Numerical simulation on heat transfer characteristics of the storage tank for concentrating solar power plant

Introduction

Energy problem is the main topic for the economic and social fields in the modern society. Solar energy is available and friendly because of energy-saving and renewable performance. Concentrating solar power (CSP) plant is a new and emerging technology, which can solve the issue of low solar flux density. At the same time, CSP system coupling with energy storage system can overcome its intermittent performance. Therefore, CSP system with energy storage is popular and trend to future design and research in renewable energy fields.^1–4 As we know, the storage energy system has three contributions: sensible heat storage (SHS), latent heat storage (LHS), and thermochemical storage. LHS has achieved most attention among three thermal storage system due to its higher energy density and nearly constant temperature exchange, which adopts the phase change material (PCM). Temperature distribution of a PCM in storage tank is crucial to system’s efficiency and stability.

Al-abidi et al. ⁵ have successively reviewed the previous studies in this field based on computational fluid dynamics (CFD) software. Utilization of CFD software in the design process of the system can save money and time, thus achieving higher efficiency of the system. Longeon et al. have been built a testing loop to analyze the influence of the heat transfer fluid (HTF) injection side on the system. The experimental test section is modeled with CFD simulations to explain the charge and discharge results. ⁶ Chaabane et al. ⁷ have investigated numerically the thermal performance of an integrated collector for storage solar water heater using Fluent tool. Tan et al. have finished a numerical research on the constrained melting of PCM inside a transparent spherical glass capsule using Fluent tool. In their works, the SIMPLE method is used to solve the governing equations and the Darcy law is adopted to the momentum equation for obtaining the effect of phase change on convection. ⁸ Xia et al. have performed an effective packed-bed thermal energy storage with a spherical PCM capsule. To investigate the effect of the PCM spheres arrangement and the PCM encapsulation on the heat transfer performance of the system, a two-dimensional (2D) numerical model via Fluent 6.2 software and SIMPLE algorithm have been used in this article. ⁹ Liang et al. have investigated the performance of sensible heat and LHS by numerical and experimental methods. Concretes and the mixture of sodium nitrate and potassium nitrate are as the materials to apply in the study. The temperature range from 250°C to 550°C and thermophysical properties have been used and calculated.^10–12 Wang et al. have investigated the efficiency and performance for a CSP system using the Fluent software. Some appliances for the system have been referred based on the physical and chemical progress.^13,14

The literatures show that the temperature distribution of a phase change storage tank is limited due to its high temperature and complex physical–chemical process. In this article, the parameters of the physical model is given first by a real experiment in the reference, then the numerical simulation and the mesh are finished by Gambit tool, and finally, the calculation results are obtained by Fluent software. The results of the temperature distribution can provide a reference to the future use for system’s design and optimization.

Physical and mathematic models

For a storage tank in CSP plant, the heat transfer model is shown in Figure 1. It can be seen from this figure that the HTF has a heat transfer process with PCM in the storage tank. The geometrical configuration of the tank has an important effect on the heat transfer efficiency. In this article, in order to investigate the heat transfer performance of the tank, sketch of thermal energy storage prototype dimension is shown in Figure 2 reported by Bayón et al. ¹⁵ The research has proposed a more detailed description, and experimental test is based on the location of Plataforma Solar de Almería. The prototype takes the KNO₃/NaNO₃ eutectic mixture as PCM and uses the expanded graphite fins to improve thermal conductivity. The prototype consists of 36 parallel tubes with six pipes arranged in six passes. PCM is 54% KNO₃/46% NaNO₃ eutectic mixture with a melting point of 221°C.

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Figure 1.

Schematic diagram of heat transfer process in the storage tank.

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Figure 2.

Physical model of the storage tank.

The main parameters of the physical model are as follows: the dimension of the tank is the length of 4310 mm, the height of 586 mm, and the width of 596 mm; the thermal properties of PCM is the mass of 2100 kg, latent heat of fusion of about 100,000 J/kg, thermal conductivity of 8 W/m k; the parameters of the fluid is inlet temperature of 234°C, the pressure of 27 bar, and the mass rate of 0.085 kg/s. In the numerical simulation, the charge process of the tank coupling the natural convection has been performed.

In this article, Fluent software is used to simulate the heat transfer process in the tank. The main equations are given as follows^16–18

Continuity equation

∂ ρ ∂ t + ∂ ( ρ u ) ∂ x + ∂ ( ρ υ ) ∂ y = 0

(1)

Momentum equations

ρ ( ∂ u ∂ t + u ∂ u ∂ x + υ ∂ u ∂ y ) = μ ( ∂ 2 u ∂ x 2 + ∂ 2 u ∂ y 2 ) − ∂ p ∂ x + S u

(2)

ρ ( ∂ υ ∂ t + u ∂ υ ∂ x + υ ∂ υ ∂ y ) = μ ( ∂ 2 υ ∂ x 2 + ∂ 2 υ ∂ y 2 ) − ∂ p ∂ y + S υ

(3)

Energy equation

ρ ( ∂ H ∂ t + u ∂ H ∂ x + υ ∂ H ∂ y ) = k C P ( ∂ 2 H ∂ x 2 + ∂ 2 H ∂ y 2 ) + S h

(4)

In the above equations, the symbol ρ is the density with the unit of kg/m³; u and υ are the fluid velocity of different directions with the unit of m/s, respectively; p is the pressure with the unit of Pa; H is the enthalpy with the unit of J; and S is the source term.

The mesh of the tank shown in Figure 3 is generated using the Gambit tool of Fluent software. A good mesh of 8506235 mesh elements is used for the tank. The material properties of water and copper in the database of the Fluent software are used. In the numerical simulation progress, the solidification and melting model has been used to calculate the temperature distribution. Boussinesq approximation is for PCMs with natural convection.

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Figure 3.

Schematic diagram of the mesh of the tank.

Results and discussions

As we know, there are three stages occurring on the charge progress for a phase change storage tank. First, the PCM is heat and the temperature obviously rises to the melting point for any phase change progress; later on, PCM melts with a constant temperature, which causes a phase change progress; Finally, PCM temperature continues to rise and go up to a constant without heat transfer when the system is for stability. It is very obvious that the temperature distribution in the final stage is very uniform with a constant temperature, which is almost same with the fluid inlet temperature. In the first and third stages, the system has performed SHS without LHS. The aim of this article is to investigate the heat transfer performance in phase change process. In this article, the total charge time is about 300 min. Therefore, the results of temperature distribution and liquid fraction in different times and different positions have been obtained in this article and shown in Figures 4–9. Due to the symmetrical performance, the temperature distribution and liquid fraction in the Y-axis positions of 128, 213, and 298 mm are proposed in this article.

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Figure 4.

Temperature distribution for the tank at position of 128 mm (Dimension is K).

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Figure 5.

Temperature distribution for the tank at position of 213 mm (Dimension is K).

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Figure 6.

Temperature distribution for the tank at position of 298 mm (Dimension is K).

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Figure 7.

Liquid fraction for the tank at position of 128 mm.

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Figure 8.

Liquid fraction for the tank at position of 213 mm.

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Figure 9.

Liquid fraction for the tank at position of 298 mm.

Figures 4–6 show that the temperature distribution of the tank of three charge times (200, 250, and 300 min) for the Y-axis positions of 128, 213, and 298 mm, respectively. It can be seen from the Figure 4 that there is a huge change along the charge time. The temperature of the tank ranges from about 495–505 K. At the same time, the top temperature of the tank is higher than the bottom. This is due to the fact that the inlet of the system is put in the top. It can be seen from the Figures 5 and 6 that there is the same trend with Figure 4. For three charge times and positions, there are common results can be obtained as follows: (1) with the change of charge time, the temperature increases with the increasing time, which represents the charge progress continues; (2) temperature distribution of the tank is nonuniform for different times and positions according to the numerical results; and (3) temperature distribution of the tank for different positions in the same charge time have a smaller change.

Figures 7–9 show that the liquid fraction of the tank of three charge times (200, 250, and 300 min) for the Y-axis positions of 128, 213, and 298 mm, respectively. It can be seen from Figure 7 that there is a phase change process at charge time of 200 min, and no phase change for the charge time of 250 and 300 min. The liquid fraction of the tank in the top is larger than one in the bottom. Also, it can be seen from Figures 8 and 9 that there is the same trend with Figure 7.

Conclusion

In this article, heat transfer performance for a phase change thermal storage tank has numerically been investigated. The main conclusions are as follows: