Transient analysis of double basin solar still

Energy Com,ers. Mgmt Vol. 23, No. 2, pp. 83-90, 1983 Printed in Great Britain. All rights reserved

0196-8904/83 $3.00+0.00 Copyright :~ 1983 Pergamon Press Ltd

TRANSIENT ANALYSIS OF DOUBLE BASIN SOLAR STILL* V. S. V. B A P E S H W A R A R A O , U. S I N G H and G. N. T I W A R I Centre of Energy Studies, Indian Institute of Technology, Hauz Khas, New Delhi 110 016. India (Received 17 M a y 1982) Abstract--The effect of water flowing over the upper glass cover of a double basin solar still on its transient performance has been presented. A comparative study of the daily distillate production of a double basin solar still with and without water flowing over the upper glass cover has been made, and some interesting conclusions have been drawn. Numerical calculations have been made for a typical hot day (viz 2 May 1980) in Delhi. Solar still

Transient analysis

Double basion

hi,. = daily distillate of water from both basins per unit basin area, kg/m z day M~.~ = heat capacity of water in upper basin per unit basin area, J / m : C M,. 2 = heat capacity of water in lower basin per unit basin area, J / m 2 C p = partial pressure of water vapour at temperature T, Pa pg = partial pressure of water vapour at glass temperature, Pa p , . = partial pressure of water vapour at water temperature, Pa Q,.v = total heat transfer from water to glass in upper basin, J/m: h Q,.L = total heat transfer from water to glass in lower basin, J/m 2 h Q~ = total heat transfer from water to glass in both basins, J/m-' h T Z- temperature, ' C To = ambient air temperature, C T~ = upper glass temperature, ' C T~2 = lower glass temperature, C Tw~ = upper basin water temperature, C Twa = lower basin water temperature, 'C T,. 3 = temperature of water flowing over upper glass cover, 'C t = time, s x = position co-ordinate, m p = density of water, kg/m 3 ~r = Stefan-Boltzman constant, 5.6697 x I 0 ~W p m 'C 4 q = fraction of energy absorbed by lower basin water z 2 = fraction of energy absorbed by basin liner , / = relative humidity 0 = temperature distribution

NOMENCLATURE b = breadth of still, m c, = specific heat of water, J/kg°C h~ : heat transfer coefficient from water in upper basin to upper glass cover, W / m 2 C h~ = heat transfer coefficient from upper glass cover to water flowing over it, W/m2°C h 3 = heat transfer coefficient from lower glass cover to water in upper basin, W/m2:'C h 4 = heat transfer coefficient from water in lower basin to lower glass cover, W/m-'~C h 5 = heat transfer coefficient from basin liner to water in lower basin, W/m2-'C h, = heat transfer coefficient from bottom of insulation to ambient air, W / m 2 ' C h h = heat transfer coefficient from basin liner to ambient air through insulation, W/m2°C h,, = convective heat transfer coefficient from top glass to ambient, W / m 2 C h~,, = radiative heat transfer coefficient from top glass to ambient, W/mZ':C h, t = evaporative heat transfer coefficient from water in upper basin to top glass cover, W/m2°C h,.L = evaporative heat transfer coefficient from water in lower basin to lower glass cover, W/m2°C h~t. = radiative heat transfer coefficient from water in upper basin to top glass cover, W/m2°C h~L = radiative heat transfer coefficient from water in lower basin to lower glass cover, W/m2°C h,z = convective heat transfer coefficient from water in upper basin to top glass cover, W/mZ~'C h~. = convective heat transfer coefficient from water in lower basin to lower glass cover, W/m2°C H s = solar nsolation on upper glass cover per unit area . . per umt ume, W/'m 2 K, = thermal conductivity of insulation, W / m ~ ' C L~ = length of still, m = latent heat of vaporization of water, J/kg rh, = a m o u n t of water distillate per unit time per unit area, kg/m 2 s M,, c = dai y distillate of water from upper basin per unit basin area, kg/m 2 day M,,L = daily distillate of water from lower basin per unit basin area, kg/m :~ day

1. I N T R O D U C T I O N D i f f e r e n t g e o m e t r i c a l c o n f i g u r a t i o n s o f s o l a r stills, s u c h as tilted tray ( A c h i l o v et al. [1]; H o w e a n d T l e i m a t [2]; T a l b e r t et al. [3]), tilted ( F r i c k a n d O m m u r f e l d [4]; T a l b e r t et al. [3]; S o d h a et al. [12, 13, 15, 17]), o r vertical wick ( C o f f e y [6]), h a v e b e e n p r o p o s e d , d u e to large a r e a r e q u i r e m e n t s o f c o n v e n t i o n a l b a s i n - t y p e s o l a r stills. A t t e m p t s h a v e also b e e n m a d e to e x p l o i t t h e m u l t i p l e effect c o n c e p t ( D u n k l e [7]; G i m m i n g s [8]; H o d g e s et al. [9]; Selcuk

*Work partially supported by commission for Additional Sources of Energy, Government of India. ~¢',~23!2 ~

83

84

RAO et al.:

TRANSIENT ANALYSIS OF DOUBLE BASIN SOLAR STILL

[10]; Telkes [11]) in solar distillation. However, the higher productivity is not desirable at the expense of cost of construction (Howe and Tleimat [2]; Talbert et al. [3]). Hence, attention has been focussed on basin type solar stills with a view to improving their performance. The daily distillate of a single basin solar still has been increased by reducing the conduction losses, viz. through bottom and side insulation (e.g. either by using a good insulating material, or by injecting a black dye in the water mass, Sodha et al. [12]), and the convection and radiation losses from the glass cover (e.g. double basin solar still, Sodha et al., [13]). In their analysis, Nayak et al. [14] and Sodha et al. [13, 15]), have used the linearised Dunkle's [7]) relation for convective and evaporative heat losses. Previous studies have shown that, in a single basin solar still, the lowering of the glass cover temperature, caused by flowing water over it, increases the daily distillate almost by a factor of two (Tiwari et al. [17]).

In this communication, the effect of water flowing over the upper glass cover of a double basin solar still on its transient performance has been studied. A comparative study has been made with the performance of the earlier system, Sodha et al.) [13], and this present model gives an increase of more than 16% in efficiency over the earlier one, with an overall efficiency of 53% at normal conditions when the energy absorbed by the basin liner has been taken as 0.8. The effect of various operating parameters has also been presented. 2. ANALYSIS A schematic representation of a double basin solar still with flowing water over the glass has been shown in Fig. la. Following Sodha et al. [12, 13, 15] and referring to Fig. l b, the energy balance equations for flowing water over the upper glass cover, water mass, lower

,," /

Drainages

/

////////

Q.~~

/ //

// ~

Blackened

,~y ~

surface

/

Saline water _ _

"" / /

__

- - ~ /

/

]/P77/2 P 7 7 / - 7 / " -s-, ./ ._ x =oLo nsulation ,

Ambient

air (a) /

L

L

"

/'V dx

/

"

Glass c o v e r

_1

ecti°fl o°f water

(b)

Fig. 1. (a) Schematic of proposed double basin solar still with water flowing over upper glass cover with uniform velocity. (b) Cross-sectional view of flowing water over upper glass cover.

RAO et al.:

TRANSIENT ANALYSIS OF DOUBLE BASIN SOLAR STILL

glass cover, and water mass in basin can be written

where

as

bMi

H-

b/~,,pc, d x ~ -

+ rh,,,c,,, ~

h-

bdx [h'..(T~t- T w 3 ) - h2(Tw3 - 7",,)

h~(T¢,-

T,~3)=h,(T,,,t-

T~, )

M..I -dt-dT"l = h3(Te2 _ T.,I ) _ h l ( T . t - Tel), h3(Te2 -- T,,,,) = h4(T.2 - L2)

hlh'~ h, + h'~

(1)

M I = h + h. + hoR~

(2)

M3 = M4 T~l + Ms M4 = h / M i

(3)

Ms=

(4)

and M"2

I~l. C.

dx =

- h o R, (T,.3 -- T.),) - hoR2(l -- 7)]

85

(h2 + hoRt 7)T. - h0 R2(1 - 7)

Mt

The solution of equation (9) with initial condition viz. dT.2

T.3=T.,

-- TI Hs

at

x=0

can be written as + hs(0x o - T,2) - h,(T,,.2- Tx2) (5) respectively, where

T.3 = M~ - (M 3 - Ti. ) e x p ( - Hx) or

rh, = bpl,, u

T . 3 = ~ 1 ft. T,3dx = M 3

h 0 = 0.013 × h,. a (Tiwari et al., 1981) h2=h,~+h~

q

HL

h,~ = 5.768[1 + 0.85(v - u)]

h~t. + h,.t~ + h,.l~

where the h's are defined in the Appendix. The energy balance for the basin liner can also be written as ~ H ~ = h s ( O ~ _ o - T,,,2)+h~(O~

o - 7",,)

d T~ti - -

dt

(6)

d T~t2

where

hh

L, --

Ki

I-

hi

After eliminating 0~_ 0 from equation (5) and (6), one gets M.,2 ~ -

(11)

+ b, T,,, + b2T,.,~=g(t)

(12)

where

1

aI=

d Tw2

+ a~ T,,t + a . T., 2 = f ( t )

and -dt

1

h.~ + (1 - h~ - h ~ M 6 M 4 ) h , g.,i

a~M,, I '

= "oH,

U2

- U~(T~2- T o ) - h4(Tw~- T.~).

(7)

b~ -

M,,2,

UI + U2 b2-

From equation (2), one has hi T.,i +

T~ -

- M~2

h'2 T,,3

h, + h;

h~

-- H ( M 3 -- T.3 )

T="C I -{- ~

(8)

Substituting the value of Tg~ from the above equation in equation (1) and neglecting the heat capacity of flowing water over the cover, equation (1), after simplification, can be written as

Tw3

(10)

With the help of equations (2). (4) and (10). equations (3) and (7) can be written as

hi = h.t, + h~t + h,.~ ha =

[exp(--HL)--l]

(9)

f(t)

=

g(t) -

t71

-

T2,

h Ih ~(M 6 M 5 + M 7 T.,30) MM

z H , + U~ 7,,

M,,2

hI

h~ + h~"

RAO et al.: TRANSIENT ANALYSIS OF DOUBLE BASIN SOLAR STILL

86

h;

t/3-

and

ht + h~'

h'4=

O,q. = hd.(T.. 2 - Te2) × 3.6

h3 ha

(16)

The hourly distillate from the upper and lower basins of the still can also be obtained as

h3 + h 4'

hhh5 UI - hh + hs'

hetl

Mev = ~ - ( T < -

U2 = h4.

7re,) x 3.6

and

The solutions of equations (11) and (12), along with initial conditions viz.

T..l=Twlo

T,.2=T,,.2o

and

at

heL

MeL = ~

(7".,2- 7"~2)× 3.6

t=0

can be written as 3. RESULTS AND DISCUSSION

T,,.I=

~ exp(-c+t)

xexp(c+t)dt-c%exp(-c

t)

f(t)

I

exp(-c~t)

g(t)

dO

x exp(-c+t)dt -exp(-c

t)dt}+{~

Numerical calculations, corresponding to a typical hot day viz. 2 May 1980 in Delhi, have been carried out, using the following relevant parameters:

;o

{

xexp(c t ) d t + ~ + ~

xexp(c

f(t)

t)

g(t)

A~exp(-c+t)

,/

(13)

- c% A_ e x p ( - c _ t ) } / A

and

T..2

1

~+ - - ~ _

[

e x p ( - c+ t)

-exp(-c

t)

f(t)exp(+c

+ ~+ e x p ( - c + t)

-~

exp(-c

;o

f ( t ) exp(c + t) dt

t)

t)dt

f0 i0

g(t)exp(-c+t)dt g(t)exp(-c

+{A+exp(-c+t)-A

exp(-c

t)dt t)}]

(14)

where

%

-- (at -- b2) +_~/(at - b2)2 + 4bl a2 2b~

and c_+ = 7".1o + % T.20.

After evaluating T,,t and T.,2 from equations (13) and (14), Tg~ and Tg2 can be obtained from equations (2) and (4) respectively. The rate of evaporation of water from the upper and lower basins of the still can be obtained as

Qeu = h,,~,(T,t- T~I) x 3.6

(15)

T,,.to = 25~C

h3 = 94.14 W/m 2'~C

Tw20= 2Y~C

h4 = 15.973 W / m 2 C

rl = 0.0

h5 = 111.95 W/m2~C

r 2 = 0.2, 0.4, 0.6, 0.8

hi = 22.71 W/m2'~C

v = 5 m/s

K/= 0.04 W/m 2°C

u = 1.5 m/s

h,+ = 8.64 W/m>~C

L = 1.0m

h,,L = 8.12W/m2 C

b = 1.0m

h,,,= - 2 1 . 3 W/m2 C

L, = 0.05 m

hh = 0.7728 W / m 2 C

p = 103 kg/m 3

c, = 4.190 kJ/kg C

hi = 16.173 W/m2~C

M.q = 2,09,500 J/m2~'C

hl = 135.0 W/m2°C

M,,.2 = 2,61,875 j/m2°C.

The hourly variation of solar intensity and ambient air temperature used in calculations has been shown in Fig. 2. In Fig. 3, the hourly variation of the temperatures of the glass and water in both basins and that of the water flowing over the upper glass cover has been plotted with the variation of ambient air temperature. The hourly variation of 0eV, QeL has been shown in Fig. 4 for a particular set of parameters (T,~t0= T,,.20= 2Y~C and r2 = 0.8) for both the cases, with and without water flowing over the glass cover (u = 1.5 m/s and 0 respectively). The dependence of the performance of the system on the temperature of water in the lower basin has been shown in Fig. 5 by keeping T,q0 constant. Figure 6 shows the dependence of hourly yield on the upper basin water temperature, when Tw20is kept constant. The effect of ~2 on the performance of the system has been shown in Fig. 7. Figure 8a, b and c show the efficiency of the present system for different cases compared with that of the double basin solar still without any water flow over the glass cover.

RAO et al.:

T R A N S I E N T ANALYSIS OF D O U B L E BASIN SOLAR STILL

50 r-

~

-] 800

Moy

~

2nd,

1980

40

600

3o

40o ~,

E - 200

20

~o,I

I

7 0 0 o.m

t

12.00

~

1

5 0 0 p.m

I000

Io

1 2 . 0 0 o.m

600

Time (h)

Fig. 2. Hourly variation of solar intensity (H.~) and ambient air temperature T, for a typical hot day (2 May 1980) in Delhi.

70 T~ o = 2 5 Twzo = 2 5

60

0 Q

r2

*C *C

= 0.8

5O

~2

P 2 ~. 40 E

~2

30

~r~, ro ,~3 2Or--7 . 0 0 a.m

I 12.00

I

I0.00

5 . 0 0 prn

Time

I 2.00o.m

I

6.00

(h)

Fig, 3. Hourly variations of temperatures of T,.L (water in upper basin), T,. 2 (water in lower basin). Te~ (upper glass cover), T~2 (lower glass cover), 7,3 (water over upper glass cover), and T~ (ambient air), when inlet water temperatures of water in both basins is 25~C and the fraction of transmittance absorbed by the basin liner (z~) is 0.8.

87

88

RAO et al.: TRANSIENT ANALYSIS OF DOUBLE BASIN SOLAR STILL 50

~o

=

T~2o

= 25

°C

u =1.5 m / s and u = 0 40

T

0 30

x .E=

"E

20

.a

tO

/ /

o

I 12.00

ZOOam

I 2 3 4

QeUwith water flow Qeuwithout water flow Qecwith water flow QeLwithout water flow

1 5.00 pm

I I0.00

I 200a.m

J 600

Time, (h)

Fig. 4. Hourly variation of useful heat in both basins separately with and without water flow over upper glass cover when T.io = T.2o = 25~'C. z2 = 0.8 and u = 1.5 cm/s, respectively.

2. The process of flowing water over the glass cover shows a good effect on the upper basin distillate output, while, in the case of the lower basin, it is not very effective (Fig. 4).

The following conclusions have been made. 1. The temperature of the flowing water over the upper glass cover is almost equal to that of the upper glass cover. The temperatures are comparable to that of ambient air (Fig. 3).

'°°F

I I I I"

'

~

\\\\

~

/ ~ 3 5

40

*C

*C

IIII

5o

I

////

~

0[ ZOOcm

~

I 1200

T2=o.s

,oo 25 oc

I 500

l prn

I0.00

l 2 . 0 0 o,rn

I 6.00

Time (h)

Fig. 5. Hourly variation of total useful heat, keeping the temperature of upper basin constant and varying that of lower basin.

RAO et al.:

TRANSIENT ANALYSIS OF DOUBLE BASIN SOLAR STILL

89

I00

0 x 50

A

Tw2o = 2 5 * C r 2 = 0.8 TWlo

0~ 7.00 o m.

I 12,00

I

- 25 *C

2

- 3 0 *C

3 4

- 3 5 *C - 4 0 *C

I

I

5 . 0 0 p.m

I0.00

I

I

2.00o.m.

6.00

Time (h)

Fig. 6. Hourly variation of total useful heat, keeping temperature of lower basin constant and varying that of upper basin.

3. Though the distillate output increases with increase of the initial water temperature in both basins, the dependence on lower basin water temperature shows more effect than that of upper one, comparatively (Figs 5 and 6).

oo[

4. It is quite obvious that the distillate o u t p u t increase with increase of r2 (Fig. 7). 5. There is a r e m a r k a b l e increase in the efficiency of the present system over t h a t of the old one in all the cases (with respect to the ratio of z2, T,,.t0, Tw2o).

T~o = 25

T~2o = 2 5

*C *C

0.4 0.6 0.8

x

"rv"

5O

111"

-~

Tr

z

o ZOO am

I 12.00

~

5.00 p.m

I0.00

I 2.00 em

6 . O O e rn.

Time (h)

Fig. 7. Hourly variation of total useful heat, keeping temperatures of water in both basins constant and varying transmittance z2.

RAO et al.: T R A N S I E N T ANALYSIS OF D O U B L E BASIN SOLAR STILL

90

(a)

(b) Dependence

(c) on

Dependence ~o

= ~2o

Dependence

Twzo

*C

T.,o = 25

r2

•r 2 = 0 . 8

on

~o

on

T.2o = 2 5 *C

=0.8

= 25°C

60

40--

20

0

I

I

I

I

0.2

04

06

08

20

[

25

r2

I

50

1

35

I

40

20

~ a o (*C)

I

I

25

I

30 r~o

35

I

40

(*C)

Fig. 8. (a) Variation of efficiency of system with z2 with and without water flow over upper glass cover (T,.t0 and T,20 being constant). (b) Variation of efficiency of system with Tw20(inlet water temperature in lower basin) in both cases (T,.10, T2 being kept constant). (c) Variation of efficiency of system with T,~0 in both cases when r 2, T,.20 are kept constant). The lower line represents the efficiency of the system when there is no water flow whereas, the upper line shows the efficiency of the present system in each of Fig. 8a, b and c.

Acknowledgement--The authors are grateful to Professor M. S. Sodha, Deputy Director, I.I.T. New Delhi for various help during this work. REFERENCES

1. B. Achilov, T. D. Zhuraev and R. A. Akhtamov, Geliote Knika 8, 78 (1972). 2. E. D, Howe and B. W. Tleimat, UNESCO Conf. The Sun in the Service of Mankind, Paris (1973). 3. S. G. Talbert, J. A. Eibling and G. O. G. Lof, Prog. Rep. No. 546, U.S. Dept of Interior Research and Development (1970). 4. G. Frick and C. Ommurfeld, Solar Energy 14, 427 (1973). 5. M. S. Sodha, Ashvini Kumar, G. N. Tiwari and R. C. Tyagi, Solar Energy 26, 127 (1981). 6. T. P. Coffey, Solar Energy 17, 373 (1975). 7. R. V. Dunkle, Int. Dev. Heat Transfer, A.S.M.E., p. 895 (1961). 8. D. C. Gimmings, Multiple effect solar still, U.S. Patent No. 2, 445 (1948). 9. C. N. Hedges, T. L. Thompson, J. E. Groh and D. H. Fricling, Prog. Rep. No. 194, U.S. Dept of Interior Research and Development (1966). 10. M. K. Selcuk, Solar Energy 8, 23 (1964). 11. M. Telkes, Prog. Rep. No. 13, U.S. Dept of Interior Research and Development (1956). 12. M. S. Sodha, A. Kumar and G. N. Tiwari, Applied Energy 7, 147 (1980).

13. M. S. Sodha, J. K. Nayak, G. N. Tiwari and A. Kumar, Energy Cony. Mgmt 20, 23 (1980). 14. J. K. Nayak, G. N. Tiwari and M. S. Sodha, Energy Res. 4, 41 (1980). 15. M. S. Sodha, Usha Singh, Ashvini Kumar and G. N. Tiwari, Energy Corn'. Mgmt 20, 191 (1980). 16. M. S. Sodha, Ashvini Kumar, A. Srivastave and G. N. Tiwari, Energy Cony. Mgmt 20, 181 (1980). 17. G. N. Tiwari, V. S. V. Bapeswara Rao and M. S. Sodha, Transient performance of single basin solar still with water flowing over the glass cover. Desalination (1982). To be published.

APPENDIX

The h's are given by Dunkle [7] and Sodha et al. [12, 13, 16]

h~u

0.9 × ~r [(T,. t + 273) 4 - (T~,I + 273) 4] (T.,i - T~,)

hey = 0.884[T,.,

(/3,1 -- Pgl )(Twl + 273)] b3 ~68.9 ~ 103 5 p ~ ]

Tgl%

and hey = (16.276 x 10 -3) × h~t. × R I and h,L , hcL and h~c have identical expressions as above with T,. I and Tel replaced by T,. 2 and Te2, respectively.