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Energy Procedia 75 (2015) 3133 - 3141

The 7th International Conference on Applied Energy - ICAE2015

Numerical investigation of concentric cylinder latent heat storage with / without gravity and buoyancy

A V Waghmare^*, A T Piseb

aGovernment College of Engineering, Maharashtra State, Karad-415124, India _bDirectorate of Technical Education, Maharashtra State, Mumbai-400001, India_

Abstract

Latent Heat Storage is used to balance temporary temperature alternations and storage of energy in several practical application areas. Numerical modelling and analysis of Latent Heat Storage is essential step in designing it for particular application. The present study explores numerically and experimentally the process of melting and solidification of a Phase Change Material in vertical concentric cylindrical unit. Two different cases are considered for analysis; first is without considering gravity and buoyancy effect and second is with considering its effect on PCM. In this analysis melting and solidification time, variation of mushy zone, solid- liquid interface have been studied for both the cases. Commercially available paraffin wax is used as a phase change material. Numerical results have a good agreement with the experimental results. The obtained results can be helpful to study the heat transfer process and designing of Latent Heat base Thermal Energy Storages.

© 2015TheAuthors.PublishedbyElsevierLtd.Thisis an open access article under the CC BY-NC-ND license

(http://creativecommons.Org/licenses/by-nc-nd/4.0/).

Peer-review under responsibility of Applied Energy Innovation Institute

Keywords: PCM, LHS, CFD, Simulation;

1 Introduction

Latent Heat Storage (LHS) using Phase Change Material (PCM) has been a part of attraction in last few years because of their high heat storage capacity. PCMs melt and solidify at a nearly constant temperature and small volume of PCM can store large amount of energy. Numerical modelling and analysis of LHS is essential step in designing it for particular application.

Literature review is done in order to know the work carried on analysis and experimentation of LHS. Abhat [1] has given the experimental analysis of different PCMs and the family of PCM. Kurklu et al. [2] have presented 2D mathematical model of concentric tube LHS. The model is based on assumptions that PCM density is same for all phases; convection heat transfer does not occur in liquid and no heat loss or

* Corresponding author. Tel.: +91 90-9612-0365; fax: +91-20-260-58943. E-mail address: avinashwaghmare1905@gmail.com

1876-6102 © 2015 The Authors. Published by Elsevier Ltd. This is an open access article under the CC BY-NC-ND license

(http://creativecommons.org/licenses/by-nc-nd/4.0/).

Peer-review under responsibility of Applied Energy Innovation Institute

doi: 10.1016/j.egypro.2015.07.646

gain from the store. Model suggests that we can eliminate some complex assumptions, existence of convection in the liquid phase, while maintaining acceptable accuracy. Hamdan and Elwar [3] have carried out theoretical analysis of 2D rectangular enclosure with all sides well insulated except one side. They carried out mathematical analysis to predict rate of melting and hence amount of energy stored in PCM based on pure conduction. Mujumdar and Xiang [4] have presented 2D Numerical model based on finite element analysis of cyclic heat transfer in shell and tube latent heat energy storage. The process of heat transfer is purely conduction controlled and density kept constant. Zivkovic and Fuzzi [5] have presented enthalpy based 2D mathematical model of rectangular and cylindrical LHS. They neglected convection in melt zone and the solution for Liquid fraction update is obtained by Finite Difference method (Gauss Seidel). Henell and Lamberg [6] reported numerical analysis of melting and solidification of PCM using FEMLAB software. The rectangular LHS is analyzed 2D with two methods enthalpy method and effective heat capacity method. Heat transfer is transient, non-linear problem is assumed moving boundary type and Navier Stoke equations used as governing equation. Boussinesq approx. used to model the buoyancy forces. Elawadi [7] has studied the solidification process of ice in a 2D cylindrical tube numerically considering the effect of unsteady natural convection in melt region. While solving problem effect of thermal expansion and radiation effect was not considered. Obtained results indicate that natural convection is dominant over conduction if Rayleigh number is greater than 5x106. Sharma and Buddhi [8] have carried out numerical simulation of 2D theoretical model based on enthalpy formulation. It is assumed that mode of heat transfer is conduction only. They also presented the effect of thermal conductivity of PCM and container material on melt fraction. Trp [9] has reported Conduction based enthalpy formulated model of concentric tube type LHS. The problem is solved using software FLUENT. The model is based on assumptions that convection in melt zone is neglected and thermo physical properties of PCM are constant. Quarnia and Adine [10] have presented Mathematical model based on conservation energy equation. The problem has been solved numerically using VOF model. Solanki et al. [11] presented the numerical model of shell and tube LHS which contains PCM balls, they studied the effect of Stefan Number on melting and solidification time and it is found that higher the Stefan Number shorter is the charging time. Ziskind and Letan [12] have validated the numerical model of PCM with experimental data for the melting process in vertical tube. Enthalpy-porosity formulation and Volume of fluid (VOF) has been used for numerical modeling using FLUENT software. From the literature review it is found that authors have studied Latent Heat Storage two dimensionally. To study melting and solidification process with consideration of gravity and buoyancy effect is important.

2 Problem Modelling

A physical model of the system is presented in detail and then the computational procedure is discussed.

2.1Configuration

A schematic view of the physical model is shown in Fig.1. The LHS is made up of concentric Stainless Steel tubes. The Heat Transfer Fluid (HTF) tube is having 38mm OD with 2 mm thickness and shell is of 101.5 mm OD with 3mm thickness. The height of LHS is 500 mm. To ensure negligible heat loss from shell surface, shell is wound with a thick asbestos rope. The annulus space between tubes is filled with PCM Paraffin Wax. Water is used as HTF and flows through the inner tube. The physical properties of PCM and Stainless steel are given in Table 1.

Consider the schematic model of LHS in Fig.1.The HTF has inlet from bottom and exit through top of inner tube. Heat is stored in PCM in the form of sensible heat and latent heat. During initial heating process sensible heat is added to PCM so conduction mode is dominant in heat transfer process and as the

phase change process takes place liquid fraction of PCM gets increased and convection mode of heat transfer becomes dominant.

Table 2. gives the location of the temperature sensors in LHS. All sensors are put at the distance calculated from the centre of HTF tube.

Assumptions:

All numerical models are based on certain assumptions. For the modelling of LHS, following assumptions have been taken.

1. The PCM is homogeneous and isotropic

2. Thermal resistance across the wall of the thermal storage is negligibly small.

3. The phase-change process is considered to be unsteady- state and two-dimensional.

4. The HTF flow is incompressible, laminar and assumed to be fully developed.

5. Heat loss to surrounding is neglected.

6. Constant temperature drop is assumed along the length of LHS for the HTF flow.

T4 13 T2 T1

Fig. 1. Schematic of LHS

Table 1. Properties of PCM and Steel

Material properties PCM Stainless Steel

Density (kg/m3) 870/960 7500

Liquid/solid

Specific heat(kJ/kg K) 2000 416

Thermal conductivity(k) 0.22 16

Melting heat (kJ) 179

Melting point (K) 331

Table 2. Sensor positions in LHS

Sensor Name Axial Position From Inlet (mm) Radial Position From HTF Tube Surface (mm)

T1/T2/T3 400 5/15/25

T4/T5/T6 300 5/15/25

T7/T8/T9 200 5/15/25

T10/T11/T12 100 5/15/25

Governing Equation:

To study heat transfer and fluid flow in 2D following governing equations are used for mathematical formulation of HTF region and PCM region.

(l)Mathematical formulation of the HTF region

dph , d (phu) d (ph v)

dt dx dy 0 (1)

d ( dv\ 9P

dp hv + (ph vv) _ dt dy dy Vr dy) dy

d(Ph Th) + d(phuTh) + d(phvTh) (3)

dt dx dy ()

= ± + ± (HJH) + 5t

dx \ch dx) dy \ch dy)

dy \ch dy)

(2) Mathematical formulation of the PCM region

In PCM region, the basic equation (The momentum source term and convection are both negligible), is-

d(ppH)

■+V(ppvH) = V(AVT)+S (4)

^\dt) dt\ dx) dt\ dy) v '

H = h +Ah (6)

The h defined as the sum of sensible enthalpy, The enthalpy change due to the phase-change ft L,

A h = ft L (7)

Boundary Conditions:

T= Tm at the HTF side wall T= Tatm and heat flux =0

Grid generation:

Two different cases considered here; case (a) is without considering gravity and buoyancy effect and case (b) with effect of those.

For case (a) horizontal cross section of the LHS is taken which result into concentric circular domain. As the process of melting and solidification is symmetric in all directions quarter circle domain has been taken to treat problem as axisymmetric. In this case gravity and buoyancy forces are not considered. Position of melt front in radial direction is studied. Time required for reaching melt front and solid front to shell is considered to be melting and solidification time respectively. From Fig.2 it is observed that first quarter circle zone is HTF tube thickness which is wall between PCM and HTF. HTF tube has thickness of 2mm so it is also considered as a solid zone and specified with material stainless steel. In second zone PCM is defined.

In second case; case (b) vertical cross section of LHS is considered which yields required axisymmetric domain. In this case effect of gravity and buoyancy on melting and solidification time is considered. This case gives the visualization of motion of melt and solid front in radial as well as axial direction. Time required for complete melting and solidification of PCM is considered to be charging and discharging time for LHS respectively.

outlet

^ Axis a I HTFtube

HTF Inlet

domain case (b)

Fig. 3 shows the domain which shows inlet and outlet of Heat Transfer Fluid (HTF) i.e. water.

The geometry is created in software GAMBIT 2.4.6 and discretized using quadrilateral grid. After successful meshing of the computational domain the meshed file is brought to the solver FLUENT 6.3. A grid system of 58435 quad cells was found to be sufficient to resolve the details of the flow and temperature fields and liquid-solid interface positions. SIMPLE pressure velocity algorithm and PRESTO scheme was adopted for the pressure correction equation. The under-relaxation factors for the velocity components, pressure correction, thermal energy, and liquid fraction were 0.3, 0.1, 1, and 0.9, respectively. In order to satisfy convergence criteria (10-6), the numbers of iterations for every time step were 200. At time t = 0, the PCM is taken to be a motionless solid that is maintained at a constant room temperature.

3 Heat Transfer Process in PCM

3.1 Process of Phase Change

PCM absorbs the heat and when it reaches the melting point it starts melting. There are two types of phase transition; Isothermal phase transition in which PCM melts at particular temperature and second is Non-Isothermal phase transition in which melting takes place over certain range of temperature. The phase-transition region (or interface) is the region that divides two different phases, i.e. divides the solid from the liquid phase. This interface, for most pure materials (pure crystalline substances and eutectics) solidifying under ordinary freezing conditions at a fixed temperature, appears locally planar and of negligible thickness (i.e. it has a sharp front). In other cases, typically resulting from super cooling and binary mixtures, the phase transition region may have apparent thickness and is referred to as a "mushy region".

3.2 Varying thermal conductivity with phase change

Thermal conductivity is the property of material which defines the capacity of material to transfer amount of heat per unit length of material and per unit temperature difference. Every material has different thermal conductivity values in its solid and liquid phase. The conductivity of PCM is assumed to be constant and its average value is taken while modelling LHS.

3.3 Varying density with temperature

The density changes with temperature, combined with gravity, produce buoyancy-driven or natural convection flow in the liquid. In order to treat the body forces, the Boussinesq approximation is employed

which considers buoyancy effect in molten PCM. Boussinesq approximation assumes density constant in the unsteady and convective terms and allows varying only in the body-force term.

4 Results and Discussion

Case (a)

It is assumed that there is uniform temperature drop in temperature of HTF from inlet to exit. HTF water enters at 85 °C and exit at 77 °C so assuming uniform temperature drop, it is considered that HTF is at 83 °C at an axial distance of 200 mm from inlet. The figures below give the results of melting. Fig. 4 shows the position of melt front after each 60min. It is observed that melting starts from surface of HTF tube and front moves in radial direction and reaches to shell in 463 min. During solidification process initially complete PCM is assumed to be at 71°C and the temperature of cooling water is taken to be 34 °C.

Fig. 5 shows the process of solidification, as the HTF flows, it carries away the latent and sensible heat from liquid PCM and PCM becomes solid. This process is called as discharging because stored heat is released. PCM starts to get solid from periphery of HTF tube and then moves radially giving away the latent heat. Case (b)

In this case gravity and buoyancy effects are taken into account. From Fig. 6 it is observed that due to gravity and buoyancy effect molten PCM moves towards top of LHS. Melt front at upper side of LHS reaches to shell very fast as compare to melt front at the lower end of LHS. Flow behaviour of molten PCM is clearly observed in the Fig. 6.

Fig. 7 shows the position of solid liquid front during the process of solidification of PCM. Convex shape of solid PCM is observed on the HTF tube surface near HTF outlet this shows the effect of gravity on the PCM. At lower end of LHS solid front reaches very fast to the shell.

(g)400 min (h)440 min (i)463 min

Fig. 4. Melt front position with time during charging

Fig. 5. Position of solid-liquid front during discharging

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Fig. 6. Melt front position during charging Fig. 7. Position of solid-liquid front during discharging

Case (b) shows that melting and solidification time is 374 min and 288 min respectively.

From the results, it is observed that in both cases melting and solidification time is different. Obtained numerical results are validated with the available experimental results.

Fig. 8 gives the values of temperature at sensor positions; it is observed that there is good agreement between the experimental and numerical results. Slight variation in the results because of the Perfect insulation is considered outside the shell surface but in practice heat loss cannot be avoided.

Fig. 9 shows the temperatures at different sensor positions. The trend of the results is good but variation in results is due to; in experimental case solidification starts from HTF surface and inner wall of shell in turn heat loss to surrounding. Initially PCM assumed to be at 71 °C but experimentally there is temperature distribution within LHS.

Fig. 10 shows the variation of temperature in axial direction. It is observed that the trend of the graph is same for experimental and numerical results. Initially curve remains less steep then after some time it becomes steeper which shows large increment in temperature within less time and again becomes flat.

To study the effect of mushy zone on melting and solidification fraction of solid, liquid and mushy zone is measured after regular interval of time for case (a). The difference between melting and solidification time may be due to role of mushy zone. For case (a) Fig. 11 gives variations of solid-liquid fraction during discharging process. It is observed that formation of mushy zone up to 70 min and then it decreases. Its effect on formation of solidification process is initially slower and then increases faster.

Fig. 8. Numerical and experimental results of charging process Fig.9. Numerical and experimental results of discharging process

Fig. 10. Variation of temperature in axial direction

Fig. 11 .Solid-Liquid fraction during solidification process

solid fraction during melting mushy zone

melt fraction during melting

120 100 80 60 40

°N 20 0

0 60 120 180 240 300 360 420 480 Time (min)

Fig. 12. Liquid-Solid fraction during melting process

Fig. 12 gives variations of liquid-solid fraction during charging (melting) process. It is observed that formation of mushy zone is slower up to 180 min, then increases up to 300 min and becomes zero at 463 min. and then it decreases. Its effect on formation of melt fraction is initially higher and then decreases. At the time of 200 min it becomes 50% and complete melt formation occurred at 462 min.

Conclusion

The present study explored numerically and experimentally the process of melting and solidification of a Phase Change Material (PCM) in vertical concentric cylindrical system. Two different cases are found important for analysis; first is without considering gravity and buoyancy effect and second is with considering its effect on PCM. In this analysis melting and solidification time, variations of mushy zone, motion of solid-liquid interface have been studied for both the cases. Numerical results have a good agreement with the experimental results. The obtained results are helpful to study the heat transfer process and designing of Latent Thermal Energy Storages.

Nomenclature

p 3 Density [kg/m ] P Percent of the liquid fraction

M Dynamic viscosity [kg /m.s] A Coefficient of heat conductivity[W/(m.K)]

k Thermal conductivity (W/m.K) L Latent heat (kJ/kg)

S Sensible enthalpy [J/kg.K] Subscript

H Enthalpy [J/mol] x y Dimensions and directions

u ,v Velocity components[m/s] P Phase Change Material

P Pressure [Pa] h Heat Transfer Fluid

References

[1]. Abhat, A., Low Temperature Latent Heat Thermal Energy Storage: Heat Storage Materials, Solar Energy Applications 13(4) 313-332, 1983

[2]. Kurklu A., Weldon A., Hadley P., Mathematical Modeling of the Thermal Performance of Phase Change Material Store: cooling cycle, Applied Thermal Engineering 16 (7) 61-623, 1996.

[3]. Hamdan, A., Elwar, F., Thermal Energy Storage Using Phase Change Materials, Solar Energy 56 (2) 183-189, 1996.

[4]. Mujumdar, A., Xiang, Z., Finite element Analysis of cyclic heat transfer in shell and tube latent heat energy storage exchanger, Applied Thermal Engineering, 17 (6) 583-591, 1997.

[5]. Zivkovic, B., Fuzzi, I., An Analysis of isothermal PCM within rectangular and cylindrical container, Solar Energy 70(1) 5161, 2001.

[6]. Henell, M., Lamberg, P., Numerical and experimental investigation of melting and freezing processes in phase change material storage, International Journal of Thermal Sciences (43) 277-287, 2004.

[7]. Elwadi, E., Phase change process with free convection in a circular enclosure, Computers & Fluids (33) 1335-1348, 2004.

[8]. Sharma, A., Buddhi, D., Numerical heat transfer studies of fatty acids for different heat exchanger materials on performance of latent heat storage system, Renewable Energy (30) 2179-2187, 2005.

[9]. Trp, A., 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) 648-660, 2005.

[10]. Qarnia H., Adine H., Numerical analysis of the thermal behavior of a shell-and-tube heat storage unit using phase change materials, Applied Mathematical Modeling (33) 648-660, 2009.

[11]. Solanki, S., Regin A., Saini, J., Heat transfer characteristics of thermal energy storage system using PCM capsules: A review, Renewable and Sustainable Energy Reviews, 12 (9) 2438-2458, 2008.

[12]. Ziskind, G., Letan, R., Study of solidification in vertical cylindrical shells, melting in a vertical cylindrical tube: Numerical investigation and comparison with experiments, International Journal of Heat and Mass Transfer (53) 4082-4091, 2008.

Authors' information

Dr. Pise Ashok Tukaram

Dy Director,

Directorate of Technical Education, (Maharashtra State), Mumbai-400001 (India) E-mail ID: ashokpise@yahoo.com

Waghmare Avinash Vishwanath

Research Scholar

Government College of Engineering, Karad Maharashtra, 415124 (India) E-mail ID:

avinashwaghmare1905@gmail.com