Nov 26, 1996 - Department of Applied Physics, Jordan University of Science and Technology,. Irbid-Jordan .... [21], Graham et al. [22] and Degelman [23].
~
Pergamon
RenewableEneryy, Vol. 11, No. 3, pp. 351 361, 1997 © 1997ElsevierScienceLtd All rights reserved.Printedin Great Britain PII : S0960-1481 (97)00005-0 0960-1481/97 $17.00+ 0.00
TECHNICAL
NOTE
Optimal design for a thermosyphon solar water heater
ADNAN SHARIAH and BASSAM SHALABI Department of Applied Physics, Jordan University of Science and Technology, Irbid-Jordan (Received 26 November 1996; accepted 12 January 1997) Abstract--Through the use of TRNSYS, a transient simulation program, optimization of design parameters for a thermosyphon solar water heater was studied for two regions in Jordan represented by two cities, namely Amman and Aqaba. The optimum value of a parameter is defined as the value which maximizes the annual solar fraction of a system. This paper includes a good deal of information concerning sizing of common components of thermosyphon solar water heaters operated under certain condition (load volume, distribution profile and temperature) using weather data of Jordan. The results indicate that the solar fraction of the system can be improved by 10 25% when a proper choice is used for each studied parameter. It is also shown that the solar fraction of a system installed in Aqaba (hot climate) is less sensitive to some parameters than the solar fraction of a similar installed in Amman (mild climate). © 1997 Elsevier Science Ltd.
INTRODUCTION Thermosyphon solar water heaters are used in Jordan for domestic applications. It is estimated that ca. 30% of households in the country have installed such systems [1]. The design of the system was developed by trial and error, because of the complexity of the variable flow rate and thermal stratification in the storage tank. The performance of the system is affected by many factors, e.g. design parameters, operating conditions and meteorological data. In the literature, a great deal of research has been conducted to improve the performance of the system by studying the effects of design parameters on the performance; e.g. Gupta and Garg [2], and Hahne [3] have studied the effect of the collector parameters on the performance of the system under steady-state conditions. Others [4-6] have conducted research on the effect of operating strategy and storage tank configuration, while some have investigated the influence of one or few parameters on the performance of the system [7 11]. Only very few researchers have studied the optimum values of design parameters of a thermosyphon solar water heater under certain operating conditions, using local weather data [12 14] for one year of operation. The author [15] conducted a comprehensive study on optimizing the design parameters using the weather data of Los Angeles. As is expected, the optimum values of design parameters of a system installed in a certain region could not necessarily be applicable to other regions of different weather data. The aim of this study is to determine the optimum values of the design parameters of a thermosyphon solar water heater operated in Jordan, for two regions representing the mild and hot climates that appear in Jordan, using the well-known simulation program TRNSYS [16]. SYSTEM DESCRIPTION AND SIMULATION MODEL The schematic diagram of the thermosyphon solar water heater investigated in this study is shown in Fig. 1. It consists of a flat-plate collector and a stratified vertical storage tank level with the top of 351
352
Technical Note LOAD TANK
MIXER
Ht Haux
Hth
MAIN
,L MAIN Hc
Ho
...................Y.......2t,........ CHECK VALVE Fig. 1. Schematic diagram of the considered system.
the collector. The reverse flow in times of low and/or no solar radiation is prevented through the use of a check valve added to the systems connecting pipes. An electric auxiliary heater and thermostat are placed 10 cm down from the top of the tank to meet the required energy for the load whenever the energy gain from the collector is not sufficient. The power of the auxiliary heater is taken as high as possible to ensure that it can meet the required energy for the load at times of low/or no radiation. Hot water at 60°C was delivered with a daily load volume of 150 1 distributed over a day according to the Rand profile [17] (Fig. 2). A flow mixer is connected between the storage tank and user to mix water from the tank with cold water from the main to ensure that hot water is delivered to the load with the desired temperature, when its temperature is above the desired load temperature. A full description of the system is presented in Table 1. The values in this table are taken from the results of Shariah et al. [15]. The storage tank is modeled as a thermally stratified tank. The number of segments (nodes) in this
k~
0
!
,
I
I
2
4
•
~
i
J I
6
,
,
,
•
,
I
I
I
8
10
12
,
•
I
,
14
t
I
16
,
,
•
I
,
18
•
I
20
D A Y T I M E (hr)
Fig. 2. The Rand hot water consumption profile.
•
I °
22
353
Technical Note Table I. System design parameters
Ac
4 m2
NBI, NB2
5
Dh
20 m m 15 m m 5 mm 21.6 kJ/h m 2 0.6 72 kg/h m 2 0.8 cm 0.95 cm 0.95 m lm 1m 0.8 cm 5m
Li, Lo N~ P~ux
(4 & 3) m 12 100 M J / h 22°C 60°C 10 kJ/h m2~C 5.4 kJ/h m2°C 150 1/day 150 1 2.2m 32 (degrees) 32 (degrees) 0.2
DI, Do D~
FRUL FR(r~).
Gtest H,u~ H~ Ho
Hr Ht Hth Lh
Tr~,.i,, T.~e~ Ui, Uo (UA)t V~ Vt W~ fl ~b pg
model is not fixed, but depends on many factors, i.e. the simulation time step, the size of the collector, load flow rates, heat losses and auxiliary input [13]. In this model the simulation starts with a certain number of segments. As the hot water leaves the top of the collector and enters the storage tank from a certain point at the top, it mixes with water at this level if their temperatures are within 0.5°C. If its temperature is lower than that at the top by more than 0.5°C it flows down and mixes with water of a segment where the temperature is within 0.5'~C of it. In the case when the temperature of water entering the storage tank is higher than that at the top of the storage tank by more than 0.5°C, a new segment is then created at the top, increasing the number of segments by one. When hot water is drawn to the load, the same case applies for cold water from the main entering the tank from the bottom, this water mixes with that at the bottom if their temperatures are within 0.5°C of each other, otherwise a new segment is created. The collector is divided into a number of segments or nodes (we used 20 nodes) normal to the flow direction. Bernouli's equation is applied to any node in the thermosyphon loop to calculate the pressure drop :
APi = Pig Ahi + PighLi.
( 1)
The temperature at the midpoint of any node k in the collector is given by [18]
Tk = T.+
FRU~q-
T~-T a
)exp
.
(2)
The total useful energy gain from the collector is calculated on the basis of the Hottel-Willier equation
Qu = rAc At[FR(ZCO.Ix - FR UL (Ti - Td)]
(3)
where r is the modification coefficient by which FR(ra) and FRUL are corrected, and given as
l /'~/cCp(l_exp(-mcFtUL~ AcF'UL
r=[
\
~
m~Cr, ( I _ e x p ( _ A c F , U L ~
LAcF'UL
//Ju~e
~
.
(4)
mccp J/]J
....
The performance of the system is characterized by the annual solar fraction, which is defined as
Q,-Q~u~ Q,
f = -
(5)
354
Technical Note
where Ql, Q.... respectively, are energy delivered to the load and energy supplied by the auxiliary heater. The parameters FR(ZC0 and FRUL, which characterize thermal and optical properties of the collector, are taken to be 0.6 and 21.6 kJ/h m2°C, respectively. These values are the average values for most of solar collectors manufactured in Jordan as reported by the Jordan Scientific Society [19]. The simulation was done using weather data for two cities in Jordan, i.e. Amman and Aqaba representing the mild northern and the hot southern half of Jordan. Weather data used in this study were provided by the Jordan Meteorological Department [20]. The required hourly meteorological data (solar radiation and dry bulb temperature) for the simulation were generated from the monthly average daily values by the Weather Data Generator component supplied by the TRNSYS. This component generates data in a manner such that their associated statistics are approximately equal to the long-term statistics at the specified location [16]. The model is based on the algorithms developed by Knight et al. [21], Graham et al. [22] and Degelman [23]. The yearly performance of the system was calculated and used as an indicator to determine the optimum values of the design parameters. The optimum value of a parameter is defined as the value which maximizes the annual solar fraction of the system. The optimization procedure followed in this work was to fix all but one parameter and find the optimum value of this parameter. Then, this parameter was fixed and another optimized, etc. until all were at an optimum. A second pass through this single variable optimization process produced no significant change in optimum values. RESULTS AND DISCUSSION The results of the simulation are given diagrammatically in Figs (3) (10). Each figure shows the plot of solar fraction vs a studied parameter. The first parameter studied was the number of risers in the absorber plate, Nr. Figure 3 shows variations in the solar fraction associated with changes in the number of risers for both Amman and Aqaba. The width of the collector was 2.2 m. Both curves have almost the same trend, where the solar fraction is strongly dependent on number of risers for small Nr values and reaches its maximum value at ca. Nr = 8. Beyond this value there is no improvement in the solar fraction as Nr increases. Clearly, due to its higher solar intensity and ambient temperature, a system installed in Aqaba operates with a solar fraction higher than that installed in 0.95
I
I
I
I
0.90
[-*
0.85 .../
//: /:
0.80
./
AQABA
// / ...................
0.75
~
I
4
i
I
i
8
I
12
AMMAN
i
I
16
i
20
Nr
Fig. 3. Variation of the annual solar fraction with the number of risers in the absorber plate for a collector of width of 2.2 m.
Technical N o t e 0.95
i
~
355
I
I
!
AQABA ..............
AMMAN
0.90
0.85
0 0.80
0.75
~
I
I
,
10
,
20
I
I
,
30
I
,
40
50
60
R~ (cm) Fig. 4. Variation o f the annual solar fraction with the risers spacing. 0.95
i
~
0.85
,
,
.........................................
0.80
o.75 0.70
:
0.65 0.60
AQABA
f
................
:
0.55
AMMAN
/
J
0.50 0.45
i
0
I
4
i
I
8
I
I
12
i
I
16
i
20
D r (ram) Fig. 5. Variation o f the annual solar fraction with the risers diameter.
A m m a n . Figure 4 shows the variation o f the solar fraction with the risers spacing, R~. It is clear that solar fraction has a m a x i m u m value at smaller Rs values and as Rs increases, starting from 8 cm, the solar fraction remains almost u n c h a n g e d up to c a . Rs = 15 cm, then it decreases with additional
356
Technical Note 1.00
t
t
I
I
I
t
I
i
t
t
0.90 0.80 0.70 0.60 0.50 0.40 0.30
t!
0.20
/
AQABA .
.
.
.
.
.
.
.
.
.
.
AMMAN
0.10 0.00 0
I
I
I
I
I
I
I
I
I
I
4
8
12
16
20
24
28
32
36
40
44
Do, Di (mm) Fig. 6. Variation of the annual solar fraction with the connecting pipes diameter. 1.00
I
t
I
'
I
AQABA AMMAN
0.95
/
f
0.90
0.85 ..,..
@
..-~
0.80 /.
,/
// ,//
0.75
0.70
'
0.0
~
0.4
I
0.8
,
I
1.2
,
I
1.6
,
2.0
Ht (in) Fig. 7. Variation of the annual solar fraction with the storage tank height. increase in R~. This decrease is faster for a system installed in Amman due to lower solar intensity and ambient temperature. Thus, the optimum or recommended value for the risers spacing is c a . 15 cm and it could be 20 cm for Aqaba. When the diameter of the risers, Dr is examined (Fig. 5) one can observe that the solar fraction is
Technical N o t e 0.95
I
l
357 I
I
0.90
0.85
0
0.80 / .,.,-
.... "
AQABA
0.75
0.70 0.0
.........
,
I
,
I
0.2
~
0.4
I
,
0.6
AMMAN
I
,
0.8
1.0
H r (m)
Fig. 8. V a r i a t i o n of the a n n u a l solar fraction with the height of the return pipe from the collector to the storage tank. 0.95
I
I
I
I
I
0.90 0.85 0.80
0.75 0.70
/:
AQABA
0.65
/
AMMAN
0.60 0.55 0.50 0.0
0.2
0.4
0.6 Ha, H m ( m )
0.8
1.0
1.2
Fig. 9. V a r i a t i o n o f the a n n u a l solar fraction with the height o f the auxiliary heater a n d t h e r m o s t a t .
extremely affected by Dr for small values a n d reaches its m a x i m u m value at c a . Dr = 5 cm. F o r larger Dr values the solar fraction has the same value. The r e c o m m e n d e d value for this p a r a m e t e r could be higher t h a n the o p t i m u m one by a certain a m o u n t , d e p e n d i n g on the quality o f water used, to
358
Technical Note 1.00
i
I
I
I
I
AQABA
AMMAN
0.95
0.90
[-, 0.85
f, ~
0.80
0.75
0.70
,
0.0
!
2.0
,
I
4.0
,
t
6.0
,
!
8.0
,
I
10.0
,
12.0
(UA)t (kJ/hr-m2-°C) Fig. 10. Variation of the annual solar fraction with the overall heat loss coefficient of the storage tank.
overcome problems like corrosion and others usually occurring in solar collectors that may be associated with the operation of the system. Figure 6 shows the effect of the diameter of the connecting pipes between the storage tank and the collector, Do, Di, on the solar fraction. It is clear that the solar fraction increases rapidly as Do, D~ increases between 3 and 12 mm, and no change is observed beyond this value. The strong dependence of the solar fraction on small values of both Do, Di and Dr, as seen in Figs 5 and 6, may be clarified as follows; when small values for Do, D~ and/or D r a r e chosen, this will result in a very low flow rate which makes the system operate with a very low solar fraction. Even a small increase in these parameters results in a large increase in the flow rate or in the solar fraction. This dependency continues until the maximum value. One of the very important design parameters affecting the operation of the thermosyphon solar water heaters is the height of the hot water storage tank, Hr. Figure 7 shows the variation of the solar fraction with this parameter as it varies from 0.4 (representing a horizontal tank) to 2 m (too long a vertical tank). Keep in mind that this parameter is studied while the bottom of the tank is at the same level as the top of the collector. A reasonable increase in the solar fraction is achieved as Ht increases from 0.4 to c a . 0.8 m (from the horizontal case to the nearly vertical one). This increase is higher for Amman which has a lower ambient temperature throughout the year. An additional increase in H~ causes further increase in the solar fraction, especially for Amman, for the same reason. Therefore, the optimum or recommended value for H t is c a . 1 m for Amman and 0.8 m for Aqaba. Quantitatively speaking, using vertical tanks instead of horizontal tanks will result in an improvement in the solar fraction of c a . 10% in Amman and c a . 7.5% in Aqaba. The dependence of the solar fraction on the height of the return pipe, Hr (height at which water from the collector enters the storage tank) is shown in Fig. 8. During the study of this parameter the height of the storage tank was taken as 1.0 m. Obviously, when hot water enters the storage tank from a point close to the bottom, this nearly mixes the tank and finally makes the entire system operate with the lowest solar fraction (Fig. 8). An increase in H r results in an improvement in the solar fraction due to the appearance of thermal stratification in the tank and lower thermal losses. Also, it can be deduced that the solar fraction is improved by c a . 10% for Amman and 7% for Aqaba when Hr increases from 0.2 to 1.0 m. Comparing
Technical Note
359
Figs 7 and 8, for Amman and Aqaba one can observe that the solar fraction for Aqaba is less sensitive to Ht and Hr due to its ambient temperature being higher than that of Amman. Another parameter that the solar fraction of the system is extremely affected by is the location of the auxiliary heater and the thermostat, Haux and Hth, respectively, in the storage tank. Figure 9 illustrates this dependency, and the solar fraction is improved quantitatively by ca. 25% for Amman and 20% for Aqaba when the auxiliary and the thermostat are located at the top of the collector, rather than near the bottom. This strong dependency can be interpreted as follows: placing the auxiliary heater and thermostat near the bottom of the tank will destroy the thermal stratification, which will force the system to operate with maximum inlet temperature and the thermal losses from the tank will be maximum. Whereas, placing them near the top of the tank will minimize the thermal losses and does not affect the thermal stratification in the tank. The optimum or recommended height for these parameters is 10 cm from the top of the tank. The importance of the insulation of the storage tank is shown in Fig. 10 by the plot of solar fraction against tank heat loss coefficient (UA),. It is clear that solar fraction decreases by ca. 12% for Amman and 7% for Aqaba when very good insulation is replaced by very bad insulation. This suggests that the storage tank should be insulated as well as possible. CONCLUSIONS The design parameters of a thermosyphon solar water heater were studied and optimized for two different climates zones in Jordan using the TRNSYS simulation program. From the results of the simulation the following conclusions can be made : (1) The solar fraction of the system can be improved by ca. 7 25% depending on the design parameter studied when the optimum or recommended value is chosen. (2) The return pipe from the collector to the storage tank and the auxiliary heater are recommended to be located as close to the top of the storage tank as possible. (3) The solar fraction of a system installed in Aqaba (hot climate) is relatively less sensitive to some design parameters than the solar fraction of a similar one installed in Amman (mild climate). (4) Using the optimum or recommended values of the design parameters for a thermosyphon system could reduce the price of the system, as well as improving the performance. research was supported by the Office of the Dean of Research at the Jordan University of Science and Technology, which the authors gratefully acknowledge.
Acknowledgement--This
NOMENCLATURE mc Dh Di, Do D~
FRUL
f F~(~)~ atest H~x
H~ Ho
H~ H~ L~ Lh L, Lo
collector area (m 2) diameter of collector's headers (m) diameter of collector's inlet and outlet connecting pipes (m) diameter of collector's risers (m) slope of the collector efficiency curve (kJ/h m2°C) annual solar fraction intercept of the collector's efficiency curves collector's test flow rate (kg/h m 2) height of the auxiliary heating element above the bottom of tank (m) vertical distance between outlet and inlet of collector (m) vertical distance between outlet of the tank and inlet of the collector (m) height of the collector's return above the bottom of the tank (m) height of the tank (m) height of the auxiliary thermostat above the bottom of the tank (m) length of the collector (m) length of the collectors headers (m) length of inlet and outlet connecting piping (m)
360
NBt, NB2
Ur Paux
Qaux Q, Tmain T~et
u~,Uo (UA)t
v, v, w~
Technical Note number of bends in the inlet and outlet connecting pipes number of parallel collector risers power of the auxiliary heater (k J/h) energy input to the tank from the auxiliary heater (J) energy delivered to the load (J) temperature of water supplied from the main (°C) temperature of water delivered to the load (°C) heat loss coefficients for inlet and outlet connecting pipes (kJ/h m2°C) overall heat loss coefficient for storage tank (kJ/h m2°C) volume of daily load (m 3) volume of storage tank (m 3) width of the collector (m)
Greek symbols /~ q5 pg
collector's tilt angle (degree) latitude (degree) ground reflectance. REFERENCES
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Technical Note
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