Parametric study of an inverted absorber double-effect solar distillation system

Transcription

1 Paraetric study of an inverted absorber double-effect solar distillation syste.2* Sangeeta Suneja 1, G.N. Tlwarl, S.N. Rai 1 l physics Departent, MMH College, Ghaziabad (UP), India 2Centre for Energy Studies, Indian Institute of Technology, New Delhi , India Tel. +91 (I1) , ext. 5040," Fax +91 (11) Received 25 October 1996; accepted 22 January 1997 Abstract An analysis of an inverted absorber double-effect solar still is presented. Energy balance equations have been written, and analytical expressions for water and condensing cover teperatures and the hourly yield have been derived. Nuerical coputations have been carried out for a typical day in Delhi. The results thus obtained have been copared with those of the conventional double effect (double basin) solar still. It was observed that an inverted absorber solar still gives a higher output than the conventional double-effect one. Keywords: Solar still; Purification of water; Solar energy I. Introduction A conventional solar still is referred to as a single effect solar still. Work has already been done on the perforance of a single-effect solar still by Sodha et al. [1], Tiwari and Madhuri [2] and Malik et al. [3]. The latent heat of vaporization lost to the abient through the condensing cover in a single-effect solar still can be reused in the heating of water in the basin above the condensing cover in a double-effect *Corresponding author. solar still. Work on a double-effect solar still has been carried out by Sodha et al. [4,5] and Tiwari et al. [6]. In a double-effect solar still, since the nuber of effect has increased, the net energy available in the basin decreases due to the presence of two water asses and two glass covers. In order to avoid reduction of available theral energy in the basin liner, an inverted absorber solar still was studied by Tiwari and Suneja [7]. In the case of an inverted absorber double-effect solar still, the reuse of latent heat can be carried out in a way siilar to that done in a double-effect solar still

2 without affecting the availability of energy in the basin liner. In this counication, analytical expressions for water and condensing cover teperatures, the various internal heat transfer coefficients and the hourly yield have been derived for an inverted absorber double-effect solar still. Nuerical coputations have been carried out for a typical day in Delhi. Effect of initial water teperature, water depth in the basin and the absorptivity of the absorber plate on the yield have also been studied. The results obtained were copared with those of an inverted absorber single-basin solar still as well as of conventional double-basin solar stills. On the basis of the nuerical coputations, the following conclusions can be drawn: The daily yield of an inverted absorber double-effect solar still varies fro 8.37 kg to 9.159kg for 2 c depth of water in each basin, and 0.95 absorptivity when the initial teperature of water in the lower basin varies fro 22 C to 35 C. The daily yield of an inverted absorber double-effect solar still varies fro kg to 7.404kg for a 30 C initial water teperature in the lower basin and 0.95 absorptivity as the depth of water in each basin varies fro 1 c to 5 c. The daily yield of an inverted absorber double-effect solar still varies fro 4.332kg to 8.855kg for 2c depth of water in each basin and at an initial teperature of 30 C in the lower basin, as the absorptivity of the absorber varies fro 0.55 to Working principle The solar radiation after transission through the glass plate gl is reflected to the inverted absorber of the solar still (Fig. 1). Most of the radiation is convected to the water ass above and a sall part is lost to the atosphere through glass plates gl and g2- The water gets heated and then there are convective, radiative and I(I)~N~ GLASS PLATE 91 qrw ~'w V~TER MASS M 2 WATER MASS M I BSOR~R PLATE p GLASS PLAT[ Fig. 1. Scheatic diagra of an inverted absorber double-basin solar still. evaporative losses to the condensing cover. The water condenses on the inner side of the condensing cover (C 0 by releasing its latent heat fro vaporization. The condensed water is collected through the channel. The latent heat of vaporization, released to C], is reused to heat the water ass in the basin above the condensing cover C 1. Again, this water ass is heated, and there are further convective, radiative and evaporative losses fro the upper water ass to the inner surface of a second condensing cover C 2. The water vapor condenses by releasing its latent heat fro vaporization, and the condensed vapor trickles down the condensing cover under gravity and is collected through the channel. 3. Energy balance The following assuptions have been ade in writing the energy balances of different coponents of the double-effect inverted absorber solar still: The heat capacities of the glass covers, the absorbing aterial, the condensing covers and the insulation are negligible. The solar distiller unit is vapor leakage proof. The area of aperture is the sae as that of the

3 absorber plate and the concentration ratio is 1:1. The inclination of the glass cover is sall. The energy balance equations are as follows: Absorber plate (p): h~+hew+hc~:hw(tw-tc) The internal heat transfer coefficients are given by h~= eefro IT+ 273) 2 +(T+273)2][T + T+ 546] T'gl~g2Dl, ppni=hcpwl(tp-twl ) Glass plate (g2): + hrpg2 (Tp- Tg2) (1) (2) h = 0.884[fT -Tc)~ (Pw-Pc)(Tw+273)] 1/3 V j hew= x 10-3xho~x (P~-Pc) Water ass (0: drw 1 hcpwl (Tp- Twt) : (l C)w dt (3) h = V 2 where Pw = exp[ ] T Condensing cover (C l): (4) P = exp[ T Water ass (2): Eeff = Ew hcl (Tcl- Tw2) = (2 C)w dtw2 dt Condensing cover (C2): (5) With the help of Eqs. (1)-(4), Eq. (3) can be rewritten as I dt +alt~l+a2tw2=f(t) where hw2 (Tw2 -- L2) "~ hc2 (Tc2 -- L ) where (6) a 1 - Uwlw2+~fWl a " _ ~WlW2., a 2 lc lc

4 f(t) = (ax)effi(t) + UWla~ ;,,') lc -1 hcpw~ ; Ups= hrpg 2 Ur -1 -~-(~,o + ~+~o)e -~' +~.(r~lo +~_r~o? -~-t (9) (at)eft = T,g I T.g 2 arr N Uwla v With the help of Eqs. (4)-(6), Eq. (5) can be written as ate2 dt where + bltwl + b2tw2 = g(t) -~,w~. u.u o b I -, b 2-2C 2C and 1 [M. (,-e-c.') rw C t M c (a-e)+~10+~+~20)e<' -(Zwl 0 + a_ T w2o)e ~ -cj I ] where M e =f+ a+g ] (lo) g _ 2 C ' hw2a + -1 a I + b 1 = C a 2 + b 2 = ac In order to get the solution to Eqs. (7) and (8), the following assuptions were ade: 1. The tie interval At (0 <t<at) is sall. 2. The functionf(t) and g(t) are constant, i.e., f(t) =fit) and g(t) = g(0 for the tie interval At. 3. al, a2, b 1 and b 2 are constant during the tie interval. 4. The initial values of water and condensing cover teperatures have been used to deterine the value of internal heat transfer coefficients. By using the above assuptions, the solutions to Eqs. (7) and (8) can be written as and (b2-al):t:i(b2-al~+4a2bl 2b 1 After knowing T w and T w, expressions for T and To2 can be obtai~aed fror~ Eqs. (4) and (6) as' h ~l 1".2 + hwl Twl L1 = hcl + hwl (11) hw2tw2 * hc2t ~ L: = (12) hw2 + he2

5 The rate of heat flux per 2 due to evaporation fro first and second effects can be obtained as 1.4 To The rate of distillation per 2 is 0ew] rh - x3600 kg/h ~] t S 0.6 o l(t) 2s~ o 20 g r~ E 0ew 2 - x3600 kg/h ew2 L [- I \ 5 4. Nuerical results and discussion In order to have a nuerical appreciation of results, the following cliatic and design paraeters have been used. The hourly variation of solar intensity and abient teperature are shown in Fig. 2. The other paraeters used are as follows: "Cg = 0.9, ~g2 1.0, tp = 0.95,0.85,0.75,0.65,0.55; r = 0.9; N = 2.5 A = l2; hrpg= 6W/2 C Ur=4.16W/2 C; h cpw I =10W/2 C C = 4190J/Kg C; o = 5.67x 10-SW/2K 4 L = 2022 x 103 J/kg 1 = 2 = 10kg, 20kg, 30kg, 40kg, 50kg hc~ = 90 W/ 2 C; he2 = 24.7 W/ 2 C The hourly variation of the solar intensity and the abient teperature is shown in Fig. 2. The hourly variation of the yield of water and O01 I I I I I ' 0 t, Tie of the day(hour) Fig. 2. Hourly variation of solar intensity and abient teperature. t C % bj >. 0, O.t, / 0.3 I, / I t X 0-2 /! \\ T~, =30"C ~.p= 0.95 / \\! \ 0.I / / x. LOWER BASIN UPPER BASIN O ~ / ~ 2 I., 6? TIM( OF TIlE DAY (HOURS} Fig. 3. Hourly variation of yield of an inverted absorber double-basin solar still.

6 dl=2c.d2= 2 c TL =30" C LOWER BASIN 0.9 O~ lc "~p = 0-95 T t = 35"C LOWER BASIF 60 UPPER BASIN UPPER BASII~ o~,,.i \ \ \ I O-5 "C 0" / / / \',\ \ \ \\%. % ; \\ IO /, 6 7 TIME OF THE DAY (hour) Fig. 4. Hourly variation of water and condensing cover teperatures of an inverted absorber double-basin solar still i 8 I~) // \ TIME OF THE DAY (hour) Fig. 6. Effect of depth of water on hourly variation of yield of an inverted absorber double-basin solar still. 0.7 dl = 2 c / 1-85 't 0.6 / \ ~ LOWER BASJN 0.5 ' lii:l' ~ o.3 j ~,4,o.~s [\ >~44///',` 7,,, 0 i ~ /, t. 6 7 TIME OF THE DAY (HOURS) Fig. 5. Effect of etp on hourly variation of a double-basin inverted absorber solar still. condensing cover teperatures of an inverted absorber double-basin solar still are shown in Figs. 3 and 4, respectively. It has been observed that the yield fro the lower basin is higher than that fro the upper basin, as expected. Fig. 5 shows the effect of absorptivity of the absorber on the hourly variation of the yield of an inverted absorber double-basin solar still. As is evident, a decrease in absorptivity decreases the output of the still. Further, the effect of depth of water in the basin on the hourly variation of the yield of an inverted absorber double-basin solar still is shown in Fig. 6. An increase in the depth of water decreases the total output of the still because of the lowering of the operating teperature at greater depths. For a coparison of the results, the daily yield/ 2 for different solar stills is given in Tables 1-5. On the basis of these tables, the following conclusions can be drawn:

7 1. As the initial water teperature is increased fro 22 C to 35 C for a particular value of absorptivity and water depth, the yield of an inverted absorber double-basin solar still Table 1 Effect of initial water teperature on the yield (in kg/ 2) of inverted absorber double- and single-basin solar stills ct Teperature, C Double-basin: Single-basin: increases by about 10% whereas the yield of an inverted absorber single-basin solar still increases by about 12% (Table 1). 2. For a particular initial water teperature and particular absorptivity, the yield of an inverted absorber double-basin solar still decreases by about 27% as the depth of water in the lower basin increases fro 1 c to 5 c, and the yield of an inverted absorber single-basin solar still decreases by 13% as the depth of water in the basin increases fro 2c to 10c (Table 2). 3. The yield of an inverted absorber doublebasin solar still increases by about 99%, whereas the yield of an inverted absorber single basin solar still increases by about 86% as the absorptivity of the absorber increases fro 0.55 to 0.95 for a particular value of water teperature and water depth (Table 1). 4. The yield of a conventional double-effect solar still increases by about 43% as the absorptivity of the absorber increases fro 0.45 to 0.65; the yield increases by about 10% as the Table 2 Effect of water depth in the basin on the yield (in kg/ 2) of inverted absorber double- and single-basin solar stills c~ Depth, c (double basin) Depth, c (single basin) Table 3 Yield (in kg/ 2) fro a conventional double-basin solar still t~ Teperature, C Depth, c

8 B n Table 4 Coparison of yield (in kg/ 2) of an inverted absorber and a conventional double-basin solar still for different initial water teperature in the lower basin Table 5 Coparison of yield (in kg/ 2) of an inverted absorber and a conventional double-basin solar still for different water depth in the basin ct Teperature, C ct Depth, c Inverted Inverted absorber absorber 0.95: 0.95: Lower Lower Upper Upper Total Total : 0.85: Lower Lower Upper Upper Total Total : 0.75: Lower Lower Upper Upper Total Total Lower Lower Upper Upper Total Total Lower Lower Upper Upper Total Total Conventional 0.65: Lower Upper Total : Lower Upper Total : Lower Upper Total Lower Upper Total Lower Upper Total Conventional 0.65: Lower Upper Total 0.60: Lower Upper Total 0.55: Lower Upper Total 0.50 Lower Upper Total 0.45 Lower Upper Total

9 - - Area initial water teperature in the lower basin increases fro 22 C to 35 C; the yield decreases by about 21% as the depth of water in each basin increases fro 2c to 5 c (Table 3). 5. Coparing Tables 1 and 2, it is seen that an inverted absorber double-effect solar still gives about 87% higher yield as copared to the inverted absorber single-effect solar still. The result is as expected because in the double-effect solar still the latent heat of vaporization, released by the evaporated water in the lower basin to its condensing cover, is reused in the heating of water in the upper basin. 6. Coparing Tables 1 and 3, we observe that an inverted absorber double-effect solar still gives about 43% higher output than the conventional double-effect solar still. This is due to the lower absorptivity of the absorber in a double-effect solar still whereas in an inverted absorber still the nuber of effects does not result in lower absorptivity. 7. As seen fro Tables 4 and 5, in the case of the inverted absorber double-basin solar still, the yield fro the lower basin is always higher than that fro the upper basin; whereas in the conventional double-basin solar still, for lower values of absorptivity and for higher depth of water in each basin, the yield fro the lower basin is less than that fro the upper basin. The reason is that in the forer case (of the inverted absorber double-basin solar still), the absorption of solar radiation is fro below, the absorber being inverted; while in the latter case, the lower value of absorptivity results in less absorption of solar radiation, and a greater water depth in the basin leads to the storage effect. 5. Sybols A C d hcp~, of the basin of the still, 2 -- Specific heat of water, J/kg C -- Depth of water in the basin, c --Convective heat transfer coefficient fro absorber plate to water ass in basin 1, W/ 2 C) h~, --Convective heat transfer coefficient fro water ass in basin 1 to condensing cover C1, W/ 2 C h~,~ --Evaporative heat transfer coefficient fro water ass in basin 1 to condensing cover C1, W/ 2 C h,~, -- Radiative heat transfer coefficient fro water ass in basin 1 to condensing cover C1, W/ 2 C hw, --Total heat transfer coefficient fro water ass in basin 1 to condensing cover C1, W/ 2 C hq --Convective heat transfer coefficient fro water ass in basin 2 to condensing cover C2, W/ 2 C h --Convective heat transfer coefficient cw 2 fro water ass in basin 2 to condensing cover C2, W/ 2 C hew: --Evaporative heat transfer coefficient fro water ass in basin 2 to condensing cover C2, W/ 2 C h -- Radiative heat transfer coefficient fro rw 2 water ass in basin 2 to condensing cover C2, W/ 2 C hw2 --Total heat transfer coefficient fro water ass in basin 2 to condensing cover C2, W/ 2 C he2 --Convective heat transfer coefficient fro condensing cover C 2 to abient, W/ 2 C l -- Solar intensity, W/ 2 L -- Latent heat of vaporization, J/kg 1 -- Mass of water in basin 1, kg 2 -- Mass of water in basin 2, kg N -- Average nuber of reflections Pc --Partial saturated vapor pressure at teperature To, N/ 2 Pw --Partial saturated vapor pressure at teperature Tw, N/ 2 r -- Reflectivity T -- Teperature, C t -- Tie, s Upa --Overall heat transfer coefficient fro absorber plate to abient, W/ 2 C U r -- Back loss coefficient, W/ 2 C

10 Uw,w2 --Overall heat transfer coefficient fro water ass in basin 1 to water ass in basin 2, W/ 2 C Uw, a --Overall heat transfer coefficient fro water ass in basin 1 to abient, W/ 2 o C Uw2 a --Overall heat transfer coefficient fro water ass in basin 2 to abient, W/ 2 o C V Greek cc o z Subscripts -- Wind velocity, /s -- Absorptivity -- Eissivity -- Stefan's constant -- Transissivity a -- Abient conditions c 1 -- Condensing cover of basin 1 c 2 -- Condensing cover of basin 2 p -- Absorber plate w I -- Water ass in basin 1 w 2 -- Water ass in basin Lower basin 2 -- Upper basin References [1] M.S. Sodha, U. Singh, A. Kuar and G.N. Tiwari, Int. J. Energy Res., 5(4) (1981) 341. [2] G.N. Tiwari and Madhuri, Desalination, 61 (1987) 67. [3] M.A.S. Malik, G.N. Tiwari, A. Kuar and M.S. Sodha, Solar Distillation, Pergaon Press, UK, [4] M.S. Sodha, J.K. Nayak, G.N. Tiwari and A. Kuar, Energy Conv. and Mgt., 20 (1980) 23. [5] M.S. Sodha, U. Singh, A. Kuar and G.N. Tiwari, Energy Conv. and Mgt., 20 (1981) 181. [6] G.N. Tiwari, C. Suedha and Y.P. Yadav, Energy Conv. and Mgt., 32 (1991) 293. [7] G.N. Tiwari and S. Suneja, Perforance evaluation of an inverted absorber solar still. Energy Conv. Mgt., in press.