- Email: [email protected]
Storage composites for the optimisation of solar water heating systems
c h e m i c a l e n g i n e e r i n g r e s e a r c h a n d d e s i g n 8 6 ( 2 0 0 8 ) 612–617
available at www.sciencedirect.com
journal homepage: www.elsevier.com/locate/cherd
Storage composites for the optimisation of solar water heating systems Didier Haillot a,b,∗ , Xavier Py a , Vincent Goetz a , Mohamed Benabdelkarim b a
PROMES CNRS UPR8521 Process, Materials and Solar Energy Laboratory, Universit´e de Perpignan Via Domitia, Rambla de la Thermodynamique Tecnosud 66100, Perpignan, France b Saunier Duval Eau Chaude Chauffage Industrie, 17 rue de la Petite Baratte, BP 44315, Nantes Cedex 03, France
a r t i c l e
i n f o
a b s t r a c t
Article history:
Composite materials based on expanded natural graphite (CENG) and various phase change
Received 21 September 2007
materials (PCM) have been developed for low temperature solar applications (323–373 K).
Accepted 24 January 2008
The integration of such composite materials directly into the solar collector could allow new storage functionality. A numerical model has been developed to describe the materials behaviour. Composites properties are presented and discussed.
Keywords:
© 2008 Published by Elsevier B.V. on behalf of The Institution of Chemical Engineers.
Phase change materials Thermal storage Solar heater Modelling
1.
Introduction
The increasing price of fossil fuels and awareness of environmental issues have caused growing interest towards renewable energy. Due to their low cost and simplicity, solar water heating systems including flat plate collectors or vacuum tube panel are the most widely commercialized systems. The optimisation of solar systems must invariably involve energy storage to smooth the influence of solar variations like day/night successions or cloud effects and to be able to manage the variations in energetic demand. Within the last decade, several configurations of solar water heating systems including integrated storage have been tested using concrete (Hazami et al., 2005), hydrated salts (Rabin et al., 1995), myristic acid (Tarhan et al., 2006) or paraffin (Mettawee and Assassa, 2004) as storage media. These systems allow rather effective heat charge and discharge steps. Nevertheless, discharge step seems to be significantly controlled by the thermal conductivity of the storage media. In the present work, composite storage materials based on phase change materials (PCM) and compressed expanded natural graphite (CENG) are presented. Two different tech-
∗
niques, leading to anisotropic properties, have been developed to elaborate these composites: cold compression (for inorganic PCM) and warm impregnation (for organic PCM). Composite thermal conductivities, storage capacities and thermal stabilities have been characterised. Dynamic modelling was carried out by using the FEMLAB software from COMSOL. The model allows the description of the composite behaviour under both the storage step under solar flux and the discharge ensured by the flow of a heat transfer fluid. Corresponding results obtained for different materials of various thermal conductivities underline the high potentiality of those new composites.
2.
Experimental investigation
2.1.
Investigated materials
Globally, there are two main PCM categories: organic PCM, and inorganic PCM also known as salts. Main characteristics of those materials are given in the following Table 1. This table presents only some of the PCM currently listed and is not thorough. We could notify, as an example, other promising organic
Corresponding author at: PROMES CNRS UPR8521, Rambla de la thermodynamique Tecnosud 66100, Perpignan, France. E-mail address: [email protected] (D. Haillot). 0263-8762/$ – see front matter © 2008 Published by Elsevier B.V. on behalf of The Institution of Chemical Engineers. doi:10.1016/j.cherd.2008.01.007
613
c h e m i c a l e n g i n e e r i n g r e s e a r c h a n d d e s i g n 8 6 ( 2 0 0 8 ) 612–617
Nomenclature cp h L rf rc t T u
calorific capacity (J kg−1 K−1 ) convective exchange coefficient (W m−2 K−1 ) tube length (m) tube radius (m) double casing radius (m) temps (s) temperature (K) velocity (m s−1 )
Symbols thermal conductivity (W m−1 K−1 ) density (kg m−3 ) H specific enthalpy of phase transition (kJ kg−1 ) Subscripts CENG compressed expanded natural graphite f fluid sf fusion/solidification PCM phase change material c composite
Fig. 1 – Composites storage capacity per volume (open symbol) and per mass (black symbol) vs. graphite matrix density.
PCM as poly(ethylene glycol) (Pielichowski and Flejtuch, 2002) or polyether (Pielichowski and Flejtuch, 2003). The criteria for the selection of the most appropriate PCM must include: price, toxicity, phase change temperature and storage capacity. According to such approach, the PCM tested in the present work are: RT65 paraffin (www.rubitherm.com), stearic acid, sodium acetate tri-hydrated (CH3 COONa·3H2 O) and barium hydroxide octa-hydrated (Ba(OH)2 ·8H2 O). The tested graphite was in the form of expanded worms obtained by the thermal exfoliation of inserted natural graphite flakes.
2.2.
PCM/CENG composite materials elaboration
Concerning the warm impregnation route, expanded graphite powders is first poured into a cubic mould of aluminium and then pressed to obtain a consolidated porous graphite matrix of a desired bulk density (Py et al., 2000). This matrix is then soaked into melted paraffin and then, regularly weighted until maximum load is reached. This technique has been found to be very relevant in the case of organic PCM but rather inefficient for inorganic PCM. Concerning the cold compression route, CENG and PCM powders are mixed together and shaped in a mould by cold axial compression (Pincemin et al., 2008). At ambient temperature, the obtained materials elaborated by the two methods are stable. These two techniques lead to an anisotropic composite structure inherited from the spatial
rearrangement of the graphen layers under axial compression. According to the graphite layers orientations, the thermal conductivity parallel to the compression axis (axial direction) is much lower than the thermal conductivity perpendicular to the compression axis (radial direction).
2.3. Theoretical storage capacity of the PCM/CENG composites In Fig. 1 are presented the theoretical storage capacities of the composite materials per unit of volume or mass, according to enthalpy values from Zalba et al. (2003) and Abhat (1983). As the graphite density in the composite increases, the relative amount of PCM and therefore the storage capacity decrease. Globally, inorganic PCMs have larger storage capacity than organic PCMs. Theoretically hydroxide barium octa-hydrated is found to be the best PCM in term of specific enthalpy per mass and per volume (240 kJ kg−1 and 50 × 104 kJ m−3 at CENG = 150 kg m−3 ). Nevertheless, as explained below, the hydrated salts present unstable behaviour above 373 K.
2.4.
Thermal analysis of the composites
The storage capacity of the materials has been measured using a Setaram C80 calorimeter. The integration of the peak surfaces during the fusion and the solidification steps lead to corresponding effective storage capacity values. The analysis of the paraffin RT65 curves leads to a latent heat of 170 kJ kg−1 and a fusion/solidification temperature of 338 ± 1 K in agree-
Table 1 – Organic/inorganic PCM comparison Advantages
Disadvantages
Organic (paraffin, fatty acids)
Low toxicity Low/or no supercooling
Segregation Inflammable Moderate storage capacity
Inorganic (pure or hydrated salts, eutectics)
High storage capacity Fireproof
Supercooling, segregation Corrosion, hygroscopic Crystallographic structure Evolution with temperature
614
c h e m i c a l e n g i n e e r i n g r e s e a r c h a n d d e s i g n 8 6 ( 2 0 0 8 ) 612–617
acid). The composite anisotropy is underlined by significantly lower axial thermal conductivity values, between 1 and 5 W m−1 K−1 . Considering that thermal storage processes could be improved by axial thermal stratification (Hasnain, 1998), the observed anisotropy of the composites favourable to the radial direction can be potentially of great interest.
3. Simulation of a solar collector including a storage composite 3.1.
Fig. 2 – Paraffin RT65 thermal analysis.
ment with the manufacturer data. This material has been also analysed using the Setsys Evolution Setaram thermobalance (Fig. 2). The stability of the thermal properties has been checked during several successive fusion/solidification cycles. The calorimetric analysis of the stearic acid leads to a storage capacity of 200 kJ kg−1 . Regarding hydrated salts, the results obtained with barium hydroxide octa-hydrated (100 kJ kg−1 ) are lower than the values found in literature (more than 200 kJ kg−1 ). In this case, a high endothermic signal has been recorded above 373 K, after which no phase change was observed any more. This could be explained by a loss of water molecules and formation of other hydrates or dehydrated salts. Similar observations were done on others hydrated salts like magnesium nitrate, aluminium sulphate, and sodium acetate.
Modelisation of the collector
As claimed in the introduction, the composites have been developed to be directly implemented inside solar collectors providing new storage functionality to them. To be efficient, the device has to: (i) store at least an amount of energy corresponding to one day of solar irradiation; (ii) release this energy when needed (for example at the end of the day) at a high level of power. The selected system corresponds to compound parabolic concentrator type collectors (CPC) with a receiver tube (Fig. 4a) at the centre of the collector. Such collector with a 90◦ “angle of acceptance” illuminates the complete perimeter of the receiver with a concentration factor equal to 1 (Fig. 4b). The PCM is placed inside the double casing of the receiver. During the charge, solar radiation (Fig. 4c) is directly absorbed by the receiver surface which is supposed to be a perfect absorber (black body). During the discharge, the energy is released, thanks to the heat transfer fluid, flowing inside the inner tube. Considering a global heat transfer coefficient between the fluid and the PCM at the inner surface of the receiver, and neglecting the sensible heat of the inner tube and the heat loss at the composites surface, the system of differential equation is given by For the fluid:
2.5.
Thermal conductivity f cpf
The experimental set-up used for thermal conductivity measurements under steady state (Olives, 1999) is composed of two standards of well know thermal conductivity (stainless steel or macor) between which the sample to be characterised is placed. The sample (in cubic shape of 2.5 cm in side), is submitted to a thermal gradient between two of its opposite faces. The measurement of the thermal gradient is realised using eight thermocouples axially placed at the centres of the standard and the sample. Then the effective thermal conductivity is identified using the Fourier’s first law. The obtained thermal conductivity versus graphite matrix density for CENG matrix and RT65/CENG, acid stearic/CENG, tri-hydrated sodium acetate/CENG and octa-hydrated barium hydroxide are presented in Fig. 3. Independently to the PCM used in the composites, the thermal conductivities obtained in radial and axial directions presents similar behaviours. At increasing bulk graphite matrix density, radial conductivities increase exponentially. Values in the range of 5–50 W m−1 K−1 are obtained, corresponding to intensification in conductivity by 10–100 compared to pure PCM (ranging from 0.2 to 1 W m−1 K−1 ). At graphite density higher than 200 kg m−3 , the best intensification is obtained by the warm impregnation method (RT65 and stearic
∂Tf + ∇(−f ∇Tf ) = −f cpf u∇Tf ∂t
Fig. 3 – PCM/CENG composites radial (open symbol) and axial (black symbol) thermal conductivities vs. graphite matrix density.
(1)
c h e m i c a l e n g i n e e r i n g r e s e a r c h a n d d e s i g n 8 6 ( 2 0 0 8 ) 612–617
615
Fig. 4 – Schematic representation of: the double casing receiver (a), the CPC solar collector and its receiver (b) and evolution of the solar radiation during 1 day (c).
For the phase change material: c cpc
∂Tc + ∇(−c ∇Tc ) = 0 ∂t
(2)
During the discharge, these equations are linked through the heat exchange at the interface between the PCM and the heat transfer fluid: ∀ z ∈ (0, L) :
− c
∂T c
∂r
r=rf
= hf/c (Tf − Tc )
(3)
In the model, the effective heat capacity cpc of the PCM takes into account its latent heat (solidification/fusion) through the following equation: H cpc = cp0 + √ sf exp 2
−(Tsf − Tc ) 2 2
2
(4)
where cp0 is the average value between the cp of the solid phase and the liquid phase. This expression is a Gauss curve based on cp0 and centred on Tsf . The surface of the Gauss curve is equal to the intrinsic latent heat. The parameter allows to fit the temperature range within which the phase change takes place. The value used in the present simulation is = 0.5 corresponding to a temperature range of 2 K. These equations with the related boundaries conditions are solved with the simulation package Comsol® which is based on the finite-element method. The geometry of the solar collector, associated to the cylindrical shape of the receiver, leads to a simple one-dimensional system during the charge. During discharge, the flowing fluid imposes to consider a twodimension system. The studied configuration of the receiver is defined by a length L of 0.5 m, a tube fluid radius rf of 0.005 m and composites radius rc of 0.05 m.
To illustrate the potential interest of the composite, simulations have been performed with two different kinds of materials: standard RT65 paraffin (with conductivity of 0.2 W m−1 K−1 and heat storage capacity of 170 kJ kg−1 , Tsf = 338 K) and the composite RT65/CENG (with conductivity equal to 15 W m−1 K−1 and a heat storage capacity of 150 kJ kg−1 ).
3.2.
Storage of the solar energy
The storage of the solar energy had been simulated in the particular case defined by a fluid velocity equal to 0 m s−1 . In Fig. 5 are presented the evolutions of the materials temperatures during the day under solar radiation. The temperatures profiles are given for different times over the tube’s radius. In the case of the pure RT65, a radial temperature gradient is observed. The solid/liquid interface location can be visualized at the curve inflection point. For the composite material, the temperature is radially homogeneous, thanks to the high conductivity. In both cases, at the end of the day all the available sun’s energy is stored in both sensible and latent heat.
3.3.
Discharge of the stored energy
In the case of the stored heat discharge, the materials temperatures are initially fixed at T = 350 K. The discharge of the previously stored energy is induced by the flow of the heat transfer fluid at a flow rate u, equal to 0.2 m s−1 and an inlet temperature of 293 K. In both cases, the heat exchange coefficient at the fluid/PCM interface is roughly close to 1000 W m−2 K−1 . The energy balance is presented in Fig. 6 for pure RT65 and RT65/CENG composite in term of released power and energy. For the particular case of the considered design and working conditions, an improvement in power is observed by use of
616
c h e m i c a l e n g i n e e r i n g r e s e a r c h a n d d e s i g n 8 6 ( 2 0 0 8 ) 612–617
Fig. 5 – Materials temperature for single paraffin (a) ( = 0.2 W m−1 K−1 ) and RT65/CENG composite (b) ( = 15 W m−1 K−1 ) at different times ((+) t = 0 s; (♦) t = 10,800 s; () t = 25,200 s; () t = 39,000 s).
Fig. 6 – Power (a) and energy (b) released to the fluid over time for pure paraffin (+) and RT65/CENG composite ().
the composite. After 3600 s, the composite released 85% of the stored energy while the pure paraffin discharged only 11% of it. This result illustrates the high potential of the highly conductive materials for solar applications.
4.
Conclusions
Composite materials based on CENG and several PCM: RT65 paraffin, stearic acid, sodium acetate tri-hydrated and barium hydroxide octa-hydrated, have been elaborated and characterised. At ambient temperature these materials are stable and a significant intensification of their thermal conductivities has been observed. Depending upon to the CENG density, the thermal conductivity of the pure PCM is in the range of 0.2–1 W m−1 K−1 while the data recorded for the composites range between 5 and 50 W m−1 K−1 . So an intensification factor of 5–100 was obtained. Hydrated salts showed unstable behaviour above 373 K due to the departure of moisture and consequently to a change in composition of the eutectic. The measured storage capacities of the RT65 paraffin and the stearic acid are respectively of 170 and 200 kJ kg−1 , hence a storage capacities of 140 and
170 kJ kg−1 for a composite with a graphite density equal to 150 kg m−3 . A numerical model has been developed to describe the material behaviours during the storage of sun radiation and the release of this energy by heat exchange with a fluid. This simulation has been realised in both cases of poorly conductive material (paraffin) and highly conductive material (PCM/CENG composite). The obtained results showed that, in both cases, the materials were able to store daily solar radiation. At the opposite, only the composite material was allowed to reach high level of thermal power during the discharge.
Acknowledgement The Saunier Duval industry part of Vaillant Group is acknowledged for financial support.
references
Abhat, A., 1983, Low temperature latent heat thermal energy storage: heat storage materials. Solar Energy, 30.
c h e m i c a l e n g i n e e r i n g r e s e a r c h a n d d e s i g n 8 6 ( 2 0 0 8 ) 612–617
Hasnain, S.M., 1998, Review on substainable thermal energy storage technologies, Part 1: heat storage materials and techniques. Energy Convers Manage, 11. Hazami, M., Kooli, S., Lazaar, M., Farhat, A. and Belghith, A., 2005, Performance of a solar storage collector. Desalination, (183): 137–172. Mettawee, E. and Assassa, G., 2004, Experimental study of a compact PCM solar collector. Energy. Olives, R., 1999, Transfert thermique dans une matrice de ´ et anisotrope, support d’un graphite poreuse, consolidee ´ es ´ energ ´ ´ ` de Doctorat, solide actif pour proced etiques, These Universite´ de Perpignan. Pielichowski, K. and Flejtuch, K., 2002, Differential scanning calorimetry studies on poly(ethylene glycol) with different molecular weights for thermal energy storage materials. Polym Adv Technol, 13: 690–696. Pielichowski, K. and Flejtuch, K., 2003, Binary blends of polyethers with fatty acids: a thermal characterization. J Appl Polym Sci, 90: 861–870.
617
Pincemin, S., Olives, R., Py, X. and Christ, M., 2008, Highly conductive composites made of phase change materials and graphite for thermal storage. Solar Energy Mater Solar Cells, 92: 603–613. Py, X., Olives, R. and Mauran, S., 2000, Paraffin/porousgraphite-matrix composite as a high and constant power thermal storage materials. Int J Heat Mass Transf, 2727–2737. Rabin, Y., Bar-Niv, I., Korin, E. and Mikic, B., 1995, Integrated solar collector storage system based on a salt hydrate phase change material. Solar Energy, 55(6): 435–444. Tarhan, S., Sari, A. and Yardim, M., 2006, Temperature distributions in trapezoidal built in storage solar water heater with/without phase change materials. Energy Convers Manage. Zalba, B., Marin, J., Cabeza, L. and Mehling, H., 2003, Review on thermal energy storage with phase change: materials, heat transfer analysis and applications. Appl Therm Eng, (23): 251–283.
available at www.sciencedirect.com
journal homepage: www.elsevier.com/locate/cherd
Storage composites for the optimisation of solar water heating systems Didier Haillot a,b,∗ , Xavier Py a , Vincent Goetz a , Mohamed Benabdelkarim b a
PROMES CNRS UPR8521 Process, Materials and Solar Energy Laboratory, Universit´e de Perpignan Via Domitia, Rambla de la Thermodynamique Tecnosud 66100, Perpignan, France b Saunier Duval Eau Chaude Chauffage Industrie, 17 rue de la Petite Baratte, BP 44315, Nantes Cedex 03, France
a r t i c l e
i n f o
a b s t r a c t
Article history:
Composite materials based on expanded natural graphite (CENG) and various phase change
Received 21 September 2007
materials (PCM) have been developed for low temperature solar applications (323–373 K).
Accepted 24 January 2008
The integration of such composite materials directly into the solar collector could allow new storage functionality. A numerical model has been developed to describe the materials behaviour. Composites properties are presented and discussed.
Keywords:
© 2008 Published by Elsevier B.V. on behalf of The Institution of Chemical Engineers.
Phase change materials Thermal storage Solar heater Modelling
1.
Introduction
The increasing price of fossil fuels and awareness of environmental issues have caused growing interest towards renewable energy. Due to their low cost and simplicity, solar water heating systems including flat plate collectors or vacuum tube panel are the most widely commercialized systems. The optimisation of solar systems must invariably involve energy storage to smooth the influence of solar variations like day/night successions or cloud effects and to be able to manage the variations in energetic demand. Within the last decade, several configurations of solar water heating systems including integrated storage have been tested using concrete (Hazami et al., 2005), hydrated salts (Rabin et al., 1995), myristic acid (Tarhan et al., 2006) or paraffin (Mettawee and Assassa, 2004) as storage media. These systems allow rather effective heat charge and discharge steps. Nevertheless, discharge step seems to be significantly controlled by the thermal conductivity of the storage media. In the present work, composite storage materials based on phase change materials (PCM) and compressed expanded natural graphite (CENG) are presented. Two different tech-
∗
niques, leading to anisotropic properties, have been developed to elaborate these composites: cold compression (for inorganic PCM) and warm impregnation (for organic PCM). Composite thermal conductivities, storage capacities and thermal stabilities have been characterised. Dynamic modelling was carried out by using the FEMLAB software from COMSOL. The model allows the description of the composite behaviour under both the storage step under solar flux and the discharge ensured by the flow of a heat transfer fluid. Corresponding results obtained for different materials of various thermal conductivities underline the high potentiality of those new composites.
2.
Experimental investigation
2.1.
Investigated materials
Globally, there are two main PCM categories: organic PCM, and inorganic PCM also known as salts. Main characteristics of those materials are given in the following Table 1. This table presents only some of the PCM currently listed and is not thorough. We could notify, as an example, other promising organic
Corresponding author at: PROMES CNRS UPR8521, Rambla de la thermodynamique Tecnosud 66100, Perpignan, France. E-mail address: [email protected] (D. Haillot). 0263-8762/$ – see front matter © 2008 Published by Elsevier B.V. on behalf of The Institution of Chemical Engineers. doi:10.1016/j.cherd.2008.01.007
613
c h e m i c a l e n g i n e e r i n g r e s e a r c h a n d d e s i g n 8 6 ( 2 0 0 8 ) 612–617
Nomenclature cp h L rf rc t T u
calorific capacity (J kg−1 K−1 ) convective exchange coefficient (W m−2 K−1 ) tube length (m) tube radius (m) double casing radius (m) temps (s) temperature (K) velocity (m s−1 )
Symbols thermal conductivity (W m−1 K−1 ) density (kg m−3 ) H specific enthalpy of phase transition (kJ kg−1 ) Subscripts CENG compressed expanded natural graphite f fluid sf fusion/solidification PCM phase change material c composite
Fig. 1 – Composites storage capacity per volume (open symbol) and per mass (black symbol) vs. graphite matrix density.
PCM as poly(ethylene glycol) (Pielichowski and Flejtuch, 2002) or polyether (Pielichowski and Flejtuch, 2003). The criteria for the selection of the most appropriate PCM must include: price, toxicity, phase change temperature and storage capacity. According to such approach, the PCM tested in the present work are: RT65 paraffin (www.rubitherm.com), stearic acid, sodium acetate tri-hydrated (CH3 COONa·3H2 O) and barium hydroxide octa-hydrated (Ba(OH)2 ·8H2 O). The tested graphite was in the form of expanded worms obtained by the thermal exfoliation of inserted natural graphite flakes.
2.2.
PCM/CENG composite materials elaboration
Concerning the warm impregnation route, expanded graphite powders is first poured into a cubic mould of aluminium and then pressed to obtain a consolidated porous graphite matrix of a desired bulk density (Py et al., 2000). This matrix is then soaked into melted paraffin and then, regularly weighted until maximum load is reached. This technique has been found to be very relevant in the case of organic PCM but rather inefficient for inorganic PCM. Concerning the cold compression route, CENG and PCM powders are mixed together and shaped in a mould by cold axial compression (Pincemin et al., 2008). At ambient temperature, the obtained materials elaborated by the two methods are stable. These two techniques lead to an anisotropic composite structure inherited from the spatial
rearrangement of the graphen layers under axial compression. According to the graphite layers orientations, the thermal conductivity parallel to the compression axis (axial direction) is much lower than the thermal conductivity perpendicular to the compression axis (radial direction).
2.3. Theoretical storage capacity of the PCM/CENG composites In Fig. 1 are presented the theoretical storage capacities of the composite materials per unit of volume or mass, according to enthalpy values from Zalba et al. (2003) and Abhat (1983). As the graphite density in the composite increases, the relative amount of PCM and therefore the storage capacity decrease. Globally, inorganic PCMs have larger storage capacity than organic PCMs. Theoretically hydroxide barium octa-hydrated is found to be the best PCM in term of specific enthalpy per mass and per volume (240 kJ kg−1 and 50 × 104 kJ m−3 at CENG = 150 kg m−3 ). Nevertheless, as explained below, the hydrated salts present unstable behaviour above 373 K.
2.4.
Thermal analysis of the composites
The storage capacity of the materials has been measured using a Setaram C80 calorimeter. The integration of the peak surfaces during the fusion and the solidification steps lead to corresponding effective storage capacity values. The analysis of the paraffin RT65 curves leads to a latent heat of 170 kJ kg−1 and a fusion/solidification temperature of 338 ± 1 K in agree-
Table 1 – Organic/inorganic PCM comparison Advantages
Disadvantages
Organic (paraffin, fatty acids)
Low toxicity Low/or no supercooling
Segregation Inflammable Moderate storage capacity
Inorganic (pure or hydrated salts, eutectics)
High storage capacity Fireproof
Supercooling, segregation Corrosion, hygroscopic Crystallographic structure Evolution with temperature
614
c h e m i c a l e n g i n e e r i n g r e s e a r c h a n d d e s i g n 8 6 ( 2 0 0 8 ) 612–617
acid). The composite anisotropy is underlined by significantly lower axial thermal conductivity values, between 1 and 5 W m−1 K−1 . Considering that thermal storage processes could be improved by axial thermal stratification (Hasnain, 1998), the observed anisotropy of the composites favourable to the radial direction can be potentially of great interest.
3. Simulation of a solar collector including a storage composite 3.1.
Fig. 2 – Paraffin RT65 thermal analysis.
ment with the manufacturer data. This material has been also analysed using the Setsys Evolution Setaram thermobalance (Fig. 2). The stability of the thermal properties has been checked during several successive fusion/solidification cycles. The calorimetric analysis of the stearic acid leads to a storage capacity of 200 kJ kg−1 . Regarding hydrated salts, the results obtained with barium hydroxide octa-hydrated (100 kJ kg−1 ) are lower than the values found in literature (more than 200 kJ kg−1 ). In this case, a high endothermic signal has been recorded above 373 K, after which no phase change was observed any more. This could be explained by a loss of water molecules and formation of other hydrates or dehydrated salts. Similar observations were done on others hydrated salts like magnesium nitrate, aluminium sulphate, and sodium acetate.
Modelisation of the collector
As claimed in the introduction, the composites have been developed to be directly implemented inside solar collectors providing new storage functionality to them. To be efficient, the device has to: (i) store at least an amount of energy corresponding to one day of solar irradiation; (ii) release this energy when needed (for example at the end of the day) at a high level of power. The selected system corresponds to compound parabolic concentrator type collectors (CPC) with a receiver tube (Fig. 4a) at the centre of the collector. Such collector with a 90◦ “angle of acceptance” illuminates the complete perimeter of the receiver with a concentration factor equal to 1 (Fig. 4b). The PCM is placed inside the double casing of the receiver. During the charge, solar radiation (Fig. 4c) is directly absorbed by the receiver surface which is supposed to be a perfect absorber (black body). During the discharge, the energy is released, thanks to the heat transfer fluid, flowing inside the inner tube. Considering a global heat transfer coefficient between the fluid and the PCM at the inner surface of the receiver, and neglecting the sensible heat of the inner tube and the heat loss at the composites surface, the system of differential equation is given by For the fluid:
2.5.
Thermal conductivity f cpf
The experimental set-up used for thermal conductivity measurements under steady state (Olives, 1999) is composed of two standards of well know thermal conductivity (stainless steel or macor) between which the sample to be characterised is placed. The sample (in cubic shape of 2.5 cm in side), is submitted to a thermal gradient between two of its opposite faces. The measurement of the thermal gradient is realised using eight thermocouples axially placed at the centres of the standard and the sample. Then the effective thermal conductivity is identified using the Fourier’s first law. The obtained thermal conductivity versus graphite matrix density for CENG matrix and RT65/CENG, acid stearic/CENG, tri-hydrated sodium acetate/CENG and octa-hydrated barium hydroxide are presented in Fig. 3. Independently to the PCM used in the composites, the thermal conductivities obtained in radial and axial directions presents similar behaviours. At increasing bulk graphite matrix density, radial conductivities increase exponentially. Values in the range of 5–50 W m−1 K−1 are obtained, corresponding to intensification in conductivity by 10–100 compared to pure PCM (ranging from 0.2 to 1 W m−1 K−1 ). At graphite density higher than 200 kg m−3 , the best intensification is obtained by the warm impregnation method (RT65 and stearic
∂Tf + ∇(−f ∇Tf ) = −f cpf u∇Tf ∂t
Fig. 3 – PCM/CENG composites radial (open symbol) and axial (black symbol) thermal conductivities vs. graphite matrix density.
(1)
c h e m i c a l e n g i n e e r i n g r e s e a r c h a n d d e s i g n 8 6 ( 2 0 0 8 ) 612–617
615
Fig. 4 – Schematic representation of: the double casing receiver (a), the CPC solar collector and its receiver (b) and evolution of the solar radiation during 1 day (c).
For the phase change material: c cpc
∂Tc + ∇(−c ∇Tc ) = 0 ∂t
(2)
During the discharge, these equations are linked through the heat exchange at the interface between the PCM and the heat transfer fluid: ∀ z ∈ (0, L) :
− c
∂T c
∂r
r=rf
= hf/c (Tf − Tc )
(3)
In the model, the effective heat capacity cpc of the PCM takes into account its latent heat (solidification/fusion) through the following equation: H cpc = cp0 + √ sf exp 2
−(Tsf − Tc ) 2 2
2
(4)
where cp0 is the average value between the cp of the solid phase and the liquid phase. This expression is a Gauss curve based on cp0 and centred on Tsf . The surface of the Gauss curve is equal to the intrinsic latent heat. The parameter allows to fit the temperature range within which the phase change takes place. The value used in the present simulation is = 0.5 corresponding to a temperature range of 2 K. These equations with the related boundaries conditions are solved with the simulation package Comsol® which is based on the finite-element method. The geometry of the solar collector, associated to the cylindrical shape of the receiver, leads to a simple one-dimensional system during the charge. During discharge, the flowing fluid imposes to consider a twodimension system. The studied configuration of the receiver is defined by a length L of 0.5 m, a tube fluid radius rf of 0.005 m and composites radius rc of 0.05 m.
To illustrate the potential interest of the composite, simulations have been performed with two different kinds of materials: standard RT65 paraffin (with conductivity of 0.2 W m−1 K−1 and heat storage capacity of 170 kJ kg−1 , Tsf = 338 K) and the composite RT65/CENG (with conductivity equal to 15 W m−1 K−1 and a heat storage capacity of 150 kJ kg−1 ).
3.2.
Storage of the solar energy
The storage of the solar energy had been simulated in the particular case defined by a fluid velocity equal to 0 m s−1 . In Fig. 5 are presented the evolutions of the materials temperatures during the day under solar radiation. The temperatures profiles are given for different times over the tube’s radius. In the case of the pure RT65, a radial temperature gradient is observed. The solid/liquid interface location can be visualized at the curve inflection point. For the composite material, the temperature is radially homogeneous, thanks to the high conductivity. In both cases, at the end of the day all the available sun’s energy is stored in both sensible and latent heat.
3.3.
Discharge of the stored energy
In the case of the stored heat discharge, the materials temperatures are initially fixed at T = 350 K. The discharge of the previously stored energy is induced by the flow of the heat transfer fluid at a flow rate u, equal to 0.2 m s−1 and an inlet temperature of 293 K. In both cases, the heat exchange coefficient at the fluid/PCM interface is roughly close to 1000 W m−2 K−1 . The energy balance is presented in Fig. 6 for pure RT65 and RT65/CENG composite in term of released power and energy. For the particular case of the considered design and working conditions, an improvement in power is observed by use of
616
c h e m i c a l e n g i n e e r i n g r e s e a r c h a n d d e s i g n 8 6 ( 2 0 0 8 ) 612–617
Fig. 5 – Materials temperature for single paraffin (a) ( = 0.2 W m−1 K−1 ) and RT65/CENG composite (b) ( = 15 W m−1 K−1 ) at different times ((+) t = 0 s; (♦) t = 10,800 s; () t = 25,200 s; () t = 39,000 s).
Fig. 6 – Power (a) and energy (b) released to the fluid over time for pure paraffin (+) and RT65/CENG composite ().
the composite. After 3600 s, the composite released 85% of the stored energy while the pure paraffin discharged only 11% of it. This result illustrates the high potential of the highly conductive materials for solar applications.
4.
Conclusions
Composite materials based on CENG and several PCM: RT65 paraffin, stearic acid, sodium acetate tri-hydrated and barium hydroxide octa-hydrated, have been elaborated and characterised. At ambient temperature these materials are stable and a significant intensification of their thermal conductivities has been observed. Depending upon to the CENG density, the thermal conductivity of the pure PCM is in the range of 0.2–1 W m−1 K−1 while the data recorded for the composites range between 5 and 50 W m−1 K−1 . So an intensification factor of 5–100 was obtained. Hydrated salts showed unstable behaviour above 373 K due to the departure of moisture and consequently to a change in composition of the eutectic. The measured storage capacities of the RT65 paraffin and the stearic acid are respectively of 170 and 200 kJ kg−1 , hence a storage capacities of 140 and
170 kJ kg−1 for a composite with a graphite density equal to 150 kg m−3 . A numerical model has been developed to describe the material behaviours during the storage of sun radiation and the release of this energy by heat exchange with a fluid. This simulation has been realised in both cases of poorly conductive material (paraffin) and highly conductive material (PCM/CENG composite). The obtained results showed that, in both cases, the materials were able to store daily solar radiation. At the opposite, only the composite material was allowed to reach high level of thermal power during the discharge.
Acknowledgement The Saunier Duval industry part of Vaillant Group is acknowledged for financial support.
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