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Experimental study of the oscillating flow characteristics for a regenerator in a pulse tube cryocooler
PII: S0011-2275(98)00037-X
Cryogenics 38 (1998) 649–656 1998 Elsevier Science Ltd. All rights reserved Printed in Great Britain 0011-2275/98/$19.00
Experimental study of the oscillating flow characteristics for a regenerator in a pulse tube cryocooler Yonglin Ju, Yan Jiang and Yuan Zhou Cryogenic Laboratory, Chinese Academy of Sciences, P.O. Box 2711, Beijing 100080, China
Received 8 December 1997; accepted 12 February 1998 A dynamic experimental apparatus was designed and constructed to investigate oscillating flow characteristics in a regenerator subjected to a periodically reversing flow established by means of a self-made linear compressor. Detailed experimental data of oscillating pressure drops and phase shift characteristics for regenerators in a high frequency pulse tube cryocooler with an operating frequency of 50 Hz were given. The correlation equations for the maximum and cycle-averaged friction factors in terms of Reynolds numbers and dimensionless distance X were obtained. It was found that the value of the cycle-averaged pressure drop in the oscillating flow across the regenerator is two to three times higher than that of a steady flow at the same Reynolds numbers based on the cross-sectional mean velocity. In addition, the relationship of the phase shifts between the velocity and pressure wave is also discussed. 1998 Elsevier Science Ltd. All rights reserved Keywords: oscillating flow; regenerator; E. pulse tube cryocooler; experimental study
Nomenclature Am Dh Dw ⌬P ⌬Pmax ⌬P¯mean ⌬Pst fmax ¯f mean fst L n
cross-sectional area of the regenerator hydraulic diameter wire diameter of screens pressure drops maximum pressure drop in one cycle cycle-averaged pressure drop in one cycle pressure drop of steady flow maximum pressure drop factor cycle-averaged pressure drop in one cycle pressure drop factor of the steady flow length of the regenerator number of stacked screens
Introduction Interest in the pulse tube cryocooler has grown rapidly in recent years owing to its no-moving component in the low temperature region. Therefore, it has merits in mechanical simplicity, high reliability, low vibration and low cost. This cryogenic cryocooler has the potential for promising applications in the cooling of infrared devices and sensors, superconducting electronic devices, etc. The significant influence of pressure characteristics in the oscillating flow regenerator on the performance of the cryocooler has been recognized recently in many papers1–3. The ability to pre-
Re um umax X
Reynolds number area-averaged fluid velocity maximum area-averaged fluid velocity dimensionless distance
Greek letters 
mesh distance dimensionless phase angle porosity pitch kinematics viscosity of fluid density of fluid oscillating frequency
dict pressure drops and phase shift in the oscillating flow regenerator is crucially important in the optimum design of pulse tube cryocoolers and other cryocoolers. As a necessary component, the oscillating flow regenerator plays an important role in the refrigeration performance of the pulse tube cryocooler. In the past, due to the lack of a friction factor and heat transfer coefficient for the oscillation flow regenerator, the regenerator was taken to be a kind of high efficiency heat exchanger that provided a way to get the gas to the low temperature region with as much cooling power as possible, which may be close to the actual performance for unidirectional steady flow or
Cryogenics 1998 Volume 38, Number 6 649
Oscillating flow characteristics for regenerator: Y. Ju et al. very low frequency regenerators. Therefore, the correlation equation of the friction factor given by Kays and London4 has been widely used. Similarly, there are also some correlations with pressure drop in regenerators5,6, but most of them are based on a unidirectional steady flow through a stack of screens. Since the pulse tube cryocooler operates under periodically reversing flow conditions, it is apparent that the correlation equations based on steady flow are not able to predicate accurately the pressure drop in the oscillating flow regenerator. For example, Yoshida et al.7, Zhao and Cheng8 and Helvensteijn et al.9 found a higher friction factor in the oscillating flow regenerator than in the steady flow at the same Reynolds numbers based on the crosssectional mean velocity. Oscillating flow characteristics for the regenerator in the pulse tube cryocooler demonstrate not only pressure drops but phase shifts. Relatively little research has been performed on the pressure drop over a stack of screens subjected to an oscillating flow regenerator. Therefore, it is important for analysis and optimum design to study the pressure drop and the phase shift in the oscillating flow regenerator. As we know, the working process in the pulse tube cryocooler is very complex due to the unsteady, oscillating compressible gas flow, the porous media in the regenerator and the addition of the orifice valve and double-inlet valve, etc. An understanding of the mechanisms associated with the pulse tube cryocooler requires a full solution of the Navies–Stocks equations. However, the complexities of these equations make an analytical solution for the pulse tube cryocooler essentially impossible. Therefore, an experimental study has been adapted and designed to investigate the oscillating flow characteristics in the regenerator subjected to a periodically reversing flow in the pulse tube cryocooler. In this paper, details of the dynamic experimental apparatus used to investigate the oscillating flow characteristics across a regenerator packed with stainless-steel wire screens are presented. The oscillating flow is established by means of a self-made linear compressor whose swept volume is 10 cc with an operating frequency of 50 Hz connected to the inlet of the regenerator through a velocity straightener. Experimental data of the pressure drops and phase shifts in the regenerator under cyclic flow conditions were obtained. The correlation equation of the friction factor during actual operation of a 50 Hz oscillating flow in a pulse tube cooler is obtained. It is found that the value of the cycle-averaged pressure drop for the 50 Hz oscillating flow is two to three times higher than that of a steady flow at the same Reynolds number based on the cross-sectional mean velocity. The relationship of the phase shifts between the velocity and the pressure wave is also obtained and discussed.
reservoir with an adjusted needle orifice valve which is connected to the end of the second velocity straightener. The oscillating flow is established by means of a self-made linear compressor. The swept volume of the compressor is 10 cc, its operating frequency is around 50 Hz. A heating resistance is provided at the cold end to maintain a constant temperature through the whole test section. Two small quartz differential pressure transducers (KISTLER, Type 601A), connected to a charge amplifier (KISTLER, Type 5011) having a high natural frequency (150 kHz), are used to measure the transient gas pressure wave at the two ends of the regenerator, as shown in Figure 1. We used a hot wire anemometer (DANTEC, Model 90N10) to measure the instantaneous cross-sectional mean velocity. The anemometer works according to the constant temperature anemometer (CTA) principle where the sensor probe forms an arm of a Whetstone bridge. It is kept in balance by the deviation signal across the bridge diagonal so that the probe resistance, and hence its temperature, is kept constant independent of the cooling from the flowing medium. Two small hot probes (DANTEC, Model 55P11) are placed at the center of the tube between the two velocity straighteners at the left side of the test section. The hot probes made of tungsten are 5 m in diameter between the probe support of 2 mm diameter and 30 mm length. The probes are suspended in the gas stream by probe supports which are electrical conductors and which also served as electrical connections for the sensors. The CTAs are operated at approximately 200 K, warmer than the temperature of the environment fluid, and the response time of the CTAs in this system is 20 s. Analog-to-digital conversions are carried out by an A/D conversion board (KEITHLEY, DAS 1601) which is plugged into a 486 personal computer. A 4-channel simultaneous sample and hold front ends are employed so that both the dynamic pressure and the velocity voltage signals are sampled simultaneously. An oscilloscope (HP 5402B) is also employed to simultaneously observe wave signals.
Experimental conditions The test section of the regenerator, 70 mm in length and 10.5 inner diameter, is made of stacks of stainless-steel plainly woven wire screens with five different mesh sizes. The properties of the number of screens n, wire diameters Dw, pitch , mesh distance , porosity and hydraulic diameter Dh for the five mesh sizes of the wire screens are listed in Table 1. Wire diameter Dw, pitch and mesh distance  are provided by the manufacturer. The hydraulic diameter Dh and the porosity of the regenerator are determined from equations given below. The working medium is helium gas, the operating frequency is 50 Hz and the system mean pressure varies from 0.6 to 0.9 MPa.
Experimental system Experimental results and discussions A schematic of the experimental apparatus is shown in Figure 1. It is designed for the experimental measurement of the dynamic pressure and mass flow rate of the oscillating flow gas at the two ends of the test section of the regenerator. The test section consists of a packed column (70 mm in length and 10.5 mm inner diameter) with both ends connected to the velocity straightener (60 mm in length and 9 mm inner diameter). The test section is connected to a
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Cryogenics 1998 Volume 38, Number 6
The raw experimental data measured from the hot wire anemometer and pressure transducers require data processing which includes velocity transformation and correction, high frequency harmonic filtration, Fourier analysis, etc. Figure 2 shows the typical variation of the instantaneous gas velocity and pressure wave at the inlet (V1,P1) and outlet (V2,P2) of the test section. They demonstrate
Oscillating flow characteristics for regenerator: Y. Ju et al.
Figure 1 Schematic diagram of experimental apparatus: 1. compressor; 2. pressure gauge; 3. velocity straightener; 4. connector; 5. regenerator; 6. orifice valve; 7. reservoir; 8. pressure transducer; 9. hot wire probe; 10. charge amplifier; 11. hot-wire anemometer; 12. A/D conversion board; 13. 486 computer Table 1 Properties of stainless-steel wire screens Mesh size
80 150 250 300 400
Number of screens, n 428 500 600 690 720
Wire diameter, Dw (mm) 0.102 0.061 0.041 0.031 0.025
Porosity,
0.735 0.6993 0.6582 0.6938 0.6677
Mesh distance,  (mm) 0.140 0.120 0.100 0.087 0.083
Hydraulic diameter, Dh (mm) 0.2828 0.1418 0.0788 0.0704 0.0504
Figure 2 Typical variation of the instantaneous gas velocity and pressure waves
the variations in the amplitude and phase relationship between the gas velocity and the dynamic pressure. It should be noted that the gas velocity and the pressure are not sinusoidal oscillations, and that the peak flows and halfcycle frequencies are not equivalent in Figure 2. Therefore, the experimentally measured phase angles were averaged over the two half-cycles. Our experimental results show that the flow characteristic depends on many factors such
as matrix porous properties, gas properties, the outlet conditions affected by orifice valve, etc. The operating frequency of the oscillating flow established by our linear compressor also affects the cycled flow pressure drops and phase shifts. The experiments in this paper focus on 50 Hz oscillation flow as an example to study the flow characteristics of an oscillating flow regenerator. In all tests, we studied experimentally the effects of dif-
Cryogenics 1998 Volume 38, Number 6 651
Oscillating flow characteristics for regenerator: Y. Ju et al. ferent orifice settings, system mean pressure and mesh sizes on the oscillating flow characteristics of pressure drops and phase shifts. Some detailed experimental data of the oscillating pressure drop ⌬P, and the phase shifts which include the phase shifts between the input pressure and output pressure ⌬P1P2, the input and output velocity ⌬V1V2 and the output pressure and velocity, ⌬P2V2 are presented.
Effects of orifice setting Figure 3a–d shows the effects of the orifice setting on the pressure drops ⌬P and the phase shifts with system mean pressure of 0.8 MPa and mesh size of 400 mesh. In the figures, position 1 indicates that the valve is closed, position 2 that the valve is opened a little (we named this the optimum position), and position 3 that it is fully opened. The pressure drop ⌬P decreased rapidly from position 1 to 2 and increased from position 2 to 3. At position 2, which we named the optimum value, the pressure drop reached its minimum value. The phase shift ⌬P2V2 decreased rapidly from position 1 to 2 and maintained an almost constant value from position 2 to 3. This shows that the opening value of the orifice valve is crucially important to the performance of the regenerator. Therefore, it should be noted in designing a pulse tube cryocooler. Position 2 (optimum value) varied with different mesh size of the stainless steel wire screens in the test section, while it remained almost constant for different system mean pressures. The experimental data reported in this paper are all based on tests at position 2 of the orifice opening value.
with a mesh size of 400 mesh are shown in Figure 4a–d. From these figures, we can clearly see the variations in the pressure drops and phase shifts between the pressure and velocity with the system mean pressure.
Effects of mesh size Figure 5a–d illustrates the influence of the mesh size on the pressure drop ⌬P and the phase shifts with a system mean pressure of 0.8 MPa. The pressure drop ⌬P and the phase shifts ⌬P1P2 increased rapidly with increasing stainless-steel mesh size. They achieved their maximum values at a mesh size of 400 stainless-steel wire screens, while the phase shifts ⌬V1V2 and ⌬P2V2 achieved their minimum values at a mesh size of 400. Thus it was demonstrate that we should adapt 400 stainless-steel mesh size in designing the pulse tube cryocooler at an operating frequency of 50 Hz to improve the performance of the regenerator.
Pressure drop and pressure drop factor Pressure drops across the regenerator in the oscillating flow under different experimental conditions including five mesh sizes and several system pressure are obtained. To compare the pressure drops over the regenerator in oscillating flow with those in steady flow, we used the following correlation equation for predicting the friction factor of a steady flow through a stack of woven screen1: 33.6 + 0.337 Re
Effects of system mean pressure
f st =
The effects of different system mean pressures on the pressure drop ⌬P and the phase shifts across the test section
where
Figure 3 Effects of orifice setting on the oscillating flow characteristics
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Cryogenics 1998 Volume 38, Number 6
(1)
Oscillating flow characteristics for regenerator: Y. Ju et al.
Figure 4 Effects of mean pressure on the oscillating flow characteristics
Figure 5 Effects of mesh size on the oscillating flow characteristics
f st =
⌬Pst/n 1 2 u 2 st
Re =
ust
(2)
(3)
where ⌬Pst is the steady flow pressure drop, ust is the crosssectional mean flow velocity in the packed column, n is the number of screens,  is the distance between meshes, and Re is the Reynolds number based on  and ust. To predict the pressure drop across the regenerator in the 50 Hz pulse tube cryocooler, the maximum friction factor is defined as follows3
Cryogenics 1998 Volume 38, Number 6 653
Oscillating flow characteristics for regenerator: Y. Ju et al. f max =
⌬PmaxDh 1 (umax )2L 2
(4)
and the cycle-averaged friction factor is ¯ ¯f mean = ⌬PmeanDh 1 (umax )2pL 2
(5)
Defining the Reynolds number Re =
umaxDh
(6)
where ⌬Pmax is the maximum pressure drop in one cycle, ⌬P¯meanis the cycle-averaged pressure drop, umax is the maximum cross-sectional mean flow velocity in the regenerator, L is the length of the test section of the regenerator, and Dh is the hydraulic diameter of the screen, which is defined as follows3 Dh =
Dw 1−
Dw√2D2w 42
(8)
1 umax 2 Dh
(9)
The maximum friction factor fmax was computed and correlated according to Equation (4) based on the experimental data. The normalized curve of fmax is shown in Figure 6. The correlation equation of the friction factor of the regenerator used in the 50 Hz pulse tube cryocooler in terms of Re and X was obtained as: f max =
冉
冊
1 1.22 × 106 2.76 × 104 + X Re
(10)
Figure 6 Correlation equation of the maximum friction factor in terms of Re and X
654
冊
(11)
The maxium deviation of the experimental data from the value calculated by Equations (10) and (11) is about 4.33%. Equations (10) and (11) can be used to predict the pressure drop in designing the regenerator of the 50 Hz pulse tube cryocooler. We compared the pressure drops predicted by Equation (11) for the oscillating flow with those from Equation (1) for the steady flow. The compared results of pressure drops of oscillating flow and steady flow are shown in Table 2. It is found that the value of the cycleaveraged pressure drop of the oscillating flow in the regenerator is two to three times higher than that of a steady flow at the same Reynolds numbers based on the crosssectional mean velocity.
Phase shift relationship
We also defined the dimensionless distance as: X=
冉
5 ¯f mean = 1 1.10 × 104 + 3.78 × 10 X Re
(7)
with being the screen porosity which is defined as1:
=1−
Based on the experimental data, the cycle-averaged friction factor ¯f mean was evaluated according to Equation (5) and is presented in Figure 7. It is shown that the experimental data are well fitted by the following correlation equation:
Cryogenics 1998 Volume 38, Number 6
Oscillating flow characteristics for the regenerator in the pulse tube cryocooler demonstrate not only pressure drops but phase shifts. Phase shifts were determined by the properties of stainless-steel wire screens and the Reynolds number of the working gas besides the orifice setting. Figure 8a–c illustrates the phase shifts between the input and the output pressure ⌬P1P2, the input and the output velocity ⌬V1V2 and the output pressure and velocity ⌬P2V2, respectively. From these figures, we can predict the phase shifts between the inlet and the outlet of pressure and velocity across the oscillating flow regenerator. Figure 8c shows that a minimum value of the phase shift ⌬P2V2 exists, between the output of the gas velocity and the pressure, which supplies a special Reynolds number for different mesh sizes of stainless-steel wire screens. Figure 9 indicates the relationship between the mesh sizes of stainless-steel wire screens and the special Reynolds number. To predict the phase shift ⌬P2V2 between the output of the gas velocity and the pressure across the oscillating flow regenerator, we define the dimensionless phase shifts as follows:
Figure 7 Correlation equation of the cycle-averaged friction factor in terms of Re and X
Oscillating flow characteristics for regenerator: Y. Ju et al. Table 2 Pressure drops of oscillatory flow compared with those of steady flow Mesh size
Re
80 150 250 300 400
5.74 5.57 5.17 5.09 4.73
⌬P¯ mean (kPa)
⌬Pst (kPa)
9.93 12.67 17.21 20.44 27.97
4.58 5.98 7.42 8.69 9.38
⌬P¯ mean/⌬Pst 2.20 2.28 2.32 2.35 2.98
Figure 9 Relationship between the special Reynolds number and the mesh sizes
Figure 10 Correlation equation of the dimensionless phase shifts with Reynolds number
mental data are well fitted by the following correlation equation:
=
36.3 − 8.05 × 10−0.049Re Re
(13)
The maximum relative deviation between Equation (13) and the experimental data is about 4.87%. Figure 8 Variation of the phase shifts between the gas velocity and the pressure
=
⌬P2V2 ⌬P1V1
(12)
Based on the experimental data, the dimensionless phase shift was calculated according to Equation (12) and is presented in Figure 10. This figure shows that the experi-
Conclusions Experimental data on the oscillating flow characteristics of the regenerator in a 50 Hz pulse tube cryocooler are presented in this paper. The oscillating flow characteristics appear not only as pressure drops but also as phase lags. Correlation equations for the maximum and cycle-averaged friction factors in terms of Reynolds numbers and dimen-
Cryogenics 1998 Volume 38, Number 6 655
Oscillating flow characteristics for regenerator: Y. Ju et al. sionless distance X are obtained. It is found that the value of the cycle-averaged pressure drop of the oscillating flow in the regenerator is two to three times higher than that of a steady flow at the same Reynolds numbers based on the cross-sectional mean velocity. In addition, the relationship of the phase shifts between the gas velocity and pressure wave is also presented.
Acknowledgements Research supported by the Foundation of Chinese Academy of Sciences.
References 1. Miyabe, H., Takahashi, S. and Hamaguchi, K., An approach to the design of Stirling engine regenerator matrix using packs of wire gauzes. Proc. 17th IECEC, 1982, 1, 1839–1844.
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2. Guo, F.Z., Chou, Y.M. and Lee, S.Z., et al., Flow characteristics of a cyclic flow regenerator. Cryogenics, 1987, 27, 152–155. 3. Tanaka, M., Yamshita, I. and Chrisaka, F., Flow and heat transfer characteristics of the Stirling engine regenerator in an oscillating flow. JSME Int. J., 1990, 33, 283–289. 4. Kays, W.M. and London, A.L., Compact Heat Exchanger, 2nd edn. McGraw-Hill, New York, 1964. 5. Tong, L.S. and London, A.L., Heat transfer and flow friction characteristics of woven-screen and cross-rod matrices. Trans. ASME, 1957, 1558–1570. 6. Walker, G. and Vasishta, V., Heat transfer and friction characteristics of wire-screen Stirling engine regenerator. Adv. Cry. Eng., 1971, 16, 324–332. 7. Yoshida, S., Ravikumar, K.V. and Frederkng, T.H.K., Friction factors of stacks of perforated regenerator plates. Cryocoolers, 1995, 8, 259–268. 8. Zhao, T.S. and Cheng, P., Oscillatory pressure drops through a woven-screen packed column subjected to a cycle flow. Cryogenics, 1996, 36, 333–341. 9. Helvensteijn, B.P.M., Kashani, A., Spivak, A.L. et al., Pressure drop over regenerators in oscillating flow. Presented at CEC/ICMC 97, Portland, Oregon, USA, July 1997.
Cryogenics 38 (1998) 649–656 1998 Elsevier Science Ltd. All rights reserved Printed in Great Britain 0011-2275/98/$19.00
Experimental study of the oscillating flow characteristics for a regenerator in a pulse tube cryocooler Yonglin Ju, Yan Jiang and Yuan Zhou Cryogenic Laboratory, Chinese Academy of Sciences, P.O. Box 2711, Beijing 100080, China
Received 8 December 1997; accepted 12 February 1998 A dynamic experimental apparatus was designed and constructed to investigate oscillating flow characteristics in a regenerator subjected to a periodically reversing flow established by means of a self-made linear compressor. Detailed experimental data of oscillating pressure drops and phase shift characteristics for regenerators in a high frequency pulse tube cryocooler with an operating frequency of 50 Hz were given. The correlation equations for the maximum and cycle-averaged friction factors in terms of Reynolds numbers and dimensionless distance X were obtained. It was found that the value of the cycle-averaged pressure drop in the oscillating flow across the regenerator is two to three times higher than that of a steady flow at the same Reynolds numbers based on the cross-sectional mean velocity. In addition, the relationship of the phase shifts between the velocity and pressure wave is also discussed. 1998 Elsevier Science Ltd. All rights reserved Keywords: oscillating flow; regenerator; E. pulse tube cryocooler; experimental study
Nomenclature Am Dh Dw ⌬P ⌬Pmax ⌬P¯mean ⌬Pst fmax ¯f mean fst L n
cross-sectional area of the regenerator hydraulic diameter wire diameter of screens pressure drops maximum pressure drop in one cycle cycle-averaged pressure drop in one cycle pressure drop of steady flow maximum pressure drop factor cycle-averaged pressure drop in one cycle pressure drop factor of the steady flow length of the regenerator number of stacked screens
Introduction Interest in the pulse tube cryocooler has grown rapidly in recent years owing to its no-moving component in the low temperature region. Therefore, it has merits in mechanical simplicity, high reliability, low vibration and low cost. This cryogenic cryocooler has the potential for promising applications in the cooling of infrared devices and sensors, superconducting electronic devices, etc. The significant influence of pressure characteristics in the oscillating flow regenerator on the performance of the cryocooler has been recognized recently in many papers1–3. The ability to pre-
Re um umax X
Reynolds number area-averaged fluid velocity maximum area-averaged fluid velocity dimensionless distance
Greek letters 
mesh distance dimensionless phase angle porosity pitch kinematics viscosity of fluid density of fluid oscillating frequency
dict pressure drops and phase shift in the oscillating flow regenerator is crucially important in the optimum design of pulse tube cryocoolers and other cryocoolers. As a necessary component, the oscillating flow regenerator plays an important role in the refrigeration performance of the pulse tube cryocooler. In the past, due to the lack of a friction factor and heat transfer coefficient for the oscillation flow regenerator, the regenerator was taken to be a kind of high efficiency heat exchanger that provided a way to get the gas to the low temperature region with as much cooling power as possible, which may be close to the actual performance for unidirectional steady flow or
Cryogenics 1998 Volume 38, Number 6 649
Oscillating flow characteristics for regenerator: Y. Ju et al. very low frequency regenerators. Therefore, the correlation equation of the friction factor given by Kays and London4 has been widely used. Similarly, there are also some correlations with pressure drop in regenerators5,6, but most of them are based on a unidirectional steady flow through a stack of screens. Since the pulse tube cryocooler operates under periodically reversing flow conditions, it is apparent that the correlation equations based on steady flow are not able to predicate accurately the pressure drop in the oscillating flow regenerator. For example, Yoshida et al.7, Zhao and Cheng8 and Helvensteijn et al.9 found a higher friction factor in the oscillating flow regenerator than in the steady flow at the same Reynolds numbers based on the crosssectional mean velocity. Oscillating flow characteristics for the regenerator in the pulse tube cryocooler demonstrate not only pressure drops but phase shifts. Relatively little research has been performed on the pressure drop over a stack of screens subjected to an oscillating flow regenerator. Therefore, it is important for analysis and optimum design to study the pressure drop and the phase shift in the oscillating flow regenerator. As we know, the working process in the pulse tube cryocooler is very complex due to the unsteady, oscillating compressible gas flow, the porous media in the regenerator and the addition of the orifice valve and double-inlet valve, etc. An understanding of the mechanisms associated with the pulse tube cryocooler requires a full solution of the Navies–Stocks equations. However, the complexities of these equations make an analytical solution for the pulse tube cryocooler essentially impossible. Therefore, an experimental study has been adapted and designed to investigate the oscillating flow characteristics in the regenerator subjected to a periodically reversing flow in the pulse tube cryocooler. In this paper, details of the dynamic experimental apparatus used to investigate the oscillating flow characteristics across a regenerator packed with stainless-steel wire screens are presented. The oscillating flow is established by means of a self-made linear compressor whose swept volume is 10 cc with an operating frequency of 50 Hz connected to the inlet of the regenerator through a velocity straightener. Experimental data of the pressure drops and phase shifts in the regenerator under cyclic flow conditions were obtained. The correlation equation of the friction factor during actual operation of a 50 Hz oscillating flow in a pulse tube cooler is obtained. It is found that the value of the cycle-averaged pressure drop for the 50 Hz oscillating flow is two to three times higher than that of a steady flow at the same Reynolds number based on the cross-sectional mean velocity. The relationship of the phase shifts between the velocity and the pressure wave is also obtained and discussed.
reservoir with an adjusted needle orifice valve which is connected to the end of the second velocity straightener. The oscillating flow is established by means of a self-made linear compressor. The swept volume of the compressor is 10 cc, its operating frequency is around 50 Hz. A heating resistance is provided at the cold end to maintain a constant temperature through the whole test section. Two small quartz differential pressure transducers (KISTLER, Type 601A), connected to a charge amplifier (KISTLER, Type 5011) having a high natural frequency (150 kHz), are used to measure the transient gas pressure wave at the two ends of the regenerator, as shown in Figure 1. We used a hot wire anemometer (DANTEC, Model 90N10) to measure the instantaneous cross-sectional mean velocity. The anemometer works according to the constant temperature anemometer (CTA) principle where the sensor probe forms an arm of a Whetstone bridge. It is kept in balance by the deviation signal across the bridge diagonal so that the probe resistance, and hence its temperature, is kept constant independent of the cooling from the flowing medium. Two small hot probes (DANTEC, Model 55P11) are placed at the center of the tube between the two velocity straighteners at the left side of the test section. The hot probes made of tungsten are 5 m in diameter between the probe support of 2 mm diameter and 30 mm length. The probes are suspended in the gas stream by probe supports which are electrical conductors and which also served as electrical connections for the sensors. The CTAs are operated at approximately 200 K, warmer than the temperature of the environment fluid, and the response time of the CTAs in this system is 20 s. Analog-to-digital conversions are carried out by an A/D conversion board (KEITHLEY, DAS 1601) which is plugged into a 486 personal computer. A 4-channel simultaneous sample and hold front ends are employed so that both the dynamic pressure and the velocity voltage signals are sampled simultaneously. An oscilloscope (HP 5402B) is also employed to simultaneously observe wave signals.
Experimental conditions The test section of the regenerator, 70 mm in length and 10.5 inner diameter, is made of stacks of stainless-steel plainly woven wire screens with five different mesh sizes. The properties of the number of screens n, wire diameters Dw, pitch , mesh distance , porosity and hydraulic diameter Dh for the five mesh sizes of the wire screens are listed in Table 1. Wire diameter Dw, pitch and mesh distance  are provided by the manufacturer. The hydraulic diameter Dh and the porosity of the regenerator are determined from equations given below. The working medium is helium gas, the operating frequency is 50 Hz and the system mean pressure varies from 0.6 to 0.9 MPa.
Experimental system Experimental results and discussions A schematic of the experimental apparatus is shown in Figure 1. It is designed for the experimental measurement of the dynamic pressure and mass flow rate of the oscillating flow gas at the two ends of the test section of the regenerator. The test section consists of a packed column (70 mm in length and 10.5 mm inner diameter) with both ends connected to the velocity straightener (60 mm in length and 9 mm inner diameter). The test section is connected to a
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Cryogenics 1998 Volume 38, Number 6
The raw experimental data measured from the hot wire anemometer and pressure transducers require data processing which includes velocity transformation and correction, high frequency harmonic filtration, Fourier analysis, etc. Figure 2 shows the typical variation of the instantaneous gas velocity and pressure wave at the inlet (V1,P1) and outlet (V2,P2) of the test section. They demonstrate
Oscillating flow characteristics for regenerator: Y. Ju et al.
Figure 1 Schematic diagram of experimental apparatus: 1. compressor; 2. pressure gauge; 3. velocity straightener; 4. connector; 5. regenerator; 6. orifice valve; 7. reservoir; 8. pressure transducer; 9. hot wire probe; 10. charge amplifier; 11. hot-wire anemometer; 12. A/D conversion board; 13. 486 computer Table 1 Properties of stainless-steel wire screens Mesh size
80 150 250 300 400
Number of screens, n 428 500 600 690 720
Wire diameter, Dw (mm) 0.102 0.061 0.041 0.031 0.025
Porosity,
0.735 0.6993 0.6582 0.6938 0.6677
Mesh distance,  (mm) 0.140 0.120 0.100 0.087 0.083
Hydraulic diameter, Dh (mm) 0.2828 0.1418 0.0788 0.0704 0.0504
Figure 2 Typical variation of the instantaneous gas velocity and pressure waves
the variations in the amplitude and phase relationship between the gas velocity and the dynamic pressure. It should be noted that the gas velocity and the pressure are not sinusoidal oscillations, and that the peak flows and halfcycle frequencies are not equivalent in Figure 2. Therefore, the experimentally measured phase angles were averaged over the two half-cycles. Our experimental results show that the flow characteristic depends on many factors such
as matrix porous properties, gas properties, the outlet conditions affected by orifice valve, etc. The operating frequency of the oscillating flow established by our linear compressor also affects the cycled flow pressure drops and phase shifts. The experiments in this paper focus on 50 Hz oscillation flow as an example to study the flow characteristics of an oscillating flow regenerator. In all tests, we studied experimentally the effects of dif-
Cryogenics 1998 Volume 38, Number 6 651
Oscillating flow characteristics for regenerator: Y. Ju et al. ferent orifice settings, system mean pressure and mesh sizes on the oscillating flow characteristics of pressure drops and phase shifts. Some detailed experimental data of the oscillating pressure drop ⌬P, and the phase shifts which include the phase shifts between the input pressure and output pressure ⌬P1P2, the input and output velocity ⌬V1V2 and the output pressure and velocity, ⌬P2V2 are presented.
Effects of orifice setting Figure 3a–d shows the effects of the orifice setting on the pressure drops ⌬P and the phase shifts with system mean pressure of 0.8 MPa and mesh size of 400 mesh. In the figures, position 1 indicates that the valve is closed, position 2 that the valve is opened a little (we named this the optimum position), and position 3 that it is fully opened. The pressure drop ⌬P decreased rapidly from position 1 to 2 and increased from position 2 to 3. At position 2, which we named the optimum value, the pressure drop reached its minimum value. The phase shift ⌬P2V2 decreased rapidly from position 1 to 2 and maintained an almost constant value from position 2 to 3. This shows that the opening value of the orifice valve is crucially important to the performance of the regenerator. Therefore, it should be noted in designing a pulse tube cryocooler. Position 2 (optimum value) varied with different mesh size of the stainless steel wire screens in the test section, while it remained almost constant for different system mean pressures. The experimental data reported in this paper are all based on tests at position 2 of the orifice opening value.
with a mesh size of 400 mesh are shown in Figure 4a–d. From these figures, we can clearly see the variations in the pressure drops and phase shifts between the pressure and velocity with the system mean pressure.
Effects of mesh size Figure 5a–d illustrates the influence of the mesh size on the pressure drop ⌬P and the phase shifts with a system mean pressure of 0.8 MPa. The pressure drop ⌬P and the phase shifts ⌬P1P2 increased rapidly with increasing stainless-steel mesh size. They achieved their maximum values at a mesh size of 400 stainless-steel wire screens, while the phase shifts ⌬V1V2 and ⌬P2V2 achieved their minimum values at a mesh size of 400. Thus it was demonstrate that we should adapt 400 stainless-steel mesh size in designing the pulse tube cryocooler at an operating frequency of 50 Hz to improve the performance of the regenerator.
Pressure drop and pressure drop factor Pressure drops across the regenerator in the oscillating flow under different experimental conditions including five mesh sizes and several system pressure are obtained. To compare the pressure drops over the regenerator in oscillating flow with those in steady flow, we used the following correlation equation for predicting the friction factor of a steady flow through a stack of woven screen1: 33.6 + 0.337 Re
Effects of system mean pressure
f st =
The effects of different system mean pressures on the pressure drop ⌬P and the phase shifts across the test section
where
Figure 3 Effects of orifice setting on the oscillating flow characteristics
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(1)
Oscillating flow characteristics for regenerator: Y. Ju et al.
Figure 4 Effects of mean pressure on the oscillating flow characteristics
Figure 5 Effects of mesh size on the oscillating flow characteristics
f st =
⌬Pst/n 1 2 u 2 st
Re =
ust
(2)
(3)
where ⌬Pst is the steady flow pressure drop, ust is the crosssectional mean flow velocity in the packed column, n is the number of screens,  is the distance between meshes, and Re is the Reynolds number based on  and ust. To predict the pressure drop across the regenerator in the 50 Hz pulse tube cryocooler, the maximum friction factor is defined as follows3
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Oscillating flow characteristics for regenerator: Y. Ju et al. f max =
⌬PmaxDh 1 (umax )2L 2
(4)
and the cycle-averaged friction factor is ¯ ¯f mean = ⌬PmeanDh 1 (umax )2pL 2
(5)
Defining the Reynolds number Re =
umaxDh
(6)
where ⌬Pmax is the maximum pressure drop in one cycle, ⌬P¯meanis the cycle-averaged pressure drop, umax is the maximum cross-sectional mean flow velocity in the regenerator, L is the length of the test section of the regenerator, and Dh is the hydraulic diameter of the screen, which is defined as follows3 Dh =
Dw 1−
Dw√2D2w 42
(8)
1 umax 2 Dh
(9)
The maximum friction factor fmax was computed and correlated according to Equation (4) based on the experimental data. The normalized curve of fmax is shown in Figure 6. The correlation equation of the friction factor of the regenerator used in the 50 Hz pulse tube cryocooler in terms of Re and X was obtained as: f max =
冉
冊
1 1.22 × 106 2.76 × 104 + X Re
(10)
Figure 6 Correlation equation of the maximum friction factor in terms of Re and X
654
冊
(11)
The maxium deviation of the experimental data from the value calculated by Equations (10) and (11) is about 4.33%. Equations (10) and (11) can be used to predict the pressure drop in designing the regenerator of the 50 Hz pulse tube cryocooler. We compared the pressure drops predicted by Equation (11) for the oscillating flow with those from Equation (1) for the steady flow. The compared results of pressure drops of oscillating flow and steady flow are shown in Table 2. It is found that the value of the cycleaveraged pressure drop of the oscillating flow in the regenerator is two to three times higher than that of a steady flow at the same Reynolds numbers based on the crosssectional mean velocity.
Phase shift relationship
We also defined the dimensionless distance as: X=
冉
5 ¯f mean = 1 1.10 × 104 + 3.78 × 10 X Re
(7)
with being the screen porosity which is defined as1:
=1−
Based on the experimental data, the cycle-averaged friction factor ¯f mean was evaluated according to Equation (5) and is presented in Figure 7. It is shown that the experimental data are well fitted by the following correlation equation:
Cryogenics 1998 Volume 38, Number 6
Oscillating flow characteristics for the regenerator in the pulse tube cryocooler demonstrate not only pressure drops but phase shifts. Phase shifts were determined by the properties of stainless-steel wire screens and the Reynolds number of the working gas besides the orifice setting. Figure 8a–c illustrates the phase shifts between the input and the output pressure ⌬P1P2, the input and the output velocity ⌬V1V2 and the output pressure and velocity ⌬P2V2, respectively. From these figures, we can predict the phase shifts between the inlet and the outlet of pressure and velocity across the oscillating flow regenerator. Figure 8c shows that a minimum value of the phase shift ⌬P2V2 exists, between the output of the gas velocity and the pressure, which supplies a special Reynolds number for different mesh sizes of stainless-steel wire screens. Figure 9 indicates the relationship between the mesh sizes of stainless-steel wire screens and the special Reynolds number. To predict the phase shift ⌬P2V2 between the output of the gas velocity and the pressure across the oscillating flow regenerator, we define the dimensionless phase shifts as follows:
Figure 7 Correlation equation of the cycle-averaged friction factor in terms of Re and X
Oscillating flow characteristics for regenerator: Y. Ju et al. Table 2 Pressure drops of oscillatory flow compared with those of steady flow Mesh size
Re
80 150 250 300 400
5.74 5.57 5.17 5.09 4.73
⌬P¯ mean (kPa)
⌬Pst (kPa)
9.93 12.67 17.21 20.44 27.97
4.58 5.98 7.42 8.69 9.38
⌬P¯ mean/⌬Pst 2.20 2.28 2.32 2.35 2.98
Figure 9 Relationship between the special Reynolds number and the mesh sizes
Figure 10 Correlation equation of the dimensionless phase shifts with Reynolds number
mental data are well fitted by the following correlation equation:
=
36.3 − 8.05 × 10−0.049Re Re
(13)
The maximum relative deviation between Equation (13) and the experimental data is about 4.87%. Figure 8 Variation of the phase shifts between the gas velocity and the pressure
=
⌬P2V2 ⌬P1V1
(12)
Based on the experimental data, the dimensionless phase shift was calculated according to Equation (12) and is presented in Figure 10. This figure shows that the experi-
Conclusions Experimental data on the oscillating flow characteristics of the regenerator in a 50 Hz pulse tube cryocooler are presented in this paper. The oscillating flow characteristics appear not only as pressure drops but also as phase lags. Correlation equations for the maximum and cycle-averaged friction factors in terms of Reynolds numbers and dimen-
Cryogenics 1998 Volume 38, Number 6 655
Oscillating flow characteristics for regenerator: Y. Ju et al. sionless distance X are obtained. It is found that the value of the cycle-averaged pressure drop of the oscillating flow in the regenerator is two to three times higher than that of a steady flow at the same Reynolds numbers based on the cross-sectional mean velocity. In addition, the relationship of the phase shifts between the gas velocity and pressure wave is also presented.
Acknowledgements Research supported by the Foundation of Chinese Academy of Sciences.
References 1. Miyabe, H., Takahashi, S. and Hamaguchi, K., An approach to the design of Stirling engine regenerator matrix using packs of wire gauzes. Proc. 17th IECEC, 1982, 1, 1839–1844.
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2. Guo, F.Z., Chou, Y.M. and Lee, S.Z., et al., Flow characteristics of a cyclic flow regenerator. Cryogenics, 1987, 27, 152–155. 3. Tanaka, M., Yamshita, I. and Chrisaka, F., Flow and heat transfer characteristics of the Stirling engine regenerator in an oscillating flow. JSME Int. J., 1990, 33, 283–289. 4. Kays, W.M. and London, A.L., Compact Heat Exchanger, 2nd edn. McGraw-Hill, New York, 1964. 5. Tong, L.S. and London, A.L., Heat transfer and flow friction characteristics of woven-screen and cross-rod matrices. Trans. ASME, 1957, 1558–1570. 6. Walker, G. and Vasishta, V., Heat transfer and friction characteristics of wire-screen Stirling engine regenerator. Adv. Cry. Eng., 1971, 16, 324–332. 7. Yoshida, S., Ravikumar, K.V. and Frederkng, T.H.K., Friction factors of stacks of perforated regenerator plates. Cryocoolers, 1995, 8, 259–268. 8. Zhao, T.S. and Cheng, P., Oscillatory pressure drops through a woven-screen packed column subjected to a cycle flow. Cryogenics, 1996, 36, 333–341. 9. Helvensteijn, B.P.M., Kashani, A., Spivak, A.L. et al., Pressure drop over regenerators in oscillating flow. Presented at CEC/ICMC 97, Portland, Oregon, USA, July 1997.