numerical investigation on phase change process of...

* Corresponding author e-mail: [email protected] Journal access: www.adpublication.org Tel.: +91 261 220 1966 © 2016 A D Publication. All rights reserved

ID: ICFTESPM2016CP140254 Proceeding of Conference, 23rd December,2016

International Conference on

Futuristic Trends in Engineering, Science, Pharmacy and Management

ISBN: 978-81-933386-0-5

Numerical Investigation on Phase Change Process of Spherical and

Rectangular Shaped Macro-encapsulated Phase Change Material

Sagar D Chaudhari, Manish K Rathod *

Mechanical Engineering Department, S V National Institute of Technology, Surat, India-395007

A B S T R A C T : Macro-encapsulation is a common way of encapsulating the Phase Change Material (PCM) for thermal energy storage applications. The container shape may be spherical, tubular, cylindrical or rectangular. The study of melting phenomena of PCM needs to be understood for the design of thermal storage systems. The constrained melting of PCM inside rectangular and spherical capsule using paraffin wax is investigated by CFD analysis. Frontal area, volume is kept same in rectangular and spherical geometry so in order to keep the mass of PCM same in both the cases. This ensures the effective comparison can be done for optimization of macro-encapsulated system. It is observed that melting time required is less in case of rectangular as compared to spherical shaped macro-encapsulated PCM.

© 2016 A D Publication. All rights reserved

Keywords:

Macro-encapsulation, Phase Change Material, Melting Time

1. Introduction Energy plays a major role in the economic prosperity and the technological competitiveness of a nation.

World energy outlook reported that the total energy demand in the countries like India and China is

expected to increase from 55% in 2010 to 65% in 2035 [1]. The utilization of readily available energy of

fossil fuels is increasing almost exponentially due to multiplying population, rapid urbanization and

progressing economy. The resource augmentation and growth in energy supply have, however, failed to

meet this increasing energy demand. Further, the energy demand in the commercial, industrial, public,

residential and utility sectors varies on a daily, weekly and seasonal basis.

Thus, the usage of non-conventional energy sources especially solar energy is essential in wide

range of applications both in urban and rural regions. However, solar energy is intermittent, unpredictable,

and available only during the day. Hence, the successful application of solar energy depends to a large

extent on the method of energy storage used. The latent heat energy storage is the most promising

means of thermal energy storage. However due to low thermal conductivity of PCM and thermal stability

over extended thermal cycles the use of latent heat storage unit (LHSU) is not as per expected [2-3].This

requires the heat transfer enhancement in such systems. The main heat transfer enhancement

techniques are using fin configuration, inserting high thermal conductivity metal matrix into a PCM,

dispersing the PCM with a high thermal conductivity particles and by micro-encapsulation of the PCMs

[4].

International Conference on Futuristic Trends in Engineering, Science, Pharmacy and Management

Page | 46

Out of many heat transfer enhancement techniques, macro-encapsulation of PCM is a new and

immersing technique [5]. Macro-encapsulation is in some form of self-assembled structure or a package

such as tubes, pouches, spheres, panels or other receptacle. These containers usually are larger than 1

cm in diameter and can be incorporated in building products as well. The main advantage of the macro-

encapsulation is its applicability to both liquid and air as heat transfer fluids and easier to ship and handle.

Macro-encapsulation of the PCM helps to overcome the barrier of low thermal conductivity by increasing

heat transfer rate. It is also helpful in forming a barrier and protecting the PCM from the outside

environment and controlling the volume changes of the PCM. It has developed interest in several

researchers especially because it can be cost effective comparative to other techniques. Spherical and

rectangular shape for encapsulation of PCM is mostly used. Since the heat transfer is dependent on

surface area there is need to investigate optimized shape for container.

Khot et al [6] investigates constrained and unconstrained melting of PCM inside a spherical

capsule using paraffin wax. They observed that, the solid PCM is restricted from sinking to the bottom of

the spherical capsule in constrained melting. They also reported that unconstrained melting results in

faster rate than constrained melting due to higher natural convection. Regin et al [7] experimentally and

numerically examined the heat transfer performance of a spherical capsule using paraffin wax PCM

placed in a convective environment during the melting process. They also observed that shorter time for

melting and higher time averaged heat flux occurs in the capsule of smaller radius and for higher Stefan

number. Maheswari and Reddy [8] investigated experimentally and numerically packed bed of spherical

macro-encapsulated PCM .They also compare results for paraffin wax and stearic acid with different sizes

of the spheres and a fin inserted in the sphere. It was observed that, the time taken to complete the

phase change in the sphere changes as the size changes and paraffin takes less time compared to

stearic acid in this cases. When a rectangular cross sectional copper as a fin is inserted into the sphere

radially the melting time taken is reduced. Khodadadi and Zhang [9] also considered the effects of natural

convection on the constrained melting of phase change materials within spherical containers, also states

that during the initial melting process, the conduction mode of the heat transfer is dominant. As the

buoyancy-driven convection is strengthened due to the increase in the melting zone, the process at top

region of the sphere is much faster than at the bottom due to the increment of the conduction mode of

heat transfer. Ismail and Henrique [10] developed parametric model for the study of the solidification of a

PCM in a spherical shell. Model is developed for pure conduction in PCM subjected to constant wall

temperature (CWT) boundary condition for spherical shaped macro-encapsulation. They found that the

increase of the size of the sphere leads to increasing the time for freezing. They also studied different

shell materials for encapsulation and concludes that shell material affects the solidification time. Freezing

was faster for metallic material (Cu, Al) followed by polyethylene, acrylic and PVC. However, the time

difference between these materials mainly metallic and non metallic was small, that still makes non

metallic capsules attractive.

Nomenclature

Cp Specific heat of PCM, Jkg-1 K-1 Liquid fraction, dimensionless

k Thermal conductivity, Wm-1 K-1 Density, kgm-3

H Specific enthalpy, Jkg-1 μ Dynamic viscosity, kgm-1 s-1

L Latent heat, Jkg-1 V fluid velocity vector

P Pressure, Pa C mushy zone constant

t Time, s g Gravitational acceleration m/s2

V Velocity, ms-1


Page | 47

Lacroix [11] presented mathematical model for the contact melting of a sub-cooled PCM inside a

heated rectangular capsule. They observed that the melted fraction from close contact melting at the

bottom of the capsule is larger, by an order of magnitude, than that from the conduction dominated

melting at the top. The melting process is chiefly governed by the magnitude of the Stefan number (Ste).

It is also strongly influenced by the side dimensions of the capsule. Muhammed et al[12] analyzed

numerically and visualized the melting characteristics of a phase change material (PCM) in different

geometries i.e. rectangular block, sphere ,cylinder and configurations using paraffin wax. Authors studied

the effect of aspect ratio on melting time. They observed that melting time strongly depends on the wall

temperature and when wall temperature changes meting time also changes in all shapes and

configurations. Jellouli [13] analyzed numerically the melting process of PCM in a horizontal cavity heated

from below, driven by the coupling of transient heat conduction in the solid phase and steady state

laminar natural convection in the liquid phase with one of the boundaries of the solution domain that

moves. The agreement between the results and those of study reported earlier was found to be good.

They stated that, as the melt layer thickness increases with time, natural convection appears in the liquid

phase and the non-uniform heat transfer distribution along the interface which reaches a steady position

when the heat transfer from the liquid phase is compensated by the heat transfer to the solid phase.

Literature shows that most of researchers focused the work in the field of macro-encapsulation

using spherical and rectangular shaped capsule. Very few literatures are found in which other than these

two shapes are considered for the analysis. The performance of the macro encapsulated PCM is

established by the key parameters like aspect ratio, boundary conditions, geometries for encapsulation,

on melting rate of PCM. However, there is need to compare/optimise these shapes for application in

thermal energy storage systems for enhancement purpose. Thus, the main objective of this research

paper is to establish the thermal performance of the PCM filled in spherical and rectangular capsule using

numerical analysis. Conceptual understanding generated through the present investigations can help to

develop LHSU for solar applications, waste heat recovery, load leveling for power generation, building

energy conservation and air-conditioning applications.

2. CFD Modelling of Macro-encapsulated PCM

2.1 Model

In order to investigate performance of PCM encapsulated in spherical and rectangular geometry, a

numerical model is developed. The physical parameters of sphere and rectangle are chosen in such a

way that frontal area and volume of the container remains same. Thus, diameter of sphere is taken as 50

mm while dimensions for rectangle are considered as 40 mm x 50 mm. The model for the numerical study

was created using pre-processor software GAMBIT 2.4.6. The GAMBIT model i.e. meshed domain is then

exported to FLUENT for processing. The pressure based unsteady solver along with solidification/melting

model with mushy zone constant of 100000 (default value, suitable for most of the engineering

applications) in FLUENT 6.3.26 was utilized for solving the governing equations. The first order upwind

differencing scheme was used for solving the energy, momentum equations and presto for pressure

discretization.


Page | 48

Fig 1. Physical model of containers

(a) (b)

Fig 2. Meshing of the model (a) Spherical Model, and (b) Rectangular Model

2.2 Governing equations

For transient 2-D heat transfer problem in latent thermal energy storage unit the governing equations are energy, momentum and continuity equations. The segregated solver is only available for solving the equations in solidification/melting model. In order to simulate phase change of PCM in above geometries, enthalpy-porosity method is used. The viscous dissipation term is considered negligible. Thus the viscous incompressible flow and the temperature distribution in the domain are described by the Navier-Stokes and thermal energy equations, respectively. The governing equations used in melting are as follows - Continuity equation :

.( ) 0Vt

(1)

Momentum equation :

2( ).( )

VV P V g S

t

(2)

2)

3

(1CS V

(3)

The momentum source term, S, contains contributions from the porosity of the mushy zone, the surface tension along the interface between the two phases, and any other external forces per unit volume. Momentum sink terms are added to the momentum equations to account for the pressure drop caused by the presence of solid material. Energy equation :

( ).( ) .( )

HVH k T

t

(4)

PCM PCM

Sphere D= 50 mm 40 mm

50

mm


Page | 49

H is the specific enthalpy, which is defined as the sum of the sensible enthalpy (h) and the latent heat (ΔH)

H h H (5)

where,

ref

T

ref p

T

h h C dT (6)

The content of the latent heat can vary between zero (for a solid) and L (for a liquid):

H L (7)

The liquid fraction (β) can be written as:

0

1

solidus

liquidus

solidussolidus liquidus

liquidus solidus

if T T

if T T

T Tif T T T

T T

(8)

The above model is developed considering following assumptions [14].

PCM is homogeneous and isotropic.

Initially PCM is in the solid phase for melting with uniform temperature.

Thermo physical properties of the PCM are constant.

Boundary condition is constant wall temperature.

The flow in the molten PCM is considered laminar, incompressible.

The viscous dissipation term is considered negligible.

2.3 Validation

Figure 3 Validation results (a) Experimental result by Gau and Viskanta [16] (b) Numerical results

obtained by present study

In order to validate the numerical model developed for rectangular and spherical capsule filled with PCM,

the present model is first validated with the experimental results published in previous research papers.

Fig. 3 shows experimental result obtained by Gau and Viskanta [16] and numerical simulation result from

present study for different melt front position.The results obtained from developed code are validated with

results obtained by Gau and Viskantha [16]. According to this, a rectangular cavity of 8.89 cm width and

6.35 cm of height is considered. Gallium is used as phase change material. The value of Density, kg/m3;

Thermal conductivity, W/mk; Latent heat, J/kg; Specific Heat, J/kg K; Dynamic viscosity, kg/ms; Melting


Page | 50

temperature, K; Coefficient of thermal expansion of Gallium are 6093, 32.0, 80160, 381.5, 0.00181,

302.78, 0.00012 respectively. Top and bottom wall are kept insulated. Left wall is given constant

temperature 311 K and right wall is kept at 301.3 K. Initial temperature of gallium is taken as 301.3 K.

Figure 4 Validation results (a) Numerical result by Darzi et al [17] (b) Numerical results obtained by present study

Fig. 4 shows numerical result obtained by Darzi et al [17] and numerical results obtained from present

study. The results obtained from developed code are validated with results obtained by Darzi et al [17].

According to this concentric cylinder with internal diameter and outer diameter as 20 mm, 40mm

respectively is considered. N-eicosane is used as PCM. The value of Density, kg/m3; Thermal

conductivity, W/mk; Latent heat, J/kg; Specific Heat, J/kg K; Dynamic viscosity, kg/ms; Melting

temperature, K; Coefficient of thermal expansion of N-eicosane are 770, 0.1505, 247600, 2460, 0.00385,

309, 0.0009 respectively. The solid PCM was sub-cooled at 308.15 K where the wall temperature of inner

cylinder fixed to the 329.15 K. Initial temperature is taken as 308.15 K.

From figs.3-4, it can be concluded that simulation results show good agreement with

experimental and numerical results. Thus, methodology used for solution is correct and further study is

based on same solution methodology.

3. Results and Discussion

The main objective of the present research paper is to develop the numerical models for rectangular and

spherical capsule filled with the PCM and compare the performance of the same in the form of melting

rate and heat transfer characteristics. For that a case study is considered in which paraffin wax is filled in

rectangular and spherical capsule as a PCM. Boundary wall of the encapsulated PCM is subjected to

620C and is assumed to be constant throughout the surface. Table 1 shows the thermo-physical

properties of paraffin-wax PCM.

Table 1 : Thermo-physical properties of Paraffin-wax [15]

Property Value

Density 861 kg/m3

Thermal conductivity 0.4 W/mK

Specific Heat 1850 J/kgK

Viscosity 0.00342 kg/m-s

Thermal expansion coefficient 0.002 /0C

Melting Heat 213000 J/kg

Solidus temperature 58 0C

Liquidus temperature 60 0C


Page | 51

Fig 5 . Contours of static temperature for sphere and rectangle at 10 min

Fig 6. Contours of liquid fraction for sphere and rectangle at 10 min

Fig. 5 shows the temperature distribution of PCM filled in sphere and rectangle after 10 min. From the

figure it is observed that PCM in vicinity of boundary starts melting uniformly. Thus, it is concluded that

conduction mode of heat transfer is dominant compared to natural convection, initially. The same results

can also be reflected from the fig. 6. Fig. 6 shows contours of liquid fraction for sphere and rectangle after

10 min. From both the figs., it is observed that melting of PCM is faster at the top than the bottom portion.

This is because after sometimes PCM starts to melt near the wall and creates a thin layer of molten PCM.

The hot molten PCM rises to top due to temperature difference induced by buoyancy forces. Thus, as

natural convection currents are flowing upwards more rapidly, top portion of rectangular capsule melts

comparatively faster than bottom.

Fig 7. Contours of liquid fraction for sphere and rectangle at 40 min


Page | 52

Fig. 7 shows contours of liquid fraction for sphere and rectangle after 40 min. From the figure it is

observed that the contours of liquid fraction for solid PCM are identical in nature after 40 min. However,

that solid PCM do not sink to bottom due to constant density assumption throughout the PCM i.e.

constrained melting is observed. Further, it is also observed that melting of PCM is faster in case of

rectangular compared to spherical one. This is due to the fact that the aspect ratio is higher in case of

rectangular. During the melting of PCM, the effect of natural convection heat transfer is significant.

Moreover, natural convection heat transfer is mostly influenced by the aspect ratio of the enclosure. This

may be the reason for higher heat transfer in case of rectangular capsule compared to spherical one.

Fig.8 Variation of temperature with respect to

time at location 10 mm below from the top

Fig.9 Variation of temperature with respect to time

at center location

Fig.10 Variation of temperature with respect to time at location 10 mm above from the bottom

Figs. 8-10 show variation of temperature with respect to time at location 10 mm below from the top, center

and 10 mm above from the bottom respectively. It is observed that melting rate at 10 mm above from the

bottom location in both the cases is same. This is due to the fact that conduction mode of heat transfer is

dominant at bottom of capsule. At location 10 mm below from the top, it is observed that initially melting

starts in spherical capsule rapidly compared to that of rectangular one. Later, after 16 min temperature of


Page | 53

PCM at that point for both the cases remains same. This may be because after 16 min PCM gets

completely melted in both the cases at location 10 mm below from the top and change in temperature in

PCM is only due to convection heat transfer only. The center portion of PCM in rectangular capsule melts

faster than spherical capsule. This is due to the effect of natural convection as discussed above. Table 2

shows comparison of time required to start melting at various locations in spherical and rectangular

capsule.

Table 2 : Comparison of melting starting time at various locations

Location Melting starting time(Minutes)

Sphere Rectangle

10 mm below from the top 20 20

Center 28 24

10 mm above from the bottom 23 20

It has been observed from the simulations that total melting time for sphere is 56 minutes & that for

rectangle is 46 minutes. Thus, total 18% reduction in melting time is observed in case of rectangle

shaped macro-encapsulated PCM than spherical one.

Conclusion

In the present research work, thermal performance of PCM encapsulated in rectangular and spherical

capsule is carried out in terms of temperature distribution and total melting time required. A numerical

code is developed in Fluent and validated with experimental results published earlier. It is observed that

PCM melts faster at top than bottom portion of enclosure. It is also concluded that melting time required

in case of macro-encapsulated PCM having rectangular shape is less compared to spherical shape by

17.85%. This research work help us to understand the potential of using efficient LHSU incorporating

macro-encapsulated PCM. It also help to increase the effectiveness of current systems with application of

rectangular shape of encapsulated PCMs and to develop an efficient LHSU in applications like small

scale textile, chemical, sugar and other processing industries.

References

[1] "World Energy Outlook",International Energy Agency,2012

[2] Rathod M K and Banerjee J, "Thermal performance of phase change material based latent heat storage unit”, Heat transfer–Asian Research, Vol. 43 (8), pp. 706-719, Wiley, 2014

[3] Rathod M K and Banerjee J, ”Numerical investigation on latent heat storage unit of different configuration”, International Journal of Engineering and Applied Sciences, Vol. 7(2), pp. 100-105, 2011

[4] Salunkhe P B and Shembekar P S, "Review on effect of phase change material encapsulation on the thermal performance of a system", Renewable and Sustainable Energy Reviews Vol. 16, pp. 5603–5616, 2012

[5] Jegadheeswaran S and Pohekar S D, "Performance enhancement in latent heat thermal storage system: A review", Renewable and Sustainable Energy Reviews, Vol. 13(9), pp. 2225-2244, 2009

[6] Khot S A, Sane N K and Gawali B S, "Experimental Investigation of Phase Change Phenomena of Paraffin Wax inside a Capsule", International Journal of Engineering Trends and Technology, Vol. 2(2), pp. 67-71, 2011


Page | 54

[7] Regin A F, Solanki S C, Saini J S, "Experimental and numerical analysis of melting of PCM inside a spherical capsule", In: Proceedings of the 9th AIAA/ASME joint thermos physics and heat transfer conference, Paper AIAA 2006-3618, pp. 1-12, 2006

[8] Maheswari C U, Reddy R M, "Thermal Analysis of Thermal Energy Storage System with Phase Change Material", International Journal of Engineering Research and Applications (IJERA), Vol. 3, Issue 4, pp.617-622, 2013

[9] Khodadadi J M, Zhang Y, "Effects of buoyancy-driven convection on melting within spherical containers", International Journal of Heat and Mass Transfer, Vol. 44, pp.1605–18, 2001

[10] Ismail K A R, Henriquez J R, "Solidification of PCM inside a spherical capsule. Energy Conversion and Management, Vol. 41, pp. 173–87, 2000

[11] Lacroix M, "Contact melting of a phase change material inside a heated parallelepedic capsule", Energy Conversion and Management, Vol. 42, pp. 35–47, 2001

[12] Muhammed S K, Aikkara R and Kadengal A, "Analysis and Optimisation of Melting Rate of Solids PCM for Various Shapes and Configurations", International Journal of Emerging Engineering Research and Technology, Vol. 2(7), pp. 173-183, 2014

[13] Jellouli Y, Chouikh R, Guizani A and Belghith A, "Numerical Study of the Moving Boundary Problem During Melting Process in a Rectangular Cavity Heated from Below", American Journal of Applied Sciences, Vol. 4 (4), pp. 251-256, 2007

[14] Zhao W, "Characterization of Encapsulated Phase Change Materials for Thermal Energy Storage" Theses and Dissertations, Lehigh University, Paper 1135, 2013

[15] Reddigari M R, Nallusamy N, Bappala A P and Konireddy H R, "Thermal energy storage system using phase change materials –constant heat source", International Scientific Journal: Thermal Science, Vol. 16(4), pp. 1097–1104, 2012

[16] Gau C and Viskanta R, “Flow visualization during solid liquid phase change heat transfer” Numerical heat transfer journal, Vol. 10(3), pp. 183-190, 1983.

[17] Darzi A A R, Farhadi M, Sedighi K," Numerical study of melting inside concentric and eccentric horizontal

annulus", Applied Mathematical Modelling, Volume 36(9), pp. 4080–4086, 2012

http://www.sciencedirect.com/science/article/pii/S0307904X11007219?np=y



http://www.sciencedirect.com/science/journal/0307904X

http://www.sciencedirect.com/science/journal/0307904X/36/9

numerical investigation on phase change process of...

Documents