M.A.Erfni Moghddm , M.R.Hssni Soukht Andni , Kh.Hosseinzdeh , , , Mohmmd Behshd Shfii , D.D.Gnji

aDepartment of Mechanical Engineering, Babol Noshirvani University of Technology, Babol, Iran

bDepartment of Mechanical Engineering, Sharif University of Technology, Tehran, Iran

Keywords:Thermal storage TCTHX Fins Melting evolution Porous media Heat exchanger

ABSTRACT It is believed that it is going to be a sizeable mismatch between supply and demand when it comes to renewable resources.Lately, researchers are on course to compensate for the unpredictabilityof such re- sources by the employment of phase change materials (PCMs).Having multiple advantages, PCMs gener- ally suffer from inadequate thermal conductivity which causes prolonged transition procedures.To tackle this issue, this study is fixated on two parameterswhich are linked to fins addition and porous media incorporation in a melting process within a triple concentric tube heat exchanger (TCTHX).The results provided by multiple cases underlined the significance of natural convection in the bare system, although finned and copper-metal-foam cases outshine buoyancy forces by roughly 45% and 97%, respectively.Ma- terial is a major determent when it comes to the selection of porous media as Al 2 O 3 registered the weak- est performance among SiC, Ni and Cu, however, it managed to speed up the process by 75% which still is much higher than the finned system, implying that porous media is of higher priority over fins.The best scenario transpiredwhile fins and copper metal foam were integrated as 26% and 97% soars in efficacy have been obtained compared to individual incorporation of porous media and fins, respectively.

Heat storage, especially in buildings attracted sizeable atten- tion in recent years due to detrimental impacts of traditional en- ergy resources, thus necessitating concerted effort into methods that enable us to store heat more efficiently.The most significant problem attributed to renewable energy is its intermittency, which was not addressed adequately during recent decades.Therefore, re- searchers have developed multiple models and inventions, one of which is thermal energy storage (TES) units which alleviate the ad- verse aspects of wind and solar energy by saving it inside these reliable systems for later usage [1] .Latent heat thermal energy storage systems (LHTESS) as a type of TES units are turned out to be the key factor of many studies in which PCMs play a crucial role due to their positive properties such as negligible tempera- ture variations, high thermal capacity, non-toxicity and unvarying performance amid plenty cycles [2] .Hence, innumerable applica- tions associated with PCMs have grownprevalent as of late leading to conspicuous jumps in efficiency for a large range of equipment, namely HVAC systems [3] , building water supply [4] , cooling and refrigeration [5] , and muchmorerange of implementations.

NomenclatureAmush mushy zone constant (kg ·m ?3 ·s)C p specific heat (J ·kg ?1 ·K ?1)C i inertia coefficientD pipe diameter (m)d f fiber diameter (m)d p pore diameter (m)f friction factorg acceleration of gravity (m ·s ?2)h heat transfer coefficient (W ·m ?2 ·K ?1)K permeability (m 2)L latent heat of fusion (kJ ·kg ?1)m mass (kg)P pressure (Pa)r radial coordinate (m)T temperature (K)T m melting point (K)t time (s)u, v fluid velocity in Cartesian coordinates (m ·s ?1)x , y Cartesian coordinates (m)Greek s y mbols β melting fractionε porosityγ thermal expansion coefficient (K ?1)λ thermal conductivityμ dynamic viscosity (kg ·m ?1 ·s ?1)ρ density (kg ·m ?3)Subscrip t se effective value i inner tube m middle tube PCM phase change material por porous media ref reference value

In spite of numerous benefits that PCMs offer, the majority of them lack sufficient thermal conductivity which in turn translates to suppressed phase-transition rates.To address this shortcom- ing, recent studies have been carried out to find effective reme- dies such as fins installation [6-8] , usage of porous media [ 9 , 10 ], nanoparticles additions [11-15] and supplemental geometrical modifications [ 16 , 17 ].A key heat promoter in LHTESS systems concerns porous media that are embedded into PCM to compen- sate for their inadequate thermal conductivity [18] .In an investi- gation into RT58 as a PCM, Zhao and Tian [19] applied metallic foam into a heat exchanger to evaluate the functionality of this technique on transition speed and they came to conclude that a staggering improvement of 3 to 10 times with respect to thermal productivity is achievable.The rationale behind this enhancement is attributed to the pores existing in porous media which occupy the whole space to hold PCM together.This extended contact area between PCM and metal results in higher overall thermal conduc- tivity which is a core parameter in LHTESS.Two primary traits for these structures are porosity and pore density.The porosity is de- termined by dividing void space by the total space available in the annulus and the pore density is calculated by the number of pores per inch (PPI).Due to its confining influence, porous media tend to engulf PCM into voids leading to suppression of buoyancy forces, thus the porosity generally is settled between 0.9 to 1 for the di- minishment of this drawback.Zheng et al.[20] proposed a sys- tem in which a rectangular cavity was selected for a 2D simulation to assess the impact of porous media application along with PCM.The final evaluations unveiled that the transition procedure was lowered by roughly 20% if PCM/metallic foam was used concur- rently.In another survey performed numerically and experimen- tally, Atal et al.[21] studied a horizontally-located heat storage in which paraffin wax was mounted inside the annulus while the in- fluence of various porosities of aluminum was to be found.They realized that varying porosities of 95% and 77% have a significant impact on phase-change evolution, with less porosity giving rise to more desirable heat transfer and higher thermal conductivity.

A conglomerationof heat transfer promotersare being widely applied into PCMs, however, the combination usage of them has just attracted many researchers.Mahdi and Nsofor [ 22 , 23 ] pre- sented two surveys in order to determine the outcome of simul- taneous effects of aluminum nanoparticles and copper foams on the melting and solidification phenomena inside a heat exchanger.The results depicted in their studies show that enhancements up to 90% and 96% can be realized for melting and solidification, re- spectively, depending on the volume fraction of nanoparticles and porosity of metallic foam.Also, many studies proposed varying porosity to compensate for the negative consequence of natural convection in the presence of metallic foams.Since the bottom of storage units are the last fractionexperiencing transition for con- duction dominancy, diverse porosity is employed in such a way that porosity gradually decreases from the bottom to the top re- sulting in a higher thermal conductivity at the lower section while the upper part enjoys better natural convection.Three different models to cast light on changing porosity technique have been considered by Yang et al.[24] namely, two linearly-changing poros- ity cases in one of which maximum porosity was at the bottom and in the other one at the top along with the third case having uniform porosity.The best performance among them is delivered byvarying porosity in which minimum porosity occurred at the top segment since this case took advantage of the buoyancy effect far better than the other two scenarios.Xu et al.[25] investigated LHT- ESS units while the annulus was partially filled with porous media to mitigate the minimization of natural convection.They reported that the comparison between the non-porous case and the full- porous case revealed a growth of roughly 6 times in presence of metallic foam.However, impregnating the metallic foam up to the lower half of the space displayed almost the same result, compared to full porous configuration, leading to approximately 28% less ma- terialand fostered natural convection.

Installation of extended surfaces or fins inside storage systems as a contributing parameter for heat transfer amplification earned a lot of attention thanks to their promising outcomes compared to unfinned systems.Incorporation of fins can happen in various forms and designs like circular fins, pins fins and longitudinal fins which are being broadly applied and produced desirable outcomes.Agyenim et al.[26] distinguished the applicability of circular fins, longitudinal fins and plain cases in a LHTESS when evaluating the charging/discharging cycles of Erythritol as the PCM.They found that the best method belonged to the longitudinal fins.Shokouh- mand and Kamkari [27] studied the functionality of adding longi- tudinal fins into a storage unit while Paraffin wax was employed to evaluate melting behavior.Their results clarified that includ- ing more fins into the system could produce a better heat trans- fer rate springing from the more available interface between highly conductive fins and PCM.Another analysis performed experimen- tally considered both design parameters like fins numbers and op- erational variables such as heat transfer fluid (HTF) temperature and mass flow rate.In this work, Blen et al [28] used a Double concentric tube heat exchanger (DCTHX) to determine which fac- tor was of more importance in the solidification process and con- cluded that geometrical procedures could affect the system more positively than operational ones.

Moreover, Seeniraj et al.[29] tried one particular fins configu- ration in which all the fins were installed from the top to the bot- tom resulting in identical separated sections in the annulus.This arrangement equalized transition rate for all parts since fins hin- dered the natural convection which otherwise made top half melt faster.Guo et al.[30] employed non-uniform fins in a numerical assessment of a vertical heat storage unit.They applied different arrangements and tilt angles of the fins as the optimization deter- minants.Non-uniformity of the fins was found to improve upon uniform configuration by as much as almost 70%.The same author [31] experimentally examined the metal foam and fins combina- tion in which roughly 83% reduction in melting phenomenon was achieved by introduction of fin-foam configuration.

A triple tube heat exchanger (TTHX) is applied in this numeri- cal analysis by Ansys 16.0 of multiple factors that can have poten- tially a major impact on the melting evolution of such systems as the majority of research has been designated to the shell-and-tube heat exchangers and employment of TTHX combined with other parameters is totally novel and innovative.This study attempts to cast light on the underlying interaction between PCM and porous media for which 4 different materials with 5% concentration have been adopted to expand our understanding of such technique in a TTHX as there is no study that investigated this aspect of heat stor- age systems.Moreover, a comparison between porous media and fins and simultaneous usage of both techniques have been made to grade the effectiveness of individual and multiple employment of primary determinants in TTHX.

A schematic configuration of a TCTHX is shown in Fig.1 .As in- dicated in Fig.1 the inner and outer tubes whose diameters are 20 and 110 mm respectively, consists of heat transfer fluid (HTF) which will maintain the melting operation.The middle tube of 80 mm diameter is occupied with paraffin (RT-82) as a PCM whose properties are tabulated in Table 1 .Throughout the melting evo- lution, constant temperature hot water is in circulation through the inner and outer tubes.For each case, the same constant mass flow rate of HTF is circulated in both inner and outer tubes.In this study, a two-dimensional cross-section of a TCTHX has been con- sidered for simulation as there is negligible variation along the ax- ial directionof the actual 500 mm length of respective heat stor- age unit.In order to reduce the computational cost, half of the annulus with a symmetry line at the middle has been modeled and analyzed.A schematic representation of the two-dimensional domain is showed in Fig.1 .Initially (att= 0) the PCM tempera- ture is set at 300 K and suddenly it’s exposed to HTF with con- vective heat transfer boundary conditions.Essentially, 7 scenarios have been considered based on porous media inclusion and fins addition in this study.These cases can be categorized in four dif- ferent groups, namely: (1) plain tube, (2) porous-embedded tube, (3) finned tube, (4) porous-embedded and finned tube.The result section of this study is presented based on these four groups to simplify the understanding.

Fig. 1. Geometry of the problem.

Table 1 Thermal-physical characteristics [ 35 , 36 ].

The dynamic viscosity of the PCM is considered as a function of temperature which is defined by [32] :

whereA= 0.819,B= -1.546 × 10?2, and 326 K ≤T≤353 K.

Equation (1) above is a correlation which is obtained from ex- perimental data points at different temperatures.Form the equa- tion it can be observed that the dynamic viscosity decreases as temperature increases.

Melting evolution of the PCM can be calculated via continuity, momentum and energy equations given as Eqs.(2) - (13) .The ensu- ing paragraph readssome assumptions for a more simplified simu- lation:

(1) The enthalpy method is applied for simulation of the heat transfer in course ofthe melting phenomenon.(2) Brinkman-Forchheimer-extended Darcy model is in place to account for un- derlying physics in the porous domain.(3) Local thermal equilib- rium conditionis assumed in effect between the given PCM and the porous mediaasmetal materialsare deemed homogeneous and isotropic.(4) Thermophysical properties of included materialsare not temperature-dependentexcept for dynamic viscosity and den- sity.(5) The streaming flow is considered laminar, unsteady, and incompressible.(6) Viscous dissipation is negligible.(7) The tem- perature variation in the HTF is negligible.(8) No-slip conditionsat boundaries are considered.(9) Boussinesq approximation, due to insignificant temperature fluctuations range, is applied to allow for density variation.(10) Volume variation related to the phase tran- sition is omitted, and (11) perfect insulation condition is assumed.For boundary conditions, with regard to aforesaid assumptions, the temperature of the inner and middle tube is considered to be 373 K and constant through the whole process as temperature fluctua- tion in HTF is somewhat minimal.

The governing equation is:

Equation (2) is the continuity equation, whereρa(bǔ)ndvdenote density and velocity vector, respectively.

Equations (3) and (4) are the momentum equations, wherePis pressure,ρis density andμis dynamic viscosity.The two source terms in the momentum equations are given as:

The momentum sink is represented by the first term on the right side of Eq.(5) .Amush denotes a number known as mushy zone constant which determines the phase transition front whose values tend to alternates from 104to 107kg ·m?3 ·s?1 .In current work,Amushis set to 105kg ·m?3·s?1 .βcan be measured from Eq.(7) and represents melting fraction while the volume-weighted averageapproach is applied.When PCM is solidified,βwillreach 0which in turn leads tourising to infinity.Avoiding division by zero,δisset to a small number, in this case 0.001.The remaining second and third terms on the right side of Eq.(5) are relatedto flow resistance due to the presence of the metal foam.Kdetermines permeability (m2) whileCirepresents inertia coeffi- cient, which is quantified by Eqs.(8) and (9) respectively.εsym- bolizes the porosity as fiber diameterdf(m) and pore diameterdp(m) arecoupled parameters related to the porosity and porous den- sity of porous media, whose correlation is depictedin Eq.(10) .The lastitem on the right side of Eq.(6) is associated with the buoyancy force due to the existence of temperature difference and thermal expansion of PCM, generating the natural convection of the liquid phase of PCM.

Energy equation:

where the effective thermal conductivityλeis obtainable by an an- alytical model [33] based on the structure of metal foams, shown in Eq.(12) :

Figure 2 demonstrates the grid network of the computational domain.As for the grid independency, Fig.3 conveys the required date on mesh analysis of the current numerical procedure.This analysis is presented to substantiate the veracity and reliability of figures and plots in this work and also to lay bare the most accu- rate results while minimizing network numbers.The most signif- icant criterion based on which the best grid network can be re- alized is liquid fraction of the PCM, therefore this independency analysis is performed contingent on respective cases.Peering over Fig.3 , it is suggested that a grid network of 10 0 0 0 elements is ca- pable of delivering accurate results successfully within reasonable precision threshold as increasing the number of elements from 10 0 0 0 to 150 0 0 doesn’t make appreciable differences to the given outcome.

Authentication of numerical results is critical for the depend- ability of the final conclusion.The unsteady numerical simulation by the inclusion of gravity force has been done by means of AN- SYS Fluent 16.0 which performs a mathematical formulation based on enthalpy-porosity technique.A SIMPLE scheme was used for pressure-velocity coupling.For spatial discretization of pressure, momentum, and energy, PRESTO (pressure staggering) and QUICK options were set, respectively.The area-weighted average temper- ature of the PCM has been chosen for the comparison with the experimental results of S.Mat et al.[34] .To delve into the details of experimented configuration, a triplex tube heat storage whose middle tube is occupied by RT82 as the PCM is the validation case.Concerning its geometry, the system’s inner tube, middle tube and outer tube have radius of 25.4 mm, 75 mm and 100 mm, respec- tively.Furthermore, 8 fins made of copper are installed within the annulus to enhance the transition rate.The initial temperature of paraffin RT82 is fixed at 300 K while the HTF with the constant temperature of 368 K sweeps across the system.Plus, the recorded data of experimental work have been registered by 15 thermo- couples for high accuracy.From Fig.4 , it is evident that the er- ror doesn’t surpass acceptable thresholds and remains below 5% which is quite justifiable when comparing numerical data with ex- perimental set-up.Therefore, the presented results are reliable for future investigations.

In order to validate a numerical study, independence of the time step for solving the equations is important.Therefore, in this section, 3 time-steps of 0.1, 0.3 and 0.05 seconds were used to nu- merically discretize the unsteady problem.As can be seen from Fig.5 , the melting fraction diagram in terms of time is shown in the three mentioned time-steps.According to the results, there is a small performance difference between the three different scenarios and the solution is completely independent in terms of time step.Hence, to continue the solution, a time step of 0.1 seconds is used to create a balance between accuracy and computational cost.

Fig. 2. Grid network of the respective computational domain.

Fig. 3. Grid independency.

Fig. 4. Comparison of the numerical and experimental average temperature.

Fig. 5. Time step independency results.

This section expounds on the distinctive melting behavior that each proposed case demonstrates inside the annulus of the storage system.At first, temporal stages of suggested scenarios in the form of liquid fraction contours are presented and then a comprehensive plot of their melting evolution is unveiled.

With regard to plain PCM, temporal contours at 250, 60 0, 10 0 0 and 1800 s after initiation of the melting (Fig.6) process imply as to how melting front in the vicinity of inner and middle tubes takes on the whole system gradually and at 1800 s, just a some- what small fraction of the annulus remained solid in the lower half of the system.The reason for this part trailing behind can be ascribed to the potent impact of natural convection that facili- tates melting transition by inducing PCM to start an upward mo- tion and forming turbulent vortices in the upper half.Therefore, in this case, where there are no other factors involved, the buoyancy force is the dominant factor in determination of melting behavior.Looking at the implementation of fins in the annulus, this case’s performance is considerably superior to that of plain PCM as con- spicuously exposed in respective contours.Initially, besides a ring- shaped melted section in the proximity of the middle tube, there is an extended liquefied PCM stretched around four fins mounted on the inner tube.As time elapses, four regions immured between each pair of fins take form all of which gradually melt completely before the 1800 s marking the quickening impact that fins can im- pose on the storage unit.It is true that fins have a negative impact on natural convection, thus making the system more symmetric; however, this disadvantage is dwarfed by the high-level protrusion of fins into the annulus leading to empowerment of conductive heat transfer which in turn registers a far faster melting duration.Although the finned case diminishes buoyancy forces,the discrep- ancy between higher and lower sections is a reflection of its pres- ence as shown more clearly at 10 0 0 s where the remaining solid PCM is quite minimal at upper half-space between two fins.

Fig. 6. Liquid fractions of PCM and its combination with fin.

Fig. 7. Liquid fractions of different metal foams.

Fig. 8. Liquid fractions of Cu metal foam with fin combination.

Porous media incorporation into PCM-based storage unit caught attraction in literature just recently and there are no required re- sources to have a consensus on its effectiveness and advantages that can be offered by its introduction into this category of applica- tions.This paper tried to clarify the impact of, firstly, the common materials which are utilized for porous media and secondly, com- pare the best material with fins installation to distinguish these two popular heat promoters in a triplex heat storage.Al2O 3 , Ni, SiC and Cu are among the selected materials for enhancing the melting evolution of the given unit.As Fig.7 depicts the contours of each porous material at different phases of their melting procedure, it is evident that, essentially, they registered much superior responsive- ness compared to plain finned and finless PCM scenarios.However, there exists some stark difference among the performance of each material, with Al 2 O 3 standing at the last place among its counter- parts, preceded by Ni, SiC and eventually Cu as the best suggested porous media.

Fig. 9. Melt fraction for all cases.

Resultant figures in the form of temporal contours also corrob- orate this gradation.Although each material’s performance differs starkly with each other with regard to melting completion time, all of them follow a similar pattern in which adjacent areas of inner and middle tubes grow melted initially and then the middle ring- shaped solid part within the annulus is liquified.This symmetri- cal paradigm in porous-media-included systems recurs regardless of the type of material, however, in a plain PCM scenario, natural convection dominates the whole process, making the upper half of the annulus be dissimilar to the lower half.The rationale be- hind this distinction is associated with the confining effect metal foam has on PCM since it limits the mobility of PCM by enclosing it inside multiple voids.The major connectivity of porous mate- rial, on the other hand, completely outweighs this disadvantage.To demonstrate the enhancing level of fins and porous material and make a better comparison, Cu and Cu-finned cases have been sim- ulated to discuss the proportional advantage each factor is offering.By presented contours in Fig.8 , it can be deduced that, although fins boost thermal responsiveness of the PCM, compared to Cu as porous media, their impact is suppressed and lowered to minimal degrees.

Fig. 10. Average temperature of finned and copper-embedded cases.

Fig. 11. Energy storage capacity of finned and copper-embedded cases.

This realization is also manifested in Fig.9 , where melting frac- tion history against time for all discussed scenarios is put up.As clearly evidenced by this plot, irrespective of material, porous me- dia inclusion benefits the whole system by a wide margin as for plain tube, it takes almost 4900 s to get fully melted followed by 2700, 1185, 534, 424 and 138 s for the finned case, Al 2 O 3 , Ni, SiC and Cu as porous media, respectively.The addition of fins into Cu as explained before doesn’t have a major and comparable impact as 26% enhancement is witnessed for this coexistence of Cu as porous material and fin which does not even come close to the 97% plunge in melting duration that Cu solely offers to the system.For better evaluation of fins and copper metal foam combination, two plots elaborating on the average temperature and stored en- ergy levels of the systems for two best scenarios are presented.As demonstrated in Fig.10 , the average temperature of the two cases started off somewhat similar, diverging around 60 s after initiation.The slope of rising temperature for copper-embedded PCM wit- nessed a reduction as fins and copper combination continued up- ward trend without any major hindrance.The total energy stored during the melting evolution (Fig.11) is more informative since, despite the steeper slope of the fin-foam scenario, the final energy storage capacity is higher for individual addition of copper into the annulus.This major observation suggests that the individual incor- poration of copper foam proved more beneficial as the energy stor- age capacity is slightly higher with negligible delay to reach fully melted status.

This study examined a numerical assessment to evaluate the impactfulness of adding fins and 4 different metal foams of vari- ous materials through the PCM melting evolution in a TTHX.Based on the given descriptions and discussions, the following points are made to outline the surveyed parameters and findings:

?Four different categories: plain system, finned tube, porous- media-included tube, and fin-porous-media combination were assessed with each of these filling up the same volume of the system.

?The problem was simulated by a 2D computational domain ac- commodating PCM, isothermally heated walls of TTHX by HTF at temperatures of 373 K.Results in the form of solid-liquid interface contours, and liquid fraction profile during varying stages of melting procedure have been shown and explained.

?It can be inferred from all the presented figures and contours that despite the fact that natural convection, in absence of porous media and fins, dominates the melting procedure, the range of improvement by a high level of intrusion that fins and porous media are offering is far more powerful, with fins and Cu metal foam increasing the responsiveness by staggering spikes of 44% and 97%, respectively.

?Furthermore, porous media with only 5% concentration proved considerably superior to fins as all material chosen as porous media outpace finned case without any exception.

?Simultaneous deployment of fins and copper metal foam also registered some enhancement of 26% compared to individual employment of copper, however, due to high level of fins vol- ume, their combination is not justified.

Declaration of Competing Interest

The authors declare that they have no known competing finan- cialinterestsor personal relationships that could have appeared to influence the work reported in this paper.