Numerical Study of an Energy Storage Container with a Flat Plate Phase Change Unit Characterized by an S-Shaped Flow Channel

Abstract

China’s rapid economic development and rising energy consumption have led to significant challenges in energy supply and demand. While wind and solar energy are clean alternatives, they do not always align with the varying energy needs across different times and regions. Concurrently, China produces substantial amounts of industrial waste heat annually. Effective recycling of this waste heat could substantially mitigate energy supply and demand issues. The Mobile Thermal Energy Storage (M-TES) system is a key solution to address these challenges, as it helps manage the uneven distribution of energy over time and space. This article establishes a packaged M-TES based on a plate-type phase change unit. Based on different placement methods of the plate-type phase change unit, different inlet temperatures and phase change temperature differences, and different inlet and outlet directions, the complete charging and discharging process of the packaged phase change thermal storage system was simulated using ANSYS FLUENT 2022 R1 software. The results showed that during the heating process of the entire system, the horizontal placement of the plate-type phase change unit and the inlet and outlet methods of the heat transfer fluid (HTF) significantly improved the heating effect of the system, increasing it by 15.9%. Increasing the temperature difference between the inlet temperature of the heat transfer fluid and the melting temperature of the phase change material (PCM) from 4 K to 19 K can increase the melting rate of PCM by approximately 54.9%

1. Introduction

Due to rapid economic development and a sharp increase in energy consumption, China faces a growing challenge regarding energy supply and demand [1]. Efficient energy utilization, energy storage, and distribution have been focal points of scholarly research. Currently, the rapid advancement of renewable energy technologies such as solar, wind, and biomass can diminish reliance on fossil fuels, guiding the reform of China’s energy structure and fostering sustainable development. However, energy generated from natural sources like solar and wind energy faces challenges such as intermittency and variability [2]. Presently, energy storage technology represents an effective approach to addressing these challenges. Energy storage technology involves converting energy into a form that can be stored and released as needed, and it can be categorized into three types based on heat storage principles: sensible heat storage, thermochemical energy storage, and phase change energy storage. Currently, research on sensible heat energy storage is relatively mature, yet it faces challenges of low energy storage density. Chemical energy storage offers higher density but entails complex heat charge and discharge processes with imperfect mechanisms. Phase change energy storage utilizes phase transitions of matter (typically between liquid and solid states) to store and release energy. Phase change materials used in energy storage typically exhibit thermal properties such as appropriate phase change temperatures, high latent heat of transformation, effective heat transfer, and physical properties including favorable phase equilibrium, high density, minimal volume change, and low vapor pressure [3]. Phase Change Thermal Energy Storage Systems [4] convert energy between forms and release it as needed, effectively addressing energy supply–demand imbalances and timing mismatches between production and consumption, thereby enhancing energy efficiency.

Based on different vessel structures and heat transfer mechanisms, phase change thermal energy storage vessels can be classified into direct-contact and non-direct-contact types. Non-direct-contact phase change thermal storage vessels include shell-and-tube and encapsulated types based on the PCM encapsulation method [5,6]. Shell-and-tube phase change heat storage vessels are the most widely used non-direct contact type, employing an immersed heat exchanger where the heat transfer medium transfers heat to the PCM material through a pipe [4,7]. In shell-and-tube systems, the HTF typically enters one end of the pipe and exits the other end, with the PCM usually surrounding the HTF pipe along its circumference. The heat transfer medium exchanges heat with the PCM through the pipe or vessel wall, causing the PCM to undergo phase change for heat storage or release.

Scholars have extensively researched phase change energy storage systems in shell-and-tube configurations. Kang et al. [8] employed computational fluid dynamics (CFD) to optimize the tube bundle arrangement and fin structure of shell-and-tube M-TES containers, enhancing loading and unloading efficiency. Guo et al. [9] used ANSYS FLUENT to simulate how various geometric parameters and heat transfer fluid injection directions affect phase change energy storage in vertical shell-and-tube systems. The results indicate that the PCM melting time increases within a certain range as pipe length increases. Seddegh et al. [10] employed numerical simulations to model thermal behavior in vertical and horizontal shell-and-tube phase change energy storage systems. They found that horizontal configurations exhibit better thermal performance during charging, and increasing the inlet temperature of the HTF significantly reduces total charging time in both configurations. Mourad et al. [11] studied how eccentricity affects transient performance in octagonal and trilobal shell-and-tube phase change thermal storage systems using the enthalpy–porosity method, employing nano-enhanced paraffin as PCM. Yang et al. [12] used numerical simulations to study how the number of fins affects melting phase change in a horizontal finned shell-and-tube thermal energy storage device. The results indicated that the maximum difference in PCM melting time due to fin number reached 72.85% for the same PCM mass. Additionally, increasing the fin number reduces local natural convection. Mohaghegh et al. [13] employed numerical methods to simulate and compare phase change heat transfer between a conventional cylindrical shell and an arbitrarily inclined conical structure. The findings indicated that increasing shell inclination from vertical to inclined enhances melting, thereby accelerating energy storage during charging while decreasing inclination improves thermal performance during discharge. Liu et al. [14] studied how T-shaped fins affect PCM melting in horizontal shell-and-tube storage units. The results indicated that T-shaped fins notably enhance PCM melting, especially those with longitudinal and transverse section length ratios exceeding 1.0. The shell-and-tube phase change heat storage system has a strong heat storage capacity in the heat storage process, but there are problems such as low heat transfer efficiency, poor flexibility, and easy leakage of PCM.

Encapsulated phase change thermal storage systems represent a novel and effective alternative to shell-and-tube vessels. They encapsulate PCM in multiple sub-vessels within the M-TES container, thereby enhancing heat transfer performance through an increased surface area for heat exchange. Sub-vessels come in cubic, cylindrical, and spherical shapes, typically crafted from materials with excellent thermal conductivity and corrosion resistance. In comparison to shell-and-tube vessels, encapsulated vessels provide higher heat transfer rates, are lighter and more cost-effective, and do not necessitate the use of fins. During the heat storage process of encapsulated phase change thermal storage vessels, the HTF completely surrounds the PCM sub-vessels, facilitating heat exchange between the vessel wall and the phase change material. Currently, PCM capsules find wide applications in construction, solar energy storage, and industrial waste heat recovery [15,16,17]. PCM capsule sizes can be tailored to specific needs, addressing issues like low heat transfer efficiency in shell-and-tube phase change heat storage systems, offering high flexibility, and preventing PCM leakage.

Numerous studies have explored encapsulated phase change thermal energy storage systems. Wang et al. [18] proposed a mobilized thermal energy storage system (M-TES) using sodium acetate trihydrate as the PCM that was filled in multiple tubular phase change units, extensively studying its thermal performance. Barba et al. [19] evaluated the thermal performance and discharge effects of PCMs in three different geometrical configurations, finding that smaller spherical capsules exhibit higher Jacobian numbers, thermal conductivity, and shorter solidification times. Ibáñez [20] used TRANSYS 16 software to simulate cooling and reheating experiments of two cylindrical PCM module tanks, concluding that hot water tank size can be reduced without compromising energy storage. Felix Regin et al. [21] developed a model for filled-bed latent heat storage using spherical capsules, studying the dynamic response under different heat transfer fluid conditions and concluding that the PCM phase change temperature range significantly impacts the system. Tat et al. [22] numerically simulated thermal performance in LHS units with cylindrical PCM packages using COMSOL Multiphysics® 6.1 software, highlighting the influence of capsule distribution on HTF flow dynamics and thermal performance. Bhagat et al. [23] conducted numerical simulations of a packed bed latent heat energy storage system using spherical encapsulated PCM, demonstrating that increasing the mass flow rate enhances the energy storage capacity while decreasing porosity reduces HTF temperature variations. Feng et al. [24] encapsulated NaNO₃-KNO₃ as the PCM in spherical containers, experimentally studying heat transfer characteristics during filling, static holding, and discharge processes. The results indicated that temperature differences inside the TES tank fluctuate with changes in average air temperature, with significant impacts from air temperature and flow rate on pressure loss in the packed bed system.

While extensive research has been conducted on spherical and cylindrical phase change units within encapsulated phase change thermal storage systems, there is comparatively less focus on plate-type phase change units. However, some studies have explored the configuration of plate-type thermal storage units within these systems. Zivkovic [25] conducted experiments with plate and cylindrical phase change heat storage vessels placed in a constant temperature bath at 60 degrees, ensuring equal PCM volume and heat transfer area. A comparison of PCM temperatures at the containers’ centers showed superior thermal performance in the plate phase change heat storage vessel compared to the cylindrical counterpart. Lin et al. [26] designed a novel multifluid pillow-plate heat exchanger using sodium acetate trihydrate (SAT) as the PCM, demonstrating excellent thermal performance, compact structure, and high heat transfer rates. Darz et al. [27] numerically simulated melting in a plate heat accumulator containing PCM, suggesting that cooling capacity can be enhanced by increasing the HTF mass flow rate. In summary, while substantial research has been conducted on spherical and cylindrical phase change thermal storage units, there is a notable lack of studies on the thermal storage performance of plate-type phase change units and containers combining multiple plate phase change units. Specifically, research is limited on whether the formation of S-shaped flow channels by multiple plate configurations impacts the energy storage effectiveness of phase change thermal storage systems. Additionally, there is scarce investigation into how the flow state of the HTF within these multi-plate phase change thermal storage containers affects the performance of PCMs.

This paper investigates the thermal performance and internal flow characteristics of plate-type phase change units and multi-plate phase change thermal storage systems by establishing a combined plate-type phase change energy storage container featuring S-shaped flow channels. First, the impact of S-shaped flow channels on the system’s charging and heat release performance is simulated, considering various placements of the container plate and different HTF flow directions. Second, the simulation explores how the temperature difference between the inlet temperature and the PCM phase transition temperature affects the melting and solidification processes of the plate-type PCM units. These simulations aim to enhance the charging and discharging efficiency of mobile phase change thermal storage systems. In practical applications, this system could be utilized in clean energy sectors such as wind and solar power, as well as in industrial waste heat recovery, offering a novel approach to thermal energy recovery and efficiency improvement.

2. Numerical Modeling

This paper numerically simulates the thermal performance of a combined plate phase change energy storage vessel with an S-shaped flow channel. The vessel contains nine plate phase change units staggered inside, forming the S-shaped flow channel. Figure 1 illustrates that the vessel dimensions are 800 mm × 500 mm × 400 mm, with each plate phase change unit measuring 400 mm × 400 mm × 20 mm. The discharge spacing between plate PCM phase change units is 60 mm, leaving 70 mm at each end. The inlet and outlet are square, sized 16.2 mm × 16.2 mm, as shown in Figure 2. HTF enters the vessel through the inlet and passes through the S-shaped flow channel, exchanging heat with the internal plate-type phase change units.

2.1. Material Selection

The organic phase change material selected was No. 46 paraffin, which has a phase change temperature (Tm) of 46 °C and a latent heat of fusion of 202 kJ/kg.

Table 1. PCM thermophysical properties [28,29].

Property	Value	Unit
Melting temperature	319.15	K
Density	880(s)/770(l)	kg/m3
Specific heat	1.8(s)/2.2(l)	kJ/(kg·K)
Thermal conductivity	0.2	W/(m·K)
Viscosity	0.01	kg/(m·s)
Enthalpy	202	kJ/kg

presents the thermophysical properties of No. 46 paraffin. The capsule material for PCM encapsulation was aluminum. The thermal conductivity of aluminum is 202.4 W/(m·K).

2.2. Governing Equations

In this paper, the numerical simulation of the charging and discharging process of the encapsulated phase change thermal storage system must adhere to the principles of conservation of mass, energy, and momentum, governed by the following control equations.

Energy equation:

$$\rho \left({\displaystyle \frac{\partial \mathrm{t}}{\partial \tau }}+u{\displaystyle \frac{\partial \mathrm{t}}{\partial x}}+\omega {\displaystyle \frac{\partial \mathrm{t}}{\partial \mathrm{z}}}\right)={\displaystyle \frac{\lambda }{C_P}}\left({\displaystyle \frac{{\partial }^2\mathrm{t}}{\partial x^2}}+{\displaystyle \frac{{\partial }^2\mathrm{t}}{\partial {\mathrm{z}}^2}}\right)+S$$

(1)

Momentum equation:

$$\rho \left({\displaystyle \frac{\partial u}{\partial \tau }}+u{\displaystyle \frac{\partial u}{\partial x}}+\omega {\displaystyle \frac{\partial u}{\partial \mathrm{z}}}\right)=\mu \left({\displaystyle \frac{{\partial }^{2}u}{\partial x^2}}+{\displaystyle \frac{{\partial }^{2}u}{\partial {\mathrm{z}}^2}}\right)-{\displaystyle \frac{\partial P}{\partial x}}+S_u$$

(2)

$$\rho \left({\displaystyle \frac{\partial \omega }{\partial \tau }}+u{\displaystyle \frac{\partial \omega }{\partial x}}+\omega {\displaystyle \frac{\partial \omega }{\partial \mathrm{z}}}\right)=\mu \left({\displaystyle \frac{{\partial }^2\omega }{\partial x^2}}+{\displaystyle \frac{{\partial }^2\omega }{\partial {\mathrm{z}}^2}}\right)-{\displaystyle \frac{\partial P}{\partial \mathrm{z}}}+S_{\omega }$$

(3)

Continuity equation:

$${\displaystyle \frac{\partial u}{\partial x}}+{\displaystyle \frac{\partial \omega }{\partial y}}=0$$

(4)

In the above equation, $\rho$ denotes the density of the phase change material, t denotes the temperature of the phase change material, $\tau$ denotes the time, $u$ and $\omega$ denote the flow rate of the liquid phase change material in the X-direction and the Z-direction, respectively, $\lambda$ is the thermal conductivity of the phase change material, $C_P$ denotes the specific heat of the phase change material, $S$ is the source term of the energy equation, $\mu$ is the kinetic viscosity of the material, P is the pressure, and $S_u$ and $S_{\omega }$ represent the source terms of momentum in the X-direction and in the Z-direction, respectively. The source term is in fact a damping term, which can be neglected in the momentum equation as the melt fraction converges infinitely to 1 and will again be a very large value as the melt fraction converges to 0.

HTF inside an encapsulated phase change heat storage vessel fluid flow and convective heat transfer can be controlled by the following equation:

$$\nabla \cdot \overrightarrow{u}=0$$

(5)

$${\rho }_H{\displaystyle \frac{\partial \overrightarrow{u}}{\partial t}}+{\rho }_H(\overrightarrow{u}\cdot \nabla )=-\nabla p+{\mu }_H{\nabla }^2\overrightarrow{u}$$

(6)

$${\rho }_H{c}_{pH}{\displaystyle \frac{\partial T}{\partial t}}+{\rho }_H{c}_{pH}\overrightarrow{u}\cdot \nabla T=\nabla \cdot (k_H\nabla T)$$

(7)

The interface between the HTF and the outer wall of the plate phase change unit involves a conjugate heat transfer at the interface, necessitating consideration of conjugate heat transfer.

$$T_H=T_{\mathrm{w}},k_H{\displaystyle \frac{\partial T_H}{\partial n}}=k_{\mathrm{w}}{\displaystyle \frac{\partial T_{\mathrm{w}}}{\partial n}}$$

(8)

Here, ${\rho }_H$, $c_{PH}$, and $k_H$ are the density, specific heat, and thermal conductivity of the thermal fluid, respectively; T is the temperature of the thermal fluid; t denotes time; and the subscripts $H$ and $W$ represent the HTF and the aluminum shell encapsulating the PCM, respectively.

2.3. Boussinesq Natural Convection and Melt-Solidification Models

During the phase transition process, solid phase change materials gradually melt over time. It is assumed that the thermophysical properties of the phase change material (PCM) and the injected heat transfer fluid (HTF) remain constant throughout the natural convection process of the molten phase. Fluid motion in the liquid phase is treated as Boussinesq free convection, where the Boussinesq approximation is used to address the influence of natural convection on melting and solidification. This approximation considers only density variations in the buoyancy term of the momentum equation, treating density as a constant in all other terms. Heat transfer during melting is governed by the energy equation, and, for simplicity, volume expansion due to paraffin melting is neglected. Local natural convection within the molten PCM is described by continuity and momentum equations. The transient phase change heat transfer and local natural convection are represented by the following equation:

$$\nabla \cdot \overrightarrow{u}=0$$

(9)

$$\rho {\displaystyle \frac{\partial \overrightarrow{u}}{\partial t}}+\rho (\overrightarrow{u}\cdot \nabla )\overrightarrow{u}=-\nabla P+\mu {\nabla }^2\overrightarrow{u}+\rho \overrightarrow{g}\beta (T-T_m)+A\overrightarrow{u}$$

(10)

$$\rho c_p{\displaystyle \frac{\partial T}{\partial t}}+\rho c_p\overrightarrow{u}\cdot \nabla T=\nabla \cdot (k\nabla T)-\rho L{\displaystyle \frac{\partial f_l}{\partial t}}$$

(11)

where the above equation is introduced as a damping coefficient for damping the velocity of the solidifying phase, given by:

$$A={\displaystyle \frac{M(1-F_l)}{N+{F_l}^3}}$$

(12)

where $M$ and $N$ are Fluent-defined coefficients suggested to be very large (1 × 10¹⁵) and very small (1 × 10⁻¹⁰), respectively, and $F_l$ is the fraction of the liquid phase in the PCM, which is determined by the representative temperature of the paste region:

$$F_l=\left\{\begin{array}{cccc}0& at& T<T_s& solid\\ {\displaystyle \frac{T-T_l}{T_l-T_s}}& at& T_s<T<T_l& mushy\\ 1& at& T>T_s& liquid\end{array}\right.$$

(13)

where $T_{\mathrm{s}}$ denotes the solid phase line melting temperature of the phase change material and $T_l$ is the liquid phase line solidification temperature of the phase change material.

2.4. Numerical Condition

In this study, the commercially available software ANSYS-Fluent 2022 R1 is utilized for three-dimensional CFD simulations. The HTF is modeled as an incompressible Newtonian fluid with laminar flow characteristics. Water, serving as the heat transfer fluid, enters the vessel through a bottom injection port with a constant inlet velocity and temperature. The inlet temperature for the heat-charging process is 323.15 K, while for the exothermic process it is 293.15 K. The inlet and outlet are set as velocity and pressure outlets, respectively. In this simulation, the water flow rate is very low at 0.07 m/s, and the inlet dimensions are 16.2 mm × 16.2 mm. Using the Reynolds number formula, a Reynolds number of 639.1 is calculated. However, due to the smooth inner wall of the container and minimal external disturbances, the critical Reynolds number is relatively high. Since the simulated Reynolds number is below this critical value, the flow is considered to be laminar in this study. The initial temperature of both the entire vessel and the PCM phase change unit is 292.95 K. During the injection of hot water, convective heat transfer occurs between the walls of the gradual PCM phase change unit via the S-type flow channel. Thermal energy is transferred through the fluid–solid interface and stored by the PCM within the plate phase change unit.

Currently, FLUENT 2022 R1 software utilizes an FVM-based approach to solve the heat transfer process during the melting of phase change materials (PCM). Numerical simulations are conducted to account for phase change heat storage during PCM melting, necessitating consideration of natural convection induced by gravity with an acceleration of −9.81 m/s² in the Z direction set in the Gravity settings. The Melting/solidification and Energy models are activated in the Models list, with the Boussinesq hypothesis used to estimate buoyancy effects due to natural convection, accounting for density changes linearly with liquid phase temperature in the Materials list. The Simple algorithm manages pressure and velocity calculations, while the Presto! method is employed for pressure correction equations, aided by under-relaxation factors (0.4 for momentum, 0.5 for pressure correction, 0.8 for energy, and 0.7 for liquid fraction) ensuring convergence (10⁻⁶ for continuity, 10⁻⁶ for momentum, and 10⁻⁹ for energy equations). Second-order upwind schemes are applied to momentum and energy equations.

In this paper, four distinct injection modes are examined: down-in-out and up-in-out with the PCM phase change unit oriented vertically and down-in-out and up-in-out with the PCM phase change unit oriented horizontally, as shown in Figure 1. The heat charging and exothermic performance of these four configurations were simulated and analyzed. Additionally, the effect of varying the temperature difference between the HTF inlet and outlet on the heat charging and exothermic efficiencies of the system is investigated based on the initial operating conditions.

2.5. Grid-Independence Validation and Time-Step Determination

Mesh-independent validation is crucial in numerical simulations to ensure the reliability of the results. By confirming the consistency of simulation results across different grid sizes, the suitability and stability of the numerical solution can be established. This validation assesses how mesh size impacts simulation accuracy and helps identify the optimal mesh size, thereby enhancing simulation reliability and accuracy. Without grid-independence validation, errors or biases due to improper mesh selection can compromise the understanding and predictive capability of the study.

Three grid configurations (503,103, 603,739, and 705,463) are utilized for grid-independence verification. As shown in Figure 3, grid 1 corresponds to 503,103, grid 2 to 603,739, and grid 3 to 705,463. The results indicate that when using 503,103 grids or more, further increases have minimal impact on the simulation results, ensuring computational stability despite slight variations among grids 1, 2, and 3. Given the small differences in results between grid 1, grid 2, and grid 3, grid configuration 603,739 is selected for its stability in subsequent calculations.

Since the average temperature change of PCM under four different time steps (1.0, 0.50, 0.10, and 0.05) is verified as shown in Figure 4, it is observed that when the time step ≤ 0.50 s, the influence on the results becomes negligible. Therefore, a time step of 0.50 s is selected for this study to balance accuracy and computational cost. To ensure precise calculation results, a grid number of 603,739 and a time step of 0.50 s are employed for the numerical simulations. Additionally, to guarantee convergence, the maximum number of iterations is capped at 20.

2.6. Validation of Experiments and Simulations

To validate the accuracy of the simulation, the results were compared with the experimental data from Diao et al. [29], as depicted in Figure 5. The simulation was simplified and modified to form a complete S-shaped flow channel by adjusting the flat phase change unit. Consequently, we excluded the HTF flow space at the top of the PCM phase change unit and disregarded the injection port of the PCM phase change unit. Additionally, heat transfer from the outer wall of the container was not considered. Initially, when the hot fluid enters the container, the simulated and experimental temperatures exhibit similar trends, with a gradual rise in temperature inside the container. However, due to the gap above the plate phase change unit in Diao et al.’s model, the hot fluid fills the container more quickly, leading to a faster temperature rise later on. In contrast, our model, which features heat transfer solely through the S-shaped flow channel and the plate phase change unit, exhibits more effective heat transfer but results in a slightly slower temperature rise in the later stages. Although there are minor discrepancies between the simulation and experimental results, the overall trends are consistent, indicating that the simulation results are reasonably accurate.

3. Results and Discussion

3.1. The Impact of Phase Change Unit Positioning and HTF Inlet/Outlet Directions on the System’s Charging and Heat Release Performance

We investigated the exothermic performance of encapsulated phase change accumulators utilizing plate-type phase change units with S-shaped flow channels under various placement conditions. Figure 6 and Figure 7 illustrate four operational configurations of the encapsulated phase change heat storage vessel under varying gravitational orientations. Condition 1 refers to HTF entering from the lower inlet and exiting from the upper outlet with the plate PCM phase change unit positioned vertically; Condition 2 refers to HTF entering from the upper inlet and exiting from the lower outlet under the same vertical orientation. Conditions 3 and 4 represent analogous inlet–outlet scenarios with the plate phase change unit positioned horizontally. Figure 8 demonstrates the consistent heating and PCM melting conditions of the plate phase change unit during the heat charging process across all four operating conditions up to 15,000 s. However, as the liquid phase rate of PCM gradually increases, the PCM within the plate phase change unit partially melts, which enhances natural convection within the PCM and thus affects the melting process across all operating conditions. Due to its plate-type design, the phase change unit exhibits a natural convection length of 400 mm in the direction of gravity when oriented vertically, leading to limited natural convection within the PCM in its molten state. In contrast, when the phase change unit is positioned horizontally, the natural convection length decreases to 20 mm in the direction of gravity, promoting more uniform and efficient internal natural convection within the molten PCM. The influence of inlet and outlet positions on the melting process of the PCM phase change unit is minimal. We observed that, regardless of whether the phase change unit is oriented horizontally or vertically, HTF entering from the top and exiting from the bottom (up-in-out) performs better than the reverse (down-in-out). This superiority of up-in-out is attributed to gravity in the S-shaped flow channel, which assists the natural flow direction, whereas down-in-out encounters resistance from gravity, thereby impeding flow efficiency.

Figure 9 illustrates the exothermic process of the plate phase change heat storage system under various placement orientations and inlet/outlet configurations. The exothermic process shows minimal variation across the four operational conditions due to the PCM solidification process. The PCM solidifies gradually from the periphery toward the interior within the plate phase change unit, exerting minimal impact on natural convection in the molten state. Consequently, this leads to convergence between the average temperature versus time curve and the liquid phase rate versus time curve for the PCM.

3.2. Influence of Temperature Difference between Inlet Temperature and Phase Change Temperature on the Heat Release Performance of the Encapsulated Phase Change Storage Vessel

The relatively small temperature difference between the PCM melting temperature of 319.15 K and the HTF inlet temperature of 293.15 K may reduce the thermal storage efficiency of the PCM. In this section of the study, we systematically varied the initial conditions by adjusting the HTF inlet temperature. Beginning with an initial ΔT of 4 K (corresponding to an HTF inlet temperature of 323.15 K), we incrementally increased ΔT by 5 K to 9 K, 14 K, 19 K, and 24 K, resulting in HTF inlet temperatures of 328.15 K, 333.15 K, 338.15 K, and 343.15 K, respectively. These conditions were analyzed to evaluate the heat charging and exothermic performance of the S-shaped flow channel-based phase change thermal storage vessel.

Figure 10 illustrates the average temperature and liquid phase rate of PCM over time during the heat charging process under different temperature differences. It is evident that, within a specific temperature range, larger disparities between the HTF inlet temperature and the PCM melting temperature lead to more pronounced changes in the PCM temperature and liquid phase rate. At temperature differences of 19 K and 24 K, the PCM experiences significantly greater temperature changes compared to 4 K, 9 K, and 14 K. The liquid-phase rate of the PCM reaches 1 more rapidly, indicating that PCM melting occurs in approximately 16,000 s under these conditions. Regarding the melting rates, at a temperature difference of 24 K, the PCM melting rate increases by approximately 59.8% compared to 4 K. At a temperature difference of 19 K, the melting rate increases by about 54.7%; at 14 K, by about 50.1%; and at 9 K, by about 15%, compared to 4 K. Under the conditions of temperature differences of 19 K and 24 K, the liquid phase rate curves are similar, and the temperature change curves align closely before 10,000 s. Consequently, we conclude that the PCM melting effect at a temperature difference of 19 K is comparable to that at 24 K. However, considering heat loss, operating with a temperature difference of 24 K increases heat loss, as energy storage is completed at around 16,000 s. The amount of heat stored in the PCM when fully melted at temperature differences of 19 K and 24 K is similar, making a temperature difference of 19 K optimal.

Figure 11 illustrates the curves of the average temperature and liquid phase rate of the PCM over time under various temperature differences during the exothermic process. After completing the heat charging process, we initiate the exothermic phase using water at 293.15 K. It is observed that the exothermic process concludes in approximately 15,000 s under each condition. Although a larger temperature difference results in a more rapid decrease in the PCM average temperature, the final exothermic time does not vary significantly. Therefore, the critical factor remains the heat charging stage.

To illustrate the charging and exothermic processes of the plate-type phase change heat storage unit with the S-shaped flow channel, cross-section A in Figure 12 presents partial cloud diagrams, while Figure 13 and Figure 14 show HTF temperature changes inside the vessel at 4000 s and 8000 s during charging and PCM melting. Figure 15 shows HTF temperature variations and PCM melting over 5000 s during the exothermic process inside the vessel. The HTF enters the encapsulated phase change heat storage vessel and exchanges heat with the plate-type phase change unit through the S-shaped flow channel, facilitating more efficient heat exchange and minimizing heat loss.

4. Conclusions

This paper investigates an encapsulated phase change thermal storage system using a multi-plate phase change unit with an S-shaped flow channel. A three-dimensional CFD model is developed to analyze how the placement orientation of the phase change thermal storage vessel and the positions of the HTF inlet and outlet affect its charging and discharging performance. Additionally, we vary the temperature difference between the HTF inlet temperature and the PCM melting temperature to evaluate its impact on the system’s charging and discharging performance. The findings reveal that:

During heat charging, the PCM melting rate is faster when the plate-type phase change unit is oriented horizontally rather than vertically, resulting in a 15% improvement in heat charging efficiency.

When the HTF flows from top to bottom, the PCM melting efficiency of the plate phase change device surpasses that of the bottom-up flow configuration, resulting in a 7.7% increase in the system’s heat charging efficiency.

With a temperature difference of 19 K between the HTF inlet temperature and the PCM melting temperature (i.e., an HTF inlet temperature of 338.15 K), the heat charging efficiency of the multi-plate phase change thermal storage system with the S-shaped flow channel improves by approximately 54.7%.

The placement of the plate unit, the HTF inlet and outlet positions, and the temperature difference exert a more significant influence on the heat charging process compared to the exothermic process.

In summary, for practical applications, the multi-plate encapsulated phase change heat storage system utilizing the S-shaped flow channel should have the plate phase change units oriented horizontally with the HTF entering through the upper inlet and exiting through the lower outlet at an inlet temperature of 338.15 K to maximize the enhancement of system charging and exothermic performance.