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A hybrid thermal energy storage system for managing simultaneously solar and electric energy
Energy Conversion and Management 47 (2006) 273–288 www.elsevier.com/locate/enconman
A hybrid thermal energy storage system for managing simultaneously solar and electric energy Zouhair Ait Hammou, Marcel Lacroix
*
Faculte´ de ge´nie, Universite´ de Sherbrooke, Sherbrooke, Que´bec, Canada J1K 2R1 Received 29 July 2004; accepted 17 January 2005 Available online 26 September 2005
Abstract A hybrid thermal energy storage system (HTESS) is proposed for managing simultaneously the storage of heat from solar and electric energy. Solar energy is stored during sunny days and released later during cloudy days or at night, and to smooth power demands, electric energy is stored during off peak periods and later used during peak periods. A heat transfer model of the HTESS is developed and validated with exact solutions and experimental data. Simulations are then performed to examine the effect of various storage materials and of the operating conditions on the thermal behaviour of the HTESS. The results indicate that the consumption of electricity for space heating is minimised when the HTESS consists of a 0.15 m thick wall comprising spherical capsules 0.065 m in diameter filled with n-octadecane. With such a system, the electric energy consumption during the month of January may be reduced by as much as 30%. 2005 Published by Elsevier Ltd. Keywords: Thermal energy storage; Phase change material; Solar energy; Electric energy
´ cole des Mines dÕAlbi Carmaux, Campus Jarlard, 81013 ALBI, Cedex 09, Corresponding author. Present address: E France. Tel.: +33 05 63 49 33 07; fax: +33 05 63 49 32 43. E-mail address: [email protected] (M. Lacroix). *
0196-8904/$ - see front matter 2005 Published by Elsevier Ltd. doi:10.1016/j.enconman.2005.01.003
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Nomenclature A Cp f h hsl k ma m_ n Q r R0 S00 t T T0 Tref T1 u U V z Greek a b q
surface (m2) heat capacity (J/kg K) liquid fraction convective heat transfer coefficient (W/m2 K) latent heat of fusion (J/kg) thermal conductivity (W/m K) mass of air in room (kg) mass flow rate (kg/s) number of spheres in a given layer energy (J) radial coordinate (m) outside radius of capsule (m) absorbed solar radiation (W/m2) time (s) temperature (K) coolant temperature (K) melting point (K) outside temperature (K) coolant velocity (m/s) overall heat transfer coefficient (W/m2 K) air volume in bed layer (m3) axial coordinate of HTESS (m) symbols inverse of Stefan number inverse of Biot number density (kg/m3)
Subscripts a air c capsule wall ex exterior f coolant j layer number in inlet l liquid N total number of horizontal layers s solid sp set point w, p, e west, centre and east control volumes
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Superscripts o old dimensionless variables *
1. Introduction In northern countries such as Canada, space heating represents the main source of electricity consumption in new homes. As a result, during harsh winter days, electric energy demand is increasingly acute in the morning and in the evening, and quite often, the distribution grid becomes overloaded. This severe problem has created the need to shift some of the on peak demand to off peak periods by making use of electric thermal storage systems. In these systems, electric energy is converted to thermal energy and stored in a material during the night and subsequently used the next day. During on peak periods, the current in the system is automatically shut off, and the storage unit discharges its heat to the living space. Of course, to agree to bear the additional cost involved in purchasing and installing a storage system, the customer benefits from lower electricity rates during off peak periods allowing him to obtain a return on his investment. An increasing number of new homes are also equipped with solar systems, passive or active, to further alleviate the problem of electricity consumption for space heating. Since the availability of solar energy is usually not coincident with the demand, heat collected from solar radiation is also stored in a thermal storage unit. For solar systems, however, heat is stored during sunny days and released later during cloudy days or at night. When both storage systems, electric and solar, are employed simultaneously, conflicting situations may arise, resulting in overheating the living space and/or poor thermal performance of the units. In spite of the fact that solar systems have been the subject of many investigations in the past [1–9], none of these studies has addressed the problem of simultaneous thermal storage of both solar and electric energy. The objective of the present paper is, therefore, to propose a system that can store and manage simultaneously and efficiently heat from both solar and electric sources. In this system, called hybrid thermal energy storage system (HTESS), solar energy is stored during sunny days and recovered later during cloudy days or at night, while thermal electric energy is stored during off peak periods and recovered during on peak periods. A mathematical model for predicting the thermal performance of the HTESS is first presented. The model is validated with exact solutions and with experimental data from a prototype. The effect of the storage media and of the operating conditions on the electricity consumption for space heating is then investigated.
2. Modelling the HTESS A schematic of the HTESS is depicted in Fig. 1. The HTESS consists chiefly of an interior wall of height H and width l filled with capsules of radius R containing either sensible heat storage material (SM) or phase change material (PCM) (Fig. 2). Heat is transferred via a stream of hot air, sometimes referred to as the coolant, coming from a solar collector and/or from an electric
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Fig. 1. Schematic of the hybrid thermal energy storage system.
Fig. 2. Capsule filled with phase change material.
heater. Heat is also collected from direct solar radiation on the wall. Openings at the bottom and at the top of the wall allow circulation of air from the room. The mass flow rate inside the storage wall is considered large enough so that the heat transfer in the coolant is convection dominated, while radial conduction heat transfer prevails inside the capsules. By dividing the bed of capsules into N horizontal layers of height Dz = 2R and assuming that within each layer, the coolant temperature is uniform [10], the energy conservation equations for the coolant, the PCM, the capsule wall and the adjacent room may be stated as
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oT f oT f _ pf þ DzmC ¼ nQ UAj ðT f T a Þ þ S 00 Aj ot oz oT ðr; tÞ 1 o of ðr; tÞ 2 oT ðr; tÞ ¼ 2 kr 0 r R0 ðPCMÞ qC p dH ot r or or ot
ðcoolantÞ V fj qf C pf
277
ð1Þ ð2aÞ
where dH ¼ qðC pl C ps ÞðT ðr; tÞ T ref Þ þ qhsl oT c ðr; tÞ 1 o 2 oT c ðr; tÞ ¼ 2 kcr ðwallÞ qc C pc R0 r R ot r or or ðroomÞ ma C pa
N X oT a _ pa ðT fN T a Þ þ U ex Aex ðT 1 T a Þ þ UAj ðT fj T a Þ ¼ mC ot j¼1
ð2bÞ ð3Þ
ð4Þ
Tf(z, t), T(r, t), Tc(r, t) and Ta(t) are the unknown coolant, phase change material, capsule wall and _ in Eq. (1), is the coolant mass flow rate defined as m_ ¼ Aj eqf u, room temperatures, respectively. m, V and e is the porosity defined as e ¼ V fjj where Vj = Aj Dz. The first term on the right hand side of Eq. (1) represents the heat transfer between the n capsules per horizontal layer and the surrounding coolant: nQ ¼ n4phR2 ðT c ðR; tÞ T f Þ
ð5Þ
h is the external heat transfer coefficient estimated with the empirical correlation proposed by Beek [11]. The second term on the right hand side of Eq. (1) represents the heat transfer between the coolant and the room, and in the last term, S00 represents the solar radiation in watts per square meter. The second term on the right hand side of Eq. (2a) accounts, via the liquid fraction f, for the solid/liquid phase change that takes place inside the PCM. For capsules made of sensible material, for example stones, this term vanishes. Finally, the second term on the right hand side of Eq. (4) represents the heat losses from the room to the outside atmosphere at temperature T1. The boundary conditions for the above set of Eqs. ((1)–(4)) are: For the coolant;
T f ðz; tÞ ¼ T in ðtÞ at z ¼ 0
ð6Þ
For the PCM and the capsule wall, oT ðr; tÞ ¼0 or k c 8 <
at r ¼ 0
ð7Þ
oT c ðr; tÞ ¼ hðT c ðr; tÞ T f Þ at r ¼ R or
oT c ðr; tÞ oT ðr; tÞ ¼ k or or : T c ðr; tÞ ¼ T ðr; tÞ k c
at r ¼ R00
ð8Þ
ð9Þ
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3. Numerical solution Eqs. (1)–(4) are solved using a finite difference solution method. The finite difference equation for the coolant, Eq. (1), is 1 T fj ¼ ðT ofj þ BT fj1 þ CT c þ DT a þ ES 00 Þ c
ð10Þ
where c¼1þ
UAj Dt m_ Dt 4pnhR2 Dt þ þ qf C pf V fj qf C pf V fj qf V fj
ð11Þ
and B¼
m_ Dt ; qf V fj
C¼
4pnhR2 Dt ; qf C pf V fj
D¼
UAj Dt ; qf C pf V fj
E¼
Aj Dt qf C pf V fj
ð12Þ
Integration of Eq. (2) over each of the control volumes in the radial direction within a capsule yields aP T P ¼ aE T E þ aW T W þ aoP T oP þ S s
ð13Þ
with aE ¼
k e ðT Þr2e ; dre
aW ¼
k w ðT Þr2w ; drw
aoP ¼ r2 qC p ðT Þ
Dr ; Dt
aP ¼ aE þ aW þ aoP
ð14Þ
and Dr re þ rw ð15Þ ; r ¼ 2 Dt The system of Eq. (13) is solved using a tri-diagonal matrix algorithm (TDMA). The central feature of the present fixed grid phase change method is the source term Ss. This source term keeps track of the latent heat evolution, and its driving element is the liquid fraction f. Its value is determined iteratively from [12] S s ¼ r2 dH P ðf f o Þ
fpmþ1 ¼ fpm þ x
ap Dt ðT p T ref Þ r2 dH P Dr
ð16Þ
where x is an under relaxation factor. The liquid fraction update Eq. (16) is applied at every node after the (m + 1)th solution of the linear system equation (13) for T. Since Eq. (16) is not adequate for every node, the correction ! <0 0 if f mþ1 p mþ1 ð17Þ fp ¼ >1 1 if f mþ1 p is applied immediately after Eq. (16). Further details concerning the numerical implementation of the present fixed grid phase change method may be found in the work of Voller [12].
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Start Initialization of the variables
t=t+dt
Read inlet coolant temperature J=1
J=J+1
Solution for capsules surface temperature Tc in layer J
Solution for coolant temperature T fj in layer J
No
J = N? Yes
Solution for room temperature Ta
No
t > tmax ? Yes Stop
Fig. 3. Overall calculation procedure.
The finite difference scheme for Eq. (3) resembles Eq. (13). Finally, integration of Eq. (4) yields ! N X 1 ð18Þ T oa þ BT 1 þ CT fN þ D Aj T fj Ta ¼ ca j¼1 where m_ Dt U ex Aex Dt ca ¼ 1 þ þ þ ma C pa ma
U Dt
N P j¼1
ma C pa
Aj ;
B¼
U ex Aex Dt ; ma C pa
C¼
m_ Dt ; ma
D¼
U Dt ma C pa
The overall calculation procedure is summarized in Fig. 3. 4. Validation The above numerical model has been thoroughly validated with analytical solutions and with numerical results available in the open literature. Two examples are reported here.
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First, the phase change model was confronted with the analytical solution reported by Shih and Chou [13] for the moving front position of a saturated liquid inside a spherical capsule (Fig. 4). k For the present exercise, the following dimensionless numbers were used: a ¼ Cps ðThrefsl T 0 Þ, b ¼ hR , r kt r ¼ R and t ¼ q Cps R2 . a is the inverse of the Stefan number, and b stands for the inverse of the s Biot number. Numerical solutions were obtained for a uniform space increment Dr = 0.001 m, a time step Dt = 2 s, a = 2 and three different values of b . As seen from Fig. 4, the agreement between the numerical predictions and the exact solution is excellent. Next, an experimental rig was set up to check the validity of the overall numerical model. The experimental prototype of the HTESS shown in Fig. 5, scale 1:6, consists of a water bath 0.5 m high, 0.5 m deep and 0.15 m wide with an adjoining 0.035 m thick storage wall made of concrete. The water reservoir is used to simulate the thermal behaviour of the room. Thermal energy is stored in the wall by means of (1) ribbon copper heaters covering uniformly its external surface in order to mimic the effect of direct solar radiation, (2) hot water flowing through vertical channels that run inside the wall in order to simulate the effect of heat transfer from a solar collector and (3) electric heaters embedded in the wall structure that simulate heat storage from electric sources. The electric power dissipated in the heaters is controlled by a power supply. Temperatures are measured with an accuracy of ±0.5 K by means of 32 copper–constantan thermocouples (type T) located in the water bath and distributed in the storage wall. Four heat flux meters and a flow meter are also used to estimate the surface heat fluxes and circulating water flow, respectively. The thermocouples, the meters and the electric heaters are all connected to a data acquisition system (32 channel multiplexer amplifiers and eight channel 12 bits A/D converter). Several laboratory experiments were performed for different heating and cooling scenarios, and numerical simulations were conducted simultaneously to mimic the observed thermal behaviour of the HTESS. As an example, Fig. 6 compares the temporal variation of the predicted and measured temperatures of the water bath for a scenario in which both the ribbon and embedded 1 Numerical prediction Exact solution Shih and Chou (1971)
0.9
Front position
0.8 ∗ β=4
0.7 0.6 ∗ β =2
0.5 0.4 ∗ β =1
0.3 0.2 0
0.5
1
1.5
2
t*/α*
Fig. 4. Comparison of the predicted phase front positions with exact solution.
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281
Fig. 5. Schematic of the experimental rig.
Fig. 6. Predicted and measured temperature of water bath.
heaters were employed. In this experiment, 250 W are first supplied to the ribbon heaters for a time period of 4788 s followed by a cooling period of 4788 s. Then, the 550 W electric heaters embedded in the concrete wall are turned on for a time period of 4788 s and finally turned off. The results shown in Fig. 6 reveal that the agreement between the numerical predictions and the data remains within the experimental uncertainty. 5. Results and discussion Now that the numerical model has been validated with numerical results and experimental data, a series of numerical simulations was conducted to assess the thermal performance of a
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typical HTESS in terms of the storage materials and the operating conditions. The room (Fig. 1) is 5 · 5 · 3 m, and the storage wall, 0.3 m thick, is filled with spherical capsules, 0.064 m in diameter, made of stone or made of polyethylene filled with different paraffin waxes. The physical properties of these materials are listed in Table 1. The simulations presented here were conducted for a time period of four consecutive days using meteorological data for the month of January in Montre´al, Canada. The corresponding solar radiation and outside air temperature are shown in Fig. 7 [14]. The initial temperatures of the room and of the HTESS were set equal to 294 K. The operating strategy for the HTESS is as follows: for the first two days, during off peak hours, i.e. from 00h00 to 07h00, the room air follows path DEB in Fig. 1. It passes through the auxiliary energy source at a rate m_ ¼ 0:08 kg s1, where its temperature increases from Ta to Tfin = 333 K. It then flows through the wall where its heat is transferred to the storage material. The total amount of electric energy consumed during the off peak hours is X X _ pa ð333 T a Þ Dt Qheat ðtÞ ¼ ð19Þ Qoff ¼ mC off -peak off -peak Table 1 Physical properties of materials
n-Octadecane (paraffin 1) Paraffine 5913 [15] (paraffin 2) Polyethylene Stone
Cpl (J/kg K)
Cps (J/kg K)
kl (W/m K)
ks (W/m K)
hsl (J/kg)
Tref (K)
q (kg/m3)
2231 2100 – –
1891 2100 2090 840
0.15 0.21 – –
0.38 0.21 0.33 0.125
243,477 189,000 – –
301.3 296 – –
773.2 900 960 1600
24
400
48
96 400 350
-2
S'' (W.m ) T∞(K)
300
300
250
250
200
200
150
150
100
100
50
50
0
0
24
48
72
× 3.610
Temperature (K)
Solar radiation (W.m-2)
350
72
0 96
3
Time (s)
Fig. 7. Hourly radiation on wall and outside air temperature during four consecutive days of January in Montre´al, Canada.
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During peak hours, which are from 07h00 to 00h00, space heating relies on direct solar radiation only. Moreover, if the temperature of the air flow emerging from the solar collector is larger than that of the room temperature, it is allowed to pass through (path AFC, Fig. 1). Otherwise, the room air flows through the wall via path CB where it retrieves some of the stored heat. During the last two days, no electricity is consumed and space heating relies entirely on the HTESS. As an example, Figs. 8 and 9 exemplify the thermal behaviour of the HTESS over the four day period using different storage materials. Paraffin 1 and 2 refers to a storage wall in which the bottom half consists of capsules filled with paraffin 1, and the top half consists of capsules filled with paraffin 2. Fig. 8 compares the energy provided by the HTESS Qprov(t) to the amount of energy that would otherwise be needed to maintain the temperature of the room at the set point Tsp = 294 K, Qnes(t). These amounts of energy are defined as " # X _ pa ðT fN T a Þ þ Qprov ðtÞ ¼ mC UAj ðT fj T a Þ Dt ð20Þ j
and Qnes ðtÞ ¼ Aex U ex ½T sp T 1 ðtÞ Dt
ð21Þ
respectively. The smaller the difference (Qnes(t) Qprov(t)), the better. Examination of these figures reveals immediately the advantages of PCMs (paraffin) over sensible materials (stones) for storing heat (Fig. 8) and for maintaining the temperature of the room at the set point Tsp = 294 K with minimal consumption of electricity. Considering the fact that a HTESS containing paraffin 1 and 2 is slightly more complicated to build, the HTESS filled with paraffin 1 is the most interesting and will be retained.
3000 Paraffin 1 Paraffin 2 Paraffin 1 and 2 Stones Qnes
2500
Energy (J)
2000
1500
1000
500
0
0
24
48
Time (s)
72
×3.6103
96
Fig. 8. Temporal variation of energy needed and energy provided by HTESS.
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290
Temperature (K)
280
270
260
Paraffin 1 Paraffin 2 Paraffin 1 and 2 Stones T∞
250
240
230 0
24
48
Time (s)
72
×3.6103
96
Fig. 9. Temporal variation of room temperature. T1 is the outside temperature.
If the room air temperature Ta(t) happens to exceed the set point Tsp, heat must be evacuated from the room. On the other hand, if Ta(t) becomes smaller than Tsp, an additional amount of electric energy Qrest must be spent to maintain the room air temperature at Tsp: X Qrest ¼ ½Qnes ðtÞ Qprov ðtÞ ð22Þ 4 days
As a result, the total amount of electric energy consumed during the course of the four day period is estimated as Qelec ¼ Qoff þ Qrest
ð23Þ
The electricity consumption for the storage materials examined here is summarized in Table 2. With no HTESS, the electricity consumption is 180 kW h, which is more than twice that of a room equipped with a HTESS filled with paraffin 1. Table 3 shows the corresponding heating costs (in monetary units) using a time-of-use rate scheme for which the peak hour rates are twice that of off peak hours.
Table 2 Energy consumption with off peak power HTESS
Qelec (off peak hours) (kW h)
Qelec (off peak hours) (kW h)
Qelec (off peak hours) (kW h)
Paraffin 1 Paraffin 2 Paraffin 1 and 2 Stones
69 73 69 89
18 27 20 62
87 100 89 151
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Table 3 Energy cost with off peak power HTESS
Cost (off peak hours) (monetary unit)
Cost (peak hours) (monetary unit)
Cost (total) (monetary unit)
Paraffin 1 Paraffin 2 Paraffin 1 and 2 Stones
69 · 1 73 · 1 69 · 1 89 · 1
18 · 2 27 · 2 20 · 2 62 · 2
105 127 109 213
The effect of the storage wall thickness on the HTESS performance was also investigated. Fig. 10 shows that as the wall thickness diminishes, energy is increasingly stored in the form of latent heat in the PCM. Consequently, the electricity consumption and the cost of the storage material is minimised for a 0.15 m thick wall (Table 4). As a final example, the thermal behaviour of a HTESS made of a 0.15 m thick wall containing capsules filled with n-octadecane was simulated for the entire month of January (Fig. 11). The control strategy retained here is similar to the one employed during the first two days of the previous simulations. The results indicate that the total electric energy consumption for space heating
60 HTESS thickness = 0.15 m HTESS thickness = 0.20 m HTESS thickness = 0.30 m HTESS thickness = 0.40 m
Molten volume fraction (%)
50
40
30
20
10
0
0
24
48
Time (s)
72
96
×3.6103
Fig. 10. Total molten volume fraction for different wall thickness.
Table 4 Electricity consumption with HTESS made of paraffin 1 Wall thickness (m) Qelec total (kW h)
0.15 83
0.2 85
0.3 87
0.4 88
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100
200
300
400
500
400
700
450 400
-2
S''( W.m ) T∞(K)
350
350
300
300
250
250
200
200
150
150
100
100
50
50
0
100
200
300
400
500
Time (s)
600
700
Temperature (K)
Solar radiation (W.m-2)
600
0
× 3.6103
Fig. 11. Hourly radiation on wall and outside air temperature for the entire month of January in Montre´al, Canada.
Table 5 Energy consumption with off peak power for one month HTESS
Qelec (off peak hours) (kW h)
Qelec (peak hours) (kW h)
Qelec (total) (kW h)
Paraffin 1
808
139
947
310
Ta T∞
300
Temperature (K)
290
280
270
260
250
240 0
100
200
300
400
Time (s)
500
600 700 ×3.6103
Fig. 12. Temporal variation of room temperature for the month of January. T1 is the outside temperature.
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is reduced from 1360 kW h (for a room without HTESS) to 947 kW h, which is a reduction of 30% (Table 5). Moreover, examination of Fig. 12 reveals that the room temperature sometimes exceeds the set point temperature of 294 K meaning that the HTESS supplies more energy than is needed. Using a more ingenious control strategy, this excess energy could be saved, and the electricity consumption further reduced. Various advanced control strategies are currently under study. The results of these investigations, which are beyond the scope of the present paper, will be reported later. 6. Concluding remarks A hybrid thermal energy storage system (HTESS) was proposed for managing simultaneously the storage of heat from solar and electric energy. A heat transfer model of the HTESS was developed and validated with exact solutions and experimental data. Simulations were conducted to examine the effect of various storage materials and of the operating conditions on the thermal behaviour of the HTESS. The results indicate that the consumption of electricity for space heating is minimised when the HTESS consists of a 0.15 m thick wall comprising spherical capsules 0.065 m in diameter filled with n-octadecane. With such a system, the electric energy consumption during the month of January in the city of Montre´al, Canada, may be reduced by as much as 30%. Further reduction in electricity consumption is expected with the implementation of an advanced control strategy. Acknowledgment The authors gratefully acknowledge the financial support of the Ministe`re des Ressources naturelles du Que´bec (projet PADTE) and of the Natural Sciences and Engineering Research Council of Canada. References [1] Duffie JA, Beckman WA. Solar engineering of thermal processes. 2nd ed. John Wiley; 1991. [2] Mbaye M, Bilgen E. Natural convection and conduction in porous wall, solar collector systems without vents. Trans ASME 1992;114:40–6. [3] Hsieh SS, Tsai JT. Transient response of the trombe wall temperature distribution applicable to passive solar heating systems. Energy Convers Manage 1988;28:21–5. [4] Abd Rabbo MF, Adam SK. Trombe wall heat transfer analysis. J Solar Energy Res 1988;6:1–19. [5] Telkes M. Thermal storage for solar heating and cooling. In: Proceedings of the workshop on solar energy storage subsystems for the heating and cooling of buildings, Virginia, USA, 1975. [6] Stritih U. Heat transfer enhancement in latent heat thermal storage system for buildings. Energy Bldgs 2003;35:1097–104. [7] Close DJ, Dunkle RV, Robeson KA. Design and performance of thermal storage air conditioner system. Mech Chem Eng Trans, Inst Engrs 1968;45. [8] Lo¨f GOG, Tybout RA. Cost of house heating with solar energy. Solar Energy 1973;14:253. [9] Evans BL, Klein SA. Combined active collection-passive storage and direct gain hybrid space systems. ASME Meeting, 1984.
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[10] Ismail KAR, Henriquez JR. Numerical and experimental study of spherical capsules packed bed latent heat storage system. Appl Thermal Eng 2002;22:1705–16. [11] Beek J. Design of packed catalytic reactors. Adv Chem Eng. 1962;3:203–71. [12] Voller VR. Fast implicit finite-difference method for the analysis of phase change problems. Numer Heat Transfer 1990;17:155–69. [13] Shih YP, Chou TC. Analytical solution for freezing a saturated liquid inside or outside spheres. Chem Eng Sci 1971;26:1787–93. [14] Available from http://www.eere.energy.gov. [15] Abhat A. Low temperature latent heat thermal energy storage: heat storage materials. Solar Energy 1983;30:313–32.
A hybrid thermal energy storage system for managing simultaneously solar and electric energy Zouhair Ait Hammou, Marcel Lacroix
*
Faculte´ de ge´nie, Universite´ de Sherbrooke, Sherbrooke, Que´bec, Canada J1K 2R1 Received 29 July 2004; accepted 17 January 2005 Available online 26 September 2005
Abstract A hybrid thermal energy storage system (HTESS) is proposed for managing simultaneously the storage of heat from solar and electric energy. Solar energy is stored during sunny days and released later during cloudy days or at night, and to smooth power demands, electric energy is stored during off peak periods and later used during peak periods. A heat transfer model of the HTESS is developed and validated with exact solutions and experimental data. Simulations are then performed to examine the effect of various storage materials and of the operating conditions on the thermal behaviour of the HTESS. The results indicate that the consumption of electricity for space heating is minimised when the HTESS consists of a 0.15 m thick wall comprising spherical capsules 0.065 m in diameter filled with n-octadecane. With such a system, the electric energy consumption during the month of January may be reduced by as much as 30%. 2005 Published by Elsevier Ltd. Keywords: Thermal energy storage; Phase change material; Solar energy; Electric energy
´ cole des Mines dÕAlbi Carmaux, Campus Jarlard, 81013 ALBI, Cedex 09, Corresponding author. Present address: E France. Tel.: +33 05 63 49 33 07; fax: +33 05 63 49 32 43. E-mail address: [email protected] (M. Lacroix). *
0196-8904/$ - see front matter 2005 Published by Elsevier Ltd. doi:10.1016/j.enconman.2005.01.003
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Nomenclature A Cp f h hsl k ma m_ n Q r R0 S00 t T T0 Tref T1 u U V z Greek a b q
surface (m2) heat capacity (J/kg K) liquid fraction convective heat transfer coefficient (W/m2 K) latent heat of fusion (J/kg) thermal conductivity (W/m K) mass of air in room (kg) mass flow rate (kg/s) number of spheres in a given layer energy (J) radial coordinate (m) outside radius of capsule (m) absorbed solar radiation (W/m2) time (s) temperature (K) coolant temperature (K) melting point (K) outside temperature (K) coolant velocity (m/s) overall heat transfer coefficient (W/m2 K) air volume in bed layer (m3) axial coordinate of HTESS (m) symbols inverse of Stefan number inverse of Biot number density (kg/m3)
Subscripts a air c capsule wall ex exterior f coolant j layer number in inlet l liquid N total number of horizontal layers s solid sp set point w, p, e west, centre and east control volumes
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275
Superscripts o old dimensionless variables *
1. Introduction In northern countries such as Canada, space heating represents the main source of electricity consumption in new homes. As a result, during harsh winter days, electric energy demand is increasingly acute in the morning and in the evening, and quite often, the distribution grid becomes overloaded. This severe problem has created the need to shift some of the on peak demand to off peak periods by making use of electric thermal storage systems. In these systems, electric energy is converted to thermal energy and stored in a material during the night and subsequently used the next day. During on peak periods, the current in the system is automatically shut off, and the storage unit discharges its heat to the living space. Of course, to agree to bear the additional cost involved in purchasing and installing a storage system, the customer benefits from lower electricity rates during off peak periods allowing him to obtain a return on his investment. An increasing number of new homes are also equipped with solar systems, passive or active, to further alleviate the problem of electricity consumption for space heating. Since the availability of solar energy is usually not coincident with the demand, heat collected from solar radiation is also stored in a thermal storage unit. For solar systems, however, heat is stored during sunny days and released later during cloudy days or at night. When both storage systems, electric and solar, are employed simultaneously, conflicting situations may arise, resulting in overheating the living space and/or poor thermal performance of the units. In spite of the fact that solar systems have been the subject of many investigations in the past [1–9], none of these studies has addressed the problem of simultaneous thermal storage of both solar and electric energy. The objective of the present paper is, therefore, to propose a system that can store and manage simultaneously and efficiently heat from both solar and electric sources. In this system, called hybrid thermal energy storage system (HTESS), solar energy is stored during sunny days and recovered later during cloudy days or at night, while thermal electric energy is stored during off peak periods and recovered during on peak periods. A mathematical model for predicting the thermal performance of the HTESS is first presented. The model is validated with exact solutions and with experimental data from a prototype. The effect of the storage media and of the operating conditions on the electricity consumption for space heating is then investigated.
2. Modelling the HTESS A schematic of the HTESS is depicted in Fig. 1. The HTESS consists chiefly of an interior wall of height H and width l filled with capsules of radius R containing either sensible heat storage material (SM) or phase change material (PCM) (Fig. 2). Heat is transferred via a stream of hot air, sometimes referred to as the coolant, coming from a solar collector and/or from an electric
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Fig. 1. Schematic of the hybrid thermal energy storage system.
Fig. 2. Capsule filled with phase change material.
heater. Heat is also collected from direct solar radiation on the wall. Openings at the bottom and at the top of the wall allow circulation of air from the room. The mass flow rate inside the storage wall is considered large enough so that the heat transfer in the coolant is convection dominated, while radial conduction heat transfer prevails inside the capsules. By dividing the bed of capsules into N horizontal layers of height Dz = 2R and assuming that within each layer, the coolant temperature is uniform [10], the energy conservation equations for the coolant, the PCM, the capsule wall and the adjacent room may be stated as
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oT f oT f _ pf þ DzmC ¼ nQ UAj ðT f T a Þ þ S 00 Aj ot oz oT ðr; tÞ 1 o of ðr; tÞ 2 oT ðr; tÞ ¼ 2 kr 0 r R0 ðPCMÞ qC p dH ot r or or ot
ðcoolantÞ V fj qf C pf
277
ð1Þ ð2aÞ
where dH ¼ qðC pl C ps ÞðT ðr; tÞ T ref Þ þ qhsl oT c ðr; tÞ 1 o 2 oT c ðr; tÞ ¼ 2 kcr ðwallÞ qc C pc R0 r R ot r or or ðroomÞ ma C pa
N X oT a _ pa ðT fN T a Þ þ U ex Aex ðT 1 T a Þ þ UAj ðT fj T a Þ ¼ mC ot j¼1
ð2bÞ ð3Þ
ð4Þ
Tf(z, t), T(r, t), Tc(r, t) and Ta(t) are the unknown coolant, phase change material, capsule wall and _ in Eq. (1), is the coolant mass flow rate defined as m_ ¼ Aj eqf u, room temperatures, respectively. m, V and e is the porosity defined as e ¼ V fjj where Vj = Aj Dz. The first term on the right hand side of Eq. (1) represents the heat transfer between the n capsules per horizontal layer and the surrounding coolant: nQ ¼ n4phR2 ðT c ðR; tÞ T f Þ
ð5Þ
h is the external heat transfer coefficient estimated with the empirical correlation proposed by Beek [11]. The second term on the right hand side of Eq. (1) represents the heat transfer between the coolant and the room, and in the last term, S00 represents the solar radiation in watts per square meter. The second term on the right hand side of Eq. (2a) accounts, via the liquid fraction f, for the solid/liquid phase change that takes place inside the PCM. For capsules made of sensible material, for example stones, this term vanishes. Finally, the second term on the right hand side of Eq. (4) represents the heat losses from the room to the outside atmosphere at temperature T1. The boundary conditions for the above set of Eqs. ((1)–(4)) are: For the coolant;
T f ðz; tÞ ¼ T in ðtÞ at z ¼ 0
ð6Þ
For the PCM and the capsule wall, oT ðr; tÞ ¼0 or k c 8 <
at r ¼ 0
ð7Þ
oT c ðr; tÞ ¼ hðT c ðr; tÞ T f Þ at r ¼ R or
oT c ðr; tÞ oT ðr; tÞ ¼ k or or : T c ðr; tÞ ¼ T ðr; tÞ k c
at r ¼ R00
ð8Þ
ð9Þ
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3. Numerical solution Eqs. (1)–(4) are solved using a finite difference solution method. The finite difference equation for the coolant, Eq. (1), is 1 T fj ¼ ðT ofj þ BT fj1 þ CT c þ DT a þ ES 00 Þ c
ð10Þ
where c¼1þ
UAj Dt m_ Dt 4pnhR2 Dt þ þ qf C pf V fj qf C pf V fj qf V fj
ð11Þ
and B¼
m_ Dt ; qf V fj
C¼
4pnhR2 Dt ; qf C pf V fj
D¼
UAj Dt ; qf C pf V fj
E¼
Aj Dt qf C pf V fj
ð12Þ
Integration of Eq. (2) over each of the control volumes in the radial direction within a capsule yields aP T P ¼ aE T E þ aW T W þ aoP T oP þ S s
ð13Þ
with aE ¼
k e ðT Þr2e ; dre
aW ¼
k w ðT Þr2w ; drw
aoP ¼ r2 qC p ðT Þ
Dr ; Dt
aP ¼ aE þ aW þ aoP
ð14Þ
and Dr re þ rw ð15Þ ; r ¼ 2 Dt The system of Eq. (13) is solved using a tri-diagonal matrix algorithm (TDMA). The central feature of the present fixed grid phase change method is the source term Ss. This source term keeps track of the latent heat evolution, and its driving element is the liquid fraction f. Its value is determined iteratively from [12] S s ¼ r2 dH P ðf f o Þ
fpmþ1 ¼ fpm þ x
ap Dt ðT p T ref Þ r2 dH P Dr
ð16Þ
where x is an under relaxation factor. The liquid fraction update Eq. (16) is applied at every node after the (m + 1)th solution of the linear system equation (13) for T. Since Eq. (16) is not adequate for every node, the correction ! <0 0 if f mþ1 p mþ1 ð17Þ fp ¼ >1 1 if f mþ1 p is applied immediately after Eq. (16). Further details concerning the numerical implementation of the present fixed grid phase change method may be found in the work of Voller [12].
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279
Start Initialization of the variables
t=t+dt
Read inlet coolant temperature J=1
J=J+1
Solution for capsules surface temperature Tc in layer J
Solution for coolant temperature T fj in layer J
No
J = N? Yes
Solution for room temperature Ta
No
t > tmax ? Yes Stop
Fig. 3. Overall calculation procedure.
The finite difference scheme for Eq. (3) resembles Eq. (13). Finally, integration of Eq. (4) yields ! N X 1 ð18Þ T oa þ BT 1 þ CT fN þ D Aj T fj Ta ¼ ca j¼1 where m_ Dt U ex Aex Dt ca ¼ 1 þ þ þ ma C pa ma
U Dt
N P j¼1
ma C pa
Aj ;
B¼
U ex Aex Dt ; ma C pa
C¼
m_ Dt ; ma
D¼
U Dt ma C pa
The overall calculation procedure is summarized in Fig. 3. 4. Validation The above numerical model has been thoroughly validated with analytical solutions and with numerical results available in the open literature. Two examples are reported here.
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First, the phase change model was confronted with the analytical solution reported by Shih and Chou [13] for the moving front position of a saturated liquid inside a spherical capsule (Fig. 4). k For the present exercise, the following dimensionless numbers were used: a ¼ Cps ðThrefsl T 0 Þ, b ¼ hR , r kt r ¼ R and t ¼ q Cps R2 . a is the inverse of the Stefan number, and b stands for the inverse of the s Biot number. Numerical solutions were obtained for a uniform space increment Dr = 0.001 m, a time step Dt = 2 s, a = 2 and three different values of b . As seen from Fig. 4, the agreement between the numerical predictions and the exact solution is excellent. Next, an experimental rig was set up to check the validity of the overall numerical model. The experimental prototype of the HTESS shown in Fig. 5, scale 1:6, consists of a water bath 0.5 m high, 0.5 m deep and 0.15 m wide with an adjoining 0.035 m thick storage wall made of concrete. The water reservoir is used to simulate the thermal behaviour of the room. Thermal energy is stored in the wall by means of (1) ribbon copper heaters covering uniformly its external surface in order to mimic the effect of direct solar radiation, (2) hot water flowing through vertical channels that run inside the wall in order to simulate the effect of heat transfer from a solar collector and (3) electric heaters embedded in the wall structure that simulate heat storage from electric sources. The electric power dissipated in the heaters is controlled by a power supply. Temperatures are measured with an accuracy of ±0.5 K by means of 32 copper–constantan thermocouples (type T) located in the water bath and distributed in the storage wall. Four heat flux meters and a flow meter are also used to estimate the surface heat fluxes and circulating water flow, respectively. The thermocouples, the meters and the electric heaters are all connected to a data acquisition system (32 channel multiplexer amplifiers and eight channel 12 bits A/D converter). Several laboratory experiments were performed for different heating and cooling scenarios, and numerical simulations were conducted simultaneously to mimic the observed thermal behaviour of the HTESS. As an example, Fig. 6 compares the temporal variation of the predicted and measured temperatures of the water bath for a scenario in which both the ribbon and embedded 1 Numerical prediction Exact solution Shih and Chou (1971)
0.9
Front position
0.8 ∗ β=4
0.7 0.6 ∗ β =2
0.5 0.4 ∗ β =1
0.3 0.2 0
0.5
1
1.5
2
t*/α*
Fig. 4. Comparison of the predicted phase front positions with exact solution.
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281
Fig. 5. Schematic of the experimental rig.
Fig. 6. Predicted and measured temperature of water bath.
heaters were employed. In this experiment, 250 W are first supplied to the ribbon heaters for a time period of 4788 s followed by a cooling period of 4788 s. Then, the 550 W electric heaters embedded in the concrete wall are turned on for a time period of 4788 s and finally turned off. The results shown in Fig. 6 reveal that the agreement between the numerical predictions and the data remains within the experimental uncertainty. 5. Results and discussion Now that the numerical model has been validated with numerical results and experimental data, a series of numerical simulations was conducted to assess the thermal performance of a
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typical HTESS in terms of the storage materials and the operating conditions. The room (Fig. 1) is 5 · 5 · 3 m, and the storage wall, 0.3 m thick, is filled with spherical capsules, 0.064 m in diameter, made of stone or made of polyethylene filled with different paraffin waxes. The physical properties of these materials are listed in Table 1. The simulations presented here were conducted for a time period of four consecutive days using meteorological data for the month of January in Montre´al, Canada. The corresponding solar radiation and outside air temperature are shown in Fig. 7 [14]. The initial temperatures of the room and of the HTESS were set equal to 294 K. The operating strategy for the HTESS is as follows: for the first two days, during off peak hours, i.e. from 00h00 to 07h00, the room air follows path DEB in Fig. 1. It passes through the auxiliary energy source at a rate m_ ¼ 0:08 kg s1, where its temperature increases from Ta to Tfin = 333 K. It then flows through the wall where its heat is transferred to the storage material. The total amount of electric energy consumed during the off peak hours is X X _ pa ð333 T a Þ Dt Qheat ðtÞ ¼ ð19Þ Qoff ¼ mC off -peak off -peak Table 1 Physical properties of materials
n-Octadecane (paraffin 1) Paraffine 5913 [15] (paraffin 2) Polyethylene Stone
Cpl (J/kg K)
Cps (J/kg K)
kl (W/m K)
ks (W/m K)
hsl (J/kg)
Tref (K)
q (kg/m3)
2231 2100 – –
1891 2100 2090 840
0.15 0.21 – –
0.38 0.21 0.33 0.125
243,477 189,000 – –
301.3 296 – –
773.2 900 960 1600
24
400
48
96 400 350
-2
S'' (W.m ) T∞(K)
300
300
250
250
200
200
150
150
100
100
50
50
0
0
24
48
72
× 3.610
Temperature (K)
Solar radiation (W.m-2)
350
72
0 96
3
Time (s)
Fig. 7. Hourly radiation on wall and outside air temperature during four consecutive days of January in Montre´al, Canada.
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283
During peak hours, which are from 07h00 to 00h00, space heating relies on direct solar radiation only. Moreover, if the temperature of the air flow emerging from the solar collector is larger than that of the room temperature, it is allowed to pass through (path AFC, Fig. 1). Otherwise, the room air flows through the wall via path CB where it retrieves some of the stored heat. During the last two days, no electricity is consumed and space heating relies entirely on the HTESS. As an example, Figs. 8 and 9 exemplify the thermal behaviour of the HTESS over the four day period using different storage materials. Paraffin 1 and 2 refers to a storage wall in which the bottom half consists of capsules filled with paraffin 1, and the top half consists of capsules filled with paraffin 2. Fig. 8 compares the energy provided by the HTESS Qprov(t) to the amount of energy that would otherwise be needed to maintain the temperature of the room at the set point Tsp = 294 K, Qnes(t). These amounts of energy are defined as " # X _ pa ðT fN T a Þ þ Qprov ðtÞ ¼ mC UAj ðT fj T a Þ Dt ð20Þ j
and Qnes ðtÞ ¼ Aex U ex ½T sp T 1 ðtÞ Dt
ð21Þ
respectively. The smaller the difference (Qnes(t) Qprov(t)), the better. Examination of these figures reveals immediately the advantages of PCMs (paraffin) over sensible materials (stones) for storing heat (Fig. 8) and for maintaining the temperature of the room at the set point Tsp = 294 K with minimal consumption of electricity. Considering the fact that a HTESS containing paraffin 1 and 2 is slightly more complicated to build, the HTESS filled with paraffin 1 is the most interesting and will be retained.
3000 Paraffin 1 Paraffin 2 Paraffin 1 and 2 Stones Qnes
2500
Energy (J)
2000
1500
1000
500
0
0
24
48
Time (s)
72
×3.6103
96
Fig. 8. Temporal variation of energy needed and energy provided by HTESS.
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290
Temperature (K)
280
270
260
Paraffin 1 Paraffin 2 Paraffin 1 and 2 Stones T∞
250
240
230 0
24
48
Time (s)
72
×3.6103
96
Fig. 9. Temporal variation of room temperature. T1 is the outside temperature.
If the room air temperature Ta(t) happens to exceed the set point Tsp, heat must be evacuated from the room. On the other hand, if Ta(t) becomes smaller than Tsp, an additional amount of electric energy Qrest must be spent to maintain the room air temperature at Tsp: X Qrest ¼ ½Qnes ðtÞ Qprov ðtÞ ð22Þ 4 days
As a result, the total amount of electric energy consumed during the course of the four day period is estimated as Qelec ¼ Qoff þ Qrest
ð23Þ
The electricity consumption for the storage materials examined here is summarized in Table 2. With no HTESS, the electricity consumption is 180 kW h, which is more than twice that of a room equipped with a HTESS filled with paraffin 1. Table 3 shows the corresponding heating costs (in monetary units) using a time-of-use rate scheme for which the peak hour rates are twice that of off peak hours.
Table 2 Energy consumption with off peak power HTESS
Qelec (off peak hours) (kW h)
Qelec (off peak hours) (kW h)
Qelec (off peak hours) (kW h)
Paraffin 1 Paraffin 2 Paraffin 1 and 2 Stones
69 73 69 89
18 27 20 62
87 100 89 151
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Table 3 Energy cost with off peak power HTESS
Cost (off peak hours) (monetary unit)
Cost (peak hours) (monetary unit)
Cost (total) (monetary unit)
Paraffin 1 Paraffin 2 Paraffin 1 and 2 Stones
69 · 1 73 · 1 69 · 1 89 · 1
18 · 2 27 · 2 20 · 2 62 · 2
105 127 109 213
The effect of the storage wall thickness on the HTESS performance was also investigated. Fig. 10 shows that as the wall thickness diminishes, energy is increasingly stored in the form of latent heat in the PCM. Consequently, the electricity consumption and the cost of the storage material is minimised for a 0.15 m thick wall (Table 4). As a final example, the thermal behaviour of a HTESS made of a 0.15 m thick wall containing capsules filled with n-octadecane was simulated for the entire month of January (Fig. 11). The control strategy retained here is similar to the one employed during the first two days of the previous simulations. The results indicate that the total electric energy consumption for space heating
60 HTESS thickness = 0.15 m HTESS thickness = 0.20 m HTESS thickness = 0.30 m HTESS thickness = 0.40 m
Molten volume fraction (%)
50
40
30
20
10
0
0
24
48
Time (s)
72
96
×3.6103
Fig. 10. Total molten volume fraction for different wall thickness.
Table 4 Electricity consumption with HTESS made of paraffin 1 Wall thickness (m) Qelec total (kW h)
0.15 83
0.2 85
0.3 87
0.4 88
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100
200
300
400
500
400
700
450 400
-2
S''( W.m ) T∞(K)
350
350
300
300
250
250
200
200
150
150
100
100
50
50
0
100
200
300
400
500
Time (s)
600
700
Temperature (K)
Solar radiation (W.m-2)
600
0
× 3.6103
Fig. 11. Hourly radiation on wall and outside air temperature for the entire month of January in Montre´al, Canada.
Table 5 Energy consumption with off peak power for one month HTESS
Qelec (off peak hours) (kW h)
Qelec (peak hours) (kW h)
Qelec (total) (kW h)
Paraffin 1
808
139
947
310
Ta T∞
300
Temperature (K)
290
280
270
260
250
240 0
100
200
300
400
Time (s)
500
600 700 ×3.6103
Fig. 12. Temporal variation of room temperature for the month of January. T1 is the outside temperature.
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287
is reduced from 1360 kW h (for a room without HTESS) to 947 kW h, which is a reduction of 30% (Table 5). Moreover, examination of Fig. 12 reveals that the room temperature sometimes exceeds the set point temperature of 294 K meaning that the HTESS supplies more energy than is needed. Using a more ingenious control strategy, this excess energy could be saved, and the electricity consumption further reduced. Various advanced control strategies are currently under study. The results of these investigations, which are beyond the scope of the present paper, will be reported later. 6. Concluding remarks A hybrid thermal energy storage system (HTESS) was proposed for managing simultaneously the storage of heat from solar and electric energy. A heat transfer model of the HTESS was developed and validated with exact solutions and experimental data. Simulations were conducted to examine the effect of various storage materials and of the operating conditions on the thermal behaviour of the HTESS. The results indicate that the consumption of electricity for space heating is minimised when the HTESS consists of a 0.15 m thick wall comprising spherical capsules 0.065 m in diameter filled with n-octadecane. With such a system, the electric energy consumption during the month of January in the city of Montre´al, Canada, may be reduced by as much as 30%. Further reduction in electricity consumption is expected with the implementation of an advanced control strategy. Acknowledgment The authors gratefully acknowledge the financial support of the Ministe`re des Ressources naturelles du Que´bec (projet PADTE) and of the Natural Sciences and Engineering Research Council of Canada. References [1] Duffie JA, Beckman WA. Solar engineering of thermal processes. 2nd ed. John Wiley; 1991. [2] Mbaye M, Bilgen E. Natural convection and conduction in porous wall, solar collector systems without vents. Trans ASME 1992;114:40–6. [3] Hsieh SS, Tsai JT. Transient response of the trombe wall temperature distribution applicable to passive solar heating systems. Energy Convers Manage 1988;28:21–5. [4] Abd Rabbo MF, Adam SK. Trombe wall heat transfer analysis. J Solar Energy Res 1988;6:1–19. [5] Telkes M. Thermal storage for solar heating and cooling. In: Proceedings of the workshop on solar energy storage subsystems for the heating and cooling of buildings, Virginia, USA, 1975. [6] Stritih U. Heat transfer enhancement in latent heat thermal storage system for buildings. Energy Bldgs 2003;35:1097–104. [7] Close DJ, Dunkle RV, Robeson KA. Design and performance of thermal storage air conditioner system. Mech Chem Eng Trans, Inst Engrs 1968;45. [8] Lo¨f GOG, Tybout RA. Cost of house heating with solar energy. Solar Energy 1973;14:253. [9] Evans BL, Klein SA. Combined active collection-passive storage and direct gain hybrid space systems. ASME Meeting, 1984.
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[10] Ismail KAR, Henriquez JR. Numerical and experimental study of spherical capsules packed bed latent heat storage system. Appl Thermal Eng 2002;22:1705–16. [11] Beek J. Design of packed catalytic reactors. Adv Chem Eng. 1962;3:203–71. [12] Voller VR. Fast implicit finite-difference method for the analysis of phase change problems. Numer Heat Transfer 1990;17:155–69. [13] Shih YP, Chou TC. Analytical solution for freezing a saturated liquid inside or outside spheres. Chem Eng Sci 1971;26:1787–93. [14] Available from http://www.eere.energy.gov. [15] Abhat A. Low temperature latent heat thermal energy storage: heat storage materials. Solar Energy 1983;30:313–32.