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Optimum operating conditions for an adsorption cryocooler: a case of activated carbon + nitrogen system
Cryogenics 45 (2005) 193–197 www.elsevier.com/locate/cryogenics
Optimum operating conditions for an adsorption cryocooler: a case of activated carbon + nitrogen system Radhika Rani Rao a, Madhu Prasad b, Kandadai Srinivasan
c,*
a
c
Department of Physics, Don Bosco Institute of Technology, Bangalore 560 074, India b Thermal Systems Group, ISRO Satellite Centre, Bangalore 560 017, India Department of Mechanical Engineering, Indian Institute of Science, Bangalore 560 012, India Received 4 June 2004; received in revised form 2 October 2004; accepted 2 October 2004
Abstract Adsorption cryocoolers are among the possible options for obtaining cryogenic temperatures, in particular for small cooling capacity applications such as cooling of infra red detectors. They need to be optimized for liquid yield. The performance of thermal compressors therein pivots around the adsorption characteristics of the adsorbent + adsorbate combination and how effectively one could pack requisite amounts of adsorbent into a given volume of the compressor housing. In addition, the overall performance of the cooler is a function of limits of operating temperatures and pressures across the compressor. This paper proposes a performance indicator—the product of liquid yield and the uptake efficiency of the compressor—and evaluates its values for various possible operating conditions for one specimen of activated carbon. It is shown that there is a limited domain of operation and that there is a condition of best performance within that domain. Ó 2004 Elsevier Ltd. All rights reserved.
1. Introduction Adsorption cryocoolers find a place among several options for low capacity cooling applications [1]. Depending upon the zone of operation of temperature, a suitable working fluid can be chosen. There have been research projects investigating nitrogen [2], methane [3] and xenon [4] as working fluids. Activated carbon is the most widely used adsorbent [5–7]. There are also reports of investigations of single [8,9] and multistage [10,11] thermal compression cycle based adsorption cryocoolers. The normal practice is to use the specific power (inverse of coefficient of performance) as a measure of performance evaluation. Its value tends to be of the order of a few 100Õs W/W of cooling. Once the temperature at which refrigeration is required is decided,
*
Corresponding author. Fax: +91 80 2360 0648. E-mail address: [email protected] (K. Srinivasan).
0011-2275/$ - see front matter Ó 2004 Elsevier Ltd. All rights reserved. doi:10.1016/j.cryogenics.2004.10.003
the lower limit of operating pressure (pL) gets fixed. This will be the saturation pressure corresponding to the temperature of refrigeration. The designer has the option of choosing the temperature at which adsorption occurs (TL) and the pressure (pH) and temperature (TH) at which desorption occurs. TH will be mostly governed by the temperature of the heat source. The design of the thermal compressors has a strong bearing on the adsorption characteristics of the adsorbent + adsorbate combination chosen and the effective packing density of the adsorbent [12]. This combined effect can be taken into account through the uptake efficiency which is analogous to the volumetric efficiency of a positive displacement compressor [13]. The performance of the cryocooler can be gauged by the mass fraction of liquid out of the working fluid that is actually compressed. It is proposed that the overall performance indicator of the adsorption cooler be represented by the product of the liquid yield and the uptake efficiency. This paper focuses on assessing an activated carbon + nitrogen cryocooler
194
R.R. Rao et al. / Cryogenics 45 (2005) 193–197
for operation in 77–120 K region, with the heat source at 400 K. It was already shown that there is a lower limit pH below which the operation of an adsorption cryocooler is not possible at all [14]. This paper brings out the existence of an upper limit and evaluates the behavior of thermal compressor in that limited domain. There is an optimal pressure at which the performance indicator attains the maximum.
2. Development of criteria Fig. 1 shows a schematic arrangement of an adsorption cryocooler and Fig. 2 shows the thermodynamic states/paths of the adsorbate on the temperature–entropy plane. The refrigerant (nitrogen in the present case) is adsorbed by microporous solid (activated carbon in the present case) at the thermodynamic state of (pL, TL = T5). The four processes of a thermal compressor are adsorption, heating, desorption and cooling (Fig. 3). Because of finite time nature of each process, a minimum of four compressors will be required. Typically, the value of pL seldom exceeds 40% of critical pressure because the saturation temperatures at this limit will be about 0.85Tc.
Fig. 2. Adsorbate states on the T–s diagram.
Fig. 3. Thermal compressor cycle. a–b: Cooling and adsorption, b–c: heating and pressurization, c–d: heating and desorption, d–a: cooling and depressurization, a–a 0 : adsorption loss due to void volume, c–c 0 : desorption loss due to void volume.
2.1. Low-side criteria pL determines the state 4g and 4f (Fig. 2), the saturated vapour and liquid states, respectively. The compactness of a refrigeration system demands that the fraction of liquid yield after throttling be as large as possible (state 3 to be as close to 4f as possible). The liquid fraction is given by Fig. 1. Schematic diagram of an adsorption cryocooler.
x¼
h4g h3 h4g h4f
ð1Þ
R.R. Rao et al. / Cryogenics 45 (2005) 193–197
One of the important parameters for the adsorption coolers is the precooler temperature (T1), to which the high pressure gas must be cooled from the state TH, prior to entering the regenerative heat exchanger where it is further cooled from T1 to T2. For a 100% effectiveness of the latter, T1 = TL = T5. It also follows that
2.2. High-side criteria In order to obtain a compact thermal compressor, one needs a large uptake difference across which it operates (cb ca, in Fig. 3). In this figure a–b–c–d is the ideal compressor cycle. However, in a practical compressor the presence of void volume reduces the uptake to (cb ca 0 ), where a 0 –b–c 0 –d is the actual cycle. The loss of uptake can be alleviated by reducing pH. But, there is a minimum pH required such that qb < qd, for nitrogen. In the previous section it was seen that increasing pH will result in a better liquid yield. The void volume effect counters that proposal. A compact compressor demands that a large quantity of activated carbon be packed into the compressor. The microporous nature of the adsorbent makes it seldom amenable to packing densities (qeff) > 800 kg/m3. The uptake efficiency of the thermal compressor is defined as follows: cb ca0 cb ca
which was shown to be reduceable to [12] q qd 1 1 gu ¼ 1 þ b cb ca qeff qs
ð6Þ
Values of a and c obtained from experimental data for specimen investigated further are 0.495 cm3/g and 0.43 mol/J respectively.
ð2Þ
Thus, for a given pH, h2 is determined by the solution to the above equation. Since h2 = h3, it also follows that liquid yield is / to (h5 h1).
gu ¼
696:94 ln ps ðMPaÞ ¼ exp 6:7228 T ðKÞ
ð3Þ
ð4Þ
where qs is the solid density of carbon. It is imminent that gu < 1, because compression implies that qb < qd. The design requirement will be to obtain the maximum liquid yield with good uptake efficiency. Thus, we define a performance indicator as ‘‘xgu’’. The evaluation of the performance indicator requires the adsorption isotherms, which in the present case are represented by the following equation based on the experimental data of Prasad et al. [15]. Ma cRT lnðps =pÞ exp c¼ ð5Þ b b For nitrogen, M = 28, b(Van der Waals volume) = 29.82 cm3/mol, the parachore, b = 251.2 J/mol. Since the adsorption is at temperatures above the critical point, a pseudo-vapour pressure equation is used, which was obtained using the vapour pressure data generated form [16]:
3. Results and discussion The analysis was carried out for Fluka specimen of activated carbon for a packing density of 450 kg/m3. The low-side pressures considered are 0.1, 0.5–2.5 MPa in steps of 0.5 MPa, the corresponding temperatures range of refrigeration being about 77–120 K. The adsorption temperature (TL) chosen are 150, 175 and 200 K which cover typical applications. The designer has to choose pH and TH. For the sake of further discussion, TH is taken as 400 K. Several other such temperatures were also considered and it was found that qualitative results are not affected. The analysis is idealized by assuming that the effectiveness of the regenerative heat exchanger is 100%. Here again, lower values do not influence the qualitative conclusions derived here. Fig. 4 shows the liquid yield variation with various pH values for a precooler temperature of 175 K. A nearly linear and monotonic increase in liquid yield is obtained at all values of pL. This behavior is governed by the thermodynamic properties of nitrogen. In the case of uptake efficiency, the first condition required is that qd(pH, TH) > qb(pL, TL). This sets a lower threshold of pH. This is again a property of the adsorbate alone. At this lower threshold gu = 1, wherein the pressure increase will be only due to isochoric heating. This obviates the use of the adsorbent itself. On the other hand the throughput of the compressor will vanish when gu = 0 which happens from Eq. (3) when,
0.6
0.4
x
ðh1 h2 Þ ¼ ðh5 h4g Þ
195
0.2
0 4
6
8
10
pH (MPa) Fig. 4. The variation of liquid yield with high side pressure for various low side pressures. Legend: s 2.5 MPa, 2 MPa, n 1.5 MPa, } 1 MPa, h 0.5 MPa, 0.1 MPa.
196
R.R. Rao et al. / Cryogenics 45 (2005) 193–197
qd qb 1 1 ¼1 cb ca qeff qs
0.5
For a given state of b (Fig. 3), the solution of the above equation yields the inter-relationship between pH and TH. These limits have been determined by Banker et al. [14]. It is pertinent to note that the above calculations assume equilibrium conditions in the thermal compressor which is essentially an adsorbent bed. To achieve this state, one has to allow for large time constants for each process in the Fig. 3. In order to limit the number of compressors and their size, it is inevitable that a part of the possible throughput of the compressor is sacrificed. Typically a loss of 37% will result if desorption is allowed for one time constant, which itself could stretch over a few 100Õs of s. Thus, if a minimum throughput of 40% is required, the uptake efficiency of the compressor should be at least 77% [13]. Fig. 5 shows the uptake efficiencies for a precooler temperature of 175 K. The continuous horizontal line represents gu = 0.77. It is evident that construction of a single stage cryocooler with pL = 0.1 MPa is not possible because the uptake efficiency is extremely low. With pL of 1 or 1.5 MPa, pH has an upper limit of about 5 and 6.3 MPa respectively. On the other hand, if refrigeration is required at saturation limits of 2 and 2.5 MPa, a minimum pressure of 5 and 7 MPa, respectively, will be required. Fig. 6 depicts the performance indicator xgu. Since liquid yield and cb cd increase with pL at a given pH, xgu also increases accordingly. However, the increase in x with pH is annulled by a decrease in gu for a given pL. As a consequence xgu shows a peak at a certain operating condition. For example, for a cryocooler at a pL = 1 MPa, (xgu)max is about 0.16 for pH between 6 and 7 MPa. As pL increases, this value increases and the maximum shifts to higher values of pH. Fig. 7 shows
0.4
1 0.8
ηu
0.6 0.4 0.2 0 4
6
8
10
pH (MPa) Fig. 5. The variation of uptake efficiency with high side pressure for various low side pressures. Legend: s 2.5 MPa, 2 MPa, n 1.5 MPa, } 1 MPa, h 0.5 MPa, 0.1 MPa.
x ηu
ð7Þ
0.3 0.2 0.1 0 4
6
8
10
pH (MPa) Fig. 6. The variation of xgu with high side pressure for various low side pressures. Legend: s 2.5 MPa, 2 MPa, n 1.5 MPa, } 1 MPa, h 0.5 MPa, 0.1 MPa.
0.4
x ηu
0.3
0.2
0.1
0 4
6
pH (MPa)
8
10
Fig. 7. Performance of the cryocooler for other precooler temperatures. Legend: s 150 K, h 175 K, n 200 K.
xgu variation with various precooler temperatures for a pL = 1 MPa. Apparently, the performance can be improved by lowering the precooler temperatures. But, this is associated with practical difficulties although thermoelectric cooling or cascading with other adsorption coolers wherein methane or krypton can be working fluids is a possibility. A comparison of 0.77x and xgu is shown in Fig. 8. For the lower limit of throughput chosen here (40%), the latter should be larger than the former. The envelope that satisfies this criterion is also shown as the shaded area for the case of pL = 2.5 MPa. In addition, (xgu)max point should be present within this envelope. This does not happen at lower values of pL. Further, the zone of operating area diminishes at lower values of pL. Thus, we observe that only a limited domain of operation satisfies all these criteria. From the above discussion it clearly emerges that a single stage activated carbon + nitrogen cryocooler will be unviable for pL < 1 MPa (temperatures below about
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197
0.5
References
0.4
[1] Wade LA. An over view of the development of sorption refrigeration. Adv Cryog Eng 1992;37B:1095–106. [2] Bard S. Development of an 80–120 K charcoal–nitrogen adsorption cryocooler. Fourth biennial international cryocooler conference, Easton, Maryland, 1986. p. 43–56. [3] Wade LA, Ryba E, Weston P, Alvarez JA. Test performance of an efficient 2 W, 137 K sorption refrigerator. Cryogenics 1992; 32:122–6. [4] Burger JF, Holland HJ, Wade LA, ter Brake HJM, Rogalla H. Thermodynamic considerations on a micro miniature sorption cooler. 10th international cryocooler conference, Monterey, California, May 26–28, 1998. [5] Bard S, Jones JA. Regenerative sorption compressor for cryogenic refrigeration. Adv Cryog Eng 1990;35:1357–65. [6] Chan CK. Optimal design of gas adsorption refrigerators for cryogenic cooling. NASA, CP 1982;2287:323–41. [7] Prakash MJ, Prasad M, Rastogi SC, Basavaraj A, Gupta PP, Narayanamurthy H, Srinivasan K. Development of a laboratory model of activated charcoal–nitrogen adsorption cryocooler. Cryogenics 2000;40(7):481–8. [8] Chan CK. Cryogenic refrigeration using low temperature heat source. Cryogenics 1981;21:391–8. [9] Rao RR, Prasad M, Bindagi SV, Srinivasan K. Effect of packing density on the performance of charcoal–nitrogen adsorption cryocoolers. Carbon 1997;35(10–11):1559–66. [10] Bard S. Improving adsorption cryocoolers by multistage compression and reducing void volume. Cryogenics 1986;26:450–8. [11] Prasad M, Rao RR, Prakash MJ, Srinivasan K. Thermodynamic analysis of a two stage charcoal–nitrogen adsorption cryocooler. In: Fundamentals of Adsorption 6. Paris: Elsevier; 1998. p. 745–50. [12] Akkimaradi BS, Prasad M, Dutta P, Srinivasan K. Effect of packing density and adsorption parameters on throughput of an adsorption compressor. Carbon 2002;40(15):2855–9. [13] Srinivasan K, Banker ND, Prasad M, Akkimaradi B. Evaluation of sorption compressor performance from isotherm data: application to activated carbon + nitrogen/HFC 134a systems. In: Saha BB, Akisawa A, Koyama S, editors. Thermally powered sorption technology, Proceedings of international seminar on thermally powered sorption technology, Kyushu University, Fukuoka, Japan, December 4–5, 2003. p. 121–33. [14] Banker NE, Rao RR, Srinivasan K, Prasad M. Limits of operating conditions for thermal compressors of adsorption cryocoolers. In: Proceedings of national seminar and conference on cryogenics and its frontier applications, Bengal Engineering College, Howrah, 25–27 March 2004. p. 143–8. [15] Prasad M, Akkimaradi B, Rastogi SC, Rao RR, Srinivasan K. Adsorption characteristics of charcoal–nitrogen system in 79– 320 K and pressures to 5 MPa. Carbon 1996;34(11):1401–6. [16] ALLPROPS—Property Package, Centre for Applied Thermodynamic Studies, University of Idaho, Moscow, Version 4.3, 1997.
xη u
0.3 0.2 0.1 0 4
6
8
10
pH (MPa) Fig. 8. Comparison of xgu with minimum requirement of 77% of uptake efficiency. Legend: xgu s 2.5 MPa, 2 MPa, n 1.5 MPa, } 1 MPa, h 0.5 MPa (continuous lines); 0.77x (broken lines). Hatched area shows the possible domain of operation with pL = 2.5 MPa.
103 K) at a packing density of 450 kg/m3. For these requirements one has to resort to two stage compression or to increase the packing density substantially. It can be expected that the specific power of the cryocooler will be the least at the point where xgu is the maximum. This can be verified from our earlier results [9].
4. Conclusions In this paper it is shown that single stage activated carbon + nitrogen cryocoolers have a very limited zone of possible operation if adequate throughput from the compressor has to be ensured. The lower limit is set by the properties of the adsorbate, while the upper by the adsorption characteristics of the two entities. Further, the packing density also plays an important role. A performance evaluation criteria has been defined. Some examples of performance are presented.
Acknowledgments The work reported in this paper was supported through grants from IISc-ISRO Space technology Cell and Defence Research and Development Organisation.
Optimum operating conditions for an adsorption cryocooler: a case of activated carbon + nitrogen system Radhika Rani Rao a, Madhu Prasad b, Kandadai Srinivasan
c,*
a
c
Department of Physics, Don Bosco Institute of Technology, Bangalore 560 074, India b Thermal Systems Group, ISRO Satellite Centre, Bangalore 560 017, India Department of Mechanical Engineering, Indian Institute of Science, Bangalore 560 012, India Received 4 June 2004; received in revised form 2 October 2004; accepted 2 October 2004
Abstract Adsorption cryocoolers are among the possible options for obtaining cryogenic temperatures, in particular for small cooling capacity applications such as cooling of infra red detectors. They need to be optimized for liquid yield. The performance of thermal compressors therein pivots around the adsorption characteristics of the adsorbent + adsorbate combination and how effectively one could pack requisite amounts of adsorbent into a given volume of the compressor housing. In addition, the overall performance of the cooler is a function of limits of operating temperatures and pressures across the compressor. This paper proposes a performance indicator—the product of liquid yield and the uptake efficiency of the compressor—and evaluates its values for various possible operating conditions for one specimen of activated carbon. It is shown that there is a limited domain of operation and that there is a condition of best performance within that domain. Ó 2004 Elsevier Ltd. All rights reserved.
1. Introduction Adsorption cryocoolers find a place among several options for low capacity cooling applications [1]. Depending upon the zone of operation of temperature, a suitable working fluid can be chosen. There have been research projects investigating nitrogen [2], methane [3] and xenon [4] as working fluids. Activated carbon is the most widely used adsorbent [5–7]. There are also reports of investigations of single [8,9] and multistage [10,11] thermal compression cycle based adsorption cryocoolers. The normal practice is to use the specific power (inverse of coefficient of performance) as a measure of performance evaluation. Its value tends to be of the order of a few 100Õs W/W of cooling. Once the temperature at which refrigeration is required is decided,
*
Corresponding author. Fax: +91 80 2360 0648. E-mail address: [email protected] (K. Srinivasan).
0011-2275/$ - see front matter Ó 2004 Elsevier Ltd. All rights reserved. doi:10.1016/j.cryogenics.2004.10.003
the lower limit of operating pressure (pL) gets fixed. This will be the saturation pressure corresponding to the temperature of refrigeration. The designer has the option of choosing the temperature at which adsorption occurs (TL) and the pressure (pH) and temperature (TH) at which desorption occurs. TH will be mostly governed by the temperature of the heat source. The design of the thermal compressors has a strong bearing on the adsorption characteristics of the adsorbent + adsorbate combination chosen and the effective packing density of the adsorbent [12]. This combined effect can be taken into account through the uptake efficiency which is analogous to the volumetric efficiency of a positive displacement compressor [13]. The performance of the cryocooler can be gauged by the mass fraction of liquid out of the working fluid that is actually compressed. It is proposed that the overall performance indicator of the adsorption cooler be represented by the product of the liquid yield and the uptake efficiency. This paper focuses on assessing an activated carbon + nitrogen cryocooler
194
R.R. Rao et al. / Cryogenics 45 (2005) 193–197
for operation in 77–120 K region, with the heat source at 400 K. It was already shown that there is a lower limit pH below which the operation of an adsorption cryocooler is not possible at all [14]. This paper brings out the existence of an upper limit and evaluates the behavior of thermal compressor in that limited domain. There is an optimal pressure at which the performance indicator attains the maximum.
2. Development of criteria Fig. 1 shows a schematic arrangement of an adsorption cryocooler and Fig. 2 shows the thermodynamic states/paths of the adsorbate on the temperature–entropy plane. The refrigerant (nitrogen in the present case) is adsorbed by microporous solid (activated carbon in the present case) at the thermodynamic state of (pL, TL = T5). The four processes of a thermal compressor are adsorption, heating, desorption and cooling (Fig. 3). Because of finite time nature of each process, a minimum of four compressors will be required. Typically, the value of pL seldom exceeds 40% of critical pressure because the saturation temperatures at this limit will be about 0.85Tc.
Fig. 2. Adsorbate states on the T–s diagram.
Fig. 3. Thermal compressor cycle. a–b: Cooling and adsorption, b–c: heating and pressurization, c–d: heating and desorption, d–a: cooling and depressurization, a–a 0 : adsorption loss due to void volume, c–c 0 : desorption loss due to void volume.
2.1. Low-side criteria pL determines the state 4g and 4f (Fig. 2), the saturated vapour and liquid states, respectively. The compactness of a refrigeration system demands that the fraction of liquid yield after throttling be as large as possible (state 3 to be as close to 4f as possible). The liquid fraction is given by Fig. 1. Schematic diagram of an adsorption cryocooler.
x¼
h4g h3 h4g h4f
ð1Þ
R.R. Rao et al. / Cryogenics 45 (2005) 193–197
One of the important parameters for the adsorption coolers is the precooler temperature (T1), to which the high pressure gas must be cooled from the state TH, prior to entering the regenerative heat exchanger where it is further cooled from T1 to T2. For a 100% effectiveness of the latter, T1 = TL = T5. It also follows that
2.2. High-side criteria In order to obtain a compact thermal compressor, one needs a large uptake difference across which it operates (cb ca, in Fig. 3). In this figure a–b–c–d is the ideal compressor cycle. However, in a practical compressor the presence of void volume reduces the uptake to (cb ca 0 ), where a 0 –b–c 0 –d is the actual cycle. The loss of uptake can be alleviated by reducing pH. But, there is a minimum pH required such that qb < qd, for nitrogen. In the previous section it was seen that increasing pH will result in a better liquid yield. The void volume effect counters that proposal. A compact compressor demands that a large quantity of activated carbon be packed into the compressor. The microporous nature of the adsorbent makes it seldom amenable to packing densities (qeff) > 800 kg/m3. The uptake efficiency of the thermal compressor is defined as follows: cb ca0 cb ca
which was shown to be reduceable to [12] q qd 1 1 gu ¼ 1 þ b cb ca qeff qs
ð6Þ
Values of a and c obtained from experimental data for specimen investigated further are 0.495 cm3/g and 0.43 mol/J respectively.
ð2Þ
Thus, for a given pH, h2 is determined by the solution to the above equation. Since h2 = h3, it also follows that liquid yield is / to (h5 h1).
gu ¼
696:94 ln ps ðMPaÞ ¼ exp 6:7228 T ðKÞ
ð3Þ
ð4Þ
where qs is the solid density of carbon. It is imminent that gu < 1, because compression implies that qb < qd. The design requirement will be to obtain the maximum liquid yield with good uptake efficiency. Thus, we define a performance indicator as ‘‘xgu’’. The evaluation of the performance indicator requires the adsorption isotherms, which in the present case are represented by the following equation based on the experimental data of Prasad et al. [15]. Ma cRT lnðps =pÞ exp c¼ ð5Þ b b For nitrogen, M = 28, b(Van der Waals volume) = 29.82 cm3/mol, the parachore, b = 251.2 J/mol. Since the adsorption is at temperatures above the critical point, a pseudo-vapour pressure equation is used, which was obtained using the vapour pressure data generated form [16]:
3. Results and discussion The analysis was carried out for Fluka specimen of activated carbon for a packing density of 450 kg/m3. The low-side pressures considered are 0.1, 0.5–2.5 MPa in steps of 0.5 MPa, the corresponding temperatures range of refrigeration being about 77–120 K. The adsorption temperature (TL) chosen are 150, 175 and 200 K which cover typical applications. The designer has to choose pH and TH. For the sake of further discussion, TH is taken as 400 K. Several other such temperatures were also considered and it was found that qualitative results are not affected. The analysis is idealized by assuming that the effectiveness of the regenerative heat exchanger is 100%. Here again, lower values do not influence the qualitative conclusions derived here. Fig. 4 shows the liquid yield variation with various pH values for a precooler temperature of 175 K. A nearly linear and monotonic increase in liquid yield is obtained at all values of pL. This behavior is governed by the thermodynamic properties of nitrogen. In the case of uptake efficiency, the first condition required is that qd(pH, TH) > qb(pL, TL). This sets a lower threshold of pH. This is again a property of the adsorbate alone. At this lower threshold gu = 1, wherein the pressure increase will be only due to isochoric heating. This obviates the use of the adsorbent itself. On the other hand the throughput of the compressor will vanish when gu = 0 which happens from Eq. (3) when,
0.6
0.4
x
ðh1 h2 Þ ¼ ðh5 h4g Þ
195
0.2
0 4
6
8
10
pH (MPa) Fig. 4. The variation of liquid yield with high side pressure for various low side pressures. Legend: s 2.5 MPa, 2 MPa, n 1.5 MPa, } 1 MPa, h 0.5 MPa, 0.1 MPa.
196
R.R. Rao et al. / Cryogenics 45 (2005) 193–197
qd qb 1 1 ¼1 cb ca qeff qs
0.5
For a given state of b (Fig. 3), the solution of the above equation yields the inter-relationship between pH and TH. These limits have been determined by Banker et al. [14]. It is pertinent to note that the above calculations assume equilibrium conditions in the thermal compressor which is essentially an adsorbent bed. To achieve this state, one has to allow for large time constants for each process in the Fig. 3. In order to limit the number of compressors and their size, it is inevitable that a part of the possible throughput of the compressor is sacrificed. Typically a loss of 37% will result if desorption is allowed for one time constant, which itself could stretch over a few 100Õs of s. Thus, if a minimum throughput of 40% is required, the uptake efficiency of the compressor should be at least 77% [13]. Fig. 5 shows the uptake efficiencies for a precooler temperature of 175 K. The continuous horizontal line represents gu = 0.77. It is evident that construction of a single stage cryocooler with pL = 0.1 MPa is not possible because the uptake efficiency is extremely low. With pL of 1 or 1.5 MPa, pH has an upper limit of about 5 and 6.3 MPa respectively. On the other hand, if refrigeration is required at saturation limits of 2 and 2.5 MPa, a minimum pressure of 5 and 7 MPa, respectively, will be required. Fig. 6 depicts the performance indicator xgu. Since liquid yield and cb cd increase with pL at a given pH, xgu also increases accordingly. However, the increase in x with pH is annulled by a decrease in gu for a given pL. As a consequence xgu shows a peak at a certain operating condition. For example, for a cryocooler at a pL = 1 MPa, (xgu)max is about 0.16 for pH between 6 and 7 MPa. As pL increases, this value increases and the maximum shifts to higher values of pH. Fig. 7 shows
0.4
1 0.8
ηu
0.6 0.4 0.2 0 4
6
8
10
pH (MPa) Fig. 5. The variation of uptake efficiency with high side pressure for various low side pressures. Legend: s 2.5 MPa, 2 MPa, n 1.5 MPa, } 1 MPa, h 0.5 MPa, 0.1 MPa.
x ηu
ð7Þ
0.3 0.2 0.1 0 4
6
8
10
pH (MPa) Fig. 6. The variation of xgu with high side pressure for various low side pressures. Legend: s 2.5 MPa, 2 MPa, n 1.5 MPa, } 1 MPa, h 0.5 MPa, 0.1 MPa.
0.4
x ηu
0.3
0.2
0.1
0 4
6
pH (MPa)
8
10
Fig. 7. Performance of the cryocooler for other precooler temperatures. Legend: s 150 K, h 175 K, n 200 K.
xgu variation with various precooler temperatures for a pL = 1 MPa. Apparently, the performance can be improved by lowering the precooler temperatures. But, this is associated with practical difficulties although thermoelectric cooling or cascading with other adsorption coolers wherein methane or krypton can be working fluids is a possibility. A comparison of 0.77x and xgu is shown in Fig. 8. For the lower limit of throughput chosen here (40%), the latter should be larger than the former. The envelope that satisfies this criterion is also shown as the shaded area for the case of pL = 2.5 MPa. In addition, (xgu)max point should be present within this envelope. This does not happen at lower values of pL. Further, the zone of operating area diminishes at lower values of pL. Thus, we observe that only a limited domain of operation satisfies all these criteria. From the above discussion it clearly emerges that a single stage activated carbon + nitrogen cryocooler will be unviable for pL < 1 MPa (temperatures below about
R.R. Rao et al. / Cryogenics 45 (2005) 193–197
197
0.5
References
0.4
[1] Wade LA. An over view of the development of sorption refrigeration. Adv Cryog Eng 1992;37B:1095–106. [2] Bard S. Development of an 80–120 K charcoal–nitrogen adsorption cryocooler. Fourth biennial international cryocooler conference, Easton, Maryland, 1986. p. 43–56. [3] Wade LA, Ryba E, Weston P, Alvarez JA. Test performance of an efficient 2 W, 137 K sorption refrigerator. Cryogenics 1992; 32:122–6. [4] Burger JF, Holland HJ, Wade LA, ter Brake HJM, Rogalla H. Thermodynamic considerations on a micro miniature sorption cooler. 10th international cryocooler conference, Monterey, California, May 26–28, 1998. [5] Bard S, Jones JA. Regenerative sorption compressor for cryogenic refrigeration. Adv Cryog Eng 1990;35:1357–65. [6] Chan CK. Optimal design of gas adsorption refrigerators for cryogenic cooling. NASA, CP 1982;2287:323–41. [7] Prakash MJ, Prasad M, Rastogi SC, Basavaraj A, Gupta PP, Narayanamurthy H, Srinivasan K. Development of a laboratory model of activated charcoal–nitrogen adsorption cryocooler. Cryogenics 2000;40(7):481–8. [8] Chan CK. Cryogenic refrigeration using low temperature heat source. Cryogenics 1981;21:391–8. [9] Rao RR, Prasad M, Bindagi SV, Srinivasan K. Effect of packing density on the performance of charcoal–nitrogen adsorption cryocoolers. Carbon 1997;35(10–11):1559–66. [10] Bard S. Improving adsorption cryocoolers by multistage compression and reducing void volume. Cryogenics 1986;26:450–8. [11] Prasad M, Rao RR, Prakash MJ, Srinivasan K. Thermodynamic analysis of a two stage charcoal–nitrogen adsorption cryocooler. In: Fundamentals of Adsorption 6. Paris: Elsevier; 1998. p. 745–50. [12] Akkimaradi BS, Prasad M, Dutta P, Srinivasan K. Effect of packing density and adsorption parameters on throughput of an adsorption compressor. Carbon 2002;40(15):2855–9. [13] Srinivasan K, Banker ND, Prasad M, Akkimaradi B. Evaluation of sorption compressor performance from isotherm data: application to activated carbon + nitrogen/HFC 134a systems. In: Saha BB, Akisawa A, Koyama S, editors. Thermally powered sorption technology, Proceedings of international seminar on thermally powered sorption technology, Kyushu University, Fukuoka, Japan, December 4–5, 2003. p. 121–33. [14] Banker NE, Rao RR, Srinivasan K, Prasad M. Limits of operating conditions for thermal compressors of adsorption cryocoolers. In: Proceedings of national seminar and conference on cryogenics and its frontier applications, Bengal Engineering College, Howrah, 25–27 March 2004. p. 143–8. [15] Prasad M, Akkimaradi B, Rastogi SC, Rao RR, Srinivasan K. Adsorption characteristics of charcoal–nitrogen system in 79– 320 K and pressures to 5 MPa. Carbon 1996;34(11):1401–6. [16] ALLPROPS—Property Package, Centre for Applied Thermodynamic Studies, University of Idaho, Moscow, Version 4.3, 1997.
xη u
0.3 0.2 0.1 0 4
6
8
10
pH (MPa) Fig. 8. Comparison of xgu with minimum requirement of 77% of uptake efficiency. Legend: xgu s 2.5 MPa, 2 MPa, n 1.5 MPa, } 1 MPa, h 0.5 MPa (continuous lines); 0.77x (broken lines). Hatched area shows the possible domain of operation with pL = 2.5 MPa.
103 K) at a packing density of 450 kg/m3. For these requirements one has to resort to two stage compression or to increase the packing density substantially. It can be expected that the specific power of the cryocooler will be the least at the point where xgu is the maximum. This can be verified from our earlier results [9].
4. Conclusions In this paper it is shown that single stage activated carbon + nitrogen cryocoolers have a very limited zone of possible operation if adequate throughput from the compressor has to be ensured. The lower limit is set by the properties of the adsorbate, while the upper by the adsorption characteristics of the two entities. Further, the packing density also plays an important role. A performance evaluation criteria has been defined. Some examples of performance are presented.
Acknowledgments The work reported in this paper was supported through grants from IISc-ISRO Space technology Cell and Defence Research and Development Organisation.