Advances in Solid Particle Thermal Energy Storage: A Comprehensive Review

Abstract

Solid particle thermal energy storage technology demonstrates extraordinary thermal stability across wide temperature ranges and possesses significant cost-effectiveness that meets stringent economic requirements for long-duration energy storage. These distinctive characteristics enable this technology to continuously support increasing decarbonization demands and drive the strategic progression of sustainable energy transformations. This review work conducts a thorough analysis of three representative reactor types: packed beds, moving beds, and fluidized beds, focusing on how particle thermophysical properties affect heat transfer and storage performance. The paper analyzes pressure drop and heat transfer correlations to reveal the coupling effects between particles and working fluids that impact system efficiency. By comparing hydrodynamic behavior across different reactor types, the study identifies optimization strategies and technical challenges. The review paper concludes by outlining future research directions for enhancing system efficiency, supporting industrial deployment, and facilitating integration with next-generation renewable energy technologies.

1. Introduction

Against the backdrop of continuously rising energy demands and increasingly stringent decarbonization policies, energy storage systems have become a vital component for enhancing renewable energy grid integration capabilities and reconciling power supply fluctuations with grid stability requirements. As a vital branch of energy storage technologies, thermal energy storage (TES) stands out due to its unique advantages of high reliability, adaptability to multiple scenarios, and relatively low investment costs [1]. At present, TES demonstrates multisectoral implementation for managing solar thermal and electrical output fluctuations [2], optimizing power plant operational efficiency [3], advancing industrial manufacturing processes [4], and enhancing thermal regulation in heating systems [5].

Current mainstream TES solutions include sensible heat storage, latent heat storage, and thermochemical energy storage. Among these technologies, although latent and thermochemical energy storage exhibit superior energy storage density to sensible heat storage, their high cost remains inadequate for industrial-scale deployment. In contrast, sensible heat storage technology features a simpler structure, lower cost, and broader operating temperature range. By 2030, the cost of sensible heat storage is projected to fall below 25 EUR/kWh, while the costs of latent heat storage and thermochemical energy storage are expected to fluctuate within the ranges of 60 to 95 EUR/kWh and 80 to 160 EUR/kWh, respectively [6]. Given its significant cost-effectiveness and sustainability benefits, this study focuses primarily on particle-based sensible heat storage technology.

Solid particle TES holds a pivotal position among thermal storage technologies due to three inherent advantages, confirmed through previous research [7,8]. These systems demonstrate excellent chemical stability with negligible performance degradation during extended high-temperature operation cycles. The implementation uses abundant raw materials with low acquisition costs and substantial global reserves, enabling significant reductions in system construction costs. Furthermore, particulate media exhibit superior thermal storage capabilities through their naturally high specific heat characteristics, enabling direct energy storage using simplified thermal insulation methods without complex conversion processes. System configurations for solid particle TES mainly include three reactor types, which are packed beds, moving beds, and fluidized beds.

Packed bed reactors enable heat and mass transfer through fluid permeation across stationary particle layers, offering structural simplicity and stable thermal performance [9]. In moving bed reactors, particle flow is regulated under countercurrent or cocurrent regimes, offering operational advantages through tunable interparticle spacing. This adjustability effectively mitigates thermal expansion stresses at elevated temperatures, thereby reducing particle fragmentation risks [10]. Fluidized bed reactors enhance heat transfer by suspending particles through fluid velocity modulation, achieving superior heat transfer coefficients with minimal pressure drop [11]. Despite their advantages, substantial engineering challenges persist, including inherent heat transfer dynamic limitations in packed and moving beds that restrict high-power-density applications, particle attrition during high-temperature transport operations in fluidized and moving beds, and critical particle conveyance technologies still requiring technological breakthroughs [12].

This comprehensive investigation examines the theoretical foundations and technological progress in solid particle TES, with the objective of defining crucial research directions and innovation pathways for efficient thermal storage systems. Section 2 systematically evaluates how particulate material properties differentially affect performance indicators in packed bed, moving bed, and fluidized bed reactor configurations. Section 3 elucidates reactor-specific mechanisms encompassing gas phase flow dynamics, particle transport behavior, and heat transfer processes. Section 4 systematically evaluates existing reactor enhancement technologies by focusing on two pivotal dimensions: breakthroughs in structural design and advancements in thermodynamic efficiency. Section 5 identifies pivotal advancement opportunities for solid particle thermal storage technology development, focusing on energy efficiency maximization and environmental impact minimization strategies.

2. Correlation Between Solid Particle Characteristics and Reactor Performance

Packed bed, moving bed, and fluidized bed reactors exhibit significant differences in their adapted particle systems due to variations in structural design. Consequently, fundamental research on solid particles must be conducted within specific reactor frameworks. The distinct structure of each reactor directly dictates significant differences in the applicable material properties, primarily including the particle diameter, shape, and size distribution.

The three types of reactors exhibit remarkable differences in the adaptability to particle diameters, which directly impact the hydrodynamic and heat transfer characteristics. In packed beds, the interstitial pore structures formed between particles facilitate fluid permeation, enabling direct thermal exchange between the fluid and the fixed solid surfaces. This structure endows packed beds with the advantages of low flow resistance and low pressure drop, with heat transfer coefficients typically ranging from 5 to 83 W/(m²·K) [13]. Packed beds are typically constructed using particles with diameters ranging from 1 mm to 100 mm to form stationary bed layers [14]. Within this range, selecting smaller particle sizes can enhance the cyclic exergy efficiency and thermal penetration coefficient of the system [15], but the significant increase in system pressure drop caused by this size reduction must be considered [16]. Moving bed particles primarily rely on gravity-driven downward flow and usually achieve indirect heat transfer via plate-type or tubular exchange surfaces, with heat transfer coefficients reaching 75 to 250 W/(m²·K) [17]. The applicable particle diameter range is approximately 0.104 mm to 50 mm [18]. However, fine particles smaller than 1 mm tend to agglomerate and form dead zones during movement, leading to significantly degraded heat transfer performance [18]. Research indicates that particles with diameters around 4 mm often exhibit optimal packing density, residence time, and heat transfer efficiency in moving beds [19]. Fluidized bed heat transfer performance is highly sensitive to variations in particle size [20], and the particle diameters were constrained to no more than 0.8 mm [14]. High-velocity fluidizing gas induces intense turbulent motion in the particles, ensuring the continuous renewal of heated particles at heat transfer surfaces. This intense gas–solid mixing enables exceptional heat transfer performance, with coefficients reaching 250 to 950 W/(m²·K) [21]. The particle movement patterns in moving beds and fluidized beds are illustrated in Figure 1.

Particle shape is a key factor influencing the flowability, packing density, and contact area of solid particles in different reactor beds. Current research largely focuses on comparing the performance of spherical versus irregular particles. In packed bed TES, irregular particles typically incur lower material costs than spherical particles due to reduced processing requirements. However, in terms of energy storage efficiency, irregular particles exhibit the best performance, followed by spherical ones [25]. In moving beds, compared to spherical particles, non-spherical particles, due to their poorer flowability, are prone to cause flow stagnation and void formation, resulting in reduced temperature distribution uniformity within the bed, decreased heat exchange efficiency, and lower average effective heat transfer coefficients [26]. In fluidized beds, spherical particles, owing to their superior flow characteristics, typically demonstrate optimal distribution uniformity, mixing efficiency, and motion characteristics, and minimum fluidization velocity [27].

Particle size distribution can substantially alter the bulk behavior of particulate systems, given that void fraction is a critical factor governing internal pressure drop in packed beds [28]. Polydisperse particle mixtures can intensify flow disorder, consequently reducing heat transfer capacity [29]. Conversely, for moving beds and fluidized beds, polydisperse particle mixtures can enhance heat transfer efficiency by reducing frictional resistance and improving flow uniformity [30]. In fluidized beds, which are multi-sized particle systems, in particular, they can enhance fluidization stability and reduce the minimum fluidization velocity through the fine particle fraction [31].

In TES systems experiencing repeated thermal cycling, thermomechanical stability is a core challenge [32]. Thermal expansion of solid particles induced by temperature fluctuations induces mechanical stresses within the system while simultaneously affecting the internal particle porosity [33]. Furthermore, particle collisions, compression, and abrasion during motion result in significant wear and fragmentation, diminishing particle cycling stability and energy storage efficiency [34]. To ensure the long-term stable operation of the system, particle materials must possess the following characteristics: high hardness to resist wear, high yield strength to avoid permanent deformation under thermal stress and maintain structural integrity, high fracture toughness to suppress brittle fracture and enhance safety, and high elongation to buffer thermal expansion through plastic deformation, thereby reducing the risk of thermal shock cracking [35].

Apart from the material properties of particles, the existing research on solid particles also primarily focuses on their key thermophysical properties. These properties are core to determining particle performance in heat exchange and TES applications. Among them, the material characteristics directly related to and crucial for the rate of thermal heat exchange and storage capacity include specific heat capacity, thermal conductivity, and volumetric heat capacity. Volumetric heat capacity characterizes a material’s ability to store thermal energy per unit volume and is the fundamental indicator determining the total energy storage capacity of a thermal storage medium. A higher volumetric heat capacity value signifies that the material can store more heat within a given volume and temperature change range [36]. Thermal conductivity describes the rate of heat conduction within a material. In solid thermal storage media, thermal conductivity governs the formation and evolution of internal temperature gradients. High thermal conductivity materials promote rapid heat transfer within particles and between particles, thereby resulting in a more uniform temperature distribution inside the thermal storage material. This uniformity is crucial for effectively suppressing thermal stratification effects [37].

From the perspective of optimizing the thermal storage performance of solid particles, achieving high-efficiency energy storage requires enhancing system energy density and reducing heat loss rates while ensuring the economic viability of material costs. Reference [38] established a multi-industry TES material database based on the ANSYS software platform (Ansys GRANTA, ANSYS, Inc., Cambridge, UK, 2024; https://www.ansys.com/products/materials, accessed on 11 May 2025). focusing on mining, construction, municipal solid waste treatment, steelmaking, and other metal industries. The study systematically analyzed the optimization relationship between the cost–volume ratio and heat storage capacity for various TES materials.

Figure 2 depicts the relationship between energy storage capacity and cost for solid particle TES systems.

Table 1. Materials from different industries for solid particle thermal energy storage.

Source	Material	Specific Heat Capacity (kJ/kg·°C)	Density (kg/m3)	Thermal Conductivity (W/m·°C)	Energy Stored per Volume (kJ/m3)	Energy Stored per Cost (kJ/EUR)
construction industry	Asbestos wastes [44]	0.80–1.03	3000–3120	1.40–2.10	2855 ± 355	2.73 ± 1.82
	Concrete [45]	0.85–1.17	2200–2400	1.25–1.50	2320 ± 380	133.85 ± 68.15
	Bricks [45]	0.70–1.07	1640–1780	0.35–0.70	1510 ± 320	659 ± 245
municipal solid waste	Fly ashes [46]	0.71–1.12	2900–2960	1.16–1.59	2080 ± 700	15.50 ± 5.69
	Bottom ashes [46]	0.71–1.12	2900–2960	1.16–1.59	2680 ± 600	34.05 ± 15.30
mining industry	Gossan [47]	0.98–1.03	3720–3780	1–3	3770 ± 100	5500 ± 4500
	Kaolinitic sludge [48]	0.70–0.90	2850	0.5–2.5	2275 ± 285	11.96 ± 4.14
steelmaking industry	Electric arc furnace slag [47,49]	0.99–1.07	3350–3390	0.53–0.64	3470 ± 140	6.68 ± 3.43
	Tundish [50,51]	1.03–1.14	3180–3410	0.64–0.85	3575 ± 215	14.46 ± 7.24
	Refractory wastes [51]	0.70–1	2970–3280	1–2.5	2655 ± 485	11.25 ± 5.75
	Mill scale [52]	0.70–1	5170–5740	0.5–1.5	4635 ± 845	11.25 ± 5.75
other metal industries	Waste from copper refinement [38]	0.5–1	1870	1–2	1402 ± 466	0.43 ± 0.29
	Dross from aluminum industry [53]	0.63–0.75	2720–3310	1.16–2	2080 ± 270	2.41 ± 1.04
	Red mud [54]	1.03–1.31	3050–3630	0.77–0.83	3905 ± 565	40.80 ± 17.80

lists several typical sensible heat storage materials. Due to their low cost, abundant resources, and mature applications, these materials are widely used [39]. In contrast, latent heat storage technology, which relies on phase change materials, is still in the early stages of commercialization. It incurs higher costs, while inherent heat discharge rate constraints may impede the full release of stored energy during peak demand periods [40]. Furthermore, thermochemical storage technology has even lower maturity and still needs to overcome key challenges such as poor controllability and a lack of demonstration projects [41]. Solid particle sensible heat storage typically exhibits an energy density ranging from 0.02 to 0.03 kWh/kg. In comparison, latent heat storage materials have an energy density of 0.5 to 1 kWh/kg [42], while thermochemical energy storage achieves an energy density ranging approximately from 0.05 to 0.1 kWh/kg [43]. Despite its relatively lower energy density, solid particle material demonstrates the most promising application potential in sensible heat storage due to its significant cost advantage. Among these options, mineral-based materials combine relatively high energy density with minimal cost, resulting in superior overall performance and positioning them as highly competitive candidates.

It is particularly noteworthy that solid particle materials demonstrate distinct thermodynamic behaviors in different reactor systems, such as fluidized beds and moving beds, with nonlinear coupling characteristics existing between operational parameters. Therefore, multi-objective optimization methods are required to achieve the systematic balancing of key performance indicators, ultimately accomplishing the engineering objective of the synergistic enhancement of the heat transfer rate and energy storage density.

3. Advances in Flow Heat Transfer Characteristics of Solid Particle Heat Storage in Different Bed Reactors

The interplay between flow dynamics and thermophysical interactions in packed bed, moving bed, and fluidized bed reactors leads to distinct performance variations in TES applications. This section comprehensively reviews fundamental advancements in solid particle thermal storage research, with a focused analysis of pressure drop correlations and heat transfer mechanisms, aiming to establish theoretical foundations for reactor scale optimization.

3.1. Heat Transfer Characteristics of Solid Particles in Packed Beds

When a fluid flows through a packed bed, it follows tortuous paths, accompanied by significant flow resistance, resulting in variations in the pressure gradient along the flow path. The pressure drop per unit bed length primarily depends on the bed porosity, effective particle diameter, particle shape, fluid dynamic viscosity, density, and flow velocity. Equations commonly used in the literature to calculate the pressure drop in packed bed systems are the Ergun equation and the Carman equation.

The Ergun equation has been demonstrated to yield reasonable accuracy for beds containing approximately spherical particles [55]. However, it systematically overestimates the pressure drop in randomly packed beds of smooth spherical particles when the Reynolds number reaches 500 or higher [56]. This model is only applicable to systems where the ratio of tube diameter to particle diameter exceeds 10 and does not account for wall effects. To address these limitations, researchers have proposed empirical correlations incorporating wall effect corrections [57]. Nevertheless, most improvements to the Ergun equation have focused on monodisperse particle systems and exhibit inadequate adaptability to polydisperse packed beds [53]. Furthermore, experimental studies on mixed packed beds of micron-sized particles reveal significant deviations between the measured pressure drop and theoretical predictions based on the Carman equation [58].

Despite continuous refinements to the Ergun and Carman equations, most advancements remain confined to monodisperse systems, limiting their application to industrially prevalent polydisperse packed beds. Key challenges include the technical limitations of real-time monitoring of particle size distribution during industrial operations, which affects parameter accuracy and increases uncertainty in model inputs. Concurrently, while irregularly shaped particles are widely used in industry, research continues to focus predominantly on regular particles. There is an urgent need for enhanced investigation into the thermo-hydrodynamic behavior of irregular particles.

Current empirical heat transfer correlations primarily target spherical particles. Wu and Hibiki [59] systematically evaluated existing models for spherical particles, reducing the mean absolute relative errors from 15.3–250% to 8.90% for turbulent flow and from 31.2–157% to 17.9% for laminar flow, respectively. For non-spherical systems, Cerantola and Lane [60] employed dimensional analysis and the discrete element method to numerically reconstruct randomly packed beds, validating the applicability of this approach in systems containing over 1000 irregular particles. Liu et al. [61] found that sphericity and porosity exert significant effects on the heat transfer process in sintered ore, and accordingly proposed a heat transfer correlation incorporating these two parameters. Based on particle-resolved direct numerical simulation (PR-DNS) results, Singhal et al. [62] proposed an improved Nusselt number (Nu) correlation. This correlation is applicable to dense packed beds with low porosity and provides more accurate simulations of heat transfer characteristics in particle beds. Their study also indicated that different particle arrangements lead to significant variations in the Nu, necessitating consideration of this structural uncertainty when establishing correlations. Using PR-DNS simulations, Sun et al. [63] investigated gas–solid heat transfer under steady-state flow conditions, deriving a correlation characterizing the relationship between the Nusselt number, Reynolds number, and porosity (ε). This expression more accurately reflects the dependence of the Nu on the Re. Heat transfer correlations applicable to packed bed particles are summarized in

Table 2. Mathematical equations related to packed beds.

Heat Transfer Correlation of $\mathbf{N}\mathbf{u}$	Definition and Scope of Application
${\mathrm{N}\mathrm{u}}_{\mathrm{D}}=0.35{\mathrm{R}\mathrm{e}}_{\mathrm{D}}^{0.7}{\mathrm{P}\mathrm{r}}^{0.33}{\left({\displaystyle \frac{{\mathrm{D}}_{\mathrm{O}}}{{\mathrm{D}}_{\mathrm{P}}}}\right)}^{0.19}$ ${\mathrm{N}\mathrm{u}}_{\mathrm{D}}=0.14{\mathrm{R}\mathrm{e}}_{\mathrm{D}}^{0.9}{\mathrm{P}\mathrm{r}}^{0.33}{\mathsf{\epsilon }}^{-0.62}{\left({\displaystyle \frac{\mathrm{L}}{{\mathrm{D}}_{\mathrm{P}}}}\right)}^{0.2}$ [59]	$1\le {\mathrm{R}\mathrm{e}}_{\mathrm{D}}\le {1.99\times 10}^5$ $0.7\le \mathrm{P}\mathrm{r}\le 17$ $0.35\le \mathsf{\epsilon }\le 0.6$ $1.27\le {\displaystyle \frac{{\mathrm{D}}_{\mathrm{O}}}{{\mathrm{D}}_{\mathrm{P}}}}\le 193$ $2\le {\displaystyle \frac{\mathrm{L}}{{\mathrm{D}}_{\mathrm{P}}}}\le 240$
$\mathrm{N}\mathrm{u}=0.430{\mathrm{R}\mathrm{e}}_{\mathrm{p}\mathrm{o}\mathrm{r}\mathrm{e}}^{0.58}{\mathrm{P}\mathrm{r}}^{1/3}+1.274$ [60]	$15\le \mathrm{R}\mathrm{e}\le 3000$
$\mathrm{N}\mathrm{u}=2.0+0.903{\left(\mathsf{\Phi }{\mathrm{R}\mathrm{e}}_{\mathrm{P}}\right)}^{0.772}{\mathsf{\epsilon }}^{0.391}{\mathrm{P}\mathrm{r}}^{1/3}$ [61]	$393<{\mathrm{R}\mathrm{e}}_{\mathrm{P}}<3319$
${\mathrm{N}\mathrm{u}}_{\mathrm{d}}=2.67\left(\pm 1.48\right)+0.53{\mathrm{P}\mathrm{r}}^{0.53}{\mathrm{R}\mathrm{e}}_{\mathrm{d}}^{0.77}$ [62]	$4<{\mathrm{R}\mathrm{e}}_{\mathrm{d}}<200$ $0.5<\mathrm{P}\mathrm{r}<1.0$
${\mathrm{N}\mathrm{u}}_{\mathrm{d}}={\displaystyle \frac{\left(-0.46+1.77\mathsf{\epsilon }+0.69{\mathsf{\epsilon }}^2\right)}{{\mathsf{\epsilon }}^3}}+\left(1.37-2.4\mathsf{\epsilon }+1.2{\mathsf{\epsilon }}^2\right){\mathrm{R}\mathrm{e}}^{0.7}{\mathrm{P}\mathrm{r}}^{1/3}$ [63]	$0.5\le \mathsf{\epsilon }\le 1.0$ $1\le \mathrm{R}\mathrm{e}\le 100$

.

While heat transfer and pressure drop studies are critical for packed bed performance evaluation, traditional isolated research approaches obscure inherent parameter coupling. Wu and Hibiki [64] developed an integrated methodology combining data augmentation, parameter optimization, and model validation to simultaneously predict pressure drop coefficients and Nusselt numbers (Nus) under varying pressure conditions. Their analog model achieved high-precision joint predictions for spherical packed beds under turbulent flow conditions with mean absolute errors of 3.10 percent for pressure drop and 8.97 percent for heat transfer coefficients. Compared to conventional methods, accuracy improved by 86.3 to 90.4 percent and 75.8 percent, respectively, with all correlations maintaining deviations within 30 percent of experimental data.

3.2. Heat Transfer Characteristics of Solid Particle Heat Storage in Moving Bed

The heat transfer characteristics that moving bed systems exhibit are strong coupled with particle flow dynamics. The continuous motion of particles disrupts the near-wall packing structure, leading relevant research to focus on two core heat transfer mechanisms: the dynamic evolution of near-wall packing structure and the flow velocity nonuniformity within the tube bundle regions [65,66]. Thermal resistance analysis based on physical mechanisms has become the dominant paradigm in this field, emphasizing the dual mechanism of synergistic interplay between contact thermal resistance and penetration thermal resistance [67]. Given that contact thermal resistance and particle thermal resistance directly govern the dynamic processes of heat storage and release, both are key parameters determining the heat storage and release performance of moving beds.

Figure 3 illustrates the thermal resistance characteristics of plate shell and tube shell moving beds. During the process where particles flow along the plate, the driving force arises from the temperature difference between the constant wall temperature in the mainstream zone and the inlet particle temperature. In this process, the local penetration resistance ($h_{\mathrm{P}\mathrm{T}\mathrm{R}}$) is given by Equation (1) [68]. The value of $h_{\mathrm{P}\mathrm{T}\mathrm{R}}$ is determined by the equivalent heat capacity (${\rho }_{\mathrm{s},\mathrm{b}}{c}_{\mathrm{p}}$) and effective thermal conductivity ($k_{\mathrm{e}\mathrm{f}\mathrm{f}}$) of a hypothetical homogeneous porous medium, and is significantly regulated by the residence time ($\tau$) of particles near the wall.

$$h_{\mathrm{P}\mathrm{T}\mathrm{R}}=\sqrt{{\displaystyle \frac{{\rho }_{\mathrm{s},\mathrm{b}}{c}_{\mathrm{p}}{k}_{\mathrm{e}\mathrm{f}\mathrm{f}}}{\pi \tau }}}$$

(1)

In the near-wall region, convection resistance ($1/h_{\mathrm{C}\mathrm{T}\mathrm{R}}$) can be expressed by Equation (2) [68], where ${\delta }_{\mathrm{n}\mathrm{w}}$ and $k_{\mathrm{n}\mathrm{w}}$, respectively, represent the effective thermal conductivity and the thickness of the air gap. The $k_{\mathrm{n}\mathrm{w}}$ is influenced by the particle diameter, the solid-to-gas thermal conductivity ratio, the near-wall porosity, and the temperature [70,71].

$$1/h_{\mathrm{C}\mathrm{T}\mathrm{R}}={\displaystyle \frac{{\delta }_{\mathrm{n}\mathrm{w}}}{k_{\mathrm{n}\mathrm{w}}}}$$

(2)

The thermal resistance characteristics of the central flow region in particle flow around a tube resemble those of flow along a plate. However, additional thermal resistances exist in the top stagnation zone and the bottom void region. The thermal resistance in the stagnation zone is governed directly by the local particle layer thickness and the effective thermal conductivity [72]. Furthermore, the convective thermal resistance of air within the void region can be approximated using correlations for natural convection between parallel plates.

Early research adopted an oversimplified piston flow continuum model for particle-mediated heat transfer processes, with its core assumption prioritizing series near-wall thermal resistances. This simplification resulted in the direct application of static bed thermal conductivity values to flow systems, while experimental constraints introduced notable deficiencies in the methodology. Adapa et al. [73] revealed fundamental discrepancies between discrete particle behavior and continuum assumptions, which were particularly evident when channel dimensions approached characteristic particle length scales. In operational moving bed systems, critical modeling parameters such as near-wall bed density and particle contact network distributions remain experimentally unmeasurable. Fang et al. [74] conducted two-dimensional numerical simulations to advance transient operational control studies of moving particle bed heat exchangers, identifying three dominant heat transfer determinants, including particle phase velocity, flow channel geometry, and particle material thermal conductivity.

Table 3. Mathematical equations related to moving beds.

Application Situation	Heat Transfer Correlation of $\mathbf{N}\mathbf{u}$	Definition and Scope of Application
Vertical channel	$0.0214\left({\mathrm{R}\mathrm{e}}^{0.8}-100\right){\mathrm{P}\mathrm{r}}^{0.4}\left[{1+\left({\displaystyle \frac{\mathrm{d}}{\mathrm{L}}}\right)}^{{\displaystyle \frac{2}{3}}}\right]{\left({\displaystyle \frac{{\mathrm{T}}_{\mathrm{m}}}{{\mathrm{T}}_{\mathrm{W}}}}\right)}^{0.48}$ [75]
Straight channel with offset rectangular fins	$0.1034{\mathrm{R}\mathrm{e}}^{0.7054}{\mathrm{P}\mathrm{r}}^{0.3489}$ [76]	$2700<\mathrm{R}\mathrm{e}<\mathrm{38,000}$ $0.8<\mathrm{P}\mathrm{r}<25$
Straight passage with offset airfoil	$0.0601{\mathrm{R}\mathrm{e}}^{0.7326}{\mathrm{P}\mathrm{r}}^{0.3453}$ [76]
Circular pipe staggered arrangement	$1.08954\mathrm{P}{\mathrm{e}}^{0.27650}{\left({\mathrm{D}}_{\mathrm{h}}/\mathrm{D}\right)}^{-0.60522}{\left({\mathrm{D}}_{\mathrm{V}}/\mathrm{D}\right)}^{0.31477}$ [77]	$\mathrm{P}\mathrm{e}={\mathsf{\rho }}_{\mathrm{s}}{\mathrm{c}}_{\mathrm{s}}{\mathrm{u}}_{\mathrm{s}}\mathrm{D}/{\mathrm{k}}_{\mathrm{s}}$ $31.328\le \mathrm{P}\mathrm{e}\le 125.312$ $\mathrm{D}\_\mathrm{h}/\mathrm{D}=1.5,2.0$ $\mathrm{D}\_\mathrm{v}/\mathrm{D}=2.0,3.0,4.0,5.0$
Circular tube alignment arrangement	$0.52290\mathrm{P}{\mathrm{e}}^{0.34654}{\left({\mathrm{D}}_{\mathrm{h}}/\mathrm{D}\right)}^{-0.44242}{\left({\mathrm{D}}_{\mathrm{V}}/\mathrm{D}\right)}^{0.16301}$ [77]
Elliptical pipe staggered arrangement	$1.14872\mathrm{P}{\mathrm{e}}^{0.34654}{\left({\mathrm{D}}_{\mathrm{h}}/\mathrm{D}\right)}^{-0.72543}{\left({\mathrm{D}}_{\mathrm{V}}/\mathrm{D}\right)}^{0.27256}$ [77]
Hexagonal pipe staggered arrangement	$1.39976\mathrm{P}{\mathrm{e}}^{0.29108}{\left({\mathrm{D}}_{\mathrm{h}}/\mathrm{D}\right)}^{-0.80822}{\left({\mathrm{D}}_{\mathrm{V}}/\mathrm{D}\right)}^{0.22398}$ [77]

summarizes the heat transfer correlations for typical flow channel configurations.

3.3. Heat Transfer Characteristics of Solid Particle Heat Storage in Fluidized Beds

In fluidized bed reactors, the characteristics of hydrodynamic resistance play a critical role in determining TES efficiency and operational reliability. The accumulation of particles within heat exchange components may lead to material clogging and uneven heat transfer, making the thorough investigation of particulate flow dynamics and fluid–particle interaction mechanisms essential. In these systems, heat transfer and pressure drop phenomena are fundamentally interconnected, with both being controlled by fluid–particle hydrodynamics. Effective heat transfer results from disruption of boundary layers caused by particles and improved thermal transport, whereas pressure drop measures the energy dissipation needed to overcome resistance from particles.

As demonstrated in [78], liquid–solid two-phase flow exhibits 16.9% to 32.0% higher pressure drops than single-phase flow, primarily caused by interparticle collisions, particle–wall contacts, and enhanced flow resistance in fluidized beds. Maximum pressure drop ratios vary dynamically with particle types and loading quantities, while increased circulation velocities effectively mitigate particle characteristic effects on pressure loss. Jiang et al. [79] identified positive correlations between pressure drop ratios and particle loading in gas–solid systems. For 0.9 mm glass beads, maximum pressure drop ratios reach 30.74%. Velocity elevation intensifies turbulence levels and particle–wall collision frequencies, consequently amplifying pressure loss magnitudes.

Further studies conducted by the Jiang research group [80] uncovered nonlinear pressure drop development patterns in circulating fluidized bed liquid–solid systems. Increasing the initial flow rate causes system pressure to rise, but exceeding critical velocity limits initiates oscillating pressure drop ratios that shift to negative values at high velocity ranges. This pressure drop reversal effect shows that introducing particles at high flow velocities can decrease total system pressure drops by reorganizing flow structures. The research additionally proves that higher circulation rates reduce pressure drop variations caused by uneven particle distributions, while greater particle settling velocities increase pressure drop fluctuation magnitudes. Current fluidized bed heat transfer correlations primarily focus on particle–wall interaction mechanisms. Zheng et al. [81] achieved the first quantitative characterization of particle distribution density effects on heat transfer by developing modified correlations through multiparameter simulations incorporating superficial gas velocity, initial phase temperature, and radiation effects. This model showed average heat transfer coefficient prediction errors below 15 percent in single and binary particle systems, while errors increased to 35 to 39 percent in multiparticle systems. Lee et al. [82] constructed state-specific wall–bed heat transfer correlations by distinguishing partially fluidized and fully fluidized states, reducing prediction errors to 5.6 percent and 3.8 percent, respectively.

Table 4. Mathematical equations related to fluidized beds.

Heat Transfer Correlation of $\mathbf{N}\mathbf{u}$	Definition and Scope of Application
$\mathrm{N}\mathrm{u}=0.01{\mathrm{R}\mathrm{e}}^{0.86}{\mathrm{P}\mathrm{e}}^{14.35}{\left({\displaystyle \frac{\mathrm{D}}{{\mathrm{d}}_{\mathrm{P}}}}\right)}^{2.76}{\left({\displaystyle \frac{{\mathrm{C}}_{\mathrm{P}\mathrm{S}}}{{\mathrm{C}}_{\mathrm{P}\mathrm{g}}}}\right)}^{-56.4}$ [81]	$3.53\le \mathrm{R}\mathrm{e}\le 28.36$ $\mathbf{12.88}\mathbf{\le }\mathbf{A}\mathbf{r}\mathbf{\le }\mathbf{22.11}$ $\mathbf{0.04}\mathbf{\le }{\mathbf{R}\mathbf{e}}_{\mathbf{P}}\mathbf{\le }\mathbf{0.63}$ $\mathrm{P}\mathrm{r}=0.7$
${\mathrm{N}\mathrm{u}}_{\mathrm{P}\mathrm{f}}=0.37{\mathrm{A}\mathrm{r}}^{0.7}{\mathrm{R}\mathrm{e}}_{\mathrm{P}}^{0.2}{\mathrm{P}\mathrm{r}}^{0.33}$ [82]
${\mathrm{N}\mathrm{u}}_{\mathrm{P}\mathrm{f},\mathrm{c}\mathrm{f}}=0.36{\mathrm{A}\mathrm{r}}^{0.69}{\left({\displaystyle \frac{{\mathsf{\rho }}_{\mathrm{s}}}{{\mathsf{\rho }}_{\mathrm{g}}}}\right)}^{0.69}{\mathrm{R}\mathrm{e}}_{\mathrm{P}}^{0.63}{\mathrm{P}\mathrm{r}}^{0.33}$ [82]	$\mathbf{12.88}\mathbf{\le }\mathbf{A}\mathbf{r}\mathbf{\le }\mathbf{22.11}$ $\mathbf{0.55}\mathbf{\le }{\mathbf{R}\mathbf{e}}_{\mathbf{P}}\mathbf{\le }\mathbf{3.29}$ $\mathbf{26.18}\mathbf{\le }{\displaystyle \frac{{\mathsf{\rho }}_{\mathbf{s}}}{{\mathsf{\rho }}_{\mathbf{g}}}}\mathbf{\le }\mathbf{92.91}$ $\mathrm{P}\mathrm{r}=0.7$

summarizes the heat transfer correlations for fluidized beds.

Industrial fluidized beds commonly face particle size nonuniformity challenges similar to those of moving bed systems. When replacing homogeneous particles with natural materials for cost reduction, nonuniformity issues intensify significantly, requiring focused research on heat transfer mechanisms between polydisperse particles and heat exchange surfaces. Current total heat transfer coefficient evaluations contain two primary uncertainty sources: unclear mechanistic relationships between particle residence time distributions and thermal performance characteristics and difficulties in predicting fluid phase flow and heat transfer behaviors during operation.

4. Advances in Solid Particle Thermal Energy Storage in Different Bed Reactors

Solid particle TES system fundamentals encompass airflow characteristics, particle motion, and heat transfer mechanisms, forming the basis for designing and optimizing thermal storage systems, including fixed beds, moving beds, and fluidized beds. This section systematically reviews optimization methods for solid particle TES systems, detailing recent optimization strategies from multiple dimensions, including flow characteristics, thermal storage performance, operational principles, and energy and exergy efficiency metrics.

4.1. Solid Particle Thermal Energy Storage of Packed Beds

The flow field distribution within packed bed reactors directly influences heat mass transfer and reaction performance, with packing structure design serving as the core control factor. Optimizing particle arrangement strategies effectively enhances the operational efficiency of packed bed thermal storage systems. Figure 4 shows several different particle packing configurations. The Van der Merwe research team [28] conducted comparative studies on gas jet co-flow dynamics in simple cubic and body-centered cubic packed beds. Utilizing 3D-printed spherical lattices and volumetric particle image velocimetry to obtain micron-level velocity field data, the results demonstrated that simple cubic structures achieved 12% to 15% higher flow uniformity than body-centered cubic arrangements under Reynolds numbers ranging from 50 to 500, while both maintained globally stable velocity distributions. Wang et al. [83] developed equivalent network models of packing structures based on Voronoi diagrams, systematically investigating flow field regulation patterns across configurations. In mono-sized particle systems, maximum flow field deviations measured 4.08%, 5.98%, and 8.43% for inline, staggered, and hexagonal packing arrangements, respectively. Disordered packing-1 and Disordered packing-2 configurations exhibited significantly enhanced flow field nonuniformity, with average deviations reaching 5.41% and 18.14%. Bidisperse hexagonal packing-2 and hexagonal packing-3 configurations reduced deviations to 4.05% and 5.33%, confirming the decisive regulatory effects of packing geometry and pore distribution on airflow patterns. Liang and Xu [84] evaluated three structural types through the parametric analysis of slender packed beds using tube-to-particle diameter ratios. Under identical inlet velocities, dense packing structures demonstrated maximum flow resistance and pressure drop. Ordered packing structures with discrete cavity channels showed pressure drop values equivalent to one-third of dense beds due to reduced flow resistance. Loose packing significantly decreased pressure drop through enhanced porosity, confirming porosity as the core regulatory parameter for packed bed hydraulic performance.

To optimize packing structures, Gui et al. [85] implemented vibration-induced particle dynamic rearrangement methods. Experimental results showed optimal comprehensive thermal performance when the vibration amplitude reached 0.25 times the particle diameter. Vibration excitation enhanced the volumetric thermal storage capacity through packing density optimization, following a nonlinear pattern characterized by rapid initial growth and subsequent stabilization. Transient and steady-state heat flux density enhancements measured 27.6 percent and 15.3 percent, respectively. Current research has shifted from packing structure optimization to systematic structural innovation. Novel packed bed designs include conical, radial flow, segmented, layered, and spray type configurations, with specific structural forms illustrated in Figure 5. The primary objective of comparative studies on packed bed designs is to reveal potential performance differences among various configurations under comparable operating conditions for identical applications. This study establishes conventional cylindrical packed beds with spherical particles as the benchmark for comparing novel packed bed TES designs, providing a basis for design selection. Key findings and conclusions from existing comparative research will be systematically summarized in the following section.

Calderon-Vasquez and Cardemil [86] conducted comparative optimization studies on four packed bed TES system configurations, including inverted conical, vertical conical, traditional cylindrical, and radial structures. Results demonstrated that radial structures achieved the optimal thermal loss and pressure drop control but exhibited the highest unit costs. Cylindrical configurations reduced unit costs by 54 percent, while both conical types outperformed cylindrical designs in thermal loss reduction and heat transfer fluid (HTF) circulation power consumption. Dual-objective optimization balancing unit cost and exergy loss identified inverted conical and radial structures as having a superior comprehensive performance.

Trevisan and Guedez [87] proposed composite multilayered thermal storage structures with radial gradient designs. Through multistage particle size gradient arrangements, the HTF sequentially flows through large-particle and small-particle zones. Experiments revealed that this nonuniform radial structure reduced pressure drops by 70 percent compared to monodisperse radial systems and by 85 percent compared to conventional cylindrical systems.

McTigue et al. [88] compared disturbance response characteristics between conventional cylindrical and segmented packed beds during charge–discharge cycles. Segmented beds demonstrated stronger disturbance resistance, with 1 to 4 percent lower pressure losses. Spray-type packed beds utilize top spray technology to form liquid HTF films through porous packing materials. Lin et al. [89] tested a 10 kW/10 kWh thermal oil/alumina spray system, achieving a round-trip thermal efficiency exceeding 90 percent, an energy efficiency of 96.06 percent, and an exergy efficiency of 54.29 percent, with under 10 percent HTF retention. This design optimized fluid distribution while significantly reducing HTF consumption.

Significant variations exist in the energy storage performance of different TES systems across practical applications, primarily influenced by system scale, design configuration, and HTF selection. For example, the quartz sand-filled cylindrical packed bed system studied by Modi et al. [90] demonstrated a high thermal capacity of approximately 33.3 ${MWh}_{th}$ when using Solar Salt molten salt; however, the heat discharge capacity decreased to about 25.8 ${MWh}_{th}$ for an equivalent system using Therminol 66 thermal oil. Eissbühler et al. [91]. experimentally and numerically investigated a circular cross-section inverted conical air–rock packed bed TES system with a storage capacity of 12 ${MWh}_{th}$, exhibiting thermal efficiencies of 77–91% and exergy efficiencies of 72–89%. The associated advanced adiabatic compressed air energy storage system achieved a round-trip electrical efficiency of 63–74%. Daschner et al. [92] conducted field tests at a pilot-scale power plant on a packed bed TES system using flue gas (charging)/air (discharging) as the HTF and featuring pebble radial flow configurations. This system achieved a maximum thermal storage capacity of 80–85 kWh, demonstrating that such radial flow systems are well-suited for operation within combined heat and power facilities. The argon–magnetite segmented packed bed system designed by McTigue and White [93] for integration with pumped TES also exhibited a high thermal storage capacity of 16 ${MWh}_{th}$. Furthermore, Türkakar’s [94] numerical simulation study explored the thermal storage potential of multilayered packed beds for solar air heating applications. The results indicated that this system could store 600 MJ of heat during a 7.5 h charging period, whereas a comparable cylindrical packed bed achieved a maximum storage capacity of approximately 450 MJ after 5.8 h of charging under identical conditions.

The structural optimization of packed beds centers on three primary objectives that involve enhancing heat transfer efficiency between HTFs and particles, suppressing thermal stratification to stabilize energy storage processes, and optimizing flow channel designs to reduce hydrodynamic resistance. Current research requires balancing thermodynamic performance with economic viability. Key technical challenges involve thermal stratification suppression mechanisms in multilayered structures, liquid retention characterization in spray beds, and scaling laws for unconventional geometries like radial flow and conical designs. The evaluation framework urgently requires standardized metrics for round-trip efficiency, exergy efficiency, and unit energy storage costs [6]. Though innovative designs increase initial costs, their operational efficiency improvements enable lifecycle cost reductions [95].

4.2. Solid Particle Thermal Energy Storage of Moving Beds

The shell plate moving bed heat exchanger enhances thermal performance by increasing solid–liquid interfacial contact area, but the continuous development of thermal boundary layers during operation reduces convective heat transfer efficiency. To address this issue, researchers proposed particle flow path optimization strategies that suppress boundary layer growth by adjusting forced particle motion trajectories, with specific optimization schemes illustrated in Figure 6.

Tian et al. [96] investigated thermal enhancement methods combining surface-engineered fin arrays with controllable vibration excitation for vertical plate heat exchangers. Their discrete element simulations revealed that particles distant from flat plates transfer heat through pin fins, while vibrational effects increase interparticle contact frequency, enhancing temperature diffusion and heat exchange efficiency. Vibrations perpendicular to particle flow direction demonstrated optimal improvement effects. The study emphasized the necessity of designing fin arrangement patterns based on particle characteristics to prevent clogging or flow separation phenomena.

Tian et al. [97] optimized thermal interfaces in shell plate moving bed heat exchangers by deploying hybrid elements on planar surfaces. Trapezoidal mixers exhibited the highest mixing rate and thermal efficiency. Near-wall regions reduced the interfacial CTR through trapezoidal obstacles, improving overall heat transfer efficiency. Characteristic velocities reached maximum values in downstream regions, disrupting thermal boundary layers and elevating particle temperatures. When flow velocity exceeded 2 mm/s, the trapezoidal configuration increased heat transfer coefficients by 9.7% compared with flat plate structures, achieving 41.5% enhancement in secondary regions. This configuration simultaneously reduced both the CTR and the permeation thermal resistance.

Yin et al. [98] established a steady-state predictive model for shell plate moving fixed beds, comparing four supercritical carbon dioxide channel fin structures. Staggered rectangular fins demonstrated optimal comprehensive heat transfer coefficients and heat flux performance, surpassing zigzag, staggered airfoil, and S-shaped fins. The optimized fin design strengthened fluid–particle thermal exchange, effectively shortening particle thermal equilibrium time and improving system efficiency.

Channel narrowing mitigates particle–wall thermal boundary layer resistance by enhancing thermal coupling through intensified particle confinement and ordered flow transitions. This geometric optimization concentrates particle flow within narrowed channels while inducing more ordered fluid flow patterns, collectively elevating heat transfer efficiency and augmenting heat transfer coefficients.

The shell tube heat exchanger utilizes annular tube units as core thermal elements, with its structure showing significant differences from planar interfaces in traditional flat shell designs. Research indicates that particle flow around horizontal tube bundles exhibits notable nonuniformity, with particle accumulation stagnation zones forming in upper regions and particle sparse cavity zones appearing below. To address this issue, geometric structure and layout optimization strategies such as adjusting tube spacing, adopting asymmetric arrangements, and implementing staggered layouts can effectively regulate particle motion trajectories, homogenize flow fields, and enhance fluid–solid interactions. These methods suppress the formation of stagnation and cavity zones, thereby improving heat exchanger efficiency and operational stability.

Ikeda’s team [99] studied particle–wall interactions during gravity-driven particle flow through circular, rhombic, hexagonal, and biaxial airfoil-shaped tubes. Rhombic and biaxial airfoil tubes reduced stagnation zones through apex angle designs, demonstrating ordered collision flow and dense packing characteristics, which significantly enhanced local heat transfer coefficients. In contrast, circular and hexagonal tubes exhibited loose packing and velocity fluctuations, leading to inferior thermal performance. Tian et al. [100] employed discrete element methods to simulate dense particle flow characteristics through circular, elliptical, and flattened elliptical tubes. Elliptical tube designs minimized stagnation and cavity zones while optimizing particle contact frequency and duration. Based on this, Tian’s team [101] developed composite elliptical tube structures that combine the thermal advantages of elliptical geometry with the fluid transport benefits of circular tubes. This hybrid design achieved superior local and global heat transfer coefficients in shell tube moving beds, particularly under higher particle outlet velocity conditions. As shown in Figure 7, when the particle outlet velocity in elliptical tubes increased from 0.5 mm/s to 8 mm/s, the local heat transfer coefficient between particles and tube walls in the third region improved by 210.0%, particle contact frequency increased by 112.3%, and the overall particle-to-wall heat transfer coefficient showed a 20.3% enhancement compared to circular tubes. The composite elliptical tubes demonstrated average improvements of 42% and 53% in particle–wall heat transfer efficiency at the tube top and bottom regions, respectively. Within the particle outlet velocity range of 4–10 mm/s, the composite elliptical tubes exhibited an average 10% increase in the particle heat transfer coefficient relative to circular tubes.

All the aforementioned heat transfer enhancement schemes for the tube/plate walls of moving beds are based on sensible heat materials. NematpourKeshteli et al. [102]. conducted a comparative study on the performance of plain tubes, corrugated tubes, and corrugated tubes with Y-shaped fins in a latent heat storage system. The study found that although the fin structure and corrugated design would inhibit natural convection to some extent, the significantly increased heat transfer area dominated the overall outcome, ultimately enhancing the system’s heat transfer performance. Therefore, for both sensible heat and latent heat storage systems, selecting fins and optimizing the tube body structure are universally applicable strategies for improving heat exchange capacity, while the material type is not the determining factor.

Substantial advancements have been achieved in tube bundle arrangement optimization. Lu et al. [103] demonstrated through comparative experiments that vertically arranged double-tube configurations fundamentally alter particulate flow dynamics relative to conventional single-tube designs. These dual tube systems promote more uniform circumferential temperature distributions while inducing characteristic particle recirculation patterns. Concurrently, Qi et al. [104] investigated horizontal tube spacing effects on solid particle flow, revealing that reduced spacing amplifies particle layer deformation and residence time fluctuations. Specifically, decreasing horizontal spacing increased flow nonuniformity by 38.1%, raised residence time standard deviation by 33.8%, and enhanced average velocity gradients by 31.4%.

Guo et al. [105] further explored the influence of tube bundle inclination angles on thermal performance. Research shows that as inclination angles increase, particle density in lower regions improves and enhances heat transfer coefficients. However, top and central regions exhibit differential behaviors, where larger inclination angles strengthen radial particle migration capacity but weaken local particle renewal efficiency. The CTR initially increases and then decreases with rising angles, while permeation thermal resistance follows an opposite trend. The study identified 15 degrees to 37.5 degrees as the optimal inclination angle range for maximizing heat transfer efficiency.

These studies collectively indicate that reconstructing forced particle trajectories through strategic motion path control effectively disrupts thermal boundary layer development. Wall region disturbance structures enable dynamic replacement of low-temperature boundary particles with high-temperature bulk particles, which serves as a key strategy for improving moving bed heat exchanger performance. This method fundamentally addresses two core issues: alleviating steep temperature gradients near wall regions and optimizing heat conduction efficiency between particles. Future research should focus on developing novel shell plate structures that integrate extended wall fins to synergistically expand heat transfer areas and regulate particle flow. Additionally, high-temperature material systems should be optimized to construct composite heat exchange architectures that combine excellent thermal stability with efficient energy transfer capabilities.

4.3. Solid Particle Thermal Energy Storage of Fluidized Beds

Fluidized bed reactors exhibit distinct technical advantages owing to their vigorous particle–fluid mixing dynamics, which amplify interphase turbulent mixing effects and maximize effective interfacial contact area [106].

Fluidized bed reactors offer distinct technological advantages derived from vigorous particle–fluid mixing dynamics, which enhance interphase turbulent mixing effects and maximize effective interfacial contact area. Ho et al. [107], employing the Analytic Hierarchy Process, evaluated and screened multiple alternatives against weighted criteria to achieve their desired objectives. This involved establishing relative importance ratios $a_{ij}$ between elements through pairwise comparisons, subject to the reciprocity constraint $a_{ij}\times a_{ji}=1$. Under conditions of perfect consistency, where the transitive relation $a_{ij}\times a_{jk}=a_{ik}$ holds, the constructed $n\times n$ matrix $a_{ij}$ yields a maximum eigenvalue ${\lambda }_{max}=n$, with all other eigenvalues being zero. In practice, inconsistency is prevalent; thus, a Consistency Index quantifies the deviation, calculated as $CI={\displaystyle \frac{{\lambda }_{max}-n}{n-1}}$, and the corresponding eigenvector, upon normalization, provides the element weights. To streamline decision-making and reduce the complexity of subjective judgments while preserving mathematical tractability, the values assigned to $a_{ij}$ are typically restricted to discrete numerical values 1, 3, 5, 7, and 9, or their reciprocals. As evidenced by the comparative analysis between fluidized beds and moving beds in

Table 5. Average scores for designs across different criteria.

	Cost	Heat Transfer Efficiency	Structural Reliability	Manufacturability	Spurious Power	Heat Loss	Expandability	Compatibility	Erosion Resistance	Corrosion Resistance
Fluidized bed	0.24	0.43	0.37	0.32	0.24	0.39	0.31	0.28	0.30	0.41
Shell-and-tube type moving bed	0.41	0.28	0.31	0.33	0.38	0.32	0.34	0.35	0.35	0.28
Plate-and-shell type moving bed	0.35	0.29	0.32	0.35	0.37	0.29	0.34	0.36	0.35	0.30

, fluidized bed systems demonstrate superior performance across multiple metrics: enhanced heat transfer coefficients, robust structural reliability, operational scalability, and simplified maintenance protocols.

Fluidized bed shell tube heat exchangers have gained attention due to their capability for noncontact heat transfer between high-temperature solid particles and secondary fluids inside tubes. Bisognin et al. [108] systematically studied parameters affecting heat transfer coefficients in gas–solid fluidized beds, identifying particle size as the dominant factor, followed by tube bundle geometric parameters, particularly tube diameter and tube spacing.

Wei et al. [109] numerically investigated heat transfer and flow characteristics of shell tube fluidized beds under different tube bundle arrangements. Results indicated that, compared to traditional inline layouts, staggered tube bundle configurations significantly enhanced heat transfer coefficients in central tube regions. Increasing the number of tube rows improved efficiency, but increasing the number of tube columns intensified bubble coalescence due to reduced intercolumn spacing, where large bubbles hindered particle–tube wall contact, thereby reducing overall thermal efficiency.

Shell tube fluidized bed heat exchangers effectively address integration challenges between particle thermal storage systems and supercritical carbon dioxide sCO₂ Brayton cycles [110], demonstrating notable advantages in thermal matching, efficiency optimization, and cost control. As shown in Figure 8, the workflow of this novel solar thermal power sCO₂ hybrid system operates as follows. High-temperature heat storage particles enter the exchanger, while sCO₂ fluidizing media are uniformly distributed through a bottom gas distributor to form ideal gas–solid fluidized states. Post heat exchange exhaust gases exit via the top outlet, and temperature-regulated sCO₂ is conveyed to downstream power cycle systems.

Gas–solid direct contact fluidized beds are a typical application of fluidized bed reactor technology. The U.S. National Renewable Energy Laboratory developed a long-term energy storage system based on particle TES [111]. As shown in Figure 9, this system adopts a direct contact continuous particle-fluidized bed heat exchanger design, effectively resolving inherent issues such as high pressure drop and high material costs in traditional fixed beds and moving beds [112]. By removing internal pipelines through direct contact architecture, the system achieves a smaller temperature approach and significant cost savings. During operation, stored particles transfer thermal energy to air working fluid via the fluidized bed heat exchanger, with heated air driving a Brayton combined cycle system. Gifford’s team [113] utilized computational fluid dynamics methods for numerical modeling and validation studies of this fluidized bed. Results showed that compared to conventional particle air heat exchangers and molten salt sCO₂ heat exchanger designs, this configuration exhibited superior performance in minimizing temperature approach and reducing pressure drop.

During heat exchanger operation, the fluidization characteristics of solid particles substantially improve heat transfer efficiency through disruption of laminar thermal boundary layers and intensification of fluid turbulence. This property enables fluidized bed systems to achieve superior heat transfer coefficients compared to conventional heat exchange devices. The dynamic particle behavior within these systems, however, creates dual effects. While enhancing thermal transfer processes, uneven particle distribution can trigger material accumulation that leads to pipeline blockage, localized overheating, and efficiency fluctuations. Research confirms that these operational defects present significant safety risks in industrial production environments [114]. Despite technical challenges, fluidized bed reactors are attracting broad attention due to their potential applications in energy fields. Current research focuses on their integration into advanced energy systems, including long-term energy storage systems, concentrated solar power plants, and industrial thermal process management.

5. Conclusions

Solid particle TES technology demonstrates significant potential in power generation and heating applications. Its exceptional heat transfer performance and cost-effectiveness have drawn substantial attention from the research community and industry. This review systematically analyzed how particle properties and reactor configurations—namely packed beds, moving beds, and fluidized beds—influence TES system performance, providing technical foundations for future research and development.

For packed bed TES systems, the absence of universal models for pressure drop and heat transfer in systems with irregular and polydisperse particles remains a key research gap. Future efforts should prioritize developing integrated models capable of predicting both flow resistance and thermal exchange characteristics under complex geometries.

For moving beds, improving particle flow uniformity is essential to maintain thermal performance. Channel structure optimization is needed to prevent stagnation zones and reduce convection and penetration resistance. Advanced modeling using discrete element methods can provide detailed insights, though computational demands remain a challenge for full-scale simulations.

For fluidized bed TES systems, reliable modeling of gas–solid interactions, especially under high-temperature and polydisperse particle conditions, is essential. Research must address phenomena such as bubble dynamics and particle agglomeration. From an engineering standpoint, practical issues, including uneven particle distribution, tube bundle vibration, and flow blockages, must be resolved to facilitate industrial-scale deployment. For all reactor types, future research must integrate materials science innovations with advanced flow control strategies to synergistically enhance energy density, thermal cycling stability, and system lifespan.

While studies on spherical particles in TES systems are relatively advanced, research on non-spherical and irregular particles remains limited. These alternative geometries offer promising interfacial heat transfer potential but present challenges in flow uniformity and pressure drop control that require deeper investigation. Moreover, although thermophysical properties of particles are well understood, dynamic mechanical behaviors such as wear, fracture, and stress accumulation in moving or fluidized environments are still underexplored—posing risks to long-term system durability. To advance TES technology, future research must adopt a holistic approach that goes beyond evaluating thermal performance alone. Integrating particle shape, structural resilience, and reactor dynamics into multi-objective optimization frameworks will be essential. Such efforts will guide the development of cost-effective, reliable TES systems suited for industrial waste heat recovery, concentrated solar power, and power-to-heat conversion pathways, which will significantly improve the overall system efficiency and environmental sustainability.