Solar & Wind Technology Vol. 3, No. 2, pp. 119-125, 1986 0741-983X/86 $3.00+ .00 Printed in Great Britain. Pergamon Press Ltd.

PERFORMANCE PREDICTION OF A REGENERATIVE SOLAR STILL

J. PRAKASHt* and A. K. KAVATHEKAR~ t Dipartimento di Energetica, Universit/L degli Studi di Firenze, Via di S. Marta, 3,1-50139 Firenze, Italy;

:~ Department of Physics, Ramjas College, University of Delhi, Delhi-t 10007, India

(Received 20 September 1985; accepted 28 October 1985)

A~traet--In this paper we have presented the design, analysis and performance of a regenerative solar still capable of giving a daily output of about 7.51 m-2 under ideal conditions. The results are compared with those for a conventional solar still.

1. INTRODUCTION

Supplying potable water to some regions (e.g. deserts, marshy lands, etc.) having no source of fresh water has always been a major problem. To do this with a distribution network connected to a centrally located distribution plant is a costly proposition, particularly in the case of thinly populated remote localities. It has been shown that in cases where the demand of potable water is small, solar distillation units are an economically viable solution. Even though the initial cost involved for the installation of such devices is high, the cost of maintenance, repair and the energy bill are practically nil, and in the ultimate cost analysis these turn out to be, economically, the most important factors. This is more so for the places where the average annual solar radiation per day exceeds 20 MJ m - 2, as in most parts of India. With the fast depleting resources of conventional fossil fuels, the relevance of an economically viable solar still becomes even more important.

In recent years a large number of models for solar stills have been suggested by various workers [1-8"i. Most of these models give a rather low daily output of 3--5 1 m-2 of potable water. It is well known that under summer conditions, as in India, in a day, about 9-101 m -2 of water evaporates from an open surface exposed to the sky. The low output in the case of most conventional solar stills is mainly due to release of large quantities oflatent heat by condensing vapours on the condensing surface, and the poor dissipation of this heat by this surface, thus increasing its temperature, which in turn results in a lowered rate of condensation as well as that of evaporation, from the basin.

* On study leave from the Department of Physics, Ramjas College, University of Delhi, Delhi-110007, India.

To enhance the still output, the following conditions must be fulfilled by the design of the still:

(1) The temperature of the condensing surface should be low; this leads to a higher rate of condensation.

(2) The temperature of the water in the basin should be high; this leads to a higher rate of evaporation.

(3) The latent heat released at the condensing surface by the water vapours at the moment of condensa- tion should be recycled to increase the temperature of water in the basin.

In this paper we present the design and the performance-prediction of a regenerative still which is capable of giving a dally output of about 7-5 1 m -2 under ideal conditions. This design has been inspired by the results of the experiments by Akhtamov et al. [9] in which they obtained an average output of 7.51 m-2 per day. Our design differs from theirs, primarily by the fact that we used two condensing surfaces instead of one, as used by them. We have found that the amount of condensate is nearly the same on both of the surfaces.

In Section 2 the design of the regenerative solar still is described. Section 3 deals with the working and the mathematical formulation of the still. The metho- dology used for numerical calculations is discussed in Section 4, while the results are discussed in Section 5.

2. DESIGN OF THE REGENERATIVE STILL

The regenerative solar still is shown in Fig. 1. It comprises a galvanized sheet-iron basin (1) having two glass covers (2 and 3) 2.5 cm apart and inclined at an angle of 10 ° to the horizontal. The surface of the basin (4) facing the sun is painted with ordinary black paint for maximum collection of solar radiation. The

119

120 J. PRAKASH and A. K. KAVATHEKAR

34. . . . - -- 6

10

8 2

4

Fig. 1. Regenerative solar still (see text for explanation).

bottom and the sides of the basin are insulated with a 5 cm thick layer of fibre-glass (5). Waters enters the still at (6) and flows in the form of a thin layer (7) between the two glass covers along the total width of the still. Water is heated along its path down the glass surface and enters through (8) into the main basin (9). The condensate is collected in two troughs (10 and 11) attached to the bottom of the glass covers. The still is oriented towards solar noon so as to collect the maximum solar radiation.

3. MATHEMATICAL FORMULATION

The solar radiation falling on the top glass cover (glass 1) travels through it. A part of the incident radiation is absorbed by glass 1 while the rest is transmitted through it to the water layer (water 1), which lies over the lower glass cover (glass 2). Part of the radiation is absorbed by water 1 and glass 2 while the rest is transmitted to the water layer (water 2) in the main basin. Here, once again, a fraction of radiation is absorbed by water 2 and the rest travels to the black surface of the basin, where it is partly absorbed by the surface and partly reflected. The reflected part, in turn, travels back through water 2. Small fractions of incident radiation are also reflected from the glass and water surfaces. Because of the absorbed radiation and the heat transfer from the black surface of the basin, the temperature of water in the basin, as well as the vapour pressure, increases. Water vapour condenses at the cooler bottom of glass 2, transferring the heat of condensation to glass 2, and then to water 1 flowing over it. This restricts the increase in the temperature of the condensing surface and thereby increases the rate of condensation at the bottom of glass 2. Water 1 transfers

heat and vapour to glass 1 in an identical manner, thus causing further condensation at its bottom. The remaining water over glass 2, at a temperature higher than the ambient temperature, enters the main basin, thus recycling a significant portion of the latent heat of condensation, which otherwise would have resulted in a much higher temperature at glass 2 and, consequently, a reduced rate of condensation. Glass 1, which is at a lower temperature, loses heat to the surroundings. Water which has condensed at the two inclined glass surfaces is collected via two troughs provided for the purpose. The flow of water between the two glass covers is adjusted continuously so that the masses of water 1 and 2 remain unchanged throughout the day.

The energy balance equations at various nodal surfaces are as follows :

A t glass 1

m,,cg dT~,/dt = c~gS(t) + hl(Tw~ - Tz, ) -- UI(T, , -- T~). (1)

A t water 1

mwtcw d T , J d t = ctwa%S(t) + nl(Tg2 - Tw,)

- h , ( T ~ , - Tg,)-q~2(Tw~- Tg 2)

+ qe, ( T w , - Tg,)) ( T w , - Ta)cw/L. (2)

At #lass 2

mg2cg dTgJdt = ctg%zw,S(t) + h2(Tw2 -- T~2)

-H~(T,~- T~). (3)

Performance prediction of a regenerative solar still

At water 2

mw~c,, dTw2/dt = ~w2~[~,,,S(t)+ H~(Tp- T,, 2) - d T , ~ - r,~ (h2-q~) ( T ~ , - Tw)cw/L). (4)

At black plate

mpCp d Tp/dt = otvZ2Zw, z ,2S( t ) - H2(T p - T,2 )

- u ~ ( ~ - ~ ) . (5)

While writing equations (1-5) we have assumed that the area of the base plate is 1 m s and is the same for the glass covers. The temperature for a particular node is assumed to be uniform. The coefficients of absorbance and transmittance of water depend on the thickness of its layer and are obtained by knowing that the intensity of solar radiation at any depth of the water layer is given by

5

I(x, t) = S(t)(1-r) ~. vj exp(-#jx), (6) j = l

121

where/~ and vj are the extinction coefficient and the corresponding weighting factor of water for the jth region of the solar spectrum.

The heat transfer coefficient h~ is given by

h, = qc, + q,, + qe,, (7)

where qo,, q,,, q,, are, respectively, convective, evaporative and radiative heat transfer coefficients between the water surface and the glass. These are approximated to their values between two infinite parallel surfaces. The relations used to describe these coefficients are as suggested by Duncle [10, 11] i.e.

( P , , - P~)(Tw, + 273)] 1/3, qc,=0"884 T,~,-TB,+ 268.9x10a_pw ' j (8)

q¢, = 16-276 x IO-aq¢,(Pw-P,,)/(T,,-T~,), (9)

q,, = 0.9 x ~r((T,,, + 2 7 3 ) ' - ( T s , + 2 7 3 ) 4 ) / ( T , , , - Ts,), (I0)

4 5

i 4O

Z

x 50

oJ

o. 25

t, 2O

e

® ® Experimenter (Ref. 12) Theoreticot (Eq.12)

I I I I I 2 0 30 40 50 60 70

Temp. (°C) II [

Fig. 2. Saturated vapour pressure curve for water.

I SO

122

where i = 1 , 2 . The mass of the condensate is given by

m, = qo,(Tw,- Ts,)/L. (11)

J. PRAKASH and A. K. KAVATHEKAR

4. NUMERICAL CALCULATIONS

The finite difference technique has been employed to solve the simultaneous differential equations for the energy balance. For this, d T / d t in these equations has been approximated as (T i + 1 - Ti)/At where T i and T ~+ ~ represent the nodal temperatures just before and just after the time interval At. The choice of the size of the time interval is important for the stability of the calculations. We found that a time interval larger than 5 s does not give consistent results, while an interval smaller than 5 s does not improve the accuracy of the results significantly, and so we have selected a time interval of 5 s for the present calculations.

In equations (8) and (9) the saturated vapour pressure P has been calculated using the expression

P(T) = 4 5 " 0 - 2 " 7 5 T + 0 ' 0 7 5 T 2. (12)

The variation of P with T as obtained by equation (12) is in good agreement, from 20 to 65"C, with the experimental values [12] as shown in Fig. 2. The

Table 1. Values of weighting factor and absorption coefficient of water for solar radiation [13]

Weighting Absorption Region factor coefficient

O') (v j) (~ j)

1 0 < 2 < 0.36 0.237 0-032 2 0-36 ~< A < 1.06 0-193 0-450 3 1.06 ~< A < 1.3 0.167 3.0 4 1.3 ~< Z < 1.6 0-179 35.0 5 1.6 ~ 2 < oo 0.224 255-0

heat transfer coefficients h~ and h 2 a r e calculated from equations (7)-(10), while the values of other heat transfer coefficients are H1 = 62 W m -2 K -1, H 2 = 106 W m - 2 K - 1 and the heat loss coefficients are U1 = 3 0 W m - 2 K - l a n d U2 = 2 ' 0 4 W m - 2 K -x .The values of weighting factors and absorption coefficients of water for solar radiations are given in Table 1.

The input parameters for the calculations, the solar radiation and the ambient temperature are shown in Fig. 3. These were measured at half-hourly intervals at the Indian Institute of Technology, New Delhi campus

50 -

40 k.)

a 30

E

20

//~"w

I I

/ SoLar radiation

/ I

/ /

/ /

/ /

/

/

! - ~

i I ~ ' . I 6.00 12.00 18.00 24.00

Time ( h )

Fig. 3. Solar radiation and ambient temperature.

700

600

500 E

g 400

300

200

I00

0

6 0 0

Performance prediction of a regenerative solar still 123

1.2

1.0

-~ 0,8

v

i 0 6

0.4

O ~

6.00

0.2

I TotoI condensote: rail = 5 kg

11" Cendensote under gloss cover 2

TIT Tatar condensate: mwl= I kg

V Condensate under gross cover 2

TE Conventional. stil.l.

t I .~., \~ / " \ \

. v \ \ / ] . / , , ",,),, /I/ I , \\,,

I / / \',x • / " \

12.(X) {8.00 Z4.00 6.(X) Time (h)

Fig. 4. Output variation vs change in water mass (m~l) on glass 2; n%, 2 = 20-0 kg.

1.2

LO

0 . 8

§ o

os

0,4

0.2

A Mass of water in basin 20 kg

B Moss of water in basin 60 kg

C Conventiot~o| stiU moss of water 60 kg

0 ~ ' " ~ , " ~ " I I I 6.00 12.00 18.00 24.00

Time (h)

Fig. 5. Output variation vs change in water mass (mw2); row, = l.O kg.

6,00

124 J. PRAKASH and A. K. KAVATHEKAR

A t

"o

E

8

8 .

20

Convent iona l

I I I 4 0 6O 80

row2 (kg )

Fig. 6. Variation of output with row2.

I ~OO

on 22 June 1982. The intermediate values are obtained by linear interpolation.

5. RESULTS AND DISCUSSION

The results of the calculation have been presented in Figs 4, 5 and 6. In Fig. 4 the hourly output of the condensate of the entire still, as well as that collected from glass 2, has been plotted. The results correspond to 20 kg of water in the basin for two different amounts of water, viz 1 and 5 kg on glass 2. The hourly output of a conventional solar still has also been shown. It is clear that the change in the amount of water on glass 2 from 1 to 5 kg does not affect the performance significantly. It can be seen from this figure that the output for the present design of the still is appreciably large compared to that for the conventional still.

The effect of the change in the amount of water in the basin, while keeping the water mass (1 kg) above glass 2 fixed, is shown in Fig. 5. The curves are for the still output for two different amounts of water in the basin; namely 20 and 60 kg. As expected, the output for the case of 60 kg, though low in the daytime, increases considerably during the night. The output for a simple

still with 60 kg of water in the basin has also been plotted.

Figure 6 represents the total distillate in a day as against the amount of water in the basin for both the present design of the still and the conventional design. The daily output decreases in both cases for larger amounts of water in the basin. Although, in the case of the regenerative solar still, the output falls more rapidly with the increase in the water mass in the basin, it is always greater than that for the conventional still.

Acknowledgements--One of the authors (J. Prakash) has carried out part of this work with the support of a grant from the "ICTP Programme for Training and Research in Italian Laboratories, Trieste, Italy". J. Prakash also wishes to thank Professor E. Carnevale and Professor F. Martelli for their interest in the work.

NOMENCLATURE

% absorption by the glass % absorption by the basin plate ~w, absorption by water cg heat capacity of the glass cover (W kg- 1 K 1) % heat capacity of the basin plate (W kg- 1 K- 1) cw heat capacity of water (W kg- 1 K- 1)

Performance prediction of a regenerative solar still 125

h z heat transfer coefficient from water above glass cover 2 to glass cover 1 ON m -z K -1)

he heat transfer coefficient from water in basin to glass cover 2 (Wm -2 K - z)

H z heat transfer coefficient from glass cover 2 to the water above it OV m -2 K - z)

H2 heat transfer coefficient from the plate of the basin to the water above it (W m -2 K -x)

L latent heat of vaporization (W kg- z) ms: mass of glass cover 1 (kg) m,z mass of glass cover 2 (kg) mp mass of basin plate (kg)

row, mass of water above glass cover 2 (kg) m,,~ mass of water in the basin (kg) mt mass of condensate collected on glass cover 1 (kg) m2 mass of condensate collected on glass cover 2 (kg) q~l convective heat transfer coefficient from the water on

glass cover 2 to glass cover 1 (Wm -2 K -1) qc~ convective heat transfer coefficient from the water in

the basin to glass cover 2 (Wm -2 K -1) qc, evaporative heat transfer coefficient from the water

on glass cover 2 to glass cover 1 (W m -2 K -z) qc~ evaporative heat transfer coefficient from water in

the basin to glass cover 2 (W m - 2 K - 1) q,~ radiative heat transfer coefficient from water on

glass cover 2 to glass cover 1 (W m -2 K -z) q,~ radiative heat transfer coefficient from water in the

basin to glass cover 2 (W m - 2 K - ~) Ps, saturated vapour pressure at glass cover 1 (N m -2) Ps~ saturated vapour pressure at glass cover 2 (N m - 2) P.,, saturated vapour pressure of water above glass

cover 1 (N m - 2) Pw~ saturated vapour pressure of water in the basin

(N m -2) S(t) solar radiation in the plane of the absorbing plate

(W m - 2) TB, temperature of#ass cover 1 (°C) T~ temperature of glass cover 2 (°C) T=, temperature of water above glass cover 1 (°C) T,, 2 temperature of water in the basin (°C)

T. ambient temperature (°C) t time (h)

zs transmittivity of glass ¢. transmittivity of water

U z heat-loss coefficient from the top of the still (W m -2 K -1)

U2 heat-loss coefficient from the bottom of the still (Wm-2 K -z )

Stefan-Boltzmann constant vj weighting factor for solar radiation in water in the

j th region of the solar spectrum ~uj absorption coefficient for solar radiation in water in

thej th region of the solar spectrum (m-t) • ~ wavelength of solar radiation (m)

REFERENCES

1. P. I. Cooper, Maximum efficiency of single effect solar stills. Solar Energy 15, 205 (1973).

2. J.W. Bloemer, J. R. Irvin, J. A. Eibling and G. O. G. Lof, A practical basin type solar still. Solar Energy 9, 197 (1965).

3. E.D. Howe and B. M. Tleimat, Twenty years of work on solar distillation at the University of California. Solar Energy 16, 97 (1974).

4. M. S. Reddy, D. J. Navin Chandra, H. K. Sehgal, S. P. Sabberwal, A. K. Bhargava and D. S. Jitha Chandra, Performance era multiple wick solar still with condenser. Appl. Energy 13, 15 (1983).

5. J. K. Nayak, G. N. Tiwari and M. S. Sodha, Periodic theory of solar still. Int. J. Energy Res. 4, 41 (1981).

6. M. S. Sodha, J. K. Nayak, G. N. Tiwari and A. Kumar, Double basin solar still. Energy Conservation 20, 23 (1980).

7. J.A. Eibling, S. G. Talbert and G. O. G. Lof, Solar stills for community use--digest of Technology. Solar Energy 13, 263 (1971).

8. S. Satcunanathan and H. P. Hanson, An investigation of some of the parameters involved in solar distillation. Sotar Energy 14, 353 (1973).

9. R. A. Akhtamov, B. M. Achilov, O. S. Kasmilov and S. Sukharov, Study of regenerative inclined stepped solar still. Geliotechnika 14, 51 (1978).

10. R. V. Dunkle, Solar water distillation, the roof type still and a multiple effect diffusion still. International Heat Transfer Conference, Part V, International Developments in Heat Transfer, p. 895. University of Colorado (1961).

11. R. V. Dunkle, A simple solar water heater and still, presented at joint AIRAH-SES Meeting, Perth, May 1971.

12. R. C. Weast (ed.), CRC Handbook of Chemistry and Physics. CRC Press, Ohio (1976).

13. N.K. Bansal and S. Singh, Analysis ofdirectly heated open and closed swimming pools. Energy Res. 9, 211 (1985).