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Thermoacoustic power effect on the refrigeration performance of thermal separators
Cryogenics 43 (2003) 493–500 www.elsevier.com/locate/cryogenics
Thermoacoustic power effect on the refrigeration performance of thermal separators S.B. Liang a, X.L. Li b, H.B. Ma a
c
c,*
Department of Mechanical and Aerospace Engineering, University of Missouri––Columbia, Columbia, MO 65211, USA b Department of Chemical Engineering, Fuzhou University, Fuzhou, PR 350002, China Department of Mechanical and Aerospace Engineering, University of Missouri––Columbia, Columbia, MO 65211, USA Received 26 September 2002; accepted 22 May 2003
Abstract An experimental investigation on the refrigeration processes occurring in a receiving tube of a thermal separator was conducted in order to determine the primary factors affecting the refrigeration performance of this new type of refrigerator. In the current investigation, the gas in the system is divided into the oscillating gas and driving gas. While the compression/expansion of the oscillating gas caused by the driving gas determines the refrigeration process occurring in the receiving tube of the thermal separator, the temperature gradient on the receiving tube significantly affects the acoustic power generation and refrigeration performance. Experimental results demonstrate that when the tube–wall temperature difference near the open end of the receiving tube increases, the refrigeration coefficient increases. Using the information presented in the paper, a new cryogenic refrigeration system was developed, and the experimental data shows that the temperature of the cryogenic air flow in the system could reach )130 °C within 50 min. It suggests that the thermal separator investigated in the paper can be employed in the field of cryogenic engineering. Ó 2003 Elsevier Ltd. All rights reserved. Keywords: Thermal separators; Thermoacoustics; Oscillating gas; Cryogenic flow
1. Introduction Thermal separators as new types of compressed gas expanders have been investigated by a number of researchers [1–7]. Based on structures and mechanisms, there are two types of thermal separators, i.e., the static thermal separator (STS) and the rotational thermal separator (RTS), as illustrated in Figs. 1 and 2, respectively. The key components in the STS are a static rectangular nozzle, an array of static receiving tubes, and two-side resonance chambers. Compressed gas flowing through the static convergence nozzle with a high speed repeatedly sweeps past a series of receiving tubes based on the Coanda effect produced by oscillating pressures in two-side chambers. Between the time intervals of two consecutive sweepings of the high-speed gas, the gas injected into the receiving tubes is exhaled into the exhaust chamber. When the driving gas in the tubes is exhausted, the gas cycle is completed. Because
*
Corresponding author. E-mail address: [email protected] (H.B. Ma).
0011-2275/$ - see front matter Ó 2003 Elsevier Ltd. All rights reserved. doi:10.1016/S0011-2275(03)00126-7
no rotational parts are used in this kind of expander, the construction is relatively simple, and the operation and maintenance are less cost. The primary issue for the STS, however, is its low oscillation frequency, and its low refrigeration efficiency caused by the mixing of fresh and exhausted gases in the STS. The RTS, as shown in Fig. 2, is composed of several rotating nozzles and a number of stationary tubes mounted radially around the periphery of rotating nozzles. During operation, the rotating nozzles sweep past a series of stationary shock tubes in order of precedence. When any shock tube aligns with a rotating nozzle, it is exposed to the high-pressure gas for a time interval. The appearance of the high-pressure gas is equivalent to the diaphragm break in a normal shock tube. As a shock wave propagates into the tube, it accelerates and compresses the gas originally in the tube. The shocked gas dissipates thermal energy through the tube wall into the environment. The wall temperature at the cold end of tube remains very low, resulting in a low-pressure and low-temperature gas being exhaled into the exhaust chamber. Currently, the refrigeration efficiency of RTS has achieved 80% in the lab and 75% in industrial
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Nomenclature i fdr L j P Q Ta To Ti u
enthalpy, kJ/kg frequency of driving gas, Hz length of receiving tube, m ratio of specific heats pressure, N/m2 heat transfer, W ambient air temperature, K outlet temperature of gas, K inlet temperature of gas, K velocity of gas, m/s
Fig. 1. Static thermal separator (STS).
Fig. 2. Rotational thermal separator (RTS).
applications [1,6,7]. Due to features such as low cost, easy operation, simple maintenance, high throughput and good anti-erosion against drops or particles, the RTS has been used more often than the STS. In 1966, Gifford and Longsworth [8] presented a new pulse tube refrigerator with a surface heat pumping cycle, and found that there was an optimum pulse rate independent of length but dependent on the equivalent diameter of the chamber squared. Due to the low frequency, the thermoacoustic power effect on the refrig-
W X
work done by the driving gas position, m
Greeks e pressure ratio, Pi =Po gs refrigeration efficiency Subscripts o outlet i inlet m average value
eration in the pulse tube refrigerator was not detected. Based on the fundamental theory of shock tube, Yu [3] described the oscillation characteristics of the working fluid in the thermal separator, and indicated that shock and rarefaction waves were the factors affecting the heating and cooling of gas in the tube during a gas cycle. Shao and Bao [7] conducted a thermodynamic analysis of the working fluid in the tube, and found that when the high-speed gas was injected into the tube, the compression effect increased the gas temperature inside the tube. This resulted in heat transfer from the high temperature gas to the tube wall, where the heat was dissipated into the environment. The energy loss directly decreased the temperature of exhausted gas. Fang et al. [6] conducted further experimental studies on the RTS. The improved design of internal gas seals in the RTS greatly reduced the mixing of fresh and exhausted gases. Expansion chambers at each closed end of the receiving tubes in the RTS were used to absorb the reflection of the shock wave, and the heating effect of the shock wave on the exhausted gas was eliminated. All these dramatically increased the refrigeration efficiency and improved the refrigeration performance of the RTS. In the current investigation, an experimental system consisting of one typical receiving tube employed in the STS or RTS was established and the effect of thermoacoustic power on the refrigeration performance was investigated in order to better understand the mechanisms occurring in this new type of refrigeration system. The results help to increase the refrigeration efficiency and improve the design of the thermal separator. Using the information presented in this paper, a cryogenic cycle system generating a cryogenic flow is investigated and the system performance discussed.
2. Experimental system The experimental system consisted of a convergence nozzle, a gas distributor, a receiving tube, a compressedgas generation unit, a driving gas frequency controller,
S.B. Liang et al. / Cryogenics 43 (2003) 493–500
an exhausted gas chamber, data acquisition systems for the temperature and pressure measurements, and a personal computer. The receiving tube was fabricated from pure copper. Three 12.0 mm diameter tubes with lengths of 2.6, 3.0, and 4.2 m, respectively, were investigated. The compressed-gas generation unit was used to generate the high-pressure gas with the flow rate up to 100.0 N m3 /h. The pressure ratio, defined by the pressure of the driving gas at the inlet of the nozzle divided by the atmospheric pressure, could be adjusted from 1.0 to 10.0. The driving gas frequency controller consisting of the gas distributor and a motor was used to control the driving gas frequency. As shown in Fig. 3, the gas distributor was fabricated from a plate with several holes, which was connected to a motor. The hole diameters were each equal to the minimum diameter of the convergence nozzle. The rotating speed of the motor and the hole number on the plate determined the frequency of the driving gas, ranging from 15 to 456 Hz. The exhausted gas chamber was fabricated from stainless steel, and a thermocouple and a pressure sensor were used to measure the temperature and pressure of the exhausted gas. T-type thermocouples were employed to measure the tube wall and gas temperatures. Micro-pressure sensors with working frequencies of 50–300 kHz were used to measure oscillating pressures of gas inside the receiving tube and exhausted gas chamber. Due to the higher working frequencies of pressure sensors, each sensor was calibrated in a pressure calibration system [4]. The working gas of the thermal separator was compressed dry air. Prior to the start of the experiment, gas leak tests were conducted to verify that all of the driving gas entered the receiving tube. Because the environment temperature directly affects the refrigeration performance, the effect of exhausted gas on the environment temperature was also conducted to maintain a constant environment. Due to the heat capacity in the system, the system was
Gas distributor Compressedgas generation unit P1 T1
allowed to equilibrate for thirty min to reach steadystate conditions. Once the test section reached steady state, temperatures and pressures were recorded and directly sent to the personal computer through the data acquisition system. In this way, effects of pressure ratio, oscillating frequency, receiving tube dimension, insulation joint, and heat transfer process on the refrigeration performance of the single-tube thermal separator were examined. The accuracy of temperature measurements for thermocouples and data acquisition system was 0.4 °C in the full range scale. The pressure sensor has an uncertainty of 4.5% for the full scale of 1.5 MPa.
3. Results and discussion The compressed air traveling through the convergence nozzle, shown in Fig. 3, obtained a high speed, prior to being injected into the receiving tube. The excited frequency of the gas inside the tube was dependent on the hole number of the gas distributor and on the rotating speed of the motor. Based on the function, the gas involved in one cycle in the receiving tube can be divided into the driving gas and the oscillating gas. The highspeed driving gas from the nozzle performs work on the oscillating gas already present in the tube. Due to the work output from the driving gas, the enthalpy and kinetic energy of the driving gas decreases similar to the compressed gas in a turbine expander. At the end of one cycle, the driving gas completely leaves the receiving tubes and enters the exhaust gas chamber, where it is removed from the thermal separator. The oscillating gas always stays in the tube and receives work from the driving gas. Due to the excitation of driving gas, the oscillating gas in the tube reciprocates, which plays an important role in the thermal separator. The receiving tube with one closed end in the thermal separator shown in Fig. 3 is considered to be a typical
Exhausted Gas chamber P0 Receiving tube T0
driving gas
ω
495
PC
motor Frequency converter
Speed sensor
Fig. 3. Experimental system.
Data Acquisition System for Pressures & temperatures
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thermoacoustic pipe [8–13]. As the driving gas strokes the gas in the tube, the oscillating gas is compressed while moving toward the closed end and expanded while moving toward the open end, resulting in the motion of the oscillating gas along the tube. Once the work on the oscillating gas is done by the driving gas, the driving gas leaves the thermal separator at the open end of the receiving tube. In order to better explain the refrigeration cycle in the system investigated here, a parcel of gas [9] is chosen as a control volume. The parcel of gas is a small volume of gas close to the tube wall that moves back and forth from the open end to the closed end in the tube. In the special case the cross-sectional area of the parcel in its moving direction is equal to the crosssectional area of the tube. The parcel volume should be large enough so that its thermodynamical description is valid. The oscillating gas in the tube may be modeled as a collection of parcels that behave in the same manner. As the parcel of the gas is stroked at location A, shown in Fig. 4, this parcel of the oscillating gas will move toward to the closed end of the receiving tube. As it reaches location B, it is compressed. If no heat exchange exists between the gas and the tube wall as the gas travels from location A to location B, the parcel of the oscillating gas is compressed adiabatically resulting in the increase of the gas temperature. When the gas temperature is higher than the wall temperature, heat rejection occurs. In the time interval between two strikes of the driving gas, the open end of the oscillating gas in the receiving tube is exposed to the atmosphere, i.e., a low pressure surrounding. The parcel of the oscillating gas will move adiabatically back to the open end, where the expansion process occurs resulting in a decrease of the gas temperature. If the surrounding temperature is higher than the gas temperature, the parcel of oscillating gas absorbs heat from the tube wall. The coefficient of performance (COP) can be calculated by COP ¼
QL W
ð1Þ
where QL is the heat absorbed in location A, and W is the work done by the driving gas. While the COP can be used to describe the refrigeration performance, it is found that the refrigeration efficiency (isentropic efficiency) can better describe the refrigeration performance
Fig. 5. Thermodynamic process of the driving gas in the tube.
of thermal separator investigated here. Fig. 5 describes the thermodynamic process of the driving gas occurring in the nozzle and receiving tube. The refrigeration efficiency (isentropic efficiency), gs , is given as gs ¼
ii io 1 To =Ti ¼ 0 ii io 1 ðPi =Po Þk1 k
where, ii , pi and Ti respectively represent the inlet enthalpy, pressure and temperature of the air compressed into the single-tube thermal separator; where io , po and To represent the outlet enthalpy, pressure and temperature of exhausted air from the single-tube thermal separator; and where j is ratio of specific heats. As shown in Eq. (2), the refrigeration efficiency depends on the outlet temperatures and outlet pressures for a given inlet condition. When the receiving tube maintains a sufficiently large temperature difference across a region where the gas experiences thermal expansion, as the pressure near the closed end of receiving tube is high, and thermal contraction, as the pressure near the open end of the receiving tube is low, the gas in the tube pumps acoustic power into the standing wave. The wave in turn provides the oscillating pressure and the oscillating motions resulting in an additional thermal expansion and contraction in the tube. In this way, the additional thermoacoustic refrigeration is generated. However, the additional thermoacoustic power generation exists only when the temperature difference is higher than the critical temperature gradient, DTcrit , defined by [9] DTcrit ¼
Fig. 4. Oscillating motion of a parcel of oscillating gas.
ð2Þ
Tm bxpis qm cp usi
ð3Þ
where Tm is the mean temperature; b ¼ ðoq=oT Þp =qm is the ordinary thermal expansion coefficient; qm is the average density; cp is the constant-pressure heat capacity per unit mass; x is equal to 2pfdr and fdr is the frequency; pis is the pressure amplitude; and usi is the velocity amplitude. It should be noted that all properties defined above are for the gas at x position inside the receiving tube.
In order to investigate the effect of the temperature gradient along the tube wall of the receiving tube on the refrigeration performance of the single-tube thermal separator shown in Fig. 3, an insulation joint made of Teflon shown in Fig. 6 was placed on the receiving tube. The receiving tube was made of copper with an inner diameter of 12 mm, a wall thickness of 1 mm and a length of 2.6 m. Fig. 7 illustrates the wall temperature distributions along a tube with an insulation joint and along a tube without such a joint. When an insulation joint was placed on the tube, the tube–wall temperature gradient increased near the open end of the tube. As shown in Fig. 7b, the maximum temperature gradient at x ¼ 0:4 m increased from 700 to 820 K/m. The increase in the temperature difference across the insulation joint would directly increase thermoacoustic power, producing additional refrigeration. As a result, the refrigeration performance of the thermal separator, as shown in Fig. 8, improved with the temperature gradient increase. In addition, the temperature gradients at x ¼ 0:4 m for both cases, as shown in Fig. 7b, are higher than the critical temperature gradient, DTcrit ¼ 626:3 K/m, calculated by Eq. (3), where pm ¼ 0:1 MPa, qm ¼ 1:5 kg/ m3 , cp ¼ 1:0 kJ/kg K, pis ¼ 0:22 MPa, and usi ¼ 105:0 m/ s, thereby providing verification that thermoacoustic power was generated in the receiving tube due to the necessary temperature difference. Furthermore, experimental results shown in Fig. 8 indicated that the improvement of the refrigeration coefficient depended on the location of insulation joint. When the insulation joint was placed in the tube between 0.0 and 1.2 m from the inlet of the receiving tube, refrigeration performance consistently improved, and a maximum refrigeration efficiency of 40.5% was found to occur for a joint located at X ¼ 0:4 m. When the insu-
Fig. 6. Schematic of insulation joint mounted in the receiving tube.
497
200 150 100 without insulation joint with insulation joint at X=0.4 m
50 0 0
0.5
1
1.5
2
2.5
-50
(a) temperature gradient (K/m)
3.1. Insulation joint effect
Tube-wall temperature, C
S.B. Liang et al. / Cryogenics 43 (2003) 493–500
tube length (X) (m) 1000 without insulation joint with insulation joint at X=0.4 m
800 600 400 200 0 -200
0
0.5
1
15 .
2
2.5
-400
(b)
tube length (x) (m)
Fig. 7. Insulation joint effect on the wall temperature along the receiving tube (a) wall temperature distribution; (b) wall temperature gradient (e ¼ 4:5, Ti ¼ 21:4 °C, Ta ¼ 15:5 °C, fdr ¼ 71:4 Hz, tube length ¼ 2.6 m, natural convection).
lation joint was placed at the location, X P 1:2 m, the temperature gradient on the receiving tube was unaffected and no improvement of refrigeration performance was observed. 3.2. Heat transfer effect The effective heat removal in the higher-temperature heat source can increase the refrigeration performance in the traditional refrigeration system such as the pulse tube refrigerator. The effects of natural and forced convections on the refrigeration performance of the receiving tube were investigated. The natural convection investigation was based on a receiving tube oriented horizontally in air at 15.5 °C. The forced convection investigation was based on forced water flow over the surface of a receiving tube, which consisted of a cooling block and cooling bath, as shown in Fig. 9. The inside diameter of the cooling block was 60.0 mm. The receiving tube was fabricated from a copper tube with an inner diameter of 12.0 mm, a wall thickness of 1.0 mm, and a full tube length of 4.2 m. Eight thermocouples were placed on the receiving tube to measure the temperature distribution. Fig. 10 illustrates the temperature distributions along the receiving tube for a natural convection condition including the pressure ratio effect. As shown, when the pressure ratio increased, the temperature drop occurring on the receiving tube increased resulting in an increase of refrigeration coefficient shown
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T1 -T0 , (C)
43
41
39
37 0
0.2
0.4
0.6
0.8
1
1.2
X (m)
Fig. 10. Temperature distributions of the tube wall (Ti ¼ 21:0 °C, Ta ¼ 15:0 °C, fdr ¼ 69:3 Hz, natural convection).
(a)
forced convection heat transfer natural convection heat transfer
43 41 39 37 35 0
0.2
0.4
0.6
0.8
1
1.2
X (m)
(b) Fig. 8. Effect of insulation joint position on the temperature drop and refrigeration efficiency (e ¼ 4:5, Ti ¼ 21:4 °C, Ta ¼ 15:5 °C, fdr ¼ 71:4 Hz, natural convection). (a) Temperature drop; (b) refrigeration efficiency.
Fig. 9. Schematic of cooling block.
in Fig. 11. The highest refrigeration coefficient occurred at the pressure ratio of e ¼ 5:0. The outlet temperature of exhausted gas in the chamber could reach )27.0 °C at for e ¼ 6:0. Fig. 12 illustrates the temperature distribution along the receiving tube in the forced convection condition. As shown the temperature drop on the receiving tube was significantly reduced by forced convection. When the cooling condition was changed from the natural convection to the forced convection, the temperature gradient near the open end of the receiving tube decreased resulting in the decrease of the acoustic
refrigeration efficiency, %
Refrigeration coefficient (%)
45
45 40 35 30 25 2
3
4
5
6
pressure ratio Fig. 11. Refrigeration efficiency with pressure ratio (Ti ¼ 21:0 °C, Ta ¼ 15:0 °C, fdr ¼ 69:3 Hz).
Fig. 12. Temperature distributions of the tube wall (Ti ¼ 21:0 °C, Ta ¼ 15:0 °C, fdr ¼ 69:3 Hz, forced convection).
power generation. At the same time the sounds heard in the natural convection experiments were not detected for the forced convection experiments. The experimental observations show that when the sound level produced in the receiving tube was louder, the refrigeration performance was better. It should be noted that the sound generated by the thermoacoustic power was quite different from the one by the driving gas. The sound generated by the thermoacoustic power was very loud and the frequency was different than that of the driving gas.
S.B. Liang et al. / Cryogenics 43 (2003) 493–500 0 -20
0
10
20
30
40
50
60
-40
T0 (C)
As a result, when heat transfer in the higher-temperature heat source increases resulting in the decrease of temperature difference on the receiving tube, the refrigeration performance of thermal separator decreases. The results show that the tube–wall temperature difference affects the thermoacoustic power and the refrigeration performance of the thermal separator.
499
-60 -80 -100 -120
Oscillating motions of gas in the receiving tube of a thermal separator play an important role in the refrigerating processes of the thermal separator. As presented above, the refrigeration occurring in the thermal separator investigated here depends not only on the pressure wave created by the compression/expansion of the oscillating gas by the driving gas, but also on the pressure wave resulting from the themoacoustic power generated by the significant temperature gradient existing in the receiving tube. Furthermore, the pressure wave due to the temperature gradient plays the more important role with respect to improving the refrigeration performance of the thermal separator. With micro-pressure sensors, pressure wave propagations inside the receiving tube of thermal separator could be readily obtained. When a relatively large temperature gradient on the receiving tube was maintained, i.e., the natural convection was employed, the second, thermoacoustic pressure wave, shown in Fig. 13, was detected. 3.4. Cryogenic refrigeration Utilizing the information discussed above, a RTS consisting of multiple receiving tubes was designed, fabricated, and employed in a refrigeration system for the generation of cryogenic flow [2]. The thermal separator consisted of three rotational nozzles and 72 re-
-140
time (minute) Fig. 14. Gas temperature at the outlet of thermal separator (Ta ¼ 19 °C).
Refrigeration coefficient variation (%)
3.3. Pressure wave propagations
16 14 12 10 8 6 4 2 0 -2 0 -4
10
20
30
40
50
60
time (minute) 0 Fig. 15. Refrigeration efficiency variation (Dg ¼ gt gg 100%) with 0 time (e ¼ 4:7; n ¼ 3480 rpm; g0 is the initial refrigeration efficiency).
ceiving tubes, as illustrated in Fig. 2. The receiving tubes were fabricated from pure copper. The inner diameter of tubes was 4.76 mm and the length of the tubes was 1.9 m. The air in the cryogenic system circulated at a flow rate of 720 N m3 /h. Fig. 14 shows the results of the outlet temperature of the thermal separator with time. As shown, the temperature of the cryogenic air flow in the system reached values as low as )130 °C within 50 min. Such a cryogenic temperature level suggests that the thermal separators can be employed in the field of cryogenic engineering [2,7,8,12]. While the closed ends of the receiving tubes were contacting with ambient air and its temperature was considered to be constant, the decrease of the outlet temperature of the driving gas increased the temperature gradient on the receiving tube, which directly generated more thermoacoustic power and increased the refrigeration coefficient shown in Fig. 15. The results further demonstrate that the temperature gradients occurring on the receiving tube affected the thermoacoustic power, and the refrigeration performance of thermal separator investigated in the paper.
4. Conclusions Fig. 13. Pressure wave propagations along the receiving tube (Ti ¼ 21:4 °C, Ta ¼ 15:5 °C, fdr ¼ 74:67 Hz, natural convection).
An experimental investigation of the mechanisms of refrigeration occurring in the receiving tube of a thermal
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separator was conducted in order to determine the primary factors affecting the refrigeration performance of this new type of refrigerator. In the current investigation, the gas in the system is divided into the oscillating gas, which always stays inside the receiving tube, and driving gas, which provides the mechanical work for the system. While the compression/expansion of oscillating gas caused by the driving gas determines the refrigeration process occurring in the receiving tube of thermal separator, the temperature gradient on the receiving tube significantly affects the acoustic power generation and the refrigeration performance. Heat transfer effect on the temperature gradient was investigated including the influences of insulation joint position, natural convection, and forced convection. Experimental results demonstrate that when the tube–wall temperature difference near the open end of the receiving tube increases, the refrigeration coefficient increases. Using the information presented in the paper, a new cryogenic refrigeration system was developed. The experimental data shows that the temperature of the cryogenic air flow in the system is capable of reaching a value as low as )130 °C within 50 min. The data further suggests that the thermal separator investigated in the paper can effectively be employed in the field of cryogenic engineering.
References [1] Rennaz MC. Wellhead gas refrigerator field strips condensate. World Oil 1971:60–1. [2] Liang S. A novel cryogenic grinding system for recycling scrap tire peels. Adv Powder Technol 2000;11(2):187–97. [3] Yu H. The flow in a thermal separator. J Dalian Inst Technol 1984;23(4):1–7. [4] Li X. The influences of axial and radial heat transfer on cooling effect of gas wave oscillating tube, Ph.D. Dissertation, Dalian University of Technology, 1996. [5] Yu H. The novel approach for generation of cryogenic test flow in a transonic wind tunnel. Exp Measurem Fluid Mech 1997;11(1): 1–5. [6] Fang Y, Zhu C. Experimental study of gas wave refrigeration. Shock Wave Proceedings, Sendai, Japan 1991;2:1335–8. [7] Shao J, Bao Y. Experimental study of a rotational-nozzle expander. J Zhejiang University 1984;18(3):52–4. [8] Gifford WE, Longsworth RC. Surface heat pumping. Adv Cryogenic Eng 1966;11:171–9. [9] Swift GW. Thermoacoustic engines. J Acoust Soc Am 1988;84:1145–80. [10] Merkli P, Thomann H. Thermoacoustic effects in a resonance tube. J Fluid Mech 1975;70:161–77. [11] Chester W. Resonant oscillations in closed tubes. J Fluid Mech 1964;18:44–64. [12] Swift GW. Thermoacoustic natural gas liquefier. In: proceedings of the DOE Natural Gas Conference. Houston, TX: March 1997. [13] Chen GB, Jin T. Experimental investigation on the onset and damping behaviour of the oscillation in a thermoacoustic prime mover. Cryogenics 1999;39(10):843–6.
Thermoacoustic power effect on the refrigeration performance of thermal separators S.B. Liang a, X.L. Li b, H.B. Ma a
c
c,*
Department of Mechanical and Aerospace Engineering, University of Missouri––Columbia, Columbia, MO 65211, USA b Department of Chemical Engineering, Fuzhou University, Fuzhou, PR 350002, China Department of Mechanical and Aerospace Engineering, University of Missouri––Columbia, Columbia, MO 65211, USA Received 26 September 2002; accepted 22 May 2003
Abstract An experimental investigation on the refrigeration processes occurring in a receiving tube of a thermal separator was conducted in order to determine the primary factors affecting the refrigeration performance of this new type of refrigerator. In the current investigation, the gas in the system is divided into the oscillating gas and driving gas. While the compression/expansion of the oscillating gas caused by the driving gas determines the refrigeration process occurring in the receiving tube of the thermal separator, the temperature gradient on the receiving tube significantly affects the acoustic power generation and refrigeration performance. Experimental results demonstrate that when the tube–wall temperature difference near the open end of the receiving tube increases, the refrigeration coefficient increases. Using the information presented in the paper, a new cryogenic refrigeration system was developed, and the experimental data shows that the temperature of the cryogenic air flow in the system could reach )130 °C within 50 min. It suggests that the thermal separator investigated in the paper can be employed in the field of cryogenic engineering. Ó 2003 Elsevier Ltd. All rights reserved. Keywords: Thermal separators; Thermoacoustics; Oscillating gas; Cryogenic flow
1. Introduction Thermal separators as new types of compressed gas expanders have been investigated by a number of researchers [1–7]. Based on structures and mechanisms, there are two types of thermal separators, i.e., the static thermal separator (STS) and the rotational thermal separator (RTS), as illustrated in Figs. 1 and 2, respectively. The key components in the STS are a static rectangular nozzle, an array of static receiving tubes, and two-side resonance chambers. Compressed gas flowing through the static convergence nozzle with a high speed repeatedly sweeps past a series of receiving tubes based on the Coanda effect produced by oscillating pressures in two-side chambers. Between the time intervals of two consecutive sweepings of the high-speed gas, the gas injected into the receiving tubes is exhaled into the exhaust chamber. When the driving gas in the tubes is exhausted, the gas cycle is completed. Because
*
Corresponding author. E-mail address: [email protected] (H.B. Ma).
0011-2275/$ - see front matter Ó 2003 Elsevier Ltd. All rights reserved. doi:10.1016/S0011-2275(03)00126-7
no rotational parts are used in this kind of expander, the construction is relatively simple, and the operation and maintenance are less cost. The primary issue for the STS, however, is its low oscillation frequency, and its low refrigeration efficiency caused by the mixing of fresh and exhausted gases in the STS. The RTS, as shown in Fig. 2, is composed of several rotating nozzles and a number of stationary tubes mounted radially around the periphery of rotating nozzles. During operation, the rotating nozzles sweep past a series of stationary shock tubes in order of precedence. When any shock tube aligns with a rotating nozzle, it is exposed to the high-pressure gas for a time interval. The appearance of the high-pressure gas is equivalent to the diaphragm break in a normal shock tube. As a shock wave propagates into the tube, it accelerates and compresses the gas originally in the tube. The shocked gas dissipates thermal energy through the tube wall into the environment. The wall temperature at the cold end of tube remains very low, resulting in a low-pressure and low-temperature gas being exhaled into the exhaust chamber. Currently, the refrigeration efficiency of RTS has achieved 80% in the lab and 75% in industrial
494
S.B. Liang et al. / Cryogenics 43 (2003) 493–500
Nomenclature i fdr L j P Q Ta To Ti u
enthalpy, kJ/kg frequency of driving gas, Hz length of receiving tube, m ratio of specific heats pressure, N/m2 heat transfer, W ambient air temperature, K outlet temperature of gas, K inlet temperature of gas, K velocity of gas, m/s
Fig. 1. Static thermal separator (STS).
Fig. 2. Rotational thermal separator (RTS).
applications [1,6,7]. Due to features such as low cost, easy operation, simple maintenance, high throughput and good anti-erosion against drops or particles, the RTS has been used more often than the STS. In 1966, Gifford and Longsworth [8] presented a new pulse tube refrigerator with a surface heat pumping cycle, and found that there was an optimum pulse rate independent of length but dependent on the equivalent diameter of the chamber squared. Due to the low frequency, the thermoacoustic power effect on the refrig-
W X
work done by the driving gas position, m
Greeks e pressure ratio, Pi =Po gs refrigeration efficiency Subscripts o outlet i inlet m average value
eration in the pulse tube refrigerator was not detected. Based on the fundamental theory of shock tube, Yu [3] described the oscillation characteristics of the working fluid in the thermal separator, and indicated that shock and rarefaction waves were the factors affecting the heating and cooling of gas in the tube during a gas cycle. Shao and Bao [7] conducted a thermodynamic analysis of the working fluid in the tube, and found that when the high-speed gas was injected into the tube, the compression effect increased the gas temperature inside the tube. This resulted in heat transfer from the high temperature gas to the tube wall, where the heat was dissipated into the environment. The energy loss directly decreased the temperature of exhausted gas. Fang et al. [6] conducted further experimental studies on the RTS. The improved design of internal gas seals in the RTS greatly reduced the mixing of fresh and exhausted gases. Expansion chambers at each closed end of the receiving tubes in the RTS were used to absorb the reflection of the shock wave, and the heating effect of the shock wave on the exhausted gas was eliminated. All these dramatically increased the refrigeration efficiency and improved the refrigeration performance of the RTS. In the current investigation, an experimental system consisting of one typical receiving tube employed in the STS or RTS was established and the effect of thermoacoustic power on the refrigeration performance was investigated in order to better understand the mechanisms occurring in this new type of refrigeration system. The results help to increase the refrigeration efficiency and improve the design of the thermal separator. Using the information presented in this paper, a cryogenic cycle system generating a cryogenic flow is investigated and the system performance discussed.
2. Experimental system The experimental system consisted of a convergence nozzle, a gas distributor, a receiving tube, a compressedgas generation unit, a driving gas frequency controller,
S.B. Liang et al. / Cryogenics 43 (2003) 493–500
an exhausted gas chamber, data acquisition systems for the temperature and pressure measurements, and a personal computer. The receiving tube was fabricated from pure copper. Three 12.0 mm diameter tubes with lengths of 2.6, 3.0, and 4.2 m, respectively, were investigated. The compressed-gas generation unit was used to generate the high-pressure gas with the flow rate up to 100.0 N m3 /h. The pressure ratio, defined by the pressure of the driving gas at the inlet of the nozzle divided by the atmospheric pressure, could be adjusted from 1.0 to 10.0. The driving gas frequency controller consisting of the gas distributor and a motor was used to control the driving gas frequency. As shown in Fig. 3, the gas distributor was fabricated from a plate with several holes, which was connected to a motor. The hole diameters were each equal to the minimum diameter of the convergence nozzle. The rotating speed of the motor and the hole number on the plate determined the frequency of the driving gas, ranging from 15 to 456 Hz. The exhausted gas chamber was fabricated from stainless steel, and a thermocouple and a pressure sensor were used to measure the temperature and pressure of the exhausted gas. T-type thermocouples were employed to measure the tube wall and gas temperatures. Micro-pressure sensors with working frequencies of 50–300 kHz were used to measure oscillating pressures of gas inside the receiving tube and exhausted gas chamber. Due to the higher working frequencies of pressure sensors, each sensor was calibrated in a pressure calibration system [4]. The working gas of the thermal separator was compressed dry air. Prior to the start of the experiment, gas leak tests were conducted to verify that all of the driving gas entered the receiving tube. Because the environment temperature directly affects the refrigeration performance, the effect of exhausted gas on the environment temperature was also conducted to maintain a constant environment. Due to the heat capacity in the system, the system was
Gas distributor Compressedgas generation unit P1 T1
allowed to equilibrate for thirty min to reach steadystate conditions. Once the test section reached steady state, temperatures and pressures were recorded and directly sent to the personal computer through the data acquisition system. In this way, effects of pressure ratio, oscillating frequency, receiving tube dimension, insulation joint, and heat transfer process on the refrigeration performance of the single-tube thermal separator were examined. The accuracy of temperature measurements for thermocouples and data acquisition system was 0.4 °C in the full range scale. The pressure sensor has an uncertainty of 4.5% for the full scale of 1.5 MPa.
3. Results and discussion The compressed air traveling through the convergence nozzle, shown in Fig. 3, obtained a high speed, prior to being injected into the receiving tube. The excited frequency of the gas inside the tube was dependent on the hole number of the gas distributor and on the rotating speed of the motor. Based on the function, the gas involved in one cycle in the receiving tube can be divided into the driving gas and the oscillating gas. The highspeed driving gas from the nozzle performs work on the oscillating gas already present in the tube. Due to the work output from the driving gas, the enthalpy and kinetic energy of the driving gas decreases similar to the compressed gas in a turbine expander. At the end of one cycle, the driving gas completely leaves the receiving tubes and enters the exhaust gas chamber, where it is removed from the thermal separator. The oscillating gas always stays in the tube and receives work from the driving gas. Due to the excitation of driving gas, the oscillating gas in the tube reciprocates, which plays an important role in the thermal separator. The receiving tube with one closed end in the thermal separator shown in Fig. 3 is considered to be a typical
Exhausted Gas chamber P0 Receiving tube T0
driving gas
ω
495
PC
motor Frequency converter
Speed sensor
Fig. 3. Experimental system.
Data Acquisition System for Pressures & temperatures
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thermoacoustic pipe [8–13]. As the driving gas strokes the gas in the tube, the oscillating gas is compressed while moving toward the closed end and expanded while moving toward the open end, resulting in the motion of the oscillating gas along the tube. Once the work on the oscillating gas is done by the driving gas, the driving gas leaves the thermal separator at the open end of the receiving tube. In order to better explain the refrigeration cycle in the system investigated here, a parcel of gas [9] is chosen as a control volume. The parcel of gas is a small volume of gas close to the tube wall that moves back and forth from the open end to the closed end in the tube. In the special case the cross-sectional area of the parcel in its moving direction is equal to the crosssectional area of the tube. The parcel volume should be large enough so that its thermodynamical description is valid. The oscillating gas in the tube may be modeled as a collection of parcels that behave in the same manner. As the parcel of the gas is stroked at location A, shown in Fig. 4, this parcel of the oscillating gas will move toward to the closed end of the receiving tube. As it reaches location B, it is compressed. If no heat exchange exists between the gas and the tube wall as the gas travels from location A to location B, the parcel of the oscillating gas is compressed adiabatically resulting in the increase of the gas temperature. When the gas temperature is higher than the wall temperature, heat rejection occurs. In the time interval between two strikes of the driving gas, the open end of the oscillating gas in the receiving tube is exposed to the atmosphere, i.e., a low pressure surrounding. The parcel of the oscillating gas will move adiabatically back to the open end, where the expansion process occurs resulting in a decrease of the gas temperature. If the surrounding temperature is higher than the gas temperature, the parcel of oscillating gas absorbs heat from the tube wall. The coefficient of performance (COP) can be calculated by COP ¼
QL W
ð1Þ
where QL is the heat absorbed in location A, and W is the work done by the driving gas. While the COP can be used to describe the refrigeration performance, it is found that the refrigeration efficiency (isentropic efficiency) can better describe the refrigeration performance
Fig. 5. Thermodynamic process of the driving gas in the tube.
of thermal separator investigated here. Fig. 5 describes the thermodynamic process of the driving gas occurring in the nozzle and receiving tube. The refrigeration efficiency (isentropic efficiency), gs , is given as gs ¼
ii io 1 To =Ti ¼ 0 ii io 1 ðPi =Po Þk1 k
where, ii , pi and Ti respectively represent the inlet enthalpy, pressure and temperature of the air compressed into the single-tube thermal separator; where io , po and To represent the outlet enthalpy, pressure and temperature of exhausted air from the single-tube thermal separator; and where j is ratio of specific heats. As shown in Eq. (2), the refrigeration efficiency depends on the outlet temperatures and outlet pressures for a given inlet condition. When the receiving tube maintains a sufficiently large temperature difference across a region where the gas experiences thermal expansion, as the pressure near the closed end of receiving tube is high, and thermal contraction, as the pressure near the open end of the receiving tube is low, the gas in the tube pumps acoustic power into the standing wave. The wave in turn provides the oscillating pressure and the oscillating motions resulting in an additional thermal expansion and contraction in the tube. In this way, the additional thermoacoustic refrigeration is generated. However, the additional thermoacoustic power generation exists only when the temperature difference is higher than the critical temperature gradient, DTcrit , defined by [9] DTcrit ¼
Fig. 4. Oscillating motion of a parcel of oscillating gas.
ð2Þ
Tm bxpis qm cp usi
ð3Þ
where Tm is the mean temperature; b ¼ ðoq=oT Þp =qm is the ordinary thermal expansion coefficient; qm is the average density; cp is the constant-pressure heat capacity per unit mass; x is equal to 2pfdr and fdr is the frequency; pis is the pressure amplitude; and usi is the velocity amplitude. It should be noted that all properties defined above are for the gas at x position inside the receiving tube.
In order to investigate the effect of the temperature gradient along the tube wall of the receiving tube on the refrigeration performance of the single-tube thermal separator shown in Fig. 3, an insulation joint made of Teflon shown in Fig. 6 was placed on the receiving tube. The receiving tube was made of copper with an inner diameter of 12 mm, a wall thickness of 1 mm and a length of 2.6 m. Fig. 7 illustrates the wall temperature distributions along a tube with an insulation joint and along a tube without such a joint. When an insulation joint was placed on the tube, the tube–wall temperature gradient increased near the open end of the tube. As shown in Fig. 7b, the maximum temperature gradient at x ¼ 0:4 m increased from 700 to 820 K/m. The increase in the temperature difference across the insulation joint would directly increase thermoacoustic power, producing additional refrigeration. As a result, the refrigeration performance of the thermal separator, as shown in Fig. 8, improved with the temperature gradient increase. In addition, the temperature gradients at x ¼ 0:4 m for both cases, as shown in Fig. 7b, are higher than the critical temperature gradient, DTcrit ¼ 626:3 K/m, calculated by Eq. (3), where pm ¼ 0:1 MPa, qm ¼ 1:5 kg/ m3 , cp ¼ 1:0 kJ/kg K, pis ¼ 0:22 MPa, and usi ¼ 105:0 m/ s, thereby providing verification that thermoacoustic power was generated in the receiving tube due to the necessary temperature difference. Furthermore, experimental results shown in Fig. 8 indicated that the improvement of the refrigeration coefficient depended on the location of insulation joint. When the insulation joint was placed in the tube between 0.0 and 1.2 m from the inlet of the receiving tube, refrigeration performance consistently improved, and a maximum refrigeration efficiency of 40.5% was found to occur for a joint located at X ¼ 0:4 m. When the insu-
Fig. 6. Schematic of insulation joint mounted in the receiving tube.
497
200 150 100 without insulation joint with insulation joint at X=0.4 m
50 0 0
0.5
1
1.5
2
2.5
-50
(a) temperature gradient (K/m)
3.1. Insulation joint effect
Tube-wall temperature, C
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tube length (X) (m) 1000 without insulation joint with insulation joint at X=0.4 m
800 600 400 200 0 -200
0
0.5
1
15 .
2
2.5
-400
(b)
tube length (x) (m)
Fig. 7. Insulation joint effect on the wall temperature along the receiving tube (a) wall temperature distribution; (b) wall temperature gradient (e ¼ 4:5, Ti ¼ 21:4 °C, Ta ¼ 15:5 °C, fdr ¼ 71:4 Hz, tube length ¼ 2.6 m, natural convection).
lation joint was placed at the location, X P 1:2 m, the temperature gradient on the receiving tube was unaffected and no improvement of refrigeration performance was observed. 3.2. Heat transfer effect The effective heat removal in the higher-temperature heat source can increase the refrigeration performance in the traditional refrigeration system such as the pulse tube refrigerator. The effects of natural and forced convections on the refrigeration performance of the receiving tube were investigated. The natural convection investigation was based on a receiving tube oriented horizontally in air at 15.5 °C. The forced convection investigation was based on forced water flow over the surface of a receiving tube, which consisted of a cooling block and cooling bath, as shown in Fig. 9. The inside diameter of the cooling block was 60.0 mm. The receiving tube was fabricated from a copper tube with an inner diameter of 12.0 mm, a wall thickness of 1.0 mm, and a full tube length of 4.2 m. Eight thermocouples were placed on the receiving tube to measure the temperature distribution. Fig. 10 illustrates the temperature distributions along the receiving tube for a natural convection condition including the pressure ratio effect. As shown, when the pressure ratio increased, the temperature drop occurring on the receiving tube increased resulting in an increase of refrigeration coefficient shown
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T1 -T0 , (C)
43
41
39
37 0
0.2
0.4
0.6
0.8
1
1.2
X (m)
Fig. 10. Temperature distributions of the tube wall (Ti ¼ 21:0 °C, Ta ¼ 15:0 °C, fdr ¼ 69:3 Hz, natural convection).
(a)
forced convection heat transfer natural convection heat transfer
43 41 39 37 35 0
0.2
0.4
0.6
0.8
1
1.2
X (m)
(b) Fig. 8. Effect of insulation joint position on the temperature drop and refrigeration efficiency (e ¼ 4:5, Ti ¼ 21:4 °C, Ta ¼ 15:5 °C, fdr ¼ 71:4 Hz, natural convection). (a) Temperature drop; (b) refrigeration efficiency.
Fig. 9. Schematic of cooling block.
in Fig. 11. The highest refrigeration coefficient occurred at the pressure ratio of e ¼ 5:0. The outlet temperature of exhausted gas in the chamber could reach )27.0 °C at for e ¼ 6:0. Fig. 12 illustrates the temperature distribution along the receiving tube in the forced convection condition. As shown the temperature drop on the receiving tube was significantly reduced by forced convection. When the cooling condition was changed from the natural convection to the forced convection, the temperature gradient near the open end of the receiving tube decreased resulting in the decrease of the acoustic
refrigeration efficiency, %
Refrigeration coefficient (%)
45
45 40 35 30 25 2
3
4
5
6
pressure ratio Fig. 11. Refrigeration efficiency with pressure ratio (Ti ¼ 21:0 °C, Ta ¼ 15:0 °C, fdr ¼ 69:3 Hz).
Fig. 12. Temperature distributions of the tube wall (Ti ¼ 21:0 °C, Ta ¼ 15:0 °C, fdr ¼ 69:3 Hz, forced convection).
power generation. At the same time the sounds heard in the natural convection experiments were not detected for the forced convection experiments. The experimental observations show that when the sound level produced in the receiving tube was louder, the refrigeration performance was better. It should be noted that the sound generated by the thermoacoustic power was quite different from the one by the driving gas. The sound generated by the thermoacoustic power was very loud and the frequency was different than that of the driving gas.
S.B. Liang et al. / Cryogenics 43 (2003) 493–500 0 -20
0
10
20
30
40
50
60
-40
T0 (C)
As a result, when heat transfer in the higher-temperature heat source increases resulting in the decrease of temperature difference on the receiving tube, the refrigeration performance of thermal separator decreases. The results show that the tube–wall temperature difference affects the thermoacoustic power and the refrigeration performance of the thermal separator.
499
-60 -80 -100 -120
Oscillating motions of gas in the receiving tube of a thermal separator play an important role in the refrigerating processes of the thermal separator. As presented above, the refrigeration occurring in the thermal separator investigated here depends not only on the pressure wave created by the compression/expansion of the oscillating gas by the driving gas, but also on the pressure wave resulting from the themoacoustic power generated by the significant temperature gradient existing in the receiving tube. Furthermore, the pressure wave due to the temperature gradient plays the more important role with respect to improving the refrigeration performance of the thermal separator. With micro-pressure sensors, pressure wave propagations inside the receiving tube of thermal separator could be readily obtained. When a relatively large temperature gradient on the receiving tube was maintained, i.e., the natural convection was employed, the second, thermoacoustic pressure wave, shown in Fig. 13, was detected. 3.4. Cryogenic refrigeration Utilizing the information discussed above, a RTS consisting of multiple receiving tubes was designed, fabricated, and employed in a refrigeration system for the generation of cryogenic flow [2]. The thermal separator consisted of three rotational nozzles and 72 re-
-140
time (minute) Fig. 14. Gas temperature at the outlet of thermal separator (Ta ¼ 19 °C).
Refrigeration coefficient variation (%)
3.3. Pressure wave propagations
16 14 12 10 8 6 4 2 0 -2 0 -4
10
20
30
40
50
60
time (minute) 0 Fig. 15. Refrigeration efficiency variation (Dg ¼ gt gg 100%) with 0 time (e ¼ 4:7; n ¼ 3480 rpm; g0 is the initial refrigeration efficiency).
ceiving tubes, as illustrated in Fig. 2. The receiving tubes were fabricated from pure copper. The inner diameter of tubes was 4.76 mm and the length of the tubes was 1.9 m. The air in the cryogenic system circulated at a flow rate of 720 N m3 /h. Fig. 14 shows the results of the outlet temperature of the thermal separator with time. As shown, the temperature of the cryogenic air flow in the system reached values as low as )130 °C within 50 min. Such a cryogenic temperature level suggests that the thermal separators can be employed in the field of cryogenic engineering [2,7,8,12]. While the closed ends of the receiving tubes were contacting with ambient air and its temperature was considered to be constant, the decrease of the outlet temperature of the driving gas increased the temperature gradient on the receiving tube, which directly generated more thermoacoustic power and increased the refrigeration coefficient shown in Fig. 15. The results further demonstrate that the temperature gradients occurring on the receiving tube affected the thermoacoustic power, and the refrigeration performance of thermal separator investigated in the paper.
4. Conclusions Fig. 13. Pressure wave propagations along the receiving tube (Ti ¼ 21:4 °C, Ta ¼ 15:5 °C, fdr ¼ 74:67 Hz, natural convection).
An experimental investigation of the mechanisms of refrigeration occurring in the receiving tube of a thermal
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separator was conducted in order to determine the primary factors affecting the refrigeration performance of this new type of refrigerator. In the current investigation, the gas in the system is divided into the oscillating gas, which always stays inside the receiving tube, and driving gas, which provides the mechanical work for the system. While the compression/expansion of oscillating gas caused by the driving gas determines the refrigeration process occurring in the receiving tube of thermal separator, the temperature gradient on the receiving tube significantly affects the acoustic power generation and the refrigeration performance. Heat transfer effect on the temperature gradient was investigated including the influences of insulation joint position, natural convection, and forced convection. Experimental results demonstrate that when the tube–wall temperature difference near the open end of the receiving tube increases, the refrigeration coefficient increases. Using the information presented in the paper, a new cryogenic refrigeration system was developed. The experimental data shows that the temperature of the cryogenic air flow in the system is capable of reaching a value as low as )130 °C within 50 min. The data further suggests that the thermal separator investigated in the paper can effectively be employed in the field of cryogenic engineering.
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