discharging process of bundled-tube LHTES units

International Journal of Heat and Mass Transfer 150 (2020) 119320

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International Journal of Heat and Mass Transfer journal homepage: www.elsevier.com/locate/hmt

Impact of using a PCM-metal foam composite on charging/discharging process of bundled-tube LHTES units Ahmed Alhusseny a,b,∗, Nabeel Al-Zurfi a,b, Adel Nasser b, Ali Al-Fatlawi a, Mohanad Aljanabi c a

Department of Mechanical Engineering, Faculty of Engineering, University of Kufa, Kufa, 54003, Najaf, Iraq Department of Mechanical, Aerospace and Civil Engineering, School of Engineering, University of Manchester, Oxford Street, Manchester, M13 9PL, Greater Manchester, United Kingdom c Daikin Industries Ltd (Iraq Branch), Al Sanater Street, Karbala, 56001, Karbala, Iraq b

a r t i c l e

i n f o

Article history: Received 12 September 2019 Revised 13 December 2019 Accepted 5 January 2020

Keywords: Phase-change materials Metal foams Thermal conductivity enhancement Tube-bundle Thermal energy storage

a b s t r a c t Due to its potentials to overcome the problems of instability and intermittency of energy through using phase change material (PCM), latent heat energy storage has been used in a variety of practical applications. However, most of the phase change materials possess poor thermal conductivity resulting in a modest charging/discharging rate. To overcome this deficit, high porosity metal foam is used to improve the overall thermal conductivity of the phase change materials leading to enhancing the heat transported, and hence, promoting the PCM melting and solidification. This proposal has been utilised to improve the performance of a thermal energy storage system formed of staggered bundled tubes, which are filled with paraffin wax as a PCM compounded to open-cell copper foam. The PCM unit is charged/discharged using a relatively hot/cold water stream flowing across the tube-bundle units. The feasibility of such a configuration is examined numerically through simulating the proposed PCM-metal foam composite units and their surrounding shell computationally using the ANSYS Fluent CFD commercial code. The impact of some design and operating parameters on the charging/discharging performance has been tested including the water flow strength as well as the tube-bundle configuration. The currently proposed design of LHTES system has been found not only easy to configure, but practically efficient as well, where the overall performance achieved is remarkably outstanding, i.e. OP=(104 ~105 ). Besides, the charging/discharging rate can be remarkably boosted through a wise selection of design parameters. Crown Copyright © 2020 Published by Elsevier Ltd. All rights reserved.

1. Introduction Daily demands of energy have drastically increased due to the rapid development of industry and human society in recent years. Consequently, increasingly large rates of polluting greenhouse gases, including CO2 and SO2 , are emitted to the atmosphere, which in turn contributes seriously to the global warming and environmental pollution [1]. Renewable resources of energy can play the role of an effective alternative to the systems powered by fossil fuels. For being abundant, environmentally friendly, and inexpensive; solar energy is nowadays considered as a promising resource of renewable en-

∗ Corresponding author at: Department of Mechanical Engineering, Faculty of Engineering, University of Kufa, Kufa, 54003, Najaf, Iraq E-mail addresses: [email protected] (A. Alhusseny), nabeelm.alzurfi@uokufa.edu.iq (N. Al-Zurfi), [email protected] (A. Nasser), [email protected] (A. Al-Fatlawi), [email protected] (M. Aljanabi).

https://doi.org/10.1016/j.ijheatmasstransfer.2020.119320 0017-9310/Crown Copyright © 2020 Published by Elsevier Ltd. All rights reserved.

ergy. However, there is a serious discrepancy between the amount of energy supplied by the sun and the energy demanded along the day. To overcome this disadvantage, solar energy systems should be supplemented with thermal energy storage units, as it is in energy-efficient buildings, solar power plants, etc. Thermal energy storage (TES) is a way to effectively balance the simultaneous mismatch between the energy supplied and energy demanded, where renewable energy resources combined with thermal energy storage can be incorporated into energy systems to ensure sustainability. Thermal energy storage can be classified into three types, i.e. sensible heat storage, latent heat storage and chemical heat storage. The simplest one to configure is the sensible heat thermal energy storage (SHTES), but its storage capacity is relatively too low due to the large-volume system required to achieve the desired storage capacity [2]. Considerably large storage capacity can be, on the other hand, offered by chemical heat storage. However, this technology is still under development and further research is required to apply it into practice. Latent heat thermal

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Nomenclature asf c cf cp d df dk dp e hsf K LH n N OP p Pr PP Red SC SCD t T u, v v V˙ w W x x, y

solid to fluid interfacial specific surface area solid specific heat foam inertial coefficient fluid specific heat modified fibre size fibre size characteristic size of representative unit cell pore diameter unit vector solid to fluid interfacial heat transfer coefficient foam permeability latent heat of fusion surface normal axis packing density overall performance pressure Prandtl Number, μcp /λ pumping power Reynolds number based on fluid velocity near the fibre, Red = ρ f |v|d/μ storage capacity storage capacity density time temperature velocity components velocity vector water flowrate twice the width of the domain considered position vector coordinates

Greek symbols λ thermal conductivity ρ density μ dynamic viscosity ∅ foam porosity β coefficient of thermal expansion ω foam pore density γ distinguishing parameter between the clear and porous flow region χ foam tortuosity δ PCM liquid volume fraction Subscripts d dispersive e effective f fluid fe fluid effective g gravitational i coordinates index in inlet condition m1 PCM solidus condition m2 PCM liquidus condition s solid se solid effective t total w water 0 initial condition

energy storage (LHTES) based on solid–liquid phase change is an effective and practical approach due to its large thermal storage capacity by involving the latent heat of melting and the nearly constant temperature during the phase change process. It is a promis-

ing alternative to either chemical or sensible heat energy storage systems due to its superiority in many design aspects such as the high storage capacity as well as chemical stability and relatively low cost. So far, LHTES has been widely employed in plenty of applications including solar energy systems, building energy conservation systems [3], air-conditioning systems [4], electricity peakshaving [5] and waste-heat recovery [6,7]. However, and as reported early by NASA, most of phase change materials possess low thermal conductivity resulting in modest charging/discharging rates [8]. Such poor levels of thermal conductivity slow down the response rate of the PCMs-based TES units which may lead to serious consequences including safety issues. To overcome this deficit, it is essential to employ an appropriate heat transfer enhancement technique that is able to accelerate the system response to an adequate level (Mahdi et al. [9]). The techniques used to enhance heat transfer in LHTES systems can, in general, be classified into two categories: indirect and direct. The first one can be accomplished through improving the thermo-physical properties of the PCM itself using micro or nano additives such as carbon nanofiber [10] carbon nanotubes [11], and metal nanoparticles [12] to improve specific heat, thermal conductivity and latent heat of fusion. The other category, which is relevant to the current work, is based on the use of high thermal conductivity inserts such as fins, heat pipes, and metal foams to improve the overall thermal conductivity of the PCM unit. Due to their ease of fabrication, relatively low cost, and high effectiveness; fins have widely been applied to enhance the phase change process in LHTES units. Various configurations of fins have been proposed to promote the melting/solidification in tube-in-tank as well as shell and tube type LHTES systems. To name a few, pinned and finned heat transfer fluid (HTF) tubes, radial fins attached to the intermediate annulus of a triplex tube, radial fins along a vertical HTF tube, radially branched fins along a HTF tube, finned shell-and-tube, and annularly as well as spirally finned HTF tubes were all examined and found effective to enhance the charging and discharging rate; see [9] for further details. Due to their potential to reduce the relatively high thermal resistance posed by phase change materials, heat pipes have also been of increasing interest in promoting the melting/solidification rate. They have been applied successfully into a variety of PCMs-based systems like heat exchangers, solar thermal storage, air-conditioning, and cooling of electronic components [13]. Another sort of the high thermal conductivity inserts used to directly enhance heat transfer in PCMs systems is the so-called metal foams, which is the core objective of the present research. Open-cell metal foams are sort of porous media having promising potentials in enhancing heat transfer. Due to their high porosity, thermal conductivity and surface area density, they have become desirable in a variety of practical and industrial applications. To name a few, they have successfully been employed in the cooling of electric generators [14–16] and compact electronic gadgets [17], heat exchangers [18], and many more [19]. Therefore, they have been proposed as a way to improve the overall thermal conductivity of the PCMs systems, and hence, promotes the melting and solidification. In the numerical investigation presented by Mesalhy et al. [20], high porosity metal matrix was recommended to enhance the melting of a PCM included in the annulus of a shell-and-tube LHTES unit. The porosity and thermal conductivity of the solid matrix were found to play a major role in promoting the TES performance. Whereas reducing porosity results in some improvement, it increases the resistance of the solid matrix to the fluid motion and reduces the volume to be occupied by the PCM, which in turn degrades both the performance and storage capacity of the LHTES unit under consideration. Accordingly, a pioneering proposal was introduced to utilise open-cell metal foams [20], as a high-porosity solid matrix with high thermal conductivity, to

A. Alhusseny, N. Al-Zurfi and A. Nasser et al. / International Journal of Heat and Mass Transfer 150 (2020) 119320

enhance heat transfer in PCM-based TES systems. A PCM–metal foam composite can be simply created through an impregnation treatment with vacuum assist to remove the air inevitably existing within the porous structure of metal foam [21]. The feasibility of this proposal has extensively been examined for both lowtemperature [22] and high-temperature LHTES systems [23,24], where the charging/discharging process has, in general, been remarkably accelerated. The influence of foam porosity and pore density on paraffin melting has been examined experimentally and numerically by Li et al. [25]. It was observed that the enhancement achieved due to the improved heat conduction outmatches the suppression in natural convection due to the flow resistance imposed by the foam matrix. It was also remarked that further heat transfer enhancement can be attained either by reducing the porosity to improve heat conduction or by increasing the pore size to promote buoyancy effects. In a related context, the melting evolution of a paraffin-copper foam composite enclosed inside a plexiglass box was experimentally examined by Zhang et al. [22] and supported with a numerical analysis based on the local thermal non-equilibrium (LTNE) principle. It was observed that heat conduction is the dominant mode of heat transfer during the early stages of charging, where the paraffin temperature was slightly less than that of copper foam. Furthermore, the considerable temperature difference recorded whether experimentally or numerically between paraffin and copper foam indicates that the LTNE model is indispensable while simulating the phase change process of a PCM embedded into a metal foam. Further numerical investigations ([26,27]) were also conducted, but considering that the foam matrix and the PCM saturated with are in local thermal equilibrium (LTE) with each other. The results acquired confirm that the presence of a metal-foam skeleton enhances the heat transfer phenomenon, and hence, upgrades the performance of PCMs-based systems. In the experimentations conducted by Mancin et al. [28], the fusion evolution has been monitored for three paraffin waxes having dissimilar melting points impregnated into a copper foam with constant porosity of 0.94 and for a range of pore densities. It was observed that the heat is well spread by the foam matrix resulting in more uniform temperature distribution, which in turn accelerates the phase-change process. A tube-in-tank configuration was considered by Yang et al. [29] to track the melting evolution of paraffin when it is embedded in a copper foam with porosity of 0.92 and pore density of 20PPI. The role played by the copper foam in enhancing the fusion process was examined compared to the case of pure paraffin with and without attaching a radial fin to the HTF tube. It was apparent how the presence of metal foam makes the temperature distribution more uniform in comparison with the case of pure paraffin, where the time required for the completion of the melting process was reduced to 33% than the pure paraffin takes. It was also reported that the HTF inlet temperature plays a more influential role than the HTF flowrate is in promoting the charging process. A PCM-copper foam composite was fabricated as an LHTES medium by Wang et al. [30], where the phase-change process was tracked experimentally and numerically. It was found that saturating the copper foam with paraffin improves the overall thermal conductivity by up to 48 times compared to the pure paraffin, which in turn shortens the charging time to only 60%. The impact of inclination angle on the melting of a PCM block embedded in an open-cell copper foam was experimentally investigated by Yang et al. [31]. It was pointed out that the time required for pure paraffin to melt is clearly affected with the variation of inclination angle unlike the case of PCM-foam composite, where buoyancy has a little contribution during the melting process, i.e. the maximum change in melting time was only 4.35%. A shell-andtube unit filled with paraffin-copper foam as a PCM was experimentally tested by Yang [32], where the evolution of solid-liquid interface during the melting process was visually monitored. It was

3

remarked that the time taken by pure paraffin to completely melt can be shortened to only 36% when paraffin-copper foam is used, where temperature distribution was seen more uniform. To improve the performance of a shell-and-tube LHTES unit, Yang et al. [33] suggested filling either the HTF tube, the shell enclosing the PCM, or both of them with an open-cell metal foam, where the outcome of this proposal was examined numerically. It was found that filling both sides with metal foam results in 88.54% reduction in the time required for melting completion with a considerable increase of 5186.91% in the comprehensive performance achieved. It was also reported that the optimum heat transfer enhancement can be attained within a certain range of foam porosity that is 0.92–0.96. When fabricated together, local thermal non-equilibrium prevails between PCM materials and metal foams due to significant difference in thermal conductivity between them. In numerical simulation, this imposes a need to model thermal transport within each of the PCM and metal ligaments separately, where an energy equation is to be solved for each phase individually. There are three principal parameters must be considered while applying the LTNE model. Those are the effective thermal conductivity ke as well as the solid-fluid interfacial specific area asf and heat transfer coefficient hsf (Alhusseny et al. [19]). However, most of former numerical investigations that dealt with heat transfer enhancement using PCM-metal foam composites have repeatedly estimated the first two parameters according to formulations found to involve serious overestimation. Plenty of them have adopted the well-known model of Boomsma and Poulikakos [34] to compute the effective thermal conductivity ke , although it was found to include some errors, in both development and presentation, which had to be corrected (Dai et al. [35]). Similarly, the solid-fluid interfacial specific area asf has mostly been computed depending on the model proposed by Calmidi and Mahajan [17], which was found to deviate up to 233% from the corresponding data measured through a μCT scan (De Schampheleire et al. [36]). Thus, the current analysis is dedicated to simulate the LTNE-based heat transport in PCM-metal foam composites using more accurate and well-validated models for the effective thermal conductivity ke [37] and solid-fluid specific area asf [38]. Overall, phase change materials embedded in metal foams have recently been employed in various configurations of LHTES units using water as a HTF, e.g. triplex-tube [39], shell-and-tube [32,33,40,41], and tube-in-tank [29,42]. However, the tube-bundle unit, which is a common configuration in heat transfer applications, has only been employed as an LHTES system based on pure paraffin as a phase-change material [43]. Due to the large surface area available for heat exchange in bundled tube structures plus the outstanding potentials of PCM-metal foam composites, their combination into an LHTES system will certainly offer promising prospects. To this end, the current work is dedicated to numerically investigate the impact of using paraffin-copper foam composite on the performance of a tube-bundle thermal energy storage unit, which is to the best of our knowledge, has not been addressed before. 2. Mathematical formulation 2.1. Description of the problem considered The thermal energy storage unit examined is configured as a staggered bundled-tube heat exchanger similar to that investigated earlier by Liu et al. [43]. It is composed of N pairs (per metre width) of alternately staggered lines of tubes, where each pair is formed of eleven staggered tubes, see Fig. 1. The bundled copper tubes that form the LHTES unit are filled with a paraffin-copper foam composite as a phase change material. On the other hand,

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A. Alhusseny, N. Al-Zurfi and A. Nasser et al. / International Journal of Heat and Mass Transfer 150 (2020) 119320

Fig. 1. Schematic description of the LHTES unit examined.

water is used as a heating or cooling fluid that flows through the void space between the tubes. The water flow directions depends on whether the system is being charged or discharged. During the charging process, hot water flows in an upward direction opposite to gravity, while cold water flows in a downward direction during the discharging period. Due to the periodic arrangement of tubes along the x-direction, only half a pair of the alternately staggered lines of pipes is adopted to implement the numerical analysis. The length, width, and depth of the unit section considered are respectively L = 500mm, W = 1000mm/N, D = 1000mm, while the length of upstream and downstream sections are LU = 50mm and LD = 71.6mm, respectively. The dimeter of the bundled-tubes is dT = 30mm with wall thickness h = 1mm, while and centre-tocentre distance in y-direction between any two subsequent tubes is fixed as S = 34.64mm. As shown in Fig. 1, the lowermost cylinder is termed as Tube1 , while the subsequent cylinders are termed as Tube2 , Tube3 , and so on.

2.2. Assumptions and governing equations The heat and fluid flow domain is composed of three physically different zones, i.e. heat transfer fluid, tubes walls, PCMmetal foam tubes. Water is used either as a heating or cooling fluid during the charging or discharging process, respectively. Copper is, on the other hand, used to form the tubes walls enclosing the PCM-metal foam composite formed of copper foam saturated with paraffin as a phase change material. Termophysical properties of the water, copper tubes, paraffin, and copper foam are all considered constant except the paraffin thermal conductivity, which varies according to the wax phase, as detailed in Table 1. The liquid-phase paraffin is considered as Newtonian and incompress-

ible fluid with employing the Boussinesq approximation to account for the density-based buoyancy effect. The copper foam used is, on the other hand, assumed to be rigid, homogeneous, and isotropic with high porosity due to its open-cell configuration. The charging/discharging processes to be investigated are basically transient due to melting/solidification phenomena incorporated, while the flow inside and outside the tubes is maintained within the laminar regime criteria. For the paraffin-copper foam tubes, the generalised model is employed to simulate the momentum equations considering both the solid and fluid phases to be in local thermal non-equilibrium with each other. Accordingly, the equations governing the conservation of mass, momentum, and energy for the three physically-different zones involved can be concisely formulated as below: Mass Conservation:

  ∂ρf + ∇ · ρf v = 0 ∂t

(1)

Momentum Conservation:

   ρ f ui 1 1 + 2 ∇ · ρ f ui v = −∇ p + ∇ · (μ∇ ui ) + γ ∂ t ∅ ∅       cf μ × − + ρ f √ ui |v| + ρ f β T f − Tm1 g∇ (eg · x ) + Si 1∂ ∅



K

K

(2)

Fluid-Phase Energy Conservation:

 ∅ρ f c p f + γ LH +γ



dδ dT f



∂ Tf + ρ f c p f (v · ∇ )T f = (1 − γ )λ f ∇ 2 T f ∂t  

 λ f e + λd ∇ 2 T f + as f hs f Ts − T f

(3)

A. Alhusseny, N. Al-Zurfi and A. Nasser et al. / International Journal of Heat and Mass Transfer 150 (2020) 119320

5

Table 1 Thermophysical properties of the materials used. Material

Water

Paraffin

Copper

Density, ρ (kg/m3 ) Specific heat, cp (J/Kg·K) Thermal conductivity, λ (W/m·K) Dynamic Viscosity, μ (Pa·sec) Coefficient of thermal expansion, β (K Latent heat of fusion, LH (J/kg) Solidus temperature, Tm 1 ( °C) Liquidus temperature, Tm 2 ( °C)

998.2 4182 0.6 0.001003 −−− −−− −−− −−−

785 2850 0.3s −0.1f 0.00365 0.0003085 175,240 54.43 64.11

8978 381 401 −−− −−− −−− −−− −−−

− 1

)

Fig. 3. Grid independency of numerical solution.

respectively set to zero and 1 in the non-porous zones, which are the fluid flow space between the bundled tubes and the solid walls enclosing the PCM tubes. In the momentum equations, the term Si stands for a source added to the momentum equations to account for the liquid fraction in pore volume and can be computed as:

Si =

( 1 − δ )2  Am ui  δ3 +

(5)

where Am is known as the mushy zone constant, which controls the amplitude of velocity damping, and its value has been set to 105 , while is another constant of small value 10−3 to avoid division by zero. The liquid volume fraction δ is, on the other hand, a function ranged from 0 to 1 depending on the wax temperature as follows:



δ= Fig. 2. The mesh used with the interfaces linking the physically different regions.

Solid-Phase Energy Conservation:

[(1 − γ ) + γ (1 − ∅ )]ρs cs ×



∂ Ts = (1 − γ )λs ∇ 2 Ts + γ ∂ t 

 λse ∇ 2 Ts + γ as f hs f T f − Ts

(4)

Depending on the parameter γ and porosity ∅, only a particular set of the above-mentioned compact equations can be assigned to the relevant zone. In the porous zones, the values of γ and ∅ are respectively set to 1 and copper foam porosity. Otherwise, they are



0, T f ≤ Tm1  T f − Tm1 /(Tm2 − Tm1 ), Tm1 < T f < Tm2 1, T f ≥ Tm2

(6)

In the same context, the foam permeability K is computed according to an analytical model that is developed based only on physical principles with no adjustable parameters to fit experimental data (Fourie and Du Plessis [38]). Unlike the model introduced earlier by Du Plessis et al. [44], which is only valid for a very narrow porosity range (0.973–0.978) and a limited range of pore density (45PPI–100PPI), the application of the currently adopted model for permeability requires no a priori knowledge of the flow behaviour across a particular metallic foam, and hence; it is applicable to metal foams within a practical range of pore sizes and porosities [38]. The foam inertial coefficient cf is, on the other hand, evaluated using the model introduced by Calmidi [45].

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A. Alhusseny, N. Al-Zurfi and A. Nasser et al. / International Journal of Heat and Mass Transfer 150 (2020) 119320 Table 2 Empirical models used for metal foam parameters. Correlation

Reference

∅2 d 2 K = 36(χ −1k )χ 2d dk = 3−χp = 2 + 2cos[ 43π + 13 cos−1 2∅ − 1 ] −0.132 d f −1.63 c f = 0.00212 1 − ∅ dp

χ

(

(

df =

)



1.18d p 1−e−(1−∅)/0.04 d p = 0.0254 ω

λe =

(

} (7)

Fourie and Du Plessis [38]

} (8)

Calmidi [45]

)

)

(1−∅) 3π

1

(ε /kA )+( (1−2ε )/kB )+(ε /kC ) √ 1+a21 2 3−4 s 6 a21 √ 1+a21 2 3−4 ] +[1 − 6 2 f a √ √ 1 2 2 (9) 2 1+a1 2 1+a1 1 − 2 + kB = 22 s 2 f a1 a21 √ √ 2 2 2 2 2 1+a1 2 1+a1 kC = 6 s + 1− 6 f a21 a21 √ 1+a21 2 = 2 . 01 3−5 , a ∅ = 1 − 62 1 2 a1 0.36 d = 1−∅ f c p f d f v (10) 0.4 0.37 0.76Red P r , 1 ≤ Red < 40 λ hs f = df 0.52Re0d.5 P r 0.37 , 40 ≤ Red < 103 0.26Re0d.6 P r 0.37 , 103 ≤ Red < 2 × 105 d = 1 − e−(1−∅)/0.04 d f 2 −1 3− (12) as f = 23d p

kA =

πε (

ε)

πε (

ε)

λ

πε

λ

(

πε

)λ

πε

λ

(

πε

)λ

πε ( ρ | |

λ

λ

(χ

Yao et al. [37]

ε)

|

( )(

}

χ)

Georgiadis and Catton [47]

} (11)

Zukauskas [48]

)

In regard to the equations governing the thermal transport, λfe and λse are respectively the effective fluid-phase and solid-phase thermal conductivity of the paraffin-copper foam composite, which have been estimated according to the analytical model derived by Yao et al. [37]. This model has considered a relatively realistic structure of open-cell metal foams by introducing concave triprism ligaments into a tetrakaidecahedron cell along with considering the impact of the filling medium and the ligament orientation on the effective thermal conductivity computed. Furthermore, the currently adopted model makes no use of non-universal empirical parameters that need to be specified experimentally. It has also been validated well against measurements of copper foams saturated with air, water, and paraffin, where the average relative deviation of the present model was only 5.70% from the ETCs measured experimentally compared to 69.74%, 11.62%, and 12.79% found for the computed ETCs using the models of Boomsma and Poulikakos [34], Dai et al. [35], and Calmidi and Mahajan [46], respectively. The dispersive thermal conductivity λd is, on the other hand, computed following the model introduced by Georgiadis and Catton [47]. To predict the interstitial solid-fluid heat transport, the correlations developed by Zukauskas [48] have been adopted to compute the local values of interfacial solid-fluid heat transfer coefficient hsf . In the same context, interfacial solid-fluid specific area asf has been estimated using the model presented by Fourie and Du Plessis [38]. The above mentioned correlations regarding the heat and fluid flow in meatal foams are all detailed in Table 2.

Fourie and Du Plessis [38]

While the conditions at the upper water boundary are:

⎫ ⎪ ⎪ ⎬   At (x, y = L, t); ⎪ ⎪ ˙ ⎪ ⎩Discharging : u = 0, v = −vin = −Vw /(N × W × D) ⎪ ⎭ ⎧ ⎪ ⎪ ⎨

 ∂u

 ∂v ∂y = ∂y = 0 ∂ Tf ∂y = 0

Charging :

T f = 22C

(15) The conditions compatible with the left and right symmetric boundaries are as follows:



At

x = 0;

  ∂u = ∂x

W , y, t ; 2



∂v = 0 ∂x

(16)

∂ Tf ∂x = 0

At the tubes outer walls in contact with the heating water, the below conditions are imposed:



At (x, y, t );

−λwater

u=

∂ T f water ∂n

v=0 ls = −λwal l s ∂ T∂s wal n



(17)

At the tubes inner walls in contact with the paraffin-copper foam composite, the below conditions are imposed:

 At (x, y, t);

ls −λwal l s ∂ T∂s wal n

 u= v=  0 ∂ Tf PCM ∂T = − λ f e + λd − λse F oam ∂f PCM n PCM ∂ n



(18) 3. Numerical procedure

2.3. Initial and boundary conditions

3.1. Grid generation

The initial conditions for the water void space, the tubes, and the PCM-metal foam cylinders are:

The problem under consideration has been meshed using the “Pointwise 18.0” software, where hexahedral elements have been employed to form an entirely structured grid everywhere in the problem domain, as shown in Fig. 2. Attention has been paid while structuring the solution grid to keep the interfaces (between the physically different regions) conformal everywhere. Also, more grid points have been clustered close to both sides of the tubes walls in order to capture the steep gradients expected there. Grid independency of numerical solution has been checked by comparing the transient development of paraffin liquid fraction at certain points on Tube6 for four grid sizes of 33,507, 59,240, 85,632, and 112,740. The tracking points have been selected to be along the vertical centreline of Tube6 and located at distance 0.1d, 0.3d, and 0.5d from

⎧  ⎫ u=v=0 ⎪ ⎪ ⎪ ⎨ Charging : T = T = 22C ⎪ ⎬ s f   At (x, y, t0 ); u=v=0 ⎪ ⎪ ⎪ ⎩Discharging : T = T = 80C ⎪ ⎭ f

(13)

s

The conditions at the lower water boundary are:  ⎫ ⎧ u = 0, v = vin = V˙ w /(N × W × D ) ⎪ ⎪ ⎪ ⎪ ⎨Charging : ⎬ T = 80C  ∂ uf ∂v  At (x, y = 0, t); = = 0 ⎪ ⎪ ⎪ ⎪ Discharging : ∂ y ∂ Tf ∂ y ⎩ ⎭ ∂y = 0

(14)

A. Alhusseny, N. Al-Zurfi and A. Nasser et al. / International Journal of Heat and Mass Transfer 150 (2020) 119320

7

Fig. 4. Transient evolution of the numerically predicted liquid-solid interface (up) in comparison with the corresponding patterns obtained experimentally by Zhang et al. [22] (down).

the lower point of the inner surface, as shown in Fig. 3. It has been found that the change in the data computed becomes quite marginal between the third and fourth mesh, and hence, mesh size of 85,632 has been used in the current analysis. 3.2. Discretisation and computational program The finite volume method has been adopted to discretise the governing equations with employing the SIMPLE algorithm to resolve the problem of velocity–pressure coupling. The heat and fluid flow has been iteratively solved using the “ANSYS FLUENT” commercial CFD code. Spatial discretisation has been done using the second-order upwinding for momentum and energy, and the PRESTO! “PREssure Staggering Option” for pressure. The temporal discretisation has been, on the other hand, done according to the second-order implicit formulation. During the iterative process, the solution has been under-relaxed to overcome convergence difficulties, where under-relaxation factors, ranged from 0.3 to 0.99, have been considered. Convergence has been monitored in terms of the change in each variable during each time-step, where the maximum residuals allowed in continuity, velocity components, and energy equations were 10−5 , 10−6 , 10−7 , respectively. When the system is either fully charged or discharged, the final solution is attained. 3.3. Validation To verify the validity of the mathematical formulations adopted along with the numerical approaches followed, the data computed numerically should be validated against some experimental data of relevance to the current problem. To this end, the configuration of paraffin-copper foam tested experimentally by Zhang et al. [22] has been simulated. As shown in Fig. 4, the temporal development of the computationally predicted liquid-solid interface is in well agreement with the data recorded experimentally. Furthermore, the local values of foam and PCM temperature at the centre of the PCM-foam composite examined by Zhang et al. [22] have also been validated against the corresponding values measured experimentally, as shown in Fig. 5, where the transient temperature development agrees well with the experiments conducted. Thus,

Fig. 5. Comparison of the foam and PCM temperature computed numerically at a selected monitor point with the corresponding data measured experimentally by Zhang et al. [22].

the reliability of the methodology adopted along with the computational program used has been confirmed and there is no concern to be worried about from employing them to track heat and fluid flow accurately in the current analysis. 3.4. Influence of time-step size To check the solution dependency upon the time-step size, the transient evolution of the paraffin temperature as well as the corresponding liquid volume fraction was monitored at the centre of each the 2nd, 6th, and 10th tubes and compared for five different time-step sizes, i.e. t = 0.25, 0.5, 1, 2, and 4 s, as shown in Fig. 6. The LHTES system considered is to be charged with V˙ w = 4m3 /h and configured of N = 20, ∅ = 0.97, and ω = 25P P I. It is observed that the change between the data computed using the first and the second time-step size has almost been identical. Hence, a time-step size of 0.5 s has been used for transient solution, where the solution was iterated 15 times per each time-step.

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Fig. 6. Impact of time-step size on transient evolution of paraffin temperature (left) and liquid volume fraction (right).

Fig. 7. Transient evolution during the charging process.

4. Results The copper foam used is of an open-cell configuration with foam pore density ω = 25P P I and high porosity of ∅ = 0.97 in order to fill the tubes with the maximum amount of paraffin. The results obtained are for ranges of some design and operating parameters including the tubes packing density 15 ≤ N ≤ 30 (Tubes Lines/meter) and water flowrate 1 ≤ V˙ w ≤ 5 (m3 /h ). 4.1. Charging process Transient development of charging process is demonstrated in Fig. 7 for a case of a storage unit with water flowrate and packing density of 3m3 /h and 20 Tubes Lines/m, respectively. During the first 60 s, it is observed that the heat transported is at the highest levels due to the considerable temperature difference between the heating water and both of the paraffin and copper foam. However, the rate of heat transported decreases sharply during this period for two reasons. The first is the rapid increase in the temperatures of paraffin-copper foam composite, while the second is the reduction occurred in the heating water temperature. As time elapses, the rate of reduction in heat transport is gradually dampened, while the water temperature starts to rise monotonically.

Meanwhile, both the foam and paraffin temperatures keep increasing but with a lesser extent than before. This is due to the fact that as the paraffin starts to melt and absorbs heat as a latent energy, its temperature remains within a range limited between the solidus and liquidus temperatures. This is obvious from the dramatic increase of paraffin liquid fraction up to the completion of melting process after about 10 0 0s. Later on, the heat is stored in the form of sensible heat up to reaching the thermal balance when the temperature of the entire system becomes equal to the heating water temperature. Temporal evolution of the melting process can be illustrated by Fig. 8 regarding the transient development of paraffin temperature contours in addition to Fig. 9 concerning the evolution of paraffin liquid volume fraction. The charging process is quite obvious whether in terms of the increase in paraffin temperature or the reduction in heating water temperature. While increasing the paraffin temperature beyond the melting temperature, the liquid fraction of paraffin starts to increase accompanied with obvious evolution of buoyancy effects, which enhances the melting process, as shown in Fig. 7. With further temporal development in the thermal field, the buoyancy effects start to vanish due to the continuous reduction occurring in the local temperature gradients of paraffin.

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Fig. 8. Evolution of temperature distribution during charging process.

Fig. 9. Evolution of paraffin liquid fraction during charging process.

It is also clear how the paraffin particles located close to the walls of the tubes are first subjected to the heating effect, and then transfer the heat gained to the next ones towards the centres of the tubes. This phenomenon can be further demonstrated by tracking the transient development of copper-foam temperature, paraffin temperature, and paraffin liquid fraction at cer-

tain points on Tube6 . These points have been selected to be along the vertical centreline of Tube6 and located at distance 0.1d, 0.3d, 0.5d, 0.7d, and 0.9d from the lower point of the inner surface, as illustrated in Fig. 10. It can be seen that the closer a paraffin particle to the tube wall is, the less time it takes to melt. It is also obvious that the copper foam plays a major role in enhanc-

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Fig. 10. Charging development of foam temperature, PCM temperature, and liquid fraction at selected points on Tube6 .

Fig. 11. Charging development of foam temperature, PCM temperature, and liquid fraction at the centres of selected tubes.

ing the heat transported to the paraffin. When the melting starts, the copper foam temperature tends to decrease indicating that it is losing its heat content to the paraffin surrounding. As the heating water losses its thermal content while flowing upward from upstream to downstream, the charging process is not expected to be alike for the locally sequent storage tubes. This can be better demonstrated by looking at Fig. 11 regarding the transient development of copper-foam temperature, paraffin temperature, and paraffin liquid fraction at centres of sequent tubes. Due to the high heat content of water at the upstream, tubes closer to the inlet are subjected to stronger heating rates, and hence, charged faster than it is for those located behind. 4.2. Discharging process Similar to what preceded in charging process, the discharging development can be demonstrated in Fig. 12 for the same water

flowrate and packing density examined before. At the beginning of the discharging process, the heat discharged is at its peak due to the considerable difference between the temperature of paraffincopper foam composite and the water to be heated. Later on, the rate of heat lost decreases remarkably due to the rapid reduction in the temperatures of thermal storage tubes besides the increase in water temperature. Then, the rate of reduction in heat transfer is damped over time, while the water temperature starts to fall monotonically. In the meantime, the paraffin starts to freeze and releases heat as a latent energy at temperature range limited between the liquidus and solidus temperatures. This is obvious from the noticeable reduction in paraffin liquid fraction up to the completion of solidification process after about 500 s, which is almost half the time required to melt the paraffin during the melting process. This is attributed to the significant role played by buoyancy during the early stages of discharging process unlike the corresponding period of fusion process.

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Fig. 12. Transient evolution during the discharging process.

Fig. 13. Evolution of temperature distribution during discharging process.

The solidification process can be better understood through Fig. 13 regarding the temporal development of paraffin temperature contours in addition to Fig. 14 concerning the evolution of paraffin liquid volume fraction. The discharging process is well demonstrated, whether in terms of the increase in water temperature or the reduction in paraffin temperature. While reducing the local temperature of paraffin particles beyond the solidification temperature, solid layers of paraffin start to form along inner sides of the tubes trapping liquid particles inside them until the paraffin completely solidifies. Similar to the melting process, the paraffin particles located close to the walls of the tubes are firstly subjected to the cooling effect, and then keep absorbing more thermal energy to heat

the particles next to them towards the centres of the tubes. This phenomenon can be better understood by monitoring the transient development of copper-foam temperature, paraffin temperature, and paraffin liquid fraction at particular points selected to be along the vertical centreline of Tube6 and located at distance 0.1d, 0.3d, 0.5d, 0.7d, and 0.9d from the lower point of the inner surface, as illustrated in Fig. 15. Apparently, the closer a paraffin particle to the tube wall is, the faster it solidifies. As the thermal content of cooling water is promoted while flowing downward, the discharging process is unlikely to be similar for the sequent tubes. Fig. 16 can help in better demonstrating this dissimilarity through the transient development of copperfoam temperature, paraffin temperature, and paraffin liquid frac-

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Fig. 14. Evolution of paraffin liquid fraction during discharging process.

Fig. 15. Discharging development of foam temperature, PCM temperature, and liquid fraction at selected points on Tube6 .

tion at centres of sequent tubes. Due to the low heat content of water at the upstream, tubes closer to the inlet are subjected to stronger cooling rates, and hence, discharged faster than it is for those located behind. 4.3. Effect of local thermal non-equilibrium In Figs. 7, 10, 11 regarding the charging process, the difference between the foam and PCM temperature is quite significant before and during the melting process indicating the strong presence of local thermal non-equilibrium between them. After that, the dominance of this phenomena, however, starts to vanish gradually as

the system full-charge draws closer, where the state of thermal equilibrium is eventually achieved. Similarly in Figs. 12, 15, 16 regarding the discharging process, the presence of the local thermal non-equilibrium phenomenon is evident from the considerable difference between the foam and PCM temperatures during and after the solidification process. However, this was not the case before, as the central zones of tubes were still in thermal equilibrium and have not been affected by the cooling process yet. To further explore this phenomenon, the transient development of local difference between the foam and PCM temperature has been plotted at the centres of tubes 2, 4, 6, 8, and 10 during both charging and discharging, as shown in Fig. 17. The importance of taking

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Fig. 16. Discharging development of foam temperature, PCM temperature, and liquid fraction at the centres of selected tubes.

Fig. 17. Temperature difference between foam and PCM temperature at the centres of selected tubes.

this phenomenon into account is quite obvious for both processes, which justify the adoption of LTNE model in such an analysis. Accordingly, a question is to be raised about the conclusion inferred by Mahdi and Nsofor [49] regarding the validity of employing the “Local Thermal Equilibrium” model for tracking heat transport across PCM-metal foam composites during solidification process. This inference might be correct; but only for limited sorts of nanoPCM-metal foams composites, where the thermal conductivity of a nanoPCM and the foam fabricated with are of a comparable order of magnitude. Thus, care should be taken in dealing with this phenomenon to avoid obtaining results might be misleading. 4.4. Influence of water flowrate The flowrate of heating water in TES unit is governed by the collector capacity and the amount of thermal energy to be shaved during the peak time, while the flowrate of cooling water used in discharging process depends on the thermal energy demands during the off-peak period. In practice, flowrate of heating/cooling water is not steady anymore and changes instantaneously depending on the amount of energy supplied and demanded. However, it is

usually dealt with as a constant quantity while optimising TES systems based on water as a heating or cooling input. Therefore, impact of water flowrate on the LHTES system under consideration has been examined and for both charging and discharging. Fig. 18 demonstrates how the charging process is affected by the flowrate of heating water supplied. In general, the charging process is noticeably accelerated while increasing the water flowrate due to increase in the heat content carried by the water, e.g. the time required to fully charge the system is trimmed to about the third when the water flow rate is raised from 1 to 5 (m3 /h), while it is halved when water flowrate is increased from 3 to 5 (m3 /h). This is attributed to the increase in heat content carried by water as well as the upgrade of the water-side heat transfer coefficient. However, such increase is accompanied with higher pressure drop as well as making the water temperature less steady during the charging process. Similar findings can be observed in the discharging process, as shown in Fig. 19, and for the same water flowrates examined before, where the solidification process is considerably accelerated.

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Fig. 18. Impact of water flowrate on transient development of foam and PCM average temperature (left) and water outlet temperature and liquid fraction (right) for N = 20 during charging.

Fig. 19. Impact of water flowrate on transient development of foam and PCM average temperature (left) and water outlet temperature and liquid fraction (right) for N = 20 during discharging.

4.5. Influence of packing density Packing density N, wherever it comes in this text, stands for the number of parallel lines of tubes stacked in one metre wide of the storage unit considered. It is expected to have a direct impact on the heat transfer rate, pressure drop, as well as the storage capacity. To explore its effect on the charging and discharging process, a storage unit with foam pore density ω = 25P P I has been examined for four packing densities N = 15, 20, 25, and 30 T ubes Lines/m. The transient development of averaged foam temperature, PCM temperature, water outlet temperature, and paraffin liquid fraction are illustrated in Figs. 20 and 21 during the charging and discharging, respectively. It is apparent that the denser the unit is packed, the faster the charging or discharging completes. This is due to the acceleration of water particles while passing through narrower voids, which in turns enhances the rate of heat exchanged between the water and the PCM-foam composite through the tubes walls. This is clear whether during charging or discharging from the remarkable reduction or increase in the water outlet temperature. However, it is observed that discharging a unit of particular packing density takes longer than it is to fully charge a corresponding LTHES unit. This can be attributed to the strong role played by buoyancy during the entire process of charging compared to the corresponding discharging process, where the buoyancy strength is less significant during the late stages of solidification as a result of

shrinking the spaces available for liquid-phase particles, which are completely trapped inside the solidified paraffin. To further demonstrate the mutual role of packing density and water flowrate on thermal performance, the heat transfer rate has been averaged over the time required to fully charge or discharge the LHTES unit for various packing density and water flowrate, as stated in Fig. 22. In general, the rate of heat transported from/to water during the charging/discharging process is enhanced with the increase whether in packing density or water flow rate due to the acceleration of water particles while passing around the tubes, which in turns improves the water-side heat transfer coefficient. However, and for the reasons mentioned earlier, the average rate of heat transfer during the discharging process is noticeably less than it is during the charging process except when the level of water flowrate was too low, i.e. V˙ w = 1m3 /h. In such cases, the water-side heat transfer coefficient is modest such that the buoyancy effect inside the tubes cannot overcome the heat transfer by conduction. Hence, more heat is transported during the discharging process as the PCM particles in the vicinity of tubes walls are mostly in the solid phase with a higher thermal conductivity than it is for the liquid-phase particles next to the walls in case of charging. Another far more significant advantage of denser packed unit is the augmentation achieved in the storage capacity density due to the increase of the overall volume occupied by the paraffin, as illustrated in Fig. 23. The storage capacity density represents the

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Fig. 20. Impact of packing density during charging on transient development of: foam and PCM average temperatures (left), water outlet temperature and paraffin liquid fraction (right).

Fig. 21. Impact of packing density during discharging on transient development of: foam and PCM average temperatures (left), water outlet temperature and paraffin liquid fraction (right).

Fig. 22. Mutual Impact of packing storage capacity and water on the time-averaged heat transfer rate.

thermal energy storage capacity per the total volume of the TES unit, i.e. (SCD = SC/Vt ). The storage capacity can be computed as follows:

   ρPCM ∅ c p PCM Tm1 − TPCM0 + Twin − Tm2 + LH   +(1 − ∅ )ρF oam cF oam Twin − TPC M0 VLHT ES (J )

SC =



(19)

Fig. 23. Impact of packing storage capacity and pressure drop for water flowrate V˙ w = 3 (m3 /h ).

Where:

Vt = L(W × N )D = 0.5m3 , and; VLHT ES = 11N

  π dT 2 /4 D

(20)

However, this gain is accompanied by unavoidable cost owing to the rise of pressure drop, which results from the increase of friction with the walls of the tubes due to the accelerated water

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Fig. 24. Variation of overall performance OP with both packing density and water flow right for charging (left) and discharging process (right).

Fig. 25. Performance comparison between the pure paraffin system and the corresponding unit based on paraffin.copper foam composite during charging process.

particles nearby. So, denser storage units are likely to be criticised in terms of the overall worth gained in practice because the improvement obtained in storage capacity is accompanied with a rise in pressure drop of almost the same order. To answer such a question, a performance measure such as the one introduced earlier by Alhusseny and Turan [50] should be used. It is called the overall performance OP and may be defined as the storage capacity to the pumping energy consumed, as follows:

OP =

SC PP

(21)

Where the pumping energy consumed can be computed as follows:





P P = V˙ w pw t (J )

(22)

Now, it is the time to have a close look at the mutual role of packing density and water flowrate on the overall performance for both charging and discharging processes, as summarised in Fig. 24. In general, the overall performance is clearly improved while increasing the packing density for a specific water flowrate, which might be confusing at first glance. This can be justified by looking closely at Eqs. (19 and 22). While storage capacity and pressure drop are raised with the same order as Fig. 23 reveals; the time required for charging or discharging is, however, reduced leading

to tone down the rate of increase in pumping energy consumed. On the other hand, the overall performance deteriorates with increasing the water flowrate V˙ w for a certain density of packing due to the increase occurred in the pumping energy consumed. Moreover, its rate of deterioration with the increase of water flowrate is worse for the lighter packed units because they need longer time to fully charge or discharge compared to the denser units. With the increase of water flow rate, there is, however, a clear discrepancy in the overall performance attained during charging compared to the discharging process. For the modest levels of water flowrate, the overall performance of the discharging process is slightly better than it is during the charging period due to the reasons mentioned earlier. Otherwise, the charging process clearly outperforms with a further increase in water flowrate and for all densities of packing. 4.6. Performance improvement using PCM-metal foam composite in lhtes systems The improvement gained using the paraffin-copper foam composite has been checked through comparing the performance obtained in both charging and discharging with that attained using only pure paraffin, as illustrated in Figs. 25 and 26, respectively. The unit used for comparison is configured of 20 (Tubes Lines/m)

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Fig. 26. Performance comparison between the pure paraffin system and the corresponding unit based on paraffin-copper foam composite during discharging process.

with water flowrate of 3m3 /hr. For both processes, it is obvious that the system adopting paraffin-copper foam composite as storage element outperforms the corresponding one employing only pure paraffin. The melting time required for the pure paraffinbased system has been reduced by 56% when using the proposed system, while the total time required for the system to fully charge has shortened by about 60%. On the other hand, the time required for the pure paraffin-based system to completely solidify has been saved by 66% when the paraffin-copper composite is used, whereas the total time required to fully discharge the system has been reduced to less than the half. This enhancement resulted in heat transfer rate can be attributed to the improvement acquired in the overall thermal conductivity of LHTES medium as a result of using the highly conductive open-cell copper foam.

Declaration of Competing Interest

5. Conclusions

Acknowledgements

High porosity copper foam has been used to improve the performance of an LHTES system formed of a staggered tubebundle structure. The tubes have been filled with paraffin wax as a phase change material compounded to an open-cell copper foam as a heat transfer enhancer. The PCM unit proposed is charged/discharged using a relatively hot/cold water stream flowing across the tube-bundle units in upward/downward manner, respectively. The feasibility of such a configuration is examined numerically through simulating the proposed PCM-metal foam composite units and their surrounding water void. Some of design and operating parameters have been examined in the light of the overall performance achieved. The results reveals that the solidification process takes, in general, half than the time required for the corresponding system to melt due to the dominant role played by buoyancy during the early stages of these processes. However, the system proposed is fully discharged slower than it takes to be fully charged due to the absence of buoyancy effect after the PCM being completely frozen. It was also found that denser storage units outperform the lighter systems in terms of storage capacity density and the time required for charging or discharging. The currently proposed design of LHTES system has been found not only easy to configure, but practically efficient as well, where the overall performance achieved is remarkably outstanding, i.e. OP=(104 ~105 ). Besides, the charging/discharging rate has been accelerated by more than 50% compared to the corresponding system adopting pure paraffin.

Our thanks to the University of Manchester for providing the computational resources required to conduct the current simulation. Also, the support presented in the Kufa Centre for Advanced Simulation in Engineering “KCASE” is quite appreciated.

None. CRediT authorship contribution statement Ahmed Alhusseny: Conceptualization, Funding acquisition, Methodology, Data curation, Software, Validation, Supervision, Project administration, Writing - original draft. Nabeel Al-Zurfi: Conceptualization, Funding acquisition, Methodology, Data curation, Software, Writing - original draft. Adel Nasser: Conceptualization, Funding acquisition, Software, Resources, Writing - original draft. Ali Al-Fatlawi: Conceptualization, Funding acquisition, Methodology, Writing - original draft. Mohanad Aljanabi: Funding acquisition, Software, Writing - original draft.

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