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Effect of inclination of external flat plate reflector of basin type still in winter
Solar Energy 81 (2007) 1035–1042 www.elsevier.com/locate/solener
Effect of inclination of external flat plate reflector of basin type still in winter Hiroshi Tanaka *, Yasuhito Nakatake Mechanical Engineering Department, Kurume National College of Technology, Komorino, Kurume, Fukuoka 830-8555, Japan Received 1 June 2006; received in revised form 24 October 2006; accepted 28 November 2006 Available online 26 December 2006 Communicated by: Associate Editor Volker Wittwer
Abstract This paper presents a theoretical analysis of a basin type solar still with an internal reflector (two sides and back walls) and an inclined flat plate external reflector on a winter solstice day at 30 N latitude. We are proposing a new geometrical method for calculating the solar radiation reflected by the inclined external reflector and then absorbed on the basin liner. Using this method, we performed a numerical analysis of heat and mass transfer in the still in order to determine the effectiveness of the inclination of the external reflector. We found that the benefit of a vertical external reflector would be smaller or even negligible for a still with a larger value for the glass cover angle, while an inclined external reflector can increase the distillate productivity of the still at any glass cover angle, and the external reflector angle should be set at about 15 from vertical on a winter solstice day. The daily amount of distillate of the still with the inclined external reflector would be about 16% greater than that with the vertical external reflector, and about 2.3 times as large as that of the still with neither the internal nor the external reflector on a winter solstice day. 2006 Elsevier Ltd. All rights reserved. Keywords: Solar still; Solar distillation; Solar desalination; Basin type; Reflector; Inclined
1. Introduction For a basin type solar still, internal and external reflectors can be a useful and inexpensive modification to increase the solar radiation incident on the basin liner as well as the distillate productivity of the still, and many reports about the effect of internal reflectors (Tamimi, 1987; El-Swify and Metias, 2002; Tripathi and Tiwari, 2004; Al-Hayek and Badran, 2004; Tanaka and Nakatake, 2006) and external reflectors (Malik et al., 1982; El-Bahi and Inan, 1999; Tanaka and Nakatake, 2006) on the distillate productivity of basin type stills have been presented. El-Swify and Metias (2002) presented a useful geometrical method for calculating the solar radiation reflected by
*
Corresponding author. Tel.: +81 942 359359; fax: +81 942 359321. E-mail address: [email protected] (H. Tanaka).
0038-092X/$ - see front matter 2006 Elsevier Ltd. All rights reserved. doi:10.1016/j.solener.2006.11.006
the internal reflector (two sides and back walls) and then absorbed on the basin liner of the basin type still. Tripathi and Tiwari (2004) performed a numerical analysis by using AUTOCAD 2000 to determine the solar fraction of the basin type still. The solar fraction was defined as the ratio of the solar radiation absorbed on the back wall to that absorbed on the basin liner in addition to the back wall of the still. El-Swify and Metias (2002) and Tripathi and Tiwari (2004) indicated that an internal reflector can remarkably increase the distillate productivity of the basin type still. We have added to this research by presenting a geometrical method (Tanaka and Nakatake, 2006) to evaluate the effect of a vertical external flat plate reflector extending from the back wall of the still, in addition to the internal reflector, on the solar radiation absorbed on the basin liner as well as on the distillate productivity of the basin type still at 30 N latitude. We found that internal and
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Nomenclature Gdf, Gdr diffuse and direct solar radiation on a horizontal surface, (W m2) lm height of external reflector, m ls length of basin liner, m Qsun,df, Qsun,dr absorption of diffuse or direct solar radiation, W Qsun,ext, Qsun,int absorption of reflected solar radiation from external or internal reflector, W w width of basin liner and external reflector, m
external reflectors can remarkably increase the distillate productivity of the basin type still throughout the year except for during the summer season. In summer, the external reflector would shade the basin liner and the direct solar radiation absorbed on the basin liner would be decreased by the external reflector during the morning and the evening, since the sun moves north and the sunrays hit from north side during the morning and the evening in summer at 30 N latitude. In addition, during the winter season, the effect of the external reflector would be smaller than that of the internal reflector, and the benefit of the external reflector would be smaller for the still with a larger value for the angle of the glass cover, and when the glass cover angle is 40, the benefit of the external reflector would be negligible. This is because the solar altitude angle decreases in winter and a large portion of the reflected sunrays from the vertical reflector cannot hit the basin liner and would escape to the ground as shown in Fig. 1. On the other hand, reflected sunrays from the inclined external reflector would not escape to the ground and can be absorbed on the basin liner even when the solar altitude angle is small as shown in Fig. 1. As mentioned above, since the vertical flat plate external reflector presented in our previous paper cannot effectively reflect the solar radiation to the basin liner in summer and
Sunray
Reflected sunrays from vertical reflector from inclined reflector External reflector
Basin type still
Fig. 1. Reflected sunrays from vertical and inclined external reflectors of a basin type still.
absorptance of basin liner incident angle of sunrays to glass cover altitude and azimuth angle of the sun altitude and azimuth angle of reflected radiation from external reflector hg angle of glass cover from horizontal hm angle of external reflector from vertical qext, qint reflectance of external and internal reflector sg transmittance of glass cover
ab b /, u /0, u0
winter, the arrangement of the flat plate external reflector has to be changed from vertical in these seasons. In this paper, we present a new geometrical method to calculate the solar radiation reflected from an inclined external reflector and then absorbed on the basin liner. The geometrical method presented in this paper differs significantly from the one for the vertical reflector described in our previous paper (Tanaka and Nakatake, 2006) and is more complicated. We also numerically analyzed the effect of the inclination of the external reflector on the distillate productivity of a basin type still on a winter solstice day at 30 N latitude. 2. Solar radiation absorbed on the basin liner of a single-slope basin type still with internal reflector and inclined flat plate external reflector The proposed still is shown in Fig. 2. The still consists of a basin liner, a glass cover, two side walls, a back wall, and an inclined flat plate external reflector of highly reflective materials such as a mirror-finished metal plate extending from the back wall of the still. The two sides and back walls are assumed to be covered with highly reflective materials, so these walls serve as the internal reflector. Direct and diffuse solar radiation and also the reflected radiation from the internal and external reflectors are transmitted through the glass cover and then absorbed on the basin liner. To simplify the following calculations, it is assumed that the same amount of solar radiation obstructed by one side wall hits the other inner side wall since both inner side walls are assumed to be covered with highly reflective materials. This assumption would be valid especially if the still’s width is great enough in relation to the still’s length. Fig. 3 shows a schematic diagram of the shadows of the internal back wall reflector and the inclined external reflector as well as the projection of the reflected sunrays from the inclined external reflector on a horizontal surface caused by direct solar radiation. ls is the length of the basin liner (ABCD), lm is the height of the external reflector (EFGH), w is the width of both the basin liner and the external reflector, hg is the angle of the glass cover (EFCD) and hm is the angle from vertical of the inclined external reflector. u and / are the azimuth and altitude angle of
H. Tanaka, Y. Nakatake / Solar Energy 81 (2007) 1035–1042
1037
where b is the incident angle of the sunrays to the glass cover. The internal back wall reflector (ABFE) makes a shadow on a horizontal surface shown as ABF00 E00 , and the solar radiation reflected by the internal back wall reflector and absorbed on the basin liner, Qsun,int, can be determined as the product of the direct solar radiation on a horizontal surface, the shadow area of the back wall reflector (ABF00 E00 ), transmittance of the glass cover, reflectance of the back wall reflector, qint, and absorptance of the basin liner, and this may be expressed as cos u ð2Þ Qsun;int ¼ Gdr sg ðbÞqint ab wls tan hg tan / The shadow and reflected projection of the inclined external reflector (EFGH) on a horizontal surface are shown as E00 F00 G00 H00 and E 0 F 0 G 0 H 0 , respectively. All of the reflected sunrays from the external reflector cannot hit the basin liner, 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 sunrays from the inclined external reflector hits the whole surface of the glass cover, the shadow of the glass cover would be an area shown as E 0 F 0 CD. The portion of the reflected radiation from the external reflector which would be absorbed on the basin liner can be determined as the overlapping area of the reflected projection of the external reflector (E 0 F 0 G 0 H 0 ) and the shadow of the glass cover (E 0 F 0 CD) shown as a trapezoid E 0 F 0 KH 0 , and the residue shown as F 0 G 0 K would escape to the ground. Since the reflected radiation from the inclined reflector would be condensed or diluted (or the lengths of the shadow (l4) and reflected projection (l1) of the inclined external reflector
Fig. 2. Schematic diagram of a basin type still with internal reflector and an inclined flat plate external reflector.
the sun. In this calculation, the still is assumed to be facing due south to maximize the solar radiation on the basin liner. The direct solar radiation absorbed on the basin liner, Qsun,dr, can be determined as the product of the direct solar radiation on a horizontal surface, Gdr, the area of the basin liner, transmittance of the glass cover, sg(b), and absorptance of the basin liner, ab, and this may be expressed as Qsun;dr ¼ Gdr sg ðbÞab wls
ð1Þ
H Sun
Inclined external reflector
θm lm
G E
Internal back wall reflector
w
Sidewall reflector
θm I ϕ φ
F
E"
H"
A
ls θg
l5
E'
ω1
Basin liner ω1 = tan
−1 l5
l4
l ω2 = tan −1 6 ls − l7
F' K
C
ω2
ω1
G' l3=l1tanω2 l6=(l7+l9)tanω1 l2=l1tanω1
l7 l1
l4
F"
B
H'
D
ω1
J
l9
l8
G"
l8 = l s tan θ g
cos ϕ tan φ
l9=lstanθgtanθm l7 =
l1 (l8 − l9 ) − l9 l4
Fig. 3. The shadow of the internal back wall reflector and the shadow and reflected projection of the inclined external reflector.
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H. Tanaka, Y. Nakatake / Solar Energy 81 (2007) 1035–1042
would not be equal), the intensity of the reflected radiation from the inclined external reflector on a horizontal surface can be determined as Gdr · l4/l1. Therefore, the solar radiation reflected from the external reflector and absorbed on the basin liner, Qsun,ext, can be determined as the product of the intensity of the reflected radiation, Gdr · l4/l1, the overlapping area of the reflected projection of the external reflector and shadow of the glass cover shown as E 0 F 0 KH 0 , reflectance of the external reflector, qext, transmittance of the glass cover and absorptance of the basin liner, and this may be expressed as l4 1 ð3Þ Qsun;ext ¼ Gdr sg ðbÞqext ab l1 w ðl2 þ l3 Þ 2 l1 To calculate Eq. (3), the lengths of l1, l4 and l5 and the angles of x1 and x2 have to be determined. Therefore, isometric and side views of an inclined flat plate reflector (EFGH), which is directly placed on a horizontal surface, are shown in Figs. 4a and b. The shadow (EFG00 H00 ) and
Sun
Inclined reflector
H
l4 = lm cos θ m
ω1 ϕ
E
G
φ
ω1 = tan −1
H''
L
l5 l4 Shadow
ω1
l5 H' w
ω1
F
l10 G'
l1
l10 = lm cos θ m
Inclined reflector
Qsun;ext ¼ Gdr
l11=lmcosθm ω 3– θm
ω 3–θm
ω3 = tan −1 ω 3–2θm θm
θm
l10 cos ϕ = tan −1 l11 tan φ
M
lm
cos b ¼ sin / cos hg þ cos / sin hg cos u
F l10 = lm cos θ m
l4 1 sinð90 x1 Þsinð90 x2 Þ sg ðbÞqext ab w2 l1 2 sinðx1 þ x2 Þ ð8Þ
In Eqs. (1)–(3), (7) and (8), the incident angle of sunrays to the glass cover, b, can be expressed as (Japan Solar Energy Society, 1985) for Eqs. (1) and (2)
φ G’
ð7Þ 3. When the overlapping area of the reflected projection and the shadow forms a triangle E 0 F 0 K as shown in Fig. 5b, Qsun,ext may be expressed as
ω 3– θm
Reflected sunray
Therefore, Qsun,ext can be determined with a length of l1 to l11 and angles of x1 to x3 shown in Figs. 3 and 4. When Qsun,ext is calculated, there are three exceptions as follows:
cos ϕ tan φ
Sun G
By drawing an additional vertical line from point G to a horizontal surface (point M) to Fig. 4a, the lengths of l4 and l5 can be determined as follows: cos u sin hm l4 ¼ lm cos hm ð5Þ tan / sin juj ð6Þ l5 ¼ lm cos hm tan /
Qsun;ext ¼ Gdr
l4
lmsinθm
ð4Þ
l4 sg ðbÞqext ab l1 1 ðls l7 Þ w ðls l7 Þðtan x1 þ tan x2 Þ 2
G''
M Reflected projection
l1 ¼ lm fcos hm tanðx3 2hm Þ þ sin hm g
1. When the length of l7 is larger than the still’s length (ls), all of the reflected sunrays would escape to the ground and Qsun,ext would be zero. 2. When the reflected projection exceeds the still’s length (l1 + l7 > ls) as shown in Fig. 5a, the overlapping area of the reflected projection of the external reflector and the shadow of the glass cover would be a trapezoid shown as E 0 F 0 CK, and Qsun,ext may be expressed as
sin | ϕ | l5 = lm cos θ m tan φ
lm
θm
cos ϕ − sin θ m tan φ
the reflected projection (EFG 0 H 0 ) of the reflector on a horizontal surface shown in Fig. 4a would be in exact accordance with those shown as E00 F00 G00 H00 and E 0 F 0 G 0 H 0 in Fig. 3. Since the incident angle and reflected angle of the sunrays for the reflector would be the same as x3–hm shown as Fig. 4b, the length of the reflected projection of the inclined reflector, l1, can be determined as follows with the angle x3 (= tan1(cos u/tan/))
cos ϕ tan φ
ð9Þ
G''
lmcosθmtan(ω 3–2θm) l1=lm{cosθmtan(ω 3–2θm) +sinθm}
Fig. 4. (a) Isometric and (b) side views of an inclined reflector on a horizontal surface.
for Eqs. (3), (7) and (8) cos b ¼ sin /0 cos hg þ cos /0 sin hg cos u0
ð10Þ
where / 0 and u 0 are the altitude and azimuth angle of the reflected sunrays from the inclined external reflector, and can be expressed as
H. Tanaka, Y. Nakatake / Solar Energy 81 (2007) 1035–1042
a
A ls
l7
ls–l7
E'
D
the glass cover for diffuse radiation from all directions in the sky dome, and can be expressed as (Tanaka and Nakatake, 2006)
Overlapping area (Trapezoid) (ls–l7)(tanω1+tanω 2)
ðsg Þdf ¼ 2:03 105 h2g 2:05 103
B
hg þ 0:667; hg ½ l1
1039
ð14Þ
K F'
H'
3. Heat and mass transfer in the still
ω2 ω1
C
Heat and mass transfer in the still was described in our previous paper in detail (Tanaka and Nakatake, 2006), and was basically the same in content as one by Dunkle (1961). The equations of the solar radiations (Qsun,dr, Qsun,int, Qsun,ext and Qsun,df) and the energy balance for basin water and the glass cover, and the equations of properties were solved together to find the solar radiation absorbed on the basin liner as well as the distillate production rate throughout a day. Temperatures of the basin water and the glass cover were set to be equal to the ambient air temperature at just before sunrise, as the initial values. The weather and design conditions are listed in Table 1.
G'
b
A
D
Overlapping area (Triangle) B
E'
ω2
ω1 90–ω1
w
ω1+ω2 90–ω2
C
F'
K
4. Results
H'
G' Fig. 5. The overlapping area of the reflected projection of the external reflector and the shadow of the glass cover when the overlapping area is: (a) trapezoid and (b) triangle.
/0 ¼ 90 ðx3 2hm Þ u0 ¼ 180 x1
ð11Þ ð12Þ
Diffuse solar radiation absorbed on the basin liner, Qsun,df, can be determined with the assumption that diffuse radiation comes uniformly from all directions in the sky dome, and may be expressed as Qsun;df ¼ Gdf ðsg Þdf ab wls
ð13Þ
where Gdf is the diffuse solar radiation on a horizontal surface, and (sg)df is the function of the angle of the glass cover, hg. This can be calculated by integrating transmittance of
Theoretical predictions of hourly variations of the global solar radiation on a horizontal surface (Global), and the distillate production rates of a still with neither the internal nor the external reflectors (called NRS), one with the internal reflector only (called IS) and one with both the internal and external reflectors (called IES) on a winter solstice day at 30 N latitude (daily global solar radiation is 12.6 MJ m2 day1) when the angle of the glass cover hg is 20 are shown in Fig. 6a. In this paper, the distillate production rate and the daily amount of distillate of the still are defined as those per unit evaporation area of basin water. The distillate production rate of each still peaks about 30 min later than that of the global solar radiation because of the heat capacity of the still. The distillate production rate is increased by using the internal and/or external reflector(s), and the daily amount of distillate of IES with reflector angle hm = 0 (3.96 kg m2 day1) is about 16% and 74% larger than that of IS (3.41 kg m2 day1) and NRS (2.27 kg m2 day1), respectively. Furthermore,
Table 1 Design and weather conditions w = 1 m, ls = 1 m, lm = 0.5 m ab = 0.9, qint = qext = 0.85 Absorptance of glass cover = 0.08 sg(b) = 2.642 cos b – 2.163 cos 2b – 0.320 cos 3b + 0.719 cos 4b (Tanaka et al., 2000) Emittance of basin liner and glass cover = 0.9 Heat capacity of basin water and glass cover = 41.7 and 6.4 kJ K1 Thermal conductivity and thickness of insulation = 0.04 W m1 K1 and 50 mm Ambient air temperature = 20 C Wind velocity = 1 m s1 Gdr: Bouguer’s equation (Japan Solar Energy Society, 1985) with transmittance of atmosphere is 0.7 and 30 N latitude Gdf: Berlage’s equation (Japan Solar Energy Society, 1985) with the solar radiation incident on the atmosphere of 1370 W m2 at 30 N latitude
H. Tanaka, Y. Nakatake / Solar Energy 81 (2007) 1035–1042
600 o
IES(θm=30 )
500
IES(θm=0o)
0.2
400
Global
0.15
IS
300 0.1 200
NRS
0.05
100
0
8 a.m.
10
2 p.m.
12
4
6
0
Fig. 6a. Hourly variation of global solar radiation on a horizontal surface and distillate production rate of NRS, IS and IES when the glass cover angle hg = 20 on a winter solstice day at 30 N latitude.
the distillate production rates of IES with the inclined external reflectors (hm = 10–30) are greater than that with the vertical external reflector (hm = 0), and there should be an optimum inclination angle of the external reflector. Hourly variations of the radiation reflected from the external reflector and absorbed on the basin liner, Qsun,ext, is shown in Fig. 6b, and the variation of the cumulative daily reflected radiation, R Qsun,ext, with the angle of the external reflector hm is shown in Fig. 6c. The reflected radiation from the external reflector, Qsun,ext, increases with an increase in the angle hm, but peaks at about hm = 13 and decreases with an increase in hm after the peak. This is because the inclined external reflector would increase the ratio of the amount of the reflected radiation which can be absorbed on the basin liner to the total amount of the reflected radiation from the external reflector as shown in Fig. 1, but on the other hand, the total amount of the reflected radiation from the inclined external reflector
3 2.5 2 1.5 1 0.5 0
0
5
10 15 20 Reflector angle θm
25
Fig. 6c. The variation of the cumulative daily reflected radiation, RQsun,ext, with a reflector angle hm when the glass cover angle hg = 20 on a winter solstice day at 30 N latitude.
would decrease with an increase in the inclination angle of the external reflector hm (or the length of l4 shown in Figs. 4 and 5 would decrease with an increase in hm). Figs. 7a–7c show the same relationships as Figs. 6a–6c when the glass cover angle hg is 40. The distillate production rates of IS (a still with an internal reflector only) and IES with reflector angle set at hm = 0 would be the same, since all of the reflected radiation from the external reflector cannot hit the basin liner and would escape to the ground and the reflected radiation from the external reflector, Qsun,ext, would be zero throughout the day, that is, the length of l7 in Fig. 3 would be longer than the still’s length ls throughout the day when hm = 0. The reflected radiation from the external reflector as well as the distillate production rate would increase with an increase in the inclination angle of the external reflector hm, and have a gentle peak around hm = 20. 0.35
200
600 IES(θm=20o)
IES(θm=10o)
150
Distillate production rate, g m–2 s–1
Reflected radiation, Qsun,ext, W
0.3 o
IES(θm=10 )
IES(θm=20o)
IES(θm=30o)
100
50
IES(θm=0o)
0
8 a.m.
10
12
500
IES(θm=30o)
0.25 400
Global IS IES(θm=0o)
0.2
300
0.15 200 0.1 NRS
100
0.05
2 p.m.
4
6
Fig. 6b. Hourly variation of reflected radiation from the external reflector and absorbed on the basin liner, Qsun,ext, when the glass cover angle hg = 20 on a winter solstice day at 30 N latitude.
30
0
Global solar radiation, W m–2
IES(θm=10o) IES(θm=20o)
Global solar radiation, W m–2
0.25 Distillate production rate, g m–2 s–1
Cumulative daily reflected radiation, ΣQsun,ext, MJ day–1
1040
8 a.m.
10
12
2 p.m.
4
0 6
Fig. 7a. Hourly variation of global solar radiation on a horizontal surface and distillate production rate of NRS, IS and IES when the glass cover angle hg = 40 on a winter solstice day at 30 N latitude.
H. Tanaka, Y. Nakatake / Solar Energy 81 (2007) 1035–1042
140
7
Reflected radiation, Qsun,ext, W
Daily amount of distillate, kg m–2 day–1
IES(θm=20o)
120 100
IES(θm=10o) IES(θm=30o)
80 60 40 20 0
8 a.m.
10
12
2 p.m.
4
θg=40o
6 5
35o 30o 25o 20o
4 3 2 1 0
6
Fig. 7b. Hourly variation of reflected radiation from the external reflector and absorbed on the basin liner, Qsun,ext, when the glass cover angle hg = 40 on a winter solstice day at 30 N latitude.
0
5
10 15 20 Reflector angle θm
25
30
Fig. 8. Daily amount of distillate of IES varying with the reflector angle hm and glass cover angle hg on a winter solstice day at 30 N latitude.
2.5
7 IES(θm=15o, lm=ls)
Daily amount of distillate, kg m–2 day–1
Cumulative daily reflected radiation, ΣQsun,ext, MJ day–1
1041
2
1.5
1
0.5
0 0
5
10 15 20 Reflector angle θm
25
30
6 5
IES(θm=15o, lm=0.5ls)
4 IES(θm=0o, lm=0.5ls)
3
IS
2
NRS
1 0 20
25
30
Glass cover angle θg
35
40
Fig. 7c. The variation of the cumulative daily reflected radiation, R Qsun,ext, with a reflector angle hm when the glass cover angle hg = 40 on a winter solstice day at 30 N latitude.
Fig. 9. Daily amount of distillate of NRS, IS and IES varying with the glass cover angle hg on a winter solstice day at 30 N latitude.
The variations of the daily amount of distillate of the still with the reflector angle hm when the glass cover angle hg is 20–40 are shown in Fig. 8. The daily amount of distillate is greater for a still with a larger glass cover angle hg at any reflector angle hm. This is mainly because the larger glass cover angle hg causes the internal back wall reflector to be higher and increases the reflected radiation from the internal reflector Qsun,int. The daily amounts of distillate peak at about hm = 15, and an increase in the daily amounts of distillate achieved by inclining the external reflector from hm = 0 (vertical) to hm = 15 would be 15% and 22% at hg = 20 and 40. The variation of the daily amount of distillate with a glass cover angle hg for NRS (the still without reflectors), IS (the still with the internal reflector only) and IES (the still with the internal and external reflectors) are shown
in Fig. 9. The results of IES are shown as that of IES with hm = 0 and lm = 0.5ls, hm = 15 and lm = 0.5ls, and hm = 15 and lm = ls. Here, for IES with hm = 0, even if the height of the external reflector lm is larger than 0.5ls, the daily amount of distillate cannot be increased at any angle hg, since the length of the overlapping area of the reflected projection of the external reflector and the shadow of the glass cover (shown as l1 + l7 in Fig. 5a) is already longer than the still’s length (ls) throughout the day even when the external reflector height lm = 0.5ls. The daily amount of distillate of NRS would remain almost the same at any glass cover angle hg, since the solar radiation incident on the basin liner would be almost the same at any hg. The daily amount of distillate of IES with hm = 0 (IES with the vertical external reflector) increases with an increase in the glass cover angle hg, but is the same as that
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H. Tanaka, Y. Nakatake / Solar Energy 81 (2007) 1035–1042
of IS when hg is larger than 35. This indicates that the benefit of the vertical flat plate external reflector would be less for a still with a larger value for hg and negligible for a still with hg > 35 in winter. The daily amounts of distillate can be increased by inclining the external reflector as well as increasing the length of the external reflector, and the daily amounts of distillate of IES with the inclined external reflector (hm = 15) and lm = 0.5ls or lm = ls would be about 14% or 34% larger than that of IES with the vertical external reflector (hm = 0) when hg = 20, and about 18% or 27% larger when hg = 40. Further, the daily amounts of distillate of IES with hm = 15 and lm = 0.5ls or lm = ls would be about 2.0 or 2.3 times as large as that of NRS when hg = 20, and about 2.6 or 2.8 times as large as that of NRS when hg = 40.
the daily amount of distillate produced by an IES type still. 4. When the angle hg is 20, the daily amount of distillate of an IES type still with an inclined external reflector (hm = 15) and lm (height of the external reflector) = 0.5 · ls (length of the still) or lm = ls would be about 14% or 34% more than that of an IES type still with a vertical external reflector (hm = 0), and about 2.0 or 2.3 times as much as that of a still without reflectors (called NRS). 5. When the angle hg = 40, the daily amount of distillate of an IES type still with hm = 15 and lm = 0.5ls or lm = ls would be about 18% or 27% larger than that of an IES type still with hm = 0, and about 2.6 or 2.8 times as large as that of a NRS type still.
5. Conclusions
References
We theoretically predicted the amount of solar radiation absorbed on the basin liner as well as the distillate productivity of a basin type solar still with an internal reflector (two sides and back walls) and an inclined flat plate external 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: 1. The distillate productivity of the basin type still with both internal and external reflectors (called IES) can be increased by inclining the external reflector in winter. 2. When the angle of the glass cover hg is 40, the benefit of a vertical external reflector is negligible, while the inclined external reflector can effectively reflect the sunrays to the basin liner. 3. When the angle hg is in the range of 20–40, the external reflector angle hm should be set at about 15 to maximize
Al-Hayek, I., Badran, O.O., 2004. The effect of using different designs of solar stills on water distillation. Desalination 169, 121–127. Dunkle, R.V., 1961. Solar water distillation: the roof type still and a multiple effect diffusion still. In: Proceedings of ASME International Developments in Heat Transfer. University of Colorado, pp. 895–902, part 5. El-Bahi, A., Inan, D., 1999. Analysis of a parallel double glass solar still with separate condenser. Renewable Energy 17, 509–521. El-Swify, M.E., Metias, M.Z., 2002. Performance of double exposure solar still. Renewable Energy 26, 531–547. Japan Solar Energy Society, 1985. Solar Energy Utilization Handbook. Onkodo Press, Tokyo, pp. 2–20. Malik, M.A.S., Tiwari, G.N., Kumar, A., Sodha, M.S., 1982. Solar Distillation. Pergamon Press Ltd., UK, p. 98. Tamimi, A., 1987. Performance of a solar still with reflectors and black dye. Solar and Wind Technology 4, 443–446. Tanaka, H., Nakatake, Y., 2006. Theoretical analysis of a basin type solar still with internal and external reflectors. Desalination 197, 205–216. Tanaka, H., Nosoko, T., Nagata, T., 2000. A highly productive basintype – multiple-effect coupled solar still. Desalination 130, 279–293. Tripathi, R., Tiwari, G.N., 2004. Performance evaluation of a solar still by using the concept of solar fractionation. Desalination 169, 69–80.
Effect of inclination of external flat plate reflector of basin type still in winter Hiroshi Tanaka *, Yasuhito Nakatake Mechanical Engineering Department, Kurume National College of Technology, Komorino, Kurume, Fukuoka 830-8555, Japan Received 1 June 2006; received in revised form 24 October 2006; accepted 28 November 2006 Available online 26 December 2006 Communicated by: Associate Editor Volker Wittwer
Abstract This paper presents a theoretical analysis of a basin type solar still with an internal reflector (two sides and back walls) and an inclined flat plate external reflector on a winter solstice day at 30 N latitude. We are proposing a new geometrical method for calculating the solar radiation reflected by the inclined external reflector and then absorbed on the basin liner. Using this method, we performed a numerical analysis of heat and mass transfer in the still in order to determine the effectiveness of the inclination of the external reflector. We found that the benefit of a vertical external reflector would be smaller or even negligible for a still with a larger value for the glass cover angle, while an inclined external reflector can increase the distillate productivity of the still at any glass cover angle, and the external reflector angle should be set at about 15 from vertical on a winter solstice day. The daily amount of distillate of the still with the inclined external reflector would be about 16% greater than that with the vertical external reflector, and about 2.3 times as large as that of the still with neither the internal nor the external reflector on a winter solstice day. 2006 Elsevier Ltd. All rights reserved. Keywords: Solar still; Solar distillation; Solar desalination; Basin type; Reflector; Inclined
1. Introduction For a basin type solar still, internal and external reflectors can be a useful and inexpensive modification to increase the solar radiation incident on the basin liner as well as the distillate productivity of the still, and many reports about the effect of internal reflectors (Tamimi, 1987; El-Swify and Metias, 2002; Tripathi and Tiwari, 2004; Al-Hayek and Badran, 2004; Tanaka and Nakatake, 2006) and external reflectors (Malik et al., 1982; El-Bahi and Inan, 1999; Tanaka and Nakatake, 2006) on the distillate productivity of basin type stills have been presented. El-Swify and Metias (2002) presented a useful geometrical method for calculating the solar radiation reflected by
*
Corresponding author. Tel.: +81 942 359359; fax: +81 942 359321. E-mail address: [email protected] (H. Tanaka).
0038-092X/$ - see front matter 2006 Elsevier Ltd. All rights reserved. doi:10.1016/j.solener.2006.11.006
the internal reflector (two sides and back walls) and then absorbed on the basin liner of the basin type still. Tripathi and Tiwari (2004) performed a numerical analysis by using AUTOCAD 2000 to determine the solar fraction of the basin type still. The solar fraction was defined as the ratio of the solar radiation absorbed on the back wall to that absorbed on the basin liner in addition to the back wall of the still. El-Swify and Metias (2002) and Tripathi and Tiwari (2004) indicated that an internal reflector can remarkably increase the distillate productivity of the basin type still. We have added to this research by presenting a geometrical method (Tanaka and Nakatake, 2006) to evaluate the effect of a vertical external flat plate reflector extending from the back wall of the still, in addition to the internal reflector, on the solar radiation absorbed on the basin liner as well as on the distillate productivity of the basin type still at 30 N latitude. We found that internal and
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Nomenclature Gdf, Gdr diffuse and direct solar radiation on a horizontal surface, (W m2) lm height of external reflector, m ls length of basin liner, m Qsun,df, Qsun,dr absorption of diffuse or direct solar radiation, W Qsun,ext, Qsun,int absorption of reflected solar radiation from external or internal reflector, W w width of basin liner and external reflector, m
external reflectors can remarkably increase the distillate productivity of the basin type still throughout the year except for during the summer season. In summer, the external reflector would shade the basin liner and the direct solar radiation absorbed on the basin liner would be decreased by the external reflector during the morning and the evening, since the sun moves north and the sunrays hit from north side during the morning and the evening in summer at 30 N latitude. In addition, during the winter season, the effect of the external reflector would be smaller than that of the internal reflector, and the benefit of the external reflector would be smaller for the still with a larger value for the angle of the glass cover, and when the glass cover angle is 40, the benefit of the external reflector would be negligible. This is because the solar altitude angle decreases in winter and a large portion of the reflected sunrays from the vertical reflector cannot hit the basin liner and would escape to the ground as shown in Fig. 1. On the other hand, reflected sunrays from the inclined external reflector would not escape to the ground and can be absorbed on the basin liner even when the solar altitude angle is small as shown in Fig. 1. As mentioned above, since the vertical flat plate external reflector presented in our previous paper cannot effectively reflect the solar radiation to the basin liner in summer and
Sunray
Reflected sunrays from vertical reflector from inclined reflector External reflector
Basin type still
Fig. 1. Reflected sunrays from vertical and inclined external reflectors of a basin type still.
absorptance of basin liner incident angle of sunrays to glass cover altitude and azimuth angle of the sun altitude and azimuth angle of reflected radiation from external reflector hg angle of glass cover from horizontal hm angle of external reflector from vertical qext, qint reflectance of external and internal reflector sg transmittance of glass cover
ab b /, u /0, u0
winter, the arrangement of the flat plate external reflector has to be changed from vertical in these seasons. In this paper, we present a new geometrical method to calculate the solar radiation reflected from an inclined external reflector and then absorbed on the basin liner. The geometrical method presented in this paper differs significantly from the one for the vertical reflector described in our previous paper (Tanaka and Nakatake, 2006) and is more complicated. We also numerically analyzed the effect of the inclination of the external reflector on the distillate productivity of a basin type still on a winter solstice day at 30 N latitude. 2. Solar radiation absorbed on the basin liner of a single-slope basin type still with internal reflector and inclined flat plate external reflector The proposed still is shown in Fig. 2. The still consists of a basin liner, a glass cover, two side walls, a back wall, and an inclined flat plate external reflector of highly reflective materials such as a mirror-finished metal plate extending from the back wall of the still. The two sides and back walls are assumed to be covered with highly reflective materials, so these walls serve as the internal reflector. Direct and diffuse solar radiation and also the reflected radiation from the internal and external reflectors are transmitted through the glass cover and then absorbed on the basin liner. To simplify the following calculations, it is assumed that the same amount of solar radiation obstructed by one side wall hits the other inner side wall since both inner side walls are assumed to be covered with highly reflective materials. This assumption would be valid especially if the still’s width is great enough in relation to the still’s length. Fig. 3 shows a schematic diagram of the shadows of the internal back wall reflector and the inclined external reflector as well as the projection of the reflected sunrays from the inclined external reflector on a horizontal surface caused by direct solar radiation. ls is the length of the basin liner (ABCD), lm is the height of the external reflector (EFGH), w is the width of both the basin liner and the external reflector, hg is the angle of the glass cover (EFCD) and hm is the angle from vertical of the inclined external reflector. u and / are the azimuth and altitude angle of
H. Tanaka, Y. Nakatake / Solar Energy 81 (2007) 1035–1042
1037
where b is the incident angle of the sunrays to the glass cover. The internal back wall reflector (ABFE) makes a shadow on a horizontal surface shown as ABF00 E00 , and the solar radiation reflected by the internal back wall reflector and absorbed on the basin liner, Qsun,int, can be determined as the product of the direct solar radiation on a horizontal surface, the shadow area of the back wall reflector (ABF00 E00 ), transmittance of the glass cover, reflectance of the back wall reflector, qint, and absorptance of the basin liner, and this may be expressed as cos u ð2Þ Qsun;int ¼ Gdr sg ðbÞqint ab wls tan hg tan / The shadow and reflected projection of the inclined external reflector (EFGH) on a horizontal surface are shown as E00 F00 G00 H00 and E 0 F 0 G 0 H 0 , respectively. All of the reflected sunrays from the external reflector cannot hit the basin liner, 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 sunrays from the inclined external reflector hits the whole surface of the glass cover, the shadow of the glass cover would be an area shown as E 0 F 0 CD. The portion of the reflected radiation from the external reflector which would be absorbed on the basin liner can be determined as the overlapping area of the reflected projection of the external reflector (E 0 F 0 G 0 H 0 ) and the shadow of the glass cover (E 0 F 0 CD) shown as a trapezoid E 0 F 0 KH 0 , and the residue shown as F 0 G 0 K would escape to the ground. Since the reflected radiation from the inclined reflector would be condensed or diluted (or the lengths of the shadow (l4) and reflected projection (l1) of the inclined external reflector
Fig. 2. Schematic diagram of a basin type still with internal reflector and an inclined flat plate external reflector.
the sun. In this calculation, the still is assumed to be facing due south to maximize the solar radiation on the basin liner. The direct solar radiation absorbed on the basin liner, Qsun,dr, can be determined as the product of the direct solar radiation on a horizontal surface, Gdr, the area of the basin liner, transmittance of the glass cover, sg(b), and absorptance of the basin liner, ab, and this may be expressed as Qsun;dr ¼ Gdr sg ðbÞab wls
ð1Þ
H Sun
Inclined external reflector
θm lm
G E
Internal back wall reflector
w
Sidewall reflector
θm I ϕ φ
F
E"
H"
A
ls θg
l5
E'
ω1
Basin liner ω1 = tan
−1 l5
l4
l ω2 = tan −1 6 ls − l7
F' K
C
ω2
ω1
G' l3=l1tanω2 l6=(l7+l9)tanω1 l2=l1tanω1
l7 l1
l4
F"
B
H'
D
ω1
J
l9
l8
G"
l8 = l s tan θ g
cos ϕ tan φ
l9=lstanθgtanθm l7 =
l1 (l8 − l9 ) − l9 l4
Fig. 3. The shadow of the internal back wall reflector and the shadow and reflected projection of the inclined external reflector.
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H. Tanaka, Y. Nakatake / Solar Energy 81 (2007) 1035–1042
would not be equal), the intensity of the reflected radiation from the inclined external reflector on a horizontal surface can be determined as Gdr · l4/l1. Therefore, the solar radiation reflected from the external reflector and absorbed on the basin liner, Qsun,ext, can be determined as the product of the intensity of the reflected radiation, Gdr · l4/l1, the overlapping area of the reflected projection of the external reflector and shadow of the glass cover shown as E 0 F 0 KH 0 , reflectance of the external reflector, qext, transmittance of the glass cover and absorptance of the basin liner, and this may be expressed as l4 1 ð3Þ Qsun;ext ¼ Gdr sg ðbÞqext ab l1 w ðl2 þ l3 Þ 2 l1 To calculate Eq. (3), the lengths of l1, l4 and l5 and the angles of x1 and x2 have to be determined. Therefore, isometric and side views of an inclined flat plate reflector (EFGH), which is directly placed on a horizontal surface, are shown in Figs. 4a and b. The shadow (EFG00 H00 ) and
Sun
Inclined reflector
H
l4 = lm cos θ m
ω1 ϕ
E
G
φ
ω1 = tan −1
H''
L
l5 l4 Shadow
ω1
l5 H' w
ω1
F
l10 G'
l1
l10 = lm cos θ m
Inclined reflector
Qsun;ext ¼ Gdr
l11=lmcosθm ω 3– θm
ω 3–θm
ω3 = tan −1 ω 3–2θm θm
θm
l10 cos ϕ = tan −1 l11 tan φ
M
lm
cos b ¼ sin / cos hg þ cos / sin hg cos u
F l10 = lm cos θ m
l4 1 sinð90 x1 Þsinð90 x2 Þ sg ðbÞqext ab w2 l1 2 sinðx1 þ x2 Þ ð8Þ
In Eqs. (1)–(3), (7) and (8), the incident angle of sunrays to the glass cover, b, can be expressed as (Japan Solar Energy Society, 1985) for Eqs. (1) and (2)
φ G’
ð7Þ 3. When the overlapping area of the reflected projection and the shadow forms a triangle E 0 F 0 K as shown in Fig. 5b, Qsun,ext may be expressed as
ω 3– θm
Reflected sunray
Therefore, Qsun,ext can be determined with a length of l1 to l11 and angles of x1 to x3 shown in Figs. 3 and 4. When Qsun,ext is calculated, there are three exceptions as follows:
cos ϕ tan φ
Sun G
By drawing an additional vertical line from point G to a horizontal surface (point M) to Fig. 4a, the lengths of l4 and l5 can be determined as follows: cos u sin hm l4 ¼ lm cos hm ð5Þ tan / sin juj ð6Þ l5 ¼ lm cos hm tan /
Qsun;ext ¼ Gdr
l4
lmsinθm
ð4Þ
l4 sg ðbÞqext ab l1 1 ðls l7 Þ w ðls l7 Þðtan x1 þ tan x2 Þ 2
G''
M Reflected projection
l1 ¼ lm fcos hm tanðx3 2hm Þ þ sin hm g
1. When the length of l7 is larger than the still’s length (ls), all of the reflected sunrays would escape to the ground and Qsun,ext would be zero. 2. When the reflected projection exceeds the still’s length (l1 + l7 > ls) as shown in Fig. 5a, the overlapping area of the reflected projection of the external reflector and the shadow of the glass cover would be a trapezoid shown as E 0 F 0 CK, and Qsun,ext may be expressed as
sin | ϕ | l5 = lm cos θ m tan φ
lm
θm
cos ϕ − sin θ m tan φ
the reflected projection (EFG 0 H 0 ) of the reflector on a horizontal surface shown in Fig. 4a would be in exact accordance with those shown as E00 F00 G00 H00 and E 0 F 0 G 0 H 0 in Fig. 3. Since the incident angle and reflected angle of the sunrays for the reflector would be the same as x3–hm shown as Fig. 4b, the length of the reflected projection of the inclined reflector, l1, can be determined as follows with the angle x3 (= tan1(cos u/tan/))
cos ϕ tan φ
ð9Þ
G''
lmcosθmtan(ω 3–2θm) l1=lm{cosθmtan(ω 3–2θm) +sinθm}
Fig. 4. (a) Isometric and (b) side views of an inclined reflector on a horizontal surface.
for Eqs. (3), (7) and (8) cos b ¼ sin /0 cos hg þ cos /0 sin hg cos u0
ð10Þ
where / 0 and u 0 are the altitude and azimuth angle of the reflected sunrays from the inclined external reflector, and can be expressed as
H. Tanaka, Y. Nakatake / Solar Energy 81 (2007) 1035–1042
a
A ls
l7
ls–l7
E'
D
the glass cover for diffuse radiation from all directions in the sky dome, and can be expressed as (Tanaka and Nakatake, 2006)
Overlapping area (Trapezoid) (ls–l7)(tanω1+tanω 2)
ðsg Þdf ¼ 2:03 105 h2g 2:05 103
B
hg þ 0:667; hg ½ l1
1039
ð14Þ
K F'
H'
3. Heat and mass transfer in the still
ω2 ω1
C
Heat and mass transfer in the still was described in our previous paper in detail (Tanaka and Nakatake, 2006), and was basically the same in content as one by Dunkle (1961). The equations of the solar radiations (Qsun,dr, Qsun,int, Qsun,ext and Qsun,df) and the energy balance for basin water and the glass cover, and the equations of properties were solved together to find the solar radiation absorbed on the basin liner as well as the distillate production rate throughout a day. Temperatures of the basin water and the glass cover were set to be equal to the ambient air temperature at just before sunrise, as the initial values. The weather and design conditions are listed in Table 1.
G'
b
A
D
Overlapping area (Triangle) B
E'
ω2
ω1 90–ω1
w
ω1+ω2 90–ω2
C
F'
K
4. Results
H'
G' Fig. 5. The overlapping area of the reflected projection of the external reflector and the shadow of the glass cover when the overlapping area is: (a) trapezoid and (b) triangle.
/0 ¼ 90 ðx3 2hm Þ u0 ¼ 180 x1
ð11Þ ð12Þ
Diffuse solar radiation absorbed on the basin liner, Qsun,df, can be determined with the assumption that diffuse radiation comes uniformly from all directions in the sky dome, and may be expressed as Qsun;df ¼ Gdf ðsg Þdf ab wls
ð13Þ
where Gdf is the diffuse solar radiation on a horizontal surface, and (sg)df is the function of the angle of the glass cover, hg. This can be calculated by integrating transmittance of
Theoretical predictions of hourly variations of the global solar radiation on a horizontal surface (Global), and the distillate production rates of a still with neither the internal nor the external reflectors (called NRS), one with the internal reflector only (called IS) and one with both the internal and external reflectors (called IES) on a winter solstice day at 30 N latitude (daily global solar radiation is 12.6 MJ m2 day1) when the angle of the glass cover hg is 20 are shown in Fig. 6a. In this paper, the distillate production rate and the daily amount of distillate of the still are defined as those per unit evaporation area of basin water. The distillate production rate of each still peaks about 30 min later than that of the global solar radiation because of the heat capacity of the still. The distillate production rate is increased by using the internal and/or external reflector(s), and the daily amount of distillate of IES with reflector angle hm = 0 (3.96 kg m2 day1) is about 16% and 74% larger than that of IS (3.41 kg m2 day1) and NRS (2.27 kg m2 day1), respectively. Furthermore,
Table 1 Design and weather conditions w = 1 m, ls = 1 m, lm = 0.5 m ab = 0.9, qint = qext = 0.85 Absorptance of glass cover = 0.08 sg(b) = 2.642 cos b – 2.163 cos 2b – 0.320 cos 3b + 0.719 cos 4b (Tanaka et al., 2000) Emittance of basin liner and glass cover = 0.9 Heat capacity of basin water and glass cover = 41.7 and 6.4 kJ K1 Thermal conductivity and thickness of insulation = 0.04 W m1 K1 and 50 mm Ambient air temperature = 20 C Wind velocity = 1 m s1 Gdr: Bouguer’s equation (Japan Solar Energy Society, 1985) with transmittance of atmosphere is 0.7 and 30 N latitude Gdf: Berlage’s equation (Japan Solar Energy Society, 1985) with the solar radiation incident on the atmosphere of 1370 W m2 at 30 N latitude
H. Tanaka, Y. Nakatake / Solar Energy 81 (2007) 1035–1042
600 o
IES(θm=30 )
500
IES(θm=0o)
0.2
400
Global
0.15
IS
300 0.1 200
NRS
0.05
100
0
8 a.m.
10
2 p.m.
12
4
6
0
Fig. 6a. Hourly variation of global solar radiation on a horizontal surface and distillate production rate of NRS, IS and IES when the glass cover angle hg = 20 on a winter solstice day at 30 N latitude.
the distillate production rates of IES with the inclined external reflectors (hm = 10–30) are greater than that with the vertical external reflector (hm = 0), and there should be an optimum inclination angle of the external reflector. Hourly variations of the radiation reflected from the external reflector and absorbed on the basin liner, Qsun,ext, is shown in Fig. 6b, and the variation of the cumulative daily reflected radiation, R Qsun,ext, with the angle of the external reflector hm is shown in Fig. 6c. The reflected radiation from the external reflector, Qsun,ext, increases with an increase in the angle hm, but peaks at about hm = 13 and decreases with an increase in hm after the peak. This is because the inclined external reflector would increase the ratio of the amount of the reflected radiation which can be absorbed on the basin liner to the total amount of the reflected radiation from the external reflector as shown in Fig. 1, but on the other hand, the total amount of the reflected radiation from the inclined external reflector
3 2.5 2 1.5 1 0.5 0
0
5
10 15 20 Reflector angle θm
25
Fig. 6c. The variation of the cumulative daily reflected radiation, RQsun,ext, with a reflector angle hm when the glass cover angle hg = 20 on a winter solstice day at 30 N latitude.
would decrease with an increase in the inclination angle of the external reflector hm (or the length of l4 shown in Figs. 4 and 5 would decrease with an increase in hm). Figs. 7a–7c show the same relationships as Figs. 6a–6c when the glass cover angle hg is 40. The distillate production rates of IS (a still with an internal reflector only) and IES with reflector angle set at hm = 0 would be the same, since all of the reflected radiation from the external reflector cannot hit the basin liner and would escape to the ground and the reflected radiation from the external reflector, Qsun,ext, would be zero throughout the day, that is, the length of l7 in Fig. 3 would be longer than the still’s length ls throughout the day when hm = 0. The reflected radiation from the external reflector as well as the distillate production rate would increase with an increase in the inclination angle of the external reflector hm, and have a gentle peak around hm = 20. 0.35
200
600 IES(θm=20o)
IES(θm=10o)
150
Distillate production rate, g m–2 s–1
Reflected radiation, Qsun,ext, W
0.3 o
IES(θm=10 )
IES(θm=20o)
IES(θm=30o)
100
50
IES(θm=0o)
0
8 a.m.
10
12
500
IES(θm=30o)
0.25 400
Global IS IES(θm=0o)
0.2
300
0.15 200 0.1 NRS
100
0.05
2 p.m.
4
6
Fig. 6b. Hourly variation of reflected radiation from the external reflector and absorbed on the basin liner, Qsun,ext, when the glass cover angle hg = 20 on a winter solstice day at 30 N latitude.
30
0
Global solar radiation, W m–2
IES(θm=10o) IES(θm=20o)
Global solar radiation, W m–2
0.25 Distillate production rate, g m–2 s–1
Cumulative daily reflected radiation, ΣQsun,ext, MJ day–1
1040
8 a.m.
10
12
2 p.m.
4
0 6
Fig. 7a. Hourly variation of global solar radiation on a horizontal surface and distillate production rate of NRS, IS and IES when the glass cover angle hg = 40 on a winter solstice day at 30 N latitude.
H. Tanaka, Y. Nakatake / Solar Energy 81 (2007) 1035–1042
140
7
Reflected radiation, Qsun,ext, W
Daily amount of distillate, kg m–2 day–1
IES(θm=20o)
120 100
IES(θm=10o) IES(θm=30o)
80 60 40 20 0
8 a.m.
10
12
2 p.m.
4
θg=40o
6 5
35o 30o 25o 20o
4 3 2 1 0
6
Fig. 7b. Hourly variation of reflected radiation from the external reflector and absorbed on the basin liner, Qsun,ext, when the glass cover angle hg = 40 on a winter solstice day at 30 N latitude.
0
5
10 15 20 Reflector angle θm
25
30
Fig. 8. Daily amount of distillate of IES varying with the reflector angle hm and glass cover angle hg on a winter solstice day at 30 N latitude.
2.5
7 IES(θm=15o, lm=ls)
Daily amount of distillate, kg m–2 day–1
Cumulative daily reflected radiation, ΣQsun,ext, MJ day–1
1041
2
1.5
1
0.5
0 0
5
10 15 20 Reflector angle θm
25
30
6 5
IES(θm=15o, lm=0.5ls)
4 IES(θm=0o, lm=0.5ls)
3
IS
2
NRS
1 0 20
25
30
Glass cover angle θg
35
40
Fig. 7c. The variation of the cumulative daily reflected radiation, R Qsun,ext, with a reflector angle hm when the glass cover angle hg = 40 on a winter solstice day at 30 N latitude.
Fig. 9. Daily amount of distillate of NRS, IS and IES varying with the glass cover angle hg on a winter solstice day at 30 N latitude.
The variations of the daily amount of distillate of the still with the reflector angle hm when the glass cover angle hg is 20–40 are shown in Fig. 8. The daily amount of distillate is greater for a still with a larger glass cover angle hg at any reflector angle hm. This is mainly because the larger glass cover angle hg causes the internal back wall reflector to be higher and increases the reflected radiation from the internal reflector Qsun,int. The daily amounts of distillate peak at about hm = 15, and an increase in the daily amounts of distillate achieved by inclining the external reflector from hm = 0 (vertical) to hm = 15 would be 15% and 22% at hg = 20 and 40. The variation of the daily amount of distillate with a glass cover angle hg for NRS (the still without reflectors), IS (the still with the internal reflector only) and IES (the still with the internal and external reflectors) are shown
in Fig. 9. The results of IES are shown as that of IES with hm = 0 and lm = 0.5ls, hm = 15 and lm = 0.5ls, and hm = 15 and lm = ls. Here, for IES with hm = 0, even if the height of the external reflector lm is larger than 0.5ls, the daily amount of distillate cannot be increased at any angle hg, since the length of the overlapping area of the reflected projection of the external reflector and the shadow of the glass cover (shown as l1 + l7 in Fig. 5a) is already longer than the still’s length (ls) throughout the day even when the external reflector height lm = 0.5ls. The daily amount of distillate of NRS would remain almost the same at any glass cover angle hg, since the solar radiation incident on the basin liner would be almost the same at any hg. The daily amount of distillate of IES with hm = 0 (IES with the vertical external reflector) increases with an increase in the glass cover angle hg, but is the same as that
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H. Tanaka, Y. Nakatake / Solar Energy 81 (2007) 1035–1042
of IS when hg is larger than 35. This indicates that the benefit of the vertical flat plate external reflector would be less for a still with a larger value for hg and negligible for a still with hg > 35 in winter. The daily amounts of distillate can be increased by inclining the external reflector as well as increasing the length of the external reflector, and the daily amounts of distillate of IES with the inclined external reflector (hm = 15) and lm = 0.5ls or lm = ls would be about 14% or 34% larger than that of IES with the vertical external reflector (hm = 0) when hg = 20, and about 18% or 27% larger when hg = 40. Further, the daily amounts of distillate of IES with hm = 15 and lm = 0.5ls or lm = ls would be about 2.0 or 2.3 times as large as that of NRS when hg = 20, and about 2.6 or 2.8 times as large as that of NRS when hg = 40.
the daily amount of distillate produced by an IES type still. 4. When the angle hg is 20, the daily amount of distillate of an IES type still with an inclined external reflector (hm = 15) and lm (height of the external reflector) = 0.5 · ls (length of the still) or lm = ls would be about 14% or 34% more than that of an IES type still with a vertical external reflector (hm = 0), and about 2.0 or 2.3 times as much as that of a still without reflectors (called NRS). 5. When the angle hg = 40, the daily amount of distillate of an IES type still with hm = 15 and lm = 0.5ls or lm = ls would be about 18% or 27% larger than that of an IES type still with hm = 0, and about 2.6 or 2.8 times as large as that of a NRS type still.
5. Conclusions
References
We theoretically predicted the amount of solar radiation absorbed on the basin liner as well as the distillate productivity of a basin type solar still with an internal reflector (two sides and back walls) and an inclined flat plate external 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: 1. The distillate productivity of the basin type still with both internal and external reflectors (called IES) can be increased by inclining the external reflector in winter. 2. When the angle of the glass cover hg is 40, the benefit of a vertical external reflector is negligible, while the inclined external reflector can effectively reflect the sunrays to the basin liner. 3. When the angle hg is in the range of 20–40, the external reflector angle hm should be set at about 15 to maximize
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