1. Introduction
Design and development of phase change material (PCM) based thermal energy storage (TES) has been widely attended recently due to the high capacity in latent heat storage without significant temperature changes in the storage unit [
1,
2]. For the heating and cooling systems in buildings when a uniform temperature is required, PCM-based TES can be more effective [
3,
4]. However, the main problem of PCM is the weak conductive property of the PCM results in low thermal diffusion inside the PCM [
4,
5]. Thus, the heat transfer process to or from the PCM is done slowly which reduces the efficiency of the system [
6,
7,
8]. Furthermore, in the heat storage process, this limited characteristic causes high charging time and also a low-performance charging process [
9,
10]. It means that, during the charging process, the PCM cannot enjoy all the capacity of the heat source. During the discharging process, the heat retrieval rate is not high enough to provide a uniform output temperature during the discharging time which reduces the efficiency of the unit outcome in limited usages of PCM-based heat storage systems [
11,
12,
13].
To solve the drawbacks of PCMs in TES applications, there are different methods which can be categorized into two main groups, i.e., (1) methods that improve the thermophysical properties of the PCM, for instance, the use of nanoparticles inside the PCM [
14,
15,
16,
17], (2) methods that increase the thermal rate inside the PCM or from the heat source to the PCM such as adding fins, adding metal foams and modifying the geometry [
18,
19,
20]. There are various works in the literature investigating the thermal improvement inside the PCM-based TES systems using one enhancement method as well as simultaneous usages of various enhancement methods [
21,
22].
Alizadeh et al. [
23] studied a finned triple-tube TES system using V-shaped fins during the discharging process. They add nanoparticles to the PCM to improve the thermal conductivity of the PCM. The outcomes revealed that adding the V-typed fins is more efficient than nanoparticles to improve the discharge rate. Elmaazouzi [
24] performed a numerical analysis on the operation of a shell and tube TES unit equipped with annular fins. They showed the importance of fins addition on the performance of the charging process. Moreover, a higher thermal rate was shown using a higher number of fins. Tiari et al. [
25] experimentally compared two different types of fins, i.e., annular and radial fins on the performance of a PCM-based TES system in comparison with the no-fined case. In the proposed configurations, radial fins show better performance through both charging and discharging compared with the annular fins. Shen et al. [
26] investigated the efficiency of a finned shell and tube PCM-based system considering the effect of thermal radiation. Yang et al. [
27] studied a non-uniform annular finned pipe TES and showed that the melting rate can be decreased by almost 63% and the heat storage rate can be improved by almost 85%. Mahdi et al. [
28] studied the performance of a horizontal finned double pipe TES equipped with longitudinal fins. They revealed that because of the convection heat transfer, fewer and smaller fins at the upper part with larger fins at the lower part are more effective to shorten the charging rate. Li et al. [
29] numerically investigated the performance of multiple PCM units considering different volume ratios and various melting points for the PCM and showed a 32% improvement in the heat storage rate compared with the PCM-only unit. Mosaffa et al. [
30] investigated the discharging process in a shell and tube TES unit and showed that the heat transfer rate is higher in the system compared with that using a rectangular shell. Ho and Gao [
31] achieved practical work on the influences of nanoparticles in a vertical PCM-based system using alumina as the nanoparticles and n-octadecane as the PCM. Kumaresan et al. [
32] examined multi-wall carbon nanotube (MWCNT) on the performance of PCM-based TES systems to improve the heat transfer rate by increasing the thermal conductivity of PCMs. Bazai et al. [
33] numerically evaluated to improve the performance of a double pipe PCM-based system using the geometry modification technique. They examined the effects of using an elliptical tube with various aspect ratios, angular positions, and diameters of the inner ellipse. They showed a maximum improvement of 61% in the heat storage rate. Li et al. [
34] examined the simultaneous effects of adding metal foam and nanoparticles on the performance of a triple pipe PCM-based TES system using RT35 as the PCM. They also examined the directions of heat transfer fluid inside the heat exchanger. They showed that in the existence of a high conductive porous medium, the impact of nanoparticle addition is insignificant.
Modifying the geometry is one technique to enhance the effectiveness of PCM-based TES heat exchangers without adding any additive to the PCM which can be one advantage of this technique compared with the other enhancement methods [
35,
36,
37]. Mahdi et al. [
38] modified a shell and tube heat storage system using multiple PCM combined with other enhancement methods, i.e., metal foam and nanoparticle addition during the solidification process. They showed that the solidification time can be reduced by up to 94% depending on the number of PCM layers and the number of metal foam segments. Shahsavar et al. [
39,
40,
41] studied the performance of double and triple pipe PCM-based heat storage units during melting and solidification using RT35 as the PCM. They modified the geometry using a wavy pipe compared with a straight pipe. They examined the effects of wavelength and wave amplitude using uniform and nonuniform wave distribution and showed the importance of geometry modification on the performance of the phase change process. Wołoszyn et al. [
42] studied a novel helical-coiled tube enhanced with spiral fins and a conical shell and showed that the melting time can be reduced by up to 60% compared with a normal TES module. Najim et al. [
43] modified the geometry of a vertical triple tube PCM storage system by adding a fin at the bottom of the storage unit during the melting process using RT35 as the PCM. Due to the natural convection effect, the PCM at the bottom melts slower compared with the PCM at the top of the storage unit. In the proposed system, they showed an almost 10% reduction in the melting time and a 9% improvement in the heat storage rate by solving the problem of a lower melting rate at the bottom of the heat storage unit.
During the fixed temperature through the phase change process, PCM based heat storage unit can be very effective in heating systems providing a uniform output temperature during the solidification [
44,
45,
46]. Thus, there are a lot of studies working on the solidification of PCMs using various enhancement techniques. Sardari et al. [
47,
48,
49] numerically developed a composite metal foam/PCM heat exchanger to warm a room using force convection air. The air passed from the middle of the composite PCM to gain heat and solidify the PCM. They showed that by using a suitable flow rate for the heat transfer flow rate, proper design, and employing the heat transfer enhancement technique, uniform output air temperature can be achieved from the TES device. In their study, the size of the heating elements as the heat source was also optimized. Talebizadehsardari et al. [
50] studied the consecutive melting and solidification of PCM-based heat storage units. They modified the geometry by employing a zigzag configuration for heat transfer fluid passage to enhance the heat transfer area in the PCM domain. They examined different angles of the zigzag plates and showed almost 33% enhancement in the heat storage rate by increasing the angle of the zigzags. Huang et al. [
51] examined the solidification process using different enhancement techniques in a triple pipe PCM-based unit. The effects of a novel configuration of fins addition and the use of multistage inner tubes were examined simultaneously and separately. They showed that the solidification performance can be improved by up to almost 50% for the best position and diameter of inner tubes.
This study aims to improve the solidification performance of a vertical triple pipe PCM-based heat exchanger using different configurations of frustum tubes for the inner, middle, and outer tubes. According to the literature review, by changing the geometry of the heat storage unit, the effect of natural convection can be changed. Thus, this study focuses on the implementation of frustum tubes in a triple tube heat exchanger to enhance the natural convection effect to improve the solidification performance of the system. The effect of heat transfer fluid flow direction is also examined in this study to improve the performance of the system without adding any additive to prevent reducing the volume of PCM. Different flow directions considering gravity direction are examined. The results of this study provide guidelines for a high-performance design of PCM heat exchangers.
2. Problem Description
In the current work, a vertical triplex tube equipped with frustum tubes as the inner and middle tubes is examined. Inside, the middle tube is filled with the PCM supported by single or multi-internal frustum tubes to improve the rate of heat transfer during the solidification. The HTF (water) flows across the inner and outer channels. Both straight and frustum tubes are considered for the inner tube where water is passed.
The height of the tube is considered 250 mm. In the system with straight tubes, the hydraulic diameters of the interior, middle, and exterior tubes are considered 20 mm, and the thickness of the interior and exterior channels is also considered 1 mm. The system with a straight tube is shown in
Figure 1a. Due to the nature of the heat transfer problem being examined and the scarcity of circumferential flow variation, the system is regarded as axisymmetric, as seen in
Figure 1b. The boundary conditions and directions of the HTF flow, as well as gravity, are also illustrated in
Figure 1b. The HTF’s input temperature and flow Reynolds number are set to 15 °C and 1000, respectively. The PCM’s initial temperature is also considered 50 °C.
In addition to the ordinary straight triplex tubes shown in
Figure 1a, there are three more scenarios considered in this study, including changing the middle tube to a frustum tube (
Figure 2a), changing the inner tube to a frustum tube (
Figure 2b), and changing both the inner and middle tube to frustum tubes (
Figure 2c). In addition to the various tube designs, different gap widths are assessed considering the hydraulic diameters of 5, 10, and 15 mm for the middle tube at the bottom of the heat exchanger. The hydraulic diameter of the middle tube at the top of the heat exchanger is then determined considering a constant volume for the PCM equal to the PCM volume in the straight triplex tube heat exchanger. It should be noted that in the case of changing the inner tube to a frustum tube, it is not possible to use 5 mm as the hydraulic diameter of the pipe at the bottom due to the slope of the frustum and dimensions of the system.
In addition, the directions of the HTF flow in the interior and exterior tubes are examined in this study during the solidification. Li et al. [
52] studied the direction of HTF flows for the melting mechanism and showed that for the counter-current flow (flow direction is similar to the gravity direction in the inner tube), the highest melting can be achieved; however, it can be varied for the solidification process which is studied in this paper considering four different scenarios as follows:
co-current (both similar gravity): the flow direction in the inner and outer tubes are in the gravity direction;
co-current (both opposite gravity): the flow direction in inner and outer tubes are opposite to the gravity direction;
counter-current (inner similar gravity): the flow direction in the inner tube is the same as gravity;
counter-current (outer similar gravity): the flow direction in the outer tube is the same as gravity.
The utilized PCM is presented in
Table 1 which is considered RT-35 which has a suitable melting point for buildings’ applications as well as integrated systems with solar and geothermal energy systems.
3. Mathematical Formulation
The simulation of phase changing of the PCM is based on the enthalpy–porosity method developed by Brent et al. [
53,
54]. In this method, the equal value of the liquid part and the porosity were assumed within each cell of the computational field. To assign the governing formulations, some assumptions are considered [
40,
41], i.e., (1) utilizing the Boussinesq approximation for buoyant influence changes, (2) considering the stream of molten PCM laminar and incompressible, (3) ignoring thermal loss to the ambient, (4) no-slip boundary conditions at the walls.
The conservation formulations of continuity, momentum, and energy are then expressed as [
55]:
(
is indicated as the velocity damping term for the phase change and it disappears at the liquid phase of the PCM and diverges at the solid phase damping the fluid velocity until zero. This term allows to solve the momentum equation in a fixed grid without tracking the location of the interface between the solid and liquid phases which is defined as [
56]:
the parameter of the mushy zone (
) equal to 10
5 based on the literature [
57,
58]. To evaluate the phase transition progression,
(the liquid part of PCM) is considered as [
59]:
The Boussinesq approximation is utilized to determine the density variations because of the temperature swipes through the PCM’s phase change progression where density is calculated as [
60]:
The source term
in the energy formula is calculated as follows [
61]:
The thermal energy released rate (solidification rate) through the discharge process is then defined as [
62]:
where
is the discharge time and
and
are the energy of the PCM at the end of discharge and initial condition.
4. Numerical Description
A combination of the SIMPLE algorithm and Green-Gauss cell-based approach was utilized within the ANSYS-FLUENT solver to assess the heat transfer and fluid flow governing equations of PCM through the phase change procedure. For the momentum and energy formulations, the QUICK differencing technique was utilized with the PRESTO scheme for the pressure correction equations [
63]. The convergence basis for terminating the iterative solution is set to be 10
−4, 10
−4, and 10
−6 for the continuity, momentum, and energy formulations, respectively.
The mesh and the time step size independency tests are performed. Therefore, the various meshing of 28,500, 43,000, and 81,620 for the base case (straight tubes) are assessed utilizing the time step size of 0.2 s for the straight triplex unit.
Table 2 describes the heat release rate for various cell numbers. As revealed, the outcomes are matching for the meshing of 43,000 and 81,620, and thus, the grid of 43,000 is selected for the next analysis.
Table 2 also presents the heat release rate for various sizes of the time step for the nominated mesh. As demonstrated, the outcome data are practically identical for the time step of 0.1, 0.2, and 0.4 s examined, principally for the values 0.2 and 0.1 s. Consequently, 0.2 s is approved as the time step in this study.
To validate the proposed applied model during the solidification process, the results of the current work are compared with the practical study of Al-Abidi et al. [
47]. Al-Abidi’s study was a reliable experimental study that, on one hand, has been employed in several studies for validation, and on the other hand, presented all the details of the geometry and PCM used and therefore is suitable for regeneration of the geometry and validation study in this paper [
64]. They examined the PCM thermal variation in a triplex-pipe PCM heat exchanger integrated with fins. As noted in
Figure 4, there is a good agreement between the PCM mean temperature of the current work and those reported by Al-Abidi et al. [
47]. This indicates that the present model accurately predicts the solidification process relative to the experimental data.
6. Conclusions
Numerical modeling of the discharge process was carried out to assess the design modification on the thermal management of a vertical triplex tube heat exchanger filled with a PCM. A three-dimensional configuration model was evaluated via commercial software (Ansys Fluent). To improve the efficiency of the cooling processes, internal frustum tubes were integrated into various scenarios compared with the ordinary straight triplex tube system. The effect of flow directions of the HTF was also examined toward the higher performance. Three different scenarios were evaluated including changing the middle tube to the frustum tube, changing the inner tube to the frustum tube, and changing both the inner and middle tube to the frustum tubes. The cases were assessed considering the solidification process duration as well as the heat release rates. The study of flow direction reveals the advantages of the heat exchanger with flowing the HTF in the gravity direction over the other directions of the HTF in the heat exchanger. For the frustum cases, a higher efficiency was found for the cases, which have a longer frustum tube diameter (δ = 15) at the top. Reducing tube diameter reduces the heat release during the discharging time because of the wide-area on the bottom side, which delays the phase change process at the center of the system. Case F3, in which only the middle tube is changed to the frustum tube, has the highest value of the heat release rate among the studied cases equal to 33.92 W, which is higher than the lowest case (case F1), case F5, and case F8 by 11.5%, 0.3%, and 0.09%, respectively. Comparing the best case using the frustum tube with the straight tube system, it was shown that there is a negligible difference between these two cases since the heat transfer mechanism is conduction through the walls which are changed from the straight tube to the frustum tube in this study. However, it can be concluded that changing the dimensions of the PCM domain affects the difference. The temperature in the case of frustum tube usage is lower than that for the system with straight tubes.