Analytical performance of a solar still integrated with a flat plate solar collector: Thermosiphon mode

Energy Convers. Mgmt Vol. 31, No. 3, pp. 255-263, 1991 Printed in Great Britain. All rights reserved

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ANALYTICAL PERFORMANCE OF A SOLAR STILL INTEGRATED WITH A FLAT PLATE SOLAR COLLECTOR: THERMOSIPHON MODE Y. P. YADAV Department o f Physics, C.M. Science College, Darbhanga, Bihar-846 004, India

(Received 14 September 1988; receivedfor publication 14 March 1990) Abstract--This paper presents a transient analysis o f a single basin solar still coupled to a flat plate solar collector using a thermosiphon mode of operation. To assess the quantitative performance o f the system, numerical calculations have been carried out for a typical day in Delhi. So as to make a performance based-choice, the proposed system has been compared with that operated using a forced circulation mode. It is observed that the system with the forced circulation mode of operation performs slightly better than the system operating using the thermosiphon mode. Despite this, the thermosiphon mode can be preferred over the forced circulation mode, as it does not need electrical power to run the pump for circulation o f water between the collector and the still. Solar

Energy

Single basin

Still

Flat plate

Collector

Thermosiphon

Mode

NOMENCLATURE Ab = Ac = Ap = Ct = Cw = D = Di=

F = F' = hop = h~ = ha = hrp = h~ = hew = ht =

h2 = h3 = hb = Hs = H'~ = Ki = L = Li = n~w = mew = Pw Ps = Mc = Mp = Mw = To = Ta = Tb = Tc = Ts = Tp =

Tw = t = T~ = T~ = Twl =

Surface area o f basin liner (m 2) Collector area (m 2) Heat transfer surface area of connecting pipe (m 2) Tube conductance (W/m 2 °C) Specific heat of water (J/kg °C) Diameter of tube Inner diameter of tube Fin efficiency factor Plate efficiency factor Convective heat transfer coefficient from glass cover to ambient 0V/m 2 °C) Convective heat transfer coefficient from water to glass cover (W/m 2 °C) Heat transfer coefficient between fluid and tube well wall (W/m 2 °C) Radiative heat transfer coefficient from galss cover to ambient (W/m 2 °C) Radiative heat transfer coefficient from water to glass (W/m 20 C) Evaporative heat transfer coefficient from water to glass (W/m 2 °C) Total heat transfer coefficient from water to glass cover (W/m 2 °C) Total heat transfer coefficient from glass cover to ambient (W/m 2 °C) Heat transfer coefficient from basin liner to water (W/m 2 °C) Overall heat transfer coefficient from basin liner to ambient through insulation 0V/m 2 °C) Solar intensity on collector (W/m 2) Solar intensity on glass cover of still (W/m 2) Thermal conductivity of insulation (W/m 2 °C) Latent heat of vaporization (J/kg) Thickness of insulation (m) Mass flow rate o f water in collector (kg/s) Mass of distillate (kg) Saturated vapour pressure at water and glass surfaces, respectively (N/m 2) Heat capacity o f collector including water (J/°C) Heat capacity o f connecting pipes including water (J/°C) Heat capacity of water in basin of still (J/°C) Initial temperature of basin water (°C) Ambient temperature (°C) Temperature of basin liner (°C) Collector plate temperature (°C) Glass cover temperature (°C) Connecting pipe temperature (°C) Water temperature (°C) Time (s) Water temperature in collector (°C) Water temperature in connecting pipes (°C) Inlet temperature of collector (°C) 255

256

YADAV: SOLAR STILL INTEGRATED WITH FLAT PLATE SOLAR COLLECTOR Two= Outlet temperature of collector (°C) Uc = Collector loss coefficient(W/m2°C) Up= Pipe overall loss coefficient(W/m2°C) W = Distance between two consecutivetubes of collector (m) (zc~)= Transmittivity-absorptivityproduct a., cry,,~b.= Phase factors co = Angular frequency(rad/s) %= Emissivity of glass cover surface Ew= Emissivity of water surface E~ = Effectiveemissivity • ~= Fraction of energy absorbed by glass cover ~2= Fraction of energy absorbed by water mass in basin T3= Fraction of energy absorbed by basin liner INTRODUCTION

Single basin solar stills have long been of considerable interest. Their performance has been studied by several authors [1-10], incorporating the effects of climatic, operational and design parameters. Earlier, a periodic analysis of a solar still was carried out by Hirschmann and Roedler [11] and Baum et al. [12]. These authors considered only the first harmonic term for the periodic physical quantities in their analysis, which is not sufficient to represent the insolation and ambient temperature. Nayak et al. [13] and Sodha et al. [14] have studied the performance of the single basin solar still based on periodic analysis taking into account an infinite number of harmonics o f the Fourier expansions of the solar intensity and ambient temperature. Their investigations reveal that the first six harmonics of the Fourier expansion of solar intensity and ambient temperature are sufficient to represent them. The output depends on the temperature difference and the absolute value of the water temperature. An increased output can be achieved at higher water temperature and reduced water-to-cover differences. This could be achieved either by feeding waste hot water into the basin or connecting a flat plate collector to the still. The case of feeding waste hot water has been studied by Sodha et al. [15], Proctor [16], Madhuri and Tiwari [17] and Rai and Tiwari [18]. The other case of feeding hot water into the basin by coupling it to the fiat plate solar collector can be performed under two kinds of modes of operation, namely the forced circulation mode and the thermosiphon mode. The former, i.e. the single basin solar still coupled to a fiat plate solar collector under the forced circulation mode, has been studied by Rai and Tiwari [19] and Tiwari and Dhiman [20]. These authors have made investigations upon the effect of heat exchanger length, flow rate of fluid in the heat exchanger loop and the depth of the water in the basin along with the temperature dependent internal heat transfer coefficients on the performance of the solar still. Further, they have suggested that such a system (high temperature distillation) is useful for extracting the essence from the flowers which is usually used for ceremonial purposes. The major limitation of the single basin solar still operated under the forced circulation mode is the requirement of electrical power to run the pump for the circulation of water in the basin. Therefore, such a system is not at all applicable for regions where electrical power is not available. That is why it will be of considerable interest to study the performance of the system under the thermosiphon mode, as this system needs neither pump nor electrical power; hence, it can be used for higher temperature distillation. In this present paper, we have presented a thermal analytical study of such a system. Based on a transient analytical approach, explicit expressions for water-temperature, glass-temperature and basin liner-temperature of the proposed system have been developed. For the quantitative assessment of the analytical results, numerical calculations have been done for the same climatic condition as used by Rai and Tiwari [19]. The results are shown graphically. ANALYSIS In order to write down the energy balance at the various components of the system, the following assumptions have been incorporated: (1) The glass cover and water surface are parallel. (2) The system is air and vapour tight.

YADAV: SOLAR STILL INTEGRATED WITH FLAT PLATE SOLAR COLLECTOR

257

(3) The heat capacity of the glass cover is negligible. (4) The surface area of glass cover, water mass and the basin liner are the same. (5) The flat plate solar collector is uncoupled from the still during low intensity/off-sunshine hours. The schematic diagram of the system is shown in Fig. 1. The energy balance at the various components of the proposed system may be expressed as follows: (a) During sunshine hours

Glazing ztH; +

hl(Tw

(1)

-- Tg) = h~(Tg - T~).

Water mass of the basin AwT2H~ + rhwCw(Two- Twl) + h3hb(Tb

-

-

Tw) =

dTw

Mw ---~-

=

(2)

h, Ab(rw - r , ) .

Basin liner T3H~ ----h3(Tb -- Tw) -F hb(Tb - Ta) where

1 1~ 1 h~=ki+hi.

(3)

Collector (thermosiphon mode) rhwCw(T~o - Twl) = F'Ac[Hs(zot) - Uc(Tw¢- 7",)] - M ¢ dT~ -~-

_

AIr

P dTp dt

UpAp(T~p

-

-

ra).

-

- - Glass cover

~---- In s u l a t l o n Water

B a s i n liner

J / ~ . ~

Flat plate sotor collector

Fig. 1. Schematic diagram of single basin solar still coupled to flat plate solar collectors under thermosiphon mode.

(4)

258

YADAV: SOLARSTILL INTEGRATEDWITH FLAT PLATE SOLARCOLLECTOR

According to Gupta and Garg [21], the body temperature of the collector is equal to its water temperature. Hence, equation (4) takes the form,

dr~,~ dr. F'A~U~(Tw¢- Ta)+Mc--~-- +Mp dt

mwC.(T~o- Tw~)=F'AcH~(z~) -

+

UpAp(T,-

7".)]. (5)

On the basis of experimental observations, Close [22] reported that the mean water temperature in the tank is the same as the mean water temperature in the absorber during sunshine hours. This will be true for the pipe temperature 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 concept leads to

Tw= Twc= Twp.

(6)

Upon substituting equation (6) into equation (5), equation (5) modifies to mwCw(T~o- T,,t)=F'A,H,(z~)- F'AcU¢(Tw- T.)+(M¢+ Mp)-~-[- + V p A p ( T w - Ta) .

(7)

Eliminating ti~Cw(T~o- T,,i) from equations (2) and (7), one obtains z2H; + F'A,H,(z~) -

[

1

F'A¢ U~(Tw- Ta) + (Me + Mp) ~

+ UpAp(T~ - Ta)

+ h, A b ( T b - Tw) = m

w dt

(8)

Equations (1) and (3) yield, zt

+

h2

ht

Ts=h,+-h2H:

h,+h2Tw+ h - ~ r .

T3

hb

h3

T..

(9) (10)

Substituting the value of Tg and Tb from equations (9) and (10), respectively, in equation (8), one gets

dT~ dt + ~Tw = f ( t ) where

oc = (F'A~U~+ UpAp + A~Ub+ U,Ab)/M f ( t ) =pH~ + qH~ + c~T~ p = F'Ac(rOO/M •

q=

h2

I-1 M

17-'

•

UbAbT3/..

(11)

YADAV:

S O L A R STILL I N T E G R A T E D W I T H F L A T P L A T E S O L A R C O L L E C T O R

259

Expression for water temperature

The solution of equation (11) subject to the initial condition Tw(t = O) = T O

(12)

f ( t ) exp(~t) dt + To exp(-~tt).

(13)

will be expressed as Tw = exp(-ctt)

Since the solar intensity and ambient temperature are periodic in nature, they can be Fourier analysed as Hs = H,o + ~ H~ exp{i(ntot - a.)}

(14)

n=l

H~ = H ~ + ~ H'~.exp{i(ntot - a;)}

(15)

n=l

T~ = T~o + ~ T~ exp{i(ntot - t#.)}.

(16)

n--I

As sufficient accuracy could be had by terminating the series at the sixth harmonic, equations (14), (15) and (16) may then take the form, 6

Hs = tI~ + ~ H~ exp{i(ntot - e.)}

(17)

n=|

6

H~ = H~ + ~ H'~exp{i(ncot -- a'.)}

(18)

n=[

6

T~ = Tao + ~ T~. exp{i(nogt - ~b.)}.

(19)

n=l

Upon substituting these values of H,, H~ and Ta from equations (17), (18) and (19) in equation (13), one obtains, Tw = T0 e x p ( - ~ t ) + (primo + q n ~ + rT~0)[1 + exp(-~t)] 6 ~.{pH~,exp( - io. ) + qH~ exp( - ia '.I) + rT~ exp( - i~b.)} + 2. . =t ~X + i nt o

L

x {exp(intot) - exp(-- ~t)} 1 .

(20)

(b) During off-sunshine hours (collector uncoupled) It has been assumed in this analysis that the still is uncoupled from the collector during off-sunshine hours. Therefore, so as to obtain the water temperature in this case, one has to put the collector terms and the solar intensity terms equal to zero in equation (20); this yields Tw = To exp(-~t't) + r'T.o[1 - exp(-~t't)] + ~. {r'Ta.exp(-idp.)} x {exp(intot) - exp(-ct't)} . = 1

(*t' +

ino~)

where ~ ' = r ' = ( A b U b + U i A b ) / m w.

(21)

260

YADAV: SOLARSTILL INTEGRATED WITH FLAT PLATE SOLAR COLLECTOR

(c) During low intensity hours (collector uncoupled) The water temperature during low intensity hours will be obtained by making only the collector terms equal to zero in equation (20). Hence, one obtains Tw = To e x p ( - ct't) + [q'H;o + r'T=0][1 - e x p ( - ~t'/)] 6 [-{q'H'~ e x p ( - ia~,) + r ' T ~ e x p ( - i~b.)}

.~- I"

(-~i~

)

{exp(imot ) - exp(-='/)}

1

where UbAbZ3\ /

q' = i[ Ut Ab z l

(22)

(d) During off-sunshine hours (collector not uncoupled) In this case, only the intensity term will vanish in the expression for water temperature, and thus, the water temperature in this case will be expressed as

T.= Toexp(-ctt)+ rT.o[1-

exp(--~t/)]+ .~=,LF{r~"exp(-i*")}(~ + ino9) {exp(inot)-exp(-~tt)}].

(23)

The amount of water distillate per unit time per unit area of the basin is given as (24)

m~. = h¢.(Tw - Tg)/L

where L = latent heat of vaporization. RESULTS AND D I S C U S S I O N The values of the parameters for the numerical calculations are as follows: (a) Still parameters hi = 16.076W/m 2 °C; h E = 4 0 . 8 8 W / m 2 ° C ; ]/3 = 137.373 W/m 2 °C; Mw = 628,500.0J/°C (corresponding to 0.15 m depth of water in the basin); z~ = 0.1 dimensionless; ¢2 = 0.0 dimensionless; T3 = 0.7 dimensionless; L i = 0.05 m; K~ = 0.04 W/m °C; hew = 8.55 W/m °C.

Ambient temperature 1/.,3 / X / X

. . . . . Solar intensity a - Horizontal surface b - Solar still

/-~_

30 20"

/,'

0

-

-800

Co.,ctor

~

//I 1./!

1 600

\V~ \~', \~)

;/i to- 2. /

o/"

c

- 1000

~

~-I 4°° " ~ - I

I £oo

7 I

&

,

8

'\,

12 Time ( hrs )

,

16

J

20

,I Jo 24

Fig. 2. Hourly variation of solar intensity and ambient temperature (after Rai and Tiwari [19]).

YADAV: SOLAR STILL INTEGRATED WITH FLAT PLATE SOLAR COLLECTOR

261

Uncoupled ......

Thermosiphon circulot ion

Forced 60

50 = 2

~0

Ck

30 20 10-

I

0

I

I

I

I

I

I

I

7AM 7PM 7AM 7PM 7AM 7PM ?AM

?AM 7PM

rE Ist doy.]__r 2nd day.J__,

3rd

dc,2J~ 4th a*yl_.

Time of day ( H r s ) Fig. 3. Variation of water temperature with time.

(b) Collector parameters F' = 0.77; Ac = 1.5 m2; Uc = 8.05 W/m 2 °C; Mc + Mp = 228,000.0 J/°C. Equations (20), (21), (22) and (23) strand for the basin water temperature during sunshine hours, off-sunshine hours (collector uncoupled), low intensity hours (collector uncoupled) and offsunshine hours (collector coupled), respectively. These expressions for the water temperatures will be useful while studying the thermal behaviour of the proposed system in the above mentioned circumstances. Sometimes, during cloudy climatic conditions, the solar intensity and ambient air temperature remain constant over short time intervals (such as 10-20 min); hence f(t) becomes constant over that time interval. In this case, equation (13) can be used to compute the water temperature very simply, and thereby, it eliminates the need to compute the Fourier coefficients Uncoupled ......

O.t,O -

Therm0siphon

t,. J¢

I

Forced circulation

q~ O~

030 -

Q. o

0.20

-

r

~.

O m

o.10

./.,~k~/

"O

I./

o

-r

o

,

'

I

7PM ?AM ?PM 7AM

i ?PM

I

I

I

?AM ?PM ?AM

L i~t d°y J znd doy± 3~ doy]~ 4th dod I-

T

-~. . . . Time of the day ( h r s )

Fig. 4. Hourly variation of distillate output.

'

262

YADAV:

SOLAR STILL I N T E G R A T E D WITH FLAT PLATE SOLAR COLLECTOR

of solar intensity and ambient temperature. The glass cover temperature and the basin liner temperature have been expressed by equations (9) and (10), respectively. Further, Fig. 2 depicts the variation of solar intensity and ambient temperature with time. Variation of water temperature with time is shown in Fig. 3, whereas the output is in Fig. 4. Moreover, in the evening or during low intensity hours, the collector is disconnected from the still in order to have the system free from collector losses; in the forced circulation mode, the pump runs until sunset.

CONCLUSIONS

The above results and discussions may be summarized as follows: (1) The system using the forced circulation mode gives 5-10% higher yield than that of the thermosiphon mode. (2) A 30-35% enhancement in the yield is observed with the proposed system as compared to the conventional system (uncoupled still). (3) For a distillation system of a fixed capacity (100 1.), the effect of increasing the collector area beyond 4.5 m 2 is insignificant. (4) The steady state condition of the system is achieved after 2-3 days (Fig. 3). Acknowledgement--The author extends his sincere thanks to Dr G. N. Tiwari, Assistant Professor at the Centre for Energy Studies, liT, Delhi, for useful discussions regarding this paper.

REFERENCES 1. 2. 3. 4. 5. 6. 7. 8. 9. 10. 11. 12. 13. 14. 15. 16. 17. 18. 19. 20. 21. 22. 23. 24.

J. W. Bloemer, J. A. Eibling, J. R. Irwin and G. O. G. Lof, Sol. Energy 9, 197 (1965). R. N. Morse and W. R. W. Read, Sol. Energy 12, 5 (1968). R. N. Morse, W. R. W. Read and R. S. Trayford, Sol. Energy 13, 99 (1970). P. I. Cooper, Sol. Energy 12, 313 (1968). P. I. Cooper, Sol. Energy 12, 333 (1969). P. I. Cooper, Sol. Energy 15, 205 (1973). P. I. Cooper, Sol. Energy 14, 454 (1973). P. I. Cooper and W. R. W. Read, Sol. Energy 16, 1 (1974). J. A. Eibling, S. G. Talbert and G. O. G. Lof, Sol. Energy 16, 263 (1971). E. D. Howe and D. W. Tleimat, Sol. Energy 16, 97 (1974). J. R. Hirschmann and S. K. Roefler, Proc. Int. Sol. Energy Congr., Melbourne, p. 402 (1980). V. A. Baum, R. B. Bayarmov and Y. N. Malevsky, Proc. Int. Sol. Energy Congr., Melbourne, p. 426 (1970). J. K. Nayak, G. N. Tiwari and M. S. Sodha, Int. J. Energy Res. 4, 41 (1980). M. S. Sodha, U. Singh, A. Kumar and G. N. Tiwari, Energy Convers. Mgmt. 20, 191 (1980). M. S. Sodha, A. Kumar and G. N. Tiwari, Desalination 37, 325 (1981). D. Proctor, Sol. Energy 14, 433 (1973). Madhuri and G. N. Tiwari, Desalination 52, 345 (1985). S. N. Rai and G. N. Tiwari, Energy Res. 8, 281 (1984). S. N. Rai and G. N. Tiwari, Energy Convers. Mgmt. 23, 145 (1983). G. N. Tiwari and N. K. Dhiman, Desalination. In press (1990). C. L. Gupta and H. P. Carg, Sol. Energy le, 163 (1968). D. J. Close, Sol. Energy 6, 33 (1962). J. Duffle and W. A. Beckman, Solar Engineering of Thermal Processes. Wiley, New York (1980). M. A. S. Malik, G. N. Tiwari, A. Kumar and M. S. Sodha, Solar Distillation. Pergamon Press, Oxford (1980).

APPENDIX The total heat transfer coefficients h~ and h2 from the water surface to the glass cover and from the glass cover to the ambient is expressed as h I = hc,~g+ hr~g + hew and h z = h¢~ + hr~, where (following Malik et al. [24]) (Pw

-

P~)(Tw + 273.15)] u3

h,wg = Gira[Tw + 273.15)4 - (Tg + 273.15) 4]

Vw-r,

YADAV:

SOLAR STILL I N T E G R A T E D WITH FLAT PLATE SOLAR COLLECTOR

Eelf =

+

;1-'

hew=16.276 x 10 -3xhcwg

\Tw-Tg]

hcsa = 5.7 + 3.8 v [(Ts + 273.15) 4 - (Ta + 261.15) 4] hrg a = Ego-

:rg- 7-,

The collector efficiency factor is given by 1 F' =

U¢

{

~

,

(Duffie and Beckmann [24]).

263