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The importance of the condenser in a solar water pump
Energy Convers. Mgmt Vol. 36, No. 12, pp. 116%1173, 1995
Pergamon
Copyright © 1995 Elsevier Science Ltd Printed in Great Britain. All rights reserved 0196-8904/95 $9.50 + 0.00
0196-8904(95)00010-0
THE
IMPORTANCE OF THE A SOLAR WATER
CONDENSER PUMP
IN
K. SUMATHY, A. VENKATESHt and V. SRIRAMULU Department of Mechanical Engineering, Indian Institute of Technology, Madras 600 036, India
(Received 12 March 1994; receivedfor publication 4 January 1995)
A k a r a c t - - A brief description of the operation and analysis of a solar water pump is given. It is shown that one of the parameters affecting the performance o f the pump is the time taken for condensation o f the working fluid in each cycle. The condensation time in each cycle is determined through heat transfer analysis o f the condenser. The effects of inlet water temperature and mass flow rate o f the cooling water to the condenser on the condensation time and the pump performance have been studied and discussed. Flat plate collector
n-Pentane
Solar water pump
Condenser analysis
NOMENCLATURE t~ = tsv = tw = do = a~ = r/~ = %= H =
Surface temperature Saturated pentane vapour temperature Average water temperature Outer diameter o f tube Inner diameter of tube Mass flow rate of cooling water Specific heat of water Enthalpy
INTRODUCTION
The pump considered here works as follows: While the vapour of a low boiling point liquid, generated in a flat plate collector, provides the motive power for lifting water from a well, the condensation of the vapour and the consequent decrease in pressure provides for the suction of water into the pump. The performance of such a pump is known to depend very much on the condensation time. Hence, the pump performance is predicted, in conjunction with the condenser analysis that evaluates the condensation time in each cycle, for a given set of parameters. Also, the effects of the mass flow rate of water and its temperature at the inlet on the condensation time are discussed. The performance of the pump has been analysed for three different discharge heads of 6, 8 and 10m.
SYSTEM
DESCRIPTION
The schematic diagram of the solar thermal water pump is shown in Fig. 1. Liquid pentane, set in motion by thermosiphon action, is heated in the flat plate collector. The saturated pentane vapour, separating in tank S, is stored in the vapour storage tank N. When the vapour in tank N reaches a pre-determined pressure (the minimum pressure needed for the pump to operate), the vapour is allowed to enter tank A (by quickly closing valve 1 and opening valves 2 and 3) which initially contains water. The pentane vapour entering tank A displaces the water in it to tank B which initially contains air at ambient conditions. The rising column of water in B t T o whom all correspondence should be addressed, 1167
1168
SUMATHY et al.:
IMPORTANCE OF THE CONDENSER IN A SOLAR WATER PUMP
compresses the air in it, and this compressed air, in turn, pushes the water in vessel C (which is immersed in well water) to the overhead tank D. At the end of pumping, valve 2 is closed and valve 1 is opened, so that tank N is replenished with pentane vapour from the collection system. Simultaneously, water from the overhead tank D is allowed to flow through the cooling coils in vessel A to condense the pentane vapour in it. Once the condensation is complete, the pump is ready for the second cycle of operation. A N A L Y S I S OF THE P U M P
A brief mention of the thermodynamic analysis of the pump, carried out in conjunction with the heat transfer analysis of the collector, is made here. The collector analysis is aimed at predicting the temperature and pressure of the pentane as a function of time. The global radiation intensity on the collector plane is assumed to vary sinusoidaUy from sunrise to sunset. Solar radiation incident on the collector heats the liquid in the collector. The temperature and pressure of the pentane gradually increase with time (process 1-2, in Fig. 2). Theoretically, at state 2, the pressure of pentane in the collector has to be such that the pump can lift the intended amount of water per cycle. This minimum pressure at state 2 is calculated based on energy and mass balance relations. When the pressure in tank N reaches the minimum pressure, a part of the pentane vapour in it (dm kg) is quickly transferred to vessel A for pumping water. After this transfer, when valve 1 is opened, after dosing valve 2, liquid pentane in the collector flashes to bring mechanical
/, .®
\
2
"////////////////////////////// A B C D N
: : : : :
Water t a n k Air tank Well t a n k Over head tank Vapour tank
S : Separation tank
/
/--Wel I / J
/
b. ~ .
Fig. 1. Schematic diagram of the solar thermal water pump.
SUMATHY et al.:
IMPORTANCE OF THE CONDENSER IN A SOLAR WATER PUMP
1169
k.
U~ r~
Specific volume---Fig. 2. p-v diagram.
equilibrium between the collector and tank N. This will cause a drop in pressure and temperature of the pentane. The pentane in the collection system, whose mass is decreased by din, is now heated from this condition. For the pump to operate again, the pressure in tank N should reach the minimum pressure. The time required to bring the pressure back to the value at state 2 is referred to as the "heating time". During the same period, the well water which has been pumped to the overhead tank D is passed through the cooling coil to cause condensation. Unless the pentane vapour is completely condensed, the condition in vessel A is not conducive for the next cycle to start. The time required for the complete condensation is referred to as "condensation time". If the heating time is less than the condensation time, the heating of the pentane has to be continued, although it is not necessary, until the condensation is completed. In such a case, at the end of heating, the pressure in the collection system reaches a value higher than that at state 2 in the previous cycle. This pressure is that corresponding to state 8 in Fig. 2. On the contrary, if the heating time is more than the condensation time, the second cycle can commence as soon as the pressure of the pentane reaches the value corresponding to that at state 2. Therefore, it is clear that the condensation time is a critical parameter which decides the cycle time. If the condensation time is higher than the heating time, the cycle time increases. As the cycle time increases, the number of cycles that the pump can perform in a day decreases. As the amount of water pumped per day is equal to the product of the number of cycles per day and the amount of water pumped per cycle, the pump performance decreases with an increase in the condensation time. To get a feel of the problem, the performance of the pump has been analysed for various assumed condensation times, in the range of 1-6 min. Figure 3 shows the performance of the pump for various assumed values of condensation time for three discharge heads, viz. 6, 8 and 10 m. For a discharge head of 6 m, the condensation time has no influence on the performance of the pump provided the condensation is complete within 2.5 min. This is so because the heating time is equal to or greater than 2.5 min, and hence, it is the heating time that dictates the cycle time. It can, therefore, be said that 2.5 min is the critical condensation time in this particular case. Once the condensation time increases beyond the critical condensation time, the cycle time is decided by the condensation time. The number of cycles, thus, decreases rapidly as the condensation takes more than 2.5 rain. The same trend is also seen in the curves corresponding to discharge heads of 8 and 10 m, although the effect of condensation time is not as pronounced. As the discharge head increases, not only the minimum pressure required to operate the pump increases, but also the pentane vapour required per cycle increases. This will obviously increase the heating time as well as the critical condensation time, as can be seen from curves 2 and 3 in Fig. 3.
1170
S U M A T H Y et al.:
I M P O R T A N C E OF T H E C O N D E N S E R IN A S O L A R W A T E R P U M P
As the pump performance is strongly linked to the condensation time, especially for pumps with low discharge heads, it is best that the pump analysis be done using the actual condensation time determined through condenser analysis rather than using an arbitrarily assumed condensation time. CONDENSER
ANALYSIS
An attempt is made here to evaluate the condensation time through heat transfer analysis of the condenser. The following are the parameters that influence the condensation time in general: (i) surface area of the condenser coil, (ii) mass flow rate of water, (iii) inlet cooling water temperature. In the condenser used here, the above parameters cannot be changed at will to get the desired condensation time. The surface area of the condenser coil cannot be increased indefinitely, as its size is limited by the volume of vessel A. The amount of cooling water available in each cycle is limited by the water lifted per cycle, as it has to come from the overhead tank D. The flow rate of cooling water can only be such that the condensation is accomplished with the available quantity of water. The inlet cooling water temperature, to,in , is subject to ambient temperatures. It is observed that, at any time of the day, tc,i, = ta - 2 where ta is the ambient temperature, which also varies with time. Figure 4 shows the schematic of vessel A with the cooling coil in it. The cooling coil is a copper tube (i.d. = 6 mm and o.d. = 11 mm), 5 m long in the form of eight coils of average diameter 20 cm. In the p - v diagram (Fig. 2), 4-5 and 5-6 show the idealized processes of cooling and condensation of the vapour, respectively, in the first cycle. During 4-5, the volume remains constant, and during 5-6, the temperature is constant. The condensation time is equal to the sum of the times taken for each of these two processes. It may be pointed out here that, although in actual practice the cooling and condensation take place simultaneously, the above simplified procedure is used in the present analysis. The flow of water in the coil is turbulent, even at as small a flow rate as 1.5 kg/min (the Reynolds Number being 7000). The water side heat transfer coefficient, h,, is evaluated using the Sieder and Tate relation [1]. The flow rate of 1.5 kg/min is used from practical considerations. The pump operating on 1 m 2 collector area can lift around 15 kg of water. Hence, the flow rate of 1.5 kg/min permits the water to pass through the condenser for 10 min--a time within which the condensation
90 80-
I = 8m head 2 = 8m head 3 = l o r e head
,~ 70~q ¢~ 60 -~ 0
550: 0 40-
• ~30ZO-
10
0
Condensation time, min Fig. 3. Effect of condensation time on p u m p performance.
SUMATHY et al.: IMPORTANCE OF THE CONDENSER IN A SOLAR WATER PUMP
1171
Cooling water in Pentone
vopour
i .... Cooling coil
Vessel
A
-....
Cooling water out
~..,
To vessel B
Fig. 4. Cooling coil in vessel A. shall positively be complete. In determining the heat transfer coefficient between the pentane vapour and the coil, the condensation is assumed to be filmwise and the appropriate correlation [2] is used. As the pentane vapour condenses, the coil is progressively submerged in liquid pentane. In order to consider the effect of condensate inundation [3], the expression for the heat transfer coefficient (hm) is modified as, hv
= hm N - I / 6
(1)
where hv = average heat transfer coefficient on the vapour side for N tubes. The surface temperature depends upon the relative magnitudes of the thermal resistances in the system. To start, ts is assumed to be equal to (tsv + tw)/2. From the second iteration onwards, the surface temperature t~ is given by ts = tw + (/pen.yap - - t , ) × (Rwat/Rtot)
(2)
where tw = average water temperature, t~nvap= saturated temperature (corresponding to the discharge pressure) o f the pentane vapour, Rw~t= thermal resistance on the water side ( = h(, l ) and Rto t = Rwa t + Rpen.vap = hw I + h~-~ , neglecting the resistance due to tube wall thickness. The overall heat transfer coefficient Uo, is given by: Uo = [(do/d~) × (hT, I + h~-l)] -~ (W/m 2 K).
(3)
The rate o f heat transfer to the cooling water is, Ol = Uo x surface area × (t~v- tw) (W).
(4)
The rate of heat transfer to the circulating water is given by, Q2 = mw x cp x At (W)
(S)
where At is the rise in temperature of the water. It is known that At = 2(tw - tc,i,) where t¢,in is the inlet water temperature, i.e. ~l and Q2 must be equal under steady conditions. If they are not equal in the first iteration, another value of tw is chosen, and the same procedure is repeated until 0~ equals 02.
1172
SUMATHYet
al.:
IMPORTANCEOF THE CONDENSER IN A SOLARWATER PUMP
The procedure adopted above is fairly easy for process 5-6 in the first cycle (Fig. 2). However, the analysis is somewhat complex for 4-5, as both pressure and temperature decrease continuously during this process. The process of cooling is divided into five parts. In each part, an average water temperature is assumed, and the convergence of 01 and Q2 is sought. The difference in enthalpies between states 3 and 4 is the total heat transfer required to cool the vapour. This quantity, when divided by the average 01 or 02 calculated for the process 4-5 will give the time required for cooling the vapour. A similar procedure is adopted for subsequent cycles as well. z4-s, the time for cooling the vapour during process 4-5, is ~,-s =
(114-
(6)
H5)104-5,
where 04-5 is the rate of heat transfer during the process 4-5, which is equal to the average 0~ in equation (4). %-6, the time for condensation during process 5-6, is given by %-6 = (H5 - H6)05-6,
(7)
where 0s-6 is the rate of heat transfer during the constant pressure process 5-6, which is evaluated using equation (5). The total time for cooling and condensation of the vapour is the sum of ~4-5 and %-6. RESULTS AND DISCUSSION The condensation time also depends on the mass of pentane vapour to be condensed in each cycle. This mass increases with increase in the discharge head. Also, the time required to generate this mass varies with the variation in solar radiation intensity and ambient temperature. So, the results in Fig. 5 are evaluated for the following assumed parameters: Noon solar radiation intensity= 1000W/m 2, collector area = 1 m 2, ambient temperature at 8.00h a.m. = 30°C and discharge head = 8 m. Under these conditions, the average heating time turns out to be 3.5 min. Figure 5 shows the effect of the mass flow rate of water on condensation time. As one would expect, the average condensation time (the average of the times taken for condensation from the first to last cycle) decreases with an increase in the mass flow rate. Though the condensation time decreases, it does not have any effect on the number of cycles performed per day for the following reason. Since the average heating time is 3.5 min, it is always greater than the condensation time for any given flow rate considered. It follows, therefore, that the performance of the pump depends only on the heating time and not on the mass flow rate in the range shown in Fig. 5. 4.0
70 ........
No. o f cycles
Head -- 8 m
C o n d e n s a t i o n time
Hma x = 1000 W / m 2
3.5
-
-
6O
3.0
m
-
50
~',
2.5
-
-40
2.0
-
-
30
z
1.5
-
-
20
e~ o
"o
8 <
1.0
I
I
I
I
I
l
2
3
4
5
l0 6
M a s s f l o w r a t e (row) F i g . 5. Effect o f m a s s f l o w r a t e o n c o n d e n s a t i o n t i m e a n d p u m p p e r f o r m a n c e .
6
et al.:
SUMATHY
IMPORTANCE
OF THE CONDENSER
5.0
..°° °°
PUMP
1173
60
°°°°°
° - ° ° ° ° ° ° ° " °°~°
4.5 --
IN A SOLAR WATER
°°,
..
". "'.
-
50
4.0 --
~" 3 s 3.0
-40
- -
.=
30
"~
-
20
Z
-
10
2.5 - <~"
2.0 - 1.5 - -
Hma x = 1000 W/m2
~ /
........
1.0 - -
0.5 25
----
,
No. of cycles Condensation time Heating time
I
I
I
I
I
]
1
I
I
26
27
28
29
30
31
32
33
34
0 35
Ambient temperature (°C) Fig° 6, Effect o f a m b i e n t t e m p e r a t u r e o n c o n d e n s a t i o n time a n d p u m p p e r f o r m a n c e ,
To find the effect of inlet cooling water temperature (/e,in) on the condensation time, the value of the ambient temperature at 8.00 h is varied in steps of 2° from 25 to 32°C, The inlet cooling water temperature at any instant is assumed to be 2° less than ambient temperature. The ambient temperature at any time of the day is obtained from a polynomial fitted using measured values. Figure 6 shows the effect of inlet cooling water temperature on condensation time and heating time. The slight decrease in heating time with an increase in ambient temperature is due to reduction of the heat losses from the collector to the surroundings. Also, the condensation time increases with an increase in t~,in. The cooling water temperature does not decrease the performance of the pump until 30°C because the heating time (curve 2 in Fig. 6) is more than the condensation time. However, the slight increase in the number of cycles up to this temperature is only due to improvement in the collection efficiency. As the ambient temperature increases, the losses from the collector decrease. As shown in Fig. 6, beyond 30°C, the inlet cooling water temperature affects the pump performance because the condensation time becomes higher than the heating time. This increase in condensation time increases the cycle time which, in turn, brings down the number of cycles that a pump can perform in a day. Also, the pump ceases to operate beyond 32°C, because it would not be possible to condense the pentane vapour in vessel A. CONCLUSIONS The performance of the pump depends on both condensation and heating times. The condensation time is predicted by heat transfer analysis of the condenser. It is seen that the change in mass flow rate has no effect on the number of cycles because the heating time is always greater than the condensation time in the range mentioned. The inlet temperature of cooling water has a significant effect on the condensation time and, in turn, on the number of cycles. While the pump can perform 58 cycles at 30°C, it can perform only 18 cycles at a temperature of 34°C. REFERENCES 1. J, P. H o l m a n , Heat Transfer, 7th edn. M c G r a w - H i l l , N e w Y o r k (1990). 2. W . H . M c A d a m s , Heat Transmission, 3rd edn. M c G r a w - H i l l , N e w Y o r k (1954). 3. D . Q , K e r n , J. Am. Inst. Chem. Engrs 4, 157 (1958).
Pergamon
Copyright © 1995 Elsevier Science Ltd Printed in Great Britain. All rights reserved 0196-8904/95 $9.50 + 0.00
0196-8904(95)00010-0
THE
IMPORTANCE OF THE A SOLAR WATER
CONDENSER PUMP
IN
K. SUMATHY, A. VENKATESHt and V. SRIRAMULU Department of Mechanical Engineering, Indian Institute of Technology, Madras 600 036, India
(Received 12 March 1994; receivedfor publication 4 January 1995)
A k a r a c t - - A brief description of the operation and analysis of a solar water pump is given. It is shown that one of the parameters affecting the performance o f the pump is the time taken for condensation o f the working fluid in each cycle. The condensation time in each cycle is determined through heat transfer analysis o f the condenser. The effects of inlet water temperature and mass flow rate o f the cooling water to the condenser on the condensation time and the pump performance have been studied and discussed. Flat plate collector
n-Pentane
Solar water pump
Condenser analysis
NOMENCLATURE t~ = tsv = tw = do = a~ = r/~ = %= H =
Surface temperature Saturated pentane vapour temperature Average water temperature Outer diameter o f tube Inner diameter of tube Mass flow rate of cooling water Specific heat of water Enthalpy
INTRODUCTION
The pump considered here works as follows: While the vapour of a low boiling point liquid, generated in a flat plate collector, provides the motive power for lifting water from a well, the condensation of the vapour and the consequent decrease in pressure provides for the suction of water into the pump. The performance of such a pump is known to depend very much on the condensation time. Hence, the pump performance is predicted, in conjunction with the condenser analysis that evaluates the condensation time in each cycle, for a given set of parameters. Also, the effects of the mass flow rate of water and its temperature at the inlet on the condensation time are discussed. The performance of the pump has been analysed for three different discharge heads of 6, 8 and 10m.
SYSTEM
DESCRIPTION
The schematic diagram of the solar thermal water pump is shown in Fig. 1. Liquid pentane, set in motion by thermosiphon action, is heated in the flat plate collector. The saturated pentane vapour, separating in tank S, is stored in the vapour storage tank N. When the vapour in tank N reaches a pre-determined pressure (the minimum pressure needed for the pump to operate), the vapour is allowed to enter tank A (by quickly closing valve 1 and opening valves 2 and 3) which initially contains water. The pentane vapour entering tank A displaces the water in it to tank B which initially contains air at ambient conditions. The rising column of water in B t T o whom all correspondence should be addressed, 1167
1168
SUMATHY et al.:
IMPORTANCE OF THE CONDENSER IN A SOLAR WATER PUMP
compresses the air in it, and this compressed air, in turn, pushes the water in vessel C (which is immersed in well water) to the overhead tank D. At the end of pumping, valve 2 is closed and valve 1 is opened, so that tank N is replenished with pentane vapour from the collection system. Simultaneously, water from the overhead tank D is allowed to flow through the cooling coils in vessel A to condense the pentane vapour in it. Once the condensation is complete, the pump is ready for the second cycle of operation. A N A L Y S I S OF THE P U M P
A brief mention of the thermodynamic analysis of the pump, carried out in conjunction with the heat transfer analysis of the collector, is made here. The collector analysis is aimed at predicting the temperature and pressure of the pentane as a function of time. The global radiation intensity on the collector plane is assumed to vary sinusoidaUy from sunrise to sunset. Solar radiation incident on the collector heats the liquid in the collector. The temperature and pressure of the pentane gradually increase with time (process 1-2, in Fig. 2). Theoretically, at state 2, the pressure of pentane in the collector has to be such that the pump can lift the intended amount of water per cycle. This minimum pressure at state 2 is calculated based on energy and mass balance relations. When the pressure in tank N reaches the minimum pressure, a part of the pentane vapour in it (dm kg) is quickly transferred to vessel A for pumping water. After this transfer, when valve 1 is opened, after dosing valve 2, liquid pentane in the collector flashes to bring mechanical
/, .®
\
2
"////////////////////////////// A B C D N
: : : : :
Water t a n k Air tank Well t a n k Over head tank Vapour tank
S : Separation tank
/
/--Wel I / J
/
b. ~ .
Fig. 1. Schematic diagram of the solar thermal water pump.
SUMATHY et al.:
IMPORTANCE OF THE CONDENSER IN A SOLAR WATER PUMP
1169
k.
U~ r~
Specific volume---Fig. 2. p-v diagram.
equilibrium between the collector and tank N. This will cause a drop in pressure and temperature of the pentane. The pentane in the collection system, whose mass is decreased by din, is now heated from this condition. For the pump to operate again, the pressure in tank N should reach the minimum pressure. The time required to bring the pressure back to the value at state 2 is referred to as the "heating time". During the same period, the well water which has been pumped to the overhead tank D is passed through the cooling coil to cause condensation. Unless the pentane vapour is completely condensed, the condition in vessel A is not conducive for the next cycle to start. The time required for the complete condensation is referred to as "condensation time". If the heating time is less than the condensation time, the heating of the pentane has to be continued, although it is not necessary, until the condensation is completed. In such a case, at the end of heating, the pressure in the collection system reaches a value higher than that at state 2 in the previous cycle. This pressure is that corresponding to state 8 in Fig. 2. On the contrary, if the heating time is more than the condensation time, the second cycle can commence as soon as the pressure of the pentane reaches the value corresponding to that at state 2. Therefore, it is clear that the condensation time is a critical parameter which decides the cycle time. If the condensation time is higher than the heating time, the cycle time increases. As the cycle time increases, the number of cycles that the pump can perform in a day decreases. As the amount of water pumped per day is equal to the product of the number of cycles per day and the amount of water pumped per cycle, the pump performance decreases with an increase in the condensation time. To get a feel of the problem, the performance of the pump has been analysed for various assumed condensation times, in the range of 1-6 min. Figure 3 shows the performance of the pump for various assumed values of condensation time for three discharge heads, viz. 6, 8 and 10 m. For a discharge head of 6 m, the condensation time has no influence on the performance of the pump provided the condensation is complete within 2.5 min. This is so because the heating time is equal to or greater than 2.5 min, and hence, it is the heating time that dictates the cycle time. It can, therefore, be said that 2.5 min is the critical condensation time in this particular case. Once the condensation time increases beyond the critical condensation time, the cycle time is decided by the condensation time. The number of cycles, thus, decreases rapidly as the condensation takes more than 2.5 rain. The same trend is also seen in the curves corresponding to discharge heads of 8 and 10 m, although the effect of condensation time is not as pronounced. As the discharge head increases, not only the minimum pressure required to operate the pump increases, but also the pentane vapour required per cycle increases. This will obviously increase the heating time as well as the critical condensation time, as can be seen from curves 2 and 3 in Fig. 3.
1170
S U M A T H Y et al.:
I M P O R T A N C E OF T H E C O N D E N S E R IN A S O L A R W A T E R P U M P
As the pump performance is strongly linked to the condensation time, especially for pumps with low discharge heads, it is best that the pump analysis be done using the actual condensation time determined through condenser analysis rather than using an arbitrarily assumed condensation time. CONDENSER
ANALYSIS
An attempt is made here to evaluate the condensation time through heat transfer analysis of the condenser. The following are the parameters that influence the condensation time in general: (i) surface area of the condenser coil, (ii) mass flow rate of water, (iii) inlet cooling water temperature. In the condenser used here, the above parameters cannot be changed at will to get the desired condensation time. The surface area of the condenser coil cannot be increased indefinitely, as its size is limited by the volume of vessel A. The amount of cooling water available in each cycle is limited by the water lifted per cycle, as it has to come from the overhead tank D. The flow rate of cooling water can only be such that the condensation is accomplished with the available quantity of water. The inlet cooling water temperature, to,in , is subject to ambient temperatures. It is observed that, at any time of the day, tc,i, = ta - 2 where ta is the ambient temperature, which also varies with time. Figure 4 shows the schematic of vessel A with the cooling coil in it. The cooling coil is a copper tube (i.d. = 6 mm and o.d. = 11 mm), 5 m long in the form of eight coils of average diameter 20 cm. In the p - v diagram (Fig. 2), 4-5 and 5-6 show the idealized processes of cooling and condensation of the vapour, respectively, in the first cycle. During 4-5, the volume remains constant, and during 5-6, the temperature is constant. The condensation time is equal to the sum of the times taken for each of these two processes. It may be pointed out here that, although in actual practice the cooling and condensation take place simultaneously, the above simplified procedure is used in the present analysis. The flow of water in the coil is turbulent, even at as small a flow rate as 1.5 kg/min (the Reynolds Number being 7000). The water side heat transfer coefficient, h,, is evaluated using the Sieder and Tate relation [1]. The flow rate of 1.5 kg/min is used from practical considerations. The pump operating on 1 m 2 collector area can lift around 15 kg of water. Hence, the flow rate of 1.5 kg/min permits the water to pass through the condenser for 10 min--a time within which the condensation
90 80-
I = 8m head 2 = 8m head 3 = l o r e head
,~ 70~q ¢~ 60 -~ 0
550: 0 40-
• ~30ZO-
10
0
Condensation time, min Fig. 3. Effect of condensation time on p u m p performance.
SUMATHY et al.: IMPORTANCE OF THE CONDENSER IN A SOLAR WATER PUMP
1171
Cooling water in Pentone
vopour
i .... Cooling coil
Vessel
A
-....
Cooling water out
~..,
To vessel B
Fig. 4. Cooling coil in vessel A. shall positively be complete. In determining the heat transfer coefficient between the pentane vapour and the coil, the condensation is assumed to be filmwise and the appropriate correlation [2] is used. As the pentane vapour condenses, the coil is progressively submerged in liquid pentane. In order to consider the effect of condensate inundation [3], the expression for the heat transfer coefficient (hm) is modified as, hv
= hm N - I / 6
(1)
where hv = average heat transfer coefficient on the vapour side for N tubes. The surface temperature depends upon the relative magnitudes of the thermal resistances in the system. To start, ts is assumed to be equal to (tsv + tw)/2. From the second iteration onwards, the surface temperature t~ is given by ts = tw + (/pen.yap - - t , ) × (Rwat/Rtot)
(2)
where tw = average water temperature, t~nvap= saturated temperature (corresponding to the discharge pressure) o f the pentane vapour, Rw~t= thermal resistance on the water side ( = h(, l ) and Rto t = Rwa t + Rpen.vap = hw I + h~-~ , neglecting the resistance due to tube wall thickness. The overall heat transfer coefficient Uo, is given by: Uo = [(do/d~) × (hT, I + h~-l)] -~ (W/m 2 K).
(3)
The rate o f heat transfer to the cooling water is, Ol = Uo x surface area × (t~v- tw) (W).
(4)
The rate of heat transfer to the circulating water is given by, Q2 = mw x cp x At (W)
(S)
where At is the rise in temperature of the water. It is known that At = 2(tw - tc,i,) where t¢,in is the inlet water temperature, i.e. ~l and Q2 must be equal under steady conditions. If they are not equal in the first iteration, another value of tw is chosen, and the same procedure is repeated until 0~ equals 02.
1172
SUMATHYet
al.:
IMPORTANCEOF THE CONDENSER IN A SOLARWATER PUMP
The procedure adopted above is fairly easy for process 5-6 in the first cycle (Fig. 2). However, the analysis is somewhat complex for 4-5, as both pressure and temperature decrease continuously during this process. The process of cooling is divided into five parts. In each part, an average water temperature is assumed, and the convergence of 01 and Q2 is sought. The difference in enthalpies between states 3 and 4 is the total heat transfer required to cool the vapour. This quantity, when divided by the average 01 or 02 calculated for the process 4-5 will give the time required for cooling the vapour. A similar procedure is adopted for subsequent cycles as well. z4-s, the time for cooling the vapour during process 4-5, is ~,-s =
(114-
(6)
H5)104-5,
where 04-5 is the rate of heat transfer during the process 4-5, which is equal to the average 0~ in equation (4). %-6, the time for condensation during process 5-6, is given by %-6 = (H5 - H6)05-6,
(7)
where 0s-6 is the rate of heat transfer during the constant pressure process 5-6, which is evaluated using equation (5). The total time for cooling and condensation of the vapour is the sum of ~4-5 and %-6. RESULTS AND DISCUSSION The condensation time also depends on the mass of pentane vapour to be condensed in each cycle. This mass increases with increase in the discharge head. Also, the time required to generate this mass varies with the variation in solar radiation intensity and ambient temperature. So, the results in Fig. 5 are evaluated for the following assumed parameters: Noon solar radiation intensity= 1000W/m 2, collector area = 1 m 2, ambient temperature at 8.00h a.m. = 30°C and discharge head = 8 m. Under these conditions, the average heating time turns out to be 3.5 min. Figure 5 shows the effect of the mass flow rate of water on condensation time. As one would expect, the average condensation time (the average of the times taken for condensation from the first to last cycle) decreases with an increase in the mass flow rate. Though the condensation time decreases, it does not have any effect on the number of cycles performed per day for the following reason. Since the average heating time is 3.5 min, it is always greater than the condensation time for any given flow rate considered. It follows, therefore, that the performance of the pump depends only on the heating time and not on the mass flow rate in the range shown in Fig. 5. 4.0
70 ........
No. o f cycles
Head -- 8 m
C o n d e n s a t i o n time
Hma x = 1000 W / m 2
3.5
-
-
6O
3.0
m
-
50
~',
2.5
-
-40
2.0
-
-
30
z
1.5
-
-
20
e~ o
"o
8 <
1.0
I
I
I
I
I
l
2
3
4
5
l0 6
M a s s f l o w r a t e (row) F i g . 5. Effect o f m a s s f l o w r a t e o n c o n d e n s a t i o n t i m e a n d p u m p p e r f o r m a n c e .
6
et al.:
SUMATHY
IMPORTANCE
OF THE CONDENSER
5.0
..°° °°
PUMP
1173
60
°°°°°
° - ° ° ° ° ° ° ° " °°~°
4.5 --
IN A SOLAR WATER
°°,
..
". "'.
-
50
4.0 --
~" 3 s 3.0
-40
- -
.=
30
"~
-
20
Z
-
10
2.5 - <~"
2.0 - 1.5 - -
Hma x = 1000 W/m2
~ /
........
1.0 - -
0.5 25
----
,
No. of cycles Condensation time Heating time
I
I
I
I
I
]
1
I
I
26
27
28
29
30
31
32
33
34
0 35
Ambient temperature (°C) Fig° 6, Effect o f a m b i e n t t e m p e r a t u r e o n c o n d e n s a t i o n time a n d p u m p p e r f o r m a n c e ,
To find the effect of inlet cooling water temperature (/e,in) on the condensation time, the value of the ambient temperature at 8.00 h is varied in steps of 2° from 25 to 32°C, The inlet cooling water temperature at any instant is assumed to be 2° less than ambient temperature. The ambient temperature at any time of the day is obtained from a polynomial fitted using measured values. Figure 6 shows the effect of inlet cooling water temperature on condensation time and heating time. The slight decrease in heating time with an increase in ambient temperature is due to reduction of the heat losses from the collector to the surroundings. Also, the condensation time increases with an increase in t~,in. The cooling water temperature does not decrease the performance of the pump until 30°C because the heating time (curve 2 in Fig. 6) is more than the condensation time. However, the slight increase in the number of cycles up to this temperature is only due to improvement in the collection efficiency. As the ambient temperature increases, the losses from the collector decrease. As shown in Fig. 6, beyond 30°C, the inlet cooling water temperature affects the pump performance because the condensation time becomes higher than the heating time. This increase in condensation time increases the cycle time which, in turn, brings down the number of cycles that a pump can perform in a day. Also, the pump ceases to operate beyond 32°C, because it would not be possible to condense the pentane vapour in vessel A. CONCLUSIONS The performance of the pump depends on both condensation and heating times. The condensation time is predicted by heat transfer analysis of the condenser. It is seen that the change in mass flow rate has no effect on the number of cycles because the heating time is always greater than the condensation time in the range mentioned. The inlet temperature of cooling water has a significant effect on the condensation time and, in turn, on the number of cycles. While the pump can perform 58 cycles at 30°C, it can perform only 18 cycles at a temperature of 34°C. REFERENCES 1. J, P. H o l m a n , Heat Transfer, 7th edn. M c G r a w - H i l l , N e w Y o r k (1990). 2. W . H . M c A d a m s , Heat Transmission, 3rd edn. M c G r a w - H i l l , N e w Y o r k (1954). 3. D . Q , K e r n , J. Am. Inst. Chem. Engrs 4, 157 (1958).