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Citation: Prieto, C.; Blindu, A.; Cabeza, L.F.; Valverde, J.; García, G. Molten Salts Tanks Thermal Energy Storage: Aspects to Consider during Design. Energies 2024,17, 22. https://doi.org/10.3390/en17010022 Academic Editors: Jesús Polo, Jose A. Almendros-Ibanez, Minerva Díaz-Heras and Maria Fernandez-Torrijos Received: 24 October 2023 Revised: 28 November 2023 Accepted: 1 December 2023 Published: 20 December 2023 Copyright: © 2023 by the authors. Licensee MDPI, Basel, Switzerland. This article is an open access article distributed under the terms and conditions of the Creative Commons Attribution (CC BY) license (https:// creativecommons.org/licenses/by/ 4.0/). energies Article Molten Salts Tanks Thermal Energy Storage: Aspects to Consider during Design Cristina Prieto 1,2,* , Adrian Blindu 1, Luisa F. Cabeza 3,* , Juan Valverde 4,5 and Guillermo García2 1Department of Energy Engineering, Universidad de Sevilla, 41092 Sevilla, Spain; [email protected] 2Build to Zero S.L, c/Gonzalo Jiménez de Quesada, 2, 41092 Sevilla, Spain; guillermo.gar[email protected] 3GREiA Research Group, Universitat de Lleida, Pere de Cabrera s/n, 25001 Lleida, Spain 4Virtualmechanics S.L, c/Arquitectura 1, 41015 Sevilla, Spain; j.valver[email protected] 5Departamento de Matemática Aplicada 2, Universidad de Sevilla, Camino de los Descubrimientos s/n, 41092 Sevilla, Spain *Correspondence: [email protected] (C.P.); [email protected] (L.F.C.) Abstract: Concentrating solar power plants use sensible thermal energy storage, a mature technology based on molten salts, due to the high storage efficiency (up to 99%). Both parabolic trough collectors and the central receiver system for concentrating solar power technologies use molten salts tanks, either in direct storage systems or in indirect ones. But even though this is a mature technology, it still shows challenges in its implementation and operation. This paper underscores the critical importance of stringent design criteria for molten salt tanks in thermal storage technology. Focusing on the potential ramifications of design failures, the study explores various dimensions where an inadequate design can lead to severe consequences, even jeopardizing the viability of the entire technology. Key areas discussed include structural integrity, corrosion, thermal shock, thermal expansions, and others. By elucidating the multifaceted risks associated with design shortcomings, this paper aims to emphasize the necessity of thorough reviews and adherence to robust design principles for ensuring the success, safety, and sustainability of thermal storage technology. Keywords: concentrating solar power (CSP); thermal energy storage (TES); molten salt tanks; challenges; design; failures; modelling 1. Introduction The energy storage technology in molten salt tanks is a sensible thermal energy storage system (TES). This system employs what is known as solar salt, a commercially prevalent variant consisting of 40% KNO 3 and 60% NaNO 3 in its weight composition and is based on the temperature increase in the salt due to the effect of energy transfer [ 1 ]. It is a mature technology that has been widely used in concentrating solar power (CSP) plants, for which it is essential. This technology gives the CSP plants the ability to store the energy of solar radiation from the hours of sunshine and convert it into electricity when required, adapting the energy source to the electricity demand of the grid. The two-tank molten salt system is the most effective technology for heat storage in CSP applications, although it still has some drawbacks [ 2 ]. The Crescent Dunes CSP project in the United States serves as an illustrative example [ 3 ]. The molten salt tank problems in this project encompassed issues of corrosion, operational reliability, thermal stress, maintenance challenges, and potential cost impacts. These challenges underscore the importance of a rigorous design and material selection in molten salt tank systems for concentrated solar power applications. The first CSP plant with a molten salt tank TES system was the Solar Electric Generating Station I, built in 1984 in the USA and decommissioned in 1999. It had 13.8 MW of nominal capacity and 3 h storage. This plant was followed by many others, such as Andasol 1, which was commissioned in 2008 in Spain. This was the first to use this technology on a large scale, with a storage capacity of 375 MWh, almost 10 times bigger than the Solar Electric Generating Station I [ 4 ]. Energies 2024,17, 22. https://doi.org/10.3390/en17010022 https://www.mdpi.com/journal/energies
Energies 2024,17, 22 2 of 19 By the end of 2021, there was already a capacity of approximately 27,500 MWh of TES from molten salt tanks installed worldwide, and it is expected to continue to increase. The two most widespread types of CSP technologies worldwide are the parabolic trough collector (PTC) and the central receiver system (CRS) [ 5 ]. The solar field of PTC technology is based on curved concentrators with a parabolic shape, called parabolic trough collectors, which concentrate solar radiation on an absorber tube. The absorber tubes are located in the focal line of these collectors. Inside these tubes, a heat transfer fluid (HTF) flows, which collects thermal energy and transports it to the TES system and the power block [ 6 ]. On the other hand, CRS technology, also known as a solar power tower (SPT), employs a heliostat solar field (HSF). The HSF is made up of a field of sun-tracking reflectors called heliostats (flat or slightly concave mirrors) that reflect and concentrate solar radiation on a central receiver positioned at the top of a tower. In the central receiver, the heat is absorbed by the HTF, which can be stored in a TES system or sent to the power cycle. PTC technology generally operates at temperatures below 400 ◦ C, while CRS reaches temperatures up to 565 ◦ C [ 7 ]. The diagrams of CSP plants with PTC and CRS technologies are shown in Figures 1and 2, respectively. Energies 2023, 16, x FOR PEER REVIEW 2 of 20 on a large scale, with a storage capacity of 375 MWh, almost 10 times bigger than the Solar Electric Generating Station I [4]. By the end of 2021, there was already a capacity of approximately 27,500 MWh of TES from molten salt tanks installed worldwide, and it is expected to continue to increase. The two most widespread types of CSP technologies worldwide are the parabolic trough collector (PTC) and the central receiver system (CRS) [5]. The solar field of PTC technology is based on curved concentrators with a parabolic shape, called parabolic trough collectors, which concentrate solar radiation on an absorber tube. The absorber tubes are located in the focal line of these collectors. Inside these tubes, a heat transfer fluid (HTF) flows, which collects thermal energy and transports it to the TES system and the power block [6]. On the other hand, CRS technology, also known as a solar power tower (SPT), employs a heliostat solar field (HSF). The HSF is made up of a field of suntracking reflectors called heliostats (flat or slightly concave mirrors) that reflect and concentrate solar radiation on a central receiver positioned at the top of a tower. In the central receiver, the heat is absorbed by the HTF, which can be stored in a TES system or sent to the power cycle. PTC technology generally operates at temperatures below 400 °C, while CRS reaches temperatures up to 565 °C [7]. The diagrams of CSP plants with PTC and CRS technologies are shown in Figures 1 and 2, respectively. Figure 1. Diagram of a parabolic trough collector (PTC) technology CSP plant with a TES system. Figure 2. Diagram of a central receiver system (CRS) technology CSP plant with a TES system. Figure 1. Diagram of a parabolic trough collector (PTC) technology CSP plant with a TES system. Energies 2023, 16, x FOR PEER REVIEW 2 of 20 on a large scale, with a storage capacity of 375 MWh, almost 10 times bigger than the Solar Electric Generating Station I [4]. By the end of 2021, there was already a capacity of approximately 27,500 MWh of TES from molten salt tanks installed worldwide, and it is expected to continue to increase. The two most widespread types of CSP technologies worldwide are the parabolic trough collector (PTC) and the central receiver system (CRS) [5]. The solar field of PTC technology is based on curved concentrators with a parabolic shape, called parabolic trough collectors, which concentrate solar radiation on an absorber tube. The absorber tubes are located in the focal line of these collectors. Inside these tubes, a heat transfer fluid (HTF) flows, which collects thermal energy and transports it to the TES system and the power block [6]. On the other hand, CRS technology, also known as a solar power tower (SPT), employs a heliostat solar field (HSF). The HSF is made up of a field of suntracking reflectors called heliostats (flat or slightly concave mirrors) that reflect and concentrate solar radiation on a central receiver positioned at the top of a tower. In the central receiver, the heat is absorbed by the HTF, which can be stored in a TES system or sent to the power cycle. PTC technology generally operates at temperatures below 400 °C, while CRS reaches temperatures up to 565 °C [7]. The diagrams of CSP plants with PTC and CRS technologies are shown in Figures 1 and 2, respectively. Figure 1. Diagram of a parabolic trough collector (PTC) technology CSP plant with a TES system. Figure 2. Diagram of a central receiver system (CRS) technology CSP plant with a TES system. Figure 2. Diagram of a central receiver system (CRS) technology CSP plant with a TES system.
Energies 2024,17, 22 3 of 19 The contemporary state-of-the-art molten salt thermal energy storage (TES) systems involve a dual-tank configuration—a “cold” tank operating at around 290 ◦ C and a hot tank reaching temperatures of approximately 395 ◦ C or 565 ◦ C—depending on the specific technology. These tanks are designed to store molten salts, and their primary function is to retain the sensible heat within until it is needed for power generation. The process involves the circulation of molten salts (MS) between the two tanks, facilitating the charging and discharging phases in a Rankine power cycle [8]. The primary motivation for incorporating salt tanks stems from their notable storage efficiency, achieving an annual efficiency of up to 99%, as evidenced in CSP plants such as Andasol and Solar Two [ 9 ]. Losses in this system primarily result from heat dissipation through tank walls and foundations, mitigated by effective insulation, and from heat exchange between various media. In contrast to alternative thermal energy storage (TES) technologies, two-tank molten salt storage systems maintain consistent power and temperature levels throughout both the charging and discharging phases. This stands in contrast to other technologies that often experience a decline in pressure, temperature, or power during the discharge process [8]. An additional notable attribute of this system is its capacity to attain high temperatures, reaching around 565 ◦ C. This allows for the storage of substantial amounts of thermal energy within a relatively compact volume, ranging from 70 kWh/m 3 to 200 kWh/m 3 [ 10 ]. Moreover, it facilitates enhanced efficiencies in the Rankine cycle during the discharge of energy. However, it is worth noting that the commonly used salts have freezing temperatures around 220 ◦ C, necessitating supplementary heating systems to prevent salt solidification. The integrity of molten salt tanks is paramount for ensuring the feasibility and success of thermal storage technology. Several key aspects defend the importance of maintaining the integrity of these tanks: • Material Compatibility and Corrosion Resistance: Molten salts, while effective for energy storage, can be corrosive. Ensuring the tanks are constructed from materials with high corrosion resistance is critical. The integrity of these materials is essential to prevent leaks, structural damage, and contamination of the stored salts. • Structural Strength and Longevity: The structural integrity of molten salt tanks is crucial for their long-term performance. The tanks must withstand thermal stresses, expansion and contraction cycles, and potential external forces. Ensuring the tanks have the structural strength to endure these conditions is vital for their longevity and reliability. • Thermal Insulation: To minimize heat losses and optimize the efficiency of the storage system, molten salt tanks must incorporate effective thermal insulation. Maintaining the integrity of this insulation is essential for preserving the temperature differentials between the hot and cold tanks, reducing energy losses during storage and retrieval processes. • Sealing and Leak Prevention: The tanks must be meticulously sealed to prevent any potential leaks. Even minor leaks can compromise the overall efficiency of the system and pose safety concerns. Regular monitoring and maintenance are crucial to identify and address any issues related to seals or potential leakage points. • Operational Safety: A breach in the integrity of molten salt tanks can result in safety hazards. Ensuring the tanks are designed and maintained with the highest standards of safety in mind is essential for preventing accidents and ensuring the well-being of personnel involved in the operation and maintenance of the storage technology. This review is particularly emphasized with the goal of enhancing the design of molten salt tanks. Section 2delves into critical insights into the design of these tanks, offering valuable considerations to bolster their efficiency and reliability. Section 3meticulously explores failure modes in molten salt tanks, highlighting corrosion, thermal shock, and thermal expansions as pivotal aspects to be addressed for improved design resilience. In Section 4, various modeling techniques are scrutinized, providing a comprehensive understanding that can inform advanced design strategies for molten salt systems. The
Energies 2024,17, 22 4 of 19 overarching aim of this review is to contribute substantively to the enhancement of molten salt tank design practices, ultimately fostering advancements in thermal storage technology. The conclusions and remarks presented in Section 5encapsulate key takeaways for driving future improvements in tank design and overall system performance. 2. Molten Salt Tank Design The main component of the storage system is the storage tanks. The total volume of the molten salt in both storage tanks is based on the storage hours at full load and the power block design turbine thermal input capacity. The thermal capacity of these tanks represents the nominal thermal storage capacity of the system. It is calculated by multiplying the hours of storage at full power cycle load by the cycle thermal input power at the design stage. There is no single unified regulation for the mechanical design of these tanks, so all existing ones can be used. Currently, the reference point for the design of salt tanks is API 650, established by the American Petroleum Institute [ 11 ]. This design is further tailored by Appendix M in API 650, which extends requirements for tanks operating at elevated temperatures, and Appendix N in API 650, addressing the use of materials not specified in the original document [ 12 ]. Another standard used is the one indicated by ASME (American Society of Mechanical Engineers), specifically ASME II D [ 13 ] for the selection of materials and ASME VIII Div II [ 14 ] for the design of tanks. These ASME standards are commonly employed to characterize material properties based on temperature for simulation purposes. Moreover, ASME VIII Div II offers guidance for Finite Element Analysis (FEA) simulations of the thermo-mechanical components, facilitating stress and fatigue checks derived from simulation results. These standards collectively contribute to ensuring the integrity and reliability of salt storage tank designs in thermal storage systems. The lack of a clear code in the design of molten salt tanks can lead to safety, efficiency, and consistency issues in the thermal storage industry, affecting both technical feasibility and regulatory acceptance of these technologies. A clear code provides a common foundation for continuous improvement and the adoption of best practices in the design and operation of molten salt tanks. The design of molten salt tanks has traditionally favored a cylindrical shape [ 15 ]. A common feature shared by both tanks is their optimal design height, set at 14 m. This specific height is a result of a trade-off consideration: as the tank height increases, thermal losses decrease. This phenomenon stems from the fact that, at the same volume, a shorter cylindrical tank exhibits a smaller heat transfer area [ 16 ]. It is noteworthy, however, that this height is constrained to 14 m [ 17 , 18 ] due to limitations in the shaft length of the salt pumps. This limitation underscores the need to balance thermal efficiency with practical engineering constraints in the design of molten salt tanks. It is crucial to note that given the absence of a standardized design criterion, the following considerations are presented as design suggestions rather than definitive guidelines. The structural integrity of the tank must be meticulously crafted to endure its own weight, the load of molten salts, and the thermal stresses associated with elevated temperatures. A comprehensive three-dimensional thermal analysis, often modeled through Finite Element Analysis (FEA), is imperative for designing the tank structure. As of now, one of the commonly employed programs for such analyses is ANSYS FLUENT. In the design of salt tanks at high temperatures, certain considerations must be taken into account: •The thermal expansions of the tank occur depending on the operating temperature. • The temperature gradients between the different internal parts of the metallic structure of the tank. •The thermal cycling that the tank is expected to experience during its design life. • Temperature differences between the bottom of the tank and the lower part of the wall. If the thermal analysis reveals a significant difference, it may be necessary to enhance the union of the bottom with the shell, introduce a thicker annular ring, or install lower plates. These considerations are vital for ensuring the reliability and longevity of the molten salt tank in high-temperature environments.
Energies 2024,17, 22 5 of 19 • The maximum temperature difference between any two points in the tank during the filling and heating procedure. Additional Design Considerations and Material Recommendations for Molten Salt Tanks in Concentrated Solar Power Applications are: • Expansion requirement design: To accommodate the free thermal expansion of molten salt tanks during the initial heating phase, all connections to main pipes or fixed equipment are designed with expansion joints. This design feature ensures seamless transitions from ambient temperature to working temperature, preventing structural stresses. • Tank Diameter and Material Correlation: The tank diameter is intricately linked to both storage capacity and molten salt temperature. Higher storage temperatures result in a reduced tank volume requirement due to the higher energy density of molten salts. However, the maximum diameter is contingent on the tank’s construction material, determined by its operating temperature. For solar power plants utilizing PTC technology, the standard of maintaining uniformity in both material and diameter for both tanks is recommended, simplifying design, construction, and maintenance processes [ 17 ]. These tanks work with salts below 400 ◦ C and may be manufactured using ASTM A516 Gr70 carbon steel [ 16 ], capable of withstanding corrosion caused by molten salts at those temperatures. In the tower plant, the molten salt works at temperatures above 500 ◦ C; commonly used materials include AISI 347H and AISI 321H, as well as other stainless steels such as AISI 316L and AISI 304 [ 16 , 17 , 19 , 20 ]. These stainless steels offer better resistance to corrosion at higher temperatures but come with increased costs and a lower maximum tank diameter of around 40 m. • Thickness Oversizing for Corrosion Protection: The oversizing of the thickness of the tank must be designed according to the annual corrosion ratio of the material in contact with the salts at these temperatures so that this may vary from one tank to another. This thickness shall be designed to consider all years of the life cycle of the storage system. Considering a plant life cycle of 30 years and corrosion rates for the cold tank (ASTM A516 Gr. 70 at 400 ◦ C) of 0.078 mm/year [ 21 ] and for the hot tank (AISI A-347H at 600 ◦ C) of 0.0088 mm/year [ 22 ], the thickness oversizing should be minimum 2.34 mm for the cold tank and 0.264 mm for the hot tank. However, for safety reasons, the thickness oversize must be higher than the minimum. • Roof Design and Impact on Tank Integrity: The design of the tank’s roof is crucial, influencing its ability to withstand vacuum and overpressure failures. The tank’s shape is also significant, determining its maximum overpressure capacity and stress in joints. Tanks with an ellipsoidal roof welded to the shell can withstand higher overpressures and generate less stress in joints compared to spherical or flat cap designs. Increasing the elevation of the roof further enhances the tank’s ability to withstand overpressure as the radius of curvature in the cylindrical shell–roof joint increases [16]. An integral aspect that demands meticulous attention in tank design is the foundation. The foundation’s robustness becomes paramount as it bears the mechanical stress stemming from the tank’s weight. Simultaneously, it must endure the temperature fluctuations inherent in the tank’s operational life cycle. Recognizing the foundation as a critical component underscores the need for precision in its design, ensuring not only structural integrity but also longevity and resilience against the dynamic interplay of mechanical forces and varying temperatures. Additionally, the goal is to minimize thermal losses from the tank to prevent a loss of efficiency in storage. Some foundation designs face the challenge of reducing the dead volume of salts, a critical space ensuring proper submersion of pumps. To address this consideration, designs utilize truncated cone bottoms. These bottoms, with their distinctive shape, not only help optimize the dead space but also provide an efficient solution to ensure effective pump operation. In conclusion, meticulous consideration is given to the thermal elongations experienced by both the shell and the tank bottom, factoring in the intricacies of the preheating
Energies 2024,17, 22 6 of 19 phase and operational cycles. The overarching design considerations are strategically aimed at averting the generation of excessive stresses in critical areas, encompassing the bottom plates, annular rings, and tank walls. Additionally, there is a focused effort to proactively mitigate the potential risk of bottom plate buckling. The foundation, a critical aspect of this design, is meticulously crafted to bear the mechanical stress imposed by the tank weight while simultaneously enduring the temperatures encountered throughout its life cycle. Comprising multiple layers of diverse materials, the foundation configuration is illustrated in Figure 3. The following sections delineate the possible layers and the materials suitable for each, providing a comprehensive overview of the foundation composition [16]: a. A layer of fine sand just after the bottom of the tank. b. A wide layer of insulating refracting bricks or expanded clay. c. A layer of insulating material, which could be made of glass foam or ceramic fiber. d. A thick layer of reinforced concrete. This concrete is cooled by an air- or watercooling system to avoid high temperatures that compromise its structural integrity, if necessary. e. A last layer of poor concrete, between the reinforced concrete and the soil. Energies 2023, 16, x FOR PEER REVIEW 6 of 20 mechanical forces and varying temperatures. Additionally, the goal is to minimize thermal losses from the tank to prevent a loss of efficiency in storage. Some foundation designs face the challenge of reducing the dead volume of salts, a critical space ensuring proper submersion of pumps. To address this consideration, designs utilize truncated cone bottoms. These bottoms, with their distinctive shape, not only help optimize the dead space but also provide an efficient solution to ensure effective pump operation. In conclusion, meticulous consideration is given to the thermal elongations experienced by both the shell and the tank bottom, factoring in the intricacies of the preheating phase and operational cycles. The overarching design considerations are strategically aimed at averting the generation of excessive stresses in critical areas, encompassing the bottom plates, annular rings, and tank walls. Additionally, there is a focused effort to proactively mitigate the potential risk of bottom plate buckling. The foundation, a critical aspect of this design, is meticulously crafted to bear the mechanical stress imposed by the tank weight while simultaneously enduring the temperatures encountered throughout its life cycle. Comprising multiple layers of diverse materials, the foundation configuration is illustrated in Figure 3. The following sections delineate the possible layers and the materials suitable for each, providing a comprehensive overview of the foundation composition [16]: a. A layer of fine sand just after the bottom of the tank. b. A wide layer of insulating refracting bricks or expanded clay. c. A layer of insulating material, which could be made of glass foam or ceramic fiber. d. A thick layer of reinforced concrete. This concrete is cooled by an air- or water-cool- ing system to avoid high temperatures that compromise its structural integrity, if necessary. e. A last layer of poor concrete, between the reinforced concrete and the soil. To ensure the safety and reliability of the foundation, the incorporation of temperature sensors is imperative. These sensors will be strategically distributed to measure the foundation’s temperature, validating that it consistently maintains safe values. The cooling system, an integral part of this design, features horizontal tubes seamlessly embedded within the reinforced concrete structure. Typically, these tubes are interlinked with fans, facilitating the passage of ambient air to dissipate heat. In scenarios demanding enhanced heat evacuation, a water-cooling system will be implemented. This system involves pumps propelling water through the tubes, providing an effective mechanism for temperature regulation and further ensuring optimal operational conditions [16]. Figure 3. Scheme of the storage tank foundation layers. Source: [16]. Figure 3. Scheme of the storage tank foundation layers. Source: [16]. To ensure the safety and reliability of the foundation, the incorporation of temperature sensors is imperative. These sensors will be strategically distributed to measure the foundation’s temperature, validating that it consistently maintains safe values. The cooling system, an integral part of this design, features horizontal tubes seamlessly embedded within the reinforced concrete structure. Typically, these tubes are interlinked with fans, facilitating the passage of ambient air to dissipate heat. In scenarios demanding enhanced heat evacuation, a water-cooling system will be implemented. This system involves pumps propelling water through the tubes, providing an effective mechanism for temperature regulation and further ensuring optimal operational conditions [16]. To conclude the design review of the tanks, it is imperative to emphasize that for the seamless operation of molten salt tanks, meticulous attention to detail is paramount. A specific requirement involves achieving a precise degree of mixing within the tank. This becomes even more critical in the cold tank, given its proximity to the melting point. The heightened importance in this context arises from the cooling effects induced by the thermal losses of the tank, which have the potential to create thermal stratification and, consequently, cold spots. To address this operational challenge, the design mandates the incorporation of internal circulation rings or a set of ejectors within the salt tanks. These elements play a pivotal role in inducing a circulation flow and facilitating the thorough mixing of salts inside the tank [ 20 ]. Their function is essential to maintaining a homogeneous temperature profile,
Energies 2024,17, 22 7 of 19 safeguarding against undesirable thermal variations. This system is intelligently designed to activate during both normal system operation and the internal recirculation mode. For a visual representation, refer to Figure 4, which illustrates the typical configuration geometry of circulation rings in a molten salt tank. This schematic elucidates the strategic placement and function of these elements, reinforcing their integral role in promoting effective mixing and ensuring a consistently uniform temperature profile. Energies 2023, 16, x FOR PEER REVIEW 7 of 20 To conclude the design review of the tanks, it is imperative to emphasize that for the seamless operation of molten salt tanks, meticulous attention to detail is paramount. A specific requirement involves achieving a precise degree of mixing within the tank. This becomes even more critical in the cold tank, given its proximity to the melting point. The heightened importance in this context arises from the cooling effects induced by the thermal losses of the tank, which have the potential to create thermal stratification and, consequently, cold spots. To address this operational challenge, the design mandates the incorporation of internal circulation rings or a set of ejectors within the salt tanks. These elements play a pivotal role in inducing a circulation flow and facilitating the thorough mixing of salts inside the tank [20]. Their function is essential to maintaining a homogeneous temperature profile, safeguarding against undesirable thermal variations. This system is intelligently designed to activate during both normal system operation and the internal recirculation mode. For a visual representation, refer to Figure 4, which illustrates the typical configuration geometry of circulation rings in a molten salt tank. This schematic elucidates the strategic placement and function of these elements, reinforcing their integral role in promoting effective mixing and ensuring a consistently uniform temperature profile. Figure 4. Configurations geometry of the circulation rings in a molten salt tank (the plane of symmetry is represented in red). Source: [15]. 3. Common Failures in Molten Salts Tanks In recent years, some incidents with tank failures in concentrated solar power plants have appeared, resulting in huge economic losses [11]. This section analyses the main causes of failures in molten salt tanks, which are mainly due to corrosion, thermal shock, and thermal deformation. 3.1. Corrosion This paper does not aim to do a comprehensive review of this topic since further information is already available in the literature [23–30]. Corrosion is defined as the thermodynamically driven degradation of materials. Molten salt at elevated temperatures is corrosive, and its level of corrosivity increases with temperature. This is the reason why the material of the tanks will depend on the temperature at which they store the salts. Corrosion can occur in various ways, among which the most common and relevant in molten salt tanks are hot corrosion, localized corrosion, mechanically assisted corrosion, and flow-accelerated corrosion [23]. Hot corrosion is defined as “accelerated corrosion of metal surfaces that results from the combined effect of oxidation and reactions with sulfur compounds and other contaminants, such as chlorides, to form a molten salt on a metal surface that fluxes, destroys, or disrupts the normal protective oxide” [31]. There are two types of hot corrosion; on the one hand, high-temperature hot corrosion (HTHC) occurs at temperatures higher than the melting temperature of the salt. On the other hand, low-temperature hot corrosion (LTHC) refers to the damage produced at Figure 4. Configurations geometry of the circulation rings in a molten salt tank (the plane of symmetry is represented in red). Source: [15]. 3. Common Failures in Molten Salts Tanks In recent years, some incidents with tank failures in concentrated solar power plants have appeared, resulting in huge economic losses [ 11 ]. This section analyses the main causes of failures in molten salt tanks, which are mainly due to corrosion, thermal shock, and thermal deformation. 3.1. Corrosion This paper does not aim to do a comprehensive review of this topic since further information is already available in the literature [23–30]. Corrosion is defined as the thermodynamically driven degradation of materials. Molten salt at elevated temperatures is corrosive, and its level of corrosivity increases with temperature. This is the reason why the material of the tanks will depend on the temperature at which they store the salts. Corrosion can occur in various ways, among which the most common and relevant in molten salt tanks are hot corrosion, localized corrosion, mechanically assisted corrosion, and flow-accelerated corrosion [23]. Hot corrosion is defined as “accelerated corrosion of metal surfaces that results from the combined effect of oxidation and reactions with sulfur compounds and other contaminants, such as chlorides, to form a molten salt on a metal surface that fluxes, destroys, or disrupts the normal protective oxide” [31]. There are two types of hot corrosion; on the one hand, high-temperature hot corrosion (HTHC) occurs at temperatures higher than the melting temperature of the salt. On the other hand, low-temperature hot corrosion (LTHC) refers to the damage produced at temperatures below the melting point of the salt. In the tanks, since the salts are molten, the type of corrosion that concerns them is HTHC. A common characteristic of hot corrosion is the change in the rate of weight loss, which makes it possible to distinguish between an initiation stage, characterized by a rate similar to that of the absence of the deposit, and a propagation stage, during which the rate is fast [23]. Localized corrosion can be defined as the appearance of small and deep indentations, known as pitting corrosion, or the preferential degradation of metals around a confined volume of electrolyte, called crevice corrosion. For this type of localized corrosion to occur, the formation of a protective layer of corrosion products is necessary. The first phase of localized corrosion can occur immediately or after weeks or even years. The absence of pitting in short intervals does not imply that the metal is resistant to this type
Energies 2024,17, 22 8 of 19 of corrosion, and it is necessary to ensure that pitting does not occur in the long term. Once corrosion has started, a pit spreads rapidly through the interior of the metal. An alternative to stop this corrosion is by clogging the pit with insoluble corrosion products [23]. One of the most relevant forms of localized corrosion in salt tanks is intragranular attack. It is the type of corrosion most commonly found in alloys exposed to molten chlorides in oxidizing atmospheres [ 32 ]. Localized corrosion becomes even more dangerous and critical if the corroded alloy is exposed to mechanical stress, as shown in [ 33 ]. Preferential attack of grain boundaries is one of the major concerns in materials used for molten salt containment [ 34 ]. Chemical species present at grain boundaries could be more likely to be oxidized, dissolved, etc., than the chemical species present in the grains, which consequently leads to a greater depth of damage where the grain boundaries are in contact with the salt [35]. Mechanically assisted corrosion encompasses stress corrosion cracking (SCC) induced by cyclic loading and corrosion fatigue resulting from thermal cyclic behavior. The confluence of mechanical stress and corrosion reactions in this scenario leads to the perilous propagation of cracks. When selecting materials for the tank shell, it becomes imperative to account for this type of corrosion, as even materials with exceptional corrosion resistance may prove inadequate when subjected to mechanical stress. The stresses requisite for such corrosion are relatively small and typically exhibit tensile characteristics [23,36]. Flow-accelerated corrosion, also known as dynamic corrosion, depends mainly on the flow velocity. At low velocities, the depletion of cathodic reactants is avoided, and the removal of soluble corrosion products is accelerated. In contrast, at higher speeds, erosion of the protective deposits may take place, and at even higher speeds, erosion of the base material may occur. In the case of erosion, the angle of impact and the turbulence of the flow are fundamental [23]. This paper focuses on the corrosion induced by solar salt. Most studies evaluate corrosion under static conditions where corrosion samples are immersed in crucibles containing molten salts, maintained at a constant temperature, and in a controlled atmosphere. These static conditions replicate the conditions inside the tanks. Nevertheless, dynamic corrosion studies are imperative for the design of piping systems and receivers. Recent experimental investigations underscore that an elevation in flow velocity typically correlates with a substantial increase in the corrosion rate [ 29 , 37 – 39 ]. The corrosion rate depends on process and film temperature, container material, and salt’ composition. This paper summarizes the behavior of the most interesting steels for the construction of TES systems. In applications with temperatures below 400 ◦ C, the industry commonly employs carbon steel, specifically the ASTM 516 Gr. 70 alloy. Conversely, for higher-temperature applications, stainless steels such as AISI 347H, AISI 316L, AISI 321, and AISI 304 are frequently utilized. The methodologies used to analyze the corrosion rates are weight gain, weight loss, weight loss by dynamic gravimetric analysis, electrochemical polarization, and electrochemical impedance spectroscopy [ 23 ]. Table 1presents the increase in the thickness of the pipelines for the service life, which is usually 25 years. Tables 2and 3values are corrosion rates in microns per year for molten salt tank materials. Table 1. Minimum corrosion thickness of molten salts pipes tested under dynamic corrosion [29,37–39]. Alloy Temperature (◦C) Minimum Corrosion Thickness [mm] A516 Gr. 70 500 9.99 A516 Gr. 70 385 2.84 AISI 304 530 0.51 AISI 347H 560 0.42 AISI 347 560 0.41 AISI 321H 560 0.50 AISI 316L 530 0.33 AISI 316L 560 0.36
Energies 2024,17, 22 9 of 19 Table 2. Summary of corrosion data in ASTM A516 Gr. 70 for molten salt tank. Alloy Test Conditions Temperature (◦C) Exposure Time (h) Corrosion Rate (µm/year) Reference A516 Gr. 70 Solar salt 400 810 78 [21] A516 Gr. 70 Solar salt 0.5 Cl wt. % 400 811 198 [21] A516 Gr. 70 Solar salt 1.0 Cl wt. % 400 804 405 [21] A516 Gr. 70 Solar salt 450 642 299 [21] A516 Gr. 70 Solar salt 0.5 Cl wt. % 450 724 734 [21] A516 Gr. 70 Solar salt 1.0 Cl wt. % 450 602 1,531 [21] A516 Gr. 70 Solar salt 390 1500 92 [40] A516 Gr. 70 Solar Salt 0.1 Cl wt. % 390 4064 5.46 [27] A516 Gr. 70 Solar salt IC * 0.1 Cl wt. % 390 4064 3.57 [27] A516 Gr. 70 Solar salt 0.1 Cl wt. % 390 8712 2.14 [27] A516 Gr. 70 Solar salt 1.2 Cl wt. % 400 1581 210 ±7 [41] A516 Gr. 70 Solar salt 3.0 Cl wt. % 400 1581 535 ±7 [41] A516 Gr. 70 Solar salt Dynamic test 500 100 333 [37] A516 Gr. 70 Solar salt Static test 500 100 215 [37] A516 Gr. 70 Solar salt 400 2165 47.4 ±3.4 [42] A516 Gr. 70 Solar salt 0.7 Cl wt. % 400 2165 47.4 ±3.4 [42] A516 Gr. 70 Solar salt 1.8 Cl wt. % 400 1504 987.3 ±18.6 [42] A516 Gr. 70 Solar salt Dynamic test 385 1000 94.6 [43] * Intermittent conditions. Partially in contact with N2and with salts, depending on the filling level of the tank. Table 3. Summary of corrosion data in stainless steels for molten salt tank. Alloy Test Conditions Temperature (◦C) Exposure Time (h) Corrosion Rate (µm/year) Reference AISI 304 Solar salt 570 7008 17.7 [44] AISI 304 Solar salt 1.0 NaCl wt. % 570 7008 26.6 [44] AISI 304 Solar salt 1.3 NaCl wt. % 570 7008 35.5 [44] AISI 304 Solar salt TC * 565 4432 15.8 [45] AISI 304 Solar salt TC 0.82 Cl wt. % 565 4432 31.6 [45] AISI 304 Solar salt 565 4584 11.5 [45] AISI 304 Solar salt 0.82 Cl wt. % 565 4584 30.6 [45] AISI 304 Solar salt 530 1960 20 [38] AISI 304 Solar salt 530 3000 12.5 [38] AISI 304 Solar salt Dynamic test 530 1960 17 [38] AISI 347H Solar salt 600 3000 8.8 [22] AISI 347H Solar salt 600 5000 51 [46] AISI 347H Solar salt Dynamic test 560 1125 14 [39]
Energies 2024,17, 22 16 of 19 The study delves into these design aspects of molten salt tanks from a multidisciplinary perspective, including factors such as material selection, insulation, and foundation design. It also encompasses a critical aspect, which is the thermal–mechanical and computational fluid dynamics modeling and analysis of this component, validating its fatigue behavior and studying losses to maximize efficiency. The study provides a state-of-the-art overview of the various forms of corrosion to which molten salt tanks may be exposed, discussing factors such as high-temperature corrosion, localized corrosion, mechanically assisted corrosion, and flow-accelerated corrosion. Corrosion rates for different materials and salt compositions are presented, underscoring the importance of material selection. This analysis has demonstrated the complexity of modeling and simulating molten salt tank systems, presenting a state-of-the-art that encompasses both global and detailed models, as well as the use of CFD models to predict temperature distributions, heat losses, and thermal behavior in molten salt tanks. The synergy of those models empowers us to fine-tune the design and operation of molten salt tanks. This extensive modeling experience is pivotal in increasing the reliability and overall effectiveness of molten salt tank-based systems. In summary, the study provides valuable insights into existing knowledge and becomes an essential reading before addressing the design, operation, and challenges associated with molten salt tanks for thermal energy storage in the CSP sector. Author Contributions: Conceptualization, C.P. and L.F.C.; methodology, C.P. and J.V.; formal analysis, L.F.C. and G.G.; investigation, C.P. and A.B.; resources, C.P. and L.F.C.; data curation, L.F.C.; writing—original draft preparation, C.P. and A.B.; writing—review and editing, L.F.C., J.V. and G.G.; visualization, C.P.; supervision, C.P. and L.F.C.; project administration, C.P. and L.F.C.; funding acquisition, C.P. and L.F.C. All authors have read and agreed to the published version of the manuscript. Funding: This work was partially funded by the Ministerio de Ciencia e Innovación de España [(PID2021-123511OB-C31—MCIU/AEI/FEDER, UE) (TED2021-132216A-I00) (RED2022-134219-T)]. Data Availability Statement: Data are available under request to the correspondence authors. Acknowledgments: The authors at University of Lleida would like to thank the Catalan Government for the quality accreditation given to their research group GREiA (2017 SGR 1537). GREiA is a certified agent TECNIO in the category of technology developers from the Government of Catalonia. This work is partially supported by ICREA under the ICREA Academia programme. Conflicts of Interest: Author Guillermo García was employed by the Build to Zero S.L. Author Cristina Prieto was Scientific Advisor at the Build to Zero S.L. Author Juan Valverde was Scientific Advisor at Virtualmechanics S.L. The remaining authors declare that the research was conducted in the absence of any commercial or financial relationships that could be construed as a potential conflict of interest. Abbreviation CSP Concentrating solar power TES Thermal Energy Storage CRS Central Receiver System PTC Parabolic Trough Collector HTF Heat Transfer Fluid SPT Solar Power Tower HSF Heliostat Solar Field MS Molten salts FEA Finite Element Analysis HTHC High Temperature hot Corrosion LTHC Low Temperature Hot Corrosion SCC Stress Corrosion Cracking WG Weight Gain biWL Weight Loss CFD Computational Fluid Dynamics
Energies 2024,17, 22 17 of 19 References 1. Prieto, C.; Cooper, P.; Fernández, A.I.; Cabeza, L.F. Review of technology: Thermochemical energy storage for concentrated solar power plants. Renew. Sustain. Energy Rev. 2016,60, 909–929. [CrossRef] 2. Py, X.; Sadiki, N.; Olives, R.; Goetz, V.; Falcoz, Q. Thermal energy storage for CSP (Concentrating Solar Power). EPJ Web Conf. 2017,148, 14. [CrossRef] 3. SolarPACES. What Happened with Crescent Dunes. Solarpaces.org, 23 August 2023. Available online: https://www.solarpaces. org/what-happened-with-crescent-dunes/ (accessed on 10 October 2023). 4. Solarpaces. Solar Electric Generating Station. CSP Project. 5 December 2021. Available online: https://solarpaces.nrel.gov/ project/solar-electric-generating-station-i (accessed on 15 August 2023). 5. Solarpaces. Concentrating Solar Power Projects. 6 Diciembre 2021. Available online: https://solarpaces.nrel.gov/ (accessed on 15 August 2023). 6. Awan, B.; Khan, M.; Zubair, M.; Bellos, E. Commercial parabolic trough CSP plants: Research trends and technological advancements. Sol. Energy 2020,211, 1422–1458. [CrossRef] 7. Zhang, H.; Baeyens, J.; Degrève, J.; Cacères, G. Concentrated solar power plants: Review and design methodology. Renew. Sustain. Energy Rev. 2013,22, 466–481. [CrossRef] 8. Bauer, T.; Odenthal, C.; Bonk, A. Molten Salt Storage for Power Generation. Chem. Ing. Tech. 2021,93, 534–546. [CrossRef] 9. Sandia National Laboratories. Final Test and Evaluation Results from the Solar Two Project. January 2002. Available online: https://www.osti.gov/biblio/793226 (accessed on 15 August 2023). 10. Palacios, A.; Barreneche, C.; Navarro, M.; Ding, Y. Thermal energy storage technologies for concentrated solar power. A review from a materials perspective. Renew. Energy 2020,156, 1244–1265. [CrossRef] 11. Wan, Z.; Wei, J.; Qaisrani, M.A.; Fang, J.; Tu, N. Evaluation on thermal and mechanical performance of the hot tank in the two-tank molten salt heat storage system. Appl. Therm. Eng. 2020,167, 114775. [CrossRef] 12. API Standard 650; Welded Tanks for Oil Storage (12th edition). American Petroleum Institute: Washington, DC, USA, 2013. 13. ASME. Section II—Materials, Part D. In ASME Boiler & Pressure Vessel Code; ASME: New York, NY, USA, 2021. 14. ASME. Section VIII—Rules for Construction of Pressure Vessels, Division 2—Alternative Rules. In ASME Boiler & Pressure Vessel Code; ASME: New York, NY, USA, 2021. 15. Iranzo, A.; Suárez, C.; Guerra, J. Mixing enhancement in thermal energy storage molten salt tanks. Energy Convers. Manag. 2018 , 168, 320–328. [CrossRef] 16. Gabbrielli, R.; Zamparelli, C. Optimal Design of a Molten Salt Thermal Storage Tank for Parabolic Trough Solar Power Plants. J. Sol. Energy Eng. 2009,131, 041001. [CrossRef] 17. González-Roubaud, E.; Pérez-Osorio, D.; Prieto, C. Review of commercial thermal energy storage in concentrated solar power plants: Steam vs. molten salts. Renew. Sustain. Energy Rev. 2017,80, 133–148. [CrossRef] 18. Angelini, G.; Lucchini, A.; Manzolini, G. Comparison of thermocline molten salt storage performances to commercial two-tank configuration. Energy Procedia 2014,49, 694–704. [CrossRef] 19. Bradshaw, R.W.; Dawson, D.B.; Rosa, W.D.L.; Gilbert, R.; Goods, S.H.; Hale, M.J.; Jacobs, P.; Jones, S.A.; Kolb, G.J.; Pacheco, J.E.; et al. Final Test and Evaluation Results from the Solar Two Project; Sandia National Laboratories: Albuquerque, NM, USA, 2002. 20. Prieto, C.; Miró, L.; Peiró, G.; Oró, E.; Gil, A.; Cabeza, L.F. Temperature distribution and heat losses in molten salts tanks for CSP. Sol. Energy 2016,135, 518–526. [CrossRef] 21. Bradshaw, R.W.; Clift, W.M. Effect of Chloride Content of Molten Nitrate Salt on Corrosion of A516 Carbon Steel; Sandia National Laboratories: Albuquerque, NM, USA, 2010. 22. Trent, M.C.; Goods, S.H.; Bradshaw, R.W. Comparison of corrosion performance of grade 316 and grade 347H stainless steels in molten nitrate salt. AIP Conf. Proc. 2016,1734, 160017. 23. Walczak, M.; Pinedaa, F.; Fernández, Á.G.; Mata-Torres, C.; Escobar, R.A. Materials corrosion for thermal energy storage systems in concentrated solar power plants. Renew. Sustain. Energy Rev. 2018,86, 22–44. [CrossRef] 24. Patel, N.S.; Pavlík, V.; Boˇca, M. High-temperature corrosion behavior of superalloys in molten salts—A review. Crit. Rev. Solid State Mater. Sci. 2016,42, 83–97. [CrossRef] 25. Fernández, Á.G.; Cabeza, L.F. Molten salt corrosion mechanisms of nitrate based thermal energy storage materials for concentrated solar power plants: A review. Sol. Energy Mater. Sol. Cells 2019,194, 160–165. [CrossRef] 26. Ma, L.; Zhang, C.; Wu, Y.; Lu, Y. Comparative review of different influence factors on molten salt corrosion characteristics for thermal energy storage. Sol. Energy Mater. Sol. Cells 2022,235, 111485. [CrossRef] 27. Ruiz-Cabañas, F.J.; Prieto, C.; Osuna, R.; Madina, V.; Fernández, A.I.; Cabeza, L.F. Corrosion testing device for in-situ corrosion characterization in operational molten salts storage tanks: A516 Gr70 carbon steel performance under molten salts exposure. Sol. Energy Mater. Sol. Cells 2016,157, 383–392. [CrossRef] 28. Ruiz-Cabañas, F.J.; Prieto, C.; Madina, V.; Fernández, A.I.; Cabeza, L.F. TES-PS10 postmortem tests: Carbon steel corrosion performance exposed to molten salts under relevant operation conditions and lessons learnt for commercial scale-up. J. Energy Storage 2019,26, 100922. [CrossRef] 29. Zhang, X.; Zhang, C.; Wu, Y.; Lu, Y. Experimental research of high temperature dynamic corrosion characteristic of stainless steels in nitrate eutectic molten salt. Sol. Energy 2020,209, 618–627. [CrossRef]
Energies 2024,17, 22 18 of 19 30. Ibrahim, A.; Peng, H.; Riaz, A.; Basit, M.A.; Rashid, U.; Basit, A. Molten salts in the light of corrosion mitigation strategies and embedded with nanoparticles to enhance the thermophysical properties for CSP plants. Sol. Energy Mater. Sol. Cells 2021 ,219, 110768. [CrossRef] 31. NACE/ASTM G193-12D; Standard Terminology and Acronyms Relating to Corrosion. American Society for Testing and Materials: West Conshohocken, PA, USA, 2013. 32. Lai, G.Y. Molten Salt Corrosion. In High-Temperature Corrosion and Materials Applications; ASM International: Almere, The Netherlands, 2007; pp. 409–421. 33. Kruizenga, M. Stainless Steel Corrosion by Molten Nitrates: Analysis and Lessons Learned; Sandia National Laboratories (SNL): Albuquerque, NM, USA; Livermore, CA, USA, 2011. 34. Liu, S.; Liu, Z.; Wang, Y.; Tang, J. A comparative study on the high temperature corrosion of TP347H stainless steel, C22 alloy and laser-cladding C22 coating in molten chloride salts. Corros. Sci. 2014,83, 396–408. [CrossRef] 35. Bell, S.; Steinberg, T.; Will, G. Corrosion mechanisms in molten salt thermal energy storage for concentrating solar power. Renew. Sustain. Energy Rev. 2019,114, 109328. [CrossRef] 36. Brown, B.F. Stress-Corrosion Cracking in High Strength Steels and in Titanium and Aluminum Alloys; Naval Research LaboratoryWashington: Washington, DC, USA, 1972. 37. García-Martín, G.; Lasanta, M.; Encinas-Sánchez, V.; Miguel, M.D.; Pérez, F. Evaluation of corrosion resistance of A516 Steel in a molten nitrate salt mixture using a pilot plant facility for application in CSP plants. Sol. Energy Mater. Sol. Cells 2017 ,161, 226–231. [CrossRef] 38. Wang, J.; Jiang, Y.; Ni, Y.; Wu, A.; Li, J. Investigation on static and dynamic corrosion behaviors of thermal energy transfer and storage system materials by molten salts in concentrating solar power plants. Mater. Corros. 2019,70, 102–109. [CrossRef] 39. Sutter, F.; Oskay, C.; Galetz, M.C.; Diamantino, T.; Pedrosa, F.; Figueira, I.; Glumm, S.; Bonk, A.; Agüero, A.; Rodríguez, S.; et al. Dynamic corrosion testing of metals in solar salt for concentrated solar power. Sol. Energy Mater. Sol. Cells 2021 ,232, 111331. [CrossRef] 40. Nithiyanantham, U.; Grosu, Y.; González-Fernández, L.; Zaki, A.; Igartua, J.M.; Faik, A. Corrosion aspects of molten nitrate salt-based nanofluids for thermal energy storage applications. Sol. Energy 2019,189, 219–227. [CrossRef] 41. Ruiz-Cabañas, F.J.; Prieto, C.; Madina, V.; Fernández, A.I.; Cabeza, L.F. Materials selection for thermal energy storage systems in parabolic trough collector solar facilities using high chloride content nitrate salts. Sol. Energy Mater. Solar Cells 2017 ,163, 134–147. [CrossRef] 42. Prieto, C.; Gallardo-González, J.; Ruiz-Cabañas, F.J.; Barreneche, C.; Martínez, M.; Segarra, M.; Fernández, A.I. Study of corrosion by Dynamic Gravimetric Analysis (DGA) methodology. Influence of chloride content in solar salt. Sol. Energy Mater. Sol. Cells 2016,157, 526–532. [CrossRef] 43. Nieto-Maestre, J.; Muñoz-Sánchez, B.; Fernández, A.G.; Faik, A.; Grosu, Y.; Gar-cía-Romero, A. Compatibility of container materials for Concentrated Solar Power with a solar salt and alumina based nanofluid: A study under dynamic conditions. Renew. Energy 2020,146, 384–396. [CrossRef] 44. Goods, S.H.; Bradshaw, R.W. Corrosion of stainless steels and carbon steel by molten mixtures of commercial nitrate salts. J. Mater. Eng. Perform. 2004,13, 78–87. [CrossRef] 45. Bradshaw, R.W.; Goods, S.H. Corrosion Resistance of Stainless Steels during Thermal Cycling in Alkali Nitrate Molten Salts; Sandia National Laboratories (SNL): Albuquerque, NM, USA; Livermore, CA, USA, 2001. 46. Dorcheh, S.; Durham, R.N.; Galetz, M.C. Corrosion behavior of stainless and low-chromium steels and IN625 in molten nitrate salts at 600 ◦C. Sol. Energy Mater. Sol. Cells 2016,144, 109–116. [CrossRef] 47. Kruizenga, A.; Gill, D. Corrosion of iron stainless steels in molten nitrate salt. Energy Procedia 2014,49, 878–887. [CrossRef] 48. Kruizenga, M.; Gill, D.D.; LaFord, M.E. Materials Corrosion of High Temperature Alloys Immersed in 600C Binary Nitrate Salt; Sandia National Laboratories (SNL): Albuquerque, NM, USA; Livermore, CA, USA, 2013. 49. Prieto, C.; Ruiz-Cabañas, J.; Madina, V.; Fernández, A.I.; Cabeza, L.F. Lessons learned from corrosion of materials with molten salts during molten salt tank preheating. Sol. Energy Mater. Sol. Cells 2022,247, 111943. [CrossRef] 50. Luengo, C.; Cardona, A.; Risso, J. Determinación de tensiones residuales en discos sometidos a grandes gradientes térmicos durante el servicio. Mecánica Comput. 2016,25, 461–472. 51. Yafei, S.; Yongjun, T.; Jing, S.; Dongjie, N. Effect of temperature and composition on thermal properties of carbon steel. In Proceedings of the 2009 Chinese Control and Decision Conference, Guilin, China, 17–19 June 2009. 52. Desai, P.D.; Ho, C.Y. Thermal Linear Expansion of Nine Selected AISI Stainless Steels; Thermophysical and Electronic Properties Information Analysis Center Lafayette IN: Washington, DC, USA, 1978. 53. Yakout, M.; Elbestawi, M.; Veldhuis, S.C. A study of thermal expansion coefficients and microstructure during selective laser melting of Invar 36 and stainless steel 316L. Addit. Manuf. 2018,24, 405–418. [CrossRef] 54. Rodríguez, I.; Pérez-Segarra, C.D.; Lehmkuhl, O.; Oliva, A. Modular object-oriented methodology for the resolution of molten salt storage tanks for CSP plants. Appl. Energy 2013,109, 402–414. [CrossRef] 55. Ghaddar, N.; Al-Marafie, A.; Al-Kandari, A. Numerical simulation of stratification behaviour in thermal storage tanks. Appl. Energy 1989,32, 225–239. [CrossRef] 56. Alizadeh, S. An experimental and numerical study of thermal stratification in a horizontal cylindrical solar storage tank. Sol. Energy 1999,66, 409–421. [CrossRef]
Energies 2024,17, 22 19 of 19 57. Pérez-Segarra, D.; Rodríguez, I.; Oliva, A.; Torras, S.; Lehmkuhl, O. Detailed numerical model for the resolution of molten salt storage tanks for CSP plants. In International Conference on Solar Heating, Cooling and Buildings; Solar energy for a Brighter Future: Book of Proceedings; EuroSun: Rijeka, Croatia, 2012. 58. Zaversky, F.; García-Barberena, J.; Sánchez, M.; Astrain, D. Transient molten salt two-tank thermal storage modeling for CSP performance simulations. Sol. Energy 2013,93, 294–311. [CrossRef] 59. Schulte-Fischedick, J.; Tamme, R.; Herrmann, U. CFD Analysis of the Cool Down Behaviour of Molten Salt Thermal Storage Systems. In Proceedings of the ASME 2008 2nd International Conference on Energy Sustainability Collocated with the Heat Transfer, Fluids Engineering, and 3rd Energy Nanotechnology Conferences, Jacksonville, FL, USA, 10–14 August 2008. 60. Suárez, C.; Iranzo, A.; Pino, F.J.; Guerra, J. Transient analysis of the cooling Process of molten salt thermal storage tanks due to standby heat loss. Appl. Energy 2015,142, 56–65. [CrossRef] 61. Suárez, C.; Pino, F.J.; Rosa, F.; Guerra, J. Heat loss from thermal energy storage ventilated tank foundations. Sol. Energy 2015 ,122, 783–794. [CrossRef] 62. Zhang, C.; Lu, Y.; Shi, S.; Wu, Y. Comparative research of heat discharging characteristic of single tank molten salt thermal energy storage system. Int. J. Therm. Sci. 2021,161, 106704. [CrossRef] 63. Tagle-Salazar, P.D.; Prieto, C.; López-Román, A.; Cabeza, L.F. A transient heat losses model for two-tank storage systems with molten salts. Renew. Energy 2023,219, 119371. [CrossRef] 64. Launder, B.; Spalding, D. The numerical computation of turbulent flows. Comput. Methods Appl. Mech. Eng. 1974 ,3, 269–289. [CrossRef] 65. Launder, B.; Sharma, B. Application of the Energy Dissipation Model of Turbulence to the Calculation of Flow Near a Spinning Disc. Lett. Heat Mass Transf. 1974,1, 131–138. [CrossRef] 66. Jones, W.; Launder, B. The calculation of low-Reynolds-number phenomena with a two-equation model of turbulence. Int. J. Heat Mass Transf. 1973,16, 1119–1130. [CrossRef] 67. Yakhot, V.; Orszag, S.A. Development of turbulence models for shear flows by a double expansion technique. Phys. Fluids A Fluid Dyn. 1992,4, 1510–1520. [CrossRef] 68. Shih, T.-H.; Liou, W.W.; Shabbir, A.; Yang, Z.; Zhu, J. A new k- eddy viscosity model for high Reynolds number turbulent flows. Comput. Fluids 1995,24, 227–238. [CrossRef] 69. Zhou, H.; Shi, H.; Zhang, J.; Zhou, M. Experimental and numerical investigation of temperature distribution and heat loss of molten salt tank foundation at different scales. Heat Mass Transf. 2020,56, 2859–2869. [CrossRef] 70. Torras, S.; Pérez-Segarra, C.; Rodríguez, I.; Rigola, J.; Oliva, A. Parametric Study of Two-tank TES Systems for CSP Plants. Energy Procedia 2015,69, 1049–1058. [CrossRef] 71. Kreith, F.; Bohn, M.S. Principles of Heat Transfer, Stamford; Cengage Learning: Boston, MA, USA, 2016. Disclaimer/Publisher’s Note: The statements, opinions and data contained in all publications are solely those of the individual author(s) and contributor(s) and not of MDPI and/or the editor(s). MDPI and/or the editor(s) disclaim responsibility for any injury to people or property resulting from any ideas, methods, instructions or products referred to in the content.