A novel shell-tube water-cooled heat exchanger for

Applied Thermal Engineering 106 (2016) 399–404

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Research Paper

A novel shell-tube water-cooled heat exchanger for high-capacity pulse-tube coolers Jingyuan Xu a,b, Jianying Hu a,⇑, Limin Zhang a, Ercang Luo a a b

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

h i g h l i g h t s A novel shell-tube water-cooled heat exchanger is proposed. The shell-tube heat exchanger achieves better heat-transfer performance. Temperature uniformity has significant effects on global cooling performance.

a r t i c l e

i n f o

Article history: Received 28 December 2015 Revised 2 June 2016 Accepted 3 June 2016 Available online 4 June 2016 Keywords: Heat exchanger Shell-tube configuration Plated-fin configuration Pulse-tube cooler Large cooling capacity

a b s t r a c t Large-capacity pulse-tube coolers are considered promising candidates for applications in hightemperature superconductivity technology, small gas liquefiers, and cryogenic storage tanks. This paper introduces a novel shell-tube heat exchanger particularly designed for such a cooler. In one heat-transfer subunit of this configuration, several small-diameter copper tubes are welded inside a large-diameter tube. This heat exchanger is characterized by small hydraulic diameter, high porosity and uniform gas temperature distribution. To verify its performance, a numerical simulation was first carried out to compare the temperature distributions of the shell-tube and plated-fin configurations. Experiments were then conducted to investigate their cooling performance. According to the experimental results, the shell-tube heat exchanger achieved better heat-transfer performance, especially with large input power. The gas temperature at the inlet of the heat exchanger and the temperature gradient in the regenerator were significantly decreased in the novel shell-tube design, which further demonstrated its better performance. Ó 2016 Elsevier Ltd. All rights reserved.

1. Introduction Since Gifford and Longsworth first introduced pulse-tube refrigerators in 1966 [1], Stirling-type pulse-tube coolers have attracted wide attention. Unlike conventional cryocoolers, such as Gifford-McMahon cryocoolers and Stirling coolers, pulse-tube coolers contain no moving parts at the cold head and are characterized by high reliability, high efficiency, and compact size. The Stirling-type pulse-tube cooler was initially used mainly in infrared detectors that required a cooling power of less than 10 W. Recently, with the large demand for small gas liquefiers, cryogenic storage tanks and high-temperature superconductivity (HTS) devices, such coolers with high-capacity cooling powers (100 W to 1 kW), which generally work in the temperature range of liquid

⇑ Corresponding author. E-mail address: [email protected] (J. Hu). http://dx.doi.org/10.1016/j.applthermaleng.2016.06.020 1359-4311/Ó 2016 Elsevier Ltd. All rights reserved.

nitrogen, are urgently needed. In 2003, a pulse-tube cooler capable of providing a cooling power of 200 W at 80 K was successfully developed by Zia [2]. A later version, with an improved cold head, achieved a cooling power of 300 W with an exergy efficiency of 19.2% [3]. In 2007, Praxair Inc. reported a pulse-tube cooler that produced a cooling power of 1100 W at 77 K [4]. Two sets of such coolers were installed in parallel to provide cryogenic environments for HTS cable [5]. Recently, a high-efficiency coaxial pulse-tube cooler was proposed, which offers more than 520 W cooling power at 80 K with an overall exergy efficiency of 18.2% [6]. The water-cooled heat exchanger (WCHX) is the core component in a pulse-tube cooler that is responsible for removing heat from the system. Many researches focus on heat transfer mechanism or new exchanger configuration [7–13]. Generally, plated-fin WCHXs (shown in Fig. 1(b)) are widely used in smallcapacity pulse-tube coolers because of their compact size and easy processing [14]; however, with large amounts of transferred heat, it is easy to cause a large temperature difference across a long fin,

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J. Xu et al. / Applied Thermal Engineering 106 (2016) 399–404

Fig. 1. Schematic diagram two types of heat exchangers: (a) shell-tube type; (b) plated-fin type.

which will lead to a large temperature difference between the gas and the cooling water. The gas-water temperature difference in the main WCHX is reported to reach as high as 50 K [6] or 57 K [15]. As a result, more effort is required for the gas to pump the heat, thereby degrading global cooling performance. To solve this problem, a shell-tube WCHX is a good choice, owing to its more uniform gas temperature distribution [16]. A conventional shelltube configuration is generally formed by many regular tubes. Unfortunately, it is difficult to simultaneously ensure a small enough hydraulic diameter and high enough porosity. Taking a frequency of 50 Hz as an example, the helium gas thermal penetration pffiffiffiffiffiffiffiffiffiffiffiffiffi depth (a characteristic length defined as 2j=x, which tells how far heat can diffuse laterally during a time interval of the period of the oscillation divided by p. j is the thermal diffusivity of the gas and x is the angular frequency) is less than 0.5 mm, so the hydraulic diameter (four times of the ratio of flow area to wetted perimeter) of each tube should be controlled to as small as 1 mm to fully exchange heat. Unfortunately, it was found that the highest porosity attained under these conditions was often less than 12%, even if the tubes were closely arranged. This regular-tube design also has an insufficient heat-exchange area on the gas side. It is because the heat-transfer coefficient on the gas side is more than an order of magnitude lower than that on the water side, whereas the heattransfer areas of the two sides are almost the same in this regular-tube design. Therefore, the heat-exchange area of the gas

side should be increased. One feasible way is to add rectangular fins inside the tubes, but with present machining process technics, it is hard to produce such fins in a small hydraulic-diameter tube. A novel shell-tube WCHX is therefore proposed to solve these problems in this paper. This novel configuration consists of a few hundred pipes, within each of which are several small-diameter tubes. In the following sections, this configuration is detailedly introduced, and a comparison with a typical plated-fin WCHX is made.

2. A novel shell-tube heat-exchanger 2.1. Configuration Fig. 1(a) presents schematic diagram of the novel shell-tube WCHX. Each large-diameter copper tube contains four smalldiameter copper tubes that act as heat-transfer fins. By adjusting the number and diameter of the smaller-diameter tubes, enough heat-exchange area at the gas side and a small enough hydraulic diameter can be obtained. Moreover, porosity of the heat exchanger can be changed in a wide range by adjusting the wall thickness and number of the small-diameter tubes. As a result, this novel design can simultaneously ensure a small enough hydraulic diameter and high enough porosity.

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Fig. 1(a) also shows the flow paths for the novel configurations. The water and working gas are isolated. Unlike the plated-fin type WCHX with the cooling water flowing through its circumference and the working gas flowing inside the fin spaces (as shown in Fig. 1(b)), the novel shell-tube-type has the water path on the outside surface of each large-diameter tube and the gas path inside each small-diameter tube and between their spaces.

water side will be less and the large-diameter tubes will be more, which is not helpful to strengthen the heat transfer on the gas side and simplify the welding processing. If too many small-diameter tubes are inserted, it is difficulty to array them when extruding the large-diameter tube. After some compromise, the number of the small-diameter tubes inserted in one large-diameter tube is chosen to be four. The more detailed parameters are shown in Table 1.

2.2. Processing procedure The processing procedures for a subunit of the shell-tube WCHX is shown in Fig. 2: (1) Coating a layer of solder on the outside surface of each small-diameter tube; (2) Putting the small-diameter tubes into a large-diameter tubes; (3) Extruding the large-diameter tube to form a surface contact between small-diameter tube and the large-diameter tube; (4) Heating the large-diameter tube to melt the solder, thus perfect thermal contact is ensured. 2.3. Parameters design The porosity and hydraulic diameter are two crucial parameters for a WCHX. Although smaller hydraulic diameter is helpful for the heat transfer, it will increase the flow resistance. Higher porosity is helpful to decrease the flow resistance, but it will lower the flow velocity and weaken the heat transfer. So these two parameters should be carefully designed for good flow condition as well as heat transfer. By numerical optimization, the optimal hydraulic diameter and porosity are about 1 mm and 20%, respectively. Three parameters—the small-tube number in one large-diameter tube, diameter of the large-diameter tube and the wall thickness, could be changed to achieve the optimal designs. If the less small-diameter tubes are inserted in the largediameter tube, the ratio of the area on the gas side to that on the

3. Theoretical analysis and discussions Fig. 3 shows temperature distributions calculated by commercial computational fluid dynamics software for the two designs as shown in Fig. 1. The structural parameters of the two WCHX designs are listed in Table 1. The temperature on the circumferential surface of each WCHX is fixed at 300 K. Transferred heat for each exchanger is 2 kW. For the shell-tube configuration, only one tube was representatively simulated: the calculation result shows that the temperature difference was only 0.2 K. This means that fairly uniform temperature distribution was obtained. If the WCHX was designed with a plated fin, the temperature difference along the fin increased sharply to 20 K, mainly because of the limited heat conduction of the long fins, which may be an obstacle to improving system efficiency. 4. Experimental investigations and results 4.1. Experimental setup Fig. 4 shows a schematic drawing and real product of the experimental setup. It consisted of a linear compressor and a pulse-tube cooler. The pulse-tube cooler included a WCHX, a regenerator, a

Fig. 2. Processing technology for one subunit of the shell-tube heat exchanger.

Table 1 Structural parameters of two types of the heat exchangers. Configuration

£ (%)

dh (mm)

Heat transfer area (m2)

Length (mm)

Typical parameters (mm)

Shell-tube

25

1.1

0.26

64

Plated-fin

26

0.78

0.38

64

Large-diameter tube inner diameter: 4.2 Small-diameter tube inner diameter: 1.2 Small-diameter tube wall thickness: 0.3 Maximum fin height: 36

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Fig. 3. Temperature distributions in two types of heat exchangers: (a) shell-tube configuration (one subunit); (b) plated-fin configuration.

cold head, a pulse-tube, a flow straightener, and a phase shifter (an inertance tube and a gas reservoir). The main geometric parameters of the cooler are listed in Table 2. The WCHX was employed either the shell-tube or plated-fin configuration. The regenerator housing was filled with a 300-mesh stainless-steel screen with porosity of 0.7. The flow straightener comprised a 40-mesh red copper screen, 3 mm in length. In this cooling system, the regenerator, cold head and pulse tube were enclosed in a vacuum chamber to decrease the ambient losses. A linear compressor was used to provide acoustic power to the pulse-tube cooler, and the acoustic power was mainly consumed in the regenerator for pumping heat from the cold head. All the heat in the system was removed by cooling water in the WCHX. The operating pressure of helium gas was 3 MPa and the working frequency was set at 55 Hz. The cooling temperature was set in the liquid nitrogen temperature range, i.e., 80 K. WCHX and the inertance tube were cooled by 293 K cooling water. In the experiment, the cooling water was cooled by an industrial chiller. The volume flow rate of the water was about 3 m3/h. If the heat rejected to the water is about 2 kW, the temperature increase of the cooling water is less than 0.6 °C. Three constantan wires heated by a direct voltage source were mounted on the cold head to simulate cooled loads. The pressure and temperature measuring points are shown in Fig. 5. A calibrated K-type sheathed thermocouple was located at the inlet of the WCHX to measure the working gas temperature (T0). The temperature of the cold head (T5) was

Fig. 4. Experimental setup: (a) schematic drawing; (b) real product.

Table 2 Main geometric parameters of the pulse-tube cooler. Component

Dimensionsa

WCHX Regenerator Cold head Pulse tube Inertance tubes Gas reservoir

Presented in Table 1 75 70 2.5 (300 mesh) 75 30 37 150 1.2 10 2300 1.5 1L

a The listed dimensions are: inner diameter length wall thickness (all in mm).


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Fig. 5. System performances for the two types of the heat exchangers. Fig. 6. Gas temperatures at the inlets of the heat exchangers.

measured by a PT-100 resistance thermometer with accuracy of ±0.1 K, while another four similar thermometers (T1–T4) were installed axially on the circumference of the regenerator. The oscillating pressures in the front and back of the linear compressor (Pf and Pb), were measured by high-precision dynamic pressure sensors supplied by PCB Piezotronics. It is noted that our major target was the cooling performance of the pulse-tube cooler—not the coupling characteristics between the cooler and the compressor; we therefore recorded the input acoustic power for the pulsetube cooler, rather than the electric-to-acoustic efficiency. The input acoustic power, W a , was calculated as:

Wa ¼

1 jp jjU f j cos hpU ; 2 f

ð1Þ

is good. The gas temperatures at the inlet of the WCHX were therefore carefully measured, as shown in Fig. 6. With 440 W input acoustic power, the gas temperatures for the two WCHX designs were similar: 297 K for the shell-tube and 299 K for the platedfin design, indicating temperature differences between the gas and the WCHX of merely 4 K and 6 K, respectively. By increasing the input acoustic power, the gas temperature increased, especially in the system with the plated-fin WCHX. When the input acoustic power was 2350 W, the gas temperature was as high as 318 K for the plated-fin WCHX, corresponding to a gas–water temperature difference of 25 K; however, the shell-tube WCHX was helpful in

where Uf was obtained from:

Uf ¼

ixV b p ; cP0 b

ð2Þ

where hpU is the phase difference between the pressure wave and the volume flow rate, x is angular frequency, V b is the back space volume of the compressor, p0 is mean pressure, and c is the specific heat ratio. 4.2. Global cooling performance Table 1 indicates that the plated-fin design definitely has advantages over that of the shell-tube in terms of a smaller hydraulic diameter and higher porosity. If better performance can be observed in the shell-tube WCHX, then this novel design is confirmed to outperform the plated-fin design. Fig. 5 presents the cooling power and overall relative Carnot efficiency (cooling power/acoustic power/Carnot efficiency) dependences on input acoustic power. Better cooling performance was achieved by employing the shell-tube WCHX, especially at large input acoustic powers. When the input acoustic power was small, the system performances for the two WCHX designs were similar; with large input acoustic power, the shell-tube WCHX obviously outperformed the plated-fin WCHX. Taking an input acoustic power of 2350 W as an example, the shell-tube WCHX system achieved a relative Carnot efficiency of 27.8% and cooling power of 246 W, whereas the system with the plated-fin WCHX only achieved an efficiency of 25.4% and cooling power of 230 W. 4.3. Gas temperature at the inlet of the heat exchanger The temperature of the working gas is generally somewhat higher than the temperature of the WCHX (assumed to be ideally cooled by water at 293 K) because of the limited heat transfer. If these two temperatures are similar, the heat transfer of the WCHX

Fig. 7. Temperature distribution in the regenerator for (a) 440 W acoustic power; (b) 2350 W acoustic power.

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cooling paths blocked (the wall temperature on this side will be higher), as shown in Fig. 8, the other with all the cooling paths unblocked. The working conditions were kept the same as described in Section 4.1. In the experiment, it was found that the surface temperature on the blocked side of the WCHX became very hot. Fig. 9 shows the experimental results. It can be found that the unblocked WCHX outperformed the blocked WCHX, especially at large input acoustic powers. This verifies the reason that the shell-tube configuration obviously outperforms the plated-fin configuration.

Fig. 8. A plated-fin heat exchanger with half of the cooling path blocked.

decreasing the gas temperature, which was effectively decreased by 16 K. 4.4. Temperature distribution in the regenerator Fig. 7 shows the temperature distribution in the regenerator for different input acoustic powers. The x-axis begins at the warm end of the regenerator and ends at its cold end. The four data points are the temperatures measured axially around the circumference of the regenerator and the straight lines are their fitted results. With an input acoustic power of 440 W, the temperature gradients for two WCHX designs were very similar; with an input acoustic power of 2350 W, the temperature gradient for the plated-fin WCHX was much higher than that for the shell-tube WCHX. As a result, more effort would be required to pump heat from the cold head to the ambient end of the regenerator. If we assume that the gas temperature was the same as that of the solid wall of the regenerator, then the temperature difference between the gas and cooling water at the ambient end of the regenerator (i.e., outlet of the WCHX) would be as high as 28 K. If the novel shell-tube WCHX design was used, the temperature difference effectively decreased by 15 K. 4.5. Influence of gas temperature nonuniformity As shown in Fig. 3, the major difference between the shell-tube and plated-fin type WCHXs is the temperature distribution on the wall: the former has more homogeneous distribution and lower average temperature while the latter has less homogeneous distribution and higher average temperature. The above experimental results implied that this difference imposes great influence on system performance. To further demonstrate the influence, experiments were conducted on plated-fin WCHXs: one with half of the

Fig. 9. Influence of gas temperature nonuniformity in the plated-fin heat exchangers.

5. Conclusions A novel shell-tube WCHX has been designed, fabricated, and tested for use in a high-capacity pulse-tube cooler. Compared with a conventional shell-tube configuration, it has an increased heatexchange area, a smaller hydraulic diameter and higher porosity. Compared with a plated-fin configuration, it is characterized by homogeneous temperature distribution, which has been proved by the numerical simulation. Comparative experiments were conducted on a pulse-tube cooler. It was found that the cooler with the novel shell-tube design always outperformed the plated-fin design, especially when the input acoustic power is large. The gas temperature at the inlet of the WCHX was greatly decreased with the shell-tube configuration and a temperature gradient drop in the regenerator was observed. The shell-tube WCHX was proved to have better heat transfer, and can be considered for use in highcapacity pulse-tube coolers. Acknowledgement This work was supported by the National Natural Science Foundation of China (Grant Nos. 51276187, 51576204 and 51506211). References [1] W.E. Gifford, R.C. Longsworth, Pulse tube refrigeration, Trans. Am. Soc. Mech. Eng. 86 (1964) 264–268. [2] J.H. Zia, A commercial pulse tube cryocooler with 200 W refrigeration at 80 K, Cryocoolers 13 (2005) 165–171. [3] J.H. Zia, A pulse tube cryocooler with 300 W refrigeration at 80 K and an operating efficiency of 19% Carnot, Cryocoolers 14 (2007) 141–147. [4] S.A. Potratz, T.D. Abbott, M.C. Johnson, Stirling-type pulse tube cryocooler with 1 kW of refrigeration at 77 K, Adv. Cryog. Eng. 53 (2007) 42–48. [5] M.C. Johnson, T.D. Abbott, K.B. Albaugh, et al., Installation of pulse tube cryocoolers for cooling of HTS cable, J. Phys: Conf. Ser. 97 (2008) 012336. [6] J.Y. Hu, L.M. Zhang, J. Zhu, et al., A high-efficiency coaxial pulse tube cryocooler with 500 W cooling capacity at 80 K, Cryogenics 62 (2014) 7–10. [7] K. Tang, J. Yu, T. Jin, Y.P. Wang, W.T. Tang, Z.H. Gan, Heat transfer of laminar oscillating flow in finned WCHX of pulse tube refrigerator, Int. J. Heat Mass Transfer 70 (2014) 811–818. [8] K. Tang, J. Yu, T. Jin, Z.H. Gan, Influence of compression-expansion effect on oscillating-flow heat transfer in a finned WCHX, J. Zhejiang Univ. (Sci. A) 14 (6) (2013) 427–434. [9] Y.Y. Chen, E.C. Luo, W. Dai, Heat transfer characteristics of oscillating flow regenerator filled with circular tubes or parallel plates, Cryogenics 47 (1) (2007) 40–48. [10] A.J. Jaworski, A. Piccolo, Heat transfer processes in parallel-plate heat exchangers of thermoacoustic devices—numerical and experimental approaches, Appl. Therm. Eng. 42 (2012) 145–153. [11] H. Shiraiwa, Y. Kita, Performance improvement of a falling-film-type heat exchanger by insertion of shafts with screw blade in a heat exchange tube, Appl. Therm. Eng. 102 (2016) 55–62. [12] W. Kamsanam, X.A. Mao, A. Jaworski, Thermal performance of finned-tube thermoacoustic heat exchangers in oscillatory flow conditions, Int. J. Therm. Sci. 101 (2016) 169–180. [13] C. Shen, H.X. Li, D.W. Zhang, et al., Study on the heat transfer characteristic of solar powered thermoacoustic prime mover at different tilted angles, Appl. Therm. Eng. 103 (2016) 1126–1134. [14] W.M. Kays, A.L. London, Compact Heat-Exchangers, second ed., McGraw Hill, New York, 1964, pp. 2–15. [15] J.Y. Hu, S. Chen, J. Zhu, L.M. Zhang, et al., An efficient pulse tube cryocooler for boil-off gas reliquefaction in liquid natural gas tanks, Appl. Energy (2015), http://dx.doi.org/10.1016/j.apenergy.2015.03.096. [16] G. Walker, Stirling Engine, Clarendon Press, Oxford, 1980, pp. 124–137.