Multi-layered solid-PCM thermocline thermal storage concept for CSP plants. Numerical analysis and perspectives

Multi-layered solid-PCM thermocline thermal storage concept for CSP plants. Numerical analysis and perspectives. Short title: MLSPCM thermocline concept for CSP P.A. Galionea,b, C.D. P´erez-Segarraa, I. Rodr´ıgueza, A. Olivaa,∗, J. Rigolaa aHeat and Mass Transfer Technological Center (CTTC),Universitat Polit`ecnica de Catalunya - BarcelonaTech, ETSEIAT, Colom 11, 08222, Terrassa (Barcelona), Spain bInstituto de Ingenier´ıa Mec´anica y Producci´on Industrial (IIMPI), Universidad de la Rep´ublica (UdelaR), Uruguay Abstract Thermocline storage concept has been considered for more than a decade as a possible solution to reduce the huge cost of the storage system in concentrated solar power (CSP) plants. However, one of the drawbacks of this concept is the decrease in its performance throughout the time. The objective of this paper is to present a new thermocline-like storage concept, which aims at circumventing this issue. The proposed concept consists of a storage tank filled with a combination of solid material and encapsulated PCMs, forming a multi-layered packed bed, with molten salt as the heat transfer fluid. The performance evaluation of each of the prototypes proposed is virtually tested by means of a detailed numerical methodology which considers the heat transfer and fluid dynamics phenomena present in these devices. The virtual tests carried out are designed so as to take into account several charging and discharging cycles until periodic state is achieved, i.e. when the same amount of energy is stored/released in consecutive charging/discharging cycles. As a result, the dependence of the storage capacity on the PCMs temperatures, the total energy and exergy stored/released, as well as the efficiencies of the storing process are compared for the different thermocline, single PCM, cascaded PCM and multi-layered solid-PCM (MLSPCM) configurations. The analysis shows that the multilayered solid-PCM concept is a promising alternative for thermal storage in CSP plants. Keywords: Thermal Energy Storage, CSP, Phase Change Materials, Thermocline, Multi-Layered Solid-PCM, Numerical Analysis ∗Corresponding author Email addresses: [email protected], [email protected] (P.A. Galione), [email protected] (A. Oliva) NOMENCLATURE ASurface area AtTransversal area of tank AwInternal surface area of tank’s lateral wall CpSpecific heat at constant pressure dpDiameter of filler PCM capsule/solid particle ecap Capsule’s shell width ex Exergy fMass liquid fraction (PCM) gGravity acceleration hSpecific total enthalpy hconv Convection coefficient kThermal conductivity keff Effective thermal conductivity Lspecific latent enthalpy m, ˙mMass and mass flux nfm Number of filler particles/capsules in tank section Nu Nusselt number NrNumber of control volumes of one filler particle/capsule NxNumber of tank sections pPressure Pe P´eclet number Pr Prandtl number rRadial direction Rcond Thermal conduction resistance of capsule shell Rconv Convection resistance between fluid and capsule/solid filler Re Reynolds number tTime TTemperature Uamb Global heat transfer convection coefficient between the fluid and the ambient vVelocity magnitude VVolume 2 ∆tTime step ∆xTank section height Volume liquid fraction (porosity) µDynamic viscosity ρDensity Superscripts and subscripts: amb ambient cap PCM capsule shell ffluid flow fm filler material (PCM or solid) iIndex of tank section/control volume i±1/2 Index of tank section’s face limiting iand i±1 in Tank inlet jIndex of capsule/solid filler control volume j±1/2 Index of filler control volume’s face limiting jand j±1 l, liq Liquid phase out Tank outlet s, sol Solid phase Abbreviations: CSP Concentrated Solar Power HTF Heat Transfer Fluid LCOE Levelized cost of Electricity MLSPCM Multi-Layered Solid-PCM PCM Phase Change Material TES Thermal Energy Storage 1. Introduction1 Thermal energy storage (TES) systems are an essential feature to make a major profit of solar2 energy. These systems allow using the thermal energy stored in hours of high solar radiation in times of3 lower radiation and higher energy demands, reducing the mismatch between the supply and demand.4 In solar power generation stations, the incorporation of TES systems produce an increase in system5 reliability and generation capacity, and a decrease of the levelized cost of electricity (LCOE) [1, 2].6 For concentrated solar power plants (CSP) the current standard for thermal energy storage is the7 3 two-tank molten salt system [3, 4], which make profit of the sensible energy changes of a heat transfer8 fluid (molten salt) under a temperature difference. In the search for investment costs reduction,9 different designs which result in lower container volumes or in the use of less and/or cheaper storage10 media have been proposed as alternatives. Some of these, making use of the materials sensible energy11 capacity, are the thermocline tanks [5, 6] and the concrete storage designs [7].12 Thermocline storage system consists of a single tank, with a volume somewhat higher than one of13 the two-tank system, filled with a solid material forming a porous packed bed through which the heat14 transfer fluid (HTF) flows. Most of the tank volume is occupied by the solid, which acts as a sensible15 energy storage medium, and therefore less of the more costly HTF is needed when compared to an16 equivalent two-tank system. Different solid materials have been considered, such as quartzite rocks,17 granite, sand [5], asbestos-containing wastes [8], etc.18 Thermocline tanks rely on the principle of thermal stratification, which occurs in a fluid having19 temperature gradients under the action of the gravitational force. The hot fluid, having a lower density20 than the cold fluid, is pushed upwards by the buoyancy force while the low temperature fluid is21 displaced downwards. Therefore, the hot fluid is placed in the upper part of a tank, while the colder22 fluid stays at the bottom. As a consequence, a vertical temperature gradient is formed which is called23 “thermocline”. The filler material helps in maintaining the thermal gradient, preventing possible24 mixing flows that may be present due to effects such as cooling through the walls (see for instance25 [9, 10]) or strong inlet flow currents [11].26 Phase change materials (PCM) can also be used to store energy, using less storage material than27 would be used with a sensible energy storage medium, taking advantage of the latent energy changes28 during a phase change. The resulting storage device should be more compact, and hopefully cheaper,29 than one that only makes use of the sensible energy changes. Thermal storage devices using encapsu-30 lated PCMs have been studied as a form of thermal storage devices for CSP applications by several31 authors. Liu et al. [12] perform an extensive review of PCMs suitable to be used in TES for CSP32 plants and of heat transfer enhancement methods. Michels and Pitz-Paal [13] studied, experimentally33 and numerically, the performance of storage systems using vertical shell and tube heat exchangers34 with different PCMs enclosed between the shell and the tubes, with different melting points (cascaded35 PCM), for parabolic trough plants. Shabgard et al. [14] studied cascaded latent heat storage with36 gravity-assisted heat pipes for CSP. They performed numerical simulations using a thermal network37 model and evaluated thermal performance of the different designs after a single charge/discharge cycle.38 Nithyanandam et al. [15] numerically analyzed packed bed thermal storage with single encapsulated39 PCMs by studying their performance after a single charging/discharging cycles and after a periodic40 4 cyclic state is reached. Parametric studies were performed and guidelines for designing latent ther-41 mocline storage systems for CSP were established. Flueckiger et al. [16] studied thermocline storage42 for solar power stations augmented with latent heat. They integrated their numerical model of the43 thermocline into a system-level model for the CSP plant and evaluated the effect of the increase of44 the storage capacity with latent heat. When compared against solid-filled thermocline, limitations in45 the thermal performance of designs including a single PCM were observed, while some improvement46 was obtained with some of the cascaded PCM configurations.47 Moreover, combination of latent and sensible storage devices has been studied for CSP plants48 with direct steam generation (DSG) [17], where a PCM storage unit is intended for vapor generation49 (evaporation) and the sensible energy units for absorbing the sensible energy of the heat transfer fluid50 (preheating and superheating).51 One of the configurations that have received the most attention is that of packed beds. Many52 numerical investigations of thermal storage in packed beds can be found in the literature. Ismail and53 Stuginsky [18] performed a comparative analysis of different packed bed models used for sensible and54 latent heat storage. Flueckiger et al. [19] reviewed different experimental and numerical studies on55 thermocline tanks for solar thermal storage. On one hand, models for packed beds of solid materials56 [6, 19, 20, 21] usually disregard the temperature gradients inside the particles. On the other hand, if57 the bed consists of PCM capsules [15, 16, 22, 23], thermal gradients inside them may be significant58 and are generally, but not always, taken into account. Karthikeyan and Velraj [24] performed a59 comparison of three one-dimensional models for packed beds of PCM spherical capsules, where the60 effect of considering the radial variation of temperature inside the capsules was tested. All these61 models are based on discretizing the conservation equations for the heat transfer fluid and the filler62 bed, and usually, several simplifying assumptions are made. Depending on the scope of the numerical63 code, one- , two- or three-dimensional simulations can be performed. However, due to the significantly64 higher computational costs associated with two- (e.g. [6, 20]) and three-dimensional (none found in65 the literature) models, one-dimensional analysis is usually chosen for studying several working cycles66 of TES systems [15, 16, 22, 23, 24].67 In this work, a new concept of thermocline-like storage system is proposed, consisting in com-68 bining low-cost solid and PCM filler materials, appropriately chosen and placed inside the tank in a69 multi-layered manner. This concept, initially presented in a congress paper [25], has been called Multi-70 Layered Solid-PCM (MLSPCM). The main idea behind MLSPCM configurations is the inclusion of71 high and low melting-point PCMs as filler materials at the ends of the tank, close to the inlet/outlet72 ports. In [25], the thermal performance of different MLSPCM designs was tested by means of a sim-73 5 plified numerical model. Preliminary results indicated that MLSPCM configurations may reduce the74 thermocline degradation occurring in the single-solid filled tanks and thus achieve a higher efficiency75 in the use of the storage capacity.76 Zanganeh et al. [26] recently studied a similar configuration using air as the heat transfer fluid,77 in which a single PCM layer of high melting point was placed at the top of a packed bed of rocks.78 They concluded that the PCM layer contributed to the stabilization of the outflow temperature but79 did not have an effect on the thermal efficiency of the system. The evaluation was performed after80 several charge/discharge cycles of the same duration.81 In this work, a numerical model for evaluating the thermal behavior and optimizing the design82 of packed bed systems is presented. The model considers axial thermal conduction within the heat83 transfer fluid and an special treatment for the convective term of the energy equation, diminishing84 the artificial numerical diffusion. Since the intention is to test both solid and PCM filler materials,85 radial variation of temperature within particles/capsules is taken into account. Numerical experiments86 are carried out in order to compare the thermal performance of the MLSPCM prototypes against87 different existent thermocline-like designs, such as solid-filled thermocline, single encapsulated PCM88 and cascaded PCM concepts. Several configurations are here analyzed, and the results are discussed in89 detail. Thermal performance is evaluated after running several charge/discharge cycles, until a periodic90 state is reached. Time operation of the processes (charge and discharge) are not fixed beforehand but91 depend on the temperature of the fluid coming out of the TES, which is limited by some temperature92 thresholds. The intention with this is to mimic the operating conditions of a real CSP plant, where93 the solar receivers and power block impose certain limits to the temperature of the HTF. Thermal94 evaluation is mainly based on terms of total energy storage, efficiency in the use total storage capacity,95 proportion of PCM effectively changing phase and exergy outputs.96 2. Mathematical modeling and numerical implementation97 Mass, momentum and energy conservation equations have to be solved in order to be able to98 simulate the thermal behavior of a thermocline-like tank. Some simplifying assumptions are made99 and empirical correlations are used. The most relevant assumptions are:100 1. One-dimensional fluid flow and temperature distribution (in the flow direction).101 2. One-dimensional heat transfer in filler particles/capsules (radial direction).102 3. Spherical shape of filler particles/capsules.103 4. Constant density of both fluid and filler bed materials (solid and PCM).104 5. Natural convection and contact melting inside the PCM capsules are neglected.105 6 6. Heat conduction between different filler material particles/capsules is not considered.106 7. Negligible radiation heat transfer.107 The energy conservation equations are discretized using the Finite Volume Method (FVM). The108 tank is divided in Nxtransversal cylindrical sections of height ∆x(see Fig. 1a). In each tank109 section, a single representative particle/capsule needs to be simulated, as all are affected by the same110 fluid temperature due to the one-dimensionality assumption. This filler particle/capsule, assumed as111 spherical, is discretized in the radial direction in Nrcontrol volumes, as shown in Fig. 1b.112 (a) Sketch representing the cylindrical container with the PCM capsules packed in a random fashion (b) Discretization details of the tank and of a representative particle/capsule, indicating the sub-indices used for tank sections (i) and capsule control volumes (j) Figure 1: Domain and discretization 2.1. Energy113 2.1.1. Heat transfer fluid (HTF)114 The semi-discrete energy conservation equation of the fluid in the ith tank section (i= 1...Nx)115 results in:116 ρfiViCp,f ∂Tf,i ∂t =Atkeff ∂Tf ∂x  i+1/2 i−1/2 −˙mCp,f (Tf,i+1/2−Tf,i−1/2) −nfm,i Tf,i −Ti,0 Rconv,i +Rcond,i −UambAw,i(Tf,i −Tamb) (1) where Ti,0is the temperature of the internal surface of the particles/capsules (boundary node in fig.117 1b). In the advective term (second in the right hand side) the fluid is assumed to be coming from118 section i−1 and going to section i+ 1. Rcond stands for the thermal resistance in the PCM capsules119 due to the capsule shell. The mass of the shell is disregarded here and is not considered to add any120 thermal inertia. The calculation of the thermal resistance due to convection between the HTF and the121 7 filler material (Rconv) requires the fluid-to-bed Nusselt number, which is calculated using the following122 correlation, obtained from [27]:123 Nu = 2.0+1.1Re0.6Pr1/3where Re =ρfvfdp µf (2) As stated in [27], the correct use of Eq. (2) should take into account the effects of solid-phase124 conduction and thermal dispersion in the diffusive term [first term on the right hand side of Eq. (1)]125 and not only molecular diffusion. Therefore, the effective thermal conductivity is evaluated as follows:126 keff =k0 eff +kdisp eff where the stagnant effective thermal conductivity (k0 eff ) is determined here as in [28]:127 k0 eff =kfm kf0.280−0.757log10()−0.057log10(kfm/kf) (3) and the effective conductivity due to thermal dispersion (kdisp eff ) is determined according to the following128 correlation [29]:129 kdisp eff kf = 0.00232Pe2where Pe =RePr In this work, some of the studied cases include one or several PCMs as filler materials. Since solid130 and liquid phases may have different thermal conductivities, a criterion is needed to determine the131 value of kfm used in Eq. (3). The criterion adopted here consists in using the thermal conductivity132 calculated at the radius of capsule that divides the sphere in two parts of the same volume.133 2.1.2. Filler material134 The energy balance for the inner nodes (j= 1...Nr) of the filler material remains:135 ρfVi,j ∂hi,j ∂t =kfmA∂T ∂r i,j−1/2 −kfmA∂T ∂r i,j+1/2 (4a) while for the boundary node (j= 0), in contact with the heat transfer fluid, results in:136 ρfVi,0 ∂hi,0 ∂t =Tf,i −Ti,0 Rconv,i +Rcond,i −kfmA∂T ∂r i,1/2 (4b) In order to solve these equations it is necessary to define a relation between the enthalpy and the137 temperature of the filler materials. Considering constant specific heats for each phase, these relations138 are:139 8 h−h0=Cp,s(T−T0), T ≤Ts h−h0=Cp,s(T−T0) + fL, Ts< T ≤Tsl h−h0=Cp,l(T−Tsl) + Cp,s(Tsl −T0) + fL, Tsl < T ≤Tl h−h0=Cp,l(T−Tsl) + Cp,s(Tsl −T0) + L, Tl< T Tsl indicates the temperature in the phase change range chosen as the transition temperature for140 the specific energy from solid to liquid, or vice versa. Mass liquid fraction (f) values range from 0141 (pure solid) to 1 (pure liquid), which, in this work, are calculated as a linear function of temperature142 in the phase change interval:143 f=T−Ts Tl−Ts (5) By taking a very narrow temperature range (Tl−Ts), fixed melting point PCMs can also be144 modeled with this approach. Hence, a unique value of hexists for each value of T, and the energy145 balance [Eq. (4)] may be expressed with Tas the only variable. It should be noted that, since the146 location of the solid-liquid interface is implicitly determined by values of f, explicit tracking of interface147 is avoided with this strategy.148 2.2. Momentum149 To determine the pressure drop in the packed bed, the following momentum equation is solved:150 δp δxi =± 5 Re1,i +0.4 Re0.1 1,i !6ρfv2 f(1 −i) dp,i3 i −ρfg(6) where Re1,i =ρfvfdp,i 6(1 −i)µf (spherical particles) and vf=˙m ρfAt Eq. (6) is the Carman correlation for packed beds, which is generally used for solid objects forming151 a bed [30]. In this equation xincreases from the bottom to the top, and therefore, the positive sign is152 used in the discharge of the tank while in the charge process the negative sign is used. The last term153 accounts for the pressure reduction/increase due to the gravitational action.154 2.3. Exergy155 For evaluating the power generating potential of the energy delivered by the thermal storage, the156 exergy global balance of the heat transfer fluid is calculated in the following manner:157 9 (a) Prototype C1 (b) Prototype D1 (c) Prototype F1 Figure 5: Sketches of some of the different filler configurations tested. Table 2: Thermo-physical properties. Quartzite rock PCM Molten Salt & sand (Qu) [20] (KOHXXX) [13] (HTF) [34] ρ(kg/m3)2500 2040 1873.8 Cp,s (J/kg K)830 1340 - Cp,l (J/kg K)- 1340 1501.5 ks(W/m K)5.69 0.5 - kl(W/m K)- 0.5 0.443 + 1.9×10−4T(ºC) µ(Pa s)- - 22.714 ×10−3−0.12 ×10−3T+ 2.281×10−7T2−1.474×10−10T3 L(J/kg)- 1.34 ×105- difference is 100℃(290℃- 390℃). It can be observed that, even in the cases where the filler material is295 only encapsulated PCM (cases B1-3 and F1-2), the sensible energy capacity is higher than the latent296 one. This is due basically to two reasons: first, the temperature jump is relatively high, making the297 sensible energy capacity of the PCMs to be equal to their latent energy capacity (Cp∆T=L); and298 second, the HTF confined inside the tank contributes with an extra sensible energy capacity.299 16 Table 3: Mass confined inside the tank and storage capacity. Mass data (ton) A B1 B2 B3 C1 C2 C4 D1 D2 F1 F2 Mass of PCM 0.0 42.0 42.0 42.0 17.0 33.9 8.5 25.0 21.0 42.0 42.0 Mass of solid filler material 71.7 0.0 0.0 0.0 42.7 13.8 57.2 28.9 35.8 0.0 0.0 Mass of confined HTF 15.2 23.4 23.4 23.4 18.5 21.8 16.8 20.1 19.3 23.4 23.4 Total mass 86.8 65.4 65.4 65.4 78.2 69.5 82.5 74.1 76.1 65.4 65.4 Storage Capacity Filler material (MWh) 1.65 3.13 3.13 3.13 2.25 2.84 1.95 2.53 2.39 3.13 3.13 Confined HTF (MWh) 0.63 0.98 0.98 0.98 0.77 0.91 0.70 0.84 0.80 0.98 0.98 Total (filler + HTF) (MWh) 2.28 4.10 4.10 4.10 3.02 3.75 2.65 3.37 3.19 4.10 4.10 Total sensible energy (%) 100.0 61.9 61.9 61.9 79.1 66.4 88.1 72.3 75.5 61.9 61.9 Total latent energy (%) 0.0 38.1 38.1 38.1 20.9 33.6 11.9 27.7 24.5 38.1 38.1 3.2. Results and discussion300 3.2.1. Case A: Solid filler material301 Table 4 shows the thermal performance results for each case. Case A (“pure” thermocline) is shown302 to behave quite poorly in terms of stored energy when compared against the rest of the cases (with303 exception of case B1). The stored energy at thermal equilibrium is 1.45 MWh,which is around 63% of304 the storage capacity. This somewhat low efficiency is due to the thermocline degradation throughout305 the several charging-discharging cycles, enforced by the assumed temperature thresholds.306 17 Table 4: Performance results for each configuration Results A B1 B2 B3 C1 C2 C4 D1 D2 F1 F2 Operation time (h)11.67 1.16 2.61 2.62 2.86 2.99 2.68 1.82 3.00 3.28 2.03 Stored Energy in Filler material (MWh) 1.05 0.63 1.42 1.43 1.72 1.71 1.65 1.11 1.83 2.00 1.25 Stored Energy (Filler + confined HTF) (MWh) 1.45 1.00 2.19 2.20 2.32 2.42 2.22 1.48 2.43 2.66 1.64 Stored Energy / Storage capacity (%) 63.4 24.5 53.4 53.5 76.9 64.5 83.7 43.8 76.2 64.9 40.0 Sensible energy stored / Total stored (%) 100.0 96.3 90.7 90.7 80.0 80.0 86.7 69.8 73.7 64.0 60.6 Latent energy stored / Total stored (%) 0.0 3.7 9.3 9.3 20.0 20.0 13.3 30.2 26.3 36.0 39.4 Effective mass of PCM changing phase (%) - 2.4 13.1 13.1 73.6 38.4 93.2 47.9 81.7 61.3 41.4 Exergy difference at charge (MWh) -0.70 -0.48 -1.05 -1.06 -1.12 -1.17 -1.07 -0.71 -1.18 -1.29 -0.79 Exergy difference at discharge (MWh) 0.69 0.48 1.04 1.05 1.11 1.15 1.06 0.70 1.16 1.27 0.78 Pressure losses due to filler bed (Pa) <400 <100 <100 <100 <250 <150 <350 <200 <250 <100 <100 aIn cases where the charge and discharge operation times are different, (e.g. B2 and B3) the mean value between processes is shown. 18 (a) 1st charge (b) 1st discharge (c) 2nd charge (d) 2nd discharge (e) Periodic state charge (f) Periodic state discharge Figure 6: Case A. Temperature maps at various instants for the first two cycles and the periodic state. The chronological order of the curves is from left to right in the charge and from right to left in the discharge. Figure 6 shows the temperature maps obtained for case A, of charge and discharge processes at307 various instants for the first two cycles and the periodic state. The degradation of the thermocline308 can be clearly observed by comparing the 1st and last cycles. The initial condition in the first charge309 process is a uniform cold temperature throughout the tank. For the 2nd cycle, the initial condition of310 19 the filler material and HTF is not anymore a uniform temperature curve, but one with the temperature311 gradient resulting from the last discharge process. This change in the initial conditions is inevitable312 due to the requirements imposed on the outgoing fluid temperature, which enforce it to lie inside the313 admissible range. Since the difference between the incoming fluid temperature and that of the filler314 material is lower than in the 1st charge process, the heat transfer rate, and thus the thermal gradient315 (in absolute value), are also lower in the 2nd charging.316 Therefore, during the consecutive charging/discharging cycles, the thermal gradient tends to get317 “flattened” until a periodic unsteady state is reached. Due to this thermocline degradation, the318 stored/released energy in this periodic state is lower than those of the previous cycles, and so is the319 operation time, since outlet thresholds are reached earlier.320 A useful way of estimating the stored/released energy in each process is to calculate the area321 between the initial temperature map and the last one, since sensible energy differences are proportional322 to the temperature jumps. From the comparison between figures 6a and 6e, a clear difference can be323 observed in the area between initial and last temperature maps of the charge processes.324 Once the periodic state is reached, symmetry between processes can be observed; and therefore,325 the energy which is stored in the charge is later delivered in the discharge. This is due to having326 disregarded the thermal losses to the ambient.327 3.2.2. Cases B1-3: Encapsulated PCM328 A first look into the storage capacity values of Table 3 can induce the reader to think that a storage329 tank filled with an encapsulated PCM should store more energy than the same tank filled with a solid330 filler material. However, results shown in Table 4 reveal a different situation.331 Prototype of case B1 is filled with a single encapsulated PCM with a fusion temperature of 360℃332 (KOH), which is well between the operating temperatures of the storage system.333 The temperature maps of the HTF inside the tank at various instants for the first two and periodic334 state cycles, are plotted in figure 7. A clear picture of the problem results from their observation. In335 the first charge, with an initially cold tank, the outlet temperature threshold is reached in a moment336 where only part of the contained PCM capsules have melted. The position inside the tank where337 the phase-changing capsules are located, can be identified by the location where there is a steep338 temperature gradient ranging from 390℃to 360℃, which for the final state is located at a distance of339 around 3.6 m from the bottom. Therefore, only a portion of the available latent heat has been used.340 Moreover, the sensible energy capacity of both the PCM and HTF is much less harnessed than in case341 A. Thus, the initial condition for the subsequent discharge is one where only a part of both the latent342 and sensible energy capacity can be exploited.343 20 (a) 1st charge (b) 1st discharge (c) 2nd charge (d) 2nd discharge (e) Periodic state charge (f) Periodic state discharge Figure 7: Case B1. Temperature maps at various instants for the first two and last cycles. The chronological order of the curves is from left to right in the charge and from right to left in the discharge. An important observation is that the melting point of KOH lies outside the admissible temperature344 ranges for both charging and discharging processes. In the figure it can be observed how the tem-345 perature of the HTF passing through the phase-changing PCM capsules is kept close to their melting346 point. Therefore, in the charging phase, the filler material located downstream of the phase-changing347 21 capsules receive the HTF with a temperature equal to the melting point, not being able to melt. Since348 the threshold temperature is lower than the melting point, the charging process ends before all the349 PCM has melted, when the capsules located at the outlet (top) cannot bring the HTF temperature350 below the threshold, with the use of their sensible energy capacity alone.351 At the periodic state, the area between the initial and last temperature curves is somewhat higher352 than those corresponding to the initial cycles (except from the 1st charge). Furthermore, the location353 of the phase-changing layers has been shifted slightly to the center of the tank.354 Cases B2 and B3 have the common feature of using PCMs whose melting points lie inside each of355 the admissible temperature ranges. In B2 a melting point of 380℃has been chosen, which is inside356 the admissible range for the outlet fluid temperature of the discharging process (375℃- 390℃); while357 a melting point of 300℃has been chosen for case B3, lying inside the admissible range of the charging358 process (290℃- 305℃).359 Temperature maps for the periodic state of both cases are shown in figures 8 and 9. A first360 observation is that the area between the initial and final maps for both cases is higher than that of361 case B1. As a result, a higher energy is stored in both cases, as can be observed in Table 4.362 In these cases, due to the more “intelligent” choice of the melting points, a higher utilization of the363 whole storage capacity has been attained. For example, in case B2, as the cold fluid comes through364 the bottom of the tank and the thermal gradient travels to the top, the layers of PCM located at365 the hot zone, which have melted in the previous charging, act as thermal “buffers” for the outgoing366 fluid, keeping its temperature close to the melting point until almost all the PCM near the outlet has367 solidified. Since this temperature is inside the admissible range, the process does not stop, and the368 rest of the upstream filler material can be thermally discharged.369 Due to the symmetry between key temperatures of cases B2 and B3 (melting points, thresholds and370 operating range), the resulting temperature maps for the periodic state are also symmetric. Charging371 process of case B2 looks the same as the discharging process of B3, with a shift of the sense in which372 both axis increase. Furthermore, the results of both cases shown in Table 4 are almost identical.373 However, a slight difference is encountered in the value of exergy delivered in the discharging phase.374 Result for case B3, with a PCM melting point of 300℃is slightly higher than that of case B2, where375 a melting point of 380℃has been adopted. This result may seem strange, since one could think that376 a higher melting point of the PCM should result in a higher amount of hot fluid coming out of the377 tank and a higher amount of exergy delivered in the discharge. The explanation for this result can378 also be extracted from the temperature maps shown in figures 8 and 9. In case B2, the temperature379 of the outgoing fluid in the discharge is seen to be the PCM melting point during most of the process380 22 (Fig. 8b); while in case B3, it is observed that during most of the discharging phase, the outlet fluid381 temperature is the maximum possible (Fig. 9b). The reason for this is that the low melting point382 PCM, acting as a thermal buffer during the charging phase, allows the upstream filler material to be383 charged of sensible energy up to the maximum temperature, while the high melting point PCM of case384 B3 is storing most of the high temperature energy (between 380℃and 390℃) in the form of latent385 heat at 380℃. On the other hand, case B2 also stores less exergy than case B3, since it needs less386 time to be charged (see figures 8a and 9a), and its final exergy efficiency (delivered/stored) is slightly387 higher in the former.388 (a) Charge (b) Discharge Figure 8: Case B2. Periodic state. Temperature maps at various instants. The chronological order of the curves is from right to left for the charge process and from left to right for the discharge. (a) Charge (b) Discharge Figure 9: Case B3. Periodic state. Temperature maps at various instants. The chronological order of the curves is from right to left for the charge process and from left to right for the discharge. 23 3.2.3. Cases C1-3, D1-2: Multi-layered solid-PCM (MLSPCM)389 Results obtained with cases B1 - B3 show that even in the best case, only a little amount of PCM390 is effectively changing phase in a cycle (less than 15%). Moreover, the results of cases B2 and B3391 show that an effective way of increasing the stored energy of an encapsulated PCM tank is to choose a392 PCM whose fusion temperature lies between an admissible temperature interval for either one of the393 processes (charge or discharge). Thus, the PCM capsules located at the end of the tank, where the394 HTF temperature is close to its melting point, act as a thermal buffer maintaining a desirable outlet395 temperature, while the rest of the tank is charged (or discharged) with sensible energy.396 Therefore, a tank which is filled with PCM in such a way that most of it can effectively undergo397 through the phase change, together with the inclusion of a cheaper solid filler material to store the398 sensible energy, should be a much more efficient and cost-effective thermal storage device.399 Hence, all the configurations studied in this section contain PCM layers at both extremes, one400 with a high melting point placed at the top of the tank (hot zone) and another with a low melting401 point placed at the bottom (cold zone), together with solid filler material placed in between.402 The symmetry of the proposed problem, given the operation conditions,induces to design the403 multi-layered prototypes using symmetric configurations, i.e. using the same width for the PCM404 layers whose melting point are at the same distance (in temperature units) from the corresponding405 outlet temperatures.406 Cases C1 (see sketch on Fig. 5a), C2 and C4 are MLSPCM configurations with only two different407 PCMs collocated at both extremes of the tank and a solid filler material (quartzite rocks & sand) in the408 middle zone, forming a 3-layer arrangement, only differing in the width of the layers. PCMs used are409 those of cases B2 (KOH380) and B3 (KOH300), having melting points lying inside the corresponding410 admissible range.411 Performance results of the three cases, in Table 4, show a significant improvement with respect412 to cases A and B1-3. The “buffering” effect of the PCM at both ends can be appreciated in figures413 10 to 12. An increase in the amount of stored/released energy in the periodic state is observed. The414 efficiency in the usage of both the total thermal capacity and the latent energy capacity are also higher.415 C2 stores the highest amount of energy of the three, but is the one with the lowest efficiencies in416 terms of utilization of both total and latent storage capacities. In fact, C4, with the least amount of417 PCM, is the best in terms of efficiency. Around 93% of the PCM is effectively changing phase between418 successive processes in the latter case, while 74% is the corresponding value for C1 and 38% for C2.419 In terms of total storage, C1 stores around 4% less than C2, while C4 is around 8% worse than C2.420 Regarding the values of fraction of energy stored in the form of latent heat, it can be observed421 24 (a) Charge (b) Discharge Figure 10: Case C1. Periodic state. Temperature maps at various instants. The chronological order of the curves is from right to left for the charge process and from left to right for the discharge. (a) Charge (b) Discharge Figure 11: Case C2. Periodic state. Temperature maps at various instants. The chronological order of the curves is from right to left for the charge process and from left to right for the discharge. that for cases C1 and C2 they are almost exactly the same and lower for case C4. This can be422 explained by the following reasoning. 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