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Modeling and simulation of solar-powered liquid desiccant regenerator for open absorption cooling cycle
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Solar Energy 85 (2011) 2977–2986 www.elsevier.com/locate/solener
Modeling and simulation of solar-powered liquid desiccant regenerator for open absorption cooling cycle El-Shafei B. Zeidan a,b, Ayman A. Aly a,c, Ahmed M. Hamed a,b,⇑ a
Department of Mechanical Engineering, Faculty of Engineering, Taif University, Al-Haweiah, P.O. Box 888, Zip Code 21974, Saudi Arabia b Department of Mechanical Power Engineering, Faculty of Engineering, Mansoura University, Mansoura, Egypt c Department of Mechanical Engineering, Faculty of Engineering, Assiut University, Assiut, Egypt Received 21 February 2010; received in revised form 19 January 2011; accepted 26 August 2011 Available online 28 September 2011 Communicated by: Associate Editor W.S. Duff
Abstract This paper presents the modeling and simulation of solar-powered desiccant regenerator used for open absorption cooling cycles. The input heat, which is the total radiation incident on an inclined surface, is evaluated via a solar radiation model in terms of the location, day of the year, and time of the day. Calcium Chloride (CaCl2) is applied as the working desiccant in this investigation. The solar radiation model is integrated with the desiccant regenerator model to produce a more realistic simulation. A finite difference method is used to simulate the combined heat and mass transfer processes that occur in the liquid desiccant regenerator. The system of equations is solved using the Matlab-Simulink platform. The effect of the important parameters, namely the regenerator length, desiccant solution flow rate and concentration, and air flow rate, on the performance of the system is investigated. It has been found that the vapor pressure difference has a maximum value for a given regenerator length. It is also shown that for specified operating conditions, a maximum value of the coefficient of performance occurs at a given range of air and solution flow rates. Therefore, it is essential to select the design parameters for each ambient condition to maximize the coefficient of performance of the system. Ó 2011 Elsevier Ltd. All rights reserved. Keywords: Modeling; Solar-powered; Desiccant; Open cycle
1. Introduction In hot areas, solar-powered absorption air-conditioning systems have been proposed as alternatives to the conventional vapor compression cooling systems. Thermal systems for producing cooling effect using solar thermal energy are based mainly on the phenomena of sorption. Several investigators have proven the visibility of the absorption cooling systems and provided theoretical limits for the performance ⇑ Corresponding author at: Department of Mechanical Engineering, Faculty of Engineering, Taif University, Al-Haweiah, P.O. Box 888, Zip Code 21974, Saudi Arabia. Tel.: +966 599121850; fax: +966 02 7255529. E-mail addresses: [email protected] (El-Shafei B. Zeidan), [email protected] (A.A. Aly), [email protected] (A.M. Hamed).
0038-092X/$ - see front matter Ó 2011 Elsevier Ltd. All rights reserved. doi:10.1016/j.solener.2011.08.035
of real systems by many researchers including Wijeysundera (2000), Chen et al. (2004, 2006). A review of the research state of art of the solar sorption (absorption and adsorption) refrigeration technologies is presented by Fan et al. (2007). Recently, solar driven LiBr/H2O absorption cooling system has been developed and installed by Agyenim et al. (2010) to demonstrate their potential use in cooling domestic scale buildings. The average coefficient of thermal performance (COP) of the system, based on the thermal cooling power output per unit of available thermal solar energy, was found to be 0.58. Combining solar collection and liquid regeneration together, a solar collector/regenerator (C/R) can be applied in an open absorption cooling cycle. In this case the condenser is eliminated and the refrigerant (water) is supplied to the evaporator from an external source. Since the introduction of open-cycle liquid-desiccant absorption
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Nomenclature A Ac a B b C c Fss H h I i L m n p Q R s T
apparent solar radiation at air mass zero, W/m2 collector surface area, m2 empirical constant (Eq. (17)) atmospheric extinction coefficient, dimensionless empirical constant (Eq. (17)) diffuse radiation factor and solution concentration empirical constant (Eq. (17)) angle factor between the surface and the sky specific enthalpy, J/kg hour angle and heat transfer coefficient, W/m2 °C solar radiation intensity, W/m2 incidence angle latitude angle and latent heat of evaporation, J/kg rate of water evaporation, kg/s day number vapor pressure, mm Hg heat rate, W tilt factor surface tilt angle, rad temperature, °C
solar-cooling system by Kakabaev and Khandurdyev (1969), the system has been investigated extensively. The feasibility of the system and the advantages it can offer in terms of energy and cost savings have been proved in different climates (see for example; Yang and Wang (1994), Grossman (2002), Krause et al. (2005), Daou et al. (2006), and Dieckmann et al. (2008). Among the advantages of liquid-desiccant systems are: ease of manipulation, low pressure drop in the contactors with the flowing air, possibility of filtering to remove dirt taken in from the air, possibility of heat exchange between spent and regenerated desiccant streams and more, also requiring lower temperature for regeneration (Factor and Grossman, 1980). A schematic of an open solar absorption cooling system is shown in Fig. 1. The weak absorbent solution is heated and subsequently concentrated in the solar collector. The strong regenerated solution leaves the collector and passes through a liquid column, to allow the strong solution to go from atmospheric pressure to reduced pressure efficiently. The strong solution then passes through a regenerative heat exchanger on its way to the absorber, where it absorbs water from the evaporator, maintaining the reduced pressure required with the energy supplied by heat from the cold space. The resultant weak solution is pumped from the absorber back to atmospheric pressure through the regenerative heat exchanger and the collector, completing the cycle. The advantages of this system would include a
UL x z
overall heat loss coefficient, W/m2 °C coordinate zenith angle
Greek symbols a solar altitude angle and surface absorptivity b mass transfer coefficient, kg/s m2 mm Hg d declination angle qg reflectance of the Earth’s surface s transmittance Subscripts a air and absorbed B beam Bn beam at normal incidence c collector d diffuse i inlet L liquid o outside max maximum s solution and surface t total and tilted
simpler collector, which also acts as a regenerator, and a reduction in thermal losses. The overall performance of the system is governed entirely by the rate at which water is driven from the solution in the collector, since this determines the flow of water that can be introduced into the evaporator as refrigerant. The rate of water evaporation from the regenerator gives a direct measure of the system cooling capacity. An analytical procedure for calculating the mass of water evaporated from the weak solution in the solar regenerator in terms of climatic conditions and solution properties at the regenerator inlet has been developed by Kakabaev and Khandurdyev (1969). Many theoretical modeling studies have been performed to simulate the system performance by Yang and Yan (1992), and Aly et al. (2010). Yang and Wang (2001) performed a computer simulation for the collector/regenerator (C/R) using a radiation processor which makes use of the statistical meteorological data for the summer season at Kaohsiung, Taiwan. Alizadeh and Saman (2002) developed a computer model using Calcium Chloride (CaCl2) as the working desiccant to study the thermal performance of a forced parallel flow solar regenerator. A parametric analysis of the system has been performed to calculate the rate of evaporation of water from the solution as a function of the system variables and the climatic conditions. However, the solar radiation intensity was assumed constant in the analysis.
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Solar collector/ regenerator
Vacuum Water supply
Absorber
Strong solution collection
Chilled water
Regenerative Cooling heat water exchanger
Reducing Valve Refrigerant
Weak solution Liquid colum
Solution pump
Refrigerant (water) pump
Fig. 1. Schematic of the solar-powered open absorption cooling system.
In this paper, a theoretical analysis of the effect of design parameters and operating conditions of solar-powered desiccant regenerator for open absorption cooling cycle has been carried out. The regenerator model is augmented with a model to simulate the solar radiation, and the system is assumed to be in operation from sunrise to sunset.
I Bn ¼ A exp
B sin a
ð2Þ
where A is an empirically determined constant which represent the apparent solar radiation at air mass zero, W/m2, B is an apparent atmospheric extinction coefficient and a is the solar altitude angle. The altitude angle a can be evaluated from the following expression:
2. Mathematical model
sin a ¼ sin L sin d þ cos L cos d cos h
2.1. Solar radiation model
where L, d and h are the latitude, declination and hour angles, respectively. The declination angle d can be calculated as a function of the day number, n as: 360 d ¼ 23:45 sin ð284 þ nÞ ð4Þ 365
Detailed solar radiation data has become more and more important with the increasing number of studies on solar energy. Any analysis of systems powered by solar energy should start with the research of the radiation data available in the region being studied. The total radiation incident on a tilted surface could be evaluated in terms of the location, day of the year and time of the day. The total perceived solar radiation can be estimated by the following relationship (Hsieh, 1986): I t ¼ RB I B þ CI Bn
1 þ cos s 1 cos s þ ðI B þ I d Þqg 2 2
The hour angle is defined by 1 h ¼ ðnumber of min from local solar noonÞ 4
where IB is beam radiation on a horizontal surface, RB is beam radiation tilt factor, IBn is beam radiation at normal incidence, W/m2, Id is the diffuse sky radiation, W/m2, C is diffuse radiation factor, s is the surface tilt angle, qg is solar reflectance of the Earth’s surface. The three terms in the above equation represent the direct, diffuse, and reflected components, respectively. The terrestrial beam radiation within the atmosphere and on the earth’s surface on a typical clear day is calculated using the following relation:
ð5Þ
where the value of h is assumed positive in the after noon period. In Eq. (1), the diffuse solar radiation is estimated from: I d ¼ CF ss I Bn
ð1Þ
ð3Þ
ð6Þ
where Fss = 0.5(1 + cos s) is the angle factor between the surface and the sky and s is the tilt angle of the solar collector. The beam radiation tilt factor RB is defined by: RB ¼
I Bt cos i ¼ I B cos z
ð7Þ
where IBt, IB are the beam radiation on a tilted surface and on the horizontal surface, respectively. The incidence angle, i, and zenith angle z are calculated from the following expressions, cos i ¼ sinðL sÞ sin d þ cosðL sÞ cos d cos h
ð8Þ
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cos z ¼ sin a
ð9Þ
ð10Þ
where ma, and ms are the mass flow rates of air and solution kg/s, respectively, Ha, and Hs are the specific enthalpies of air and solution J/kg, respectively, m is the mass of evaporated water, kg/s, hfg is latent heat of water, J/kg, To is the outside temperature, and UL is the overall heat loss coefficient, W/m2 °C.
The solar radiation absorbed by the solution in the collector/regenerator can be obtained from,
2.2.2. Energy balance for the air stream passing through the regenerator-segment
The day length, which is the period from sunrise to sunset, can be evaluated from, daylength ¼
2 cos1 ð tan L tan dÞ 15
I a ¼ I t ð1 qÞsa
ð11Þ
ma dH a ¼ ha ðT s T a Þdx hs ðT a T o Þdx
ð13Þ
where q and s are the reflectance and transmittance of the glass cover on the collector surface, respectively, and a is the regenerator absorptivity.
where ha and hs are heat transfer coefficients for the air and solution sides, each in W/m2 °C.
2.2. Collector/regenerator (C/R) model
2.2.3. The amount of water evaporated from the weak solution
A schematic representation of the forced flow C/R is shown in Fig. 2. The C/R employs an inclined flat blackened surface over which the absorbent solution to be concentrated trickles down as a thin liquid film. 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 air stream may flow parallel or counter to the liquid film. The channel is divided into a large number of equal segments of width dx with the assumption of constant properties within the segment (air vapor pressure, pa, and temperature, Ta, and vapor pressure on the solution surface, ps, temperature, Ts, and concentration, Cs). The main equations include the energy balance and mass balance for each segment of the open-cycle regenerator. These equations are summarized as follows Aly et al. (2010): 2.2.1. Energy balance for the regenerator-segment I a dx ¼ ms dH s þ ma dH a þ U L ðT s T o Þ þ mhfg
ð12Þ
m ¼ 0:622
ma ðp pai Þ pb a
ð14Þ
where pb and pai are the barometric pressure and initial vapor pressure in air at the regenerator inlet, in mm Hg, respectively. 2.2.4. The rate of mass transport of water vapor dm ¼ bðps pa Þ dx
ð15Þ
where b is the mass transfer coefficient, kg/s m2 mm Hg. And the relation between the mass of evaporated water and solution flow rates is given by: m C s ¼ C si = 1 ð16Þ ms where Csi is the initial concentration of the solution at regenerator inlet. The relationship between the solution temperature, concentration and vapor pressure for Calcium Chloride is given by,
Fig. 2. Open-cycle solar collector regenerator.
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ps ¼ a þ bT s þ
c Cs
ð17Þ
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multiplying the rate of water evaporation, m, by the latent heat of water L at the evaporator pressure i.e.,
where a, b and c are empirical constants (Alizadeh and Saman, 2002) .
Qe ¼ mL
2.2.5. System coefficient of performance (COP) The overall coefficient of performance of the system can be evaluated from the following expression:
The above mentioned analysis shows the dependence of the regeneration process on operational parameters such as air and liquid mass flow rates as well as the vapor pressure of inlet air. In this study, the performance of soft computing methodology, is used for the system performance analysis.
COP ¼
Qe I t Ac
ð19Þ
ð18Þ 2.3. Simulation procedure
where Ac is the collector area and Qe is the cooling rate of the desiccant cooling system, which can be evaluated by
Fig. 3. Scheme of Matlab-Simulink.
2.3.1. Solving the equations The theoretical model is constituted from coupled algebraic and 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 current study, a numerical solution is obtained by the finite difference technique. These equations are solved using the Matlab-Simulink platform. Simulink allows the system to be modeled by drawing a block diagram directly on the screen. The Simulink representation of the system of equations is presented in Fig. 3. Each
Fig. 4. Sub-block for calculating the mass of evaporated water.
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block represent a calculation unit and may be composed of other more detailed sub-systems. The sub-system for calculating the mass of evaporated water is shown in Fig. 4. A Matlab computer code is written to perform the computations and visualize the results. The ordinary differential equations are solved using the fourth-order Runge–Kutta scheme with variable time steps (Chapra and Canale, 2006). As the time step decreases, the total time for running the simulation increases. The time step was set as 1 min in the solar radiation calculations. 2.3.2. Solar radiation module The sunshine period is evaluated for the specified location (defined by the latitude angle, L) by knowledge of the day number of the year, n, evaluating the declination angle, d (Eq. (4)), then substituting in Eq. (10). Eq. (1) is used to evaluate the instantaneous value of total radiation on the tilted surface during the sunshine period. The parameters in Eq. (1) are calculated from Eqs. (2)–(9). For 21 June, which is selected as a representative day in this analysis, values of radiation constants A, B and C are A = 1087.61 W/m2, B = 0.205 and C = 0.134 (Hsieh, 1986). 2.3.3. Collector/regenerator module The system of equations from (12)–(17) have six unknowns; which are: m, Ta, Ts, pa, ps and Cs. Given the input values of mass flow rates of air and solution, air temperature, and solution concentration at the inlet of any segment, along with the physical properties of the working desiccant, 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 obtain a numerical solution with the criterion set apriori. The heat and mass transfer coefficients are evaluated by using available correlations from the literature (McCabe et al., 1985). 3. Results and discussion The performance of the solar collector/regenerator is influenced by design parameters (regenerator length, solution flow rate, working solution concentration and air flow rate) and ambient conditions (air temperature and vapor pressure in the flowing air). These key parameters are
investigated in the following sub-sections. A sensitivity analysis is performed by varying the parameters of interest one at a time, while keeping all others fixed at given values. 3.1. Effect of air mass flow rate In order to analyze the effect of air mass flow rate on the regeneration process, the solution mass flow rate, ms, is settled at 20 kg/h and the range of air mass flow rate, ma, is considered in the range (10–200 kg/h), then the vapour pressure difference between the regenerated solution and flowing air is plotted versus the regenerator length. For a given regenerator length, the vapour pressure, which is the mass transfer potential, is directly proportional with the rate of water evaporation, when the mass transfer coefficient is assumed constant. As shown in Fig. 5, the vapor pressure difference has a maximum for a given length of the regenerator. The results obtained by Alizadeh and Saman (2002) were compared with that presented in Fig. 5. The trend of the results of both the vapor pressure difference and evaporation rate agree very well along with the regenerator length, which validates the present model. However, the rate of water evaporation could be obtained by multiplying the vapor pressure difference by the mass transfer coefficient. The length, at which the maximum rate of evaporation occurs, increases with the air flow rate. Concerning the effect of solution inlet concentration on regeneration process, the decrease of solution concentration can effectively improve the regenerator performance, though it sacrifices solution outlet concentration. It can be noted that the vapor pressure difference rapidly decreases, after reaching the peak value, with decrease in air flow rate (see Fig. 5, at Ma = 10 kg/h). This can be explained as follows: as a result of continuous evaporation from the collector surface, evaporated water is accumulated in the flowing airstream and consequently the vapor pressure in air increases with regenerator length. This leads to a decrease in vapor pressure difference between desiccant and air. 3.2. Effect of solution flow rate Fig. 6, demonstrates the variation of the solution temperature during the regeneration period. This period lasts
Fig. 5. Variation of vapor pressure at regenerator exit with different values of air flow rate, at noon time.
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Fig. 6. Variation of solution temperature during the day time for different values of solution flow rate.
from sun rise to sun set. As the solution flows from the regenerator inlet to exit, it is expected that the solution temperature will be maximum at the end of the regenerator. On the other hand, the maximum temperature of the solution will follow the solar radiation intensity along the day time. It can be observed that the solution temperature increases with the decrease in the flow rate. In Fig. 7, the solution concentration at the regenerator exit is plotted versus the regenerator length, for different values of the solution flow rate, at noon time (maximum intensity of solar radiation). It is clear that the solution concentration increases with the increase of the regenerator length as well as the decrease of solution flow rate. The explanation for this is as follow: with a lower solution flow rate and a longer regenerator a higher outlet solution temperature can be achieved, thus a higher vapour pressure and consequently a higher evaporation rate. The increase in evaporation rate results in increase in the solution concentration at the end of the regeneration process. It can be observed that the effect of solution flow rate is significant at its lower values (see Fig. 7). When the flow rate decreases from 20 kg/h to 10 kg/h, the solution concentration increases by about 8% (from 47% to 55%), whereas the solution concentration increases about 1% with decrease in the flow rate from 100 kg/h to 80 kg/h, for a regenerator with 5 m length. It is evident from Eq. (15) that the change in the solution concentration (Cs Csi) is inversely proportional
with the solution flow rate, ms. However the increase in the solution concentration must be limited by the crystallization of the solution which is dependent on the concentration and temperature. The solution temperature at the end of regenerator at noon time is plotted versus regenerator length for different values of solution flow rate as shown in Fig. 8. It can be noted that the temperature increases gradually with regenerator length. However, the rate at which the temperature increases is dependent on the solution flow rate. For lower values of solution flow rate (for example, ms = 10 kg/h.), solution temperature reaches 80 °C at the regenerator end of 5 m length, whereas this temperature is limited to about 55 °C when the flow rate is 100 kg/h. It can be also noted that the solution temperature slightly decreases at the regenerator inlet. This can be explained by the cold evaporation of water from the solution at this region. This evaporation of vapour from the solution surface occurs without heating due to the difference in vapor pressure between the solution and flowing air. The vapor pressure in air at regenerator inlet is 20 mm Hg and for the solution at the specified inlet conditions (Tsi = 40 °C, Csi = 40%), the evaluated pressure exceeds 35 mm Hg and consequently vapor transfers from solution to air with subsequent cooling of the solution. The drop in solution temperature increases with the flow rate (see Fig. 9). For lower values of solution flow rate (10 kg/h) it can be noted that the
Fig. 7. Variation of solution concentration at regenerator exit for different values of solution flow rate.
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Fig. 8. Variation of solution temperature at regenerator exit for different values of air flow rate, at noon time.
Fig. 9. Variation of vapor pressure at the regenerator exit for different values of solution flow rate, at noon time.
vapor pressure difference decreases sharply after reaching the maximum value. This sharp decrease vapor pressure difference can be explained by the rapid increase in solution concentration with evaporation of water from the solution surface. An increase in solution concentration decreases the vapor pressure on the solution surface and consequently the potential for mass transfer. 3.3. Effect of regenerator length The daily accumulated amount of water that evaporates from the regenerator surface is plotted versus time for various values of regenerator length, as shown in Fig. 10. It is
clear that the accumulated mass of evaporated water, at regenerator length of x = 3 m, is close to 6 kg/day, whereas a regenerator having 4 m length produces about 7 kg of water per day. On the other hand, when the length is limited by 1 m, more than 2.5 kg of water evaporates from the solution, at the same conditions. This means that, for the specified operating conditions, the relative value of daily water evaporation decreases with the increase of the solar regenerator. However, an increase in regenerator length results in increasing the solution concentration in the evaporator with subsequent decrease in the evaporator temperature. Therefore, when selecting the regenerator length, the consideration of the system COP, which is directly dependent on
Fig. 10. Amount of daily accumulated water evaporation from the regenerator surface.
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the mass of evaporated water per day per unit, and the required evaporator temperature must be taken into account. 3.4. Effect of solution concentration
Mass of Water per unit area, kg/m sq.
The effect solution concentration at regenerator exit is depicted in Fig. 11. For the solar-powered systems it is objected to maximize the mass of water evaporated per unit collector area. Therefore, the mass of evaporated water per unit area is shown versus the regenerator length for a complete day of operation. It is evident that the effect of solution concentration is significant for a regenerator length up to about 2 m. Also, for the solution concentration of 30%, a shorter regenerator is more efficient from the point of view of regenerator cost. On the other hand, values of solution concentration more than 40% have a maximum at a given value of regenerator length; this length is dependent on the concentration. However, the solution concentration at the end of regeneration process determines the vapor pressure in the absorber and consequently the evaporator temperature. Lower temperatures in the evaporator could be obtained at higher values of solution concentration, this of course on the account of the mass of evaporated vapour as well as the system coefficient of performance.
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3.5. System coefficient of performance A set of independent parameters control the performance of the system. However, some of these parameters are uncontrollable such as the ambient conditions (temperature and humidity). Other design parameters must be selected to optimize the system performance. From the results presented in Figs. 5–11 it is evident that the most important of the design parameters are regenerator length, solution flow rate and air flow rate. Variation of coefficient of performance (COP) of the system is illustrated in the surface plot shown in Fig. 12. For the specified operating conditions, a maximum value of the COP occurs at a given range of air and solution flow rates. However, the maximum value of COP is dependent of the design parameters and operating conditions, therefore it is essential to select the design parameters for each ambient condition to maximize the COP of the system. Values of COP presented in Fig. 12. summarize the dependence of system performance on the controllable design variables. A maximum value of 0.34 could be obtained when the vapor pressure in the atmospheric air is 20 mm Hg. However, higher values could be attained when the vapor pressure decreases. Also, it is expected that a decrease in the solution concentration increases the value of COP.
5
Ma=100kg/hr To=40 oC Tsi=40 oC Csi=40% Pai=20mmHg Day 21 June
4 Cs=30%
3
Cs=40% Cs=50%
2 1 0 0.5
1
1.5
2
2.5
3
3.5
4
4.5
5
Regenerator Length, m Fig. 11. Mass of evaporated water per unit area for different values of inlet concentration.
Fig. 12. Surface plot showing the variation of system COP with air and solution flow rates.
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4. Conclusion The modeling and simulation of solar-powered desiccant regenerator used for open absorption cooling cycle are presented. The source of input heat is assumed to be the total solar radiation incident on a tilted surface. A finite difference method is used to simulate the combined heat and mass transfer processes that occur in the liquid desiccant regenerator. The model is implemented using the MatlabSimulink platform and its feasibility is established. It has been shown that the use of the proposed methodology results in some desirable characteristics. It is also concluded that the proposed model can be successfully used for predicting the overall performance of the system. The simulation has shown that the vapor pressure difference has a maximum value for a given regenerator length. It is also shown that for specified operating conditions, a maximum value of the coefficient of performance occurs at a given range of air and solution flow rates. Therefore, it is essential to select the design parameters for each ambient condition to maximize the coefficient of performance of the system. References Agyenim, F., Knight, I., Rhodes, M., 2010. Design and experimental testing of the performance of an outdoor LiBr/H2O solar thermal absorption cooling system with a cool store. Solar Energy 84 (5), 735– 744. Alizadeh, S., Saman, W.Y., 2002. Modeling and performance of a forced flow solar collector/regenerator using liquid desiccant. Solar Energy 72 (2), 143–154. Aly, A.A., Zeidan, E.B., Hamed, A.M., 2010. Performance evaluation of open-cycle solar regenerator using artificial neural network technique. Energy and Buildings 43 (2/3), 454–457.
Chapra, S.C., Canale, R.P., 2006. Numerical Methods for Engineers. McGraw-Hill, New York. Chen, L., Zhengm, T., Sun, F., Wu, C., 2004. Optimal cooling load and COP relationship of a four-heat-reservoir endoreversible absorption refrigeration cycle. Entropy 6 (3), 316–326. Chen, L., Zheng, T., Sun, F., Wu, C., 2006. Irreversible four-temperaturelevel absorption refrigerator. Solar Energy 80 (3), 347–360. Daou, K., Wang, R.Z., Xia, Z.Z., 2006. Desiccant cooling air conditioning: a review. Renewable and Sustainable Energy Reviews 10, 55–77. Dieckmann, J., Roth, K., Brodrick, J., 2008. Liquid desiccant air conditioners. ASHRAE Journal (October). Factor, H., Grossman, G.A., 1980. A packed bed dehumidifier/regenerator for solar air conditioning with liquid desiccant. Solar Energy 24, 541–550. Fan, Y., Luo, L., Souyri, B., 2007. Review of solar sorption refrigeration technologies: development and applications. Renewable & Sustainable Energy Reviews 11, 1758–1775. Grossman, G., 2002. Solar-powered systems for cooling, dehumidification and air-conditioning. Solar Energy 72 (1), 53–62. Hsieh, K., 1986. Solar Energy Engineering. Prentice- Hall Inc., Englewood Cliffs, New Jersey, USA. Kakabaev, A., Khandurdyev, A., 1969. Absorption solar refrigeration unit with open regeneration of solution. Gliotekhnika 5 (4), 28–32. Krause, M., Saman, W., Vajen, K., 2005. Open cycle liquid desiccant air conditioning systems – Theoretical and experimental investigations. In: ANZSES Conference Solar, Dunedin, New Zealand. McCabe, W.L., Smith, J.C., Harriott, P., 1985. Unit Operation of Chemical Engineering. McGraw-Hill, New York. Wijeysundera, N.E., 2000. An irreversible-thermodynamic model for solar-powered absorption cooling systems. Solar Energy 68 (1), 69–75. Yang, R., Wang, P.L., 1994. Experimental study of a forced convection solar collector/regenerator for open cycle absorption cooling. Transactions ASME Journal of Solar Energy Engineering 116, 194–199. Yang, R., Wang, P.L., 2001. A simulation study of the performance evaluation of single-glazed and double-glazed collectors/regenerators for an open-cycle absorption solar cooling system. Solar Energy 71 (4), 263–268. Yang, R., Yan, W.J., 1992. Simulation study for an open-cycle absorption solar-cooling system operated in a humid area. Energy 17 (7), 649–655.
Solar Energy 85 (2011) 2977–2986 www.elsevier.com/locate/solener
Modeling and simulation of solar-powered liquid desiccant regenerator for open absorption cooling cycle El-Shafei B. Zeidan a,b, Ayman A. Aly a,c, Ahmed M. Hamed a,b,⇑ a
Department of Mechanical Engineering, Faculty of Engineering, Taif University, Al-Haweiah, P.O. Box 888, Zip Code 21974, Saudi Arabia b Department of Mechanical Power Engineering, Faculty of Engineering, Mansoura University, Mansoura, Egypt c Department of Mechanical Engineering, Faculty of Engineering, Assiut University, Assiut, Egypt Received 21 February 2010; received in revised form 19 January 2011; accepted 26 August 2011 Available online 28 September 2011 Communicated by: Associate Editor W.S. Duff
Abstract This paper presents the modeling and simulation of solar-powered desiccant regenerator used for open absorption cooling cycles. The input heat, which is the total radiation incident on an inclined surface, is evaluated via a solar radiation model in terms of the location, day of the year, and time of the day. Calcium Chloride (CaCl2) is applied as the working desiccant in this investigation. The solar radiation model is integrated with the desiccant regenerator model to produce a more realistic simulation. A finite difference method is used to simulate the combined heat and mass transfer processes that occur in the liquid desiccant regenerator. The system of equations is solved using the Matlab-Simulink platform. The effect of the important parameters, namely the regenerator length, desiccant solution flow rate and concentration, and air flow rate, on the performance of the system is investigated. It has been found that the vapor pressure difference has a maximum value for a given regenerator length. It is also shown that for specified operating conditions, a maximum value of the coefficient of performance occurs at a given range of air and solution flow rates. Therefore, it is essential to select the design parameters for each ambient condition to maximize the coefficient of performance of the system. Ó 2011 Elsevier Ltd. All rights reserved. Keywords: Modeling; Solar-powered; Desiccant; Open cycle
1. Introduction In hot areas, solar-powered absorption air-conditioning systems have been proposed as alternatives to the conventional vapor compression cooling systems. Thermal systems for producing cooling effect using solar thermal energy are based mainly on the phenomena of sorption. Several investigators have proven the visibility of the absorption cooling systems and provided theoretical limits for the performance ⇑ Corresponding author at: Department of Mechanical Engineering, Faculty of Engineering, Taif University, Al-Haweiah, P.O. Box 888, Zip Code 21974, Saudi Arabia. Tel.: +966 599121850; fax: +966 02 7255529. E-mail addresses: [email protected] (El-Shafei B. Zeidan), [email protected] (A.A. Aly), [email protected] (A.M. Hamed).
0038-092X/$ - see front matter Ó 2011 Elsevier Ltd. All rights reserved. doi:10.1016/j.solener.2011.08.035
of real systems by many researchers including Wijeysundera (2000), Chen et al. (2004, 2006). A review of the research state of art of the solar sorption (absorption and adsorption) refrigeration technologies is presented by Fan et al. (2007). Recently, solar driven LiBr/H2O absorption cooling system has been developed and installed by Agyenim et al. (2010) to demonstrate their potential use in cooling domestic scale buildings. The average coefficient of thermal performance (COP) of the system, based on the thermal cooling power output per unit of available thermal solar energy, was found to be 0.58. Combining solar collection and liquid regeneration together, a solar collector/regenerator (C/R) can be applied in an open absorption cooling cycle. In this case the condenser is eliminated and the refrigerant (water) is supplied to the evaporator from an external source. Since the introduction of open-cycle liquid-desiccant absorption
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Nomenclature A Ac a B b C c Fss H h I i L m n p Q R s T
apparent solar radiation at air mass zero, W/m2 collector surface area, m2 empirical constant (Eq. (17)) atmospheric extinction coefficient, dimensionless empirical constant (Eq. (17)) diffuse radiation factor and solution concentration empirical constant (Eq. (17)) angle factor between the surface and the sky specific enthalpy, J/kg hour angle and heat transfer coefficient, W/m2 °C solar radiation intensity, W/m2 incidence angle latitude angle and latent heat of evaporation, J/kg rate of water evaporation, kg/s day number vapor pressure, mm Hg heat rate, W tilt factor surface tilt angle, rad temperature, °C
solar-cooling system by Kakabaev and Khandurdyev (1969), the system has been investigated extensively. The feasibility of the system and the advantages it can offer in terms of energy and cost savings have been proved in different climates (see for example; Yang and Wang (1994), Grossman (2002), Krause et al. (2005), Daou et al. (2006), and Dieckmann et al. (2008). Among the advantages of liquid-desiccant systems are: ease of manipulation, low pressure drop in the contactors with the flowing air, possibility of filtering to remove dirt taken in from the air, possibility of heat exchange between spent and regenerated desiccant streams and more, also requiring lower temperature for regeneration (Factor and Grossman, 1980). A schematic of an open solar absorption cooling system is shown in Fig. 1. The weak absorbent solution is heated and subsequently concentrated in the solar collector. The strong regenerated solution leaves the collector and passes through a liquid column, to allow the strong solution to go from atmospheric pressure to reduced pressure efficiently. The strong solution then passes through a regenerative heat exchanger on its way to the absorber, where it absorbs water from the evaporator, maintaining the reduced pressure required with the energy supplied by heat from the cold space. The resultant weak solution is pumped from the absorber back to atmospheric pressure through the regenerative heat exchanger and the collector, completing the cycle. The advantages of this system would include a
UL x z
overall heat loss coefficient, W/m2 °C coordinate zenith angle
Greek symbols a solar altitude angle and surface absorptivity b mass transfer coefficient, kg/s m2 mm Hg d declination angle qg reflectance of the Earth’s surface s transmittance Subscripts a air and absorbed B beam Bn beam at normal incidence c collector d diffuse i inlet L liquid o outside max maximum s solution and surface t total and tilted
simpler collector, which also acts as a regenerator, and a reduction in thermal losses. The overall performance of the system is governed entirely by the rate at which water is driven from the solution in the collector, since this determines the flow of water that can be introduced into the evaporator as refrigerant. The rate of water evaporation from the regenerator gives a direct measure of the system cooling capacity. An analytical procedure for calculating the mass of water evaporated from the weak solution in the solar regenerator in terms of climatic conditions and solution properties at the regenerator inlet has been developed by Kakabaev and Khandurdyev (1969). Many theoretical modeling studies have been performed to simulate the system performance by Yang and Yan (1992), and Aly et al. (2010). Yang and Wang (2001) performed a computer simulation for the collector/regenerator (C/R) using a radiation processor which makes use of the statistical meteorological data for the summer season at Kaohsiung, Taiwan. Alizadeh and Saman (2002) developed a computer model using Calcium Chloride (CaCl2) as the working desiccant to study the thermal performance of a forced parallel flow solar regenerator. A parametric analysis of the system has been performed to calculate the rate of evaporation of water from the solution as a function of the system variables and the climatic conditions. However, the solar radiation intensity was assumed constant in the analysis.
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Solar collector/ regenerator
Vacuum Water supply
Absorber
Strong solution collection
Chilled water
Regenerative Cooling heat water exchanger
Reducing Valve Refrigerant
Weak solution Liquid colum
Solution pump
Refrigerant (water) pump
Fig. 1. Schematic of the solar-powered open absorption cooling system.
In this paper, a theoretical analysis of the effect of design parameters and operating conditions of solar-powered desiccant regenerator for open absorption cooling cycle has been carried out. The regenerator model is augmented with a model to simulate the solar radiation, and the system is assumed to be in operation from sunrise to sunset.
I Bn ¼ A exp
B sin a
ð2Þ
where A is an empirically determined constant which represent the apparent solar radiation at air mass zero, W/m2, B is an apparent atmospheric extinction coefficient and a is the solar altitude angle. The altitude angle a can be evaluated from the following expression:
2. Mathematical model
sin a ¼ sin L sin d þ cos L cos d cos h
2.1. Solar radiation model
where L, d and h are the latitude, declination and hour angles, respectively. The declination angle d can be calculated as a function of the day number, n as: 360 d ¼ 23:45 sin ð284 þ nÞ ð4Þ 365
Detailed solar radiation data has become more and more important with the increasing number of studies on solar energy. Any analysis of systems powered by solar energy should start with the research of the radiation data available in the region being studied. The total radiation incident on a tilted surface could be evaluated in terms of the location, day of the year and time of the day. The total perceived solar radiation can be estimated by the following relationship (Hsieh, 1986): I t ¼ RB I B þ CI Bn
1 þ cos s 1 cos s þ ðI B þ I d Þqg 2 2
The hour angle is defined by 1 h ¼ ðnumber of min from local solar noonÞ 4
where IB is beam radiation on a horizontal surface, RB is beam radiation tilt factor, IBn is beam radiation at normal incidence, W/m2, Id is the diffuse sky radiation, W/m2, C is diffuse radiation factor, s is the surface tilt angle, qg is solar reflectance of the Earth’s surface. The three terms in the above equation represent the direct, diffuse, and reflected components, respectively. The terrestrial beam radiation within the atmosphere and on the earth’s surface on a typical clear day is calculated using the following relation:
ð5Þ
where the value of h is assumed positive in the after noon period. In Eq. (1), the diffuse solar radiation is estimated from: I d ¼ CF ss I Bn
ð1Þ
ð3Þ
ð6Þ
where Fss = 0.5(1 + cos s) is the angle factor between the surface and the sky and s is the tilt angle of the solar collector. The beam radiation tilt factor RB is defined by: RB ¼
I Bt cos i ¼ I B cos z
ð7Þ
where IBt, IB are the beam radiation on a tilted surface and on the horizontal surface, respectively. The incidence angle, i, and zenith angle z are calculated from the following expressions, cos i ¼ sinðL sÞ sin d þ cosðL sÞ cos d cos h
ð8Þ
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cos z ¼ sin a
ð9Þ
ð10Þ
where ma, and ms are the mass flow rates of air and solution kg/s, respectively, Ha, and Hs are the specific enthalpies of air and solution J/kg, respectively, m is the mass of evaporated water, kg/s, hfg is latent heat of water, J/kg, To is the outside temperature, and UL is the overall heat loss coefficient, W/m2 °C.
The solar radiation absorbed by the solution in the collector/regenerator can be obtained from,
2.2.2. Energy balance for the air stream passing through the regenerator-segment
The day length, which is the period from sunrise to sunset, can be evaluated from, daylength ¼
2 cos1 ð tan L tan dÞ 15
I a ¼ I t ð1 qÞsa
ð11Þ
ma dH a ¼ ha ðT s T a Þdx hs ðT a T o Þdx
ð13Þ
where q and s are the reflectance and transmittance of the glass cover on the collector surface, respectively, and a is the regenerator absorptivity.
where ha and hs are heat transfer coefficients for the air and solution sides, each in W/m2 °C.
2.2. Collector/regenerator (C/R) model
2.2.3. The amount of water evaporated from the weak solution
A schematic representation of the forced flow C/R is shown in Fig. 2. The C/R employs an inclined flat blackened surface over which the absorbent solution to be concentrated trickles down as a thin liquid film. 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 air stream may flow parallel or counter to the liquid film. The channel is divided into a large number of equal segments of width dx with the assumption of constant properties within the segment (air vapor pressure, pa, and temperature, Ta, and vapor pressure on the solution surface, ps, temperature, Ts, and concentration, Cs). The main equations include the energy balance and mass balance for each segment of the open-cycle regenerator. These equations are summarized as follows Aly et al. (2010): 2.2.1. Energy balance for the regenerator-segment I a dx ¼ ms dH s þ ma dH a þ U L ðT s T o Þ þ mhfg
ð12Þ
m ¼ 0:622
ma ðp pai Þ pb a
ð14Þ
where pb and pai are the barometric pressure and initial vapor pressure in air at the regenerator inlet, in mm Hg, respectively. 2.2.4. The rate of mass transport of water vapor dm ¼ bðps pa Þ dx
ð15Þ
where b is the mass transfer coefficient, kg/s m2 mm Hg. And the relation between the mass of evaporated water and solution flow rates is given by: m C s ¼ C si = 1 ð16Þ ms where Csi is the initial concentration of the solution at regenerator inlet. The relationship between the solution temperature, concentration and vapor pressure for Calcium Chloride is given by,
Fig. 2. Open-cycle solar collector regenerator.
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ps ¼ a þ bT s þ
c Cs
ð17Þ
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multiplying the rate of water evaporation, m, by the latent heat of water L at the evaporator pressure i.e.,
where a, b and c are empirical constants (Alizadeh and Saman, 2002) .
Qe ¼ mL
2.2.5. System coefficient of performance (COP) The overall coefficient of performance of the system can be evaluated from the following expression:
The above mentioned analysis shows the dependence of the regeneration process on operational parameters such as air and liquid mass flow rates as well as the vapor pressure of inlet air. In this study, the performance of soft computing methodology, is used for the system performance analysis.
COP ¼
Qe I t Ac
ð19Þ
ð18Þ 2.3. Simulation procedure
where Ac is the collector area and Qe is the cooling rate of the desiccant cooling system, which can be evaluated by
Fig. 3. Scheme of Matlab-Simulink.
2.3.1. Solving the equations The theoretical model is constituted from coupled algebraic and 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 current study, a numerical solution is obtained by the finite difference technique. These equations are solved using the Matlab-Simulink platform. Simulink allows the system to be modeled by drawing a block diagram directly on the screen. The Simulink representation of the system of equations is presented in Fig. 3. Each
Fig. 4. Sub-block for calculating the mass of evaporated water.
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block represent a calculation unit and may be composed of other more detailed sub-systems. The sub-system for calculating the mass of evaporated water is shown in Fig. 4. A Matlab computer code is written to perform the computations and visualize the results. The ordinary differential equations are solved using the fourth-order Runge–Kutta scheme with variable time steps (Chapra and Canale, 2006). As the time step decreases, the total time for running the simulation increases. The time step was set as 1 min in the solar radiation calculations. 2.3.2. Solar radiation module The sunshine period is evaluated for the specified location (defined by the latitude angle, L) by knowledge of the day number of the year, n, evaluating the declination angle, d (Eq. (4)), then substituting in Eq. (10). Eq. (1) is used to evaluate the instantaneous value of total radiation on the tilted surface during the sunshine period. The parameters in Eq. (1) are calculated from Eqs. (2)–(9). For 21 June, which is selected as a representative day in this analysis, values of radiation constants A, B and C are A = 1087.61 W/m2, B = 0.205 and C = 0.134 (Hsieh, 1986). 2.3.3. Collector/regenerator module The system of equations from (12)–(17) have six unknowns; which are: m, Ta, Ts, pa, ps and Cs. Given the input values of mass flow rates of air and solution, air temperature, and solution concentration at the inlet of any segment, along with the physical properties of the working desiccant, 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 obtain a numerical solution with the criterion set apriori. The heat and mass transfer coefficients are evaluated by using available correlations from the literature (McCabe et al., 1985). 3. Results and discussion The performance of the solar collector/regenerator is influenced by design parameters (regenerator length, solution flow rate, working solution concentration and air flow rate) and ambient conditions (air temperature and vapor pressure in the flowing air). These key parameters are
investigated in the following sub-sections. A sensitivity analysis is performed by varying the parameters of interest one at a time, while keeping all others fixed at given values. 3.1. Effect of air mass flow rate In order to analyze the effect of air mass flow rate on the regeneration process, the solution mass flow rate, ms, is settled at 20 kg/h and the range of air mass flow rate, ma, is considered in the range (10–200 kg/h), then the vapour pressure difference between the regenerated solution and flowing air is plotted versus the regenerator length. For a given regenerator length, the vapour pressure, which is the mass transfer potential, is directly proportional with the rate of water evaporation, when the mass transfer coefficient is assumed constant. As shown in Fig. 5, the vapor pressure difference has a maximum for a given length of the regenerator. The results obtained by Alizadeh and Saman (2002) were compared with that presented in Fig. 5. The trend of the results of both the vapor pressure difference and evaporation rate agree very well along with the regenerator length, which validates the present model. However, the rate of water evaporation could be obtained by multiplying the vapor pressure difference by the mass transfer coefficient. The length, at which the maximum rate of evaporation occurs, increases with the air flow rate. Concerning the effect of solution inlet concentration on regeneration process, the decrease of solution concentration can effectively improve the regenerator performance, though it sacrifices solution outlet concentration. It can be noted that the vapor pressure difference rapidly decreases, after reaching the peak value, with decrease in air flow rate (see Fig. 5, at Ma = 10 kg/h). This can be explained as follows: as a result of continuous evaporation from the collector surface, evaporated water is accumulated in the flowing airstream and consequently the vapor pressure in air increases with regenerator length. This leads to a decrease in vapor pressure difference between desiccant and air. 3.2. Effect of solution flow rate Fig. 6, demonstrates the variation of the solution temperature during the regeneration period. This period lasts
Fig. 5. Variation of vapor pressure at regenerator exit with different values of air flow rate, at noon time.
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Fig. 6. Variation of solution temperature during the day time for different values of solution flow rate.
from sun rise to sun set. As the solution flows from the regenerator inlet to exit, it is expected that the solution temperature will be maximum at the end of the regenerator. On the other hand, the maximum temperature of the solution will follow the solar radiation intensity along the day time. It can be observed that the solution temperature increases with the decrease in the flow rate. In Fig. 7, the solution concentration at the regenerator exit is plotted versus the regenerator length, for different values of the solution flow rate, at noon time (maximum intensity of solar radiation). It is clear that the solution concentration increases with the increase of the regenerator length as well as the decrease of solution flow rate. The explanation for this is as follow: with a lower solution flow rate and a longer regenerator a higher outlet solution temperature can be achieved, thus a higher vapour pressure and consequently a higher evaporation rate. The increase in evaporation rate results in increase in the solution concentration at the end of the regeneration process. It can be observed that the effect of solution flow rate is significant at its lower values (see Fig. 7). When the flow rate decreases from 20 kg/h to 10 kg/h, the solution concentration increases by about 8% (from 47% to 55%), whereas the solution concentration increases about 1% with decrease in the flow rate from 100 kg/h to 80 kg/h, for a regenerator with 5 m length. It is evident from Eq. (15) that the change in the solution concentration (Cs Csi) is inversely proportional
with the solution flow rate, ms. However the increase in the solution concentration must be limited by the crystallization of the solution which is dependent on the concentration and temperature. The solution temperature at the end of regenerator at noon time is plotted versus regenerator length for different values of solution flow rate as shown in Fig. 8. It can be noted that the temperature increases gradually with regenerator length. However, the rate at which the temperature increases is dependent on the solution flow rate. For lower values of solution flow rate (for example, ms = 10 kg/h.), solution temperature reaches 80 °C at the regenerator end of 5 m length, whereas this temperature is limited to about 55 °C when the flow rate is 100 kg/h. It can be also noted that the solution temperature slightly decreases at the regenerator inlet. This can be explained by the cold evaporation of water from the solution at this region. This evaporation of vapour from the solution surface occurs without heating due to the difference in vapor pressure between the solution and flowing air. The vapor pressure in air at regenerator inlet is 20 mm Hg and for the solution at the specified inlet conditions (Tsi = 40 °C, Csi = 40%), the evaluated pressure exceeds 35 mm Hg and consequently vapor transfers from solution to air with subsequent cooling of the solution. The drop in solution temperature increases with the flow rate (see Fig. 9). For lower values of solution flow rate (10 kg/h) it can be noted that the
Fig. 7. Variation of solution concentration at regenerator exit for different values of solution flow rate.
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Fig. 8. Variation of solution temperature at regenerator exit for different values of air flow rate, at noon time.
Fig. 9. Variation of vapor pressure at the regenerator exit for different values of solution flow rate, at noon time.
vapor pressure difference decreases sharply after reaching the maximum value. This sharp decrease vapor pressure difference can be explained by the rapid increase in solution concentration with evaporation of water from the solution surface. An increase in solution concentration decreases the vapor pressure on the solution surface and consequently the potential for mass transfer. 3.3. Effect of regenerator length The daily accumulated amount of water that evaporates from the regenerator surface is plotted versus time for various values of regenerator length, as shown in Fig. 10. It is
clear that the accumulated mass of evaporated water, at regenerator length of x = 3 m, is close to 6 kg/day, whereas a regenerator having 4 m length produces about 7 kg of water per day. On the other hand, when the length is limited by 1 m, more than 2.5 kg of water evaporates from the solution, at the same conditions. This means that, for the specified operating conditions, the relative value of daily water evaporation decreases with the increase of the solar regenerator. However, an increase in regenerator length results in increasing the solution concentration in the evaporator with subsequent decrease in the evaporator temperature. Therefore, when selecting the regenerator length, the consideration of the system COP, which is directly dependent on
Fig. 10. Amount of daily accumulated water evaporation from the regenerator surface.
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the mass of evaporated water per day per unit, and the required evaporator temperature must be taken into account. 3.4. Effect of solution concentration
Mass of Water per unit area, kg/m sq.
The effect solution concentration at regenerator exit is depicted in Fig. 11. For the solar-powered systems it is objected to maximize the mass of water evaporated per unit collector area. Therefore, the mass of evaporated water per unit area is shown versus the regenerator length for a complete day of operation. It is evident that the effect of solution concentration is significant for a regenerator length up to about 2 m. Also, for the solution concentration of 30%, a shorter regenerator is more efficient from the point of view of regenerator cost. On the other hand, values of solution concentration more than 40% have a maximum at a given value of regenerator length; this length is dependent on the concentration. However, the solution concentration at the end of regeneration process determines the vapor pressure in the absorber and consequently the evaporator temperature. Lower temperatures in the evaporator could be obtained at higher values of solution concentration, this of course on the account of the mass of evaporated vapour as well as the system coefficient of performance.
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3.5. System coefficient of performance A set of independent parameters control the performance of the system. However, some of these parameters are uncontrollable such as the ambient conditions (temperature and humidity). Other design parameters must be selected to optimize the system performance. From the results presented in Figs. 5–11 it is evident that the most important of the design parameters are regenerator length, solution flow rate and air flow rate. Variation of coefficient of performance (COP) of the system is illustrated in the surface plot shown in Fig. 12. For the specified operating conditions, a maximum value of the COP occurs at a given range of air and solution flow rates. However, the maximum value of COP is dependent of the design parameters and operating conditions, therefore it is essential to select the design parameters for each ambient condition to maximize the COP of the system. Values of COP presented in Fig. 12. summarize the dependence of system performance on the controllable design variables. A maximum value of 0.34 could be obtained when the vapor pressure in the atmospheric air is 20 mm Hg. However, higher values could be attained when the vapor pressure decreases. Also, it is expected that a decrease in the solution concentration increases the value of COP.
5
Ma=100kg/hr To=40 oC Tsi=40 oC Csi=40% Pai=20mmHg Day 21 June
4 Cs=30%
3
Cs=40% Cs=50%
2 1 0 0.5
1
1.5
2
2.5
3
3.5
4
4.5
5
Regenerator Length, m Fig. 11. Mass of evaporated water per unit area for different values of inlet concentration.
Fig. 12. Surface plot showing the variation of system COP with air and solution flow rates.
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4. Conclusion The modeling and simulation of solar-powered desiccant regenerator used for open absorption cooling cycle are presented. The source of input heat is assumed to be the total solar radiation incident on a tilted surface. A finite difference method is used to simulate the combined heat and mass transfer processes that occur in the liquid desiccant regenerator. The model is implemented using the MatlabSimulink platform and its feasibility is established. It has been shown that the use of the proposed methodology results in some desirable characteristics. It is also concluded that the proposed model can be successfully used for predicting the overall performance of the system. The simulation has shown that the vapor pressure difference has a maximum value for a given regenerator length. It is also shown that for specified operating conditions, a maximum value of the coefficient of performance occurs at a given range of air and solution flow rates. Therefore, it is essential to select the design parameters for each ambient condition to maximize the coefficient of performance of the system. References Agyenim, F., Knight, I., Rhodes, M., 2010. Design and experimental testing of the performance of an outdoor LiBr/H2O solar thermal absorption cooling system with a cool store. Solar Energy 84 (5), 735– 744. Alizadeh, S., Saman, W.Y., 2002. Modeling and performance of a forced flow solar collector/regenerator using liquid desiccant. Solar Energy 72 (2), 143–154. Aly, A.A., Zeidan, E.B., Hamed, A.M., 2010. Performance evaluation of open-cycle solar regenerator using artificial neural network technique. Energy and Buildings 43 (2/3), 454–457.
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