CrossMark

Available online at www.sciencedirect.com

ScienceDirect

Energy Procedia 109 (2017) 314 - 321

International Conference on Recent Advancement in Air Conditioning and Refrigeration, RAAR 2016, 10-12 November 2016, Bhubaneswar, India

Influence of Mushy Zone Constant on Thermohydraulics of a PCM

Mathura Kumara, D. Jaya Krishna^*

aGraduate student, bAssistant professor, Department of Mechanical Engineering, National Institute of Technology, Warangal 506004, India

Abstract

PCM (Phase Change Material) can be considered as an attractive option for thermal energy storage due to its high energy density and isothermal process. The understanding of melting characteristics of a PCM is very much necessary for the effective storage/dissipation of heat. One of the important parameters which influences the melting behaviour is mushy zone constant. The present study aims to address the influence of mushy zone constant on the melting characteristics of a PCM by performing 2-D transient numerical simulations in a rectangular cavity. The PCM considered for the study is gallium. The investigation has been carried out using a commercial CFD code ANSYS Fluent 16.0.

The mushy zone constant is varied from 103 to 108, and its influence on the melt fraction and the amount of heat stored has been studied. Results are presented in terms of melt fraction and stream function contours, melt fraction and heat stored. Based on the study, it is observed that the mushy zone constant significantly influence the thermohydraulics of a PCM. © 2017 The Authors.Publishedby 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 the organizing committee of RAAR 2016. Keywords:Mushy zone constant; melt fraction; phase change material; thermohydraulics; gallium.

1. Introduction

The fossil fuels are not going to last long and also the blind use and over exploitation of these fossil fuels have adversely affected the environment. To overcome this, the use of eco-friendly and renewable energy sources is to be promoted. Solar energy is abundantly available in nature and is free of cost. Nowadays, to harvest the available solar energy effectively and to store it for a longer period, PCMs are employed to store the solar energy as a latent thermal energy [1,2]. This stored energy can be used for domestic purposes such as house heating and warming water [2]. Owing to their advantages such as high phase change enthalpy, low volumetric change during phase change, high

* D. Jaya Krishna. Tel.: +91-870-246-2323; fax: +91-870-245-9547. E-mail address: djayakrishna@nitw.ac.in

1876-6102 © 2017 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 the organizing committee of RAAR 2016. doi:10.1016/j.egypro.2017.03.074

energy density and non-toxic nature [1,3], PCMs are also used in air-conditioning units, in radiators of automobiles, in industries for waste energy recovery, for catering services and in electronic equipments for maintaining low temperatures[2,4,5].

Melting is a constant temperature process and during solid-liquid phase transition, for most of the cases the volumetric change due to melting is small. Also, melting process (latent heat transfer method) is accompanied by a large rate of heat transfer compared to that of sensible heat storage methods for a particular temperature range [1,5]. At the onset of phase change, only conduction effect is observed, but, as the phase change progresses the natural convection effect is dominant in the melt region. Gau and Vishkanta [6] conducted an experiment and investigated the influence of natural convection on solid-liquid interface and heat transfer during solidification and melting of a pure metal (gallium) on a vertical wall. Brent et al.[7] numerically investigated the melting of gallium in a rectangular cavity using enthalpy-porosity approach to model combined convection-diffusion phase change. Pal and Joshi [4] computationally and experimentally studied the melting of ra-triacontane in a tall enclosure of aspect ratio 10 having constant heat flux and adiabatic boundary conditions. Kant et al. [3] computationally evaluated the heat storage capacity of six different phase change materials in a square aluminium cavity with constant wall temperature at one side and the other three sides as adiabatic walls. Francisco et al. [8] used the volume averaging approach to estimate the permeability of the porous media and found that for the same porosity value, the permeability is significantly influenced by the flow channel distribution. Kheirabadi et al. [9] numerically studied the effect of the variation of Amush and AT in a rectangular cavity filled with lauric acid and observed that the melting rate of PCM is dependent on Amush and AT. Koller et al. [10] performed a transient numerical investigation of the melting and solidification behaviour of NaNO3 in a wire matrix and observed that the use of wire matrix enhances the heat transfer into the PCM (NaNO3). Omari et al. [11] numerically analysed the impact of shape of containers and the relative position of the cooled surface on the heat transfer and flow characteristics during the melting of PCM in a container for the passive cooling of the electronic devices.

Mushy zone is a semi-solid region existing as an interface between the melted and the un-melted region of PCMs [4,7-9]. This region significantly influences the heat transfer and flow characteristics during melting and solidification of a PCM [3,9]. Due to its semi-solid state and porous nature [4,7-9], the influence of mushy zone during melting and solidification process is unpredictable till date. This paper presents the numerical investigation of variation of Amush and its effect on the melt fraction, vortex strength and the amount of heat stored.

Nomenclature

Ac porosity function, kg/m3s Greek symbols

Amush mushy zone constant, kg/m3s ß thermal expansion coefficient, K-1

Cp constant pressure specific heat, J/kgK £ computational constant

H total enthalpy, J/kg Y liquid fraction of molten PCM

AH latent heat of fusion, J/kg M dynamic viscosity, kg/m-s

h sensible enthalpy, J/kg P density, kg/m3

k thermal conductivity, W/mK

L latent heat, J/kg

P pressure, N/m2 Subscripts

S source term in momentum equation, N/m3 c cold wall

Se source term in energy equation, N/m3 h hot wall

T temperature, K m melting point

t time, s i> j components

u velocity, m/s ref reference value

x coordinate

X length of rectangular enclosure, m Abbreviations

Y height of rectangular enclosure, m PCM Phase Change Material

2. Numerical methodology

2.1. Physical model

A schematic view of the two-dimensional physical model is shown in Fig. 1. The base dimension of the rectangular cavity containing a pure metal, gallium is 8.89 cmx6.35 cm. The left side of the rectangular enclosure is hot, Th= 311 K and the right side of the enclosure is cold, Tc= 301.3 K. The top and bottom walls of the enclosure are subjected to adiabatic conditions. The initial temperature of the enclosure is set at 301.3 K. The thermo-physical properties of the gallium [7] considered in the present study is given in Table 1.

PCM T, 1

Fig. 1. Schematic view of a 2D rectangular enclosure

Following assumptions have been made while solving the above mentioned problem:

• Gallium (PCM) is homogeneous and isotropic.

• Boussinesq approximation is taken into account for natural convection effect.

• Temperature difference between solidus and liquidus temperature is taken as 0.001 K. The difference of 0.001K is considered to avoid an undefined value for melt fraction, when calculated analytically [Eq. (6)].

Table 1. Thermo-physical properties of gallium

Properties Symbol Numerical value

Density P 6093 kg/m3

Melting temperature Tm 302.78 K

Latent heat of fUsion L 80160 J/kg

Thermal conductivity k 32 W/mK

Dynamic viscosity M 0.00181 kg/m-s

Specific heat capacity CP 381.5 J/kgK

Thermal expansion coefficient ß 0.00012 K-1

2.2. Governing equations

The enthalpy-porosity approach [7] is used to solve the problem. It is very difficult to explicitly track the solidliquid interface during melting of PCM. To counter this problem, a quantity called liquid or melt fraction, which is defined as the ratio of the volume of molten PCM to the total volume of PCM, is used. The governing equations pertaining to present study are given below [Eqs. (1-8)].

^ .dp d(puj) ^ ...

Continuity equation: — + gx =0 (1)

d(pUj) d(pUiUj) g2Uj dp

Momentum equation:—--1---—— = ---—h Acui + Si (2)

UL U Xi U Xi Xi U Xi

Energy equation.+ = V. (kVT) + SE

The enthalpy of the material is written as the sum of the sensible enthalpy, h, and the latent heat, AH, H = h + AH

Where,

h = href + £refCpdT

The liquid fraction y is defined as: Y = 0 if T <Tsolldus

y=l if T >Tliquidus

T~TSolidus

, if Tsolidus < T <Ti

Hquidus

Tliquidus Tsolidus

The latent heat content AH in equation can now be written in terms of the latent heat of the material L, AH = yL

Am.ush(,l~Y)2

The term Ac in momentum equation is defined as, Ac = — -

yd+ £

Where, e is a small computational constant (0.001) to prevent division by zero.

2.3. Grid independence and validation

The above mentioned problem is solved in ANSYS Fluent 16.0. The computational geometry is equally divided into 42x32 cells and after further refinement of geometry to 60x50 cells, variation in the results is found to be less than 2%. A time step size of 0.01 second is chosen with convergence criterion for continuity, velocity components in x-and y-directions, and energy to be 10-3, 10-4 and 10-6 respectively. For pressure-velocity coupling, SIMPLE scheme is used. The solutions of the present calculation is compared with the experiments performed by Gau and Vishkanta [6]. Here, the value of mushy zone constant is taken as 1.6x106. Fig. 2 shows the existence of good agreement between the present numerical study and the experimental study carried out by Gau and Vishkanta [6]. Thus, the present computational procedure is reliable and it can be utilised for further studies.

Fig. 2. Comparison of melt fraction interfaces

3. Results and discussions

The present study aims at understanding the influence of mushy zone constant on thermohydraulics of a PCM. Therefore, the mushy zone constant has been varied from 103 to 108 for the time intervals of 2 min, 6 min, 10 min and 18 min. The following section provides the details pertaining to the above considered range of mushy zone constant in terms of melt fraction contours, stream function contours, melt fraction and the amount of heat stored.

Fig. 3 shows the melt fraction contours for considered time intervals and range of mushy zone constants. Based on the figures, it may be noted that as the time duration increases the shape of the contour gets more skewed for all Amush values. This is due to the increased buoyancy effect showing the dominance of convective currents in the upper part compared to bottom part of the melted region. Mathematically, in Eq. 2, if Amush value increases, then the diffusion term also increases, which means that convective term is getting overpowered by diffusion term. Also with the increase in Amush value, decrease in heat transfer rate may be observed. This decrease in heat transfer rate is due to the decrease in convection strength.

As the Amush value increases from 103 to 108, for each time interval the skewness of the melt fraction interface is decreasing and also the melt fraction interface is becoming smooth. For Amush = 106,107 and108, at t=2 min, the melt fraction interface is almost parallel to the vertical face, which shows the dominance of diffusion when compared to that of convection. Thus, for Amush = 106,107 and108, at t=2 min, the heat transfer is observed to be by conduction, while for other cases, both conduction and convection effects are supporting the heat transfer. Eqs. (4-7) are used to calculate the thermal energy stored in PCM during its phase change. Table 2 shows the amount of thermal energy stored in PCM during its melting for different time intervals with the variation of Amush values.

Fig. 3. Melt fraction contours for Am„i,: (a) 103; (b) 104; (c) 105; (d) 106; (e) 107; (f) 108

Fig. 4 shows the variation of melt fraction with time for Amush values ranging from 103 to 108. Based on the figure, it may be noted that for Amush = 103, the rate of increase in melt fraction is high and is observed to decrease with the

increase of Amush i.e., from 104 to 108.The primary reason for the decrease in melt fraction with increase in Amush is due to decrease in convective strength, which can be inferred from the melt fraction contours shown in Fig.3.

Table 2. Amount of energy stored (in J/ kg) during melting of PCM for different Amush values and time intervals

Energy stored (J/kg)

Amush (kg/m3s) 103 104 105 106 107 108

Time (min)

2 6 10 18

16374.86 13537.49 12135.10 11771.77

41395.19 31439.44 25011.52 22749.45

59677.35 46228.83 36971.12 32478.61

81857.53 65567.08 58012.48 51444.46

11710.48 11526.66

22193.13 21726.22

31273.15 30450.66

49043.23 47546.81

0 2 4 6 8 10 12 14 16 18 20

Time (min)

Fig. 4. Variation of melt fraction with time for different values of Amush

Fig. 5 shows the stream function contours for different mushy zone constants with the increase in time interval. As it can be seen from the figure that with the increase in time interval the size of the vortex increases for all Amush values. Also, for a given time interval with the increase in Amush value a decrease in size of the wake is observed. It may be noted that as the molten PCM is getting confined to a smaller region the vortex region decreases with the increase in Amush for all time intervals. In Fig. 5 (a) for 18 min, the vortex region is bigger than the other cases, and is almost capturing the whole computational geometry. This means that the circulation of the molten PCM is taking thoroughly for Amush=103 for 18 min, implying the dominance of natural convection. From Table 2, it is noted that for Amush=103, for each time intervals, the amount of heat energy stored is more than the other Amush values for the corresponding time intervals. This implies that for smaller mushy zone constants, the rate of heat transfer taking place is more than that of the larger mushy zone constants. Thus, it is noted that the vortex size or the wake region shows the strength of natural convection, which in turn indicates the fraction of PCM melted and the rate of heat transfer.

Fig. 5. Stream function contours for Amush (a) 103; (b) 104; (c) 105; (d) 106; (e) 107; (f) 108

4. Conclusions

In the present study, 2-D transient numerical investigation of the melting characteristics of pure gallium in a rectangular enclosure has been carried out for different mushy zone constants ranging from 103 to 108. The simulations have been performed in ANSYS Fluent 16.0. SIMPLE algorithm has been employed for pressure-velocity coupling. Based on the study, it can be noted that the thermohydraulics of a PCM is significantly influenced by Amush. The study could reveal that with the increase in Amush, the convection strength is observed to decrease, which further leads to decrease in heat transfer rate. Therefore, proper selection of mushy zone constant is very much necessary for the accurate prediction of heat transfer characteristics of a PCM.

Acknowledgements

The authors would like to thank SERB-DST, Government of India for funding the research work (SB/FTP/ETA-0130/2014).

References

[1] Sanjay Kumar R, Jaya Krishna D. Differential scanning calorimetry (DSC) analysis of latent heat storage materials for low temperature (40-80°C) solar heating applications. Int J Eng Res Tech2013;2(8):429-455.

[2] Karunesh Kant, Shukla A, Atul Sharma.Performance evaluation of fatty acids as phase change material for thermal energy storage.J Energy Storage2016;6:153-162.

[3] Mahfuz MH, Anisur MR, Kibria MA, Saidur R, Metselaar IHSC. Performance investigation of thermal energy storage system with phase change material (PCM) for solar water heating application. Int Commun Heat Mass 2014;57:132-139.

[4] Debabrata Pal, Joshi Yogendra K. Melting in a side heated tall enclosure by a uniformly dissipating heat source.Int J Heat Mass Tran 2001;44:375-387.

[5] Ben Xu, Peimen Li, Cholik Chan. Application of phase change materials for thermal energy storage in a concentrated solar thermal power plants: a review to recent developments. Appl Energ 2015;160:286-307.

[6] GauC, ViskantaR. Melting and solidification of a pure metal on a vertical wall. J Heat Transf 1986;108:174-181.

[7] Brent AD, Voller VR, Reid KJ. Enthalpy-porosity technique for modeling convection-diffusion phase change: application to the melting of a pure metal. Numer Heat Transfer 1988;13:297-318.

[8] Francisco Valdes-Parada J, Alberto Ochoa-Tapia J, Jose Alvarez-Ramirez. Validity of the permeability Carman-Kozeny equation: a volume averaging approach. Physica A 2009; 388:789-798.

[9] Kheirabadi Ali C, Dominic Groulx. The effect of the mushy-zone constant on simulated phase change heat transfer. Int Symp Adv Comput Heat Transf 2015.

[ 10] Martin Koller, Heimo Walter, Michael Hameter. Transient numerical simulation of the melting and solidification behavior of NaNO3 using a wire matrix for enhancing the heat transfer. Energies 2016; 9:205.

[11] Kamal El Omari, Tank Kousksou, Yves Le Guer. Impact of shape of container on natural convection and melting inside enclosures used for passive cooling of electronic devices. Appl Therm Eng 2011; 31 (14-15):3022-3035.