Effect of porous material properties on thermal efficiencies of a thermocline storage tank

Highlights

• TES are investigated using a model for turbulent heat transfer in porous media.

• Decreasing the thermal conductivity ratio at lower Re improved system efficiency.

• Increasing Reynolds lowered thermal efficiency for low thermal capacity ratios.

Abstract

Thermocline energy storage systems can be adapted to store energy in a tank where the hot fluid is pumped in during a charging cycle and cold fluid during a discharging cycle, substituting the need for two storage tanks. Here, a numerical investigation of a hot air flow transferring thermal energy to a solid porous bed is performed to evaluate the influence of the thermal conductivity and capacity ratios on the efficiency of a charging cycle of a thermocline storage tank. The numerical model considers the mixed convection turbulent flow (k-ε model) through clear and porous media using the Local Thermal Non-Equilibrium approach to provide solutions for the solid and fluid phases separately. Macroscopic equations are obtained by the method of volume averaging and numerically processed by finite volume method. The system was modelled as a vented axisymmetric cavity, partially filled with a porous medium, with hot fluid inflow from the top and outflow at the bottom. The investigation included changing Reynolds number (Re_t from 8.3 × 10³ to 5 × 10⁴), thermal conductivity ratios ($k_s/k_f$ from 3.5 to 1062) and thermal capacity ratio (${\rho }_s{c}_{\mathit{ps}}/{\rho }_f{c}_{\mathit{pf}}$ from 1483 to 7415). It was found that lower $k_s/k_f$ ratios decrease the heat loss throughout the charging cycle which allow for higher temperatures in the later stages of the cycle and thus improve charging efficiency. However, this effect decreases in importance as the system undergoes higher Re_t number flows. On the other hand, increasing the ${\rho }_s{c}_{\mathit{ps}}/{\rho }_f{c}_{\mathit{pf}}$ ratio affects the entire cycle, increasing the temperature difference between phases, lowering the velocity in which the solid raises its temperature but storing heat more efficiently. Finally, a design consideration is highlighted as the importance of the $k_s/k_f$ ratio on the thermal efficiency is predominant at lower Re_t flows, whereas as Re_t increases, ${\rho }_s{c}_{\mathit{ps}}/{\rho }_f{c}_{\mathit{pf}}$ becomes the dominant parameter providing efficiency gains.

Introduction

Thermal Energy Storage (TES) systems use thermal energy to heat up a storage material that will release energy during a discharge cycle later. This storage systems are particularly important for concentrating solar power plants (CSP) since the thermal energy produced during daytime can be directly stored for later usage, improving the overall efficiency of the power plant [1]. Currently, the types of TES available are sensible heat storage, latent heat storage and thermo-chemical heat storage. Amongst these, sensible heat storage is the predominant technology [2]. As for the TES system, it can be comprised of a two-tank system, where hot and cold fluid are stored separately, or of a single tank system, alias Thermocline TES. In a thermocline TES, a hot fluid can be used to provide thermal energy for a solid medium (packed bed) in a charging cycle, and later be used to heat up cold fluid in a discharging cycle [3]. Sensible heat storage thermocline TES have been studied since 2002 [4] and most focused on molten-salt as Heat Transfer Fluid (HTF) due to its thermal stability at high temperatures or heat transfer oils due to good thermo-mechanical properties [5], [6], [7], [8], [9], [10], [11], [12].

However, using air as a HTF has been proposed to avoid temperature constraints, enable close to ambient operating pressures, eliminate the need for heat exchangers and reduce costs [13]. Experimental work on TES systems with air as HTF was further investigated by Zanganeh et al. [14], where a pilot scale 6.5 MWh_th thermal storage tank was constructed and used to demonstrate thermocline formation and validate a numerical heat transfer model for charging and discharging cycles. Also, in Anderson et al. [15] an experimental setup was used to evaluate a numerical one-equation approach with focus on Biot number analysis and thermophysical properties. A prototype thermocline thermal storage tank with 42kWh_th was fabricated combining sensible and latent heat storage by Zanganeh et al. [16] and Cascetta et al. [17] compared CFD simulation results with data obtained from an experimental setup demonstrating the matching temperature distributions across the tank and during the transitory.

Numerically, Bayón and Rojas [18] developed a single-phase one-dimensional simplified model to develop design guidelines for thermocline tanks and Andreozzi et al. [19] used the commercial CFD Fluent software to perform a parametric analysis of a thermocline TES with air as HTF and a honeycomb shaped porous medium. In Bonanos and Votyakov [20] a sensitivity analysis indicated that tank height and thermophysical properties of the solid filler were the most influential parameters in tank efficiency.

For heat transfer and flow in porous media the books by Nield and Bejan [21] and Ingham and Pop [22] described several models and applications for analyzing this type of media, which often use the volume-averaging technique [23], [24], [25]. Also, for thermal energy storage applications, the difference in temperature between the solid and fluid phases may influence the charging cycle and a local thermal non-equilibrium (LTNE) model may be required to improve model accuracy [26], [27] In addition, studies on porous cavity, including oblique enclosures [28] and the use of nanofluids [29], [30], [31] have also been presented in the literature, showing the importance of the LTNE model for accurate thermal prediction.

In a series of articles, a general model for turbulent flow and heat transfer in porous media was investigated and applied to a number of steady-state cases, including heat transfer under thermal non-equilibrium [32], turbulent flow in hybrid media [33], heat transfer in impinging jets [34] and turbulent combustion burners [35], to mention a few. Those developments were later compiled and published in a book [36]. Although tested in a number of geometries and flows of different types, the general model detailed in [36] has never been applied to investigate the effects of solid-to-fluid thermal conductivity and thermal capacity ratios in situations involving simultaneously different models, namely, turbulence, porous media, hybrid systems (clear region and porous medium), transient analysis and ventilated cavities. The two parameters, $k_s/k_f$ and ${\rho }_s{c}_{\mathit{ps}}/{\rho }_f{c}_{\mathit{pf}}$, affect thermal transport and storage and indirectly the flow field due to the inherent velocity-temperature coupling.

Therefore, the contribution herein consists in investigating the transient behavior of temperature fields and thermocline thicknesses of Thermal Energy Storage systems as a function of $k_s/k_f$ and ${\rho }_s{c}_{\mathit{ps}}/{\rho }_f{c}_{\mathit{pf}}$, considering simultaneously the models mentioned above. Also examined is the overall thermal efficiency of the system, η. This is done with the hope of expanding the understanding of the thermal behavior of thermocline TES systems and, ultimately, predicting their charging efficiencies with a greater accuracy. As such, we expect that design and analysis of such systems benefit from the work herein.