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
]. 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
]. 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
]. 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 role in a large number of fields, like temperature-adjustable greenhouses [12
], 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
]. 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 super-cooling 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
≥ 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
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
= 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 PCM-capsuled 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.
3. Experimental Set-Up and Measuring Procedure
3.1. General Description
In Section 1
, it was mentioned that the tested PCM is dedicated to working in a special storage heat exchanger/tank [38
]. It was decided that the PCM, due to the design of the heat exchanger, should be studied in a cylindrical system for the conditions most similar to those in which it will be operated later. For this purpose, a wind tunnel, as presented in Figure 4
, was used that met the operational and functional parameters. The obtained range of the Reynolds numbers (15,260–52,767) is fully turbulent and the heat transfer conditions (temperature and the Nusselt numbers) are similar to the considered storage tank.
The experimental set-up consists of four basic sections, operated in an open circuit suction mode. The first section is related to the air inlet. It is composed of a lamellar exchanger with a cross-section of 0.75 m × 0.74 mm in which it was possible to control the temperature in the range of −15 °C to 35 °C while using a chiller with a maximum cooling capacity of 4 kW. Subsequently, a stabilisation flow section was installed behind the lamellar exchanger. The stabilisation section is made of three net layers with a mesh size of approximately 1.5 mm × 1.5 mm. Such a system ensured a stable flow, without recirculation zones while also eliminating potential turbulence behind the lamellar exchanger. The next section is the so-called the Witoszyński nozzle, whose task is to shape a flat velocity profile in the measuring section. This special velocity profile allowed for homogeneous thermal-flow parameters along the entire length of the tested module to be obtained. The measuring section had a square cross section with dimensions of 0.25 m × 0.25 m and a length of 0.52 m. In order to eliminate the impact of the installed fan, between the measuring section and the fan a 0.9 m long channel with an identical cross-section as the measuring section was installed. The purpose of this channel was to stabilise the fan working conditions and eliminate any possible flow disorders that are caused by its operation. The fan that is installed in the experimental set-up provides the opportunity to achieve three mean values of velocity in the measuring section equal to 0.92, 2.27, and 3.18 m/s, respectively, which correspond to the Reynolds numbers 15,260, 37,688, and 52,767, based on the channel height of the test section. In order to achieve different mean value of air velocities, the fan power was regulated by a capacitor system. Generally, the maximum volume air flow rate was 1000 m3/h, which was generated for the maximum electrical power of the fan engine, equal to 150 W.
The parameters of inlet air, such as ambient temperature, pressure, and humidity, were measured just before the lamellar exchanger by a high-precision digital temperature, humidity, and airflow meter Testo 480 with Testo Robust Humidity Probe.
3.2. Tested Module
The PCM was experimentally tested in a special cylindrical module made of copper, as presented in Figure 5
. This module was characterised by a fixed height and a wall thickness of 250 mm and 1 mm, respectively. Three different outer diameters of 15, 22, and 28 mm were studied. At the ends of the module, two pipe caps that were made of the same material with a height of 15 mm were mounted. Additionally, three T-type thermocouples have been installed in situ in the axis of the module, at half height, and one-third above and below, as is shown in Figure 5
. The module was then placed and tested in the measuring section, as depicted in Figure 4
and Figure 6
The PCM mass contribution in the module varied from 25.23% to 37.82%, (see Table 2
). The theoretical heat transfer from the air to the modules were estimated and presented in Table 2
, according to the producer information, as described in Table 1
and assumptions concerning paraffin and copper properties used during the numerical calculations, as summarised in Table 4. For paraffin, it varies from 2.87 kJ to 10.19 kJ for sensible heat and from 2.46 kJ to 8.74 kJ for latent heat. For copper the heat transfer varies from 1.62 kJ to 3.71 kJ. The heat storage in copper is 23.31% for d
= 15 mm, 20.78% for d
= 22 mm and 16.37% for d
= 28 mm of the total system, respectively. Those estimations show that PCM phase change plays an important role during the heating of the module that is filled with the PCM.
3.3. Preparation of the Module to the Test
The module has been specially prepared in order to test the thermal behaviour of the module filled with the PCM for various thermal-flow conditions. First, before filling with the PCM, the module was degreased with propyl alcohol and thoroughly dried. Next, three T-type thermocouples with an accuracy of ±0.5 °C were placed in the prepared arrangement in the configuration that is shown in Figure 5
. Subsequently, the module was filled with the phase change material. Before testing, the module was placed in a freezer for about 4 h to cool to a temperature of about −18 °C. The freezing process was completed when the material obtained the same temperature in the entire volume, which was monitored by thermocouples that were placed inside the module. The module prepared in this way was then mounted in the wind tunnel measuring section. Figure 6
presents the measuring section with the installed PCM module.
3.4. Measurement and Control Systems
The experimental set-up was equipped with two types of measurement system: one was based on Testo devices and the second one on the National Instruments module 4-Slot USB CompactDAQ Chassis (cDAQ 9174) working under the LabView environment. The high-precision digital temperature, humidity, and airflow meter Testo 480 had a build-in absolute pressure meter with an accuracy of ±3 hPa and allowed for up to three probes to be connected. The first Testo device was a Robust Humidity Probe, which was used to measure humidity and temperature of the suction air with an accuracy of temperature ±0.5 °C (from −20 °C to 0 °C) and ±0.4 °C (from 0.1 °C to 50 °C), relative humidity: ±2% RH (from 2.1 to 98% RH). The second installed device was a Thermal Flow Velocity Probe, Testo 480, which was used to measure the velocity profile. The device is characterised by the accuracy of measured velocity profile amounting to ±0.03 m/s + 5% of the measured velocity.
A special thermocouples net system was installed in order to measure inlet and outlet air temperatures at the measured section. At the inlet to the section, eight T-type thermocouples were installed and used to determine the average inlet temperature. At the outlet, one T-type thermocouples type of temperature sensor was mounted. The accuracy of installed T-type thermocouples was ±0.5 °C.
The combination of the National Instruments equipment and LabView software allowed for the measurement of temperature with a high resolution and frequency. During the experiments, it was sufficient that the measurements were carried out with a frequency of 0.2 Hz (every 5 s).
3.5. Velocity Profiles at the Inlet and Outlet of the Measurement Section
A special construction of the inlet section with the installed Witoszyński nozzle contributes to the formation of quasi-uniform thermal and velocity profiles in the measurement section, as mentioned in Section 3
Before the measurement campaign, the velocity profiles at the inlet and outlet were determined. The measurements of the velocity profile were carried out at a distance of 20 mm from the inlet and outlet edges of the measuring section. The velocity profiles were determined at measuring points 33, 73, and 105 mm from the channel’s symmetry axis.
In total, seven holes have been made in the top of the measuring section cover for measurement purposes. The thermal flow velocity probe that was connected to the Testo 480 module has been inserted into these holes, mounted on a special measuring instrument. A measuring device, similar to a caliper allowed for precise measurement of the velocity profile along with the channel height with an accuracy of ±0.1 mm. In total, one profile was determined while using 19 measurements, concentrated in the central part of the channel. The results of the obtained profiles at the inlet and outlet of the measuring section for different powers of the fan are presented in Figure 7
, where a larger number represents higher air velocity.
The measurements that are presented in Figure 7
showed that, for all the tested ranges of fan power, the velocity profiles are characterised by a flat profile. The obtained flat velocity profile is a consequence of the use of a specially shaped inlet contraction section designed according to the Witoszynski curve equation [41
]. The analysis points out that the differences between the average values determined do not exceed 7.4% of the local value of velocity. Table 3
summarises the test results. In addition, for further analysis, each analysed value of average speed: 0.0, 0.92, 2.18, and 3.18 m/s was defined as Case 0, Case I, Case II, and Case III, respectively.