 Graduate University of Chinese Academy of Sciences, Beijing 100049, China

New phenomena discovered in the experimental research of the ultra-high frequency pulse tube cryo-cooler 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.

pulse tube cryocooler, DC flow, fluid network theory, flow resistance

Pulse tube cryocooler (PTC) is a small-scale refrigerator capable of reaching cryogenic temperature. It has been widely researched both at home and abroad due to its advantages of no moving components at low tempera-ture as well as its simplicity, low cost, low vibration at cold head and long life time. With its rapid development in recent 20 years, the performance of the PTC has been greatly improved especially for adopting new structures and operations. As a result, the refrigeration efficiency of the PTC is at or close to the level of Stirling cooler so that it has found a wide range of applications in both infrared devices in space and scientific research equip-ment. For example, in 1990s, NASA applied the PTC to infrared device in space as the cold resource, and the GM-type pulse tube refrigerator operating at low fre-quency has been the high-tech product of Cryomech Company in USA for a long time. It can be expected that the PTC will continue to play an important role in scien-tific research as well as in industries such as communi-cation and aerospace in the future.

The working fluid in the PTC is characterized as the oscillating flow (AC flow). However, it is well known that in the PTC there are two types of DC flow called Gedeon streaming[1] and Rayleigh streaming[2] caused by the double-inlet design and the boundary layer effect,

respectively. Furthermore, our recent experimental re-sults of the ultra-high frequency PTC showed that in addition to the two types of DC flow mentioned above, there is also a third type DC flow. Since the DC flow not only deteriorates the performance of the PTC but also affects the stability of the refrigeration temperature, fur-ther study on the mechanism and the suppression meth-ods of this new DC flow is needed and of both academic and application value. It will help to improve not only the performance of the PTC operating at ultra-high fre-quency, but also the COP and the refrigeration tempera-ture stability of PTC operating at high (30―60 Hz) and low frequencies.

In this paper, the fluid network theory will be used to analyze characteristics of the oscillating flow resistance of the pulse tube refrigeration system. The concept of the third type DC flow will also be established. More-over, the mechanism of the third type DC flow and the corresponding suppression methods will be presented.

Received March 26, 2009; accepted June 6, 2009 doi: 10.1007/s11431-009-0287-x †Corresponding author (email: zhouyuan@mail.ipc.ac.cn) Supported by the Major Project of National Natural Science Foundation of China (Grant No. 50890181) and National Natural Science Foundation of China (Grant No. 50676100)

3492 Zhou Y et al. Sci China Ser E-Tech Sci | Dec. 2009 | vol. 52 | no. 12 | 3491-3496

1 Two known types of DC flow in the pulse tube cryocooler

In order to improve the refrigeration performance and cooling temperature stability, two types of DC flow have been discovered through deep theoretical analysis and experimental investigations. In June 1996, Gedeon pre-sented his research in the 9th International Cryocooler Conference, indicating that there was a potential for DC flow in Stirling cooler and double-inlet pulse tube re-frigerator. Through Gedeon’s analysis[1], he pointed out that a closed-loop flow path exists in the double-inlet pulse tube refrigerator, which connects the pulse tube to the regenerator by double inlet valve. Due to the peri-odic oscillation of the density and pressure in the PTC, a mass imbalance of the inflow and outflow is formed in one cycle along the cross-section of the PTC. Thus it causes a net mass flow in one direction, which leads to a stable circulating flow, the Gedeon streaming in the closed-loop. Ju Y L et al.[3] observed DC flow phe-nomenon through the experimental investigation of the double-inlet pulse tube refrigerator which verified the existence of Gedeon streaming. Gedeon streaming car-ries the additional enthalpy flow by itself from the warm end to the cold end of the pulse tube, which will increase the heat load of the cold end heat exchanger. Although the magnitude of the mass flow of Gedeon streaming is small, the additional heat carried by Gedeon streaming is on the same order of the theoretical refrigeration power of the PTC, which significantly reduces cooling effi-ciency and deteriorates refrigeration temperature stabil-ity of the PTC. This, therefore, attracted a lot of atten-tion in this field.

In addition to Gedeon DC flow, Rayleigh DC flow also exists in the PTC. Since there is a temperature gra-dient along the pulse tube and the viscosity of gas parcel at high temperature is larger than that at low temperature, the moving gas parcel does not return to its starting point in one cycle, resulting in a displacement in the pulse tube. These displacements of the gas parcel cause a time-averaged mass flow flux in the boundary layer. Due to the mass conservation principle, there will be the Rayleigh streaming which is a time-averaged mass flow flux in the opposite direction near the wall. Rayleigh DC flow will also carry additional heat from the warm end to the cold end of the pulse tube, deteriorating the cool-ing performance. Swift et al.[4] have made a more de-tailed analysis of the Rayleigh streaming in the pulse

tube refrigerator. Researchers have been using several methods such as

the second orifice[5], multi-bypass[6] technology to sup-press Gedeon DC flow and Rayleigh DC flow. Suppres-sion of DC flow is achieved by eliminating the closed-loop or providing additional gas flow, which has made some progress in the low frequency and high fre-quency pulse tube refrigerator.

2 New phenomena discovered in the ul-tra-high frequency pulse tube cryocooler

As the ultra-high frequency PTC operating at hundreds of Hz has the advantages of small size and high energy density, it can be potentially applied to small scale cryogenic cooling. We have discovered some new phe-nomena in our research of the ultra-high frequency PTC.

A pulse tube cryocooler driven by 300 Hz standing wave thermoacoustic engine was used in the experiment. Figure 1 shows the schematic of the experimental sys-tem[7], which is composed of the ultra-high frequency standing-wave engine, PTC and inertance tube as phase shifter. Yang J L et al.[8] have done a series of experi-ments on this ultra-high frequency PTC. Figure 2 is a typical cooling curve of the experiments[9]. It can be concluded from the curve that compared with the Stir-ling type PTC operating at tens of Hz, the cold head temperature of ultra-high frequency PTC can’t be stable as it fluctuates after reaching the lowest value. It is also found in the experiment that the time needed for ul-tra-high frequency PTC is longer than that for Stirling type PTC operating at tens of Hz with similar structure to reach the same refrigeration temperature. These phe-nomena are similar to the typical DC flow effects, which

Figure 1 Schematic of ultra-high frequency pulse tube cryocooler. ① Thermal buffer; ② hot end exchanger; ③ stack; ④ ambient heat ex-changer; ⑤ resonator; ⑥ ambient heat exchanger; ⑦ regenerator; ⑧ cold head; ⑨ pulse tube; ⑩ ambient end; inertance tube.

Zhou Y et al. Sci China Ser E-Tech Sci | Dec. 2009 | vol. 52 | no. 12 | 3491-3496 3493

Figure 2 Cooling curve of ultra-high frequency PTC (Inner-diameter of the inertance tube is 2.5 mm). encourages us to make a deep investigation on the cause of the temperature instability.

As the inertance tube is the only phase shifter, dou-ble-inlet structure is eliminated in the ultra-high fre-quency PTC. As a result, there is no closed-loop flow path and consequently no Gedeon DC flow. On the other hand, Rayleigh streaming mainly occurs in the boundary layer[10]. The viscous and thermal boundary layer thick-ness are defined as the viscous and thermal penetration depth, respectively as follows.

2 ,υυδω

= (1)

2 ,kp

kc

δωρ

= (2)

where υ is the kinematic viscosity of gas, k is its thermal conductivity, ρ is its density, cp is its isobaric specific heat capacity, andω is the angular frequency. According to eqs. (1) and (2), the viscous and thermal penetration depth will decrease so that the viscous and thermal boundary layer thickness will decrease correspondingly with the increase of frequency. Moreover, the maximum displacement of gas parcels in the ultra-high frequency PTC is smaller than that in the lower frequency PTC. Hence, Rayleigh DC flow has a minor influence on the refrigeration performance.

The analysis presented above indicates that a third type DC flow exists in the PTC besides Gedeon DC flow and Rayleigh DC flow since they are not the major factors causing these DC flow phenomena in the ex-periments. The third type DC flow exists in all the pulse tube cryocoolers operating at different frequencies. It’s also the main factor causing the deterioration of the per-

formance and the instability of the refrigeration tem-perature of the PTC. The analysis of the mechanism of the third type DC flow will be presented as follows.

3 Mechanism of the third type DC flow

We now consider the mechanism of the third type DC flow in the PTC without any closed-loop flow path caused by double-inlet structure. The only phase shifter of this kind of PTC is the inertance tube.

The flow resistance of the regenerator in one cycle is investigated. Figure 3 is the schematic of the typical flow resistance of the regenerator in PTC. Due to the different characteristics of the flow resistances of the inlet, outlet and intermediate part of the regenerator re-spectively, the three parts should be discussed separately and a simple model of the flow resistance is established. The inlet part is defined as the warm end which connects the regenerator to the flow path from the pressure oscil-lator, and the inflow and outflow resistances of this part are R1 and 1R′ , respectively. The outlet part is defined as the cold end which connects the regenerator to the flow path to the pulse tube, and the inflow and outflow resis-tances of this part are R3 and 3R′ , respectively. The in-termediate part is in the middle of the inlet and outlet parts, and the inflow and outflow resistances of this part are R2 and 2R′ , respectively.

Figure 3 Schematic of the flow resistance of the regenerator in PTC. ① Pressure oscillator; ② regenerator; ③ hot heat exchanger; ④ pulse tube; ⑤ ambient heat exchanger; ⑥ inertance tube.

The inflow and outflow resistances of each part of the

regenerator are assumed to be steady flow resistances in one cycle. According to the fluid network theory[11], steady flow resistance is equal to pressure drop pΔ divided by mass flow qm:

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.m

pRqΔ

= (3)

The inflow and outflow resistances of each part of the regenerator are investigated as follows. For the interme-diate part, the regenerator is considered equivalent to a bundle of capillary tubes since it is filled with metal meshes. Capillary tube is steady flow resistance and both the flow capacity and flow inductance can be ne-glected in qualitative analysis. Hence, the inflow and outflow resistances of the intermediate part can be ex-pressed as linear equations as follows[11]:

2 22 4

2

128,

πl

RDυ

= (4)

2 22 4

2

128,

πl

RDυ′′ = (5)

where l2 and D2 are characteristic length and diameter of the capillary tube, respectively, 2υ and 2υ′ are kine-matic viscosity of inflow and outflow resistances of gas. As there is a large temperature gradient along the regen-erator, kinematic viscosity should be the equivalent av-erage value of different temperatures:

h

lh l

1 d .T

TTT

T Tυ υ=

− ∫ (6)

Hence, the influence of temperature is so small that it can be neglected for average kinematic viscosity of the gas in one cycle. As the inflow average pressure of the gas in the regenerator is larger than the outflow one in one cycle, the inflow kinematic viscosity is smaller than the outflow one due to fluid mechanics and thermal properties of the gas at cryogenic temperature[12]. That is, 2 2.υ υ′< (7)

Substituting eq. (7) into eqs. (4) and (5), we obtain 2 2 ,R R′< (8) which means that the inflow resistance is smaller than the outflow resistance of the intermediate part of the regenerator.

For the inlet and outlet parts of the regenerator, the flow resistance can be expressed[11] as the sum of the two parts due to the sudden change of the geometry pa-rameters. ,AR R Rζ= + (9)

where RA is the non-linear flow resistance due to non-uniformity of the flow path cross-section, Rζ is the flow resistance caused by loss of local resistance. For

the inlet part, as the inflow path is from narrow to wide and outflow path is from wide to narrow, we obtain 1 1.R R′< (10)

For the same reason, for the outlet part we obtain 3 3.R R′> (11)

From eqs. (8), (10) and (11), we can hardly get a con-clusion of the relationship between the inflow and out-flow resistances. However we can get a possible answer if we make some simple assumptions.

Due to the symmetry of the inflow and outflow paths, we assume that the two non-linear flow resistances are equal to each other. However, the flow resistance caused by loss of local resistance depends on ζ, which is the coefficient of local resistance. Hence, Rζ depends on gas viscosity. As temperature of the inlet part (warm end) is much higher than that of the outlet part (cold end), gas viscosity of the inlet part is higher than that of the outlet part. So is the flow resistance, i.e., 1 3 1 3.R R R R′ ′+ < + (12)

From eqs. (8) and (12), we can obtain 1 2 3 1 2 3.R R R R R R′ ′ ′+ + < + + (13)

The above analysis is just appropriate for one possible circumstance. As the flow resistances of the inlet part and outlet part are quite complicated, more specific study should be done in the future research. But we can conclude that the inflow and outflow resistances of the regenerator are not equal.

We assume that the average inflow and outflow pres-sure drops of the regenerator are steady in one cycle, defined as pΔ and p′Δ , respectively. As the PTC of-ten uses reservoir or inertance tube with large volume as the phase shifter, we assume the inflow and outflow pressure drops to be the same, namely .p p′Δ ≈ Δ (14)

From eq. (3) we can get the inflow mass of the regen-erator is

1 2 3

,mpq

R R RΔ

=+ +

(15)

and outflow mass of the regenerator is

1 2 3

.mpq

R R R′Δ′ =

′ ′ ′+ + (16)

From eqs. (13)―(16), we can obtain .m mq q′> (17)

From the above qualitative analysis for the simple model of the PTC, we can conclude that the inflow mass

Zhou Y et al. Sci China Ser E-Tech Sci | Dec. 2009 | vol. 52 | no. 12 | 3491-3496 3495

and outflow mass of the regenerator are not equal to each other in one cycle, mainly because of the charac-teristic of oscillating flow, asymmetry of the structure and resistances of the refrigeration system (due to the difference of the local loss of resistance) and the change of gas viscosity (due to the change of temperature and pressure). Thus, the mass flow imbalance will gradually accumulate in the cold end of the regenerator, causing increase (or decrease) of average pressure of the “gas displacer” in the pulse tube. While the average pressure exceeds a critical value (at that time, p p′Δ < Δ ), mass flow will be transported from the warm end of the pulse tube to the cold end of the pulse tube, the regenerator, and the compressor. That is the mechanism of the third type DC flow.

As regenerator in the PTC is a porous medium, an amount of gas is filled in the void volume in the regen-erator. Due to the fluctuations of the temperature and pressure, the gas will compress or expand, resulting in the unequal mass flow along cross-section of the regen-erator. After all, the oscillating flow of the regenerator is very complicated and our model based on some assump-tions needs more detailed calculations in the future. However, we can get the conclusion that the third type DC flow is of universal significance and exists in PTC operating at any frequency. It makes some sense that Jiang Y L et al.[13] researched on double-inlet PTC with a closed-loop and realized the importance of the inequality of the inflow and outflow resistances in Gedeon DC flow.

As the third type DC flow carries heat from cold end to warm end in the PTC, transportation of mass and en-thalpy flow will cause deterioration of the refrigeration performance and instability of the cooling temperature. For the Stirling cooler with a real displacer, only a small amount of the third type DC flow will occur in a limited region due to the obstacle of the displacer. Hence, it will hardly have any influence on the refrigeration perform-ance and temperature stability. But for PTC with “gas displacer” it is totally different. Mass and interior pres-sure of “gas displacer” are changing with time. As the maximum oscillatory displacement of gas parcel is not large especially at ultra-high frequencies, it costs a long time for the average pressure of the system behind the cold end of the regenerator to reach the critical value and return to the average value of overall system. Thus, it has great influence on the temperature stability for the

third type DC flow.

4 Discussion on suppression ways of the third type DC flow

It is of great importance to study suppression ways of the third type DC flow since it carries additional heat from the cold end to warm end in the PTC, which leads to decrease of refrigeration power and instability of cooling temperature. Considering the root of the third type DC flow, asymmetrical oscillating flow resistance of the system should be eliminated. However, flow re-sistance of regenerator can not be changed easily. Hence we consider several indirect means to suppress the third type DC flow as follows.

1) As double-inlet structure is not applied to the ul-tra-high frequency PTC due to negative experimental results, the suppression means of DC flow for dou-ble-inlet PTC are not appropriate for the third type DC flow. Yang J L[9] indicated that refrigeration temperature would be relatively stable if inertance tube with a small diameter was used.

Compared with Figure 2, Figure 4 is a cooling curve with smaller diameter which is much more stable. The reason of this phenomenon is that volume of the iner-tance tube will dramatically decrease with the decrease of inner-diameter. Hence, the time needed will decrease for the average pressure of the system behind the cold end of the regenerator to reach the critical value and re-turn to the average value of the overall system. So, iner-tance tube of a small inner-diameter is suggested to sup-press the third type DC flow.

2) A second orifice and multi-bypass structure are

Figure 4 Cooling curve of ultra-high frequency PTC (Inner-diameter of the inertance tube is 1.6 mm).

3496 Zhou Y et al. Sci China Ser E-Tech Sci | Dec. 2009 | vol. 52 | no. 12 | 3491-3496

efficient for suppression of Gedeon and Rayleigh DC flow in experimental study. As a result, it’s recom-mended to connect inertance tube to pressure oscillator with asymmetrical nozzle or retaining valve just like a second orifice to stabilize cooling temperature. Multi- bypass structure can also be used to partially suppress the third type DC flow.

3) As the inflow time and outflow time are controlla-ble, cam mechanism can be used to replace linear com-pressor as pressure oscillator for Stirling type PTC. For the same reason, rotating valve of the GM type PTC can be used to adjust the difference between inflow and out-flow time to maintain the average pressure of refrigera-tion system at a steady value as well as the second

orifice to suppress the DC flow.

5 Conclusion According to the experimental results of the ultra-high frequency pulse tube cryocooler, we conclude that there’s a third type DC flow in PTC. From the simple regenerator model analysis, it’s derived that asymmetry of the oscillating flow resistances of the refrigeration system is the main factor of the third type DC flow. The third type DC flow exists in PTC operating at any fre-quency and it will deteriorate cooling performance and cause temperature instability of pulse tube cryocooler. We will investigate more suppression means in the fu-ture.

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