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An approach to optimization of double slope solar still geometry for maximum collected solar energy
Alexandria Engineering Journal (2015) xxx, xxx–xxx
H O S T E D BY
Alexandria University
Alexandria Engineering Journal www.elsevier.com/locate/aej www.sciencedirect.com
ORIGINAL ARTICLE
An approach to optimization of double slope solar still geometry for maximum collected solar energy Wael M. El-Maghlany Mechanical Engineering Department, Faculty of Engineering, Alexandria University, Alexandria, Egypt Received 19 April 2015; revised 12 June 2015; accepted 15 June 2015
KEYWORDS Solar still; Solar energy; Double slope; Optimum inclination
Abstract This investigation represents the optimum inclination angles of the glass cover of the double slope solar still, and orientation for maximum collected solar energy that could be captured by the solar still glass cover. The results will be displayed for different latitudes (/ = 24, / = 27.2, / = 30 and / = 31.2) to cover Egypt geographically. The double slope solar still has two opposite inclined surface; so it has two surfaces azimuth angles (c1 and c2) according to |c1| + |c2| = 180, with opposite signs, these values are (c1 = 0 and c2 = 180), (c1 = 90 and c2 = 90), (c1 = 45 and c2 = 135) which is equivalent to (c1 = 45 and c2 = 135); consequently, the total energy is the summation of the collected energy by the two surfaces represents the double slope solar still surface area. The inclination angle (b) is changed from 10 to 60 on both sides of the glass cover to get independently the optimum inclination angles for each side that not necessary to be the same. ª 2015 Faculty of Engineering, Alexandria University. Production and hosting by Elsevier B.V. This is an open access article under the CC BY-NC-ND license (http://creativecommons.org/licenses/by-nc-nd/4.0/).
1. Introduction Egypt is interested in finding new resources and new processes to provide fresh water. This need for water is mainly due to the population progress and to the rapid industrial growth also the reduction of River Nile water due to El-Nahda dam in Ethiopia. Solar desalination can be one of the proposed future solutions for the production of fresh water since the country is characterized by an extra ordinary intensity of solar radiation during most days of the year. Numerous experimental and numerical studies have been done on different configurations of solar stills to reach the optimum design by examining the effect of operational and design parameters on its E-mail addresses: [email protected], [email protected] Peer review under responsibility of Faculty of Engineering, Alexandria University.
performance. One of the key parameters is the cover tilt angle. Experimental and theoretical studies were performed for single slope solar still [1–11], these studies were investigated for different climate conditions, also at different periods of the year as well as all a year investigation. The performance of double slope solar still was performed experimentally and theoretically by many researches [12–18], their studies were concerned with the effect of inclination angle of the glass cover on its performance for different locations and orientation of the solar still. 2. Scope, objective, and methodology From the previous survey, more attention was focused on the performance of single slope solar still while the double slope performance had fewer attentions. Also, the previous studies were performed on the effect of cover inclination at only
http://dx.doi.org/10.1016/j.aej.2015.06.010 1110-0168 ª 2015 Faculty of Engineering, Alexandria University. Production and hosting by Elsevier B.V. This is an open access article under the CC BY-NC-ND license (http://creativecommons.org/licenses/by-nc-nd/4.0/). Please cite this article in press as: W.M. El-Maghlany, An approach to optimization of double slope solar still geometry for maximum collected solar energy, Alexandria Eng. J. (2015), http://dx.doi.org/10.1016/j.aej.2015.06.010
2
W.M. El-Maghlany
Nomenclature a EG Gb Gbn Gd Gdn HG I L
basin length to the cover length ratio the total radiation absorbed on the tilted surfaces (W/m2) instantaneous beam radiation on the surface (W/m2) beam radiation on a plane normal to the sun’s rays (W/m2) instantaneous diffuse radiation on the surface (W/m2) diffuse radiation coming from the sun (W/m2) total transmitted energy absorbed on a surface per year (J/m2) extra-terrestrial solar radiation (W/m2) glass cover total length (m)
symmetrical glass cover (b1 = b2). This study aimed to the optimum inclination angles (b1 and b2) for both the two different facing surfaces of the glass cover (c1 and c2) to get the optimum one for maximizing the transmitted solar energy through still double glass cover. Also, the selected geometry of the solar still was based on the total amount of the transmitted solar energy through the year, i.e. the solar still efficient performance will be year around. The methodology followed to achieve these objectives, via analytical analysis. 3. Modeling of the double slope solar still glass cover Fig. 1 illustrates the double slope solar still glass cover. The lengths of the two sides of the glass cover changed with respect to the optimum inclination angles (b1 and b2) with total length (L) that generates the basin width (W), so the results will be related to the glass cover total length (L) as: L1 þ L2 ¼ L
ð1Þ
L1 cos b1 þ L2 cos b2 ¼ W
ð2Þ
From Eqs. (1) and (2) after simplification
n W Z
number of days basin width (m) width of the still glass cover in depth direction (m)
Greek Symbols a polar angle b inclination angle of a tilted surface c azimuth of a tilted surface d declination angle h incident angle of beam radiation to tilted surface / latitude angle s transmittance of the atmosphere X hour angle
Lða cos b2 Þ and ðcos b1 cos b2 Þ Lða cos b1 Þ L2 ¼ with b1 –b2 ðcos b2 cos b1 Þ L1 ¼
ð3Þ
1 þb2 Þ where a ¼ W ¼ sinsinðb < 1. b1 þsin b2 L The double glass cover has two azimuth angles (c1 and c2) for the surfaces according to |c1| + |c2| = 180, with opposite signs of both c1 and c2. For this reason, the average beam radiation per unit (Z) for the inclined flat surfaces at inclination angles b1 and b2 can be obtained by: Gb ¼ L1 sgb Gbn cos h c¼c þ L2 sgb Gbn cos h c¼c ð4Þ 1
b1
2
b2
From Eqs. (3) and (4), the average beam radiation per unit area (L · Z) for the inclined flat surfaces at inclination angles (b1 and b2) can be obtained by: ða cos b2 Þ Gb ¼ sgb Gbn cos h c¼c 1 b ðcos b1 cos b2 Þ 1 ða cos b1 Þ þ sgb Gbn cos h c¼c2 ð5Þ b2 ðcos b2 cos b1 Þ Transmissivity of the glass cover, sgb (h) is the function of the incident angle h and may be presented as [18] and presented in Eq. (7). The angle h is incident angle of beam radiation to tilted surface and related to the declination d, the latitude /, the slope of the surface b, the azimuth of the surface c and the hour angle X as given below
Zenith
cos h ¼ M cos b þ N sin b
ð6Þ
where M ¼ sin dsin u þ cos dcos ucos X
β2
γ2
γ1
W
Figure 1
Flat surface double slope solar still.
N ¼ cos dsin ucos ccos X sin dcos u cos c þ cos dsin c sin X
β1
ð7Þ
sgb ¼ 2:642 cos h 2:163 cos2 h 0:32 cos3 h þ 0:719 cos4 h
In the above equations, north is positive for /, due south is zero for c with east negative and west positive, and the hour angle X is negative in the morning and positive in the afternoon.
Please cite this article in press as: W.M. El-Maghlany, An approach to optimization of double slope solar still geometry for maximum collected solar energy, Alexandria Eng. J. (2015), http://dx.doi.org/10.1016/j.aej.2015.06.010
An approach onto optimization of double slope solar still geometry Substitute in Eq. (5) to get the instantaneous average beam radiation that transmitted through the glass cover of the double slope solar still. In the above Eq. (5), the beam radiation Gbn is instantaneously constant with respect to the hour angle (X). Isotropic sky models will be used for estimation of diffuse radiation. Isotropic sky models are simple models that assume a uniform distribution of the diffuse radiation over the sky dome and circumsolar and horizontal brightening parts are considered to be zero. According to the simple model of an isotropic sky, the diffuse radiation per unit (Z) for the inclined flat surfaces at inclination angles b1 and b2 on the tilted surface Gd can be obtained according to: Gd ¼ L1 sgd Gdn ½1 þ cos b c¼c 1 b 1 þ L2 sgd Gdn ½1 þ cos b c¼c ð8Þ 2
b2
From Eqs. (3) and (8), the diffuse radiation per unit area (L · Z) for the inclined flat surfaces at inclination angles b1 and b2 can be obtained by: ða cos b2 Þ Gd ¼ sgd Gdn ½1 þ cos b c¼c 1 b ðcos b1 cos b2 Þ 1 ða cos b1 Þ þ sgd Gdn ½1 þ cos b c¼c ð9Þ 2 b ðcos b2 cos b1 Þ 2 Transmissivity of the glass cover, sgd (b) is the function of the glass cover angle, b, and may be presented as [18]. sgd ¼ 0:667 2:05 103 b 2:03 105 b2 ;
with bð Þ
ð10Þ
The total radiation absorbed on the tilted surfaces per unit surface area (L · Z) is the sum of the average beam and diffuse radiations as following EG ¼ Gb þ Gd
ð11Þ
Both values of the beam Gbn and diffuse Gdn radiation for optimization are calculated with Bouguer’s and Berlage’s equation, respectively [19] 1 Gbn ¼ Isasin as ð12Þ 0 1 1 sin as 0:25I sin a s 1 sa B C Gdn ¼ @ A 1 1:4 ln s
ð13Þ
where 360ðn 2Þ I ¼ 1370 1 þ 0:033 cos 365
ð14Þ
sin as ¼ sin d sin u þ cos d cos u cos X ¼ M
ð15Þ
Here n is the number of days from the first of January, and sa is the transmittance of the atmosphere that is calculated according to Hottel [20]. For generalization of the obtained results, it is interested to compare the performance of double slope solar still over one year. The total solar energy received (HG) per unit area (L · Z) for a total number of days (n = 365) will be obtained as Z 365 Z Xsunset HG ¼ EG dX ð16Þ 1
Xsunrise
3
4. Results and discussion The purpose of this section is to determine quantitatively the amount of collected transmitted solar energy through the two surfaces of the solar still throughout the year. The inclination angles b1 and b2 represent the inclination of the two sides of the glass cover are stated corresponding to the optimum inclination to receive maximum possible solar energy. The results are presented in two scenarios, the first one is for double slope with same inclination angles (b1 = b2) and the second for modified double slope solar still with optimum inclination angles (b1 and b2) optimum. 4.1. Total energy captured by the same slope (b1 = b2) solar still over one year for different azimuth and latitude angles By solving Eqs. (4) and (8) with same both side length (L1 = L2); led to (b1 = b2) and different azimuth and latitude angles, the total amount of transmitted solar energy (HG) per square meter of the total surface area (L · Z) through the solar still could be obtained by Eq. (16) and is represented in Fig. 2 for inclination angles (b = b1 = b2) from 10 to 60 while the basin to cover length ratio (a = W/L = cos b) varies from 0.984 to 0.5. From the results that are represented in Fig. 2, as the inclination angle increases the total transmitted solar energy through the glass cover decreases and the orientation with respect to the south has a noticeable effect. This is explained as, at small inclination angle the inflation of both surfaces led to horizontal flat plat and maximum energy could be received on both sides, this only for double slope but if the surface is only single slope located in north sphere the optimum slope (b) is around the latitude angle of the location (/ ). The maximum solar energy that transmitted is at b = 10 without no effect of the orientation (c1 and c2). At conventional inclination angle (b = /) for different locations, the total solar energy that transmitted is at the orientation of c1 = 90 and c2 = 90 with values less than that at b = 10, Table 1. 4.2. Total energy captured by the modified double slope solar still (optimum b1 and b2) over one year for different azimuth and latitude angles The first step in the calculations is to get the optimum inclination angles (b1 and b2) for both coupled pair of surfaces (c1 = 0 and c2 = 180), (c1 = 90 and c2 = 90), (c1 = 45 and c2 = 135) which is equivalent to (c1 = 45 and c2 = 135); that construct the solar still surface. By solving Eqs. (4) and (8) we get EG and consequently HG with only one azimuth angles (c = 0, ±45, ±90, ±135 and 180), the results are represented in Fig. 3 and the optimum inclination angles (b) are extracted and listed in Table 2 for different latitudes (/) taking into account that at |c| > 90 the optimum inclination angle (b) will be the same as |c| = 90. At the optimum inclination angles (b1 and b2) as well as the corresponding basin to cover length ratio (a = W/L) as listed in Table 2, Eqs. (5) and (9) are solved to get EG and consequently HG for both surfaces with the two pairs of the azimuth angles (c1 = 0 and c2 = 180), (c1 = 90 and c2 = 90), (c1 = 45 and c2 = 135) which is equivalent to (c1 = 45 and c2 = 135). Fig. 4 represents the total amount of transmitted
Please cite this article in press as: W.M. El-Maghlany, An approach to optimization of double slope solar still geometry for maximum collected solar energy, Alexandria Eng. J. (2015), http://dx.doi.org/10.1016/j.aej.2015.06.010
4
W.M. El-Maghlany
Figure 2 b1 = b2.
The annual total transmitted solar energy by the glass cover of the double slope solar still for different inclination angles with
Table 1 Total transmitted energy through the still surface at b1 = b2 for different latitude angles. /
(24)
b1 = b2 HG (GJ/m2/ year)
10 6.3
(27.2) 24 5.88
10 6.08
(30) 27.2 5.56
10 5.87
(31.2) 30 5.26
10 5.77
31.2 5.14
solar energy through the glass cover of the solar still for different latitudes and orientations at the optimum inclination angles that are listed in Table 2. The maximum transmitted energy for (/ = 24) is 6.488 GJ/m2/year with orientation of c1 = 45 and c2 = 135, for (/ = 27.2) is 6.1045
GJ/m2/year with orientation of c1 = 45 and c2 = 135, for (/ = 30) is 5.87 GJ/m2/year with orientation of c1 = 90 and c2 = 90, and for (/ = 31.2) is 5.77 GJ/m2/year with orientation of c1 = 90 and c2 = 90. 4.3. On the relation between cover tilt angles and latitude angle The inclination of the locus of the sun differs with the latitude angle. Consequently, the transmitted radiation from the still cover varies with the latitude angle (/) of the test zone. An optimum cover tilt angle that is close or almost equal to the latitude angle was established for single glass solar still, Fig. 3, with facing to the south direction (c = 0) while the optimum tilt of the symmetrical double slope (b1 = b2) was established at b1 = b2 = 10 far apart the latitude angles with
Please cite this article in press as: W.M. El-Maghlany, An approach to optimization of double slope solar still geometry for maximum collected solar energy, Alexandria Eng. J. (2015), http://dx.doi.org/10.1016/j.aej.2015.06.010
An approach onto optimization of double slope solar still geometry
Figure 3
5
The annual total transmitted solar energy by single glass solar still.
Table 2 Optimum declination angles (b1 and b2) for different azimuth (c1 and c2) and latitude angles (/). c1 = 0 and c2 = 180
(/ = 24) a = W/L (/ = 27.2) a = W/L (/ = 30) a = W/L (/ = 31.2) a = W/L
c1 = 90 and c2 = 90
c1 = 45 and c2 = 135
b1
b2
b1
b2
b1
b2
19 0.971 22 0.966 25 0.961 26 0.96
10
10 0.98 10 0.98 10 0.98 10 0.98
10
15 0.977 17 0.974 20 0.969 22 0.966
10
10 10 10
10 10 10
10 10 10
Figure 4 The annual total transmitted solar energy by the glass cover of the double slope solar still for different latitudes and orientations at optimum inclination angles b1 and b2.
Please cite this article in press as: W.M. El-Maghlany, An approach to optimization of double slope solar still geometry for maximum collected solar energy, Alexandria Eng. J. (2015), http://dx.doi.org/10.1016/j.aej.2015.06.010
6 south orientation independence. With the novel approach, the optimum tilt of the cover glass of the double slope (b1 and b2) has different optimum values for the two sides, as the surface direction go towards the south, the optimum inclination angle closed to the latitude angle (c 6 45) while the other side need an inflation (b = 10), for maximum transmitted solar energy, Table 2. 5. Conclusion In this study, the amount of transmitted solar energy through the surface of the glass cover of the double slope solar still during the year is estimated for latitude angles between 24 and 31.2. The main obtained results could be concluded as: The mathematical expression for the transmitted solar energy through the surface of the glass cover of the double slope solar still is obtained. For single glass solar still, the optimum cover tilt angle that is close or almost equal to the latitude angle with facing to the south direction (c = 0). b1 = b2 = 10 are the optimum tilt of the symmetrical double slope solar still without any effect of the orientation due south. The optimum tilt of the cover glass of the double slope solar still not necessary to be symmetrical but has values depend on the direction of each surface with respect to the south direction.
References [1] K.B. Baibutaev, B.M. Achilov, Comparative testing of a solar distiller, Appl. Solar Energy 4 (1968) 69–72. [2] A.S. Al-Jubouri, A.J.N. Khalifa, An experimental study on the performance of solar still in Iraq, in: Passive and Low Energy Alternatives International Conference, Bermuda, September, 1982, pp. 1–7. [3] A.K. Tiwari, G.N. Tiwari, An optimization of slope of condensing cover of solar still for maximum yield: in summer climatic condition, Centre for Energy Studies, Indian Institute of Technology Hauz Khas, New Delhi, India, 2004.
W.M. El-Maghlany [4] M. Abd Elkader, An investigation of the parameters involved in simple solar still with inclined yute, Renewable Energy 14 (1998) 333–338. [5] S. Kumar, G.N. Tiwari, H.N. Singh, Annual performance of an active solar distillation system, Desalination 127 (2000) 79–88. [6] A.S. Nafey, M. Abdelkader, A. Abdelmotalip, A.A. Mabrouk, Parameters affecting solar still productivity, Energy Convers. Manage. 41 (2000) 1797–1809. [7] M.N. Bahadori, F.E. Edlin, Improvement of solar stills by the surface treatment of the glass, Sol. Energy 14 (1973) 339–352. [8] G.N. Tiwari, J.M. Thomas, E. Khan, Optimisation of glass cover inclination for maximum yield in a solar still, Heat Recov. Syst. CHP 14 (1994) 447–455. [9] R. Dev, G.N. Tiwari, Characteristic equation of a passive solar still, Desalination 245 (2009) 246–265. [10] H. Aybar, H. Assefi, Simulation of a solar still to investigate water depth and glass angle, Desalination Water Treat. 7 (2009) 35–40. [11] W.A. Kamal, A theoretical and experimental study of the basintype solar still under the Arabian Gulf climatic conditions, Solar Wind Technol. 5 (1988) 147–157. [12] S. Aboul-Enein, A.A. El-Sebaii, E. El-Bialy, Investigation of a single-basin solar still with deep basins, Renewable Energy 14 (1998) 299–305. [13] K.B. Baibutaev, B.M. Achilov, Effect of the inclination of the transparent solar still surface on the condensation and collection processes, Appl. Solar Energy 6 (1970) 34–38. [14] H.P. Garg, H.S. Mann, Effect of climatic, operational and design parameters on the year round performance of singlesloped and double-sloped solar still under Indian arid zone conditions, Sol. Energy 18 (1976) 159–163. [15] H. Al-Hinai, M.S. Al-Nassri, B.A. Jubran, Effect of climatic, design and operational parameters on the yield of a simple solar still, Energy Convers. Manage. 43 (2002) 1639–1650. [16] A. Omri, J. Orfi, S.B. Nasrallah, Natural convection effects in solar stills, Desalination 183 (2005) 173–178. [17] T. Abderachid, K. Abdenacer, Effect of orientation on the performance of a symmetric solar still with a double effect solar still (comparison study), Desalination 329 (2013) 68–77. [18] H. Tanaka, Y. Nakatake, Theoretical analysis of a basin type solar still with internal and external reflectors, Desalination 197 (2006) 205–216. [19] Japan Solar Energy Society, Solar Energy Utilization Handbook, Japan Solar Energy Society, Tokyo, 1985, p. 20. [20] H.C. Hottel, A simple model for estimating the transmittance of direct solar radiation through clear atmospheres, Sol. Energy 18 (1976) 129–134.
Please cite this article in press as: W.M. El-Maghlany, An approach to optimization of double slope solar still geometry for maximum collected solar energy, Alexandria Eng. J. (2015), http://dx.doi.org/10.1016/j.aej.2015.06.010
H O S T E D BY
Alexandria University
Alexandria Engineering Journal www.elsevier.com/locate/aej www.sciencedirect.com
ORIGINAL ARTICLE
An approach to optimization of double slope solar still geometry for maximum collected solar energy Wael M. El-Maghlany Mechanical Engineering Department, Faculty of Engineering, Alexandria University, Alexandria, Egypt Received 19 April 2015; revised 12 June 2015; accepted 15 June 2015
KEYWORDS Solar still; Solar energy; Double slope; Optimum inclination
Abstract This investigation represents the optimum inclination angles of the glass cover of the double slope solar still, and orientation for maximum collected solar energy that could be captured by the solar still glass cover. The results will be displayed for different latitudes (/ = 24, / = 27.2, / = 30 and / = 31.2) to cover Egypt geographically. The double slope solar still has two opposite inclined surface; so it has two surfaces azimuth angles (c1 and c2) according to |c1| + |c2| = 180, with opposite signs, these values are (c1 = 0 and c2 = 180), (c1 = 90 and c2 = 90), (c1 = 45 and c2 = 135) which is equivalent to (c1 = 45 and c2 = 135); consequently, the total energy is the summation of the collected energy by the two surfaces represents the double slope solar still surface area. The inclination angle (b) is changed from 10 to 60 on both sides of the glass cover to get independently the optimum inclination angles for each side that not necessary to be the same. ª 2015 Faculty of Engineering, Alexandria University. Production and hosting by Elsevier B.V. This is an open access article under the CC BY-NC-ND license (http://creativecommons.org/licenses/by-nc-nd/4.0/).
1. Introduction Egypt is interested in finding new resources and new processes to provide fresh water. This need for water is mainly due to the population progress and to the rapid industrial growth also the reduction of River Nile water due to El-Nahda dam in Ethiopia. Solar desalination can be one of the proposed future solutions for the production of fresh water since the country is characterized by an extra ordinary intensity of solar radiation during most days of the year. Numerous experimental and numerical studies have been done on different configurations of solar stills to reach the optimum design by examining the effect of operational and design parameters on its E-mail addresses: [email protected], [email protected] Peer review under responsibility of Faculty of Engineering, Alexandria University.
performance. One of the key parameters is the cover tilt angle. Experimental and theoretical studies were performed for single slope solar still [1–11], these studies were investigated for different climate conditions, also at different periods of the year as well as all a year investigation. The performance of double slope solar still was performed experimentally and theoretically by many researches [12–18], their studies were concerned with the effect of inclination angle of the glass cover on its performance for different locations and orientation of the solar still. 2. Scope, objective, and methodology From the previous survey, more attention was focused on the performance of single slope solar still while the double slope performance had fewer attentions. Also, the previous studies were performed on the effect of cover inclination at only
http://dx.doi.org/10.1016/j.aej.2015.06.010 1110-0168 ª 2015 Faculty of Engineering, Alexandria University. Production and hosting by Elsevier B.V. This is an open access article under the CC BY-NC-ND license (http://creativecommons.org/licenses/by-nc-nd/4.0/). Please cite this article in press as: W.M. El-Maghlany, An approach to optimization of double slope solar still geometry for maximum collected solar energy, Alexandria Eng. J. (2015), http://dx.doi.org/10.1016/j.aej.2015.06.010
2
W.M. El-Maghlany
Nomenclature a EG Gb Gbn Gd Gdn HG I L
basin length to the cover length ratio the total radiation absorbed on the tilted surfaces (W/m2) instantaneous beam radiation on the surface (W/m2) beam radiation on a plane normal to the sun’s rays (W/m2) instantaneous diffuse radiation on the surface (W/m2) diffuse radiation coming from the sun (W/m2) total transmitted energy absorbed on a surface per year (J/m2) extra-terrestrial solar radiation (W/m2) glass cover total length (m)
symmetrical glass cover (b1 = b2). This study aimed to the optimum inclination angles (b1 and b2) for both the two different facing surfaces of the glass cover (c1 and c2) to get the optimum one for maximizing the transmitted solar energy through still double glass cover. Also, the selected geometry of the solar still was based on the total amount of the transmitted solar energy through the year, i.e. the solar still efficient performance will be year around. The methodology followed to achieve these objectives, via analytical analysis. 3. Modeling of the double slope solar still glass cover Fig. 1 illustrates the double slope solar still glass cover. The lengths of the two sides of the glass cover changed with respect to the optimum inclination angles (b1 and b2) with total length (L) that generates the basin width (W), so the results will be related to the glass cover total length (L) as: L1 þ L2 ¼ L
ð1Þ
L1 cos b1 þ L2 cos b2 ¼ W
ð2Þ
From Eqs. (1) and (2) after simplification
n W Z
number of days basin width (m) width of the still glass cover in depth direction (m)
Greek Symbols a polar angle b inclination angle of a tilted surface c azimuth of a tilted surface d declination angle h incident angle of beam radiation to tilted surface / latitude angle s transmittance of the atmosphere X hour angle
Lða cos b2 Þ and ðcos b1 cos b2 Þ Lða cos b1 Þ L2 ¼ with b1 –b2 ðcos b2 cos b1 Þ L1 ¼
ð3Þ
1 þb2 Þ where a ¼ W ¼ sinsinðb < 1. b1 þsin b2 L The double glass cover has two azimuth angles (c1 and c2) for the surfaces according to |c1| + |c2| = 180, with opposite signs of both c1 and c2. For this reason, the average beam radiation per unit (Z) for the inclined flat surfaces at inclination angles b1 and b2 can be obtained by: Gb ¼ L1 sgb Gbn cos h c¼c þ L2 sgb Gbn cos h c¼c ð4Þ 1
b1
2
b2
From Eqs. (3) and (4), the average beam radiation per unit area (L · Z) for the inclined flat surfaces at inclination angles (b1 and b2) can be obtained by: ða cos b2 Þ Gb ¼ sgb Gbn cos h c¼c 1 b ðcos b1 cos b2 Þ 1 ða cos b1 Þ þ sgb Gbn cos h c¼c2 ð5Þ b2 ðcos b2 cos b1 Þ Transmissivity of the glass cover, sgb (h) is the function of the incident angle h and may be presented as [18] and presented in Eq. (7). The angle h is incident angle of beam radiation to tilted surface and related to the declination d, the latitude /, the slope of the surface b, the azimuth of the surface c and the hour angle X as given below
Zenith
cos h ¼ M cos b þ N sin b
ð6Þ
where M ¼ sin dsin u þ cos dcos ucos X
β2
γ2
γ1
W
Figure 1
Flat surface double slope solar still.
N ¼ cos dsin ucos ccos X sin dcos u cos c þ cos dsin c sin X
β1
ð7Þ
sgb ¼ 2:642 cos h 2:163 cos2 h 0:32 cos3 h þ 0:719 cos4 h
In the above equations, north is positive for /, due south is zero for c with east negative and west positive, and the hour angle X is negative in the morning and positive in the afternoon.
Please cite this article in press as: W.M. El-Maghlany, An approach to optimization of double slope solar still geometry for maximum collected solar energy, Alexandria Eng. J. (2015), http://dx.doi.org/10.1016/j.aej.2015.06.010
An approach onto optimization of double slope solar still geometry Substitute in Eq. (5) to get the instantaneous average beam radiation that transmitted through the glass cover of the double slope solar still. In the above Eq. (5), the beam radiation Gbn is instantaneously constant with respect to the hour angle (X). Isotropic sky models will be used for estimation of diffuse radiation. Isotropic sky models are simple models that assume a uniform distribution of the diffuse radiation over the sky dome and circumsolar and horizontal brightening parts are considered to be zero. According to the simple model of an isotropic sky, the diffuse radiation per unit (Z) for the inclined flat surfaces at inclination angles b1 and b2 on the tilted surface Gd can be obtained according to: Gd ¼ L1 sgd Gdn ½1 þ cos b c¼c 1 b 1 þ L2 sgd Gdn ½1 þ cos b c¼c ð8Þ 2
b2
From Eqs. (3) and (8), the diffuse radiation per unit area (L · Z) for the inclined flat surfaces at inclination angles b1 and b2 can be obtained by: ða cos b2 Þ Gd ¼ sgd Gdn ½1 þ cos b c¼c 1 b ðcos b1 cos b2 Þ 1 ða cos b1 Þ þ sgd Gdn ½1 þ cos b c¼c ð9Þ 2 b ðcos b2 cos b1 Þ 2 Transmissivity of the glass cover, sgd (b) is the function of the glass cover angle, b, and may be presented as [18]. sgd ¼ 0:667 2:05 103 b 2:03 105 b2 ;
with bð Þ
ð10Þ
The total radiation absorbed on the tilted surfaces per unit surface area (L · Z) is the sum of the average beam and diffuse radiations as following EG ¼ Gb þ Gd
ð11Þ
Both values of the beam Gbn and diffuse Gdn radiation for optimization are calculated with Bouguer’s and Berlage’s equation, respectively [19] 1 Gbn ¼ Isasin as ð12Þ 0 1 1 sin as 0:25I sin a s 1 sa B C Gdn ¼ @ A 1 1:4 ln s
ð13Þ
where 360ðn 2Þ I ¼ 1370 1 þ 0:033 cos 365
ð14Þ
sin as ¼ sin d sin u þ cos d cos u cos X ¼ M
ð15Þ
Here n is the number of days from the first of January, and sa is the transmittance of the atmosphere that is calculated according to Hottel [20]. For generalization of the obtained results, it is interested to compare the performance of double slope solar still over one year. The total solar energy received (HG) per unit area (L · Z) for a total number of days (n = 365) will be obtained as Z 365 Z Xsunset HG ¼ EG dX ð16Þ 1
Xsunrise
3
4. Results and discussion The purpose of this section is to determine quantitatively the amount of collected transmitted solar energy through the two surfaces of the solar still throughout the year. The inclination angles b1 and b2 represent the inclination of the two sides of the glass cover are stated corresponding to the optimum inclination to receive maximum possible solar energy. The results are presented in two scenarios, the first one is for double slope with same inclination angles (b1 = b2) and the second for modified double slope solar still with optimum inclination angles (b1 and b2) optimum. 4.1. Total energy captured by the same slope (b1 = b2) solar still over one year for different azimuth and latitude angles By solving Eqs. (4) and (8) with same both side length (L1 = L2); led to (b1 = b2) and different azimuth and latitude angles, the total amount of transmitted solar energy (HG) per square meter of the total surface area (L · Z) through the solar still could be obtained by Eq. (16) and is represented in Fig. 2 for inclination angles (b = b1 = b2) from 10 to 60 while the basin to cover length ratio (a = W/L = cos b) varies from 0.984 to 0.5. From the results that are represented in Fig. 2, as the inclination angle increases the total transmitted solar energy through the glass cover decreases and the orientation with respect to the south has a noticeable effect. This is explained as, at small inclination angle the inflation of both surfaces led to horizontal flat plat and maximum energy could be received on both sides, this only for double slope but if the surface is only single slope located in north sphere the optimum slope (b) is around the latitude angle of the location (/ ). The maximum solar energy that transmitted is at b = 10 without no effect of the orientation (c1 and c2). At conventional inclination angle (b = /) for different locations, the total solar energy that transmitted is at the orientation of c1 = 90 and c2 = 90 with values less than that at b = 10, Table 1. 4.2. Total energy captured by the modified double slope solar still (optimum b1 and b2) over one year for different azimuth and latitude angles The first step in the calculations is to get the optimum inclination angles (b1 and b2) for both coupled pair of surfaces (c1 = 0 and c2 = 180), (c1 = 90 and c2 = 90), (c1 = 45 and c2 = 135) which is equivalent to (c1 = 45 and c2 = 135); that construct the solar still surface. By solving Eqs. (4) and (8) we get EG and consequently HG with only one azimuth angles (c = 0, ±45, ±90, ±135 and 180), the results are represented in Fig. 3 and the optimum inclination angles (b) are extracted and listed in Table 2 for different latitudes (/) taking into account that at |c| > 90 the optimum inclination angle (b) will be the same as |c| = 90. At the optimum inclination angles (b1 and b2) as well as the corresponding basin to cover length ratio (a = W/L) as listed in Table 2, Eqs. (5) and (9) are solved to get EG and consequently HG for both surfaces with the two pairs of the azimuth angles (c1 = 0 and c2 = 180), (c1 = 90 and c2 = 90), (c1 = 45 and c2 = 135) which is equivalent to (c1 = 45 and c2 = 135). Fig. 4 represents the total amount of transmitted
Please cite this article in press as: W.M. El-Maghlany, An approach to optimization of double slope solar still geometry for maximum collected solar energy, Alexandria Eng. J. (2015), http://dx.doi.org/10.1016/j.aej.2015.06.010
4
W.M. El-Maghlany
Figure 2 b1 = b2.
The annual total transmitted solar energy by the glass cover of the double slope solar still for different inclination angles with
Table 1 Total transmitted energy through the still surface at b1 = b2 for different latitude angles. /
(24)
b1 = b2 HG (GJ/m2/ year)
10 6.3
(27.2) 24 5.88
10 6.08
(30) 27.2 5.56
10 5.87
(31.2) 30 5.26
10 5.77
31.2 5.14
solar energy through the glass cover of the solar still for different latitudes and orientations at the optimum inclination angles that are listed in Table 2. The maximum transmitted energy for (/ = 24) is 6.488 GJ/m2/year with orientation of c1 = 45 and c2 = 135, for (/ = 27.2) is 6.1045
GJ/m2/year with orientation of c1 = 45 and c2 = 135, for (/ = 30) is 5.87 GJ/m2/year with orientation of c1 = 90 and c2 = 90, and for (/ = 31.2) is 5.77 GJ/m2/year with orientation of c1 = 90 and c2 = 90. 4.3. On the relation between cover tilt angles and latitude angle The inclination of the locus of the sun differs with the latitude angle. Consequently, the transmitted radiation from the still cover varies with the latitude angle (/) of the test zone. An optimum cover tilt angle that is close or almost equal to the latitude angle was established for single glass solar still, Fig. 3, with facing to the south direction (c = 0) while the optimum tilt of the symmetrical double slope (b1 = b2) was established at b1 = b2 = 10 far apart the latitude angles with
Please cite this article in press as: W.M. El-Maghlany, An approach to optimization of double slope solar still geometry for maximum collected solar energy, Alexandria Eng. J. (2015), http://dx.doi.org/10.1016/j.aej.2015.06.010
An approach onto optimization of double slope solar still geometry
Figure 3
5
The annual total transmitted solar energy by single glass solar still.
Table 2 Optimum declination angles (b1 and b2) for different azimuth (c1 and c2) and latitude angles (/). c1 = 0 and c2 = 180
(/ = 24) a = W/L (/ = 27.2) a = W/L (/ = 30) a = W/L (/ = 31.2) a = W/L
c1 = 90 and c2 = 90
c1 = 45 and c2 = 135
b1
b2
b1
b2
b1
b2
19 0.971 22 0.966 25 0.961 26 0.96
10
10 0.98 10 0.98 10 0.98 10 0.98
10
15 0.977 17 0.974 20 0.969 22 0.966
10
10 10 10
10 10 10
10 10 10
Figure 4 The annual total transmitted solar energy by the glass cover of the double slope solar still for different latitudes and orientations at optimum inclination angles b1 and b2.
Please cite this article in press as: W.M. El-Maghlany, An approach to optimization of double slope solar still geometry for maximum collected solar energy, Alexandria Eng. J. (2015), http://dx.doi.org/10.1016/j.aej.2015.06.010
6 south orientation independence. With the novel approach, the optimum tilt of the cover glass of the double slope (b1 and b2) has different optimum values for the two sides, as the surface direction go towards the south, the optimum inclination angle closed to the latitude angle (c 6 45) while the other side need an inflation (b = 10), for maximum transmitted solar energy, Table 2. 5. Conclusion In this study, the amount of transmitted solar energy through the surface of the glass cover of the double slope solar still during the year is estimated for latitude angles between 24 and 31.2. The main obtained results could be concluded as: The mathematical expression for the transmitted solar energy through the surface of the glass cover of the double slope solar still is obtained. For single glass solar still, the optimum cover tilt angle that is close or almost equal to the latitude angle with facing to the south direction (c = 0). b1 = b2 = 10 are the optimum tilt of the symmetrical double slope solar still without any effect of the orientation due south. The optimum tilt of the cover glass of the double slope solar still not necessary to be symmetrical but has values depend on the direction of each surface with respect to the south direction.
References [1] K.B. Baibutaev, B.M. Achilov, Comparative testing of a solar distiller, Appl. Solar Energy 4 (1968) 69–72. [2] A.S. Al-Jubouri, A.J.N. Khalifa, An experimental study on the performance of solar still in Iraq, in: Passive and Low Energy Alternatives International Conference, Bermuda, September, 1982, pp. 1–7. [3] A.K. Tiwari, G.N. Tiwari, An optimization of slope of condensing cover of solar still for maximum yield: in summer climatic condition, Centre for Energy Studies, Indian Institute of Technology Hauz Khas, New Delhi, India, 2004.
W.M. El-Maghlany [4] M. Abd Elkader, An investigation of the parameters involved in simple solar still with inclined yute, Renewable Energy 14 (1998) 333–338. [5] S. Kumar, G.N. Tiwari, H.N. Singh, Annual performance of an active solar distillation system, Desalination 127 (2000) 79–88. [6] A.S. Nafey, M. Abdelkader, A. Abdelmotalip, A.A. Mabrouk, Parameters affecting solar still productivity, Energy Convers. Manage. 41 (2000) 1797–1809. [7] M.N. Bahadori, F.E. Edlin, Improvement of solar stills by the surface treatment of the glass, Sol. Energy 14 (1973) 339–352. [8] G.N. Tiwari, J.M. Thomas, E. Khan, Optimisation of glass cover inclination for maximum yield in a solar still, Heat Recov. Syst. CHP 14 (1994) 447–455. [9] R. Dev, G.N. Tiwari, Characteristic equation of a passive solar still, Desalination 245 (2009) 246–265. [10] H. Aybar, H. Assefi, Simulation of a solar still to investigate water depth and glass angle, Desalination Water Treat. 7 (2009) 35–40. [11] W.A. Kamal, A theoretical and experimental study of the basintype solar still under the Arabian Gulf climatic conditions, Solar Wind Technol. 5 (1988) 147–157. [12] S. Aboul-Enein, A.A. El-Sebaii, E. El-Bialy, Investigation of a single-basin solar still with deep basins, Renewable Energy 14 (1998) 299–305. [13] K.B. Baibutaev, B.M. Achilov, Effect of the inclination of the transparent solar still surface on the condensation and collection processes, Appl. Solar Energy 6 (1970) 34–38. [14] H.P. Garg, H.S. Mann, Effect of climatic, operational and design parameters on the year round performance of singlesloped and double-sloped solar still under Indian arid zone conditions, Sol. Energy 18 (1976) 159–163. [15] H. Al-Hinai, M.S. Al-Nassri, B.A. Jubran, Effect of climatic, design and operational parameters on the yield of a simple solar still, Energy Convers. Manage. 43 (2002) 1639–1650. [16] A. Omri, J. Orfi, S.B. Nasrallah, Natural convection effects in solar stills, Desalination 183 (2005) 173–178. [17] T. Abderachid, K. Abdenacer, Effect of orientation on the performance of a symmetric solar still with a double effect solar still (comparison study), Desalination 329 (2013) 68–77. [18] H. Tanaka, Y. Nakatake, Theoretical analysis of a basin type solar still with internal and external reflectors, Desalination 197 (2006) 205–216. [19] Japan Solar Energy Society, Solar Energy Utilization Handbook, Japan Solar Energy Society, Tokyo, 1985, p. 20. [20] H.C. Hottel, A simple model for estimating the transmittance of direct solar radiation through clear atmospheres, Sol. Energy 18 (1976) 129–134.
Please cite this article in press as: W.M. El-Maghlany, An approach to optimization of double slope solar still geometry for maximum collected solar energy, Alexandria Eng. J. (2015), http://dx.doi.org/10.1016/j.aej.2015.06.010