Packed Bed Latent Thermal Energy Research Articles

Thermal analysis of packed bed thermal energy storage system with dimpled spherical capsules

The thermal storage potential of a packed bed filled with paraffin wax capsules was examined. Heat transfer fluid (HTF) at 70 °C inlet temperature for dimpled and plain stainless-steel capsules was compared for three different flow rates, 1 L/min, 3 L/min and 5 L/min. In general, dimpled spherical capsules sustain more heat than plain spherical capsules at the same flow rate, according to instantaneous and cumulative heat stored. Spherical capsules with dimples exhibited a 30 % improvement in charging rate compared to smooth spheres, particularly at elevated flow rates. Specifically, at a flow rate of 5 L/min, dimpled capsules achieved faster charging and sustained higher temperature compared to plain capsules. Higher flow rates (3 and 5 L/min) result in steeper temperature increases and an earlier peak temperature phase compared to the lower flow rate (1 L/min). Key dimensionless heat transfer numbers were examined. The Stefan number was found to be 0.1966 for an HTF inlet temperature of 70 °C and a latent heat of fusion (Lm) of 213 kJ/kg. Heat transfer increases when Reynolds numbers increased from laminar (123.8 at 1 L/min) to turbulent (619.1 at 5 L/min). Rayleigh number decreased over time but increased for dimpled capsules, indicating improved convection. Dimpled capsules had higher Nusselt numbers and increases with flow rate, indicating better convective heat transfer. Dimpled capsules absorbed heat faster and stored more energy, giving them a viable and efficient Packed Bed Latent Thermal Energy Storage system design.

Identifying driving factors in cascaded packed bed latent thermal energy storage: An experimental validation

The cascaded packed bed latent thermal energy storage (PBLTES) system, an innovative and efficient technique, remains unexplored experimentally in terms of driving factors and cyclic stability. To address this gap, this study designed a cascaded PBLTES system, employing three phase-change-materials with varied phase transition temperatures. Parametric experiments were conducted to measure phase transition in capsules and temperature changes in heat transfer fluid. Pearson's correlation coefficients were used to establish relationships between driving factors and thermal performance metrics. This study developed multiple linear regression models based on experimental correlations to evaluate and predict thermal performance under various conditions. These results indicated that the employed multiple regression models are capable of making reliable quantitative predictions regarding the thermal behavior of cascaded PBLTES systems. The models showed a good fit to the experiment data (lowest R2 value at 0.776). The results also showed that the flow rate significantly affected total and phase transition times of the cascaded PBLTES for charging/discharging, with substantial Standardized Linear Regression Coefficients of −0.79/-0.8 and −0.74/-0.72, respectively. In contrast, inlet temperature, with coefficients of −0.18/0.15 and −0.34/0.21, has about a quarter of the flow rate's impact. These findings provide compelling experimental substantiation for the design of cascaded PBLTES.

Optimal design and evaluation for sphere capsules in the packed bed latent thermal energy storage

The high-performance PLTES basically relies on the heat transfer inside the sphere capsule. To achieve a high cost-performance enhancement, the sphere capsule with the copper foam partially filled is proposed, depending on the full utilization of the foam enhancement and natural convection. The melting performance of the partly filled sphere capsule and the optimization, including the geometric shape and foam material usage, is numerically investigated. The economic assessment of these initial cases and the optimized cases is also conducted to evaluate the economic feasibility. The numerical results indicate the partially filled strategy is effective and the optimal design is the spherical capsule with a copper foam geometric shape that resembles a high cone with a prominent center. This is because the buoyancy-driven natural convection is fully used to enhance the heat transfer in the upper section and the foam is used to enhance the heat transfer in the bottom section. Based on this analysis, a better effect can be obtained by maintaining consistent angle size while changing the height of the vertex of the high cone. Through this optimization, the usage of copper foam is reduced by 24.48 % at the same melting rate.

An improved effectiveness-NTU method for streamlining the design and optimization of packed bed latent thermal energy storage

The packed bed thermal energy storage system (PBLTES) is one of the promising and effective ways to solve the contradiction between the supply and demand of renewable energy. As a simplified mathematical representation, the effectiveness-number of transfer units (NTU) method can characterize the PBLTES faster than numerical simulation, which is convenient for PBLTES design, analysis, and optimization. The p factor, which is a key parameter for calculating the equivalent thermal resistance in the effectiveness-NTU method, is used to define the path of charging and discharging of the PBLTES, that is, the synchronization of phase change processes of phase change materials in different layers, which determines the accuracy of the model. In this paper, the calculation method of average effectiveness is further refined based on existing studies and mathematical derivations. The phase change duration characteristic of the PBLTES is incorporated into the method. Then, a numerical simulation model of PBLTES with spherical capsules was established to investigate the influence of relevant parameters on the p-factor and the impact mechanism. Finally, the p-factor was fitted based on numerical simulation. The results show that the effectiveness solved by the fitting p-factor equation has a maximum error of less than 10 % and an average error of 5.11 % compared to the experimental results. The establishment of the p-factor calculation equation allows the effectiveness-NTU method to be used more accurately and quickly for the design and optimization of the structural and operating parameters of the PBLTES, which can advance the engineering applications of PBLTES.

A predictive method for pipe in pipe, cylindrical modules and spherical packed bed latent thermal energy storage systems

Due to the transient operation of latent thermal energy storage (LTES) heat exchangers, methods from classical heat exchanger theory such as the effectiveness number of transfer unit method are not applicable. As a result, the study of these systems lacks a general theoretical framework. Recently, an approximate analytical solution method was developed which integrates phase fraction under a constant boundary condition to an LTES heat exchanger with a varying heat transfer fluid temperature. In this paper, the method is applied to three geometries: pipe in pipe, cylindrical modules and spherical packed bed geometries. The resulting model predicts the phase change fraction and effectiveness as a function of time, based on one-dimensional solutions for the movement of the phase change front. The predictions of the analytical model are compared to results of a simplified numerical method of an LTES heat exchanger. The average deviation of the predicted phase change fraction is 3.3 10−2 %, 4.6 10−1 % and 3.7 10−1 % for the pipe in pipe, cylindrical and spherical module respectively. The difference in model performance stems from the description of the fundamental heat transfer behavior. In a second validation step, the outlet temperature predicted by the model is compared to an experimental dataset for a LTES shell and tube heat exchanger. The predictions of the model can be improved further by including sensible heat, heat losses and allowing time-varying inlet conditions.

Numerical heat transfer analysis of the packed bed latent heat storage system based on an effective packed bed model

Due to the complexity of the fluid flow and heat transfer in packed bed latent thermal energy storage (LTES) systems, many hypotheses were introduced into the previous packed bed models, which consequently influenced the accuracy and authenticity of the numerical calculation. An effective packed bed model was therefore developed, which could investigate the flow field as the fluid flows through the voids of the phase change material (PCM), and at the same time could account for the thermal gradients inside the PCM spheres. The proposed packed bed model was validated experimentally and found to accurately describe the thermo-fluidic phenomena during heat storage and retrieval. The proposed model was then used to do a parametric study on the influence of the arrangement of the PCM spheres and encapsulation of PCM on the heat transfer performance of LTES bed, which was difficult to perform with the previous packed bed models. The results indicated that random packing is more favorable for heat storage and retrieval as compared to special packing; both the material and the thickness of the encapsulation have the apparent effects on the heat transfer performance of the LTES bed.