Advance in research of several types of streaming of pulse tube refrigerators

SCIENCE CHINA Technological Sciences

© Science China Press and Springer-Verlag Berlin Heidelberg 2013 tech.scichina.com www.springerlink.com

*Corresponding author (email: [email protected])

Progress of Projects Supported by NSFC November 2013 Vol.56 No.11: 2690–2701

doi: 10.1007/s11431-013-5327-x

Advance in research of several types of streaming of pulse tube refrigerators

GU Chao1,2, TANG JianBo1,2, WANG JunJie1 & ZHOU Yuan1*

1 Key Laboratory of Cryogenics, Technical Institute of Physics and Chemistry, Chinese Academy of Sciences, Beijing 100190, China; 2 University of Chinese Academy of Sciences, Beijing 100049, China

Received April 22, 2013; accepted August 12, 2013; published online September 12, 2013

The pulse tube refrigerator (PTR) is a promising small-scale cryocooler. This paper first briefly introduces the history of the pulse tube refrigerator. It has pointed out that technology improvements and theoretical developments of the pulse tube refrig-erator closely relate with the internal streaming effects. Then the discovering history and classification of the streaming or DC (direct current) flow effect are summarized. It proposes for the first time that the physical significance of the streaming con-tains the driving mechanisms and the transport mechanisms. It demonstrates that the driving mechanisms are the asymmetry of fluid flow and temperature while the transport mechanisms are a loop or vorticity, which transmits nonlinear dissipations. The important advancements have been made over the past two decades all over the world in research of streaming of the pulse tube refrigerator including Gedeon DC flow, Rayleigh streaming, the third type of DC flow and the regenerator circulation. With regard to Gedeon DC flow, theoretical and experimental analyses have been made and different suppression methods are summarized. In the aspect of Rayleigh streaming, it mainly focuses on the analytical solution of the second-order mass flow and the research of tapered pulse tubes. In particular, limited research on the third type of DC flow and regenerator circulation is presented. The experimental measurement techniques of streaming also are summarized. Finally, this paper briefly discusses the key scientific and technical issues of the current research, and foretells the future development trends of streaming research in PTR.

pulse tube refrigerator, streaming, asymmetry, closed loop, vorticity

Citation: Gu C, Tang J B, Wang J J, et al. Advance in research of several types of streaming of pulse tube refrigerators. Sci China Tech Sci, 2013, 56: 2690 2701, doi: 10.1007/s11431-013-5327-x

1 Introduction

The pulse tube refrigerator (PTR) is a promising small-scale cryocooler for a wide range of applications. With no mov-ing parts at low temperature, it has the advantages of low mechanical vibration, electromagnetic interference, long lifetime as well as simple structure and high reliability. Since the invention of basic PTR in 1963, the PTR technol-ogy has matured in infrared devices in space, high-temperature superconductivity etc., and the GM-type pulse tube

refrigerator operating at low frequency has been commer-cialized as high-tech product. On the other hand, from the surface heat pumping theory, phase shift theory to small perturbations thermoacoustic theory, theories focusing on the interior oscillating flow in PTR also made many im-portant breakthroughs for the further innovation and opti-mization of refrigeration technology, which is the new high-light in oscillating flow and heat transfer area [1].

Since the internal gas of PTR works as the alternating cur-rent (AC) flow, the technological and theoretical develop-ments are two major directions in PTR researching. The first one is to enhance the positive effect to make full use of the acoustic power provided by the compressor. Researching

Gu C, et al. Sci China Tech Sci November (2013) Vol.56 No.11 2691

work gradually aims at optimizing the phase shift between the pressure wave and mass flow of the internal working gas ever since the phase shift theory proposed. The other direction is to reduce the negative effects, including flow and heat transfer and other losses [2]. Streaming problem in the PTR system closely relates with these two strategic directions.

Historically, the main methods of adjusting the phase shift experienced three important innovations. Mikulin et al. [3] first proposed orifice and reservoir implementation. On this basis, Zhou [4] obtained the lowest temperature of 49 K and sought the practical application prospect of PTR. The second breakthrough came from Zhu et al. [5], who pro-posed double-inlet structure. Since then the cooling perfor-mance of the single-stage PTR became comparable to Stir-ling-type cryocooler, which greatly expanded the applica-tion range. The latest achievement is the invention of in-ertance tube by Kanao et al. [6]. It made the cooling per-formance of high-frequency inertance tube PTR better than the orifice PTR. At the same time, the double-inlet structure formed a closed loop in the PTR system, bringing the DC (direct current) flow problem. Oscillating working medium works as periodic reciprocating main flow, while DC flow refers to the small unidirectional current among the main flows. Researchers tried various methods to suppress the DC flow effects ever since its discovery.

The DC flow problem began with the invention of dou-ble-inlet structure, but with the development of thermo-acoustic technology, people realized that the DC flow prob-lem commonly existed in thermoacoustic engines and re-frigerators in which the medium works as oscillating flow. According to acoustics theory, streaming is a second order mass flow or velocity, which is driven by the first order velocity and pressure oscillations. In thermoacoustic en-gines, streaming can be both an undesirable loss mechanism and a way of convective heat transfer, hence its suppression becomes very important. In 1999, Backhaus et al. [7] de-veloped the world’s first thermoacoustic Stirling engine. Backhaus pointed out that the key factor of his success was the suppressing of streaming. In PTRs even without dou-ble-inlet, other types of streaming may be generated, caus-ing great heat loss and fluctuations of the refrigeration tem-perature. In order to reduce various losses in PTR, figuring out the generation mechanism of streaming and finding practical suppressing method both are of great significance.

We will review and classify all the types of streaming according to the different generation mechanisms. This pa-per will systematically discuss the streaming effects based on the physical nature of the oscillating and DC flow. Moreover, the theoretical and experimental suppressing methods are also mentioned.

1.1 Discovery and classification of streaming in PTR

Seki et al. [8] pointed out that temperature fluctuations, which resulted from the double-inlet valve that brings cir-

culating flow, existed in long-operating double-inlet PTR in the 16th ICEC in 1996. In June 1996, Gedeon [9] presented his research in the 9th International Cryocooler Conference, indicating that there was a potential for DC flow in Stir-ling-type cooler and double-inlet pulse tube refrigerator, whereby DC flow effect was formally proposed and at-tracted wide attentions. Thereafter, the streaming caused by the double-inlet valve was named Gedeon flow. Gedeon flow is the traveling wave acoustic streaming as shown in Figure 1(a) [10].

Streaming effect is a classic problem in acoustics and fluid mechanics. Due to different boundary conditions and initial conditions, there will be different types and generat-ing mechanisms. Therefore, after the discovery of Gedeon flow, exploration of other types of streaming has become a popular area. Olson and Swift [11] analyzed the streaming in oscillating boundary layer and tested the performance of the tapered pulse tube structure on suppressing the stream-ing in 1997. The earliest research work of boundary layer streaming can be traced back to Rayleigh et al. [12] who studied standing wave between the parallel walls in acoustic field, so the boundary layer streaming is referred to Ray-leigh flow (Figure 1(b)).

Whether there are other types of streaming in PTR and other thermoacoustic systems remains controversy. Some researchers claimed to discover other new types of stream-ing. In 2002, Mironov and Gusev [13] put forward a theory that thermoacoustic stack with temperature gradient would cause a new type of streaming, and asymmetrical stress was the main generating mechanism. In 2007, Liang and de Waele et al. [14] observed a new type of streaming caused by asymmetrical stresses due to the flow resistance of the straightener and viscous effects of the wall in a numerical research. In 2009, Zhou et al. [15] pointed out the third type of DC gas flow in PTR. Then Gu et al. [16, 17] verified and systematically studied this new streaming through theoreti-cal analysis, experiments and numerical simulations. The streaming caused by flow and thermal asymmetries existed in PTR and other thermoacoustic system. Its essence is the vortex generated by the jet flow shown in Figure 1(c). These researches not only clarified the vague understanding,

Figure 1 Schematic of the four types of streaming in PTR [10] . (a) Gedeon flow; (b) Rayleigh flow; (c) jet flow; (d) circulating flow in regen-erator.

2692 Gu C, et al. Sci China Tech Sci November (2013) Vol.56 No.11

but also formed a complete theoretical system. Moreover, in 2007 Dietrich et al. [18] discovered a cir-

culating flow in the regenerator of a high-power Stir-ling-type PTR (Figure 1(d)). As most of the regenerators filled with screens or other porous medium, the internal unevenness as well as the temperature gradient may lead to a small annular acoustic streaming, which caused heat loss-es in the direction of temperature gradient.

1.2 Physical significance of streaming in PTR

Alternating current (AC) flow cyclically changes in the flow direction. The basic governing equations for PTR and ther-moacoustic heat engines are the N-S equations, and the driven pressure gradient term can be regarded as harmonic functions. Qualitatively speaking, fluid particles reciprocate in their equilibrium positions in the range of heat penetra-tion away from the wall, and exchange heat and acoustic power with the surrounding medium. All the fluid particles produce the periodic energy transportation and transfor-mation.

Unlike AC flow, DC flow does not change its flow direc-tion. The DC component is the imbalance mass flow at every cross section during the positive and negative half- cycles in one period. The concept of AC flow and DC flow is borrowed from electricity. Direct and alternating currents are both power source (electromotive force) determined current, but DC flow is much more complicated than AC flow even they are driven by the same pressure wave gener-ator. The physical mechanism of DC flow or streaming has two elements, the driving mechanism and transmission mechanism. The aforementioned different types of stream-ing are mainly classified by their driving mechanisms. The flow and temperature asymmetry are the two most im-portant factors, which produce the unidirectional driving stress. Driven by the driving stress, a part of working me-dium originally in AC form shows DC flow features. Then, the DC momentum is continuously transported in the form of the closed-loop or vortex streaming, and finally com-pletes the nonlinear dissipation process.

In most cases, the formation of acoustic streaming is as-sociated with the generation of vortex. The alternating cur-rent momentum equation [19] is shown as

2

3

Dp

Dt

uu u . (1)

After convolution and tensor transformation, the linear term of eq. (1) becomes

2 ( ) ( ) 0

tu u . (2)

According to Boluriaan and Morris [20], eq. (2) deter-mines the vorticity evolution when the characteristic length and the viscous penetration depth have the same order of

magnitude. The characteristic length of Rayleigh flow is its oscillatory boundary layer thickness, and it has the same order of magnitude as its viscous penetration depth, so eq. (2) can be applied to the flow distribution of Rayleigh flow. When the characteristic length is far less than the viscous penetration depth, the time differential term can be neglect-ed, and then eq. (2) can be simplified as Laplace equation. It indicates that it is the wall and not the flow itself that in-duces the vortexes. Another case that the characteristic length is far more than the viscous penetration depth will not appear due to the limited operation frequency at present. Therefore, the flow pattern in the PTR system does not in-clude Eckert flow.

The characteristic scale of the vortexes in Rayleigh flow is the same order of magnitude as the boundary layer depth and far less than the length of its acoustic wave. Unlike the Rayleigh flow, the characteristic scale of the vortexes in the third type of DC flow is equivalent to the length of its acoustic wave. The vortexes in the third type of DC flow are induced by the shear stress caused boundary layer separa-tion at the cross sections in the PTR system. The vortexes go through generating, evolution and shading process dur-ing the oscillating motion of the main flow. Periodically, vortexes motion forms a special flow pattern that we call vortex wave [17, 21].

Similarly, the generation mechanism of Gedeon flow and the regenerator circulation can also attribute to the asym-metry of the oscillating flow and the temperature gradient. Nevertheless, vorticity and vortex may not appear in these two kinds of DC flow. The transport mechanisms of these two kinds of DC flow are looped traveling-wave acoustic streaming. The closed loop is an important feature of these two kinds of DC flow and their nonlinear dissipation and momentum transformation. Therefore, these two kinds of DC flow are distinct from Rayleigh flow and the third type of DC flow.

2 Progress in streaming research

2.1 Progress in Gedeon flow research

Based on thermodynamics, Gedeon proposed the first theo-retical model to study streaming in the PTR system. The pressure drop of the low Reynolds number working fluid caused by each resistance component was regarded as linear function of velocity. Under the assumption that the pressure and density have a sinusoidal vibration and all the high- order terms are negligible, the time-averaged mass flow rate can be described as [9]

2 0 0 1 1

1( cos )

2 M p p , (3)

where α is the phase shift between density and pressure drop. Gedeon pointed out that asymmetries or closed loop


needed to form the second order mass flow described in eq. (3). It can be the asymmetrical resistance of the flow chan-nels, like double-inlet structure, or the heterogeneity of den-sity, pressure and temperature. Moreover, if all these asymmetries and closed loop are absent, the system will adjust itself to suppression DC flow as shown in

0 1

1 0

1cos( )

2

p

p. (4)

Eq. (4) also gives guidance to suppression Gedeon flow. Gedeon calculated the DC mass flow rate. The result shows that the DC mass flow rate accounts for about 1%‒3% of the main oscillating flow.

Ju et al. [22] tested and verified DC flow in a double- inlet PTR for the first time. Ju used a hot-wire anemometer to measure the mass flow rate and the pressure. The result in Figure 2 shows a mass flow rate imbalance during positive semi-period and negative semi-period. He also investigated the effect opening of the double-inlet valve on the mass flow rate, as well as the pressure oscillation. The double- inlet structure had been verified to be an effective DC flow suppression structure [22, 23].

Charles et al. [24] proposed that the mass flow rate and the direction of DC flow could be predicated by measuring the PTR wall temperature distribution. Figure 3 shows the temperature distribution from the hot head of the regenera-tor to the hot head of the pulse tube. In Charles’s point of view, the temperature along the regenerator should have a linear distribution with no DC flow effect. When DC flow takes effect, the curves transform into concave and convex shapes. Whether the curves take a concave change or con-vex change depends on the direction of DC flow. Because the resistance and asymmetry of many components, like the double-inlet valve, may influence DC flow and change its direction, Charles’s method shows great reference value in later researches. It requires no precise mass-flow-meter but

Figure 2 Mass flow rate and pressure at the cold head of the PTR in Ju’s experiment [22].

Figure 3 The mass flow rate and the direction of DC flow predicated by Charles based on wall temperature distribution [24].

still has a great practicability. This makes it a widely used standard to detect DC flow in cryocooler systems.

Gedeon flow causes heat transfer between cold head and hot head, which consequently decreases the refrigeration performance. Therefore, how to suppress Gedeon flow be-comes the key issue to the problem. The most astonishing success by applying the DC flow suppression method is found in a Stirling thermoacoustic engine. Backhaus and Swift at Los Alamos laboratory installed a jet pump above the main cold heat exchanger in a Stirling thermoacoustic engine, as shown in Figure 4. The structure of the jet pump includes two parallel-arranged rectangular channels with bevels at the exit sections. The flow resistance coefficient, which affects the pressure gradient that suppresses Gedeon flow can be manually controlled by changing the outlet to the inlet area ratio. Experiment shows that the thermoacous-tic engine could deliver 710 W acoustic power to the reso-nator with a relative Carnot efficiency of 42% and a thermal

Figure 4 Schematic of the Stirling thermoacoustic engine at the Las Alamos laboratory [25].


efficiency of 0.3 [7, 25]. Using the jet pump to suppress Gedeon flow is thought to be the main reason of the suc-cess.

Although the double-inlet structure is used infrequently in high frequency PTRs along with the invention of the in-ertance tube, it is still widely used in PTRs designed to reach extremely low temperature. Gendeon flow suppress-ing remains the crucial problem to the refrigeration temper-ature and its stability. Wang et al. [26] used two double- inlet needle valves with inverse asymmetry to control the DC mass flow rate. Moreover, Wang et al. [27] found that DC flow with a negative direction could increase the cool-ing capacity in a 4 K PTR. Zhou [28] proposed two struc-tures, namely the asymmetric nozzle and the multi- bypass, to suppress DC flow. Chen et al. [29] combined a second orifice with the regular one and reached 3.1 K with a two- stage PTR. Figure 5 shows the scheme of the two-orifice PTR system. Chen et al. connected a second orifice reser-voir to the low-pressure outlet of the compressor. Appar-ently, the mass flow from the reservoir towards the second orifice counterbalances the potential Gedeon flow in the loop and at the same time causes a minor capacity loss. Yang’s further research [30] shows that the direction of DC flow may switch under different working conditions or with the change of the system structure. Based on his work, Yang suggested a new method which connected the reservoir and the high-pressure outlet of the compressor. Shiraishi et al. [31] used a smoke-wire flow visualization technique to au-thenticate the effect of the second orifice method on sup-pressing Gedeon flow.

Swift et al. [32] suggested that elastic sphere could be used to cut off DC flow. As a follow-up design, Hu et al. [33] set a membrane between (Figure 6) the entrance of PTR and the double inlet valve. The membrane was made of silicon rubber. The elasticity of this material makes it capable of nearly no-loss acoustic power transfer while it still could cut off Gedeon flow. At present, the elastic sphere structure was mostly used on thermoacoustic engines. Whether it can be applied to PTRs or not needs further study.

In recent years, Zhu et al. [34] analyzed Gedeon flow using CFD code. Zhu found out that in symmetrically ar-ranged double inlet by-pass PTR system, the opening of the metering valve is a crucial parameter to Gedeon flow in

Figure 5 Schematic of two-orifice PTR [30].

Figure 6 Schematic of diaphragm unit [32].

turbulence flow, but has little relevance when the flow re-mains laminar (Figure 7).

2.2 Progress in Rayleigh flow research

Acoustic streaming within the boundary layer is considered to be the most sufficiently-studied streaming among all kinds of DC flows due to the thorough understanding of this problem in the compressible flow field. In 1970s, Rott [35] improved Rayleigh’s theory and completed the linear ana-lytical solution of the velocity profile of the acoustic streaming influenced by temperature gradient. Rott’s work laid the foundation of Rayleigh streaming study in PTR.

Lee et al. [36] used smoke-wire flow visualization tech-nique to observe acoustic streaming in PTRs. The acoustic streaming flows along the pulse tube wall towards the ori-fice valve then its counter current flows back to middle of the pulse tube. In Lee’s opinion, the magnitude of acoustic enthalpy streaming is inversely proportional to the diameter of the tube. Lee suggested that both reducing the flow rate at the hot end of the pulse tube and using the tapered pulse tube can suppress Rayleigh flow. Lee et al. [37] also ana-lyzed the dissipation of momentum and heat caused by acoustic enthalpy flow by using a two-dimensional axial symmetry linear equation. Lee pointed out that Reynlods stress was the driving mechanism of Rayleigh flow.

Figure 7 Influence of the valve closing angle on Gedeon DC mass flow rate [34].


Olson and Swift [11] explained how Rayleigh flow formed (Figure 8). The temperature gradient along the pulse tube within the boundary layer leads to viscosity difference among the gas parcels. Generally, the gas parcels’ viscosity is higher at higher temperature than that at lower tempera-ture. Consequently, the gas parcels cannot return to their original positions after every cycle. The macroscopic effect of the gas parcels is the formation of a boundary layer streaming from the hot side to the cold side. According to the principle of mass conservation, a counter flow near the wall must exist. Apparently, Rayleigh flow drives the en-thalpy convection inside the pulse tube and causes an in-crease of the cold heat exchanger load, which is undesirable to the refrigerator. Olson and Swift also tested the tapered pulse tube (Figure 9) to see the effect on suppressing Ray-leigh flow and found out the theoretical optimum cross- section formula.

Though Swift [10] declared that several coincidences made tapered pulse tube suppress Rayleigh flow, this method has become a focus in DC flow suppression. Sang et al. [38] analyzed a two-dimensional model and found that the enthalpy loss caused by acoustic streaming would in-crease with the increase of the operating frequency (Figure 10). In cases that the viscosity penetration depth is far less than the inner diameter of the pulse tube, increasing the inclined angle of the pulse tube could significantly reduce the mass flow rate as well as the temperature fluctuations. Finally, the heat loss is reduced. Shiraishi et al. [39] com-pared the shrunk pulse tube and enlarged pulse tube. The velocity distribution of the acoustic streaming in the con-

Figure 8 Formation mechanism of Rayleigh flow [11].

Figure 9 Schematic of tapered pulse tube refrigerator [11].

Figure 10 Influence of the inclined angle and frequency on streaming induced enthalpy loss [38].

vergence pulse tube was flatter than that in the enlarged pulse tube and the radical velocity of the gas parcels in the convergence pulse tube was more distinct, while the streaming of the divergence pulse tube was more evident. Consequently, the performance of the convergence PTR structure is better than the divergence PTR structure. He et al. [40, 41] carried out early numerical researches on ta-pered PTRs. He’s work showed that an optimum inclined angle existed and oversized inclined angle would exacerbate the performance of PTR (Figure 11). He also pointed out that the tapered pulse tube could not only suppress the DC mass flow rate, but also optimize the velocity distribution of the acoustic streaming. Therefore, the tapered pulse tube structure could improve the refrigerating capacity as well as the refrigerating temperature. Recently, Antao et al. [42] analyzed PTR with an asymmetric thermodynamic model.


Figure 11 Influence of the inclined angle on the time-averaged streaming. (a)φ=0; (b)φ=0.105 rad (optimum inclined angle); (c)φ=0.11 rad [41].

The result showed that the diameter of the hot heat ex-changer had a great influence on the optimum inclined an-gle and an identical hot heat exchanger diameter with the tapered pulse tube could significantly decrease the velocity of the DC flow at the hot end.

In recent years, the CFD method is widely applied to the PTR studies. Another numerical study of Antao et al. [43] discovered that vortex streaming existed in pulse tube as shown in Figure 12. This kind of streaming was different from other kinds of streaming in some respects. One is that the structure of the vortex ring was very sensitive to the oper-

Figure 12 Numerical results of temperature and streamline distribution in the pulse tube of Antao [43].

ating frequency. The vortex ring became smaller as the oper-ating frequency increased. The other was that the symmetric counter-rotating vortex rings formed a buffer zone that in-sulated the heat transfer between the cold end and the hot end (Figure 12(a)). This kind of velocity distribution was desirable for good performance. While when the vortex rings joined each other instead of forming a buffer zone, distinct convection between the cold end and the hot end occurred (Figure 12(b)). Heat and mass convection between the cold end and the hot end would deteriorate the perfor-mance of PTR. The interesting flow pattern needs further investigation. This kind of streaming has something differ-ent from the known Rayleigh flow and it is somewhat like the third type of DC flow that will be mentioned later.

2.3 Progress in the third type of DC flow research

Jet flow, which is usually accompanied with vortex and flow loss, is a common phenomenon occurring when fluid runs through cross sections or curved channels. The steady jet inflow has been well studied while other kinds of jet flow still need further research. Swift’s rough calculation [10] of the jet flow inside the channel showed that the high- Reynolds-number jet divergence angle in free space is about 10°. This kind of jet flow can stretch very far away and en-hance heat transfer in the channel. When it comes to PTR, the jet flow would enlarge the dissipation. Swift then sug-gested adding few screen meshes at both ends of the pulse tube to suppress jet flow.

Cross sections or curved channels are common in the PTR systems and thermal acoustic systems, so jet flow has substantial influences on the system. The oscillating flow and large temperature gradient along the flow direction are two striking features of these systems. The working condi-tion makes the jet flow unique and complicated, and its mechanism has not been cognized until quite recently. Mironov and Gusev’s [13] theoretical study showed that just like Reynlods stress driving Rayleigh flow, the asym-metrical local stress loss was also a driving mechanism. Liang and Waele [14] reported a new kind of streaming in PTR based on their numerical study. In fact, it was a kind of jet flow. Zhou et al. [15] clarified the vague concept about the jet flow in the PTR system and proposed to classify this kind of streaming as the third type of DC flow in order to distinguish it from Gedeon flow and Rayleigh flow. Zhou et al. [15] used fluid network theory to analyze the third type of DC flow and pointed out that where there was dynamic asymmetry or thermal asymmetry, there existed the third type of DC flow. Based on Zhou’s analysis and Cha’s [44] CFD work, Gu et al. [17] carried out a numerical study of the nonlinear process in pulse tube shown in Figure 13. Gu found periodic vertex evolution in the pulse tube and at-tributed this to the asymmetry of the PTR system. The vor-tex streaming was the driving mechanism of the third type DC flow. Apparently, it is different from the driving mech-


Figure 13 Numerical result of the temperature field and the streaming line in the pulse tube during one cycle [17].

anism of Gedeon, which is the closed loop. During every cycle, the vortex developed differently due to the differ-ences of Strohal number and temperature gradient. Larger Strohal number resulted in fewer vortexes. The vortexes carried momentum and heat during the periodic motion and created drastic heat and mass transfer. Moreover, the mass flow rate and the direction of the third type of DC flow were found to be very sensitive to the operating frequency. To PTR used in Gu’s numerical study, the mass flow rate of the third type of DC flow under 30 and 45 Hz was at an order of magnitude of 10−5 kg s−1, and the order of magnitude de-creased to 10−6 kg s−1 when the operating frequency in-creased to 60 Hz.

Gu et al. [16] tried to connect the back volume of the compressor and the reservoir to suppress the third type of DC flow. In some cases, this method could achieve lower refrigeration temperature. However, its applicability needs further experimental verification. Moreover, the mul-ti-bypass structure [45] is also a practical method to sup-press the third type DC flow. Compared to the well-studied Gedeon flow and Rayleigh flow, the newly proposed third type DC flow still requires more comprehensive study and search for more effective suppressing methods.

2.4 Progress in regenerator circulation research

The high-power PTR is not the simple magnification of the miniature PTR. Some unique flow patterns and heat transfer problems only exist in the high-power PTR. The regenerator circulation and regenerator non-uniformity are two critical problems in the high-power PTR researching. So et al. [46] thought that the nonlinear resistance was not equal between AC flow and DC flow. This is the main reason for the insta-bility of the regenerator. Moreover, the enthalpy flow car-ried by the acoustic wave as well as the axial and radial conduction of the regenerator packing also contributes to the instability. By comparing the limitation calculation of the stability and the experiment result, So et al. pointed out that the regenerator circulation only existed in the high- power PTR with large temperature gradient. So also added that it would not present in thermal acoustic devices due to the declining (or enhancing) of the perturbance. The present solution is sandwiching brass mess or red copper mess in the regenerator packing in order to weaken the instable temperature effect caused by the non-uniformity resistance and heat transfer (Figure 14).

A high-power Stirling PTR designed by Dietrich et al. [18] showed distinct regenerator circulation when the


Figure 14 Schematic of PTR that So used to detect regenerator circula-tion [46].

refrigeration temperature was below a critical point. The regenerator circulation appeared to be influenced by the temperature gradient, mass flow rate and the horizontal conductivity coefficient. Dietrich monitored the temperature of three sampling points placed evenly around the midsec-tion of the regenerator. The temperature of the sampling points varied more greatly when input power increased (Figure 15). This phenomenon indicated the existence of the non-uniform circulation in the regenerator. In addition, the repeated experiments showed that the positions of high temperature or low temperature occurred randomly at the sampling points. According to this, a conclusion could be made that the asymmetry of the regenerator was not the only reason for the non-uniform circulation. High conduc-tivity sandwiched mesh could substantially reduce the loss caused by the regenerator circulation. A refrigeration tem-perature reached 34.5 K with the input power of 6.3 kW and a refrigerating capacity of 50 W obtained at 45 K.

Sun et al. [47] studied the temperature variety of the re-generator on a two-stage thermally-coupled U-type high- power Stirling PTR. Sun found that the uneven inter-stage cooling also contributed to the regenerator instability. The regenerator non-uniform firstly was induced in the interme-diate heat exchanger and amplification occurred in the form of inner streaming inside the regenerator. The biggest radi-cal temperature difference could reach 30‒40 K. This indi-cated that any asymmetry, even the temperature variety

Figure 15 Relationship between the sampling points and the input P-V power [18].

outside the regenerator, could influence the regenerator non-uniform and circulation.

The inducing mechanism of the streaming came down to three parts, according to the numerical study of Andersen et al. [48], namely, the deviation between the pressure wave of the both ends of the regenerator and the standard sinusoidal wave, the instantaneous mass flow rate determined by the instantaneous pressure and temperature difference between the two ends of the regenerator, and the temperature fluctu-ation of the regenerator. Andersen firstly suggested to use parallel-connected regenerator model to analyze the regen-erator circulation. Liu et al. [49] improved Andersen’s model and quantitatively predicted the temperature differ-ence in the regenerator.

In 2008, Imura et al. [50] designed a high-power PTR, which had a temperature difference of 150 K around the midsection of the regenerator. The temperature difference was reduced to 37 K by adding lower mesh number copper screen into the interlayer of the stainless steel screen. Better performance of PTR was also obtained and PTR produced a refrigeration capacity of 180 W at 80K.

The driving mechanisms of the regenerator circulation are also hydrodynamic asymmetry and thermodynamic asymmetry, the same as the third type of DC flow. However, the transport mechanism of the regenerator circulation is the closed loop, different from that of the third type of DC flow, which is vortex streaming. Most of the researches about the regenerator circulation are qualitative at present. Further quantitative study requires better experimental techniques as well as more appropriate CFD models.

2.5 Overview of the DC flow detecting methods

Experimental research is the highest priority methodology in refrigeration and cryogenics, so it is necessary to summa-


rize the DC flow detecting methods. It is very important to measure all kinds of DC flows in

the PTR system quantitatively and precisely, but the oscil-lating nature and the difficulty in measuring the velocity and the phase of the working medium make it difficult. Ju et al. [22, 23] firstly used hot wire anemometer to verify DC flow in a double-inlet PTR. However, hot wire anemometer and other traditional flow meters require complex operating and provide unsatisfying precision in detecting the velocity and phase of the small DC flow among the main oscillating flow; further researches merely used hot wire anemometer and other traditional flow meters. Nowadays, flow visuali-zation technique and temperature, or pressure, indirect measurement are the methods that are widely used in DC flow detecting.

Flow visualization techniques include smoke-wire tech-nique, infrared thermography technique, laser Doppler an-emometry technique (LDA), particle image velocimetry technique, etc. The smoke wire technique was used in most of the early flow visualization experiments. Lee et al. [36], Shiraishi et al. [39] both recorded the movements and changes of the smoke wire during typical cycle to demon-strate Rayleigh flow in PTR. In 2008, Garaway et al. [51] observed jet flow in the high-power PTR by using LDA as shown in Figure 16.

LDA can provide more distinct results while metal is still used as wall material when compared to smoke wire tech-nique, which can only use transparent non-metal material. Both of them can only roughly show the flow details and cannot function well in cryogenic and oscillating flow con-dition. LDV technique, however, can achieve quantitative detecting with the help of high-speed camera. Biwa et al. [52] successfully measured the Lagrangian speed of the acoustic streaming by tracking the tracer particle in a jet-pump thermoacoustic engine. Later, he obtained the Eu-lerian speed with the assistance of LDV, and then calculated the acoustic power, mass flow rate, heat transfer loss, etc. with the detected pressure. LDV technique provides precise results; also, it requires transparent non-metal wall material. Chen et al. [53] measured the flow field with PIV and the transient pressure with PCB pressure sensor, respectively. Chen et al., who combined LDV with phase-locked method,

Figure 16 LDA results of jet flow in high-power PTR (a) and its effects of instability (b) [51].

visualized the flow field of the cross section and the induc-ing mechanism of the jet flow and the vortex. PIV technique has few restrictions, so it is expected to have a bright pro-spect in DC flow detecting.

Indirect-measure technique means qualitatively detecting the mass flow rate and direction of DC flow by using indi-rect measurements like temperature, pressure, etc. when it lacks direct-measure equipment. The above-mentioned DC flow predicting methods like detecting the temperature dif-ference around the midsection of the regenerator and meas-uring the temperature gradient along the regenerator and the pulse tube are both indirect-measurements. Gu [16] found that the accumulation of DC flow in the PTR system would eventually build up a pressure difference between the res-ervoir and the back volume of the compressor in the third type of DC flow. The accumulating effect was hopefully used to predict the direction of the DC flow.

3 Prospects

Great progress has been achieved on research of different types of streaming in PTR both theoretically and experi-mentally, though some problems remain. Further studies targeted these problems which may become a new area of research focus.

1) The understanding of the inducing mechanism of the streaming is inadequate due to the lack of knowledge in some crucial areas like high amplitude strong nonlinear os-cillating problems in PTR and thermoacoustic systems. The present theory can only match experiments qualitatively. Moreover, if turbulence appears in any channel of the sys-tem, new problems occurs. Unfortunately, no fully devel-oped theory or model can describe any streaming mingled with oscillating flow at present. In addition, different types of streaming may occur simultaneously. Their interaction effect makes the situation more complicated. So full under-standing of the inducing mechanism and quantitative analy-sis of different types of streaming especially their transport mechanism are urgent requirements not only in the PTR technique, but also in thermoacoustics and fluid mechanics. As an important supplementary method, numerical studies assisted with SAGE, FLUENT, etc. and other new CFD methods, like wavelet analysis, neural net analysis, need to be promoted.

2) The ultimate goal of the DC flow study is to find ef-fective suppressing methods. No practical method has ever been found until now and the present suppressing methods are accompanied with side effects. The above-mentioned suppressing structural modifications, i.e. jet pump, dia-phragm unit or tapered pulse tube, have not been promoted until now. Finding simple practical suppressing methods for specific problem or wide-applicable suppressing methods are the two future trends. For example, regenerator circula-tion suppression is the crucial problem in high-power PTRs


while the multi-bypass structure can effectively suppress the combined DC flow effects in miniature PTRs.

3) Researches on the third type of DC flow and the re-generator circulation are not as insufficient as that of Gede-on flow and Rayleigh flow. However, these two kinds of DC flow are of great significance because of their extensive existence in PTRs and thermoacoustic engines. Moreover, a full understanding of these two types of DC flow and find-ing practical suppressing methods will greatly benefits the development of the high-power PTR and the future super- normal PTR.

4) Generally speaking, DC flow has negative influence on the PTR performance. In dialectical view, DC flow may also be used to improve the PTR performance. The jet flow formed at the jet pump creates a pressure difference to sup-press Gedeon flow. Wang found that the negative direction DC flow could increase the refrigeration capacity. Chen’s second orifice arrangement in low frequency PTR was in fact an artificially introduced DC flow that was used to im-prove the refrigeration performance. These are examples of the positive effects of DC flow. different types and direc-tions of DC flow can be combined to achieve better heat- work conversion.

5) Although quantitative experiment is very important in DC flow researching, many problems remain. Advanced technologies like LDV, PIV should be applied to more and more experiments to obtain better understanding of the in-ducing mechanism and transport mechanism of all types of DC flow.

This work was supported by the National Natural Science Foundation of China (Grant No. 51176198).

1 Radebaugh R. A review of pulse tube refrigeration. Adv Cryogenic Eng, 1990, 35: 1191−1205

2 Radebaugh R. Cryocoolers: the state of the art and recent develop-ments. J Phys: Conden Matter, 2009, 21: 4219−4228

3 Mikulin E I, Tarasov A A, Shkrebyonock M P. Low temperature ex-pansion pulse tubes. Adv Cryogen Eng, 1984, 29: 629−637

4 Liang J T, Zhou Y, Zhu W X. Development of a single-stage pulse tube refrigerator capable of reaching 49 K. Cryogenics, 1990, 30: 49−51

5 Zhu S W, Wu P Y, Chen Z Q. Double inlet pulse tube refrigerators: an important improvement. Cryogenics, 1990, 30: 514−520

6 Kanao K, Watanabe N, Kanazawa Y. A miniature pulse tube refrig-erator for temperatures below 100K. Cryogenics, 1994, 34(Suppl): 167−170

7 Backhaus S, Swift G W. A thermoacoustic-Stirling heat engine. Na-ture, 1999, 399: 335−338

8 Seki N, Yamasaki S, Yuyama J, et al. Temperature Stability of Pulse Tube Refrigerators. Proceedings of the 16th International Cryogenic Engineering Conference, Japan, 1996

9 Gedeon D. DC gas flows in Stirling and pulse tube cryocoolers. Cry-ocoolers, 1996, 9: 385−392

10 Swift G W. Thermoacoustics: A unifying perspective for some en-gines and refrigerators. Los Alamos: Acoustical Society of America, 1999

11 Olson J R, Swift G W. Acoustic streaming in pulse tube refrigerators: Tapered pulse tubes. Cryogenics, 1997, 37: 769−776

12 Rayleigh L. On the circulation of air observed in Kundt’s tubes, and on some allied acoustical problems. Philos Trans Roy Soc London Ser A, 1883, 175: 1−21

13 Mironov M, Gusev V, Auregan Y, et al. Acoustic streaming related to minor loss phenomenon in differentially heated elements of ther-moacoustic devices. J Acoust Soc Amer, 2002, 112: 441−445

14 Liang W, De Waele. A new type of streaming in pulse tubes. Cryo-genics, 2007, 47: 468−473

15 Zhou Y, Gu C, Cai H K. The third type DC flow in pulse tube cry-ocooler. Sci China Ser E-Tech Sci, 2009, 52: 3491−3496

16 Gu C, Zhou Y, Wang J J, et al. Experimental discovery and verifica-tion of the third type of DC gas flow in pulse tube cryocooler. Cryo-genics, 2011, 51: 157−160

17 Gu C, Zhou Y, Wang J J, et al. CFD analysis of nonlinear processes in pulse tube refrigerators: Streaming induced by vortices. Int J Heat Mass Transfer, 2012, 55: 7410−7418

18 Dietrich M, Yang L W, Thummes G. High-power Stirling-type pulse tube cryocooler: Observation and reduction of regenerator tempera-ture-inhomogeneities. Cryogenics, 2007, 47: 306−314

19 Landau L D, Lifshitz E M. Fluid Mechanics. New York: Pergamon Press, 1987

20 Boluriaan S, Morris J. Acoustic streaming: from Rayleigh to today. Int J Aeroacoust, 2003, 2: 255−292

21 Sobey I. Observation of waves during oscillatory channel flow. J Fluid Mech, 1985, 151: 395−426

22 Ju Y L, Wang C, Zhou Y. Dynamic experimental investigation of a multi-bypass pulse tube refrigerator. Cryogenics, 1997, 37: 357−361

23 Ju Y L, Wang C, Zhou Y. Dynamic experimental investigation of a multi-bypass pulse tube refrigerator (in Chinese). J Eng Thermophys, 1997, 18: 413−416

24 Charles I, Duband L, Ravex A. Permanent flow in low and high fre-quency pulse tube coolers—Experimental results. Cryogenics, 1999, 39:777−782

25 Backhaus S, Swift G W. A thermoacoustic-Stirling heat engine：Detailed study. J Acoust Soc Am, 2000, 107: 3148−3166

26 Wang C, Thummes G, Heiden C. Control of DC gas flow in a single- stage double-inlet pulse tube cooler. Cryogenics, 1998, 38: 843−847

27 Wang C, Thummes G, Heiden C. Effects of DC gas flow on perfor-mance of two-stage 4 K pulse tube coolers. Cryogenics, 1998, 38: 689−695

28 Liang J T, Zhou Y, Zhu W X, et al. Study on miniature pulse tube cryocooler for space application. Cryogenics, 2000, 40: 229−233

29 Chen G, Qui L, Zheng J, et al. Experimental study on a double-orifice two-stage pulse tube refrigerator. Cryogenics, 1997, 37: 271−273

30 Yang L W, Zhou Y, Liang J T. DC flow analysis and second orifice version pulse tube refrigerator. Cryogenics, 1999, 39: 187−192

31 Shiraishi M, Takamatsu K, Murakami M. Visualization of DC gas flows in a double-inlet pulse tube refrigerator with a second orifice valve. Cryocoolers, 2002, 11: 371−379

32 Swift G W, Gardner D L, Backhaus S. Acoustic recovery of lost power in pulse tube refrigerators. J Acoust Soc Am, 1999, 105: 711− 724

33 Hu J Y, Luo E C, Wu Z H, et al. Investigation of an innovative method for DC flow suppression of double-inlet pulse tube coolers. Cryogenics, 2007, 47: 287−291

34 Zhu S W, Nogawa M, Inoue T. Analysis of DC gas flow in GM type double inlet pulse tube refrigerators. Cryogenics, 2009, 49: 66−71

35 Rott N. Thermal driven acoustic oscillations, Part 3: Second order heat flux. Z Angew Math Phys, 1975, 26: 43−49

36 Lee J M, Kittel P, Timmerhaus K D, et al. Flow patterns intrinsic to the pulse tube refrigerator. Proceedings of the 7th International Cry-ocooler Conference, Santa Fe, 1992. 125−139

37 Lee J M, Kittel P, Timmerhaus K D, et al. Steady secondary momen-tum and enthalpy streaming in the pulse tube refrigerator. Cryocool-ers, 1995, 8: 359−369

38 Sang H B, Eun S J, Sangkwon J. Two-dimensional model for tapered pulse tubes. Part 2: Mass streaming and streaming-driven enthalpy flow loss. Cryogenics, 2000, 40: 387−392


39 Shiraishi M, Ikeguchi T, Murakami M. Visualization of oscillatory flow phenomena in tapered pulse tube refrigerators. Adv Cryogen Eng, 2002, 47: 768−775

40 He Y L, Gao C M, Xu M Y, et al. Numerical simulation of conver gent and divergent tapered pulse tube cryocoolers and experimental verification. Cryogenics, 2001, 41: 699−704

41 He Y L, Zhao C F, Ding W J, et al. Two-dimensional numerical sim-ulation and performance analysis of tapered pulse tube refrigerator. Appl Therm Eng, 2007, 27: 1876−1882

42 Antao D S, Farouk B. Numerical simulations of transport processes in a pulse tube cryocooler: Effects of taper angle. Int J Heat Mass Transfer, 2011, 54: 4611−4620

43 Antao D S, Farouk B. Computational fluid dynamics simulations of an orifice type pulse tube refrigerator: Effects of operating frequency. Cryogenics, 2011, 51: 192−201

44 Cha J S, Ghiaasiaan S M, Desai P V, et al. Multi-dimensional flow effects in pulse tube refrigerators. Cryogenics, 2006, 46: 658−665

45 Gu C, Jin H, Zhou Y, et al. A novel Stirling type pulse tube cry-ocooler suppressing the third type of dc gas flow. Adv Cryogen Eng, 2012, 57: 214−220

46 So J H, Swift G W, Backhaus S. An internal streaming instability in regenerators. J Acoust Soc Am, 2006, 120: 1898−1909

47 Sun D M, Dietrich M, Thummes G. Study on temperature inhomo-geneity in regenerator of Stirling-type pulse tube cryocoolers. Chin Sci Bull, 2008, 53: 3062−3066

48 Andersen S K, Dietrich M, Carlsen H. Numerical study on transverse asymmetry in the temperature profile of a regenerator in a pulse tube cooler. Int J Heat Mass Transfer, 2007, 50: 2795–2804

49 Liu D H, Qiu L M, Gan Z H, et al. Study on temperature inhomoge-neity in regenerator of high-power Stirling-type pulse tube cryocool-ers based on two parallel regenerator model (in Chinese). Cryogenics, 2011, 6: 1−5

50 Imura J, Iwata N, Yamamoto H. Optimization of regenerator in high capacity Stirling type pulse tube cryocooler. Physica C, 2008, 468: 2178−2180

51 Garaway I, Taylor R, Lewis M, et al. Characterizing flow and tem-perature Iistabilities within pPulse tube cryocoolers using infrared imaging. Cryocoolers, 2009, 15: 233−240

52 Biwa T, Tashiro Y, Ishigaki M. Measurements of acoustic streaming in a looped-tube thermoacoustic engine with a jet pump. J Appl Phys, 2007, 101: 064914

53 Chen Y Y, Zhang Y K, Dai W, et al. Minor losses of oscillating flow through a sudden change area (in Chinese). J Eng Thermophys, 2012, 33: 186−190

Documents

Advance in research of several types of streaming of pulse tube refrigerators