Packed-bed Thermal Energy Storage System Research Articles

Performance analysis of a molten salt packed-bed thermal energy storage system using three different waste materials

Concentrated Solar Power (CSP) is a critical technology for the renewable energy transition, offering high power output at elevated temperatures. However, further integration of CSP plants requires a reduction in investment costs. This study investigates the use of cost-effective, sustainable, waste-based TES materials—such as Electric Arc Furnace Black Slag (BS) and Tundish (TN) from the steel industry, as well as Demolition Waste (DW) from urban regeneration projects—as packing materials in TES systems to reduce the capital expenditure of CSP plants. A One-Dimensional Continuous Solid Phase (1D-2P) model was employed to evaluate and compare the performance of DW, TN, and BS. The results revealed that all materials demonstrated comparable properties, with TN exhibiting the highest energy storage capacity (44.7 kWh) and energy storage density (296 kWh/m³). With high utilization rates of 73–75 %, waste-based TES systems show strong potential for application in CSP plants. The TES systems were scaled for a 110 MW CSP plant, which currently operates with a 2-tank molten salt TES system providing 4648.4 MWh of storage capacity. TN required the smallest storage volume of 22,273 m³ for the 110 MW CSP plant. The reduction of molten salt usage by up to 31,000 tons in the waste-based packed-bed TES system could significantly enhance the economic feasibility of CSP plants.

On the analytical solution of the one-dimensional convection–conduction equation for packed-bed thermal energy storage systems

Temperature distribution modeling within packed-bed thermal energy storage (PBTES) systems is crucial to simulate its integration into heat sources and perform techno-economic analyses to assess the actual benefits associated with its use. This article proposes a one-dimensional convection–conduction equation to model a fluid–solid system by assuming volume-averaged properties for the energy balance and determines the analytic solution through Integral Transforms. The present study analyzes the applicability of this analytic solution considering different operational conditions of PBTES systems. The article revealed that the Péclet number (Pe) and the fluid-to-solid capacity ratio (κ) must be limited to obtain stable solutions, while the dimensionless time τ cannot be arbitrary despite computing an analytic solution. A sensitivity study of the solution for parameter a=κPe/2 defined the minimum dimensionless time required for the solution to be stable. This stability was assessed with existing experimental setups, indicating the solution’s feasibility for air–solid PBTES systems.

Multi-scale investigation of heat and momentum transfer in packed-bed TES systems up to 800 K

With the rising cost of energy and the advancement of corporate social responsibility, there is a growing interest in addressing the challenge of recovering and storing high-temperature waste heat. Sensible heat storage in packed beds stands out as a cost-effective and seemingly straightforward solution for high-temperature Thermal Energy Storage (TES). Engineering models developed to design low-temperature TES systems were tentatively used to design this new generation of high-temperature systems. Delving into the physics of coupled heat and mass transfer reveals a lack of validation of this approach. This study seeks to establish a comprehensive bottom-up methodology - from the particle scale up to the system level - to provide informed and validated engineering models for the design of high-temperature TES systems. To achieve this goal, we developed a multi-scale numerical model to explore the physics of heat and momentum transfer in packed-bed TES systems. At the microscopic scale (pore/particle), we consider the flow of a compressible high-temperature gas between the particles, coupled to transient heat conduction within the particles, with particular attention given to incorporating accurate temperature-dependent viscosity for the gas phase and thermal conductivity and density for both solid and gas phases. At the macroscopic scale (engineering), we propose a high-temperature extension of state-of-the-art two-equation TES models. The governing equations considered are the volume-average conservation laws for gas-mass, gas-momentum and energy of both phases. The multi-scale strategy is applied to a randomly packed bed of spherical particles generated with the discrete element method (DEM) software LIGGGHTS. Numerical models for both scales were implemented in the Porous material Analysis Toolbox based on OpenFoam (PATO), which is made available in Open Source by NASA. Microscopic scale simulations were used to infer the effective parameters needed to inform the macroscopic model, namely, permeability, Forchheimer coefficient, effective thermal conductivities, and the heat transfer coefficient. The informed macroscopic model reproduces with excellent accuracy the average temperature fields of the physics-based microscopic model. Pore-scale analysis shows highly three-dimensional flow characterized by reverse flow and strong cross-flow in the packed bed system. Moreover, it indicates the coupling between temperature and velocity fields, where a nonuniform velocity field results in uneven temperature distributions across the fluid and the solid spheres within the packed bed, subsequently affecting the macroscopic heat transfer coefficient. The overall strategy is validated by comparison to available experimental data. This bottom-up methodology contributes to the understanding and opens new perspectives for a more precise design and monitoring of high-temperature TES systems.

Numerical and experimental analysis of instability in high temperature packed-bed rock thermal energy storage systems

Due to heat losses of preferential areas of packed-bed energy storage systems, transverse temperature variations may occur during the charging, discharging and standby processes. Furthermore, the heat losses of preferential areas of the storage tank cause a lower pressure drop in these areas resulting in an increased mass flow rate and further cooling, and thereby an enhanced transverse temperature variation, in a positive feedback loop – a phenomenon called instability. The transverse temperature variations may deteriorate the performance and thereby the economic feasibility of packed-bed energy storage systems. In this paper, numerical and experimental investigations of an air-based packed-bed rock thermal energy storage system for large-scale high temperature applications are presented. The objective of the study is to predict the instability and to analyze the effect of different standby durations and storage size on the instability of the air-based packed-bed system. Transient axisymmetric computational fluid dynamics models were developed for the standby and discharging processes of the packed-bed thermal energy storage systems. In addition, experimental investigations were carried out at a test facility located at Stiesdal Storage, Denmark, using magnetite rocks as heat storage material and air as heat transfer fluid. The results suggest that the numerical predictions are in good agreement with the test data. The instability phenomenon is found to increase with the standby duration, resulting in a maximum difference of 161 K between the maximum rock temperature and the outlet air temperature for a standby period of 10 h followed by a discharging process. Moreover, the results indicate that the maximum difference between the rock temperature and outlet temperature is 73 K and 56 K for a reduced-scale and a full-scale system (no standby period), respectively.

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.

Effects of EPCM particle properties on creep damage of the molten salt packed-bed thermal energy storage system

One of the concerned aspects in the design of molten salt packed-bed thermal energy storage (TES) tank with encapsulated phase change materials (EPCMs) is to evaluate the creep damage because of molten salt tanks have to withstand elevated temperature and stress level in charging and discharging processes. This paper aims at estimating the creep damage and investigating the effects of EPCM particle properties on creep damage performance of EPCM-TES tank. First, a commercial scale molten salt EPCM-TES tank applied in 50MWe tower plant is designed. Second, a method to evaluate the creep damage of packed-bed tank in service life is developed based on the integration model coupling FVM and FEM. Then, the effects of particle diameter and melting temperature of EPCMs on creep damage are discussed. Finally, a novel diameter-changed and melting temperature-changed two-layered EPCMs packed-bed structure with lower creep damage is proposed. The results are concluded as follows. (1) The creep damage of bottom wallboard is more significant than that of other wallboards in operation. (2) The EPCMs with smaller particle diameter or higher melting temperature is helpful to reduce the creep damage of tank. When particle diameter decreases from 42 mm to 20 mm or melting point rise from 365 °C to 395 °C, the creep damage of bottom wallboard can be reduced by 4.8 times and 58 %, respectively. (3) The creep damage of novel two-layered EPCM-TES configuration with lower creep damage time and stress is weaker than single-layered form. Compared with single-layered form filling with higher particle diameter and melting temperature of EPCMs, the creep damage of bottom wallboard in two-layered structure can be reduced by 53 %. This work can provide insights on the optimization design of the EPCM packed-bed TES configuration for lower creep damage in service life.

Chloroplast-granum inspired phase change capsules accelerate energy storage of packed-bed thermal energy storage system

Packed-bed thermal energy storage (PBTES) systems utilizing phase change capsules have found extensive applications in thermal energy harvesting and management to alleviate energy supply-demand imbalances. Nevertheless, the sluggish thermal charging rate of phase change materials (PCMs) capsules remains a significant impediment to the rapid advancement of PBTES. Here, bionic PCMs capsules are proposed by mimicking the internal and external structure of chloroplast-granum. The heat transfer and flow characteristics of the bionic PCMs capsules in the packed-bed are analyzed by experiments and numerical simulations. The results illustrate that the chloroplast-fin type PCMs capsule exhibits significantly faster heat storage compared to the sphere type PCMs capsule. This improvement is attributed to the bionic folded shape and inner membrane structure, which generate multiple local vortices to enhance heat convection, and shorten the heat transfer distance between the capsule wall and center PCMs to facilitate heat conduction. The PCMs capsules are further filled into the packed-bed in a staggered arrangement, resulting in increased heat transfer area and enhanced disturbance flow as compared to an aligned arrangement. Consequently, the melting time of the packed-bed filled with chloroplast-fin type capsules is reduced by 33.2%, meanwhile the average exergy storage rate and exergy efficiency are enhanced by 48.4% and 8.3%, respectively, compared to the packed-bed filled with sphere type capsules. This research offers a novel approach for designing high-performance PBTES system utilizing bionic capsules.

Experimental and numerical study of epoxy resin-based composite phase change material in packed-bed thermal energy storage system for ventilation

Air heating of ventilation system occupies large energy consumption of buildings. Using phase change material (PCM) in active thermal energy storage system (TES) has practical significant to avoid unstable input and improve energy capacity. This work proposed a packed-bed TES system with solar collector for ventilation, by employing the novel epoxy resin-based composite PCM without capsule shell as fillers. In experiment, two types composites were first prepared and compared: the epoxy resin-based composite with Al additives has loading capacity up to 65% and a latent heat of 116.7 J kg−1, which shows better thermal performance than that of the Al-based composite (maximum 25%, 46.92 J kg−1). Then, a numerical model of TES system was built, validated, and then used to simulate the outlet temperature variation of air. Simulation results shows the designed TES system is beneficial to stabilize output temperature. Therefore, when the energy storage process is from 7:30 am to 17:30 pm, the utilization efficiency for composite filler system of 51.1 % is higher than that of pure PCM filler system of 49.7 %. At last, determining the phase change temperature of the composite at around 25 °C leads to an efficiency improvement around 22 %.

Combining entropy weight and TOPSIS method for selection of tank geometry and filler material of a packed-bed thermal energy storage system

Thermocline thermal energy storage systems are promising alternatives for recovering waste heat lost by industry around the world. The aim of this work is to extend the methodology presented in previous work, by optimising an existing industrial packed-bed storage system on two geometric optimisation variables, considering exergy, environmental and economic aspects. Seven filler materials are compared for the same heat transfer fluid, to include discrete variables in the model. The multi-objective optimisation problem is solved using the NSGA-II multi-objective genetic algorithm. For each filler material, a Pareto set is obtained. The non-dominated solutions within the union of the different Pareto sets are then selected, which give a new single set of optimised solutions. A multi-criteria decision-making method (TOPSIS) is then applied to obtain the optimal solution. To avoid any subjective choice from the decision-maker by determining the objective weights of each of the optimisation criteria, the Shannon entropy is used. The combination of TOPSIS and Shannon entropy led to the selection of a recycled ceramic obtained from hard coal ashes as the best filler. This solution has a stocky tank shape (2.4 m diameter, 2.1 m height) and a small particle diameter (7 mm). The exergy and environmental performance is improved compared to the reference storage. They reach 98.0% (vs 95.6%) and 58 hab.year (vs 67 hab.year) respectively. The levelised cost of energy is close to that of the reference tank (3.35 vs 3.31 c€/kWhth).

Optimization of capsule diameters in cascade packed-bed thermal energy storage tank with radial porosity oscillations based on genetic algorithm

The packed-bed thermal energy storage system (PBTES) has broad application prospects in renewable energy, such as for solar, hydraulics, biomass, and geothermal. This study varied the capsule diameter arrangement of the PBTES using a genetic algorithm (GA) to optimize the thermal performance of the cascaded three-layer PBTES during charging. When considering the oscillatory distribution of the radial porosity, the thermal energy storage (TES) rate density was used as an objective function to evaluate the system’s thermal performance. The TES rate density of PBTES was calculated for more than 4000 capsule diameter arrangements. The results indicate that the tank-to-capsule diameter ratio significantly affects the radial porosity distribution, velocity, and temperature distribution of PBTES. The optimal capsule diameter arrangement in the range of 15 mm ≤d≤ 40 mm was obtained as d1 = 15.58 mm, d2 = 21.78 mm, and d3 = 27.68 mm. Compared with the original model, the optimal model’s charging time was reduced by 33.90%, the TES rate density improved by 37.07%, and the cost per unit of heat storage increased by 92.41%. The results show that the GA is a powerful tool for optimizing PBTES structures.

Albizzia pollen-inspired phase change capsules accelerate energy storage of packed-bed thermal energy storage system

Packed-bed thermal energy storage (PBTES) system using phase change capsules has been widely applied for thermal energy harvesting and management to alleviate unbalanced energy supply and demand problems. However, the slow thermal energy charging is always a daunting challenge limiting its fast development. Here, a bionic phase change materials (PCMs) capsule by mimicking the natural structure of albizzia pollen is proposed. The heat storage performance and economy of capsules with different internal fin structures are investigated numerically and experimentally. The thermal charging of pollen-type PCMs capsules is the fastest, whose melting time prominently reduces by 19 %, 24 %, 41 % and 61 % compared to the plate-type, ring-type, column-type, and pure PCMs capsules, respectively. That is because the contact area between the skeleton and the capsule wall is increased and the average distance between PCMs and the heat transfer surface is shortened. The pollen-type capsules exhibit the best economy with the exergy efficiency is improved by 15 % compared to pure PCMs capsule. By optimizing the ratio of fin length to radius (L/R) to 5/6, the melting time can be further reduced by 62 % and the exergy efficiency can be improved by 16 % owing to the enhanced heat transfer rate in the center of the pollen-type capsules. A PBTES system is further built based on optimized pollen-based capsules, and faster heat storage rate is successfully demonstrated in experiments. These results provide alternative solutions for optimizing PBTES systems and improving their thermal energy storage performances.

Optimization design and performance investigation on the cascaded packed-bed thermal energy storage system with spherical capsules

Most of the previous researches on the cascaded packed-bed latent heat storage (CPTES) system are the thermal performance optimization based on numerical calculation. Experimental studies are few and mainly focus on single design parameter at low-temperature conditions. Lack of the detailed temperature - flow field experimental data and optimization scheme for the CPTES system. In this paper, an optimized two-layered filling structure of packed-bed heat storage system (OT-PTES) was proposed, which considers melting temperature of phase change material (PCM), capsule diameter, and filling volume ratio. The heat transfer process of PCM capsule and heat transfer fluid (HTF) during charging/discharging process were studied in detail by experiments. Under consistent working conditions, the average charging/discharging rate, total heat capacity, overall efficiency, and exergy efficiency was evaluated. And the influences of HTF inlet flow and the volume filling ratio of two-layered on thermal performance were analyzed. Finally, the concentric diffusion model was used to simulate the system to further optimize its hierarchical structure. The results are concluded as follows: (1) The temperature difference between PCM capsule and HTF at the interface changes continuously, and there is also an obvious temperature gradient in the radial direction of HTF, which improves the heat transfer efficiency. (2) Through experiments, the packed-bed with single large/small size PCM capsules are compared with the OT-PTES system. The overall efficiency of the latter is 74.2%, increased by 3.38% and 8.28%, and the exergy efficiency is 62.7%, increased by 7.5% and 52%. It is proved that the OT-PTES system has better charging/discharging performance. (3) When the volume filling rate = 1/2, the system has the best thermal performance (75.04%) and exergy efficiency (67.1%). (4) The numerical simulation results show that the overall performance of the packed-bed is optimal when the capsule size composition is 20–30 mm and the temperature difference of PCMs melting point is 60 ℃. In summary, OT-PTES is an optimized system with better heat storage performance. This study can provide experimental data support for the optimal design of the PLTES system and useful guidance for industrial applications.

Techno-economic optimization of packed-bed thermal energy storage system combined with CSP plant using DOE: design of experiment technique and Taguchi method

Techno-economic optimization of packed-bed thermal energy storage system combined with CSP plant using DOE: design of experiment technique and Taguchi method

Numerical study of high-temperature cascaded packed bed thermal energy storage system

The thermal energy storage system (TES) in the form of packed bed with encapsulated phase change materials (EPCMs) can further improve the thermal performance of ordinary TES. This study presents a numerical model for a three-dimensional cascaded packed bed thermal energy storage system (PBTES), in which an effective thermal conductivity model is used by consisering the natural convection effects in each EPCM based on its volume average liquid fraction. To examine the system-storage thermal energy and exergy in PBTES accurately, a thermodynamic analysis approach is also given. The high-temperature PCMs are grouped as KNO3, NaNO3, and NaNO2 according to the phase transition temperature from high to low in the packed bed stage. The effects of element stages on the thermal performance of PBTES are studied. Results show that the total thermal energy storage of cascaded-PBTES is 38.5% higher than that of single-PBTES (KNO3), and the total thermal exergy storage is 30.8% higher than single-PBTES. The average exergy efficiency possessed by cascaded-PBTES is 5% higher than that of single-PBTES. Furthermore, the effects of heat transfer fluid (HTF) inlet temperature and mass flow rate on the thermal performance of cascaded-PBTES are discussed. The increase of inlet temperature and mass flow rate can promote the charging process and influence the exergy efficiency. However, increasing the inlet mass flow rate will not lead to an increase in maximum thermal energy and exergy storage capacity.

Coupled Thermal and Mechanical Dynamic Performances of the Molten Salt Packed-Bed Thermal Energy Storage System

Coupled Thermal and Mechanical Dynamic Performances of the Molten Salt Packed-Bed Thermal Energy Storage System

Performance analysis and optimization of packed-bed TES systems based on ensemble learning method

Most existing studies that focused on the performance analysis and optimization of packed bed thermal energy storage systems (PBTESS) have ignored some impact factors, which decreased the accuracy of the system performance prediction. In this work, the Latin Hypercube Sampling (LHS) and numerical simulation were used to construct the training database, and a full-parameter prediction model of PBTESS was constructed with the help of the LightGBM (LGBM), the naive Bayes optimization algorithm was then used to further optimize the performance of PBTESS. The prediction model considered all parameters of the system and the rationality was verified through the numerical simulation. The results showed that LGBM was effective in predicting actual heat release time, actual heat storage, and actual utilization rate of the material with R-square of 0.960, 0.962, 0.956. Meanwhile, the trained prediction model could analyze the effects of all parameters on the performance of PBTESS by the characteristic importance method. The optimization results showed that actual heat release time, actual heat storage, and actual utilization rate of the material of PBTESS were improved by 410%, 14.11%, and 39.86%.

Design optimization on characteristics of packed-bed thermal energy storage system coupled with high temperature gas-cooled reactor pebble-bed module

The packed-bed thermal energy storage (PBTES) coupled with the high temperature gas-cooled reactor pebble-bed module (HTR-PM) system is of emerging interest which can ensure the economy, safety and reliability operation of the HTR-PM. For the coupled PBTES system, multi-parameters need to be considered and there is a need to propose an integral method to help the design and optimization. In this work, firstly, the numerical results are compared and validated with the experiment data. Then, the thermal characteristics of the coupled PBTES system including the overall heat storage quantity, heat release quantity, average charging power, average discharging power, charging/discharging/total enthalpy efficiency and charging/discharging/total exergy efficiency are systematically evaluated with the orthogonal design optimization. At last, the typical non-dimensional numbers including the ReP number, Nu number and Pr number of the high temperature fluid (HTF) are illustrated for the optimal scheme. The results indicate that the calculation results agree well (relative error within 7.0%) with the experiment data. Additionally, the most optimal scheme is determined as 26 mm of the capsule diameter, “K2CO3-Li2CO3 (65–35 wt%)”+“LiF-NaF-KF (29–12–59 wt%)” of the phase change materials (PCMs), 0.229 m3·s−1 of the inlet HTF flow rate and 850℃ of the inlet HTF temperature or initial PCMs temperature. It demonstrates an integral method including the numerical model calculation, orthogonal design optimization, thermal characteristics evaluation, range and variance analysis, enthalpy and exergy efficiency and dimensionless number for the design of the coupled PBTES system.

Numerical modelling and optimization of packed-bed thermal-energy storage system

In this work, numerical modelling (including convection and radiation heat transfer) of Packed-bed storage systems (PBSS) is carried out and the effect of various system parameters affecting the efficiency and temperature is studied. One dimensional forms of the time-dependent, coupled partial differential equations for energy conservation of the heat transfer fluid (HTF) and the packing materials are solved using the finite difference method to design a PBSS for a given mass flow rate for 0.125 MWh (0.45 GJ). The packed-bed material is assumed to be spherical with an average diameter, and the mass flow rate, void fraction, packed bed material diameter, heat transfer fluid (HTF), and the packed-bed materials are varied for optimal efficiency during charging (i.e. when the temperature of HTF is greater than that of the packed bed). The results are compared with the analytical solutions for validation. Present solutions (considering only convection) are found to be matching reasonably well with the analytical data. With the validated model, the radiation heat transfer effect on the packed-bed is modelled (along with the convection) and void fraction, mass flow rate of HTF, a diameter of the packed-bed material, different HTF, various packed-bed materials are compared for maximum efficiency. From the present work, a PBSS design with void fraction =0.45, mass flow rate =1.8 kg/s, the average diameter of the packed-bed material = 0.02 m, water as HTF, and brick as packed-bed material is found to give the maximum efficiency along the length of the packed-bed.

Optimization Design and Performance Investigation on the Two-Layered Filling Structure of Packed-Bed Thermal Energy Storage System with Spherical Pcm Capsules

Optimization Design and Performance Investigation on the Two-Layered Filling Structure of Packed-Bed Thermal Energy Storage System with Spherical Pcm Capsules

Analysis and optimisation of packed bed thermocline energy storage tank for CSP power plant

A 17 kWhth packed bed thermal energy storage (PBTES) system for concentrated solar power application (CSP) has been investigated by using a two-phase energy model. The PBTES system used in this study consists of quartzite as storage material and caloria HT-43 as a heat transfer fluid (HTF). Simulation of 17 kWhth packed bed system has been utilised to study the effect of void fraction, storage material on charging efficiency and pressure drop at varying mass flow rate (0.01∼0.04 kg/s) of HTF. In this study, parametric optimisation using the Taguchi method has also been done to get the optimum parameter for maximum efficiency and minimum pressure drop. Results show that void fraction has more effect on charging efficiency as compared to pebbles diameter. The percentage decrease in charging efficiency is 8.1% for pebbles diameter varying from 0.03 to 0.05 and 13.5% for void fraction varying from 0.3 to 0.5.