**1. Introduction**

The electrical and power generation equipment's application generally faces a considerable heat flux [1–3]. The operation of these machines may be thermally affected if the applicable thermal control measure is absent, causing a failure in the operation process [4–6]. Latent heat thermal energy storage (LHTES) could consider as a passive heat control measure for related thermal applications [7,8]. The phase change material (PCM) based in the LHTES can hold the temperature at a constant value by releasing or absorbing heat during the phase change process [9–11]. The simple structure, high and constant performance, and no extra power spending, make the LHTES appropriate for space application [12,13]. Still, a major concern for the LHTES system is PCM's minimal thermal

**Citation:** Sun, X.; Mahdi, J.M.; Mohammed, H.I.; Majdi, H.S.; Zixiong, W.; Talebizadehsardari, P. Solidification Enhancement in a Triple-Tube Latent Heat Energy Storage System Using Twisted Fins. *Energies* **2021**, *14*, 7179. https:// doi.org/10.3390/en14217179

Academic Editor: Luisa F. Cabeza

Received: 16 September 2021 Accepted: 28 October 2021 Published: 1 November 2021

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efficiency, which decreases the phase change rate [14–17]. Researchers developed several techniques to improve the heat transfer rate of such systems, including the expansion of the heat transfer surface area [18–20], adding micro or nano-sized particles [21–24], using cascade layer PCM [25], encapsulation techniques [26,27], changing the location of the heat transfer fluid (HTF) channel [28–30], fins combinations [31–33], conductive foams [34–36], and using magnetic fields [37,38].

A lot of studies related to enhancing the thermal performance in the solidification process have been achieved [39]. Tao [40] was the first researcher to investigate the solidification process in cylindrical geometry. He developed a numerical model to predict interface moving issues during the phase change process. Gortych et al. [41] experimentally and numerically analysed the discharge process of the PCM located in a horizontal annular channel. They assumed a constant wall temperature, which is not a real condition, and they detected a moderate range of the natural convection coefficient. Abdollahzadeh and Esmaeilpour [42] investigated the thermal energy storage (TES) with a wavy wall, and nanofluid used as HTF. They found that the configuration of the system and the nanofluid have great influences on the thermal performance of the system. Shahsavar et al. [43] examined the effect of the wavy channel combined with the metal foam on the latent heat system (LHS). They found that the system configuration and the porous medium have a considerable effect on the thermal performance of the solidification process due to increasing the heat transfer surface area and enhancing the average thermal conductivity of the system. Choi and Kim [44] evaluated the circular fins for the discharging improvement in the LHS. Their work stated that the fins enhance the heat transfer coefficient by 3 times over the case without fins. Wang et al. [45] numerically studied the solidification process in a 2-D zigzag shape heat exchanger. Unlike the inlet velocity, they found that the average velocity of the HTF has a noticeable influence on the thermal performance. Sardari et al. [46] studied the modification of the LHS using a zigzag configuration. They confirm that the unit with the zigzag angle of 60◦ accelerated the storage time by 1/3 times over the time of the case with a 30◦ zigzag angle.

Applying double and triple pipe as the heat exchanger has been widely used in the TES to steady the effects of various parameters such as fins, temperature, and velocity of HTF [47,48]. Shokouhmand and Kamkari [49] numerical evaluated the charging process of the PCM in the double pipe heat exchanger. They stated that the phase change process is strongly affected by the fins placed in the inner tube. Bazai et al. [50] numerically studied an elliptical tube implanted in an annulus channel, they investigated the effects of various aspect ratios and the angular position of the inner ellipse diameters during the charging process. They found that the maximum charging rate accelerated by 61% and the system performance improved by 26%. Shahsavar et al. [51] numerically studied the phase change processes in a wavy double-pipe LHTES unit. They found that the essential time to charge and discharge the PCM decreases by 29% and 58%, respectively, utilising wavy tubes compared with the straights. In a separate study, Shahsavar et al. [52] assessed the efficiency of the phase change process in a wavy double-channel TES system. Increasing the inlet temperature, average velocity, and wave amplitude increases the performance of the system. Xu et al. [53,54] examined a horizontal double-pipe TES combined with a porous medium and optimised the position of the porous injected in the system. They found that the system with a partially filled foam at the base part has the same effect as the system with totally filled by the foam with 80% enhancement of the melting rate. Researchers also applied triple pipe in the TES heat exchanger. Ghalambaz et al. [55] studied the impact of the fins array in a triple-tube LHTES during the melting process. They found that the charging rate for the case of utilising four straight fins was 8.3% lower than that compared with the fins-less case. In two separate works, Mahdi et al. [56,57] studied the performance of the charging rate of the PCM in a triplex tube system. Li et al. [58] studied the effect of the metal foam and nanoparticles on the PCM in a triplex tube LHS. The main outcome of their work was that increasing the loading of nanoparticles or decreasing the porosity of the porous medium accelerates the phase change rate of the PCM.

Fins are considered the best technique to solve the issue of the low thermal conductivity of the PCM and improve the general heat transfer performance in the LHS. Longitudinal, annular, pin, triangular, radial, array, and tree-like fins are the shapes studied by the researcher [59]. Mat et al. [60] utilised a longitudinal fin in the LHS, and they detected a 58% reduction in the phase change time at the constant HTF velocity and 86% under a constant inlet temperature of the HTF. Darzi et al. [61] numerically analysed the solidification process for the PCM in the TES combined with radial fins. They stated that utilising fins increase the solidification process due to increasing the surface area of the heat transfer, and this effect diminishes during the melting process due to annihilation of the natural convection. Pizzolato et al. [62] detected an increase in the melting and solidification rates by 37% and 15%, respectively, when high conductive fins were implanted in a small size TES. Yıldız et al. [63] studied the effect of the fins dimensions and structure (using tree-shaped fins) on the phase change rate, and they found that the rectangular shape has a stronger influence on the system. Yu et al. [64] studied the performance of the LHS using tree-shaped fins, they found that using such fins decreases the melting time by 27% and increases the heat storage rate by 45% than the conventional fins. Rathod and Banerjee [65] stated that the fins improve the TES with both charging and discharging processes. The main enhancements were found as 11%, 12%, and 15% with utilising internal, internal with external, and external triangle fins over the case with longitudinal fins. The rectangular fins supply an improvement rate of 15% over the triangle fins when the evaluation of the fins' configuration is achieved by Abdulateef et al. [66]. Shahsavar et al. [67] examined the influence of the fins locations in the vertical pipe LHS for the charging and discharging systems. The time of the melting and solidification reduces by 41% and 10% by using a uniform fins array compared with the non-uniform array.

Twisted fins have been recently used to improve the heat transfer characteristics in heat exchangers [68]. Providing a higher heat transfer area in the length unit of the heat exchanger is the main advantage of twisted-fins implementation in heat exchangers. Moreover, they generate a swirling flow in the liquid phase, leading to an enhancement in flow mixing and thermal boundary layer disturbance which in turn increases the heat transfer [69]. There are limited studies in the literature on the use of twisted-fins array in latent heat storage systems. Ghalambaz et al. [9,55] studied the twisted-fin array as an advanced form for increasing the phase change rate of the PCM in the shell-and-tube unit during the melting process. They stated that in a double-tube heat exchanger after optimising the geometrical parameters of the fin [9], the use of five twisted fins array improves the melting rate by 42% and the storage rate by 63% compared with the case with straight longitudinal fins using similar geometrical parameters. In a triple-tube heat exchanger, they showed that the use of four twisted fins reduced the melting time and melting rate by 18% and 25%, respectively, compared with the cases of using the same number of straight fins and no-fins considering a similar PCM mass.

In this study, three-dimensional numerical modelling of the PCM solidification process is simulated in a triplex tube LHS combined with twisted fins. The use of twisted fins along the inner perimeter of the annulus hosting the PCM in the triple-tube heat exchanger during the solidification is considered a new contribution to the existing literature. Fins are inserted into the PCM in the centre of the tube and located in a staggered alignment. According to the above comprehensive review, there is no published study regarding twisted-fins application in the triple-tube heat exchanger for intensifying the PCM solidification. It should be noted that the authors studied a similar geometry in their previous study [55] during the melting mode of the PCM and in this study, the solidification process is investigated as the process of heat transfer is different during the solidification compared with the melting due to natural convection especially for vertical geometries. Different simulations were run via ANSYS FLUENT 17.0 (Canonsburg, PA, USA) to evaluate the effectiveness of the innovative design of the fins compared to the base cases of straight fins and no-fins during the solidification. The main purpose was to find suitable and efficient fins number and the best values of the mass flow rate and the inlet temperature of the HTF. Liquid and temperature contour plots and solidification rates are analysed scientifically to evaluate the discharge process. The results of this work provide guidelines for the novel structure of latent heat storage units.

#### **2. Problem Description**

A triple-tube LHS system with twisted fins (Figure 1a) was investigated during the solidification process compared with no-fin and straight fin cases, shown in Figure 1. The system was positioned vertically, and the PCM region was located in the middle tube. Hot water with the uniform inlet temperature of 10, 15, and 20 ◦C and Reynolds numbers of 500, 1000, and 1500 passed through the inner and outer tubes using RT35 as the PCM. Note that the Reynolds number is changed by the variation of inlet velocity of the HTF. The velocity of the HTF for the Reynolds number of 1000 is 0.055 m/s. The adiabatic outer tube was chosen to neglect heat loss from the system to the environment. A pressure outlet was applied for the outlet, and uniform inlet temperature and velocity were employed for the inlet. For the wall surfaces, the no-slip boundary condition was applied. Note that because of the advantages of counter-current flow directions for the working fluid to have a higher melting rate, this method was employed in this study [58]. The inner, middle, and outer diameters of the system were 20, 42, and 64 mm, respectively. The thickness of the inner and middle tubes was considered 2 mm, considering copper for the material of the fins and inner tube. To compare the effect of twisted fins addition with straight fins and no-fin cases, four copper fins were added to the system which the fins were externally and internally attached to the inner and the middle tubes, respectively, as shown in Figure 1. Then, a different number of 2, 4, and 6 fins with twisted configurations were also investigated. The fin pitch for the case of twisted fins was 3 cm. The initial temperature of the PCM is considered 50 ◦C. It is worth noting that this work was achieved with analysis of the numerical results only, and no experiment works were included.

**Figure 1.** The schematic of the proposed double-tube heat exchanger with twisted fins using: (**a**) no fins, (**b**) straight fins, and (**c**) twisted fins.

The properties of RT35 as the employed PCM are presented in Table 1.


**Table 1.** Thermo-physical properties of RT35 [70].

#### **3. Mathematical Modeling**

To calculate the phase change process numerically, the enthalpy–porosity approach was employed where, in each cell, the porosity and the liquid fraction were considered equal [71]. The Newtonian free convection flow of melted PCM was generated because of the buoyancy forces, which were transient and placed in the laminar flow regime because of the range of fluid velocity in the domain. The Boussinesq approximation was also employed in the momentum equation because of the small temperature gradient. Thus, the governing equations were derived based on these assumptions and are as follows neglecting Viscous dissipation [72]:

$$\frac{\partial \rho}{\partial t} + \nabla .\rho \stackrel{\rightarrow}{V} = 0 \tag{1}$$

$$\rho \frac{\partial \overrightarrow{V}}{\partial t} + \rho \left(\overrightarrow{V}.\nabla\right) \overrightarrow{V} = -\nabla P + \mu \left(\nabla^2 \overrightarrow{V}\right) - A\_m \frac{\left(1-\lambda\right)^2}{\lambda^3 + 0.001} \overrightarrow{V} - \rho\_{ref} \beta \left(T - T\_{ref}\right) \overrightarrow{g} \tag{2}$$

$$\frac{\rho \mathbb{C}\_p \partial T}{\partial t} + \nabla \left( \rho \mathbb{C}\_p \vec{V} T \right) = - \left[ \frac{\partial \rho \lambda L\_f}{\partial t} + \nabla \left( \rho \vec{V} \lambda L\_f \right) \right] + \nabla \left( k \nabla T \right) \tag{3}$$

where <sup>→</sup> *V*, *T*, *λ*, and *P* are the velocity vector, temperature, liquid volume fraction, and pressure, respectively; while *t* is time. *Tref* and *ρref* are the reference temperature and density. The third term on the right-hand side of Equation (2) represents the momentum sink for the phase change in the mushy zone [56]. The symbols *Lf* , *ρ*, *Cp*, *k*, *μ*, *Am*, and *β* are the latent heat of fusion, density, specific heat capacity, thermal conductivity, dynamic viscosity, mushy, and volume expansion coefficient, respectively.

It is worth mentioning that the volume expansion of the PCM changing from the solid-state to the liquid-state was neglected, and the mushy zone constant was considered 10−<sup>5</sup> based on the validation process and literature [71]. To simulate the flow of the water in the inner tube, the governing equations were the same as the above equations, ignoring the additional source of body forces and phase change. The liquid fraction, *λ*, is introduced as per Equation (4) [73]:

$$\lambda = \frac{\Delta H}{L\_f} = \left\{ \begin{array}{c} 0 \\ \frac{(T - T\_S)}{(T\_L - T\_S)} \\ 1 \end{array} \begin{array}{c} if \quad T \le T\_S \\\ if \ T\_S < T < T\_L \\\ if \ T \ge T\_L \end{array} \right\},\tag{4}$$

where the subscripts *S* and *L* denote the solidus and liquidus states of PCM, and Δ*H* is the enthalpy variation during the phase change. The solidification or discharging rate . *Q* is introduced as per Equation (5) [53]:

$$\dot{Q} = \frac{Q}{t\_m} = \frac{m\left(\int\_S \mathbb{C}\_p dT + L\_f + \int\_L \mathbb{C}\_p dT\right)}{t\_m},\tag{5}$$

where *tm* is the melting time and m is the mass of PCM. The total enthalpy (*H*) is achieved as per Equation (6):

$$H = \Delta H + h\_{\prime} \tag{6}$$

where,

$$h = \int\_{T\_{ref}}^{T} \mathbb{C}\_p dT + h\_{ref} \tag{7}$$

A detailed description of the mathematical model can be found in the author's previous work [71].

#### **4. Numerical Process**

ANSYS computational fluid dynamic software (FLUENT) was employed to solve the problem using the SIMPLE algorithm for the pressure–velocity coupling scheme. The QUICK scheme was used to discretise the terms of the derivatives in the momentum and energy equations, while the PRESTO scheme was used for the continuity equation. For different equations governed, 10−<sup>6</sup> was used as the convergence criteria. The grid independence analysis was performed before the main simulations considering different mesh and time-step sizes to determine the results independent from the grid number and the time step size. The grid independence test was performed using different cell numbers of 2,302,000, 2,357,000, and 2,451,000 for the case with six twisted fins shown in Figure 1c. The melting time was considered as the criteria to find the mesh independent from the number of cells. The melting time for the system with different cell numbers of 2,302,000, 2,357,000, and 2,451,000 are 2004, 2083, and 2098 s, respectively. The results showed that for the case of twisted f0.33inned triple-tube with six fins, 2,357,000 cells were enough to have independent results from the number of grids tested. The difference between the melting times for the cases with 2,357,000 and 2,451,000 cells is less than 0.3%. Different time step sizes of 0.1, 0.2, and 0.4 s are studied to find the results independent from the size of the time step. The results showed similar melting times for different sizes of time step, and therefore, the size of the time step was also selected equal to 0.2 s. The configuration of the final mesh is shown in Figure 2.

**Figure 2.** The configuration of the mesh after grid independence analysis.

The numerical model is verified using the experimental and numerical results of Mat et al. [60], where the effect of fins attached to both outer and inner surfaces of the tubes in the PCM zone (RT58) in a double-tube LHSHE unit was studied. In this study, constant wall temperature was implemented for the walls of the heat exchanger. As seen from Figure 3, the presented results are in line with the experimental data as well as numerical results for the temperature and numerical data for the melt fraction of Mat et al. [60]. It should be noted that the study of Mat et el. has been used in various studies in the literature to validate different codes.

**Figure 3.** Verification of the numerical model.

#### **5. Results and Discussion**

Several simulation tests have been conducted in order to assess the potential of twisted fins on intensifying the solidification rate of paraffin (RT35) in the vertical TES triple-tube system. Three cases with no fins, straight fins, and twisted fins, are dealt with in this study. There are two, four, and six fins involved in the case of twisted fins. The total mass of PCM is fixed at 0.335 kg, which is equal to the mass of the PCM in the case without any fins, in all of these cases to enable making meaningful performance comparisons. It should be noted that including a denser material of the enhancer (fins) does help faster rates of solidification but also impact the mass/volume of PCM being occupied in the TES unit. Therefore, the storage capacity of the system is negatively affected. To reveal the impact of twisted fins on the system's thermal response, the present results were studied in terms of the liquid-fraction contours, isothermal contour distribution, and temporal fluid-fraction profiles. In any of these cases, it was supposed that the scenario to achieve the total solidification started when the PCM at an initial temperature (*Tint* = 305 K) was above the PCM liquidus temperature (*Ts* = 302 K) while the HTF (water) circulating at a lower temperature (*THTF* = 323 K). This supports the formation of a solidifying layer next to the thermally-active walls so that the PCM molecules near the cooling walls initiate the solidifying phase earlier than the other PCM parts. Over time the layers grow progressively to intrude the entire PCM domain when additional amounts of heat are removed by the heat-transfer fluid (HTF) flowing outside. The presence of twisted or straight fins serves as an extra promoter for better heat communication between the HTF and PCM so that faster heat removal rates from the PCM are achieved, as seen in the next sections. It would be worthy to mention that achieving a faster time response for heat removal in actual TES application is a critical part to consider when designing a TES system. It indicates the TES system's ability to achieve a continuous and stable operation of the energy recovery [74]. If the system fails to timely respond to the energy discharging duties on the PCM side, this causes delays in attaining the cyclic solidification within the time limit, and consequently, a failure of the system's design becomes more probable.
