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A valve operated absorption refrigerator
Applied Thermal Engineering 23 (2003) 417–429 www.elsevier.com/locate/apthermeng
A valve operated absorption refrigerator I.W. Eames, S. Wu
*
The School of Built Environment, The University of Nottingham, Nottingham NG7 2RD, UK Received 20 July 2002; accepted 25 October 2002
Abstract This paper presents a lithium bromide absorption refrigerator that does not use a mechanical pump for solution circulation. In this refrigerator, the solution circulation is achieved by making use of pressure in the generator. To achieve this, the generator is designed to carry out two functions namely desorption and circulation alternatively, which is served by two operational valves. A mathematic model for the solution circulation is developed to predict the refrigeratorÕs performance. Results from the model shows that this refrigerator can give a similar COP to that from single-effect refrigerators with mechanical pump circulation. This paper also discusses some structural effects to the refrigeratorÕs performance based on the mathematic model. Ó 2002 Elsevier Science Ltd. All rights reserved. Keywords: Absorption refrigeration; Bubble pump; Heat powered refrigerator
1. Introduction This paper describes and evaluates a novel ÔpumplessÕ water–lithium bromide absorption cycle refrigerator. In conventional absorption refrigeration systems, a mechanical pump is usually used to circulate the working fluids. Although the power consumption on the pump is only a small portion of total energy input, the use of electricity for a heat-powered system is not so convenient in cases where electricity supply is not available. For a heat-powered system, it is desirable to use heat for the circulation to keep the supply source simple. The idea utilising heat to circulate working fluids in absorption refrigeration cycle is not new. Around 1920, a diffusion–absorption refrigeration cycle was pioneered. In this cycle, a bubble pump is used to circulate the working fluid. This cycle has been investigated extensively since its invention [1]. The diffusion–absorption
*
Corresponding author. E-mail address: [email protected] (S. Wu).
1359-4311/02/$ - see front matter Ó 2002 Elsevier Science Ltd. All rights reserved. PII: S 1 3 5 9 - 4 3 1 1 ( 0 2 ) 0 0 2 1 0 - 7
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Nomenclature A=B d D hTG hTH hTG;g hTH;g hfg hr hs;i hs;pipe H L L1 L2 mG mP mPH ms ms;i mr ms;Gen ms;pipe p PA PG P PH Qe Qin QPG P QP PH Qde R S Spipe TG TP
volume ratio of the vapour to the liquid in a cylinder generator vessel during desorption period diameter of rising pipe, m diameter of generator vessel, m enthalpy of solution at temperature TG , kJ kg1 enthalpy of solution at temperature TH , kJ kg1 enthalpy of vapour at temperature TG , kJ kg1 enthalpy of vapour at temperature TH , kJ kg1 latent heat, kJ kg1 enthalpy of refrigerant, kJ kg1 enthalpy of solution entering the generator, kJ kg1 enthalpy of solution in the rising pipe, kJ kg1 solution level change in the generator related to the amount of the solution pumped into the absorber, m solution level in the rising pipe, m solution level in the rising pipe during non-pumping period, m highest solution level in the rising pipe, m mass of vapour in the generator at beginning of pumping period, kg mass of vapour in the generator when the rising pipe is just full, kg mass of vapour in the generator at the end of pumping period, kg mass of solution in the generator at the beginning of pumping period, kg mass of solution entering the generator, kg mass of refrigerant leaving the generator at non-pumping period, kg mass of solution in the generator at the end of pumping period, kg mass of solution in the rising pipe at the end of pumping period, kg pressure, N m2 absorber pressure, N m2 generator pressure at the beginning of pumping period, N m2 generator pressure when the rising pipe is just full, N m2 generator pressure at the end of pumping period, N m2 cooling load, kJ total heat input, kJ heat input to fill the rising pipe from L1 to L2 , kJ heat input to push the solution into absorber, kJ heat input in the non-pumping period, kJ gas constant, kJ kg1 K1 cross-sectional section area of generator vessel, m2 cross-sectional area of the rising pipe, m2 solution temperature at the beginning of pumping period, K solution temperature when the rising pipe is just full, K
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TPH V VG VP VPH WL1 L2 WP PH xd xc c DH q e
419
solution temperature at the end of pumping period, K volume, m3 vapour volume in the generator at the beginning of pumping period, m3 vapour volume in the generator when the rising pipe is just full, m3 vapour volume in the generator at the end of pumping period, m3 work required to fill rising pipe, kJ work required to pump the solution, kJ mass fraction of the weak solution, % mass fraction of the strong solution, % specific weight of solution, N m3 solution level change in the generator related to the amount of the solution to fill the riser to L2 , m density, kg m3 pumping rate
refrigeration cycle typically uses a mixture of ammonia–water–hydrogen as its working fluid. The roles of ammonia and water are familiar from conventional absorption cycle experience. Hydrogen is added to equalise the pressure throughout the cycle and so permit the use of a bubble pump to circulate the working fluids. However, the presence of hydrogen increases the resistance for the mass transfer and therefore the COP of this system tends to be significantly lower than a conventional water–lithium bromide absorption cycle. Recently, a two-fluid bubble pump system was investigated by Pfaff et al. [2]. Based on a water– lithium bromide vapour absorption refrigerator, their system used a bubble-pump to transfer the refrigerant-poor solution between the absorber and generator. The rising refrigerant vapour bubbles push the solution into the generator in slug flow pattern. Saravana and Maiya [3,4], also reported the influence of the working fluids and the effect of component pressure drops on a similar two-fluid bubble pump refrigerator. Karthikeyan et al. [5] reported a transfer-tank operated vapour absorption refrigeration systems. Their system used three valves to control pumping stages and part of the refrigerant, which was used to pump the solution, was directly discharged to the absorber after pumping period. Obviously, a reduction in COP is inevitable as a result of such an arrangement.
2. System description The proposed system, shown in Fig. 1, is a single-effect absorption refrigerator using water– lithium bromide solution as its working pair of fluids. In this system, the working fluid is pumped intermittently from the generator to the absorber by the pressure difference between them. This is achieved by controlling the opening and closing of two valves, V0 and V1 . During the pumping phase, both valves, V0 and V1 , are closed. However, heat continues to be supplied to the generator causing the vapour pressure to rise which pushes
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I.W. Eames, S. Wu / Applied Thermal Engineering 23 (2003) 417–429 L2
A bsorber
Evaporator
L1 V1
V0
L0 ∆H
Generator
Condenser
Fig. 1. Diagram of the system.
the solution up the fluid transfer tube. If the pressure is high enough to lift the working fluid to level L2 , the concentrated solution will flow into the absorber. At the end of the pumping phase, both valves are opened and the system enters a desorption phase. In this phase, the generator pressure will fall until it equals the condenser pressure and the weak solution flows from the absorber to the generator by virtue of its hydrostatic head. This phase will last until the solution level returns to the previous level at which the pumping phase started. A solution circulation is completed by the end of the desorption phase. The quantity of solution transferred to the absorber can be controlled by duration of valve closing time. Although the circulation of the working fluid is intermittent, the system can still provide continuous cooling because absorption process is not disrupted. Even the desorption process does not stop as the close of valve V0 does not stop vapour evolving from the solution in the generator. At the end of the pumping phase, when valve V0 is opened, the flow of water vapour from the generator to the condenser will be more rapid due to greater pressure difference. What is more, when the valve is opened the energy stored in the solution will accelerate the desorption process. Therefore, the overall performance of absorption and desorption in this system should be similar to that in the conventional absorption system, which uses a mechanical pump to circulate the fluids, apart from slightly higher solution temperature in generator required during the pumping phase. An aim of the design process is to minimise the hydraulic head difference between them in order to minimise pump work needed to transfer the solution. In previous diffusion absorption systems, the solution was pumped from absorber to the generator. Because the generator pressure is greater than absorber pressure, if the solution is to be pumped vertically from absorber to generator then the pump must overcome a pressure difference between generator and absorber plus the hydraulic head difference. In the proposed arrangement, shown in Fig. 1, the pumping head is reduced because the generator pressure now acts in the direction of the flow, tending to raise the fluid in the transfer pipe, towards the absorber. Fig. 2 shows the pressure balance between the generator and the absorber. The height of the solution in the transfer pipe, L, at which this balance, between vapour pressure and hydraulic head, is achieved, can be determined from L¼
Pg Pa c
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∆L
Pa
421
A bsorber
L
Pg Generator Fig. 2. Pressure balance between the generator and absorber.
In practice the level of the solution may need to be slightly higher than L for the solution to flow back to the generator by gravity. Obviously, to pump the solution from the generator to the absorber, slightly more pressure is required at the generator to overcome the additional hydraulic head cDL. However, this will probably be much less than the pressure difference Pg Pa . As DL approaches zero, the pumping head should also approach zero. Therefore, with this arrangement the pumping work reduces with the rate at which the solution is circulated. As a consequence of this the thermal efficiency of the system is improved.
3. Model of the pumping and desorption processes 3.1. Pumping phase Referring to Fig. 1: At the end of the desorption phase, we assume the solution levels are L0 in the generator and L1 the transfer pipe, or riser. At the beginning of the pumping phase, valves V0 and V1 are closed and this causes the solution level in the riser to increase whilst that in the generator falls, if heat continues to be added. Because the change in volume occupied by the solution in the generator must equal that in the riser then the following relationship can be derived. VP VG ¼ SDH ¼ Spipe ðL L1 Þ where DH equals the change in solution level in the generator and L is the increase of the level from L0 . The pressure in the generator can be calculated from following equation: p ¼ cL þ PA þ cDH Eq. (1) can be re-written as follows: L Spipe L þ 1 þ PA p ¼ cL1 L1 L1 S
ð1Þ
ð2Þ
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To raise the solution from L1 to L2 , the minimum generator pressure required is L2 Spipe L2 P ¼ cL1 þ 1 þ PA L1 S L1
ð3Þ
The solution temperature in the generator is a function of the vapour pressure and the solution concentration. However, the change of the solution concentration is very small in the pumping period so that we can assume that the concentration remains constant in order to simplify our analysis. With this assumption, vapour pressure becomes a function of solution temperature only. The required temperature increase can be calculated from following equation: TP TG ¼ f ðP Þ f ðPG Þ
ð4Þ
where f ðP Þ is a function that represents the relationship between temperature and pressure of the working fluid. As the solution level increases in the riser the vapour volume in the generator also increases. This volume changes from VG , at the start of the pumping phase to VP at its end, when the solution level equals L2 Since the vapour in the generator is superheat and at low pressure, the mass difference of vapour contained by the generator can be obtained from ideal gas law, 1 PVP PG VG mP mG ¼ ð5Þ R TP TG where, VP ¼ VG þ Spipe ðL2 L1 Þ. Therefore, the thermal energy input to the generator for the pumping process can be calculated from an energy balance: QPG P ¼ mP hTP ;g þ ðms mP þ mG ÞhTP ms hTG mG hTG;g
ð6Þ
where, ms ¼ qðV VG Þ. This equals the amount of solution in the generator at the start of pumping phase and V is the total volume of the generator. The work required for the solution to be lift from L1 to L2 can be determined as follows: Z Z L2 L Spipe L Spipe cL1 þ 1 þ PA dL ð7Þ WL1 L2 ¼ p dV ¼ L1 L1 S L1 Integration of Eq. (7) yields WL1 L2
Spipe cL21 ¼ 2
L22 Spipe 1þ 2 L1 S
L2 1 L1
2 !
þ PA Spipe L1
L2 1 L1
ð8Þ
The total amount of thermal energy input to the generator during the pumping phase, to raise the solution to level L2 , equals the sum of Eqs. (6) and (8). Once the solution level reaches the L2 in the riser any further fall in the quantity of solution in the generator will equal that which enters the absorber. At the end of pumping phase the pressure in generator equal PH , L2 Spipe L2 PH ¼ cL1 ð9Þ þ 1 þ PA þ cH L1 S L1 where, H equals the change in level in the generator due to the solution pumped into the absorber. In another words, H represents the amount of solution pumped to the absorber.
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The work required to pump this amount of solution can be calculated from the following: Z Z H L2 Spipe L2 WP PH ¼ pH dV ¼ cL1 ð10Þ þ 1 þ PA þ cH S dH L1 S L1 0 On integration of Eq. (10), therefore, the work required to pump the solution into absorber can be obtained from following: L2 Spipe L2 cH 2 WP PH ¼ cL1 þ 1 H þ PA H þ S ð11Þ L1 S L1 2 As first order approach, we consider the temperature change during the pumping period is linear with the vapour pressure, which is acceptable when the pressure change is not large, Spipe L2 cL 1 þ 1 þ cH 1 S L1 PH PG TPH TG ¼ ¼ ð12Þ k k Here, k is a constant that represents linear relationship between the vapour pressure and temperature and is related to properties of the working fluid. The required heat input to produce this increase solution temperature is given by, QP PH ¼ mPH hTH;g þ ðms mPH þ mG ÞhTH ðms mP þ mG ÞhTP mP hTP ;g
ð13Þ
The change in mass of vapour contained in the generator during the pumping process only (when solution is actually transferred into the absorber), is given by, 1 PH VPH PP VP mPH mP ¼ R TPH TP The mass of the solution pumped into the absorber is given by, m ¼ qSH
ð14Þ
Overall, from the start of the pumping phase, the total amount of vapour generated from the solution is mPH mG , which can be obtained from the following, 1 PH VPH PG VG mPH mG ¼ ð15Þ R TPH TG This amount of vapour can be regarded as forming part of product of the desorption process and it will flow to the condenser once the valves are opened. 3.2. Desorption phase After the pumping phase, both valves are again opened. Once this occurs the generator pressure will fall back to equal the condenser pressure and the level in the riser will fall to L1 . Once the pressure in the generator equals that in the condenser then the weak solution will begin to flow under gravity from the absorber to the generator. This phase will last until the solution level in the generator rises to height of L0 . The required heat input for this period can be calculated from following equation:
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Qde ¼ ms hTG;g ms;Gen hTH þ mr hr ms;i hs;i ms;pipe hs;pipe
ð16Þ
Here, ms;Gen equals the amount of the solution remaining in the generator after the pumping phase. This is equal to qðV VPH Þ. The amount of solution returning back to the generator, ms;i equals ðxc =xd ÞqSH and the refrigerant evolved from the solution during this period, mr , equals ððxc =xd Þ 1ÞqSH . The amount of the solution in the rising pipe returns to the generator, ms;pipe , equals qSpipe ðL2 L1 Þ.
4. Cop of the system The total heat input to the system during the pumping and desorption phases equals the sum of Eqs. (6), (8), (11), (13) and (16), which can be written as follows: Qin ¼ Qde þ QP PH þ QPG P þ WP PH þ WL1 L2
ð17Þ
The total cooling capacity can be determined from, Qe ¼ ðmPH mG þ mr Þhfg
ð18Þ
Therefore, the COP of the system can be written as follows: COP ¼
Qe ðmPH mG þ mr Þhfg ¼ Qin Qde þ QP PH þ QPG P þ WP PH þ WL1 L2
ð19Þ
Compared with conventional single-effect absorption refrigeration systems, which use mechanical solution pumps to circulate the solution, the thermally driven circulation absorption system described here needs extra energy, the amount of which equals the sum of QPG P and QP PH . These are stored in the solution and the vapour which actually contribute to the desorption process when the valves are opened. However, it is important to reduce the energy consumption during the pumping period in order to improve the COP value. 4.1. Non-back flow arrangement In the previous discussion, the solution in the riser is assumed to flow back to the generator at the start of the desorption process. Therefore, additional work is required at the beginning of each pumping phase to raise the solution level to L2 . Consequently, the COP of the system will be affected negatively. This problem can be eliminated if a one-way valve is installed in the riser so that the solution can be held in the pipe during desorption period. With such an arrangement, not only is the energy needed to fill the riser saved but also this will reduce heat losses in the solution heat exchanger. Consequently, the COP of the system can be improved. In this case, it can be expressed as follows: COP ¼
Qe ðmPH mG þ mr Þhfg ¼ Qin Qde þ QPG PH þ WP PH
ð20Þ
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5. Structural effects to the system performance As previously discussed, additional energy is required to transfer the solution into the absorber. The quantity of the additional energy is the sum of the works of WL1 L2 and WP PH as expressed in Eqs. (8) and (10), respectively, and the heat to increase the solution temperature in the generator vessel as expressed in Eqs. (6) and (13). According to Eq. (19), COP of the system can be improved if less additional energy is used to circulate the solution. To reduce this part of energy input, the increase of solution temperature in the generator vessel should be kept minimum for the pumping purpose. As Eq. (12) indicates that this can be done by adjusting the hydraulic head ratio L2 =L1 , the cross-sectional area ratio Spipe =S as well as solution level change H that is related to circulation flow rate. To show how these structural parameters affect the system performance, we apply the equations previously derived to a particular case. We will assume that the generator vessel is cylindrical and the solution heat exchanger is not included in the design. The following operating conditions are then assumed: the solution temperature in the generator is 75 °C during desorption phase; the evaporator temperature is 5 °C and the absorber and condenser temperatures are both 30 °C; the equilibrium solution concentration in the absorber and generator are 54% and 59% respectively. In the following sections, the crosssectional area ratio is represented by diameter ratio d=D. We also introduce pumping ratio, e, which represents the ratio of solution level fall H to the original level in the generator, to replace H .
5.1. The height of the riser
0.65 0.64 0.63 0.62 0.61 0.6 0.59 0.58
95 90 85
T HP,˚C
COP
The height, L2 , of the riser has significant effect to the solution temperature in the generator since the required pressure to lift the solution increases with its height. It also affects the COP of the system because additional energy is needed to build up the necessary pressure. As the hydraulic head and the ratio L2 =L1 increases, higher solution temperature is required to operate the system, which causes the COP to deteriorate. The results shown in Fig. 3 show that the solution temperature increases almost linearly with the ratio of L2 =L1 . The results shown in Fig. 3 also show that there is no benefit to the performance of the system by increasing the height of riser, L2 . Therefore, this ratio should be kept as low as possible.
80 1
1.2
1.4
1.6
1.8
Height ratio, L 2/L1
2
75 2.2
COP TPH
Fig. 3. Effect of the height ratio L2 =L1 on solution temperature and COP (d=D ¼ 0:05, A=B ¼ 3, A ¼ 0:2 m, d ¼ 0:025 m, e ¼ 0:5).
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However, a minimum height must be met to provide enough hydraulic head to ensure that the solution is able to flow back to the generator by gravity. 5.2. The cross-sectional area ratio of the generator vessel to the riser The riser must be filled with solution before any can be pumped into the absorber. Clearly, the greater the cross-sectional area of the riser then more solution is needed to fill it. This means that the level of solution in the generator must fall further before the flow enters the absorber. The consequence of this is that the solution temperature in the generator vessel needs to be higher. Since the solution remaining in the rising pipe does not have any positive contribution to the circulation system, the cross-sectional area of the riser should be as small as practicable in order to reduce the amount of the solution it contains. In contrast, a generator vessel with a large crosssectional area can reduce the level change of the solution, DH consequently, reduce the vapour pressure to fill the riser. Therefore, the cross-sectional area ratio of the generator vessel to the riser, Spipe =S, should be as small as possible. Fig. 4 shows the effects of this ratio on both COP and solution temperature. When determining the cross-sectional area of the riser, the resistance to the flow may also need to consider in balancing the gains and losses. 5.3. Pumping ratio In this proposed system, the circulation of solution is intermittent. The solution leaving and returning the generator takes place during different phases of the cycle. The amount of the solution pumped to the absorber in a whole circulation cycle determines the cooling capacity of the system. For a cylindrical generator, the amount of solution pumped is proportional to the level change, H , in the generator vessel, therefore proportional to pumping ratio e. The greater the pumping ratio, the larger the level change will be. This will result in higher solution temperatures and more work and heat transfer needed to produce the pumping effect, as indicated in Eqs. (12)– (14). Figs. 5 and 6 show the theoretical results for the variation in solution temperature, cooling capacity and COP change, with the pumping ratio. These results indicate that the solution temperature and cooling capacity increase proportionally with the pumping ratio. However, COP increases sharply with the pumping ratio in the range of e from 0.001 to 0.16. When the pumping ratio is above 0.33, COP is almost a constant with downward tendency. Figs. 5 and 6 also give 0.63
84
COP
83.2
0.62
82.8
0.615 0.61 0.05
TPH, ˚C
83.6
0.625
82.4 0.15
0.25
Area ratio, d/D
82 0.35
COP TPH
Fig. 4. Effect of cross-sectional area ratio on COP and solution temperature.
0.7
85
0.6
84
0.5
83
0.4 0.3
82
0.2
81 0
0.2
0.4
0.6
0.8
427
TPH,˚C
COP
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COP TPH
1
Pumping ratio, ε
cooling capacity, kJ
Fig. 5. Effect of the pumping rate on COP and solution temperature.
6000 5000 4000 3000 2000 1000 0 0
0.2
0.4
0.6
0.8
1
Pumping ratio, ε
Fig. 6. Effect of the pumping ratio on cooling capacity.
some guidance for choosing an optimum-pumping ratio. This is suggested to lie between 0.16 and 0.33. 5.4. Back flow to non-back flow arrangements
COP
It was earlier pointed that the non-back flow arrangement can reduce the energy needed for circulation and therefore, increase the COP of the system, as shown in Fig. 7. However, according to our calculations this does not always occur. The COP of a non-back flow system is indicated to be higher than that of back flow arrangement when the height ratio L2 =L1 is large. Fig. 7 shows the COP of two arrangement with cross-sectional area ratio d=D ¼ 0:05 while Fig. 8 is that with d=D ¼ 0:1. In Fig. 7, COP of non-back flow arrangement is only higher when L2 =L1 is greater than 2 while this takes place earlier (L2 =L1 ¼ 1:5) in Fig. 8. The result indicates that non-flow back 0.66 0.64 0.62 0.6 0.58 0.56 0.54
Back Flow
1
2
3
4
Non-back Flow
Height ratio, L2/L1
Fig. 7. Comparison of two arrangements with d=D ¼ 0:05.
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I.W. Eames, S. Wu / Applied Thermal Engineering 23 (2003) 417–429 0.66 0.64 COP
0.62 Back Flow
0.6
Non-back Flow
0.58 0.56 0.54 1
2
3
4
Height ratio, L2/L1
Fig. 8. Comparison of two arrangements with d=D ¼ 0:1.
arrangement is worth to consider in the case of high lift of the solution and big cross-sectional area ratio, which may be necessary for big capacity system. Other than that, it may not be worthwhile since the non-back flow arrangement could result in complexity of the system.
6. Design strategy From previous discussion, we suggest that the dimensions of the riser and generator vessel play an important role in COP of the system. To achieve the best COP from the system, the following are recommended: 1. Keep the lift height, L2 , of the solution as low as possible, but maintain necessary hydraulic head for the solution to flow back to the generator vessel under gravity. 2. The cross-sectional area ratio of the riser to the generator vessel should be as small as possible. A generator with a large cross-sectional area is preferred as this seems help to reduce the operating temperature for the same pumping rate in addition to reducing the cross- sectional area ratio. 3. For small capacity refrigerator, use the flow back arrangement as non-flow back one does not improve COP significantly but increases complex.
7. Conclusions A valve operated pump free absorption refrigerator using water–lithium bromide as working fluid has been described and evaluated. This refrigerator has the advantages of being simple in construction and easy to operate. A mathematical model was described and the calculation results from this model shows that COP of this system is laid between 0.61 and 0.64 when L2 =L1 ¼ 1 and d=D ¼ 0:1 are used. This COP value is similar to its conventional counterpart. To achieve it, the valve-operated system requires higher generator temperature to establish enough pumping pressure. The temperature of the generator increases with the hydraulic head ratio L2 =L1 and crosssectional area ratio d=D. Compared with a similar but conventional vapour absorption system, the minimum temperature increase required by this system is 7.1 °C when L2 =L1 ¼ 1, this increase
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could be as high as 21.5 °C when L2 =L1 ¼ 2:2 if we assume minimum generator temperature is 70 °C for a conventional system. It is worth mentioning here that COP of the system will decrease as hydraulic ratio increases. To make the system practically useful, an automatic valve operating system is required. This could be either electrical or mechanical one as long as they meet operation requirements. A mechanical valve control system will enable the refrigerator to run without electricity. A small PV panel may be sufficient to supply electricity to an electronic control device for the refrigerator. Therefore, it could be used in the cases that electricity supply is not viable and is possibly worthwhile for further investigation.
References [1] K.E. Herold, R. Radermacher, S.A. Klein, Absorption Chillers and Heat Pumps, CRC Press, Inc, 1996. [2] M. Pfaff, R. Saravanan, M.P. Maiya, S.S. Murthy, Studies on bubble pump for a water–lithium bromide vapour absorption refrigerator, International Journal of Refrigeration 21 (6) (1998) 452–562. [3] R. Saravanan, M.P. Maiya, Influence of thermodynamic and thermophysical properties of water-based working fluids for bubble pump operated vapour absorption refrigerator, Energy Conversion and Management 40 (1999) 845–860. [4] R. Saravanan, M.P. Maiya, Effect of component pressure drops in two-fluid pumpless continuous vapour absorption refrigerator, Energy Conversion and Management 38 (18) (1997) 1823–1832. [5] G. Karthikeyan, A. Mani, S. Srinivasa Murthy, Performance of different working fluids in transfer-tank operated vapour absorption refrigeration systems, Renewable Energy 6 (7) (1995) 835–842.
A valve operated absorption refrigerator I.W. Eames, S. Wu
*
The School of Built Environment, The University of Nottingham, Nottingham NG7 2RD, UK Received 20 July 2002; accepted 25 October 2002
Abstract This paper presents a lithium bromide absorption refrigerator that does not use a mechanical pump for solution circulation. In this refrigerator, the solution circulation is achieved by making use of pressure in the generator. To achieve this, the generator is designed to carry out two functions namely desorption and circulation alternatively, which is served by two operational valves. A mathematic model for the solution circulation is developed to predict the refrigeratorÕs performance. Results from the model shows that this refrigerator can give a similar COP to that from single-effect refrigerators with mechanical pump circulation. This paper also discusses some structural effects to the refrigeratorÕs performance based on the mathematic model. Ó 2002 Elsevier Science Ltd. All rights reserved. Keywords: Absorption refrigeration; Bubble pump; Heat powered refrigerator
1. Introduction This paper describes and evaluates a novel ÔpumplessÕ water–lithium bromide absorption cycle refrigerator. In conventional absorption refrigeration systems, a mechanical pump is usually used to circulate the working fluids. Although the power consumption on the pump is only a small portion of total energy input, the use of electricity for a heat-powered system is not so convenient in cases where electricity supply is not available. For a heat-powered system, it is desirable to use heat for the circulation to keep the supply source simple. The idea utilising heat to circulate working fluids in absorption refrigeration cycle is not new. Around 1920, a diffusion–absorption refrigeration cycle was pioneered. In this cycle, a bubble pump is used to circulate the working fluid. This cycle has been investigated extensively since its invention [1]. The diffusion–absorption
*
Corresponding author. E-mail address: [email protected] (S. Wu).
1359-4311/02/$ - see front matter Ó 2002 Elsevier Science Ltd. All rights reserved. PII: S 1 3 5 9 - 4 3 1 1 ( 0 2 ) 0 0 2 1 0 - 7
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Nomenclature A=B d D hTG hTH hTG;g hTH;g hfg hr hs;i hs;pipe H L L1 L2 mG mP mPH ms ms;i mr ms;Gen ms;pipe p PA PG P PH Qe Qin QPG P QP PH Qde R S Spipe TG TP
volume ratio of the vapour to the liquid in a cylinder generator vessel during desorption period diameter of rising pipe, m diameter of generator vessel, m enthalpy of solution at temperature TG , kJ kg1 enthalpy of solution at temperature TH , kJ kg1 enthalpy of vapour at temperature TG , kJ kg1 enthalpy of vapour at temperature TH , kJ kg1 latent heat, kJ kg1 enthalpy of refrigerant, kJ kg1 enthalpy of solution entering the generator, kJ kg1 enthalpy of solution in the rising pipe, kJ kg1 solution level change in the generator related to the amount of the solution pumped into the absorber, m solution level in the rising pipe, m solution level in the rising pipe during non-pumping period, m highest solution level in the rising pipe, m mass of vapour in the generator at beginning of pumping period, kg mass of vapour in the generator when the rising pipe is just full, kg mass of vapour in the generator at the end of pumping period, kg mass of solution in the generator at the beginning of pumping period, kg mass of solution entering the generator, kg mass of refrigerant leaving the generator at non-pumping period, kg mass of solution in the generator at the end of pumping period, kg mass of solution in the rising pipe at the end of pumping period, kg pressure, N m2 absorber pressure, N m2 generator pressure at the beginning of pumping period, N m2 generator pressure when the rising pipe is just full, N m2 generator pressure at the end of pumping period, N m2 cooling load, kJ total heat input, kJ heat input to fill the rising pipe from L1 to L2 , kJ heat input to push the solution into absorber, kJ heat input in the non-pumping period, kJ gas constant, kJ kg1 K1 cross-sectional section area of generator vessel, m2 cross-sectional area of the rising pipe, m2 solution temperature at the beginning of pumping period, K solution temperature when the rising pipe is just full, K
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TPH V VG VP VPH WL1 L2 WP PH xd xc c DH q e
419
solution temperature at the end of pumping period, K volume, m3 vapour volume in the generator at the beginning of pumping period, m3 vapour volume in the generator when the rising pipe is just full, m3 vapour volume in the generator at the end of pumping period, m3 work required to fill rising pipe, kJ work required to pump the solution, kJ mass fraction of the weak solution, % mass fraction of the strong solution, % specific weight of solution, N m3 solution level change in the generator related to the amount of the solution to fill the riser to L2 , m density, kg m3 pumping rate
refrigeration cycle typically uses a mixture of ammonia–water–hydrogen as its working fluid. The roles of ammonia and water are familiar from conventional absorption cycle experience. Hydrogen is added to equalise the pressure throughout the cycle and so permit the use of a bubble pump to circulate the working fluids. However, the presence of hydrogen increases the resistance for the mass transfer and therefore the COP of this system tends to be significantly lower than a conventional water–lithium bromide absorption cycle. Recently, a two-fluid bubble pump system was investigated by Pfaff et al. [2]. Based on a water– lithium bromide vapour absorption refrigerator, their system used a bubble-pump to transfer the refrigerant-poor solution between the absorber and generator. The rising refrigerant vapour bubbles push the solution into the generator in slug flow pattern. Saravana and Maiya [3,4], also reported the influence of the working fluids and the effect of component pressure drops on a similar two-fluid bubble pump refrigerator. Karthikeyan et al. [5] reported a transfer-tank operated vapour absorption refrigeration systems. Their system used three valves to control pumping stages and part of the refrigerant, which was used to pump the solution, was directly discharged to the absorber after pumping period. Obviously, a reduction in COP is inevitable as a result of such an arrangement.
2. System description The proposed system, shown in Fig. 1, is a single-effect absorption refrigerator using water– lithium bromide solution as its working pair of fluids. In this system, the working fluid is pumped intermittently from the generator to the absorber by the pressure difference between them. This is achieved by controlling the opening and closing of two valves, V0 and V1 . During the pumping phase, both valves, V0 and V1 , are closed. However, heat continues to be supplied to the generator causing the vapour pressure to rise which pushes
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I.W. Eames, S. Wu / Applied Thermal Engineering 23 (2003) 417–429 L2
A bsorber
Evaporator
L1 V1
V0
L0 ∆H
Generator
Condenser
Fig. 1. Diagram of the system.
the solution up the fluid transfer tube. If the pressure is high enough to lift the working fluid to level L2 , the concentrated solution will flow into the absorber. At the end of the pumping phase, both valves are opened and the system enters a desorption phase. In this phase, the generator pressure will fall until it equals the condenser pressure and the weak solution flows from the absorber to the generator by virtue of its hydrostatic head. This phase will last until the solution level returns to the previous level at which the pumping phase started. A solution circulation is completed by the end of the desorption phase. The quantity of solution transferred to the absorber can be controlled by duration of valve closing time. Although the circulation of the working fluid is intermittent, the system can still provide continuous cooling because absorption process is not disrupted. Even the desorption process does not stop as the close of valve V0 does not stop vapour evolving from the solution in the generator. At the end of the pumping phase, when valve V0 is opened, the flow of water vapour from the generator to the condenser will be more rapid due to greater pressure difference. What is more, when the valve is opened the energy stored in the solution will accelerate the desorption process. Therefore, the overall performance of absorption and desorption in this system should be similar to that in the conventional absorption system, which uses a mechanical pump to circulate the fluids, apart from slightly higher solution temperature in generator required during the pumping phase. An aim of the design process is to minimise the hydraulic head difference between them in order to minimise pump work needed to transfer the solution. In previous diffusion absorption systems, the solution was pumped from absorber to the generator. Because the generator pressure is greater than absorber pressure, if the solution is to be pumped vertically from absorber to generator then the pump must overcome a pressure difference between generator and absorber plus the hydraulic head difference. In the proposed arrangement, shown in Fig. 1, the pumping head is reduced because the generator pressure now acts in the direction of the flow, tending to raise the fluid in the transfer pipe, towards the absorber. Fig. 2 shows the pressure balance between the generator and the absorber. The height of the solution in the transfer pipe, L, at which this balance, between vapour pressure and hydraulic head, is achieved, can be determined from L¼
Pg Pa c
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∆L
Pa
421
A bsorber
L
Pg Generator Fig. 2. Pressure balance between the generator and absorber.
In practice the level of the solution may need to be slightly higher than L for the solution to flow back to the generator by gravity. Obviously, to pump the solution from the generator to the absorber, slightly more pressure is required at the generator to overcome the additional hydraulic head cDL. However, this will probably be much less than the pressure difference Pg Pa . As DL approaches zero, the pumping head should also approach zero. Therefore, with this arrangement the pumping work reduces with the rate at which the solution is circulated. As a consequence of this the thermal efficiency of the system is improved.
3. Model of the pumping and desorption processes 3.1. Pumping phase Referring to Fig. 1: At the end of the desorption phase, we assume the solution levels are L0 in the generator and L1 the transfer pipe, or riser. At the beginning of the pumping phase, valves V0 and V1 are closed and this causes the solution level in the riser to increase whilst that in the generator falls, if heat continues to be added. Because the change in volume occupied by the solution in the generator must equal that in the riser then the following relationship can be derived. VP VG ¼ SDH ¼ Spipe ðL L1 Þ where DH equals the change in solution level in the generator and L is the increase of the level from L0 . The pressure in the generator can be calculated from following equation: p ¼ cL þ PA þ cDH Eq. (1) can be re-written as follows: L Spipe L þ 1 þ PA p ¼ cL1 L1 L1 S
ð1Þ
ð2Þ
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To raise the solution from L1 to L2 , the minimum generator pressure required is L2 Spipe L2 P ¼ cL1 þ 1 þ PA L1 S L1
ð3Þ
The solution temperature in the generator is a function of the vapour pressure and the solution concentration. However, the change of the solution concentration is very small in the pumping period so that we can assume that the concentration remains constant in order to simplify our analysis. With this assumption, vapour pressure becomes a function of solution temperature only. The required temperature increase can be calculated from following equation: TP TG ¼ f ðP Þ f ðPG Þ
ð4Þ
where f ðP Þ is a function that represents the relationship between temperature and pressure of the working fluid. As the solution level increases in the riser the vapour volume in the generator also increases. This volume changes from VG , at the start of the pumping phase to VP at its end, when the solution level equals L2 Since the vapour in the generator is superheat and at low pressure, the mass difference of vapour contained by the generator can be obtained from ideal gas law, 1 PVP PG VG mP mG ¼ ð5Þ R TP TG where, VP ¼ VG þ Spipe ðL2 L1 Þ. Therefore, the thermal energy input to the generator for the pumping process can be calculated from an energy balance: QPG P ¼ mP hTP ;g þ ðms mP þ mG ÞhTP ms hTG mG hTG;g
ð6Þ
where, ms ¼ qðV VG Þ. This equals the amount of solution in the generator at the start of pumping phase and V is the total volume of the generator. The work required for the solution to be lift from L1 to L2 can be determined as follows: Z Z L2 L Spipe L Spipe cL1 þ 1 þ PA dL ð7Þ WL1 L2 ¼ p dV ¼ L1 L1 S L1 Integration of Eq. (7) yields WL1 L2
Spipe cL21 ¼ 2
L22 Spipe 1þ 2 L1 S
L2 1 L1
2 !
þ PA Spipe L1
L2 1 L1
ð8Þ
The total amount of thermal energy input to the generator during the pumping phase, to raise the solution to level L2 , equals the sum of Eqs. (6) and (8). Once the solution level reaches the L2 in the riser any further fall in the quantity of solution in the generator will equal that which enters the absorber. At the end of pumping phase the pressure in generator equal PH , L2 Spipe L2 PH ¼ cL1 ð9Þ þ 1 þ PA þ cH L1 S L1 where, H equals the change in level in the generator due to the solution pumped into the absorber. In another words, H represents the amount of solution pumped to the absorber.
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The work required to pump this amount of solution can be calculated from the following: Z Z H L2 Spipe L2 WP PH ¼ pH dV ¼ cL1 ð10Þ þ 1 þ PA þ cH S dH L1 S L1 0 On integration of Eq. (10), therefore, the work required to pump the solution into absorber can be obtained from following: L2 Spipe L2 cH 2 WP PH ¼ cL1 þ 1 H þ PA H þ S ð11Þ L1 S L1 2 As first order approach, we consider the temperature change during the pumping period is linear with the vapour pressure, which is acceptable when the pressure change is not large, Spipe L2 cL 1 þ 1 þ cH 1 S L1 PH PG TPH TG ¼ ¼ ð12Þ k k Here, k is a constant that represents linear relationship between the vapour pressure and temperature and is related to properties of the working fluid. The required heat input to produce this increase solution temperature is given by, QP PH ¼ mPH hTH;g þ ðms mPH þ mG ÞhTH ðms mP þ mG ÞhTP mP hTP ;g
ð13Þ
The change in mass of vapour contained in the generator during the pumping process only (when solution is actually transferred into the absorber), is given by, 1 PH VPH PP VP mPH mP ¼ R TPH TP The mass of the solution pumped into the absorber is given by, m ¼ qSH
ð14Þ
Overall, from the start of the pumping phase, the total amount of vapour generated from the solution is mPH mG , which can be obtained from the following, 1 PH VPH PG VG mPH mG ¼ ð15Þ R TPH TG This amount of vapour can be regarded as forming part of product of the desorption process and it will flow to the condenser once the valves are opened. 3.2. Desorption phase After the pumping phase, both valves are again opened. Once this occurs the generator pressure will fall back to equal the condenser pressure and the level in the riser will fall to L1 . Once the pressure in the generator equals that in the condenser then the weak solution will begin to flow under gravity from the absorber to the generator. This phase will last until the solution level in the generator rises to height of L0 . The required heat input for this period can be calculated from following equation:
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Qde ¼ ms hTG;g ms;Gen hTH þ mr hr ms;i hs;i ms;pipe hs;pipe
ð16Þ
Here, ms;Gen equals the amount of the solution remaining in the generator after the pumping phase. This is equal to qðV VPH Þ. The amount of solution returning back to the generator, ms;i equals ðxc =xd ÞqSH and the refrigerant evolved from the solution during this period, mr , equals ððxc =xd Þ 1ÞqSH . The amount of the solution in the rising pipe returns to the generator, ms;pipe , equals qSpipe ðL2 L1 Þ.
4. Cop of the system The total heat input to the system during the pumping and desorption phases equals the sum of Eqs. (6), (8), (11), (13) and (16), which can be written as follows: Qin ¼ Qde þ QP PH þ QPG P þ WP PH þ WL1 L2
ð17Þ
The total cooling capacity can be determined from, Qe ¼ ðmPH mG þ mr Þhfg
ð18Þ
Therefore, the COP of the system can be written as follows: COP ¼
Qe ðmPH mG þ mr Þhfg ¼ Qin Qde þ QP PH þ QPG P þ WP PH þ WL1 L2
ð19Þ
Compared with conventional single-effect absorption refrigeration systems, which use mechanical solution pumps to circulate the solution, the thermally driven circulation absorption system described here needs extra energy, the amount of which equals the sum of QPG P and QP PH . These are stored in the solution and the vapour which actually contribute to the desorption process when the valves are opened. However, it is important to reduce the energy consumption during the pumping period in order to improve the COP value. 4.1. Non-back flow arrangement In the previous discussion, the solution in the riser is assumed to flow back to the generator at the start of the desorption process. Therefore, additional work is required at the beginning of each pumping phase to raise the solution level to L2 . Consequently, the COP of the system will be affected negatively. This problem can be eliminated if a one-way valve is installed in the riser so that the solution can be held in the pipe during desorption period. With such an arrangement, not only is the energy needed to fill the riser saved but also this will reduce heat losses in the solution heat exchanger. Consequently, the COP of the system can be improved. In this case, it can be expressed as follows: COP ¼
Qe ðmPH mG þ mr Þhfg ¼ Qin Qde þ QPG PH þ WP PH
ð20Þ
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5. Structural effects to the system performance As previously discussed, additional energy is required to transfer the solution into the absorber. The quantity of the additional energy is the sum of the works of WL1 L2 and WP PH as expressed in Eqs. (8) and (10), respectively, and the heat to increase the solution temperature in the generator vessel as expressed in Eqs. (6) and (13). According to Eq. (19), COP of the system can be improved if less additional energy is used to circulate the solution. To reduce this part of energy input, the increase of solution temperature in the generator vessel should be kept minimum for the pumping purpose. As Eq. (12) indicates that this can be done by adjusting the hydraulic head ratio L2 =L1 , the cross-sectional area ratio Spipe =S as well as solution level change H that is related to circulation flow rate. To show how these structural parameters affect the system performance, we apply the equations previously derived to a particular case. We will assume that the generator vessel is cylindrical and the solution heat exchanger is not included in the design. The following operating conditions are then assumed: the solution temperature in the generator is 75 °C during desorption phase; the evaporator temperature is 5 °C and the absorber and condenser temperatures are both 30 °C; the equilibrium solution concentration in the absorber and generator are 54% and 59% respectively. In the following sections, the crosssectional area ratio is represented by diameter ratio d=D. We also introduce pumping ratio, e, which represents the ratio of solution level fall H to the original level in the generator, to replace H .
5.1. The height of the riser
0.65 0.64 0.63 0.62 0.61 0.6 0.59 0.58
95 90 85
T HP,˚C
COP
The height, L2 , of the riser has significant effect to the solution temperature in the generator since the required pressure to lift the solution increases with its height. It also affects the COP of the system because additional energy is needed to build up the necessary pressure. As the hydraulic head and the ratio L2 =L1 increases, higher solution temperature is required to operate the system, which causes the COP to deteriorate. The results shown in Fig. 3 show that the solution temperature increases almost linearly with the ratio of L2 =L1 . The results shown in Fig. 3 also show that there is no benefit to the performance of the system by increasing the height of riser, L2 . Therefore, this ratio should be kept as low as possible.
80 1
1.2
1.4
1.6
1.8
Height ratio, L 2/L1
2
75 2.2
COP TPH
Fig. 3. Effect of the height ratio L2 =L1 on solution temperature and COP (d=D ¼ 0:05, A=B ¼ 3, A ¼ 0:2 m, d ¼ 0:025 m, e ¼ 0:5).
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However, a minimum height must be met to provide enough hydraulic head to ensure that the solution is able to flow back to the generator by gravity. 5.2. The cross-sectional area ratio of the generator vessel to the riser The riser must be filled with solution before any can be pumped into the absorber. Clearly, the greater the cross-sectional area of the riser then more solution is needed to fill it. This means that the level of solution in the generator must fall further before the flow enters the absorber. The consequence of this is that the solution temperature in the generator vessel needs to be higher. Since the solution remaining in the rising pipe does not have any positive contribution to the circulation system, the cross-sectional area of the riser should be as small as practicable in order to reduce the amount of the solution it contains. In contrast, a generator vessel with a large crosssectional area can reduce the level change of the solution, DH consequently, reduce the vapour pressure to fill the riser. Therefore, the cross-sectional area ratio of the generator vessel to the riser, Spipe =S, should be as small as possible. Fig. 4 shows the effects of this ratio on both COP and solution temperature. When determining the cross-sectional area of the riser, the resistance to the flow may also need to consider in balancing the gains and losses. 5.3. Pumping ratio In this proposed system, the circulation of solution is intermittent. The solution leaving and returning the generator takes place during different phases of the cycle. The amount of the solution pumped to the absorber in a whole circulation cycle determines the cooling capacity of the system. For a cylindrical generator, the amount of solution pumped is proportional to the level change, H , in the generator vessel, therefore proportional to pumping ratio e. The greater the pumping ratio, the larger the level change will be. This will result in higher solution temperatures and more work and heat transfer needed to produce the pumping effect, as indicated in Eqs. (12)– (14). Figs. 5 and 6 show the theoretical results for the variation in solution temperature, cooling capacity and COP change, with the pumping ratio. These results indicate that the solution temperature and cooling capacity increase proportionally with the pumping ratio. However, COP increases sharply with the pumping ratio in the range of e from 0.001 to 0.16. When the pumping ratio is above 0.33, COP is almost a constant with downward tendency. Figs. 5 and 6 also give 0.63
84
COP
83.2
0.62
82.8
0.615 0.61 0.05
TPH, ˚C
83.6
0.625
82.4 0.15
0.25
Area ratio, d/D
82 0.35
COP TPH
Fig. 4. Effect of cross-sectional area ratio on COP and solution temperature.
0.7
85
0.6
84
0.5
83
0.4 0.3
82
0.2
81 0
0.2
0.4
0.6
0.8
427
TPH,˚C
COP
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COP TPH
1
Pumping ratio, ε
cooling capacity, kJ
Fig. 5. Effect of the pumping rate on COP and solution temperature.
6000 5000 4000 3000 2000 1000 0 0
0.2
0.4
0.6
0.8
1
Pumping ratio, ε
Fig. 6. Effect of the pumping ratio on cooling capacity.
some guidance for choosing an optimum-pumping ratio. This is suggested to lie between 0.16 and 0.33. 5.4. Back flow to non-back flow arrangements
COP
It was earlier pointed that the non-back flow arrangement can reduce the energy needed for circulation and therefore, increase the COP of the system, as shown in Fig. 7. However, according to our calculations this does not always occur. The COP of a non-back flow system is indicated to be higher than that of back flow arrangement when the height ratio L2 =L1 is large. Fig. 7 shows the COP of two arrangement with cross-sectional area ratio d=D ¼ 0:05 while Fig. 8 is that with d=D ¼ 0:1. In Fig. 7, COP of non-back flow arrangement is only higher when L2 =L1 is greater than 2 while this takes place earlier (L2 =L1 ¼ 1:5) in Fig. 8. The result indicates that non-flow back 0.66 0.64 0.62 0.6 0.58 0.56 0.54
Back Flow
1
2
3
4
Non-back Flow
Height ratio, L2/L1
Fig. 7. Comparison of two arrangements with d=D ¼ 0:05.
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I.W. Eames, S. Wu / Applied Thermal Engineering 23 (2003) 417–429 0.66 0.64 COP
0.62 Back Flow
0.6
Non-back Flow
0.58 0.56 0.54 1
2
3
4
Height ratio, L2/L1
Fig. 8. Comparison of two arrangements with d=D ¼ 0:1.
arrangement is worth to consider in the case of high lift of the solution and big cross-sectional area ratio, which may be necessary for big capacity system. Other than that, it may not be worthwhile since the non-back flow arrangement could result in complexity of the system.
6. Design strategy From previous discussion, we suggest that the dimensions of the riser and generator vessel play an important role in COP of the system. To achieve the best COP from the system, the following are recommended: 1. Keep the lift height, L2 , of the solution as low as possible, but maintain necessary hydraulic head for the solution to flow back to the generator vessel under gravity. 2. The cross-sectional area ratio of the riser to the generator vessel should be as small as possible. A generator with a large cross-sectional area is preferred as this seems help to reduce the operating temperature for the same pumping rate in addition to reducing the cross- sectional area ratio. 3. For small capacity refrigerator, use the flow back arrangement as non-flow back one does not improve COP significantly but increases complex.
7. Conclusions A valve operated pump free absorption refrigerator using water–lithium bromide as working fluid has been described and evaluated. This refrigerator has the advantages of being simple in construction and easy to operate. A mathematical model was described and the calculation results from this model shows that COP of this system is laid between 0.61 and 0.64 when L2 =L1 ¼ 1 and d=D ¼ 0:1 are used. This COP value is similar to its conventional counterpart. To achieve it, the valve-operated system requires higher generator temperature to establish enough pumping pressure. The temperature of the generator increases with the hydraulic head ratio L2 =L1 and crosssectional area ratio d=D. Compared with a similar but conventional vapour absorption system, the minimum temperature increase required by this system is 7.1 °C when L2 =L1 ¼ 1, this increase
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could be as high as 21.5 °C when L2 =L1 ¼ 2:2 if we assume minimum generator temperature is 70 °C for a conventional system. It is worth mentioning here that COP of the system will decrease as hydraulic ratio increases. To make the system practically useful, an automatic valve operating system is required. This could be either electrical or mechanical one as long as they meet operation requirements. A mechanical valve control system will enable the refrigerator to run without electricity. A small PV panel may be sufficient to supply electricity to an electronic control device for the refrigerator. Therefore, it could be used in the cases that electricity supply is not viable and is possibly worthwhile for further investigation.
References [1] K.E. Herold, R. Radermacher, S.A. Klein, Absorption Chillers and Heat Pumps, CRC Press, Inc, 1996. [2] M. Pfaff, R. Saravanan, M.P. Maiya, S.S. Murthy, Studies on bubble pump for a water–lithium bromide vapour absorption refrigerator, International Journal of Refrigeration 21 (6) (1998) 452–562. [3] R. Saravanan, M.P. Maiya, Influence of thermodynamic and thermophysical properties of water-based working fluids for bubble pump operated vapour absorption refrigerator, Energy Conversion and Management 40 (1999) 845–860. [4] R. Saravanan, M.P. Maiya, Effect of component pressure drops in two-fluid pumpless continuous vapour absorption refrigerator, Energy Conversion and Management 38 (18) (1997) 1823–1832. [5] G. Karthikeyan, A. Mani, S. Srinivasa Murthy, Performance of different working fluids in transfer-tank operated vapour absorption refrigeration systems, Renewable Energy 6 (7) (1995) 835–842.