Solar & Wind Te~hnoh#¢) Vol. 5, No. 4, pp. 433 44(I, 1988 0741 983X,88 $3.00 +.IX} Printed in Great Britain. Pergamon Press pie

TECHNICAL NOTE

Effect of tracking on the performance of a built-in-storage type solar water heater

J. PRAKASH,* H . P . G A R G t a n d D . S. HRISHIKESANt

* Department of Physics, Ramjas College, University of Delhi, Delhi-110 007, India t Centre for Energy Studies, Indian Institute of Technology, New Delhi- 110 016, India

(Received 25 April 1987 ; accepted 21 October 1987)

Abstraet--A mathematical model based on the forward time step marching technique is developed for predicting the thermal behaviour of a built-in-storage type solar water heater. Using the model, the performance of such a system is studied with and without night insulation as well as for various flow patterns like continuous flow, intermittent flow, instantaneous withdrawal, min imum temperature limit withdrawal, constant temperature withdrawal etc., under three types of orientation, viz. fixed surface, single axis tracking and double axis tracking. It is observed that the sysem performs better under single axis tracking mode as compared to fixed surface mode but the improvement in the performance over single axis tracking is marginal when double axis tracking is employed.

N O M E N C L A T U R E

Cg specific heat of glass (670 J/kg "C) Cp specific heat of the absorbing plate (420 J/kg 'C) C~ specific heat of water (4190 J/kg "C) heg heat transfer coefficient between the glazing and

the air enclosed between the glass and the plate (W/m 2 °c)

hep heat transfer coefficient between the plate and the air enclosed between the glass and the plate (W/m 2 °C)

hpw heat transfer coefficient between the plate and the water in the heater (W/m 2 'C)

hrpg radiative heat transfer coefficient between the plate and the glass (W/m 2 ~C)

Id intensity of diffuse radiation (W/m 2) lr~ intensity of beam radiation (W/m 2) Iv intensity of global radiation (W/m 2)

Mg mass of the glass (7.5 kg) Mp mass of the plate (7.07 kg) Mw mass of water (100 kg) rn w mass flow rate of water (kg/s)

S(t) instantaneous value of solar radiation incident on unit area of collector (W/m 2)

t time coordinate (s) T. ambient air temperature ( 'C) To temperature of air enclosed between the plate and

the glass CC) Tg glass temperature C C) T,n inlet water temperature (15~C) T v plate temperature CC) Tw temperature of water in the heater CC) U~ top loss coefficient (W/m: °C) U2 bot tom loss coefficient (W/m-" "C)

Greek letters absorbance of the plate (0.9)

C~g absorbance of the glass (0.06)

[~ tilt angle of the absorbing surface At time step p ground reflectance (0.2)

transmittance of glass and enclosed air (0.94) Oh angle of incidence of solar radiation on horizontal

surface O~ angle of incidence of solar radiation on tilted sur-

face.

I N T R O D U C T I O N

Built-in-storage type solar water heaters, which are simple and compact systems for collecting solar energy at low tem- perature, have many applications in the domestic as well as the industrial sector. Earlier work in this field was carried out by Garg and Rant [1]. To improve the efficiency of the system Prakash et al. [2,3] studied its performance under various conditions such as incorporation of a baffle plate and application of night insulation etc. They also investigated the effect of withdrawal of hot water from the system both continuously and intermittently at different mass flow rates and for different duty cycles.

Instead of incorporating a baffle plate for improving the performance of the system the authors felt it was worth investigating the possibility of achieving the same result by arranging the orientation of the collector in such a way as to receive increased solar radiation. The three possible modes of orientation considered are: (i) The fixed surface orien- tation : the tilt of the collector is fixed at a value which is optimized for the month and the azimuth angle kept equal to zero. Here, it is required to adjust the tilt of the collector only once in a month. This system is very simple, inexpensive, saves a lot of labour and reduces the wear and tear since there is no moving part. (it) Single axis tracking: the tilt of the collector is fixed at a value which is optimized for the month and the azimuth angle is continuously adjusted equal to that of the sun. (iii) Double axis tracking: the azimuth

433

434 Technical Nolo

angle of the collector is adjusted so that it is always equal to that of the sun and the collector tilt is adjusted so that the normal to the collector surface is collinear with the sun beams. Double axis tracking is more cumbersome compared to the two previous modes and the problems of wear and lear as well as maintenance are more acute.

The performance of the system was studied under different operating conditions for various duty cycles, such as no- flow (with and without night insulation), continuous flow, intermittent flow and instantaneous withdrawal for these three modes of orientation. The studies were also extended to the system which is adjusted so that water flows at a fixed flow rate through it only when the water temperature is above a fixed value. Due to the withdrawal of thermal energy in the form of hot water or fall in input energy if the water temperature falls below this limit, the flow would auto- matically stop. Another case studied was constant tem- perature withdrawal, where as soon as the temperature reaches a certain value, the flow starts. Thereafter, the mass flow rate automatically gets adjusted so that the temperature of the water in the heater remains constant. The flow of water will stop when the input energy is sufficiently low and the temperature falls below the fixed value. For all the cases mentioned above, the improvement in performance of the system for single axis tracking over a lixed surface mode is fairly significant while the difference between those of single axis tracking and double axis tracking is nominal.

DESIGN OF THE SYSTEM

The built-in-storage type solar water heater, as shown in Fig. 1, consists of a closed rectangular box of G.I. Sheets (0.914 mm) of dimensions 100× 100× 10 cm 3 made leak- proof by welding along the edge. The top surface of the box is blackened by an ordinary blackboard paint, so that it acts as a good absorber. The bottom and sides of the box are insulated using 5 cm thick libre glass insulation and the top is provided with a glazing of 3 mm thick glass sheet, with an air gap of 2.5 cm above the plate. Solar radiation, after passing through the glass sheet and tb~ air gap, is incident

on the blackened surlkicc, which being a good absorber ~,! solar radiation, heats up. The thermal energy thus gamed b.~ the plate is convectively transferred to the water in contact with it, raising its temperature, which is maintained uniform by virtue of convective currents set up in the water mass

The system is provided with an inlet lk~r cold water at the bottom and an outlet for warm water at the top. A valve i~ attached to the inlet, which prevents water from Ilowing oa~ of the system through the inlet. By forcing water through the inlet an equal amount of water is withdrawn from the sytem through the outlet.

The tracking of the system is achieved by lixing it on a flame which can be so adjusted as to keep the water heater at any tilt angle. A turntable, on which the whole set-up is mounted, facilitates the adjustments of the azimuth angle of the system.

ANALYSIS

An analysis of the system, described above, is performed under the following assumptions.

(l) Due to flee convective currents, thorough mixing of water is assumed to take place and hence a thermal stratification within the water mass avoided.

(2) The plate and the glass are assumed to have a uniform temperature.

(3) The air mass enclosed between the plate and the glass is considered to be at a uniform temperature, equal to the mean value of glass and plate temperatures.

(4) The initial values of the temperature of the glass which is in contact with the ambient air and that of the plate which is in contact with water in the heater are assumed to be equal to that of the ambient air and water tem- perature respectively.

(5) The edge losses are taken care of while calculating the bottom loss coefficients.

Considering the area of the absorbing surface and the glazing to be unity, the energy balance equations at various

Fig. I. Schematic representation of a built-in-storage water heater.

- - Night insulation

- - Water outlet

Gloss cover

Water

Insulation

Technical Note 435

interfaces of the system are given as :

For glazing,

dT~ MgCg dt =,%S(t)+h~g(Te Tg)+h~vg(Tp-- Tg)

U,(T s T~).

For the absorbing plate,

d G MpCp d / = ~zS(t)--hpw(Tr -- Tw)--hcp(Tp-- T~)

- h~pg( Tp - Tg).

And for water,

dT M,~Cw d/w = hv~(T p Tw)--U2(T~--T~)

(1)

(2)

--rhwCw(T~-- Ti.). (3)

The temperature of the enclosed air is given by

T e = T p + T g 2

Converting the differential equations (I 3) into difference equations and rearranging we get

AI T(i) (1) (1) (i) + - - [ h e g c +hrpgTp +U,T~ + ~ S ] (4) Mg Cg

o = _fl MpcvAt h ) T~ '+ [hpw q- co q- hrpg]~ T~p °

At T~ +hepT ~ +hrpgTg +~T S ] (5) + M, Co[h~ W ~,) .) 0~ .)

1 1

At l - M - c , [hp +U,+,n c l

+ At [hvwT~'~+U~T")+rh C~7~,] (6) MwCw " " w . , •

The superscripts i and i + 1 refer to time instants just before and just after the time interval At.

The average system efficiency is defined as

f24 m~Cw(Tw(/) T,.)dt+MwC~(Twl,_24--Twlt=o)

q --[2, S(t) dt

(7)

Where the first term in the numerator denotes the total energy withdrawn during 24 h in the form of hot water, the second term stands for the energy stored in the system after the same period, while the denominator stands for the total input energy.

The instantaneous values of solar radiation incident on a tilted surface of any orientation is obtained by the well known result of Liu and Jordan [4]

ID . (1 +COS /~) (1 --COS /3) S(t) = cos Oh COS 0, + ld - - f + pl~

(8)

N U M E R I C A L C O M P U T A T I O N S

Making use of eq. (8) and the hourly average values of solar radiation [5] in Delhi, the energy incident on a tilted surface is calculated [6]. The three orientations of the surfaces chosen for calculation are: (i) fixed surface, where the azi- muth angle is kept equal to zero and the tilt is kept at a particular value (= 52 ° for the mon th of January), which was found to be opt imum for a fixed surface; (ii) single axis tracking, where the azimuth angle of the surface is kept equal to that of the sun and the tilt angle is fixed at a value ( - 56 c~ for the same month) which is opt imum for single axis tracking; (iii) double axis tracking, where the azimuth angle of the surface is kept equal to that of the sun and the tilt angle is kept complementary to solar altitude angle. The tilt angle in the first case is optimized for the noon value while in the second case it is optimized for the complete period of sunshine hours. The hourly values of solar radiation, thus obtained, and that of ambient air temperature for January are plotted in Fig. 2. The increase in total solar radiation, in a day in January, incident on the surface, in Delhi, with single axis tracking over that on a fixed surface is found to be 15.5%, whereas the corresponding value for a double axis tracking mode is 17.3%. This shows that in winter months the double axis tracking, in spite of its complexity, does not increase the input energy incident on the collector surface substantially compared to single axis tracking, which is much easier to achieve. Since the average tap water temperature in Delhi during the mon th of January is experimentally observed as 15'~C, the value of T,, is assumed to be a constant, equal to 15"C.

To find the water temperature inside the heater, eqs (1 3) are solved simultaneously using the forward time step marching technique, with a time step of 10 s. It is observed that this time step is op t imum for a good convergence of the results.

N U M E R I C A L RESULTS AND DISCUSSION

Water temperature for fixed surface, single axis tracking and double axis tracking modes are plotted in Fig. 2, along with the values of solar radiation incident on the absorbing surface for the three modes of orientation. From the figure, it can be seen that there is a noticeable improvement in the thermal performance of the system under single axis tracking compared to the fixed surface mode, whereas the difference in the thermal behaviour between the systems under single and double axis tracking modes is nominal. The increase in the max imum water temperature for the single axis tracking case over the fixed surface case is 9.5%, whereas for the double axis tracking case it is 10.5%. This is in fair agreement with the increase in solar radiation incident on the surface due to the tracking of the system.

In Fig, 3(a) the effect of night insulation used over the heater is illustrated. Here, the night insulation cover is con- sidered to be employed at three different times of the day viz. 1700, 1800 and 2000 h. For all three modes of orientation, the difference in water temperature, at 0600 h next morning, between the three cases mentioned above is not large, but it is found that for single and double axis tracking the water temperature after covering the system at 1800 h is higher ( though not appreciably) than that of the system when it is covered at 1700 h. The opposite is found to be true using a fixed surface. This can be attributed to the higher energy input during this period of I h in the former case. This shows

436 Tcchnical Nolo

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In order to study the effect of withdrawal of hot water on the system performance, the model is simulated for two flow rates, 10 and 20 kg/h. The water temperatures in all three cases of orientation are shown in Fig. 3(b). When the flow rate is kept at 10 kg/h, the temperature of water reaches 30~C at 1230 h in the case of the fixed surface and water above this temperature can be withdrawn for 7 h continuously. In the cases of the single and double axis tracking modes, the temperature reaches 30°C at 1200 h and remains above this value for 8~ h. When the flow rate is raised to 20 kg/h, the 30°C limit is reached at 1330 h and falls below this value only after 3~ h for the fixed surface. In single and double axis

tracking, water temperature reaches 3 0 C at 1230 h and continues to be above this value for 5~ h.

The behaviour of the system for two duty cycles, viz. in- termittent flow and instantaneous withdrawal are depicted in Fig. (4a, b). For intermittent flow, hot water is withdrawn con- tinuously for a period of 1 h starting at 1200, 1700 and 2000 h at two flow rates of 10 and 20 kg/h. The time-dependent variation of water temperature for these two flow rates for the three types of orientation are given in Fig. 4(a). In the case of the fixed surface, when the flow starts at 1200 h, the temperature is just 30°C. For the flow rate of 10 kg/h, the water temperature at 1700 h is 46°C and falls to 42~'C 1 h thereafter, and at 2000 h in 1 h the water temperature falls from 39°C to 35.5°C. For a flow rate of 20 kg, the corres- responding values at 1700 h are 44.5'C and 39°C and at 2000h they are 36°C and 31°C. For single axis tracking, when the flow starts at 1200 h the water temperature is 33'C. For a flow rate of I0 kg/h, at 1700 h the water temperature is

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Technical Note 439

between 50'C and 46.5"C and at 2000 h it is between 42.5°C and 38.5"C. For a flow rate of 20 kg/h the temperature is between 48.5°C and 42°C at 1700 h and at 2000 h it is between 39°C and 33.5'~C. In the case of double axis tracking, at 1200 h the temperature of water is 33°C. For a flow rate of 10 kg/h at 1700 h, the water temperature is between 50°C and 47°C and at 2000 h, it is between 43°C and 39°C. When the flow rate in this case was raised to 20 kg/h it is seen that at 1700 h the water temperature is between 49°C and 43"C and at 2000 h it is between 39°C and 33.5°C.

For the instantaneous withdrawal case, 30 I of water are withdrawn within a period of 5 min, starting at 1200, 1700 and 2000 h. The water temperature, for all the three types of configuration, are given in Fig. 4(b). For the fixed surface, water is available at a temperature of 30°C, 44°C and 33~'C at 1200, 1700 and 2000 h respectively. For single axis tracking the corresponding values are 33°C, 48°C and 36.5°C respec- tively while for double axis tracking the corresponding values are 0.5'C higher than those of single axis tracking.

It was felt worth studying the possibility of hot water withdrawal fixing a minimum limit of the water temperature, above which the water flows at a fixed flow rate. The system is supposed to be fitted with a temperature-sensitive valve allowing the withdrawal of hot water at a fixed flow rate only when the water temperature is above a certain value (in our case 40°C). When the flow rate is 10 kg/h, the flow starts at 1400 h and continues for about 3 h for the fixed surface orientation. Here, it is observed that for the last 10 min, the flow stops for short periods of 10 s. In the single axis tracking mode, the flow starts at 1325 h and continues for nearly 4" h while for the double axis tracking mode the flow starts at 1325 h and continues for 4 h and 40 min. When the flow is increased to 20 kg/h, the flow pattern is quite different. For the fixed surface mode, the flow starts at 1400 h and continues intermittently for 3 h. In the beginning when the flow starts, the flow is seen to be for short periods of 1 min with intervals of no flow of 10 s in between. Towards the end, these intervals increase to about 2 min with the periods of flow reduced to

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440 Technical Note

Table 1. Average efficiency of the built-in-storage type solar water heater

Average efficiency (%)

Flow rate Fixed Single axis Operating conditions (kg/h) surface tracking

Double axis tracking

1. Without night insulation 0.0 27.0 27.5 27.6 2. System covered with night insulation

at : (a) 1700 h 0.0 43.37 43.5 43.5 (b) 1800 h 0.0 42.39 42.62 42.65 (c) 2000 h 0.0 39.75 39.98 40.01

3. Cont inuous flow (a) 10.0 51.18 51.69 51.74 (b) 20.0 61.25 61.75 61.80

4. Intermittent flow (a) t 0.0 34.14 34.60 34.64 (b) 20.0 39.91 40.35 40.39

5. Instantaneous withdrawal 360.0 44.35 44.83 44.87 6. Fixed flow when temperature is > 40~'C

(a) 10.0 35.75 39.68 39.98 (b) 20.0 36.09 41.02 41.45

7. Constant temperature withdrawal variable 36.09 41.01 41.44 (40°C)

10 s. For both single and double axis tracking modes the flow starts at 1325 h and continues intermittently for 3 h. In the former case, the durations of flow in the beginning is 2.5 min with 10 s intervals of no flow in between and finally periods of flow reduce to 10 s. In the latter case when the flow starts, the periods of flow are for 3 min with intervals of no flow of 10 s and the periods of flow reduce to l0 s towards the end. In all the three modes o f orientation, when the flow rate is fixed at 10 kg/h the flow is seen to be continu- ous, and during this period the temperature is above 40°C. When the flow rate is 20 kg/h the flow is intermittent and the water temperature normally does not go above 40°C. These findings prompted us to probe into the possibility of with- drawal of hot water at a fixed temperature, with a varying mass flow rate.

The system is supposed to be fitted with a temperature- sensitive flow regulating valve, which adjusts the flow rate in such a way as to keep the water temperature at a fixed value. In order to have a mathematical appreciation of this system, initially the water temperature is allowed to increase to a certain fixed value and after that the hot water is withdrawn from the system at varying flow rate, rhw, which is obtained by substituting dTUdt = 0. The hot water continues to flow until its temperature falls below the fixed value. The variation in water temperature and flow rate with respect to time, for all the three modes of orientation, are plotted in Fig. 5. For the fixed surface the water temperature reaches 40°C at 1400 h. At this instant the flow is set with a rate of 17.2 kg/h. Water continues to flow for 3~ h, and the flow rate gradually decreases to zero and thereafter the water tem- perature starts falling below 40°C. In both the single and double axis tracking modes, the flow starts at 1330 h and continues for 4 h. The initial values of flow rates are 18.7 kg/h in the former case and 18.9 kg/h in the latter. The flow

pattern in both these cases is the same as that in the fixed surface case.

The average efficiency of the system for the three modes of orientation under various operating conditions as cal- culated by employing eq. (7) is given in Table 1. This in brief is the summary of the work in this paper.

C O N C L U S I O N S

(l) The performance of the system, in terms of the thermal energy output , can be improved by employing a tracking device so as to follow the direction o f the sun.

(2) The double axis tracking mode does not improve the performance of the system substantially more than the single axis tracking mode.

REFERENCES

1. H. P. Garg and U. Rani, Theoretical and experimental studies on collector/storage type solar water heater. Solar Energy 29, 467 (1982).

2. J. Prakash, G. Datta and H. P. Garg, Effect of baffle plate on the performance of a built-in-storage type solar water heater. Energy 8, 381 387 (1983).

3. J. Prakash, (3. Dat ta and H. P. Garg, A solar water heater with a built-in latent heat storage. Energy Conversion and Management 25, 51-56 (1985).

4. B. Y. Liu and R. C. Jordan, Daily insolation on surfaces tilted towards equator. ASHRAEJ. 3, 53 59 (1961).

5. A. Mani and S. Rangarajan, Solar Radiation Over Imh'a. Allied Publishers, New Delhi (1982).

6. H. P. Garg and S. N. Garg, Model evaluation and opti- mum collector slope for a tropical country. Eneryy Con- version and Mana#ement 21,299-312 (1981).