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Performance study of a partitioned thermally stratified storage tank in a solar powered absorption air conditioning system
Applied Thermal Engineering 22 (2002) 1207–1216 www.elsevier.com/locate/apthermeng
Performance study of a partitioned thermally stratified storage tank in a solar powered absorption air conditioning system Z.F. Li, K. Sumathy
*
Department of Mechanical Engineering, University of Hong Kong, Hong Kong Received 20 September 2001; accepted 21 February 2002
Abstract Accurate modeling of solar heating or cooling with storage generally requires an accounting of the stratification within such storage tank, since overall system performance is significantly affected by the storage temperature distribution. In this study, a simple one-dimensional multi-node approach, taking into account of the axial heat conduction between nodes, has been used to theoretically analyze temperature stratification in the thermal storage tank. The results indicate that, for less collector area, the heat removal factor plays a major role in increasing the system performance, than the thermal stratification. Also, an optimum ratio of tank volume over collector area exists for a solar powered absorption air conditioning system. This paper also reviews the state of the art on different kinds of variable inlet design, and a simple new inlet design (partitioning the tank) has been introduced to effect better thermal stratification in storage tank. 2002 Elsevier Science Ltd. All rights reserved. Keywords: Stratification; Partitioned storage tank; Solar energy; Absorption air conditioning
1. Introduction The efficiency of thermal energy systems can usually be improved by providing storage for hot and cold water depending on the load [1]. For conventionally operated large air-conditioning systems, utility costs may be considerably reduced by operating the equipment at night, when offpeak electricity rates are low, and make use of the chilled water that was stored during the night to meet the next day’s load demand. Likewise, the performance of the entire solar cooling/heating
*
Corresponding author. Fax: +852-2858-5415. E-mail address: [email protected] (K. Sumathy).
1359-4311/02/$ - see front matter 2002 Elsevier Science Ltd. All rights reserved. PII: S 1 3 5 9 - 4 3 1 1 ( 0 2 ) 0 0 0 4 8 - 0
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Nomenclature ai , bi , CP m m_ C m_ L Tb Ta TCr TLr TS;i UA k
ci , d coefficient and constant specific heat at constant pressure, J kg1 K1 mass of fluid, kg collector flow rate, kg s1 load flow rate, kg s1 temperature at the bottom of storage tank, K ambient temperature, K temperature of collector return flow, K temperature of load return flow, K temperature in the storage tank node i, K loss coefficient-area product, W K1 heat conduction coefficient, W m1 K1
Superscripts and subscripts C collector i ith node in the stratified storage tank L load N N th node in the stratified storage tank S storage tank system can be improved positively by an appropriate design of the thermally stratified storage tank. The success of this approach depends on the design of the inlet. Duffie and Beckman [2], Kleinbach et al. [3] have promoted two basic approaches (multi-node and plug flow) to be used when modeling the temperature distribution in thermal storage tanks for solar domestic hot water system. They have also incorporated the plume entrainment in their TRNSYS program [4], ensuring a realistic approach has been made in creating the temperature distribution in storage tanks. Though several other works have been carried out in achieving a thermally stratified temperature profile in the storage tank, some methods behave more complicated when introduced in the simulation of entire solar powered air conditioning systems. Hence, in the present study, a simple multi-node approach has been used to analyze the performance of the hot water storage tank. Energy balance has been made for N nodes inside the storage tank. In order to predict the temperature profile more accurately, the axial heat conduction in the fluid has also been taken into account, and the derived general discretization equations has been easily solved by the method of Tridiagonal-Matrix Algorithm (TDMA) [5].
2. Theoretical analysis The storage system considered in this analysis is a vertical cylinder of diameter D and length L as shown in Fig. 1. The tank is divided into N equal elements (nodes) in the longitudinal direction
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Fig. 1. Stratified water storage tank.
with energy balances written for each node in the tank. The energy equation takes into account of the energy gain from the collector (QU ), energy lost to surrounding, and energy utilized by the load (LS ), which results in a set of N differential equations that can be solved to obtain the temperatures of the N nodes as a function of time. For temperature stratified water tank, having a variable inlet design, a collector control function FiC is defined to identify which node receives water from the collector [2,3]; the liquid returning from the load can be controlled in a similar manner with a load return control function FiL . Along with the above given control functions, and taking into account of the axial heat conduction between nodes, an energy balance on node i can be expressed as: oTS;i ¼ ðUAÞi ðTa TS;i Þ þ FiC FCO m_ C CP ðTCr TS;i Þ þ FiL FAU CP m_ L ðTLr TS;i Þ þ kADx ot o2 TS;i _ þ Qinter ð1Þ ox2 Eq. (1) gives the heat balance on node i. The first term on the right side of the equation expresses the heat loss from the layer of the node to the surrounding; the following three terms denotes the heat gain from the collector circulation, heat utilized by load and the heat conduction between nodes, respectively. The last term refers to the heat exchange caused by fluid flow either by the upward or downward motion, from neighboring nodes. The heat conduction term in Eq. (1) can be expanded in the following form by using the central difference scheme: mi CP
kADx
o2 TS;i TS;iþ1 þ TS;i1 2TS;i ¼ kA 2 ox Dx
ð2Þ
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For the convenience of computer programming, the expressions of Q_ inter for interior points can be combined into a compact form by the use of a special symbol Max( ), which stands for the largest of the quantities contained within it. Thus, Q_ inter ¼ Maxðm_ m;i ; 0ÞCP ðTS;i1 TS;i Þ þ Maxðm_ m;i ; 0ÞCP ðTS;i TS;iþ1 Þ
ð3Þ
where ‘m_ m;i ’ denotes the net flow in the storage tank as a resultant of the collector down-flow and the load up-flow streams. Substituting Eqs. (2) and (3) into Eq. (1), and integrating over the time interval from t to t þ Dt, Eq. (1) can be presented in a generalized form of TDMA: ai TS;i ¼ bi TS;iþ1 þ ci TS;i1 þ di
ð4Þ
3. Results and discussion A solar powered air conditioning system has been designed and installed on the roof of Yam Pak building, at the University of Hong Kong. The collector which is used as the heat source is a type of high-performance, single-glassed, selective absorption coated flat-plate collector, with an effective area of 40 m2 , and with a flow rate of 0.38 kg/s. A WFC-1.3 chiller manufactured by YAZAKI Company [6] with a rated capacity of 4.7 kW was tested in this study. The chiller has a generator inlet temperature range of 75–100 C, and a cooling water inlet temperature range of 24–31 C, and attains its rated capacity of 4.7 kW under the following conditions: • Generator inlet temperature ¼ 88 C. • Cooling water inlet temperature ¼ 29.5 C. • Chilled water outlet temperature ¼ 9 C. A storage tank with a volume of 2.75 m3 has been employed in the system to store heat from the collector in order to drive the chiller at the required operating temperature (Fig. 2). A new variable inlet design (partitioned storage tank) has been introduced in the tank to effect better stratification and thereby further improves the thermal efficiency of the system. 3.1. Effect of parameters on the performance of the storage tank In the present study, as said earlier, multi-node approach has been used to predict the temperature profile, in which it is assumed that the number of nodes remains stable throughout the simulation process. In order to maintain the stability of the system, the chosen number of nodes must not be too many, as the amount of water flowing into the storage tank (either load flow or collector flow) in a given time step should not be greater than the amount of water occupied in each node of the storage tank. Kleinbach et al. [3] have suggested that 15 nodes may be chosen as the maximum number for a multi-node approach. On the other hand, the number of nodes cannot be too low, as it would under-predict the output of the system by nearly 10%. In general, the main governing parameters in limiting the maximum number of nodes are the flow rates (collector flow and load flow), volume of the storage tank and the time step. The
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Fig. 2. Front view of the storage tank.
collector flow rate plays a major role in effecting the number of nodes compared to the load flow rate. It was reported [7] that the optimum flow rate for a conventional fully mixed storage tank is about 0.014 kg/s per square meter of the collector area, which corresponds to a value of 0.57 kg/s with a total collector area of 40 m2 . For a stratified tank, it is preferred to have the flow rate lower than this value. Hence, in the present study, a comparative study was made for three different flow rates; i.e., (i) 0.38 kg/s (as recommended by the manufacturer, for this system), (ii) 0.57 kg/s (commonly used for a fully mixed storage tank), (iii) 0.83 kg/s (a higher collector flow rate). Fig. 3 shows the influence of the collector flow rate on the performance of the solar powered air conditioning system, for a given tank volume of 2.75 m3 (present experimental set-up). It is seen that, the system COP increases initially with the increase in collector flow rate. This initial increase can be attributed to the improvement in heat removal factor with increase in flow rate. It is interesting to note that, for a given collector flow rate, once the system attains its highest value of COPsystem , the performance reduces with further increase in collector area. This is due to the fact that, the system performance is also influenced by thermal stratification in the storage tank. Hence, higher collector flow rate generally tends to decline the thermocline (though the heat removal factor is higher) and further affect the system performance. The next deciding parameter in limiting the maximum number of nodes is the volume of the storage tank. In the present study, in order to study the effect of tank volume on the system
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Fig. 3. Effect of collector flow rate on system performance.
performance, tank volume of sizes 1–4 m3 are used to simulate the results (1 m3 represents a supposed minimum volume, whereas 4 m3 stands for a relatively large volume of the tank, for the chosen collector area (40 m2 ) in the experimental work). Fig. 4 shows the combined effect of tank volume and collector area on the system performance, while operating in partitioned mode. It is seen that, in general, the system COP is low with the increase in tank volume. Nevertheless, if the tank volume is too small, e.g. 1 m3 , then, with increase in collector area, the system COP decreases sharply beyond certain point. This is mainly because of the below given reasons: (i) by using small tank volume, the system could not effect solar cooling in the late afternoon and therefore the effective operation period is reduced; (ii) a small volume of tank generally reflects a relatively higher bulk temperature in the tank, which reduces the collector efficiency;
Fig. 4. Effect of tank volume on system COP.
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(iii) a too small storage tank would not be able to effectively balance the fluctuation of solar radiation, which might cause the frequent on–off of the chiller, and in turn results in a tremendous heat loss during the transitional period of stable operating condition. Hence, the system performance deteriorates significantly if too small tank volume is chosen. Therefore, while designing a solar powered air conditioning system, a proper/optimum size of storage tank should be chosen, such that it could serve as a heat reservoir, not only to balance the fluctuation of solar radiation, but also to provide enough thermal energy to drive the chiller in late afternoon (when solar insolation is insufficient to effect cooling). Hence, there exists an optimum ratio of tank volume over collector area. Also, in the present multimode approach, two recommended extreme cases such as 4 and 15 noded tanks have been chosen, to identify the number of nodes that is required to predict the temperature profile in the tank. It is shown that, 4 nodes are enough to accurately predict the temperature distribution in the system. 3.2. Modification of the variable inlet design Another important aspect of the storage system is the stratification, which in turn is highly dependent on the inlet design of the storage tank. A relatively simple new baffle inlet technique was introduced by Davis and Bartera [8], to maintain stratification. Fig. 5(a) shows the schematic of the baffle inlet storage tank, in which two solid baffle plates were placed near the inlet of the tank having a clearance of about 5 cm from the wall. The flow from the solar collector and from the load enters the tank through two inlet ports at mid-height and impinges on the plates where it
Fig. 5. (a) Inlet configuration used by Davis and Bartera [8]. (b) Modified inlet configuration for stratified thermal storage tank.
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gets diverted vertically up or down depending on the difference between the inlet and local tank fluid temperatures. However, this approach was not fully explored by the investigators, and the tests conducted were not comprehensive since they treated only a special case wherein the thermocline (the region between the hot and cold portions of fluid) location was already above the level of collector return water (mid-height of the tank) when the pump was turned on. Also, the collector return-flow, as well as load return-flow had been connected to the middle in the tank, which may not be a preferable design. Hence, in the present study, an attempt has been made to modify the Davis and Bartera inlet design, in such a way that the collector return-flow is connected to the upper part and the load flow to the lower part of the tank. Accordingly, the baffle plates have been redesigned. In order to further improve the system performance, the storage tank is partitioned into two parts (upper part and lower part). In the morning, the system would be operated with the upper part of the tank, while in the afternoon, the whole tank would be used to provide heat to the load (absorption chiller). Fig. 5(b) shows the schematic diagram of the partitioned storage tank design. As seen, the partition of the storage tank is achieved by positioning two baffle plates horizontally in the upper part of the tank, so that the tank is divided into two parts. The effect of volume ratio of upper part over entire storage tank has been analyzed [9]. For optimum system design, the upper part has one-fourth volume of the entire tank. The two plates are perforated, so that in the whole-tank mode, the collector return-flow in between the plates can locate at a position with the temperature close to its own. With the modified inlet design, both simulation and experimental works have been carried out. Fig. 6 shows the temperature profile in the storage tank during one-day operation, for a 4 noded tank, and being operated in the partitioned mode. The temperatures in the upper part (node 1) and lower part (node 4) of the tank alone are presented in order to give a simple profile of temperature distribution in the tank. It could be seen that, during the morning hours (until about 12:30 h), there is a wide fluctuation in the temperature profile in the upper part of the tank. This is because, the incident solar radiation being not sufficient to energize the chiller continuously, and the auxiliary heater being initiated, whenever the temperature level was below the required value
Fig. 6. Temperature distribution in the storage tank with time of the day (partitioned storage tank).
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(about 75 C). It is important to note that, when the air conditioning system is coupled to a partitioned mode storage tank, in addition to a better thermal stratification in the tank, the water can attain the required temperature to drive the chiller, by about 10:30 h. Whereas, when being operated using the conventional whole-tank mode, the water could attain the required temperature level, only at 12:30 h, delaying the operation about 2 h. It is also seen that, experimental data agrees reasonably well with the simulated results. Hence, a stratified storage tank with partitioned mode is recommended for solar air conditioning system and it is preferable to restrict the upper part of the tank to 1/4 of its entire volume, to achieve a higher COP.
4. Conclusion Stratified storage tank has an advantage of obtaining higher heat energy output when compared to a conventional fully mixed hot water storage tank. That is, the energy delivered by a forced-flow solar system can be increased substantially by thermal stratification. In this study, a multi-node model with variable inlets was chosen to analyze the temperature distribution in storage tanks. Care should be taken in choosing the number of nodes, such that, in any given time-step, the amount of water flowing into the storage tank should not be greater than the amount of water occupied in each node of the tank; if not, the system would become unstable. In order to effect thermal stratification, a modified inlet design has been made, and the tank was partitioned with the upper part having one-fourth volume of the entire tank. Results show that, the system operating in partitioned mode can provide cooling effect much earlier compared to conventional whole-tank designs, and achieve a higher system COP.
Acknowledgements The authors wish to express their thanks to the Committee on Research and Conference Grants (CRCG), the University of Hong Kong, Hong Kong, for its financial support.
References [1] F.J. Oppel, A.J. Ghajar, P.M. Moretti, A numerical and experimental study of stratified thermal storage, ASHRAR Trans. 92 (2A) (1986) 293–309. [2] J.A. Duffie, W.A. Beckman, Solar Engineering of Thermal Processes, Chapter 8 (Energy Storage), Wiley, New York, 1991. [3] E.M. Kleinbach, W.A. Beckman, S.A. Klein, Performance study of one-dimensional models for stratified thermal storage tanks, Solar Energy 50 (2) (1993) 155–166. [4] S.A. Klein et al., TRNSYS 13.1 User’s manual, Engineering Experimental Station Report 38-13, Solar Energy Laboratory, University of Wisconsin-Madison 1990. [5] S.V. Patankar, Numerical Heat Transfer and Fluid Flow, Chapter 4 (Heat Conduction), Hemisphere Publishing Corporation, New York, 1980. [6] Co. Yazaki, Installation and Service Manual of the Absorption Chiller and Catalog of Blue Panel Solar Collector (1982).
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[7] K.G.T. Hollands, M.F. Lightstone, A review of low-flow, stratified-tank solar water heating systems, Solar Energy 43 (2) (1989) 97–105. [8] E.S. Davis, R. Bartera, in: Stratification in solar water heater storage tanks. Pro. Workshop on Solar Energy Storage Subsystems for the Heating and Cooling of the Buildings, Charlottesville, Virginia, 1975, pp. 38–42. [9] Z.F. Li, K. Sumathy, Simulation of a solar absorption air conditioning system, Energy Convers. Mgmt. 4 (2000) 1–15.
Performance study of a partitioned thermally stratified storage tank in a solar powered absorption air conditioning system Z.F. Li, K. Sumathy
*
Department of Mechanical Engineering, University of Hong Kong, Hong Kong Received 20 September 2001; accepted 21 February 2002
Abstract Accurate modeling of solar heating or cooling with storage generally requires an accounting of the stratification within such storage tank, since overall system performance is significantly affected by the storage temperature distribution. In this study, a simple one-dimensional multi-node approach, taking into account of the axial heat conduction between nodes, has been used to theoretically analyze temperature stratification in the thermal storage tank. The results indicate that, for less collector area, the heat removal factor plays a major role in increasing the system performance, than the thermal stratification. Also, an optimum ratio of tank volume over collector area exists for a solar powered absorption air conditioning system. This paper also reviews the state of the art on different kinds of variable inlet design, and a simple new inlet design (partitioning the tank) has been introduced to effect better thermal stratification in storage tank. 2002 Elsevier Science Ltd. All rights reserved. Keywords: Stratification; Partitioned storage tank; Solar energy; Absorption air conditioning
1. Introduction The efficiency of thermal energy systems can usually be improved by providing storage for hot and cold water depending on the load [1]. For conventionally operated large air-conditioning systems, utility costs may be considerably reduced by operating the equipment at night, when offpeak electricity rates are low, and make use of the chilled water that was stored during the night to meet the next day’s load demand. Likewise, the performance of the entire solar cooling/heating
*
Corresponding author. Fax: +852-2858-5415. E-mail address: [email protected] (K. Sumathy).
1359-4311/02/$ - see front matter 2002 Elsevier Science Ltd. All rights reserved. PII: S 1 3 5 9 - 4 3 1 1 ( 0 2 ) 0 0 0 4 8 - 0
1208
Z.F. Li, K. Sumathy / Applied Thermal Engineering 22 (2002) 1207–1216
Nomenclature ai , bi , CP m m_ C m_ L Tb Ta TCr TLr TS;i UA k
ci , d coefficient and constant specific heat at constant pressure, J kg1 K1 mass of fluid, kg collector flow rate, kg s1 load flow rate, kg s1 temperature at the bottom of storage tank, K ambient temperature, K temperature of collector return flow, K temperature of load return flow, K temperature in the storage tank node i, K loss coefficient-area product, W K1 heat conduction coefficient, W m1 K1
Superscripts and subscripts C collector i ith node in the stratified storage tank L load N N th node in the stratified storage tank S storage tank system can be improved positively by an appropriate design of the thermally stratified storage tank. The success of this approach depends on the design of the inlet. Duffie and Beckman [2], Kleinbach et al. [3] have promoted two basic approaches (multi-node and plug flow) to be used when modeling the temperature distribution in thermal storage tanks for solar domestic hot water system. They have also incorporated the plume entrainment in their TRNSYS program [4], ensuring a realistic approach has been made in creating the temperature distribution in storage tanks. Though several other works have been carried out in achieving a thermally stratified temperature profile in the storage tank, some methods behave more complicated when introduced in the simulation of entire solar powered air conditioning systems. Hence, in the present study, a simple multi-node approach has been used to analyze the performance of the hot water storage tank. Energy balance has been made for N nodes inside the storage tank. In order to predict the temperature profile more accurately, the axial heat conduction in the fluid has also been taken into account, and the derived general discretization equations has been easily solved by the method of Tridiagonal-Matrix Algorithm (TDMA) [5].
2. Theoretical analysis The storage system considered in this analysis is a vertical cylinder of diameter D and length L as shown in Fig. 1. The tank is divided into N equal elements (nodes) in the longitudinal direction
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Fig. 1. Stratified water storage tank.
with energy balances written for each node in the tank. The energy equation takes into account of the energy gain from the collector (QU ), energy lost to surrounding, and energy utilized by the load (LS ), which results in a set of N differential equations that can be solved to obtain the temperatures of the N nodes as a function of time. For temperature stratified water tank, having a variable inlet design, a collector control function FiC is defined to identify which node receives water from the collector [2,3]; the liquid returning from the load can be controlled in a similar manner with a load return control function FiL . Along with the above given control functions, and taking into account of the axial heat conduction between nodes, an energy balance on node i can be expressed as: oTS;i ¼ ðUAÞi ðTa TS;i Þ þ FiC FCO m_ C CP ðTCr TS;i Þ þ FiL FAU CP m_ L ðTLr TS;i Þ þ kADx ot o2 TS;i _ þ Qinter ð1Þ ox2 Eq. (1) gives the heat balance on node i. The first term on the right side of the equation expresses the heat loss from the layer of the node to the surrounding; the following three terms denotes the heat gain from the collector circulation, heat utilized by load and the heat conduction between nodes, respectively. The last term refers to the heat exchange caused by fluid flow either by the upward or downward motion, from neighboring nodes. The heat conduction term in Eq. (1) can be expanded in the following form by using the central difference scheme: mi CP
kADx
o2 TS;i TS;iþ1 þ TS;i1 2TS;i ¼ kA 2 ox Dx
ð2Þ
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For the convenience of computer programming, the expressions of Q_ inter for interior points can be combined into a compact form by the use of a special symbol Max( ), which stands for the largest of the quantities contained within it. Thus, Q_ inter ¼ Maxðm_ m;i ; 0ÞCP ðTS;i1 TS;i Þ þ Maxðm_ m;i ; 0ÞCP ðTS;i TS;iþ1 Þ
ð3Þ
where ‘m_ m;i ’ denotes the net flow in the storage tank as a resultant of the collector down-flow and the load up-flow streams. Substituting Eqs. (2) and (3) into Eq. (1), and integrating over the time interval from t to t þ Dt, Eq. (1) can be presented in a generalized form of TDMA: ai TS;i ¼ bi TS;iþ1 þ ci TS;i1 þ di
ð4Þ
3. Results and discussion A solar powered air conditioning system has been designed and installed on the roof of Yam Pak building, at the University of Hong Kong. The collector which is used as the heat source is a type of high-performance, single-glassed, selective absorption coated flat-plate collector, with an effective area of 40 m2 , and with a flow rate of 0.38 kg/s. A WFC-1.3 chiller manufactured by YAZAKI Company [6] with a rated capacity of 4.7 kW was tested in this study. The chiller has a generator inlet temperature range of 75–100 C, and a cooling water inlet temperature range of 24–31 C, and attains its rated capacity of 4.7 kW under the following conditions: • Generator inlet temperature ¼ 88 C. • Cooling water inlet temperature ¼ 29.5 C. • Chilled water outlet temperature ¼ 9 C. A storage tank with a volume of 2.75 m3 has been employed in the system to store heat from the collector in order to drive the chiller at the required operating temperature (Fig. 2). A new variable inlet design (partitioned storage tank) has been introduced in the tank to effect better stratification and thereby further improves the thermal efficiency of the system. 3.1. Effect of parameters on the performance of the storage tank In the present study, as said earlier, multi-node approach has been used to predict the temperature profile, in which it is assumed that the number of nodes remains stable throughout the simulation process. In order to maintain the stability of the system, the chosen number of nodes must not be too many, as the amount of water flowing into the storage tank (either load flow or collector flow) in a given time step should not be greater than the amount of water occupied in each node of the storage tank. Kleinbach et al. [3] have suggested that 15 nodes may be chosen as the maximum number for a multi-node approach. On the other hand, the number of nodes cannot be too low, as it would under-predict the output of the system by nearly 10%. In general, the main governing parameters in limiting the maximum number of nodes are the flow rates (collector flow and load flow), volume of the storage tank and the time step. The
Z.F. Li, K. Sumathy / Applied Thermal Engineering 22 (2002) 1207–1216
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Fig. 2. Front view of the storage tank.
collector flow rate plays a major role in effecting the number of nodes compared to the load flow rate. It was reported [7] that the optimum flow rate for a conventional fully mixed storage tank is about 0.014 kg/s per square meter of the collector area, which corresponds to a value of 0.57 kg/s with a total collector area of 40 m2 . For a stratified tank, it is preferred to have the flow rate lower than this value. Hence, in the present study, a comparative study was made for three different flow rates; i.e., (i) 0.38 kg/s (as recommended by the manufacturer, for this system), (ii) 0.57 kg/s (commonly used for a fully mixed storage tank), (iii) 0.83 kg/s (a higher collector flow rate). Fig. 3 shows the influence of the collector flow rate on the performance of the solar powered air conditioning system, for a given tank volume of 2.75 m3 (present experimental set-up). It is seen that, the system COP increases initially with the increase in collector flow rate. This initial increase can be attributed to the improvement in heat removal factor with increase in flow rate. It is interesting to note that, for a given collector flow rate, once the system attains its highest value of COPsystem , the performance reduces with further increase in collector area. This is due to the fact that, the system performance is also influenced by thermal stratification in the storage tank. Hence, higher collector flow rate generally tends to decline the thermocline (though the heat removal factor is higher) and further affect the system performance. The next deciding parameter in limiting the maximum number of nodes is the volume of the storage tank. In the present study, in order to study the effect of tank volume on the system
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Fig. 3. Effect of collector flow rate on system performance.
performance, tank volume of sizes 1–4 m3 are used to simulate the results (1 m3 represents a supposed minimum volume, whereas 4 m3 stands for a relatively large volume of the tank, for the chosen collector area (40 m2 ) in the experimental work). Fig. 4 shows the combined effect of tank volume and collector area on the system performance, while operating in partitioned mode. It is seen that, in general, the system COP is low with the increase in tank volume. Nevertheless, if the tank volume is too small, e.g. 1 m3 , then, with increase in collector area, the system COP decreases sharply beyond certain point. This is mainly because of the below given reasons: (i) by using small tank volume, the system could not effect solar cooling in the late afternoon and therefore the effective operation period is reduced; (ii) a small volume of tank generally reflects a relatively higher bulk temperature in the tank, which reduces the collector efficiency;
Fig. 4. Effect of tank volume on system COP.
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(iii) a too small storage tank would not be able to effectively balance the fluctuation of solar radiation, which might cause the frequent on–off of the chiller, and in turn results in a tremendous heat loss during the transitional period of stable operating condition. Hence, the system performance deteriorates significantly if too small tank volume is chosen. Therefore, while designing a solar powered air conditioning system, a proper/optimum size of storage tank should be chosen, such that it could serve as a heat reservoir, not only to balance the fluctuation of solar radiation, but also to provide enough thermal energy to drive the chiller in late afternoon (when solar insolation is insufficient to effect cooling). Hence, there exists an optimum ratio of tank volume over collector area. Also, in the present multimode approach, two recommended extreme cases such as 4 and 15 noded tanks have been chosen, to identify the number of nodes that is required to predict the temperature profile in the tank. It is shown that, 4 nodes are enough to accurately predict the temperature distribution in the system. 3.2. Modification of the variable inlet design Another important aspect of the storage system is the stratification, which in turn is highly dependent on the inlet design of the storage tank. A relatively simple new baffle inlet technique was introduced by Davis and Bartera [8], to maintain stratification. Fig. 5(a) shows the schematic of the baffle inlet storage tank, in which two solid baffle plates were placed near the inlet of the tank having a clearance of about 5 cm from the wall. The flow from the solar collector and from the load enters the tank through two inlet ports at mid-height and impinges on the plates where it
Fig. 5. (a) Inlet configuration used by Davis and Bartera [8]. (b) Modified inlet configuration for stratified thermal storage tank.
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gets diverted vertically up or down depending on the difference between the inlet and local tank fluid temperatures. However, this approach was not fully explored by the investigators, and the tests conducted were not comprehensive since they treated only a special case wherein the thermocline (the region between the hot and cold portions of fluid) location was already above the level of collector return water (mid-height of the tank) when the pump was turned on. Also, the collector return-flow, as well as load return-flow had been connected to the middle in the tank, which may not be a preferable design. Hence, in the present study, an attempt has been made to modify the Davis and Bartera inlet design, in such a way that the collector return-flow is connected to the upper part and the load flow to the lower part of the tank. Accordingly, the baffle plates have been redesigned. In order to further improve the system performance, the storage tank is partitioned into two parts (upper part and lower part). In the morning, the system would be operated with the upper part of the tank, while in the afternoon, the whole tank would be used to provide heat to the load (absorption chiller). Fig. 5(b) shows the schematic diagram of the partitioned storage tank design. As seen, the partition of the storage tank is achieved by positioning two baffle plates horizontally in the upper part of the tank, so that the tank is divided into two parts. The effect of volume ratio of upper part over entire storage tank has been analyzed [9]. For optimum system design, the upper part has one-fourth volume of the entire tank. The two plates are perforated, so that in the whole-tank mode, the collector return-flow in between the plates can locate at a position with the temperature close to its own. With the modified inlet design, both simulation and experimental works have been carried out. Fig. 6 shows the temperature profile in the storage tank during one-day operation, for a 4 noded tank, and being operated in the partitioned mode. The temperatures in the upper part (node 1) and lower part (node 4) of the tank alone are presented in order to give a simple profile of temperature distribution in the tank. It could be seen that, during the morning hours (until about 12:30 h), there is a wide fluctuation in the temperature profile in the upper part of the tank. This is because, the incident solar radiation being not sufficient to energize the chiller continuously, and the auxiliary heater being initiated, whenever the temperature level was below the required value
Fig. 6. Temperature distribution in the storage tank with time of the day (partitioned storage tank).
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(about 75 C). It is important to note that, when the air conditioning system is coupled to a partitioned mode storage tank, in addition to a better thermal stratification in the tank, the water can attain the required temperature to drive the chiller, by about 10:30 h. Whereas, when being operated using the conventional whole-tank mode, the water could attain the required temperature level, only at 12:30 h, delaying the operation about 2 h. It is also seen that, experimental data agrees reasonably well with the simulated results. Hence, a stratified storage tank with partitioned mode is recommended for solar air conditioning system and it is preferable to restrict the upper part of the tank to 1/4 of its entire volume, to achieve a higher COP.
4. Conclusion Stratified storage tank has an advantage of obtaining higher heat energy output when compared to a conventional fully mixed hot water storage tank. That is, the energy delivered by a forced-flow solar system can be increased substantially by thermal stratification. In this study, a multi-node model with variable inlets was chosen to analyze the temperature distribution in storage tanks. Care should be taken in choosing the number of nodes, such that, in any given time-step, the amount of water flowing into the storage tank should not be greater than the amount of water occupied in each node of the tank; if not, the system would become unstable. In order to effect thermal stratification, a modified inlet design has been made, and the tank was partitioned with the upper part having one-fourth volume of the entire tank. Results show that, the system operating in partitioned mode can provide cooling effect much earlier compared to conventional whole-tank designs, and achieve a higher system COP.
Acknowledgements The authors wish to express their thanks to the Committee on Research and Conference Grants (CRCG), the University of Hong Kong, Hong Kong, for its financial support.
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[7] K.G.T. Hollands, M.F. Lightstone, A review of low-flow, stratified-tank solar water heating systems, Solar Energy 43 (2) (1989) 97–105. [8] E.S. Davis, R. Bartera, in: Stratification in solar water heater storage tanks. Pro. Workshop on Solar Energy Storage Subsystems for the Heating and Cooling of the Buildings, Charlottesville, Virginia, 1975, pp. 38–42. [9] Z.F. Li, K. Sumathy, Simulation of a solar absorption air conditioning system, Energy Convers. Mgmt. 4 (2000) 1–15.