New effective thermal conductivity model for the analysis of whole thermal storage tank

https://doi.org/10.1016/j.ijheatmasstransfer.2018.11.122Get rights and content

Highlights

Abstract

In this paper, a new effective thermal conductivity model is proposed and used to numerically investigate a whole tank designed for latent-heat thermal energy storage (LHTES). The tank was filled with phase-change materials (PCM) inside 9 × 9 × 20 spherical capsules. Previous studies have focused on the performance of only one capsule under the assumption that one capsule could represent the performance of the whole tank. The analysis of phase change involves much complexity, even for one capsule; thus it is challenging to analyze a whole tank due to the tremendous amounts of calculation time and memory capacity required. The new effective thermal conductivity model includes the effect of the natural convection in molten PCM, and estimates charging/discharging performance in the full scale system with reduced calculation time. This new effective thermal conductivity model can appropriately predict dissimilar melting behavior depending on the unique position of each capsule in the tank. The model was validated by comparison with experimental data, and also by rigorous numerical analysis including natural convection.

Introduction

Soaring demand for electric power has increased interest in energy storage systems. Latent-heat thermal energy storage (LHTES) systems have been highlighted as one of the more efficient energy storage systems for its high energy storage density. It is hard to accurately estimate the performance of LHTES systems because the phenomena involved with phase change is very complicated.

Much effort has been devoted to numerical analysis of phase change phenomena. Chung et al. [1] analyzed flow transition during the melting process in a horizontal cylinder with extended Rayleigh number to demonstrate the effect of thermal instability on solid-liquid interfaces. Khodadadi and Zhang [2] conducted a computational study of constrained melting within spherical containers and showed that the Rayleigh number was more significant than the Stefan number, for natural convection. They also demonstrated the important role of the Prandtl number in melting patterns at a fixed Rayleigh number. Assis et al. [3] explored how a phase change process depends on thermal and geometric parameters. They suggested a correlation of molten fraction as a function of Fourier, Stefan, and Grashof numbers. Elghnam et al. [4] performed an experimental study on the charging and discharging process inside a spherical capsule with variations in size, capsule material, and temperature of the heat transfer fluid (HTF). They discovered that the charging performance improved when using bigger size, metallic materials, at lower HTF temperature. Lee et al. [5] investigated thermal storage performance more practically by including the convection effect outside a spherical capsule. They confirmed that the inclusion of forced convection surrounding the capsule resulted in much lower discharging performance.

In order to understand phase change phenomena better, many researchers conducted studies under diverse conditions. Sparrow and Geiger [6] provided an experimental and numerical comparison between constrained and unconstrained melting in a horizontal tube. They demonstrated that melting was faster in unconstrained mode where the movement of solid PCM was allowed, and that the melting became faster as the solid PCM sank closer to the tube wall. Tan [7] used spherical capsules experimentally to demonstrate that melting in unconstrained mode was faster than in constrained mode. These results correspond to the conclusions of Sparrow and Geiger [6]. The same author [8] also conducted numerical analysis to compare the results of the experiments and validated the conclusions. Hong et al. [9] analytically examined unconstrained melting inside a spherical capsule, varying the conditions of capsule size, material, and wall temperature. They discussed the limitation of analytical approach in the high Stefan number. There have been many studies on phase change phenomena; however, there is still an ongoing need for the complexity of these phenomena to be considered, such as movement of solid phase-change material (PCM), the effect of natural convection in molten PCM, the thermal instability on solid-liquid interfaces, and the external conditions surrounding the capsule.

Although it is important to analyze an entire tank to predict the proper performance of thermal energy storage systems, previous studies have focused on only one capsule or one coil under the assumption that it could represent the performance of the whole tank. Considering that phase change even for one capsule is very complex, it is not feasible to analyze a whole tank due to the tremendous amounts of calculation time and memory capacity required. Because of these difficulties, there have been few studies of whole tanks, and these have been subject to the following assumptions: (1) if two phases are regarded one single phase, which ignores the temperature differences between solid and liquid, we can call it a single-phase model, or (2) if the solid and liquid phases are treated separately, we can call it a two-phase model. There are two typical variations of the two-phase model: continuous solid phase and concentric dispersion. In the continuous solid phase model, the phase change material is assumed to be a porous medium. Ismail and Stuginsky [10] conducted a numerical comparison of four models, that is, the continuous solid phase model, Schumann's model, a single phase model, and a thermal diffusion model. They compared the computation time required for each model to solve a test problem, and investigated the influence of various parameters, such as size, void fraction, material, flow rate, and working fluid inlet temperature. They discovered that the working fluid inlet temperature had a greater influence on the wall-heat-losses in all models and that the mass flow rate had the least effect. Arkar and Medved [11] investigated the influence of the PCM thermal properties on the thermal responses of LHTES-containing spheres filled with paraffin. Using a continuous solid phase model, they compared the numerical results with an experiment consisting of 35 rows of spheres and validated them in slow running processes. Erek and Dincer [12] developed a heat transfer coefficient correlation using 120 numerical simulations for an ice TES system. Their conclusions from using a concentric dispersion model emphasized the importance of taking into account the variable heat transfer coefficient for analyzing thermal energy storage (TES) systems. Peng et al. [13] conducted numerical analysis of thermal behavior for LHTES systems by investigating radial heat transfer and wall heat losses. Using the concentric dispersion model, their study showed that charging efficiency could be increased under the following conditions: decrease in capsule size and fluid inlet velocity, or increase in the storage height.

From a literature review, even though analysis of entire tanks have been extensive, we can see the limitations in their assumptions: the single-phase model has limited accuracy because it does not consider phase change behavior. The continuous solid-phase model also has shortcomings because the temperature differences in the two phases are ignored. The other concentric dispersion model, which takes temperature differences into account, improved the accuracy to some extent; however, it does not include the natural convective effect, and thus retains a limit on its accuracy. Furthermore, these models do not reflect the differences in thermal behavior of capsules regarding their position; thus we cannot estimate the true charging and discharging performance because the melting/solidification will be different depending on the capsule position: near the tank top or tank bottom, or near the tank center or tank edge.

In this study, an efficient, accurate approach is proposed for estimating the melting/solidification behaviors in a full tank. By introducing effective thermal conductivity that reflects the effect of natural convection in the molten PCM, we are able to investigate the performance of the full-scale tank within a much shorter calculation time. First, we validated the proposed model for a single capsule by comparing experimental results. Second, we checked whether the model could be applied over much wider conditions in relation to different capsule sizes, wall temperatures, and initial temperatures. In addition, we created 12-layer capsules in a vertical column to show that the present model is superior to the previous effective thermal conductivity model. Finally, we accomplish our goal of analyzing a whole tank containing 1692 spherical capsules (9 × 9 × 20 array).

Section snippets

Mathematical model

Hirata and Nishida [14] proposed an effective thermal conductivity model. The constrained melting model is shown in Fig. 1(a). This model ignores the movement of solid PCM due to the density difference between liquid PCM and solid PCM. Natural convection plays an important role and accelerates melting in the upper part of solid PCM. However, this process is the main cause of the tremendous computation time required in simulation of melting and solidification. Thus, a combination of the

Validation by experimental results VS Natural Convection Model VS keff Model

The proposed keff model was compared with the experimental results from Tan [7] as well as the constrained melting model including natural convection of molten PCM. The latter was used as a reference when there was no experimental result. We also used the result of the previous keff for comparison. The validation was conducted in a spherical capsule of diameter 101.66 mm. We used n-octadecane as the PCM and its properties are shown in Table 1. The initial temperature was 1 °C below the melting

Conclusions

In this study, a new effective thermal conductivity model was proposed and used to investigate numerically the whole tank of a latent heat thermal energy storage (LHTES) system filled with phase-change materials (PCM) in an array of 9 × 9 × 20 spherical capsules. Most of previous approaches assumed the charging/discharging performance of the entire tank would be the same as that of one capsule inside the tank due to the tremendous computation time required to simulate the natural convection in

Conflict of interest

The authors declared that there is no conflict of interest.

Acknowledgement

This research was supported by Basic Science Research Program through the National Research Foundation of Korea (NRF) funded by the Ministry of Education (No. 2017R1D1A1B05030422).

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