Experimental and Numerical Study of a Laboratory-Scale Salt-Based Thermal Energy Storage (TES) System Focusing on Latent Heat

Abstract

Molten salt-based thermal energy storage (TES) systems are widely deployed for large-scale energy storage; however, they currently utilize only sensible heat, limiting their energy density and overall efficiency. The utilization of latent heat in molten salts has the potential to significantly increase the extractable energy, but its practical implementation remains largely unexplored due to challenges related to solidification control, thermal stresses, and structural integrity. Addressing this gap is essential for improving the performance and economic viability of TES systems in renewable energy applications. This work presents the first combined experimental and numerical study demonstrating the controlled utilization of latent heat in a molten salt TES system at laboratory scale. A vertical shell-and-tube heat exchanger integrated into a salt tank was investigated experimentally, enabling controlled melting and solidification of solar salt under realistic operating conditions. High-resolution spatial and temporal measurements of temperature and heat flux were used to establish detailed energy balances and characterize the thermal response during phase change. In addition, a three-dimensional CFD model was developed and validated against the measured temperature histories to predict the corresponding crystallization behaviour and support system optimization and scale-up. The combined experimental–numerical analysis provides new insights into molten salt solidification. While the thermal response was validated experimentally, the spatial distribution and temporal evolution of the solid phase were inferred from the validated CFD simulations. It is shown that complete solidification can increase the thermal energy yield by approximately 10%. However, a configuration-specific recommended operating limit is identified at approximately 60% solidification, corresponding to an energy storage capacity of approximately 1300 kJ/kg (normalized to the mass of solar salt) over a temperature range from above 550 °C down to 200 °C. Beyond this point, heat transfer is significantly reduced due to the formation of insulating solid layers. These findings demonstrate the technical feasibility of controlled latent heat utilization in the investigated molten salt TES configuration and provide new insight into the mechanisms governing frozen-layer growth and discharge performance under high-temperature operating conditions.

1. Introduction

Thermal energy storage (TES) is an essential technology for balancing fluctuating renewable-energy generation and energy demand. Global energy demand increased by 2.2% in 2025, surpassing the average growth rate over the past decade [1], which emphasizes the urgent need for clean, reliable, and dispatchable energy. This poses a significant challenge of our time: supplying the world with clean and stable energy [2]. However, the unpredictable nature of renewable energy, including wind and solar, poses inherent challenges to the stability of the power grid [3]. To address this, thermal energy storage (TES) systems provide a promising solution by decoupling energy generation from consumption [4], enabling flexible load management [5], and allowing electricity to be converted into heat and back at times of high demand [6]. Other energy-storage and conversion technologies, including electrochemical batteries and fuel cells, complement TES by providing rapid electrical response and efficient energy conversion. Their performance is strongly influenced by thermal management and internal transport processes, as recently demonstrated for liquid-cooled power batteries and proton exchange membrane fuel cells [7,8]. Molten salt is among the most established storage media for high-temperature TES applications. Molten salt-based TES systems are among the most mature and widely deployed technologies for large-scale energy storage [9]. Their high operating temperatures, typically exceeding 500 °C and, in advanced systems, targeting temperatures of up to 800 °C [10], favourable thermophysical properties, and proven integration in concentrated solar power (CSP) plants [11] make them suitable for industrial-scale applications [12]. At such temperature levels, stored thermal energy can be directly utilized for applications such as saturated steam generation or feedwater preheating, significantly enhancing overall system efficiency [13]. Historically, these systems have focused primarily on sensible heat storage, which involves storing energy through temperature changes in the molten salt without inducing a phase change. Conventional molten salt TES systems primarily employ sensible heat storage, in which energy is stored through a change in salt temperature without a phase transition. Sensible heat storage is well understood, robust, and easy to implement using established heat exchanger designs, such as shell-and-tube and U-tube configurations [14]. This approach offers predictable operation, manageable pressure drops, and well-characterized thermal performance, which has contributed to the successful deployment of molten salt TES in several commercial CSP plants and industrial settings [15]. Combining molten salt TES with power-to-heat energy storage systems provides fast and flexible load control [16], significantly outperforming conventional coal-fired power plants [17]. Despite the widespread use of sensible heat systems, their energy density is inherently limited, and the full potential of the storage medium is not realized [18]. Latent heat storage uses the solid–liquid phase transition of a phase change material (PCM) to increase the extractable thermal energy. PCMs can store and release substantial amounts of energy over a narrow temperature range [19], increase the extractable thermal energy [20], improve system efficiency [21], reduce temperature swings [22], and enhance operational flexibility and environmental sustainability [23]. By exploiting latent heat, existing storage volumes can store more energy without enlarging the system footprint [24], and thermal management can be optimized to align with grid or process requirements [25]. These benefits of molten salt PCMs are particularly attractive for industrial applications where space, energy efficiency, low costs, and fast load control are critical [26]. The thermal performance of a latent heat storage system depends not only on the latent heat of the PCM but also on the heat-exchanger geometry and the progression of melting and solidification. Recent developments include compact heat exchanger concepts based on pillow-plate heat exchangers, finned structures, and optimized internal geometries, where the overall storage performance is likewise governed by the interaction between heat exchanger topology, phase-change progression, and internal heat transfer [27]. In particular, recent analytical and CFD investigations of pillow-plate latent heat storage systems demonstrated that melting and solidification performance is controlled by the evolution of thermal resistance within the PCM, emphasizing the importance of exchanger-controlled heat transfer rather than solely the latent heat capacity of the storage material. These studies highlight that identifying the governing heat-transfer mechanisms is equally important as maximizing latent heat storage capacity. However, conventional PCM materials such as paraffins or polymers are typically limited to low and moderate temperature ranges, rendering them unsuitable for high-temperature applications above 500 °C [28]. In contrast, molten salts uniquely enable latent heat storage at these elevated temperatures, making them highly attractive for industrial-scale TES systems [29]. Despite this potential, the active utilization of latent heat in molten salt systems remains largely unexplored in practical applications. Salt crystallization and solidification remain major challenges for the practical use of latent heat in high-temperature molten salt systems. Most studies either circumvent the solidification process experimentally [30] or avoid it in numerical models due to concerns over structural integrity, thermal stress, and controllability. Consequently, hybrid TES concepts combining sensible and latent heat remain largely conceptual or limited to small-scale laboratory experiments [31]. In addition, key engineering aspects such as pressure drop, manufacturability, and cost implications are often neglected, limiting the feasibility of latent heat TES for real-world deployment. This indicates that although latent heat storage is promising, more research is needed to create solutions for large-scale energy storage systems [32]. Computational fluid dynamics provides access to phase-change quantities that cannot readily be measured inside opaque high-temperature storage systems. The enthalpy–porosity method can predict liquid-fraction evolution, natural-convection decay, and frozen-layer development, while experiments provide the temperature and heat-transfer measurements required for thermal validation. Recent research on other complex thermo-fluid applications explored non-intrusive reduced-order modelling to reproduce spatially and temporally resolved flow behaviour at lower computational cost [33]. Although such approaches demonstrate the increasing importance of efficient data-driven numerical methods, high-fidelity three-dimensional CFD remains necessary in the present study to resolve the strongly coupled heat-transfer and phase-change mechanisms in the molten salt domain. Because liquid fraction and frozen-layer thickness cannot be measured directly in the present test rig, these quantities must be interpreted as CFD-based predictions supported indirectly by experimental thermal validation. Against this background, the present study combines laboratory-scale experiments with a three-dimensional CFD model to investigate the controlled utilization of sensible and latent heat in solar salt. Addressing these gaps, this study presents a combined experimental and numerical investigation of a molten salt TES system designed to actively utilize latent heat under practical operating conditions (≥550 °C). The system is based on a laboratory-scale vertical U-tube shell-and-tube heat exchanger, reflecting designs already implemented in CSP plants [34]. This design ensures low pressure drop, high robustness, and straightforward manufacturability [35]. The selected geometry was chosen to reflect industrially relevant design principles and operating conditions. This enables investigation of latent heat utilization under conditions that are substantially closer to industrial practice than those typically reported in laboratory-scale studies. Solar salt is used as the storage medium surrounding the heat transfer tubes, while air flows inside the tubes to enable controlled charging and discharging, allowing both sensible and latent heat to be harvested in an operationally relevant manner. A key objective of this work is to quantify the additional energy that can be extracted per cycle through latent heat utilization compared to purely sensible heat operation. The experimental campaign represents the first documented attempt to melt and solidify molten salt in a laboratory-scale test rig, combining electrical and compressed air heating. Comprehensive measurements of temperature distributions and heat fluxes were conducted under diverse and realistic boundary conditions, and precise energy balances were established. To investigate spatially resolved phase change phenomena beyond the capability of direct experimental diagnostics, a high-fidelity three-dimensional CFD model was developed to predict the solidification process. The model was extensively validated against the experimentally measured thermal response over a wide range of operating conditions and provides physically consistent predictions of crystallization behaviour and frozen-layer evolution. This combined experimental–numerical approach enables investigation of the governing mechanisms controlling latent heat utilization and supports the identification of configuration-specific operating conditions that balance heat transfer performance and latent heat recovery. These results demonstrate that latent heat in molten salt TES systems can be partially exploited, providing several practical engineering advantages: higher energy yield from existing storage volumes [36], improved operational flexibility [37], and better alignment with energy demand profiles. This work bridges the gap between theoretical concepts and deployable engineering solutions. By demonstrating controlled latent heat utilization in a laboratory-scale molten salt TES system, validated by high-fidelity CFD simulations, the study offers a pathway to increase energy density, efficiency, and operational flexibility of existing and future storage systems, demonstrating the feasibility of practical latent heat utilization in real-world applications. It should be noted that the methodology developed in this work, particularly the reconstruction of the liquid fraction evolution from temperature measurements and the associated validation strategy, was developed and validated specifically for solar salt under the investigated operating conditions. Solar salt exhibits only a relatively small density difference between the liquid and solid phases, which limits volumetric changes during phase transition. Consequently, the quantitative findings and the demonstrated accuracy of the proposed methodology cannot be directly generalized to phase change materials exhibiting substantially larger density variations, different phase transition characteristics, or significantly different operating conditions. Extension of the methodology to such systems would require dedicated validation and assessment of density-related effects.

2. Materials and Methods

The materials used and the design of the laboratory-scale test rig are briefly explained.

2.1. Materials

Solar salt, a mixture of 60 wt% sodium nitrate (NaNO₃) and 40 wt% potassium nitrate (KNO₃), is a widely utilized thermal storage medium in concentrated solar power (CSP) systems. Its efficacy is attributed to its favourable thermophysical properties, such as low melting point, high heat capacity, and thermal stability. While it is a prevalent choice, its performance is constrained at temperatures exceeding 600 °C due to thermal degradation [38]. This salt is also inexpensive and readily available [21]. The low melting point of 222 °C makes it easy to work at the phase change point and gain experience with latent heat and salt crystallization [39]. The solar salt used was prepared in-house, and its melting point was measured experimentally. When lower temperature levels are desired, a switch to different salts [40,41] is also feasible. In instances where reduced melting points are desired, the incorporation of pure salts has been demonstrated to result in a substantial reduction in melting points without compromising the energy storage capacity [42]. Adding nanoparticles could potentially further increase the heat storage capacity [43], thermal conductivity [44] and performance [45]. Previous research confirms that choosing the right material is essential for components in contact with liquid salt. Earlier studies have shown that Ni-alloys with at least 15% chromium are most effective in solar salt applications [46]. Therefore, the salt tank was constructed using the nickel-based Alloy 600 (NiCr15Fe; 2.4816). After more than 200 thermal load cycles and roughly 2400 h of operation, no signs of material degradation were observed. The phase change temperature was repeatedly measured (at least 150 times) and remained constant, indicating stable thermophysical properties of the salt. In addition, the experimental discharge curves were found to be highly reproducible, confirming the absence of performance degradation of the salt over time. No indications of corrosion or thermo-mechanical fatigue were detected in the storage tank. These results demonstrate the suitability of solar salt as a stable and reliable phase change material under the investigated operating conditions. Long-term corrosion behaviour, thermo-mechanical stresses, fatigue resistance, and alternative construction materials must be evaluated before the system can be transferred to larger-scale or industrial applications. It is also possible to build the salt tank from less alloyed steel, which can lower costs [47]. Alloy 600 was chosen as a reliable material for all types of salts [48].

2.2. System Description and Test Rig Design

As shown in the test rig flow diagram in Figure 1, the test rig consists of the core element (salt tank; inner dimensions: 400 mm × Ø82.7 mm) in which the salt is melted and heated using a heating element. The salt tank was filled with a total of 2009 g of solar salt. Compressed air is used as the heat transfer medium on the test rig to simulate steam or supercritical CO₂ for industrial applications [49]. The test rig is constructed in the form of a vertical U-tube shell and tube heat exchanger, featuring a single U-tube (341 mm height; 50 mm pipe spacing). This design has been proven on an industrial scale [50] and performs slightly better than coil types [51]. A vertical alignment was chosen for practical reasons; it is easier to refill the salt tank, and the salt tank can be reopened using the flange. In the heat exchanger, the compressed air is contained within the pipe, while the salt is located around the pipe. A total length of 270 mm air pipe covers the salt; the rest of the pipe is in the gas chamber. The upscaling of the experimental data is also favourable with a U-tube heat exchanger [52]. The U-tube was designed to achieve high Reynolds numbers in the turbulence range of Re > 10,000 on the air side. Previous work has investigated low Reynolds numbers, where the arrangement of salt and air is reversed [53]. Shell and tube heat exchangers are the most cost-effective design in concentrated solar power applications [54]. The test rig is connected to the institute’s compressed air line on the air side, with a maximum available air pressure of 8 bar absolute. To determine the flow rate and pressure in the air line, a volume flow sensor and a pressure sensor were installed in the cold air line before the tube furnace. The cold compressed air flows through a tube furnace, which can regulate the air to any desired temperature (with a maximum temperature of the tube furnace of 1200 °C). The (tempered) compressed air flows into the U-tube heat exchanger, whereby energy in the form of heat is transferred from the salt to the compressed air during the extraction of thermal energy. Thermal loading can also work in reverse, transferring energy from the compressed air to the salt. At the outlet of the U-tube heat exchanger, a temperature-resistant valve is located, allowing the back pressure to be adjusted to achieve a maximum absolute pressure of 8 bar absolute in the U-pipe heat exchanger. A pressure sensor monitors the gas pressure in the gas chamber above the salt. Suppose a specified gas pressure or a specified salt temperature in the system is exceeded. In that case, the heating element automatically switches off, ensuring operational safety, and a pressure relief valve can evacuate the gas chamber in the event of an emergency. When designing the test rig, the heating surfaces were dimensioned following the VDI Heat Atlas [55]. The true-to-scale structure of the salt tank, including the measurement points, is shown in Figure 2. A thermocouple is located at the inlet and outlet of the U-tube heat exchanger to measure the air temperatures (T_in and T_out). Twenty additional thermocouples measure the salt temperatures radially and axially within the salt tank (T_i,salt). The green lines represent the thermocouples, which measure the temperature at the inner shell of the salt tank. The blue lines represent the thermocouples that measure the salt temperature at the very inside of the salt tank. The salt temperatures are measured by placing a thermocouple in a welded-on cladding tube to ensure the imperviousness of the salt tank. Two thermocouples (yellow) are located directly above the U-tube in a welded-on cladding tube to determine the temperature in the gas chamber above the salt level. The heating element (red) is located within a casing tube that is welded to the salt tank. Above the heating element there is a welded-on cylinder, which is connected to the gas chamber above the salt. This design avoids the formation of high-pressure zones or liquid salt pockets during melting by ensuring the liquid salt can always flow upward into the gas chamber. The air pipes are installed from below, as only in this construction can the flange be disassembled again when cold (due to frozen salt). This design is also advantageous for crystallization. Suppose thermal energy is extracted by compressed air through the U-tube; the highest temperature gradient will be at the bottom of the U-tube (inlet and outlet), as the warm salt circulates upward due to natural convection. Especially, the inlet section will have the highest temperature gradients; therefore, the salt crystallizes from the bottom to the top, and no areas of high pressure can develop during crystallization. A dotted orange line indicates the liquid salt level; the filling level changes minimally during operation due to the thermal expansion of the solar salt. The filling level of the liquid salt is approximately 1 cm below the flange sealing. All data is recorded using LabVIEW.

Figure 1. Test rig flow diagram.

Figure 2. Salt tank with measurement points and liquid salt filling level in 2 cross sections.

3. Experimental

The stationary tests provide the heat losses and the boundary conditions for subsequent numerical CFD investigations. The transient experiments provide insight into the system’s performance, with a focus on the phase change of the solar salt.

3.1. Stationary Testing

The salt tank was insulated in three layers to reduce heat loss to an acceptable minimum, as shown in Figure 3. In the first layer, the central cylinder was roughly sheathed. In the following two layers, the insulating material was also wrapped around the flange. The fully insulated cylinder was operated either with the heating element or with hot compressed air until a stationary operating state was reached, allowing for the measurement of heat losses. The maximum salt temperature of T = 560 °C was never exceeded because of the thermal stability of the solar salt [56]. The heat loss in stationary operation using hot air was calculated via Equation (1), where ${\dot{Q}}_{\mathit{air}}$ is the heat loss, ${\dot{m}}_{\mathit{air}}$ is the mass flow of air, T_in and T_out are the air temperatures, measured at the inlet and outlet, and c_p is the heat capacity of air at the median temperature.

$${\dot{Q}}_{\mathit{air}} = {\dot{m}}_{\mathit{air}}·{\left.c_p\right|}_{T_{\mathit{in}}}^{T_{\mathit{out}}}·(T_{\mathit{out}} - T_{\mathit{in}})$$

(1)

Figure 3. Thermal insulation of salt tank; 1 layer—(left), 3 layers (right)—of thermal insulation.

The heat loss in stationary operation using the heating element was measured using the data recorded in LabVIEW. Several stationary tests were conducted within the relevant salt temperature range of 220 °C to above 550 °C. When the salt tank temperature is optimized, annual costs of an extensive system can be significantly reduced [57]. During the stationary tests, an infrared camera and many thermocouples were used to determine the maximum wall temperature of the insulation. With the now-known values of the salt temperature, wall temperature, heat flux, and geometry, the heat losses were calculated with high accuracy. The thermal conductivity of the entire storage tank was now determined using the known values of heat flux, temperature, and geometry. It was assumed that the salt tank was a cylinder. The heat loss of a cylindrical system is calculated using Equation (2), where ${\dot{Q}}_{\mathit{loss}}$ denotes the heat loss, L represents the height of the cylinder, and k is the thermal conductivity of the insulation material. As illustrated in Figure 2, R_i corresponds to the radius of the outer wall of the salt tank (i.e., the metallic shell), while R_a denotes the outer radius of the thermal insulation. The temperature T_hull refers to the temperature of the metallic shell at radius R_i, which is assumed to be equal to the salt temperature at this location. In contrast, T_insulation represents the temperature at the outer boundary of the insulation, measured at radius R_a. If the formula is converted to the desired value of thermal conductivity, the result is Equation (3).

$${\dot{Q}}_{\mathit{loss}} = {\displaystyle \frac{2·\pi ·L·k·\left(T_{\mathit{hull}} - T_{\mathit{insulation}}\right)}{\ln \left(\frac{R_a}{R_i}\right)}}$$

(2)

$$k = {\displaystyle \frac{{\dot{Q}}_{\mathit{loss}}·\ln \left(\frac{R_a}{R_i}\right)}{2·\pi ·L·\left(T_{\mathit{hull}} - T_{\mathit{insulation}}\right)}}$$

(3)

The values determined for the thermal conductivity of the entire salt tank, as a function of the salt temperature, will be used as boundary conditions for the CFD model to recreate the heat losses and are also relevant in Section 3.3 Energy Balance. The results of the thermal conductivity over the hull temperature (assuming the salt temperature equals the metal hull temperature) are shown in Figure 4. All data necessary for creating the figure are included in the Supplementary Materials in Table S1 “Measurement data of stationary heat loss experiments”. Stationary experiments were conducted in either compressed air mode (blue dots) or with the heating element in operation (red squares). The standard deviation of the stationary tests with air is slightly higher (4–5% of the measured value) than the standard deviation of the tests with the heating element (2–3%). This can be explained by the greater number of measurement readings in the air tests than in those with the heating element. In the stationary tests with the heating element, there are only two measurement variables, namely voltage and current. In the tests with compressed air, there are four measurement variables: pressure, volume flow, and the inlet and outlet air temperatures of the U-tube. The values of the thermal conductivity of the entire salt tank were also compared with the manufacturer’s values for the thermal conductivity of the insulating fleece (green triangles). It can be seen that the thermal conductivity of the whole system is approximately 3 times higher than the manufacturer’s values. This corresponds well with the experience of other systems, where compression on the insulation has been observed [58,59,60,61]. As the insulation is often compressed during installation, its insulating capacity decreases [62]. In practice, the insulation is built up in several layers [63]. The insulation structure always creates compacted regions and small air spaces [64]. This can be counteracted in practice by increasing the insulation thickness [65], as shown in Figure 3. Three layers of thermal insulation were applied here, resulting in a total insulation thickness of approximately 17 cm. In an industrial setting, optimising insulation thickness and electric heating can reduce power loss by an additional 10% and operating costs by 15%, further reducing heat loss [66]. Recent studies of ORC-based Carnot batteries demonstrate that storage temperature and heat-exchange losses substantially influence overall system efficiency [67].

Figure 4. Thermal conductivity of the insulation of the salt tank as a function of the salt temperature under steady-state operating conditions.

3.2. Transient Testing (Storage Tests)

The primary objective of the transient experiments was to characterize the thermal response associated with salt solidification and to identify the conditions governing the evolution of the solid salt layer during discharge. To this end, the storage tank was instrumented with 20 thermocouples distributed throughout the salt domain, enabling spatially and temporally resolved monitoring of the phase-change process. The salt tank was thermally charged using an internal heating element until the salt reached an average temperature of approximately 550 °C. The heating element was then switched off and compressed air was introduced into the U-tube heat exchanger, initiating the thermal discharge process. During discharge, heat extraction progressively cooled the molten salt until crystallization occurred and a solid salt layer developed around the heat exchanger surfaces. The experiments were continued until near-complete, or complete solidification was achieved, corresponding to average salt temperatures below approximately 220 °C. Figure 5 summarizes the measured thermal response during a representative discharge experiment. The transient inlet and outlet air temperatures shown in Figure 5a provide information on the heat extraction process, while the heat flux presented in Figure 5b quantifies the thermal power transferred from the storage medium (salt) to the air stream. A steady decrease in the heat flux over time can be observed when the storage tank is discharged, as the temperature spread from salt to air becomes increasingly smaller throughout the experiment. The heat flux per tube area is plotted on the right-hand ordinate. This is calculated by dividing the heat flux in watts by the outer surface area of the U-pipe covered by salt, which amounts to 0.0348 m². The order of magnitude of the heat flux density is in agreement with previous results from molten salt storage systems [68]. More importantly, the temperature measurements within the salt domain shown in Figure 5c provide direct experimental evidence of the phase-change process. As the salt approaches its crystallization temperature, characteristic temperature plateaus and reduced temperature gradients are observed, indicating latent heat release and the progressive formation of a solid salt layer. These thermal signatures form the experimental basis for interpreting the crystallization behaviour and for validating the corresponding CFD analysis. The temperature measurements provide detailed information on the thermal evolution within the instrumented region of the salt domain (T_i,salt—Figure 2). Due to geometrical constraints of the flange in the experimental setup, no thermocouples could be installed in the uppermost liquid region of the storage tank. Consequently, the local thermal conditions and potential crystallization behaviour in this region cannot be observed directly. Additional support for the predictive capability of the CFD model in this region is provided in the Supplementary Materials (Figure S20—Transient gas temperature—above the salt domain), where the transient gas temperatures above the salt domain are compared with the corresponding experimental measurements. The excellent agreement between the CFD and experimental results demonstrates that the model accurately captures the thermal response in the upper part of the storage tank, thereby providing increased confidence in the predicted temperature field and the inferred crystallization behaviour in this otherwise inaccessible region. The corresponding solidification patterns are therefore inferred from the validated CFD model and should be interpreted as model-based predictions supported by experimentally measured thermal response data. The standard deviation of the experimental data across all transient tests can be derived from Section 3.1, Stationary testing (σ_Air = 4–5%). The heat flux of air in the U-pipe, calculated using Equation (1), and the heat flux density are shown for several experiments in Figure 6a. The lines are sorted in descending order by inlet air temperature. The inlet air temperature depicted in the diagram pertains to the temperature attained after approximately 30 min. The mass flow rate of the air was 0.0052 kg/s in all experiments shown in Figure 6, with a maximum back pressure of 8 bar absolute, corresponding to the minimum air mass flow. The blue line with an air inlet temperature of 230 °C was specified as a reference. In this reference case, the temperature did not fall below the freezing point of the salt; only the sensible heat of the heat storage was transferred to the air. The inlet temperature specified in the legend represents the constant temperature set after the approximately 30 min run-in phase, as shown in Figure 5. The thermal energy quantity shown in the legend represents the thermal energy of the air. This is calculated by integrating the heat flow over time, as shown in Equation (4), where ${\dot{m}}_{\mathit{air}}$ is the mass flow of air in the U-pipe, c_p is the heat capacity of air at the median temperature, and T_in and T_out are the inlet and outlet air temperatures of the U-pipe heat exchanger. The absolute value is applied to ensure the thermal energy during discharge is positive. The integration was performed using the trapezoidal method, with a time step of 1 s. The transient salt temperature at the end of the experiment is plotted in the graph near the end of each curve (Sensor T₅).

$$E_{\mathit{air}} = \left|\int {\dot{Q}}_{\mathit{air}}\mathit{dt}\right| = \left|\int {\dot{m}}_{\mathit{air}}·{\left.c_p\right|}_{T_{\mathit{in}}}^{T_{\mathit{out}}}·\left(T_{\mathit{out}} - T_{\mathit{in}}\right)\mathit{dt}\right|$$

(4)

Figure 5. Measurement data of transient heat storage experiments.

Figure 6. Thermal discharging process with constant air mass flow of 0.0052 kg/s and variable inlet air temperature.

If the air mass flow remains constant in the experiments and the inlet temperature varies, this has no significant effect on the heat flow. When the phase change occurs (around 45 min), no decrease in heat flux is observed. This can be attributed to the release of latent heat. The measured values of the transient salt temperature for sensor T₅ are shown in Figure 6b. The average salt temperature is the arithmetic mean of the 20 temperature sensors that determine the axial and radial salt temperatures, Equation (5). The transient salt temperature drops relatively steadily until around the 45 min mark, after which the gradient decreases. This is due to the start of the crystallization process. The release of latent heat in the salt creates a “plateau” in the salt temperature around the 60 min mark. After the salt has crystallized and the latent heat has been released, the salt temperature drops again more rapidly. For comparison with the blue reference curve (no salt crystallization), this plateau is missing; no latent heat was released in this specific experiment. A hysteresis of the transient salt temperature is included in the Supplementary Materials (Figure S1—transient salt temperature from measurement data—heating hysteresis) to provide a better understanding of the test procedure and the salt temperature during the experiment. The temperature difference over the test duration is illustrated in Figure 6c. In the experiments, the temperature difference always refers to the average temperature difference between the air and the salt. The mean air temperature was calculated as the mean value of the inlet and outlet temperature, Equation (6). The temperature difference is then calculated from the average values of salt and air temperature, Equation (7), and is shown on the ordinate. With this temperature difference related to the mean temperature values of air and salt, it is easy to estimate how much of a temperature rise the air experiences during the experiment. When the crystallization temperature of the salt is reached, a plateau or a slight increase in the temperature difference is observed, especially in the experiments with lower inlet air temperature. This is because the transient salt temperature changes only slightly due to crystallization and the release of latent heat in the salt. To provide a more detailed physical interpretation of the observed temperature profiles, the thermal discharge process can be divided into distinct stages governed by different heat transfer mechanisms. Initially, heat transfer is dominated by sensible cooling of the liquid salt, supported by natural convection, resulting in a continuous decrease in salt temperature and heat flux. As the salt approaches the phase-change temperature (222 °C), the onset of crystallization leads to the release of latent heat, which manifests as a characteristic temperature plateau in the salt temperature and a stabilization of the heat flux. During this phase, the balance between latent heat release and heat extraction governs the thermal response. As solidification progresses, a solid salt layer forms around the heat exchanger surfaces, suppressing convective motion and shifting the dominant heat transfer mechanism toward conduction. This mechanism becomes dominant once the frozen salt layer reaches a thickness of approximately 3–4 mm, as predicted by the CFD model, resulting in a progressive reduction in heat flux during continued heat extraction. The influence of operating conditions is evident from the variation in inlet temperature and air mass flow rate (Figure 6 and Figure 7). While the timing and intensity of the individual stages vary, the underlying thermal behaviour remains consistent across all investigated cases, confirming the robustness of the observed phase-change dynamics under different thermal and pneumatic conditions. Additional transient experimental data beyond the manuscript are provided in the Supplementary Materials (Figure S21—thermal discharge process of all experiments beyond the manuscript, and Table S4—parameters of additional transient experimental cases). To explicitly highlight the utilization of latent heat in the thermal discharge process, the experimental procedure was designed to allow the salt to fully solidify, or reach near-solidification. As the salt reaches its phase-change temperature (≈222 °C), the onset of crystallization leads to the release of latent heat, which is directly transferred to the air stream. This manifests as a characteristic plateau in the salt temperature and a stabilization of the heat flux, effectively prolonging and sustaining the energy output beyond what is achievable through sensible heat alone. By controlling the inlet air temperature and mass flow rate, it is possible to regulate the rate of latent heat extraction and optimize the balance between heat flux and total energy yield. The cumulative energy release over time for cases with and without phase change is presented in the Supplementary Materials (Figure S7—Integral of air heat flux vs. stored energy in TES), providing a clear quantitative illustration of the latent heat contribution to the overall energy storage and discharge behaviour.

$$T_{\mathit{air}-\mathit{avg}} = {\displaystyle \frac{T_{\mathit{in}} + T_{\mathit{out}}}{2}}$$

(5)

$$T_{\mathit{salt}-\mathit{avg}}(t) = {\displaystyle \frac{1}{20}}{\displaystyle \sum _{i=1}^{20}}{T}_{i,\mathit{salt}}(t)$$

(6)

ΔT = T_salt−avg − T_air−avg

(7)

Figure 7. Thermal discharging process with variable air mass flow and constant inlet air temperature of 85 °C.

Figure 7 illustrates the same scenario as in Figure 6, except that the air mass flow is variable and the inlet air temperature is held constant. The tube furnace was switched off during the experiments in Figure 7. The air was, nevertheless, slightly preheated, as the pipe sections had heated up before entering the salt tank due to heat conduction. The air inlet temperature for all experiments in Figure 7 was 85 °C. The curves are sorted in ascending order by air mass flow. The calculated pressure drop is 3800 Pa for the maximum air mass flow rate of 0.0091 kg/s and 1500 Pa for the minimum air mass flow rate of 0.0052 kg/s. The pressure drop was calculated over the entire flow path, including the inlet section, the vertical U-tube heat exchanger, and the outlet section, corresponding to a total flow length of approximately 1.1 m. Figure 7a shows the heat transfer rate and heat flux of the air over time. Due to the higher mass flow rates, significantly higher heat flow peaks are achieved. The peak heat transfer rate at maximum (5 min) air flow of 1260 W at 0.0091 kg/s is also almost twice as high as the peak heat transfer rate at minimum air flow of 680 W at 0.0052 kg/s. The extraction time is correspondingly shorter due to the low inlet temperature and high air flow rates. The maximum heat flux (green line, approximately 5 min) is 35,000 Wm⁻² and corresponds well with other experimental research [69]. After 30 min, the heat transfer rate decreases to approx. 550 W (15,000 Wm⁻²). At 60 min, corresponding to the onset of crystallisation around the tubes, it further declines to approximately 300 W (9000 Wm⁻²). After 90 min, when crystallisation around the U-tubes is well underway, the heat transfer rate is reduced to about 200 W (5500 Wm⁻²). The transient salt temperature of the experiments (Sensor T₅) is shown in Figure 7b. The phase change occurs at all curves, and the characteristic “crystallization plateau” of the salt temperature begins at an transient salt temperature of approximately 250 °C. In experiments with higher mass flow, crystallization begins approximately 25 min after the start (green curve). In the experiments with lower mass flow (blue curve), crystallization begins only after approximately 60 min. The heat flow decreases the most during the crystallization process in experiments with the highest mass flow. This can be explained by a salt layer forming around the U-tube, which restricts heat transfer from the salt to the air. At the beginning of crystallization, when the solid salt layer around the U-tube is just forming, heat transfer is hardly restricted. However, as this solid salt layer continues to grow, convection ceases, and heat can only be transferred by pure conduction. In this case, the salt layer surrounding the U-tube acts as thermal insulation, reducing the achievable heat flow. Suppose the aim is to operate with the highest possible heat flows. In that case, it is important to understand the crystallization process in detail and identify an optimal condition that maximizes latent heat yield while simultaneously maximizing heat flow. The experimental results indicate that the discharge behaviour is governed by the evolution of the solid salt layer surrounding the U-tubes. At the onset of crystallization, latent heat release maintains high heat transfer rates despite the decreasing salt temperature. As the evolution of the solid salt layer progresses, the growing frozen layer increasingly restricts heat transfer by suppressing natural convection and introducing an additional conductive thermal resistance between the remaining liquid salt and the heat transfer surface. Consequently, system performance is not primarily determined by the total amount of latent heat available, but by the evolution of the solid salt layer and its associated increase in conductive thermal resistance during discharge. The measured thermal response therefore provides indirect information on the evolution of the solid salt layer and the progression of crystallization. Combined with the validated CFD simulations, these measurements enable detailed investigation of the evolution of the solid salt layer and support the identification of configuration-specific operating conditions that maximize latent heat utilization while limiting the formation of excessively thick insulating salt layers. The temperature difference in the experiments with variable air mass flow is illustrated in Figure 7c. Due to the lower inlet temperature resulting from the inactive tube furnace, slightly higher temperature differences between the salt and air can be observed. The plateau, which occurs when the salt reaches its phase change, is recognizable in all these experiments after approximately 30–60 min. The analysis concludes that the highest heat fluxes and the largest temperature spread ΔT are achieved at maximum air mass flow and minimum inlet air temperature. This was to be expected, as the heat transfer value is strongly dependent on the flow velocity and temperature spread. Parameters such as charging and discharging rates, as well as transient temperature profiles, are key considerations in the design of salt-based phase change material (PCM) storage systems [70]. The thermal energy quantity of the storage tank when it is completely discharged and the latent heat is used is more than 3000 kJ. However, some of this heat is available at a very low temperature level. At an average salt temperature of 200 °C, a temperature spread from salt to fluid of approximately ΔT = 100 °C can be achieved (Figure 7c). On an industrial scale, it is not valuable to have fluid temperatures at a lower level. Therefore, the amount of energy in the storage tank up to this salt temperature is of interest. The thermal energy stored in the tank, transferred to the compressed air, is approximately 2600 kJ when the average salt temperature ranges from 550 °C to 200 °C. The amount of energy was calculated using Equation (1). When considering the salt quantity of 2009 g of solar salt, the thermal energy, related to salt mass, is calculated according to Equation (8). The thermal energy associated with salt mass in the temperature range from 550 °C to 200 °C is approximately 1300 kJ/kg (normalized by the mass of solar salt), assuming the latent heat is utilized. This value is consistent with the existing literature in terms of magnitude for molten salt thermal energy storage systems [71]. A detailed propagation of the experimental measurement uncertainties is provided in the Supplementary Materials in Section S17. For a representative temperature decrease of approximately 350 K, the temperature-measurement contribution to the expanded uncertainty of the sensible energy is approximately 0.7%; uncertainties associated with the heat capacities, latent heat, and CFD-predicted solidification level are treated separately as material-property and model uncertainties. At the configuration-specific recommended operating point, the calculated latent-energy benefit is (6.00 ± 0.04) percentage points as an expanded experimental measurement uncertainty (k = 2), corresponding to an interval of approximately 5.96–6.04%. This interval includes the propagated temperature- and salt-mass-measurement contributions entering the storage-side energy ratio but excludes the separately considered uncertainties in the heat capacities, latent heat based on the literature, and CFD-predicted solidification level; varying the assumed latent heat from 161 to 110 kJ kg⁻¹ reduces the calculated benefit from approximately 6% to approximately 4%.

$$e = E/m_{\mathit{salt}}\left[{\displaystyle \frac{\mathrm{kJ}}{\mathrm{kg}}}\right]$$

(8)

The experimental campaign covers a range of operating conditions to ensure the robustness of the thermal storage system under transient operation. In addition to a reference case with no salt crystallization, constant inlet temperature and constant air mass flow, experiments with varying inlet temperatures as well as varying mass flow rates were conducted. These variations allow for the assessment of the system behaviour under different thermal and pneumatic driving conditions, which are representative of typical waste heat recovery scenarios. The results show that, despite significant changes in inlet temperature and mass flow rate, the characteristic phase-change behaviour, including the latent heat-induced temperature plateau and the associated modification of the heat flux evolution, remains consistently observable. This confirms that the observed thermal response is not limited to a single operating point but persists across a relevant range of operating conditions, covering both thermal-dominated and flow-dominated regimes. With the gathered experimental data, an energy balance was conducted to better understand the proportion of heat in the storage tank that comes from the salt.

3.3. Energy Balance

The thermal energy extracted from the storage tank by the heat-transfer fluid was determined using Equation (4). The energy balance relates the energy transferred to the airflow and the heat released to the surroundings to the decrease in the stored energy of the salt and the salt-contacting metallic components, as expressed by Equation (9). The heat losses were evaluated transiently using the experimentally determined heat-loss correlation described in Section 3.1. At each time step, the representative storage temperature was calculated as the instantaneous spatial average of the 20 simultaneously measured thermocouple temperatures according to Equation (6). The instantaneous heat-loss rate was then integrated over the complete discharge period. Therefore, the term “average salt temperature” used in the following refers to a time-dependent spatial average, (T_salt−avg(t)), and not to a single temperature averaged over the entire experiment. The same instantaneous spatially averaged temperature was used to estimate the sensible energy released by the approximately 12.5 kg of metallic components in direct thermal contact with the solar salt. Thermocouples T1–T20 are installed in metallic protective sheaths distributed throughout the salt domain and are therefore thermally coupled to the salt-contacting metal at 20 different positions. Their spatial average provides an experimentally based approximation of the mean transient temperature of the included metallic components. External structural components not represented by these measurements were excluded from the metal-energy contribution. This treatment constitutes a lumped-capacitance approximation because the complete spatial temperature distribution within all salt-contacting metallic components could not be measured directly. However, the approximation is supported by the direct salt–metal contact, the higher thermal conductivity of Alloy 600 relative to solar salt, and the distributed transient temperature measurements. The heat-capacity values were evaluated at the mean temperature of the respective material over the considered temperature interval. The latent heat of fusion of salt is well-established in the literature, amounting to 161 kJ/kg [72]. It should be noted that different values are reported in the literature (e.g., around 100–110 kJ/kg), depending on the exact salt composition and measurement approach. In this study, the value provided by SQM was used, as it is considered most representative for the solar salt employed in the experiments. The average salt temperature was used as the reference temperature to calculate the thermal energy in the metal. The heat capacity values correspond to the median temperature of the respective material. Figure 8 shows a bar chart comparing the thermal energy quantities for several experiments. All data in the diagram is provided in the Supplementary Materials in Table S2—Measurement data of transient experiments—Energy balance. The blue bars represent the thermal energy of the air, minus the heat losses through the insulation, i.e., the left-hand side of Equation (9). The stacked bars indicate the thermal energy stored in the storage tank. They are composed of the thermal energy in the salt (orange), the thermal energy in the metal (yellow), and the latent heat of the salt (purple), i.e., the right-hand side of Equation (9). The bars are arranged by air mass flow on the x-axis. The different heights of the bars result from different operating parameters, such as test duration and temperature difference. Listed on top of each bar is the average salt temperature at the end of the experiment. The average salt temperatures range from above 550 °C to a minimum of 97 °C (at 0.009 kg/s). It can be concluded that only about half of the thermal energy in the storage tank comes from the salt (E_salt = 52%). In contrast, the remaining portion originates from the metal (E_metal = 48%). Even in larger thermal energy storage systems, substantial amounts of the sensible energy is provided by the shell [73]. To quantify the contribution of latent heat to the overall energy storage capacity of the system, an additional evaluation of the energy components was performed based on the results shown in Figure 8. In particular, the ratio of latent heat to the total stored energy was determined. The analysis shows that the latent heat accounted for up to approximately 11% of the calculated total TES energy under the investigated conditions. This result indicates that latent-heat utilization can provide an additional, although parameter-dependent, contribution to the recoverable energy of the investigated storage configuration. Consequently, the inclusion of latent heat provides a measurable increase in the overall storage capacity, demonstrating the benefit of the phase change material within the investigated configuration. Reducing the latent heat from 161 to 110 kJ/kg decreased the calculated total TES energy by approximately 3–4%, depending on the investigated operating case. The additional energy recovery associated with approximately 60% solidification decreased from approximately 6% to approximately 4%. For the investigated configuration, approximately 60% solidification corresponds to an additional energy recovery of approximately 6%, a CFD-predicted frozen-layer thickness of 3–4 mm, and a 70–80% reduction in heat-transfer rate relative to the start of the experiment, depending on the operating conditions. For conditions approaching complete solidification, the calculated energy-yield increase decreased from approximately 10% to approximately 7%. Similarly, the maximum latent-heat contribution to the total TES energy decreased from approximately 11% to approximately 8%. These results demonstrate that the magnitude of the reported benefit depends directly on the assumed latent heat. Nevertheless, the sensitivity assessment does not change the qualitative conclusion that partial crystallization provides additional recoverable energy relative to purely sensible operation under the investigated conditions. A detailed breakdown of the individual energy contributions and the corresponding ratio of latent heat to total stored energy is provided in the Supplementary Materials (Table S2—Measurement data of transient experiments—Energy balance), enabling a quantitative assessment of the impact of phase change on the storage capacity. The test rig consists of 2009 g of solar salt and approximately 12.5 kg of metal, which yields a salt-to-metal ratio of 0.161. These results show that the ratio of salt to metal is a decisive design parameter in the construction of thermal energy storage units. On a larger scale, the salt-to-metal ratio should be reversed from this small design, leading to a higher proportion of E_salt. The temperature of the complete metallic structure was not measured directly; therefore, using the spatially averaged salt temperature for the approximately 12.5 kg of metal represents a lumped-capacitance approximation. Possible spatial and transient temperature differences between the salt and the metal introduce uncertainty into the calculated sensible-metal contribution and, consequently, the quantitative partitioning of the total TES energy. In the calculation of thermal energy, it was assumed that all the salt had crystallized, meaning that all the latent heat of the salt had been utilized. The CFD analysis indicates that small pockets of molten salt may remain within the salt domain at the end of some experiments, corresponding to a residual liquid fraction of approximately 2%. Since latent heat accounts for a maximum of approximately 11% of the total TES energy, the influence of these remaining liquid regions on the overall energy balance is less than approximately 0.3% and can therefore be considered negligible. The CFD analysis was used to predict when and where phase change occurs and to quantify the temporal evolution of the liquid fraction within the salt domain. Additionally, the conservation of energy within the CFD model was verified by comparing the temporal change in total enthalpy in the computational domain with the net heat transfer (air + losses). A detailed comparison between the CFD-based energy content of the air domain and the experimentally derived total energy balance is provided in the Supplementary Materials (Figure S6—Thermal energy comparison between experiment and CFD), showing excellent agreement with a deviation of only +0.9%.

$$\begin{array}{l}\int {\dot{m}}_{\mathit{air}}·{\left.c_{p\mathit{air}}\right|}_{T_{\mathit{in}}}^{T_{\mathit{out}}}·\left(T_{\mathit{out}}-T_{\mathit{in}}\right)\mathit{dt} + \int {\dot{Q}}_{\mathit{loss}}\left({T_{\mathit{salt}}}_{\mathit{avg}}\left(t\right),T_{\mathit{amb}}(t)\right)\mathit{dt}\\ =m_{\mathit{salt}}·{\left.c_{p\mathit{salt}}\right|}_{T_{\mathit{end}}}^{550°\mathrm{C}}·\Delta T_{\mathit{salt}} + E_{\mathit{latent}\mathit{heat}\mathit{salt}} + m_{\mathit{metal}}·{\left.c_{p\mathit{metal}}\right|}_{T_{\mathit{end}}}^{550°\mathrm{C}}·\Delta T_{\mathit{salt}}\end{array}$$

(9)

Figure 8. Energy balance of experimental data—air vs. TES (salt + metal + latent heat).

4. Numerical Study of Salt Phase Change

This chapter presents the CAD geometry of the salt tank, the resulting mesh for the simulation, and the results of the 3-D transient CFD simulations, including a comparison with the measured data. The primary focus of this study was the salt phase change, particularly crystallization. The melting process is not illustrated in this study due to space constraints.

4.1. Geometry and Model Structure

The construction of the numerical domain was performed using the academic software package ANSYS Design Modeler (version 2024 R2). The geometry was simplified; no radii, weld seams, or the like were considered. The geometry consists only of cylinders, truncated cones, or similar simple geometric shapes. The construction consists of five domains: salt (orange), metal (Alloy 600, green), compressed air (blue), a gas space above the salt (grey), and a separating layer between the salt and gas domains (red), as shown in Figure 9. The salt volume in the numerical model is constant, which slightly contradicts the physical reality on the test bench, as the salt expands as the temperature rises. A fill level at a 400 °C salt temperature was selected for the CFD model. The U-tube that separates the compressed air from the salt does not have a continuous radius, as the bending radius could not be realized in practice, so the U-tube was welded together in cylinder segments. The casing tube, located in the middle of the salt cylinder, has a cylinder welded to its end. This was provided for practical reasons to ensure a constant thermal connection between the salt domain and the gas chamber. This is beneficial during melting because it enables the hot liquid salt to ascend to the top, and this design can help decrease thermal stresses. The compressed air domain is located within a cylinder in the U-tube; the inlet is positioned at the bottom left, and the outlet is located at the bottom right corner (indicated by blue arrows). The separation layer between the salt and gas domains was necessary for solver convergence; direct contact between the salt and gas led to problems in Fluent. The geometry is not rotationally symmetrical, but it can be mirrored around the center axis in both the plane of the U-tube and the plane of the thermocouples. The metal shell and thermal insulation of the salt tank were not designed to limit the total number of cells. Both the metal shell and thermal insulation were simulated in Fluent with a 2-layer shell conduction model.

Figure 9. CAD geometry of the experimental setup.

4.2. Meshing

ANSYS Mesher^® (version 2024 R2) was used to generate the mesh. The default size of the elements was 2 mm with a growth rate of 1.2. A total of 5 inflation layers were inserted in the compressed air domain to determine suitable y+ values (y+ = 10–20). The maximum skewness is less than 0.8, indicating good mesh quality. The final mesh comprises approximately 1.6 million cells, as illustrated in Figure 10, which shows a sectional view of the mesh. The mesh consists mainly of tetrahedra, and approximately 89% of the total elements are tetrahedra. The rest consists of 4% Hexahedra, 6% Wedges, and 1% Pyramids. The Alloy 600 U-tube has a thickness of approximately 2.6 mm and consists of two elements in depth. The Interface has a thickness of 1 mm and consists of one element in depth. The high number of tetrahedra is visible in the gas and salt domains. A grid independence study was conducted using 3, 10, and 30 million cells, respectively. The grid-independence study showed deviations of less than 1% in the key parameters, including transient outlet temperature, heat flux, spatially resolved salt temperature, and liquid-fraction evolution, between the investigated meshes. Therefore, the final mesh was considered sufficiently grid-independent. The initially generated mesh contained approximately 3 million predominantly tetrahedral cells. Before performing the transient CFD simulations, the tetrahedral mesh was converted into a polyhedral mesh using the corresponding mesh-conversion functionality in ANSYS Fluent. This conversion reduced the total number of computational cells to approximately 1.6 million while preserving the spatial resolution of the original mesh. Therefore, the 3-million-cell mesh used in the grid-independence study and the final 1.6-million-cell polyhedral mesh represent the same spatial discretization before and after polyhedral conversion, respectively.

Figure 10. Final mesh in 2 sectional views.

4.3. Physical Model and Boundary Conditions

A three-dimensional solver that considers the conservation of energy, mass, and momentum equations in a transient case was implemented using a Realizable k-ε-turbulence model with enhanced wall treatment in the air domain. The salt domain was set to the Laminar turbulence model. The Solidification & Melting Tool was also activated to model the phase change of the salt. An enthalpy-porosity method [74] is employed in FLUENT to model the solidification and melting processes. The enthalpy-porosity method is well-established for developing numerical models of phase change materials. With this approach, the melt interface is not tracked explicitly. Each cell in the domain is assigned a value known as liquid fraction β, which represents the part of the cell volume that is liquid. The liquid fraction is calculated at each iteration based on an enthalpy balance. The mushy zone is an area where the liquid fraction varies from 0 to 1. It is modeled as a “pseudoporous” medium in which porosity decreases from 1 to 0 as the material solidifies. When a cell’s material is fully solidified, the porosity drops to zero, and the velocities also reduce to zero. The enthalpy of the phase change material is computed as the sum of the sensible heat (h_sensible) and the latent heat (h_latent), according to Equation (10) [75]:

H = h_sensible + h_latent

(10)

The sensible heat of the material is defined by Equation (11);

$$h = h_{\mathit{ref}} + {\int }_{T_{\mathit{ref}}}^T{c}_p\mathit{dT}$$

(11)

where h_ref is the reference enthalpy and c_p is the specific heat at constant pressure. When the temperature of a cell is below the solidus temperature, the liquid fraction β is equal to 0. If the temperature is above the liquidus state, the liquid fraction β equals 1. For a material undergoing phase change over a finite temperature interval, the liquid fraction is commonly defined by Equation (12).

$$\beta = \left\{\begin{array}{ccc}0,& T \le T_{\mathit{solidus}},& \\ {\displaystyle \frac{T - T_{\mathit{solidus}}}{T_{\mathit{liquidus}} - T_{\mathit{solidus}}}},& T_{\mathit{solidus}} < T < T_{\mathit{liquidus}},& T_{\mathit{liquidus}} > T_{\mathit{solidus}}\\ 1,& T \ge T_{\mathit{liquidus}},& \end{array}\right.$$

(12)

This expression applies only when a finite phase-change interval is specified. In the present simulations, both temperatures were set to the nominal melting temperature of solar salt, (T_solidus = T_liquidus = T_melt = 222 °C), corresponding to an idealized isothermal phase transition. For this sharp-transition case, the intermediate linear expression is not evaluated directly. Instead, the enthalpy–porosity implementation in ANSYS Fluent incorporates the latent heat into the enthalpy solution at the melting temperature and determines the local phase state iteratively. Accordingly, the isothermal model represents a limiting sharp-transition formulation rather than a zero-width substitution into the finite-interval equation.

The latent heat content can now be written using the latent heat of the material, L. The latent heat, expressed in Equation (13), can vary between 0 (solid) and L (liquid). For solar salt, L is 161 kJ/kg. When identical solidus and liquidus temperatures are specified, Fluent treats the phase transition as isothermal. In this limiting case, no finite temperature-based mushy interval is defined. Instead, latent heat is incorporated through the enthalpy balance at the phase-change temperature, and the liquid fraction is updated iteratively as the latent enthalpy is released or absorbed.

h_latent = β·L

(13)

For problems involving solidification and melting, the energy equation in the solver can be written as Equation (13), where H is the enthalpy of the phase change material (Equation (10)), ρ is the density, $\overrightarrow{v}$ is the fluid velocity, T is the temperature, and S is the source term.

$${\displaystyle \frac{\mathit{\partial }}{\mathit{\partial }t}}\left(\rho H\right) + \nabla ·\left(\rho \overrightarrow{v}H\right) = \nabla ·\left(k\nabla T\right) + S$$

(14)

The solution for temperature is fundamentally a reiteration of the energy equation (Equation (14)) and the liquid fraction equation (Equation (13)). As the material transitions from a solid to a liquid state or vice versa, it becomes porous, a phenomenon known as the ‘mushy zone’. The porosity of the material depends on the liquid fraction. When the cell is fully solidified, the porosity is zero, which extinguishes velocities in these solid regions. The mushy-zone constant was set to 200,000. The corresponding momentum sink progressively suppresses the velocity as the liquid fraction decreases and reduces the velocity to approximately zero in fully solidified regions. The selected value provided the closest agreement with the experimentally observed transient temperature evolution. The predicted liquid-fraction distribution and frozen-layer thickness should therefore be interpreted as model-dependent quantities supported by thermal validation rather than as directly measured values. The mushy-zone constant was calibrated using one reference experiment and subsequently kept fixed for all remaining validation cases. A sensitivity assessment using values of (50,000), (200,000), and (500,000) showed only minor effects on the outlet-air temperature, salt temperature at position T5, and domain-averaged liquid-fraction evolution. Further details are provided in the Supplementary Materials in Section S20 (Figure S24—Sensitivity of the CFD results to mushy zone constants). The heat losses of the salt tank to the environment were modelled using a two-layer shell conduction approach. The first layer represents the metallic structure (Alloy 600). As the numerical implementation requires constant layer thicknesses, the total mass of the metal in direct thermal contact with the salt, including additional components such as the flange, was converted into an equivalent uniform wall thickness to preserve the overall thermal mass. This resulted in an effective thickness of 9 mm for the metallic layer. The second layer represents the thermal insulation, which was modelled with a thickness of 170 mm, consistent with the experimental setup shown in Figure 3. Heat losses to the surroundings were defined using an ambient temperature of 22 °C and an external heat transfer coefficient of 5.5 W/m²K, based on the stationary experiments described in Section 3.1. At the fluid boundaries, a mass-flow-inlet condition was applied at the air inlet and a pressure-outlet condition at the outlet. The remaining external surfaces, corresponding to the outer walls of the inlet and outlet pipes, were modelled as adiabatic. This assumption is justified by the short distance between the measurement locations and the storage tank, where no significant temperature change in the air was observed experimentally. A schematic overview of all described boundary conditions is provided in the Supplementary Materials (Figure S8—boundary conditions in CFD). The material properties of air were specified as those of an ideal gas, and the database for material values of ρ, k, μ, and c_p, stored by ANSYS Fluent^®, was used. A corresponding clarification has been added to the Supplementary Materials (Section S4). The thermal energy of the air is evaluated based on the enthalpy difference between inlet and outlet mass flow rates as obtained from the CFD solution, ensuring consistency with the energy conservation equations in the fluid domain. The material properties of the solar salt, based on its phase state, were assumed as follows:

Data from the literature indicate that the density of solar salt changes only by approximately 4–5% across the solid–liquid phase transition [76]. In the present model, this discontinuous density change associated with melting and solidification was neglected. However, the density of the liquid salt remained temperature dependent according to the implemented density correlation, allowing buoyancy-driven natural convection to be resolved throughout the liquid phase. This modelling approach neglects only the volumetric expansion and contraction associated with melting and solidification, while preserving the influence of thermal expansion on the flow field. The assumption was adopted because the fixed computational mesh cannot represent moving boundaries or volume changes during phase change. For the investigated test rig, the resulting change in salt level is only a few millimetres and therefore has a negligible influence on the quantities of interest. A more detailed insight into the behavior of the TES with respect to volume expansion and contraction during thermal charging and discharging is provided in the Supplementary Materials, in the Section S3. The viscosity in the solid state is higher than 100 Pa s, but with viscosity jumps greater than 10⁵, there were problems in Fluent. Therefore, this value was chosen for the solid aggregate state of the salt. Since the thermal conductivity and specific heat of the solar salt do not change significantly over the temperature range, and to accelerate the solver’s convergence, these material values were assumed to be constant. The latent heat released by the phase change of solar salt was considered to be 161 KJ/kg. The material values used for Alloy 600 originate from the manufacturer. The property values of salt were used as the material values of the interface between salt and air. The thermophysical properties of salt can also be further enhanced when nanoparticles are added. The area for inserting the boundary condition of the heating element is in the very center of the salt tank and is shown in Figure 10. The thermal boundary condition was modeled via convection, with the heat transfer coefficient set to h = 250 (W/m²K), and the corresponding heating temperature was set to the same value as in the experiment. The modelling via convection was necessary to accurately reproduce the heat contact between the casing tube and the heating element.

4.4. Solver-Setup Transient

The transient solver of ANSYS Fluent^® was used in this study. The pressure–velocity coupling scheme was set to SIMPLE; the spatial discretization schemes were put to second-order upwind for the energy, momentum, turbulent dissipation rate, and turbulent kinetic energy equations. The pressure discretization scheme was set to PRESTO!. The convergence criterion was deactivated, and the simulation duration was adjusted to match the experiment duration. A time-step sensitivity study using time-step sizes of 2.5, 5, and 10 s is provided in Section S19 (Figure S23—Time step sensitivity study using time step sizes of 2.5, 5 and 10 s) of the Supplementary Materials. The selected time step of 5 s closely reproduced the temperature evolution and phase-change progression obtained with the finer 2.5 s reference while requiring substantially lower computational effort. The residual histories provided in Section S18 (Figure S22—Scaled residual histories of the transient CFD simulation) of the Supplementary Materials demonstrate stable convergence within the individual time steps without systematic residual accumulation or numerical divergence. Within the fixed 35 iterations per time step, the final scaled residuals typically reached orders of magnitude of 10⁻⁴–10⁻³ for continuity, 10⁻⁹ for velocity, 10⁻⁸ for energy, 10⁻⁶ for turbulent kinetic energy, and 10⁻⁵ for the turbulent dissipation rate. The temperature distribution of the salt at the end of the loading process is the starting condition for the transient thermal discharging simulations. In the thermal loading experiments, only the heating element was active. The initial salt temperature at the start of the transient simulations was set to the same value as in the corresponding experimental trials. There is almost no temperature stratification in the radial direction in the salt. In future work, the temperature stratification could be optimized using composite materials, which improve thermal conductivity [77]; however, thermal stability becomes more challenging with the addition of composites [78].

4.5. Validation

The ultimate purpose of the validation is not merely to reproduce measured temperatures but to establish confidence that the model captures the physical mechanisms governing frozen-layer growth and the associated degradation of heat-transfer performance during discharge. Particular attention was given to the onset and progression of crystallization, as these phenomena govern the evolution of the insulating solid salt layer and ultimately determine the thermal performance of the storage system. To this end, spatially resolved salt temperatures distributed throughout the storage domain were used as the primary validation metric. Additional validation quantities included transient salt temperatures, heat transfer rates, and transient gas temperatures. Figure 11 summarizes the comparison between experimentally measured and CFD-predicted temperature histories at five representative thermocouple locations (T1, T3, T5, T7, and T9), spanning the vertical extent of the storage tank. Thermocouple T1 is located in the upper region of the storage domain, whereas T9 is positioned near the bottom. The exact sensor locations of the experiment and numerical simulation are provided in Figure S2—20 temperature points CFD vs. experimental of the Supplementary Materials. Figure 11a presents results for cases of minimum and maximum air mass flow rates ($\dot{\mathrm{m}}=0.0052{\displaystyle \frac{\mathrm{kg}}{\mathrm{s}}}$ and $\dot{\mathrm{m}}=0.0091{\displaystyle \frac{\mathrm{kg}}{\mathrm{s}}}$, respectively), while Figure 11b shows the corresponding comparison for minimum and maximum inlet air temperatures at constant mass flow rate. All simulations and experiments were initialized at an identical initial average salt temperature of approximately 550 °C. The experimental datasets shown in Figure 11 correspond to the same measurement campaigns as those previously presented in Figure 6 and Figure 7. Across all cases, the results reveal a consistent stratified temperature distribution within the molten salt domain, with higher temperatures in the upper region and progressively lower temperatures toward the bottom of the salt tank. The thermocouples located near the mid-height of the domain (T3 & T5) closely follow the evolution of the volume-averaged salt temperature. A comparison of transient salt temperature and outlet air temperature between CFD and experiments is provided in Figure S9—Transient salt and air outlet temperature CFD vs. experiment—of the Supplementary Materials. As shown in Figure 11a, increasing the air mass flow rate leads to a significantly accelerated thermal discharge of the storage system. The onset of phase change at approximately 222 °C occurs at around 40 min (at sensor T9) in the high-mass-flow case, whereas it is delayed to approximately 65 min (at sensor T9) under low-mass-flow conditions. During the phase transition, a pronounced temperature plateau is observed as latent heat is released and a solid salt layer progressively forms on the heat-exchanger tube, increasing the thermal resistance. Once the local phase transition is complete, the temperature decreases further. The numerical model consistently reproduces the characteristic plateau and the overall transient thermal response under both operating conditions. However, the experimental temperature plateau is smoother and extends over a broader temperature range than its numerical counterpart, indicating that the effective crystallization behaviour of the investigated solar salt is more gradual than an ideal isothermal transition. In the CFD model, the phase change was represented by an idealized sharp-transition formulation with identical solidus and liquidus temperatures of 222 °C. This assumption facilitated a numerically stable simulation of the transient crystallization process but represents a simplification of the experimentally observed behaviour. Consequently, localized deviations between the measured and calculated temperatures occur within the phase-transition region. Moreover, although the model reproduces the measured overall thermal response, this thermal validation does not demonstrate that the predicted liquid-fraction evolution or phase-boundary position is insensitive to the selected solidus–liquidus interval. Because no sensitivity calculation using a finite phase-change interval was performed, the associated model uncertainty could not be quantified. The reported liquid-fraction evolution, frozen-layer thickness, and solidification level associated with the configuration-specific recommended operating point should therefore be interpreted as CFD-based predictions conditional on the adopted sharp-transition model. This difference explains the localized deviations observed during the onset and completion of crystallization, particularly around 40 min for the high-mass-flow case and approximately 65 min for the low-mass-flow case. Additional insight into the solidification process is provided by the liquid fraction evolution shown in Figure S10—evolution of liquid fraction for different operating conditions—of the Supplementary Materials. Since the liquid fraction cannot be measured directly in the present experimental setup, these results should be interpreted as model-based predictions derived from the validated thermal response. Nevertheless, the predicted progression of the solidification front is consistent with the experimentally observed temperature plateaus and changes in local cooling rates associated with latent heat release. This is further confirmed by the time-averaged RMSE values reported in Figure S11—RMSE between sensor positions for different operating conditions—of the Supplementary Materials, which demonstrate consistent predictive accuracy across all investigated operating conditions. After completion of phase change in the vicinity of the thermocouple locations, the temperature decreases with a significantly lower gradient compared to the liquid phase. This behaviour is primarily attributed to the substantial reduction in the effective overall heat transfer coefficient caused by the formation of a solid salt layer around the heat exchanger tubes. Once crystallization occurs, the solidified salt acts as an insulating barrier between the airflow inside the heat exchanger and the remaining molten salt domain, thereby limiting further heat transfer. In addition, the continuously decreasing temperature difference between the airflow and the salt further reduces the thermal driving force during the later stages of discharge. A detailed analytical assessment of the thermal resistance contributions and the resulting overall heat transfer coefficient is provided in Figure S12—schematic pipe section for thermal resistance analysis and Figure S13—thermal resistance analysis for a growing salt layer around the heat exchanger tube—of the Supplementary Materials. The analysis demonstrates that even thin solid salt layers rapidly dominate the overall thermal resistance of the system. In particular, the resistance fraction associated with the solidified salt layer becomes the dominant contribution already at sub-millimeter solid layer thicknesses, resulting in a pronounced reduction in the overall heat transfer coefficient. This behaviour explains the reduced thermal gradients observed experimentally after the completion of local phase change. Although the growing solid salt layer substantially increases the conductive thermal resistance, latent heat release during crystallization partially compensates for this effect during the active phase-change period. Once solidification is nearly complete, however, heat transfer is governed predominantly by conduction through the solid salt layer, leading to the observed reduction in temperature gradients. The most important outcome of the present investigation is that the thermal performance of the storage system is governed primarily by the evolution of the solid salt layer rather than by the total amount of latent heat available. The thermal resistance analysis presented in Figures S12 and S13 demonstrates that the resistance associated with the solidified salt layer rapidly becomes the dominant contribution to the overall heat-transfer resistance, even at relatively small frozen-layer thicknesses. Consequently, the transition from convection-dominated to conduction-dominated heat transfer occurs much earlier than complete solidification. This transition represents the fundamental mechanism controlling TES performance during discharge. While latent heat release initially sustains high heat-transfer rates, continued frozen-layer growth progressively suppresses natural convection and introduces an increasingly insulating conductive barrier around the heat-transfer surfaces. As a result, further latent heat utilization becomes progressively less beneficial despite additional energy remaining stored within the salt. The CFD analysis indicates that this transition occurs when the frozen salt layer reaches approximately 3–4 mm thickness, corresponding to about 60% overall solidification in the present system. Beyond this point, the increase in thermal resistance outweighs the benefits associated with additional latent heat recovery, thereby defining the practical operating limit of the investigated storage concept. Complete solidification of the storage medium is reached after approximately 150–165 min, at which point the experiments were terminated. Figure 11b compares CFD and experimental results for varying inlet air temperatures under constant air mass flow. As expected, the largest initial temperature gradients occur at the beginning of the discharge process, when the salt is at its initial temperature of approximately 550 °C. The onset of phase change occurs at approximately 70 min (at sensor T9) in both cases, with a slight shift depending on inlet temperature. Specifically, the case with lower inlet air temperature (104 °C) exhibits an earlier onset of phase change (approximately 10 min earlier) compared to the case with higher inlet temperature (146 °C), while maintaining identical mass flow conditions. Following the characteristic phase-change plateau at 222 °C, the temperature decreases again with a reduced gradient until the end of the discharge process. Additional experimental results, including the comparison of maximum and minimum gas pressure in the gas chamber above the salt domain, are provided in Figure S14—spatially resolved temperature for maximum and minimum pressure in the gas chamber above the salt domain—of the Supplementary Materials. It should be emphasized that the present validation is based on experimentally measured thermal quantities, including transient temperature distributions and heat transfer response. The spatial evolution of the crystallization field and frozen salt layer thickness cannot be measured directly with the available experimental techniques and are therefore inferred from the validated CFD model. Consequently, the predicted solidification patterns should be interpreted as model-based predictions supported by extensive thermal validation rather than directly validated quantities.

Figure 11. Spatially resolved salt temperature—Validation—Experiment vs. CFD.

The experimental validation presented in this work, including spatially resolved temperature measurements, liquid fraction evolution, RMSE analysis, for multiple operating conditions, demonstrates that the applied numerical methodology captures the dominant thermal and phase-change dynamics with good accuracy and reproducibility. Figure 12a presents the spatially resolved temperature evolution during the discharge process for different density assumptions used in the numerical model. The experimental measurements are shown in blue. The orange curves represent the CFD simulation using a density of 2192 kg/m³ for both the liquid and solid phases, corresponding to the values listed in Table 1. The yellow curves represent a CFD simulation using a constant density of 2090 kg/m³ for both the liquid and solid phases. According to data from the literature and material datasheets for solar salt, the density of the solid phase is approximately 2192 kg/m³, whereas the liquid-phase density is approximately 2090 kg/m³. These two density values were therefore selected to investigate the influence of density variation on the transient thermal behaviour of the storage system. The thermal discharge process begins at an initial salt temperature of approximately 550 °C and decreases continuously until the onset of phase change at approximately 222 °C. In the CFD simulations, crystallization starts after approximately 90 min. During phase transition, latent heat release causes a substantial reduction in the local temperature gradients, resulting in the characteristic plateau behaviour of the temperature curves. After completion of local phase change, the temperature decreases further under predominantly conduction-controlled heat transfer conditions within the solidified salt domain until the end of the experiment after approximately 225 min. Among the investigated density assumptions, the configuration using the higher density value (orange curves, Table 1) provides the closest agreement with the experimentally measured spatially resolved temperatures and was therefore selected for the numerical analysis presented in this work. The corresponding RMSE values are provided in Figure S4—time averaged temperature: absolute, difference and RMSE—of the Supplementary Materials. Overall, the comparison demonstrates that the density variation from 2090 to 2192 kg/m³ has only a minor influence on both the local temperature evolution and the overall transient discharge behaviour of the thermal energy storage system. The Supplementary Materials provides the corresponding spatially resolved temperature fields, time-averaged deviations, and RMSE values for all investigated cases. Once crystallization begins and the salt transitions into the solid state with simultaneous latent heat release (approximately 90 min), the agreement between experimental and numerical results improves significantly.

Figure 12. Air temperature at the inlet and outlet, transient salt temperature, and liquid fraction—experimental vs. CFD.

Table 1. Material properties of solar salt.

Phase State	ρ [kg/m3] [79]	cp [J/kgK] [80]	k [W/mK] [81]	μ [kg/ms] [82]
Liquid (T > 222 °C)	2192 − 0.636·T [°C]	1550	0.52	0.075439 − 0.000277·T [°C] +3.49·10−7·T2 [°C] −1.474·10−10·T3 [°C]
Solid (T ≤ 222 °C)	2192	1550	0.52	100

This behaviour is additionally influenced by the crystallization of salt around the thermocouple casing tubes, which affects the experimentally measured local temperatures. Additional sensitivity analyses investigating more pronounced density variations of up to +25%, as well as the influence of the phase-dependent density change from 2090 kg/m³ (liquid) to 2192 kg/m³ (solid), are provided in Figure S15—Influence of 25% increased salt density on TES system—of the Supplementary Materials. Figure 12b compares the transient outlet air temperatures obtained experimentally and numerically. For clarity, only the results for the ρ_max case is shown, as the differences between the ρ_max and ρ_min simulations are negligible. The results indicate that neglecting the phase-change-induced density discontinuity is appropriate for solar salt under the investigated operating conditions. However, the additional sensitivity analysis demonstrates that larger density differences may significantly affect the predicted phase-change behaviour. Consequently, the validity of the present modelling approach should be interpreted within the context of the investigated material system and should not be generalized to phase change materials exhibiting substantially larger density-induced volume changes without further validation. The inlet air temperature was imposed in the CFD model using a polynomial fit of the experimental data and therefore exhibits no deviation between simulation and experiment. The outlet air temperature agrees very well with the measurements, with maximum deviations remaining below approximately 2% of the instantaneous temperature value. The numerical model slightly overpredicts heat transfer from the salt to the airflow during the first half of the discharge process, corresponding to the liquid-state regime, while heat transfer is slightly underpredicted during the later stages after solidification. This trend is consistent with the behaviour observed for the salt temperatures and is directly reflected in the transient outlet air temperature evolution. The heat flux comparison from measurement data to ρ_max simulation results can be found in the Supplementary Materials under Figure S16—Heat flux during thermal discharge CFD vs. experiment.

The phase state of the salt is represented using the liquid fraction parameter, where a value of 1 corresponds to fully liquid salt and 0 corresponds to fully solid salt. Figure 12c presents the evolution of the domain-averaged liquid fraction for the ρ_max (orange) and ρ_min (yellow) simulations. Up to approximately 90 min, the salt domain remains fully liquid. As thermal discharge progresses, an increasing number of computational cells reach the crystallization temperature of 222 °C, initiating solidification throughout the storage domain. At the end of the experiment, nearly the entire salt domain is solidified, with only approximately 2% remaining in either liquid or partially molten state. The dotted red lines in Figure 12c represent several key points in time during the thermal discharge process, which are illustrated in Figure 13. The elements in the salt domain in Figure 13 are coloured according to their liquid fraction state, where red represents a liquid state, and orange, yellow, green, and turquoise indicate a phase change state, or a mushy zone. The CFD simulations predict that crystallization initiates in the vicinity of the air tubes, where the largest local temperature gradients exist, as shown in Figure 13a. Based on the validated thermal response, the model predicts a progressive growth of the solidification front from the heat exchanger surfaces into the surrounding salt domain. The resulting frozen-layer evolution provides a physically consistent explanation for the experimentally observed reduction in heat transfer during the later stages of discharge. A cross-section of the solid fraction shown in Figure 13a can be found in the Supplementary Materials under Figure S17—Cross sectional view of the solid fraction 127 min after start. As soon as the salt around the air pipes is completely crystallized, the crystallization front begins to spread toward the heating element, as shown in Figure 13b. If thermal discharge is continued, the solid salt also grows from the bottom to the top of the heating element’s casing tube. Now, the outer surface of the salt domain is entirely covered with solid salt; only liquid “salt pockets” remain, which change phase from bottom to top as the thermal discharge progresses, transitioning into the solid phase. At the end of the thermal discharge process, almost the entire salt domain is in a solid state, as shown in Figure 13c. The proportion of liquid melt or salt that is in the transition area between liquid and solid is in the low single-digit percentage range at the end of the experiment. A video of the crystallization process (for salt densities ρ_max and ρ_min) is available in the Supplementary Materials document. When the salt crystallizes, the heat transfer from the tube to the salt decreases significantly in the pipe areas where the salt has solidified, as shown in Figure 14. This reduction in heat flux occurs because natural convection occurs only on the outer surface of the pipe when it is in the liquid aggregate state. As soon as the salt crystallizes and adopts a solid aggregate state, a thermal insulation layer of solid salt forms around the U-tube. If this salt layer continues to grow, only pure heat conduction will occur at the U-tube. Dead zones in the flow course are a further limiting factor for heat transfer [83]. When the crystallization front reaches the casing tube of the heating element, it poses a problem in industrial operation. Suppose the casing tube of the heating element is completely enclosed by solid salt; only very low temperature gradients can be used during heating, otherwise, material fatigue and thermal stresses occur. This is audible through loud cracking noises. Flexible operation, achieved by quickly switching loads, can significantly reduce costs when favourable electricity prices are available [84]. Hybrid molten-salt thermal energy storage systems that utilize both sensible and latent heat can dramatically enhance the flexibility of a coal-fired power plant [85]. Suppose operation with solar salt is initiated at a salt temperature of 550 °C. In that case, the salt tank can be thermally discharged for approximately two to three hours (depending on the operating parameters) until the recommended operating point, approximately 60% salt crystallization, is reached (163 min after start in Figure 13b; and Figure 12c). At this point, the next thermal loading cycle should be initiated. In that case, the total usable thermal energy increases by roughly 6%, due to latent heat. If 60% of the latent heat is used, the layer of frozen salt around the U-tube is approximately 3–4 mm thick. These CFD findings refine the experimental data presented in Section 3.2. This operating duration is consistent with other experimental TES studies in which latent heat was utilised [86]. Based on the experimentally validated CFD model, the progression of the phase-change process can be predicted with sufficient accuracy to identify practical operating limits and discharge strategies [87]. The maximum increase in thermal energy output resulting from the use of the latent heat of the salt is 10%, as shown in Figure 8. The design can be optimized to increase the amount of salt that can crystallize and maximize the latent heat yield. In an optimization, the distance between the heat source (heating element) and the heat sink (air pipes) would be increased [88], as the freezing of the salt around the heating element severely restricts the operating mode, making rapid load changes impossible. The optimization could be further enhanced using existing models for phase change materials in heat exchangers [89]. Previous work has demonstrated that targeted adjustments to the geometry and operating temperature can significantly improve the performance of phase change material-based heat storage systems [90]. It is not optimal if the entire salt domain crystallizes completely, as this leads to unnecessarily long reloading times due to the low temperature gradients of the heating element. However, if thermal discharging is carried out up to the recommended operating point, approximately 60% of the latent heat of the salt can be utilized. To further illustrate the internal flow dynamics within the molten salt phase and to demonstrate the high spatial and temporal resolution achieved by the CFD model, Figure 15a presents the velocity vectors, while Figure 15b shows the corresponding contours of velocity magnitude at four characteristic time steps. Natural convection within the molten salt phase is explicitly resolved in the CFD model by incorporating gravity and temperature-dependent density, thereby enabling buoyancy-driven flow. During the early stage of thermal discharge (t = 1 min), the salt is fully liquid and convection is strongest, exhibiting pronounced circulation patterns that enhance heat transfer within the molten region, with a maximum velocity of 0.01082 m/s and a volume-averaged velocity of 0.00155 m/s. As solidification begins (t = 85 min), the liquid fraction decreases and natural convection weakens significantly (maximum velocity 0.00286 m/s, volume-averaged velocity 0.000337 m/s), reflecting the gradual suppression of convective motion. In the intermediate stage (t = 127 min, liquid fraction ≈ 0.8), convection is further reduced due to the growing solid regions and diminished temperature gradients, while at t = 163 min (liquid fraction ≈ 0.37), fluid motion is extinguished and heat transfer becomes predominantly conduction-driven. This progressive decrease in velocity magnitude clearly illustrates the transition from convection-dominated to conduction-dominated heat transfer during solidification, a key mechanism governing overall system performance. Simplified one-dimensional models generally fail to capture these effects, as phase-change heat transfer in molten salts is inherently three-dimensional and involves local processes such as the formation of insulating solid layers at heat-transfer surfaces and the decay of buoyancy-driven flow. These phenomena are fully resolved in the present CFD model. Similar conclusions have been reported for reduced-order modelling approaches, where high-fidelity CFD remains necessary to resolve local melting, solidification, and heat-transfer mechanisms in latent heat TES systems [91]. To provide a more detailed view of the flow structures, a region in the upper part of the salt domain is highlighted in Figure 15a (dashed black box) for the first three time steps, and the corresponding magnified views are presented in Figure S19, “Zoomed in view of selected velocity vector plots”, in the Supplementary Materials. The observed transition from convection-dominated to conduction-dominated heat transfer has important implications for practical applications such as waste heat recovery systems. The results suggest that high flow rates or low inlet temperatures can accelerate solid layer formation on the heat exchanger surface, reducing heat transfer performance. Therefore, an optimal operating strategy should balance heat extraction rate and phase-change progression to maximize both heat flux and latent heat utilization. Overall, the numerical predictions show good agreement with the experimental observations across all investigated operating conditions. The CFD model successfully reproduces the measured thermal response associated with thermal stratification, latent heat release, and the transition from convection-dominated to conduction-dominated heat transfer. Based on this extensive thermal validation, the model provides physically consistent predictions of crystallization dynamics and frozen-layer evolution within the storage domain.

Figure 13. Liquid fraction on relevant time steps during the crystallization process.

Figure 14. Liquid Fraction and Heat Flux 127 min after start in sectional view.

Figure 15. Flow within the molten salt phase (natural convection) during thermal discharge and salt solidification.

Remaining local discrepancies are considered acceptable for such strongly coupled transient phase-change systems and can be attributed to a combination of experimental limitations, including the finite spatial resolution of the thermocouple network, sensor encapsulation effects, and potential minor thermocouple displacements caused by thermal expansion and mechanical stresses during operation. The validation presented in this work comprises spatially resolved salt temperatures, transient salt temperatures, transient gas temperatures, heat transfer rates, RMSE analyses, and multiple operating conditions. These experimentally validated thermal quantities provide confidence that the numerical methodology captures the dominant thermo-physical processes governing solidification. The resulting liquid fraction evolution and frozen-layer development should therefore be interpreted as model-based predictions supported by extensive thermal validation rather than directly validated quantities. The additional sensitivity analyses further indicate that neglecting the phase-change-induced density discontinuity represents an appropriate simplification for solar salt and similar PCM systems exhibiting only small density differences between the liquid and solid phases. Based on the combined experimental and numerical results, the proposed frozen-layer limits and discharge recommendations are considered valid for the investigated storage configuration, the applied heat exchanger geometry, the examined operating conditions, and comparable molten-salt PCM systems. However, the results also demonstrate that the recommended frozen-layer thickness (as inferred from CFD analysis) is not a universal parameter but depends strongly on the thermophysical properties of the PCM, heat exchanger design, thermal conductivity, operating conditions, and storage scale. Consequently, systems employing different PCM materials, alternative heat exchanger configurations, or exhibiting substantially larger density variations during phase change may exhibit different recommended operating points. In such cases, more advanced numerical approaches, including moving-mesh or deformable-interface methods, may be required to accurately capture interface movement, volume contraction, thermal stresses, and scale-dependent effects. Therefore, the conclusions presented in this work should be interpreted within the context of the investigated solar salt TES system and similar storage concepts rather than as universally applicable design rules for latent heat thermal energy storage systems.

5. Conclusions

This study experimentally investigated the deliberate utilization of latent heat in a laboratory-scale solar-salt thermal energy storage system and developed a three-dimensional CFD model to analyse the associated phase-change behaviour. More than 40 transient experiments provided spatially and temporally resolved temperature and heat-transfer data for model validation. The main conclusions are as follows:

(1)

The CFD model reproduced the experimentally measured thermal response across the investigated operating conditions. For the detailed validation case, the RMSE values of the spatially resolved salt temperatures ranged from approximately 4.3 to 12.7 °C (Figure S4c). Across the additional operating conditions, the local temperature RMSE values ranged from approximately 4.0 to 25.6 °C (Figure S11a,b), with the lowest deviations observed near the center of the salt domain and higher deviations near its upper and lower boundaries. In addition, the transient outlet-air temperature showed close agreement between the experimental and numerical results, as shown in Figure S9. Based on this thermal validation, the model was used to predict the liquid-fraction evolution and frozen-layer development. Since these quantities could not be measured directly, they should be interpreted as CFD-based predictions supported indirectly by the experimental thermal measurements.

(2)

Frozen-layer growth at the heat-exchanger surface governs the practical operating limit of the investigated system. For the considered geometry and operating conditions, the CFD model predicts that a frozen-layer thickness of approximately 3–4 mm marks the onset of substantially reduced heat-transfer performance, as the increasing conductive resistance progressively limits further energy extraction.

(3)

The system achieved heat fluxes of up to 35,000 W/m² and released approximately 1300 kJ per kg of solar salt between approximately 550 °C and 200 °C. This value represents the total TES energy—including the sensible energy of the salt, the latent heat of the salt, and the sensible energy of the metallic structure—normalized by the salt mass; it should not be interpreted as the intrinsic specific storage capacity of solar salt.

(4)

A configuration-specific recommended operating limit was identified at approximately 60% solidification, corresponding to a CFD-predicted frozen-layer thickness of approximately 3–4 mm and an additional energy recovery of approximately 6% relative to purely sensible heat utilization. Depending on the operating conditions, the heat-transfer rate had decreased by approximately 70–80% relative to its initial value at this point. Further solidification could increase the additional energy recovery to a maximum of approximately 10%, but only at a progressively reduced heat-transfer rate and with longer discharge and subsequent recharge durations. Under the investigated conditions, the recommended operating limit was reached after approximately 2–3 h of discharge.

The reported liquid-fraction evolution, frozen-layer thickness, and configuration-specific recommended operating limit of approximately 60% solidification are CFD-based predictions supported indirectly by the experimental thermal validation. These predictions are specific to the investigated solar salt, storage geometry, operating conditions, and modelling assumptions and should not be interpreted as universally applicable design criteria. In particular, the CFD model assumes an isothermal phase transition at 222 °C. Since no sensitivity analysis employing a finite solidus–liquidus interval was performed, the resulting uncertainty in the predicted phase distribution and phase-boundary position could not be quantified. The reported quantities should therefore be regarded as model-dependent predictions rather than directly validated phase-distribution measurements. Further validation is also required before applying the modelling approach to phase-change materials with substantially larger density variations or different phase-transition characteristics. Within these limitations, the results indicate that latent-heat utilization in the investigated system is governed primarily by the increasing thermal resistance of the solidified salt layer rather than by the available latent heat alone.