**1. Introduction**

Thermal Energy Storage (TES) technology has gained increasing worldwide attention, because it, among others, has been regarded as an effective way to compensate for the intermittence of renewable sources [1,2]. Among various TES technologies, Latent Heat Thermal Energy Storage, (LHTES), utilising Phase Change Materials, (PCMs), is one of the most attractive forms, with a relatively high storage density and small temperature changes from storage to retrieval [3]. PCMs are substances with the property of heat absorption when they undergo a phase change from solid to liquid, liquid to gas, or vice versa [4–6]. These PCMs are widely applicable in a broad range of industrial areas. For instance, they can be encapsulated in building materials, e.g., gypsum plasterboard, cubicle, and wall board in order to enhance the thermal storage capacity [7,8]. PCMs are also considered to improve the frosting/defrosting operating performance of air source heat pumps [9]. Likewise, PCMs are frequently used in order to produce thermoregulated textiles, where they are generally entrapped in micro/nano-capsules to prevent leakage [10]. PCMs-assisted packaging is an innovative technology, which can plenarily control temperature-sensitive food products under different conditions [11]. In addition, PCMs also play an important

**Citation:** Ochman, A.; Chen, W.-Q.; Błasiak, P.; Pomorski, M.; Pietrowicz, S. The Use of Capsuled Paraffin Wax in Low-Temperature Thermal Energy Storage Applications: An Experimental and Numerical Investigation. *Energies* **2021**, *14*, 538. https://doi.org/10.3390/en14030538

Received: 21 December 2020 Accepted: 17 January 2021 Published: 21 January 2021

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role in a large number of fields, like temperature-adjustable greenhouses [12,13], waste heat recovery [14], and building air-conditioning [15]. High-temperature PCMs have attracted considerable interests over the past decade, which is extraordinarily promising in the concentrated solar thermal field and other high-temperature-required domains [16–18]. On the other hand, Amin et al. [19] considered a different temperature interval with a focus on low-temperature PCMs that are encapsulated in spheres.

PCMs can be generally classified into two types: organic and inorganic. Most inorganic PCMs are barely applicable to the TES system due to their toxicity, corrosivity, and supercooling properties. In contrast, organic PCMs are relatively safe, chemically inert and ecologically friendly [20]. Among diverse organic PCMs, paraffin wax is one of the most common materials, with several remarkable properties, e.g., high energy storage density, relatively low cost in commerce, and a small super-cooling trend. Paraffin wax (usually extracted from ozokerite, petroleum, natural gas, etc.) has a wide range of phase change temperatures and it has a general chemical formula C*n* H2*n*+<sup>2</sup> (*n* ≥ 4, the higher the value of *n* the higher the melting temperature) [21]. Consequently, an ideal scheme seems to be to use capsuled paraffin wax as a storage material and proposals for such a method have already been tackled by groups of researchers [22,23].

Plenty of investigations on the mathematical models and numerical analyses with PCMs that are capsuled in different configurations have been performed and reported in the literature. Shamsundar and Sparrow [24] resolved the enthalpy equation using the finite difference approach and performed an analysis of the multidimensional transient solidification process with the change of density and an increasing shrinkage cavity. The authors noted that the highest impact of the density ratio and the Stefan number on the heat transfer occurred at almost the end of solidification. In a horizontal tube with unfixed solid PCMs inside, the thermal behaviours of the PCMs (heat flux densities, geometric shape, melting rates, etc.) were obtained by Bareiss and Beer [25] through neglecting the inertial force. The authors pointed out that the gravity of the solid PCMs and pressure forces in a thin liquid layer jointly formed a force balance. Bilir and Ilken [26] investigated PCMs capsuled in a spherical/cylindrical container employing the third kind of boundary condition. The authors derived correlations that utilise the Biot number, the Stefan number and the dimensionless surface temperature to present the dimensionless total solidification time of PCMs. Verma et al. [27] studied the mathematical models that are based on the first and second law of thermodynamics regarding the LHTES system with PCMs inside. The authors indicated that the model based on the first law of thermodynamics had been experimentally validated, and could be employed to model PCMs. However, the model based on the second law of thermodynamics required additional work related to its experimental verification. A numerical model regarding the solidification process of PCMs in a triplex tube with external and internal fins was proposed by Al-Abidi et al. [28]. The authors noted that factors, including the fin length, the fin thickness, and the numbers of fins, had a considerable impact on the heat transfer. However, the effect of the fin thickness was assessed to be less than that of the fin length. Similarly, Li et al. [29] explored the enhancement effect of aluminium oxide on phase change heat transfer in the triplex tube with fins. The conducted research revealed that an extra alumina contributed to a stronger conduction and the best discharging rate was determined in the case of *dp* = 40 nm. The entropy optimization method was applied in order to study the solidification behaviour of nanoparticle-enhanced PCMs in the LHTES system affected by a magnetic field by Shah et al. [30]. The authors indicated that the Lorentz force, caused by the Hartmann number, and buoyancy forces had positive and negative impacts on the solidification rate of nanoparticle-enhanced PCMs, respectively. Jourabian et al. [31] utilised the enthalpy-based Lattice Boltzmann method and double distribution function to explore the melting process of the ice within a semicircle enclosure. The authors noticed that the concentration of nanoparticles had a positive and an adverse effect on the thermal conductivity and the latent heat of PCMs, respectively, but a negligible impact on the average Nusselt number. A novel PCM-air tubular heat exchanger and the corresponding

analytical solution were proposed by Dubovsky et al. [32]. The authors successfully predicted the results of separate tubes and verified the applicability of the analytical solution to the practical heat exchangers. Darzi et al. [33] presented several simulations of the symmetric melting process between two cylinders in an eccentric and concentric position using N-eicosane as the PCM. The authors pointed out that the downward movement of the inner cylinder caused a significant increase in the melting rate due to the dominance of convective heat transfer in most areas of the PCM. Mahdaoui et al. [34] proposed a numerical model involving the natural convection phenomenon in the PCM-melted region around a horizontal cylinder. As a result of the conducted research, the authors assessed that regardless of the assumed boundary conditions, (constant temperature of the cylinder walls, constant heat flux), the melting of the PCM in the lower part was ineffective since the energy was transferred mainly by convection to the top of the cylinder. Regin et al. [35] focused on the cylindrical PCM-melting model integrated into the LHTES system, which was combined with a solar water heating collector. The conducted analyses indicated that the melting of PCMs was primarily dependent on the magnitude of the temperature range of the phase transformation, the Stefan number, and the capsule radius. Although these papers have successfully studied diverse mathematical and numerical PCM melting/solidification models employing different constraints. Additionally, it was considered various influencing factors and configurations, none of them pays attention to the changes in the internal structure of the PCMs during the phase change process. Furthermore, most of them only deal with the PCMs capsuled in horizontal cylinders and heat transfer is uniformly along the circumference of the circular cylinder. Accordingly, we have made an attempt to investigate the case of PCMs capsuled in the vertical position of a cylinder, which will undergo several heat-flow processes of the cross-flow of air with different velocities. We are highly expecting to test and compare the capabilities of the mixture of paraffin wax and water in different heat flux environments and to more explicitly describe the characteristic parameters of five-phase change regions of the mixed PCMs. In addition, a Scanning Electron Microscope (SEM) will be expedient in confirming the specific changes in the internal structure of the mixed PCMs during the phase transition.

The motivation to undertake the analyses carried out in the article is to design a container for storing/accumulating cold "energy" cooperating with the heat pump. The presented literature analysis shows that one of the most promising candidates that can be directly applied in the analysed device and its ranges of the temperature is the PCMcapsuled paraffin wax. This container unit filled with PCM has to operate with a system named a Flower Shape Oscillating Heat Pipe (FSOHP), which was described in detail by Czajkowski et al. in [36] and it has also been patented in [37] by Pietrowicz et al. Thus, an integral element in the innovative system for cooling mixed substances is a special exchanger that contains the PCM described and studied in this paper. The operational parameters of the exchanger have been defined and described by Ochman and Pietrowicz in [38], and have also been patented by Pietrowicz et al. [39]. What is important, due to the required technological process, PCMs are expected to store the "cold" energy in the range of 4 ◦C to 6 ◦C. The paraffin wax, due to its thermodynamic and functional properties, is a pertinent candidate for this novel system, as it was mentioned.

Thus, when preparing the design procedures that are dedicated for a storage tank, the authors of the article needed to have a complete, validated mathematical model of the thermal-flow processes occurring in the tested phase change material and to have knowledge of the impact of the operating conditions of the designed storage tank on the temperature change in the PCMs, depending on the total applied mass of the PCM. It was also important to determine the time that is needed for the phase changes and to compare them with different values of the supplied heat flux. The authors of the article also believe that the developed numerical procedures together with the conducted research will help in the future during the optimization process of the construction of a cold accumulator cooperating with a heat pump and a mixing/dissolver device.

In the presented article, the thermal-flow processes occurring in the low-temperature PCM were experimentally tested and then numerically investigated. The experiments were carried out for fully turbulent flow (15,250 < Re < 52,750) and for three cylindrical modules filled with a PCM with fixed heights of 250 mm and with outer diameters of 15, 22, and 28 mm, respectively. For this purpose, a special set-up was designed and constructed, in which a wind tunnel is the main element. Additionally, special test procedures were developed and adapted. Subsequently, a mathematical model of thermal-flow processes existing in the phase change material, based on the enthalpy porosity method, was proposed and validated. Finally, the numerical calculations, during the transient processes, were carried out for various boundary conditions that are close to those expected during the real operation of the device.

The structure of the article consisted of the following elements: Section 2 describes the tested phase change material, with a description of the thermophysical properties and the analysis of the internal structure while using a SEM. The test stand, tested modules filled with PCM and measurement procedures are described in Section 3. Section 4 presents the mathematical model and numerical procedures, numerical domains with the applied boundary conditions and applied thermal properties. The experimental studies are detailed and discussed in Section 5. Additionally, this Section compares the results of the numerical studies with the experimental data and summarizes them by the relative error analysis. Section 6 concludes the work, where the most important results and observations from the conducted research are presented.

#### **2. Phase Change Material (PCM)**

#### *2.1. General Description of the PCM*

To meet the thermal requirements, i.e., the phase change temperature range and usability, the research was conducted on a commercial phase-change material, which was paraffin wax capsules in a melamine-formaldehyde membrane and water mixture, produced by the *MikroCaps* company [40]. Table 1 shows the selected thermophysical properties describing the tested PCM.


**Table 1.** The thermophysical properties of the Phase Change Material (PCM) used during the experiments [40].

#### *2.2. Analysis of the PCM's Internal Structure*

#### 2.2.1. Test Conditions and Testing Procedures

The purpose of the analysis described in this section was to observe whether and how the internal structure of the PCM changes at the characteristic temperature points. The structure of the material was studied while using a Scanning Electron Microscope (SEM). A *Prisma* E scanning electron microscope from Thermo Fisher Scientific was used for this purpose. A special table with a Peltier system was installed in the test chamber in order to regulate the sample temperature in the phase transition range, i.e., from 0 ◦C to 16 ◦C. Figure 1 shows the system with the studied sample along with the details of the test chamber.

(**a**) Test chamber with mounted the Peltier system and sample. (**b**) Prepared

**Figure 1.** Description of the Scanning Electron Microscope (SEM) chamber and the prepared sample.

> During the measurements, the focusing beam power was set from 20 to 25 kV. Those values were experimentally selected to ensure the right quality of contrast and sharpness of an image. It should be mentioned that the power of the selected high-energy electron beam allowed for the analysis of the sample without its visible degradation of the sample.

sample.

Efforts were made to keep the relative humidity value in the measuring chamber at 17 ÷ 42% in order to maintain the emulsion structure of the sample during the analyses of the PCM structure. Maintaining these parameters ensured that the evaporation of water from the material was minimized by achieving thermal conditions far from saturation conditions. Figure 2 presents the change in sample temperature and humidity during the experiment.

**Figure 2.** Temperature and relative humidity profiles maintained during measurement.

## 2.2.2. SEM Analysing

Figure 3 presents the results of the SEM's investigation of the PCM structure for selected temperature points that were defined at 0 ◦C, 5.5 ◦C, and 15 ◦C.

(**a**) 15 ◦C, 500×

(**d**) 5.5 ◦C, 3000×

(**e**) 0 ◦C, 3000×

(**c**) 5.5 ◦C, 2000×

(**f**) 0 ◦C, 6000×

**Figure 3.** Analysis of the PCM internal structure, made for different temperatures and magnifications obtained while using the SEM.

> Those temperatures have been selected, because the potential changes in the structure were expected. Thus, the temperature of 15 ◦C (Figure 3a,b) is significantly separated from the phase transition temperature, which was estimated at between 4 ◦C and 6 ◦C (Figure 3c,d). Because the analysed substance is an emulsion of two components-paraffin wax and water, analysis at 0 ◦C (Figure 3e,f) was also potentially considered, due to the phase change of the water.

> The investigation showed that the diameter of the analysed paraffin capsules is between 3 and 8 μm. This differs from the values declared by the manufacturer and described

in Table 1. Additionally, it was observed from Figure 3e,f, that, for 0 ◦C, the distances between microcapsules increase in comparison with other tested temperatures, which are a consequence of the presence of water in the form of ice and a higher value of the specific volume compared to other temperature tests. Generally, it can be concluded that, in the studied temperature ranges, no significant changes in the internal structure were noticed. This is an important fact that was used later during numerical simulations. The substance that is taken into account is homogeneous and the separation of components, i.e., sedimentation, is not later considered.

#### **3. Experimental Set-Up and Measuring Procedure**
