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Regenerator performance improvement of a single-stage pulse tube cooler reached 11.1 K
Cryogenics 47 (2007) 49–55 www.elsevier.com/locate/cryogenics
Regenerator performance improvement of a single-stage pulse tube cooler reached 11.1 K L.M. Qiu *, Y.L. He, Z.H. Gan, X.B. Zhang, G.B. Chen Institute of Refrigeration and Cryogenic Engineering, Zhejiang University, Hangzhou 310027, China Received 14 July 2006; received in revised form 26 August 2006; accepted 9 September 2006
Abstract In order to improve the cooling performance of pulse tube cooler (PTC) at 20–40 K, hybrid regenerators are often employed. In this paper a three-layer regenerator, which consists of woven wire screen, lead sphere and Er3Ni is optimized to enhance the cooling performance and explore the lowest attainable refrigeration temperature for a single-stage PTC. The efforts focus on the temperature range of 80–300 K, where woven wire screens are used. Theoretical and experimental studies are carried out to study the metal material and the mesh size effect of woven wire screens on the performance of the single-stage G-M type PTC. A lowest no-load refrigeration temperature of 11.1 K was obtained with an input power of 6 kW. The PTC can supply 17.8 W at 20 K and 39.4 W at 30 K, respectively. 2006 Elsevier Ltd. All rights reserved. Keywords: Pulse tube cooler (E); Regenerator (E); Heat transfer (C); Pressure drop
1. Introduction In comparison with the traditional regenerative cryocoolers such as G-M and Stirling coolers, the pulse tube cooler (PTC) with no moving parts in low temperature range has the advantages of simple structure, low cost, high reliability, low mechanical vibration and low electromagnetic noise [1]. With the development of phase shift method, flexure bearing compressor and magnetic regenerator material, the efficiency of PTCs working at 77 K and 4.2 K was significantly enhanced [2–4], which can be comparable with that of G-M and Stirling coolers. The development of single-stage G-M type PTC at 20–40 K is also promising for the applications of superconductor cooling, cryopump and so on. A refrigeration temperature of 13 K was obtained by a single-stage PTC with an input power of 13 kW at University of Giessen in 2003 [5]. However, the cooling performance of single-stage PTC at 20–40 K is still lower than that of G-M coolers [6]. The
*
Corresponding author. Tel./fax: +86 571 87952793. E-mail address: [email protected] (L.M. Qiu).
0011-2275/$ - see front matter 2006 Elsevier Ltd. All rights reserved. doi:10.1016/j.cryogenics.2006.09.004
regenerator losses become especially large at low temperature range, at which the matrix heat capacities of known regenerator materials becomes less than that of helium gas and leads to increased losses. Besides, the PTC needs relatively bigger mass flow rate compared to the G-M cooler, which further decreases the efficiency of regenerator. Obviously, a small reduction in these losses can lead to a significant increase in the net refrigeration power for the same power input [7]. An efficient regenerator must have a large thermal inertia per unit volume to support high volumetric heat transfer with the working fluid, and at the same time with small pressure drops. Meeting all these goals is evidently not feasible in practice, and optimization and compromise are often needed. In order to improve the performance of the PTC working at 20–40 K, we performed the study of regenerator optimization. In 2004 a G-M type single-stage PTC was designed and manufactured at Zhejiang University. A lowest no-load refrigeration temperature of 13.8 K and cooling capacity of 55.9 W at 40 K were obtained when the regenerator was packed with phosphor–bronze screens in the warm part and lead spheres in the cold part with an input power of 6 kW [4]. In order to further improve the
L.M. Qiu et al. / Cryogenics 47 (2007) 49–55
The detailed experimental setup of the single-stage double-inlet PTC can be found in Refs. [4,8]. A three-layer matrix, consisting of woven wire screens, lead spheres and Er3Ni from warm to cold end of regenerator was used. The volume ratios of the three types of regenerator materials are fixed as 77.0%, 18.4% and 4.6%, respectively. Experiments were first carried out to compare the performance of the regenerator packed with screens between stainlesssteel and phosphor–bronze. With 250# stainless-steel screens packed at the warm part, we define this set of experiments as CASE-SS; for 250# phosphor–bronze screens we call it CASE-PH. In these two cases lead spheres and Er3Ni packed at the cold part remains unchanged. If not otherwise stated, the operating frequency of the PTC is 1.4 Hz, the rotary valve timing (defined as time ratio of exhaust process to intake process of rotary valve) is 1.22 and the rated input power of the compressor (Leybold CP6000) is 6 kW. Fig. 1 shows the performance comparison of the PTC between stainless-steel and phosphor–bronze screens with filling pressure of 1.7 MPa. Lower refrigeration temperature and higher cooling capacity have been obtained for CASE-SS. With the filling pressure of 1.4 MPa, a no-load refrigeration temperature as low as 12.2 K was obtained, which is 0.4 K lower than that in CASE-PH. When the filling pressure is 1.7 MPa, a cooling capacity of 37.5 W at 30 K has been obtained, which is 0.5 W larger than that of CASE-PH; the maximum coefficient of performance (COP, i.e. cooling capacity over the actual input power to the compressor) of the PTC was 2.5 · 103 at 20 K and 5.7 · 103 at 30 K, respectively.
40
0.008
30
0.006
20
0.004
10
0.002
0 10
15
20
25
30
35
COP
0.010
CASE-PH CASE-SS
0.000 40
T (K) Fig. 1. Performance comparison of PTC between stainless-steel and phosphor–bronze screens with filling pressure of 1.7 MPa.
The experimental results are reasonable if we compare the thermodynamic properties of stainless-steel and phosphor–bronze. Fig. 2 shows the volumetric specific heat capacity and heat conductivity of phosphor–bronze and stainless-steel from 30 to 300 K. We can find that the volumetric specific heat capacity and bulk heat conductivity of phosphor–bronze and stainless-steel both increase with the increase of temperature. Though the heat capacity difference between phosphor–bronze and stainless-steel is not so big, the heat conductivity of phosphor–bronze is almost 4 times bigger than that of stainless-steel, which will introduce larger axial conduction loss in the regenerator.
4.0x106
72
Stainless-steel Phosphor-bronze
3.5x106
63
3.0x106
54
2.5x106
45
2.0x106
36
1.5x106
27
1.0x106
18
5.0x105
9
0.0 0
50
100
150
200
250
300
Heat conductivity (W/m*K)
2. Performance comparison of PTC with the regenerator packed with stainless-steel and phosphor–bronze woven wire screens
50
Cooling capacity (W)
efficiency of regenerator below 20 K, the regenerator was modified to a three-layer structure with Er3Ni located in the coldest part in 2005. A lowest no-load refrigeration temperature of 12.6 K and cooling capacity of 59.0 W at 40 K were obtained with an input power of 6 kW [8]. In this paper we focus on regenerator improvement at temperature range of 80–300 K. Woven wire screens have the advantages of low pressure drop, low axial conduction, high heat transfer area and high heat capacity at 80–300 K. Woven wire screens made of phosphor–bronze and stainless-steel are commonly used. Theoretical calculation and experimental study were carried out about the metal material and mesh size effect of woven wire screens on the performance of single-stage G-M type PTC. Experimental results show that the cooling performance with stainless-steel woven wire screens are better than that with phosphor–bronze screens. Then heat transfer capacity and pressure drop of stainless-steel screens of different mesh sizes were calculated to find the optimum mesh size number for the PTC. At last the results of calculations and experiments are compared and analyzed.
Volumetric specific capacity (J/K*m3)
50
0
T (K) Fig. 2. Comparison of volumetric specific heat capacity and heat conductivity between stainless-steel and phosphor–bronze from 30 to 300 K.
L.M. Qiu et al. / Cryogenics 47 (2007) 49–55
3. Performance comparison of PTC with the regenerator packed with different mesh sizes of stainless-steel woven wire screens Above experiments show that the PTC can be improved if we use stainless-steel screens other than phosphor– bronze screens. In order to further improve the PTC performance theoretical and experimental study are carried out to find the optimal mesh size number of stainless-steel screen.
3.1. Thermodynamic calculations of regenerator performance factor The performance of regenerator, which essentially is a compact heat exchanger, is mainly depended on the heat transfer capacity of the matrix and the pressure drop of gas through the regenerator. But for woven wire screens the heat transfer between matrix and working gas and the pressure drop through regenerator both increase with the increase of mesh size number. It is necessary to select the optimal mesh size of screen to compromise between heat transfer and pressure drop loss. In order to evaluate the regenerator performance, we introduce the concept of regenerator performance factor (RPF) [9], which is defined as follows:
Rpf ¼
51
As h dp=dx
ð1Þ
where Rpf is RPF; As is the surface area of regenerator material per unit length of regenerator; h is the convection heat transfer coefficient between gas and regenerator material; dp/dx is the pressure drop per unit length of regenerator. Table 1 shows the geometric properties of stainless-steel woven wire screens from 200 to 397 mesh. Area density means the surface area of screens per unit volume. In order to calculate RPF for different mesh sizes, we assume that the mean mass flow rate of 4He through the regenerator is 0.01 kg/s; the mean pressure in the regenerator is 1.5 MPa; the axial spacing between different layers of screen is zero. The diameter of the regenerator can be seen in Ref. [8]. The convection heat transfer coefficient h can be calculated by the empirical expression [10]: StPr2=3 ¼ 0:375Re00:375
ð2Þ
where St = h/(Gcp); G is the mass flow rate of 4He per unit flow area; cp is the constant-pressure specific heat of 4He; Pr is the Prandtl number of 4He; Re 0 is the modified Reynolds number, whose definition can be seen in Ref. [10]. Calculation results from Eq. (2) are given in Fig. 3. We can find that the convection heat transfer coefficient h
Table 1 Properties of stainless-steel wire screensa Mesh size
Wire diameter (mm)
Mesh distance (mm)
Open area ratio (%)
Porosity (%)
Hydraulic diameter (mm)
Area density (m2/m3)
200 247 295 397
0.056 0.04 0.036 0.028
0.071 0.063 0.05 0.036
31 37 34 32
65.36 69.50 67.12 65.63
0.09194 0.08223 0.06499 0.04665
24740.16 30504.85 36534.88 49093.75
Data selected from website: http://www.metel.de/tabelle3.pdf.
10000
Heat transfer coefficient (W/m2-K)
a
Mesh size: 200 Mesh size: 247 Mesh size: 295 Mesh size: 397
9000
8000
7000
6000
5000 50
100
150
200
250
T (K) Fig. 3. Convection heat transfer coefficients calculated from Eq. (2).
300
52
L.M. Qiu et al. / Cryogenics 47 (2007) 49–55
between 4He and screens is proportional to the mesh size number of screen and the temperature. For the calculation of pressure drop in regenerator, friction factor f is commonly used. Pressure drop can be expressed as dp f qu2 ¼ dx d h 2
ð3Þ
where f is the friction factor; dh is the hydraulic diameter of screens; q and u are the density and velocity of 4He. Ref. [11] summarized an empirical expression which can be used to calculate the friction factor f for low frequency oscillatory flow. Based on this expression, Fig. 4 gives the calculation results of pressure drop in regenerator for different mesh sizes of screens and temperature. We can find that the pressure drop of the regenerator increases with the increase of mesh size and temperature. The influence of mesh
size on the pressure drop becomes small with the decrease of temperature. Fig. 5 gives the RPFs calculated from the results shown in Figs. 3 and 4. With the decrease of temperature the influence of mesh size on the RPF becomes remarkable, which indicates that in order to reach lower temperature, it is important to select an optimum mesh size. Calculation results show that for low frequency oscillatory flow RPF is highest when the mesh size is 247 from 80 to 300 K, which coincides with the mesh size of screens used in Refs. [12–14]. 3.2. Thermodynamic calculations of a In Refs. [10,15] a, which is similar to RPF and defined as a = (StPr2/3)/f, is used. A high value of a are desired since it gives a high heat transfer for a given pressure drop.
3.5
T=300 K T=250 K T=200 K T=150 K T=80 K
3.0
dP/dX (MPa/m)
2.5 2.0 1.5 1.0 0.5 0.0 200
250
300
350
400
Mesh size Fig. 4. Pressure drop of fluid flowing through regenerator calculated from Eq. (3).
6
RPF (W/K-Pa)
5
T=300 K T=250 K T=200 K T=150 K T=80 K
4
3
2
1 200
250
300
350
Mesh size Fig. 5. RPFs calculated from the results of Figs. 3 and 4.
400
L.M. Qiu et al. / Cryogenics 47 (2007) 49–55
Fig. 6 shows the calculated curves of a based on Eq. (2) and empirical expression in Ref. [11] as a function of Reynolds number for different mesh sizes of stainless-steel screens. Calculated results show that when the mesh size is 247 higher heat transfer can be expected for a given pressure drop, which is similar with the results shown in Fig. 5.
0.030
0.025
295#
247#
397#
200#
α
0.020
0.015
0.010
0.005
40
80
120
160
200
Re Fig. 6. Curves of a as a function of Reynolds number for different mesh sizes of stainless-steel screens.
53
3.3. Experimental results Based on above analysis, we experimentally investigated the mesh size effect of stainless-steel woven wire screen on the performance of PTC. Three sets of experiments with different mesh sizes (247, 295 and 397, respectively) of stainless-steel screens were performed. For comparison and analysis, lead spheres and Er3Ni packed at the cold part remains unchanged. Figs. 7 and 8 show the mean pressure and pressure amplitude measured at the hot end of regenerator and pulse tube under the lowest attainable refrigeration temperature with the filling of 1.4 and 1.7 MPa, respectively. The mean pressure in the regenerator didn’t change much during three sets of experiments. The pressure ratio and pressure amplitude at the hot end of the regenerator increase with the increase of mesh size number, but at the hot end of the pulse tube they are biggest when the mesh size number is 295. As the pressure drop through pulse tube is very small, we can consider the pressure at the hot end of pulse tube as that of cold end. The difference of pressure ratio and amplitude between hot end of regenerator and pulse tube increases with the increase of mesh size, which indicates the pressure drop across regenerator increases with the increase of mesh size, coinciding with the results of Fig. 4. Figs. 9 and 10 give the cooling performance of the PTC. When the mesh size is 247, 295 and 397, respectively, the lowest no-load refrigeration temperature is 12.2, 11.1 and 11.3 K and the cooling capacity at 20 K is 15.7, 17.8 and 16.7 W, respectively. From Figs. 7 and 8 we can find the
Mean pressure (MPa)
Pressure amplitude (MPa)
Measured at the hot end of the regenerator Measured at the hot end of the pulse tube 0.6
0.5
0.4
0.3 240
260
280
300
320
340
360
380
400
320
340
360
380
400
1.4
1.3
1.2
Filling pressure: 1.4 MPa 1.1 240
260
280
300
Mesh size Fig. 7. Mean pressure and pressure amplitude measured at the hot end of regenerator and pulse tube under the lowest attainable refrigeration temperature with the filling of 1.4 MPa.
54
L.M. Qiu et al. / Cryogenics 47 (2007) 49–55
Pressure amplitude (MPa)
Measured at the hot end of the regenerator Measured at the hot end of the pulse tube 0.60 0.55 0.50 0.45 0.40 240
260
280
300
320
340
360
380
400
320
340
360
380
400
Mean pressure (MPa)
1.60
1.55
1.50
Filling pressure: 1.7 MPa 1.45 240
260
280
300
Mesh size Fig. 8. Mean pressure and pressure amplitude measured at the hot end of regenerator and pulse tube under the lowest attainable refrigeration temperature with the filling of 1.7 MPa.
pressure ratio and pressure amplitude at the hot end of pulse tube, which can be regarded as the pressure of cold end of pulse tube, are biggest when the mesh size is 297. The performance of PTC increases with the increase of pressure ratio at the cold end of regenerator. The performance of PTC is optimum when the mesh size is 297. This result is a little deviated from the calculation results shown
in Fig. 5. We can conclude that increasing mesh size properly from 247 to 295 will increase friction factor and pressure drop loss, but the increase in heat transfer can more than offset a large friction factor increase. If we further increase the mesh size, the pressure drop across the regenerator will increase rapidly and the performance of regenerator and PTC will deteriorate.
Filling pressure: 1.4 MPa Filling pressure: 1.7 MPa Q @ 30 K (W)
40 38 36 34
Q @ 20 K (W)
32 18
240
260
280
300
320
340
360
380
400
240
260
280
300
320
340
360
380
400
240
260
280
300
320
340
360
380
400
17 16 15 14
T (K)
12.5 12.0 11.5 11.0
Mesh size Fig. 9. Cooling capacity comparisons of different mesh sizes of stainless-steel screens.
L.M. Qiu et al. / Cryogenics 47 (2007) 49–55
55
COP @ 30 K
6.2x10-3
6.0x10-3
5.8x10-3
5.6x10-3 250
300
350
400
COP @ 20 K
3.00x10-3
2.75x10-3
2.50x10-3
Filling pressure: 1.4 MPa Filling pressure: 1.7 MPa
2.25x10-3 250
300
350
400
Mesh size Fig. 10. COP comparisons of different mesh sizes of stainless-steel screens.
4. Conclusion The regenerator of a single-stage G-M type PTC was optimized to improve the efficiency at the temperature range of 80–300 K. Experiments show that the performance can be improved if we use stainless-steel screens other than phosphor–bronze screens. Regenerator performance factor (RPF) and a are introduced to evaluate the performance of regenerator for different mesh sizes of screen. Calculations show that 247 mesh stainless-steel screen can give optimum performance. The experimental results indicate that appropriately increase the mesh size to 295 can enhance the heat transfer capacity and improve the efficiency of regenerator with the pressure drop increased a little. After optimization a lowest no-load refrigeration temperature of 11.1 K was obtained with an input power of 6 kW. The cooling capacity and COP at 20 K are 17.8 W and 2.95 · 103. Acknowledgements This work was supported by the Science and Technology Department of Zhejiang Province, China under contract No. 2006C24G2010027 and Natural Sciences Foundation of Zhejiang Province, China under contract No. Y105519. References [1] Radebaugh R. The development and application of cryocoolers since 1985. In: Chen GB, Hebral B, Chen GM, editors. Proceedings of ICCR’ 2003. International Academic Publishers/Beijing World Publishing Corporation; 2003. p. 858–70.
[2] Tward E, Chan CK, Raab J, et al. High efficiency pulse tube cooler. In: Ronald Jr G Ross, editor. Cryocoolers 11. Kluwer Aademic/ Plenum Publishers; 2001. p. 163–7. [3] Jiang N, Lindemann U, Giebeler F, et al. A 3He pulse tube cooler operating down to 1.3 K. Cryogenics 2004;44:809–16. [4] Qiu LM, He YL, Gan ZH, et al. A separate two-stage pulse tube cooler working at liquid helium temperature. Chinese Sci Bull 2005;50:1030–3. [5] Haefner HU, Giebeler F, Thummes G. Einstufiger 25 K Pulsrohrkuehler fuer HTS-energie-applikationen. DKV-Tagungsbericht 2003:173–83. [6] http://www.cryomech.com/products.cfm?item_type=p&prod_id=9&op= one. [7] Radebaugh R, Marquardt E, Bradley P. Development of a pulse tube refrigerator for millimeter array sensor cooling: Phase I, ALMA Memo #281, 1999. [8] Qiu LM, He YL, Gan ZH, et al. A single-stag pulse tube cooler reached 12.6 K. Cryogenics 2005;45:641–3. [9] Bin-Nun U, Manitakos D. Low cost and high performance screen laminate regenerator matrix. Cryogenics 2004;44:439–44. [10] Ackermann Robert A. Cryogenic regenerative heat exchangers. New York: Plenum press; 1997. [11] Tanaka M, Yamshita I, Chrisaka F. Flow and heat transfer characteristics of the stirling engine regenerator in an oscillating flow. JSME Int J 1990;33:283–9. [12] Wang C, Thummes G, Heiden C. A two-stage pulse tube cooler operating below 4 K. Cryogenics 1997;37:159–64. [13] Chen GB, Qiu LM, Zhen JY, et al. Experimental study on a doubleorifice two-stage pulse tube refrigerator. Cryogenics 1997;37:271–3. [14] Jiang YL, Chen GB, Thummes G. Experimental investigation on DC flow control in a single-stage pulse tube refrigerator operating below 20 K. In: Chen GB, Hebral B, Chen GM, editors. Proceedings of ICCR’ 2003. International Academic Publishers/Beijing World Publishing Corporation; 2003. p. 77–80. [15] Radebaugh R, Louie B. A simple, First step to the optimization of regenerator geometry. In: Proceedings of the third cryocooler conference NBS special publication 698, Boulder, CO; 1985. p. 177–98.
Regenerator performance improvement of a single-stage pulse tube cooler reached 11.1 K L.M. Qiu *, Y.L. He, Z.H. Gan, X.B. Zhang, G.B. Chen Institute of Refrigeration and Cryogenic Engineering, Zhejiang University, Hangzhou 310027, China Received 14 July 2006; received in revised form 26 August 2006; accepted 9 September 2006
Abstract In order to improve the cooling performance of pulse tube cooler (PTC) at 20–40 K, hybrid regenerators are often employed. In this paper a three-layer regenerator, which consists of woven wire screen, lead sphere and Er3Ni is optimized to enhance the cooling performance and explore the lowest attainable refrigeration temperature for a single-stage PTC. The efforts focus on the temperature range of 80–300 K, where woven wire screens are used. Theoretical and experimental studies are carried out to study the metal material and the mesh size effect of woven wire screens on the performance of the single-stage G-M type PTC. A lowest no-load refrigeration temperature of 11.1 K was obtained with an input power of 6 kW. The PTC can supply 17.8 W at 20 K and 39.4 W at 30 K, respectively. 2006 Elsevier Ltd. All rights reserved. Keywords: Pulse tube cooler (E); Regenerator (E); Heat transfer (C); Pressure drop
1. Introduction In comparison with the traditional regenerative cryocoolers such as G-M and Stirling coolers, the pulse tube cooler (PTC) with no moving parts in low temperature range has the advantages of simple structure, low cost, high reliability, low mechanical vibration and low electromagnetic noise [1]. With the development of phase shift method, flexure bearing compressor and magnetic regenerator material, the efficiency of PTCs working at 77 K and 4.2 K was significantly enhanced [2–4], which can be comparable with that of G-M and Stirling coolers. The development of single-stage G-M type PTC at 20–40 K is also promising for the applications of superconductor cooling, cryopump and so on. A refrigeration temperature of 13 K was obtained by a single-stage PTC with an input power of 13 kW at University of Giessen in 2003 [5]. However, the cooling performance of single-stage PTC at 20–40 K is still lower than that of G-M coolers [6]. The
*
Corresponding author. Tel./fax: +86 571 87952793. E-mail address: [email protected] (L.M. Qiu).
0011-2275/$ - see front matter 2006 Elsevier Ltd. All rights reserved. doi:10.1016/j.cryogenics.2006.09.004
regenerator losses become especially large at low temperature range, at which the matrix heat capacities of known regenerator materials becomes less than that of helium gas and leads to increased losses. Besides, the PTC needs relatively bigger mass flow rate compared to the G-M cooler, which further decreases the efficiency of regenerator. Obviously, a small reduction in these losses can lead to a significant increase in the net refrigeration power for the same power input [7]. An efficient regenerator must have a large thermal inertia per unit volume to support high volumetric heat transfer with the working fluid, and at the same time with small pressure drops. Meeting all these goals is evidently not feasible in practice, and optimization and compromise are often needed. In order to improve the performance of the PTC working at 20–40 K, we performed the study of regenerator optimization. In 2004 a G-M type single-stage PTC was designed and manufactured at Zhejiang University. A lowest no-load refrigeration temperature of 13.8 K and cooling capacity of 55.9 W at 40 K were obtained when the regenerator was packed with phosphor–bronze screens in the warm part and lead spheres in the cold part with an input power of 6 kW [4]. In order to further improve the
L.M. Qiu et al. / Cryogenics 47 (2007) 49–55
The detailed experimental setup of the single-stage double-inlet PTC can be found in Refs. [4,8]. A three-layer matrix, consisting of woven wire screens, lead spheres and Er3Ni from warm to cold end of regenerator was used. The volume ratios of the three types of regenerator materials are fixed as 77.0%, 18.4% and 4.6%, respectively. Experiments were first carried out to compare the performance of the regenerator packed with screens between stainlesssteel and phosphor–bronze. With 250# stainless-steel screens packed at the warm part, we define this set of experiments as CASE-SS; for 250# phosphor–bronze screens we call it CASE-PH. In these two cases lead spheres and Er3Ni packed at the cold part remains unchanged. If not otherwise stated, the operating frequency of the PTC is 1.4 Hz, the rotary valve timing (defined as time ratio of exhaust process to intake process of rotary valve) is 1.22 and the rated input power of the compressor (Leybold CP6000) is 6 kW. Fig. 1 shows the performance comparison of the PTC between stainless-steel and phosphor–bronze screens with filling pressure of 1.7 MPa. Lower refrigeration temperature and higher cooling capacity have been obtained for CASE-SS. With the filling pressure of 1.4 MPa, a no-load refrigeration temperature as low as 12.2 K was obtained, which is 0.4 K lower than that in CASE-PH. When the filling pressure is 1.7 MPa, a cooling capacity of 37.5 W at 30 K has been obtained, which is 0.5 W larger than that of CASE-PH; the maximum coefficient of performance (COP, i.e. cooling capacity over the actual input power to the compressor) of the PTC was 2.5 · 103 at 20 K and 5.7 · 103 at 30 K, respectively.
40
0.008
30
0.006
20
0.004
10
0.002
0 10
15
20
25
30
35
COP
0.010
CASE-PH CASE-SS
0.000 40
T (K) Fig. 1. Performance comparison of PTC between stainless-steel and phosphor–bronze screens with filling pressure of 1.7 MPa.
The experimental results are reasonable if we compare the thermodynamic properties of stainless-steel and phosphor–bronze. Fig. 2 shows the volumetric specific heat capacity and heat conductivity of phosphor–bronze and stainless-steel from 30 to 300 K. We can find that the volumetric specific heat capacity and bulk heat conductivity of phosphor–bronze and stainless-steel both increase with the increase of temperature. Though the heat capacity difference between phosphor–bronze and stainless-steel is not so big, the heat conductivity of phosphor–bronze is almost 4 times bigger than that of stainless-steel, which will introduce larger axial conduction loss in the regenerator.
4.0x106
72
Stainless-steel Phosphor-bronze
3.5x106
63
3.0x106
54
2.5x106
45
2.0x106
36
1.5x106
27
1.0x106
18
5.0x105
9
0.0 0
50
100
150
200
250
300
Heat conductivity (W/m*K)
2. Performance comparison of PTC with the regenerator packed with stainless-steel and phosphor–bronze woven wire screens
50
Cooling capacity (W)
efficiency of regenerator below 20 K, the regenerator was modified to a three-layer structure with Er3Ni located in the coldest part in 2005. A lowest no-load refrigeration temperature of 12.6 K and cooling capacity of 59.0 W at 40 K were obtained with an input power of 6 kW [8]. In this paper we focus on regenerator improvement at temperature range of 80–300 K. Woven wire screens have the advantages of low pressure drop, low axial conduction, high heat transfer area and high heat capacity at 80–300 K. Woven wire screens made of phosphor–bronze and stainless-steel are commonly used. Theoretical calculation and experimental study were carried out about the metal material and mesh size effect of woven wire screens on the performance of single-stage G-M type PTC. Experimental results show that the cooling performance with stainless-steel woven wire screens are better than that with phosphor–bronze screens. Then heat transfer capacity and pressure drop of stainless-steel screens of different mesh sizes were calculated to find the optimum mesh size number for the PTC. At last the results of calculations and experiments are compared and analyzed.
Volumetric specific capacity (J/K*m3)
50
0
T (K) Fig. 2. Comparison of volumetric specific heat capacity and heat conductivity between stainless-steel and phosphor–bronze from 30 to 300 K.
L.M. Qiu et al. / Cryogenics 47 (2007) 49–55
3. Performance comparison of PTC with the regenerator packed with different mesh sizes of stainless-steel woven wire screens Above experiments show that the PTC can be improved if we use stainless-steel screens other than phosphor– bronze screens. In order to further improve the PTC performance theoretical and experimental study are carried out to find the optimal mesh size number of stainless-steel screen.
3.1. Thermodynamic calculations of regenerator performance factor The performance of regenerator, which essentially is a compact heat exchanger, is mainly depended on the heat transfer capacity of the matrix and the pressure drop of gas through the regenerator. But for woven wire screens the heat transfer between matrix and working gas and the pressure drop through regenerator both increase with the increase of mesh size number. It is necessary to select the optimal mesh size of screen to compromise between heat transfer and pressure drop loss. In order to evaluate the regenerator performance, we introduce the concept of regenerator performance factor (RPF) [9], which is defined as follows:
Rpf ¼
51
As h dp=dx
ð1Þ
where Rpf is RPF; As is the surface area of regenerator material per unit length of regenerator; h is the convection heat transfer coefficient between gas and regenerator material; dp/dx is the pressure drop per unit length of regenerator. Table 1 shows the geometric properties of stainless-steel woven wire screens from 200 to 397 mesh. Area density means the surface area of screens per unit volume. In order to calculate RPF for different mesh sizes, we assume that the mean mass flow rate of 4He through the regenerator is 0.01 kg/s; the mean pressure in the regenerator is 1.5 MPa; the axial spacing between different layers of screen is zero. The diameter of the regenerator can be seen in Ref. [8]. The convection heat transfer coefficient h can be calculated by the empirical expression [10]: StPr2=3 ¼ 0:375Re00:375
ð2Þ
where St = h/(Gcp); G is the mass flow rate of 4He per unit flow area; cp is the constant-pressure specific heat of 4He; Pr is the Prandtl number of 4He; Re 0 is the modified Reynolds number, whose definition can be seen in Ref. [10]. Calculation results from Eq. (2) are given in Fig. 3. We can find that the convection heat transfer coefficient h
Table 1 Properties of stainless-steel wire screensa Mesh size
Wire diameter (mm)
Mesh distance (mm)
Open area ratio (%)
Porosity (%)
Hydraulic diameter (mm)
Area density (m2/m3)
200 247 295 397
0.056 0.04 0.036 0.028
0.071 0.063 0.05 0.036
31 37 34 32
65.36 69.50 67.12 65.63
0.09194 0.08223 0.06499 0.04665
24740.16 30504.85 36534.88 49093.75
Data selected from website: http://www.metel.de/tabelle3.pdf.
10000
Heat transfer coefficient (W/m2-K)
a
Mesh size: 200 Mesh size: 247 Mesh size: 295 Mesh size: 397
9000
8000
7000
6000
5000 50
100
150
200
250
T (K) Fig. 3. Convection heat transfer coefficients calculated from Eq. (2).
300
52
L.M. Qiu et al. / Cryogenics 47 (2007) 49–55
between 4He and screens is proportional to the mesh size number of screen and the temperature. For the calculation of pressure drop in regenerator, friction factor f is commonly used. Pressure drop can be expressed as dp f qu2 ¼ dx d h 2
ð3Þ
where f is the friction factor; dh is the hydraulic diameter of screens; q and u are the density and velocity of 4He. Ref. [11] summarized an empirical expression which can be used to calculate the friction factor f for low frequency oscillatory flow. Based on this expression, Fig. 4 gives the calculation results of pressure drop in regenerator for different mesh sizes of screens and temperature. We can find that the pressure drop of the regenerator increases with the increase of mesh size and temperature. The influence of mesh
size on the pressure drop becomes small with the decrease of temperature. Fig. 5 gives the RPFs calculated from the results shown in Figs. 3 and 4. With the decrease of temperature the influence of mesh size on the RPF becomes remarkable, which indicates that in order to reach lower temperature, it is important to select an optimum mesh size. Calculation results show that for low frequency oscillatory flow RPF is highest when the mesh size is 247 from 80 to 300 K, which coincides with the mesh size of screens used in Refs. [12–14]. 3.2. Thermodynamic calculations of a In Refs. [10,15] a, which is similar to RPF and defined as a = (StPr2/3)/f, is used. A high value of a are desired since it gives a high heat transfer for a given pressure drop.
3.5
T=300 K T=250 K T=200 K T=150 K T=80 K
3.0
dP/dX (MPa/m)
2.5 2.0 1.5 1.0 0.5 0.0 200
250
300
350
400
Mesh size Fig. 4. Pressure drop of fluid flowing through regenerator calculated from Eq. (3).
6
RPF (W/K-Pa)
5
T=300 K T=250 K T=200 K T=150 K T=80 K
4
3
2
1 200
250
300
350
Mesh size Fig. 5. RPFs calculated from the results of Figs. 3 and 4.
400
L.M. Qiu et al. / Cryogenics 47 (2007) 49–55
Fig. 6 shows the calculated curves of a based on Eq. (2) and empirical expression in Ref. [11] as a function of Reynolds number for different mesh sizes of stainless-steel screens. Calculated results show that when the mesh size is 247 higher heat transfer can be expected for a given pressure drop, which is similar with the results shown in Fig. 5.
0.030
0.025
295#
247#
397#
200#
α
0.020
0.015
0.010
0.005
40
80
120
160
200
Re Fig. 6. Curves of a as a function of Reynolds number for different mesh sizes of stainless-steel screens.
53
3.3. Experimental results Based on above analysis, we experimentally investigated the mesh size effect of stainless-steel woven wire screen on the performance of PTC. Three sets of experiments with different mesh sizes (247, 295 and 397, respectively) of stainless-steel screens were performed. For comparison and analysis, lead spheres and Er3Ni packed at the cold part remains unchanged. Figs. 7 and 8 show the mean pressure and pressure amplitude measured at the hot end of regenerator and pulse tube under the lowest attainable refrigeration temperature with the filling of 1.4 and 1.7 MPa, respectively. The mean pressure in the regenerator didn’t change much during three sets of experiments. The pressure ratio and pressure amplitude at the hot end of the regenerator increase with the increase of mesh size number, but at the hot end of the pulse tube they are biggest when the mesh size number is 295. As the pressure drop through pulse tube is very small, we can consider the pressure at the hot end of pulse tube as that of cold end. The difference of pressure ratio and amplitude between hot end of regenerator and pulse tube increases with the increase of mesh size, which indicates the pressure drop across regenerator increases with the increase of mesh size, coinciding with the results of Fig. 4. Figs. 9 and 10 give the cooling performance of the PTC. When the mesh size is 247, 295 and 397, respectively, the lowest no-load refrigeration temperature is 12.2, 11.1 and 11.3 K and the cooling capacity at 20 K is 15.7, 17.8 and 16.7 W, respectively. From Figs. 7 and 8 we can find the
Mean pressure (MPa)
Pressure amplitude (MPa)
Measured at the hot end of the regenerator Measured at the hot end of the pulse tube 0.6
0.5
0.4
0.3 240
260
280
300
320
340
360
380
400
320
340
360
380
400
1.4
1.3
1.2
Filling pressure: 1.4 MPa 1.1 240
260
280
300
Mesh size Fig. 7. Mean pressure and pressure amplitude measured at the hot end of regenerator and pulse tube under the lowest attainable refrigeration temperature with the filling of 1.4 MPa.
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L.M. Qiu et al. / Cryogenics 47 (2007) 49–55
Pressure amplitude (MPa)
Measured at the hot end of the regenerator Measured at the hot end of the pulse tube 0.60 0.55 0.50 0.45 0.40 240
260
280
300
320
340
360
380
400
320
340
360
380
400
Mean pressure (MPa)
1.60
1.55
1.50
Filling pressure: 1.7 MPa 1.45 240
260
280
300
Mesh size Fig. 8. Mean pressure and pressure amplitude measured at the hot end of regenerator and pulse tube under the lowest attainable refrigeration temperature with the filling of 1.7 MPa.
pressure ratio and pressure amplitude at the hot end of pulse tube, which can be regarded as the pressure of cold end of pulse tube, are biggest when the mesh size is 297. The performance of PTC increases with the increase of pressure ratio at the cold end of regenerator. The performance of PTC is optimum when the mesh size is 297. This result is a little deviated from the calculation results shown
in Fig. 5. We can conclude that increasing mesh size properly from 247 to 295 will increase friction factor and pressure drop loss, but the increase in heat transfer can more than offset a large friction factor increase. If we further increase the mesh size, the pressure drop across the regenerator will increase rapidly and the performance of regenerator and PTC will deteriorate.
Filling pressure: 1.4 MPa Filling pressure: 1.7 MPa Q @ 30 K (W)
40 38 36 34
Q @ 20 K (W)
32 18
240
260
280
300
320
340
360
380
400
240
260
280
300
320
340
360
380
400
240
260
280
300
320
340
360
380
400
17 16 15 14
T (K)
12.5 12.0 11.5 11.0
Mesh size Fig. 9. Cooling capacity comparisons of different mesh sizes of stainless-steel screens.
L.M. Qiu et al. / Cryogenics 47 (2007) 49–55
55
COP @ 30 K
6.2x10-3
6.0x10-3
5.8x10-3
5.6x10-3 250
300
350
400
COP @ 20 K
3.00x10-3
2.75x10-3
2.50x10-3
Filling pressure: 1.4 MPa Filling pressure: 1.7 MPa
2.25x10-3 250
300
350
400
Mesh size Fig. 10. COP comparisons of different mesh sizes of stainless-steel screens.
4. Conclusion The regenerator of a single-stage G-M type PTC was optimized to improve the efficiency at the temperature range of 80–300 K. Experiments show that the performance can be improved if we use stainless-steel screens other than phosphor–bronze screens. Regenerator performance factor (RPF) and a are introduced to evaluate the performance of regenerator for different mesh sizes of screen. Calculations show that 247 mesh stainless-steel screen can give optimum performance. The experimental results indicate that appropriately increase the mesh size to 295 can enhance the heat transfer capacity and improve the efficiency of regenerator with the pressure drop increased a little. After optimization a lowest no-load refrigeration temperature of 11.1 K was obtained with an input power of 6 kW. The cooling capacity and COP at 20 K are 17.8 W and 2.95 · 103. Acknowledgements This work was supported by the Science and Technology Department of Zhejiang Province, China under contract No. 2006C24G2010027 and Natural Sciences Foundation of Zhejiang Province, China under contract No. Y105519. References [1] Radebaugh R. The development and application of cryocoolers since 1985. In: Chen GB, Hebral B, Chen GM, editors. Proceedings of ICCR’ 2003. International Academic Publishers/Beijing World Publishing Corporation; 2003. p. 858–70.
[2] Tward E, Chan CK, Raab J, et al. High efficiency pulse tube cooler. In: Ronald Jr G Ross, editor. Cryocoolers 11. Kluwer Aademic/ Plenum Publishers; 2001. p. 163–7. [3] Jiang N, Lindemann U, Giebeler F, et al. A 3He pulse tube cooler operating down to 1.3 K. Cryogenics 2004;44:809–16. [4] Qiu LM, He YL, Gan ZH, et al. A separate two-stage pulse tube cooler working at liquid helium temperature. Chinese Sci Bull 2005;50:1030–3. [5] Haefner HU, Giebeler F, Thummes G. Einstufiger 25 K Pulsrohrkuehler fuer HTS-energie-applikationen. DKV-Tagungsbericht 2003:173–83. [6] http://www.cryomech.com/products.cfm?item_type=p&prod_id=9&op= one. [7] Radebaugh R, Marquardt E, Bradley P. Development of a pulse tube refrigerator for millimeter array sensor cooling: Phase I, ALMA Memo #281, 1999. [8] Qiu LM, He YL, Gan ZH, et al. A single-stag pulse tube cooler reached 12.6 K. Cryogenics 2005;45:641–3. [9] Bin-Nun U, Manitakos D. Low cost and high performance screen laminate regenerator matrix. Cryogenics 2004;44:439–44. [10] Ackermann Robert A. Cryogenic regenerative heat exchangers. New York: Plenum press; 1997. [11] Tanaka M, Yamshita I, Chrisaka F. Flow and heat transfer characteristics of the stirling engine regenerator in an oscillating flow. JSME Int J 1990;33:283–9. [12] Wang C, Thummes G, Heiden C. A two-stage pulse tube cooler operating below 4 K. Cryogenics 1997;37:159–64. [13] Chen GB, Qiu LM, Zhen JY, et al. Experimental study on a doubleorifice two-stage pulse tube refrigerator. Cryogenics 1997;37:271–3. [14] Jiang YL, Chen GB, Thummes G. Experimental investigation on DC flow control in a single-stage pulse tube refrigerator operating below 20 K. In: Chen GB, Hebral B, Chen GM, editors. Proceedings of ICCR’ 2003. International Academic Publishers/Beijing World Publishing Corporation; 2003. p. 77–80. [15] Radebaugh R, Louie B. A simple, First step to the optimization of regenerator geometry. In: Proceedings of the third cryocooler conference NBS special publication 698, Boulder, CO; 1985. p. 177–98.