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Study on pulse tube refrigeration Part 3: Experimental verification
Cryogenics 36 (1996) 101-106 0 1996 Elsevier Science Limited Printed in Great Britain. All rights reserved OOII-2275/96/$15.00 ELSEVIER
Study on pulse tube refrigeration Part 3: Experimental verification J. Liang*,
A. Ravex
and P. Roland
Service des Basses Temperatures, Centre d’Etudes des Martyrs, 38054 Grenoble, Cedex 9, France Received 8 May
Nucleaires
de Grenoble,
17 rue
1995
A large number of experiments have been systematically carried out in order to validate the theoretical model described in the preceding parts of this study. The influences of the important parameters, including opening of the orifice and double-inlet valve, frequency, average pressure, pressure oscillation amplitude in the pulse tube, and the diameter of the pulse tube on the refrigeration performance are intensively investigated. The cold end temperature and the net cooling power at 100 K are used as criteria of refrigeration performance. Real-time measurements of gas temperature and pressure at various positions in the pulse tube refrigerator are performed in order to reveal the internal physical processes. The experimental results are found to be in good agreement with the theoretical predictions. Keywords:
pulse tube; refrigeration
Tc2
Nomenclature f P&i” PB
P DR P ER P -.. ?I?
P.ST
QF
TC T,,
Frequency (Hz) Average pressure (bar) Pressure in gas reservoir (bar) Pressure drop across regenerator (bar) Pressure at hot end of regenerator (bar) Pressure at cold end of regenerator (bar) Pressure at hot end of pulse tube (bar) Net cooling power (W) Cold end temperature of pulse tube (K) Gas temperature at hot end of regenerator
Tc3 Tc4
V1 V,
Greek letters (K)
In the previous two parts of this study, we have developed a theoretical model for pulse tube refrigerators. Such a model is not utilizable before it is experimentally verified for a wide range of parameters. In this paper we present the experiments conducted to validate the theoretical model’. The experimental results are analysed and compared with the corresponding theoretical results.
Experimental
apparatus
An experimental apparatus has been constructed in order to experimentally investigate the pulse tube refrigerator and verify the theoretical model. A general view of the exper-
*Present address: Cryogenic Laboratory, Chinese Academy Sciences, PO Box 2711, Beijing 100080, China
Gas temperature at cold end of regenerator (K) Gas temperature at cold end of pulse tube (K) Gas temperature at hot end of pulse tube (K) Opening of orifice (turns) Opening of double-inlet valve (turns)
of
6 AP
Thickness of thermal viscous layer (m) Pressure amplitude in pulse tube (bar)
imental apparatus is given in Figure I. The important components are illustrated in detail. The whole apparatus comprises mainly two systems: refrigeration and measurement. The refrigeration system (pulse tube refrigerator) includes the pressure wave generator, regenerator, pulse tube, cold and hot end heat exchangers, orifice, double-inlet valve, gas reservoir, and connecting tubing. The working fluid is helium gas. Two kinds of pressure wave generator were used in the experiments: one is a helium compressor with a rotatory or electromagnetic gas distributor; the other is a directly coupled compressor, with no gas distribution devices. The regenerator used in the experiments is a stainless steel tube of 18 mm internal diameter (i.d.), 19 mm external diameter (e.d.), and 170 mm in length, filled with stainless steel screens. The three pulse tubes tested are all 200 mm long thin-walled stainless steel tubes: 1, 19.5 mm i.d., 20mm e.d.; 2, 14mm i.d., 15 mm e.d; and 3, 10mm
Cryogenics
1996 Volume
36, Number
2
101
Pulse tube refrigeration.
Part 3: J. Liang et al.
i ?as reservoir Zooling water I
pressures. A resistor of 48 a, attached to the cold end copper block, is used to supply heating power to the cold end heat exchanger of the pulse tube. When the temperature of the cold end block is stabilized, the heating power provided by the heater is equivalent to the net cooling power of the pulse tube. To measure the compression power in the case of a directly coupled compressor, a pressure sensor and a displacement sensor are used. The pressure-volume (P-V) relationship of the compressor is recorded using a digital oscilloscope.
Results and discussions Regenerator
Pulse tube
Heat exchanger Heater
Figure 1
Experimental
apparatus
i.d., 10.4 mm e.d. At each end of the pulse tubes, about 40 copper gauze discs are brazed in a copper block for both flow straightening and heat exchange. A coiled water-conducting copper tube is soldered around the hot end copper block in order to maintain a constant temperature. The regenerator, pulse tube, and other low temperature parts are placed in a cylindrical vacuum vessel, in which a low pressure of 1 x 1O-5-1 x 10m6mbar is maintained for thermal insulation from the environment. The thermal insulation is further improved by the installation of a radiation screen composed of = 10 layers of aluminized polyester film. Two identical continuously adjustable needle valves serve as the orifice and the double-inlet valve. A stainless steel container of 300 cm3 volume is used as the gas reservoir. A valve is annexed to it for the purpose of system purging. The measurement system includes devices to measure pressure, temperature, and the net cooling power. It also includes measurement devices for compression power, in the case of a directly coupled compressor. As shown in Figure 1, PER, PSR, P,,, and PB are measured with piezoesistive pressure sensors; P,, is measured with a differential piezoresistive pressure sensor. Temperature measurements of the system include static and dynamic temperature measurements. Platinum and carbon resistance thermometers are inserted in the copper block of the cold end heat exchanger in order to detect the cold end temperature. Similarly, a platinum thermometer is used to measure the wall temperature of the hot end heat exchanger. Another 10 platinum thermometers are employed in order to measure the temperature gradients along the pulse tube and the regenerator, with five thermometers placed on each of them in good thermal contact. Four thermoelectric couples are used to measure the dynamic gas temperatures Tc,, T,,, Tc3, and Tc4. A computer data-acquisition system is used for the real-time measurements of the dynamic temperatures and
102
Cryogenics
1996 Volume
36, Number
2
Using the experimental apparatus described above, three main series of experiments have been carried out. The first series was performed to systematically study the influences of the principal parameters on the cold end temperature. Parameters studied include the opening of the orifice and the double-inlet valve, the frequency, the average pressure, the pressure amplitude in the pulse tube, the cooling load, and the diameter of the pulse tube. As we study the influences of one parameter, all the other parameters are kept constant. In the experiments, when the cold end temperature is stabilized, we note the temperature and record the pressures P,,, PST, and P,. Then we change only one parameter and repeat the process after the cold end temperature is stabilized once again. About 920 points of measurement have been made in this way for this series of experiments. Calculations corresponding to all the experimental results have been done. Some examples of the experimental and calculation results are presented in Figures 2-7. As can be seen from these figures, the theoretical curves have the same shapes as the corresponding experimental curves, showing a general agreement between the theoretical and experimental results. Figures 2 and 5 show that an optimum frequency always exists, corresponding to the minimum cold end temperature for each operation condition. This can be understood using the theoretical model. When the frequency decreases, the thickness of the thermal
250
200
150
8 c 100
30 t 5 f
Figure2
(Hz)
Temperature versus frequency for pulse V, = 8 turns, f’_ = 12 bar, AP= 2.5 bar
V, = 10 turns,
10
tube
1,
Pulse tube refrigeration. -
Experiment
- - - - Calculation
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Figure5 Temperature versus frequency for pulse V, = 12 turns, V, =4 turns, Pa, = 12 bar, AP= 2.5bar
P,, (t-1 Figure 3 Temperature versus average pressure for pulse tube 1, V, = 10 turns, V2 = 8 turns, f= 2 Hz, BP= 2.5bar
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viscous layer, 6, will increase, and eventually the gross refrigeration power will decrease more than the regenerator inefficiency loss. This will lead to an increase in the cold end temperature: when frequency increases, 6 will decrease, and the increase of refrigeration power will eventually be surpassed by that of the regenerator inefficiency loss, which will also lead to an increase of the cold end temperature. Therefore, at a certain frequency, the cold end temperature is the lowest. As shown in Figures 2 and 5, the optimum frequency is increased when the pulse tube works in a higher temperature range. The cold end temperature
Figure 6 Temperature versus average pressure for pulse tube 2, V, = 12 turns, V, = 4 turns, f= 5 Hz,AP= 2.5bar
increases as the cooling load increases; consequently the thermal diffusivity and thermal conductivity of the gas will also increase. Therefore, 6 will be increased and the optimum frequency becomes higher. From the experiments performed for pulse tubes 1, 2, and 3, we find that the optimum frequency increases as the pulse tube diameter decreases. For pulse tube 1, the optimum frequency falls in the range l-3 Hz; for pulse tube 2, 3-6 Hz; and for pulse tube 3, 6-14 Hz. This is because the pulse tubes with smaller diameters must work at higher frequencies in order to reduce the proportion of 6 to the radius. Another reason is that for the same regenerator, the regenerator inefficiency loss is smaller for smaller pulse tubes and increases less significantly with the increase of frequency compared to larger pulse tubes.
Cryogenics
1996 Volume
36, Number
2
103
Pulse tube refrigeration.
Part 3: J. Liang et al. 20 -
250
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Figure8 Measurement for pulse tube 1
5
AP (bar) Figure 7
Temperature
versus pressure oscillation amplitude
for pulse tube 2, V, = 12 turns, V, = 4 turns, f= 5 Hz, P,, = 12 bar
Figures 3 and 6 indicate that the cold end temperature decreases with decreasing average pressure, under the same pressure amplitude. Since the pressure amplitude is kept constant, the pressure ratio will be increased as the average pressure decreases. According to the theoretical model, the refrigeration power given by the thermodynamic nonsymmetric effect tends to increase with increasing pressure ratio and decreases with decreasing average pressure. The first tendency outweighs the second. Therefore, the cold end temperature decreases with decreasing average pressure, but the losses of cooling increase with decreasing cold end the decrease of temperature temperature. Therefore, becomes less evident at lower temperatures and lower average pressures. The differences between the theoretical and the experimental results in Figures 3 and 6 imply that the actual losses of cooling are greater than those calculated using the theoretical model. From Figures 4 and 7, we can see that at small pressure oscillation amplitudes the increase of AP, defined as the difference between the maximum and minimum pressures in the pulse tube, brings about a significant decrease in the cold end temperature, and that this tendency becomes less evident at higher values of AP, which is not surprising. The increase of AP leads to an increase in the gross refrigeration power of the pulse tube, and consequently a decrease in the cold end temperature. However, with the increase of pressure amplitude and the decrease of the cold end temperature, the regenerator inefficiency loss will be greatly increased, which will partially or completely counteract the gain of gross refrigeration power. Therefore, the cold end temperature becomes insensitive to pressure amplitude when the latter is greater than ~5 bar. In this series of experiments, the pressure amplitude is controlled by adjusting the bypass valve of the helium compressor. The refrigeration performances of the three pulse tubes at the full capacity of the compressor (bypass valve closed) have also been investigated. A minimum tempera-
104
Cryogenics
1996 Volume
36, Number
2
results of net cooling
power at 100 K
ture of 28 K and 16 W of net cooling power at 80 K have been achieved with pulse tube 2 (reference 2). In the second series of experiments, the effects of frequency, and the opening of the orifice and the double-inlet valve on the net cooling power at 100 K are investigated for the three pulse tubes. The cold end temperature is maintained at 100 K by a temperature regulator. The bypass valve of the helium compressor is always closed. This means that the pressure amplitude is not controlled. The variations of PER, PST. and PB are recorded for each point of measurement. The average pressure is 12 bar for all the experiments. Figures 8 and 9 show the experimental results for pulse tubes 1 and 2. Figures 10 and II show the corresponding calculation results for pulse tubes 1 and 2, respectively. Both the theoretical and the experimental results indicate that a pulse tube with a smaller diameter has higher optimum frequencies.
“1 “1 i- 0 12 16 18 18 18 18 18
0 0 0
4 8 12 16
f (Hz) Figure 9 Measurement for pulse tube 2
results of net cooling power at 100 K
Pulse tube refrigeration.
20
t
15
“1
“2
4
0 0 0 0 0 4 8 12 16
8 12 I6 18 18 IX 18 18
T s
10
5
L 0
5 f
Figure 10 tube 1
Calculated
(Hz)
net cooling
power
Part 3: J. Liang et al.
result shown in Figure 12. From these figures, we find that the experimental results are generally in good agreement with the theoretical results. The third series of experiments has been performed with a directly coupled compressor, in order to investigate the compression power and the refrigeration efficiency, and to verify the theoretical model concerning the calculation of the directly coupled compressor. The calculated compression powers are about 50% higher than those given by the P-V relationship measured in the experiments. Two factors may be responsible for this discrepancy. The first is the overestimation of the pressure drop across the regenerator in the calculation. The second is the indirect measurement of the displacement of the piston, which may result in significant errors in the magnitude of the volume and the phase angle between the pressure and volume. In the experiments, a displacement sensor with a small scope of measurement (1.4 mm) is installed to an inclined plane at the end of the axis of the compressor. A sensor with a sufficiently large scope of measurement should be installed within the top cover of the cylinder in order to directly measure the displacement of the piston.
at 100 K for pulse
Conclusions
-0 I 5
0
f (Ilz) Figure 11 tube 2
Calculated
net cooling
power
at 100 K for pulse
For each of the pulse tubes tested, real-time measurements of the dynamic gas temperatures and pressures, as well as measurements of the temperature gradients along the regenerator and the pulse tube, have been made under various operation conditions. Figure 12 shows the gas temperature measured at the cold end of pulse tube. For reference, the synchronous PER is also shown in the figure. We can see that when gas flows into the cold end of the pulse tube, its temperature is almost constantly at 98 K, possibly the temperature of the inner wall of the cold end heat exchanger; when gas flows out of the cold end of the pulse tube, its temperature is much lower than 98 K. Therefore, a certain amount of refrigeration power is produced in the cold end heat exchanger. This is in good agreement with the theoretical analyses presented in Part 1. Figure 13 gives the calculation result corresponding to the experimental
In order to verify the theoretical model, an experimental apparatus has been set up and three main series of experiments have been carried out. The first series of experiments has focused on the influences of the principal parameters on the cold end temperature. The optimum frequency is found to increase with decreasing pulse tube diameter, other parameters being constant; it is higher when the pulse tube works in higher temperature regions. Under the same pressure amplitude, the cold end temperature decreases as the average pressure decreases. The increase in the pressure amplitude brings about improvements of performance when the pressure amplitude is not too great. In the second series of experiments, the net cooling power at 100 K has been measured at various frequencies and openings of the orifice and double-inlet valve for the three pulse tubes of different diameters. Under the same operation condition, the smaller diameter pulse tube has higher optimum frequencies. The real-time measurements of gas temperatures and pressures reveal the internal physical processes and confirm the theoretical analyses. In the last series of experiments, conducted with a directly coupled compressor, the P-V relationship and the refrigeration efficiency have been measured under various operation conditions. The results of the above experiments have been compared with the corresponding theoretical results, and fairly good agreements have been found between them. Many important experimental phenomena have been successfully explained using the theoretical model. Accordingly, the theoretical model is considered valid and utilizable.
Acknowledgements The authors would like to thank Dr G. Claudet and Professor Y. Zhou for their support and valuable discussions. The help give by Mr M. Desmaris with the experiments and the figures is also gratefully acknowledged.
Cryogenics
1996 Volume
36, Number
2
105
Pulse tube refrigeration.
Part 3: J. Liang et al.
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measured
References loo
1
95 g w
2 90-
and experimental verification of a theoretical model for pulse tube refrigeration PhD Thesis CENG/DRFMC/SBT, Grenoble (1993) Ravex, A., Rolland, P. and Liang, J. Experimental study and modelization of pulse tube refrigerator Proc 14th ICEC Cryogenics Suppl. (1992)
85 80 0
I
I
I
I
I
I
SO
100
150
200
250
300
t (ms)
Figure 13
Calculated temperature variation of gas at the cold end of pulse tube 1, V, = 18 turns, V, closed, f=3 Hz, T,= 100 K
106
Liang, J. Development
Cryogenics
1996 Volume
36, Number
2
32 9
Study on pulse tube refrigeration Part 3: Experimental verification J. Liang*,
A. Ravex
and P. Roland
Service des Basses Temperatures, Centre d’Etudes des Martyrs, 38054 Grenoble, Cedex 9, France Received 8 May
Nucleaires
de Grenoble,
17 rue
1995
A large number of experiments have been systematically carried out in order to validate the theoretical model described in the preceding parts of this study. The influences of the important parameters, including opening of the orifice and double-inlet valve, frequency, average pressure, pressure oscillation amplitude in the pulse tube, and the diameter of the pulse tube on the refrigeration performance are intensively investigated. The cold end temperature and the net cooling power at 100 K are used as criteria of refrigeration performance. Real-time measurements of gas temperature and pressure at various positions in the pulse tube refrigerator are performed in order to reveal the internal physical processes. The experimental results are found to be in good agreement with the theoretical predictions. Keywords:
pulse tube; refrigeration
Tc2
Nomenclature f P&i” PB
P DR P ER P -.. ?I?
P.ST
QF
TC T,,
Frequency (Hz) Average pressure (bar) Pressure in gas reservoir (bar) Pressure drop across regenerator (bar) Pressure at hot end of regenerator (bar) Pressure at cold end of regenerator (bar) Pressure at hot end of pulse tube (bar) Net cooling power (W) Cold end temperature of pulse tube (K) Gas temperature at hot end of regenerator
Tc3 Tc4
V1 V,
Greek letters (K)
In the previous two parts of this study, we have developed a theoretical model for pulse tube refrigerators. Such a model is not utilizable before it is experimentally verified for a wide range of parameters. In this paper we present the experiments conducted to validate the theoretical model’. The experimental results are analysed and compared with the corresponding theoretical results.
Experimental
apparatus
An experimental apparatus has been constructed in order to experimentally investigate the pulse tube refrigerator and verify the theoretical model. A general view of the exper-
*Present address: Cryogenic Laboratory, Chinese Academy Sciences, PO Box 2711, Beijing 100080, China
Gas temperature at cold end of regenerator (K) Gas temperature at cold end of pulse tube (K) Gas temperature at hot end of pulse tube (K) Opening of orifice (turns) Opening of double-inlet valve (turns)
of
6 AP
Thickness of thermal viscous layer (m) Pressure amplitude in pulse tube (bar)
imental apparatus is given in Figure I. The important components are illustrated in detail. The whole apparatus comprises mainly two systems: refrigeration and measurement. The refrigeration system (pulse tube refrigerator) includes the pressure wave generator, regenerator, pulse tube, cold and hot end heat exchangers, orifice, double-inlet valve, gas reservoir, and connecting tubing. The working fluid is helium gas. Two kinds of pressure wave generator were used in the experiments: one is a helium compressor with a rotatory or electromagnetic gas distributor; the other is a directly coupled compressor, with no gas distribution devices. The regenerator used in the experiments is a stainless steel tube of 18 mm internal diameter (i.d.), 19 mm external diameter (e.d.), and 170 mm in length, filled with stainless steel screens. The three pulse tubes tested are all 200 mm long thin-walled stainless steel tubes: 1, 19.5 mm i.d., 20mm e.d.; 2, 14mm i.d., 15 mm e.d; and 3, 10mm
Cryogenics
1996 Volume
36, Number
2
101
Pulse tube refrigeration.
Part 3: J. Liang et al.
i ?as reservoir Zooling water I
pressures. A resistor of 48 a, attached to the cold end copper block, is used to supply heating power to the cold end heat exchanger of the pulse tube. When the temperature of the cold end block is stabilized, the heating power provided by the heater is equivalent to the net cooling power of the pulse tube. To measure the compression power in the case of a directly coupled compressor, a pressure sensor and a displacement sensor are used. The pressure-volume (P-V) relationship of the compressor is recorded using a digital oscilloscope.
Results and discussions Regenerator
Pulse tube
Heat exchanger Heater
Figure 1
Experimental
apparatus
i.d., 10.4 mm e.d. At each end of the pulse tubes, about 40 copper gauze discs are brazed in a copper block for both flow straightening and heat exchange. A coiled water-conducting copper tube is soldered around the hot end copper block in order to maintain a constant temperature. The regenerator, pulse tube, and other low temperature parts are placed in a cylindrical vacuum vessel, in which a low pressure of 1 x 1O-5-1 x 10m6mbar is maintained for thermal insulation from the environment. The thermal insulation is further improved by the installation of a radiation screen composed of = 10 layers of aluminized polyester film. Two identical continuously adjustable needle valves serve as the orifice and the double-inlet valve. A stainless steel container of 300 cm3 volume is used as the gas reservoir. A valve is annexed to it for the purpose of system purging. The measurement system includes devices to measure pressure, temperature, and the net cooling power. It also includes measurement devices for compression power, in the case of a directly coupled compressor. As shown in Figure 1, PER, PSR, P,,, and PB are measured with piezoesistive pressure sensors; P,, is measured with a differential piezoresistive pressure sensor. Temperature measurements of the system include static and dynamic temperature measurements. Platinum and carbon resistance thermometers are inserted in the copper block of the cold end heat exchanger in order to detect the cold end temperature. Similarly, a platinum thermometer is used to measure the wall temperature of the hot end heat exchanger. Another 10 platinum thermometers are employed in order to measure the temperature gradients along the pulse tube and the regenerator, with five thermometers placed on each of them in good thermal contact. Four thermoelectric couples are used to measure the dynamic gas temperatures Tc,, T,,, Tc3, and Tc4. A computer data-acquisition system is used for the real-time measurements of the dynamic temperatures and
102
Cryogenics
1996 Volume
36, Number
2
Using the experimental apparatus described above, three main series of experiments have been carried out. The first series was performed to systematically study the influences of the principal parameters on the cold end temperature. Parameters studied include the opening of the orifice and the double-inlet valve, the frequency, the average pressure, the pressure amplitude in the pulse tube, the cooling load, and the diameter of the pulse tube. As we study the influences of one parameter, all the other parameters are kept constant. In the experiments, when the cold end temperature is stabilized, we note the temperature and record the pressures P,,, PST, and P,. Then we change only one parameter and repeat the process after the cold end temperature is stabilized once again. About 920 points of measurement have been made in this way for this series of experiments. Calculations corresponding to all the experimental results have been done. Some examples of the experimental and calculation results are presented in Figures 2-7. As can be seen from these figures, the theoretical curves have the same shapes as the corresponding experimental curves, showing a general agreement between the theoretical and experimental results. Figures 2 and 5 show that an optimum frequency always exists, corresponding to the minimum cold end temperature for each operation condition. This can be understood using the theoretical model. When the frequency decreases, the thickness of the thermal
250
200
150
8 c 100
30 t 5 f
Figure2
(Hz)
Temperature versus frequency for pulse V, = 8 turns, f’_ = 12 bar, AP= 2.5 bar
V, = 10 turns,
10
tube
1,
Pulse tube refrigeration. -
Experiment
- - - - Calculation
250
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P,, (t-1 Figure 3 Temperature versus average pressure for pulse tube 1, V, = 10 turns, V2 = 8 turns, f= 2 Hz, BP= 2.5bar
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viscous layer, 6, will increase, and eventually the gross refrigeration power will decrease more than the regenerator inefficiency loss. This will lead to an increase in the cold end temperature: when frequency increases, 6 will decrease, and the increase of refrigeration power will eventually be surpassed by that of the regenerator inefficiency loss, which will also lead to an increase of the cold end temperature. Therefore, at a certain frequency, the cold end temperature is the lowest. As shown in Figures 2 and 5, the optimum frequency is increased when the pulse tube works in a higher temperature range. The cold end temperature
Figure 6 Temperature versus average pressure for pulse tube 2, V, = 12 turns, V, = 4 turns, f= 5 Hz,AP= 2.5bar
increases as the cooling load increases; consequently the thermal diffusivity and thermal conductivity of the gas will also increase. Therefore, 6 will be increased and the optimum frequency becomes higher. From the experiments performed for pulse tubes 1, 2, and 3, we find that the optimum frequency increases as the pulse tube diameter decreases. For pulse tube 1, the optimum frequency falls in the range l-3 Hz; for pulse tube 2, 3-6 Hz; and for pulse tube 3, 6-14 Hz. This is because the pulse tubes with smaller diameters must work at higher frequencies in order to reduce the proportion of 6 to the radius. Another reason is that for the same regenerator, the regenerator inefficiency loss is smaller for smaller pulse tubes and increases less significantly with the increase of frequency compared to larger pulse tubes.
Cryogenics
1996 Volume
36, Number
2
103
Pulse tube refrigeration.
Part 3: J. Liang et al. 20 -
250
Experimcn~
r
4 8
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18 18 18 18
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;:
5 100
0
5
50
f (Hz) 0
Figure8 Measurement for pulse tube 1
5
AP (bar) Figure 7
Temperature
versus pressure oscillation amplitude
for pulse tube 2, V, = 12 turns, V, = 4 turns, f= 5 Hz, P,, = 12 bar
Figures 3 and 6 indicate that the cold end temperature decreases with decreasing average pressure, under the same pressure amplitude. Since the pressure amplitude is kept constant, the pressure ratio will be increased as the average pressure decreases. According to the theoretical model, the refrigeration power given by the thermodynamic nonsymmetric effect tends to increase with increasing pressure ratio and decreases with decreasing average pressure. The first tendency outweighs the second. Therefore, the cold end temperature decreases with decreasing average pressure, but the losses of cooling increase with decreasing cold end the decrease of temperature temperature. Therefore, becomes less evident at lower temperatures and lower average pressures. The differences between the theoretical and the experimental results in Figures 3 and 6 imply that the actual losses of cooling are greater than those calculated using the theoretical model. From Figures 4 and 7, we can see that at small pressure oscillation amplitudes the increase of AP, defined as the difference between the maximum and minimum pressures in the pulse tube, brings about a significant decrease in the cold end temperature, and that this tendency becomes less evident at higher values of AP, which is not surprising. The increase of AP leads to an increase in the gross refrigeration power of the pulse tube, and consequently a decrease in the cold end temperature. However, with the increase of pressure amplitude and the decrease of the cold end temperature, the regenerator inefficiency loss will be greatly increased, which will partially or completely counteract the gain of gross refrigeration power. Therefore, the cold end temperature becomes insensitive to pressure amplitude when the latter is greater than ~5 bar. In this series of experiments, the pressure amplitude is controlled by adjusting the bypass valve of the helium compressor. The refrigeration performances of the three pulse tubes at the full capacity of the compressor (bypass valve closed) have also been investigated. A minimum tempera-
104
Cryogenics
1996 Volume
36, Number
2
results of net cooling
power at 100 K
ture of 28 K and 16 W of net cooling power at 80 K have been achieved with pulse tube 2 (reference 2). In the second series of experiments, the effects of frequency, and the opening of the orifice and the double-inlet valve on the net cooling power at 100 K are investigated for the three pulse tubes. The cold end temperature is maintained at 100 K by a temperature regulator. The bypass valve of the helium compressor is always closed. This means that the pressure amplitude is not controlled. The variations of PER, PST. and PB are recorded for each point of measurement. The average pressure is 12 bar for all the experiments. Figures 8 and 9 show the experimental results for pulse tubes 1 and 2. Figures 10 and II show the corresponding calculation results for pulse tubes 1 and 2, respectively. Both the theoretical and the experimental results indicate that a pulse tube with a smaller diameter has higher optimum frequencies.
“1 “1 i- 0 12 16 18 18 18 18 18
0 0 0
4 8 12 16
f (Hz) Figure 9 Measurement for pulse tube 2
results of net cooling power at 100 K
Pulse tube refrigeration.
20
t
15
“1
“2
4
0 0 0 0 0 4 8 12 16
8 12 I6 18 18 IX 18 18
T s
10
5
L 0
5 f
Figure 10 tube 1
Calculated
(Hz)
net cooling
power
Part 3: J. Liang et al.
result shown in Figure 12. From these figures, we find that the experimental results are generally in good agreement with the theoretical results. The third series of experiments has been performed with a directly coupled compressor, in order to investigate the compression power and the refrigeration efficiency, and to verify the theoretical model concerning the calculation of the directly coupled compressor. The calculated compression powers are about 50% higher than those given by the P-V relationship measured in the experiments. Two factors may be responsible for this discrepancy. The first is the overestimation of the pressure drop across the regenerator in the calculation. The second is the indirect measurement of the displacement of the piston, which may result in significant errors in the magnitude of the volume and the phase angle between the pressure and volume. In the experiments, a displacement sensor with a small scope of measurement (1.4 mm) is installed to an inclined plane at the end of the axis of the compressor. A sensor with a sufficiently large scope of measurement should be installed within the top cover of the cylinder in order to directly measure the displacement of the piston.
at 100 K for pulse
Conclusions
-0 I 5
0
f (Ilz) Figure 11 tube 2
Calculated
net cooling
power
at 100 K for pulse
For each of the pulse tubes tested, real-time measurements of the dynamic gas temperatures and pressures, as well as measurements of the temperature gradients along the regenerator and the pulse tube, have been made under various operation conditions. Figure 12 shows the gas temperature measured at the cold end of pulse tube. For reference, the synchronous PER is also shown in the figure. We can see that when gas flows into the cold end of the pulse tube, its temperature is almost constantly at 98 K, possibly the temperature of the inner wall of the cold end heat exchanger; when gas flows out of the cold end of the pulse tube, its temperature is much lower than 98 K. Therefore, a certain amount of refrigeration power is produced in the cold end heat exchanger. This is in good agreement with the theoretical analyses presented in Part 1. Figure 13 gives the calculation result corresponding to the experimental
In order to verify the theoretical model, an experimental apparatus has been set up and three main series of experiments have been carried out. The first series of experiments has focused on the influences of the principal parameters on the cold end temperature. The optimum frequency is found to increase with decreasing pulse tube diameter, other parameters being constant; it is higher when the pulse tube works in higher temperature regions. Under the same pressure amplitude, the cold end temperature decreases as the average pressure decreases. The increase in the pressure amplitude brings about improvements of performance when the pressure amplitude is not too great. In the second series of experiments, the net cooling power at 100 K has been measured at various frequencies and openings of the orifice and double-inlet valve for the three pulse tubes of different diameters. Under the same operation condition, the smaller diameter pulse tube has higher optimum frequencies. The real-time measurements of gas temperatures and pressures reveal the internal physical processes and confirm the theoretical analyses. In the last series of experiments, conducted with a directly coupled compressor, the P-V relationship and the refrigeration efficiency have been measured under various operation conditions. The results of the above experiments have been compared with the corresponding theoretical results, and fairly good agreements have been found between them. Many important experimental phenomena have been successfully explained using the theoretical model. Accordingly, the theoretical model is considered valid and utilizable.
Acknowledgements The authors would like to thank Dr G. Claudet and Professor Y. Zhou for their support and valuable discussions. The help give by Mr M. Desmaris with the experiments and the figures is also gratefully acknowledged.
Cryogenics
1996 Volume
36, Number
2
105
Pulse tube refrigeration.
Part 3: J. Liang et al.
‘ER
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Gas temperature
variation
at the cold end of pulse tube 1, V, = 18 turns, V, closed, f= 3 Hz, T,= 100 K
measured
References loo
1
95 g w
2 90-
and experimental verification of a theoretical model for pulse tube refrigeration PhD Thesis CENG/DRFMC/SBT, Grenoble (1993) Ravex, A., Rolland, P. and Liang, J. Experimental study and modelization of pulse tube refrigerator Proc 14th ICEC Cryogenics Suppl. (1992)
85 80 0
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100
150
200
250
300
t (ms)
Figure 13
Calculated temperature variation of gas at the cold end of pulse tube 1, V, = 18 turns, V, closed, f=3 Hz, T,= 100 K
106
Liang, J. Development
Cryogenics
1996 Volume
36, Number
2
32 9