Numerical and experimental investigation of a new conceptual fluoride salt freeze valve for Thorium based Molten Salt Reactor

Numerical and experimental investigation of a new conceptual fluoride salt freeze valve for Thorium based Molten Salt Reactor 1 2 first-author https://orcid.org/0000-0001-7205-6992 1 1 2 1 1 corresp Corresponding author, wangnaxiu@sinap.ac.cn Corresponding author, wangnaxiu@sinap.ac.cn wangnaxiu@sinap.ac.cn Shanghai Institute of Applied Physics, Chinese Academy of Sciences, Shanghai 201800, China Shanghai Institute of Applied Physics, Chinese Academy of Sciences, Shanghai 201800, China University of Chinese Academy of Sciences, Beijing 100049, China University of Chinese Academy of Sciences, Beijing 100049, China To improve the reliability and reduce energy consumption, a conceptual design of a freeze valve is proposed for the Thorium-based Molten Salt Reactor (TMSR) concept. Fins were utilized in this new design to enhance heat transfer and realize passive shut-off function, which could not be realized by the previous design. An experimental apparatus using the fluoride salt FLiNaK was constructed to conduct a series of preliminary solidification and melting experiments. In addition, the enthalpy–porosity method of ANSYS ® Fluent solver was applied to simulate the solidification process of the salt at a specified operating temperature. Temperature distributions of the fluoride salt, solidification/melting time, and frozen plug effect were analyzed under natural convection heat transfer in an open space. The calculated salt temperatures exhibited good agreement with the experimental values. The results indicated that the range of effective operating temperature is 530–600 °C for the finned freeze valve. In this study, the ideal set operating temperature of the finned freeze valve was chosen as 560 °C to achieve competent performance. Moreover, 560 °C is additionally the highest set operating temperature for maintaining excellent cooling performance and sustaining deep-frozen condition of the salt plug. At this set operating temperature, the simulation data indicated that the molten salt in the flat part of the finned freeze valve will completely solidify at 10.5 min. The percentage of solid salt in the flat and lower transitional parts of the valve reaches 29.60% in 30.0 min. Furthermore, the surface temperature of the proposed freeze valve is 11.10% lower compared with that of the TMSR freeze valve at a cooling gas supply of 173 m 3 /h. Therefore, the new freeze valve was proven to be capable of reducing the energy consumption and realizing the passive shut-off function. Fin Natural convection Freeze valve Fluoride salt Solidification Molten salt reactor 1. Introduction 1 Molten salt reactor (MSR) is one of the six candidates identified by the Generation IV International Forum (GIF), which has numerous advantages, including inherent safety, excellent neutron economy, and online reprocessing [ 1 1 , 2 2 ]. The MSRs were first proposed by Ed Bettis and Ray Briant of Oak Ridge National Laboratory (ORNL) during the post-World War II period in an attempt to design a nuclear-powered aircraft [ 3 3 ]. The first liquid-fuel r eactor technology of the world was developed by Eugene Wigner and Alvin Weinberg in 1945, which used uranium sulfate fuel dissolved in water [ 4 4 ]. In 1953, Weinberg realized this concept as a homogeneous reactor experiment (HRE) by using light water, and generated 150 kW of electricity [ 5 5 ]. The potential for extremely high temperature and power density was the point of interest in the aircraft propulsion project. As a product of the Aircraft Nuclear Propulsion program, the Aircraft Reactor Experiment (ARE) was conceptualized and operated at ORNL in 1954. It reached a maximum operating temperature of 880 ℃ and demonstrated the nuclear feasibility of operating a molten-salt-fueled reactor at high temperature [ 6 6 ]. Although this program was subsequently abandoned, the potential of MSRs for civilian power production was recognized [ 7 7 ]. This effort led to the design and construction of the Molten-Salt Reactor Experiment (MSRE), which was successfully operated in 1965–69. During operation, it demonstrated extraordinarily high levels of operability, availability, and maintainability [ 8 8 ]. Subsequently, some conceptual design works were carried on to construct a Molten Salt Breeder Reactor (MSBR). It focused on developing full‐scale reactor designs and utilizing the thorium-uranium fuel cycle to minimize electricity costs [ 9 9 ]. The MSBR effort was interrupted in 1972, resumed as a technology-development program (no conceptual work) in 1974, and finally ended in 1976 [ 10 10 ]. After the US program was discontinued, the research of MSRs entered a period of stagnation. Recently, much effort has been made by several countries toward studying MSRs. Japan proposed the design of FUJI MSR based on the MSBR design and conducted a series of studies [ 11 11 ]. The Safety assessment of the molten salt fast reactor (SAMOFAR) project focused on assessing the key safety features of the molten salt fast reactor (MSFR) proposed by the Centre National de la Recherche Scientifique (CNRS) in 2004 [ 12 12 , 13 13 ]. In China, the thorium-based molten salt reactor (TMSR) nuclear energy system was proposed as a strategic pilot technology special project [ 14 14 ] by the Shanghai Institute of Applied Physics (SINAP) of the Chinese Academy of Sciences (CAS), based on the liquid-fueled thorium molten salt reactor (TMSR-LF) [ 15 15 ] and solid-fueled thorium molten salt reactor (TMSR-SF) [ 16 16 , 17 17 ]. In this study, a key safety component of the TMSR is investigated. An important feature of the MSRs is enhanced safety. The experience gained from previous nuclear disasters indicate that passively removing the decay heat from the reactor core is preferable, i.e., without mechanical or electrical supply. The freeze valve provides inherent safety to MSRs to quickly drain the molten salt. The freeze valve, which is not a mechanical valve but a frozen-seal special-shaped pipe, has been proposed as one of the most important devices for the passive salt draining system in MSRs, because it has no moving parts and achieves zero leakage rate and safe draining of an overheated core. A typical freeze valve system mainly comprises a valve body and corresponding heating/cooling devices. Under normal operating conditions, the molten salt in the freeze valve is cooled to form a salt plug through an external cooling device, which can effectively block the flow of liquid salt in the pipeline. If accidents occur (such as power failure and core overheating) or the cooling device is turned off, the solid plug begins to melt. After the solid salt thaws, the fuel salt in the core is immediately and passively evacuated by gravitation draining into emergency discharge tanks. The freeze valve technology was first proposed by ORNL in the 1960s as a safety component of the MSRE system. The MSRE freeze valve was made from Schedule 40 INOR-8 pipe of size 1-1/2″, featuring a flattened section of 1-1/2″ in the middle [ 18 18 ]. There were 12 freeze valves in the MSRE, of which one was a passive salt draining valve. However, the other valves acted similar to a normally closed shut-off valve, which can be melted by external heaters. Further, SINAP developed a freeze valve prototype for molten salt loading and discharging based on the MSRE freeze valve design [ 19 19 ]. A high-temperature freeze valve engineering test facility and a high-temperature fluoride salt test loop were established to investigate the performance of the prototype valve. The prototype valve was extruded by a Hastelloy C (nickel-based alloy) tube of diameter 48.3 mm at room temperature. The height and length of the flat part were respectively 20.7 mm and 50 mm. The prototype valve had non-passive safety features. It utilized an external high-frequency induction coil to melt the salt plug and freeze the salt using the cooling gas supplied by an external high-pressure fan. Julien Giraud et al. [ 20 20 ] constructed two experimental facilities to improve the freeze valve design for molten salt application. Indarta Kuncoro Aji et al. [ 21 21 ] conducted a fundamental experiment to determine the thawing time of a typical salt. This experiment was conducted by pouring a liquid high transfer salt (HTS) on the top of a frozen HTS to detach the metal rod inserted in the frozen HTS. The actual freeze valve configuration was not utilized in this experiment. Recent numerical studies on the freeze valve mainly focused on calculating the passive draining time. Generally, the draining time is longer than the melting time. The specific discharge time is related to the liquid salt volume in the core tank above the freeze valve. The Delft University of Technology conducted several simulation investigations on the draining time of the salt plug [ 22 22 ]. Further, Qinhua Zhang [ 19 19 ] studied the comprehensive properties of the TMSR freeze valve in a high-temperature engineering test facility and found good performance of the TMSR freeze valve in a high temperature (up to 700 ℃) molten salt loop. Qiming Li et al. [ 23 23 , 24 24 ] investigated the thermal-structural performances of the TMSR freeze valve using the Finite Element numerical simulation method, and proved a reasonable agreement with the experimental data from the FLiNaK engineering test loop. Shisheng Wang et al. [ 25 25 ] analytically evaluated the draining time of a freeze valve by varying the draining tube diameter and length, and varying the solidification extent of a salt plug for SAMOFAR. Marco Tiberga et al. [ 26 26 ] preliminarily investigated the freeze-plug melting behavior and assessed the influence of various design configurations and parameters for MSFR, and found that it may be impossible to heat the salt plug to melt it only using the decay heat from a reactor core based on this freeze plug design. The objective of this study is to upgrade the design of the TMSR freeze valve for improving its reliability and reducing the energy consumption. A novel finned freeze valve was devised for this purpose. Moreover, an experimental system using the fluoride salt FLiNaK was built to investigate the effect of different set operating temperatures on the solidification time and melting time of the salt in the finned freeze valve. To investigate the solidification process of the salt, the enthalpy-porosity method adopted by ANSYS ® Fluent, Release 14.5 was selected to simulate the salt in the finned freeze valve at a specified operating temperature. Further, the temperature distributions of the fluoride salt were obtained and analyzed. The solidification time, melting time, and frozen plug effect of the finned freeze valve were analyzed as well. 2. Experimental study 1 2.1 Finned freeze valve unit 2 A new conceptual freeze valve, called the finned freeze valve, was invented by welding four similar longitudinal rectangular fins to the flat part of the TMSR freeze valve. The valve body of the finned freeze valve was the same as that of the TMSR freeze valve. Fig. 1 Fig. 1 displays the structure of the finned freeze valve. The finned freeze valve consisted of two straight parts, two transitional parts, a flat part, and four fins. The length of each part was 50 mm, and the total length was thus 250 mm. Table 1 Table 1 lists the main valve parameters. 1 1 Parameter 1 1 Value 1 1 Parameter 1 1 Value 1 1 Material of the finned freeze valve 1 1 Hastelloy C-276 alloy 1 1 Distance between the upper flat part and the top fin, d uf (mm) 1 1 2.5 1 1 Maximum operating temperature (℃) 1 1 700 1 1 Distance between the lower flat part and the bottom fin, d lf (mm) 1 1 2.5 1 1 Maximum operating pressure (MPa) 1 1 0.5 1 1 Length of each fin, l f (mm) 1 1 86.12 1 1 Outer diameter, OD (mm) 1 1 48.3 1 1 Thickness of each fin, t f (mm) 1 1 36.7 1 1 Inner diameter, ID (mm) 1 1 37.22 1 1 Height of each fin, H f (mm) 1 1 8 1 1 Height of the flat part, l a (mm) 1 1 75.68 1 1 Space between each fin, s f (mm) 1 1 3 1 1 Thickness of the flat part, t a (mm) 1 1 20.7 1 1 Width of each fin, w f (mm) 1 1 3 Subsequently, a finned freeze valve unit was constructed to conduct the following experiment. As illustrated in Fig. 2 Fig. 2 , the finned freeze valve unit was fabricated with a finned freeze valve, two extension tubes, an internal tube, two gas pipes, a valve support, three internal thermocouples, and ten surface thermocouples. The extension tubes, maintaining adequate flow of molten salt in the finned freeze valve, shared the diameter with the finned freeze valve. The upper extension tube was 100 mm long, whereas its lower counterpart was 50 mm long. The internal tube with an outer diameter of 8 mm was used to prevent the internal thermocouples from severe corrosion of the salt. The total length of the internal tube was 425 mm, 325 mm of which was immersed in the valve. Two gas pipes were connected to the upper heads of the finned freeze valve unit. The gas pipes were both 120 mm long and had a diameter of 6 mm. Afterward, the valve support, which had a diameter of 20 mm, was connected into the lower heads of the finned freeze valve. All the components were connected only by welding to achieve excellent airtightness. Most components of the finned freeze valve unit were made of Hastelloy C-276 alloy because of its outstanding corrosion resistance, whereas the inner tube and the gas pipes were made of Stainless steel 316 to ensure accessible small sizes. The FLiNaK (LiF-NaF-KF, 46.5-11.5-42.0 mol%) was used in this system for its excellent heat transfer characteristics in most of the molten salt; however, FLiNaK is a highly corrosive salt [ 27 27 ]. For reducing corrosion of the valve unit, highly pure salt must be used in this system. The FLiNaK powder of 0.6 kg with a purity of 90% was deposited and compressed into the finned freeze valve. After heating, the liquid molten salt was filled to half of the finned freeze valve because the volume decreases when the solid salt melts to become liquid salt. Therefore, the distance between the liquid salt level and the lower head of the finned freeze valve is approximately 175 mm, as shown in Fig. 2 Fig. 2 . Because temperature is the most important parameter in this experiment, three sheathed K‐type thermocouples were used to measure the salt temperature at three vertical locations in the finned freeze valve. Ten K‐type thermocouples were welded on the layer of the finned freeze valve to measure the surface temperatures; their positions are shown in Fig. 2 Fig. 2 . The distance between the internal thermocouples and the lower heads of the finned freeze valve unit are 175, 125, and 75 mm, respectively, from top to bottom. The surface thermocouples were at the midpoint of each part of the finned freeze valve and the midpoint of the top of the third fin. The errors in temperatures measured by the thermocouples were ±1 ℃. 2.2 Experimental system 2 The experiment was conducted in an open space and the ambient temperature was approximately 10 °C. As shown in Fig. 3(a) Fig. 3(a) , the experimental system includes a finned freeze valve unit, two electric heaters, a data acquisition and control system, and an argon loop. Fig. 3(b) Fig. 3(b) shows that the experimental system was placed in an experimental cabinet. The data acquisition and control system located was in the lower part of this experimental cabinet. The residual components were in the upper part of this experimental cabinet. All the data signals were collected and converted by the data acquisition and control system. The top and bottom of the extension tubes and the straight part of the finned freeze valve were completely enveloped by two heaters with heat insulation. The lengths of the upper and lower heaters were 150 mm and 100 mm, respectively. The uniform diameter and rated power of the two heaters were respectively 248 mm and 1.2 kW. The two heaters were heated independently and controlled by the data acquisition and control system. Under most scenarios, the two heaters were set to the same specific operating temperature. With an automatic controller, the temperature accuracy of the two heaters was less than ±1 °C. An argon loop was used to remove oxygen and water vapor from the valve. This argon loop included a high-pressure argon tank, pressure regulator, intake valve, exhaust valve, and gas pipelines. The argon gas used in this experimental system was supplied by a high‐pressure argon tank and had a purity of 99.9999%. The experimental system was built in-house by the Zhenjiang Sanwei Electric Heater Co., Ltd. Moreover, most of the products used in this experimental system, including fins, heaters, thermocouples, and the data acquisition and control system, were manufactured by and bought from Zhenjiang Sanwei Electric Heater Co., Ltd. 2.3 Experimental procedure 2 The specific operational procedures of the experimental system are as follows: (1) Prior to the experiment, argon gas should be injected from the high‐pressure argon tank and discharged into air to create an oxygen-free environment inside the valve. Aluminum silicate fiber blankets are wrapped around the transitional parts, flat part, and fins of the finned freeze valve for heat insulation. (2) Both the heaters are slowly heated beyond the melting temperature of FLiNaK of 454 °C. Simultaneously, a small flow of argon gas is continuously pumped to purge water vapor and impure vapor. (3) After purging, the intake and exhaust valves should be closed, and argon gas supply is stopped. The electric heaters are heated to a specific temperature and preserved for 12 h. (4) After the temperatures of the electric heaters reach the specified values, the aluminum silicate fiber blankets should be removed. The molten salt in the finned freeze valve is cooled to solidify under natural convection condition. (5) After the temperature distributions of the valve reach a steady-state condition, the blankets are enveloped around the transitional parts and the flat part of the valve again. The solid salt is heated to be melted. (6) When T 11 is above the melting point of the salt, the electric heaters are adjusted to the next target temperature. This temperature should be maintained for 12 h. (7) Step 4–6 are repeated to measure the melting and solidification process of the salt when the electric heaters are both set to 500 °C, 515 °C, 530 °C, 550 °C, 560 °C, 590 °C, 600 °C, 620 °C and 650 °C. (8) After completion of all the experiments, the blankets should be removed. The high‐pressure argon tank and the power supply of the experimental system should then be turned off. 2.4 Uncertainty analysis 2 The uncertainties of the experimental results include instrumentation errors and data acquisition system errors. The maximum error of the data acquisition and control system is 0.02%. For heat transfer analysis, the uncertainty of the Rayleigh number of the salt was determined using the Kline and Moffat method [ 28 28 ]. The uncertainties of the variables used in this study are listed in Table 2 Table 2 . As listed in Table 2 Table 2 , the uncertainty of the Rayleigh number of the salt is 31%. 1 1 Type 1 1 Parameter 1 1 Maximum uncertainty 1 11 Directly measured variables 1 1 T 1 – T 4 1 1 0.55% 1 1 T 5 1 1 2.71% 1 1 T 6 1 1 4.42% 1 1 T 7 1 1 10.88% 1 1 T 8 1 1 4.56% 1 1 T 9 1 1 8.79% 1 1 T 10 1 1 3.59% 1 1 T 11 1 1 3.64% 1 1 T 12 1 1 2.14% 1 1 T 13 1 1 1.06% 1 1 Mass of the salt 1 1 2.83% 1 4 Properties of the salt 1 1 Density 1 1 2% 1 1 Thermal conductivity 1 1 5% 1 1 Specific heat 1 1 10% 1 1 Viscosity 1 1 10% 1 1 Variables in empirical correlations 1 1 Rayleigh number of the salt 1 1 31% 3. Numerical approach 1 Directly analyzing the actual salt solidification process is difficult because of the impenetrable metal walls of the finned freeze valve. The main purpose of this simulation is to analyze the solidification process of the salt at a specific operating temperature using ANSYS ® Fluent solver [ 29 29 ]. To obtain more accurate numerical results, the boundary conditions and the material properties in this simulation were set as close as possible to their real experimental counterparts. For the same reason, the static experimental data at the selected operating temperature are used to determine the initial conditions of the time-dependent simulation, which takes 30 min. Moreover, the following assumptions are made to simplify the analysis: (1) Laminar flow, (2) Incompressible fluid, (3) Negligible viscous dissipation, (4) Negligible thermal contact resistance between the surface of the valve and the fins, (5) Assuming air exists only in the internal tube, the gas tubes and the internal thermocouples are neglected, (6) Air and molten salt are not blended, (7) Negligible fins in the thickness direction of the flat part of the finned freeze valve. 3.1 Computational model and boundary conditions 2 According to the work of Vogel and Thess [ 30 30 ], a 2D model is sufficient to accurately calculate the phase change material under natural convection condition. In this study, an approximate 2D model was utilized to simulate the solidification process of the salt. The 2D model considered the wall thickness of the valve surfaces, internal tube, and fins. As illustrated in Fig. 4 Fig. 4 , the top of the red liquid salt reaches the center of the flat part of the finned freeze valve. The surfaces of the valves wrapped by two heaters were assumed to have a constant temperature. This computational model lost heat predominantly by natural convection and heat radiation to room. The detailed parameters of the boundary conditions for this computational model are listed in Table 3 Table 3 . 1 1 Parameters of boundary conditions 1 1 Values 1 1 Specific temperature of both heaters, T h (°C) 1 1 560 1 1 Ambient temperature, T ∞ (°C) 1 1 10 1 1 Average convective heat transfer coefficient of the surfaces (W/m 2 /K) 1 1   1 1 Left fins, <math id="M1"><mrow><msub><mover accent="true"><mi>h</mi><mo>¯</mo></mover><mrow><mtext>lf</mtext></mrow></msub></mrow></math> 1 1 5.11 1 1 Right fins, <math id="M2"><mrow><msub><mover accent="true"><mi>h</mi><mo>¯</mo></mover><mrow><mtext>rf</mtext></mrow></msub></mrow></math> 1 1 5.13 1 1 Left flat part of the valve, <math id="M3"><mrow><msub><mover accent="true"><mi>h</mi><mo>¯</mo></mover><mrow><mtext>1s</mtext></mrow></msub></mrow></math> 1 1 4.21 1 1 Right flat part of the valve, <math id="M4"><mrow><msub><mover accent="true"><mi>h</mi><mo>¯</mo></mover><mrow><mtext>rs</mtext></mrow></msub></mrow></math> 1 1 4.06 1 1 Upper transitional part of the valve, <math id="M5"><mrow><msub><mover accent="true"><mi>h</mi><mo>¯</mo></mover><mrow><mtext>ut</mtext></mrow></msub></mrow></math> 1 1 4.23 1 1 Lower transitional part of the valve, <math id="M6"><mrow><msub><mover accent="true"><mi>h</mi><mo>¯</mo></mover><mrow><mtext>lt</mtext></mrow></msub></mrow></math> 1 1 4.33 Because of the highly complex geometry of the valve and the combination of the dynamic natural convection and radiation heat transfer at high temperature, accurately calculating the heat transfer between the valve and ambient air is difficult. In this research, therefore, an approximate calculation of the average natural convective heat transfer coefficients for the flat and transitional parts of the valve ( <math id="M7"><mrow><mover accent="true"><mrow><msub><mi>h</mi><mtext>s</mtext></msub></mrow><mo stretchy="true">¯</mo></mover></mrow></math> ) and the fins of the valve ( <math id="M8"><mrow><mover accent="true"><mrow><msub><mi>h</mi><mtext>f</mtext></msub></mrow><mo stretchy="true">¯</mo></mover></mrow></math> ) was performed as follows. The correlation of the Nusselt numbers ( Nu s ) for the flat and transitional parts of the valve was adopted from the empirical correlations for the vertical plate [ 31 31 ]. For the fins in the finned freeze valve, the correlation for Nusselt numbers ( Nu f ) was defined by the empirical correlations for the vertical heat sink [ 32 32 ]. The following equations were used to calculate them: <math display="block" id="M9"><mrow><mi>R</mi><mi>a</mi><mo>=</mo><mi>G</mi><mi>r</mi><mo>×</mo><mi>Pr</mi><mo>=</mo><mfrac><mrow><mn>2</mn><mi>g</mi><msup><mi>l</mi><mn>3</mn></msup><mi>Pr</mi></mrow><mrow><msup><mi>ν</mi><mn>2</mn></msup></mrow></mfrac><mo>×</mo><mfrac><mrow><mn>1</mn><mo>−</mo><mfrac><mrow><msub><mi>T</mi><mi>∞</mi></msub></mrow><mrow><msub><mi>T</mi><mtext>s</mtext></msub></mrow></mfrac></mrow><mrow><mn>1</mn><mtext>+</mtext><mfrac><mrow><msub><mi>T</mi><mi>∞</mi></msub></mrow><mrow><msub><mi>T</mi><mtext>s</mtext></msub></mrow></mfrac></mrow></mfrac><mo>,</mo></mrow></math> <math display="block" id="M10"><mrow><mi>R</mi><msub><mi>a</mi><mtext>s</mtext></msub><msup><mrow/><mo>′</mo></msup><mo>=</mo><mi>G</mi><mi>r</mi><mo>×</mo><mi>Pr</mi><mo>×</mo><mfrac><mrow><msub><mi>s</mi><mtext>f</mtext></msub></mrow><mrow><msub><mi>H</mi><mtext>f</mtext></msub></mrow></mfrac><mo>,</mo></mrow></math> <math display="block" id="M11"><mrow><mi>R</mi><msub><mi>a</mi><mtext>f</mtext></msub><msup><mrow/><mo>′</mo></msup><mo>=</mo><mi>G</mi><mi>r</mi><mo>×</mo><mi>Pr</mi><mo>×</mo><msup><mrow><mrow><mo>(</mo><mrow><mfrac><mrow><msub><mi>H</mi><mtext>f</mtext></msub></mrow><mrow><msub><mi>l</mi><mtext>f</mtext></msub></mrow></mfrac></mrow><mo>)</mo></mrow></mrow><mrow><mn>0.5</mn></mrow></msup><mo>×</mo><mfrac><mrow><msub><mi>s</mi><mtext>f</mtext></msub></mrow><mrow><msub><mi>H</mi><mtext>f</mtext></msub></mrow></mfrac><mo>,</mo></mrow></math> <math display="block" id="M12"><mrow><mi>N</mi><msub><mi>u</mi><mtext>s</mtext></msub><mo>=</mo><mn>0.59</mn><mo>×</mo><msup><mrow><mrow><mo>(</mo><mrow><mi>R</mi><msub><msup><mi>a</mi><mo>′</mo></msup><mtext>s</mtext></msub></mrow><mo>)</mo></mrow></mrow><mrow><mn>0.25</mn></mrow></msup><mo>,</mo></mrow></math> <math display="block" id="M13"><mrow><mi>N</mi><msub><mi>u</mi><mtext>f</mtext></msub><mo>=</mo><mn>0.0929</mn><mo>×</mo><msup><mrow><mrow><mo>(</mo><mrow><mi>R</mi><msub><msup><mi>a</mi><mo>′</mo></msup><mtext>f</mtext></msub></mrow><mo>)</mo></mrow></mrow><mrow><mn>0.5</mn></mrow></msup><mo>,</mo></mrow></math> <math display="block" id="M14"><mrow><msub><mi>h</mi><mtext>s</mtext></msub><mo>=</mo><mfrac><mrow><mi>N</mi><msub><mi>u</mi><mtext>s</mtext></msub><mo>×</mo><mi>k</mi></mrow><mrow><msub><mi>l</mi><mtext>s</mtext></msub></mrow></mfrac><mo>,</mo></mrow></math> <math display="block" id="M15"><mrow><msub><mi>h</mi><mtext>f</mtext></msub><mo>=</mo><mfrac><mrow><mi>N</mi><msub><mi>u</mi><mtext>f</mtext></msub><mo>×</mo><mi>k</mi></mrow><mrow><msub><mi>l</mi><mtext>f</mtext></msub></mrow></mfrac><mo>,</mo></mrow></math> <math display="block" id="M16"><mrow><mover accent="true"><mrow><msub><mi>h</mi><mtext>s</mtext></msub></mrow><mo stretchy="true">¯</mo></mover><mtext>=</mtext><mfrac><mrow><mstyle displaystyle="true"><munderover><mo>∑</mo><mrow><mi>i</mi><mo>=</mo><mn>1</mn></mrow><mi>t</mi></munderover><mrow><msub><mi>h</mi><mrow><mtext>s</mtext><mo>,</mo><mi>i</mi></mrow></msub></mrow></mstyle></mrow><mi>t</mi></mfrac><mo>,</mo></mrow></math> <math display="block" id="M17"><mrow><mover accent="true"><mrow><msub><mi>h</mi><mtext>f</mtext></msub></mrow><mo stretchy="true">¯</mo></mover><mtext>=</mtext><mfrac><mrow><mstyle displaystyle="true"><munderover><mo>∑</mo><mrow><mi>i</mi><mo>=</mo><mn>1</mn></mrow><mi>t</mi></munderover><mrow><msub><mi>h</mi><mrow><mtext>f</mtext><mo>,</mo><mi>i</mi></mrow></msub></mrow></mstyle></mrow><mi>t</mi></mfrac><mo>,</mo></mrow></math> where Ra , Gr , and Pr represent the Rayleigh number, Grashof number, and Prandtl number, respectively; <math id="M18"><mrow><mi>R</mi><msubsup><mi>a</mi><mtext>s</mtext><mo>'</mo></msubsup></mrow></math> is modified by the ratio of the fin width to the fin height [ 33 33 ] and <math id="M19"><mrow><mi>R</mi><msubsup><mi>a</mi><mtext>f</mtext><mo>'</mo></msubsup></mrow></math> is a modified Rayleigh number [ 32 32 ]; subscript i represents the different experimental time ranging from 1 to t ; t is the total experimental interval; <math id="M20"><mrow><mo> </mo><msub><mi>h</mi><mrow><mtext>s</mtext><mo>,</mo><mi>i</mi></mrow></msub></mrow></math> is the convective heat transfer coefficient for the flat and transitional parts of the valve at different experimental times; <math id="M21"><mrow><msub><mi>h</mi><mrow><mtext>f</mtext><mo>,</mo><mi>i</mi></mrow></msub></mrow></math> is the convective heat transfer coefficient for the fins of the valve at different experimental times; g is the gravitational constant, and <math id="M22"><mrow><msub><mi>l</mi><mtext>s</mtext></msub></mrow></math> and <math id="M23"><mrow><msub><mi>l</mi><mtext>f</mtext></msub></mrow></math> are respectively the characteristic length of the surfaces and fins of the valve; V is the kinematic viscosity of air; <math id="M24"><mrow><msub><mi>T</mi><mtext>s</mtext></msub></mrow></math> represents the surface temperatures of the valve; <math id="M25"><mrow><msub><mi>T</mi><mi>∞</mi></msub></mrow></math> represents the temperature of ambient air; k is the thermal conductivity of ambient air. The definitions of H f , L f , and s f can be found in Table 1 Table 1 . Based on the Kline and Moffat method [ 28 28 ], the uncertainties of <math id="M26"><mrow><mover accent="true"><mrow><msub><mi>h</mi><mtext>s</mtext></msub></mrow><mo stretchy="true">¯</mo></mover></mrow></math> and <math id="M27"><mrow><mover accent="true"><mrow><msub><mi>h</mi><mtext>f</mtext></msub></mrow><mo stretchy="true">¯</mo></mover></mrow></math> are respectively 57.79% and 58.32%. The heat transfer coefficient distributions in the finned freeze valve unit are asymmetric because of the corresponding asymmetric experimental data distributions. For the same reason, the salt solidification process is different between the left and right parts of the finned freeze valve unit. 3.2 Materials 2 Table 4 Table 4 and Table 5 Table 5 summarize the material properties used in this paper. The molten salt used in this paper is FLiNaK. The Hastelloy C-276 alloy is used to make the finned freeze valve unit. However, a few open sources have reported emissivity of Hastelloy C-276 alloy. Based on the engineering experience, the emissivity of this alloy is assumed to be 0.25 in this study. 1 1 Property 1 1 FLiNaK [ 34 34 ] 1 1 Stainless steel 316 1 1 Air 1 1 Density (kg/m 3 ) 1 1 ρ =2579-0.624 × T 1 1 8030 1 1 Incompressible ideal gas 1 1 Thermal conductivity (W/m/°C) 1 1 k =0.36-0.00056 × T 1 1 14.6 1 1 0.0242 1 1 Specific heat capacity (J/kg/°C) 1 1 c solid = 1299.259 - 0.97796 × T + 1.533 × 10 -3 × T 2 1 1 450 1 1 1006.43 1 1 Viscosity (kg/m/s) 1 1 μ =0.04e 4170/ T 1 1 - 1 1 1.7894e-05 1 1 Latent heat (J/kg) 1 1 403,800 1 1 - 1 1 - 1 1 Melting temperature (°C) 1 1 454 1 1 - 1 1 - 1 1 Temperature (°C) 1 1 Density (kg/m 3 ) 1 1 Emissivity 1 1 Thermal conductivity (W/m/°C) 1 1 Specific heat capacity (J/kg/°C) 1 1 20 1 1 8890 1 1 0.25 1 1 10.2 1 1 426 1 1 100 1 1 8890 1 1 0.25 1 1 11.6 1 1 438 1 1 200 1 1 8890 1 1 0.25 1 1 13.4 1 1 453 1 1 300 1 1 8890 1 1 0.25 1 1 15.1 1 1 469 1 1 400 1 1 8890 1 1 0.25 1 1 16.7 1 1 483 1 1 500 1 1 8890 1 1 0.25 1 1 18.1 1 1 493 1 1 600 1 1 8890 1 1 0.25 1 1 20.2 1 1 515 1 1 700 1 1 8890 1 1 0.25 1 1 25.7 1 1 609 1 1 800 1 1 8890 1 1 0.25 1 1 25.8 1 1 605 1 1 900 1 1 8890 1 1 0.25 1 1 25.9 1 1 609 1 1 1000 1 1 8890 1 1 0.25 1 1 27.2 1 1 605 3.3 Grid independence test and solving method 2 In this study, an unstructured grid with 259166 cells was selected for the transient calculation of the solidification process of the salt. A grid independence test allowed the determination of an adequate mesh resolution, the results of which are provided in Table 6 Table 6 . It can be seen that the percentage difference of T 11 between the mesh counts of 259166 cells and 649609 cells is 0.03%. Similarly, this difference is respectively 0.01%, 0.08%, and 0.07% for T 5 , T 8 , and T 9 . Thus, an unstructured grid with 259166 cells was selected for the transient calculation in this research. The enthalpy-porosity method adopted by the solidification and melting model was used to investigate the solidification process of the salt. The mushy zone parameter was set to 10 5 . The Discrete Ordinates (DO) model was used to resolve the radiation equation. The first order upwind scheme for the DO model was used in this paper. The first order implicit formulation was used for the transient time scheme. The pressure-implicit with splitting of operators (PISO) algorithm was used to solve the pressure and velocity fields in this simulation. The residual errors of energy and DO intensity were less than 10 -7 and the residual errors of other equations were smaller than 10 -4 . Based on the Courant–Friedrichs–Lewy (CFL) condition, the time step was set to 0.01 s. The number of maximum iterations per time step was set as 500, which ensured that the calculation in every iteration was converged. Furthermore, the values of T 5 , T 11 , T 12 , and T 13 at 90 s were compared when the time steps were 0.01 s and 0.001 s. As shown in Table 7 Table 7 , the maximum deviation between T 5 , T 11 , T 12 , and T 13 is 0.087%. Thus, the time step of 0.01 s was proven to be sufficiently small to calculate the solidification process of the salt. 1 2 Cell numbers 4 1 Temperature (°C) 1 1 T 5 1 1 T 8 1 1 T 9 1 1 T 11 1 1 73848 1 1 424.125 1 1 329.862 1 1 325.6 1 1 323.379 1 1 131656 1 1 420.339 1 1 321.197 1 1 318.63 1 1 321.492 1 1 259166 1 1 420.288 1 1 320.983 1 1 318.432 1 1 321.274 1 1 649609 1 1 420.231 1 1 320.726 1 1 318.199 1 1 321.014 1 2 Time step (s) 4 1 Temperature (°C) 1 1 T 5 1 1 T 11 1 1 T 12 1 1 T 13 1 1 0.01 1 1 502.638 1 1 511.189 1 1 544.045 1 1 553.999 1 1 0.001 1 1 502.742 1 1 511.509 1 1 544.520 1 1 553.885 1 1 Deviation 1 1 0.021% 1 1 0.063% 1 1 0.087% 1 1 -0.021% 3.4 Model validation and sensitivity analysis of the numerical results 2 To check the capability of the present 2D model, the experimental results of T 11 and T 12 were compared with those of the simulation data at the set operating temperature of 560 ℃. As presented in Fig. 5(a) and (b) Fig. 5(a) and (b) , the simulation results of T 11 and T 12 are in agreement with the experimental values. The deviations between the experimental and the numerical results are less than 8.14% under all conditions. The present model is acceptable for engineering analysis, considering the complex geometry and the dynamic heat transfer process in this experiment. From Fig. 5(a) Fig. 5(a) , it is observed that the experimental results are better than the simulation results at the beginning of the experiment because of the remaining thermal inertia immediately after the aluminum silicate fiber blankets are removed. The simulated results of T 11 show an approximate step at the time ranging from 3.5 min to 5 min because the salt in the flat part of the valve is in the phase change zone. However, the corresponding step is undetectable in the experimental results of T 11 during this period, because the simulated model is a simplified 2D model and the fins in the thickness direction of the flat part are neglected. Therefore, the actual heat loss in the flat part of this valve is higher than that simulated, and the energy is thus insufficient to sustain the heat balance of the phase change zone. For the same reason, the measured values of T 11 in the later stages of the experiment are lower than the simulated values. In Fig. 5(b) Fig. 5(b) , it can be seen that the experimental results of T 12 in the later stages of the experiment are higher than the simulation results. The main reason is that the heat flux of the lower heater became the determining factor, which affected the value of T 12 in the later stages of the experiment. Considering the relatively large uncertainties of the salt properties, a sensitivity analysis of the numerical results was performed. Fig. 6 Fig. 6 shows the deviations of the calculation results with the uncertainties of the salt properties from the original simulation data. All simulation results were obtained at 90 s. Fig. 6 Fig. 6 indicates that the effect of salt properties on the numerical results is in the order of specific heat > heat conductivity > density > viscosity. 4. Results and discussion 1 4.1 Solidification time and melting time of the fluoride salt in the finned freeze valve with different set operating temperatures 2 The operational experience of MSRE suggested that the minimum surface temperature must be 343.33 °C to form a deep-frozen salt plug in the flat part of the freeze valve [ 18 18 ]. Based on this experience, it is assumed that the salt in the flat part of the finned freeze valve is solidified to a deep-frozen condition, when T 11 reaches 350 °C, in this study. Three key time definitions are made as follows. The solidification time is the interval when T 11 cools from the initial temperature of the salt to the melting point of the salt in the solidification experiment. The deep-frozen time is the interval when T 11 decreases from the initial temperature of the salt to 350 °C. The melting time is the interval when T 11 increases from the salt temperature at the end of the solidification experiment to the melting point of the salt. Fig. 7 Fig. 7 shows the distributions of T 11 and T 12 at the beginning and the end of the solidification experiment when the temperature of both the electric heaters are set to 500 °C, 515 °C, 530 °C, 550 °C, 560 °C, 590 °C, 600 °C, 620 °C, and 650 °C. With the increase in the set operating temperature, both T 11 and T 12 increase. T 11-b and T 11-e represent the values of T 11 at the beginning and the end of the solidification experiment, respectively, and T 12-b and T 12-e represent the values of T 12 at the beginning and the end of the solidification experiment, respectively. When the set operating temperature is below 515 °C, T 11-b is below the melting point of FLiNaK, and the salt plug is already formed in the flat part of the valve before measurements can be performed, making the solidification experiment impossible to be conducted. The temperature of T 11-e is higher than the melting point of FLiNaK with the set operating temperature of above 620 °C. At this temperature, the salt in the flat part of the finned freeze valve would still be thawing after the solidification experiment. Therefore, the effective set operating temperature range of the solidification and melting experiments is 530–600 °C in this study. Fig. 8 Fig. 8 depicts the variations of the key intervals with increasing set operating temperature. The solidification time and the deep-frozen time of FLiNaK increased with the increasing set operating temperature, whereas the melting time decreases. No data are shown for the deep-frozen time after the set operating temperatures exceed 560 °C because T 11 did not cool down to 350 °C within 30 min under these operating conditions. There is no definitive assessment for the frozen plug effect of the finned freeze valve. However, a competent finned freeze valve requires the shortest melting time possible when achieving a deep-frozen state, because it is essential to thaw the formed salt plug as quickly as possible for opening the valve alongside increasing the intensity of the salt plug. From Fig. 8 Fig. 8 , it is seen that the molten salt in the flat part of the finned freeze valve achieves the deep-frozen state within 23 min and melts within 16.5 min, when the operating temperature is set to 560 °C. Thus, the ideal set operating temperature is 560 °C for a competent performance of the finned freeze valve in this study. 4.2 Effects of the set operating temperatures on the cooling rates of the salt 2 Fig. 9 Fig. 9 shows the cooling rates of the salt with increasing set operating temperatures in this solidification experiment. It can be observed that the cooling rate of T 11 and T 12 is higher than that of T 13 because the heat insulations are not provided for the flat and lower parts of the valve. When T h is less than 560 ℃, the cooling rate of T 11 remains almost constant. Further, when T h is higher than 560 ℃, the cooling rate of T 11 decreases because of the effect of stronger heat flux from the lower heater. For the same reason, T 12 and T 13 have the same cooling rate when T h is higher than 590 ℃. At this condition, the heat flux from the lower heater is sufficiently strong for T 12 to agree with T 13 . This suggests that the finned freeze valve has a good heat loss performance when T h is less than 560 ℃. Once T h exceeds 560 ℃, the increase in temperature caused by the heat radiation of heaters is larger than the temperature loss caused by natural convection between the fins of the valve and ambient air, and the cooling rate of T 11 decreases. Thus, the temperature of the heaters should be below 560 ℃ to maintain the excellent cooling performance of the finned freeze valve. 4.3 Comparison of the effects of salt plug on finned freeze valve and TMSR freeze valve 2 Fig. 10 Fig. 10 compares the effects of salt plug between the experimental results of the finned freeze valve and the experimental data of the TMSR freeze valve reported in [ 36 36 ], when the set operating temperature is 600 ℃. T 8t represents the surface temperature at the right midpoint of the flat part of the TMSR freeze valve with the cooling gas flux of 173 m 3 /h. The figure shows that T 8 is lower than T 8t by 11.10% in 30 min. This suggests that the heat loss performance of the finned freeze valve is better than that of the TMSR freeze valve with the cooling gas flux of 173 m 3 /h. Therefore, energy consumption can be reduced by adding fins to the surface of the freeze valve. For opening the valve, it is important to ensure that the melting time of the finned freeze valve is good. Thus, the melting times of the finned freeze valve and the TMSR freeze valve with a set operating temperature of 550 °C were compared. The melting times of the finned freeze valve and TMSR freeze valve were 21.5 min and 20 min, respectively [ 36 36 ]. It was found that the melting time of the finned freeze valve was slightly longer than that of the previous design because the fins enhance the heat dissipation in the finned freeze valve. 4.4 Simulation of the solidification process of salt at a specific operating temperature 2 Fig. 11 Fig. 11 shows the solidification process of the salt in the flat and lower transitional parts of the finned freeze valve with increasing time. The areas in red and blue represent liquid and solid states, respectively, and the residual areas represent the solid–liquid coexistence zone. At t = 3.0 min, the salt near the edge of the valve body starts to solidify. At t = 4.0 min, the salt at the location of the thermocouple probe of T 11 begins to solidify. At t = 5.0 min, the salt at the location of T 11 is completely solidified. At t = 7.0 min, the salt at the lower transitional part starts to solidify. At t = 10.5 min, the molten salt at the flat part is completely solidified. At t = 30.0 min, the liquid salt did not reach the height of T 12 . Therefore, it can be concluded that the frozen plug effect of the finned freeze valve is excellent beyond the experimental time of 10.5 min. Furthermore, the percentage of solid salt in the flat and lower parts of the valve increased from 0.09% at 3.0 min to 29.60% at 30.0 min, as shown in Fig. 12 Fig. 12 . In summary, the solidification time estimated in this simulation work is conservative. The top of the frozen surface is flat as shown in Fig. 11 Fig. 11 . In actuality, the frozen layer is not smooth because of the volume expansion caused by the transformation of liquid salt to solid salt. The volume expansion of the salt pushes the liquid salt down and accelerates the solidification process. Therefore, the actual solidification time is less than the simulated time. In addition, the volume expansion phenomenon contributes to the temperature deviations shown in Fig. 5 Fig. 5 . Further, the salt at the internal edges of the valve is frozen well before the salt at the external edges of the internal tube freezes. The size of the internal tube is expected to affect the freezing process of the salt in the valve. However, this factor was not studied in this preliminary research, and will be considered in future research. 5. Conclusion 1 The main aspect of this study was the idea of fins–freeze valve combination, based on which a novel freeze valve was proposed for TMSR. It acts as a passive shut-off valve in the TMSR, allowing for the salt to be crystallized without external cooling devices. An experimental apparatus was built to test the preliminary performance of the finned freeze valve. The solidification and melting processes of FLiNaK in the valve with different set operating temperatures were investigated at the condition of natural convection heat transfer. Moreover, the enthalpy-porosity method was applied to simulate the solidification process of FLiNaK over time at a specified operating temperature. From this study, the following main conclusions and recommendations for future studies can be drawn: (1) The effective temperature range of the finned freeze valve is 530–600 °C. If the set operating temperature is lower than 530 °C, the valve should not melt to open. If the set operating temperature is higher than 600 °C, the salt plug should not form. (2) With the increasing set operating temperature, the solidification time and the deep-frozen time of the finned freeze valve increase, whereas the melting time decreases. (3) The ideal operating temperature is 560 °C to achieve competent performance of the finned freeze valve, i.e., the melting time of the salt plug is as short as possible when the valve achieves the deep-frozen state. In addition, 560 °C is the maximum set operating temperature to prevent attractive heat loss from occurring because of the heat radiation generated by the lower heater, and realize the deep-frozen state of the salt plug in the flat part of the finned freeze valve. (4) The surface temperature of the finned freeze valve under natural convection decreases by 11.10% compared with that of the TMSR freeze valve at a cooling gas supply of 173 m 3 /h. (5) The salt simulation results at the center of the flat and lower transitional parts are in good agreement with the experimental values, whose errors are less than 8.14%. The simulation results indicate that the molten salt of the flat part solidifies completely at 10.5 min, when the operating temperature is set to 560 ℃. Additionally, the percentage of salt plug in the flat and lower transitional parts of the valve is 29.60% in 30.0 min. Consequently, it can be concluded that the novel finned freeze valve design is suitable for reducing the energy consumption by adding fins to the surface of the TMSR freeze valve and realizing the passive shut-off function. Future research scope encompasses improving the experiment, developing more accurate models, and investigating the effect of internal tubes of different sizes on the freezing process of the salt. For improving the experiment, the finned freeze valve should be filled with liquid salt. 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Su et al ., Structural design and finite element analysis of a normally-closed finned freeze valve , Nuclear Power Engineering , 2019 . http://kns.cnki.net/kcms/detail/51.1158.tl.20190626.1045.003.html http://kns.cnki.net/kcms/detail/51.1158.tl.20190626.1045.003.html (in Chinese) Structural design and finite element analysis of a normally-closed finned freeze valve 10.1007/s41365-020-0729-5 This work was supported by the National Natural Science Foundation of China (No. 91326201) and the Strategic Pilot Technology Chinese Academy of Sciences (No. XDA0201002). 2019-09-24 2019-12-31 2020-01-01 2020-01-31 2020-02-01 2021-04-10 © China Science Publishing & Media Ltd. (Science Press), Shanghai Institute of Applied Physics, the Chinese Academy of Sciences, ChineseNuclear Society and Springer Nature Singapore Pte Ltd. 2020 This is a post-peer-review, pre-copyedit version of an article published in Nuclear Science and Techniques. The final authenticated version is available online at: http://dx.doi.org/10.1007/s41365-020-0729-5 http://dx.doi.org/10.1007/s41365-020-0729-5 . 2020 Nuclear Science and Techniques 2 31