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Study of the performance of the solar heating system of a multifamily building
Energy and Buildings, 13 (1989) 109 - 118
109
Study of the Performance of the Solar Heating System of a Multifamily Building F. O. FLOUQUET and N. KERNEVEZ Centre de Recherches sur les Tr@s Basses Tempdratures, CNRS, BP 166 X, 38042 Grenoble-C~dex (France) (Received March 9, 1988; accepted May 8, 1988; revised paper received September 6, 1988)
ABSTRACT
The computer program T R N S Y S was used to simulate the heating system o f the Bourgoin-Jallieu experimental solar building and added quantitative results to the survey o f several years o f monitoring. The building, situated near Lyon, France, consists of two identical three-storey blocks; the south face is a curtain wall with water solar collectors (the parameters o f the solar system can be varied). The floors are equipped with coils of water imbedded in the concrete. The heating system was simulated by a model which took into account the independent electric auxiliary heating and the thermal capacitance o f the floor and o f the walls. It gave good information about the energy balance according to the experiments. The overall performance o f the system has been investigated by the Chang model and the concept o f decay constant was analyzed. It was shown to be relevant only for intermediate solar radiation, to be a function o f the utilizability and to be inversely proportional to the load o f the building. It was also shown that the most interesting solution is to use the largest storage allowed by the tanks, although the direct use o f the concrete mass o f the floor could achieve nearly equivalent energy performance at a lower cost.
1. INTRODUCTION
The Bourgoin-Jallieu building is a twelveapartment, low-income, solar building. It was designed in 1977 as a facility to study the effects o f varying the parameters of the system and of testing c o m p u t e r models of active solar systems. Thus the building consists of t w o geometrically and thermally identical
blocks, containing the same system components and insulated from each other [1, 2]. In this way, parameters concerning the storage or collector system can be varied on one side and performances can be compared with those on the second side, for identical meteorological conditions. The solar heating system is detailed in Section 2. The monitoring of the solar Bourgoin building was performed b y CNRS (Centre National de la Recherche Scientifique) and was discontinued after 1986. Experimental studies on variations of storage volume, collector area and water flow rate were performed for periods of a few weeks and have led to qualitative results [3]. In addition, during one year, all the water storage tanks were bypassed on one side in order to compare the classic storage system with a direct solar space-heating floor using only the thermal capacitance of the concrete [4]. During another full year, the tank on one side of the building was equipped with cans which contained a material with a phase transition close to 40 °C, and the comparison with the water storage was analyzed in a separate report [5]. In order to control the behaviour of the solar heating system, and to draw more quantitative conclusions from the experiments, a theoretical model was first proposed in 1980 [2]. The transient simulation program TRNSYS [6] was able to give a good description of the solar heating system. It was necew sary to develop later an original subroutine, to simulate the space heating flow through the floor, taking into account the load of the house as well as the floor and wall thermal capacitance [7, 8]. (To test the computer models, periods varying from one to five weeks were selected based on favourable sunshine conditions in addition to wellfunctioning solar and data-logging systems.) Elsevier Sequoia/Printed in The Netherlands
110
The analytical model and its different assumptions are described in Section 3, where it is shown that only t w o differential equations are necessary, involvingtwo main parameters: the temperature of the floor on the one hand, and the temperature of walls and indoor air on the other. The results of the simulation in Section 4.1 give information regarding the interaction between the solar and auxiliary heating systems. The exponential relationship between auxiliary energy and collector area, worked o u t b y Chang, is discussed again and optimized b y TRNSYS runs in Section 4.2. Analytical laws known in the literature for active solar systems and useful in simplified computer programs are also used to define all the parameters occurring in the decay constant k expression. In this way, it could be seen whether k is a good indicator of the overall performance of the system, i.e., whether this parameter is indeed independent of building load and meteorological conditions.
2. DESCRIPTION OF THE SOLAR HEATING SYSTEM
Figure 1 shows a schematic representation of the solar system. The south face of the building is a curtain wall with forty modules
of single-glazedwater collectors.The collector area can be varied from 0 to 152.5 m 2. The p u m p of the collector's circuit is controlled by a photoelectric cell and operates from sunrise to sunset. The water-glycol solution does not flow through the heat exchanger unless the temperature difference between the entrance to the diverter and the storage tank exceeds a chosen A T (5 °C). The controller simultaneously triggers the diverter and turns on, or off, the p u m p of the secondary circuit. Storage is provided by three main water tanks that can be connected in series or in parallel in order to vary the storage volume from 0.2 m a to 30.2 m a. Water circulated through the coil in the solar tank to preheat domestic h o t water (DHW) which is then transferred to an electric water heater operating during off-peak hours only; its temperature is finally boosted to the required tap temperature by an electrical auxiliary heater. Heat is transferred from the storage tank to the house by means of coils imbedded in the four floors. The upper and lower floors are insulated from outside and only radiate inwards. The walls are insulated by 8 cm o f polystyrene and the windows are doubleglazed. The auxiliary heating is provided b y means of electriC convectors and is independent. The average annual heating consumption measured for one half-building and during three years is 156 GJ (floor area 573 m 2 and 24 inhabitants). The building loss coefficient is 1.29 kW/°C. The solar heating fraction is 44% and corresponds to 450 MJ/m 2 of collector area. At the same time the solar energy provides 38% of the annual DHW needs corresponding to 128 MJ/m ~ of collector area. The accuracy of the solar energy measured at the distribution varies from 10% to 20%.
3. COMPUTER SIMULATION WITH TRNSYS
.~.flOw meter (diagrQm) J .--.thermome~m" (Pt msistonc~ Fig. 1. Schematic representation of the solar heating system.
Figure 2 shows the schematic representation of the solar main system and the DHW distribution with standard TRNSYS components. The system characteristics are detailed in the Appendix. The horizontal cylindrical tanks have an observed loss coefficient of 30 W/°C each, and
111
card reclderl ~
~
'
~
i'"
-.I p'p'I
]
/
/~3~';ump
| /
T
~ IDHWprofilel
pump Fig. 2. Information flow diagram of the solar heating system with TRNSYS components.
the tertiary pipes between the storage and the house, which have a coefficient of 10 W/ °C, are incorporated with the storage tank(s) in the simulation. F o r all the other pipes, t y p e 31 was used, with the observed loss and heat capacity coefficients. The solar tank for DHW with an internal heat exchange coil was modelled as a mixing tank. For DHW consumption, a profile was determined b y referring to average daily totals observed in the building and load vs. time of day schedule proportional to that given b y the national standard. The floor heating and its regulation are shown in Fig. 3. A first controller switches on the floor p u m p only if the upper storage temperature exceeds a set point Tset (22 °C). (The corresponding o n / o f f controller parameter in T R N S Y S is then 7~ = 1.) A three-way m o t o r valve mixes warm water (at temperature T~) from the storage tank and water (at temperature To) flowing back from the floor. To regulate the temperature Te at the entrance of the coils, the valve is adjusted b y an electronic controller so that this temperature Te is compared to a function Tc = x --YTa where Ta is the ambient temperature and x, y, are positive
I
I
Fig. 3. Space heating and its regulation.
adjustable constants. These constants x and y are different for night and day. The flow-diverter of TRNSYS, with progressive flow rate partition, was used for the three-way m o t o r valve (corrective parameter 7): - - i f Te ~ To, 7 = 1, the storage is t o o cold to reach Tc and the water flowing in the coils, comes entirely from the storage tank (7 = 0 otherwise and the water then flows in a closed circuit, bypassing the storage); --if T e = To, 7 takes an intermediate value given by the expression 7 = [(Tc -- T o ) / ( T , - - To)] To simulate the controller, an algebraic subroutine was used. The o n / o f f controller which turns on the p u m p is included in the same calculation unit (7~)- The final corrective parameter of the valve is thus 7 X 7~. A special module was developed using the heat transfer differential equations of IENER [9]. An electrical analogy was used to reduce the problem to that of a single r o o m with an equivalent internal temperature and with a single floor equivalent to the four real ones. First, a simplified module with one differential equation (associated with the floor) assuming a constant air temperature (Ti = Tic) was tested. C ~ l ( d T d d t ) = {~s -- Qt
(1)
Ctl = 13 000 kJ/°C and is the floor thermal capacity drawn from the volume and thermal characteristics of the concrete; T~ is the floor temperature. As shown in Fig. 3, {~s is the rate of heat flow supplied from water to the floor, and
112
0 f is the rate of heat flow transmitted from the concrete to the internal air and to the building. Qs = er~cp(Te
Tf)
--
(2)
e = 1 -- [ e x p - (hTrdl/tnCp)]
(3)
Q~
(4)
=
oa4fz(Tf
--
Ti)
where rh, Cp = flow rate and heat capacity of the water in coils, respectively; d, l = coil diameter and length respectively; e = emittance of the coils; h, ~ = heat exchange coefficients for w a t e r - f l o o r and floor-house, respectively. The heat exchange coefficients h and were first chosen according to the value given by IENER. The module for the floor was run separately with input files containing data of the water temperature and flow rate at the floor inlet. To test the response of the model, we plotted first the experimental and simulated data for the water temperature at the floor outlet (Fig. 4). To fit simultaneously the capacitances involved and the heat exchange coefficients, several observed periods in winter were used. With only one differential equation associated with the floor (eqn. (1)), the simulated curve of the water temperature was distorted and out of phase compared to the experimental plot. In addition, the simulation of the complete system led to the required electric auxiliary heating being much greater from the calculation than from the experiment. The air temperature is controlled, n o t only by the thermal capacitance of the air b u t b y the building concrete. Thus a second equation associated with the air and building was added, with a heat capacity Ci including the effect of the concrete. To keep only two equations and a skeleton model, the first equation related to a floor layer containing coils; in the second equation the heat
To('C)
capacity Ct was thus fitted to relate the building itself (10% of the total mass) and the remaining section of the floor (90% of the mass of the floor) (Ci was taken as 200 000 kJ/°C). The internal and variable temperature Ti concerns b o t h the air and a big concrete mass supposed to be at the same equivalent temperature at every moment. Cl(dTl/dt) = Qf + Qaux + Qw - {~L
(5)
QL = (UA)L(Ti -- A T -
(6)
Ta)
where {~L represents the needs of the building (heating losses minus the internal gains) and Qw the heat solar gains through the windows. A controller maintains the internal temperature above a set.point Tic by adjusting the auxiliary heat flow Qaux : Q.ux = 0
i f T i > Tic
O.ux = e L --
Q,
-- Cw
(7) T, < Tic
(8)
The electrical equivalent network of the heating of the building is shown in Fig. 5.
T
e
~
T
Q
Fig. 5. Electrical equivalent network of the heating of the building. The building loss coefficient (UA)L = 4650 kJ/h °C is predicted b y taking the fresh air admission into account (0.8 air change per hour determined b y measurement). The free internal heat gains in degrees have been evaluated to AT = 1.9 °C + 0.2 °C from both the daily average electric and gas consumption for the appliance (including lights) (32 k w h per block) and the occupancy (100 W/person; 2.5 occupancy per fiat). The solar gains through the windows Qw are predicted each timestep b y the type 35 of TRNSYS with an equivalent south window area of 21 m 2. The heat exchange coefficients were determined:
/"
h=1000kJ/h°Cm
ii0
, 20
310
, 40
, 50
i 60 hr
Fig. 4. Comparison of predicted (dot line) and measured (full line) temperature of the water at the floor outlet (Cfl = 13000 kJ/°C, Ci = 200000 kJ/°C, ~ = 72 kJ/h Cm2).
2 and
a=72kJ/h°Cm
2
4. ANALYSIS AND RESULTS 4.1. General results o f the system The accuracy of the simulation results can be judged b y performing an energy balance on
113
while the auxiliary energy was predicted to be 3537 MJ (3330 MJ measured). There is no measurement for the real temperature Ti in the apartments or for the temperature Tic. Moreover, b o t h these temperatures in the model are n o t representative of the indoor air alone, b u t concern also, as already said, a large part of the mass of the walls and floor. The time constants of the exponents in the floor and air-building equations are much greater than the time step (At = 0.031 s):
the storage. The two quantities A (=energy input to storage) and B (=losses+energy delivered by the storage + change of internal energy) should be equal. An error of the simulation given by 2 [ A - - B [ / ( A + B) less than 0.5% was achieved. Simulation gives information about gains and losses of the solar system and they are in good agreement with measured energies available at every circuit outlet of the system (Table 1). For the whole month of March, the energy Q e c h supplied at the primary heat exchanger is divided into 33% for the total losses and 67% for the useful energy Qs delivered to the load. The energies Qech and Qs are different from their corresponding experimental values by 3% and 6% respectively
T 1 = C ~ l / ( e r h C p + o~4fl) = 1.95 (h)
+ ~A~l] = 5 (h) For the period of March, the calculated set temperature Tic = 15 °C, however indi-
1"2 = C i [ ( U A ) L
TABLE 1 M e a s u r e d a n d c a l c u l a t e d energies f o r t h e solar Date 1984
/~ Ta ( M J / m 2 (°C) day)
heating
system
Energy at exchanger Qech (MJ)
Energy to the floor Qs ( M J )
meas.
meas.
calc.
calc.
March 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31
13.2 6.6 8.0 5.1 6.3 20.7 14.0 19.3 8.4 4.1 9.7 18.7 10.6 20.3 7.3 7.6 9.8 0.9
9.7 7.5 6.7 2.5 2.3 5.4 10.1 14.6 12.2 13~8 15.9 18.5 15.1 13.2 13.8 13.6 12.6 10.9
731 209 324 61 112 1429 929 1335 342 230 569 1250 583 1296 0 367 450 0
710 100 161 60 46 1443 1041 1358 159 181 604 1328 527 1340 272 264 269 0
634 155 169 0 0 997 605 857 464 142 425 230 889 713 350 234 378 0
572 0 0 0 0 1170 853 560 576 129 425 230 866 552 887 67 179 0
April 1 2 3 4 5 6 7 8 9
3.6 4.2 11.5 4.9 4.4 9.5 9.8 16.0 16.6
10.4 11.4 11.8 11.6 12.6 12.4 15.6 16.8 16.1
0 112 749 0 112 565 529 1163 1091
0 41 724 0 41 368 434 1091 1066
0 0 634 0 0 425 392 403 608
0 0 490 0 0 165 358 638 459
14538
13629
8915
9176
Totals
Electric Qaux (MJ)
44 100 533 1066 1077 501 ----
-----
----
----181 ---
Solar e n e r g y in t h e h o u s e Qf (MJ)
E n e r g y gain E n e r g y t h r o u g h t h e load windows QL Qw (MJ) (MJ)
17.2 15 15 15 15 19.4 20.9 22.8 22.3 20.3 21.6 22.9 ~23 ~23 ~23 ~23 21.9 18.5
553 30 0 0 0 1121 833 514 617 150 407 196 854 559 909 170 193 45
278 134 163 110 126 435 295 406 177 125 204 393 222 427 153 176 205 19
572 750 780 1234 1266 1079 794 516 963 660 326 292 663 880 809 849 902 799
16.2 15.4 17.9 16.4
31 10 436 21
7 88 240 39 93 200 204 324 337
560 267 364 416 210 321 129 195 489
Ti
(°C)
16,0
35 --
--3537
16.4 18.6 21.7 23
6
140 326 544 452
114
cates that inhabitants use very little auxiliary electrical energy above that temperature. This behaviour of saving energy at the beginning or at the end of the heating period was previously noticed elsewhere [8 ]. When the solar energy supplied Almost all the needs of the house (sequence of 15 days from March 19, in Table 1), an average indoor temperature Ti = 20.9 °C is found. Taking into account the internal gains and the solar gains through the windows, this should result in a base temperature Tb = 17 °C. The difference from Tic = 15 °C is due to solar energy through the floors (the overheating is chosen in the calculation to be evacuated through the open windows above 23 °C). However, it can be shown that the concept of a base temperature is nearly irrelevant since the load is a scattered linear function of the ambient temperature for that period. 4.2. Overall performance and decay constant Optimization formulations for solar hot water systems have been suggested by Chang and Minardi [10, 11]. An exponential relationship was found between electrical auxiliary energy and collector area Ac. The slope of the curve, defined as the energy decay constant ~, was proposed as an indicator of the overall performance of a solar system. Qaux = Qm e-kAc
The same relationship (Fig. 6) is found here for space heating for one m o n t h (one week of auxiliary heating use}. The decay value of = 0.56 × 10 -2 m -2 is close to the value i
i
i
8.8
found with the same system for domestic hot water alone in a previous paper [7]. It is found to be m u c h lower than the average constant of X = 0.3 m -2 indicated by Chang for a standard D H W heating system for one
family unit (Ac = 2.5 m2). A series of TRNSYS Simulations was run to determine the effect on the energy decay k of varying the solar heating system parameters. The effect on auxiliary (Qaux) values was determined for t w o collector surface areas of A1 = 91.5 m 2 and A2 = 152.5 m 2. The decay coefficient could be found b y applying the following equation, as used by Chang [10]: k = [ln(Qaux. I/Qa,~.2)]/(A2 -- A1)
(9)
The studied parameter is the ratio b between the tank volume and the collector area. Figure 7 shows the results concerning the effect of this parameter. Differently from Chang's results, an optimized point is found for b - 0 . 1 3 m and ~ = 0 . 7 0 × 1 0 -2 m -2. However, for a given collector area A max= 152.5 m 2, the auxiliary heating is continuously decreasing with the increase of the tank volume. Previous experiments [3] have already showed an increase of the solar heating energy used, by a b o u t 12% for a water storage variation of 10 - 30 m 3. It is interesting to develop an analytical expression and the physical meaning of the decay coefficient X, in order to determine if this parameter is independent of the collector area Ac and of the chosen meteorological period, as seemed to be indicated b y Chang et aL who give X as a good indicator of the overall performance. When the solar heating is not used, the needs are totally supplied by the electrical heating system (Qm = QL).
A I
"~8.6 o .o
~ 0.7
I optimized . _...t'~ point
I
c
~ 0.6
8.4
"\
"~ 0.5 8.2
0
I 50
100 150 collector a r e a ( m 2 )
Fig. 6. E x p o n e n t i a l r e l a t i o n s h i p given b y t h e m o d e l b e t w e e n t h e auxiliary e n e r g y a n d t h e c o l l e c t o r a r e a : Qaux = Qm e x p ( - - k A c ) in M a r c h ( o n e w e e k o f auxiliary h e a t i n g ) .
0.4 0.07
!
I
!
0.1
0.15 volume to area rotio
0.2 b(m)
Fig. 7. T h e e f f e c t o n t h e d e c a y c o n s t a n t ~, o f varying b, t h e r a t i o o f t h e t a n k v o l u m e t o c o l l e c t o r area.
115
Qaux = Q L exp(--kAc)
(i0)
The solar load ratio and the solar heating fraction are defined as functions of the heating needs only:
fo = Qech/QL,
fs = Qs/QL
Therefore: Q..x = QL(1 -- A)
(11)
For a period of N days and average daily radiation /~ (MJ/day), the solar energy available at the primary heat exchanger is a function of the collector parameters and of the utilizabilityq studied by Klein [12]:
Qech = AcF~(~"d)NH~o
(12)
The efficiency F~ of the primary circuit is a function of the collector heat removal factor FR and the effectiveness of the heat exchanger taken as a constant (E = 0.8).
Fh=FRE FR = thoco/AcUc [1 -- exp(--F' AcUc/rhoCo ) ]
(13) The present case of great flowrate of the fluid in the primary circuit (th 0 = 1 5 0 0 0 kg/h) gives a ratio of 14.64 for rhoco/A~U ~ and a removal factor of FR = 0.967 ( F ' is taken = 1). The solar load ratio is then varying as follows:
fo = 0.60AcNIV-I~O/QL
(14)
As in any solar active heating system, from the solar energy supplied to the house, the heat transfer of the available energy at the exchanges depends on the intermediate storage. One or more tanks and also part of the whole of the heating floor concrete play that role. The laws for no-stratified storage given b y Phillips [13] were adopted. f~ = 1 - - e x p [ - - e l f 0 ( 1 + C2f0)]
(15)
C1 is the efficiency of the system for weak values of the solar load ratio and gives then fs if f0 is known. Its expression was empirically developed from correlation functions and was used to develop simplified computational models able to give solar systems performances (European model ESM1 using m o n t h l y data [14]). The coefficient C2 was calculated to minimize the quadratic error of the solar annual ratio (by means of annual simulations with a transient simulation program).
C1 = 1 . 0 2 0 5 1 1 - 0.47 exp(--1.785Cs)]
(16)
Cs is a dimensionless term giving the "storage correction".
C~ = (MCp)~torage/tR AcF~ Uc
(17)
ta=21.06 hours is the storage-collector reference time. The effect of C2 only occurs for high heat capacitance of the storage (MCp> 100 MJ/K) and values of f0 >~ 0.3. Consequently, the decay coefficient can be drawn, from eqns. (10), (11) and (15): kAc = Cxf0(1 + C2fo) in o t h e r terms, in first approximation and taking account of eqn. (14): ;k = 0.60 C 1NH~p/QL The utilizability ~0 can be drawn from cumulated frequency tables [15] and is varying as well as the daily solar radiation with the given period. The most important parameter in the expression of ;k is the size of the load. This explains the t w o orders of magnitude factor for k between the case studied here of a multifamily building heating and the case studied by Chang of a family domestic hot water heating. Empirical laws used above give correct performances of the present system: for the period of March, simulated results of Qech, Qs and Qaux (cf. Table 1) lead to f0 = 1.07 and fs = 0.72, while with the same f0, empirical laws (for MCp = 58 MJ/K) lead to fs = 0.70 (C, = 0.93, C2 = 0.19). It is also interesting to check from the analytical role of the storage the experimental results obtained when the system was used for direct solar floor heating (DSFH). For almost an entire year, with Vtank = 10 m 3 on one side of the building, the results were Qech = 66 GJ and Qs = 48.8 GJ; the corresponding values on the other side with the D S H F are found to be Q~ch = 60 GJ and Qs = 51.8 GJ [4]. Equation (15) with a storage thermal capacitance of 58 MJ/K gives (with f~xp = 0.60) a solar heating fraction f~ = 0.46 in very good agreement with the experiments (0.44}. A more important part of the floor can be supposed to be involved in terms of its thermal capacitance in the D S F H case. The value f~xP= 0.54 is almost similar for both sides
116
and would lead with the thermal capacitance of the floor alone (87 MJ/K) to f, = 0.455 or fs = 0.46 if the walls are also supposed to be involved. The experimental value of fsexp~-0.47 is therefore probably overestimated inside the limits of error (every energy measurement has a 10% accuracy corresponding to an uncertainty for fs of +0.10). Whatever the case, a maximum storage thermal capacitance (300 MJ/K) would n o t allow (for annual f0 -~ 0.6) a solarratio greater than fs = 0.54, close to the values calculated above. The conclusion of this Section is that t h e solar heating system always increases the auxiliary energy savings by increasing the storage volume (the o p t i m u m working conditions being a b o u t two tanks and the maxim u m collector area). The opposite case Vtank = 0 similar to a D S F H installation could lead to comparable energy performance. The energy gain which seems to have been found by experiments in that case is smaller than the uncertainty on the corresponding energies.
b y the importance of the load in winter and the size of the system which is designed for six families. The analysis using the decay constant allows the optimum working conditions of the system with a storage volume close to 20 m 3 to be determined while the cheaper installation in a direct solar floor heating system would lead to performances almost as favourable.
ACKNOWLEDGEMENTS
The authors are grateful to G. Kuhn and P. Pataud for their help. This work was supported by C N R S (Centre National de la Recherche Scientifique) and A F M E (Agence Fran~aise pour la Ma£trise de l'Energie).
LIST OF SYMBOLS
Ac All
b 5. CONCLUSIONS
The TRNSYS program appeared to be very well adapted to describe the active solar heating system of a collective building. It gave reasonable computational costs in spite of the large size of the system. For reasons of cost, it was necessary to use a simplified model with only two differential equations for the space heating. The proposed model yielded accurate-enough energy values: the energy differences between calculations and the experimental values are several percent. The simulation gave interesting information on the distribution of heat losses and their magnitude, on the thermal capacitance effect of the building, and on the energy balance of the whole heating system. To represent the overall system performance, the analysis was based u p o n the interesting notion of decay constant )~ given previously by Chang and Minardi. The exponential relationship between the electrical auxiliary and the collector area was first checked. Then the )~ value was found to be 20 times lower for the p~esent system than for a standard DHW system for one family. This difference could be explained essentially
collector area (m 2) floor area (m 2) ratio of tank volume to collector area heat capacitance of the floor (kJ/
°c) Cl
Cp c0
FR f0 f, H h rh
rh0 Qaux Qech
Qm Q,
QL
heat capacitance of part of walls and floor (kJ/°C) specific heat of water (kJ/°C kg) specific heat of water-glycol (kJ/ °C kg) primary circuit effectiveness collector heat removal factor solar heat ratio solar heating fraction solar radiation (MJ) w a t e r - f l o o r heat exchange coefficient (kJ/h °C m 2) mass flow rate of the water in the coils (kg/s) mass flow rate of the water-glycol in the collector circuit (kg/s) auxiliary energy used (MJ) energy delivered at the heat exchanger (MJ) energy transmitted from the floor to the house (MJ) maximum auxiliary energy used (MJ) energy supplied from the storage to the floor (MJ) needs of the building (MJ)
117
QW
% Ti Tio AT
T, T, To Uo (UA)L V e (x k T
solar energy gains through windows (MJ) balance temperature (°C) floor temperature (°C) indoor temperature (°C) indoor set temperature (°C) temperature increase from
Modelling, Policy and Decision in Energy Systems, San Francisco, June, 1981, Acta Press.
the 8
the
i n t e r n a l gains (°C) temperature of the water entering tile f l o o r (°C) Tset (22 °C) t e m p e r a t u r e o f t h e s t o r a g e (°C) a m b i e n t t e m p e r a t u r e (°C) t e m p e r a t u r e o f t h e w a t e r at t h e f l o o r o u t l e t (°C) c o l l e c t o r loss c o e f f i c i e n t (MJ/°C m 2) h e a t losses c o e f f i c i e n t o f t h e building e n v e l o p e (MJ/°C) t a n k v o l u m e ( m 3) e m i t t a n c e e f f i c i e n c y o f t h e coils floor-air heat exchange coefficient ( K J / h °C m 2) e n e r g y d e c a y c o n s t a n t ( m -2) time constant(s)
N. Kernevez and F. Flouquet, Simulation with TRNYS of the heating system and of its regulation for the Bourgoin solar building, Proc. CEE International Conference, System Simulation in Buildings, Lidge, Belgium, December, 1982, XII/ 425/83-EN. 9 A. Gardel, B. Saugy and J. C. Hadorn, Simulation d'une Installation Solaire Active avec le programme TRNS YS, N 706.101/Sg.Hd/mp, Insti-
10 11 12 13
14
15 REFERENCES
1 W. Palz and T. C. Steemers, Solar Houses in Europe -- How They Have Worked, Commission of European Communities, Pergamon Press, Oxford, 1981. 2 F. Flouquet, N. Galanis, P. Pataud and A. Cordier, The Bourgoin-Jallieu experimental apartment building: simulation for different solar system characteristics. Proc. IASTED Energy Symposia -Modelling, Policy and Decision in Energy Systems, Montreal, May, 1980, Int. J. Energy Systems, 1
(3) (1981). 3 F. Flouquet, G. Kuhn and P. Pataud, Influence des param~tres du circuit capteur et de la dimension des cuves sur le systdme de stockage, CoUoque Stockage de rEnergie Solaire, Lyon, January, 1981, COFEDES Press, Paris.
4 G. Kuhn and P. Pataud, The Solar Building of Bourgoin-Jallieu, Proc. INTERSOL '85, Montreal, Pergamon Press, Oxford. 5 C. Aubert-Dmme, Comparaison d'un syst~me de stockage /t eau et d'un systtme de stockage par mat~riau ~ changement de phase sur l'immeuble solaire de Bourgoin-Jallieu, 3dme Cycle Thesis, Inst. Nat. Polytech. de Grenoble, France, June, 1981. 6 TRNSYS -- A
Transient Simulation Program,
The University of Wisconsin, Madison, 1982. 7 F. Flouquet, The Bourgoin-Jallieu experimental apartment building: optimization of the collector system, Proc. IASTED Energy S y m p o s i a -
tut d'Economie and Am~nagements Energ~tiques, Lausanne, Switzerland, December, 1980. K. K. Chang and A. Minardi, An optimization formulation for solar heating systems, Solar Energy, 24 (1980) 99 - 104. K. K. Chang, A. Minardi and T. Clay, Parametric study of the overall performance of a solar hot water system, Solar Energy, 29 (1982) 513 - 521. S. A. Klein, Calculation of fiat-plate utilizability, Solar Energy, 21 (1978) 393. W. F. Phillips, Integrated performance of liquidbased solar heating systems, Solar Energy, 24 (1980) 287. Effects of stratification on the performance of liquid-based solar heating systems, Solar Energy, 29 (2) (1982) 111. J. Adnot, B. Bourges and B. Peuportier, Moddlisation Solaire Active, Rapport, Centre d'Energ~tique, Ecole Nationale Sup~rieure des Mines de Paris, 1984. B. Bourges, Les courbes de fr~quences cumul~es de l'~clairement solaire: Analyse statistique et applications, Thdse de Docteur-lngdnieur, Universit~ Paris, June, 1980.
APPENDIX The T R N S Y S program analysis was made with the system data listed below: COLLECTOR: m o d e 1, area (Ac) = 152.5 m 2, efficiency factor (F')= 1, black painted steel absorber-type, single glazing of 6 m m , product transmittance absorptance (~-~)= 0.95 × 0.82, loss coefficient (Uc) = 25.2 kJ/h m 2 °C, water-glycol thermal capacitance Co = 3.75 kJ/kg °C, flow rate of the fluid in the collector circuit rho = 15 000 kg/h. MAIN
STORAGE:
tank volume (V)= 10.75
m 3 (or X2, or X3), t a n k h e i g h t (H) = 2 m , loss coefficient of the equivalent rectangular tank and tertiary incorporated pipes = 5.86 kJ/m 2 °C, 3 s t r a t i f i c a t i o n s e g m e n t s . C O L L E C T O R C I R C U I T PIPES: loss coeffic i e n t = 162 k J / h °C, h e a t c a p a c i t a n c e = 300
kJ/°C.
118
STORAGE C I R C U I T PIPES: loss coefficient = 200 kJ/h °C, heat capacitance = 550 kJl°C. SOLAR AND ELECTRIC DHW TANKS: volume = 1.5 m 3, height= 2.15 m, loss coefficient = 1.95 kJ/h m 2 °C, supply water temperature = 10 °C, tap temperature = 60 °C. F L O W R A T E S : 1000 kg/h in the solar D H W circuit, 15 000 kg/h in the collector and secondary circuits. PUMP
CONTROLLERS:
upper dead band =
5 °C and lower dead band = 0 °C for the secondary circuit, upper and lower dead band = 0 °C for DHW circuit.
Building data Ventilation = 0.8 air change per hour, loss coefficient (UA)T. = 4650 k J / h °C = 1.29 KW/ °C, temperature difference from the internal gains (AT) = 1.9 °C -+ 0.2 °C, coils diameter and length: ( d ) = 1.8 cm and (l)ffi 1512 m, floor area (A~l) = 550 m 2, flow rate in the coils (rh) = 5500 kg/h.
109
Study of the Performance of the Solar Heating System of a Multifamily Building F. O. FLOUQUET and N. KERNEVEZ Centre de Recherches sur les Tr@s Basses Tempdratures, CNRS, BP 166 X, 38042 Grenoble-C~dex (France) (Received March 9, 1988; accepted May 8, 1988; revised paper received September 6, 1988)
ABSTRACT
The computer program T R N S Y S was used to simulate the heating system o f the Bourgoin-Jallieu experimental solar building and added quantitative results to the survey o f several years o f monitoring. The building, situated near Lyon, France, consists of two identical three-storey blocks; the south face is a curtain wall with water solar collectors (the parameters o f the solar system can be varied). The floors are equipped with coils of water imbedded in the concrete. The heating system was simulated by a model which took into account the independent electric auxiliary heating and the thermal capacitance o f the floor and o f the walls. It gave good information about the energy balance according to the experiments. The overall performance o f the system has been investigated by the Chang model and the concept o f decay constant was analyzed. It was shown to be relevant only for intermediate solar radiation, to be a function o f the utilizability and to be inversely proportional to the load o f the building. It was also shown that the most interesting solution is to use the largest storage allowed by the tanks, although the direct use o f the concrete mass o f the floor could achieve nearly equivalent energy performance at a lower cost.
1. INTRODUCTION
The Bourgoin-Jallieu building is a twelveapartment, low-income, solar building. It was designed in 1977 as a facility to study the effects o f varying the parameters of the system and of testing c o m p u t e r models of active solar systems. Thus the building consists of t w o geometrically and thermally identical
blocks, containing the same system components and insulated from each other [1, 2]. In this way, parameters concerning the storage or collector system can be varied on one side and performances can be compared with those on the second side, for identical meteorological conditions. The solar heating system is detailed in Section 2. The monitoring of the solar Bourgoin building was performed b y CNRS (Centre National de la Recherche Scientifique) and was discontinued after 1986. Experimental studies on variations of storage volume, collector area and water flow rate were performed for periods of a few weeks and have led to qualitative results [3]. In addition, during one year, all the water storage tanks were bypassed on one side in order to compare the classic storage system with a direct solar space-heating floor using only the thermal capacitance of the concrete [4]. During another full year, the tank on one side of the building was equipped with cans which contained a material with a phase transition close to 40 °C, and the comparison with the water storage was analyzed in a separate report [5]. In order to control the behaviour of the solar heating system, and to draw more quantitative conclusions from the experiments, a theoretical model was first proposed in 1980 [2]. The transient simulation program TRNSYS [6] was able to give a good description of the solar heating system. It was necew sary to develop later an original subroutine, to simulate the space heating flow through the floor, taking into account the load of the house as well as the floor and wall thermal capacitance [7, 8]. (To test the computer models, periods varying from one to five weeks were selected based on favourable sunshine conditions in addition to wellfunctioning solar and data-logging systems.) Elsevier Sequoia/Printed in The Netherlands
110
The analytical model and its different assumptions are described in Section 3, where it is shown that only t w o differential equations are necessary, involvingtwo main parameters: the temperature of the floor on the one hand, and the temperature of walls and indoor air on the other. The results of the simulation in Section 4.1 give information regarding the interaction between the solar and auxiliary heating systems. The exponential relationship between auxiliary energy and collector area, worked o u t b y Chang, is discussed again and optimized b y TRNSYS runs in Section 4.2. Analytical laws known in the literature for active solar systems and useful in simplified computer programs are also used to define all the parameters occurring in the decay constant k expression. In this way, it could be seen whether k is a good indicator of the overall performance of the system, i.e., whether this parameter is indeed independent of building load and meteorological conditions.
2. DESCRIPTION OF THE SOLAR HEATING SYSTEM
Figure 1 shows a schematic representation of the solar system. The south face of the building is a curtain wall with forty modules
of single-glazedwater collectors.The collector area can be varied from 0 to 152.5 m 2. The p u m p of the collector's circuit is controlled by a photoelectric cell and operates from sunrise to sunset. The water-glycol solution does not flow through the heat exchanger unless the temperature difference between the entrance to the diverter and the storage tank exceeds a chosen A T (5 °C). The controller simultaneously triggers the diverter and turns on, or off, the p u m p of the secondary circuit. Storage is provided by three main water tanks that can be connected in series or in parallel in order to vary the storage volume from 0.2 m a to 30.2 m a. Water circulated through the coil in the solar tank to preheat domestic h o t water (DHW) which is then transferred to an electric water heater operating during off-peak hours only; its temperature is finally boosted to the required tap temperature by an electrical auxiliary heater. Heat is transferred from the storage tank to the house by means of coils imbedded in the four floors. The upper and lower floors are insulated from outside and only radiate inwards. The walls are insulated by 8 cm o f polystyrene and the windows are doubleglazed. The auxiliary heating is provided b y means of electriC convectors and is independent. The average annual heating consumption measured for one half-building and during three years is 156 GJ (floor area 573 m 2 and 24 inhabitants). The building loss coefficient is 1.29 kW/°C. The solar heating fraction is 44% and corresponds to 450 MJ/m 2 of collector area. At the same time the solar energy provides 38% of the annual DHW needs corresponding to 128 MJ/m ~ of collector area. The accuracy of the solar energy measured at the distribution varies from 10% to 20%.
3. COMPUTER SIMULATION WITH TRNSYS
.~.flOw meter (diagrQm) J .--.thermome~m" (Pt msistonc~ Fig. 1. Schematic representation of the solar heating system.
Figure 2 shows the schematic representation of the solar main system and the DHW distribution with standard TRNSYS components. The system characteristics are detailed in the Appendix. The horizontal cylindrical tanks have an observed loss coefficient of 30 W/°C each, and
111
card reclderl ~
~
'
~
i'"
-.I p'p'I
]
/
/~3~';ump
| /
T
~ IDHWprofilel
pump Fig. 2. Information flow diagram of the solar heating system with TRNSYS components.
the tertiary pipes between the storage and the house, which have a coefficient of 10 W/ °C, are incorporated with the storage tank(s) in the simulation. F o r all the other pipes, t y p e 31 was used, with the observed loss and heat capacity coefficients. The solar tank for DHW with an internal heat exchange coil was modelled as a mixing tank. For DHW consumption, a profile was determined b y referring to average daily totals observed in the building and load vs. time of day schedule proportional to that given b y the national standard. The floor heating and its regulation are shown in Fig. 3. A first controller switches on the floor p u m p only if the upper storage temperature exceeds a set point Tset (22 °C). (The corresponding o n / o f f controller parameter in T R N S Y S is then 7~ = 1.) A three-way m o t o r valve mixes warm water (at temperature T~) from the storage tank and water (at temperature To) flowing back from the floor. To regulate the temperature Te at the entrance of the coils, the valve is adjusted b y an electronic controller so that this temperature Te is compared to a function Tc = x --YTa where Ta is the ambient temperature and x, y, are positive
I
I
Fig. 3. Space heating and its regulation.
adjustable constants. These constants x and y are different for night and day. The flow-diverter of TRNSYS, with progressive flow rate partition, was used for the three-way m o t o r valve (corrective parameter 7): - - i f Te ~ To, 7 = 1, the storage is t o o cold to reach Tc and the water flowing in the coils, comes entirely from the storage tank (7 = 0 otherwise and the water then flows in a closed circuit, bypassing the storage); --if T e = To, 7 takes an intermediate value given by the expression 7 = [(Tc -- T o ) / ( T , - - To)] To simulate the controller, an algebraic subroutine was used. The o n / o f f controller which turns on the p u m p is included in the same calculation unit (7~)- The final corrective parameter of the valve is thus 7 X 7~. A special module was developed using the heat transfer differential equations of IENER [9]. An electrical analogy was used to reduce the problem to that of a single r o o m with an equivalent internal temperature and with a single floor equivalent to the four real ones. First, a simplified module with one differential equation (associated with the floor) assuming a constant air temperature (Ti = Tic) was tested. C ~ l ( d T d d t ) = {~s -- Qt
(1)
Ctl = 13 000 kJ/°C and is the floor thermal capacity drawn from the volume and thermal characteristics of the concrete; T~ is the floor temperature. As shown in Fig. 3, {~s is the rate of heat flow supplied from water to the floor, and
112
0 f is the rate of heat flow transmitted from the concrete to the internal air and to the building. Qs = er~cp(Te
Tf)
--
(2)
e = 1 -- [ e x p - (hTrdl/tnCp)]
(3)
Q~
(4)
=
oa4fz(Tf
--
Ti)
where rh, Cp = flow rate and heat capacity of the water in coils, respectively; d, l = coil diameter and length respectively; e = emittance of the coils; h, ~ = heat exchange coefficients for w a t e r - f l o o r and floor-house, respectively. The heat exchange coefficients h and were first chosen according to the value given by IENER. The module for the floor was run separately with input files containing data of the water temperature and flow rate at the floor inlet. To test the response of the model, we plotted first the experimental and simulated data for the water temperature at the floor outlet (Fig. 4). To fit simultaneously the capacitances involved and the heat exchange coefficients, several observed periods in winter were used. With only one differential equation associated with the floor (eqn. (1)), the simulated curve of the water temperature was distorted and out of phase compared to the experimental plot. In addition, the simulation of the complete system led to the required electric auxiliary heating being much greater from the calculation than from the experiment. The air temperature is controlled, n o t only by the thermal capacitance of the air b u t b y the building concrete. Thus a second equation associated with the air and building was added, with a heat capacity Ci including the effect of the concrete. To keep only two equations and a skeleton model, the first equation related to a floor layer containing coils; in the second equation the heat
To('C)
capacity Ct was thus fitted to relate the building itself (10% of the total mass) and the remaining section of the floor (90% of the mass of the floor) (Ci was taken as 200 000 kJ/°C). The internal and variable temperature Ti concerns b o t h the air and a big concrete mass supposed to be at the same equivalent temperature at every moment. Cl(dTl/dt) = Qf + Qaux + Qw - {~L
(5)
QL = (UA)L(Ti -- A T -
(6)
Ta)
where {~L represents the needs of the building (heating losses minus the internal gains) and Qw the heat solar gains through the windows. A controller maintains the internal temperature above a set.point Tic by adjusting the auxiliary heat flow Qaux : Q.ux = 0
i f T i > Tic
O.ux = e L --
Q,
-- Cw
(7) T, < Tic
(8)
The electrical equivalent network of the heating of the building is shown in Fig. 5.
T
e
~
T
Q
Fig. 5. Electrical equivalent network of the heating of the building. The building loss coefficient (UA)L = 4650 kJ/h °C is predicted b y taking the fresh air admission into account (0.8 air change per hour determined b y measurement). The free internal heat gains in degrees have been evaluated to AT = 1.9 °C + 0.2 °C from both the daily average electric and gas consumption for the appliance (including lights) (32 k w h per block) and the occupancy (100 W/person; 2.5 occupancy per fiat). The solar gains through the windows Qw are predicted each timestep b y the type 35 of TRNSYS with an equivalent south window area of 21 m 2. The heat exchange coefficients were determined:
/"
h=1000kJ/h°Cm
ii0
, 20
310
, 40
, 50
i 60 hr
Fig. 4. Comparison of predicted (dot line) and measured (full line) temperature of the water at the floor outlet (Cfl = 13000 kJ/°C, Ci = 200000 kJ/°C, ~ = 72 kJ/h Cm2).
2 and
a=72kJ/h°Cm
2
4. ANALYSIS AND RESULTS 4.1. General results o f the system The accuracy of the simulation results can be judged b y performing an energy balance on
113
while the auxiliary energy was predicted to be 3537 MJ (3330 MJ measured). There is no measurement for the real temperature Ti in the apartments or for the temperature Tic. Moreover, b o t h these temperatures in the model are n o t representative of the indoor air alone, b u t concern also, as already said, a large part of the mass of the walls and floor. The time constants of the exponents in the floor and air-building equations are much greater than the time step (At = 0.031 s):
the storage. The two quantities A (=energy input to storage) and B (=losses+energy delivered by the storage + change of internal energy) should be equal. An error of the simulation given by 2 [ A - - B [ / ( A + B) less than 0.5% was achieved. Simulation gives information about gains and losses of the solar system and they are in good agreement with measured energies available at every circuit outlet of the system (Table 1). For the whole month of March, the energy Q e c h supplied at the primary heat exchanger is divided into 33% for the total losses and 67% for the useful energy Qs delivered to the load. The energies Qech and Qs are different from their corresponding experimental values by 3% and 6% respectively
T 1 = C ~ l / ( e r h C p + o~4fl) = 1.95 (h)
+ ~A~l] = 5 (h) For the period of March, the calculated set temperature Tic = 15 °C, however indi-
1"2 = C i [ ( U A ) L
TABLE 1 M e a s u r e d a n d c a l c u l a t e d energies f o r t h e solar Date 1984
/~ Ta ( M J / m 2 (°C) day)
heating
system
Energy at exchanger Qech (MJ)
Energy to the floor Qs ( M J )
meas.
meas.
calc.
calc.
March 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31
13.2 6.6 8.0 5.1 6.3 20.7 14.0 19.3 8.4 4.1 9.7 18.7 10.6 20.3 7.3 7.6 9.8 0.9
9.7 7.5 6.7 2.5 2.3 5.4 10.1 14.6 12.2 13~8 15.9 18.5 15.1 13.2 13.8 13.6 12.6 10.9
731 209 324 61 112 1429 929 1335 342 230 569 1250 583 1296 0 367 450 0
710 100 161 60 46 1443 1041 1358 159 181 604 1328 527 1340 272 264 269 0
634 155 169 0 0 997 605 857 464 142 425 230 889 713 350 234 378 0
572 0 0 0 0 1170 853 560 576 129 425 230 866 552 887 67 179 0
April 1 2 3 4 5 6 7 8 9
3.6 4.2 11.5 4.9 4.4 9.5 9.8 16.0 16.6
10.4 11.4 11.8 11.6 12.6 12.4 15.6 16.8 16.1
0 112 749 0 112 565 529 1163 1091
0 41 724 0 41 368 434 1091 1066
0 0 634 0 0 425 392 403 608
0 0 490 0 0 165 358 638 459
14538
13629
8915
9176
Totals
Electric Qaux (MJ)
44 100 533 1066 1077 501 ----
-----
----
----181 ---
Solar e n e r g y in t h e h o u s e Qf (MJ)
E n e r g y gain E n e r g y t h r o u g h t h e load windows QL Qw (MJ) (MJ)
17.2 15 15 15 15 19.4 20.9 22.8 22.3 20.3 21.6 22.9 ~23 ~23 ~23 ~23 21.9 18.5
553 30 0 0 0 1121 833 514 617 150 407 196 854 559 909 170 193 45
278 134 163 110 126 435 295 406 177 125 204 393 222 427 153 176 205 19
572 750 780 1234 1266 1079 794 516 963 660 326 292 663 880 809 849 902 799
16.2 15.4 17.9 16.4
31 10 436 21
7 88 240 39 93 200 204 324 337
560 267 364 416 210 321 129 195 489
Ti
(°C)
16,0
35 --
--3537
16.4 18.6 21.7 23
6
140 326 544 452
114
cates that inhabitants use very little auxiliary electrical energy above that temperature. This behaviour of saving energy at the beginning or at the end of the heating period was previously noticed elsewhere [8 ]. When the solar energy supplied Almost all the needs of the house (sequence of 15 days from March 19, in Table 1), an average indoor temperature Ti = 20.9 °C is found. Taking into account the internal gains and the solar gains through the windows, this should result in a base temperature Tb = 17 °C. The difference from Tic = 15 °C is due to solar energy through the floors (the overheating is chosen in the calculation to be evacuated through the open windows above 23 °C). However, it can be shown that the concept of a base temperature is nearly irrelevant since the load is a scattered linear function of the ambient temperature for that period. 4.2. Overall performance and decay constant Optimization formulations for solar hot water systems have been suggested by Chang and Minardi [10, 11]. An exponential relationship was found between electrical auxiliary energy and collector area Ac. The slope of the curve, defined as the energy decay constant ~, was proposed as an indicator of the overall performance of a solar system. Qaux = Qm e-kAc
The same relationship (Fig. 6) is found here for space heating for one m o n t h (one week of auxiliary heating use}. The decay value of = 0.56 × 10 -2 m -2 is close to the value i
i
i
8.8
found with the same system for domestic hot water alone in a previous paper [7]. It is found to be m u c h lower than the average constant of X = 0.3 m -2 indicated by Chang for a standard D H W heating system for one
family unit (Ac = 2.5 m2). A series of TRNSYS Simulations was run to determine the effect on the energy decay k of varying the solar heating system parameters. The effect on auxiliary (Qaux) values was determined for t w o collector surface areas of A1 = 91.5 m 2 and A2 = 152.5 m 2. The decay coefficient could be found b y applying the following equation, as used by Chang [10]: k = [ln(Qaux. I/Qa,~.2)]/(A2 -- A1)
(9)
The studied parameter is the ratio b between the tank volume and the collector area. Figure 7 shows the results concerning the effect of this parameter. Differently from Chang's results, an optimized point is found for b - 0 . 1 3 m and ~ = 0 . 7 0 × 1 0 -2 m -2. However, for a given collector area A max= 152.5 m 2, the auxiliary heating is continuously decreasing with the increase of the tank volume. Previous experiments [3] have already showed an increase of the solar heating energy used, by a b o u t 12% for a water storage variation of 10 - 30 m 3. It is interesting to develop an analytical expression and the physical meaning of the decay coefficient X, in order to determine if this parameter is independent of the collector area Ac and of the chosen meteorological period, as seemed to be indicated b y Chang et aL who give X as a good indicator of the overall performance. When the solar heating is not used, the needs are totally supplied by the electrical heating system (Qm = QL).
A I
"~8.6 o .o
~ 0.7
I optimized . _...t'~ point
I
c
~ 0.6
8.4
"\
"~ 0.5 8.2
0
I 50
100 150 collector a r e a ( m 2 )
Fig. 6. E x p o n e n t i a l r e l a t i o n s h i p given b y t h e m o d e l b e t w e e n t h e auxiliary e n e r g y a n d t h e c o l l e c t o r a r e a : Qaux = Qm e x p ( - - k A c ) in M a r c h ( o n e w e e k o f auxiliary h e a t i n g ) .
0.4 0.07
!
I
!
0.1
0.15 volume to area rotio
0.2 b(m)
Fig. 7. T h e e f f e c t o n t h e d e c a y c o n s t a n t ~, o f varying b, t h e r a t i o o f t h e t a n k v o l u m e t o c o l l e c t o r area.
115
Qaux = Q L exp(--kAc)
(i0)
The solar load ratio and the solar heating fraction are defined as functions of the heating needs only:
fo = Qech/QL,
fs = Qs/QL
Therefore: Q..x = QL(1 -- A)
(11)
For a period of N days and average daily radiation /~ (MJ/day), the solar energy available at the primary heat exchanger is a function of the collector parameters and of the utilizabilityq studied by Klein [12]:
Qech = AcF~(~"d)NH~o
(12)
The efficiency F~ of the primary circuit is a function of the collector heat removal factor FR and the effectiveness of the heat exchanger taken as a constant (E = 0.8).
Fh=FRE FR = thoco/AcUc [1 -- exp(--F' AcUc/rhoCo ) ]
(13) The present case of great flowrate of the fluid in the primary circuit (th 0 = 1 5 0 0 0 kg/h) gives a ratio of 14.64 for rhoco/A~U ~ and a removal factor of FR = 0.967 ( F ' is taken = 1). The solar load ratio is then varying as follows:
fo = 0.60AcNIV-I~O/QL
(14)
As in any solar active heating system, from the solar energy supplied to the house, the heat transfer of the available energy at the exchanges depends on the intermediate storage. One or more tanks and also part of the whole of the heating floor concrete play that role. The laws for no-stratified storage given b y Phillips [13] were adopted. f~ = 1 - - e x p [ - - e l f 0 ( 1 + C2f0)]
(15)
C1 is the efficiency of the system for weak values of the solar load ratio and gives then fs if f0 is known. Its expression was empirically developed from correlation functions and was used to develop simplified computational models able to give solar systems performances (European model ESM1 using m o n t h l y data [14]). The coefficient C2 was calculated to minimize the quadratic error of the solar annual ratio (by means of annual simulations with a transient simulation program).
C1 = 1 . 0 2 0 5 1 1 - 0.47 exp(--1.785Cs)]
(16)
Cs is a dimensionless term giving the "storage correction".
C~ = (MCp)~torage/tR AcF~ Uc
(17)
ta=21.06 hours is the storage-collector reference time. The effect of C2 only occurs for high heat capacitance of the storage (MCp> 100 MJ/K) and values of f0 >~ 0.3. Consequently, the decay coefficient can be drawn, from eqns. (10), (11) and (15): kAc = Cxf0(1 + C2fo) in o t h e r terms, in first approximation and taking account of eqn. (14): ;k = 0.60 C 1NH~p/QL The utilizability ~0 can be drawn from cumulated frequency tables [15] and is varying as well as the daily solar radiation with the given period. The most important parameter in the expression of ;k is the size of the load. This explains the t w o orders of magnitude factor for k between the case studied here of a multifamily building heating and the case studied by Chang of a family domestic hot water heating. Empirical laws used above give correct performances of the present system: for the period of March, simulated results of Qech, Qs and Qaux (cf. Table 1) lead to f0 = 1.07 and fs = 0.72, while with the same f0, empirical laws (for MCp = 58 MJ/K) lead to fs = 0.70 (C, = 0.93, C2 = 0.19). It is also interesting to check from the analytical role of the storage the experimental results obtained when the system was used for direct solar floor heating (DSFH). For almost an entire year, with Vtank = 10 m 3 on one side of the building, the results were Qech = 66 GJ and Qs = 48.8 GJ; the corresponding values on the other side with the D S H F are found to be Q~ch = 60 GJ and Qs = 51.8 GJ [4]. Equation (15) with a storage thermal capacitance of 58 MJ/K gives (with f~xp = 0.60) a solar heating fraction f~ = 0.46 in very good agreement with the experiments (0.44}. A more important part of the floor can be supposed to be involved in terms of its thermal capacitance in the D S F H case. The value f~xP= 0.54 is almost similar for both sides
116
and would lead with the thermal capacitance of the floor alone (87 MJ/K) to f, = 0.455 or fs = 0.46 if the walls are also supposed to be involved. The experimental value of fsexp~-0.47 is therefore probably overestimated inside the limits of error (every energy measurement has a 10% accuracy corresponding to an uncertainty for fs of +0.10). Whatever the case, a maximum storage thermal capacitance (300 MJ/K) would n o t allow (for annual f0 -~ 0.6) a solarratio greater than fs = 0.54, close to the values calculated above. The conclusion of this Section is that t h e solar heating system always increases the auxiliary energy savings by increasing the storage volume (the o p t i m u m working conditions being a b o u t two tanks and the maxim u m collector area). The opposite case Vtank = 0 similar to a D S F H installation could lead to comparable energy performance. The energy gain which seems to have been found by experiments in that case is smaller than the uncertainty on the corresponding energies.
b y the importance of the load in winter and the size of the system which is designed for six families. The analysis using the decay constant allows the optimum working conditions of the system with a storage volume close to 20 m 3 to be determined while the cheaper installation in a direct solar floor heating system would lead to performances almost as favourable.
ACKNOWLEDGEMENTS
The authors are grateful to G. Kuhn and P. Pataud for their help. This work was supported by C N R S (Centre National de la Recherche Scientifique) and A F M E (Agence Fran~aise pour la Ma£trise de l'Energie).
LIST OF SYMBOLS
Ac All
b 5. CONCLUSIONS
The TRNSYS program appeared to be very well adapted to describe the active solar heating system of a collective building. It gave reasonable computational costs in spite of the large size of the system. For reasons of cost, it was necessary to use a simplified model with only two differential equations for the space heating. The proposed model yielded accurate-enough energy values: the energy differences between calculations and the experimental values are several percent. The simulation gave interesting information on the distribution of heat losses and their magnitude, on the thermal capacitance effect of the building, and on the energy balance of the whole heating system. To represent the overall system performance, the analysis was based u p o n the interesting notion of decay constant )~ given previously by Chang and Minardi. The exponential relationship between the electrical auxiliary and the collector area was first checked. Then the )~ value was found to be 20 times lower for the p~esent system than for a standard DHW system for one family. This difference could be explained essentially
collector area (m 2) floor area (m 2) ratio of tank volume to collector area heat capacitance of the floor (kJ/
°c) Cl
Cp c0
FR f0 f, H h rh
rh0 Qaux Qech
Qm Q,
QL
heat capacitance of part of walls and floor (kJ/°C) specific heat of water (kJ/°C kg) specific heat of water-glycol (kJ/ °C kg) primary circuit effectiveness collector heat removal factor solar heat ratio solar heating fraction solar radiation (MJ) w a t e r - f l o o r heat exchange coefficient (kJ/h °C m 2) mass flow rate of the water in the coils (kg/s) mass flow rate of the water-glycol in the collector circuit (kg/s) auxiliary energy used (MJ) energy delivered at the heat exchanger (MJ) energy transmitted from the floor to the house (MJ) maximum auxiliary energy used (MJ) energy supplied from the storage to the floor (MJ) needs of the building (MJ)
117
QW
% Ti Tio AT
T, T, To Uo (UA)L V e (x k T
solar energy gains through windows (MJ) balance temperature (°C) floor temperature (°C) indoor temperature (°C) indoor set temperature (°C) temperature increase from
Modelling, Policy and Decision in Energy Systems, San Francisco, June, 1981, Acta Press.
the 8
the
i n t e r n a l gains (°C) temperature of the water entering tile f l o o r (°C) Tset (22 °C) t e m p e r a t u r e o f t h e s t o r a g e (°C) a m b i e n t t e m p e r a t u r e (°C) t e m p e r a t u r e o f t h e w a t e r at t h e f l o o r o u t l e t (°C) c o l l e c t o r loss c o e f f i c i e n t (MJ/°C m 2) h e a t losses c o e f f i c i e n t o f t h e building e n v e l o p e (MJ/°C) t a n k v o l u m e ( m 3) e m i t t a n c e e f f i c i e n c y o f t h e coils floor-air heat exchange coefficient ( K J / h °C m 2) e n e r g y d e c a y c o n s t a n t ( m -2) time constant(s)
N. Kernevez and F. Flouquet, Simulation with TRNYS of the heating system and of its regulation for the Bourgoin solar building, Proc. CEE International Conference, System Simulation in Buildings, Lidge, Belgium, December, 1982, XII/ 425/83-EN. 9 A. Gardel, B. Saugy and J. C. Hadorn, Simulation d'une Installation Solaire Active avec le programme TRNS YS, N 706.101/Sg.Hd/mp, Insti-
10 11 12 13
14
15 REFERENCES
1 W. Palz and T. C. Steemers, Solar Houses in Europe -- How They Have Worked, Commission of European Communities, Pergamon Press, Oxford, 1981. 2 F. Flouquet, N. Galanis, P. Pataud and A. Cordier, The Bourgoin-Jallieu experimental apartment building: simulation for different solar system characteristics. Proc. IASTED Energy Symposia -Modelling, Policy and Decision in Energy Systems, Montreal, May, 1980, Int. J. Energy Systems, 1
(3) (1981). 3 F. Flouquet, G. Kuhn and P. Pataud, Influence des param~tres du circuit capteur et de la dimension des cuves sur le systdme de stockage, CoUoque Stockage de rEnergie Solaire, Lyon, January, 1981, COFEDES Press, Paris.
4 G. Kuhn and P. Pataud, The Solar Building of Bourgoin-Jallieu, Proc. INTERSOL '85, Montreal, Pergamon Press, Oxford. 5 C. Aubert-Dmme, Comparaison d'un syst~me de stockage /t eau et d'un systtme de stockage par mat~riau ~ changement de phase sur l'immeuble solaire de Bourgoin-Jallieu, 3dme Cycle Thesis, Inst. Nat. Polytech. de Grenoble, France, June, 1981. 6 TRNSYS -- A
Transient Simulation Program,
The University of Wisconsin, Madison, 1982. 7 F. Flouquet, The Bourgoin-Jallieu experimental apartment building: optimization of the collector system, Proc. IASTED Energy S y m p o s i a -
tut d'Economie and Am~nagements Energ~tiques, Lausanne, Switzerland, December, 1980. K. K. Chang and A. Minardi, An optimization formulation for solar heating systems, Solar Energy, 24 (1980) 99 - 104. K. K. Chang, A. Minardi and T. Clay, Parametric study of the overall performance of a solar hot water system, Solar Energy, 29 (1982) 513 - 521. S. A. Klein, Calculation of fiat-plate utilizability, Solar Energy, 21 (1978) 393. W. F. Phillips, Integrated performance of liquidbased solar heating systems, Solar Energy, 24 (1980) 287. Effects of stratification on the performance of liquid-based solar heating systems, Solar Energy, 29 (2) (1982) 111. J. Adnot, B. Bourges and B. Peuportier, Moddlisation Solaire Active, Rapport, Centre d'Energ~tique, Ecole Nationale Sup~rieure des Mines de Paris, 1984. B. Bourges, Les courbes de fr~quences cumul~es de l'~clairement solaire: Analyse statistique et applications, Thdse de Docteur-lngdnieur, Universit~ Paris, June, 1980.
APPENDIX The T R N S Y S program analysis was made with the system data listed below: COLLECTOR: m o d e 1, area (Ac) = 152.5 m 2, efficiency factor (F')= 1, black painted steel absorber-type, single glazing of 6 m m , product transmittance absorptance (~-~)= 0.95 × 0.82, loss coefficient (Uc) = 25.2 kJ/h m 2 °C, water-glycol thermal capacitance Co = 3.75 kJ/kg °C, flow rate of the fluid in the collector circuit rho = 15 000 kg/h. MAIN
STORAGE:
tank volume (V)= 10.75
m 3 (or X2, or X3), t a n k h e i g h t (H) = 2 m , loss coefficient of the equivalent rectangular tank and tertiary incorporated pipes = 5.86 kJ/m 2 °C, 3 s t r a t i f i c a t i o n s e g m e n t s . C O L L E C T O R C I R C U I T PIPES: loss coeffic i e n t = 162 k J / h °C, h e a t c a p a c i t a n c e = 300
kJ/°C.
118
STORAGE C I R C U I T PIPES: loss coefficient = 200 kJ/h °C, heat capacitance = 550 kJl°C. SOLAR AND ELECTRIC DHW TANKS: volume = 1.5 m 3, height= 2.15 m, loss coefficient = 1.95 kJ/h m 2 °C, supply water temperature = 10 °C, tap temperature = 60 °C. F L O W R A T E S : 1000 kg/h in the solar D H W circuit, 15 000 kg/h in the collector and secondary circuits. PUMP
CONTROLLERS:
upper dead band =
5 °C and lower dead band = 0 °C for the secondary circuit, upper and lower dead band = 0 °C for DHW circuit.
Building data Ventilation = 0.8 air change per hour, loss coefficient (UA)T. = 4650 k J / h °C = 1.29 KW/ °C, temperature difference from the internal gains (AT) = 1.9 °C -+ 0.2 °C, coils diameter and length: ( d ) = 1.8 cm and (l)ffi 1512 m, floor area (A~l) = 550 m 2, flow rate in the coils (rh) = 5500 kg/h.