This paper deals with the Exergetic optimisation stutdy of the PCM’s slabs- Solar Energy Storage Tank (SEST). Both melting temperature and the maximum power output taking into account the phase change process are determined.Peer ReviewedPostprint (published version

Al Omar Mesnaoui, Anas

Illa Alibés, Josep

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 __________________________________________________________________________________________________ 9ième Congrès de Mécanique, FS Semlalia, Marrakech                                                                                                         313 Exergetic optimisation of a solar energy installation  F. Aghbalou, F. Badia, J. Illa and A. Al Omar*  Escuela Politécnica Superior, Universidad de Lleida, Calle Jaume II,  69, Campus Cappont. E 25001. LLeida, Spain *Departamento de Ingeniería Mecánica, EPSEM, Universidad Politécnica de Cataluña, Avenida Bases de Manresa 61 – 73, 08240 Manresa, Barcelona, Spain  Abstract: This paper deals with the Exergetic optimisation stutdy of the PCM’s slabs- Solar Energy Storage Tank (SEST). Both melting temperature and the maximum power output taking into account the phase change process are determined.   Key words: Exergy, Optimisation, Solar energy, Phase change material.   Introduction One of the key for Solar Energy success resides without any doubt, in an effective thermal storage. Among solar thermal energy storage techniques, we mention: • The thermally stratified storage (sensible heat), which is an effective technique, that’s widely used in energy conservation and load management applications.  Analytical, experimental, and numerical studies have been carried out on its performance [1-3].  • Reversible chemical heat storage which is based on the conversion of solar radiation into-high temperature heat.  It consists of a closed loop [4-6] or open-loop [7] system of reactants passing to endothermic “Solar energy storage” and exothermic “solar energy recovery” reactors.   • Latent heat thermal energy storage. Solar energy is stored in phase change material (PCM). The main features of PCM are their high-energy storage density and their ability to give up the stored energy at a constant temperature. These characteristics motivate for their applications. The most analysed latent heat energy storage unit is the shell and tube one, with the PCM filling the shell and the heat transfer fluid flowing through the tubes [8]. A detailed discussion on the solar energy storage using PCM can be found in [9].  The installation was treated as a transient –continue system using finite difference. The analysis of PCM melting process, which falls into the moving boundaries problems, was performed using the enthalpy formulation. The PCM slabs were considered to be bathed in two different fluids.  Several methodologies for Thermal Energy Storage (TES) evaluation and comparison have been investigated [10,11] concluding that the only adequate method providing illuminating information is that based on the Second Law of Thermodynamics, that’s, availability analysis. In fact, energy efficiency which is the ratio of the energy returned from the storage to the energy originally delivered to the storage, does not take into account all the considerations necessary in Thermal energy storage evaluation as could be storage duration, and the temperatures of the supplied and recovered thermal energy and the surroundings. Availability analysis yields efficiencies which provide a true measure of how nearly actual performance approaches the ideal, and identifies more clearly than energy analysis the causes and locations of thermodynamics losses.  Consequently, the availability analysis can assist in improving and optimising TES designs.    The purpose of this article is the presentation of a most general exergetic optimisation of the PCM’s slabs- solar energy storage tank (hereafter SEST), Fig. 1, and to determine both optimal melting temperature and the maximum power output taking into account the phase change process.    Fig. 1 Solar Installation  2. Availability maximisation of SEST with PCM Once the hot stream of a flow rate m at temperature inT  comes in contact with a PCM, a fractional energy of the hot stream is released to a PCM and consequently hot stream’s temperature falls to outT . Assuming both steady state and PCM at the melting temperature (saturated solid state), mT , it could be deduced therefore that;  tuNminmout eTTTT−−+= )(   (1)  wherewwtu CpmUAN = , A  is the heat transfer area between the hot stream and PCM and U is the overall heat transfer coefficient based on A . Considering that SEST with PCM performs like a heat engine using Carnot cycle, that’s, heat leaves the high temperature reservoir at temperature mT  and goes into the heat engine. The heat engine does work,W , and reject heat into the low temperature reservoir at temperature LT .   Then   __________________________________________________________________________________________________ 9ième Congrès de Mécanique, FS Semlalia, Marrakech                                                                                                         314 mLoutinww TTTTCpmW−=−1)(    (2)  and after combining with Eq. (1), it yields )1)(1)((mLNminww TTeTTCpmW tu −−−= −  (3) optmT ,  maximising Eq. (3) is  21,)( Linoptm TTT =    (4)  This result coincide with the optimal latent heat storage temperature  proposed by Lim et al. [12], however the expression of the maximum power output  deduced by Lim et al. does not reflect the phase change process  as the following equation obtained after substituting Eq. (4) in Eq. (3) [ ]221)(1)1(inLNinww TTeTCpmW tu −−= −  (5) 3. Case study A complete solar installation situated at Lleida city in Catalunya, Spain, is studied. For all calculations of parameter’s design and optimisation, we consider a March’s representative day, that’s, date 16. Tubing thermal losses between SC and SEST with PCM are neglected. The tuN  is of a great usefulness and significance. In fact, it gives precious information for design as if number of slabs should be changed or not. The fractional energy, ,Ψ  given up by the melted PCM of a melting temperature, mT , and recovered by the entering water is defined as  the actual energy given by the PCM in time t divided by the total energy, That’s,minmmeanTTTT−−=Ψ . The water’s mean temperature bathing each PCM’s hourly section is evaluated simply by2inoutmeanTTT+= .  The other important key design in this problem is the melted thickness, )(tδ , which is, function of a PCM thermal properties, thickness and boundary conditions, that’s, h  and meanT . Fig 2 shows the variation of the PCM’s optimal melting temperature, optmT ,  and the water’s mean temperature bathing the PCM’s slabs, meanT , with the PCM’s slabs height during the first six hours, i.e.; hr9  to hr15 . As the PCM’s slab’s height increase, optmT ,  and meanT  decrease. Thus, for ml 135.0= , optmT , =363ºK and meanT =365ºK when for ml 38.0= , optmT , =327ºK and meanT =332ºK. From hr15 to hr18  and depending on the chosen PCM’s melting temperature, a fractional energy, Ψ , will be given up by the melted PCM to the entering water. Fig 3, shows that for m135,0l = , Ψ is of about %54,58  and for m38,0l = , Ψ is of 25,49%.  Considering RT-PCM products and from Fig.4, for optmT , =327ºK, the recovered energy by the entering water is of 612,18 kJ when the energy to be recovered  is of 1836,54 kJ. However, for optmT , =363ºK, the recovered energy by the entering water is of 561 kJ and the energy to be recovered is 406kJ. Thus, the energy quality to be delivered at optmT , =363ºK is 5 times better than the energy to be delivered at optmT , =327ºK.  3203303403503603703800,02 0,12 0,22 0,32 0,42PCM's slabs height (m)Temperature (K)Tm, optTmean  Fig. 2 Variation of PCM’s optimal melting temperature and water’s mean temperature bathing PCM’s slabs with the PCM’s slabs height 00,20,40,60,810 0,1 0,2 0,3 0,4PCM's slabs height (m)Recovered fractional energy (%)Fig. 3 Variation of the recovered fractional energy as a function of PCM’s slabs height  0300600900120015001800320 330 340 350 360 370Tm, opt (K)Energy (kJ)Recovered byentering waterNot recovered byentering waterFig. 4 Variation of recovered and not recovered energy with the chosen PCM’s optimal temperature   __________________________________________________________________________________________________ 9ième Congrès de Mécanique, FS Semlalia, Marrakech                                                                                                         315 4. Conclusion  A most general exergetic optimisation of the whole solar energy installation has been carried out for March representative day at Lleida Spanish city. As a result, the exergetic optimisation study of the PCM’s slabs- SEST gives optimal melting temperature. Results show that Tm ranges between 327ºK and 363ºK.  For each melting temperature corresponds its PCM’s slabs height. Thus, for Tm=327K, l=0,38 m when for Tm=363K, l=0,135 m. The fractional energy, Ψ, function of Tm, given up by the PCM’s slabs to the entering water has been also examined. As a result, for Tm=363K, Ψ=58,54%  and for Tm= 327K, Ψ=25,49% . Therefore, the energy to be recovered at Tm=363K is five times better in point of view of quality.    References  [1] H. Yoo, C-J. Kim and C. W. Kim, 1998, Approximate analytical solutions for stratified thermal storage under variable inlet temperature, Solar Energy, Vol. 66, No. 1, pp. 47-56 [2] J. E. B. Nelson, A. R. Balakrishnan and S. Srinivasa Murthy., 1999, Experiments on stratified chilled-water tanks. Int. J. Refrigeration. 22, pp. 216-234. [3] J. E. B.Nelson, A. R. Balakrishnan and S. Srinivasa Murthy, 1999, Parametric studies on thermally studied chilled water storage systems. Applied thermal Eng. 19, pp. 89-115 [4] K. Lovegrove, A. Luzzi and H. Kreetz , 1999, A solar driven ammonia-based thermochemical energy storage system. Solar Energy, Vol. 67, Nos. 4-6, pp.309-316 [5] H. Kreetz and K. Lovegrove, 1999, Theoretical analysis and experimental results of a 1 kW chem ammonia synthesis reactor for a solar thermochemical energy storage system. Solar Energy, Vol. 67, Nos. 4-6, pp.287-296 [6] K. Lovegrove, A. Luzzi, M. Mccann and O. Freitag , 1999, Exergy analysis of ammonia-based solar thermochemical power systems. Solar Energy, Vol. 66, No. 2, pp.103-115 [7] F. Aghbalou, A. Touzani, M. Mada, M. Charia and A. Bernatchou, 1998, A parabolic solar collector heat pipe heat exchanger reactor assembly for cyclohexane’s dehydrogenation: A simulation study. Renewable energy, Vol. 14, Nos. 1-4, pp.61-67 [8] M. Esen, A. Durmus, A. Durmus, 1998, Geometric design of solar-aided latent heat store depending on various parameters and phase change materials. Solar Energy, Vol. 62, No. 1, pp. 12-28 [9] F. Aghbalou, F. Badia and J. Illa, 2002, Design and analysis of a thermal solar energy storage using PCM, FIER 2002 Proceeding, Vol. 2, pp. 395-401 [10] M.A. Rosen and I. Dincer, 2003, Exergy methods for assessing and comparing thermal storage systems, Energy research, 27, pp. 415-430 [11] I. Dincer, 1999, Evaluation and selection of energy storage systems for solar thermal applications. Energy research , 23, pp. 1017-1028 [12] J.S. Lim, A. Bejan and J.H Kim, 1992, Thermodynamics optimisation of phase change energy storage using two or more materials. Energy resources  Technology, 114, pp. 84-90   

Exergetic optimisation of a solar energy installation

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Exergetic optimisation of a solar energy installation

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