- Email: [email protected]
Modeling and simulation of solar absorption system performance in Beirut
Renewable Energy, Vol. 10, No. 4, pp. 539-558, 1997 © 1997, Elsevier Science Ltd Printed in Great Britain. All rights reserved
Pergamon
PII : S0960-1481 (96)00039-0
0960-1481/97$17.00+ 0.00
MODELING AND SIMULATION OF SOLAR ABSORPTION SYSTEM PERFORMANCE IN BEIRUT N. K. GHADDAR, M. SHIHAB and F. BDEIR Department of Mechanical Engineering, American University of Beirut, P.O. Box 11-236, Beirut, Lebanon (Received 11 June 1996 ; accepted 8 July 1996)
Abstract--An analytical study is performed on solar energy utilization in space cooling of a small residential application using a solar lithium bromide absorption system. A simulation program for modeling and performance evaluation of the solar-operated absorption cycle is done for all possible climatic conditions of Beirut. The results have shown that for each ton of refrigeration it is required to have a minimum collector area of 23.3 m 2 with an optimal water storage tank capacity ranging from 1000 to 1500 liters for the system to operate solely on solar energy for about seven hours a day. The monthly solar fraction o f total energy use in cooling is determined as a function of solar collector area and storage tank capacity. An economic assessment is performed based on current cost of conventional cooling systems. It is found that the solar cooling system is marginally competitive only when combined with domestic water heating. © 1997, Elsevier Science Ltd. All rights reserved.
INTRODUCTION
Active solar energy systems for space conditioning are becoming an attractive alternative for designers due to the fact that the peak solar radiation is in phase with the maximum cooling loads in buildings. One of the methods to achieve cooling by solar energy is by use of an absorption cycle [1, 2]. Absorption cooling systems essentially require a heat source and have been in standard production for several decades in gas fired applications. A waterlithium bromide absorption system operates moderately well with delivery temperatures of 65-95°C to the generator [3]. Flat-plate solar collectors can generally heat fluids up to those temperatures which stimulated a considerable amount of research and development into adaptation and use of absorption systems for solar air-conditioning [1, 4]. Commercial residential units are available from 8 to 140 kW [5]. Performance predictions of absorption solar cooling systems for small residential applications have been reported by Tsilingiris [6] where a 7 kW system was modeled and optimized. The yearly solar fraction was found to be proportional to the collector area. For double glazed collectors of 50 m 2 area and 1000 1 storage tank capacity, the yearly solar fraction in Greece would reach values of up to 45% [6]. For a system to be econ539
540
N. K. GHADDAR et al.
omically feasible and for better solar energy utilization in space cooling, Kilkis used the absorption system with radiant ceiling cooling panels which shaved the peak cooling load by 25% and improved the cooling coefficients of performance [7, 8]. A 3.5 kW waterammonia and absorption system needed only 30 m -2 of fiat-plate collector area in a case design that involved an 81 m 2 solar house in Turkey [8]. Other investigations based on computer models have allowed accurate assessment of solar air-conditioning using detailed meterological data [9, 10]. In the present work, the performance of a 10.5 kW solar driven lithium bromide absorption cooling system is investigated numerically. Thermodynamic behavior of the cooling system cycle is simulated under various ambient conditions. In parallel, modeling and simulation is also done for proper sizing of fiat-plate solar collectors with a water storage tank to match the load needed to the generator of the absorption system. A parametric study is performed under Beirut's local conditions to determine the monthly and yearly solar fraction of total energy use in a residential building. An economic assessment will follow based on the payback period of the system and the net present worth.
ABSORPTION CYCLE MODEL AND ANALYSIS The general arrangement of the solar lithium bromide water system is shown in Fig. 1. Solar heated water can be provided at up to 85-90°C and is used to supply heat to the generator where the water vapor is released from the saturated solution of H20-LiBr. Heat rejection is accomplished by circulating water through the cooling tower. The total heat rejection at both the absorber and the condenser is generally double that of electrically driven equipment at a given cooling capacity [5]. The system will be designed to provide a substantial portion of the summer load and domestic hot water requirements for a 150 m 2 house requiring a 10.5 kW cooling load. Since the storage tank heat source strongly relies on weather and solar radiation data, which are time dependent, it is necessary to evaluate the absorption cycle performance with variable generator and condenser temperatures. The coefficient of performance of cooling is defined as : COP = - Q~v/(Qg~,+ Wp),
(1)
where Qev is the rate of heat gain at the evaporator, Qgen is the heat gain at the generator and Wp is the input power to the pump. Standard mass and energy balances are performed on the various components of the absorption system and a computer simulation program is developed for the cycle analysis. The various enthalpies of the refrigerant and carrier are calculated through simulating concentration charts by equations [11, 12]. The enthalpies of H20 are expressed as a second order polynomial in terms of respective temperatures at evaporator, condenser and generator as suggested by Stoeker [11]. The enthalpy h of the solution of H 2 0 - L i B r is expressed in a multi-variable polynomial in terms of the solution temperature, T (°C), and solution concentration, X, through the absorber and generator unit as given in A S H R A E charts by : 4
4
4
h = ~ A.X" + T~' B.X" + T z 2 C.X", 0
0
(2)
0
where A, B and C are constant coefficients and are listed in A S H R A E [12]. Equation (2)
541
Solar absorption system performance
!f . . . . I
I ! I I I I
Heating Mode
I
I II I
I
I
I
I
I
I
I
t i i
I l I
I
I
i !
Storage Tank
Solar Collector
Heat
I
ExchangerJ
t
I
r I
Is
i i
I
!I
i I I i I
h
I
l
t
generator
r ~
Absorber Expansion [Valve
I
I
Evaporator
t i J I
Pump
Fig. 1. The general arrangement of a lithium bromide water system.
applies for the concentration range 40% < X < 70% o f LiBr and temperature range o f 15°C < T < 165°C. The error e in simulation equations is c o m p u t e d as: l i s t e d v a l u e - computed_value e=
listed value
'
(3)
where the listed value is the value obtained either f r o m tables or charts. The solution concentration which is the ratio o f the mass o f LiBr to the mass o f the solution o f water and LiBr depends on the temperature and is usually determined f r o m A S H R A E charts [12] by allocating the other two properties o f the state point. In the simulation p r o g r a m it was m o r e convenient to use the Stoeker a p p r o x i m a t i o n o f a multivariable polynomial given by [11] :
542
N.K. GHADDAR et al. f(x,y,z)
= ao + a l x 2 + a 2 x + a 3 y 2 + a 4 y + a s z 2 + a 6 z + a 7 x y + a s y z + a 9 x z + a l o x y
2
+a~x2y+a~2y2z+a~3z2y+a~4x2z+a~sz2x+al6xyz+a~7x2yz+a~sxy2z + a l 9xyz 2 q- a20x2y2g d- a21 xZY Z2 -}- a22xY 22'2 -k-a23 x2y 2z2 + a24x2y 2
(4)
+ a25y2z 2 + a26x2z 2,
where the ais are empirical constants, and x, y, and z are the temperatures of which the concentration is a function. The concentration at the absorber exit is a function of Tab and Tev and the ai constants of eq. (4) are taken from Ref. [11]. The calculated concentrations at the absorber exit using the above simulation equations incur a maximum e of about 0.1 when compared with the values obtained from A S H R A E concentration charts [12]. The concentration of the strong solution at the 9enerator exit depends on the generator and condenser temperatures and the ai coefficients of eq. (4) in this case are obtained from Ref. [11]. The concentrations at the generator exit obtained by using eq. (4) incur a maximum e of about 0.02 compared with the values obtained from A S H R A E charts. The input range of temperatures for the simulation program compatible with available energy from solar fiat-plate collectors are as follows : System nominal capacity Generator temperature range Condenser temperature range Evaporator temperature range Absorber temperature Ambient temperature range Generator and condenser pressure Evaporator and absorber pressure Mass flow rate from generator to condenser Mass flow rate from absorber to generator Mass flow rate from generator to absorber
= = = = = = = = = = =
10.53 kW 50-85°C 20-35°C 5-12°C 22-40°C 22-38°C 24-42.2 mm Hg 9.2 mm Hg 0.004--0.0044 kg/s 0.0075-0.272 kg/s 0.006-0.267 kg/s.
The rate of heat transfer at the generator, Qge,, and the corresponding coefficient of performance are calculated for various values of generator temperature and condenser temperature using the developed simulation program. In optimization of an absorption cooling system, the temperature of the generator directly affects the COP of the system when other design conditions are fixed. The relationship between the COP and the generator temperature is shown in Fig. 2 of our simulated LiBr absorption cycle for various evaporator temperatures at fixed condenser and absorber temperatures of 25°C and 27°C, respectively. It can be seen that the COP is highest (=0.778 corresponding to Qge, = 13.56 kW) at a generator temperature of 75-80°C with acceptable values for Tgen above 60°C. So the evaporator temperature in the given range does not influence the cycle performance unless the generator temperature goes below 60°C. The variation of COP with Tgen at various condenser temperatures is shown in Fig. 3a, while COP variation with Tgo, at various absorber temperatures is shown in Fig. 3b. The absorption cycle performance is enhanced with lower condenser and absorber temperatures which may be accomplished by means of night cooling of water. In the operating range of the solar absorption system, the required load Q~n is between 12 and 14.5 kW for acceptable performance of the system when heat is supplied at Tg~ > 60°C.
Solar absorption system performance
543
0.780 0.770 0.760 0.750 0.740 O.
O 0.730 ¢3 0.720 0.710 0.700 I 0.690
Te=0C0.337 ......
0.680 55
- - - - - - Te=7C 0.339
Te=10C 0.340
Te=l 2C 0.340
{
I
l
l
I
I
6O
65
70
75
80
85
gO
95
TO
Fig. 2. The relationship between the COP and the generator temperature of the simulated LiBr absorption cycle for various evaporator temperatures at fixed condenser and absorber temperatures of 25°C and 27°C, respectively.
SOLAR COLLECTOR-TANK SYSTEM MODEL The solar collector field is composed of several units of widely spread non-selective single glazing that collects and stores solar energy in a water storage tank. Each unit has an effective surface area of 2.872 m 2. The absorber plate is a black painted steel plate with emissivity o f 0.91 and absorptivity of 0.91 and it has 12 welded longitudinal copper tubes of 15 mm diameter. The collectors are-used in forced circulation mode and are set at a ~ - 1 5 ° tilt angle facing south where q5 is the latitude and is equal to 33.9 ° for Beirut. The performance of the collector-tank system is simulated numerically using the theory of Hottel and Whillier presented by Duffle and Beckman [13]. The useful heat gain of water in the collector is obtained by applying an energy balance that indicates the distribution of incident solar energy into useful heat gain, thermal losses and optical losses with a time step between 0.0833 and 0.15 hours, depending on system flow rate. An expression for the useful heat gain is given by [13] : Q , = A c F R { S - - UL(Tci- Ta)},
(5)
where Ac is the aperture area of the collector, S is the solar radiation absorbed by the plate, Tel is the inlet water temperature to the collector, Ta is the ambient air temperature, UL is the overall heat transfer loss coefficient and FR is the heat removal factor. The collector efficiency is calculated on hourly basis as rl = Q , / ( A j T ) ,
(6)
544
N. K. GHADDAR et al.
0.800 ..
0.700
°°
. . . . . . . .
° .....
. . . . . . . . . . . . . .
. . . . . . . . .
-'°
°
oO°
0.600 BD
0.500
o*
L
e
o
o
0.400
B# B •m
0.300 • Tc=25C
Tc=30C . . . . . .
Tc=35C I
0.200 0.100 6o
[
I
I
I
65
70
75
80
85
Tg(C)
(a) 0.800
0.750 .°
oO°.O'"
0.700
Q. 0 0.650
O o
o
B f O
0.600
P
Ta=25C
Ta=30C . . . . . .
Ta=35C I
0.550
0.500 60
(b)
I
;
I
I
65
70
75
80
85
Tg (CI
Fig. 3. The variation of COP with Tgo.at (a) various condenser temperatures and (b) various absorber temperatures. where IT is the solar energy incident per hour on the collector's surface. The required heat from the solar system to satisfy the cooling load is given by : QL = Q~v/COP,
(7)
where COP is calculated based on the absorption cycle performance at the supply hot water temperature to the generator from the storage tank. An energy balance on the associated storage tank which is assumed to be well mixed gives : Q~ = p C p V d T ~ / d t = Q u - ( Q t +QIh + Q L ) ,
(8)
Solar absorption system performance
545
where Qt is the tank loss, QJh is the hose loss from collector to tank, p is the water density, Cp is the specific heat of water, V is the tank volume and Ts is the storage tank temperature. The extracted energy for the cooling load QL is taken as zero at times when the tank temperature is below 65°C. The temperature drop between the heat source and the generator is taken as 5°C. The combined system hourly efficiency is :
?]sys
=
(9)
(Qs + QL)/AclT.
Equation (8) will be used to predict the water tank temperature as a function of time. The yearly solar fraction is then defined as the ratio of the cooling provided by solar-driven absorption system to the total cooling needed which is given by :
YSF=
{m~=ld~=lt~_l[Qc]}
,
(10)
m=l d=l t=l where D is the number of days per month, m is the number of months from 1 to 5 corresponding from May to September, Qc is the heat delivery from the collectors, and QL is the extracted load. The calculations of the solar collector-tank system proceed at an initial temperature of the storage tank and inlet water temperature to the collectors equal to the ambient temperature for the given day. The hourly values of direct and diffuse components of solar radiation incident on the collectors and the values of ambient temperatures, wind speed and direction are derived directly from actual hourly measured weather data files and are used directly in the simulation program. The program integrates eqs (5) and (8) at discrete 0.25 hour intervals for the entire period between May and September, and calculates the useful heat gain, the storage tank temperature, the generator temperature which is generally 5°C lower than the tank temperature, COP, the extracted load from the system, collector and system efficiencies, and the mean plate temperatures. The collector-tank simulation has previously been verified with experimental data on solar water heaters without load extraction [14, 15].
RESULTS AND DISCUSSION The computer model is a powerful tool for system performance evaluation and optimization with respect to flat-plate total collector area, the storage tank volume and the mass flow rate. At fixed flow rate, the increase in the ratio of collector area to tank volume increases the tank temperature but decreases the efficiency of the collector due to increased losses. The tank temperature is not allowed to exceed 95°C to prevent change of phase occurrence. The collector is increased in multiples of 2.87 m 2 collector unit. The simulation code is run in terms of number of unit. For example, 20 units corresponds to 57.4 m 2 and so on. The load required for the generator is calculated based on Tev = 10°C and Tcond= dew point temperature of ambient air. The cooling power at the evaporator, Qev, is modeled as a variable load with an average capacity of 10.5 kW and a peak load during sunshine hours
546
N . K . GHADDAR et al.
as seen in Fig. 4 which shows the cooling power as a function of the time of the day. The constant load model has also been used in our calculations for comparison purposes. Figure 5 shows the variation of the tank mixed mean temperature as a function of time for a typical day of each of the summer months (May through September) for different numbers of units corresponding to areas from 57 m 2 to 86 m 2 at tank volume of 1000 1, water volume flow rate of 3.5 m3/h and with variable load extraction starting when the tank mixed mean temperature is above 65°C. As the collector area is increased, the absorption system will be run for longer times on the solar source up to 7 h for the 30 unit system, and the tank mean temperature in this case also attains higher values. The number of units cannot be increased indefinitely as seen in Fig. 6 which shows the collector outlet temperature as a function of time of the day of a typical day in June. The water exiting from the collector is found to be generally 2-5°C higher than the tank mixed temperature during the active period and it gets close to 100°C when the number of units is 30. A similar performance is observed for the other summer months. The storage tank size has a major effect on the system performance and the length of the extraction period. Figure 7 shows, for the months of M a y and August, the mixed mean tank temperature as a function of time at a fixed collector area of 80.4 m 2 (28 units) for tank volumes of 1000, 1300, 1500 and 1800 1. As the tank volume is increased the m a x i m u m temperature decreases and the starting time for extraction is generally delayed in the morning and is extended in the afternoon. The yearly solar fraction can be calculated from the extraction periods for all the summer months to optimize the tank volume. Figure 8 shows plots of the YSF of (a) constant and (b) variable evaporator load versus tank size for different collector areas. The yearly solar fraction reaches 43% with variable load extraction compared with 26% with constant load extraction. The reason for this better performance is due to the fact that the peak load in the variable load system is coincident with peak solar energy extraction while less load is required during night hours unlike the constant load case. For collector areas larger than 68 m :, the YSF increases with an increase
16 14 12 A
4
|
~
1
1
~
1
~
I
I
~
1
;
~
1
~
~
~
~
~
~
~
',
I
~
1
1
~
',
~ 1
~.~
1 1 ~
~
1
~
1
~
1
1
~ ~
~
~
~ ~
~
',
~
1
I
~
',
',
~
1
1
~
~ ~" !
~
TIME
Fig. 4. The cooling power required at the evaporator as a function of the time of day.
~
I
~
Solar absorption
system performance
547
90.000 80.000
70.000 60.000
40.000 30.000 Ac= 57.44 rn2
......
Ac= 71,8 m2
Ac= 86.2 m2
10.000 I
I
I
i
I
I
;
i
;
;
;
;
;
;
;
i
i
I
I
;
J
I
;
[
I
I
I
I
;
;
i
I
I
I
I
',
i
I
I
i
I
I
I
I
I
TIME"
g0.000
(b) J u n e
...-" .......
80.000 70.000 60.000
.~.~ 40.1~ Ac= 57.44 m2 . . . . . .
Ac= 71.8 m2
Ac= 86.2 m2
0.000
TIME 100.000
90.000 80.000 , o°° o°°°oo-° "° °° o°°" - ° - - " . . . . . . . . . . . . . . .
70.000
~ ° ° °° .°°°
60.000
A
~i0.000 I=40.000 30.000
Ac= 57.44 m2 Ac= 86.2 m2
20.000
......
Ac= 71.8 m2
[
I
10.000 0.000
8
g• ' ~g
g,, 8~
~~
~in ~~
~ .8..8.~ 8
~
8~
8. ~8
8,'
8
~
8"- ~8
8," ~8
8"
8
~
8"-
F i g . 5. T h e v a r i a t i o n o f t h e t a n k m i x e d m e a n t e m p e r a t u r e a s a f u n c t i o n o f t i m e f o r a t y p i c a l d a y o f each of the summer months (May through September) for different numbers of units corresponding t o a r e a s f r o m 4 3 m 2 t o 8 6 m 2 a t a t a n k v o l u m e o f 1000 1, a n d w i t h l o a d e x t r a c t i o n s t a r t i n g w h e n t h e t a n k m i x e d m e a n t e m p e r a t u r e is a b o v e 6 5 ° C .
548
N. K. GHADDAR et al. 100.000 90.000 80.000 70.000 60.000 50.000
k-
40.000 30.000 I
20.000
~
Ac= 57.44 m2
......
Ac= 71.8 m2
J
I
• Ac= 86.2 m2
10.000 0.000 m
m
m
m
~
m
m
~
m
m
m
m
m
m
m
m
m
m
m
m
m
m
m
m
TIME 90.000 80.000 70.000 60.000 .-50.000 1-40.000 30.000 20.000
I
~
Ac= 57.44 m2
10.000
J
~
Ac= 86.2 m2
0.000,
',
;
:
',
:
:
;
~ ~
;
;,
:
:
~
',
""
:
',
~ ~
--
""
'.
~
:
;
"TIME
',
',
.
......
:
;
.
:
.
',
;
.
;
Ac= 71.8 m2
'.
.
',
.
;
:
.
;
.
:
:
.
;
:
.
:
'.
:
:
',
.
Fig. 5. Continued.
in volume, then maintains a m a x i m u m for a tank size ranging from about 1000 to 1500 1 and then decreases monotonically with increased volume as seen from Fig. 8. The optimal conditions for maximizing the yearly solar fraction for our 3 ton absorption cooling system would then be easily specified to be for a volume to area ratio, A / V , from 13 to 19 l/m 2. The minimum required collector area per kW delivered is then 6.6 m2/kW corresponding to a m a x i m u m YSF of 0.37 and the m a x i m u m allowed collector area is 8.2 m2/kW corresponding to a m a x i m u m of 0.435. The effect of water flow rate in the solar water heating system on the tank mixed mean temperature is studied. Figure 9 shows the mean tank temperature as it varies with time for a typical day in M a y for a system area of 80 m 2 and 1000 1 at different flow rates starting
Solar absorption system performance
549
100.000 90.000 80.000 70.000 60.000
E 40.000
20.000
10.000
I
Ac= 57.44 m2 . . . . . . Ac= 86.2 m2
Ac= 71.8 m2 I
:::::::::::::::::::::::::::::::::::::::::::::::::::::::::
8 8~ o~ 80i 8~ 8tii 8 tii8 ti-i-~ 8 8 "'8 ~6 8 8'" t;6 8 8"" 8ti'i 8"" 8Oi 8"" 8=ii8 ""8 8 8 TIME
Fig. 6. The collector outlet temperature as a function of the time of day of a typical day in June for different numbers of units corresponding to areas from 57 m2 to 86 m 2 at a tank volume of i000 1.
from 0.5 to 11 m3/h. Increasing flow rate increases the tank temperature up to a limit at 6 m3/h, after which any further increase in flow rate hardly changes the tank temperature. It is of interest to evaluate the system performance in the optimal range conditions for maximum YSF which are set now for the case of the 1300 1 tank, 80.6 m 2 collector area and a flow rate of 7 m3/h. Figure 10a shows the useful heat gain and overall heat loss from the system as a function of time for a typical day of May, while Fig. 10b shows the collector and system efficiencies. It is clear that the system operates with higher efficiency in the morning and with increasing collector temperature, the useful heat gain decreases and system loss increases. The load extraction has a positive effect on system performance as seen from the decrease in the slope of the efficiency curve when extraction starts at 9:45 a.m. This improvement is obvious when comparing the system performance when load extraction is present and when load extraction is zero. Figure 1 la shows the useful heat gain versus time for both cases of zero load extraction and full load extraction and Fig. 11 b shows the tank mean temperature versus time for both cases. Direct energy extraction reduces heat loss, increases useful heat gain and reduces tank mean temperature.
SYSTEM OPTIMIZATION AND ECONOMICS The proposed solar absorption system will be cost effective when its investment cost is equal to or less than the present value of the energy savings over the life of the system
550
N. K. GHADDAR
et al.
100.000 90.000 80.000
70.000 60.000 50.000 40.000 30.000
Vt=lO001 Vt=1500~
20.000
10.000
......
Vt=13001 I Vt=18001
0.000
TIME 100.000 90.000
(b)
August
80.000 70.000 60.000 o 1-
S0.000 40.00030.000
10.000 -
- .....
Vt=18001
Vt=lfi001
0.000 , I : ; ', : ', ', : ', ' I I ', ; : : ; : ', : ', ', : ', : : ', ; : : : : ', ~ ', ; : : : ', : ', : ', : ',
.o° ~ ~ ~ .o°..o°. ~ ~ 8..8..8 .8. 8 8..8 8..8 .8 .8. 8. 8. 8..8..8. TIME F i g . 7. T h e m i x e d m e a n t a n k t e m p e r a t u r e as a f u n c t i o n o f t i m e at fixed c o l l e c t o r a r e a o f 80.4 m 2 (28 u n i t s ) f o r t a n k v o l u m e s o f 1000, 1300, 1500 a n d 1800 l, f o r t h e m o n t h s o f (a) M a y a n d (b) A u g u s t .
which
is a f u n c t i o n
capital
investment
of fuel escalation
rates and the expected
of the solar-absorption
real return
system can be expressed
C = CcAc+CsVs+AC+AT,
on investment.
The
as" (11)
Solar absorption system performance
(a)
55 I
(CONSTANT LOAD EXTRACTION)
0.3
O
: : :: ::: i _ i
tL )"
o., '-
'iiiiiiii i"
0.1
i
0.05 0
I 500
~
750
1000
'I
......
=
I
1300
1500
1800
2200
2500
Vt (Liter)
(b)
(VARIABLE LOAD EXTRACTION)
0.45 .-
--..-'.--_..._..:~.. .... L~-- "-:.:_'~ ......
0,
.............
0.35
u.
,
0.25
0.15
.
0.1
......
o.os
AC=71.83 '"
0
500
- ....... A¢=57"5
A~=,3.1A~=,3.1
.,,
I
N
II
,'
J
i
I
750
1000
1300
1500
\
~._ ~
1800
q.
2200
2500
Vt(Liter)
Fig. 8. Plots of the YSF of (a) constant and (b) variable evaporator load versus tank size for different collector areas. The YSF versus tank size for collectors area of 80.4 m 2. where Cc is the unit cost of the solar collector equal to $220/m :, Ac is the area of used solar collectors (m2), Cs is the unit cost for a thermally insulated low pressure galvanized steel storage tank ($500/m3), V, is the volume of the storage tank, AC is the fixed cost of the absorption chiller ($5000), and A T is the fixed cost of the small cooling tower plus an additional pump ($500). Installation cost is assumed to be included in all the above items. For 1.3 m 3 tank, and 80.4 m 2 collector area the investment cost would be $23,938. The annual cost o f such a system is composed of electrical cost, which is very small, plus
552
N. K. G H A D D A R et al. 100.000
90.000 80.000 70.000 is IS
60.000 =E U.I I-. ,¢ Z
50.000 40.000
. . ~
. . . .
8 M3/HR
......
4 M3/HR
J
6 M3/HR
30.000
- - - - - - 2 M3/HR
20.000
~ 0 . 5
M3/HR
10.000 0.000 O O O O O O O O
TIME
Fig. 9. The mean tank temperature variation with time for a typical day in May at different flow rates in the system starting from 0.5 m3/h to 11 m3/h. maintenance cost. This annual cost is considered to be m = $100. The domestic hot water cost is assumed to be zero since the hot water that remains in the storage tank after use can be used for domestic purposes using an inflation rate figure e = 8% and interest rate r = 11%. Then the annual cost o f the absorption system can be found by the formula [6] :
(l+e 7 l+e\ a = m*
*
l+e l+r
1
'
(12)
where a is the annual cost, N is the time in years. F o r a conventional vapor-compression air conditioning unit, the cost o f 10.5 k W is a b o u t $2500, and it consumes 3.2 k W / h electric power and the domestic hot water use is assumed to be 10 k W daily. The daily c o n s u m p t i o n o f electric power is: P = 3 . 2 " u + 10,
(13)
where u is the daily usage time for the system. The m o n t h l y electric c o n s u m p t i o n and cost can then be calculated using the Lebanese tariff for a usage time equivalent to the solar extraction time o f the absorption system. The annual cost for usage o f the conventional air conditioning unit for the same period o f the solar-absorption system is $393.3. The interest rate is considered to be r = 11%, and the electric energy inflation rate is taken to be e = 4%.
553
Solar absorption system performance
(a)
25.000 20.000
15.000 10.000
i
. . . . .i i i i i
5.000 0.000 -5.000 °10.000 -15.000
TIME QU(kj/sec) 60.000
. . . . . . QL(kj/sec) (b)
50.000¸ 40.000
I,k
30.000
16
~u 20.000 10.000 0.000 o10.000 TIME
Fig. 10. Plots of (a) useful heat gain and overall heat loss from the system as a function of time for a representative day of May and (b) the collector and system efficiencies as a function of time for a representative day of May.
N. K. GHADDAR et al.
554 35000
QU 30000
"'-"
" ~
-.
without
extraction
25000
extraction
20000
15000 0 10000
5000
. ,
0
=,
. . . . . . . . . . . . .
,0
,~ ~ ~
=..
,
:_
. . . . . . .
~
.
,
. ,
~ .~
,
-, ~
r
, ,
, ,
,~ .
,
. ,
~' =
,
.
* ,
=~
,
.
~-
~
~
, , .
Time (hr)
(a) 120
deg. C 100
8o 1-
1--
60 4O
20
Ib)
Iime(hr)
Fig. l l. Plots of (a) useful heat gain versus time and of (b) tank mixed mean temperature versus time for both cases of zero load extraction and full load extraction. The electric energy consumption for the coming years can then be calculated using eq. (12). Figure 12a shows the predicted annual operation cost of the solar refrigeration system and Fig. 12b the annual electric cost of the vapor compression system for the coming years. It is seen that electrical cost will have a detrain increase due to expected electrical inflation rate. For our system of 80.4 m 2, V = 1500 1 and with a life cycle of 20 years, the payback period, Np in years, of the solar absorption system versus the vapor compression system is given by : I + ~) B* 1 ÷ i (l--~r) *
\7-~/ I÷m*
l+i
l+r
--1
-(T~r)*
- 1
l+e
, -, -+-el+r
(14)
1
where Iis the capital cost of the solar absorption system minus that of the vapor compression system.
Solar absorption system performance
555
6000 5000 4000 3000 2000 1000
electrical
cost]
0
time (years)
(a) 1800 1600 1400 $ 1200 1000 800 600 400 200 0
I
I
I
3
I
I
5
I
',
7
',
',
9
',
;
11
',
',
',
13
;
15
',
',
17
',
',
',
19
',
',
',
,
21 23
time (years)
(b)
Fig. 12. Plots of (a) the predicted annual operation cost of the solar refrigeration system and of (b) the annual electric cost of the vapor compression system for the coming years. Figure 13 shows the predicted cumulative system cost for both the solar-absorption system and the conventional system as a function of time in years for three different collector 70000 60000 50000
• Cumilativeelectrical --II-- 170 $/m^2 220 $/m^2
4
b
f
40000 30000 20000 i
~
10000 0
,
,
,
,
I
,
,
time (yr) Fig. 13. The predicted cumulative system cost for both the solar-absorption system and the conventional system as a function of time in years for three different collector area prices of 170, 220 and $270/mL
N, K. GHADDAR et al.
556
area prices of 170, 220 and $270/m 2. The break-even points will range from 12 to 16 years. Current costs of solar collectors in general are expected to decrease dramatically with mass production and this may then make such systems economically viable. The use of solar systems should be combined with passive designs of buildings, so as to reduce the required air conditioning load and this may double the yearly solar fraction of the system. Earlier studies of G h a d d a r and Bsat [16] on conservation measures applied to residential building in Beirut, have shown a substantial decrease in cooling requirements.
CONCLUSIONS The lithium bromide absorption refrigeration system operates well when combined with a solar hot water source. The acceptable operating range of the solar absorption system is when the supplied hot water from the solar system is between 65 and 85°C corresponding to a required generator load between 12 and 14.5 kW. An optimal performance of the solar absorption system was attained at a tank volume to collector area ratio (Vs/Ac) of 13 to 19 l/m 2 which corresponded to a solar fraction of 20% to 26% for constant load extraction and to a solar fraction of 38% to 44% for a variable load extraction. The minimum (Vs/A¢) permitted so that boiling in the system does not occur, is found to be 11.6 1/m2. The minimum required collector area per kW delivered is then 6.6 mZ/kW and the m a x i m u m allowed collector area is 8.2 m2/kW. The solar absorption system can be marginally competitive with conventional vapor compression air conditioning when collector manufacturing prices reach values less than $120/m 2. The prospects of solar air conditioning are expected to further improve with the growth of solar industry and the escalation of fuel costs.
Acknowledgements--The support for this research by the American University of Beirut Research Board under grant number 11304048118, is thankfully acknowledged by the authors.
NOMENCLATURE a AC AT Cp COP D e FR h IT N Q r S T
annual cost solar-absorption system absorption chiller cost cooling tower cost heat capacity coefficient of performance number of days per month inflation rate collector heat removal factor enthalpy hourly radiation time in years heat transfer interest rate absorbed solar radiation temperature
Solar absorption system performance t U u V X YSF
557
time overall heat transfer coefficient daily usage time of vapor compression system volume concentration, variable, data point coordinate yearly solar fraction
Greek characters ct thermal diffusivity fl collector tilt angle error r/ efficiency p density, reflectance Subscripts a abs bot c cond ev gen L m s u
absorber, ambient, absorption, air absorber bottom collector condenser evaporator generator extracted load number of summer months from May to September storage tank useful.
REFERENCES
1. P. J. Wilbur and C. E. Mitchell, Solar absorption air-conditioning alternatives. Solar Energy 17, 193-199 (1975). 2. S. Alizadeh, F. Bahar and F. Geoola, Design and optimization of an absorption refrigeration system operated by solar energy. Solar Energy 24, 149-154 (1979). 3. A. Karakas, N. Egrican and S. Uygur, Second-law analysis of solar absorption-cooling cycles using ammonia/water as working fluids. Applied Energy 37, 169-187 (1990). 4. F. Sakkal, N. Ghaddar and J. Diab, Solar collectors for Beirut climate. Applied Energy 45, 313-325 (1993). 5. F. J. Kreider and F. Kreith, Solar Energy HandBook. McGraw Hill, U.S.A. (1981). 6. P. T. Tsilingiris, Theoretical modeling of a solar air conditioning system for domestic applications. Energy Convers. Mgmt 34, 523-531 (1993). 7. B. Kilkis, Panel cooling and heating of buildings using solar energy. Solar Energy in the 1990s. ASME-SED 10, 1-9 (1990). 8. B. Kilkis, Radiant ceiling cooling with solar energy fundamentals, modeling and a case design. ASHRAE Trans. Part 2 (1993). 9. E. H. Perry, Theoretical performance of the lithium bromide-water intermittent absorption refrigeration cycle. Solar Energy 17, 321-323 (1975). 10. Y. Shiran, A. Shitzer and D. Degani, Computerized design and economic evaluation of an aqua-ammonia solar operated absorption system. Solar Energy 29, 43-54 (1982). 11. W. F. Stoeker, Refrigeration and Air Conditioning, international edn. McGraw Hill, Singapore (1987). 12. ASHRAE Handbook of Fundamentals. ASHRAE, Atlanta, U.S.A. (1985). 13. J. m. Duffle and W. A. Beckman, Solar En#ineerin# of Thermal Processes. Wiley, New York (1980).
558
N. K. GHADDAR et al.
14. N. K. Ghaddar, Stratified storage tank influence on performance of solar water heating system tested in Beirut. Renewable Energy 4, 911-926 (1994). 15. N. Ghaddar and I. Kebbe, Experimental and numerical study of stratified tank solar water heating system in Beirut. Proc. Fourth Arab Int. Solar Energy Conf., Royal Scientific Society of Jordan, Amman, Jordan, November 1993. 16. N. Ghaddar and A. Bsat, Energy conservation of residential buildings in Beirut. Applied Energy, in press.
Pergamon
PII : S0960-1481 (96)00039-0
0960-1481/97$17.00+ 0.00
MODELING AND SIMULATION OF SOLAR ABSORPTION SYSTEM PERFORMANCE IN BEIRUT N. K. GHADDAR, M. SHIHAB and F. BDEIR Department of Mechanical Engineering, American University of Beirut, P.O. Box 11-236, Beirut, Lebanon (Received 11 June 1996 ; accepted 8 July 1996)
Abstract--An analytical study is performed on solar energy utilization in space cooling of a small residential application using a solar lithium bromide absorption system. A simulation program for modeling and performance evaluation of the solar-operated absorption cycle is done for all possible climatic conditions of Beirut. The results have shown that for each ton of refrigeration it is required to have a minimum collector area of 23.3 m 2 with an optimal water storage tank capacity ranging from 1000 to 1500 liters for the system to operate solely on solar energy for about seven hours a day. The monthly solar fraction o f total energy use in cooling is determined as a function of solar collector area and storage tank capacity. An economic assessment is performed based on current cost of conventional cooling systems. It is found that the solar cooling system is marginally competitive only when combined with domestic water heating. © 1997, Elsevier Science Ltd. All rights reserved.
INTRODUCTION
Active solar energy systems for space conditioning are becoming an attractive alternative for designers due to the fact that the peak solar radiation is in phase with the maximum cooling loads in buildings. One of the methods to achieve cooling by solar energy is by use of an absorption cycle [1, 2]. Absorption cooling systems essentially require a heat source and have been in standard production for several decades in gas fired applications. A waterlithium bromide absorption system operates moderately well with delivery temperatures of 65-95°C to the generator [3]. Flat-plate solar collectors can generally heat fluids up to those temperatures which stimulated a considerable amount of research and development into adaptation and use of absorption systems for solar air-conditioning [1, 4]. Commercial residential units are available from 8 to 140 kW [5]. Performance predictions of absorption solar cooling systems for small residential applications have been reported by Tsilingiris [6] where a 7 kW system was modeled and optimized. The yearly solar fraction was found to be proportional to the collector area. For double glazed collectors of 50 m 2 area and 1000 1 storage tank capacity, the yearly solar fraction in Greece would reach values of up to 45% [6]. For a system to be econ539
540
N. K. GHADDAR et al.
omically feasible and for better solar energy utilization in space cooling, Kilkis used the absorption system with radiant ceiling cooling panels which shaved the peak cooling load by 25% and improved the cooling coefficients of performance [7, 8]. A 3.5 kW waterammonia and absorption system needed only 30 m -2 of fiat-plate collector area in a case design that involved an 81 m 2 solar house in Turkey [8]. Other investigations based on computer models have allowed accurate assessment of solar air-conditioning using detailed meterological data [9, 10]. In the present work, the performance of a 10.5 kW solar driven lithium bromide absorption cooling system is investigated numerically. Thermodynamic behavior of the cooling system cycle is simulated under various ambient conditions. In parallel, modeling and simulation is also done for proper sizing of fiat-plate solar collectors with a water storage tank to match the load needed to the generator of the absorption system. A parametric study is performed under Beirut's local conditions to determine the monthly and yearly solar fraction of total energy use in a residential building. An economic assessment will follow based on the payback period of the system and the net present worth.
ABSORPTION CYCLE MODEL AND ANALYSIS The general arrangement of the solar lithium bromide water system is shown in Fig. 1. Solar heated water can be provided at up to 85-90°C and is used to supply heat to the generator where the water vapor is released from the saturated solution of H20-LiBr. Heat rejection is accomplished by circulating water through the cooling tower. The total heat rejection at both the absorber and the condenser is generally double that of electrically driven equipment at a given cooling capacity [5]. The system will be designed to provide a substantial portion of the summer load and domestic hot water requirements for a 150 m 2 house requiring a 10.5 kW cooling load. Since the storage tank heat source strongly relies on weather and solar radiation data, which are time dependent, it is necessary to evaluate the absorption cycle performance with variable generator and condenser temperatures. The coefficient of performance of cooling is defined as : COP = - Q~v/(Qg~,+ Wp),
(1)
where Qev is the rate of heat gain at the evaporator, Qgen is the heat gain at the generator and Wp is the input power to the pump. Standard mass and energy balances are performed on the various components of the absorption system and a computer simulation program is developed for the cycle analysis. The various enthalpies of the refrigerant and carrier are calculated through simulating concentration charts by equations [11, 12]. The enthalpies of H20 are expressed as a second order polynomial in terms of respective temperatures at evaporator, condenser and generator as suggested by Stoeker [11]. The enthalpy h of the solution of H 2 0 - L i B r is expressed in a multi-variable polynomial in terms of the solution temperature, T (°C), and solution concentration, X, through the absorber and generator unit as given in A S H R A E charts by : 4
4
4
h = ~ A.X" + T~' B.X" + T z 2 C.X", 0
0
(2)
0
where A, B and C are constant coefficients and are listed in A S H R A E [12]. Equation (2)
541
Solar absorption system performance
!f . . . . I
I ! I I I I
Heating Mode
I
I II I
I
I
I
I
I
I
I
t i i
I l I
I
I
i !
Storage Tank
Solar Collector
Heat
I
ExchangerJ
t
I
r I
Is
i i
I
!I
i I I i I
h
I
l
t
generator
r ~
Absorber Expansion [Valve
I
I
Evaporator
t i J I
Pump
Fig. 1. The general arrangement of a lithium bromide water system.
applies for the concentration range 40% < X < 70% o f LiBr and temperature range o f 15°C < T < 165°C. The error e in simulation equations is c o m p u t e d as: l i s t e d v a l u e - computed_value e=
listed value
'
(3)
where the listed value is the value obtained either f r o m tables or charts. The solution concentration which is the ratio o f the mass o f LiBr to the mass o f the solution o f water and LiBr depends on the temperature and is usually determined f r o m A S H R A E charts [12] by allocating the other two properties o f the state point. In the simulation p r o g r a m it was m o r e convenient to use the Stoeker a p p r o x i m a t i o n o f a multivariable polynomial given by [11] :
542
N.K. GHADDAR et al. f(x,y,z)
= ao + a l x 2 + a 2 x + a 3 y 2 + a 4 y + a s z 2 + a 6 z + a 7 x y + a s y z + a 9 x z + a l o x y
2
+a~x2y+a~2y2z+a~3z2y+a~4x2z+a~sz2x+al6xyz+a~7x2yz+a~sxy2z + a l 9xyz 2 q- a20x2y2g d- a21 xZY Z2 -}- a22xY 22'2 -k-a23 x2y 2z2 + a24x2y 2
(4)
+ a25y2z 2 + a26x2z 2,
where the ais are empirical constants, and x, y, and z are the temperatures of which the concentration is a function. The concentration at the absorber exit is a function of Tab and Tev and the ai constants of eq. (4) are taken from Ref. [11]. The calculated concentrations at the absorber exit using the above simulation equations incur a maximum e of about 0.1 when compared with the values obtained from A S H R A E concentration charts [12]. The concentration of the strong solution at the 9enerator exit depends on the generator and condenser temperatures and the ai coefficients of eq. (4) in this case are obtained from Ref. [11]. The concentrations at the generator exit obtained by using eq. (4) incur a maximum e of about 0.02 compared with the values obtained from A S H R A E charts. The input range of temperatures for the simulation program compatible with available energy from solar fiat-plate collectors are as follows : System nominal capacity Generator temperature range Condenser temperature range Evaporator temperature range Absorber temperature Ambient temperature range Generator and condenser pressure Evaporator and absorber pressure Mass flow rate from generator to condenser Mass flow rate from absorber to generator Mass flow rate from generator to absorber
= = = = = = = = = = =
10.53 kW 50-85°C 20-35°C 5-12°C 22-40°C 22-38°C 24-42.2 mm Hg 9.2 mm Hg 0.004--0.0044 kg/s 0.0075-0.272 kg/s 0.006-0.267 kg/s.
The rate of heat transfer at the generator, Qge,, and the corresponding coefficient of performance are calculated for various values of generator temperature and condenser temperature using the developed simulation program. In optimization of an absorption cooling system, the temperature of the generator directly affects the COP of the system when other design conditions are fixed. The relationship between the COP and the generator temperature is shown in Fig. 2 of our simulated LiBr absorption cycle for various evaporator temperatures at fixed condenser and absorber temperatures of 25°C and 27°C, respectively. It can be seen that the COP is highest (=0.778 corresponding to Qge, = 13.56 kW) at a generator temperature of 75-80°C with acceptable values for Tgen above 60°C. So the evaporator temperature in the given range does not influence the cycle performance unless the generator temperature goes below 60°C. The variation of COP with Tgen at various condenser temperatures is shown in Fig. 3a, while COP variation with Tgo, at various absorber temperatures is shown in Fig. 3b. The absorption cycle performance is enhanced with lower condenser and absorber temperatures which may be accomplished by means of night cooling of water. In the operating range of the solar absorption system, the required load Q~n is between 12 and 14.5 kW for acceptable performance of the system when heat is supplied at Tg~ > 60°C.
Solar absorption system performance
543
0.780 0.770 0.760 0.750 0.740 O.
O 0.730 ¢3 0.720 0.710 0.700 I 0.690
Te=0C0.337 ......
0.680 55
- - - - - - Te=7C 0.339
Te=10C 0.340
Te=l 2C 0.340
{
I
l
l
I
I
6O
65
70
75
80
85
gO
95
TO
Fig. 2. The relationship between the COP and the generator temperature of the simulated LiBr absorption cycle for various evaporator temperatures at fixed condenser and absorber temperatures of 25°C and 27°C, respectively.
SOLAR COLLECTOR-TANK SYSTEM MODEL The solar collector field is composed of several units of widely spread non-selective single glazing that collects and stores solar energy in a water storage tank. Each unit has an effective surface area of 2.872 m 2. The absorber plate is a black painted steel plate with emissivity o f 0.91 and absorptivity of 0.91 and it has 12 welded longitudinal copper tubes of 15 mm diameter. The collectors are-used in forced circulation mode and are set at a ~ - 1 5 ° tilt angle facing south where q5 is the latitude and is equal to 33.9 ° for Beirut. The performance of the collector-tank system is simulated numerically using the theory of Hottel and Whillier presented by Duffle and Beckman [13]. The useful heat gain of water in the collector is obtained by applying an energy balance that indicates the distribution of incident solar energy into useful heat gain, thermal losses and optical losses with a time step between 0.0833 and 0.15 hours, depending on system flow rate. An expression for the useful heat gain is given by [13] : Q , = A c F R { S - - UL(Tci- Ta)},
(5)
where Ac is the aperture area of the collector, S is the solar radiation absorbed by the plate, Tel is the inlet water temperature to the collector, Ta is the ambient air temperature, UL is the overall heat transfer loss coefficient and FR is the heat removal factor. The collector efficiency is calculated on hourly basis as rl = Q , / ( A j T ) ,
(6)
544
N. K. GHADDAR et al.
0.800 ..
0.700
°°
. . . . . . . .
° .....
. . . . . . . . . . . . . .
. . . . . . . . .
-'°
°
oO°
0.600 BD
0.500
o*
L
e
o
o
0.400
B# B •m
0.300 • Tc=25C
Tc=30C . . . . . .
Tc=35C I
0.200 0.100 6o
[
I
I
I
65
70
75
80
85
Tg(C)
(a) 0.800
0.750 .°
oO°.O'"
0.700
Q. 0 0.650
O o
o
B f O
0.600
P
Ta=25C
Ta=30C . . . . . .
Ta=35C I
0.550
0.500 60
(b)
I
;
I
I
65
70
75
80
85
Tg (CI
Fig. 3. The variation of COP with Tgo.at (a) various condenser temperatures and (b) various absorber temperatures. where IT is the solar energy incident per hour on the collector's surface. The required heat from the solar system to satisfy the cooling load is given by : QL = Q~v/COP,
(7)
where COP is calculated based on the absorption cycle performance at the supply hot water temperature to the generator from the storage tank. An energy balance on the associated storage tank which is assumed to be well mixed gives : Q~ = p C p V d T ~ / d t = Q u - ( Q t +QIh + Q L ) ,
(8)
Solar absorption system performance
545
where Qt is the tank loss, QJh is the hose loss from collector to tank, p is the water density, Cp is the specific heat of water, V is the tank volume and Ts is the storage tank temperature. The extracted energy for the cooling load QL is taken as zero at times when the tank temperature is below 65°C. The temperature drop between the heat source and the generator is taken as 5°C. The combined system hourly efficiency is :
?]sys
=
(9)
(Qs + QL)/AclT.
Equation (8) will be used to predict the water tank temperature as a function of time. The yearly solar fraction is then defined as the ratio of the cooling provided by solar-driven absorption system to the total cooling needed which is given by :
YSF=
{m~=ld~=lt~_l[Qc]}
,
(10)
m=l d=l t=l where D is the number of days per month, m is the number of months from 1 to 5 corresponding from May to September, Qc is the heat delivery from the collectors, and QL is the extracted load. The calculations of the solar collector-tank system proceed at an initial temperature of the storage tank and inlet water temperature to the collectors equal to the ambient temperature for the given day. The hourly values of direct and diffuse components of solar radiation incident on the collectors and the values of ambient temperatures, wind speed and direction are derived directly from actual hourly measured weather data files and are used directly in the simulation program. The program integrates eqs (5) and (8) at discrete 0.25 hour intervals for the entire period between May and September, and calculates the useful heat gain, the storage tank temperature, the generator temperature which is generally 5°C lower than the tank temperature, COP, the extracted load from the system, collector and system efficiencies, and the mean plate temperatures. The collector-tank simulation has previously been verified with experimental data on solar water heaters without load extraction [14, 15].
RESULTS AND DISCUSSION The computer model is a powerful tool for system performance evaluation and optimization with respect to flat-plate total collector area, the storage tank volume and the mass flow rate. At fixed flow rate, the increase in the ratio of collector area to tank volume increases the tank temperature but decreases the efficiency of the collector due to increased losses. The tank temperature is not allowed to exceed 95°C to prevent change of phase occurrence. The collector is increased in multiples of 2.87 m 2 collector unit. The simulation code is run in terms of number of unit. For example, 20 units corresponds to 57.4 m 2 and so on. The load required for the generator is calculated based on Tev = 10°C and Tcond= dew point temperature of ambient air. The cooling power at the evaporator, Qev, is modeled as a variable load with an average capacity of 10.5 kW and a peak load during sunshine hours
546
N . K . GHADDAR et al.
as seen in Fig. 4 which shows the cooling power as a function of the time of the day. The constant load model has also been used in our calculations for comparison purposes. Figure 5 shows the variation of the tank mixed mean temperature as a function of time for a typical day of each of the summer months (May through September) for different numbers of units corresponding to areas from 57 m 2 to 86 m 2 at tank volume of 1000 1, water volume flow rate of 3.5 m3/h and with variable load extraction starting when the tank mixed mean temperature is above 65°C. As the collector area is increased, the absorption system will be run for longer times on the solar source up to 7 h for the 30 unit system, and the tank mean temperature in this case also attains higher values. The number of units cannot be increased indefinitely as seen in Fig. 6 which shows the collector outlet temperature as a function of time of the day of a typical day in June. The water exiting from the collector is found to be generally 2-5°C higher than the tank mixed temperature during the active period and it gets close to 100°C when the number of units is 30. A similar performance is observed for the other summer months. The storage tank size has a major effect on the system performance and the length of the extraction period. Figure 7 shows, for the months of M a y and August, the mixed mean tank temperature as a function of time at a fixed collector area of 80.4 m 2 (28 units) for tank volumes of 1000, 1300, 1500 and 1800 1. As the tank volume is increased the m a x i m u m temperature decreases and the starting time for extraction is generally delayed in the morning and is extended in the afternoon. The yearly solar fraction can be calculated from the extraction periods for all the summer months to optimize the tank volume. Figure 8 shows plots of the YSF of (a) constant and (b) variable evaporator load versus tank size for different collector areas. The yearly solar fraction reaches 43% with variable load extraction compared with 26% with constant load extraction. The reason for this better performance is due to the fact that the peak load in the variable load system is coincident with peak solar energy extraction while less load is required during night hours unlike the constant load case. For collector areas larger than 68 m :, the YSF increases with an increase
16 14 12 A
4
|
~
1
1
~
1
~
I
I
~
1
;
~
1
~
~
~
~
~
~
~
',
I
~
1
1
~
',
~ 1
~.~
1 1 ~
~
1
~
1
~
1
1
~ ~
~
~
~ ~
~
',
~
1
I
~
',
',
~
1
1
~
~ ~" !
~
TIME
Fig. 4. The cooling power required at the evaporator as a function of the time of day.
~
I
~
Solar absorption
system performance
547
90.000 80.000
70.000 60.000
40.000 30.000 Ac= 57.44 rn2
......
Ac= 71,8 m2
Ac= 86.2 m2
10.000 I
I
I
i
I
I
;
i
;
;
;
;
;
;
;
i
i
I
I
;
J
I
;
[
I
I
I
I
;
;
i
I
I
I
I
',
i
I
I
i
I
I
I
I
I
TIME"
g0.000
(b) J u n e
...-" .......
80.000 70.000 60.000
.~.~ 40.1~ Ac= 57.44 m2 . . . . . .
Ac= 71.8 m2
Ac= 86.2 m2
0.000
TIME 100.000
90.000 80.000 , o°° o°°°oo-° "° °° o°°" - ° - - " . . . . . . . . . . . . . . .
70.000
~ ° ° °° .°°°
60.000
A
~i0.000 I=40.000 30.000
Ac= 57.44 m2 Ac= 86.2 m2
20.000
......
Ac= 71.8 m2
[
I
10.000 0.000
8
g• ' ~g
g,, 8~
~~
~in ~~
~ .8..8.~ 8
~
8~
8. ~8
8,'
8
~
8"- ~8
8," ~8
8"
8
~
8"-
F i g . 5. T h e v a r i a t i o n o f t h e t a n k m i x e d m e a n t e m p e r a t u r e a s a f u n c t i o n o f t i m e f o r a t y p i c a l d a y o f each of the summer months (May through September) for different numbers of units corresponding t o a r e a s f r o m 4 3 m 2 t o 8 6 m 2 a t a t a n k v o l u m e o f 1000 1, a n d w i t h l o a d e x t r a c t i o n s t a r t i n g w h e n t h e t a n k m i x e d m e a n t e m p e r a t u r e is a b o v e 6 5 ° C .
548
N. K. GHADDAR et al. 100.000 90.000 80.000 70.000 60.000 50.000
k-
40.000 30.000 I
20.000
~
Ac= 57.44 m2
......
Ac= 71.8 m2
J
I
• Ac= 86.2 m2
10.000 0.000 m
m
m
m
~
m
m
~
m
m
m
m
m
m
m
m
m
m
m
m
m
m
m
m
TIME 90.000 80.000 70.000 60.000 .-50.000 1-40.000 30.000 20.000
I
~
Ac= 57.44 m2
10.000
J
~
Ac= 86.2 m2
0.000,
',
;
:
',
:
:
;
~ ~
;
;,
:
:
~
',
""
:
',
~ ~
--
""
'.
~
:
;
"TIME
',
',
.
......
:
;
.
:
.
',
;
.
;
Ac= 71.8 m2
'.
.
',
.
;
:
.
;
.
:
:
.
;
:
.
:
'.
:
:
',
.
Fig. 5. Continued.
in volume, then maintains a m a x i m u m for a tank size ranging from about 1000 to 1500 1 and then decreases monotonically with increased volume as seen from Fig. 8. The optimal conditions for maximizing the yearly solar fraction for our 3 ton absorption cooling system would then be easily specified to be for a volume to area ratio, A / V , from 13 to 19 l/m 2. The minimum required collector area per kW delivered is then 6.6 m2/kW corresponding to a m a x i m u m YSF of 0.37 and the m a x i m u m allowed collector area is 8.2 m2/kW corresponding to a m a x i m u m of 0.435. The effect of water flow rate in the solar water heating system on the tank mixed mean temperature is studied. Figure 9 shows the mean tank temperature as it varies with time for a typical day in M a y for a system area of 80 m 2 and 1000 1 at different flow rates starting
Solar absorption system performance
549
100.000 90.000 80.000 70.000 60.000
E 40.000
20.000
10.000
I
Ac= 57.44 m2 . . . . . . Ac= 86.2 m2
Ac= 71.8 m2 I
:::::::::::::::::::::::::::::::::::::::::::::::::::::::::
8 8~ o~ 80i 8~ 8tii 8 tii8 ti-i-~ 8 8 "'8 ~6 8 8'" t;6 8 8"" 8ti'i 8"" 8Oi 8"" 8=ii8 ""8 8 8 TIME
Fig. 6. The collector outlet temperature as a function of the time of day of a typical day in June for different numbers of units corresponding to areas from 57 m2 to 86 m 2 at a tank volume of i000 1.
from 0.5 to 11 m3/h. Increasing flow rate increases the tank temperature up to a limit at 6 m3/h, after which any further increase in flow rate hardly changes the tank temperature. It is of interest to evaluate the system performance in the optimal range conditions for maximum YSF which are set now for the case of the 1300 1 tank, 80.6 m 2 collector area and a flow rate of 7 m3/h. Figure 10a shows the useful heat gain and overall heat loss from the system as a function of time for a typical day of May, while Fig. 10b shows the collector and system efficiencies. It is clear that the system operates with higher efficiency in the morning and with increasing collector temperature, the useful heat gain decreases and system loss increases. The load extraction has a positive effect on system performance as seen from the decrease in the slope of the efficiency curve when extraction starts at 9:45 a.m. This improvement is obvious when comparing the system performance when load extraction is present and when load extraction is zero. Figure 1 la shows the useful heat gain versus time for both cases of zero load extraction and full load extraction and Fig. 11 b shows the tank mean temperature versus time for both cases. Direct energy extraction reduces heat loss, increases useful heat gain and reduces tank mean temperature.
SYSTEM OPTIMIZATION AND ECONOMICS The proposed solar absorption system will be cost effective when its investment cost is equal to or less than the present value of the energy savings over the life of the system
550
N. K. GHADDAR
et al.
100.000 90.000 80.000
70.000 60.000 50.000 40.000 30.000
Vt=lO001 Vt=1500~
20.000
10.000
......
Vt=13001 I Vt=18001
0.000
TIME 100.000 90.000
(b)
August
80.000 70.000 60.000 o 1-
S0.000 40.00030.000
10.000 -
- .....
Vt=18001
Vt=lfi001
0.000 , I : ; ', : ', ', : ', ' I I ', ; : : ; : ', : ', ', : ', : : ', ; : : : : ', ~ ', ; : : : ', : ', : ', : ',
.o° ~ ~ ~ .o°..o°. ~ ~ 8..8..8 .8. 8 8..8 8..8 .8 .8. 8. 8. 8..8..8. TIME F i g . 7. T h e m i x e d m e a n t a n k t e m p e r a t u r e as a f u n c t i o n o f t i m e at fixed c o l l e c t o r a r e a o f 80.4 m 2 (28 u n i t s ) f o r t a n k v o l u m e s o f 1000, 1300, 1500 a n d 1800 l, f o r t h e m o n t h s o f (a) M a y a n d (b) A u g u s t .
which
is a f u n c t i o n
capital
investment
of fuel escalation
rates and the expected
of the solar-absorption
real return
system can be expressed
C = CcAc+CsVs+AC+AT,
on investment.
The
as" (11)
Solar absorption system performance
(a)
55 I
(CONSTANT LOAD EXTRACTION)
0.3
O
: : :: ::: i _ i
tL )"
o., '-
'iiiiiiii i"
0.1
i
0.05 0
I 500
~
750
1000
'I
......
=
I
1300
1500
1800
2200
2500
Vt (Liter)
(b)
(VARIABLE LOAD EXTRACTION)
0.45 .-
--..-'.--_..._..:~.. .... L~-- "-:.:_'~ ......
0,
.............
0.35
u.
,
0.25
0.15
.
0.1
......
o.os
AC=71.83 '"
0
500
- ....... A¢=57"5
A~=,3.1A~=,3.1
.,,
I
N
II
,'
J
i
I
750
1000
1300
1500
\
~._ ~
1800
q.
2200
2500
Vt(Liter)
Fig. 8. Plots of the YSF of (a) constant and (b) variable evaporator load versus tank size for different collector areas. The YSF versus tank size for collectors area of 80.4 m 2. where Cc is the unit cost of the solar collector equal to $220/m :, Ac is the area of used solar collectors (m2), Cs is the unit cost for a thermally insulated low pressure galvanized steel storage tank ($500/m3), V, is the volume of the storage tank, AC is the fixed cost of the absorption chiller ($5000), and A T is the fixed cost of the small cooling tower plus an additional pump ($500). Installation cost is assumed to be included in all the above items. For 1.3 m 3 tank, and 80.4 m 2 collector area the investment cost would be $23,938. The annual cost o f such a system is composed of electrical cost, which is very small, plus
552
N. K. G H A D D A R et al. 100.000
90.000 80.000 70.000 is IS
60.000 =E U.I I-. ,¢ Z
50.000 40.000
. . ~
. . . .
8 M3/HR
......
4 M3/HR
J
6 M3/HR
30.000
- - - - - - 2 M3/HR
20.000
~ 0 . 5
M3/HR
10.000 0.000 O O O O O O O O
TIME
Fig. 9. The mean tank temperature variation with time for a typical day in May at different flow rates in the system starting from 0.5 m3/h to 11 m3/h. maintenance cost. This annual cost is considered to be m = $100. The domestic hot water cost is assumed to be zero since the hot water that remains in the storage tank after use can be used for domestic purposes using an inflation rate figure e = 8% and interest rate r = 11%. Then the annual cost o f the absorption system can be found by the formula [6] :
(l+e 7 l+e\ a = m*
*
l+e l+r
1
'
(12)
where a is the annual cost, N is the time in years. F o r a conventional vapor-compression air conditioning unit, the cost o f 10.5 k W is a b o u t $2500, and it consumes 3.2 k W / h electric power and the domestic hot water use is assumed to be 10 k W daily. The daily c o n s u m p t i o n o f electric power is: P = 3 . 2 " u + 10,
(13)
where u is the daily usage time for the system. The m o n t h l y electric c o n s u m p t i o n and cost can then be calculated using the Lebanese tariff for a usage time equivalent to the solar extraction time o f the absorption system. The annual cost for usage o f the conventional air conditioning unit for the same period o f the solar-absorption system is $393.3. The interest rate is considered to be r = 11%, and the electric energy inflation rate is taken to be e = 4%.
553
Solar absorption system performance
(a)
25.000 20.000
15.000 10.000
i
. . . . .i i i i i
5.000 0.000 -5.000 °10.000 -15.000
TIME QU(kj/sec) 60.000
. . . . . . QL(kj/sec) (b)
50.000¸ 40.000
I,k
30.000
16
~u 20.000 10.000 0.000 o10.000 TIME
Fig. 10. Plots of (a) useful heat gain and overall heat loss from the system as a function of time for a representative day of May and (b) the collector and system efficiencies as a function of time for a representative day of May.
N. K. GHADDAR et al.
554 35000
QU 30000
"'-"
" ~
-.
without
extraction
25000
extraction
20000
15000 0 10000
5000
. ,
0
=,
. . . . . . . . . . . . .
,0
,~ ~ ~
=..
,
:_
. . . . . . .
~
.
,
. ,
~ .~
,
-, ~
r
, ,
, ,
,~ .
,
. ,
~' =
,
.
* ,
=~
,
.
~-
~
~
, , .
Time (hr)
(a) 120
deg. C 100
8o 1-
1--
60 4O
20
Ib)
Iime(hr)
Fig. l l. Plots of (a) useful heat gain versus time and of (b) tank mixed mean temperature versus time for both cases of zero load extraction and full load extraction. The electric energy consumption for the coming years can then be calculated using eq. (12). Figure 12a shows the predicted annual operation cost of the solar refrigeration system and Fig. 12b the annual electric cost of the vapor compression system for the coming years. It is seen that electrical cost will have a detrain increase due to expected electrical inflation rate. For our system of 80.4 m 2, V = 1500 1 and with a life cycle of 20 years, the payback period, Np in years, of the solar absorption system versus the vapor compression system is given by : I + ~) B* 1 ÷ i (l--~r) *
\7-~/ I÷m*
l+i
l+r
--1
-(T~r)*
- 1
l+e
, -, -+-el+r
(14)
1
where Iis the capital cost of the solar absorption system minus that of the vapor compression system.
Solar absorption system performance
555
6000 5000 4000 3000 2000 1000
electrical
cost]
0
time (years)
(a) 1800 1600 1400 $ 1200 1000 800 600 400 200 0
I
I
I
3
I
I
5
I
',
7
',
',
9
',
;
11
',
',
',
13
;
15
',
',
17
',
',
',
19
',
',
',
,
21 23
time (years)
(b)
Fig. 12. Plots of (a) the predicted annual operation cost of the solar refrigeration system and of (b) the annual electric cost of the vapor compression system for the coming years. Figure 13 shows the predicted cumulative system cost for both the solar-absorption system and the conventional system as a function of time in years for three different collector 70000 60000 50000
• Cumilativeelectrical --II-- 170 $/m^2 220 $/m^2
4
b
f
40000 30000 20000 i
~
10000 0
,
,
,
,
I
,
,
time (yr) Fig. 13. The predicted cumulative system cost for both the solar-absorption system and the conventional system as a function of time in years for three different collector area prices of 170, 220 and $270/mL
N, K. GHADDAR et al.
556
area prices of 170, 220 and $270/m 2. The break-even points will range from 12 to 16 years. Current costs of solar collectors in general are expected to decrease dramatically with mass production and this may then make such systems economically viable. The use of solar systems should be combined with passive designs of buildings, so as to reduce the required air conditioning load and this may double the yearly solar fraction of the system. Earlier studies of G h a d d a r and Bsat [16] on conservation measures applied to residential building in Beirut, have shown a substantial decrease in cooling requirements.
CONCLUSIONS The lithium bromide absorption refrigeration system operates well when combined with a solar hot water source. The acceptable operating range of the solar absorption system is when the supplied hot water from the solar system is between 65 and 85°C corresponding to a required generator load between 12 and 14.5 kW. An optimal performance of the solar absorption system was attained at a tank volume to collector area ratio (Vs/Ac) of 13 to 19 l/m 2 which corresponded to a solar fraction of 20% to 26% for constant load extraction and to a solar fraction of 38% to 44% for a variable load extraction. The minimum (Vs/A¢) permitted so that boiling in the system does not occur, is found to be 11.6 1/m2. The minimum required collector area per kW delivered is then 6.6 mZ/kW and the m a x i m u m allowed collector area is 8.2 m2/kW. The solar absorption system can be marginally competitive with conventional vapor compression air conditioning when collector manufacturing prices reach values less than $120/m 2. The prospects of solar air conditioning are expected to further improve with the growth of solar industry and the escalation of fuel costs.
Acknowledgements--The support for this research by the American University of Beirut Research Board under grant number 11304048118, is thankfully acknowledged by the authors.
NOMENCLATURE a AC AT Cp COP D e FR h IT N Q r S T
annual cost solar-absorption system absorption chiller cost cooling tower cost heat capacity coefficient of performance number of days per month inflation rate collector heat removal factor enthalpy hourly radiation time in years heat transfer interest rate absorbed solar radiation temperature
Solar absorption system performance t U u V X YSF
557
time overall heat transfer coefficient daily usage time of vapor compression system volume concentration, variable, data point coordinate yearly solar fraction
Greek characters ct thermal diffusivity fl collector tilt angle error r/ efficiency p density, reflectance Subscripts a abs bot c cond ev gen L m s u
absorber, ambient, absorption, air absorber bottom collector condenser evaporator generator extracted load number of summer months from May to September storage tank useful.
REFERENCES
1. P. J. Wilbur and C. E. Mitchell, Solar absorption air-conditioning alternatives. Solar Energy 17, 193-199 (1975). 2. S. Alizadeh, F. Bahar and F. Geoola, Design and optimization of an absorption refrigeration system operated by solar energy. Solar Energy 24, 149-154 (1979). 3. A. Karakas, N. Egrican and S. Uygur, Second-law analysis of solar absorption-cooling cycles using ammonia/water as working fluids. Applied Energy 37, 169-187 (1990). 4. F. Sakkal, N. Ghaddar and J. Diab, Solar collectors for Beirut climate. Applied Energy 45, 313-325 (1993). 5. F. J. Kreider and F. Kreith, Solar Energy HandBook. McGraw Hill, U.S.A. (1981). 6. P. T. Tsilingiris, Theoretical modeling of a solar air conditioning system for domestic applications. Energy Convers. Mgmt 34, 523-531 (1993). 7. B. Kilkis, Panel cooling and heating of buildings using solar energy. Solar Energy in the 1990s. ASME-SED 10, 1-9 (1990). 8. B. Kilkis, Radiant ceiling cooling with solar energy fundamentals, modeling and a case design. ASHRAE Trans. Part 2 (1993). 9. E. H. Perry, Theoretical performance of the lithium bromide-water intermittent absorption refrigeration cycle. Solar Energy 17, 321-323 (1975). 10. Y. Shiran, A. Shitzer and D. Degani, Computerized design and economic evaluation of an aqua-ammonia solar operated absorption system. Solar Energy 29, 43-54 (1982). 11. W. F. Stoeker, Refrigeration and Air Conditioning, international edn. McGraw Hill, Singapore (1987). 12. ASHRAE Handbook of Fundamentals. ASHRAE, Atlanta, U.S.A. (1985). 13. J. m. Duffle and W. A. Beckman, Solar En#ineerin# of Thermal Processes. Wiley, New York (1980).
558
N. K. GHADDAR et al.
14. N. K. Ghaddar, Stratified storage tank influence on performance of solar water heating system tested in Beirut. Renewable Energy 4, 911-926 (1994). 15. N. Ghaddar and I. Kebbe, Experimental and numerical study of stratified tank solar water heating system in Beirut. Proc. Fourth Arab Int. Solar Energy Conf., Royal Scientific Society of Jordan, Amman, Jordan, November 1993. 16. N. Ghaddar and A. Bsat, Energy conservation of residential buildings in Beirut. Applied Energy, in press.