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Increase in distillate productivity by inclining the flat plate external reflector of a tilted-wick solar still in winter
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Solar Energy 83 (2009) 785–789 www.elsevier.com/locate/solener
Brief Note
Increase in distillate productivity by inclining the flat plate external reflector of a tilted-wick solar still in winter Hiroshi Tanaka *, Yasuhito Nakatake Mechanical Engineering Department, Kurume National College of Technology, Komorino, Kurume, Fukuoka 830-8555, Japan Received 18 January 2007; received in revised form 25 November 2008; accepted 8 December 2008 Available online 27 December 2008 Communicated by: Associate Editor G.N. Tiwari
Abstract This paper presents a theoretical analysis of a tilted-wick solar still with an inclined flat plate external reflector on a winter solstice day at 30°N latitude. The daily amount of distillate of a still with an inclined reflector would be about 15% or 27% greater than that with a vertical reflector when the reflector’s length is a half of or the same as the still’s length. Ó 2008 Elsevier Ltd. All rights reserved. Keywords: Solar still; Solar distillation; Solar desalination; Tilted-wick; Reflector; Inclined
1. Introduction An external reflector can be a useful and inexpensive modification to increase the distillate productivity of single-effect stills. Single-effect stills with the external flat plate reflector have been studied for basin type stills (Malik et al., 1982; Al-Karaghouli and Minasian, 1995; El-Bahi and Inan, 1999) and tilted-wick stills (Al-Karaghouli and Minasian, 1995), but a detailed and quantitative analysis of the effect of the external reflector on both the basin type still and the tilted-wick still had not been presented. Therefore, we have added to this research by presenting a geometrical model for a basin type still (Tanaka and Nakatake, 2006) and a tilted-wick still (Tanaka and Nakatake, 2007b) to evaluate the effect of a vertical flat plate external reflector extending from the back wall of the still, on the solar radiation absorbed on the basin liner or the evaporating wick, as well as on the distillate productivity of both the stills. We found that a vertical flat plate external reflector can remarkably increase the distillate produc-
*
Corresponding author. Tel.: +81 942 359359; fax: +81 942 359321. E-mail address: [email protected] (H. Tanaka).
0038-092X/$ - see front matter Ó 2008 Elsevier Ltd. All rights reserved. doi:10.1016/j.solener.2008.12.001
tivity of both stills throughout the year except for during the summer season. In addition, during the winter season, the effect of the vertical reflector would be less than during spring and autumn, and further, the benefit of the external reflector would decrease with an increase in the inclination of the glass cover from horizontal, and when the glass cover inclination exceeded about 35°, the benefit of the vertical external reflector would be negligible for both the stills. This is because the solar altitude angle deceases in winter and most of the reflected sunrays from the vertical reflector could not hit the basin liner or the evaporating wick and would escape to the ground. As mentioned above, the arrangement of the external flat plate reflector has to be changed from vertical in the summer and winter seasons for both types of stills. During the winter season, the external reflector, which is inclined slightly forward, would be able to make the reflected radiation hit the basin liner or the evaporating wick even when the solar altitude angle is small. Therefore, we have presented an additional analysis for the basin type still to calculate the solar radiation reflected from the inclined external reflector and then absorbed on the basin liner (Tanaka and Nakatake, 2007a). We found that the inclined
786
H. Tanaka, Y. Nakatake / Solar Energy 83 (2009) 785–789
Nomenclature Gdr
Direct solar radiation on a horizontal surface, W m2 Length of reflector, m Length of still, m Rate of absorption of reflected solar radiation, W Width of still and reflector, m Absorptance of wick Incident angle of sunrays to glass cover, °
lm ls Qsun,re w aw b
external reflector can increase the distillate productivity of the still at any inclination of the glass cover. The external reflector inclination should be set at about 15° from vertical. This would produce approximately a 16% increase in distillate over a basin type still with a vertical reflector when the reflector was half as long as the basin liner. The geometrical model to predict the effect of inclining an external flat plate reflector on a basin type still described in our previous paper (Tanaka and Nakatake, 2007a) differs significantly from one with a vertical reflector (Tanaka and Nakatake, 2006), and is more complicated. For the tilted-wick still, the geometrical model for the inclined external reflector would also be more complicated than one with a vertical reflector (Tanaka and Nakatake, 2007b), but the geometrical model for the inclined reflector of basin type still can be easily applied to the tilted-wick still with some modifications. In this paper, we numerically
Inclined flat plate reflector
θm
Solar radiation
Feeding saline water
Evaporating wick Glass cover
Insulation
Distilled water Brine to waste
θs
Fig. 1. Schematic diagram of a tilted-wick still with an inclined flat plate external reflector.
u, / u0 , / 0 c hm hs qm sg
Azimuth and altitude angle of the sun, ° Azimuth and altitude angle of reflected radiation from reflector, ° Azimuth angle of still, ° Inclination of reflector from vertical, ° Inclination of still from horizontal, ° Reflectance of reflector Transmittance of glass cover
analyze the effect of the inclination of the external reflector on the distillate productivity of a tilted-wick still on a winter solstice day at 30°N latitude. The analysis includes the effect of the tilt inclination of the still and the length of the external reflector. 2. Solar radiation absorbed on the evaporating wick of a tilted-wick still with an inclined flat plate external reflector The proposed still is shown in Fig. 1. The still consists of an evaporating wick, a glass cover and an inclined flat plate reflector of highly reflective materials such as a mirror-finished metal plate extending from the back wall of the still. Direct and diffuse solar radiation and also the reflected solar radiation from the reflector are transmitted through the glass cover and then absorbed on the wick. To simplify the following calculations to determine the absorption of solar radiation on the wick, the walls of the still are disregarded, since the height of the walls (10 mm) is negligible in relation to the still’s length (1 m) and width (1 m). In this calculation, the still is assumed to be facing due south to maximize the solar radiation on the wick. Fig. 2 shows a schematic diagram of the shadows of the still and the inclined reflector as well as the projection of the reflected sunrays from the inclined reflector on a horizontal surface caused by direct solar radiation. Here, the shadows of the glass cover and the evaporating wick would be exactly the same since the walls are disregarded as mentioned above. The way to determine the amount of absorption of direct and diffuse solar radiation onto the wick was described in our previous paper (Tanaka and Nakatake, 2007b). The shadow and reflected projection of the inclined reflector (ABFE) on a horizontal surface are shown as A00 B00 F00 E00 and A0 B0 F0 E0 , respectively. All of the reflected sunrays from the reflector cannot hit the wick, and some portion of the reflected sunrays would escape to the ground. Assuming that the radiation which has the same azimuth and altitude angle as the reflected radiation from
H. Tanaka, Y. Nakatake / Solar Energy 83 (2009) 785–789
787
Fig. 2. The shadow of the still and the shadow and reflected projection of the inclined reflector.
the reflector hits the whole surface of the still, the shadow of the still would be an area shown as A0 B0 CD. The portion of the reflected radiation from the reflector which would be absorbed on the wick can be determined as the overlapping area of the reflected projection of the reflector (A0 B0 F0 E0 ) and the shadow of the still (A0 B0 CD) shown as a trapezoid A0 B0 GE0 , and the residue shown as a triangle B0 F0 G would escape to the ground. Since the reflected radiation from the inclined reflector would be concentrated or diluted, the intensity of the reflected radiation from the inclined reflector on a horizontal surface can be determined as Gdr l4/l1. Therefore, the solar radiation reflected from the reflector and absorbed on the wick, Qsun,re, can be determined as l4 1 ð1Þ Qsun;re ¼ Gdr sg ðbÞqm aw l1 w ðl2 þ l3 Þ l1 2 The lengths of l1, l4 and l5 cannot be directly determined from Fig. 2. The way to determine these lengths was described in our previous paper in detail (Tanaka and Nakatake, 2007a). l1, l4 and l5 do not depend on the still’s length ls and inclination hs, but on the reflector’s length lm and inclination hm, and can be expressed as follows: l1 ¼ lm fcos hm tanðx3 2hm Þ þ sin hm g where x3 ¼ tan1 ðcosðu cÞ= tan /Þ cosðu cÞ l4 ¼ lm cos hm sin hm tan /
ð2Þ ð3Þ
Therefore, Qsun,re can be determined with lengths of l1 to l9 and angles of x1 to x3 shown in Fig. 2. When Qsun,re is calculated, there are three exceptions as follows: 1. When l7 > ls cos hs, Qsun,re would be zero. 2. When l1 + l7 > ls cos hs, Qsun,re may be expressed as l4 Qsun;re ¼ Gdr sg ðbÞqm aw ðls cos hs l7 Þ l 1 1 w ðls cos hs l7 Þðtan x1 þ tan x2 Þ 2
3. When the overlapping area of the reflected projection and the shadow forms a triangle, Qsun,re may be expressed as l4 1 sg ðbÞqm aw w2 l1 2 sinð90 x1 Þ sinð90 x2 Þ sinðx1 þ x2 Þ
Qsun;re ¼ Gdr
ð4Þ
ð6Þ
The details concerning these exceptions was also described in our previous paper (Tanaka and Nakatake, 2007a). The incident angle of reflected sunrays to the glass cover, b, can be expressed as (Japan Solar Energy Society, 1985) cos b ¼ sin /0 cos hs þ cos /0 sin hs cos u0 0
sin ju cj l5 ¼ lm cos hm tan /
ð5Þ
0
ð7Þ
where u and / are the azimuth and altitude angle of the reflected sunrays from the inclined external reflector, and can be expressed as
H. Tanaka, Y. Nakatake / Solar Energy 83 (2009) 785–789
/0 ¼ 90 ðx3 2hm Þ 0
u ¼ 180 x1
ð8Þ
5
ð9Þ
3. Heat and mass transfer in the still Heat and mass transfer in the still was described in our previous paper in detail (Tanaka and Nakatake, 2007b), and was basically the same in content as one by Elsayed (1983) and Tanaka et al. (2000). The equations for the respective solar radiation, the energy balance for the evaporating wick and the glass cover, and the equations of properties were solved together to find the solar radiation absorbed on the wick, temperatures in the still and the distillate production rate throughout the day. Temperatures of the wick and the glass cover were set to be equal to the ambient air temperature at just before sunrise as the initial conditions. The weather and design conditions are listed in Table 1. Here, the rate of brine discharge would be changed due to changed gravitational force caused by changing in inclination of the still. Sodha et al. (1981) presented a multiple wick still, which consists of several wicks and polyethylene sheets sandwiched between wicks, to flow saline water properly and keep good wettability of the wick. However, these problems would be able to be negligible if the cloth which is wettable enough such as cotton flannel would be used as an evaporating wick. 4. Results The variations of the daily amount of distillate from a still with a reflector inclination of hm when the still’s inclination hs is 10–40° are shown in Fig. 3. The daily amounts of distillate peaks at around hm = 15°, and an increase in the daily amounts of distillate achieved by inclining the reflector from hm = 0° to hm = 15° would about 3% and 18% at hs = 10° and 40°. The variations of the daily amount of distillate with the still’s inclination hs for NS (a still without an external reflector) and RS (a still with an external reflector) are shown in Fig. 4. The results of RS are shown as that of the reflector’s inclination hm = 0° and the reflector’s length is half of the still’s length (lm = 0.5ls), hm = 15° and lm = 0.5ls, and hm = 15° and lm = ls. Here, for RS with hm = 0°, even if the reflector’s length lm is more than
Daily amount of distillate, kg/m2day
788
4
θs=40o
35o
20o
15o 10o
3
2
1
0
0
5
10 15 20 Reflector inclination θm
25
30
Fig. 3. Daily amount of distillate from RS varying with the reflector inclination hm.
0.5ls, the daily amount of distillate cannot be increased at any inclination of the still hs, since the length of the overlapping area of the reflected projection of the reflector and the shadow of the still (shown as l1 + l7 in Fig. 2) is already more than the length of ls cos hs throughout the day even when lm = 0.5ls. The daily amount of distillate of each still increases with an increase in the still’s inclination hs, since the direct solar radiation absorbed on the wick increases with an increase in the still’s inclination hs for each still on a winter solstice day. The daily amount of distillate of RS with hm = 0° (a still with a vertical external reflector) is the same as that of NS when hs is larger than about 35°. This indicates that the benefit of a vertical flat plate external reflector would be less for a still with a larger value for hs and negligible for a still with hs > 35° on a winter solstice day. The daily amount of distillate produced by a tilted-wick still can be increased by inclining the reflector as well as increasing the length of the reflector. The daily amount of distillate from RS with an inclined reflector (hm = 15°) and lm = 0.5ls or lm = ls would be about 12% or 27% more than that of RS with a vertical reflector (hm = 0°) when hs = 20°, and about 18% or 26% more when hs = 40°.
Table 1 Design and weather conditions. w = 1 m, ls = 1 m, lm = 0.5 m, c = 0° (still is orienting due south) Diffusion gap between wick and glass cover = 10 mm Heat capacity of glass cover = 6.4 kJ/K aw = 0.9, qm = 0.85 sg(b) = 2.642 cos b 2.163 cos2 b 0.320 cos3 b + 0.719 cos4 b (Tanaka et al., 2000) Ambient air temperature = 20 °C Wind velocity = 1 m/s Thermal conductivity and thickness of bottom insulation = 0.04 W/mK and 50 mm Gdr: Bouguer’s equation with transmissivity of atmosphere is 0.7 and 30°N latitude (Japan Solar Energy Society, 1985)
H. Tanaka, Y. Nakatake / Solar Energy 83 (2009) 785–789
reflector extending from the back wall of the still on a winter solstice day at 30°N latitude, and the results of this work are summarized as follows:
6 o
Daily amount of distillate, kg/m2day
RS(θm=15 , lm=ls) 5
RS(θm=15o, lm=0.5ls)
(1) The inclined reflector can increase the distillate productivity of the still at any still’s inclination hs, and the reflector’s inclination hm should be set at about 15° from vertical. (2) The daily amount of distillate produced by a still with an inclined reflector is predicted to be about 15% or 27% more than one with a vertical reflector when the reflector’s length is a half of or the same as the still’s length, and this augmentation is almost the same as the results for a basin type still with an external reflector.
o
RS(θm=0 , lm=0.5ls)
4
NS
3
2
1
0
789
References 20
25
30
35
40
Inclination of the still θs Fig. 4. Daily amount of distillate from NS and RS varying with the inclination of the still hs.
For the basin type still, the augmentation of the daily amount of distillate achieved by inclining the external flat plate reflector on a winter solstice day (Tanaka and Nakatake, 2007a) was predicted to be almost the same as that of the tilted-wick still reported in this study. Therefore, inclining the external flat plate reflector in winter season is profitable for both of the typical single-effect stills: the basin type still and the tilted-wick still. 5. Conclusions We theoretically predicted the distillate productivity of a tilted-wick solar still with an inclined flat plate external
Al-Karaghouli, A.A., Minasian, A.N., 1995. A floating-wick type solar still. Renewable Energy 6–1, 77–79. El-Bahi, A., Inan, D., 1999. Analysis of a parallel double glass solar still with separate condenser. Renewable Energy 17, 509–521. Elsayed, M.M., 1983. Comparison of transient performance predictions of a solar-operated diffusion-type still with a roof-type still. Journal of Solar Energy Engineering, Transactions of the ASME 105, 23–28. Japan Solar Energy Society, 1985. Solar Energy Utilization Handbook, Onkodo Press, Tokyo, p. 2, 20. Malik, M.A.S., Tiwari, G.N., Kumar, A., Sodha, M.S., 1982. Solar Distillation. Pergamon Press Ltd., UK, p. 98. Sodha, M.S., Kumar, A., Tiwari, G.N., Tyagi, R.C., 1981. Simple multiple wick solar still: analysis and performance. Solar Energy 26, 127–131. Tanaka, H., Nosoko, T., Nagata, T., 2000. A highly productive basintype–multiple-effect coupled solar still. Desalination 130, 279–293. Tanaka, H., Nakatake, Y., 2006. Theoretical analysis of a basin type solar still with internal and external reflectors. Desalination 197, 205–216. Tanaka, H., Nakatake, Y., 2007a. Effect of inclination of external flat plate reflector of basin type still in winter. Solar Energy 81, 1035–1042. Tanaka, H., Nakatake, Y., 2007b. Improvement of the tilted wick solar still by using flat plate reflector. Desalination 216, 139–146.
Solar Energy 83 (2009) 785–789 www.elsevier.com/locate/solener
Brief Note
Increase in distillate productivity by inclining the flat plate external reflector of a tilted-wick solar still in winter Hiroshi Tanaka *, Yasuhito Nakatake Mechanical Engineering Department, Kurume National College of Technology, Komorino, Kurume, Fukuoka 830-8555, Japan Received 18 January 2007; received in revised form 25 November 2008; accepted 8 December 2008 Available online 27 December 2008 Communicated by: Associate Editor G.N. Tiwari
Abstract This paper presents a theoretical analysis of a tilted-wick solar still with an inclined flat plate external reflector on a winter solstice day at 30°N latitude. The daily amount of distillate of a still with an inclined reflector would be about 15% or 27% greater than that with a vertical reflector when the reflector’s length is a half of or the same as the still’s length. Ó 2008 Elsevier Ltd. All rights reserved. Keywords: Solar still; Solar distillation; Solar desalination; Tilted-wick; Reflector; Inclined
1. Introduction An external reflector can be a useful and inexpensive modification to increase the distillate productivity of single-effect stills. Single-effect stills with the external flat plate reflector have been studied for basin type stills (Malik et al., 1982; Al-Karaghouli and Minasian, 1995; El-Bahi and Inan, 1999) and tilted-wick stills (Al-Karaghouli and Minasian, 1995), but a detailed and quantitative analysis of the effect of the external reflector on both the basin type still and the tilted-wick still had not been presented. Therefore, we have added to this research by presenting a geometrical model for a basin type still (Tanaka and Nakatake, 2006) and a tilted-wick still (Tanaka and Nakatake, 2007b) to evaluate the effect of a vertical flat plate external reflector extending from the back wall of the still, on the solar radiation absorbed on the basin liner or the evaporating wick, as well as on the distillate productivity of both the stills. We found that a vertical flat plate external reflector can remarkably increase the distillate produc-
*
Corresponding author. Tel.: +81 942 359359; fax: +81 942 359321. E-mail address: [email protected] (H. Tanaka).
0038-092X/$ - see front matter Ó 2008 Elsevier Ltd. All rights reserved. doi:10.1016/j.solener.2008.12.001
tivity of both stills throughout the year except for during the summer season. In addition, during the winter season, the effect of the vertical reflector would be less than during spring and autumn, and further, the benefit of the external reflector would decrease with an increase in the inclination of the glass cover from horizontal, and when the glass cover inclination exceeded about 35°, the benefit of the vertical external reflector would be negligible for both the stills. This is because the solar altitude angle deceases in winter and most of the reflected sunrays from the vertical reflector could not hit the basin liner or the evaporating wick and would escape to the ground. As mentioned above, the arrangement of the external flat plate reflector has to be changed from vertical in the summer and winter seasons for both types of stills. During the winter season, the external reflector, which is inclined slightly forward, would be able to make the reflected radiation hit the basin liner or the evaporating wick even when the solar altitude angle is small. Therefore, we have presented an additional analysis for the basin type still to calculate the solar radiation reflected from the inclined external reflector and then absorbed on the basin liner (Tanaka and Nakatake, 2007a). We found that the inclined
786
H. Tanaka, Y. Nakatake / Solar Energy 83 (2009) 785–789
Nomenclature Gdr
Direct solar radiation on a horizontal surface, W m2 Length of reflector, m Length of still, m Rate of absorption of reflected solar radiation, W Width of still and reflector, m Absorptance of wick Incident angle of sunrays to glass cover, °
lm ls Qsun,re w aw b
external reflector can increase the distillate productivity of the still at any inclination of the glass cover. The external reflector inclination should be set at about 15° from vertical. This would produce approximately a 16% increase in distillate over a basin type still with a vertical reflector when the reflector was half as long as the basin liner. The geometrical model to predict the effect of inclining an external flat plate reflector on a basin type still described in our previous paper (Tanaka and Nakatake, 2007a) differs significantly from one with a vertical reflector (Tanaka and Nakatake, 2006), and is more complicated. For the tilted-wick still, the geometrical model for the inclined external reflector would also be more complicated than one with a vertical reflector (Tanaka and Nakatake, 2007b), but the geometrical model for the inclined reflector of basin type still can be easily applied to the tilted-wick still with some modifications. In this paper, we numerically
Inclined flat plate reflector
θm
Solar radiation
Feeding saline water
Evaporating wick Glass cover
Insulation
Distilled water Brine to waste
θs
Fig. 1. Schematic diagram of a tilted-wick still with an inclined flat plate external reflector.
u, / u0 , / 0 c hm hs qm sg
Azimuth and altitude angle of the sun, ° Azimuth and altitude angle of reflected radiation from reflector, ° Azimuth angle of still, ° Inclination of reflector from vertical, ° Inclination of still from horizontal, ° Reflectance of reflector Transmittance of glass cover
analyze the effect of the inclination of the external reflector on the distillate productivity of a tilted-wick still on a winter solstice day at 30°N latitude. The analysis includes the effect of the tilt inclination of the still and the length of the external reflector. 2. Solar radiation absorbed on the evaporating wick of a tilted-wick still with an inclined flat plate external reflector The proposed still is shown in Fig. 1. The still consists of an evaporating wick, a glass cover and an inclined flat plate reflector of highly reflective materials such as a mirror-finished metal plate extending from the back wall of the still. Direct and diffuse solar radiation and also the reflected solar radiation from the reflector are transmitted through the glass cover and then absorbed on the wick. To simplify the following calculations to determine the absorption of solar radiation on the wick, the walls of the still are disregarded, since the height of the walls (10 mm) is negligible in relation to the still’s length (1 m) and width (1 m). In this calculation, the still is assumed to be facing due south to maximize the solar radiation on the wick. Fig. 2 shows a schematic diagram of the shadows of the still and the inclined reflector as well as the projection of the reflected sunrays from the inclined reflector on a horizontal surface caused by direct solar radiation. Here, the shadows of the glass cover and the evaporating wick would be exactly the same since the walls are disregarded as mentioned above. The way to determine the amount of absorption of direct and diffuse solar radiation onto the wick was described in our previous paper (Tanaka and Nakatake, 2007b). The shadow and reflected projection of the inclined reflector (ABFE) on a horizontal surface are shown as A00 B00 F00 E00 and A0 B0 F0 E0 , respectively. All of the reflected sunrays from the reflector cannot hit the wick, and some portion of the reflected sunrays would escape to the ground. Assuming that the radiation which has the same azimuth and altitude angle as the reflected radiation from
H. Tanaka, Y. Nakatake / Solar Energy 83 (2009) 785–789
787
Fig. 2. The shadow of the still and the shadow and reflected projection of the inclined reflector.
the reflector hits the whole surface of the still, the shadow of the still would be an area shown as A0 B0 CD. The portion of the reflected radiation from the reflector which would be absorbed on the wick can be determined as the overlapping area of the reflected projection of the reflector (A0 B0 F0 E0 ) and the shadow of the still (A0 B0 CD) shown as a trapezoid A0 B0 GE0 , and the residue shown as a triangle B0 F0 G would escape to the ground. Since the reflected radiation from the inclined reflector would be concentrated or diluted, the intensity of the reflected radiation from the inclined reflector on a horizontal surface can be determined as Gdr l4/l1. Therefore, the solar radiation reflected from the reflector and absorbed on the wick, Qsun,re, can be determined as l4 1 ð1Þ Qsun;re ¼ Gdr sg ðbÞqm aw l1 w ðl2 þ l3 Þ l1 2 The lengths of l1, l4 and l5 cannot be directly determined from Fig. 2. The way to determine these lengths was described in our previous paper in detail (Tanaka and Nakatake, 2007a). l1, l4 and l5 do not depend on the still’s length ls and inclination hs, but on the reflector’s length lm and inclination hm, and can be expressed as follows: l1 ¼ lm fcos hm tanðx3 2hm Þ þ sin hm g where x3 ¼ tan1 ðcosðu cÞ= tan /Þ cosðu cÞ l4 ¼ lm cos hm sin hm tan /
ð2Þ ð3Þ
Therefore, Qsun,re can be determined with lengths of l1 to l9 and angles of x1 to x3 shown in Fig. 2. When Qsun,re is calculated, there are three exceptions as follows: 1. When l7 > ls cos hs, Qsun,re would be zero. 2. When l1 + l7 > ls cos hs, Qsun,re may be expressed as l4 Qsun;re ¼ Gdr sg ðbÞqm aw ðls cos hs l7 Þ l 1 1 w ðls cos hs l7 Þðtan x1 þ tan x2 Þ 2
3. When the overlapping area of the reflected projection and the shadow forms a triangle, Qsun,re may be expressed as l4 1 sg ðbÞqm aw w2 l1 2 sinð90 x1 Þ sinð90 x2 Þ sinðx1 þ x2 Þ
Qsun;re ¼ Gdr
ð4Þ
ð6Þ
The details concerning these exceptions was also described in our previous paper (Tanaka and Nakatake, 2007a). The incident angle of reflected sunrays to the glass cover, b, can be expressed as (Japan Solar Energy Society, 1985) cos b ¼ sin /0 cos hs þ cos /0 sin hs cos u0 0
sin ju cj l5 ¼ lm cos hm tan /
ð5Þ
0
ð7Þ
where u and / are the azimuth and altitude angle of the reflected sunrays from the inclined external reflector, and can be expressed as
H. Tanaka, Y. Nakatake / Solar Energy 83 (2009) 785–789
/0 ¼ 90 ðx3 2hm Þ 0
u ¼ 180 x1
ð8Þ
5
ð9Þ
3. Heat and mass transfer in the still Heat and mass transfer in the still was described in our previous paper in detail (Tanaka and Nakatake, 2007b), and was basically the same in content as one by Elsayed (1983) and Tanaka et al. (2000). The equations for the respective solar radiation, the energy balance for the evaporating wick and the glass cover, and the equations of properties were solved together to find the solar radiation absorbed on the wick, temperatures in the still and the distillate production rate throughout the day. Temperatures of the wick and the glass cover were set to be equal to the ambient air temperature at just before sunrise as the initial conditions. The weather and design conditions are listed in Table 1. Here, the rate of brine discharge would be changed due to changed gravitational force caused by changing in inclination of the still. Sodha et al. (1981) presented a multiple wick still, which consists of several wicks and polyethylene sheets sandwiched between wicks, to flow saline water properly and keep good wettability of the wick. However, these problems would be able to be negligible if the cloth which is wettable enough such as cotton flannel would be used as an evaporating wick. 4. Results The variations of the daily amount of distillate from a still with a reflector inclination of hm when the still’s inclination hs is 10–40° are shown in Fig. 3. The daily amounts of distillate peaks at around hm = 15°, and an increase in the daily amounts of distillate achieved by inclining the reflector from hm = 0° to hm = 15° would about 3% and 18% at hs = 10° and 40°. The variations of the daily amount of distillate with the still’s inclination hs for NS (a still without an external reflector) and RS (a still with an external reflector) are shown in Fig. 4. The results of RS are shown as that of the reflector’s inclination hm = 0° and the reflector’s length is half of the still’s length (lm = 0.5ls), hm = 15° and lm = 0.5ls, and hm = 15° and lm = ls. Here, for RS with hm = 0°, even if the reflector’s length lm is more than
Daily amount of distillate, kg/m2day
788
4
θs=40o
35o
20o
15o 10o
3
2
1
0
0
5
10 15 20 Reflector inclination θm
25
30
Fig. 3. Daily amount of distillate from RS varying with the reflector inclination hm.
0.5ls, the daily amount of distillate cannot be increased at any inclination of the still hs, since the length of the overlapping area of the reflected projection of the reflector and the shadow of the still (shown as l1 + l7 in Fig. 2) is already more than the length of ls cos hs throughout the day even when lm = 0.5ls. The daily amount of distillate of each still increases with an increase in the still’s inclination hs, since the direct solar radiation absorbed on the wick increases with an increase in the still’s inclination hs for each still on a winter solstice day. The daily amount of distillate of RS with hm = 0° (a still with a vertical external reflector) is the same as that of NS when hs is larger than about 35°. This indicates that the benefit of a vertical flat plate external reflector would be less for a still with a larger value for hs and negligible for a still with hs > 35° on a winter solstice day. The daily amount of distillate produced by a tilted-wick still can be increased by inclining the reflector as well as increasing the length of the reflector. The daily amount of distillate from RS with an inclined reflector (hm = 15°) and lm = 0.5ls or lm = ls would be about 12% or 27% more than that of RS with a vertical reflector (hm = 0°) when hs = 20°, and about 18% or 26% more when hs = 40°.
Table 1 Design and weather conditions. w = 1 m, ls = 1 m, lm = 0.5 m, c = 0° (still is orienting due south) Diffusion gap between wick and glass cover = 10 mm Heat capacity of glass cover = 6.4 kJ/K aw = 0.9, qm = 0.85 sg(b) = 2.642 cos b 2.163 cos2 b 0.320 cos3 b + 0.719 cos4 b (Tanaka et al., 2000) Ambient air temperature = 20 °C Wind velocity = 1 m/s Thermal conductivity and thickness of bottom insulation = 0.04 W/mK and 50 mm Gdr: Bouguer’s equation with transmissivity of atmosphere is 0.7 and 30°N latitude (Japan Solar Energy Society, 1985)
H. Tanaka, Y. Nakatake / Solar Energy 83 (2009) 785–789
reflector extending from the back wall of the still on a winter solstice day at 30°N latitude, and the results of this work are summarized as follows:
6 o
Daily amount of distillate, kg/m2day
RS(θm=15 , lm=ls) 5
RS(θm=15o, lm=0.5ls)
(1) The inclined reflector can increase the distillate productivity of the still at any still’s inclination hs, and the reflector’s inclination hm should be set at about 15° from vertical. (2) The daily amount of distillate produced by a still with an inclined reflector is predicted to be about 15% or 27% more than one with a vertical reflector when the reflector’s length is a half of or the same as the still’s length, and this augmentation is almost the same as the results for a basin type still with an external reflector.
o
RS(θm=0 , lm=0.5ls)
4
NS
3
2
1
0
789
References 20
25
30
35
40
Inclination of the still θs Fig. 4. Daily amount of distillate from NS and RS varying with the inclination of the still hs.
For the basin type still, the augmentation of the daily amount of distillate achieved by inclining the external flat plate reflector on a winter solstice day (Tanaka and Nakatake, 2007a) was predicted to be almost the same as that of the tilted-wick still reported in this study. Therefore, inclining the external flat plate reflector in winter season is profitable for both of the typical single-effect stills: the basin type still and the tilted-wick still. 5. Conclusions We theoretically predicted the distillate productivity of a tilted-wick solar still with an inclined flat plate external
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