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DC flow analysis and second orifice version pulse tube refrigerator
Cryogenics 39 (1999) 187–192
DC flow analysis and second orifice version pulse tube refrigerator Luwei Yang *, Yuan Zhou, Jingtao Liang Cryogenic Laboratory, Chinese Academy of Sciences, Post Box 2711, Beijing, 100080, People’s Republic of China Received 7 September 1998; accepted 4 February 1999
Abstract This paper analyzes direct current flow (DC flow) due to double-inlet, and introduces a second orifice version pulse tube refrigerator experiment to diminish DC flow. Analysis based on some assumptions shows that DC flow through the double-inlet valve in the pulse tube refrigerator is not generally zero, and the DC flow direction may change when the pressure wave changes. Thus, different schemes should be developed for different DC flow directions. In experiments, through measuring the change of temperature near the hot end of the pulse tube, DC flow direction different from former in pulse tube is decided. The second orifice is arranged from the second-stage reservoir to high pressure of the compressor, instead of the traditional arrangement of from the reservoir to low pressure. Experiments with the newly arranged second orifice show that the lowest temperature is about 4 K lower than without the second orifice. 1999 Elsevier Science Ltd. All rights reserved. Keywords: Pulse tube refrigerator; DC flow and its direction; Second orifice; Experiment
1. Introduction The development of the pulse tube refrigerator has been done very quickly, and the double-inlet version proposed by Zhu et al. in 1990 [1] became one of the most important improvements. In 1997, Professor Chen proposed the concept of a second-orifice or double-orifice [2] based on a doubleinlet, and acquired the lowest temperature of 3.02 K with a two-stage pulse tube refrigerator. His explanation was that the second orifice could pull heat from the pulse tube, for near the hot end part of the pulse tube the wall temperature is as high as about 350 K. This high temperature phenomenon is also described in [3,4], too. Earlier than the development of the second orifice, using a hot wire anemometer in experiments, Ju et al. observed flow rate imbalance at the cold end of the pulse tube when the double-inlet valve was open [5]. The imbalance means the mass flowing in is not equal to the mass flowing out. This flow rate imbalance resulting from the double-inlet valve is called DC flow, or net flow. Recently, Wang et al. analyzed the effect of DC flow on a 4 K pulse tube cryocooler [6].
* Corresponding author.
The present authors also found the possibility of flow rate imbalance resulting from a double-inlet in our research on a pulse tube refrigerator [7]. In this paper, DC flow in a double-inlet version pulse tube refrigerator is analyzed. In experiments, the DC flow problem is speculated and a different version of the second orifice is proposed to improve the performance of the pulse tube refrigerator. 2. Analysis 2.1. Amplitude and direction of DC flow Occurrence of DC flow in a pulse tube refrigerator has two prerequisites: One is a closed circuit, which is the result of opening the double inlet valve, as shown in Fig. 1. Regenerator, pulse tube and double-inlet valve form one circuit. The other is imbalance of the flow rate in a cycle or a period, which is theoretically possible at present. Assume that the pressure wave in a flow system is a sinusoidal wave with a second-order harmonic wave. Taking flow resistance into consideration, the pressures before and after regenerator pc(t) and ppt(t) can be written as: pc(t) = pave + pa1cos(t + ) + pa1cos(2t + )
0011-2275/99/$ - see front matter 1999 Elsevier Science Ltd. All rights reserved. PII: S 0 0 1 1 - 2 2 7 5 ( 9 9 ) 0 0 0 2 9 - 6
(1)
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L. Yang et al. / Cryogenics 39 (1999) 187–192
(5). Thus, in Eq. (5), due to the average high pressure flowing into the pulse tube from the inlet of the regenerator being on average higher than that of the reverse process, the net flow amount in a whole period is not generally zero. For convenience, the net flow or DC flow resulting from the double-inlet is defined as follows: ⌬d ⫽ 2养md dt/养兩md兩 dt
Fig. 1.
DC flow in a double-inlet version PTR and pressure waves.
ppt(t) ⫽ pave ⫹ pa2cos(t) ⫹ pa2cos(2t)
(2)
where pave is the average pressure, pa1 and pa2 the amplitude of fundamental wave respectively for pc(t) and ppt(t), the angular frequency, and  the coefficient of second-order harmonic wave. ⫽ cos−1(pa2/pa1) is phase difference between two pressure waves. This result is deduced from three assumptions: (a) quasi-steady state, that is “gas can only flow from high pressure toward low pressure”, (b) closure of orifice, and (c) closure of double-inlet valve. These pressures and their relation are as shown in Fig. 1. When the orifice is open, may diminish and such a change will not affect the analysis result in this paper. The steady state flow formula through the double-inlet valve due to pressure difference is as follows: md ⫽ ·⑀·A√2H(pH ⫺ pL)
冪
⫽ ·⑀·A ⫽ ·⑀·A
2
(3)
(4)
where md is the transient flow rate through the doubleinlet valve, the flow coefficient, ⑀ the coefficient due to gas compressibility, A the flow area, H the gas density of high pressure, pH high-pressure, and pL low pressure. Neglect the change of flow coefficient , ⑀ and the temperature, and the mass flow of the double-inlet is in direct proportion to √2pH(pH ⫺ pL): md⬀√2pH(pH ⫺ pL)
in which, let’s define md as positive when pc > ppt, and negative when pc ⬍ ppt, then positive ⌬d means the DC flow is from the regenerator to the pulse tube through the double-inlet valve, and negative ⌬d from the pulse tube to the regenerator. On the basis of the above analysis, calculation is carried out and the results are as follows: For  ⫽ 0, fundamental wave, the authors find that (a) ⌬d is always larger than 0. (b) When pa2/pa1 decreases, ⌬d increases; when pressure ratio is 1.5 for pc(t) and pa2/pa1 is near 0, the largest value of ⌬d is about 6.8%. A group of typical results is shown in Fig. 2(a). The upper two curves are two pressure waves and their phase difference. The lower curve shows the change of flow rate md. In the flow rate curve, the average value is given, which is a little larger than 0. (Note: in Fig. 2, pressures and flow rate have no dimension.) (c) In order to eliminate this flow imbalance, average pressure in the pulse tube is increased to make ⌬d ⫽ 0. At the limit condition pa2/pa1 ⫽ 0, the increase of average pressure in the pulse tube is within 0.5% of average pressure. In fact, pressures are generally not fundamental sinusoidal waves, so  is considered and the calculation result shows:
pH (p ⫺ pL) RT H
pave √2pH/pave·(pH ⫺ pL)/pave √RT
(6)
(5)
As shown in Fig. 1, a cycle is divided into two parts, A and B. The average pressure of pc in part A is larger than that of ppt in part B, and these two average pressures are pH when calculating the mass flow in Eqs. (4) and
(a) When  increases, ⌬d decreases, evidently. When  is about 0.10–0.20, ⌬d becomes 0. (b) Compared to Fig. 2(a), a typical result is shown in Fig. 2(b). Curves of pressure waves and flow rate are a little changed, and the average flow rate is smaller than 0. In order to further explain this phenomenon, a curve of ⌬d versus  is shown in Fig. 3. ⌬d changes from greater than 0 to smaller than 0 as  increases. (c) ⌬d ⬍ 0 means that the DC flow direction may change when the pressure wave form changes. (d) There are three factors leading to the direction change of ⌬d. Two are the times of parts A and B in Fig. 1 are unbalanced and the time for part B is longer, the average pressure of part B is increased; the square root in Eq. (5) diminishes the flow imbalance. The above calculation shows: (1) generally, ⌬d is
L. Yang et al. / Cryogenics 39 (1999) 187–192
Fig. 2.
189
Calculated pressure waves and flow rates. (a) Waves with  ⫽ 0; (b) waves with ⫽0.
With the double-inlet open, though DC flow may exist, but due to potential average pressure change and flow resistance of the double-inlet valve and regenerator, net flow should be very small. Even if a very small DC flow exists, its effect on performance of a pulse tube cooler is quite great. Suppose that ⌬d flows to the hot end or the cold end of a pulse tube directly, then loss of heat due to temperature difference will be: ⌬Qc ⫽ 养兩md兩 dt·⌬d/2·(Th ⫺ tc)·Cp
(7)
The cooling capacity of the pulse tube is: ˙ c ⫽ mc·⌬Tc·Cp Q
Fig. 3. Effect of  on ⌬d.
greater than 0, but smaller than 7%; (2) the existing condition of  or the pressure of another irregular form, may change the direction of ⌬d to negative. Though the above results are simple and based on some assumptions, they explain the essence of DC flow and its features. 2.2. DC flow’s effect on the performance of a pulse tube cooler For a pulse tube refrigeration system without a double-inlet (no closed circuit), it is impossible to get DC flow at the cold end of the pulse tube. But the flow resistance of the regenerator still exists. If the net flow is not zero, average pressure would change to make up the difference automatically.
(8)
where mc is the cold tip average flow rate and ⌬Tc is the average temperature difference between the temperature of the gas flowing into the pulse tube and the temperature of the gas flowing out of the pulse tube. Then: ⌬Qc/Qc ⫽ ⌬d/2·养兩md兩 dt/mc·(Th ⫺ Tc)/⌬Tc
(9)
The heat loss will be rather large when the refrigeration temperature is as low as 80 K.
3. Experiments and analysis If DC flow exists, and once its direction is decided, a suitable design of second orifice may diminish it or make the DC flow amount smaller. It is speculated that the too high temperature or too low temperature near the pulse tube hot end with doubleinlet opening is caused by the DC flow, and a second orifice is a good method to improve it. Thus, the authors
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measured the temperature near the hot end of the pulse tube. The following is the authors’ experiment on this issue. 3.1. Experiment system and measurement The pulse tube refrigerator is driven by a nominal 2.2 kW G-M compressor. A two-stage separate-version pulse tube refrigerator is set up as in Fig. 4. The main dimensions are as follows: Second-stage regenerator including two parts, the first part is a 28 mm outside diameter, 0.45 mm thick wall, 120 mm long stainless steel tube, filled with 250 mesh stainless steel screen; the other part is a 24.4 mm outside diameter, 0.2 mm thick wall, 80 mm long stainless steel tube, filled with 0.2–0.3 mm diameter Pb. Second-stage pulse tube is an 18.4 mm outside diameter, 0.2 mm thick wall, and 200 mm long stainless steel tube. The first-stage regenerator is a 28 mm outside diameter, 0.45 mm thick wall, 120 mm long stainless steel tube, filled with 250 mesh stainless steel screen; first-stage pulse tube is the same as the second-stage pulse tube. In experiments, the main parameters measured include: 1. The temperatures at the cold tip Tc, at the middle of the regenerator Tm, 60 mm from the hot end of pulse tube Th, as shown in Fig. 4. These temperatures were measured by gold–iron or copper–constantan ( > 50 K) thermocouple, calibrated by the Cryogenics Temperature Calibration Station, Chinese Academy of Sciences. 2. Pressure wave amplitude, including average pressure, high pressure and low pressure, and pressure wave. The pressure was measured through a pressure transducer, and was shown using an HP 54602B Oscilloscope. 3. Operation frequency, recorded through an Oscilloscope. 4. Cooling capacity, using HP6634A system DC power supply (0–100 V/0–1 A, 100 W). 5. Vacuum degree, Generally 1.5–2 Pa.
Fig. 4.
A separated version two-stage pulse tube refrigerator.
3.2. Experiment and analysis On the basis of the above-said analysis, the effect of the second-stage double-inlet valve on the hot end temperature Th is measured as shown in Fig. 5. Before the opening of the double-inlet, Th and Tc are 180 K and 35 K, respectively. When the double-inlet is opened to 1.2 turns (one turn means one circle), Th reaches its highest value of 200 K; when the double inlet opens further, Th begins to drop quickly, and when the double-inlet valve stays at 2.4 turns, Th ⫽ 90 K. And the lowest temperature of Tc is 22.5 K when the double-inlet valve stays at 2.0 turns. Through Fig. 5, it can be concluded that the direction of the DC flow should be from the cold tip of the pulse tube to the hot end, because cold gas flows to the hot end of the pulse tube to lower the wall temperature. Thus, in Fig. 4, the connection of the second-stage reservoir and high-pressure pipe of the compressor forms the typical second orifice. This is different from that in reference [2], where the connection is between the second-stage reservoir and the low-pressure pipe of the compressor. An experiment with this new second orifice valve were carried out. In the experiment, Th is a main controlling parameter. When the second orifice opens, Th evidently increases, and with a small change of the second orifice valve, the change of Th may change from 200 K to 350 K. This means that a small DC flow has a large effect on the wall temperature distribution. When Th is higher than room temperature, and the double-inlet valve is opened further, Th will drop. Through continuous adjustment of the double-inlet valve and the second orifice valve, Th can be adjusted to about 300 K. The final opening status of valves were double-inlet 5 turns, and second orifice 13/50 turn. And without the second
Fig. 5. Effect of the double-inlet on the hot end temperature of the second-stage pulse tube.
L. Yang et al. / Cryogenics 39 (1999) 187–192
orifice, the double-inlet valve shows the best performance at 2 turns, as shown in Fig. 5. (Note: this paragraph has no figure explanation, but experimental phenomena are depicted and the result is given.) After adjusting the second orifice, several groups of results were obtained. They show the effect of this newly arranged second orifice. Firstly, the stability of the second orifice is tested. As shown in Fig. 6(a), cooling down curves of temperatures are given. It is clear that the hot end temperature Th rises to 410 K quickly in 5 minutes, then it drops slowly to near 300 K. And for the cold tip temperature, in 40 minutes Tc reached 20 K, and finally Tc reached the lowest temperature of 18.7 K. This means the second orifice is stable in lowering the refrigeration temperature further. For the purpose of comparison, cooling down curves of temperatures without a second orifice are shown in
191
Fig. 7. A typical characteristics curve of a second orifice valve’s effect on temperature.
Fig. 6(b). Obviously, the cooling down rate is faster than that with the second orifice open. The final temperature is 22.5 K for Tc and 205 K for Th. Another test to verify the second orifice is shown in Fig. 7. With the second orifice closed and the doubleinlet at 5 turns, the compressor is started. In the first 15 minutes, Tc and Th reach 50 K and 140 K, respectively. In the second 15 minutes, Tc and Th gradually rise by about 10 K. At about the 31st minute, the second orifice is opened to its best value of 13/50 turn, and Th rises to 350 K quickly, then drops gradually to 300 K. Tc also drops quickly at the beginning, then slowly, and reaches 18.7 K at last. The final results of the temperatures are same as Fig. 6(a). Cooling performance is very important to a cryocooler. Experimental results are shown in Fig. 8. For the double-inlet version, the temperature rises 4 K for 2 W, and for the second orifice version, temperature rises
Fig. 6. Two cooling down curves, with and without the second orifice.
Fig. 8.
Refrigeration capacity change versus temperature.
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L. Yang et al. / Cryogenics 39 (1999) 187–192
1. The second orifice is effective to lower the temperature if DC flow exists; 2. The second orifice should be arranged according to DC flow direction; 3. The second orifice in this experiment has a negative effect on cooling capacity.
4. Conclusion Analysis of a pulse tube refrigerator shows that by opening the double-inlet valve, the DC flow will occur in a circuit of a pulse tube, regenerator and double-inlet valve. For a one-order sinusoidal wave, direction of the DC flow is from the hot end of the pulse tube to the cold end; but in the case of a second-order harmonics sinusoidal wave, the DC flow direction may be changed. Through experiments, the possible direction of the DC flow is decided, and a different second orifice is arranged to connect the second-stage reservoir to the high pressure part of the compressor, instead of as traditionally connecting the reservoir to the low pressure part of the compressor. Tests show that using this arrangement of second orifice, the DC flow can be suppressed and the cold tip temperature can be lowered further. Acknowledgements This research was supported by the National Superconductor Center of China, No. 863-CD040201 and National Natural Science Fund, No. 59636190. Fig. 9.
Pressure waves in the experiments.
References 5.6 K for 2 W. The reason for this different temperature rise at the same cooling capacity needs further research. But it is clear that the difference is due to the second orifice. Pressure waves were measured during the experiments, as shown in Fig. 9. The relatively larger one is that before the regenerator pc, and the smaller one is that in the hot end of the second stage pulse tube ppt2. With the cold tip temperature dropping, the pressure wave obviously changes, and the pressure ratio decreases and the curve becomes smooth. In all cases, the pressure wave is different from the calculated pressure. From these experiments, the following conclusions can be drawn:
[1] Zhu S, Wu P, Chen Z. Double inlet pulse tube refrigerators: an important improvement. Cryogenics 1990;30:514. [2] Chen G, Qui L, Zheng J, Yan P, Gan Z, Bai X, Huang Z. Experimental study on a double-orifice two-stage pulse tube refrigerator. Cryogenics 1997;37:271. [3] Gao J, Matsubara Y. Experimental investigation of 4 K pulse tube refrigerator. Cryogenics 1994;34:25. [4] Wang C, Ju YL, Zhou Y. The experimental investigation of a twostage pulse tube refrigerator. Cryogenics 1996;36:605. [5] Ju YL, Wang C, Zhou Y. Dynamic experimental investigation of a multi-bypass pulse tube refrigerator. Cryogenics 1997;37:357. [6] Wang C, Thummes G, Heiden C. Effects of DC gas flow on performance of two-stage 4 K pulse tube coolers. Cryogenics 1998;38:689. [7] Yang LW, Zhou Y, Liang JT. Analysis, experiment and improvement of double-inlet version pulse tube refrigerator. J of Engineering Thermophysics (China) 1999;20(2):147.
DC flow analysis and second orifice version pulse tube refrigerator Luwei Yang *, Yuan Zhou, Jingtao Liang Cryogenic Laboratory, Chinese Academy of Sciences, Post Box 2711, Beijing, 100080, People’s Republic of China Received 7 September 1998; accepted 4 February 1999
Abstract This paper analyzes direct current flow (DC flow) due to double-inlet, and introduces a second orifice version pulse tube refrigerator experiment to diminish DC flow. Analysis based on some assumptions shows that DC flow through the double-inlet valve in the pulse tube refrigerator is not generally zero, and the DC flow direction may change when the pressure wave changes. Thus, different schemes should be developed for different DC flow directions. In experiments, through measuring the change of temperature near the hot end of the pulse tube, DC flow direction different from former in pulse tube is decided. The second orifice is arranged from the second-stage reservoir to high pressure of the compressor, instead of the traditional arrangement of from the reservoir to low pressure. Experiments with the newly arranged second orifice show that the lowest temperature is about 4 K lower than without the second orifice. 1999 Elsevier Science Ltd. All rights reserved. Keywords: Pulse tube refrigerator; DC flow and its direction; Second orifice; Experiment
1. Introduction The development of the pulse tube refrigerator has been done very quickly, and the double-inlet version proposed by Zhu et al. in 1990 [1] became one of the most important improvements. In 1997, Professor Chen proposed the concept of a second-orifice or double-orifice [2] based on a doubleinlet, and acquired the lowest temperature of 3.02 K with a two-stage pulse tube refrigerator. His explanation was that the second orifice could pull heat from the pulse tube, for near the hot end part of the pulse tube the wall temperature is as high as about 350 K. This high temperature phenomenon is also described in [3,4], too. Earlier than the development of the second orifice, using a hot wire anemometer in experiments, Ju et al. observed flow rate imbalance at the cold end of the pulse tube when the double-inlet valve was open [5]. The imbalance means the mass flowing in is not equal to the mass flowing out. This flow rate imbalance resulting from the double-inlet valve is called DC flow, or net flow. Recently, Wang et al. analyzed the effect of DC flow on a 4 K pulse tube cryocooler [6].
* Corresponding author.
The present authors also found the possibility of flow rate imbalance resulting from a double-inlet in our research on a pulse tube refrigerator [7]. In this paper, DC flow in a double-inlet version pulse tube refrigerator is analyzed. In experiments, the DC flow problem is speculated and a different version of the second orifice is proposed to improve the performance of the pulse tube refrigerator. 2. Analysis 2.1. Amplitude and direction of DC flow Occurrence of DC flow in a pulse tube refrigerator has two prerequisites: One is a closed circuit, which is the result of opening the double inlet valve, as shown in Fig. 1. Regenerator, pulse tube and double-inlet valve form one circuit. The other is imbalance of the flow rate in a cycle or a period, which is theoretically possible at present. Assume that the pressure wave in a flow system is a sinusoidal wave with a second-order harmonic wave. Taking flow resistance into consideration, the pressures before and after regenerator pc(t) and ppt(t) can be written as: pc(t) = pave + pa1cos(t + ) + pa1cos(2t + )
0011-2275/99/$ - see front matter 1999 Elsevier Science Ltd. All rights reserved. PII: S 0 0 1 1 - 2 2 7 5 ( 9 9 ) 0 0 0 2 9 - 6
(1)
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L. Yang et al. / Cryogenics 39 (1999) 187–192
(5). Thus, in Eq. (5), due to the average high pressure flowing into the pulse tube from the inlet of the regenerator being on average higher than that of the reverse process, the net flow amount in a whole period is not generally zero. For convenience, the net flow or DC flow resulting from the double-inlet is defined as follows: ⌬d ⫽ 2养md dt/养兩md兩 dt
Fig. 1.
DC flow in a double-inlet version PTR and pressure waves.
ppt(t) ⫽ pave ⫹ pa2cos(t) ⫹ pa2cos(2t)
(2)
where pave is the average pressure, pa1 and pa2 the amplitude of fundamental wave respectively for pc(t) and ppt(t), the angular frequency, and  the coefficient of second-order harmonic wave. ⫽ cos−1(pa2/pa1) is phase difference between two pressure waves. This result is deduced from three assumptions: (a) quasi-steady state, that is “gas can only flow from high pressure toward low pressure”, (b) closure of orifice, and (c) closure of double-inlet valve. These pressures and their relation are as shown in Fig. 1. When the orifice is open, may diminish and such a change will not affect the analysis result in this paper. The steady state flow formula through the double-inlet valve due to pressure difference is as follows: md ⫽ ·⑀·A√2H(pH ⫺ pL)
冪
⫽ ·⑀·A ⫽ ·⑀·A
2
(3)
(4)
where md is the transient flow rate through the doubleinlet valve, the flow coefficient, ⑀ the coefficient due to gas compressibility, A the flow area, H the gas density of high pressure, pH high-pressure, and pL low pressure. Neglect the change of flow coefficient , ⑀ and the temperature, and the mass flow of the double-inlet is in direct proportion to √2pH(pH ⫺ pL): md⬀√2pH(pH ⫺ pL)
in which, let’s define md as positive when pc > ppt, and negative when pc ⬍ ppt, then positive ⌬d means the DC flow is from the regenerator to the pulse tube through the double-inlet valve, and negative ⌬d from the pulse tube to the regenerator. On the basis of the above analysis, calculation is carried out and the results are as follows: For  ⫽ 0, fundamental wave, the authors find that (a) ⌬d is always larger than 0. (b) When pa2/pa1 decreases, ⌬d increases; when pressure ratio is 1.5 for pc(t) and pa2/pa1 is near 0, the largest value of ⌬d is about 6.8%. A group of typical results is shown in Fig. 2(a). The upper two curves are two pressure waves and their phase difference. The lower curve shows the change of flow rate md. In the flow rate curve, the average value is given, which is a little larger than 0. (Note: in Fig. 2, pressures and flow rate have no dimension.) (c) In order to eliminate this flow imbalance, average pressure in the pulse tube is increased to make ⌬d ⫽ 0. At the limit condition pa2/pa1 ⫽ 0, the increase of average pressure in the pulse tube is within 0.5% of average pressure. In fact, pressures are generally not fundamental sinusoidal waves, so  is considered and the calculation result shows:
pH (p ⫺ pL) RT H
pave √2pH/pave·(pH ⫺ pL)/pave √RT
(6)
(5)
As shown in Fig. 1, a cycle is divided into two parts, A and B. The average pressure of pc in part A is larger than that of ppt in part B, and these two average pressures are pH when calculating the mass flow in Eqs. (4) and
(a) When  increases, ⌬d decreases, evidently. When  is about 0.10–0.20, ⌬d becomes 0. (b) Compared to Fig. 2(a), a typical result is shown in Fig. 2(b). Curves of pressure waves and flow rate are a little changed, and the average flow rate is smaller than 0. In order to further explain this phenomenon, a curve of ⌬d versus  is shown in Fig. 3. ⌬d changes from greater than 0 to smaller than 0 as  increases. (c) ⌬d ⬍ 0 means that the DC flow direction may change when the pressure wave form changes. (d) There are three factors leading to the direction change of ⌬d. Two are the times of parts A and B in Fig. 1 are unbalanced and the time for part B is longer, the average pressure of part B is increased; the square root in Eq. (5) diminishes the flow imbalance. The above calculation shows: (1) generally, ⌬d is
L. Yang et al. / Cryogenics 39 (1999) 187–192
Fig. 2.
189
Calculated pressure waves and flow rates. (a) Waves with  ⫽ 0; (b) waves with ⫽0.
With the double-inlet open, though DC flow may exist, but due to potential average pressure change and flow resistance of the double-inlet valve and regenerator, net flow should be very small. Even if a very small DC flow exists, its effect on performance of a pulse tube cooler is quite great. Suppose that ⌬d flows to the hot end or the cold end of a pulse tube directly, then loss of heat due to temperature difference will be: ⌬Qc ⫽ 养兩md兩 dt·⌬d/2·(Th ⫺ tc)·Cp
(7)
The cooling capacity of the pulse tube is: ˙ c ⫽ mc·⌬Tc·Cp Q
Fig. 3. Effect of  on ⌬d.
greater than 0, but smaller than 7%; (2) the existing condition of  or the pressure of another irregular form, may change the direction of ⌬d to negative. Though the above results are simple and based on some assumptions, they explain the essence of DC flow and its features. 2.2. DC flow’s effect on the performance of a pulse tube cooler For a pulse tube refrigeration system without a double-inlet (no closed circuit), it is impossible to get DC flow at the cold end of the pulse tube. But the flow resistance of the regenerator still exists. If the net flow is not zero, average pressure would change to make up the difference automatically.
(8)
where mc is the cold tip average flow rate and ⌬Tc is the average temperature difference between the temperature of the gas flowing into the pulse tube and the temperature of the gas flowing out of the pulse tube. Then: ⌬Qc/Qc ⫽ ⌬d/2·养兩md兩 dt/mc·(Th ⫺ Tc)/⌬Tc
(9)
The heat loss will be rather large when the refrigeration temperature is as low as 80 K.
3. Experiments and analysis If DC flow exists, and once its direction is decided, a suitable design of second orifice may diminish it or make the DC flow amount smaller. It is speculated that the too high temperature or too low temperature near the pulse tube hot end with doubleinlet opening is caused by the DC flow, and a second orifice is a good method to improve it. Thus, the authors
190
L. Yang et al. / Cryogenics 39 (1999) 187–192
measured the temperature near the hot end of the pulse tube. The following is the authors’ experiment on this issue. 3.1. Experiment system and measurement The pulse tube refrigerator is driven by a nominal 2.2 kW G-M compressor. A two-stage separate-version pulse tube refrigerator is set up as in Fig. 4. The main dimensions are as follows: Second-stage regenerator including two parts, the first part is a 28 mm outside diameter, 0.45 mm thick wall, 120 mm long stainless steel tube, filled with 250 mesh stainless steel screen; the other part is a 24.4 mm outside diameter, 0.2 mm thick wall, 80 mm long stainless steel tube, filled with 0.2–0.3 mm diameter Pb. Second-stage pulse tube is an 18.4 mm outside diameter, 0.2 mm thick wall, and 200 mm long stainless steel tube. The first-stage regenerator is a 28 mm outside diameter, 0.45 mm thick wall, 120 mm long stainless steel tube, filled with 250 mesh stainless steel screen; first-stage pulse tube is the same as the second-stage pulse tube. In experiments, the main parameters measured include: 1. The temperatures at the cold tip Tc, at the middle of the regenerator Tm, 60 mm from the hot end of pulse tube Th, as shown in Fig. 4. These temperatures were measured by gold–iron or copper–constantan ( > 50 K) thermocouple, calibrated by the Cryogenics Temperature Calibration Station, Chinese Academy of Sciences. 2. Pressure wave amplitude, including average pressure, high pressure and low pressure, and pressure wave. The pressure was measured through a pressure transducer, and was shown using an HP 54602B Oscilloscope. 3. Operation frequency, recorded through an Oscilloscope. 4. Cooling capacity, using HP6634A system DC power supply (0–100 V/0–1 A, 100 W). 5. Vacuum degree, Generally 1.5–2 Pa.
Fig. 4.
A separated version two-stage pulse tube refrigerator.
3.2. Experiment and analysis On the basis of the above-said analysis, the effect of the second-stage double-inlet valve on the hot end temperature Th is measured as shown in Fig. 5. Before the opening of the double-inlet, Th and Tc are 180 K and 35 K, respectively. When the double-inlet is opened to 1.2 turns (one turn means one circle), Th reaches its highest value of 200 K; when the double inlet opens further, Th begins to drop quickly, and when the double-inlet valve stays at 2.4 turns, Th ⫽ 90 K. And the lowest temperature of Tc is 22.5 K when the double-inlet valve stays at 2.0 turns. Through Fig. 5, it can be concluded that the direction of the DC flow should be from the cold tip of the pulse tube to the hot end, because cold gas flows to the hot end of the pulse tube to lower the wall temperature. Thus, in Fig. 4, the connection of the second-stage reservoir and high-pressure pipe of the compressor forms the typical second orifice. This is different from that in reference [2], where the connection is between the second-stage reservoir and the low-pressure pipe of the compressor. An experiment with this new second orifice valve were carried out. In the experiment, Th is a main controlling parameter. When the second orifice opens, Th evidently increases, and with a small change of the second orifice valve, the change of Th may change from 200 K to 350 K. This means that a small DC flow has a large effect on the wall temperature distribution. When Th is higher than room temperature, and the double-inlet valve is opened further, Th will drop. Through continuous adjustment of the double-inlet valve and the second orifice valve, Th can be adjusted to about 300 K. The final opening status of valves were double-inlet 5 turns, and second orifice 13/50 turn. And without the second
Fig. 5. Effect of the double-inlet on the hot end temperature of the second-stage pulse tube.
L. Yang et al. / Cryogenics 39 (1999) 187–192
orifice, the double-inlet valve shows the best performance at 2 turns, as shown in Fig. 5. (Note: this paragraph has no figure explanation, but experimental phenomena are depicted and the result is given.) After adjusting the second orifice, several groups of results were obtained. They show the effect of this newly arranged second orifice. Firstly, the stability of the second orifice is tested. As shown in Fig. 6(a), cooling down curves of temperatures are given. It is clear that the hot end temperature Th rises to 410 K quickly in 5 minutes, then it drops slowly to near 300 K. And for the cold tip temperature, in 40 minutes Tc reached 20 K, and finally Tc reached the lowest temperature of 18.7 K. This means the second orifice is stable in lowering the refrigeration temperature further. For the purpose of comparison, cooling down curves of temperatures without a second orifice are shown in
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Fig. 7. A typical characteristics curve of a second orifice valve’s effect on temperature.
Fig. 6(b). Obviously, the cooling down rate is faster than that with the second orifice open. The final temperature is 22.5 K for Tc and 205 K for Th. Another test to verify the second orifice is shown in Fig. 7. With the second orifice closed and the doubleinlet at 5 turns, the compressor is started. In the first 15 minutes, Tc and Th reach 50 K and 140 K, respectively. In the second 15 minutes, Tc and Th gradually rise by about 10 K. At about the 31st minute, the second orifice is opened to its best value of 13/50 turn, and Th rises to 350 K quickly, then drops gradually to 300 K. Tc also drops quickly at the beginning, then slowly, and reaches 18.7 K at last. The final results of the temperatures are same as Fig. 6(a). Cooling performance is very important to a cryocooler. Experimental results are shown in Fig. 8. For the double-inlet version, the temperature rises 4 K for 2 W, and for the second orifice version, temperature rises
Fig. 6. Two cooling down curves, with and without the second orifice.
Fig. 8.
Refrigeration capacity change versus temperature.
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L. Yang et al. / Cryogenics 39 (1999) 187–192
1. The second orifice is effective to lower the temperature if DC flow exists; 2. The second orifice should be arranged according to DC flow direction; 3. The second orifice in this experiment has a negative effect on cooling capacity.
4. Conclusion Analysis of a pulse tube refrigerator shows that by opening the double-inlet valve, the DC flow will occur in a circuit of a pulse tube, regenerator and double-inlet valve. For a one-order sinusoidal wave, direction of the DC flow is from the hot end of the pulse tube to the cold end; but in the case of a second-order harmonics sinusoidal wave, the DC flow direction may be changed. Through experiments, the possible direction of the DC flow is decided, and a different second orifice is arranged to connect the second-stage reservoir to the high pressure part of the compressor, instead of as traditionally connecting the reservoir to the low pressure part of the compressor. Tests show that using this arrangement of second orifice, the DC flow can be suppressed and the cold tip temperature can be lowered further. Acknowledgements This research was supported by the National Superconductor Center of China, No. 863-CD040201 and National Natural Science Fund, No. 59636190. Fig. 9.
Pressure waves in the experiments.
References 5.6 K for 2 W. The reason for this different temperature rise at the same cooling capacity needs further research. But it is clear that the difference is due to the second orifice. Pressure waves were measured during the experiments, as shown in Fig. 9. The relatively larger one is that before the regenerator pc, and the smaller one is that in the hot end of the second stage pulse tube ppt2. With the cold tip temperature dropping, the pressure wave obviously changes, and the pressure ratio decreases and the curve becomes smooth. In all cases, the pressure wave is different from the calculated pressure. From these experiments, the following conclusions can be drawn:
[1] Zhu S, Wu P, Chen Z. Double inlet pulse tube refrigerators: an important improvement. Cryogenics 1990;30:514. [2] Chen G, Qui L, Zheng J, Yan P, Gan Z, Bai X, Huang Z. Experimental study on a double-orifice two-stage pulse tube refrigerator. Cryogenics 1997;37:271. [3] Gao J, Matsubara Y. Experimental investigation of 4 K pulse tube refrigerator. Cryogenics 1994;34:25. [4] Wang C, Ju YL, Zhou Y. The experimental investigation of a twostage pulse tube refrigerator. Cryogenics 1996;36:605. [5] Ju YL, Wang C, Zhou Y. Dynamic experimental investigation of a multi-bypass pulse tube refrigerator. Cryogenics 1997;37:357. [6] Wang C, Thummes G, Heiden C. Effects of DC gas flow on performance of two-stage 4 K pulse tube coolers. Cryogenics 1998;38:689. [7] Yang LW, Zhou Y, Liang JT. Analysis, experiment and improvement of double-inlet version pulse tube refrigerator. J of Engineering Thermophysics (China) 1999;20(2):147.