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Transient analysis of double-basin solar still integrated with collector
Desalination, 71 (1989) 151-164 Elsevier Science Publishers B.V., Amsterdam -
151 Printed in The Netherlands
Transient Analysis of Double-Basin Solar Still Integrated with Collector Y .P. YADAV* Department of Physics, C.M. Science College Darbhunga, 846004 Bihar (India), Tel. 2582 (Received May 24,1988) SUMMARY
A transient analysis of a double-basin solar still coupled to a flat plate solar collector is presented. The analysis has been carried out for both the natural (thermosiphon) and forced circulation of water between the collector and the still. Explicit expressions for the temperatures of water mass, glass cover, and basin liner of the proposed system have been developed. Effect of water depth on the distillate output and efficiency of the proposed system has been studied in detail. For appreciation of the analytical results, numerical calculations have been made for a typical day under Delhi climatic conditions. Performance of the proposed system has also been compared with that of the uncoupled double-basin solar still. Keywords: double-basin solar still, collector, transient analysis.
SYMBOLS &
-
A,
-
A, A,
-
Am.1
-
A,
-
CW
-
F’
-
FR hb hl
-
h 1U
-
Basin area Collector area Surface area of connecting pipe Area of the lower glass cover Area of the water surface in the lower basin Area of the water surface in the upper basin Specific heat of water Collector efficiency factor Heat removal factor of the collector Bottom heat loss coefficient Total heat transfer coefficient from the water surface to the glass cover of the lower basin Total heat transfer coefficient from the water surface to the glass cover of the upper basin
(m”)
gz;
g:,’ b”)
(J kg-’
‘C-l)
( Wmm2 ‘C-l) (WmB2 “C-l) ( Wmm2 oC-1)
*Present address: SSO-II, Centre for Energy Studies, IIT, Delhi, Hauz Khas, New Delhi 110016, India. OOll-9164/89/$03.50
0 1989 Elsevier Science Publishers B.V.
-
-
-
Total heat transfer coefficient from glass cover of lower basin to water Total heat transfer coefficient from the glass cover of the upper basin to ambient Heat transfer coefficient from the basin liner to water Total heat transfer coefficient from the bottom of the still to the ambient Solar intensity incident on still Solar intensity on collector Thermal conductivity of the insulation material Thickness of insulation Hourly distillate output Distillate output per unit time per unit surface area of the lower basin Distillate output per unit time per unit surface area of the upper basin Mass flow rate of water in the collector Total heat capacity of the lower basin and the collector Heat capacity of collector and water within it Heat capacity of connecting pipes and water within them Heat capacity of water mass in the lower basin Heat capacity of water mass in the upper basin Temperature of collector and water within it Water temperature of the lower basin Temperature of connecting pipe and water within it Collector inlet temperature Collector outlet temperature Temperature of water mass in the upper basin Overall heat loss coefficient of the collector Heat loss coefficient of connecting pipes
Greek symbols - Absorptivity of collector - Fraction of energy absorbed by the basin liner of : the still &I, rgu - Fraction of energy absorbed by the glass cover of lower and upper basin respectively
(Wmm2 ‘C-l) ( Wmw2 ‘C-l)
(Wmm2 ‘C-l) (Wmw2 ‘C-l) ( Wmm2) ( Wmm2) ( Wmm2 oC-l)
(m) (kgmw2 h-l) (kgmm2 s-l) (kgmm2 s-l) (kg s-2) (J ‘C-l) (J OC--l) (J ‘C-l) (J ‘C-l) (J ‘C-l ) (“C) (“C) (’ C) (“C) (“C) (’ C) (WmM2 “C-l)
153
Lb Ll
-
(@)
-
? 6”
Fraction of energy absorbed by the water mass in the lower and the upper basin respectively Effective transmittance-absorbance product Efficiency of the still Energy available from the collector (W mw2)
INTRODUCTION
The basin-type solar still, also referred to as the green-house roof-type, simple or conventional solar still, is in an advanced stage of development. Several researchers (Cooper [ 11, Frick [ 21 and Hirschmann and Roefler [ 31) have investigated the effect of climatic, operational and design parameters on the performance of such stills. Periodic and transient analyses have been presented by Baum et al. [ 41, Nayak et al. [ 51 and Sodha et al. [ 61, and enhancement of the performance of the still has been studied. In order to enhance the distillate output of the still, it is important to consider the losses suffered by solar stills. These losses are (i) conduction losses from the base, sides and edges, (ii) leakage of water vapor and (iii) convective and radiative losses from the glass cover to the ambient. The conduction losses can be reduced by using proper insulation on the base and the sides of the still. For further reducing the conduction losses, Sodha et al. [ 71 suggested maintaining the temperature of the basin water at a higher value than the blackened base of the still by dissolving a dye in the basin water. The losses due to leakage of water vapor can be prevented by perfect sealing, i.e. by providing rubber gaskets just below the glass cover. The convective and radiative heat losses from the glass cover to the ambient arise from the latent heat given by the water vapor at the inner surface of the glass cover. This latent heat ultimately increases the temperature of the glass cover thereby reducing the temperature difference between the water and the glass cover and consequently decreasing the distillate production rate. To make use of the latent heat of vaporization of water, a concept of the double-basin solar still has been suggested by Malik [8]. Sodha et al. [9] analysed the performance of this system based on periodic analysis and reported that the daily distillate production increased by 36% as compared to the single-basin still. However, the performance of the double-basin solar still may further be improved by integrating it with a flat plate collector, which increases the temperature difference between the water mass and the glass cover of the lower basin resulting in an enhanced distillate output. Moreover, the distillation is accomplished at a higher temperature; therefore, this system is very useful for extraction of essence from flowers, seeds, etc. The double-basin solar still coupled to a flat plate collector can be operated in two modes, namely the thermosiphon mode and the forced circulation mode, depending upon the way of circulation of water between the collector and the still. In the thermosiphon mode, natural circulation of water between the collector and the still occurs due to a density gradient while in the forced circulation
154
mode, a water pump is used for the circulation of water between the still and the collector. The former mode requires no electrical power for operation of the system while in the latter mode, it is necessary to run the pump. However, the double-basin solar still coupled to a collector in the thermosiphon mode is useful for high-temperature distillation in remote places where electrical power is not available. Therefore, it appears to be of considerable interest to study the performance of the proposed system. The present paper deals with the performance studies of the double-basin solar still coupled to a flat plate collector in both thermosiphon and forced circulation modes, based on a transient analytical approach. Apart from this, the performance of the uncoupled double-basin solar still has also been studied so as to make an assessment of the improvement obtained by coupling the still to the collector. Explicit expressions for the water and basin liner temperatures, hourly distillate output and efficiency of the proposed system have been developed. In order to appreciate the analytical results, numerical calculations have been carried out for a typical day under climatic conditions prevailing in Delhi. From the results obtained it is concluded that the double-basin solar still coupled to a flat plate collector performs better in the forced circulation mode than in the thermosiphon mode; however, these performances are still better than those of the uncoupled double-basin solar still. Apart from this, the effect of water depth and heat capacity of the water mass on the daily distillate output and efficiency has also been studied in detail. Illustration of the proposed system The schematics of the double-basin solar still, uncoupled and coupled to a flat plate collector, in thermosiphon modes of operation are shown in Figsla-
SUN
+
SUN
*
Fig. 1. (a) Schematic of uncoupled double-basin solar still. (b) Schematic of the double-basin solar still coupled to a collector in the thermosiphon mode. (c) Schematic of double-basin solar still coupled to a collector in the forced circulation mode.
155
c. The lower and upper heaters of the flat plate collector are connected to the bottom and the top of the lower basin of the still for both the thermosiphon and the forced circulation modes (Figs. lb and lc, respectively). For the thermosiphon mode, the double-basin solar still is kept above the upper heater of the flat plate collector in order to provide an adequate heat for the natural circulation of water in the proposed system; in the forced circulation mode it is not essential to place the still above the outlet heater of the collector. TRANSIENT ANALYSIS
The following assumptions have been made for the energy balance under various conditions of the proposed system. (1) Glass cover and water surface are parallel. (2 ) Heat capacities of the glass cover and the insulation are negligible as compared to the heat capacity of water mass in the basin. (3 ) The system is air- and vapor-tight. (4) There does not exist a temperature gradient along the glass thickness and the water depth. (5 ) Sides and bottom of the still are insulated. (6) The surface area of glass cover and water mass in the basin and the basin liner are the same. (7) The flat plate collector is uncoupled to the still during off-sunshine hours. During sunshine hours Upper basin Glass cover (1)
r,H,+h,,(T,,-T,)=h,,(T,-T,) Water mass dT A,i,,H,+Aglh21(Tgl-Twu)=Mwu~+Awuhlu
(7%~T,)
(2)
Lower basin Glass cover r,,H,+h,,(T,,-T,,)=h,,(T,,-T,,)
(3)
Water mass dT,, A,,i,,H,+B,+Abh3(Tb-Tw,)=Mwl~+Awlhll(Twl-Tgl)
(4)
156
Basin liner
(5)
rbH*=hB(Tb-T,1)+hb(Tb-T,) where h
Expressions for hi, h, and h2 are obtained by following Malik et al. [lo]. Here, 0, is the energy available from the collector and its values, for uncoupled still and still coupled to collector in the thermosiphon mode and forced circulation mode are respectively as follows Uncoupled double basin solar still (Fig. la) :
(6)
e,=o
Still coupled to collector in thermosiphon mode (Fig. lb): bu=l;t, Cw(Tw,-Twi)
(7) Still coupled to collector in forced circulation mode (Fig. 1~): &=A,&
[(ra!).ffH,,-u~(T,-T,)l
(8)
For the thermosiphon mode, the body temperature of the collector is equal to its water temperature [ 111. Therefore, one can write T, = T,,
Tp=Twp Hence, Eqn. (7) takes the form
&,=F’A,(@v)~,H,,-
dT
[
F’A,U,(T,,-T,)+M,dt+M,dt+
&A,
VW-T,)
dT
1
(9)
On the basis of the experimental observations, Close [ 121 reported that the mean water temperature in the tank is the same as the mean water temperature in the absorber during the sunshine hours. This will be true for the pipe tem-
157
perature too. Hence the mean water temperature in the basin of the still might be considered to be the same as that in the absorber. This leads to T,=T,,=T,
(10)
Upon substituting Eqn. (10) into Eqn. (9)) Eqn. (9) modifies to b,=F’A,(&&H,,-
[
F’A,UL(Tw-Ta)+
(N+&.)
%+U,A,((T,v-Te,)
1 (11)
Eqns. (l), (3) and (5) give
(12) (13)
and (14)
Now substituting the values of I$, Tgu,Tgland Tb from Eqns. (ll), (12), (13) and ( 14) respectively in Eqns. (2 ) and (4) and rearranging the terms, one can obtain dT
$+aT,,
+bT,, =g(t)
(15)
and
dTw,
dt+a’Tw,+bTw=g’(t)
where a=-
(A, u,)
WVU
(16)
158 -1
U,=
(7Et,;> 1U
+w,
g(t) =BH,
B= j&
a,
-
_
2u
[(A,&
wu
u,)l(h,,)+A,r,,+A,,r,U,l
F’A, UL+ UpA, + GA, +&I U, M2
x
>
F’A, U, + L&A, +A,, U, MZ
(neglecting
pipe losses )
>
A,, Ul “=-M g’
(t)
2
=A’&
+B’H,
+C’T,
A, _F’A,W,,, M2
c,
= WA, UL.+ UA,) M2
M,=M,+M,+M,, By multiplying one obtains dW YfPd,
Eqn. (16) throughout
dTwl+ (a+j3a’)T,,+
by /3 and adding the results to Eqn. (15))
(b+pb’)T,,=g(t)+pg’(t)
(17)
Now, choosing a value for m so that m=b+pb
(18)
and mp=a+/?a’ and substituting
(19) the value of m from Eqn. (18)in Eqn. (19)
b’P2+ (b-a’)/?-a=0 gives
(20)
159
p+ = _ (b-u’)
2 J(b-a’)2+4ab’
2b’ Hence m+ =b+j?,b’
(21)
Now Eqn. (17) may be written as
(22) where
S+(t) =&f(t) +&g’ (t) The solution of Eqn. (22) subjected to the initial conditions T,,(kO)
=T,, (23)
can be expressed as (24)
From Eqn. (24 ), one can obtain, after a simple algebraic manipulation, 1 TVA= (P+ -p-)
[I
2
[l-exp(-
[1-exp(
m+t)] -2
-m-t)]
I
+
1 (25)
{(T~,+p+T,,~)exP(-m+t)-((T-,+p_T,l,)exp(-m_t)} and
P+S-
Tw”=(p+ -P-)m[l-exp(-m+t)]+
[1-exp(
-m-t)]
-
B-S+ (P+ -P-
)m+ ‘IB_) + (26)
The values of T, and T, can be determined by substituting the values of T,, and T, from Eqns. (25) and (26) respectively in Eqns. (12) and (13).
160
During off-sunshine hours During off-sunshine hours, only the solar intensity and the collector terms will vanish; otherwise the analysis will be the same. Expression for the distillate output The amount of the distillate output obtained from the upper and the lower basin per unit time per unit basin area will be expressed respectively as (27) and
where _Y= latent heat of vaporization of water. Hence, the total hourly distillate output obtained from the proposed system will be given by r;t, = (tie, + &i) x 3600.0
(29)
For the forced circulation mode Eqn. (8) will be used instead of Eqn. (2 ) and Eqn. (4) and then the similar procedure will be followed. Expression for efficiency of the system The efficiency of the proposed system may be expressed as (30) where At refers to the time interval over which the solar intensity is measured. RESULTS AND DISCUSSION
In order to appreciate the analytical results, numerical calculations have been carried out for a typical day, i.e. 16th February 1986, at Delhi. The numerical values of the relevant parameters taken for calculations are as follows: Still parameters = 1.0 m2 = 1.0 m2 = 1.0m2 = 1.0m2 = 15.973 Wme2 ‘C-l = 94.14 Wmm2 “C-l
Ab A, A,1 AWlI hl, hz,
161
h 1U h 2u h3 he, h iiU Li _Y Mw, M,, r 91 r WI
= =
= = = = = = = = = =
16.173 Wm-’ “C-l 70.47 Wm-’ “C-’ 111.95 Wm-’ “C-l 8.12 Wm-’ “C-l 8.64 Wm-’ “C-’ 0.04 Wm-’ “C-’ 0.05 m 2.37252 x lo6 J kg-’ 261,875.0 J “C-l 209,500 J ‘C--l 0.0 0.0 0.0 0.5
Collectorparameters = 1.5m2 A, F = 0.77 = 8 05 Wm-’ ‘C-l UL. M,+M, = 2b2,897.0 J ‘C-l = 0.81 (&La
0
4
12 Time
16
( hours
20
24
)
Fig. 2. Hourly variation of solar intensity and the ambient temperature in Delhi on 16February 1986. (-) Ambient temperature; (- - -) Solar intensity; (I) Horizontal surface; (II) Solar still; (III) Collector.
162
o7AM
11AM
3PM lime
7PM of the
1lPM
3AM
day (hours
7AM
I
Fig. 3. Hourly variation of basin water temperature. (--------) Uncoupled; (- - -) Coupled in thermosiphon mode; (-) Coupled in forced circulation mode. Z’,, = water temperature of lower basin; T, = water temperature of upper basin; M,, = 261,875.0 J ’ C; Mm= 209,500.O J ” C. 0.50-
-; OM.k N & E .z 5a o.30 2 B t f = o.zor” Lg
O.lO-
7AM 1lAM
3PM Time
7PN of the
11PM day (hours
3AM
7AM
1
Fig. 4. Hourly variation of distillate output. (- . - a)Uncoupled; mode; (-) Coupled in forced circulation mode.
(- - -) Coupled in thermosiphon
163
Fig. 5. Effect of water depth in the basin on the daily distillate output and the efficiency of the proposed system. (-) Distillate output; (- - - ) Efficiency; ( 0 ) Uncoupled; (A ) Thermosiphon mode; ( 0 ) Forced circulation mode.
The hourly variation of solar intensity and ambient temperature is shown in Fig. 2. Fig. 3 depicts the hourly variation of the basin water temperature for the uncoupled still, thermosiphon and forced circulation modes of operation. The hourly variation of the distillate output for the uncoupled still, thermosiphon mode and forced circulation mode is shown in Fig. 4. Effect of water depth in the lower basin on daily distillate output and efficiency is shown in Fig. 5. The daily distillate output and efficiency decrease with increasing water depth because of the increasing heat capacity of the water mass, which are expected results. CONCLUSIONS
On the basis of numerical results, the following conclusions have been drawn: (1) The efficiency of the high-temperature distillation system is less than that of the conventional system. (2) The performance of the forced circulation mode is better than that of the thermosiphon mode. (3 ) The temperature of the basin water mass can be further increased by increasing the area of the collector panel.
164
(4) The efficiency of the high-temperature increasing area of the collector panel.
distillation
system decreases
with
ACKNOWLEDGEMENT
The author is thankful
to G.N. Tiwari for useful discussions.
REFERENCES 1 2 3 4 5 6 7 8 9 10 11 12
P.I. Cooper, Digital simulation of experimental solar still data, Sol. Energy, 14 (1973) 451. B. Frick and J.V. Sommerfeld, Solar stills of inclined evaporating cloth, Sol. Energy, 14 (1973) 427. J.R. Hirschmann and S.K. Roefler, Thermal inertia of solar stills and its influence on performance, Proc. International Solar Energy Congress, Melbourne, 1970, p. 402. V.A. Baum, R.B. Bayaramov and Y.M. Malevsky, The solar still in the desert, Proc. International Solar Energy Congress, Melbourne, 1970, p. 426. J.K. Nayak, G.N. Tiwari and M.S. Sodha, Periodic theory of solar still, Int. J. Energy Res., 4 (1980) 141. M.S. Sodha, A. Kumar, Usha Singh and G.N. Tiwari, Transient analysis of solar still, Energy Convers. Manage., 20 (1980) 191. MS. Sodha, A. Kumar, G.N. Tiwari and G.C. Pandey, Effect of dye on thermal performance of solar still, Appl. Energy, 7 (1980) 147. M.A.S. Malik, V.M. Puri and H. Aburshiad, Use of double stage solar still for nocturnal production, Proc. 6th International Symposium on Fresh Water From the Sea, 2 (1978) 367. M.S. Sodha, J.K. Nayak, G.N. Tiwari and A. Kumar, Double basin solar still, Energy Convers. Manage., 20 (1980) 23. M.A.S. Malik, G.N. Tiwari, A. Kumar and M.S. Sodha, Solar Distillation, Pergamon, London and New York, 1982. C.L. Gupta and H.P. Garg, System design in solar water heater with natural circulation, Sol. Energy, 12 (1968) 103. D.J. Close, The performance of solar water heater with natural circulating, Sol. Energy, 6 (1962) 33.
151 Printed in The Netherlands
Transient Analysis of Double-Basin Solar Still Integrated with Collector Y .P. YADAV* Department of Physics, C.M. Science College Darbhunga, 846004 Bihar (India), Tel. 2582 (Received May 24,1988) SUMMARY
A transient analysis of a double-basin solar still coupled to a flat plate solar collector is presented. The analysis has been carried out for both the natural (thermosiphon) and forced circulation of water between the collector and the still. Explicit expressions for the temperatures of water mass, glass cover, and basin liner of the proposed system have been developed. Effect of water depth on the distillate output and efficiency of the proposed system has been studied in detail. For appreciation of the analytical results, numerical calculations have been made for a typical day under Delhi climatic conditions. Performance of the proposed system has also been compared with that of the uncoupled double-basin solar still. Keywords: double-basin solar still, collector, transient analysis.
SYMBOLS &
-
A,
-
A, A,
-
Am.1
-
A,
-
CW
-
F’
-
FR hb hl
-
h 1U
-
Basin area Collector area Surface area of connecting pipe Area of the lower glass cover Area of the water surface in the lower basin Area of the water surface in the upper basin Specific heat of water Collector efficiency factor Heat removal factor of the collector Bottom heat loss coefficient Total heat transfer coefficient from the water surface to the glass cover of the lower basin Total heat transfer coefficient from the water surface to the glass cover of the upper basin
(m”)
gz;
g:,’ b”)
(J kg-’
‘C-l)
( Wmm2 ‘C-l) (WmB2 “C-l) ( Wmm2 oC-1)
*Present address: SSO-II, Centre for Energy Studies, IIT, Delhi, Hauz Khas, New Delhi 110016, India. OOll-9164/89/$03.50
0 1989 Elsevier Science Publishers B.V.
-
-
-
Total heat transfer coefficient from glass cover of lower basin to water Total heat transfer coefficient from the glass cover of the upper basin to ambient Heat transfer coefficient from the basin liner to water Total heat transfer coefficient from the bottom of the still to the ambient Solar intensity incident on still Solar intensity on collector Thermal conductivity of the insulation material Thickness of insulation Hourly distillate output Distillate output per unit time per unit surface area of the lower basin Distillate output per unit time per unit surface area of the upper basin Mass flow rate of water in the collector Total heat capacity of the lower basin and the collector Heat capacity of collector and water within it Heat capacity of connecting pipes and water within them Heat capacity of water mass in the lower basin Heat capacity of water mass in the upper basin Temperature of collector and water within it Water temperature of the lower basin Temperature of connecting pipe and water within it Collector inlet temperature Collector outlet temperature Temperature of water mass in the upper basin Overall heat loss coefficient of the collector Heat loss coefficient of connecting pipes
Greek symbols - Absorptivity of collector - Fraction of energy absorbed by the basin liner of : the still &I, rgu - Fraction of energy absorbed by the glass cover of lower and upper basin respectively
(Wmm2 ‘C-l) ( Wmw2 ‘C-l)
(Wmm2 ‘C-l) (Wmw2 ‘C-l) ( Wmm2) ( Wmm2) ( Wmm2 oC-l)
(m) (kgmw2 h-l) (kgmm2 s-l) (kgmm2 s-l) (kg s-2) (J ‘C-l) (J OC--l) (J ‘C-l) (J ‘C-l) (J ‘C-l ) (“C) (“C) (’ C) (“C) (“C) (’ C) (WmM2 “C-l)
153
Lb Ll
-
(@)
-
? 6”
Fraction of energy absorbed by the water mass in the lower and the upper basin respectively Effective transmittance-absorbance product Efficiency of the still Energy available from the collector (W mw2)
INTRODUCTION
The basin-type solar still, also referred to as the green-house roof-type, simple or conventional solar still, is in an advanced stage of development. Several researchers (Cooper [ 11, Frick [ 21 and Hirschmann and Roefler [ 31) have investigated the effect of climatic, operational and design parameters on the performance of such stills. Periodic and transient analyses have been presented by Baum et al. [ 41, Nayak et al. [ 51 and Sodha et al. [ 61, and enhancement of the performance of the still has been studied. In order to enhance the distillate output of the still, it is important to consider the losses suffered by solar stills. These losses are (i) conduction losses from the base, sides and edges, (ii) leakage of water vapor and (iii) convective and radiative losses from the glass cover to the ambient. The conduction losses can be reduced by using proper insulation on the base and the sides of the still. For further reducing the conduction losses, Sodha et al. [ 71 suggested maintaining the temperature of the basin water at a higher value than the blackened base of the still by dissolving a dye in the basin water. The losses due to leakage of water vapor can be prevented by perfect sealing, i.e. by providing rubber gaskets just below the glass cover. The convective and radiative heat losses from the glass cover to the ambient arise from the latent heat given by the water vapor at the inner surface of the glass cover. This latent heat ultimately increases the temperature of the glass cover thereby reducing the temperature difference between the water and the glass cover and consequently decreasing the distillate production rate. To make use of the latent heat of vaporization of water, a concept of the double-basin solar still has been suggested by Malik [8]. Sodha et al. [9] analysed the performance of this system based on periodic analysis and reported that the daily distillate production increased by 36% as compared to the single-basin still. However, the performance of the double-basin solar still may further be improved by integrating it with a flat plate collector, which increases the temperature difference between the water mass and the glass cover of the lower basin resulting in an enhanced distillate output. Moreover, the distillation is accomplished at a higher temperature; therefore, this system is very useful for extraction of essence from flowers, seeds, etc. The double-basin solar still coupled to a flat plate collector can be operated in two modes, namely the thermosiphon mode and the forced circulation mode, depending upon the way of circulation of water between the collector and the still. In the thermosiphon mode, natural circulation of water between the collector and the still occurs due to a density gradient while in the forced circulation
154
mode, a water pump is used for the circulation of water between the still and the collector. The former mode requires no electrical power for operation of the system while in the latter mode, it is necessary to run the pump. However, the double-basin solar still coupled to a collector in the thermosiphon mode is useful for high-temperature distillation in remote places where electrical power is not available. Therefore, it appears to be of considerable interest to study the performance of the proposed system. The present paper deals with the performance studies of the double-basin solar still coupled to a flat plate collector in both thermosiphon and forced circulation modes, based on a transient analytical approach. Apart from this, the performance of the uncoupled double-basin solar still has also been studied so as to make an assessment of the improvement obtained by coupling the still to the collector. Explicit expressions for the water and basin liner temperatures, hourly distillate output and efficiency of the proposed system have been developed. In order to appreciate the analytical results, numerical calculations have been carried out for a typical day under climatic conditions prevailing in Delhi. From the results obtained it is concluded that the double-basin solar still coupled to a flat plate collector performs better in the forced circulation mode than in the thermosiphon mode; however, these performances are still better than those of the uncoupled double-basin solar still. Apart from this, the effect of water depth and heat capacity of the water mass on the daily distillate output and efficiency has also been studied in detail. Illustration of the proposed system The schematics of the double-basin solar still, uncoupled and coupled to a flat plate collector, in thermosiphon modes of operation are shown in Figsla-
SUN
+
SUN
*
Fig. 1. (a) Schematic of uncoupled double-basin solar still. (b) Schematic of the double-basin solar still coupled to a collector in the thermosiphon mode. (c) Schematic of double-basin solar still coupled to a collector in the forced circulation mode.
155
c. The lower and upper heaters of the flat plate collector are connected to the bottom and the top of the lower basin of the still for both the thermosiphon and the forced circulation modes (Figs. lb and lc, respectively). For the thermosiphon mode, the double-basin solar still is kept above the upper heater of the flat plate collector in order to provide an adequate heat for the natural circulation of water in the proposed system; in the forced circulation mode it is not essential to place the still above the outlet heater of the collector. TRANSIENT ANALYSIS
The following assumptions have been made for the energy balance under various conditions of the proposed system. (1) Glass cover and water surface are parallel. (2 ) Heat capacities of the glass cover and the insulation are negligible as compared to the heat capacity of water mass in the basin. (3 ) The system is air- and vapor-tight. (4) There does not exist a temperature gradient along the glass thickness and the water depth. (5 ) Sides and bottom of the still are insulated. (6) The surface area of glass cover and water mass in the basin and the basin liner are the same. (7) The flat plate collector is uncoupled to the still during off-sunshine hours. During sunshine hours Upper basin Glass cover (1)
r,H,+h,,(T,,-T,)=h,,(T,-T,) Water mass dT A,i,,H,+Aglh21(Tgl-Twu)=Mwu~+Awuhlu
(7%~T,)
(2)
Lower basin Glass cover r,,H,+h,,(T,,-T,,)=h,,(T,,-T,,)
(3)
Water mass dT,, A,,i,,H,+B,+Abh3(Tb-Tw,)=Mwl~+Awlhll(Twl-Tgl)
(4)
156
Basin liner
(5)
rbH*=hB(Tb-T,1)+hb(Tb-T,) where h
Expressions for hi, h, and h2 are obtained by following Malik et al. [lo]. Here, 0, is the energy available from the collector and its values, for uncoupled still and still coupled to collector in the thermosiphon mode and forced circulation mode are respectively as follows Uncoupled double basin solar still (Fig. la) :
(6)
e,=o
Still coupled to collector in thermosiphon mode (Fig. lb): bu=l;t, Cw(Tw,-Twi)
(7) Still coupled to collector in forced circulation mode (Fig. 1~): &=A,&
[(ra!).ffH,,-u~(T,-T,)l
(8)
For the thermosiphon mode, the body temperature of the collector is equal to its water temperature [ 111. Therefore, one can write T, = T,,
Tp=Twp Hence, Eqn. (7) takes the form
&,=F’A,(@v)~,H,,-
dT
[
F’A,U,(T,,-T,)+M,dt+M,dt+
&A,
VW-T,)
dT
1
(9)
On the basis of the experimental observations, Close [ 121 reported that the mean water temperature in the tank is the same as the mean water temperature in the absorber during the sunshine hours. This will be true for the pipe tem-
157
perature too. Hence the mean water temperature in the basin of the still might be considered to be the same as that in the absorber. This leads to T,=T,,=T,
(10)
Upon substituting Eqn. (10) into Eqn. (9)) Eqn. (9) modifies to b,=F’A,(&&H,,-
[
F’A,UL(Tw-Ta)+
(N+&.)
%+U,A,((T,v-Te,)
1 (11)
Eqns. (l), (3) and (5) give
(12) (13)
and (14)
Now substituting the values of I$, Tgu,Tgland Tb from Eqns. (ll), (12), (13) and ( 14) respectively in Eqns. (2 ) and (4) and rearranging the terms, one can obtain dT
$+aT,,
+bT,, =g(t)
(15)
and
dTw,
dt+a’Tw,+bTw=g’(t)
where a=-
(A, u,)
WVU
(16)
158 -1
U,=
(7Et,;> 1U
+w,
g(t) =BH,
B= j&
a,
-
_
2u
[(A,&
wu
u,)l(h,,)+A,r,,+A,,r,U,l
F’A, UL+ UpA, + GA, +&I U, M2
x
>
F’A, U, + L&A, +A,, U, MZ
(neglecting
pipe losses )
>
A,, Ul “=-M g’
(t)
2
=A’&
+B’H,
+C’T,
A, _F’A,W,,, M2
c,
= WA, UL.+ UA,) M2
M,=M,+M,+M,, By multiplying one obtains dW YfPd,
Eqn. (16) throughout
dTwl+ (a+j3a’)T,,+
by /3 and adding the results to Eqn. (15))
(b+pb’)T,,=g(t)+pg’(t)
(17)
Now, choosing a value for m so that m=b+pb
(18)
and mp=a+/?a’ and substituting
(19) the value of m from Eqn. (18)in Eqn. (19)
b’P2+ (b-a’)/?-a=0 gives
(20)
159
p+ = _ (b-u’)
2 J(b-a’)2+4ab’
2b’ Hence m+ =b+j?,b’
(21)
Now Eqn. (17) may be written as
(22) where
S+(t) =&f(t) +&g’ (t) The solution of Eqn. (22) subjected to the initial conditions T,,(kO)
=T,, (23)
can be expressed as (24)
From Eqn. (24 ), one can obtain, after a simple algebraic manipulation, 1 TVA= (P+ -p-)
[I
2
[l-exp(-
[1-exp(
m+t)] -2
-m-t)]
I
+
1 (25)
{(T~,+p+T,,~)exP(-m+t)-((T-,+p_T,l,)exp(-m_t)} and
P+S-
Tw”=(p+ -P-)m[l-exp(-m+t)]+
[1-exp(
-m-t)]
-
B-S+ (P+ -P-
)m+ ‘IB_) + (26)
The values of T, and T, can be determined by substituting the values of T,, and T, from Eqns. (25) and (26) respectively in Eqns. (12) and (13).
160
During off-sunshine hours During off-sunshine hours, only the solar intensity and the collector terms will vanish; otherwise the analysis will be the same. Expression for the distillate output The amount of the distillate output obtained from the upper and the lower basin per unit time per unit basin area will be expressed respectively as (27) and
where _Y= latent heat of vaporization of water. Hence, the total hourly distillate output obtained from the proposed system will be given by r;t, = (tie, + &i) x 3600.0
(29)
For the forced circulation mode Eqn. (8) will be used instead of Eqn. (2 ) and Eqn. (4) and then the similar procedure will be followed. Expression for efficiency of the system The efficiency of the proposed system may be expressed as (30) where At refers to the time interval over which the solar intensity is measured. RESULTS AND DISCUSSION
In order to appreciate the analytical results, numerical calculations have been carried out for a typical day, i.e. 16th February 1986, at Delhi. The numerical values of the relevant parameters taken for calculations are as follows: Still parameters = 1.0 m2 = 1.0 m2 = 1.0m2 = 1.0m2 = 15.973 Wme2 ‘C-l = 94.14 Wmm2 “C-l
Ab A, A,1 AWlI hl, hz,
161
h 1U h 2u h3 he, h iiU Li _Y Mw, M,, r 91 r WI
= =
= = = = = = = = = =
16.173 Wm-’ “C-l 70.47 Wm-’ “C-’ 111.95 Wm-’ “C-l 8.12 Wm-’ “C-l 8.64 Wm-’ “C-’ 0.04 Wm-’ “C-’ 0.05 m 2.37252 x lo6 J kg-’ 261,875.0 J “C-l 209,500 J ‘C--l 0.0 0.0 0.0 0.5
Collectorparameters = 1.5m2 A, F = 0.77 = 8 05 Wm-’ ‘C-l UL. M,+M, = 2b2,897.0 J ‘C-l = 0.81 (&La
0
4
12 Time
16
( hours
20
24
)
Fig. 2. Hourly variation of solar intensity and the ambient temperature in Delhi on 16February 1986. (-) Ambient temperature; (- - -) Solar intensity; (I) Horizontal surface; (II) Solar still; (III) Collector.
162
o7AM
11AM
3PM lime
7PM of the
1lPM
3AM
day (hours
7AM
I
Fig. 3. Hourly variation of basin water temperature. (--------) Uncoupled; (- - -) Coupled in thermosiphon mode; (-) Coupled in forced circulation mode. Z’,, = water temperature of lower basin; T, = water temperature of upper basin; M,, = 261,875.0 J ’ C; Mm= 209,500.O J ” C. 0.50-
-; OM.k N & E .z 5a o.30 2 B t f = o.zor” Lg
O.lO-
7AM 1lAM
3PM Time
7PN of the
11PM day (hours
3AM
7AM
1
Fig. 4. Hourly variation of distillate output. (- . - a)Uncoupled; mode; (-) Coupled in forced circulation mode.
(- - -) Coupled in thermosiphon
163
Fig. 5. Effect of water depth in the basin on the daily distillate output and the efficiency of the proposed system. (-) Distillate output; (- - - ) Efficiency; ( 0 ) Uncoupled; (A ) Thermosiphon mode; ( 0 ) Forced circulation mode.
The hourly variation of solar intensity and ambient temperature is shown in Fig. 2. Fig. 3 depicts the hourly variation of the basin water temperature for the uncoupled still, thermosiphon and forced circulation modes of operation. The hourly variation of the distillate output for the uncoupled still, thermosiphon mode and forced circulation mode is shown in Fig. 4. Effect of water depth in the lower basin on daily distillate output and efficiency is shown in Fig. 5. The daily distillate output and efficiency decrease with increasing water depth because of the increasing heat capacity of the water mass, which are expected results. CONCLUSIONS
On the basis of numerical results, the following conclusions have been drawn: (1) The efficiency of the high-temperature distillation system is less than that of the conventional system. (2) The performance of the forced circulation mode is better than that of the thermosiphon mode. (3 ) The temperature of the basin water mass can be further increased by increasing the area of the collector panel.
164
(4) The efficiency of the high-temperature increasing area of the collector panel.
distillation
system decreases
with
ACKNOWLEDGEMENT
The author is thankful
to G.N. Tiwari for useful discussions.
REFERENCES 1 2 3 4 5 6 7 8 9 10 11 12
P.I. Cooper, Digital simulation of experimental solar still data, Sol. Energy, 14 (1973) 451. B. Frick and J.V. Sommerfeld, Solar stills of inclined evaporating cloth, Sol. Energy, 14 (1973) 427. J.R. Hirschmann and S.K. Roefler, Thermal inertia of solar stills and its influence on performance, Proc. International Solar Energy Congress, Melbourne, 1970, p. 402. V.A. Baum, R.B. Bayaramov and Y.M. Malevsky, The solar still in the desert, Proc. International Solar Energy Congress, Melbourne, 1970, p. 426. J.K. Nayak, G.N. Tiwari and M.S. Sodha, Periodic theory of solar still, Int. J. Energy Res., 4 (1980) 141. M.S. Sodha, A. Kumar, Usha Singh and G.N. Tiwari, Transient analysis of solar still, Energy Convers. Manage., 20 (1980) 191. MS. Sodha, A. Kumar, G.N. Tiwari and G.C. Pandey, Effect of dye on thermal performance of solar still, Appl. Energy, 7 (1980) 147. M.A.S. Malik, V.M. Puri and H. Aburshiad, Use of double stage solar still for nocturnal production, Proc. 6th International Symposium on Fresh Water From the Sea, 2 (1978) 367. M.S. Sodha, J.K. Nayak, G.N. Tiwari and A. Kumar, Double basin solar still, Energy Convers. Manage., 20 (1980) 23. M.A.S. Malik, G.N. Tiwari, A. Kumar and M.S. Sodha, Solar Distillation, Pergamon, London and New York, 1982. C.L. Gupta and H.P. Garg, System design in solar water heater with natural circulation, Sol. Energy, 12 (1968) 103. D.J. Close, The performance of solar water heater with natural circulating, Sol. Energy, 6 (1962) 33.