Cascaded thermal storage, consisting of multiple Phase Change Materials (PCMs) with different melting temperatures, has been proposed to solve the problem of poor heat transfer caused by unavoidable decrease of temperature differences during heat exchange process. This paper conducts a theoretical study of the overall thermal performance for a cascaded thermal storage system. Both heat transfer rate and exergy efficiency are taken into account. The main findings are: the cascaded

arrangement of PCMs enhances the heat transfer rate by up to 30%, whilst it does not always improve the exergy efficiency (-15 to +30%). Enhanced heat transfer and reduced exergy efficiency can both be attributed to the larger temperature differences caused by the cascaded arrangement. A new parameter hex (exergy transfer rate) has been proposed to measure the overall thermal

performance. It is defined as the product of heat transfer rate and exergy efficiency, representing the

transfer rate of the utilisable thermal energy. The simulation results indicate that the cascaded thermal storage has higher overall thermal performance than the single-staged storage despite of higher exergy efficiency loss

Lapkin, Alexei

Tian, Y. (Yuan)

Zhao, Changying

English

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http://go.warwick.ac.uk/lib-publications          Original citation: Tian, Y. et al. (2012). Exergy Optimisation for Cascaded Thermal Storage. Proceedings of the 12th International Conference on Energy Storage.  Lleida, Spain. 16-19 May  Permanent WRAP url: http://wrap.warwick.ac.uk/49188   Copyright and reuse: The Warwick Research Archive Portal (WRAP) makes the work of researchers of the University of Warwick available open access under the following conditions.  Copyright © and all moral rights to the version of the paper presented here belong to the individual author(s) and/or other copyright owners.  To the extent reasonable and practicable the material made available in WRAP has been checked for eligibility before being made available.  Copies of full items can be used for personal research or study, educational, or not-for-profit purposes without prior permission or charge.  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For more information, please contact the WRAP Team at: wrap@warwick.ac.uk  Innostock 2012The 12th International Conference on Energy StorageINNO-SP-78Exergy Optimisation for Cascaded Thermal StorageYuan Tian1, Changying Zhao 2, Alexei Lapkin11School of Engineering, University of Warwick, CV4 7AL, Coventry, United Kingdom,Phone: 44-2476522654, email: Y.Tian.4@warwick.ac.uk2School of Mechanical Engineering, Shanghai Jiaotong University, 200240, Shanghai, China,Phone: 86-21-34204541, Email: Changying.zhao@sjtu.edu.cnAbstractCascaded thermal storage, consisting of multiple Phase Change Materials (PCMs) with differentmelting temperatures, has been proposed to solve the problem of poor heat transfer caused byunavoidable decrease of temperature differences during heat exchange process. This paper conductsa theoretical study of the overall thermal performance for a cascaded thermal storage system. Bothheat transfer rate and exergy efficiency are taken into account. The main findings are: the cascadedarrangement of PCMs enhances the heat transfer rate by up to 30%, whilst it does not alwaysimprove the exergy efficiency (-15 to +30%). Enhanced heat transfer and reduced exergy efficiencycan both be attributed to the larger temperature differences caused by the cascaded arrangement. Anew parameter hex (exergy transfer rate) has been proposed to measure the overall thermalperformance. It is defined as the product of heat transfer rate and exergy efficiency, representing thetransfer rate of the utilisable thermal energy. The simulation results indicate that the cascadedthermal storage has higher overall thermal performance than the single-staged storage despite ofhigher exergy efficiency loss.NomenclatureBi Biot number, hd/λ (dimensionless)cp specific heat of HTF (kJ/kg)cs specific heat of PCMs (kJ/kg)d characteristic length (m)dA differential thermal area (m2)dq differential heat flow (kJ)m。mass flow rate (kg/s)h system dimension (m)h heat transfer coefficient (W/m2 K)hs enthalpy of PCMs (kJ/kg)HL latent heat (kJ/kg)L system length (m)Nu Nusselt number, hd/λ(dimensionless)P pressure (Pa)Pr Prandtl number, Cpμ/λ (dimensionless)q overall heat exchange rate (W/m2)Re Reynolds number, ud/ν (dimensionless)Rg ideal gas constant (kJ/kg K)s specific entropy (kJ/kg℃)T temperature (℃)T0 ambient temperature (℃)Tf0 inlet HTF temperature (℃)Innostock 2012The 12th International Conference on Energy Storageu flow velocity (m/s)X anergy (kJ)Greek symbolsλ thermal conductivity of HTF (W/m K)ρ density (kg/m3)μ dynamic viscosity of HTF (Ns/m2)ν kinetic viscosity of HTF (m2/s)ηex exergy efficiency (%)Subscriptsf HTF –heat transfer fluidm meltings PCMs1. IntroductionIn a Thermal Energy Storage (TES) system, the temperature differences undergo an unavoidabledecrease during heat exchange process, which worsens the heat transfer. In order to tackle thisproblem, a new concept of cascaded thermal storage has been proposed [1–3]. A cascaded thermalstorage system consists of multiple Phase Change Materials (PCMs) with staged meltingtemperatures, so that a relatively high temperature difference can be maintained to achieve higherheat transfer rate during the charging/discharging process. The concept of cascaded thermal storagewas tested by Michelsa and Pitz-Paal [4] for high-temperature molten salt storage system, and theirresults indicated that cascaded arrangement of PCMs increased the charging/discharging rate.Watanabe et al. [5] also identified a significant heat transfer enhancement in their ‘three-type’storage system.However, most previous studies on cascaded storage have focused on heat transfer rate, andtherefore failed to reflect an important energy conversion factor –exergy. Exergy is the useful partof thermal energy in PCMs which can be converted into electricity. Krane [6] employed the ε–NTUanalysis to conduct an exergy study of a TES system, but only sensible heat was considered. It isnecessary to make an overall thermal performance analysis of a TES system, not only consideringsensible heat, but also latent heat. This study aims to investigate the overall thermal performance ofa cascaded thermal storage system, considering both heat transfer performance and exergyefficiency.2. Problem descriptionFor comparison, two systems are presented in this study: the Cascaded Storage (CS) and the Single-staged Storage (SS). Fig. 1 (a) illustrates the CS system, and Fig. 1 (b) illustrates the SS system.The CS system was formed by staging three PCMs (different physical properties) along the flowdirection of HTF (heat transfer fluid), whilst the SS system was formed by using only one PCM.In Fig. 1, HL (kJ/kg) and Tm (℃) denote latent heat and melting temperature, respectively; h and Lshow the dimensions of the two systems. Heat transfer fluid (HTF) enters each system from the left(inlet temperature Tf0 = 100℃), and exits each system from the right (temperature Tf(t), varyingfrom time). The thermal properties of PCMs used in this study are shown in Table 1. The meltingpoint of PCM 4 (the SS system) was roughly chosen to have the average value of three PCMs usedin the Cascaded Storage (CS) system, and thus a comparison made between two systems can bejustified. The initial temperatures of two systems were both 20℃, and the ambient temperature was20℃.Innostock 2012The 12th International Conference on Energy StoragexxFig. 1. Cascaded Storage (CS) vs. Single-staged Storage (SS)Table 1 Thermal properties of PCMsPCMs Meltingtemperature(℃)Density(kg/m3)Latent heat(kJ/kg)Specific heat(kJ/kg℃)Thermalconductivity(W/m K)PCM 1 31 880.0 169.0 2.1 0.2PCM 2 50 880.0 168.0 2.1 0.2PCM 3 82 880.0 176.0 2.1 0.2PCM 4 55 880.0 172.0 2.1 0.23. Mathematical description3.1. Exergy analysisThe entropy change [3] of a system from state ‘1’to state ‘2’can be written as:2 1 2 1 2 1ln( / ) ln( / )p gs s c T T R P P   (1)The unusable part of the thermal energy (i.e. anergy X), depends on the irreversible entropyincrease, which is shown in Eq. (2).Tf0 Tf (x, t)OHTFHTFh1 h2PCM 4HL4, Tm4(b) single-staged storageL1Tf0 Tf ( t)OHTFHeat Transfer Fluid (HTF)h1 h2L2 L3PCM 1HL1, Tm1PCM 2HL2, Tm2PCM 3HL3, Tm3(a) cascaded storageyyInnostock 2012The 12th International Conference on Energy Storage 0 2 1 0 2 1 2 1ln( / ) ln( / )p gX T s s T c T T R P P      (2)Thus the percentage of the usable energy can be calculated by using Eq. (3):  2 12 1pexpc T T Xc T T  (3)Substituting Eq.(2) into Eq. (3), exergy efficiency is given in Eq. (4):  2 1 0 2 1 2 12 1ln( / ) ln( / )p p gexpc T T T c T T R P Pc T T    (4)Eq. (4) can be reduced to Eq. (5), under the assumption of PCM incompressibility.  2 1 0 2 12 1ln( / )p pexpc T T c T T Tc T T  (5)In this study, Eq. (5) has been used to obtain the exergy efficiency for both the Cascade Storage andSingle-staged Storage system.3.2. Heat transfer analysis on the HTF sideConsidering the charging process of each system, heat transfer comes from high-temperature heattransfer fluid (HTF) to low-temperature PCMs. Thermal resistance of heat transfer consists twoparts: HTF-side resistance and PCMs-side resistance. The effective heat transfer coefficient on theHTF side can be obtained by simply employing the Dittus–Boelter Equation [7].0.8 0.40.023Re PrNu (6)In this study, water was used as HTF: u = 0.5 (flow velocity), v = 0.553×10-6 m2/s (kineticviscosity at 50℃), Pr = 3.56 (Prandtl number at 50℃), characteristic length d = (h2-h1)/2 = 0.01m.By employing the Dittus–Boelter Equation shown in Eq. (6), the effective heat transfer coefficient hwas calculated as 1117.7W/m2 (h = 0.023λRe0.8Pr0.4/d).Biot number was also obtained as follows:55.9 1hdBi    (7)Biot number [7] roughly represents how many times bigger the thermal resistance on the PCMs sideis than that on the HTF side. Since Biot number is far more than 1, the thermal resistance on theHTF can be reasonably neglected, which gives much convenience to the following analyses.3.3. Heat transfer analysisPerfect thermal insulation was assumed in the study, so the heat transfer equations can beestablished by employing the Energy Conservation Law: PCMs absorb the same amount of thermalenergy as HTF releases, which is reflected in Eq. (8).( )f s f sdq dq h T T dA    (8)dqf and dqs in Eq. (8) can be expanded as follows:ff f fT xdq c mx t   (9)1h ss shdq dAt (10)Innostock 2012The 12th International Conference on Energy StorageThe last term on the right hand side of Eq. (9) is equal to the flow velocity of HTF, which is shownin Eq. (11).x ut (11)Thus Eq. (8) can be rewritten as Eq. (12).1h ( )f sf f s f sT hc m u dA h T T dAx t      (12)To tackle the phase change problem, the Enthalpy Method [8] has been employed. The PCMenthalpy hs shown in Eq. (10) has the following relationship with the PCM temperature Ts [8–10]. , (0, ), ,, ( , )ss s mss m s s m s m Ls Ls s m Lsh h c TcT T h c T c T Hh H h c T Hc             (13)4. Numerical procedureAs stated in the earlier section, Eq. (12) and (13) are the equations governing such particular heattransfer phenomena. These equations are solved simultaneously by the Finite Difference Method(FDM) under the workspace of Matlab®. Three thousand uniform meshes were used in the x-direction to ensure the simulation accuracy. Mesh independency was also examined, and it wasfound that 6000 meshes could only improve the accuracy by 0.17% compared to the case of 3000meshes. The Implicit Iteration was adopted as the Difference Scheme, because the simulationindicated that Explicit Iteration made the results divergent whilst Implicit Iteration made the resultsconvergent and accurate. Numerical simulations were set to stop when the error between twoconsecutive iterations was less than 10-4 (i.e. 0.01%).5. Results and discussionFigure 2 shows the comparison of heat transfer rates between the CS and SS system. It indicatesthat the cascaded arrangement of PCMs (CS) enhanced heat transfer rate by up to 30% (overall).However, it needs to be noted that the heat transfer rate of CS system was lower than that of SSsystem when PCM 2 finished melting process. The low heat transfer rate (CS) can be attribute totwo reasons: firstly, the temperatures in the CS system increased rapidly (sensible heat only) whenPCM 2 (50℃) finished phase change; secondly, at the same time when the temperatures in the CSsystem rose rapidly, the temperatures in the SS system kept relatively constant because PCM 4 (55℃) is still melting (latent heat). The rapidly-rising temperatures caused the decrease of temperaturedifferences between PCMs and HTF, resulting in a lower heat transfer rate.The phase change regions of PCM 1, PCM 2, PCM 3 and PCM 4 can also be seen in Fig. 2. Thefigure also indicates that PCM 3 used the most time to finish phase change, because temperaturedifferences for PCM 3 were much smaller than others. As temperature differences decreased, PCM2 and PCM 3 took more time to be melted than PCM 1.Innostock 2012The 12th International Conference on Energy StorageFig. 2. A comparison of heat transfer rate q (W/m2)The comparison of exergy efficiency between the two systems is shown in Fig. 3. The CS systemdoes not always have higher exergy efficiency than the SS system (-15% to +30%). The exergyefficiency of the CS system was lower than that of the SS system in early stages before PCM 4started to melt, because PCM 1 and PCM 2 in the CS system delayed the increase of temperaturerise due to their latent heat. Since lower temperatures mean lower quality of energy, the CS systemhad lower exergy efficiency at this time. However, the situation was changed when PCM 2 finishedphase change and PCM 4 started its phase change. From this time on, the temperatures in the CSsystem began to increase rapidly (sensible heat) whilst the temperatures in the SS system keptrelatively constant (latent heat), which leaded to a higher exergy efficiency of the CS system thanthe SS system.Fig. 3. A comparison of Exergy Efficency η(%)Innostock 2012The 12th International Conference on Energy StorageThe Second Law of Thermodynamics states that not 100% of q (shown in Eq. (8)) can be convertedinto electricity, meaning that heat transfer rate cannot reflect the real efficiency of a TES system.Thus, a new concept of exergy transfer rate hex was proposed in the study to evaluate the overallthermal performance of the CS and SS systems.hex = q×ηex (W/m2) (14)hex denotes the effective exergy transfer rate, representing how much useful thermal energy istransferred from HTF to PCMs during charging processes.Figure 4 shows the comparison of effective exergy transfer rates (hex) between the CS and SSsystem, it can be concluded that the CS system nearly always produced higher exergy flow rate (upto 23%) than the SS system. It needs to be noted that the CS system gave slightly lower exergy flowrate than the SS system, only when PCM 1 started phase change and after PCM 4 finished phasechange. The probable reasons are as follows: when PCM 1 started its phase change, the CS systemhad lower exergy efficiency than the SS system although it had slightly higher heat transfer ratethan the SS system; after PCM 4 finished its phase change, the heat transfer rate of the SS systemwas higher than the CS system due to the long-time delay of temperature rise (latent heat of PCM 4),but the exergy efficiency of the SS system was much lower than the CS system (shown in Fig. 3)due to its low temperatures after phase change.Fig. 4. A comparison of the equivalent Exergy Flow hex6. ConclusionsAn overall comparative study for the Cascaded Storage system and the Single-staged Storagesystem was carried out. In order to take energy conversion efficiency into account, effective exergytransfer rate was first introduced to measure the real energy efficiency of a Thermal Energy Storagesystem. The main findings are: although the Cascaded Storage system shows lower exergyefficiency (-15%), it has much higher heat transfer performance (30%), making its overall thermalperformance still superior (23%) to the Single-staged Storage system.7. Future workThis work has neglected natural convection and the heat conduction in vertical direction (y-direction). It is necessary to conduct further work that incorporates a multi-dimensional numericalsimulation on the coupled natural convection and heat conduction.Innostock 2012The 12th International Conference on Energy StorageAcknowledgementsThis work was supported by the UK Engineering and Physical Sciences Research Council (EPSRCgrant number: EP/F061439/1), and the National Natural Science Foundation of China (NSFC grantnumber: 51176110).References[1] M. Medrano, A. Gil, I. Martorell, X. Potou. L.F. Cabeza. State of the art on high-temperaturethermal energy storage for power generation. Part 2: Case studies. Renew. Sust. Energ. 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A Numerical Investigation of Heat Transfer in Phase Change Materials (PCMs) Embedded in Porous Metals.

A Second Law analysis of the optimum design and operation of thermal energy storage systems.

Cascaded latent heat storage for parabolic trough solar power plants.

Enhancement of charging and discharging rates in a latent heat storage system by use of PCM with different melting temperatures. Heat Recov.

Heat and cold storage with PCM.

Heat transfer enhancement for thermal energy storage using metal foams embedded within phase change materials (PCMs).

Heat transfer, 8 th Edition, McGraw-Hill Companies,

Natural Convection Investigations in Porous Phase Change Materials.

State of the art on high-temperature thermal energy storage for power generation. Part 2: Case studies.

Thermal Energy Storage: Systems and Applications, 2 nd Edition,

Exergy optimisation for cascaded thermal storage

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Exergy optimisation for cascaded thermal storage

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