Journal Pre-proofs Migration and phase change study of leaking molten salt in tank foundation material Hao Zhou, Hua Shi, Zhenya Lai, Yuhang Zuo, Shihao Hu, Mingxi Zhou PII: DOI: Reference:
S1359-4311(19)34803-3 https://doi.org/10.1016/j.applthermaleng.2020.114968 ATE 114968
To appear in:
Applied Thermal Engineering
Received Date: Revised Date: Accepted Date:
12 July 2019 7 January 2020 17 January 2020
Please cite this article as: H. Zhou, H. Shi, Z. Lai, Y. Zuo, S. Hu, M. Zhou, Migration and phase change study of leaking molten salt in tank foundation material, Applied Thermal Engineering (2020), doi: https://doi.org/ 10.1016/j.applthermaleng.2020.114968
This is a PDF file of an article that has undergone enhancements after acceptance, such as the addition of a cover page and metadata, and formatting for readability, but it is not yet the definitive version of record. This version will undergo additional copyediting, typesetting and review before it is published in its final form, but we are providing this version to give early visibility of the article. Please note that, during the production process, errors may be discovered which could affect the content, and all legal disclaimers that apply to the journal pertain.
© 2020 Published by Elsevier Ltd.
Migration and phase change study of leaking molten salt in tank foundation material Hao Zhou *, Hua Shi, Zhenya Lai, Yuhang Zuo, Shihao Hu, Mingxi Zhou
State Key Laboratory of Clean Energy Utilization, Institute for Thermal Power Engineering, Zhejiang University, Hangzhou 310027, China
Permanent Postal Address: State Key Laboratory of Clean Energy Utilization, Zhejiang University, Zheda Road 38, Hangzhou 310027, China. *Corresponding author. E-mail: [email protected]
(H. Zhou), Tel.: +86-0571-87952598.
Abstract Molten salt is widely used as a heat transfer and thermal storage medium in concentrated solar power plants. This paper mainly focuses on the migration and phase change characteristics of molten salt leaking from a high-temperature storage tank to the thermal-steady porous foundation materials. The effects of the different conditions, including material structure, leakage pore size, operating temperature and leaking molten salt mass, are investigated via the self-designed experimental system that models the actual leaking process. Results show that the molten salt migrates rapidly in the porous foundation material during the leaking process and begins to solidify on the bottom, hindering molten salt from further flowing down. After molten salt leakage, the thermal equilibrium temperature of foundation material increases. It is found that the molten salt migration depth distinctly decreases with the smaller porosity of the porous material. When the leakage pore size diminishes or the operating temperature increases, the migration depth obviously increases, while the migration diameter decreases. Nevertheless, within a certain range, the leaking molten salt mass has some effect on the migration diameter but has little effect on the migration depth. These results provide quantitative references for the pollution control and disposition of molten salt leakage accidents. Keywords: Molten salt; foundation material; migration; solidification
1. Introduction Molten salt has the advantages of a large specific heat and energy density, a low vapor pressure and melting point, and thermal chemistry stability [1,2], and molten salt is widely used as a heat
transfer and thermal storage medium in concentrated solar power (CSP) plants and other industrial systems. During the application process, the environmental pollution from molten salt mainly includes the migration of leaking molten salt and the emission of nitrogen oxides caused by the decomposition of nitrate and nitrite at local high temperatures . On the one hand, the storage tank is loaded by gravity and pressure from the molten salt [4,5], and thermal stress is caused by the charge and discharge cyclic processes. On the other hand, molten salt has a significant corrosive effect on tank materials during long-term operation, especially at high operating temperatures [6,7]. Therefore, tank leakage and corrosion can take place. There have been several molten salt storage tank leakage accidents in operating CSP plants. The Crescent Dunes CSP plant was shut down for 8 months because of a leak from the molten salt tank in 2016 [8,9], and the Gemasolar Thermosolar Plant also suffered from serious tank leakage accidents . Moreover, the thorium-based molten salt reactor (TMSR), one of the six advanced reactor concepts, also faces great challenges with its leakage and sealing technology [11,12]. When breakage of molten salt storage tanks occurs, molten salt flows into the tank foundation and surrounding insulation layers and even into the soil and groundwater. Meanwhile, the leaking molten salt transfers heat with these materials and solidifies when the temperature of the molten salt is lower than its freezing point. This is an unsteady multiphase flow process involving fluid dynamics, heat transfer and phase changes. Many studies have investigated the transport and crystallization of ambient temperature salt solutions in porous granular mediums by means of X-ray microtomography [13–15], light transmission systems  and time domain reflectometry . Zafari M et al.  studied the fluid flow and heat transfer in open cell metal foams by a microtomography-based numerical simulation and obtained a correlation for the mean Nusselt 3
number in terms of parameters such as the percentage of porosity and Reynolds number. Weisbrod N  investigated the migration process of concentrated NaNO3 solutions in homogeneous packs of pre-wetted silica sands through a light transmission system. The crystallization and upward percolation of the sodium chloride salt inside porous granular media were investigated by Robert Hird and Malcolm D. Bolton . Song M and Viskanta R experimentally and theoretically studied the lateral freezing of porous media in a saturated brine solution . In molten salt thermocline storage tanks, high-temperature molten salt flows through porous granules such as quartzite rocks and sands and transfers thermal energy to each other during the charge and discharge processes. Some research has focused on the thermal characteristics of the molten salt thermocline in the porous packed bed tank by numerical simulation [19–24]. A model considering the heat transfer between molten salt and the filling material in the tank was established, and the influence of the environmental boundary conditions on the performance of the thermocline was studied by Zhen Yang and Suresh V. Garimella . Chao Xu et al.  implemented a transient numerical study on the heat transfer and fluid dynamics in a packed bed molten salt thermocline thermal storage system, and they estimated the effect of the interstitial heat transfer coefficient, the thermal conductivity of solid fillers and the effective thermal conductivity. Zheshao Chang et al.  established a transient two-dimensional and dual temperature model to study the heat transfer and fluid dynamics performance of a molten salt thermocline thermal energy storage system TES, and they studied the effect of the boundary conditions of the insert liner and sloped wall with an entropy generation analysis. K.S. Reddy et al.  studied the thermal characteristics of a single-tank thermocline storage system, including the temperature distribution and discharge efficiency, with different heat transfer fluids. There has been little research studying the thermal 4
characteristics of molten salt thermocline storage tanks by experiments [25,26]. Huibin Yin et al.  analyzed the performances of molten salt thermocline porous packed bed tanks during the charge and discharge processes through experiments and numerical simulations based on the local heat balance theory of porous media. Xiaoping Yang  conducted an experimental study on the heat transfer characteristics of a molten salt thermocline storage tank and obtained the temperature distribution and thermal storage capacity during the charging process, which verified the availability of the numerical simulation reports. In addition, Zhirong Liao et al. [27–29] studied the heat transfer and phase change dynamics process of cold filling with molten salt into a receiver tube by using VOF and CSF models. Jinqiao Wu and Yuanyuan Zhang et al. [30,31] numerically and experimentally studied the migration and phase change phenomena of molten salt leaking into cold soil and sand. Experimental and mechanistic studies are extremely lacking on the flow and phase change processes of leaking molten salt when the molten salt storage tank breaks down. Only a few articles have studied molten salt migration in cold porous materials, which is not consistent with actual leakage accident scenarios. As far as the authors know, there has been no research conducted on the migration of leaking molten salt in the thermal foundation material, which has a significant effect on the leaking molten salt heat transfer and phase change. In the present work, the migration and heat transfer characteristics of high-temperature molten salt in thermal steady-state storage tank foundation materials were first investigated experimentally via a self-designed test rig. The effects of the porous media gradation, leakage pore size, operating temperature and leaking molten salt mass on the migration depth and diameter were discussed by a straightforward visualization method. The results obtained from this study would be useful for a gaining a better understanding of the 5
leakage and migration processes of molten salt and for taking effective measures to reduce economic loss and safety risks of leaking accidents.
2. Materials and methods 2.1 Materials The commercial thermal storage medium called Solar Salt, which is a mixture of 60 wt.% sodium nitrate and 40 wt.% potassium nitrate, is used in the present experiments. The mixture was provided by Zhejiang Lianda Chemical Co., Ltd., and the level of impurities in the salt mixture is given in Table 1. The physical characteristics of Solar Salt are shown in Table 2 . During the process of decreasing temperature, the molten salt begins to crystallize at 237.85 °C and is completely solidified at 220.85 °C, and the latent heat is 113.03 kJ/kg . Table 1 The reported level of impurities in the nitrate salt mixture. Impurity
Table 2 Properties of the molten salt . Property
molten salt (T, °C)
The typical molten salt storage tank foundation consists of multiple layer insulation materials and a concrete slab with passive ventilation or an active cooling system. Stacked light expanded clay aggregate (LECA) is used in the foundation . In this work, LECAs with different gradations were used as foundation materials for the study of the leaking molten salt migration. The particle size distribution, bulk density and porosity are shown in Table 3. The appearances of the LECA with three different gradations are shown in Fig. 1. The LECA with different particle size distributions has the largest bulk density and the smallest porosity. Table 3 Properties of LECA. Property
LECA 3 3.35-6.3 mm
Bulk density (kg/m3)
(a) LECA 1
(b) LECA 2
(c) LECA 3
Fig. 1. Appearances of LECA with the three different gradations.
2.2 Methods A schematic diagram of the experimental system used in this investigation is shown in Fig. 2. A muffle furnace is used to heat the molten salt to a prescribed temperature. The complex molten salt storage tank is replaced by a ceramic sheathed electrical resistance heater with a temperature control range from 30 °C to 800 °C, which implements the thermal effect of high-temperature molten salt in the tank on the foundation materials. Both the temperature resolution of the muffle furnace and heater control device are ±1 °C. The sidewall of the test rig and the top of the heater are insulated with refractory bricks. The height of the test rig is 760 mm, the internal diameter is 345 mm, and the height of the heater is 60 mm. The bottom tray can be opened to discharge the filling foundation materials. The temperature evolution is recorded through thermocouples and a data acquisition instrument. There are sixteen K-type thermocouples with an accuracy of ±0.1 °C that measure the temperature distribution of the foundation materials and the migration of leaking molten salt, which are inserted into the center axis on a height spacing of 40 mm.
Fig. 2. Schematic diagram of the experimental system. 8
The experiment includes three processes: the foundation material heating process, molten salt leakage process, and molten salt migration and cooling process after leakage. First, the LECA foundation material was filled to the test rig, and the electrical resistance heater was turned on. The temperature of the heater reached the predesigned operating temperature of the molten salt tank and then remained at that temperature; meanwhile, the temperature of the LECA gradually increased. In the present experiment, the foundation temperature was assumed to reach a steady state when the temperature difference was below 0.5 °C for 3 hours. The molten salt was melted and kept at the predesigned operating temperature for 5 hours in the muffle furnace. The crucible was also preheated to the same temperature as the molten salt to reduce the heat transfer between the molten salt and crucible. Then, the heater was pulled up, and the crucible, designed with a leaking hole on the bottom, was placed at the center and top of the LECA. The high-temperature molten salt was poured into the crucible. After the molten salt leakage occurred, the heater was pulled back immediately and continued to maintain the operating temperature during the solidifying and cooling process. The leaking molten salt migrated and solidified in the foundation material, and the foundation material reached a new thermal equilibrium state. Then, the heater was turned off, and the molten salt and the LECA were cooled down. During the whole process, the temperatures of the LECA/molten salt were recorded. After the molten salt was completely cooled, the solid molten salt block with the LECA was removed, and the depth and diameter were further measured with an accuracy of ±1 mm. Before the start of the leakage process, the heater was maintained at the operating temperature until the foundation material achieved the thermal steady state. The composition of the molten salt is consistent with the salt used in plants, and the molten salt and crucible, designed with the leaking 9
hole used to model the leaking process of the tank, were heated to a uniform temperature. During the migrating and cooling processes, the heater under the operating temperature was always kept above the foundation material. These measures ensure the accurate modeling of the leakage process of accident scenarios. The experimental conditions of the tested cased are shown in Table 4. The tests in cases A1-A3 studied the effect of the porous foundation material structure on the migration characteristics. Compared with case A3, cases B1 and B2 have different leakage hole diameters, cases C1-C3 have different operating temperatures, and cases D1 and D2 have different leaking molten salt masses. Table 4 Experimental conditions of the tested cases. Operating Case
Mass of leaking
3. Results and discussion 3.1 Temperature evolution and flow dynamics characteristics Before the molten salt leakage process, the upper heater was maintained at the predetermined operating temperature, and the foundation material temperature gradually increased and reached a thermal equilibrium state. The temperature evolution of the foundation materials during the heating process of case A3 is shown in Fig. 3, where the operating temperature was 300 °C and the porous foundation material was LECA 3. The heater was heated to 300 °C at a rate of 10 °C/min and then maintained at a constant temperature. In general, the temperature evolution trends are very similar at different depths. At the depth of 40 mm, the temperature increases rapidly to 200 °C at 156 min and then increases slowly to the equilibrium temperature of 237 °C at 1897 min. At the depth of 80 mm, the temperature increases rapidly to 95 °C at 512 min and then increases slowly to the equilibrium temperature of 120 °C at 2491 min. At the depth of 120 mm, the temperature increases rapidly to 71 °C at 679 min and then increases slowly to the equilibrium temperature of 90 °C at 3426 min. As the heat was conducted downward, the temperature of the foundation material increased in turn and, finally, an equilibrium state was reached. As the depth increases, the equilibrium temperature decreases. After 72 hours, the temperatures of the foundation material reached an overall equilibrium state.
Fig. 3. Temperature evolution of the foundation materials during the heating process of case A3. Fig. 4 presents the temperature evolution during the molten salt leakage and migration process of case A3, where the diameter of the leakage hole is 10 mm and the mass of the leaking molten salt is 600 g. When the molten salt flows through the foundation material, the temperature at this position increases rapidly and reaches the peak value, and then the temperature gradually decreases due to heat loss, which is consistent with previous investigations . The maximum temperatures are 271.9 °C, 188.1 °C and 150.4 °C for y = 40 mm, 120 mm, 320 mm, respectively. As the foundation depth y increases, the peak values of the temperature generally decrease where the molten salt flows through. However, the maximum temperature of the positions increases and is more than 200 °C for depths of 240 mm and 280 mm, which is also common in other cases.
Fig. 4. Temperature evolution during the molten salt leakage and migration processes of case A3. Fig. 5 shows the temperature evolution of the foundation material along the axial direction during the leakage and migration processes of case A3. During the leakage process, the molten salt continuously leaked from the hole and flowed into the foundation material. The leaking molten salt migrated rapidly among the foundation material. Before 30 s, the temperature of the foundation material increased rapidly where the molten salt flowed through. From 0 s to 16 s, the temperature began to increase almost simultaneously where the depth y was in the range of 0 mm to 300 mm. From 20 s to 30 s, the temperature increased faster at depths of 240 mm and 280 mm than at other positions, and the peak temperature was more than the value at depths of 80~200 mm. This increase was observed because the foundation material in the bottom where the depth was more than 300 mm had a temperature below 50 °C; the molten salt began to first solidify in the bottom when the temperature of the molten salt dropped to the freezing point, which hindered the molten salt flowing further downward. The molten salt accumulated in the upper part of the solidified layer, which is consistent with the shape of the molten salt and LECA block and with the position of the maximum
migration diameter presented in Fig. 6(c). The heat of the molten salt continued to transfer to the ambient air and foundation materials at a lower temperature. The flow velocity decreased to zero, and the molten salt gradually solidified into a solid state. The temperature of the foundation material increased slowly from 30 s to 100 s, and then the temperature no longer increased after 100 s.
Fig. 5. Temperature evolution of the foundation material along the axial direction during the leakage and migration processes of case A3. After molten salt migration and solidification, the temperature of the foundation material and molten salt decreased gently and finally reached a new steady state, as shown in Fig. 4. The new thermal equilibrium temperatures of the foundation materials and leaking molten salt were higher than the stable temperature values of the foundation before the molten salt leakage. This increase is caused by the thermal conductivity of the leaking molten salt that has been solidified in pores being greater than that of the air among the foundation material granules. According to Fourier’s law of heat conduction, the heat flux can be interpreted as ,
q kgrad (T ) where q is the heat flux, W/m2, and k is the thermal conductivity, W/(m*k). 14
For multilayer wall heat conduction, the heat flux can be interpreted as
T1 Tn 1 n
k i 1
and for each layer material,
q ki where
Ti Ti 1
i is the thickness of material i , m, and ki is the thermal conductivity, W/(m*k).
The effective conductivity of the porous material structure is modeled by the effective medium theory (EMT) equation :
(1 2 )
k1 ke k k 2 2 e 0 k1 2ke k 2 2ke
which can be rewritten to be explicit for ke :
ke 1/ 4 (3 2 1)k2 3 1 2 1 k1
(3 2 1)k2 (3(1 2 ) 1)k1
where ke , k1 and k2 are the effective thermal conductivity and thermal conductivity of component 1 and component 2, W/(m*k), and
2 is the volume fraction of the material component
2. According to equation (5), the leaking molten salt filling into the porous material causes an increase in the effective thermal conductivity of the upper porous material. Therefore, the heat flux increases based on equation (2). Since the temperature on the top and bottom of porous material are constant, it is obtained from equation (3) that the temperature gradient increases for the porous material without molten salt on the bottom, while the temperature gradient decreases for the porous material with molten salt. Therefore, the equilibrium temperature in the foundation material 15
increases. Due to molten salt leakage, the temperature of the foundation materials may be more than the maximum allowable temperature, and the heat loss of the molten salt tank through the foundation would increase.
3.2 Migration characteristics under different conditions Once molten salt tank leakage occurs, the leaking molten salt flows into the foundation material and changes the thermal characteristics of the foundation. In the cases where the temperatures of the foundation materials exceed the maximum allowable temperatures, the foundation would partially cave in because of the breakage of the concrete slab. It is important to ascertain the migration range of leaking molten salt for pollution control of leakage accidents under different conditions. To further study the migration characteristics of leaking molten salt in the foundation material, the effects of the factors, including the leaking conditions and the foundation material structure parameters, were investigated in the experiments.
3.2.1 Effect of porous material parameters on migration characteristics
The structural parameters of porous media remarkably affect the migration process of leaking molten salt in the foundation material. The solid molten salt blocks with LECA with different structural parameters in cases A1, A2 and A3 are shown in Fig. 6, and the migration results are shown in Fig. 7. The solid block shape of LECA 1 and LECA 3 is similar to a circular truncated cone, but the block shape of LECA 2 is similar to a circular column. The molten salt migration depth with LECA 2 is significantly larger, and the migration diameter is much smaller than that with LECA 1 and LECA 3. Compared with LECA 1 of the single small size particle, the migration depth of LECA 3 with different particle size grades is slightly smaller, and the migration diameter has 16
little difference. These results are mainly caused by the difference in the pore structure of the LECA. As the porosity increases from 0.433 to 0.464, the migration depth increases from 322 mm to 586 mm, and the maximum migration diameter decreases from 141 mm to 104 mm. The results are in good agreement with those of a previous investigation . The foundation material with a small particle size has a relatively high density and small porosity, which would increase the resistance of the molten salt to flow. Therefore, a small particle size and reasonable grades can effectively control the molten salt migration depth, while the migration diameter increases.
(a) LECA 1 (case A1)
(b) LECA 2 (case A2)
(c) LECA 3 (case A3)
Fig. 6. Solid molten salt block with LECAs with different structure parameters.
Fig. 7. Molten salt migration characteristics with different gradation LECAs. Fig. 8 shows the thermal equilibrium temperatures of the foundation material before and after molten salt leakage. The thermal equilibrium temperatures of cases A1, A2 and A3 are not much different before molten salt leakage. After molten salt leakage, the thermal equilibrium temperatures all increase. The thermal equilibrium temperatures in case A1 change obviously among the foundation material with molten salt. The porosity of LECA 2 is the largest, and the migration depth in case A2 is the largest. Because the proportion of molten salt in the pores is the smallest in case A2, the thermal equilibrium temperature changes slightly. The change in the thermal equilibrium temperature is mainly related to the molten salt content in the pores of the foundation material.
Fig. 8. Thermal equilibrium temperatures of the foundation material before and after molten salt leakage.
3.2.2 Effect of leakage hole size on migration characteristics
The effect of the leakage hole size on the migration characteristics was investigated in cases B1, A3 and B2, where the diameter of the round leakage hole is 5 mm, 10 mm, and 15 mm, respectively. The solid molten salt blocks with LECAs under different leakage hole sizes are shown in Fig. 9. The shapes are similar to circular truncated cones, and the diameter increases as the depth increases. The migration depth and diameter are shown in Fig. 10, and the leakage pore size has a significant influence on the migration range. When the leakage pore diameter increases from 5 mm to 15 mm, the migration depth decreases from 380 mm to 289 mm, while the maximum migration diameter increases from 130 mm to 152 mm. When the leakage pore size becomes larger, the crosssectional area of molten salt leakage grows, and a larger amount of molten salt migrates to the periphery; therefore, the molten salt migration diameter increases. Since the total mass of molten
salt is consistent, the leaking time is shortened, and the migration depth of the leaking molten salt decreases.
(a) φ=5 mm (case B1)
(b) φ=10 mm (case A3)
(c) φ=15 mm (case B2)
Fig. 9. Solid molten salt block with LECAs with different leakage hole sizes.
Fig. 10. Molten salt migration characteristics with different leakage hole sizes.
3.2.3 Effect of operating temperature on migration characteristics
Fig. 11 presents the thermal equilibrium temperatures of the foundation material along the axial
direction with different operating temperatures in cases A3, C1, C2, and C3. The temperature trend is very similar, and the equilibrium temperature increases as the operating temperature increases. The solid molten salt blocks with LECAs under different operating temperatures are shown in Fig. 12, and the migration depth and diameter are shown in Fig. 13. When the operating temperature increases, the shape of the solid block changes from a circular truncated cone to a circular cone shape. The operating temperature has a significant effect on the migration characteristics. The migration depth under the operating temperature of 300 °C is much larger than that under the coldstate experiment, while the maximum migration diameter is not much different. Compared with the cold-state experiment, the migration depth for the 300 °C operating temperature increases obviously from 174 mm to 322 mm. When the operating temperature increases from 300 °C to 400 °C in the thermal state experiments, the migration depth increases from 322 mm to 581 mm, while the maximum migration diameter decreases from 141 mm to 99 mm. The effect of molten salt temperature on migration characteristics on cold porous materials has been researched by Jinqiao Wu  and Yuanyuan Zhang , and the change trend in migration depth and diameter is the same as the experimental results in this paper. However, the migration characteristics of hot porous materials are highly dependent on temperature in the present work, while the changes in migration characteristics are small in previous cold-state studies. It is necessary to study the migration characteristics and phase change of leaking molten salt in high-temperature foundation materials.
Fig. 11. Thermal equilibrium temperatures of the foundation material with different operating temperatures.
(a) cold-state (case C1)
(b) 300 °C (case A3)
(c) 350 °C (case C2)
(d) 400 °C (case C3)
Fig. 12. Solid molten salt block with LECAs at different operating temperatures.
Fig. 13. Molten salt migration characteristics at different operating temperatures.
3.2.4 Effect of leaking molten salt mass on migration characteristics
The effect of the leaking molten salt mass on the migration characteristics of cases A3, D1 and D2 was investigated, where the masses of leaking molten salt were 400 g, 600 g, and 800 g, respectively. The solid molten salt blocks with LECAs with different leaking molten salt masses are shown in Fig. 14, and the migration depth and diameter are shown in Fig. 15. The three solid blocks are all in the shape of a truncated cone, and the diameter becomes larger as the depth increases. When the leaking molten salt mass increases from 400 g to 800 g, the maximum migration diameter increases from 106 mm to 155 mm, while the migration depth decreases slightly from 329 mm to 311 mm. Within a certain range, the leaking molten salt mass mainly affects the migration diameter rather than the migration depth due to the temperature distribution of the foundation at different heights; the temperature of the foundation material gradually decreases with increasing depth, as shown in Fig. 3. During the molten salt migration process, the molten salt temperature rapidly
decreases, as shown in Fig. 4 and Fig. 5, and molten salt solidifies once the temperature is lower than the freezing point and prevents molten salt from migrating to a deeper position.
(a) 400 g (case D1)
(b) 600 g (case A3)
(c) 800 g (case D2)
Fig. 14. Solid molten salt block with LECAs under different leaking molten salt masses.
Fig. 15. Molten salt migration characteristics under different leaking molten salt masses.
4. Conclusions An experimental system was utilized to evaluate the migration and phase change processes of
leaking molten salt under different conditions. The conclusions can be given as follows. (1) During the molten salt leakage process, the molten salt migrates rapidly among the porous foundation material, and the molten salt begins to solidify from the bottom to the top due to the heat transfer from the high-temperature molten salt to the foundation materials or to the air. After molten salt migration and solidification, the new thermal equilibrium temperature of the foundation material is higher than the temperature value before molten salt leakage because the thermal conductivity of the leaking molten salt is greater than that of the air among the foundation material granules. (2) As the porosity of the foundation material diminishes, the migration depth decreases, and the maximum migration diameter increases. With the leaking pore diameter increasing from 5 mm to 15 mm, the migration depth of molten salt decreases by 91 mm, and the maximum migration diameter increases by 22 mm. Nevertheless, the mass of leaking molten salt within a certain range has no obvious impact on the migration depth but has a direct impact on the migration diameter. (3) Compared with the cold-state foundation, the migration depth has an increase of 148 mm under the operating temperature of 300 °C. When the operating temperature increases from 300 °C to 400 °C, the migration depth increases from 322 mm to 581 mm. It is obvious that the molten salt operating temperature has a significant influence on the migration characteristics. The experiments in the present work produced new and consolidated results on the temperature evolution and migration characteristics of leaking molten salt in porous foundation materials. All results are intended to provide a benchmark for further improvements of the numerical migration model in future work. 25
Acknowledgement This work was supported by the National Science Fund for Distinguished Young Scholars (51825605).
G.J. Janz, Molten salts handbook, Academic Publisher, 1967.
D. Kearney, U. Herrmann, P. Nava, B. Kelly, R. Mahoney, J. Pacheco, R. Cable, N. Potrovitza, D. Blake, H. Price, Assessment of a molten salt heat transfer fluid in a parabolic trough solar field, J. Sol. Energy Eng. Trans. ASME. 125 (2003) 170–176. doi:10.1115/1.1565087.
Y.L. He, K. Wang, Y. Qiu, B.C. Du, Q. Liang, S. Du, Review of the solar flux distribution in concentrated solar power: Non-uniform features, challenges, and solutions, Appl. Therm. Eng. 149 (2019) 448–474. doi:10.1016/j.applthermaleng.2018.12.006.
Q. Ge, F. Xiong, X. Peng, Method study for finite element modeling of large oil storage tanks, Appl. Mech. Mater. 166–169 (2012) 471–476. doi:10.4028/www.scientific.net/AMM.166169.471.
S. Flueckiger, Z. Yang, S. V. Garimella, An integrated thermal and mechanical investigation of molten-salt thermocline energy storage, Appl. Energy. 88 (2011) 2098–2105. doi:10.1016/j.apenergy.2010.12.031.
A. Gomes, M. Navas, N. Uranga, T. Paiva, I. Figueira, T.C. Diamantino, High-temperature corrosion performance of austenitic stainless steels type AISI 316L and AISI 321H, in molten Solar Salt, Sol. Energy. 177 (2019) 408–419. doi:10.1016/j.solener.2018.11.019.
A. Kruizenga, D. Gill, Corrosion of iron stainless steels in molten nitrate salt, Energy Procedia. 49 (2014) 878–887. doi:10.1016/j.egypro.2014.03.095. 26
David Jacobs, Salt Leak Shuts Down Crescent Dunes Solar Plant Outside Tonopah, TimesBonanza Goldf. News. (2016). https://pvtimes.com/tonopah/salt-leak-shuts-down-crescentdunes-solar-plant-outside-tonopah/.
David Jacobs, 8-month outage ends at solar plant near Tonopah, Times-Bonanza Goldf. News. (2017). https://pvtimes.com/news/8-month-outage-ends-at-solar-plant-near-tonopah/.
Z. Wan, J. Wei, M.A. Qaisrani, J. Fang, N. Tu, Evaluation on thermal and mechanical performance of the hot tank in the two-tank molten salt heat storage system, Appl. Therm. Eng. 167 (2020) 114775. doi:10.1016/j.applthermaleng.2019.114775.
Q. Li, J. Tian, C. Zhou, N. Wang, A new method to evaluate the sealing reliability of the flanged connections for Molten Salt Reactors, Nucl. Eng. Des. 287 (2015) 90–94. doi:10.1016/j.nucengdes.2015.03.003.
C. Shi, M. Cheng, G. Liu, Development and application of a system analysis code for liquid fueled molten salt reactors based on RELAP5 code, Nucl. Eng. Des. 305 (2016) 378–388. doi:10.1016/j.nucengdes.2016.05.034.
M. Zafari, M. Panjepour, M.D. Emami, M. Meratian, Microtomography-based numerical simulation of fluid flow and heat transfer in open cell metal foams, Appl. Therm. Eng. 80 (2015) 347–354. doi:10.1016/j.applthermaleng.2015.01.045.
X. Ou, X. Zhang, T. Lowe, R. Blanc, M.N. Rad, Y. Wang, N. Batail, C. Pham, N. Shokri, A.A. Garforth, P.J. Withers, X. Fan, X-ray micro computed tomography characterization of cellular SiC foams for their applications in chemical engineering, Mater. Charact. 123 (2017) 20–28. doi:10.1016/j.matchar.2016.11.013.
M.A.B. Promentilla, T. Sugiyama, T. Hitomi, N. Takeda, Quantification of tortuosity in 27
hardened cement pastes using synchrotron-based X-ray computed microtomography, Cem. Concr. Res. 39 (2009) 548–557. doi:10.1016/j.cemconres.2009.03.005. 
N. Weisbrod, M.R. Niemet, M.L. Rockhold, T. McGinnis, J.S. Selker, Migration of saline solutions in variably saturated porous media, J. Contam. Hydrol. 72 (2004) 109–133. doi:10.1016/j.jconhyd.2003.10.013.
R. Hird, M.D. Bolton, Migration of sodium chloride in dry porous materials, Proc. R. Soc. A Math. Phys. Eng. Sci. 472(2186): (2016). doi:10.1098/rspa.2015.0710.
M. Song, R. Viskanta, Lateral freezing of an anisotropic porous medium saturated with an aqueous salt solution, Int. J. Heat Mass Transf. 44 (2001) 733–751. doi:10.1016/S00179310(00)00132-0.
Z. Yang, S. V. Garimella, Molten-salt thermal energy storage in thermoclines under different environmental boundary conditions, Appl. Energy. 87 (2010) 3322–3329. doi:10.1016/j.apenergy.2010.04.024.
C. Xu, Z. Wang, Y. He, X. Li, F. Bai, Sensitivity analysis of the numerical study on the thermal performance of a packed-bed molten salt thermocline thermal storage system, Appl. Energy. 92 (2012) 65–75. doi:10.1016/j.apenergy.2011.11.002.
Z. Chang, X. Li, C. Xu, C. Chang, Z. Wang, The effect of the physical boundary conditions on the thermal performance of molten salt thermocline tank, Renew. Energy. 96 (2016) 190–202. doi:10.1016/j.renene.2016.04.043.
K.S. Reddy, V. Jawahar, S. Sivakumar, T.K. Mallick, Performance investigation of single-tank thermocline storage systems for CSP plants, Sol. Energy. 144 (2017) 740–749. doi:10.1016/j.solener.2017.02.012. 28
A. Abdulla, K.S. Reddy, Effect of operating parameters on thermal performance of molten salt packed-bed thermocline thermal energy storage system for concentrating solar power plants, Int. J. Therm. Sci. 121 (2017) 30–44. doi:10.1016/j.ijthermalsci.2017.07.004.
M. Wu, C. Xu, Y. He, Cyclic behaviors of the molten-salt packed-bed thermal storage system filled with cascaded phase change material capsules, Appl. Therm. Eng. 93 (2015) 1061–1073. doi:10.1016/j.applthermaleng.2015.10.014.
H. Yin, J. Ding, R. Jiang, X. Yang, Thermocline characteristics of molten-salt thermal energy storage in porous packed-bed tank, Appl. Therm. Eng. 110 (2017) 855–863. doi:10.1016/j.applthermaleng.2016.08.214.
X. Yang, X. Yang, F.G.F. Qin, R. Jiang, Experimental investigation of a molten salt thermocline storage tank, Int. J. Sustain. Energy. 35 (2016) 606–614. doi:10.1080/14786451.2014.930465.
L. Jianfeng, D. Jing, Y. Jianping, Solidification and melting behaviors and characteristics of molten salt in cold filling pipe, Int. J. Heat Mass Transf. 53 (2010) 1628–1635. doi:10.1016/j.ijheatmasstransfer.2010.01.033.
I. Im, W. Kim, K. Lee, A unified analysis of filling and solidification in casting with natural convection, Int. J. Heat Mass Transf. 44 (2001) 1507–1515. doi:10.1016/s00179310(00)00197-6.
Z. Liao, X. Li, Z. Wang, C. Chang, C. Xu, Phase change of molten salt during the cold filling of a receiver tube, Sol. Energy. 101 (2014) 254–264. doi:10.1016/j.solener.2014.01.002.
J. Wu, J. Ding, J. Lu, W. Wang, Migration and phase change phenomena and characteristics of molten salt leaked into soil porous system, Int. J. Heat Mass Transf. 111 (2017) 312–320. 29
Y. Zhang, J. Wu, W. Wang, J. Ding, J. Lu, Experimental and numerical studies on molten salt migration in porous system with phase change, Int. J. Heat Mass Transf. 129 (2019) 397–405. doi:10.1016/j.ijheatmasstransfer.2018.09.122.
R. Ferri, A. Cammi, D. Mazzei, Molten salt mixture properties in RELAP5 code for thermodynamic solar applications, Int. J. Therm. Sci. 47 (2008) 1676–1687. doi:10.1016/j.ijthermalsci.2008.01.007.
M. Chieruzzi, G.F. Cerritelli, A. Miliozzi, J.M. Kenny, L. Torre, Heat capacity of nanofluids for solar energy storage produced by dispersing oxide nanoparticles in nitrate salt mixture directly at high temperature, Sol. Energy Mater. Sol. Cells. 167 (2017) 60–69. doi:10.1016/j.solmat.2017.04.011.
J. Bonilla, M.M. Rodríguez-garcía, L. Roca, A. De, Design and experimental validation of a computational effective dynamic thermal energy storage tank model, Energy. 152 (2018) 840– 857. doi:10.1016/j.energy.2017.11.017.
S. Yang, W. Tao, Heat Transfer, Higher education press, n.d.
J.K. Carson, S.J. Lovatt, D.J. Tanner, A.C. Cleland, Thermal conductivity bounds for isotropic, porous materials, Int. J. Heat Mass Transf. 48 (2005) 2150–2158. doi:10.1016/j.ijheatmasstransfer.2004.12.032.
Thermal equilibrium temperature of foundation increases after leakage.
The operating temperature affects significantly migration characteristics.
Migration process of leaking molten salt are investigated experimentally.
Author statement Hao Zhou: Conceptualization, Methodology, Resources, Data Curation, Supervision, Project administration, Funding acquisition Hua Shi: Validation, Investigation, Writing- Original draft, Writing- Reviewing and Editing, Visualization Zhenya Lai: Investigation Yuhang Zuo: Investigation Shihao Hu: Investigation Mingxi Zhou: Writing- Reviewing and Editing.