Scholarly article on topic 'Thermal behavior of latent thermal energy storage unit using two phase change materials: Effects of HTF inlet temperature'

Thermal behavior of latent thermal energy storage unit using two phase change materials: Effects of HTF inlet temperature Academic research paper on "Materials engineering"

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{"Thermal energy storage" / "Phase change materials" / "Heat transfer fluid" / "Charging process" / "Melting time"}

Abstract of research paper on Materials engineering, author of scientific article — Fouzi Benmoussa, Ahmed Benzaoui, Hocine Benmoussa

Abstract This work presents a numerical study of the thermal behavior of shell-and-tube latent thermal energy storage (LTES) unit using two phase change materials (PCMs). The heat transfer fluid (HTF) flow through the inner tube and transfer the heat to PCMs. First, a mathematical model is developed based on the enthalpy formulation and solved through the governing equations. Second, the effects of HTF inlet temperature on the unsteady temperature evolution of PCMs, the total energy stored evolution as well as the total melting time is studied. Numerical results show that for all HTF inlet temperature, melting rate of PCM1 is the fastest and that of PCM2 is the slowest; increasing the HTF inlet temperature considerably increases the temperature evolution of PCMs. The maximum energy stored is observed in PCM2 with high melting temperature and high specific heat; heat storage capacity is large for high HTF inlet temperature. When the HTF inlet temperature increases from 338K to 353K, decreasing degree of melting time of PCM2 is the biggest from 1870s to 490s, which reduces about 73.8%; decreasing degree of melting time of PCM1 is the smallest from 530s to 270s, which reduces about 49.1%.

Academic research paper on topic "Thermal behavior of latent thermal energy storage unit using two phase change materials: Effects of HTF inlet temperature"

Author's Accepted Manuscript

Thermal behavior of latent thermal energy storage unit using two phase change materials: Effects of HTF inlet temperature

Fouzi Benmoussa, Ahmed Benzaoui, Hocine Benmoussa

CASE STUDIES IN THERMAL ENGINEERING

www.elsevier.com'locate/csite

PII: S2214-157X(17)30211-3

DOI: https://doi.org/10.1016/j.csite.2017.10.010

Reference: CSITE228

To appear in: Case Studies in Thermal Engineering

Received date: 26 August 2017 Revised date: 9 October 2017 Accepted date: 16 October 2017

Cite this article as: Fouzi Benmoussa, Ahmed Benzaoui and Hocine Benmoussa, Thermal behavior of latent thermal energy storage unit using two phase change materials: Effects of HTF inlet temperature, Case Studies in Thermal Engineering, https://doi.org/10.1016/j.csite.2017.10.010

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Thermal behavior of latent thermal energy storage unit using two phase change materials: Effects of HTF inlet temperature

Fouzi Benmoussaa*, Ahmed Benzaouib, Hocine Benmoussaa aLESEI Laboratory, Faculty of Technology, Mechanics Department, University of Batna-2,

Batna, Algeria

bFaculty of Physics, University of Sciences and Technology Houari Boumedienne, Algiers,

Algeria

*E-mail: benmoussa_fouzi@yahoo.fr; a1benzaoui@yahoo.fr; hocine_b@hotmail.com

Abstract

This work presents a numerical study of the thermal behavior of shell-and-tube latent thermal energy storage (LTES) unit using two phase change materials (PCMs). The heat transfer fluid (HTF) flow through the inner tube and transfer the heat to PCMs. First, a mathematical model is developed based on the enthalpy formulation and solved through the governing equations. Second, the effects of HTF inlet temperature on the unsteady temperature evolution of PCMs, the total energy stored evolution as well as the total melting time is studied. Numerical results show that for all HTF inlet temperature, melting rate of PCM1 is the fastest and that of PCM2 is the slowest; increasing the HTF inlet temperature considerably increases the temperature evolution of PCMs. The maximum energy stored is observed in PCM2 with high melting temperature and high specific heat; heat storage capacity is large for high HTF inlet temperature. When the HTF inlet temperature increases from 338 K to 353 K, decreasing degree of melting time of PCM2 is the biggest from 1870 s to 490 s, which reduces about 73.8 %; decreasing degree of melting time of PCM1 is the smallest from 530 s to 270 s, which reduces about 49.1 %.

Keywords: Thermal energy storage; Phase change materials; Heat transfer fluid; Charging process; Melting time.

1. Introduction

ACCEPTED MANUSCRIPT

The shell-and-tube latent thermal energy storage (LTES) using phase change materials (PCMs) has attracted a large number of applications in recent years, such as solar energy due to its advantages of high energy storage density and its isothermal operating characteristics during charging and discharging processes. In a latent heat storage system, thermal energy is stored during melting while it is recovered during solidification of PCMs. The development of LTES involves the understanding of heat transfer in PCMs when they undergo solid-to-liquid phase transition in the required operating conditions. A number of studies have been performed to examine the overall thermal behaviors of the LTES unit with single PCM. Trp et al. [1]-[2] established a mathematical model in order to analyze the transient heat transfer phenomena of melting and solidification of paraffin wax in a cylindrical shell. They concluded that the operating conditions and geometric parameters should be chosen carefully to optimize the thermal performance of the storage unit. Tao et al. [3] investigated the performance of high temperature molten salt LTES under variable conditions, the effects of heat transfer fluid (HTF) inlet temperature, velocity and tube geometric parameters. The results show that within the studied parameters, the HTF inlet temperature has the largest effect on heat storage rate. Kibria et al. [4] numerically and experimentally investigated a thermal storage unit of phase change process under various flow parameters and system dimensions. The thermal energy storage involves a shell-and-tube, where paraffin wax is used as PCM. Experimental setup has been designed to examine the physical validity of the numerical results. Lacroix [5] numerically studied the effects of temperature difference between HTF inlet temperature and melting point of PCM, HTF inlet mass flow rate on heat charging and heat discharging performance. The layout of the phase change storage unit considered consists of a shell-and-tube type. The annulus space is filled with PCM (n-octadecane).

However, the low thermal conductivity of most PCM ranging from 0.1 to 0.6 W.m-1.K-1 limits heat transfer rates during both charging and discharging processes. In order to enhance the heat transfer exchange during such processes, multiple PCMs with different melting temperatures were employed. Akgun et al. [6]-[7] analyzed the LTES system of the shell-and-tube type with three kinds of paraffin as PCMs. A novel tube-in-shell storage geometry was introduced and the effects of the Reynolds number on the melting and solidification behaviors were examined. Ait Adine and El Qarnia [8] performed numerical studies of LTES unit consisting of a shell-and-tube type. The storage unit consists of an inner tube, outer tube and an annulus space filled with two PCMs, P116 and n-octadecane. In order to compare the thermal performances of the unit using two PCMs and single PCM, a mathematical model was developed and validated with experimental data. Farid and Kanzawa [9] numerically and

experimentally studied th

LTES unit using different PCMs of 11 i

howed that, compared to the LTES

different melting temperatures,

using single PCM, some improvement in the thermal performance of the unit may be achieved. El Qarnia [10] developed a theoretical and numerical analysis to predict the thermal performance of a coupled solar collector LTES unit using multiple PCMs. The effects of the HTF flow rate on its outlet temperature are determined. Results showed that, the selection of PCMs should be done carefully in order to produce hot water in acceptable range of temperature. Li et al. [11] developed a mathematical model of a shell-and-tube LTES unit of three kinds of PCMs, having different high melting temperature for solar thermal power, air is used as HTF. Instantaneous solid-liquid interface positions, liquid fractions and melting times of each PCM have been obtained by a series of numerical calculations and represented graphically. Fang and Chen [12] presented a theoretical model for the performance of a shell-and-tube LTES unit using multiple PCMs. Numerical simulations are carried out to investigate the effects of different multiple PCMs on the melted fraction, stored thermal energy and fluid outlet temperature of the LTES unit.

The search in the literature shows that the numerical analysis reported by Ait Adine and El Qarnia [8] is the most related investigation to the present work. However, the effects of the HTF inlet temperatures on the thermal behavior of the LTES unit and on the variation of different parameters have not been analyzed. In the present study, in order to study the transient thermal behavior of the LTES unit under different HTF inlet temperature, a physical and mathematical model was established for the shell-and-tube LTES unit with two kinds of PCMs named PCM1 and PCM2 having different melting temperature. The simulation for the LTES process was based on the enthalpy method which takes into account phase change phenomenon. Numerical simulations are carried out to investigate the effects of HTF inlet temperature on the unsteady temperature evolution of PCM1 and PCM2; the total energy stored evolution in different zone of PCMs as well as the total melting time of each PCM.

2. Physical model and governing equations

2.1. Physical model

The shell-and-tube PCMs storage unit considered in the present study is shown in Fig. 1a, which is similar to the model used by Ait Adine and El Qarnia [8]. It consists of an inner tube, an outer tube and an annulus filled with two PCMs named PCM1 and PCM2, having different melting temperatures (323 K and 333 K, respectively). HTF (water) flows through the inner tube and exchanges heat with PCMs. During charging process, hot water circulates in the direction of the melting temperature increase. The thermo-physical properties of the HTF and PCMs are listed in Table 1. The two-dimension physical model to be analysed is represented

by a geometry shown in Fig. 1b. The dimensions of the unit are: L1= 0.47 m, L2= 0.53 m, Ri= 0.635 cm and Ro= 1.135 cm. Initially each PCM are in solid phase; its temperatures are set to 303 K. Analysis has been performed for three different HTF inlet temperatures above the melting point of PCM2 (338 K, 343 K and 353 K). The HTF inlet velocity was maintained constant during the numerical tests to a value of 0.03 m/s.

Fig. 1a. Schematic representation of the LTES unit with two PCMs.

Fig. 1b. Physical model for numerical calculations.

Table 1. Thermo-physical properties of the HTF and PCMs

2.2. Assumptions

In order to simplify the physical and mathematical model, the following assumptions are adopted.

• The HTF is incompressible and can be considered as a Newtonian fluid;

• The HTF flow is laminar, HTF inlet temperature and inlet velocity are both constant;

• The thermo-physical properties of the HTF and PCMs are independent of temperature;

• Initial temperature of the unit is uniform, the PCMs are in solid phase;

• The outer surface of the shell side is treated as an adiabatic boundary;

• The problem is axisymmetric

2.3. Governing equations

Based on the above assumptions, the LTES melting process in the shell-and-tube unit can be treated as an axisymmetric model. The enthalpy method is used to deal with the moving boundary problem in PCMs melting process. The energy equations for the HTF and PCMs are shown as follows: • For the HTF region

8Tf (x,r,t) , ,8Tf (x,r,t)) ¡82Tf (x,r,t) l 8Tf (x,r t) 82Tf (x,r,t)

+ Uf (r)

x y 0, 0 ^ r ^ R, t y 0

Where p is the density of fluid, C the specific heat, U the fluid velocity and k the thermal conductivity

For the PCMs region

(pCp ) Mpcm (x,r,t) = k

820pcm (x, r, t) 1 8 i 80pcm (x, r, t)■ - -2--1---r---

8x r 8r 8r

-p AH — Ppcm 8t

x y 0, R ■< r ■< R0, t > 0

Where: 6pcm =(t - Tm ),

(\ ^ v ^ T

CMPTED MAh

L < x < l2

/ is the PCMs melting fraction. The melting fraction during charging process is determined as:

/ = 0, 6 < 0 Solid

0 ^ / < 1, 6 = 0 Solid + Liquid I (4)

/ = 1, 6 > 0 Liquid

The Eq. (2) is formulated by using the enthalpy method (Voller [16]), in which the total enthalpy is split into sensible heat and latent heat:

H (t) = h (t)+p/AH (5)

Where: h(T )= \pCpdT (6)

2.4. Initial and boundary conditions • Initial conditions

For the HTF region:

Tf (x,0 < r < R, t = 0) = T Uf (x,0 ^ r < R, t = 0) = U

f ,ini

f ,ini

For the PCMs region:

Tpcmi = Tpcm2 (x, R < r < R, t = 0) = 303 K

Boundary conditions

For the HTF region:

Tf (0,0 < r < R, t) = Tf ,in Uf (0,0 < r < R, t) = 0.03 m / s

dUf (x, r, t )

dTf (x, r, t )

x ^ 0, t > 0

(8a) (8b)

For the PCMs region:

d#pcm (x r, t)

d^pcml (x r, t)

d^pcm2 (x r, t)

x ^ 0, t > 0

R < r < R, t ^ 0

(8c) (8d)

, SOpcm1 (X, r,t)

kpcm1 Sx

^pcml (x = L1, r, t)pcm i = &pCm2 (x = L1, r>t)P

At the inner surface boundary:

hf (0f -0(x, r = Ri, t ))=- kpcmi

Mpm (x, r, t)

x y 0, r = R, t y 0

Where h is local convective heat transfer coefficient (W/m2.K)

The total energy stored capacity for each zone of PCM during charging process can be represented by the following expression:

EPCMi \(mCp )PCMdT + (mAH)PCMlfl + \(mCp )pcMdT

EPCMi = (mCp )PCMl (TMi - TPCMi ) + (mAHS)PCMi fi + (mCp )PCMi (Tf in - TPCMi )

The first term of the Eq. (10) represents the sensible heat charging period, when each PCM temperature increase from its initial temperature to the phase change. The second term represents the latent heat charging during the phase change period. The third term represents the second sensible heat charging period under a fusion form until reaching the steady state.

3. Simulation model

3.1. Numerical Computations

Numerical computations are performed by adopting commercial CFD code Fluent 6.3.26, which employs the finite volume method (FVM) described by Patankar [17] and uses the enthalpy-porosity technique for modeling the melting process. The energy equations were discretized with the first order upwind scheme. The time integration has been performed fully implicitly and control volumes of a uniform size and constant time steps were used. An enthalpy-porosity technique is used for modeling the melting process. In this technique, the liquid melt fraction in each cell is computed every iteration, based on enthalpy balance. The mushy zone is the region where the porosity increases from 0 to 1 as the PCM melts. When the region is complete solid, the porosity is zero. Details on the computational fluid dynamics application in the latent heat thermal energy storage can be found in Al-Abidi et al. [18].

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In order to validate the solution independency of the computational grid size, six different grid sizes for the same working conditions are tested: (100x20), (100x30), (100x40), (300x20), (300x30) and (300x40). Fig. 2 shows the different computation grids used in the preliminary calculations. In charging process, the results of the temperature variation of PCM (Tm=300.7 K) respecting to time using the six different grid sizes are shown in Fig. 3a. As shown in the figure, the grid sizes of (300x20), (300x30) and (300x40) are not suitable. The relative solution deviations with grid sizes of (100x20), (100x30) and (100x40) are small. By enlarging the result as shown in Fig. 3b, the grid sizes of (100x30) and (100x40) presents some perturbations around the melting temperature of PCM, on the other hand, the temperature evolution for the grid size (100x20) during the melting time is very stable and keeps a fixed value (value of melting temperature). The grid size of (100x20) can be regarded as a grid size through which grid independent results can be obtained.

Fig. 2. Different computation grids used in the preliminary calculations.

Fig. 3a. Temperature variation of PCM for different grid sizes.

Fig. 3b. Temperature variation of PCM for different grid sizes (Enlarging results).

4. Analysis of computational results

The transient thermal behavior of the shell-and-tube LTES including two kinds of PCMs having different melting temperature is presented in this section. A large set of numerical tests have been conducted in order to analyze the heat transfer process inside the unit under the effects of different HTF inlet temperature. The variation of temperature respecting to time at locations T1 (x=0.235, r=0.00885) m inside PCM1 and T2 (x=0.735, r=0.00885) m inside PCM2, the variation of total energy stored in different zone of PCMs as well as the total melting time of each PCM have been obtained by a series of numerical calculations and represented graphically.

4.1. Effects of HTF inlet temperature on PCMs temperature evolution

Figs. 4(a-b-c) show the unsteady temperature evolution of PCM1 and PCM2 for three different HTF inlet temperatures (338 K, 343 K and 353 K, respectively). The transient thermal behavior of the unit shows three distinct periods. During the first period, an increasing in temperature of each PCM was observed from the start of heating process until the beginning of the phase change, corresponding to the melting point of each PCM (Tm1=323 K and Tm2=333 K), the two PCMs stores energy primarily by sensible heat. During the second period, the thermal energy is mainly charged by latent heat and the temperature

evolution of each PCM keeps constant for a period of time. At the third period, each PCM temperature starts to increase again, reaches its maximum value, then remains constant and equals to the HTF inlet temperature; during this period, the energy is charged only by sensible heat under a fusion form.

It can be seen that, the melting rate of PCM1 is the fastest and that of PCM2 is the slowest for all three different HTF inlet temperatures. The PCM1 temperature evolution increases rapidly with time during the heating process, which can be explained by the fact that the melting point of PCM1 is lower than PCM2, the PCM1 temperature reaches quickly the melting point, then enter to the second period before PCM2.

Increasing the HTF inlet temperature considerably increases the temperature evolutions of each PCM until reaching the steady state. The effects of HTF inlet temperature show that for high temperature difference between HTF inlet temperature and melting point of each PCM, charging process is rapidly reached. An increase in temperature difference will lead to an increase in the heat transfer rates as a result of rapidly increasing of temperature evolution until reaching the steady state.

Fig. 4a. Unsteady temperature evolution of PCM1 and PCM2 (Tf,in=338 K, Uf,in= 0.03 m/s).

Fig. 4b. Unsteady temperature evolution of PCM1 and PCM2 (Tf,in=343 K, Uf,in= 0.03 m/s).

Fig. 4c. Unsteady temperature evolution of PCM1 and PCM2 (Tf,in=353 K, Uf,in= 0.03 m/s).

4.2. Effects of HTF inlet temperature on total energy stored evolution

Figs. 5(a-b-c) depict the unsteady total energy stored evolution in different zone of PCMs for three different HTF inlet temperatures; for all the cases reported in Figs. 5(a-b-c), the HTF inlet velocity is maintained constant during the numerical tests to a value of 0.03 m/s. As shown in the figures, when the HTF inlet temperature increases from 338 K to 353 K, the thermal energy carried by the HTF enhances, then, the heat transmitted to each PCM becomes important and the charging process is rapidly reached.

The results show also that, for each HTF inlet temperature, the maximum thermal energy stored is observed in PCM2 with high melting temperature, high specific heat and high latent heat of fusion.

It's very clear to observe that, heat storage capacity is large for high temperature difference between HTF inlet temperature and melting point of each PCM. The total energy stored reaches its maximum value, then remains constant at the end of charging process and equals to: (265600 J for PCM1and 282600 J for PCM2) for HTF inlet temperature 338 K; (273800 J for PCM1 and 291800 J for PCM2) for HTF inlet temperature 343 K; (290300 J for PCM1 and 310300 J for PCM2) for HTF inlet temperature 353 K.

Fig. 5b. Unsteady total energy stored evolution in PCM1 and PCM2 (Tf,in=343 K, Uf,in= 0.03 m/s).

Fig. 5c. Unsteady total energy stored evolution in PCM1 and PCM2 (Tf,in=353 K, Uf,in= 0.03 m/s).

Fig. 6 illustrates the amount of total energy stored in each PCM for the three different HTF inlet temperatures. Due to the same reason, the thermal energy carried by the HTF enhances for high HTF inlet temperature. It can be seen from Fig. 6, for each HTF inlet temperature, the maximum energy stored is observed in PCM2.

Fig.6. The amount of total energy stored in each PCM 4.3. Effects of HTF inlet temperature on total melting time

The effects of HTF inlet temperature on the total melting time (time required for each PCM completely melted) is shown in Fig. 7. For different HTF inlet temperature, melting time of PCM2 decrease considerably with increase in HTF inlet temperature compared to PCM1. The effects of increasing in HTF inlet temperature is considerably observed in PCM with high melting temperature. With high temperature difference between HTF inlet temperature and melting point of each PCM, the heat transfer rate increase, so, each PCM melting time reduce. when the HTF inlet temperature increases from 338 K to 353 K, decreasing degree of melting time of PCM2 is the biggest from 1870 s to 490 s, which reduces about 73.8 %; decreasing degree of melting time of PCM1 is the smallest from 530 s to 270 s, which reduces about 49.1 %.

Fig. 7. Effects of HTF inlet temperature on total melting time (Uf,in= 0.03 m/s). 5. Conclusions

A two-dimension mathematical model formulated in two-dimensional cylindrical coordinates based on the enthalpy formulation is developed in order to study the transient thermal behavior of a shell-and-tube LTES unit using two phase change materials named PCM1 and PCM2 having different melting temperatures. A variety of numerical tests were conducted in order to analyze the effect of HTF inlet temperature on the unsteady temperatures evolution

of PCM1 and PCM2, the total energy stored evolution in different zone of PCMs as well as

the total melting time of each PCM. According to the results and discussions, the following

conclusions can be derived:

(01) The transient thermal behavior of the LTES unit shows three distinct periods for the change of PCMs temperatures regarding to time;

(02) For a given HTF inlet temperature, melting rate of PCM1 is the fastest and that of PCM2 is the slowest;

(03) For high temperature difference between HTF inlet temperature and melting point of PCMs, the higher the heat transfer rate is observed; and the charging process is rapidly reached;

(04) For each HTF inlet temperature, the maximum energy stored is observed in PCM2 with high melting temperature, high specific heat and high latent heat of fusion;

(05) Heat storage capacity is large when the temperature difference between HTF inlet temperature and melting point of each PCM is large;

(06) The higher HTF inlet temperature, the smaller melting times is needed.

Nomenclature

0, Specific heat, (J/kg.K)

E Total energy stored, (J)

f PCM melting fraction

h Convective heat transfer coefficient, (W/m2.K)

k Thermal conductivity, (W/m.K)

L Length of the tube, (m)

m Mass of the PCMs, (Kg)

R Inner tube radius, (m)

Ro Outer tube radius, (m)

r Radial coordinate, (m)

T Temperature, (K)

T1, T2 Representative locations inside PCM1 and PCM2, respectively

TM Melting temperature, (K)

Tf,in HTF inlet temperature, (K)

Tpcm Temperature of PCM, (K)

t Time, (s)

U Velocity, (m/s)

x Axial coordinate, (m)

Greek symbols

M Dynamic viscosity, (Kg/m.s)

P Density, (Kg/m3)

AH Latent heat of fusion, (kJ/kg)

6 Relative temperature, (K)

Abbreviations

CFD Computational fluid dynamics

FVM Finite volume method

HTF Heat transfer fluid

LTES Latent thermal energy storage

PCMs Phase change materials

Subscripts f

Phase change material Melting temperature Inlet boundary Initial condition

Heat transfer fluid

M in ini

Research Highlights

• We studied the thermal behavior of LTES unit using two PCMs.

• The effects of HTF inlet temperature on the transient thermal behavior are studied.

• Charging process is rapidly reached for high HTF inlet temperature.

• Heat storage capacity is large for high HTF inlet temperature.

• The higher HTF inlet temperature, the smaller melting time is needed.

References

[1] A. Trp, An experimental and numerical investigation of heat transfer during technical grade paraffin melting and solidification in a shell-and-tube latent thermal energy storage unit, Solar Energy, 79 (2005) 648-660.

[2] A. Trp, K. Lenic, and B. Frankovic, Analysis of the influence of operating conditions and geometric parameters on heat transfer in water-paraffin shell-and-tube latent thermal energy storage unit, Applied Thermal Engineering, 26 (2006) 1830-1839.

[3] Y.B. Tao, M.J. Li, Y.L. He and W.Q. Tao, Effects of parameters on performance of high temperature molten salt latent heat storage unit, Applied Thermal Engineering, 72 (2014)

[4] M.A. Kibria, M.R. Anisur, M.H. Mahfuz, R. Saidur and I.H.S.C. Metselaar, Numerical and experimental investigation of heat transfer in a shell-and-tube thermal energy storage system, International Communications in Heat and Mass Transfer, 53 (2014) 71-78.

[5] M. Lacroix, Numerical simulation of a shell-and-tube latent heat thermal energy storage unit, Solar Energy, 50 (1993) 357-367.

48-55.

M. Akgun, O. Aydin and K. Kaygusuz, Experimental study on melting/solidification characteristics of a paraffin as PCM, Energy Conversion and Management, 48 (2007) 669678.

[7] M. Akgun, O. Aydin and K. Kaygusuz, Thermal energy storage performance of paraffin in a novel tube-in-shell system, Applied Thermal Engineering, 28 (2008) 405-413.

[8] H. Ait Adine and H. El Qarnia, Numerical analysis of the thermal behavior of a shell-and-tube heat storage unit using phase change materials, Applied Mathematical Modelling, 33 (2009) 2132-2144.

[9] M.M. Farid and A. Kanzawa, Thermal performance of a heat storage module using PCMs with different melting temperatures: mathematical modeling, Transactions of the ASME, Journal of Solar Energy Engineering, 111 (1989) 152-157.

[10] H. El Qarnia, Numerical analysis of a coupled solar collector latent heat storage unit using various phase change materials for heating the water, Energy Conversion and Management, 50 (2009) 247-254.

[11] Y.Q Li, Y.L He, H.J Song, C Xu and W.W Wang, Numerical analysis and parameters optimization of shell-and-tube heat storage unit using three phase change materials, Renewable Energy, 59 (2013) 92-99.

[12] M. Fang and G. Chen, Effects of different multiple PCMs on the performance of a latent thermal energy storage system. Applied Thermal Engineering 27 (2007) 994-1000.

[13] T. Watanabe, H. Kikuchi and A. Kanzawa, Enhancement of charging and discharging rates in a latent heat storage system by use of PCM with different melting temperatures, Heat Recovery Systems & CHP, 13 (1993) 57-66.

[14] L. Yang, X. Zhang and G. Xu, Thermal performance of a solar storage packed bed using spherical capsules filled with PCM having different melting points, Energy and Buildings, 68 (2014) 639-646.

[15] F.P. Incropera, D.P. Dewitt, T.L. Bergman and A.S. Lavine, Fundamentals of heat and mass transfer, Sixth edition, Wiley, New York 1996.

[16] V.R. Voller, Fast implicit finite-difference method for the analysis of phase change problems, Numerical Heat Transfer, 17 (1990) 155-169.

[17] S.V. Patankar, Numerical Heat Transfer and Fluid Flow, Hemisphere Publishing Corporation, New York, 1980.

[18] A.A. Al-Abidi, S.B. Mat, K. Sopian, M.Y. Sulaiman and A.Th. Mohammed, CFD applications for latent heat thermal energy storage: a review, Renewable and Sustainable Energy Reviews, 20 (2013) 353-363.

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Table 1

Thermo-physical properties of the HTF and PCMs [13-14-15]

HTF (T= 343 K) PCM 1 PCM 2

Fusion temperature, Tm (K) / 323 333

Density, p (Kg/ m3) 976 848 861

Thermal conductivity, k (W/ m.K) 0.668 0.4 0.4

Specific heat, Cp (J/ kg.K) 4191 1650 1850

Latent heat of fusion, AH (kJ/ kg) 3.34.102 2.00.102 2.09.102

Dynamic viscosity, p (Kg/ m.s) 389.10-6 5.6.10-3 6.3.10-3

Time (Seconds)

Fig. 1a. Schematic representation of the LTES unit with two PCMs.

Tm=323 K

Tm=333 K

htf (tin=338 k) htf (tin=343 k) htf (tin=353 k)

HTF PCM1 PCM2

-► - _ ---- ---- - — - - - —

► PCM1 PCM2

0.47 m

0.53 m

Fig. 1b. Physical model for numerical calculations.

Fig. 2. Different computation grids used in the preliminary calculations.

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I | I-1 I |-1-1-1-1 I | I | l~[ I | T

400 800 1200 1600 2000 2400 2800 3200 3600 4000

Time (Seconds)

Fig. 3a. Temperature variation of PCM for different grid sizes.

300,76 300,75 300,74 300,73 300,72 300,71 Q 300,70 300,69 3 300,68 2 300,67

& 300,66 £

S 300,65 ^ 300,64 300,63 300,62 300,61 300,60

0 100 200 300 400 500 600 700 800 900 1000 1100 1200

Time (Seconds)

—---- —-L-1 i_i | 1___i ---

f'-""™' I"'

i ■ \

11" m j

pn jgt i I | i

L i.. p , . H „ 1,

----—■■ - - — —■— i Grid size 1 (100*20)

f —•— i Grid size 2 (100*30)

t, _____jj f —▲— i Grid size 3(100*40)

J —1 Grid size 4 (300*20)

1 —♦— i Grid size 5 (300*30)

1 —4-I Grid size 6 (300*40)

Fig. 3b. Temperature variation of PCM for different grid sizes (Enlarging results).

1000 1250 1500 1750 2000 2250

Time (Seconds)

Fig. 4a. Unsteady temperature evolution of PCM1 and PCM2 (Tf,in=338 K, Uf,in= 0.03 m/s).

345 342 339 336 333 330 327 324 321 318 315 312 309 306 303 300

---1— J m

< j.....i T j—rn 1-- "j-----

m I f * •

1 T =343 K t,Bl U. =0.03 m/s t.in

j 1 2 ——PCM I (T =323 K) M

—pcm: 2 (TM=333 K)

250 500 750 1000 1250 1500 1750 2000 2250

Time (Seconds)

Fig. 4b. Unsteady temperature evolution of PCM1 and PCM2 (Tf,in=343 K, Ufin= 0.03 m/s).

=3 327

g, 321

H 318 O

H 315 312 309 306 303 300

-250 0 250 500 750 1000 1250 1500 1750 2000 2250

Time (Seconds)

P ■ f a T A /---1--i ft : i

IE.....

1.......1

T, = 353 K

1 I.Bl Uc= 0.03 m/s

PCMi (TM=323 K) -PCM2 (T..=333 K) M

1-•-1-1-1-1-1-1-1-'-1-'-1-I-1-I—r

Fig. 4c. Unsteady temperature evolution of PCM1 and PCM2 (Tf,m=353 K, Uf,in= 0.03 m/s).

Time (Seconds)

Fig. 5a. Unsteady total energy stored evolution in PCM1 and PCM2 (Tf,in=338 K, Uf,in= 0.03 m/s).

Time (Seconds)

Fig. 5b. Unsteady total energy stored evolution in PCM1 and PCM2 (Tf,in=343 K, Uf,in= 0.03 m/s).

Time (Seconds)

Fig. 5c. Unsteady total energy stored evolution in PCM1 and PCM2 (Tf,in=353 K, Uf,in= 0.03 m/s).

320000

310000 -

300000 -

290000 -

^ 280000 -T3

§ 270000™ 260000 -&

£ 250000 -S

« 240000 -§ 230000 -

220000 -

210000 -200000 -

Fig.6. The amount of total energy stored in each PCM

310300

282600

291800

273800

T =338 K T =343 K T =3S3K

l,Lll I.LlI Llii

HTF inlet temperature

Fig. 6. Effects of HTF inlet temperature on total melting time (Uf,in= 0.03 m/s).