1

ACTS-P00539

NUMERICAL STUDY ON THE MELTING PROCESS OF PCM WITH

DIFFERENT CONTAINER GEOMETRIES FOR THERMAL ENERGY

RECOVERY

Zhen Qin1, 2, Chenzhen Ji

1, 2, Swapnil Dubey

1, Fook Hoong Choo

1, Fei Duan

2*

1Energy Research Institute @ NTU, Nanyang Technological University, Singapore

2School of Mechanical and Aerospace Engineering, Nanyang Technological University, Singapore

Presenting Author: qinzhen@ntu.edu.sg

*Corresponding Author: feiduan@ntu.edu.sg

ABSTRACT

Latent heat thermal energy storage utilizing phase change materials (PCMs) is a popular approach for the exhaust

gas waste heat recovery. This paper performs three dimensional, time dependent numerical simulations to

investigate the effects of the container geometry on the PCM melting process during heat storage. Under the same

volume of PCM, three container geometries including one baseline cuboid container, one concave container and one

protruding container are considered. Two groups of studies were subsequently carried out with or without natural

convection. The simulation results indicate that natural convection greatly accelerates the PCM melting process.

Especially for the protruding type III container, PCM fully melts at 3330 s with natural convection, while with no

natural convection PCM achieves fully liquid state until 10000 s. Besides, PCM container geometry is proved to

significantly affect the PCM melting speed from two aspects. Firstly, the increasing contact area enhances the heat

transfer process. Secondly, the geometry shape also significantly affects the natural convection process during PCM

melting. It is also worthwhile to draw the conclusion that the protruding type III container performs better than the

concave type II container, while they are both better than the cuboid type I. The simulation results have a guidance

meaning for the future PCM container design.

KEYWORDS: Latent heat energy storage, Phase change material, Numerical modelling, Natural convection

1. INTRODUCTION

Waste heat recovery has a great importance in improving the gas turbine power generation efficiency. In a simple

gas turbine power generation cycle, the energy efficiency is typically only about 30%, while nearly two-third of the

input energy is wasted through high temperature exhaust gas. [1] Thus it is of great meaning to store the heat from

the exhaust gas for reuse. One of the popular ways to store the waste heat is using latent heat storage with PCMs.

Although featuring a high latent heat storage capacity, PCMs normally have a low thermal conductivity that is less

than 0.5 Wm/K. [2] Regarding this disadvantage, various heat transfer enhancement methods have been proposed,

such as installing fins [3], embedding high thermal conductivity nano particles [4] and introducing metal forms [5].

Apart from these methods, it will also affect the heat transfer process inside PCMs to change the PCM container

geometries. In an exhaust gas waste heat recovery application, the PCM container geometries affect the heat

recovery performance not only from changing the container surface area, but also influencing the natural convection

inside liquid PCM. Thus investigating the effect of PCM containers helps optimize the PCM heat recovery

performance. Normally higher thermal energy recovery efficiency means less PCM melting time. Therefore, in order

to investigate the effect of PCM container geometries on the thermal energy recovery efficiency, it is very interesting

to observe the PCM melting process under different PCM containers geometries.

Proceedings of the Asian Conference on Thermal Sciences 2017, 1st ACTS March 26-30, 2017, Jeju Island, Korea

2

In the present work, two groups of three dimensional and transient numerical studies were carried out for an exhaust

gas waste heat recovery with PCMs in three types of container geometries. One group of them involved natural

convection in liquid PCM, while another group only considered conduction. The PCM temperatures in specific

locations were compared and the PCM melting fractions varying with time were plotted. The effects of PCM

containers geometries on the PCM melting process were analyzed according to the simulation results.

2. MODEL DESCRIPTION AND RESULTS

2.1 NUMERICAL MODEL DESCRIPTION

The computational domain includes the air part and the PCM part, as shown in Fig. 1 a). To simplify the model,

some assumptions were made. Firstly, the thermal resistance of the PCM container shell was negligible due to the

higher thermal conductivity of aluminum compared with the PCM. Therefore, the thickness of the PCM container

shell was not ignored. Secondly, the volume change of the PCM during phase change was negligible, and the PCM

was homogeneous and isotropic. Thirdly, the exhaust air was incompressible and considered as the Newtonian fluid.

The inlet flow rate and the temperature of the exhaust air were constant. Lastly, the air inlet temperature into the duct

was uniform. The duct was well insulated outside, thus the heat loss to the environment was negligible.

The investigated three types of PCM container geometries are presented in Fig. 1 b). Three geometry types are

proposed. Except for the original cuboid container geometry type I, one concave type II and one protruding type III

are considered. The volume and the mass of PCM are kept the same in all cases, while the difference lies in the

contact areas. The geometry type II and type III have 1.08 times surface area of type I. Besides, as the three cases

have different cross section areas in the middle x-y plane perpendicular to the gravity direction, the natural

convection inside the three containers will be different from each other.

100

mm

10 mm

y

z

50 mm

P1

P2

P3

Point 1 (200, 100, 50)

Point 2 (200, 100, 75)

Point 3 (200, 100, 25)

b)

III IIIa)

300 mm

Air Flow

Wind Tunnel

PCM Container (Type I)

10 mm

α αx

z

y

200 mm

100 mm

Fig. 1 a) Schematic diagram of the whole computational domain, b) The schematic of three types of PCM containers

and the three investigation positions.

Based on the above-mentioned assumptions, a numerical model was built in three dimensional coordinates, which

can describe the transient heat transfer and melting process of the PCM coupled with the transient heat transfer and

flow of the exhaust air. The governing equations including continuity, momentum, and energy equations were

formulated as below. Unsteady, incompressible Navier-Stokes equations are solved by commercial software

COMSOL Multiphysics 5.1:

0u , (1)

2u

u u p u Ft

, (2)

( ) 0p p

Tc c u T k T

t

, (3)

where (1 ( ))l mF T T g is the buoyance force for natural convection in the PCM domain. To account for

the latent heat absorbed during melting, the effective heat capacity method was used.

3

The hot air velocity in the inlet was set to be 0.5 m/s and inlet temperature was 357.15 K. The PCM selection was

paraffin wax, whose material properties were shown in the previous work. [6] To validate the model, the previous

hot air heat recovery with paraffin wax experiment test section was modelled. [6] The experimental and numerical

temperature evolution at the specific the upper position and the lower point inside the PCM is plotted in Fig. 2 for

comparison and it was found that the numerical results fit well with the experiment results. After model validation,

Mesh independency was studied and the grid size of around 100 k non-structure elements was selected for each case.

0 2000 4000 6000 8000 100001200014000

30

40

50

60

70

80

Tem

per

atu

re (℃

)

Time (s)

Tu (Exp.)

Td (Exp.)

Tu (Sim.)

Td (Sim.)

Fig. 2 Comparison of PCM temperature obtained from experiment and simulation at upper uT and lower dT point.

2.2 RESULTS AND DISCUSSION

Without natural convection effect. The group of simulations without natural convection effect was firstly carried

out in COMSOL Multiphysics 5.1. The simulation results are summarized in Fig. 3. Fig. 3 a) presents the

comparison of PCM temperature profiles in the three selected positions for all cases. It indicates that at point 2 and 3

locations, PCM temperature increases faster and reaches a higher temperature to around 344 K at 10000 s for

geometry type II and type III than type I. This is obviously caused by the higher surface areas of type II and type III

than type I. Similar phenomenon can be observed at point 1. In spite of a longer heat conduction length from surface

wall to point 1 for type II at y direction, it still has a very close temperature increasing trend compared with type I.

Fig. 3 b) shows the melting fraction evolution with time in the three types of geometries. Although with different

melting speeds, all the PCM in the three cases finally melted at around 10000 s, which means that changing the

geometry shapes brings little effect on the melting time of PCM under no natural convection condition.

0 2500 5000 7500 10000

300

320

340

360b)a)

Time (s)

Point 3Point 2Point 1

Tem

per

atu

re (

K)

Type I

Type II

Type III

0 2500 5000 7500 10000

Time (s)

0 2500 5000 7500 10000

Time (s)

0 2500 5000 7500 100000.0

0.2

0.4

0.6

0.8

1.0

Type I

Type II

Type III

Mel

tin

g F

ract

ion

Time (s)

Fig. 3 a) Comparison of PCM temperature in the three locations with no natural convection effect considered, b)

melting fraction of PCM in the three types of containers with no natural convection considered.

To visualize the melting process in the three types of geometry containers, the isothermal contours in PCM domain

are plotted in Fig. 4, where the unmelted PCM is displayed. It is interesting to find that type II and type III have

larger melting fractions and unique melting front shapes. The melting front of PCM has the symmetry shape along

the respective container mid-plane. For the baseline geometry type I, PCM melts evenly from four sides of the

containers to the inside, while the PCM in other containers differ from each other. In the concave type II, PCM melts

firstly in the front part of the center plane, while in protruding type III, PCM melts firstly from the upper and lower

part of the container then to the center, which is easily observed in 4000 s.

4

Fig. 4 Comparison of PCM melting processes in different time steps without natural convection effect.

With natural convection effect. The other group of simulations was performed involving natural convection effect.

The gravity and buoyancy force will drive the liquid PCM to flow, thus enhancing the melting process. Fig. 5 a)

presents the temperature profiles of PCM at the three selected positions. In all cases the sudden temperature jump

after melting is observed, which is different from the gently temperature increase in Fig. 3 a) where natural

convection is not involved. In Fig. 5 a) all positions, type II and type III have a higher temperature increasing speed

than type I. Especially at the lower position point 3, type II and type III achieve the sudden temperature jump around

2500 s earlier than type I. At 10000 s, all three types container PCM reach near the inlet air temperature, 357.15 K.

In contrast, PCM only achieves maximum temperature of 350 K at 10000 s for all cases without natural convection

shown in Fig. 3 a). Correspondingly, the PCM melting fraction evolution with time is presented in Fig. 5 b). It is

observed that the PCM melting fraction of all three cases has a smooth increasing rate and all the PCM becomes

liquid within 10000 s. Of all the three types, type III reaches fully melted state firstly at 3330 s, followed by type II

at 4240 s and lastly type I at 6130 s. Both of Fig. 5 a) and b) prove the advantage of changing geometries on

enhancing the heat transfer in PCM.

0 2500 5000 7500 10000

300

320

340

360b)a)

Time (s)

Point 3Point 2Point 1

Tem

per

atu

re (

K)

Type I

Type II

Type III

0 2500 5000 7500 10000

Time (s)

0 2500 5000 7500 10000

Time (s)

0 2500 5000 7500 100000.0

0.2

0.4

0.6

0.8

1.0

Type I

Type II

Type III

Mel

tin

g F

ract

ion

Time (s)

Fig. 5 a) Comparison of PCM temperature histories in the three locations with natural convection effect considered,

b) melting fraction of PCM in the three types of containers with natural convection considered.

This opinion can also be supported by Fig. 6, which provides the temperature contours of solid PCM at 2000 s and

4000 s respectively. As seen at 4000 s, PCM in type III geometry has already completely melted and becomes fully

liquid. In stark contrast, type I still has almost one third unmelted PCM. As to type II, only a small part of solid PCM

exists at 4000 s. Compared to type II, although with the same contact area, type III has a better heat storage

performance. It is because the concave container shape of type II has limited the natural convection due to its less

mid-plane cross section area. The analysis above proves that the container geometry affects PCM melting speed both

from contact surface area and natural convection space.

5

Fig. 6 Comparision of PCM melting process in different time steps with natural convection effect.

3. CONCLUSIONS

In a summary, a three dimensional transient numerical model was built in COMSOL Multiphysics to investigate the

effect of PCM container geometries on the PCM melting process. A concave type and a protruding type PCM

container were modelled in order to compare with the baseline cuboid container. Two groups of simulations with or

without natural convection were performed. It is found that natural convection greatly accelerates the PCM melting

process in all the three types of PCM containers and convection has a dominant effect in melting compared to pure

conduction. Especially for protruding type III container, PCM fully melts at 3330 s with natural convection, while

with no natural convection PCM achieves fully liquid state until 10000 s. What’s more, PCM container geometry

greatly affects the PCM melting speed when natural convection is involved. Comparing to type I, both type II and

type III have helped improve heat storage performance. Last but not least, it can be concluded that the protruding

type container performs better than concave type container. With a same contact area, the PCM in protruding type III

container melts faster due to a larger natural convection space compared to type II, thus gaining a better result.

ACKNOWLEDGMENT

The authors would like to thank National Research Foundation, Energy Innovation Programme Office, and Energy

Market Authority (EMA) of Singapore for their full support for the work carried out in this paper under a research

Grant No.NRF2013EWT-EIRP001-017.

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