Method for analyzing melting and solidification characteristics of liquid metal fast reactor fuel

Abstract

The invention discloses a liquid metal fast reactor fuel melting and solidification characteristic analysis method. The method comprises the following steps: 1, calculating a heat exchange coefficient; 2, determining an interface temperature; 3, calculating net energy transfer at an interface; 4, calculating a non-equilibrium mass transfer rate; and 5, calculating the equilibrium solidification process. As a whole, the analysis process aims at two parts of non-equilibrium fusion and solidification calculation and equilibrium fusion and solidification calculation; according to the method, the solidification process of the molten fuel on the structure surface is considered from the microscopic mechanism level, and reasonable modeling analysis is carried out on the basis. The mass transfer rate in the non-equilibrium process is determined by the net energy transfer rate and melting latent heat at the interface of the melt and the structure, the mass transfer rate in the equilibrium process is calculated based on thermodynamic energy driving, and the heat exchange coefficient and the interface temperature need to be reasonably determined in the process to obtain the accurate mass transfer rate. According to the method, the basic mechanism of solidification of the fuel in the narrow channel is reasonably explained, and a result which is relatively consistent with that of an experiment is obtained for fuel solidification and relocation calculation.

Description

Technical Field

[0001] The invention belongs to the technical field of nuclear reactor safety analysis, and in particular relates to a method for analyzing the melting and solidification characteristics of liquid metal fast reactor fuel. Background Art

[0002] As a typical type of fourth-generation advanced nuclear reactor, the liquid metal fast reactor meets the requirements of safety, economy, sustainability and nuclear non-proliferation, and plays an important role in the field of nuclear reactors. Therefore, safety analysis and evaluation of liquid metal fast reactors is an indispensable subject.

[0003] A major issue in fast reactor safety is that in the event of a hypothetical core disruptive accident (CDA), the molten material is released after the fuel breaks, and then migrates, diffuses, and relocates. It may be suspended or settled in the coolant, and there is a possibility of aggregation and deposition at the bottom of the core, which may further cause the core to return to criticality. However, if the fuel can be quickly moved out of the core area under the action of buoyancy, natural circulation, etc., and the fuel accumulates on the surface of the structure, the possibility of the core returning to criticality will be reduced to a certain extent, and the main factor affecting this process is the relocation process of the molten fuel.

[0004] Under CDA, the molten fuel diffuses and migrates in the core, and exists mostly in the form of solid fuel particles in the coolant, which may cause a certain degree of blockage and promote the core to return to criticality. Therefore, it is extremely necessary to reasonably simulate the solidification process of the molten fuel in the core on the surface of the structure. At present, the SIMMER series of programs are mostly used internationally to calculate and analyze this process, and computational fluid dynamics (CFD) programs are mostly used in China to study the fuel diffusion process during CDA of liquid metal reactors, including fuel accumulation, but there is still a lack of specialized analysis tools. Summary of the invention

[0005] In order to solve the problems existing in the above-mentioned prior art, the purpose of the present invention is to provide a method for analyzing the melting and solidification characteristics of liquid metal fast reactor fuel. The present invention is based on the microscopic solidification mechanism, and through reasonable simulation of the supercooling temperature, the heat transfer coefficient and the specified corresponding solidification behavior criterion, a more reasonable simulation prediction of the solidification behavior of the melt in the steel tube wall is achieved, which is of great significance to the field of safety analysis under CDA of my country's nuclear reactors.

[0006] In order to achieve the above object, the present invention adopts the following technical solution:

[0007] The method for analyzing the melting and solidification characteristics of liquid metal fast reactor fuel is characterized by comprising five steps: five steps: step 1. calculating the heat transfer coefficient; step 2. determining the interface temperature; step 3. calculating the net energy transfer at the interface; step 4. calculating the non-equilibrium mass transfer rate; step 5. calculating the equilibrium solidification process.

[0008] Step 1: Calculation of heat transfer coefficient

[0009] The melt initially contacts the structure at discrete points and is cooled by heat transfer at these contact points. During the cooling process, the melt near the surface of the structure is cooled below its liquidus temperature and forms a supercooled layer containing some solid particles. If the supercooled layer is then sufficiently cooled, it may further solidify to form a hard shell. For the above heat and mass transfer process, the heat transfer coefficient involved in the calculation must first be obtained. The heat transfer coefficient expression of the melt under turbulent conditions is shown in formula (1):

[0010] h l =(κ l / D h )Nu (1)

[0011] Nu=2.0+0.023Re 0.8 Pr 0.3 (2)

[0012] Nu=5.0+0.025Re 0.8 Pr 0.8 (3)

[0013] Where: h l represents the melt heat transfer coefficient, κ l Denotes the thermal conductivity of the melt, D h represents the hydraulic diameter, Nu, Re, and Pr represent the Nusselt number, Reynolds number, and Prandtl number, respectively; Formulas (2)-(3) represent the total Nusselt number of thermal conductivity and convection heat transfer of the fluid, which is used to calculate the heat transfer coefficient on the melt side; for liquid metals with low Prandtl numbers (Pr < 0.1), their thermal conductivity is relatively strong, and the thermal conductivity Nusselt number is 5.0; for liquid oxide materials, their thermal conductivity Nusselt number is 2.0, and the DB formula is used for convection heat transfer calculation;

[0014] The heat transfer coefficient on the structural side is defined as the ratio of thermal conductivity to semi-penetration length. The specific expression is as follows:

[0015] h s =2κ s / L s (4)

[0016] Where: h s represents the heat transfer coefficient on the structural side, κ s represents the structural thermal conductivity, L s It represents the heat penetration length on the structure side, characterizing the thermal response speed of the structure. It is defined by the structure density, specific heat and time constant. Assuming that the transient temperature distribution is approximately a parabola, the heat penetration length on the structure side is expressed as follows:

[0017]

[0018] Where: τ s , s 、c s are the time constant, density and heat capacity of the structure respectively; to ensure the stability of the numerical solution, the time constant should be no less than 6 times the time step;

[0019] Formulas (1) and (4) are the standard heat transfer coefficient calculation methods for the melt and structure sides. However, in actual processes, there is a certain gap between the melt and the structure surface. Therefore, it is necessary to consider the thermal resistance of the melt in contact with the structure at discrete points. The contact points are idealized as circles with a radius of r, and the separation distance between the contact points is D. The interfacial resistance-corrected heat transfer coefficients on the melt side and the structure side are given by formulas (6) and (7), respectively:

[0020]

[0021]

[0022] ω(n)=1-1.40925n+0.40925n 3 (8)

[0023]

[0024] η=r / D (10)

[0025] Where: It represents the heat transfer coefficient corrected by the interface resistance on the melt side, represents the heat transfer coefficient corrected by the interface resistance on the structure side, η is the ratio of the contact point radius to the contact point separation distance, ω(η) is the empirical relationship about η, υ l represents the melt velocity, the contact density N in formula (9) is calculated according to the mainstream velocity, and a and b are empirical constants. After solid particles are generated in the melt, assuming that turbulent transport makes the particles and the melt evenly mixed, the effective viscosity of the fluid gradually increases, and when the proportion of particles in the fluid exceeds a certain value, the flow stops due to the rapid increase in effective viscosity. The effective viscosity of the melt is modeled, and the expression of the particle viscosity factor changing with the particle volume fraction is as follows:

[0026]

[0027] The particle viscosity factor defined in formula (11) will be applied to the momentum exchange function to solve the momentum equation and update the velocity field; where f is the particle viscosity factor, F represents the original melt viscosity part, the default value is 1.0, k is the coefficient in the particle viscosity formula, the default value is 5.0, α Mp The maximum filling fraction that characterizes the particle viscosity factor, the default value is 0.62; α p is the particle volume fraction;

[0028] When the supercooled layer is completely solidified, the energy of the flowing melt will be transferred to the hard shell. The criterion for defining the transition from the supercooled layer to the hard shell is given by the width of the supercooled layer. The expression of the hard shell transformation criterion is as follows:

[0029]

[0030] Where: Δ c Indicates the hard shell thickness, W crust is the empirical constant in the hard shell thickness judgment criterion, and its default value is 0.5. When the hard shell is formed, the discrete contact between the melt and the structural surface is converted into the contact thermal resistance between the hard shell and the structural surface. The equivalent heat transfer coefficient of the interface resistance between the hard shell and the structure is given by the following formula:

[0031]

[0032] Where: represents the equivalent heat transfer coefficient of the interface resistance between the hard shell and the structure, κ c represents the thermal conductivity of the hard shell;

[0033] The total heat transfer coefficient between the hard shell and the structure is given by equation (14):

[0034]

[0035] h c =2κ c / Δ c (15)

[0036] Where: h c,s represents the total heat transfer coefficient between the shell and the structure, h c is the shell-side heat transfer coefficient; for non-equilibrium processes, the mainstream temperature of the melt or the structure temperature usually does not meet the phase change conditions, and mass transfer occurs at the interface. When the energy transferred from the flowing melt to the supercooled layer exceeds the energy that the structure can absorb under non-melting conditions, the structure undergoes non-equilibrium melting; similarly, when the energy obtained through the supercooled layer exceeds the energy transferred from the flowing melt to the supercooled layer, the melt undergoes non-equilibrium solidification; if both conditions are not met, it is considered that non-equilibrium mass transfer process does not occur; the judgment criteria for non-equilibrium melting and solidification processes are expressed by equations (16) and (17), respectively:

[0037]

[0038]

[0039]

[0040] Where: T l represents the melt temperature, represents the interface temperature of the supercooled layer, T s represents the structural temperature, T s,sol represents the solidus temperature of the structure, h scl,s Represents the total heat transfer coefficient between the supercooling layer and the structure;

[0041] Step 2: Determine the interface temperature

[0042] The expression for the interface temperature between the melt and the structure is defined as follows:

[0043]

[0044] Where: T I represents the interface temperature between the melt and the structure, ρ l 、c p,l They represent the density and specific heat at constant pressure of the melt, ρ s 、c p,s represent the density and specific heat at constant pressure of the structure respectively; if the interface temperature calculated by equation (19) is lower than the liquidus temperature, the supercooling limit needs to be considered additionally. This process is determined by the following relationship:

[0045]

[0046] Where: ΔT sc represents the interface supercooling, T liq represents the liquidus temperature of the material, and the undercooling of the interface does not exceed the value obtained by equation (20);

[0047] Assume that before the crust is formed, the interface temperature between the melt and the structure is I It is defined by the temperature of the supercooled layer and determined by an input constant value; the latent heat of fusion of the melt may reach several times the thermal energy of the melt, so the definition of the supercooled temperature has a significant impact on the final penetration length of the melt; assuming that the melt contacts the structural surface at the contact point and no phase change occurs, the initial contact temperature can be considered by the instantaneous steady-state heat flux density, and the expression is as follows:

[0048]

[0049] Combining equations (6)-(7), the initial temperature of the melt and structure interface is obtained as follows:

[0050]

[0051] Step 3: Calculation of net energy transfer at the interface

[0052] In the nonequilibrium melting and solidification calculation process, the mainstream temperature of the melt when mass transfer occurs at the melt-structure interface usually does not meet the phase change conditions. The net energy transfer rate at the interface is expressed as follows:

[0053]

[0054] Where: represents the net energy transfer rate at the melt and structure interface, represents the melt and structure interface area concentration;

[0055] Step 4: Calculation of nonequilibrium mass transfer rate

[0056] When the value of equation (23) is zero, sensible heat exchange occurs at the interface without phase change. When the value of equation (23) is negative, energy is gained at the interface, indicating that melting occurs on the structural surface. When the value of equation (23) is positive, energy is lost at the interface, indicating that solidification of the melt occurs. The corresponding mass transfer rates when melting and solidification occur are determined by the following equations:

[0057]

[0058]

[0059] Where: represents the nonequilibrium melting rate at the interface, represents the non-equilibrium solidification rate at the interface, e liq,s represents the specific thermodynamic energy of the structure liquidus, e s represents the specific thermodynamic energy of the structure, e l represents the specific thermodynamic energy of the melt, e sol,l Represents the specific thermodynamic energy of the melt solidus; after the non-equilibrium process is completed, the energy change rate of the melt is determined by the following formula:

[0060]

[0061] Where: Indicates the macroscopic density of the melt;

[0062] Step 5: Calculation of the equilibrium solidification process

[0063] The equilibrium solidification process is driven by thermodynamic energy. When the thermodynamic energy of the mainstream melt is less than the thermodynamic energy of its liquidus line, the solidification calculation under the equilibrium process is performed. The expression of the melt solidification rate is as follows:

[0064]

[0065] After the melt solidifies on the surface of the structure, there is a possibility that it will be heated and melted again. That is, when the thermodynamic energy of the structure is higher than the thermodynamic energy of its solidus line, the melting calculation under the equilibrium process is performed. The expression of the solid phase melting rate is as follows:

[0066]

[0067] Where: represents the equilibrium solidification rate, represents the equilibrium melting rate, represents the macroscopic density of the structure, and Δt represents the calculation time step.

[0068] The present invention obtains a hybrid solidification model that combines an overall solidification model in which solid particles are generated at the melt front to increase the melt viscosity and cause blockage, and a thermal conductivity limitation model in which a hard shell forms blockage flow. This model can obtain analysis results that are relatively consistent with experiments, and is of great significance in the field of safety analysis under CDA of nuclear reactors in my country.

[0069] Compared with the prior art, the present invention has the following advantages:

[0070] 1. The modeling process is sufficient. The present invention fully considers the non-equilibrium mass transfer process determined by the net energy transfer at the interface when the temperature of the main component does not meet the phase change temperature, and the overall equilibrium mass transfer process driven by thermodynamic energy when the temperature of the main component meets the phase change temperature. It is more in line with the understanding of the actual heat and mass transfer process, and can achieve a full and reasonable modeling analysis of the entire solidification physical process.

[0071] 2. Conform to the microscopic mechanism. When the melt flows in the flow channel, the front melt is supercooled to produce some solid particles. The solid particles are mixed in the melt, resulting in an increase in melt viscosity and increased flow resistance. This effect is taken into account in the present invention. As the supercooled layer develops and reaches the conditions for hard shell formation, a hard shell will form on the surface of the structure, which will lead to a decrease in the hydraulic diameter and further affect the flow of the melt. The solid particles are equiaxed grains distributed at the front of the melt. The hard shell formed by columnar crystals lags behind the generation of equiaxed grains and is distributed on the surface of the structure. The simulation of the melt-solidification behavior of the present invention achieves good consistency in the explanation based on its microscopic mechanism.

[0072] 3. Flexible selection of interface temperature. The present invention is more flexible in calculating the contact temperature between the melt and the structure. On the one hand, the initial value of the interface temperature can be estimated by the instantaneous steady-state interface heat flux density, and implanted into the model calculation process in the form of an input constant. This method has high requirements on the estimated initial temperature value, and requires some parameter sensitivity analysis and experimental comparison. When the initial temperature value is filled in more accurately, better calculation results can be obtained. On the other hand, the interface temperature can be calculated by weighted assumption of non-steady-state pure heat conduction. This case requires fewer parameter analysis and is easier to operate. At the same time, supercooling limits are used to avoid non-physical calculation results. BRIEF DESCRIPTION OF THE DRAWINGS

[0073] Figure 1 It is a conceptual flowchart of the analysis method of the present invention;

[0074] Figure 2A schematic diagram of the component distribution of the melt and its solidification obtained by simulating the THEFIS experiment by the method of the present invention;

[0075] Figure 3 This is a comparison chart of the calculation results of the method of the present invention and the melt penetration length results obtained by THEFIS experiment. DETAILED DESCRIPTION

[0076] The method of the present invention is further described in detail below in conjunction with the accompanying drawings and specific embodiments:

[0077] The method for analyzing the melting and solidification characteristics of liquid metal fast reactor fuel of the present invention comprises five steps: step 1. calculating the heat transfer coefficient; step 2. determining the interface temperature; step 3. calculating the net energy transfer at the interface; step 4. calculating the non-equilibrium mass transfer rate; and step 5. calculating the equilibrium solidification process.

[0078] Step 1: Calculation of heat transfer coefficient

[0079] The melt initially contacts the structure at discrete points and is cooled by heat transfer at these contact points. During the cooling process, the melt near the surface of the structure is cooled below its liquidus temperature and forms a supercooled layer containing some solid particles. If the supercooled layer is then sufficiently cooled, it may further solidify to form a hard shell. For the above heat and mass transfer process, the heat transfer coefficient involved in the calculation must first be obtained. The heat transfer coefficient expression of the melt under turbulent conditions is shown in formula (1):

[0080] h l =(κ l / D h )Nu (1)

[0081] Nu=2.0+0.023Re 0.8 Pr 0.3 (2)

[0082] Nu=5.0+0.025Re 0.8 Pr 0.8 (3)

[0083] Where: h l represents the melt heat transfer coefficient, κ l Denotes the thermal conductivity of the melt, D h represents the hydraulic diameter, Nu, Re, and Pr represent the Nusselt number, Reynolds number, and Prandtl number, respectively; Formulas (2)-(3) represent the total Nusselt number of thermal conductivity and convection heat transfer of the fluid, which is used to calculate the heat transfer coefficient on the melt side; for liquid metals with low Prandtl numbers (Pr < 0.1), their thermal conductivity is relatively strong, and the thermal conductivity Nusselt number is 5.0; for liquid oxide materials, their thermal conductivity Nusselt number is 2.0, and the DB formula is used for convection heat transfer calculation;

[0084] The heat transfer coefficient on the structural side is defined as the ratio of thermal conductivity to semi-penetration length. The specific expression is as follows:

[0085] h s =2κ s / L s (4)

[0086] Where: h s represents the heat transfer coefficient on the structural side, κ s represents the structural thermal conductivity, L s It represents the heat penetration length on the structure side, characterizing the thermal response speed of the structure. It is defined by the structure density, specific heat and time constant. Assuming that the transient temperature distribution is approximately a parabola, the heat penetration length on the structure side is expressed as follows:

[0087]

[0088] Where: τ s , s 、c s are the time constant, density and heat capacity of the structure respectively; to ensure the stability of the numerical solution, the time constant should be no less than 6 times the time step;

[0089] Formulas (1) and (4) are the standard heat transfer coefficient calculation methods for the melt and structure sides. However, in actual processes, there is a certain gap between the melt and the structure surface. Therefore, it is necessary to consider the thermal resistance of the melt in contact with the structure at discrete points. The contact points are idealized as circles with a radius of r, and the separation distance between the contact points is D. The interfacial resistance-corrected heat transfer coefficients on the melt side and the structure side are given by formulas (6) and (7), respectively:

[0090]

[0091]

[0092] ω(n)=1-1.40925n+0.40925n 3 (8)

[0093]

[0094] η=r / D (10)

[0095] Where: It represents the heat transfer coefficient corrected by the interface resistance on the melt side, represents the heat transfer coefficient corrected by the interface resistance on the structure side, η is the ratio of the contact point radius to the contact point separation distance, ω(η) is the empirical relationship about η, υ lrepresents the melt velocity, the contact density N in formula (9) is calculated according to the mainstream velocity, and a and b are empirical constants. After solid particles are generated in the melt, assuming that turbulent transport makes the particles and the melt evenly mixed, the effective viscosity of the fluid gradually increases, and when the proportion of particles in the fluid exceeds a certain value, the flow stops due to the rapid increase in effective viscosity. The effective viscosity of the melt is modeled, and the expression of the particle viscosity factor changing with the particle volume fraction is as follows:

[0096]

[0097] The particle viscosity factor defined in formula (11) will be applied to the momentum exchange function to solve the momentum equation and update the velocity field; where f is the particle viscosity factor, F represents the original melt viscosity part, the default value is 1.0, k is the coefficient in the particle viscosity formula, the default value is 5.0, α Mp The maximum filling fraction that characterizes the particle viscosity factor, the default value is 0.62; α p is the particle volume fraction;

[0098] When the supercooled layer is completely solidified, the energy of the flowing melt will be transferred to the hard shell. The criterion for defining the transition from the supercooled layer to the hard shell is given by the width of the supercooled layer. The expression of the hard shell transformation criterion is as follows:

[0099]

[0100] Where: Δ c Indicates the hard shell thickness, W crust is the empirical constant in the hard shell thickness judgment criterion, and its default value is 0.5. When the hard shell is formed, the discrete contact between the melt and the structural surface is converted into the contact thermal resistance between the hard shell and the structural surface. The equivalent heat transfer coefficient of the interface resistance between the hard shell and the structure is given by the following formula:

[0101]

[0102] Where: represents the equivalent heat transfer coefficient of the interface resistance between the hard shell and the structure, κ c represents the thermal conductivity of the hard shell;

[0103] The total heat transfer coefficient between the hard shell and the structure is given by equation (14):

[0104]

[0105] h c =2κ c / Δ c (15)

[0106] Where: h c,s represents the total heat transfer coefficient between the shell and the structure, hc is the shell-side heat transfer coefficient; for non-equilibrium processes, the mainstream temperature of the melt or the structure temperature usually does not meet the phase change conditions, and mass transfer occurs at the interface. When the energy transferred from the flowing melt to the supercooled layer exceeds the energy that the structure can absorb under non-melting conditions, the structure undergoes non-equilibrium melting; similarly, when the energy obtained through the supercooled layer exceeds the energy transferred from the flowing melt to the supercooled layer, the melt undergoes non-equilibrium solidification; if both conditions are not met, it is considered that non-equilibrium mass transfer process does not occur; the judgment criteria for non-equilibrium melting and solidification processes are expressed by equations (16) and (17), respectively:

[0107]

[0108]

[0109]

[0110] Where: T l represents the melt temperature, represents the interface temperature of the supercooled layer, T s represents the structural temperature, T s,sol represents the solidus temperature of the structure, h scl,s Represents the total heat transfer coefficient between the supercooling layer and the structure;

[0111] Step 2: Determine the interface temperature

[0112] The expression for the interface temperature between the melt and the structure is defined as follows:

[0113]

[0114] Where: T I represents the interface temperature between the melt and the structure, ρ l 、c p,l They represent the density and specific heat at constant pressure of the melt, ρ s 、c p,s represent the density and specific heat at constant pressure of the structure respectively; if the interface temperature calculated by equation (19) is lower than the liquidus temperature, the supercooling limit needs to be considered additionally. This process is determined by the following relationship:

[0115]

[0116] Where: ΔT sc represents the interface supercooling, T liq represents the liquidus temperature of the material, and the undercooling of the interface does not exceed the value obtained by equation (20);

[0117] Assume that before the crust is formed, the interface temperature between the melt and the structure is IIt is defined by the temperature of the supercooled layer and determined by an input constant value; the latent heat of fusion of the melt may reach several times the thermal energy of the melt, so the definition of the supercooled temperature has a significant impact on the final penetration length of the melt; assuming that the melt contacts the structural surface at the contact point and no phase change occurs, the initial contact temperature can be considered by the instantaneous steady-state heat flux density, and the expression is as follows:

[0118]

[0119] Combining equations (6)-(7), the initial temperature of the melt and structure interface is obtained as follows:

[0120]

[0121] Step 3: Calculation of net energy transfer at the interface

[0122] In the nonequilibrium melting and solidification calculation process, the mainstream temperature of the melt when mass transfer occurs at the melt-structure interface usually does not meet the phase change conditions. The net energy transfer rate at the interface is expressed as follows:

[0123]

[0124] Where: represents the net energy transfer rate at the melt and structure interface, represents the melt and structure interface area concentration;

[0125] Step 4: Calculation of nonequilibrium mass transfer rate

[0126] When the value of equation (23) is zero, sensible heat exchange occurs at the interface without phase change. When the value of equation (23) is negative, energy is gained at the interface, indicating that melting occurs on the structural surface. When the value of equation (23) is positive, energy is lost at the interface, indicating that solidification of the melt occurs. The corresponding mass transfer rates when melting and solidification occur are determined by the following equations:

[0127]

[0128]

[0129] Where: represents the nonequilibrium melting rate at the interface, represents the non-equilibrium solidification rate at the interface, e liq,s represents the specific thermodynamic energy of the structure liquidus, e s represents the specific thermodynamic energy of the structure, e l represents the specific thermodynamic energy of the melt, e sol,l Represents the specific thermodynamic energy of the melt solidus; after the non-equilibrium process is completed, the energy change rate of the melt is determined by the following formula:

[0130]

[0131] Where: Indicates the macroscopic density of the melt;

[0132] Step 5: Calculation of the equilibrium solidification process

[0133] The equilibrium solidification process is driven by thermodynamic energy. When the thermodynamic energy of the mainstream melt is less than the thermodynamic energy of its liquidus line, the solidification calculation under the equilibrium process is performed. The expression of the melt solidification rate is as follows:

[0134]

[0135] After the melt solidifies on the surface of the structure, there is a possibility that it will be heated and melted again. That is, when the thermodynamic energy of the structure is higher than the thermodynamic energy of its solidus line, the melting calculation under the equilibrium process is performed. The expression of the solid phase melting rate is as follows:

[0136]

[0137] Where: represents the equilibrium solidification rate, represents the equilibrium melting rate, represents the macroscopic density of the structure, and Δt represents the calculation time step.

[0138] The THEFIS experiment was used as a verification object to simulate the flow process of molten alumina in a quartz tube. The method of the present invention was used to calculate the amount of alumina particles converted from molten alumina to obtain the material distribution during the flow of molten alumina. Figure 2 According to the position of the melt front, the penetration length of molten alumina at different times can be obtained. The comparison between the variation curve of the penetration length of molten alumina and the experimental results is shown in the attached figure. Figure 3 As shown. Figure 3 It can be seen that the overall variation trend of the penetration length of molten alumina is consistent with the experimental results, which verifies the applicability of the heat and mass transfer calculation model of the melting and solidification process adopted in the method of the present invention.

[0139] The above content is a further detailed description of the present invention in combination with a specific preferred embodiment. It cannot be determined that the specific embodiments of the present invention are limited to this. For ordinary technicians in the technical field to which the present invention belongs, several simple deductions or substitutions can be made without departing from the concept of the present invention, which should be regarded as belonging to the present invention and the scope of patent protection determined by the submitted claims.

Claims

1. A method for analyzing the melting and solidification characteristics of liquid metal fast reactor fuel, characterized in that: It includes the following five steps: Step 1: Calculation of heat transfer coefficient The melt initially contacts the structure at discrete points and is cooled by heat transfer at these contact points. During the cooling process, the melt near the surface of the structure is cooled below its liquidus temperature and forms a supercooled layer containing some solid particles. If the supercooled layer is then sufficiently cooled, it may further solidify to form a hard shell. For the above heat and mass transfer process, it is first necessary to obtain the heat transfer coefficient involved in the calculation. The heat transfer coefficient expression of the melt under turbulent state is shown in formula (1): h l =(κ l / D h )No (1) Now=2.0+0.023Re 0.8 Per 0.3 (2) Now=5.0+0.025Re 0.8 Per 0.8 (3) Where: h l represents the melt heat transfer coefficient, κ l Denotes the thermal conductivity of the melt, D h represents the hydraulic diameter, Nu, Re, and Pr represent the Nusselt number, Reynolds number, and Prandtl number, respectively; Formulas (2)-(3) represent the total Nusselt number of thermal conductivity and convection heat transfer of the fluid, which is used to calculate the heat transfer coefficient on the melt side; for liquid metals with low Prandtl numbers (Pr < 0.1), their thermal conductivity is relatively strong, and the thermal conductivity Nusselt number is 5.0; for liquid oxide materials, their thermal conductivity Nusselt number is 2.0, and the DB formula is used for convection heat transfer calculation; The heat transfer coefficient on the structural side is defined as the ratio of thermal conductivity to semi-penetration length. The specific expression is as follows: h s =2κ s / L s (4) Where: h s represents the heat transfer coefficient on the structural side, κ s represents the structural thermal conductivity, L s It represents the heat penetration length on the structure side, characterizing the thermal response speed of the structure. It is defined by the structure density, specific heat and time constant. Assuming that the transient temperature distribution is approximately a parabola, the heat penetration length on the structure side is expressed as follows: Where: τ s , s 、c s are the time constant, density and heat capacity of the structure respectively; to ensure the stability of the numerical solution, the time constant should be no less than 6 times the time step; Formulas (1) and (4) are the standard heat transfer coefficient calculation methods for the melt and structure sides. However, in actual processes, there is a certain gap between the melt and the structure surface. Therefore, it is necessary to consider the thermal resistance of the melt in contact with the structure at discrete points. The contact points are idealized as circles with a radius of r, and the separation distance between the contact points is D. The interfacial resistance-corrected heat transfer coefficients on the melt side and the structure side are given by formulas (6) and (7), respectively: ω(η)=1-1.40925η+0.40925η 3 (8) η=r / D (10) Where: It represents the heat transfer coefficient corrected by the interface resistance on the melt side, represents the heat transfer coefficient corrected by the interface resistance on the structure side, η is the ratio of the contact point radius to the contact point separation distance, ω(η) is the empirical relationship about η, υ l represents the melt velocity, the contact density N in formula (9) is calculated according to the mainstream velocity, and a and b are empirical constants. After solid particles are generated in the melt, assuming that turbulent transport makes the particles and the melt evenly mixed, the effective viscosity of the fluid gradually increases, and when the proportion of particles in the fluid exceeds a certain value, the flow stops due to the rapid increase in effective viscosity. The effective viscosity of the melt is modeled, and the expression of the particle viscosity factor changing with the particle volume fraction is as follows: The particle viscosity factor defined in equation (11) will be applied to the momentum exchange function to solve the momentum equation and update the velocity field; where; f is the particle viscosity factor, F represents the original melt viscosity part, the default value is 1.0, k is the coefficient in the particle viscosity formula, the default value is 5.0, α Mp The maximum filling fraction that characterizes the particle viscosity factor, the default value is 0.62; α p is the particle volume fraction; When the supercooled layer is completely solidified, the energy of the flowing melt will be transferred to the hard shell. The criterion for defining the transition from the supercooled layer to the hard shell is given by the width of the supercooled layer. The expression of the hard shell transformation criterion is as follows: Where: Δ c Indicates the hard shell thickness, W crust is the empirical constant in the hard shell thickness judgment criterion, and its default value is 0.

5. When the hard shell is formed, the discrete contact between the melt and the structural surface is converted into the contact thermal resistance between the hard shell and the structural surface. The equivalent heat transfer coefficient of the interface resistance between the hard shell and the structure is given by the following formula: Where: represents the equivalent heat transfer coefficient of the interface resistance between the hard shell and the structure, κ c represents the thermal conductivity of the hard shell; The total heat transfer coefficient between the hard shell and the structure is given by equation (14): h c =2k c / D c (15) Where: h c,s represents the total heat transfer coefficient between the shell and the structure, h c is the shell-side heat transfer coefficient; for non-equilibrium processes, the mainstream melt temperature or the structure temperature usually does not meet the phase change conditions, and mass transfer occurs at the interface. When the energy transferred from the flowing melt to the supercooled layer exceeds the energy that the structure can absorb under non-melting conditions, non-equilibrium melting of the structure occurs; Similarly, when the energy obtained through the supercooling layer exceeds the energy transferred from the flowing melt to the supercooling layer, the melt undergoes nonequilibrium solidification; if both conditions are not met, it is considered that the nonequilibrium mass transfer process does not occur; the judgment criteria for the nonequilibrium melting and solidification processes are expressed by equations (16) and (17), respectively: Where: T l represents the melt temperature, represents the interface temperature of the supercooled layer, T s represents the structural temperature, T s,sol represents the solidus temperature of the structure, h scl,s Represents the total heat transfer coefficient between the supercooling layer and the structure; Step 2: Determine the interface temperature The expression for the interface temperature between the melt and the structure is defined as follows: Where: T I represents the interface temperature between the melt and the structure, ρ l 、c p,l They represent the density and specific heat at constant pressure of the melt, ρ s 、c p,s represent the density and specific heat at constant pressure of the structure respectively; if the interface temperature calculated by equation (19) is lower than the liquidus temperature, the supercooling limit needs to be considered additionally. This process is determined by the following relationship: Where: ΔT sc represents the interface supercooling, T liq represents the liquidus temperature of the material, and the undercooling of the interface does not exceed the value obtained by equation (20); Assume that before the crust is formed, the interface temperature between the melt and the structure is T I It is defined by the temperature of the supercooled layer and determined by an input constant value; the latent heat of fusion of the melt may reach several times the thermal energy of the melt, so the definition of the supercooled temperature has a significant impact on the final penetration length of the melt; assuming that the melt contacts the structural surface at the contact point and no phase change occurs, the initial contact temperature can be considered by the instantaneous steady-state heat flux density, and the expression is as follows: Combining equations (6)-(7), the initial temperature of the melt and structure interface is obtained as follows: Step 3: Calculation of net energy transfer at the interface In the nonequilibrium melting and solidification calculation process, the mainstream temperature of the melt when mass transfer occurs at the melt-structure interface usually does not meet the phase change conditions. The net energy transfer rate at the interface is expressed as follows: Where: represents the net energy transfer rate at the melt and structure interface, represents the melt and structure interface area concentration; Step 4: Calculation of nonequilibrium mass transfer rate When the value of equation (23) is zero, sensible heat exchange occurs at the interface without phase change. When the value of equation (23) is negative, energy is gained at the interface, indicating that melting occurs on the structural surface. When the value of equation (23) is positive, energy is lost at the interface, indicating that solidification of the melt occurs. The corresponding mass transfer rates when melting and solidification occur are determined by the following equations: Where: represents the nonequilibrium melting rate at the interface, represents the non-equilibrium solidification rate at the interface, e liq,s represents the specific thermodynamic energy of the structure liquidus, e s represents the specific thermodynamic energy of the structure, e l represents the specific thermodynamic energy of the melt, e sol,l Represents the specific thermodynamic energy of the melt solidus; after the non-equilibrium process is completed, the energy change rate of the melt is determined by the following formula: Where: Indicates the macroscopic density of the melt; Step 5: Calculation of the equilibrium solidification process The equilibrium solidification process is driven by thermodynamic energy. When the thermodynamic energy of the mainstream melt is less than the thermodynamic energy of its liquidus line, the solidification calculation under the equilibrium process is performed. The expression of the melt solidification rate is as follows: After the melt solidifies on the surface of the structure, there is a possibility that it will be heated and melted again. That is, when the thermodynamic energy of the structure is higher than the thermodynamic energy of its solidus line, the melting calculation under the equilibrium process is performed. The expression of the solid phase melting rate is as follows: Where: represents the equilibrium solidification rate, represents the equilibrium melting rate, represents the macroscopic density of the structure, and Δt represents the calculation time step.

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