- Email: [email protected]
Performance evaluation of open-cycle solar regenerator using artificial neural network technique
Energy and Buildings 43 (2011) 454–457
Contents lists available at ScienceDirect
Energy and Buildings journal homepage: www.elsevier.com/locate/enbuild
Performance evaluation of open-cycle solar regenerator using artificial neural network technique Ayman A. Aly, El-Shafei B. Zeidan, Ahmed M. Hamed ∗ Department of Mechanical Engineering, Faculty of Engineering, Taif University, Al-hawyah, P.O. Box 888, Saudi Arabia
a r t i c l e
i n f o
Article history: Received 31 January 2010 Received in revised form 27 September 2010 Accepted 30 September 2010 Keywords: Solar energy Open-cycle Regeneration Lithium chloride Absorption Liquid desiccant Neural network Back-propagation algorithm
a b s t r a c t Theoretical investigation on the performance of lithium chloride (LiCl) absorption cooling system using an artificial neural network (ANN) model is presented. Tabulated data from the literature are used to construct the ANN model. Solar collector desiccant/regenerator is applied to re-concentrate the working solution. Using the proposed model, the effect of system design parameters; namely regenerator length, and air flow rate on the performance of the system is demonstrated. The variation of the thermo-physical parameters along the regenerator length is highlighted. © 2010 Elsevier B.V. All rights reserved.
1. Introduction Solar-powered air conditioning has seen renewed interest in recent years due to the growing awareness of environmental problems. Significant progress has been achieved in the development of absorption cooling systems considered as a serious alternative to traditional vapor compression systems [1–8]. Solar air liquid collector/regenerator (C/R) systems can achieve liquid regeneration at lower temperatures, which is suitable to buildings with high outdoor air requirements in high humidity areas [9,10]. Alizadeh and Saman [11] studied the performance of forced flow solar collector/regenerator using liquid desiccant. To analyze the performance of absorption system, the partial pressure of water vapor of the desiccant solution must be known in terms of temperature and concentration. Empirical expressions generally provide vapor pressure with limited accuracy. Further, the expressions currently in use are tedious and valid for narrow ranges and must be adjusted continuously [12]. Artificial neural network (ANN) models are capable of relating output to input variables for cases where no theoretical model works satisfactorily in a realistic time frame. An ANN model can be
∗ Corresponding author. E-mail addresses: ayman [email protected] (A.A. Aly), [email protected] (E.-S.B. Zeidan), [email protected] (A.M. Hamed). 0378-7788/$ – see front matter © 2010 Elsevier B.V. All rights reserved. doi:10.1016/j.enbuild.2010.09.032
used to create a black box model that simulates exactly the real situation. ANN models have become very popular recently to overcome some of the limitations of physical modeling [12,13]. This study is part of the ongoing investigation onto the concept and operation of an open-cycle absorption cooling systems. The present work proposes the use of an ANN based model in order to capture the relations between the thermo-physical properties of the desiccant solution to feed the simulation model which investigates the performance of the solar-powered open collector regenerator. Before the application of the ANN model, the data given in literature is treated and the model is trained and tested. It is also objected to evaluate the variation of the most effective output parameters (vapor pressure difference and mass of evaporated water) along the regenerator length. 2. The artificial neural network model The artificial neural network (ANN) is a new form of computing, inspired by biological models and composed of a large number of processing elements organized into layers. A computing system, made up of a number of simple, highly interconnected processing elements, which processes information by its dynamic state response to external inputs. The ANN is supposed to consist of artificial neurons or processing elements [14,15]. If we denote the ith input as xi and the output as y, then we can write the mapping from the inputs to the output performed by the
A.A. Aly et al. / Energy and Buildings 43 (2011) 454–457
455
Nomenclature C g H ha
solution concentration gradient specific enthalpy, J/kg heat transfer coefficient from air stream to ambient atmosphere, W/m2 ◦ C heat transfer coefficient from solution to air stream, W/m2 ◦ C latent heat of water, kJ/kg solar radiation intensity, kW/m2 fluid mass flow rate or rate of water evaporation, kg/s pressure, mmHg temperature, ◦ C target output overall heat loss coefficient, W/m2 ◦ C weight factors regenerator length, m inputs to the ANN model output from the ANN model
hs hfg Ia m P T t UL wij x xi yi
Greek symbols ˛ learning rate ˇ mass transfer coefficient, kg/s m2 mmHg Subscripts a air b barometric i inlet k iteration level o outside s solution
Fig. 2. ANN analysis algorithm.
Generally, the goal of a neural network is to modify the weights to minimize the response error. Nudge the weights in the direction that will minimize the difference between the measured and desired outputs. The technique for modifying weights in the appropriate direction and magnitude eluded researchers for years. However, the recent development of the back propagation learning scheme has solved this problem. Since the advent of ‘backpropagation’, neural networks have enjoyed renewed emphasis and application. Several studies have found that a three-layered neural network with one hidden layer can approximate any nonlinear function to any desired accuracy [16]. The network consists of input layer, hidden layer and output layer. The method is based on an analysis of how a change in any particular weight influences the output of the network. After such analysis is done, the designer understands how to change the weights to achieve the specified values for the outputs. First of all, one must construct a chain similar to Fig. 2. This chain examines the influence of any weight factor on the output value and, hence, on the error value. We consider as an error the difference between the actual output and the desired one. The performance function is the sum square error (SSE) which is defined as the sum of square of the difference between target output (expected) and the actual output from the NN: SSE =
m
(tk − yk )2
(2)
k=1
processing elements in this case as y = f(
xi wij + b)
(1)
Layers are connected together composing an ANN. Inputs could be connected to many nodes with various weights, resulting in a series of outputs, one per node (Fig. 1). The connections are multiplied by the weights associated with that particular node with which they interconnect. They convey analog values. Note that there are many more connections than nodes. The network is said to be fully connected if every output from one layer is passed along to every node in the next layer.
Learning rule gradually adjusts the weights until the performance function (SSE) falls below a certain threshold or minimised. Back-propagation learning updates the network weights and biases in the direction in which the performance function decreases most rapidly, i.e., the negative of the gradient: ¯ k+1 = w ¯ k − ˛k g¯ k w
(3)
where wk+1 are updated weights, wk are current weights, gk is current gradient of performance function, and (k is the learning rate. In this paper the network has two input elements and one output. Ten element hidden layers are assigned. 3. Mathematical model The forced flow C/R employs an inclined flat blackened surface over which the absorbent solution to be concentrated trickles down as a thin liquid film. The schematic of the C/R is shown in Fig. 3. The weak solution flows over the absorber as a thin film and the forced air stream flows parallel or counter to the solution. In order to reduce top losses and eliminate contamination of the solution with dust, the C/R is covered by a single or double glazing. Due to absorption of solar energy by the plate, water evaporates from the liquid surface and is removed by a forced air stream. The steady-state energy balance equations for the open cycle regenerator-segment of unit width is written as [11]: Ia dx = ms dHs + ma dHa + UL (Ts − T0 ) + mhfg
(4)
The energy balance for the air stream passing through the regenerator-segment is written as Fig. 1. A schematic of multilayer neural network.
ma dHa = ha (Ts − Ta )dx − hs (Ta − T0 )dx
(5)
456
A.A. Aly et al. / Energy and Buildings 43 (2011) 454–457
Fig. 5. Absolute error of the evaluated concentration from the ANN model.
4. Results and discussion
Fig. 3. Schematic diagram of solar liquid collector/regenerator system.
The amount of water evaporated from the weak solution and the rate of mass transport are given by m = 0.622
ma (pa − pai ) pb
dm = ˇ(ps − pa ) dx
(6)
(7)
and the relation between the mass of evaporated water and solution flow rates is given by Cs =
Csi (1 − (m/ms )
(8)
The model described above consists of coupled non-linear ordinary differential equations which link the characteristic parameters of air and desiccant solution. An analytical solution is rather difficult and could only be obtained for simplified situations that allow the reduction of the basic equations. In the present study, a numerical solution is obtained by a finite difference technique. The regenerator is divided into a large number of segments with the assumption of constant properties within the segment. Given the input values of mass flow rates of air and solution, air temperature, and solution concentration at the inlet of any segment, the output values are obtained using the above equations by a step-by-step analysis up to the outlet. An iterative procedure is used to get a converged steady-state solution. In the present study, lithium chloride (LiCl) is used as the absorbent. The properties of the solution are obtained from the ANN model to feed the numerical simulation model. The heat and mass transfer coefficients are evaluated by using available correlations from the literature [17]. A computer code is written in MATLAB to perform the computations and visualize the results. The convergence criterion is taken as 0.1 ◦ C for the air temperature and 1 × 10−6 kg/s for the mass of evaporated water.
To validate the ANN model, the thermo-physical properties of LiCl which are given in [18] are plotted versus the numerical data obtained from the model (see Fig. 4). It can be observed that a good agreement between the model results and the original data set. The error analysis of the data is presented in Fig. 5. The most important value of applying the ANN model is that it makes it possible to evaluate any of the three properties in terms of the other two properties at any value within the treated range of data. Moreover, it is possible to link the model with other models used to analyze the performance of the systems which use the desiccant solutions. The developed ANN model for the LiCl solution is applied in this study to analyze the performance of the open desiccant cooling cycle powered by solar energy. By applying the mathematical model described above, the regenerator thermal performance is carried out. The regenerator performance is analyzed for the conditions given in Table 1. The temperature of the desiccant solution as well as air temperature are plotted versus the regenerator length, x, at air flow rate equals 10 kg/s, as shown in Fig. 6. It can be observed that the difference between the two temperatures increases with x, which explains the accumulation of energy in both solution and air streams. It is expected that the solution and air temperatures will be affected by the air and solution flow rates for the same radiation intensity. The vapor pressure difference, which is the mass transfer potential or the driving force for evaporation of water from the surface of the solution is plotted with generator length, for the three cases of air flow rates (10, 20 and 30 kg/h), as illustrated in Fig. 7. For the specified operating conditions, the vapor pressure difference at regenerator inlet is negative, where the solution vapor pressure is lower than that of the inlet air stream; this of course results in a negative flow of vapor or negative absorption. As soon as the solution vapor pressure exceeds that of the air stream, evaporation of water starts. The rate of evaporation is expected to be 90.0
Air Temperature Solution temperature
Temperature, C
80.0 70.0 60.0 50.0 40.0 30.0 0.0
0.1
0.2
0.3
0.4
0.5
0.6
0.7
0.8
0.9
1.0
Regenerator length,m Fig. 4. ANN model validation.
Fig. 6. Variation of solution and air temperatures with regenerator length.
A.A. Aly et al. / Energy and Buildings 43 (2011) 454–457
457
Table 1 System operating conditions. Pa , mmHg
Ps , mmHg
ma , kg/h
ms , kg/h
Tai , ◦ C
Tsi , ◦ C
To , ◦ C
Ia , kW
25
20
18.75
10, 20, 30
20
33
33
33
1
Vapour pressure difference, mm Hg
Csi , %
5. Conclusion
70.0 60.0 50.0
Air mass flow rate 10 kg/hr 20 kg/hr 30 kg/hr
40.0 30.0 20.0 10.0 0.0 0.0
0.1
0.2
0.3
0.4
0.5
0.6
0.7
0.8
0.9
1.0
Regenerator length,m
Rate of water evaporation, kg/hr
Fig. 7. Vapor pressure difference versus regenerator length.
0.6
Air flow rate 10 kg/hr 20 kg/hr 30 kg/hr
0.4
References
0.2
0.0
-0.2 0.0
0.1
0.2
0.3
The problem associated with the application of a neural network (ANN) model to evaluate the instantaneous values of the thermo-physical properties of LiCl and consequently feed the outputs of the model into the numerical simulation model for an open solar-regenerator is treated. The neural network model is implemented and its feasibility is established. Good agreement between the outputs from the ANN model and the corresponding data is found. It is seen that the use of the proposed methodology results in some desirable characteristics. More accurate values of the solution properties can be obtained over a wide range of pressure and temperature values without any need to empirical correlations. From the investigation of the variation of desiccant parameters along the regenerator length, it is found that an appropriate length must be selected in terms of solution and air flow rates. It is also concluded that the proposed model can be successfully used for predicting the overall performance of the system and investigating the effect of operating parameters under different ambient conditions.
0.4
0.5
0.6
0.7
0.8
0.9
1.0
Regenerator length,m Fig. 8. Rate of water evaporation versus evaporator length.
maximum at the peak value of vapor pressure difference. This can be explained by the effect of desiccant concentration on the vapor pressure, where the concentration is minimum at the regenerator inlet and rapidly increases with temperature. Successive evaporation of water increases the solution concentration and consequently the increase in solution vapor pressure with temperature will be lower than that of the solution with lower concentration. On the other hand, the air vapor pressure increases gradually with x due to the accumulation of evaporated vapor in the flowing air stream. As the cooling effect of the desiccant cooling system is directly dependent on the mass of evaporated water, for a given rate of heat addition, it is objected to evaluate the effect of flow rates of air and solution on the optimum length of the regenerator. To select the appropriate length of the regenerator, the accumulated mass of evaporated water is plotted against the regenerator length as shown in Fig. 8. It can be noted that, for a given length, the mass of water varies with air flow rate. However, this analysis is carried out at constant value of solar radiation. For actual conditions, the system must be optimized on the light of the nature of the heating system. Some desiccant systems are powered by solar as well as waste heat sources. However, the analysis here highlights the effect of the design parameters, more extensive study must be considered for selecting the design point on the basis of the ambient conditions as well as the system design parameters
[1] V.C. Mei, Z. Lavan, Performance of cross-cooled desiccant dehumidifiers, Transactions of the ASME Journal for Solar Energy Engineering 105 (1983) 300–304. [2] P. Gandhidasan, A simple analysis of an open regeneration system, Solar Energy 31 (1983) 343–345. [3] D.J. Nelson, B.D. Wood, Evaporation rate model for a natural convection glazed collector/regenerator, Transactions of the ASME Journal for Solar Energy Engineering 12 (1990) 51–57. [4] Y. Saito, Regeneration characteristics of adsorbent in the integrated desiccant/collector, Transactions of the ASME Journal for Solar Energy Engineering 115 (1993) 169–175. [5] A.A. Pesaran, Desiccant degradation in desiccant cooling systems: a system study, Transactions of the ASME Journal for Solar Energy Engineering 115 (1993) 237–240. [6] A. Hajji, S. Khalloufi, Improving the performance of adsorption heat exchangers using a finned structure, International Journal of Heat and Mass Transfer 39 (8) (1996) 1677–1686. [7] R. Yang, P.L. Wang, Experimental study of a forced convection solar collector/regenerator for open cycle absorption cooling, Transactions of the ASME Journal for Solar Energy Engineering 116 (1994) 194–199. [8] M.S. Hatamipour, H. Mahiyr, M. Taheri, Evaluation of existing cooling systems for reducing cooling power consumption, Energy and Buildings 39 (2007) 105–112. [9] G.I. Sultan, A.M. Hamed, A.A. Sultan, The effect of inlet parameters on the performance of packed tower-regenerator, Renewable Energy 26 (2002) 271–283. [10] A.M. Hamed, A.A. Sultan, G.I. Sultan, Regeneration of calcium chloride in packed tower for operation with open solar absorption cooling system, Mansoura Engineering Journal 23 (4) (1998) 81–91. [11] S. Alizadeh, W.Y. Saman, Modeling and performance of a forced flow solar collector/regenerator using liquid desiccant, Solar Energy 72 (2) (2002) 143–154. [12] P. Gandhidasan, M.A. Mohandes, Predictions of vapor pressures of aqueous desiccants for cooling applications by using artificial neural networks, Applied Thermal Engineering 28 (3) (2008) 126–135. [13] J.M. Cejudo, R. Moreno, A. Carrillo, Physical and network models of a silica-gel desiccant wheel, Energy and Buildings 34 (8) (2002) 837–844. [14] J. Farrell, W. Baker, Learning control systems, in: P.J. Antsaklis, K.M. Passino (Eds.), An Introduction to Intelligent and Autonomous Control, Kluwer Academic, 1992, pp. 237–262. [15] S.Y. Kung, Digital Neural Networks, Prentice Hall, Englewood Cliffs, 1993. [16] A.A. Aly, Flow rate control of variable displacement piston pump with pressure compensation using neural network, Journal of Engineering Science 33 (1) (2007) 199–209. [17] A.M. Hamed, A.A. Sultan, Mass transfer in vertical cloth layers impregnated with calcium chloride for recovery of water from air, Renewable Energy 27 (2002) 13–25. [18] E.D. Zaetsev, G.G. Aseev, Physical-Chemical Properties of Binary Non-organic Solutions, Khemia, Leningrad, 1988.
Contents lists available at ScienceDirect
Energy and Buildings journal homepage: www.elsevier.com/locate/enbuild
Performance evaluation of open-cycle solar regenerator using artificial neural network technique Ayman A. Aly, El-Shafei B. Zeidan, Ahmed M. Hamed ∗ Department of Mechanical Engineering, Faculty of Engineering, Taif University, Al-hawyah, P.O. Box 888, Saudi Arabia
a r t i c l e
i n f o
Article history: Received 31 January 2010 Received in revised form 27 September 2010 Accepted 30 September 2010 Keywords: Solar energy Open-cycle Regeneration Lithium chloride Absorption Liquid desiccant Neural network Back-propagation algorithm
a b s t r a c t Theoretical investigation on the performance of lithium chloride (LiCl) absorption cooling system using an artificial neural network (ANN) model is presented. Tabulated data from the literature are used to construct the ANN model. Solar collector desiccant/regenerator is applied to re-concentrate the working solution. Using the proposed model, the effect of system design parameters; namely regenerator length, and air flow rate on the performance of the system is demonstrated. The variation of the thermo-physical parameters along the regenerator length is highlighted. © 2010 Elsevier B.V. All rights reserved.
1. Introduction Solar-powered air conditioning has seen renewed interest in recent years due to the growing awareness of environmental problems. Significant progress has been achieved in the development of absorption cooling systems considered as a serious alternative to traditional vapor compression systems [1–8]. Solar air liquid collector/regenerator (C/R) systems can achieve liquid regeneration at lower temperatures, which is suitable to buildings with high outdoor air requirements in high humidity areas [9,10]. Alizadeh and Saman [11] studied the performance of forced flow solar collector/regenerator using liquid desiccant. To analyze the performance of absorption system, the partial pressure of water vapor of the desiccant solution must be known in terms of temperature and concentration. Empirical expressions generally provide vapor pressure with limited accuracy. Further, the expressions currently in use are tedious and valid for narrow ranges and must be adjusted continuously [12]. Artificial neural network (ANN) models are capable of relating output to input variables for cases where no theoretical model works satisfactorily in a realistic time frame. An ANN model can be
∗ Corresponding author. E-mail addresses: ayman [email protected] (A.A. Aly), [email protected] (E.-S.B. Zeidan), [email protected] (A.M. Hamed). 0378-7788/$ – see front matter © 2010 Elsevier B.V. All rights reserved. doi:10.1016/j.enbuild.2010.09.032
used to create a black box model that simulates exactly the real situation. ANN models have become very popular recently to overcome some of the limitations of physical modeling [12,13]. This study is part of the ongoing investigation onto the concept and operation of an open-cycle absorption cooling systems. The present work proposes the use of an ANN based model in order to capture the relations between the thermo-physical properties of the desiccant solution to feed the simulation model which investigates the performance of the solar-powered open collector regenerator. Before the application of the ANN model, the data given in literature is treated and the model is trained and tested. It is also objected to evaluate the variation of the most effective output parameters (vapor pressure difference and mass of evaporated water) along the regenerator length. 2. The artificial neural network model The artificial neural network (ANN) is a new form of computing, inspired by biological models and composed of a large number of processing elements organized into layers. A computing system, made up of a number of simple, highly interconnected processing elements, which processes information by its dynamic state response to external inputs. The ANN is supposed to consist of artificial neurons or processing elements [14,15]. If we denote the ith input as xi and the output as y, then we can write the mapping from the inputs to the output performed by the
A.A. Aly et al. / Energy and Buildings 43 (2011) 454–457
455
Nomenclature C g H ha
solution concentration gradient specific enthalpy, J/kg heat transfer coefficient from air stream to ambient atmosphere, W/m2 ◦ C heat transfer coefficient from solution to air stream, W/m2 ◦ C latent heat of water, kJ/kg solar radiation intensity, kW/m2 fluid mass flow rate or rate of water evaporation, kg/s pressure, mmHg temperature, ◦ C target output overall heat loss coefficient, W/m2 ◦ C weight factors regenerator length, m inputs to the ANN model output from the ANN model
hs hfg Ia m P T t UL wij x xi yi
Greek symbols ˛ learning rate ˇ mass transfer coefficient, kg/s m2 mmHg Subscripts a air b barometric i inlet k iteration level o outside s solution
Fig. 2. ANN analysis algorithm.
Generally, the goal of a neural network is to modify the weights to minimize the response error. Nudge the weights in the direction that will minimize the difference between the measured and desired outputs. The technique for modifying weights in the appropriate direction and magnitude eluded researchers for years. However, the recent development of the back propagation learning scheme has solved this problem. Since the advent of ‘backpropagation’, neural networks have enjoyed renewed emphasis and application. Several studies have found that a three-layered neural network with one hidden layer can approximate any nonlinear function to any desired accuracy [16]. The network consists of input layer, hidden layer and output layer. The method is based on an analysis of how a change in any particular weight influences the output of the network. After such analysis is done, the designer understands how to change the weights to achieve the specified values for the outputs. First of all, one must construct a chain similar to Fig. 2. This chain examines the influence of any weight factor on the output value and, hence, on the error value. We consider as an error the difference between the actual output and the desired one. The performance function is the sum square error (SSE) which is defined as the sum of square of the difference between target output (expected) and the actual output from the NN: SSE =
m
(tk − yk )2
(2)
k=1
processing elements in this case as y = f(
xi wij + b)
(1)
Layers are connected together composing an ANN. Inputs could be connected to many nodes with various weights, resulting in a series of outputs, one per node (Fig. 1). The connections are multiplied by the weights associated with that particular node with which they interconnect. They convey analog values. Note that there are many more connections than nodes. The network is said to be fully connected if every output from one layer is passed along to every node in the next layer.
Learning rule gradually adjusts the weights until the performance function (SSE) falls below a certain threshold or minimised. Back-propagation learning updates the network weights and biases in the direction in which the performance function decreases most rapidly, i.e., the negative of the gradient: ¯ k+1 = w ¯ k − ˛k g¯ k w
(3)
where wk+1 are updated weights, wk are current weights, gk is current gradient of performance function, and (k is the learning rate. In this paper the network has two input elements and one output. Ten element hidden layers are assigned. 3. Mathematical model The forced flow C/R employs an inclined flat blackened surface over which the absorbent solution to be concentrated trickles down as a thin liquid film. The schematic of the C/R is shown in Fig. 3. The weak solution flows over the absorber as a thin film and the forced air stream flows parallel or counter to the solution. In order to reduce top losses and eliminate contamination of the solution with dust, the C/R is covered by a single or double glazing. Due to absorption of solar energy by the plate, water evaporates from the liquid surface and is removed by a forced air stream. The steady-state energy balance equations for the open cycle regenerator-segment of unit width is written as [11]: Ia dx = ms dHs + ma dHa + UL (Ts − T0 ) + mhfg
(4)
The energy balance for the air stream passing through the regenerator-segment is written as Fig. 1. A schematic of multilayer neural network.
ma dHa = ha (Ts − Ta )dx − hs (Ta − T0 )dx
(5)
456
A.A. Aly et al. / Energy and Buildings 43 (2011) 454–457
Fig. 5. Absolute error of the evaluated concentration from the ANN model.
4. Results and discussion
Fig. 3. Schematic diagram of solar liquid collector/regenerator system.
The amount of water evaporated from the weak solution and the rate of mass transport are given by m = 0.622
ma (pa − pai ) pb
dm = ˇ(ps − pa ) dx
(6)
(7)
and the relation between the mass of evaporated water and solution flow rates is given by Cs =
Csi (1 − (m/ms )
(8)
The model described above consists of coupled non-linear ordinary differential equations which link the characteristic parameters of air and desiccant solution. An analytical solution is rather difficult and could only be obtained for simplified situations that allow the reduction of the basic equations. In the present study, a numerical solution is obtained by a finite difference technique. The regenerator is divided into a large number of segments with the assumption of constant properties within the segment. Given the input values of mass flow rates of air and solution, air temperature, and solution concentration at the inlet of any segment, the output values are obtained using the above equations by a step-by-step analysis up to the outlet. An iterative procedure is used to get a converged steady-state solution. In the present study, lithium chloride (LiCl) is used as the absorbent. The properties of the solution are obtained from the ANN model to feed the numerical simulation model. The heat and mass transfer coefficients are evaluated by using available correlations from the literature [17]. A computer code is written in MATLAB to perform the computations and visualize the results. The convergence criterion is taken as 0.1 ◦ C for the air temperature and 1 × 10−6 kg/s for the mass of evaporated water.
To validate the ANN model, the thermo-physical properties of LiCl which are given in [18] are plotted versus the numerical data obtained from the model (see Fig. 4). It can be observed that a good agreement between the model results and the original data set. The error analysis of the data is presented in Fig. 5. The most important value of applying the ANN model is that it makes it possible to evaluate any of the three properties in terms of the other two properties at any value within the treated range of data. Moreover, it is possible to link the model with other models used to analyze the performance of the systems which use the desiccant solutions. The developed ANN model for the LiCl solution is applied in this study to analyze the performance of the open desiccant cooling cycle powered by solar energy. By applying the mathematical model described above, the regenerator thermal performance is carried out. The regenerator performance is analyzed for the conditions given in Table 1. The temperature of the desiccant solution as well as air temperature are plotted versus the regenerator length, x, at air flow rate equals 10 kg/s, as shown in Fig. 6. It can be observed that the difference between the two temperatures increases with x, which explains the accumulation of energy in both solution and air streams. It is expected that the solution and air temperatures will be affected by the air and solution flow rates for the same radiation intensity. The vapor pressure difference, which is the mass transfer potential or the driving force for evaporation of water from the surface of the solution is plotted with generator length, for the three cases of air flow rates (10, 20 and 30 kg/h), as illustrated in Fig. 7. For the specified operating conditions, the vapor pressure difference at regenerator inlet is negative, where the solution vapor pressure is lower than that of the inlet air stream; this of course results in a negative flow of vapor or negative absorption. As soon as the solution vapor pressure exceeds that of the air stream, evaporation of water starts. The rate of evaporation is expected to be 90.0
Air Temperature Solution temperature
Temperature, C
80.0 70.0 60.0 50.0 40.0 30.0 0.0
0.1
0.2
0.3
0.4
0.5
0.6
0.7
0.8
0.9
1.0
Regenerator length,m Fig. 4. ANN model validation.
Fig. 6. Variation of solution and air temperatures with regenerator length.
A.A. Aly et al. / Energy and Buildings 43 (2011) 454–457
457
Table 1 System operating conditions. Pa , mmHg
Ps , mmHg
ma , kg/h
ms , kg/h
Tai , ◦ C
Tsi , ◦ C
To , ◦ C
Ia , kW
25
20
18.75
10, 20, 30
20
33
33
33
1
Vapour pressure difference, mm Hg
Csi , %
5. Conclusion
70.0 60.0 50.0
Air mass flow rate 10 kg/hr 20 kg/hr 30 kg/hr
40.0 30.0 20.0 10.0 0.0 0.0
0.1
0.2
0.3
0.4
0.5
0.6
0.7
0.8
0.9
1.0
Regenerator length,m
Rate of water evaporation, kg/hr
Fig. 7. Vapor pressure difference versus regenerator length.
0.6
Air flow rate 10 kg/hr 20 kg/hr 30 kg/hr
0.4
References
0.2
0.0
-0.2 0.0
0.1
0.2
0.3
The problem associated with the application of a neural network (ANN) model to evaluate the instantaneous values of the thermo-physical properties of LiCl and consequently feed the outputs of the model into the numerical simulation model for an open solar-regenerator is treated. The neural network model is implemented and its feasibility is established. Good agreement between the outputs from the ANN model and the corresponding data is found. It is seen that the use of the proposed methodology results in some desirable characteristics. More accurate values of the solution properties can be obtained over a wide range of pressure and temperature values without any need to empirical correlations. From the investigation of the variation of desiccant parameters along the regenerator length, it is found that an appropriate length must be selected in terms of solution and air flow rates. It is also concluded that the proposed model can be successfully used for predicting the overall performance of the system and investigating the effect of operating parameters under different ambient conditions.
0.4
0.5
0.6
0.7
0.8
0.9
1.0
Regenerator length,m Fig. 8. Rate of water evaporation versus evaporator length.
maximum at the peak value of vapor pressure difference. This can be explained by the effect of desiccant concentration on the vapor pressure, where the concentration is minimum at the regenerator inlet and rapidly increases with temperature. Successive evaporation of water increases the solution concentration and consequently the increase in solution vapor pressure with temperature will be lower than that of the solution with lower concentration. On the other hand, the air vapor pressure increases gradually with x due to the accumulation of evaporated vapor in the flowing air stream. As the cooling effect of the desiccant cooling system is directly dependent on the mass of evaporated water, for a given rate of heat addition, it is objected to evaluate the effect of flow rates of air and solution on the optimum length of the regenerator. To select the appropriate length of the regenerator, the accumulated mass of evaporated water is plotted against the regenerator length as shown in Fig. 8. It can be noted that, for a given length, the mass of water varies with air flow rate. However, this analysis is carried out at constant value of solar radiation. For actual conditions, the system must be optimized on the light of the nature of the heating system. Some desiccant systems are powered by solar as well as waste heat sources. However, the analysis here highlights the effect of the design parameters, more extensive study must be considered for selecting the design point on the basis of the ambient conditions as well as the system design parameters
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