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Enhanced solar still performance using a radiative cooling system
Renewable Energy 21 (2000) 459±469 www.elsevier.com/locate/renene
Enhanced solar still performance using a radiative cooling system O.M. Haddad*, M.A. Al-Nimr, A. Maqableh Mechanical Engineering Department, Jordan University of Science and Technology, P.O. Box 3030, Irbid, Jordan Received 20 October 1999; accepted 6 March 2000
Abstract A basin type solar still is integrated with a packed bed storage tank which is used as an external condenser for the still. The packed bed condenser is cooled during the night using a radiative cooling panel by circulating pure water into the packed bed condenser and the radiative cooling panel. At the end of the cooling process, the packed bed tank attains low temperature, which is very close to the eective sky temperature. At the begining of daylight, the vapor produced by the solar still is sucked naturally by the packed bed condenser and condenses within it. A mathematical model describing the behavior of the modi®ed still is proposed. The eects of dierent designs, climate and operating parameters on the still performance are investigated. 7 2000 Elsevier Science Ltd. All rights reserved.
1. Introduction Solar distillation represents one of the oldest techniques for the production of fresh water from brackish or saline water. Numerous eorts have been made to enhance the system eciency so that the distillate output is obtained at a reasonable cost and utilizes a minimum amount of land surface. These eorts involve the use of active solar distillation, in which the basin of the solar still is integrated with a panel of collectors through heat exchangers [1], enhancing the
* Corresponding author. 0960-1481/00/$ - see front matter 7 2000 Elsevier Science Ltd. All rights reserved. PII: S 0 9 6 0 - 1 4 8 1 ( 0 0 ) 0 0 0 7 9 - 3
460
O.M. Haddad et al. / Renewable Energy 21 (2000) 459±469
Nomenclature A c G h hfg m m' m_ e me PT Px qxÿy qe t td T Ta Ti Tsky a e r s
surface area (m2) speci®c heat capacity (J kgÿ1 Kÿ1) instantaneous solar radiation normal to glass cover (W mÿ2) convective heat transfer coecient (W mÿ2 8Cÿ1). latent heat of condensation (J kgÿ1) mass of the rock in the packed bed tank (kg) mass of water per unit basin area (kg mÿ2) instantaneous distillate output per unit basin area (kg mÿ2s ÿ1) accumulated distillate output per unit basin area; during a given period of time, a certain period of time (kg mÿ2) total pressure (Pa) water vapor partial pressure at temperature x (Pa) heat ¯ux from x to y (W mÿ2) heat ¯ux due to evaporation (W mÿ2) time (s) number of hours of the daylight (h) temperature (K) ambient temperature (K) temperature of the packed bed condenser at the end of the charging process (K) eective sky temperature (K) absorption coecient emissivity density (kg mÿ3) Stefan±Boltzmann constant (W mÿ2 Kÿ4)
Subscripts a ambient b basin c convection mode of heat transfer g glass cover r radiation mode of heat transfer t packed bed storage tank
solar still performance by cooling the glass cover with water ®lm [2], using thermal-electrical solar still in which the water vapor is removed from the basin by a low power fan and then passing the vapor through external condenser [3]. Other techniques involve the use of double basin solar still [4], upward-type double eect solar distillers [5], double basin solar still integrated with collectors [6], solar still with an internal condenser [7], multi-eect active distillation system [8] and using solar still with dye [9]. Malik et al. [10] have presented a
O.M. Haddad et al. / Renewable Energy 21 (2000) 459±469
461
comprehensive review of other types of solar stills, such as the tilted wick type still, tilted tray inclined stepped stills and wiping spherical stills, etc . . . It is well known that enhancing the performance of the solar still may be achieved by reducing the thermal losses from the still. These losses are: (i) conduction losses from the base, side and edges; (ii) leakage of water vapor; and (iii) convective and radiative losses from the glass cover to the ambient. The rate of evaporation of water from the basin depends on the temperature dierence between the water surface and glass cover and also on the presence of saturated water vapor in the space between the glass cover and the water base. As warm humidi®ed air rises, it comes into contact with the relatively cool inner surface of the glass cover above the water surface where it condenses. The latent heat of condensation of vapor on the inner surface of the glass raises the temperature of the glass cover, which in turn reduces the temperature dierence between the water and the glass cover and consequently decreases the still productivity and still eciency. In the present work, a radiative cooling system is integrated with the still to improve the still performance. The radiative cooling system consists of radiative cooling panel and packed bed storage tank. The radiative cooling panel is used to utilize the cold eective sky temperature, which is normaly 10±258C lower than the ambient temperature. Cooling is achieved by circulating the working ¯uid within the packed bed storage tank and the radiative cooling panel during night. As a result of this circulation, the cold ¯uid exiting the radiative panel charges the rock domain within the packed bed storage tank with coldness. This process continues during night untill the tank attains the lowest possible temperature, which is very near to the eective sky temperature, provided that the radiative cooling panel area is large enough. At the begining of the daylight, water is evacuated from the packed bed tank and it is used as a condenser to condense the vapor produced by the still. The sizes of the radiative panel, storage tank and solar still are designed in such a way that the storage tank is able to condense all of the vapor produced by the still during the daylight. The packed bed tank is installed at a higher level than the solar still level and is connected to the still by a vertical duct. The buoyancy eect and the reduced back pressure, created in the condenser due to vapor condensation, are the driving forces which are sucking the vapor from the still. As a result, no external driving force is required in the proposed system. The levels of temperatures attained in the packed bed condenser are much lower than that attained in the conventional condensers which utilize cold water from ambient conditions. The temperature dierence between the ambient and the eective sky temperature varies within the range of 15±258C. Also, the packed bed condenser is a direct heat exchanger which has better performance than the conventional indirect heat exchangers. In addition, the packed bed condenser provides much larger surface area for the vapor condensation than that provided by the conventional condenser. Using the above modi®ed still, ®ve goals can be achieved: (i) the temperature of the glass cover is reduced and as a result the thermal losses from the still through glass are reduced; (ii) the vapor pressure and temperature inside the still are
462
O.M. Haddad et al. / Renewable Energy 21 (2000) 459±469
reduced and as a result the thermal losses from the vapor are reduced; (iii) vapor leakage from the still is reduced; (iv) the vapor partial pressure inside the still is reduced and this enhances the evaporation rate from the still; (v) the low level of temperature in the packed bed condenser enhances the condensation rate inside the condenser. In the present work, a mathematical model is proposed to describe the performance of the modi®ed solar still. The model is solved numerically and the eects of dierent designs, climate and operational parameters on the performance of the modi®ed system are investigated. 2. Analysis Refering to Fig. 1, the modi®ed still consists of solar still, packed bed storage tank and radiative cooling panel. The theoretical model of the still is obtained by writing simple energy balance of glass, water and packed bed storage tank as: For the basin: Gta qr, bÿg qe, bÿt qe, bÿg qc, bÿg qc, bÿt qr, bÿt m 0 c b
@Tb @t
1
For the glass: qr, bÿg qe, bÿg qc, bÿg qc, gÿa qr, gÿa For the packed bed storage tank:
Fig. 1. Schematic diagram of the enhanced still.
2
O.M. Haddad et al. / Renewable Energy 21 (2000) 459±469
mct
@ Tt Ab qe, bÿt qc, bÿt @t
463
3
Eqs. (1)±(3) assume the following initial conditions: Tb 0 T a ,
Tt 0 Ti
4
In Eq. (1) the radiation between the basin and the tank qr, bÿt may be neglected and in Eq. (2) it is assumed that the glass thermal capacity is negligible. Also, in Eq. (4), it is assumed that the storage tank is charged with coldness during night and its temperature at the end of the charging process is Ti : The remaining terms in Eqs. (1)±(3) are given as: ÿ qr, bÿg 0:9s T 4b ÿ T 4g , qc, gÿa hc, gÿa Tg ÿ Ta , hc, gÿa 5:7 ÿ qr, gÿa eg s T 4g ÿ T 4a , qc, bÿg hc, bÿg Tb ÿ Tg ,
qc, bÿt hc, bÿt Tb ÿ Tt
At Ab
"
hc, bÿg
#0:333 Pb ÿ Pg Tb 0:884 Tb ÿ Tg , 2:65PT, 1 ÿ Pb ÿ
hc, bÿt
Pb ÿ Pt Tb 0:884 Tb ÿ Tt 2:65PT, 2 ÿ Pb
PT, 1 rair Rair
qe, bÿg
Tb Tg 2
0:333
Pb ,
PT, 2 rair Rair
Tb Tt 2
Pb
# " ÿ Pb ÿ Pg PT Mw hfg ÿ , hc, bÿg PT ÿ Pb PT ÿ Pg Mair cp, air
qe, bÿt
Pb ÿ Pt PT Mw hfg At hc, bÿt PT ÿ Pb PT ÿ Pt Ab Mair cp, air
and the still instantaneous yield of distilled water per unit basin surface area is given as: m_ e
qe, bÿg qe, bÿt hfg
5
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In Eq. (5), qe, bÿg may be neglected as compared to qe, bÿt : The performance of the conventional solar still may be considered as a special case of the modi®ed one. The conventional still is described by Eqs. (1) and (2) after dropping Eq. (3), and qe; bÿt , qc; bÿt and qr, bÿt from Eq. (1). Eqs. (1)±(3) are nonlinear coupled ®rst order ordinary dierential equations. These equations are solved numerically using the ®rst order accurate backward dierence formula. All terms in Eqs. (1)±(3), except @@Ttb and @@Ttc , are evaluated at the temperatures of the previous time step. The calculations are continued untill the end of the daylight. 3. Mechanism of work of the modi®ed still As shown in Fig. 1, the modi®ed still consists of basin still, packed bed storage tank and radiative cooling panel. The radiative cooling panel consists of two parallel plates. The upper surface of the upper plate should be a very good black emitter and the lower one is well insulated. The radiative cooling method is a method which utilizes the cold sky, which has low eective temperature, as a heat sink [11,12]. Radiative cooling of a given surface may be achieved if the emitted radiation from the surface exceeds the absorbed radiation. Enhancing the emitted radiation to the sky is achieved with a very good black body emitter, and under clean and clear weather conditions which improve the atmospheric transmissivity to long wave length (infrared) radiation [11,12]. On the other hand, the absorbed radiation is decreased if the cooling system operates with no imposed heat ¯ux and with no convective heat gain from the ambient. Convective heat gain is reduced with low ambient temperature and low wind speed. Also, heat gain by the radiator may be reduced by constructing an evacuated or stationary air gap over the black body emitter. This may be achieved by replacing the traditional glass cover by a polyethylene ®lm. Polyethylene has very high transmissivity for long wave length radiation and very low transmissivity for short wave length radiation which is the major part in the incident solar radiation. As a result, polyethylene ®lm has the role of reducing the thermal convective gain from the ambient without preventing the long wave thermal radiation losses to the sky. Also, polyethylene ®lm prevents the diuse and direct short wavelength radiation, emitted from the sun during daylight or re¯ected from the moon during night. The last goal is attained if the upper surface of the polyethylene cover is coated with a highly re¯ective material [11,12]. During night, pure water is circulated through the radiative panel and the packed bed tank. The circulation process continues until the packed bed tank is charged completely with coldness and this is achieved when the entire contents of the tank reach the lowest temperature Ti which is very close to the eective sky temperature. At the begining of the daylight, the packed bed storage tank is evacuated completely of water and the vapor produced by the still is passed through the packed bed condenser. The packed bed storage tank is a well insulated tank in which the bed is packed
O.M. Haddad et al. / Renewable Energy 21 (2000) 459±469
465
with high thermal capacity small rocks. Using small rocks provides a large surface area for the vapor condensation. At the bottom of the packed bed condenser, a small collecting tank is attached to collect the condensed pure water. 4. Results and discussion Our results here are based on the assumption that the instantaneous solar radiation varies sinusoidaly with time as: t G Gmax sin 2td where td is the number of hours of the daylight and Gmax is the maximum instantaneous solar radiation. In addition, the following reference values are assumed for the following parameters: Ta 303,
Tsky 273,
td 10,
Gmax 400,
Ti Tsky
Fig. 2 shows the transient instantaneous productivity of the still for dierent instantaneous maximum solar radiation constants. It is clear from this ®gure that
Fig. 2. Eect of maximum solar radiation intensity on the instantaneous condensation of water.
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O.M. Haddad et al. / Renewable Energy 21 (2000) 459±469
the response of the still is very slow at the begining of its work due to the thermal capacity of the still. At the begining of its work, the still stores part of the incident radiation within its structure. Also, it is clear that the productivity of the still is not zero at the begining of its work. The water in the still may evaporate at any temperature, provided that the basin temperature is larger than the saturation temperature corresponding to the vapor partial pressure. Also, it is clear from this ®gure that the still productivity increases by increasing the solar radiation, however, the still eciency decreases. As an example, by increasing Gmax from 200 to 1000 W m 2 (i.e. ®ve times the original value), leads to an increase in the still yield by only three times. This is due to the increase in the thermal losses of the still, which results from the increase in the still basin temperature. Also, as Gmax increases, it is clear that the still maximum productivity occurs at earlier times. As we mentioned above, the delay in the response of the still is due to its thermal capacity, which consumes part of the incident radiation at early stages of time. As the incident radiation increases, the still stores this part within a shorter period of time and this causes the advance in the time at which the still maximum productivity occurs. Also, this stored part will enhance the still productivity during the second half of the daylight, as shown in Fig. 2, as the solar radiation starts to decrease. The eect of Gmax on the transient accumulated condensation rate is shown in Fig. 3.
Fig. 3. Eect of maximum solar radiation intensity on the instantaneous condensation of water.
O.M. Haddad et al. / Renewable Energy 21 (2000) 459±469
467
The eect of ambient temperature on the accumulated productivity of the still is depicted in Fig. 4. Increasing the ambient temperature improves the still productivity. As ambient temperature increases, the thermal losses from the still to the surrounding decreases. As is clear from this ®gure, the eect of the ambient temperature on the still performance accumulates as time proceeds. Also, it is clear that the eect of the ambient temperature on the still performance is linear, since the thermal losses from the still are linearly proportional to the ambient temperature. In conventional solar stills, increasing ambient temperature may destroy the still performance because condensation on the inner surface of the glass cover decreases. In enhanced solar stills, condensation mainly occurs in the packed bed tank and it is not aected by increasing the ambient temperature. The eect of the eective sky temperature on the still performance is depicted in Fig. 5. It is clear from this ®gure that the eective sky temperature has no signi®cant eect on the still performance. In fact, the eective sky temperature varies within a very narrow range. Also, the eective sky temperature has only one direct eect on the still performance and this is represented by the initial
Fig. 4. Eect of ambient temperature on the accumulated condensation of water.
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O.M. Haddad et al. / Renewable Energy 21 (2000) 459±469
temperature of the packed bed condenser. However, if the condenser has enough cooling capacity, then the eect of the eective sky temperature is not signi®cant.
5. Conclusions In this study, the performance of a basin type solar still is enhanced by using a packed bed storage tank as an external condenser for the still. The packed bed storage tank is charged with coldness during night using a radiative cooling panel. A mathematical model describing the behavior of the modi®ed still is proposed. The eects of dierent designs, climate and operating parameters on the still performance are investigated. Some of these parameters are found to be the ambient temperature, the eective sky temperature, the incident solar radiation and the sizes of the solar still, the packed bed condenser and the radiative cooling panel relative to each other.
Fig. 5. Eect of eective sky temperature on the accumulated condensation of water.
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469
It is found that the still productivity increases by increasing the solar radiation, however, the still eciency decreases. Also, as Gmax increases, the still maximum productivity occurs at earlier times, while increasing the ambient temperature improves the still productivity. Finally, the eective sky temperature does not aect the still performance signi®cantly. References [1] Tiwari GN, Saxena P, Thakur K. Thermal analysis of active solar distillation system. Energy Convers Mgmt 1994;35(1):51±9. [2] Abu-Hijleh B. Enhanced solar still performance using water ®lm cooling of the glass cover. Desalination 1996;107:233±42. [3] Nijegorodov N, Jain P, Carlsson S. Thermal±electrical, high eciency solar stills. Renewable Energy 1994;4(1):123±7. [4] Yadav Y. Parametric studies on a double basin solar still. Int J Solar Energy 1994;16:137±50. [5] Yeh H, Chen Z. Energy balances for upward-type, double-eect solar distillers with air ¯ow through the second-eect unit. Energy 1994;19(6):619±26. [6] Yadav Y. Transient analysis of double basin solar still integrated with collector. Desalination 1989;71:151±64. [7] Ahmed ST. Study of single-eect solar still with an internal condenser. Solar and Wind Technology 1988;5(6):637±43. [8] Tiwari GN, Singh AK, Saxena P, Rai S. The performance of multi-eect active distillation system. Int J Solar Energy 1993;13:277±87. [9] Lawrence SA, Gupta SP, Tiwari GN. Experimental validation of thermal analysis of solar still with dye. Int J Solar Energy 1988;6:291±305. [10] Malik M, Tiwari G, Kumar A, Sodha M. Solar distillation. Oxford: Pergamon Press, 1982. [11] Al-Nimr MA, Tahat M, Al-Rashdan MA. night cold storage system enhanced by radiative cooling Ð a modi®ed Australian cooling system. Applied Thermal Engineering 1999;19:1013±26. [12] Argiriou A, Santamouris M, Balaras C, Jeter S. Potential of radiation cooling in southern europe. Int J Solar Energy 1993;13:189±96.
Enhanced solar still performance using a radiative cooling system O.M. Haddad*, M.A. Al-Nimr, A. Maqableh Mechanical Engineering Department, Jordan University of Science and Technology, P.O. Box 3030, Irbid, Jordan Received 20 October 1999; accepted 6 March 2000
Abstract A basin type solar still is integrated with a packed bed storage tank which is used as an external condenser for the still. The packed bed condenser is cooled during the night using a radiative cooling panel by circulating pure water into the packed bed condenser and the radiative cooling panel. At the end of the cooling process, the packed bed tank attains low temperature, which is very close to the eective sky temperature. At the begining of daylight, the vapor produced by the solar still is sucked naturally by the packed bed condenser and condenses within it. A mathematical model describing the behavior of the modi®ed still is proposed. The eects of dierent designs, climate and operating parameters on the still performance are investigated. 7 2000 Elsevier Science Ltd. All rights reserved.
1. Introduction Solar distillation represents one of the oldest techniques for the production of fresh water from brackish or saline water. Numerous eorts have been made to enhance the system eciency so that the distillate output is obtained at a reasonable cost and utilizes a minimum amount of land surface. These eorts involve the use of active solar distillation, in which the basin of the solar still is integrated with a panel of collectors through heat exchangers [1], enhancing the
* Corresponding author. 0960-1481/00/$ - see front matter 7 2000 Elsevier Science Ltd. All rights reserved. PII: S 0 9 6 0 - 1 4 8 1 ( 0 0 ) 0 0 0 7 9 - 3
460
O.M. Haddad et al. / Renewable Energy 21 (2000) 459±469
Nomenclature A c G h hfg m m' m_ e me PT Px qxÿy qe t td T Ta Ti Tsky a e r s
surface area (m2) speci®c heat capacity (J kgÿ1 Kÿ1) instantaneous solar radiation normal to glass cover (W mÿ2) convective heat transfer coecient (W mÿ2 8Cÿ1). latent heat of condensation (J kgÿ1) mass of the rock in the packed bed tank (kg) mass of water per unit basin area (kg mÿ2) instantaneous distillate output per unit basin area (kg mÿ2s ÿ1) accumulated distillate output per unit basin area; during a given period of time, a certain period of time (kg mÿ2) total pressure (Pa) water vapor partial pressure at temperature x (Pa) heat ¯ux from x to y (W mÿ2) heat ¯ux due to evaporation (W mÿ2) time (s) number of hours of the daylight (h) temperature (K) ambient temperature (K) temperature of the packed bed condenser at the end of the charging process (K) eective sky temperature (K) absorption coecient emissivity density (kg mÿ3) Stefan±Boltzmann constant (W mÿ2 Kÿ4)
Subscripts a ambient b basin c convection mode of heat transfer g glass cover r radiation mode of heat transfer t packed bed storage tank
solar still performance by cooling the glass cover with water ®lm [2], using thermal-electrical solar still in which the water vapor is removed from the basin by a low power fan and then passing the vapor through external condenser [3]. Other techniques involve the use of double basin solar still [4], upward-type double eect solar distillers [5], double basin solar still integrated with collectors [6], solar still with an internal condenser [7], multi-eect active distillation system [8] and using solar still with dye [9]. Malik et al. [10] have presented a
O.M. Haddad et al. / Renewable Energy 21 (2000) 459±469
461
comprehensive review of other types of solar stills, such as the tilted wick type still, tilted tray inclined stepped stills and wiping spherical stills, etc . . . It is well known that enhancing the performance of the solar still may be achieved by reducing the thermal losses from the still. These losses are: (i) conduction losses from the base, side and edges; (ii) leakage of water vapor; and (iii) convective and radiative losses from the glass cover to the ambient. The rate of evaporation of water from the basin depends on the temperature dierence between the water surface and glass cover and also on the presence of saturated water vapor in the space between the glass cover and the water base. As warm humidi®ed air rises, it comes into contact with the relatively cool inner surface of the glass cover above the water surface where it condenses. The latent heat of condensation of vapor on the inner surface of the glass raises the temperature of the glass cover, which in turn reduces the temperature dierence between the water and the glass cover and consequently decreases the still productivity and still eciency. In the present work, a radiative cooling system is integrated with the still to improve the still performance. The radiative cooling system consists of radiative cooling panel and packed bed storage tank. The radiative cooling panel is used to utilize the cold eective sky temperature, which is normaly 10±258C lower than the ambient temperature. Cooling is achieved by circulating the working ¯uid within the packed bed storage tank and the radiative cooling panel during night. As a result of this circulation, the cold ¯uid exiting the radiative panel charges the rock domain within the packed bed storage tank with coldness. This process continues during night untill the tank attains the lowest possible temperature, which is very near to the eective sky temperature, provided that the radiative cooling panel area is large enough. At the begining of the daylight, water is evacuated from the packed bed tank and it is used as a condenser to condense the vapor produced by the still. The sizes of the radiative panel, storage tank and solar still are designed in such a way that the storage tank is able to condense all of the vapor produced by the still during the daylight. The packed bed tank is installed at a higher level than the solar still level and is connected to the still by a vertical duct. The buoyancy eect and the reduced back pressure, created in the condenser due to vapor condensation, are the driving forces which are sucking the vapor from the still. As a result, no external driving force is required in the proposed system. The levels of temperatures attained in the packed bed condenser are much lower than that attained in the conventional condensers which utilize cold water from ambient conditions. The temperature dierence between the ambient and the eective sky temperature varies within the range of 15±258C. Also, the packed bed condenser is a direct heat exchanger which has better performance than the conventional indirect heat exchangers. In addition, the packed bed condenser provides much larger surface area for the vapor condensation than that provided by the conventional condenser. Using the above modi®ed still, ®ve goals can be achieved: (i) the temperature of the glass cover is reduced and as a result the thermal losses from the still through glass are reduced; (ii) the vapor pressure and temperature inside the still are
462
O.M. Haddad et al. / Renewable Energy 21 (2000) 459±469
reduced and as a result the thermal losses from the vapor are reduced; (iii) vapor leakage from the still is reduced; (iv) the vapor partial pressure inside the still is reduced and this enhances the evaporation rate from the still; (v) the low level of temperature in the packed bed condenser enhances the condensation rate inside the condenser. In the present work, a mathematical model is proposed to describe the performance of the modi®ed solar still. The model is solved numerically and the eects of dierent designs, climate and operational parameters on the performance of the modi®ed system are investigated. 2. Analysis Refering to Fig. 1, the modi®ed still consists of solar still, packed bed storage tank and radiative cooling panel. The theoretical model of the still is obtained by writing simple energy balance of glass, water and packed bed storage tank as: For the basin: Gta qr, bÿg qe, bÿt qe, bÿg qc, bÿg qc, bÿt qr, bÿt m 0 c b
@Tb @t
1
For the glass: qr, bÿg qe, bÿg qc, bÿg qc, gÿa qr, gÿa For the packed bed storage tank:
Fig. 1. Schematic diagram of the enhanced still.
2
O.M. Haddad et al. / Renewable Energy 21 (2000) 459±469
mct
@ Tt Ab qe, bÿt qc, bÿt @t
463
3
Eqs. (1)±(3) assume the following initial conditions: Tb 0 T a ,
Tt 0 Ti
4
In Eq. (1) the radiation between the basin and the tank qr, bÿt may be neglected and in Eq. (2) it is assumed that the glass thermal capacity is negligible. Also, in Eq. (4), it is assumed that the storage tank is charged with coldness during night and its temperature at the end of the charging process is Ti : The remaining terms in Eqs. (1)±(3) are given as: ÿ qr, bÿg 0:9s T 4b ÿ T 4g , qc, gÿa hc, gÿa Tg ÿ Ta , hc, gÿa 5:7 ÿ qr, gÿa eg s T 4g ÿ T 4a , qc, bÿg hc, bÿg Tb ÿ Tg ,
qc, bÿt hc, bÿt Tb ÿ Tt
At Ab
"
hc, bÿg
#0:333 Pb ÿ Pg Tb 0:884 Tb ÿ Tg , 2:65PT, 1 ÿ Pb ÿ
hc, bÿt
Pb ÿ Pt Tb 0:884 Tb ÿ Tt 2:65PT, 2 ÿ Pb
PT, 1 rair Rair
qe, bÿg
Tb Tg 2
0:333
Pb ,
PT, 2 rair Rair
Tb Tt 2
Pb
# " ÿ Pb ÿ Pg PT Mw hfg ÿ , hc, bÿg PT ÿ Pb PT ÿ Pg Mair cp, air
qe, bÿt
Pb ÿ Pt PT Mw hfg At hc, bÿt PT ÿ Pb PT ÿ Pt Ab Mair cp, air
and the still instantaneous yield of distilled water per unit basin surface area is given as: m_ e
qe, bÿg qe, bÿt hfg
5
464
O.M. Haddad et al. / Renewable Energy 21 (2000) 459±469
In Eq. (5), qe, bÿg may be neglected as compared to qe, bÿt : The performance of the conventional solar still may be considered as a special case of the modi®ed one. The conventional still is described by Eqs. (1) and (2) after dropping Eq. (3), and qe; bÿt , qc; bÿt and qr, bÿt from Eq. (1). Eqs. (1)±(3) are nonlinear coupled ®rst order ordinary dierential equations. These equations are solved numerically using the ®rst order accurate backward dierence formula. All terms in Eqs. (1)±(3), except @@Ttb and @@Ttc , are evaluated at the temperatures of the previous time step. The calculations are continued untill the end of the daylight. 3. Mechanism of work of the modi®ed still As shown in Fig. 1, the modi®ed still consists of basin still, packed bed storage tank and radiative cooling panel. The radiative cooling panel consists of two parallel plates. The upper surface of the upper plate should be a very good black emitter and the lower one is well insulated. The radiative cooling method is a method which utilizes the cold sky, which has low eective temperature, as a heat sink [11,12]. Radiative cooling of a given surface may be achieved if the emitted radiation from the surface exceeds the absorbed radiation. Enhancing the emitted radiation to the sky is achieved with a very good black body emitter, and under clean and clear weather conditions which improve the atmospheric transmissivity to long wave length (infrared) radiation [11,12]. On the other hand, the absorbed radiation is decreased if the cooling system operates with no imposed heat ¯ux and with no convective heat gain from the ambient. Convective heat gain is reduced with low ambient temperature and low wind speed. Also, heat gain by the radiator may be reduced by constructing an evacuated or stationary air gap over the black body emitter. This may be achieved by replacing the traditional glass cover by a polyethylene ®lm. Polyethylene has very high transmissivity for long wave length radiation and very low transmissivity for short wave length radiation which is the major part in the incident solar radiation. As a result, polyethylene ®lm has the role of reducing the thermal convective gain from the ambient without preventing the long wave thermal radiation losses to the sky. Also, polyethylene ®lm prevents the diuse and direct short wavelength radiation, emitted from the sun during daylight or re¯ected from the moon during night. The last goal is attained if the upper surface of the polyethylene cover is coated with a highly re¯ective material [11,12]. During night, pure water is circulated through the radiative panel and the packed bed tank. The circulation process continues until the packed bed tank is charged completely with coldness and this is achieved when the entire contents of the tank reach the lowest temperature Ti which is very close to the eective sky temperature. At the begining of the daylight, the packed bed storage tank is evacuated completely of water and the vapor produced by the still is passed through the packed bed condenser. The packed bed storage tank is a well insulated tank in which the bed is packed
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with high thermal capacity small rocks. Using small rocks provides a large surface area for the vapor condensation. At the bottom of the packed bed condenser, a small collecting tank is attached to collect the condensed pure water. 4. Results and discussion Our results here are based on the assumption that the instantaneous solar radiation varies sinusoidaly with time as: t G Gmax sin 2td where td is the number of hours of the daylight and Gmax is the maximum instantaneous solar radiation. In addition, the following reference values are assumed for the following parameters: Ta 303,
Tsky 273,
td 10,
Gmax 400,
Ti Tsky
Fig. 2 shows the transient instantaneous productivity of the still for dierent instantaneous maximum solar radiation constants. It is clear from this ®gure that
Fig. 2. Eect of maximum solar radiation intensity on the instantaneous condensation of water.
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the response of the still is very slow at the begining of its work due to the thermal capacity of the still. At the begining of its work, the still stores part of the incident radiation within its structure. Also, it is clear that the productivity of the still is not zero at the begining of its work. The water in the still may evaporate at any temperature, provided that the basin temperature is larger than the saturation temperature corresponding to the vapor partial pressure. Also, it is clear from this ®gure that the still productivity increases by increasing the solar radiation, however, the still eciency decreases. As an example, by increasing Gmax from 200 to 1000 W m 2 (i.e. ®ve times the original value), leads to an increase in the still yield by only three times. This is due to the increase in the thermal losses of the still, which results from the increase in the still basin temperature. Also, as Gmax increases, it is clear that the still maximum productivity occurs at earlier times. As we mentioned above, the delay in the response of the still is due to its thermal capacity, which consumes part of the incident radiation at early stages of time. As the incident radiation increases, the still stores this part within a shorter period of time and this causes the advance in the time at which the still maximum productivity occurs. Also, this stored part will enhance the still productivity during the second half of the daylight, as shown in Fig. 2, as the solar radiation starts to decrease. The eect of Gmax on the transient accumulated condensation rate is shown in Fig. 3.
Fig. 3. Eect of maximum solar radiation intensity on the instantaneous condensation of water.
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The eect of ambient temperature on the accumulated productivity of the still is depicted in Fig. 4. Increasing the ambient temperature improves the still productivity. As ambient temperature increases, the thermal losses from the still to the surrounding decreases. As is clear from this ®gure, the eect of the ambient temperature on the still performance accumulates as time proceeds. Also, it is clear that the eect of the ambient temperature on the still performance is linear, since the thermal losses from the still are linearly proportional to the ambient temperature. In conventional solar stills, increasing ambient temperature may destroy the still performance because condensation on the inner surface of the glass cover decreases. In enhanced solar stills, condensation mainly occurs in the packed bed tank and it is not aected by increasing the ambient temperature. The eect of the eective sky temperature on the still performance is depicted in Fig. 5. It is clear from this ®gure that the eective sky temperature has no signi®cant eect on the still performance. In fact, the eective sky temperature varies within a very narrow range. Also, the eective sky temperature has only one direct eect on the still performance and this is represented by the initial
Fig. 4. Eect of ambient temperature on the accumulated condensation of water.
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temperature of the packed bed condenser. However, if the condenser has enough cooling capacity, then the eect of the eective sky temperature is not signi®cant.
5. Conclusions In this study, the performance of a basin type solar still is enhanced by using a packed bed storage tank as an external condenser for the still. The packed bed storage tank is charged with coldness during night using a radiative cooling panel. A mathematical model describing the behavior of the modi®ed still is proposed. The eects of dierent designs, climate and operating parameters on the still performance are investigated. Some of these parameters are found to be the ambient temperature, the eective sky temperature, the incident solar radiation and the sizes of the solar still, the packed bed condenser and the radiative cooling panel relative to each other.
Fig. 5. Eect of eective sky temperature on the accumulated condensation of water.
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It is found that the still productivity increases by increasing the solar radiation, however, the still eciency decreases. Also, as Gmax increases, the still maximum productivity occurs at earlier times, while increasing the ambient temperature improves the still productivity. Finally, the eective sky temperature does not aect the still performance signi®cantly. References [1] Tiwari GN, Saxena P, Thakur K. Thermal analysis of active solar distillation system. Energy Convers Mgmt 1994;35(1):51±9. [2] Abu-Hijleh B. Enhanced solar still performance using water ®lm cooling of the glass cover. Desalination 1996;107:233±42. [3] Nijegorodov N, Jain P, Carlsson S. Thermal±electrical, high eciency solar stills. Renewable Energy 1994;4(1):123±7. [4] Yadav Y. Parametric studies on a double basin solar still. Int J Solar Energy 1994;16:137±50. [5] Yeh H, Chen Z. Energy balances for upward-type, double-eect solar distillers with air ¯ow through the second-eect unit. Energy 1994;19(6):619±26. [6] Yadav Y. Transient analysis of double basin solar still integrated with collector. Desalination 1989;71:151±64. [7] Ahmed ST. Study of single-eect solar still with an internal condenser. Solar and Wind Technology 1988;5(6):637±43. [8] Tiwari GN, Singh AK, Saxena P, Rai S. The performance of multi-eect active distillation system. Int J Solar Energy 1993;13:277±87. [9] Lawrence SA, Gupta SP, Tiwari GN. Experimental validation of thermal analysis of solar still with dye. Int J Solar Energy 1988;6:291±305. [10] Malik M, Tiwari G, Kumar A, Sodha M. Solar distillation. Oxford: Pergamon Press, 1982. [11] Al-Nimr MA, Tahat M, Al-Rashdan MA. night cold storage system enhanced by radiative cooling Ð a modi®ed Australian cooling system. Applied Thermal Engineering 1999;19:1013±26. [12] Argiriou A, Santamouris M, Balaras C, Jeter S. Potential of radiation cooling in southern europe. Int J Solar Energy 1993;13:189±96.