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Choice of thermal energy system for solar absorption cooling
Sohzr Idnergy Vol. 32. No. 2, pp. 181-187. 1984 Printed in Great Britain.
00384)92X/84 $3.00 + .00 Pergamon Press Ltd.
CHOICE OF T H E R M A L ENERGY SYSTEM FOR SOLAR ABSORPTION COOLING R. K. SURI, K. AL-MADANI and S. AVYASH Solar Energy Department, Engineering Division, Kuwait Institute for Scientific Research, P.O. Box 24885, Safat, Kuwait
(Receired 10 January 1983) Abstract--It is essential to operate a solar vapour absorption cooling system only at design conditions in order to maximize the saving of conventional electrical energy. The paper deals x~fth the analysis of a solar thermal energy system by coupling the collector field, an auxiliary thermal energy source, the thermal energy reservoir and the generator of the'absorption chiller in a single closed loop, thus ensuring optimum performance of the chiller at design conditions. This analysis is preceded by a quasi steady-state analysis for the system xxithout the auxiliary source to obtain the temperature history of the reservoir, the hourly thermal energy availability and the resulting cooling effect. The comparative results of the two systems highlight the importance of auxiliary thermal energy source in maximizing the electrical energy saying. The utility of auxiliary energy input is highly attractive because of its high effective COP and higher equivalent electrical conversion efficiency. INTRODUCTION
The use of solar energy to operate a vapour absorption cooling system has its attraction in its ability to conserve commercial form of energy [1, 2]. The quantum of saving is however critically dependent upon the temperature of the generator, the cooling water and the chilled water. In separate studies of commercially available Water-Lithium Bromide absorption chillers, the authors [3, 4] have made engineering estimates on the extent of electrical energy saving with solar absorption system when compared to the conventional vapour compression units of equivalent cooling capacity. These studies indicate that as a rough approximation, one can save about 50 per cent electrical energy consumption by using solar absorption chillers operating at design conditions. The studies also show that for a desired chilled water temperature, the cooling capacity of the chiller drops drastically, if either the cooling water temperature increases above the design conditions (due to adverse humidity conditions) or if the generator input temperature drops (based on technique adopted for solar thermal energy collection-storage subsystem) below the design value. Coupled with this is the fact that the electrical power consumption of the total absorption system (pumps and fans) is at its full rated capacity irrespective of the operating characteristics of the chiller. As a result, the electrical power consumption per unit of refrigeration (kW electrical]kW cooling) can increase to a level that it becomes equal to that needed by a vapour compression system to produce the same quantum of cooling effect. Such a situation will correspond to absorption chiller operating at nearly 50 per cent of its rated capacity; the conditions quite common with many of the installed solar absorption cooling systems. It is therefore of interest to evaluate the feasibility of coupling solar collector field, and auxiliary thermal energy reservoir, thus ensuring optimum performance of the chiller at design conditions. The paper deals
with analytical studies of such a system to obtain cumulative thermal energy transfer pattern in the system components for a typical summer day operation in Kuwait. This analysis is preceded by the quasi steady-state solutions for the proposed system but without an auxiliary thermal energy source. The results show that for the system without the auxiliary source, the daily average COP is much lower than the design value at which the proposed system operates throughout the day. Thus, at the expense of source fuel for the required quantum of auxiliary thermal energy, it is possible to save electrical energy to a maximum extent with the proposed system and virtually nothing for the system without the ,auxiliary source. The analytical results have been obtained in a generalized form to study the important parameters which influence the performance of the two solar thermal energy collection-storage-utilization systems. DESIGN CONFIGURATION AND ENERGY TRANSFER PROCESS
The simplified versions of the two single loop solar thermal energy systems are shown in Fig. l, without (Fig. la) and with (Fig. lb) the auxiliary thermal source in the circuit. In the first system (Fig. la), the temperature t of the thermal energy reservoir which is a time dependent function, is the inlet temperature of the solar collector field. This temperature is raised to t, after passage through the collector field. The absorption chiller is thus supplied thermal energy at a temperature t~, which is a time dependent function. Based on the governing value of chiller's coefficient of performance (COP), the fluid enters the thermal energy reservoir at a temperature t2 after passage through the generator. The instantaneous energy transfer process for the quasi steady-state system is thus given by:
(1) The symbols have been defined in the nomenclature. 181
182
R.K. SuRI et al. % %~'J
(te) C~JLLER * ( GEN~KATOR) J BY.P~5
M~XED TEki~ RESERVOIR
/f/.,,,o-
Mal~$ : M Sp Heat : Cp Temp t !
(t) pUMP
(a)
WITHOUT AUXILIARY ENERGY 50URCE
THERMAL
%
,e-
\
^/--I
l---I
~q~
I ----rT
CHIIIER I (GENERATOR)
SOURCE
Ml]~En TIrMp RESERVOIR
Mal$ ; M S~ Heal t Cp Te~p t 1 l
I
.
~'I J
02)
( b ) WffH
AXILIARY
THERMAL
ENERGY SOURCE
Fig. 1. Solar thermal energy systems.
The rate of energy inflow/outflow from the reservoir is responsible for the rate of change of its temperature (dt/dO); where 0 is the time parameter. In the second system (Fig. lb), the reservoir temperature t2 (constant; chiller generator outlet design temperature) is the inlet temperature of the collector field. This temperature rises to te after passage through the collector field and is further boosted to fl; the fixed generator inlet temperature as specified by the manufacturer for the optimum design cooling capacity performance of the vapour absorption chiller. Depending upon the operating COP, the fluid temperature h drops to t2 after passage through the generator of the chiller, which is also the constant steady-state temperature of the reservoir. The energy transfer processes for this system is thus given by:
THEORETICAL ANALYSIS
The text to follow gives the analysis for the two systems: S o l a r T h e r m a l E n e r g y S j ' s t e m W i t h o u t A u x i l iary S o u r c e : Referring to Fig. l(a), let M and Cp represent, respectively, the total mass of the fluid in the reservoir and its specific heat. The temperatures of the fluid at other locations in the closed loop circuit have been indicated in the diagram. Let lit be the fluid flow rate (constant). The energy balance for the reservoir for the quasi steady-state conditions as defined by eqn (1), can be simplified and written as, (MfliO(dt/dO)
= (t, - t) - (t, - t2).
(3)
Figure 2 shows the collector field efficiency curve (representative); assumed linear and defined by the equation:
(2) d~Cp(te - t)/(l.Ae) = oc[(t~ + t)12 -- t,]/I + ft.
In this case, the reservoir operates under steady-state conditions (dt /dO = 0). Under the circumstances when the chiller unit is not in operation (during the non-occupancy period of the day), both systems act as simple thermal energy collection devices, as shown by the dotted by-pass line (/~ = L'g = 0 and/~R # 0 in eqn 2).
(4)
The above equation can be expressed explicitly in terms o f t , as follows: t, = (X~t + f l l -- ~ ta)lX2
(5)
where, X~, X2, ~ and fl have been defined in the nomenclature.
Choice of thermal energy system for solar absorption cooling
183
Referring to Fig. l(b), the energy transfer processes for this case are governed by eqn (2) and given by: fflCr(t, - t2) + / ~ a - - ,hCp(tl - t2) = 0.
(11)
The collector field outlet temperature t, in this case will be given by: t, = ( X , t2 + f l l - ~ta)/X2.
(12)
Similarly, the chiller cooling rate will now be given by: 6 = vdlCp(tt - h )
[(te, t
(13)
Substituting t, from eqn (12) and t~ from eqn (13), the auxiliary thermal energy supply rate (Ea) from eqn (11) can be expressed in terms of fi, the fixed temperature for the optimum performance of the chiller:
)/2-t,a ] / I
Fig. 2. Collector field efficiency curve (representative). f: o = ( x , / x g ( r /v ) - OhCpt~ t)/ X2 -- coilCp(t I - t~)/X z.
The cooling rate (fi) provided by the chiller at its operating COP (v) is given by: 6 = v t i z C p ( t , - h).
(6)
Substitution of t, in (t, - t) from eqn (5) and (t, - t2) from eqn (6) in eqn (3) gives the differential equation describing the reservoir temperature as a single dependent parameter: (Mhh)(dt[dO)
-- ( ~ l X 2 ) ( t - 0 = i l l / X 2 -- 5 l v ~ C p
(7)
In order to normalize the above differential e_quation, the following temperature (u) and time (0) parameters have been defined: u = (t -- Q / ( t , - -
to) and /Y= 0/0o.
Equation (7) can now be expressed in the nondimensional form: (du/d#) - ( . u / X , ) = ~,
(8)
where ~l is given by: ~, = q 3 l ) / [ X z ( t , -
t,,)] - 6 [ v , h C p ( h - O]-
(9)
Using the initial condition, u(ff = 0) = 1, the solution of eqn (8) is given by: u = [1 "t- (~lX2/ct) e "#lx2 -- (~1X21~).
(10)
During the period of the day when the system acts as a simple thermal energy collection device, the solution is also given by eqn (10) with ~ modified by using 6 = 0. Solar thermal energy system with auxiliary source.
SE Vol. 32. No. 2-.--C
(14)
The above equation shows that for non-sunny conditions, if the chiller has to be operated under optimum conditions on auxiliary source alone, it must supply thermal energy at full rate, i. e. E~ = 6 / v ; since I = 0, ct = 0 and X t = Xz. RESULTS
The expression for ~1 given by eqn (9) has two distinct terms, one having solar collector field parameters and the other consisting of absorption chiller terms. The collector field term can be evaluated for known values of ct and fl and for the actual hourly values of insolation (I) and ambient temperature (to). The second term has to be evaluated by using the performance curves of the absorption chiller to obtain 6 and v for different values of generator inlet temperature (equal to t,, see Fig. la), the chilled water temperature and the cooling water temperature. Figure 3 shows the diagrammatic representation of the vapour absorption chiller with the three temperature potentials which basically define its thermodynamic performance. Depending upon a set of these operating temperatures, the 6 and v values can be read off the performance curves supplied by the manufacturer of the chiller (Ref: Yazaki Solar System Equipment-Installation and Service Manual for Model WFC-3000). For the purpose of demonstrating the use of analysis, a 140 kW solar cooling project already installed in a kindergarten in Kuwait has been taken as an example. The pertinent parameters of the project, wherever used in the text to follow are given in the nomenclature. For the first case (Fig. la), in order to obtain quantitative values of performance of the chiller at varying generator input temperatures, the chilled
R.K. Sugl et al.
184
/
VAPC(.~
ABSORPTI(~N(~HILLEIR
g /~" C a w
1
w
CO~4DENSER / ABSORBER
t 7~,"- rhc,,w
Fig. 3. Energy transfer model of absorption chiller.
water temperature (tch,) and the cooling water temperature (to,) have been chosen as 9~ and 29.5~ respectively. The governing equations describing the cooling output (R) of the chiller and its COP (v) for different generator inlet temperatures (ts; equal to t,) have been discussed in Ref. [4] and are reproduced below: R = 23.86r - 4 . 2 3 ; from Ref. [4] v = 0.03tz - 1.9 for tx < 85~ from manufacturer's data v = 0.267t~ - 1.62 for tt > 85~ from manufacturer's data. The parameters R, r, and tt have been defined in the nomenclature. The solution of the quasi steady-state problem, given by eqn (10), can be applied for short intervals of half or one hour duration during which the insolation (I) and ambient temperature (ta) can be assumed to remain constant as an average hourly value. The result will give reservoir temperature at the end of the interval. This value can then become the initial temperature (ti) of the reservoir for the next time interval (0) . The repetitive interval solutions will thus yield the temperature history of the reservoir during the day. The initial and the final temperature (t) of the reservoir for any time interval can then be used to obtain the corresponding temperatures t, and h- From the average temperature differentials it is thus possible to obtain the net energy inflow/outflow from the reservoir, the chiller (generator) and the collector field. For low insolation conditions, the collector field will be cut-off and the chiller (generator) will have energy supply from the hot water reservoir. The solution under these circumstances will be given by using eqn (7) with c~= 0 and I = 0. In the second case (Fig. lb), eqn (14) gives the rate
of auxiliary thermal energy input to the system for optimum performance of the chiller as per design conditions. This equation can be applied for short intervals of one hour duration to obtain E= on hourly basis. The energy available from the collector field and that needed for the chiller (generator) can be easily deduced. Figure 4 shows the insolation (inclined plane) and the ambient temperature during the day for a typical summer day (June) in Kuwait. Figure 5 shows the cumulative values of ER, L',, L', and E8 for the two cases discussed earlier in the text. The cooling produced in the two cases has also been shown in the same diagram. DISCUSSIONSAND CONCLUSIONS An exact solution of the quasi steady-state problem gives the performance of the solar thermal energy system without the additional auxiliary thermal energy source. During the process of normalizing the differential equation, describing the reservoir temperature history, two parameters of importance have been brought out, these are: ~j, and 00. Each of these parameters subscribe the variation of the reservoir temperature and thereby the performance of the individual subsystem i.e. energy collection, energy storage and energy utilization. With the use of auxiliary thermal energy source in series with the collector field, it is possible to obtain much higher daily cooling output from an already installed system at the operating COP equal to the optimum design value of the chiller. This is evident from the quantitative values from Fig. 5 which have been reproduced in Table 1. The table shows that for a full day operation, the system without the auxiliary thermal source has a much lower daily average COP (0.51) as compared to the system's design value (0.72) obtainable with the proposed system. The table also shows the electrical energy saving possible with the two systems when compared to an equivalent capacity vapour compression system. The criteria and norms used for estimating the electrical power saving have
185
Choice of thermal energy system for solar absorption cooling i
i
i
i
i
i
i
I
900
t t,
E o
S
s INSOLATION AMBIENI TEMPERATURE
700
z o
IF . . . . r------qL - -
5 i. . . .
z
l i J
~0
I i
r .... J
....
~r
I L ....
I I i ]
l I
1
.see
or
&OO
0~' ~
I
I
1;" I
!
1~' I
]I
13s I
I
I
,g" I
I
I
3C
I
HOURS OF DAY
Fig. 4. Solar insolation and ambient temperature distribution June day.
Table I. Comparative performance of two systems Parameters
1.
System w i t h Auxiliary Source
1120
a.
From C o l l e c t o r
1200
b.
From A u x i l i a r y Source
ZERO
765
e.
From R e s e r v o i r
365
ZERO
TOTAL COOLING PRODUCED ( K ~ r )
3.
AVERAGE DALLY COP
4.
ADDITIONAL COLLECTOR AREA FOR RECOUPING RESERVOIR ENERGY DRAINAGE
5.
System w i t h no A u x i l i a r y Source
THER}~L ENERGY INPUT (KWHr)
2.
(1565)
(1885)
8OO
1360
0.51
0.72
30
ZERO
266
452
257
257
9
195
0.04
0.50
(%)
ELECTRIC ENERGY FOR EQUIVALENT VAPOUR COMPRESSION SYSTEM (k%~r); see 'a' below.
6.
PARASITIC ENERGY NEEDED BY ABSORPTION SYSTEM (Kk~r); see 'b' below.
7.
ELECTRIC ENERGY SAVED ( K ~ r )
8.
KW e SAVING/TON OF COOLING
DATA FROM REFERENCE (4) : a.
Power needed for conventional system = 1.16 KWe/Ten
b.
Parasitic power needed for absorption system = 0.66 KWelTon
DEDUCTIONS e.
Thermal e n e r g y i n p u t from a u x i l i a r y s o u r c e (projected) using equal collector area
d.
COP o f p r o j e c t e d
e.
Equivalent electric conversion efficiency o f p r o j e c t e d a u x i l i a r y e n e r g y needed
auxiliary
e n e r g y needed
=r to iz t~
I I I i
:
-600
4~
I -~-
lBB5 - 1120 x 429 k%'llr (1360 (195 43Z
800) 9)/429
1.3 /429
= 1.3
186
R. K. SURI et al. T
r
T
/t
1600 .1500
///////~ IHERMAL
ENERGY
IN PUT TO CHILLER
/
GENERATOR . . . .
/~OOLIN G /
//
/i
OUTPUT / / "
~"
//
//. I
/
zr
i/
z
/ t.--
/
/ i/'
//
/
/
t
'
COOL /
/t
/i
///
I//
500
tol
.~It/ENE~Y SUPPLYBY
5"
~-""
8
\
AUXILIARYSOURCE
LEGEND
CASE:F=gute I.o
_ _
CASE P,gure l.b . . . . .
THERMAL RESERVOIR \INPUT/OUTPUT
37 ~
06' HOURS OF DAY
Fig. 5. Cumulative energy pattern for the subsystems.
already been discussed earlier in the text. These results have been reproduced in Table I from Ref. [4]. The analysis and the results (see Table 1) highlight the importance of auxiliary heating source in maximising the saving of conventional electrical energy from a mere 9 kWhr/day to 195 kWhr/day. The utility of the thermal energy supplied by the auxiliary booster is highly attractive; its equivalent electrical conversion efficiency is 43 per cent and its effective COP is 1.3 as against apparent value of 0.72 (see Table 1). In addition, the incorporation of an auxiliary thermal energy source, in the manner proposed in the paper, facilitates the designer to optimize the size of the collector field for its effective round the year usage. With the proposed system, there is now no need to provide a backup vapour compression system, thereby lowering the total cost of cooling hardware and thus improving the techno-economics remarkably. The analyses presented in the paper predict without
doubt that the use of auxiliary heat source in a solar absorption cooling system is unavoidable, if the ultimate objective is to save electrical power for summer cooling. NOMENCLATURE A c collector area (window); m2; 344 1 average inclined surface insolation; hourly basis; Watt/m2; June data (see Fig. 4) 0 time period; hr to average ambient temperature; hourly basis; cC June data (see Fig. 4) collector field performance curve factor (slope linear plot of Fig. 2); kcal/hrm 2 cC; - 4.0 collector field performance curve factor (intercept on the vertical axis of Fig. 2); dimensionless; 0.7 Cp specific heat of fluid (water); kcal/Kgrn cC: 1.0 mass flow rate of fluid; kgm/hr; 35000 M mass of fluid in reservoir; kgm; 25000 ti initial temperature of reservoir; ~C; 85 6 cooling output of chiller; kW; 4 units (total 140kW cooling)
Choice of thermal energy system for solar absorption cooling v coefficient of performance (COP) of chiller; dimensionless t~h. chilled water outlet temperature from chiller; ~ 9 to,. cooling water inlet temperature to chiller; cC; 29.5 t~ generator inlet temperature under design conditions; ~ 87 0o normalising time quantity; hr. = M[th X, parameter: Kcal/hrm2~ = (rhCp/Ac) + (:t]2) X2 parameter: Kcal/hr m ~~ = (rhCp/A~) - (~/2) ~l parameter; dimensionless = (fll) /[X2(t i - t~)] - 3 /[~'rhCp(ts- t~)] * parameter; dimensionless = I - (tchw+ 273)/(tx + 273) R cooling capacity ratio; dimensionless = (actual cooling capacity in kW/design capacity in kW) time parameter; dimensionless = O[Oo u reservoir temperature parameter; dimensionless= (t -- t , ) / ( t , - ta) t 2 generator outlet temperature; ~ t, collector field outlet temperature; ~ t~ generator inlet temperature; ~
187
~ea rate of thermal energy input from the auxiliary source; kw rate of thermal energy gained by the collector field; kw ~c rate of thermal energy supplied to chiller generator; kw E, rate of thermal energy inflow/outflow to the reservoir; kw REFERENCES 1. T. Ishibashi, The result of cooling operating of Yazaki experimental solar house "one". Solar Energy 21, I1 (1978). 2. D. Van Hattem and P. Actis Dato, Description and performance of an active solar cooling system--using a LiBr-H20 absorption machine. Energy and Building 3, 169 (1981). 3. S. Ayyash, Power saving in solar absorption cooling systems. Third M I C A E S , Florida, U.S.A., (1980). 4. R. K. Suri and S. Ayyash, Solar absorption cooling-effect of operational parameters on power saving. Int. J. Refrig. 5, 274 (1982).
00384)92X/84 $3.00 + .00 Pergamon Press Ltd.
CHOICE OF T H E R M A L ENERGY SYSTEM FOR SOLAR ABSORPTION COOLING R. K. SURI, K. AL-MADANI and S. AVYASH Solar Energy Department, Engineering Division, Kuwait Institute for Scientific Research, P.O. Box 24885, Safat, Kuwait
(Receired 10 January 1983) Abstract--It is essential to operate a solar vapour absorption cooling system only at design conditions in order to maximize the saving of conventional electrical energy. The paper deals x~fth the analysis of a solar thermal energy system by coupling the collector field, an auxiliary thermal energy source, the thermal energy reservoir and the generator of the'absorption chiller in a single closed loop, thus ensuring optimum performance of the chiller at design conditions. This analysis is preceded by a quasi steady-state analysis for the system xxithout the auxiliary source to obtain the temperature history of the reservoir, the hourly thermal energy availability and the resulting cooling effect. The comparative results of the two systems highlight the importance of auxiliary thermal energy source in maximizing the electrical energy saying. The utility of auxiliary energy input is highly attractive because of its high effective COP and higher equivalent electrical conversion efficiency. INTRODUCTION
The use of solar energy to operate a vapour absorption cooling system has its attraction in its ability to conserve commercial form of energy [1, 2]. The quantum of saving is however critically dependent upon the temperature of the generator, the cooling water and the chilled water. In separate studies of commercially available Water-Lithium Bromide absorption chillers, the authors [3, 4] have made engineering estimates on the extent of electrical energy saving with solar absorption system when compared to the conventional vapour compression units of equivalent cooling capacity. These studies indicate that as a rough approximation, one can save about 50 per cent electrical energy consumption by using solar absorption chillers operating at design conditions. The studies also show that for a desired chilled water temperature, the cooling capacity of the chiller drops drastically, if either the cooling water temperature increases above the design conditions (due to adverse humidity conditions) or if the generator input temperature drops (based on technique adopted for solar thermal energy collection-storage subsystem) below the design value. Coupled with this is the fact that the electrical power consumption of the total absorption system (pumps and fans) is at its full rated capacity irrespective of the operating characteristics of the chiller. As a result, the electrical power consumption per unit of refrigeration (kW electrical]kW cooling) can increase to a level that it becomes equal to that needed by a vapour compression system to produce the same quantum of cooling effect. Such a situation will correspond to absorption chiller operating at nearly 50 per cent of its rated capacity; the conditions quite common with many of the installed solar absorption cooling systems. It is therefore of interest to evaluate the feasibility of coupling solar collector field, and auxiliary thermal energy reservoir, thus ensuring optimum performance of the chiller at design conditions. The paper deals
with analytical studies of such a system to obtain cumulative thermal energy transfer pattern in the system components for a typical summer day operation in Kuwait. This analysis is preceded by the quasi steady-state solutions for the proposed system but without an auxiliary thermal energy source. The results show that for the system without the auxiliary source, the daily average COP is much lower than the design value at which the proposed system operates throughout the day. Thus, at the expense of source fuel for the required quantum of auxiliary thermal energy, it is possible to save electrical energy to a maximum extent with the proposed system and virtually nothing for the system without the ,auxiliary source. The analytical results have been obtained in a generalized form to study the important parameters which influence the performance of the two solar thermal energy collection-storage-utilization systems. DESIGN CONFIGURATION AND ENERGY TRANSFER PROCESS
The simplified versions of the two single loop solar thermal energy systems are shown in Fig. l, without (Fig. la) and with (Fig. lb) the auxiliary thermal source in the circuit. In the first system (Fig. la), the temperature t of the thermal energy reservoir which is a time dependent function, is the inlet temperature of the solar collector field. This temperature is raised to t, after passage through the collector field. The absorption chiller is thus supplied thermal energy at a temperature t~, which is a time dependent function. Based on the governing value of chiller's coefficient of performance (COP), the fluid enters the thermal energy reservoir at a temperature t2 after passage through the generator. The instantaneous energy transfer process for the quasi steady-state system is thus given by:
(1) The symbols have been defined in the nomenclature. 181
182
R.K. SuRI et al. % %~'J
(te) C~JLLER * ( GEN~KATOR) J BY.P~5
M~XED TEki~ RESERVOIR
/f/.,,,o-
Mal~$ : M Sp Heat : Cp Temp t !
(t) pUMP
(a)
WITHOUT AUXILIARY ENERGY 50URCE
THERMAL
%
,e-
\
^/--I
l---I
~q~
I ----rT
CHIIIER I (GENERATOR)
SOURCE
Ml]~En TIrMp RESERVOIR
Mal$ ; M S~ Heal t Cp Te~p t 1 l
I
.
~'I J
02)
( b ) WffH
AXILIARY
THERMAL
ENERGY SOURCE
Fig. 1. Solar thermal energy systems.
The rate of energy inflow/outflow from the reservoir is responsible for the rate of change of its temperature (dt/dO); where 0 is the time parameter. In the second system (Fig. lb), the reservoir temperature t2 (constant; chiller generator outlet design temperature) is the inlet temperature of the collector field. This temperature rises to te after passage through the collector field and is further boosted to fl; the fixed generator inlet temperature as specified by the manufacturer for the optimum design cooling capacity performance of the vapour absorption chiller. Depending upon the operating COP, the fluid temperature h drops to t2 after passage through the generator of the chiller, which is also the constant steady-state temperature of the reservoir. The energy transfer processes for this system is thus given by:
THEORETICAL ANALYSIS
The text to follow gives the analysis for the two systems: S o l a r T h e r m a l E n e r g y S j ' s t e m W i t h o u t A u x i l iary S o u r c e : Referring to Fig. l(a), let M and Cp represent, respectively, the total mass of the fluid in the reservoir and its specific heat. The temperatures of the fluid at other locations in the closed loop circuit have been indicated in the diagram. Let lit be the fluid flow rate (constant). The energy balance for the reservoir for the quasi steady-state conditions as defined by eqn (1), can be simplified and written as, (MfliO(dt/dO)
= (t, - t) - (t, - t2).
(3)
Figure 2 shows the collector field efficiency curve (representative); assumed linear and defined by the equation:
(2) d~Cp(te - t)/(l.Ae) = oc[(t~ + t)12 -- t,]/I + ft.
In this case, the reservoir operates under steady-state conditions (dt /dO = 0). Under the circumstances when the chiller unit is not in operation (during the non-occupancy period of the day), both systems act as simple thermal energy collection devices, as shown by the dotted by-pass line (/~ = L'g = 0 and/~R # 0 in eqn 2).
(4)
The above equation can be expressed explicitly in terms o f t , as follows: t, = (X~t + f l l -- ~ ta)lX2
(5)
where, X~, X2, ~ and fl have been defined in the nomenclature.
Choice of thermal energy system for solar absorption cooling
183
Referring to Fig. l(b), the energy transfer processes for this case are governed by eqn (2) and given by: fflCr(t, - t2) + / ~ a - - ,hCp(tl - t2) = 0.
(11)
The collector field outlet temperature t, in this case will be given by: t, = ( X , t2 + f l l - ~ta)/X2.
(12)
Similarly, the chiller cooling rate will now be given by: 6 = vdlCp(tt - h )
[(te, t
(13)
Substituting t, from eqn (12) and t~ from eqn (13), the auxiliary thermal energy supply rate (Ea) from eqn (11) can be expressed in terms of fi, the fixed temperature for the optimum performance of the chiller:
)/2-t,a ] / I
Fig. 2. Collector field efficiency curve (representative). f: o = ( x , / x g ( r /v ) - OhCpt~ t)/ X2 -- coilCp(t I - t~)/X z.
The cooling rate (fi) provided by the chiller at its operating COP (v) is given by: 6 = v t i z C p ( t , - h).
(6)
Substitution of t, in (t, - t) from eqn (5) and (t, - t2) from eqn (6) in eqn (3) gives the differential equation describing the reservoir temperature as a single dependent parameter: (Mhh)(dt[dO)
-- ( ~ l X 2 ) ( t - 0 = i l l / X 2 -- 5 l v ~ C p
(7)
In order to normalize the above differential e_quation, the following temperature (u) and time (0) parameters have been defined: u = (t -- Q / ( t , - -
to) and /Y= 0/0o.
Equation (7) can now be expressed in the nondimensional form: (du/d#) - ( . u / X , ) = ~,
(8)
where ~l is given by: ~, = q 3 l ) / [ X z ( t , -
t,,)] - 6 [ v , h C p ( h - O]-
(9)
Using the initial condition, u(ff = 0) = 1, the solution of eqn (8) is given by: u = [1 "t- (~lX2/ct) e "#lx2 -- (~1X21~).
(10)
During the period of the day when the system acts as a simple thermal energy collection device, the solution is also given by eqn (10) with ~ modified by using 6 = 0. Solar thermal energy system with auxiliary source.
SE Vol. 32. No. 2-.--C
(14)
The above equation shows that for non-sunny conditions, if the chiller has to be operated under optimum conditions on auxiliary source alone, it must supply thermal energy at full rate, i. e. E~ = 6 / v ; since I = 0, ct = 0 and X t = Xz. RESULTS
The expression for ~1 given by eqn (9) has two distinct terms, one having solar collector field parameters and the other consisting of absorption chiller terms. The collector field term can be evaluated for known values of ct and fl and for the actual hourly values of insolation (I) and ambient temperature (to). The second term has to be evaluated by using the performance curves of the absorption chiller to obtain 6 and v for different values of generator inlet temperature (equal to t,, see Fig. la), the chilled water temperature and the cooling water temperature. Figure 3 shows the diagrammatic representation of the vapour absorption chiller with the three temperature potentials which basically define its thermodynamic performance. Depending upon a set of these operating temperatures, the 6 and v values can be read off the performance curves supplied by the manufacturer of the chiller (Ref: Yazaki Solar System Equipment-Installation and Service Manual for Model WFC-3000). For the purpose of demonstrating the use of analysis, a 140 kW solar cooling project already installed in a kindergarten in Kuwait has been taken as an example. The pertinent parameters of the project, wherever used in the text to follow are given in the nomenclature. For the first case (Fig. la), in order to obtain quantitative values of performance of the chiller at varying generator input temperatures, the chilled
R.K. Sugl et al.
184
/
VAPC(.~
ABSORPTI(~N(~HILLEIR
g /~" C a w
1
w
CO~4DENSER / ABSORBER
t 7~,"- rhc,,w
Fig. 3. Energy transfer model of absorption chiller.
water temperature (tch,) and the cooling water temperature (to,) have been chosen as 9~ and 29.5~ respectively. The governing equations describing the cooling output (R) of the chiller and its COP (v) for different generator inlet temperatures (ts; equal to t,) have been discussed in Ref. [4] and are reproduced below: R = 23.86r - 4 . 2 3 ; from Ref. [4] v = 0.03tz - 1.9 for tx < 85~ from manufacturer's data v = 0.267t~ - 1.62 for tt > 85~ from manufacturer's data. The parameters R, r, and tt have been defined in the nomenclature. The solution of the quasi steady-state problem, given by eqn (10), can be applied for short intervals of half or one hour duration during which the insolation (I) and ambient temperature (ta) can be assumed to remain constant as an average hourly value. The result will give reservoir temperature at the end of the interval. This value can then become the initial temperature (ti) of the reservoir for the next time interval (0) . The repetitive interval solutions will thus yield the temperature history of the reservoir during the day. The initial and the final temperature (t) of the reservoir for any time interval can then be used to obtain the corresponding temperatures t, and h- From the average temperature differentials it is thus possible to obtain the net energy inflow/outflow from the reservoir, the chiller (generator) and the collector field. For low insolation conditions, the collector field will be cut-off and the chiller (generator) will have energy supply from the hot water reservoir. The solution under these circumstances will be given by using eqn (7) with c~= 0 and I = 0. In the second case (Fig. lb), eqn (14) gives the rate
of auxiliary thermal energy input to the system for optimum performance of the chiller as per design conditions. This equation can be applied for short intervals of one hour duration to obtain E= on hourly basis. The energy available from the collector field and that needed for the chiller (generator) can be easily deduced. Figure 4 shows the insolation (inclined plane) and the ambient temperature during the day for a typical summer day (June) in Kuwait. Figure 5 shows the cumulative values of ER, L',, L', and E8 for the two cases discussed earlier in the text. The cooling produced in the two cases has also been shown in the same diagram. DISCUSSIONSAND CONCLUSIONS An exact solution of the quasi steady-state problem gives the performance of the solar thermal energy system without the additional auxiliary thermal energy source. During the process of normalizing the differential equation, describing the reservoir temperature history, two parameters of importance have been brought out, these are: ~j, and 00. Each of these parameters subscribe the variation of the reservoir temperature and thereby the performance of the individual subsystem i.e. energy collection, energy storage and energy utilization. With the use of auxiliary thermal energy source in series with the collector field, it is possible to obtain much higher daily cooling output from an already installed system at the operating COP equal to the optimum design value of the chiller. This is evident from the quantitative values from Fig. 5 which have been reproduced in Table 1. The table shows that for a full day operation, the system without the auxiliary thermal source has a much lower daily average COP (0.51) as compared to the system's design value (0.72) obtainable with the proposed system. The table also shows the electrical energy saving possible with the two systems when compared to an equivalent capacity vapour compression system. The criteria and norms used for estimating the electrical power saving have
185
Choice of thermal energy system for solar absorption cooling i
i
i
i
i
i
i
I
900
t t,
E o
S
s INSOLATION AMBIENI TEMPERATURE
700
z o
IF . . . . r------qL - -
5 i. . . .
z
l i J
~0
I i
r .... J
....
~r
I L ....
I I i ]
l I
1
.see
or
&OO
0~' ~
I
I
1;" I
!
1~' I
]I
13s I
I
I
,g" I
I
I
3C
I
HOURS OF DAY
Fig. 4. Solar insolation and ambient temperature distribution June day.
Table I. Comparative performance of two systems Parameters
1.
System w i t h Auxiliary Source
1120
a.
From C o l l e c t o r
1200
b.
From A u x i l i a r y Source
ZERO
765
e.
From R e s e r v o i r
365
ZERO
TOTAL COOLING PRODUCED ( K ~ r )
3.
AVERAGE DALLY COP
4.
ADDITIONAL COLLECTOR AREA FOR RECOUPING RESERVOIR ENERGY DRAINAGE
5.
System w i t h no A u x i l i a r y Source
THER}~L ENERGY INPUT (KWHr)
2.
(1565)
(1885)
8OO
1360
0.51
0.72
30
ZERO
266
452
257
257
9
195
0.04
0.50
(%)
ELECTRIC ENERGY FOR EQUIVALENT VAPOUR COMPRESSION SYSTEM (k%~r); see 'a' below.
6.
PARASITIC ENERGY NEEDED BY ABSORPTION SYSTEM (Kk~r); see 'b' below.
7.
ELECTRIC ENERGY SAVED ( K ~ r )
8.
KW e SAVING/TON OF COOLING
DATA FROM REFERENCE (4) : a.
Power needed for conventional system = 1.16 KWe/Ten
b.
Parasitic power needed for absorption system = 0.66 KWelTon
DEDUCTIONS e.
Thermal e n e r g y i n p u t from a u x i l i a r y s o u r c e (projected) using equal collector area
d.
COP o f p r o j e c t e d
e.
Equivalent electric conversion efficiency o f p r o j e c t e d a u x i l i a r y e n e r g y needed
auxiliary
e n e r g y needed
=r to iz t~
I I I i
:
-600
4~
I -~-
lBB5 - 1120 x 429 k%'llr (1360 (195 43Z
800) 9)/429
1.3 /429
= 1.3
186
R. K. SURI et al. T
r
T
/t
1600 .1500
///////~ IHERMAL
ENERGY
IN PUT TO CHILLER
/
GENERATOR . . . .
/~OOLIN G /
//
/i
OUTPUT / / "
~"
//
//. I
/
zr
i/
z
/ t.--
/
/ i/'
//
/
/
t
'
COOL /
/t
/i
///
I//
500
tol
.~It/ENE~Y SUPPLYBY
5"
~-""
8
\
AUXILIARYSOURCE
LEGEND
CASE:F=gute I.o
_ _
CASE P,gure l.b . . . . .
THERMAL RESERVOIR \INPUT/OUTPUT
37 ~
06' HOURS OF DAY
Fig. 5. Cumulative energy pattern for the subsystems.
already been discussed earlier in the text. These results have been reproduced in Table I from Ref. [4]. The analysis and the results (see Table 1) highlight the importance of auxiliary heating source in maximising the saving of conventional electrical energy from a mere 9 kWhr/day to 195 kWhr/day. The utility of the thermal energy supplied by the auxiliary booster is highly attractive; its equivalent electrical conversion efficiency is 43 per cent and its effective COP is 1.3 as against apparent value of 0.72 (see Table 1). In addition, the incorporation of an auxiliary thermal energy source, in the manner proposed in the paper, facilitates the designer to optimize the size of the collector field for its effective round the year usage. With the proposed system, there is now no need to provide a backup vapour compression system, thereby lowering the total cost of cooling hardware and thus improving the techno-economics remarkably. The analyses presented in the paper predict without
doubt that the use of auxiliary heat source in a solar absorption cooling system is unavoidable, if the ultimate objective is to save electrical power for summer cooling. NOMENCLATURE A c collector area (window); m2; 344 1 average inclined surface insolation; hourly basis; Watt/m2; June data (see Fig. 4) 0 time period; hr to average ambient temperature; hourly basis; cC June data (see Fig. 4) collector field performance curve factor (slope linear plot of Fig. 2); kcal/hrm 2 cC; - 4.0 collector field performance curve factor (intercept on the vertical axis of Fig. 2); dimensionless; 0.7 Cp specific heat of fluid (water); kcal/Kgrn cC: 1.0 mass flow rate of fluid; kgm/hr; 35000 M mass of fluid in reservoir; kgm; 25000 ti initial temperature of reservoir; ~C; 85 6 cooling output of chiller; kW; 4 units (total 140kW cooling)
Choice of thermal energy system for solar absorption cooling v coefficient of performance (COP) of chiller; dimensionless t~h. chilled water outlet temperature from chiller; ~ 9 to,. cooling water inlet temperature to chiller; cC; 29.5 t~ generator inlet temperature under design conditions; ~ 87 0o normalising time quantity; hr. = M[th X, parameter: Kcal/hrm2~ = (rhCp/Ac) + (:t]2) X2 parameter: Kcal/hr m ~~ = (rhCp/A~) - (~/2) ~l parameter; dimensionless = (fll) /[X2(t i - t~)] - 3 /[~'rhCp(ts- t~)] * parameter; dimensionless = I - (tchw+ 273)/(tx + 273) R cooling capacity ratio; dimensionless = (actual cooling capacity in kW/design capacity in kW) time parameter; dimensionless = O[Oo u reservoir temperature parameter; dimensionless= (t -- t , ) / ( t , - ta) t 2 generator outlet temperature; ~ t, collector field outlet temperature; ~ t~ generator inlet temperature; ~
187
~ea rate of thermal energy input from the auxiliary source; kw rate of thermal energy gained by the collector field; kw ~c rate of thermal energy supplied to chiller generator; kw E, rate of thermal energy inflow/outflow to the reservoir; kw REFERENCES 1. T. Ishibashi, The result of cooling operating of Yazaki experimental solar house "one". Solar Energy 21, I1 (1978). 2. D. Van Hattem and P. Actis Dato, Description and performance of an active solar cooling system--using a LiBr-H20 absorption machine. Energy and Building 3, 169 (1981). 3. S. Ayyash, Power saving in solar absorption cooling systems. Third M I C A E S , Florida, U.S.A., (1980). 4. R. K. Suri and S. Ayyash, Solar absorption cooling-effect of operational parameters on power saving. Int. J. Refrig. 5, 274 (1982).