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Simulation of the vapor mixture condensation in the condenser of seawater greenhouse using two models
Desalination 317 (2013) 152–159
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Simulation of the vapor mixture condensation in the condenser of seawater greenhouse using two models T. Tahri a,⁎, M. Douani a, S.A. Abdul-Wahab b, M. Amoura a, A. Bettahar a a b
Faculty of Technology, Hassiba Ben Bouali University, P.O. Box 151, Chlef 02000, Algeria College of Engineering, Sultan Qaboos University, P.O. Box 33, Al-khod 123, Oman
H I G H L I G H T S • Simulation of the condenser of seawater greenhouse using heat transfer model • Simulation of the condenser of seawater greenhouse using mass transfer model • The effects of operational parameters
a r t i c l e
i n f o
Article history: Received 9 February 2012 Received in revised form 28 February 2013 Accepted 28 February 2013 Available online 9 April 2013 Keywords: Condenser Modeling Heat model Mass model Seawater greenhouse Oman
a b s t r a c t The aim of this paper is the development of a mathematical model, based on mass transfer, in order to compare the simulation results with those obtained by the model developed by Tahri et al. for the analysis of the seawater greenhouse (SWGH) condenser operating. This last model was depending on heat balance according to the thermodynamic model of Nusselt for simulating the physical process of condensation of the humid air in the condenser of SWGH that is located in Muscat, Oman. The present model was a mathematical one that was based on mass balance development in order to improve the description of phenomena in a humidification-dehumidification seawater greenhouse desalination system. The values of the predicted condensate calculated by the two models were compared with those of the measured values. Using the model developed in this work, the predicted mass condensate rates calculated by mass model was much closer to the measured condensate rates than that calculated by the heat model. Furthermore, the effects of relative humidity, dry bulb temperature, seawater temperature, humid air velocity and solar radiation on condensate values are also discussed. © 2013 Elsevier B.V. All rights reserved.
1. Introduction The lack of potable water poses a big problem in arid regions of the world where freshwater is becoming very scarce and expensive. The areas with the severest water shortages are the warm arid countries of the Middle East and North Africa (MENA) [1]. The consequences of water scarcity will be especially seen in arid and semiarid areas of the planet. Currently, agriculture accounts for around 70% of fresh water use. In arid countries, this figure can exceed up to 90%. Scarcity of water is very detrimental to agriculture and it is expected that the growth in world population will aggravate the situation further. This goes above 85% in the MENA and it is about 94% in Oman [2]. As expected, irrigation demands will put a considerable pressure on the water resources that are going to lead to groundwater scarcity. The economic and social consequences are apparent in many coastal regions of arid countries, such as Oman, where the overuse of ⁎ Corresponding author. Tel.: +213 551591304; fax: +213 27721794. E-mail address: [email protected] (T. Tahri). 0011-9164/$ – see front matter © 2013 Elsevier B.V. All rights reserved. http://dx.doi.org/10.1016/j.desal.2013.02.025
groundwater has caused saline intrusion, which in turn has reduced the ability to grow crops and resulted in agricultural land being discarded [3]. As the resources of freshwater are limited, there is an inexorable and continuous pressure to reduce the agricultural uses of the water. Desalination has become the main source of freshwater in many parts of the world, especially in the MENA countries. The most widely used desalination technologies are thermal and reverse osmosis [4]. Desalination is an appropriate way in coastal regions or other locations where access to saline or brackish water is not a constraint. The high operational cost of desalination (multi-stage flash and reverse osmosis) has not rendered these techniques feasible for arid land agriculture [5]. Today most of the desalination systems are using fossil fuels, and thus are contributing to the increased levels of greenhouse gases. There have been numerous voices inclined towards a more ecological and safer approach to the problem proposing the use of renewable energy sources, fundamentally wind and solar, for small-scale seawater desalination. Recently, a considerable attention has been given to the use of renewable energy in desalination, especially in remote areas
T. Tahri et al. / Desalination 317 (2013) 152–159
Nomenclature As C Cp Cs D DAB f H h hfg k Le L m _ m N P Pr Q RH Sc St T
heat transfer area number specific heat humid heat diameter mass diffusivity friction factor absolute humidity enthalpy latent heat of vaporization Thermal conductivity Lewis number length mass mass flux number pressure Prandtl number heat flux relative humidity Schmidt number Stanton number temperature
Greek symbols α Thermal diffusivities ρ density
153
on the amount of the condensed water, which can be gained at a certain ambient condition and a certain type of crops. Having noted discrepancies between the experimental results and those obtained by the model of heat transfer presented by Douani et al. [17], we developed the mass transfer model within the framework of this study. Our task was focused on simulating the condenser of a seawater greenhouse by using two models that were based on heat and mass transfer. Application of both developed models using FORTRAN was conducted to validate its theoretical development. The effect of the relative humidity, the dry bulb temperature, the seawater temperature, the humid air velocity and the solar radiation on condensate values were also addressed. 2. Methodology 2.1. Condenser process description The condenser of the solar greenhouse is a heat exchanger where seawater is the coolant and humid air is the hot fluid (Fig. 1). The tubes are organized in such a way to ensure passage of the coolant from one tube to another forming a row of coiled tubes. Seawater is introduced, at a constant speed (usw) and at a known temperature (Tswin), in the first line of the tube bundle to an exit tube located upstream of the greenhouse after an increase in temperature. The condenser unit consists of a set of 302 rows of parallel tubes which arranged semi-vertically at an angle of 30 degrees to the direction of the flow of moist air. Each line consists of 16 vertical tubes, identical diameter (D) of 33 mm, and a height (L) of 1.8 m [9]. Values of different design parameters of the condenser unit are listed in Table 1. 2.2. Modeling of heat and mass exchange in the condenser
Subscripts air air c condensate D degrees of freedom db dry bulb in inner sat saturation sw seawater swin seawater inlet swout seawater outlet vap vapor
and islands. This is mainly because of the high cost of fossil fuels, the difficulties to obtain it taking account with their progressive scarcity, the attempts to preserve it for future generations, while envisaging a contribution to the reduction of the atmospheric pollution related to the combustion rejects during the electrical energy generation [1]. Solar desalination methods are well suited for the arid and sunny regions of the world as in the Arabian Peninsula. In the desalination context, it is relevant to use the technologies which facilitate more efficient water in agriculture. The Seawater Greenhouse (SWGH) provides a perfect environment in which the transpiration loss from plants is minimized. At the same time, sufficient water for its own use is produced through a process of solar distillation [6]. Indeed, the projects of solar desalination have been demonstrated in several locations around the world. The humidification-dehumidification method was used in a greenhousetype structure for desalination and for crop growth as a pilot plant at Al-Hail, Muscat, in the Sultanate of Oman [7,8]. Sablani et al. shown that the dimension of the greenhouse had the greatest overall effect on water production and energy consumption [21]. Among other parameters, cooling the condenser(s) of the SWGH has a direct impact
2.2.1. Heat transfer model Steam condensation occurs when its temperature is reduced below its saturation temperature at a given pressure. The presence of non-condensable gases (air) in the gas mixture leads to a significant reduction in the heat flow and during condensation. This is because of the formation non-condensable gases, bind to the wall film that will prevent the diffusion of vapor through the bulk liquid film [11]. Analysis of the kinetics of heat transfer for film condensation outside vertical tubes was originally treated for laminar film by Nusselt in 1916 [12]. In this work, the simulation of the condenser of the seawater greenhouse was done on the basis of a model that developed previously by Tahri et al. [9] at Al-Hail, Muscat. Data of dry bulb temperature of air together with its relative humidity are collected only at the inlet and the exit of the condenser of the seawater greenhouse. However, simulation of the operation of the condenser requires that the saturation temperature to be known at each tube of the condenser. Equations used in this work can be found in Sherwood and Comings [13]. Saturation temperature (Tsat) was calculated for the first and the last tube in the row of the condenser [10] according to Eq. (1): H sat −H C ¼− s T sat −T db hfg
ð1Þ
Cs is the mass humid heat (kJ/kg °C) [19] which was calculated according to Eq. (2): C s ¼ C pair þ H C pvap
ð2Þ
The temperature of seawater flowing inside the tubes of the condenser is only known at the entrance and exit of the condenser. In
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T. Tahri et al. / Desalination 317 (2013) 152–159
Fig. 1. Process schematic of one vertical tube of the condenser unit.
this work, parabolic interpolations were used to find the temperature of seawater at the entrance and the exit for each tube of the condenser by utilizing the information that are known at the entrance and the exit of the condenser. As a basis of calculation, the temperature of seawater at the entrance and the exit of intermediate tubes are unknown. To resolve this problem, linear profile of seawater temperature along the row of the condenser was adopted. The temperature at the entrance of each tube was calculated according to Eq. (3): T swin ðjÞ ¼
ðT swout ð16Þ−T swin ð1ÞÞ ðj−1Þ þ T swin ð1Þ 16
ð3Þ
However, this hypothesis was subsequently corrected by introducing a coefficient of weighting [17] that was used to adjust the value of the entrance seawater temperature for each tube. If the total number of tubes in the condenser is Ntot, then the total flow of condensate will be:
_ ctot ¼ m
NL X NT X
mij
ð4Þ
j¼1 i¼1
Moreover, it was considered that the outlet seawater temperature of one tube of the row (Tswout) was equal to the inlet seawater temperature (Tsin) of the next tube. Also, it was assumed known both the inner (TWin) and the outer wall (TWout) temperatures for the first
Table 1 Design parameters of the condenser unit [10]. Dimensions of condenser Thickness of vertical tube (δ) Height of vertical tube (L) Diameter of vertical tube (Dout) Number of longitudinal tubes (NL) Number of transverse tubes (NT) Total number of tubes (Ntot)
tube in the row of condenser. This value of TWout will be used in Eq. (9) to find out the heat flux (Q). The average heat transfer coefficient for a laminar film condensation over a vertical tube of height (L) was calculated [12] for each tube of the condenser according to Eq. (5): " have ¼ 0:943
#1 4
ð5Þ
According to Çengel [14], Rohsenow [15] showed that the cooling of a liquid below its saturation temperature can be accounted for ∗ , deby replacing hfg by the modified latent heat of vaporization hfg fined as
hfg ¼ hfg þ 0:68 C pL ðT sat −T Wout Þ
ð6Þ
In the presence of noncondensble gases (e.g., air), the average heat transfer coefficient for film condensation (have) was corrected (hvert) according to the graph of Sacadura [16] as shown in Eq. (7). According to Tahri et al. [12], correction is a function of the noncondensable gas mass fraction (X) hvert ¼ have f ðX Þ
ð7Þ
X is the mass fraction of the noncondensable gases (kg noncondensable gas/kg humid air) which was calculated for each tube according to Eq. (8): X¼
(15 × 19 × 0.8)m 200 μm 1.8 m 33 mm 16 302 4832
3
g ρL ðρL −ρv ÞkL hfg μ L ðT sat −T Wout ÞL
mNC 1 ¼ mtot 1 þ H
ð8Þ
Calculation of Q The heat flux (Q) in the film condensation was calculated for the first tube according to Eq. (9): Q ¼ hvert Aout ðT sat −T Wout Þ
ð9Þ
T. Tahri et al. / Desalination 317 (2013) 152–159
Calculation of hin The inner heat transfer coefficient hin was calculated [10] according to Eq. (10): hin ¼
Nu ksw Din
ð10Þ
Calculation of (TWout)cal The outer wall temperature (TWout)cal was then calculated for the first tube [14] according to Eq. (11): Q ¼ 2 π L ktub
ðT Wout Þcal −ðT Win Þ ln DDout
ð11Þ
in
Calculation of (TWin)cal The inner wall temperature (TWin)cal was then calculated for the first tube [10] according to Eq. (12): Q ¼ hin Ain
ðT Win Þcal −T swin − ðT Win Þcal −T swout ððT Þ −T Þ ln ðT WinÞ cal−T swin ð Win cal swout Þ
ð12Þ
Firstly, the values of (TWout)cal and (TWin)cal are calculated from Eqs. (11) to (12) respectively. Their values were compared with the guessed initial values of TWout and TWin. If the difference between the compared values does not verify a criterion of convergence, the values of (TWout)cal and (TWin)cal will be again used in Eqs. (5) and (11) to calculate the new values of (TWout)cal and (TWin)cal. The process was repeated until the values of (TWout)cal and (TWin)cal with successive trials did not change. The mass flux of condensate for the first tube was determined by Eq. (13): _ c1 ¼ m
hvert Aout ðT sat −T Wout Þ hfg
ð13Þ
The heat flux transferred from humid air to seawater (Qsw) was calculated in the first tube according to Eq. (14): 2
Q sw ¼ ρsw usw C P sw π
ðDin Þ ðT swout −T swin Þ 4
ð14Þ
The enthalpy of air (Hair) was calculated at the entrance of the first tube according to Eq. (15): ðH air Þin ¼ C Pair
0 T db þ H C Pvap T db þ hfg
ð15Þ
The heat flux of air (Qair) was calculated at the entrance of the first tube according to Eq. (16): _ air ðQ air Þin ¼ ðHair Þin m
ð16Þ
The heat flux of air (Qair) was calculated at the outlet of the first tube according to Eq. (17): ðQ air Þout ¼ ðQ air Þin −Q−Q sw
ð17Þ
The humidity of air (H) at the dry bulb temperature was calculated at the outlet of the first tube according to Eq. (18): _ c1 m H out ¼ Hin − _ air m
ð18Þ
155
The dry bulb temperature Tdb was calculated at the outlet of the first tube according to Eq. (19):
T dbout ¼
ðQ air Þout _ air − m
Hout h0fg
C Pair þ H out C Pvap
ð19Þ
The calculated humidity of air (Hout)cal from Eq. (18) and dry bulb temperature (Tdbout)cal from Eq. (19) in outlet first tube were used in Eq. (1) to set the saturation temperature (Tsat) of the second tube in the row of the condenser. Simulation of the condenser operation required that the saturation temperature to be known at each tube in the condenser. For this purpose, Eqs. (1)–(19) were repeated for _ c1tot Þcal from each tube. Next, the total mass flow calculated ðm _ ctot Þm Eq. (4) was compared with the measured total mass flow ðm on the day of 25 December 2005. If the model was not valid, then new values were proposed for the coefficients of weighting of parabolic interpolation for seawater temperature at different tubes in the condenser [17]. The trial was repeated until the values of _ c1tot Þcal and ðm _ ctot Þm did not change with successive trials. ðm 2.2.2. Mass transfer model For this model, Eqs. (1)–(12) were repeated for the first tube to defined (Tsat) and (TWout). The Reynolds analogy is very useful relation, and it is certainly desirable to extend it to a wider range of Pr and Sc number. Several attempts were done in this regards, but the simplest and the best know was the one suggested by Chilton and Colburn in 1934 as [18]: f 2=3 2=3 ¼ StPr ¼ St mass Sc 2
ð20Þ
For 0.6 b Pr > 60 and 0.6 b Sc > 3000. This equation is known as the Chilton–Colburn analogy. Using the definition of heat and mass Stanton numbers, the analogy between heat and mass transfer was expressed more conveniently as: 2=3 hvert Sc ¼ ρair C pair Pr hmass
ð21Þ
For air-vapor mixtures at 298 K, the mass and thermal diffusivities were D = 2.5 10 −5 m 2/s and α = 2.18 10 −5 m 2/s, respectively. Hence, Lewis number was calculated from Eq. (22): Le ¼
α ¼ 0:872 D
ð22Þ
Next, (α/D)2/3 = 0.872 2/3 was calculated as 0.913, where the value was close to unity. The Lewis number was relatively insensitive to variations in temperature. Therefore, for air–water vapor mixture, the relation between heat and mass transfer coefficients was expressed with a good accuracy as: hmass ≅
hvert ρair C pair
ð23Þ
where ρair and Cpair are the density and specific heat of air at film temperature. The film temperature (Tfilm) was given by [14] according to Eq. (24): T film ¼
T db þ T Wout 2
ð24Þ
The condensate rate of fresh water produced for the first tube was calculated by the following relation: _ c2 ¼ hmass π Dout L ρvapdb −ρvapWout m
ð25Þ
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T. Tahri et al. / Desalination 317 (2013) 152–159
Fig. 2. Comparison of the diurnal measured and calculated mass condensate rate of condenser.
where ρvapdb and ρvapWout are the density of vapor at dry bulb and external wall temperature which were calculated by Eq. (26), according to [20]: ρsat ðT Þ ¼
2910 expð9:48654−3892:7=ðT−42:6776ÞÞ 8314 T
ð26Þ
Where ρvapdb ¼ ρsat T vapdb ρvapWout ¼ ρsat T vapWout
_ c2tot Þcal from Eq. (4) which is compared with the meacalculated ðm _ ctot Þm on the day of 25 December 2005. If sured total mass flow ðm the model is not valid, then new values are proposed for the coefficients of weighting of parabolic interpolation for seawater temperature at different tubes in the condenser [17]. The trial calculation is _ c2tot Þcal and ðm _ ctot Þm don’t change. repeated until the values of ðm 3. Results and discussion
ð27Þ
3.1. Comparison between the measured and predicted mass condensate rate
The simulation of the condenser operation requires that the saturation temperature to be known at each tube in the condenser. To this end and knowing the dry air properties (Hdry, Tdb), we use the Eq. (1) to determinate it for each tube. For all the tubes, the total mass flow
Fig. 2 illustrates the calculated and measured mass condensate rates according to the hours of a one day period. It can be seen that there was a time gap between the calculated [9] and the measured condensate rates. This gap was attributed to the tipping bucket
Fig. 3. Comparison of the diurnal mass condensate rate and the solar radiation inside the SWGH.
T. Tahri et al. / Desalination 317 (2013) 152–159
157
Fig. 4. Comparison of the diurnal mass condensate rate and the inlet dry bulb temperature in the condenser.
gauge which did not register outflow from the condenser due to the low production rate of condensate. Formation of the water droplets on the tubes of the condensers were observed, but only a small fraction of the droplets made their way to the gutter collecting the condensate. It should be noted that the measured condensate mass rates were taken from the freshwater tank by the tipping bucket gauge, whereas the predicted condensate mass rates were calculated directly as droplets formed at the outer surface of the tubes of the condenser [9]. Therefore it was observed that the trend of the predicted and the measured mass condensate rates were close, a gap was clearly seen between them. The trend of the predicted mass condensate rates calculated in this work by mass model was much closer to the measured condensate rates than that calculated by heat model.
3.2. Impact of the meteorological variables on mass condensate rates Fig. 3 shows the variation of the measured and predicted mass condensate rates together with solar radiation values of a one day period. It can be seen that the solar radiation values were observed only during the interval from 08:00 to 18:00 and it was zero during the night time. Hence, the trend of the calculated and measured mass condensate rates went hand-in-hand with solar radiation. Fig. 4 shows the diurnal variation of the measured mass condensate rate, the predicted mass condensate rate and the dry bulb temperature for one day period. It can be noted that the two plots of the measured and predicted mass condensate rates follow the same trend of the diurnal variations of dry bulb temperature. We note that its shapes are typically Gaussian which reach its maximum at
Fig. 5. Comparison of the diurnal mass condensate rate and inlet relative humidity in the condenser.
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T. Tahri et al. / Desalination 317 (2013) 152–159
Fig. 6. Comparison of the diurnal mass condensate rate and the inlet seawater temperature in the condenser.
12 h 00. In any rigor, we mention that the mass condensate rate is strongly influenced by the pinch of temperature (Tsat–Tdb) according to Eq. (1). For a condenser, where the condensation of vapor place inside the tubes bank immersed in a tank, filled by seawater [20], the results of the operating analysis show that the trends of Tdb, and _ ctot Þcal versus the time confirm the results obtained by the model ðm developed within the framework of this work. Indeed, the maximum values are also reached at 12 h 00. Fig. 5 depicts the diurnal variation of the measured mass condensate rate, the predicted mass condensate rate and the relative humidity of a one day period. It can be seen that the relative humidity values were high (100%) between 08:00 and 14:00, while their lower values (RH = 65%) were seen during the rest of the day. It should be noted that in the interval extended from 08:00 to 14:00, the seawater greenhouse produce 98% of the total daily freshwater. This result is in perfect agreement with the conditions of condensation of the water vapor which require a preliminary saturation of the air
(100%). However, the tiny quantities of condensate appear beyond 14:00 where the air is unsaturated. Fig. 6 depicts the variation of the measured and predicted mass condensate rates together with the inlet seawater temperature values to condenser for one day period. It shows that the condensation of steam in the condenser happened between 08:00 and 18:00 with an average temperature of cold fluid (seawater) below 20 °C. The quantity of the condensate is the consequence of the interference of the installation operating parameters so that it is impossible to obtain an obvious conclusion for a variation of the inlet seawater temperature in such a restricted interval (20 to 24 °C) which is an exterior uncontrollable parameter, dictated by ambient condition. Fig. 7 depicts the diurnal variation of the measured mass condensate rate, the predicted mass condensate rate and the air speed values of a one day period. In our experiences, the air speed is selected according to the degree of saturation of the air in order to favorite the mass transfer. From previous results, these selected air speeds
Fig. 7. Comparison of the diurnal mass condensate rate and air speed inside the SWGH.
T. Tahri et al. / Desalination 317 (2013) 152–159
are maximum within the interval time 09:00 to 17:00. We see that the measured and predicted mass condensate rates went hand-inhand with the air speed values inside SWGH whereas the seawater greenhouse produced 98% of the total daily freshwater during this period when air speed was maximum (7 m/s). 4. Conclusions This paper discussed the modeling of the heat and mass exchange in the condenser of a seawater greenhouse (SWGH) at Al Hail in Muscat, Oman. In this work, two theoretical models were developed in order to describe the process of condensation by using model of heat and mass transfer equations. A comparison was made between the mass condensate rates values calculated by the two models. The predicted values were also compared with that of the measured values. The trend of the predicted mass condensate rates calculated by mass model in this work was found much closer to the measured mass condensate rates. The results indicated that the comparison was more consistent with the mass model used in this work. The effect of solar radiation, relative humidity, dry bulb temperature, seawater temperature, and air speed was also discussed to see their effects on the condensate. Acknowledgments The first author would like to acknowledge the valuable assistance of his advisors: Prof. Dr. Sabah Ahmed Abdul-Wahab, (College of Engineering, Sultan Qaboos University) and Prof. Dr Bettahar Ahmed (College of Engineering, Chlef University). The first author would like also to thank Dr. Douani Mustapha (College of Engineering, Chlef University) for his assistance in describing the models. References [1] H.M. Qiblawey, F. Banat, Solar thermal desalination technologies, Desalination 220 (2008) 633–644. [2] C. Paton, P. Davies, The seawater greenhouse cooling, fresh water and fresh produce from seawater, The 2nd International Conference on Water Resources in Arid Environments, Riyadh, 2006.
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[3] J.S. Perret, A.M. Al-Ismaili, S.S. Sablani, Development of humidification–dehumidification system in a quonset greenhouse for sustainable crop production in arid regions, Biosyst. Eng. 91 (2005) 349–359. [4] M.F.A. Goosen, S.S. Sablani, W.H. Shayya, C. Paton, H. Al-Hinai, Thermodynamic and economic considerations in solar desalination, Desalination 129 (2000) 63–89. [5] M.F.A. Goosen, H. Al-Hinai, S.S. Sablani, Capacity building strategies for desalination: activities, facilities and educational programs in Oman, Desalination 141 (2001) 181–190. [6] P.A. Davies, C. Paton, The Seawater Greenhouse in the United Arab Emirates: thermal modelling and evaluation of design options, Desalination 173 (2005) 103–111. [7] C. Paton, A. Davis, The seawater greenhouse for arid lands, Proc. Mediterranean Conf. on Renewable Energy Sources for Water Production, Santorini, 10–12 June, 1996. [8] B. Dawoud, Y.H. Zurigat, B. Klitzing, T. Aldoss, G. Theodoridis, On the possible techniques to cool the condenser of seawater greenhouse, Desalination 195 (2006) 119–140. [9] T. Tahri, S.A. Abdul-Wahab, A. Bettahar, M. Douani, H. Al-Hinai, Y. Al-mulla, Simulation of the condenser of the seawater greenhouse. Part II: application of the developed theoretical model, J. Therm. Anal. Calorim. 96 (2009) 43–47. [10] N.K. Maheshwari, D. Saha, R.K. Sinha, M. Aritomiet, Investigation on condensation in presence of a noncondensable gas for a wide range of Reynolds number, Nucl. Eng. Des. 227 (2004) 219–238. [11] W. Nusselt, Die oberflachen Kondensation des Wasserdampes, Z. Ver. Deut. Ing. 60 (2) (1916) 541–546. [12] T. Tahri, S.A. Abdul-Wahab, A. Bettahar, M. Douani, H. Al-Hinai, Y. Al-mulla, Simulation of the condenser of the seawater greenhouse. Part I: theoretical development, J. Therm. Anal. Calorim. 96 (2009) 35–42. [13] T.K. Sherwood, E.W. Comings, An experimental study of the wet bulb hygrometer, Trans. Am. Inst. Chem. Eng. 28 (1932) 88. [14] Y.A. Çengel, Heat Transfer: a practical approach, second ed. McGrRAW-HILL, New York, 2003. [15] W.M. Rohsenow, A method of correlating heat transfer data for surface boiling of liquid, ASME Trans. 74 (1952) 969–975. [16] J.F. Sacadura, Initition aux transferts thermiques, Edit, Techniques et documentation, 1982. [17] M. Douani, T. Tahri, S.A. Abdul-Wahab, A. Bettahar, H. Al-Hinai, Y. Al-mulla, Modeling heat exchange in the condenser of a seawater greenhouse in Oman, Chem. Eng. Commun. 198 (2011) 1–15. [18] Y.A. Çengel, Heat Transfer: A Practical Approach, second ed. McGraw-Hill, New York, 2003. 754–759. [19] Perry's Chemical Engineers' Handbook, McGraw-Hill, 1999, p. 3 (Section 12). [20] H. Mahmoudi, N. Spahis, S. Abdul-Wahab, S.S. Sablani, F.A. Goosen, Improving the performance of a Seawater Greenhouse desalination system by assessment of simulation models for different condensers, Renew. Sustain. Energy Rev. 14 (2010) 2182–2188. [21] S.S. Sablani, M.F.A. Goosen, C. Paton, W.H. Shayya, H. Al-Hinai, Simulation of fresh water production using a humidification–dehumidification seawater greenhouse, Desalination 159 (2003) 283–288.
Contents lists available at SciVerse ScienceDirect
Desalination journal homepage: www.elsevier.com/locate/desal
Simulation of the vapor mixture condensation in the condenser of seawater greenhouse using two models T. Tahri a,⁎, M. Douani a, S.A. Abdul-Wahab b, M. Amoura a, A. Bettahar a a b
Faculty of Technology, Hassiba Ben Bouali University, P.O. Box 151, Chlef 02000, Algeria College of Engineering, Sultan Qaboos University, P.O. Box 33, Al-khod 123, Oman
H I G H L I G H T S • Simulation of the condenser of seawater greenhouse using heat transfer model • Simulation of the condenser of seawater greenhouse using mass transfer model • The effects of operational parameters
a r t i c l e
i n f o
Article history: Received 9 February 2012 Received in revised form 28 February 2013 Accepted 28 February 2013 Available online 9 April 2013 Keywords: Condenser Modeling Heat model Mass model Seawater greenhouse Oman
a b s t r a c t The aim of this paper is the development of a mathematical model, based on mass transfer, in order to compare the simulation results with those obtained by the model developed by Tahri et al. for the analysis of the seawater greenhouse (SWGH) condenser operating. This last model was depending on heat balance according to the thermodynamic model of Nusselt for simulating the physical process of condensation of the humid air in the condenser of SWGH that is located in Muscat, Oman. The present model was a mathematical one that was based on mass balance development in order to improve the description of phenomena in a humidification-dehumidification seawater greenhouse desalination system. The values of the predicted condensate calculated by the two models were compared with those of the measured values. Using the model developed in this work, the predicted mass condensate rates calculated by mass model was much closer to the measured condensate rates than that calculated by the heat model. Furthermore, the effects of relative humidity, dry bulb temperature, seawater temperature, humid air velocity and solar radiation on condensate values are also discussed. © 2013 Elsevier B.V. All rights reserved.
1. Introduction The lack of potable water poses a big problem in arid regions of the world where freshwater is becoming very scarce and expensive. The areas with the severest water shortages are the warm arid countries of the Middle East and North Africa (MENA) [1]. The consequences of water scarcity will be especially seen in arid and semiarid areas of the planet. Currently, agriculture accounts for around 70% of fresh water use. In arid countries, this figure can exceed up to 90%. Scarcity of water is very detrimental to agriculture and it is expected that the growth in world population will aggravate the situation further. This goes above 85% in the MENA and it is about 94% in Oman [2]. As expected, irrigation demands will put a considerable pressure on the water resources that are going to lead to groundwater scarcity. The economic and social consequences are apparent in many coastal regions of arid countries, such as Oman, where the overuse of ⁎ Corresponding author. Tel.: +213 551591304; fax: +213 27721794. E-mail address: [email protected] (T. Tahri). 0011-9164/$ – see front matter © 2013 Elsevier B.V. All rights reserved. http://dx.doi.org/10.1016/j.desal.2013.02.025
groundwater has caused saline intrusion, which in turn has reduced the ability to grow crops and resulted in agricultural land being discarded [3]. As the resources of freshwater are limited, there is an inexorable and continuous pressure to reduce the agricultural uses of the water. Desalination has become the main source of freshwater in many parts of the world, especially in the MENA countries. The most widely used desalination technologies are thermal and reverse osmosis [4]. Desalination is an appropriate way in coastal regions or other locations where access to saline or brackish water is not a constraint. The high operational cost of desalination (multi-stage flash and reverse osmosis) has not rendered these techniques feasible for arid land agriculture [5]. Today most of the desalination systems are using fossil fuels, and thus are contributing to the increased levels of greenhouse gases. There have been numerous voices inclined towards a more ecological and safer approach to the problem proposing the use of renewable energy sources, fundamentally wind and solar, for small-scale seawater desalination. Recently, a considerable attention has been given to the use of renewable energy in desalination, especially in remote areas
T. Tahri et al. / Desalination 317 (2013) 152–159
Nomenclature As C Cp Cs D DAB f H h hfg k Le L m _ m N P Pr Q RH Sc St T
heat transfer area number specific heat humid heat diameter mass diffusivity friction factor absolute humidity enthalpy latent heat of vaporization Thermal conductivity Lewis number length mass mass flux number pressure Prandtl number heat flux relative humidity Schmidt number Stanton number temperature
Greek symbols α Thermal diffusivities ρ density
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on the amount of the condensed water, which can be gained at a certain ambient condition and a certain type of crops. Having noted discrepancies between the experimental results and those obtained by the model of heat transfer presented by Douani et al. [17], we developed the mass transfer model within the framework of this study. Our task was focused on simulating the condenser of a seawater greenhouse by using two models that were based on heat and mass transfer. Application of both developed models using FORTRAN was conducted to validate its theoretical development. The effect of the relative humidity, the dry bulb temperature, the seawater temperature, the humid air velocity and the solar radiation on condensate values were also addressed. 2. Methodology 2.1. Condenser process description The condenser of the solar greenhouse is a heat exchanger where seawater is the coolant and humid air is the hot fluid (Fig. 1). The tubes are organized in such a way to ensure passage of the coolant from one tube to another forming a row of coiled tubes. Seawater is introduced, at a constant speed (usw) and at a known temperature (Tswin), in the first line of the tube bundle to an exit tube located upstream of the greenhouse after an increase in temperature. The condenser unit consists of a set of 302 rows of parallel tubes which arranged semi-vertically at an angle of 30 degrees to the direction of the flow of moist air. Each line consists of 16 vertical tubes, identical diameter (D) of 33 mm, and a height (L) of 1.8 m [9]. Values of different design parameters of the condenser unit are listed in Table 1. 2.2. Modeling of heat and mass exchange in the condenser
Subscripts air air c condensate D degrees of freedom db dry bulb in inner sat saturation sw seawater swin seawater inlet swout seawater outlet vap vapor
and islands. This is mainly because of the high cost of fossil fuels, the difficulties to obtain it taking account with their progressive scarcity, the attempts to preserve it for future generations, while envisaging a contribution to the reduction of the atmospheric pollution related to the combustion rejects during the electrical energy generation [1]. Solar desalination methods are well suited for the arid and sunny regions of the world as in the Arabian Peninsula. In the desalination context, it is relevant to use the technologies which facilitate more efficient water in agriculture. The Seawater Greenhouse (SWGH) provides a perfect environment in which the transpiration loss from plants is minimized. At the same time, sufficient water for its own use is produced through a process of solar distillation [6]. Indeed, the projects of solar desalination have been demonstrated in several locations around the world. The humidification-dehumidification method was used in a greenhousetype structure for desalination and for crop growth as a pilot plant at Al-Hail, Muscat, in the Sultanate of Oman [7,8]. Sablani et al. shown that the dimension of the greenhouse had the greatest overall effect on water production and energy consumption [21]. Among other parameters, cooling the condenser(s) of the SWGH has a direct impact
2.2.1. Heat transfer model Steam condensation occurs when its temperature is reduced below its saturation temperature at a given pressure. The presence of non-condensable gases (air) in the gas mixture leads to a significant reduction in the heat flow and during condensation. This is because of the formation non-condensable gases, bind to the wall film that will prevent the diffusion of vapor through the bulk liquid film [11]. Analysis of the kinetics of heat transfer for film condensation outside vertical tubes was originally treated for laminar film by Nusselt in 1916 [12]. In this work, the simulation of the condenser of the seawater greenhouse was done on the basis of a model that developed previously by Tahri et al. [9] at Al-Hail, Muscat. Data of dry bulb temperature of air together with its relative humidity are collected only at the inlet and the exit of the condenser of the seawater greenhouse. However, simulation of the operation of the condenser requires that the saturation temperature to be known at each tube of the condenser. Equations used in this work can be found in Sherwood and Comings [13]. Saturation temperature (Tsat) was calculated for the first and the last tube in the row of the condenser [10] according to Eq. (1): H sat −H C ¼− s T sat −T db hfg
ð1Þ
Cs is the mass humid heat (kJ/kg °C) [19] which was calculated according to Eq. (2): C s ¼ C pair þ H C pvap
ð2Þ
The temperature of seawater flowing inside the tubes of the condenser is only known at the entrance and exit of the condenser. In
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Fig. 1. Process schematic of one vertical tube of the condenser unit.
this work, parabolic interpolations were used to find the temperature of seawater at the entrance and the exit for each tube of the condenser by utilizing the information that are known at the entrance and the exit of the condenser. As a basis of calculation, the temperature of seawater at the entrance and the exit of intermediate tubes are unknown. To resolve this problem, linear profile of seawater temperature along the row of the condenser was adopted. The temperature at the entrance of each tube was calculated according to Eq. (3): T swin ðjÞ ¼
ðT swout ð16Þ−T swin ð1ÞÞ ðj−1Þ þ T swin ð1Þ 16
ð3Þ
However, this hypothesis was subsequently corrected by introducing a coefficient of weighting [17] that was used to adjust the value of the entrance seawater temperature for each tube. If the total number of tubes in the condenser is Ntot, then the total flow of condensate will be:
_ ctot ¼ m
NL X NT X
mij
ð4Þ
j¼1 i¼1
Moreover, it was considered that the outlet seawater temperature of one tube of the row (Tswout) was equal to the inlet seawater temperature (Tsin) of the next tube. Also, it was assumed known both the inner (TWin) and the outer wall (TWout) temperatures for the first
Table 1 Design parameters of the condenser unit [10]. Dimensions of condenser Thickness of vertical tube (δ) Height of vertical tube (L) Diameter of vertical tube (Dout) Number of longitudinal tubes (NL) Number of transverse tubes (NT) Total number of tubes (Ntot)
tube in the row of condenser. This value of TWout will be used in Eq. (9) to find out the heat flux (Q). The average heat transfer coefficient for a laminar film condensation over a vertical tube of height (L) was calculated [12] for each tube of the condenser according to Eq. (5): " have ¼ 0:943
#1 4
ð5Þ
According to Çengel [14], Rohsenow [15] showed that the cooling of a liquid below its saturation temperature can be accounted for ∗ , deby replacing hfg by the modified latent heat of vaporization hfg fined as
hfg ¼ hfg þ 0:68 C pL ðT sat −T Wout Þ
ð6Þ
In the presence of noncondensble gases (e.g., air), the average heat transfer coefficient for film condensation (have) was corrected (hvert) according to the graph of Sacadura [16] as shown in Eq. (7). According to Tahri et al. [12], correction is a function of the noncondensable gas mass fraction (X) hvert ¼ have f ðX Þ
ð7Þ
X is the mass fraction of the noncondensable gases (kg noncondensable gas/kg humid air) which was calculated for each tube according to Eq. (8): X¼
(15 × 19 × 0.8)m 200 μm 1.8 m 33 mm 16 302 4832
3
g ρL ðρL −ρv ÞkL hfg μ L ðT sat −T Wout ÞL
mNC 1 ¼ mtot 1 þ H
ð8Þ
Calculation of Q The heat flux (Q) in the film condensation was calculated for the first tube according to Eq. (9): Q ¼ hvert Aout ðT sat −T Wout Þ
ð9Þ
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Calculation of hin The inner heat transfer coefficient hin was calculated [10] according to Eq. (10): hin ¼
Nu ksw Din
ð10Þ
Calculation of (TWout)cal The outer wall temperature (TWout)cal was then calculated for the first tube [14] according to Eq. (11): Q ¼ 2 π L ktub
ðT Wout Þcal −ðT Win Þ ln DDout
ð11Þ
in
Calculation of (TWin)cal The inner wall temperature (TWin)cal was then calculated for the first tube [10] according to Eq. (12): Q ¼ hin Ain
ðT Win Þcal −T swin − ðT Win Þcal −T swout ððT Þ −T Þ ln ðT WinÞ cal−T swin ð Win cal swout Þ
ð12Þ
Firstly, the values of (TWout)cal and (TWin)cal are calculated from Eqs. (11) to (12) respectively. Their values were compared with the guessed initial values of TWout and TWin. If the difference between the compared values does not verify a criterion of convergence, the values of (TWout)cal and (TWin)cal will be again used in Eqs. (5) and (11) to calculate the new values of (TWout)cal and (TWin)cal. The process was repeated until the values of (TWout)cal and (TWin)cal with successive trials did not change. The mass flux of condensate for the first tube was determined by Eq. (13): _ c1 ¼ m
hvert Aout ðT sat −T Wout Þ hfg
ð13Þ
The heat flux transferred from humid air to seawater (Qsw) was calculated in the first tube according to Eq. (14): 2
Q sw ¼ ρsw usw C P sw π
ðDin Þ ðT swout −T swin Þ 4
ð14Þ
The enthalpy of air (Hair) was calculated at the entrance of the first tube according to Eq. (15): ðH air Þin ¼ C Pair
0 T db þ H C Pvap T db þ hfg
ð15Þ
The heat flux of air (Qair) was calculated at the entrance of the first tube according to Eq. (16): _ air ðQ air Þin ¼ ðHair Þin m
ð16Þ
The heat flux of air (Qair) was calculated at the outlet of the first tube according to Eq. (17): ðQ air Þout ¼ ðQ air Þin −Q−Q sw
ð17Þ
The humidity of air (H) at the dry bulb temperature was calculated at the outlet of the first tube according to Eq. (18): _ c1 m H out ¼ Hin − _ air m
ð18Þ
155
The dry bulb temperature Tdb was calculated at the outlet of the first tube according to Eq. (19):
T dbout ¼
ðQ air Þout _ air − m
Hout h0fg
C Pair þ H out C Pvap
ð19Þ
The calculated humidity of air (Hout)cal from Eq. (18) and dry bulb temperature (Tdbout)cal from Eq. (19) in outlet first tube were used in Eq. (1) to set the saturation temperature (Tsat) of the second tube in the row of the condenser. Simulation of the condenser operation required that the saturation temperature to be known at each tube in the condenser. For this purpose, Eqs. (1)–(19) were repeated for _ c1tot Þcal from each tube. Next, the total mass flow calculated ðm _ ctot Þm Eq. (4) was compared with the measured total mass flow ðm on the day of 25 December 2005. If the model was not valid, then new values were proposed for the coefficients of weighting of parabolic interpolation for seawater temperature at different tubes in the condenser [17]. The trial was repeated until the values of _ c1tot Þcal and ðm _ ctot Þm did not change with successive trials. ðm 2.2.2. Mass transfer model For this model, Eqs. (1)–(12) were repeated for the first tube to defined (Tsat) and (TWout). The Reynolds analogy is very useful relation, and it is certainly desirable to extend it to a wider range of Pr and Sc number. Several attempts were done in this regards, but the simplest and the best know was the one suggested by Chilton and Colburn in 1934 as [18]: f 2=3 2=3 ¼ StPr ¼ St mass Sc 2
ð20Þ
For 0.6 b Pr > 60 and 0.6 b Sc > 3000. This equation is known as the Chilton–Colburn analogy. Using the definition of heat and mass Stanton numbers, the analogy between heat and mass transfer was expressed more conveniently as: 2=3 hvert Sc ¼ ρair C pair Pr hmass
ð21Þ
For air-vapor mixtures at 298 K, the mass and thermal diffusivities were D = 2.5 10 −5 m 2/s and α = 2.18 10 −5 m 2/s, respectively. Hence, Lewis number was calculated from Eq. (22): Le ¼
α ¼ 0:872 D
ð22Þ
Next, (α/D)2/3 = 0.872 2/3 was calculated as 0.913, where the value was close to unity. The Lewis number was relatively insensitive to variations in temperature. Therefore, for air–water vapor mixture, the relation between heat and mass transfer coefficients was expressed with a good accuracy as: hmass ≅
hvert ρair C pair
ð23Þ
where ρair and Cpair are the density and specific heat of air at film temperature. The film temperature (Tfilm) was given by [14] according to Eq. (24): T film ¼
T db þ T Wout 2
ð24Þ
The condensate rate of fresh water produced for the first tube was calculated by the following relation: _ c2 ¼ hmass π Dout L ρvapdb −ρvapWout m
ð25Þ
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T. Tahri et al. / Desalination 317 (2013) 152–159
Fig. 2. Comparison of the diurnal measured and calculated mass condensate rate of condenser.
where ρvapdb and ρvapWout are the density of vapor at dry bulb and external wall temperature which were calculated by Eq. (26), according to [20]: ρsat ðT Þ ¼
2910 expð9:48654−3892:7=ðT−42:6776ÞÞ 8314 T
ð26Þ
Where ρvapdb ¼ ρsat T vapdb ρvapWout ¼ ρsat T vapWout
_ c2tot Þcal from Eq. (4) which is compared with the meacalculated ðm _ ctot Þm on the day of 25 December 2005. If sured total mass flow ðm the model is not valid, then new values are proposed for the coefficients of weighting of parabolic interpolation for seawater temperature at different tubes in the condenser [17]. The trial calculation is _ c2tot Þcal and ðm _ ctot Þm don’t change. repeated until the values of ðm 3. Results and discussion
ð27Þ
3.1. Comparison between the measured and predicted mass condensate rate
The simulation of the condenser operation requires that the saturation temperature to be known at each tube in the condenser. To this end and knowing the dry air properties (Hdry, Tdb), we use the Eq. (1) to determinate it for each tube. For all the tubes, the total mass flow
Fig. 2 illustrates the calculated and measured mass condensate rates according to the hours of a one day period. It can be seen that there was a time gap between the calculated [9] and the measured condensate rates. This gap was attributed to the tipping bucket
Fig. 3. Comparison of the diurnal mass condensate rate and the solar radiation inside the SWGH.
T. Tahri et al. / Desalination 317 (2013) 152–159
157
Fig. 4. Comparison of the diurnal mass condensate rate and the inlet dry bulb temperature in the condenser.
gauge which did not register outflow from the condenser due to the low production rate of condensate. Formation of the water droplets on the tubes of the condensers were observed, but only a small fraction of the droplets made their way to the gutter collecting the condensate. It should be noted that the measured condensate mass rates were taken from the freshwater tank by the tipping bucket gauge, whereas the predicted condensate mass rates were calculated directly as droplets formed at the outer surface of the tubes of the condenser [9]. Therefore it was observed that the trend of the predicted and the measured mass condensate rates were close, a gap was clearly seen between them. The trend of the predicted mass condensate rates calculated in this work by mass model was much closer to the measured condensate rates than that calculated by heat model.
3.2. Impact of the meteorological variables on mass condensate rates Fig. 3 shows the variation of the measured and predicted mass condensate rates together with solar radiation values of a one day period. It can be seen that the solar radiation values were observed only during the interval from 08:00 to 18:00 and it was zero during the night time. Hence, the trend of the calculated and measured mass condensate rates went hand-in-hand with solar radiation. Fig. 4 shows the diurnal variation of the measured mass condensate rate, the predicted mass condensate rate and the dry bulb temperature for one day period. It can be noted that the two plots of the measured and predicted mass condensate rates follow the same trend of the diurnal variations of dry bulb temperature. We note that its shapes are typically Gaussian which reach its maximum at
Fig. 5. Comparison of the diurnal mass condensate rate and inlet relative humidity in the condenser.
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T. Tahri et al. / Desalination 317 (2013) 152–159
Fig. 6. Comparison of the diurnal mass condensate rate and the inlet seawater temperature in the condenser.
12 h 00. In any rigor, we mention that the mass condensate rate is strongly influenced by the pinch of temperature (Tsat–Tdb) according to Eq. (1). For a condenser, where the condensation of vapor place inside the tubes bank immersed in a tank, filled by seawater [20], the results of the operating analysis show that the trends of Tdb, and _ ctot Þcal versus the time confirm the results obtained by the model ðm developed within the framework of this work. Indeed, the maximum values are also reached at 12 h 00. Fig. 5 depicts the diurnal variation of the measured mass condensate rate, the predicted mass condensate rate and the relative humidity of a one day period. It can be seen that the relative humidity values were high (100%) between 08:00 and 14:00, while their lower values (RH = 65%) were seen during the rest of the day. It should be noted that in the interval extended from 08:00 to 14:00, the seawater greenhouse produce 98% of the total daily freshwater. This result is in perfect agreement with the conditions of condensation of the water vapor which require a preliminary saturation of the air
(100%). However, the tiny quantities of condensate appear beyond 14:00 where the air is unsaturated. Fig. 6 depicts the variation of the measured and predicted mass condensate rates together with the inlet seawater temperature values to condenser for one day period. It shows that the condensation of steam in the condenser happened between 08:00 and 18:00 with an average temperature of cold fluid (seawater) below 20 °C. The quantity of the condensate is the consequence of the interference of the installation operating parameters so that it is impossible to obtain an obvious conclusion for a variation of the inlet seawater temperature in such a restricted interval (20 to 24 °C) which is an exterior uncontrollable parameter, dictated by ambient condition. Fig. 7 depicts the diurnal variation of the measured mass condensate rate, the predicted mass condensate rate and the air speed values of a one day period. In our experiences, the air speed is selected according to the degree of saturation of the air in order to favorite the mass transfer. From previous results, these selected air speeds
Fig. 7. Comparison of the diurnal mass condensate rate and air speed inside the SWGH.
T. Tahri et al. / Desalination 317 (2013) 152–159
are maximum within the interval time 09:00 to 17:00. We see that the measured and predicted mass condensate rates went hand-inhand with the air speed values inside SWGH whereas the seawater greenhouse produced 98% of the total daily freshwater during this period when air speed was maximum (7 m/s). 4. Conclusions This paper discussed the modeling of the heat and mass exchange in the condenser of a seawater greenhouse (SWGH) at Al Hail in Muscat, Oman. In this work, two theoretical models were developed in order to describe the process of condensation by using model of heat and mass transfer equations. A comparison was made between the mass condensate rates values calculated by the two models. The predicted values were also compared with that of the measured values. The trend of the predicted mass condensate rates calculated by mass model in this work was found much closer to the measured mass condensate rates. The results indicated that the comparison was more consistent with the mass model used in this work. The effect of solar radiation, relative humidity, dry bulb temperature, seawater temperature, and air speed was also discussed to see their effects on the condensate. Acknowledgments The first author would like to acknowledge the valuable assistance of his advisors: Prof. Dr. Sabah Ahmed Abdul-Wahab, (College of Engineering, Sultan Qaboos University) and Prof. Dr Bettahar Ahmed (College of Engineering, Chlef University). The first author would like also to thank Dr. Douani Mustapha (College of Engineering, Chlef University) for his assistance in describing the models. References [1] H.M. Qiblawey, F. Banat, Solar thermal desalination technologies, Desalination 220 (2008) 633–644. [2] C. Paton, P. Davies, The seawater greenhouse cooling, fresh water and fresh produce from seawater, The 2nd International Conference on Water Resources in Arid Environments, Riyadh, 2006.
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