A calculation method, system, medium and device for Zr element migration and redistribution

Abstract

The present invention discloses a calculation method, system, medium and equipment for Zr element migration and redistribution. The method calculates the alloy phase in the metal fuel based on a U-Zr pseudo-binary phase diagram with a fixed Pu content, and on the basis of the calculation, calculates the Zr element migration process in the ternary metal fuel and the concentration distribution at each moment in the process by coupling Fick's law with thermal diffusion (Soret effect), and corrects the diffusion process. The present invention develops a Zr element migration and redistribution model for U-Pu-Zr ternary metal fuel based on the existing U-Zr pseudo-binary phase diagram with a fixed Pu content and Fick's law and thermal diffusion empirical formula of U and Zr, and compares it with literature data. The comparison shows that the calculation results using the model are basically consistent with the experimental data. Therefore, the Zr element migration process and concentration distribution inside the U-Pu-Zr metal fuel obtained by the present invention are more accurate.

Description

Technical Field

[0001] The invention relates to the field of thermal performance analysis of nuclear reactor fuel rods, and in particular to a calculation method, system, medium and equipment for migration and redistribution of Zr elements in U-Pu-Zr ternary metal fuel. Background Art

[0002] Traditional nuclear reactors are divided into thermal neutron reactors and fast neutron reactors. The most widely used and mature one is the pressurized water reactor (PWR), which belongs to the thermal neutron reactor type. However, the PWR will produce a large amount of nuclear waste and the utilization efficiency of nuclear fuel is low. Fast neutron reactors have the characteristics of high power and high heat release per unit. The use of fast neutron reactors can make full use of nuclear fuel in nature. Compared with traditional PWRs, fast neutron reactors have better performance in preventing nuclear proliferation. Sodium-cooled fast reactors (SFR) and lead-cooled fast reactors (LFR) are typical representatives. In order to prevent the occurrence of fuel melting and cladding failure caused by the overall high temperature of the fuel in the fast reactor, it is necessary to use fuel with good thermal performance at high temperature. Among them, metal fuel has the characteristics that thermal conductivity and heat capacity increase with the increase of temperature, so it has excellent thermal performance, among which U-Pu-Zr ternary metal fuel is the representative. However, the service behavior of metal fuel in fast neutron reactor is accompanied by complex physical and chemical processes, among which the most important phenomenon is the migration and redistribution of internal Zr elements in ternary metal fuel during service. This phenomenon greatly affects the heat capacity and thermal conductivity of metal fuel, and thus greatly affects the fuel performance of fuel rods during the operation of the entire nuclear reactor. At present, there is no calculation method for the migration of Zr elements in U-Pu-Zr ternary metal fuel. Therefore, it is necessary to propose a reliable and accurate calculation method for the migration and redistribution of Zr elements in U-Pu-Zr ternary metal fuel. Summary of the invention

[0003] In order to overcome the defects and shortcomings of the prior art, the first purpose of the present invention is to provide a calculation method for the migration and redistribution of the Zr element in the U-Pu-Zr ternary metal fuel, which adopts the fully coupled calculation method of Fick's law, Soret effect (thermal diffusion phenomenon) and heat conduction to calculate the concentration distribution of the Zr element in the fuel pellets and the temperature distribution of the fuel pellets and the cladding at each moment, and at the same time considers the correction method for the migration rate of the Zr element to obtain accurate and reliable calculation results.

[0004] The second object of the present invention is to provide a computing system for the migration and redistribution of Zr elements in U-Pu-Zr ternary metal fuel.

[0005] A third object of the present invention is to provide a storage medium.

[0006] A fourth object of the present invention is to provide a computing device.

[0007] In order to achieve the above object, the present invention provides a method for calculating the migration and redistribution of Zr elements in U-Pu-Zr ternary metal fuel, which uses a one-dimensional non-steady-state heat conduction equation to calculate the temperature distribution of fuel pellets and cladding, and uses Fick's law and Soret effect (thermally induced diffusion phenomenon) to calculate the concentration distribution of Zr elements in fuel pellets, which specifically includes the following steps:

[0008] (1) determining the initial concentration percentages of U, Pu and Zr in the metal fuel, and obtaining a U-Zr pseudo-binary phase diagram at the Pu content;

[0009] (2) calculating the temperature distribution of the fuel pellets and the cladding at each time based on the fuel pellet linear power of the metal fuel and the physical properties of the fuel pellets, the cladding, and the gap between the fuel pellets and the cladding;

[0010] (3) Based on the temperature distribution in the fuel pellet of the metal fuel and the U-Zr pseudo-binary phase diagram, a criterion for determining the alloy phase at each time and position in the fuel pellet is established to obtain the distribution of the alloy phase;

[0011] (4) Based on the distribution of alloy phases at various times and locations in the fuel pellets in the metal fuel, the diffusion and redistribution process of Zr is calculated using Fick's law of Zr metal and the empirical formula for thermal diffusion under different U-Pu-Zr elemental phase states, and the Zr concentration distribution at various times and locations in the fuel pellets is obtained.

[0012] As a preferred technical solution, the heat transfer calculation of the fuel pellets, cladding and the gap between the fuel pellets and cladding in the metal fuel is specifically calculated as follows:

[0013] (1)

[0014] in, is the density of the material, is the heat capacity of the fuel pellet or cladding, is the uncorrected temperature of the fuel pellet or cladding, For time, is the thermal conductivity of the fuel pellet or cladding, is the distance from the centerline of the fuel pellet, is the heat generation rate per unit volume of the fuel pellet. Formula (1) is used to calculate the heat transfer process and temperature distribution in the fuel pellet. As for the heat transfer process and temperature distribution in the cladding and the gap between the fuel pellet and the cladding, since there is no heat source, the source term in Formula (1) is rounding.

[0015] As a preferred technical solution, a temperature correction is performed for the heat transfer calculation, and the calculated temperature is reduced by 58K, thereby relatively increasing the phase transition temperature by 58K:

[0016] (2)

[0017] Formula (1) and formula (2) are calculated using the solid heat transfer module in COMSOL.

[0018] As a preferred technical solution, according to the U-Pu-Zr element at a fixed Pu concentration contained in the metal fuel pellet, a phase discrimination criterion of the U-Pu-Zr element is established, and the U-Pu-Zr element phase at each position of the fuel pellet at each time is determined according to the discrimination criterion. The specific steps are as follows:

[0019] (1) Determine the Pu concentration in the U-Pu-Zr element used in the calculation of the metal fuel, and refer to the relevant U-Zr pseudo-binary phase diagram based on the Pu concentration;

[0020] (2) Based on the U-Zr pseudo-binary phase diagram consulted in step (1), determine the phase type of Zr (α phase, β phase, etc.), and determine the conditions that the U-Pu-Zr elements must meet in each phase, such as:

[0021] ① If a certain condition is met alone or a combination of certain conditions is met (condition one, condition two...; condition combination a, condition combination b...), the U-Pu-Zr element is in the α phase.

[0022] ② If a certain condition is met alone or a combination of certain conditions is met (condition A, condition B...; condition combination I, condition combination II...), the U-Pu-Zr elements are in the β phase.

[0023] …

[0024] Similar to the above, for each phase of the U-Pu-Zr element, the conditions that need to be met for the U-Pu-Zr element to be in the phase are determined.

[0025] As a preferred technical solution, the alloy phase distribution at each location of the fuel pellet at each time is calculated to determine the migration rate and migration direction of Zr at that location at that time. Zr is in a non-steady-state diffusion state in the metal fuel pellet, and its diffusion equation is:

[0026] (3)

[0027] in, is the concentration of Zr element, is the Fick's law diffusion coefficient of Zr element, is the diffusion coefficient of thermal diffusion of Zr element, is the concentration gradient, is the temperature gradient, is the Hamiltonian operator, T is the corrected temperature, For time.

[0028] For the above two diffusion coefficients, a unified calculation method is used:

[0029] For single-phase area:

[0030] (4)

[0031] (5)

[0032] in, represent Fick's law diffusion rate of the phase, Refers to any phase that an alloy may be in. is the diffusion pre-exponential factor, represent The Fick's law diffusion pre-exponential factor of the phase, is the diffusion activation energy, represents the universal gas constant under standard conditions, represent The thermal diffusion rate of the phase, for Fick's law diffusion coefficient of phase Zr element, is the concentration of Pu metal element in the metal fuel pellet, for Thermal diffusion of phases effectively transports heat; for the two-phase region:

[0033] (6)

[0034] (7)

[0035] in , They refer to different alloy phases. For the alloy The volume fraction of the phase, is the dissolution enthalpy.

[0036] For different phases, the calculation parameters under different alloy phases are given as follows:

[0037]

[0038] For the two-phase region, the lever law is used to calculate the volume fractions of different phases:

[0039] (8)

[0040] (9)

[0041] in , Zr is Mutually, The Zr concentration at a certain calculated time on the solid solubility curve of the phase and at a temperature calculated at a certain location of the metal fuel pellet. , The calculation time and location of the U-Pu-Zr ternary alloy are Mutually, The concentration of the phase. Formulas (3)-(9) are calculated using the domain partial differential equation module in COMSOL.

[0042] In order to achieve the above-mentioned second purpose, the present invention provides a calculation system for the migration and redistribution of Zr elements in U-Pu-Zr ternary metal fuel, including: a heat conduction module, an alloy phase judgment module, and a Zr migration and redistribution calculation module.

[0043] The heat conduction module is used to calculate the temperature change and distribution of the fuel pellets, the cladding and the gap between them;

[0044] The alloy phase judgment module is used to judge the phase of the alloy at each position of the fuel pellet at each moment;

[0045] The Zr migration and redistribution calculation module is used to calculate the Zr concentration distribution inside the fuel pellet at each time and the migration rate and direction of the Zr element at each time.

[0046] As a preferred technical solution, a correction module is also included for correcting the phase transition temperature of the ternary alloy to increase the phase transition temperature by 58 K.

[0047] In order to achieve the third purpose mentioned above, the present invention provides a storage medium storing a program, which, when executed by a processor, implements the calculation method for the migration and redistribution of the Zr element in the U-Pu-Zr ternary metal fuel as mentioned above.

[0048] In order to achieve the fourth purpose mentioned above, the present invention provides a computing device, including a processor and a memory for storing a program executable by the processor, and when the processor executes the program stored in the memory, it implements the calculation method of the migration and redistribution of the Zr element in the above-mentioned U-Pu-Zr ternary metal fuel.

[0049] Compared with the prior art, the present invention has at least the following beneficial effects:

[0050] (1) The present invention adopts Fick's law, Soret effect (thermal diffusion) and heat conduction coupling to calculate the migration and redistribution of Zr element in U-Pu-Zr ternary metal fuel, establishes the judgment criterion of the alloy phase, and can accurately calculate the concentration distribution of Zr element in ternary metal fuel, and then accurately calculate the thermal conductivity of metal fuel affected by the concentration distribution of Zr element, so that the heat transfer calculation and temperature distribution of metal fuel are more accurate, thereby making the prediction of the thermal performance of the metal fuel more accurate.

[0051] (2) The present invention uses a newer Zr migration calculation formula, which makes the calculated Zr concentration distribution and migration rate and direction more accurate;

[0052] (3) The present invention is applicable to the migration and redistribution of Zr elements in a large number of U-Pu-Zr ternary metal fuels, and the calculation method has a certain degree of universality. BRIEF DESCRIPTION OF THE DRAWINGS

[0053] Figure 1 Schematic diagram of a flow chart of a method for calculating the migration and redistribution of Zr elements in a ternary metal fuel according to an embodiment of the present invention;

[0054] Figure 2 This is the pseudo-binary phase diagram of the U-71Pu-10Zr ternary metal fuel when the Pu element content is fixed;

[0055] Figure 3 This is a comparison chart of the migration and redistribution results of the Zr element in the U-Pu-Zr ternary metal fuel calculated by the present invention and the existing recorded results. DETAILED DESCRIPTION

[0056] In order to make the purpose, technical solution and advantages of the present invention more clearly understood, the present invention is further described in detail below in conjunction with the accompanying drawings and embodiments. It should be understood that the specific embodiments described herein are only used to explain the present invention and are not intended to limit the present invention.

[0057] The present invention provides a calculation method for the migration and redistribution of Zr elements in a U-Pu-Zr ternary metal fuel. The metal fuel contains three metal elements, U, Pu and Zr, and the Pu element is considered to have a fixed content and not diffuse. A U-Zr pseudo-binary phase diagram with a fixed Pu content is used to establish a phase discrimination condition for metal Zr. A fully coupled calculation is performed using Fick's law, the Soret effect (thermal diffusion) and a series of other physical and chemical processes caused by heat generation of metal fuel pellets to obtain the migration rate, direction and concentration distribution of the Zr element inside the ternary metal fuel pellet.

[0058] Example 1

[0059] See also Figure 1 The present invention provides a method for calculating the migration and redistribution of Zr elements in a U-Pu-Zr ternary metal fuel, comprising the following steps:

[0060] S1: determining the initial concentration percentages of U, Pu and Zr in the metal fuel, and obtaining a pseudo-binary phase diagram of U-Zr at the Pu content;

[0061] In this embodiment, the initial mass fractions of the metal elements in the ternary metal fuel are respectively U: 71%; Pu: 19%; Zr: 10% (hereinafter referred to as U-19Pu-10Zr). Of course, in other embodiments, the initial mass fractions may also be other values, and a phase diagram of the metal fuel corresponding to the initial mass fraction percentage of the other values ​​needs to be obtained.

[0062] S2: Calculate the temperature distribution of the fuel pellets and the cladding at each moment based on the fuel pellet linear power of the metal fuel and the physical properties of the fuel pellets, the cladding, and the gap between the fuel pellets and the cladding.

[0063] The physical properties of the gap between the fuel pellet and the cladding are the thermodynamic properties of the gap material.

[0064] The calculation formula for the temperature distribution of the fuel pellets and the cladding at each moment is as follows:

[0065] (1)

[0066] In the formula, is the density of the material, is the heat capacity of the fuel pellet or cladding, is the uncorrected temperature of the fuel pellet or cladding, For time, is the thermal conductivity of the fuel pellet or cladding, is the distance from each position inside the fuel pellet to the centerline of the fuel pellet, is the heat generation rate per unit volume of fuel pellets.

[0067] Formula (1) is used to calculate the heat transfer process and temperature distribution in the fuel pellets. As for the heat transfer process and temperature distribution in the cladding and the gap between the fuel pellets and the cladding, since there is no heat source, the source term in Formula (1) is Give up, that is, at this time =0.

[0068] In this step, the phase transition temperature of the ternary alloy was also corrected, and the phase transition temperature was increased by 58 K, that is,

[0069] The temperature in formula (1) is corrected to increase the phase transition temperature by 58K:

[0070] (2)

[0071] In the formula, is the uncorrected temperature of the fuel pellet or cladding and T is the corrected temperature.

[0072] Formula (1) and formula (2) are both calculated using the solid heat transfer module in COMSOL.

[0073] S3: In combination with the pseudo-binary phase diagram of the alloy used in the ternary metal fuel pellet, and based on the temperature calculation result in S2, establish a criterion for determining the alloy phase at each time and each position in the fuel pellet to obtain the distribution of the alloy phase.

[0074] In some embodiments of the present invention, the pseudo binary phase diagram of the ternary alloy (which can be obtained after determining the initial concentration percentages of the three elements) is as follows: Figure 2 As shown, based on the phase diagram, the alloy phase judgment criteria are as follows:

[0075] (1) When the temperature-Zr molar concentration state of the ternary alloy (obtained from the analytical equation of the solvus line in the binary phase diagram) is Figure 1 When the state point is located in the area to the left of line 1 and below line 3, the alloy is in the α phase, wherein lines 1, 2, 3, 4, and 6 in the figure represent the solvus line between α and α+δ phases, the solvus line between α+δ and δ phases, the temperature line of transformation from α and δ phases to β and γ phases, the solvus line between β and β+γ phases, the solvus line between β+γ and γ phases, and the temperature line of transformation from β+γ phase to γ ​​phase, respectively;

[0076] (2) When the temperature-Zr molar concentration state of the ternary alloy is Figure 1 When the state point in is located in the area between the right side of line 1, the left side of line 2, and the bottom side of line 3, the alloy is in the α+δ phase;

[0077] (3) When the temperature-Zr molar concentration state of the ternary alloy is Figure 1When the state point in is located to the right of line 2 and below line 3, the alloy is in the δ phase;

[0078] (4) When the temperature-Zr molar concentration state of the ternary alloy is Figure 1 When the state point in is located above line 3, to the left of line 4 and below line 6, the alloy is in the β phase;

[0079] (5) When the temperature-Zr molar concentration state of the ternary alloy is Figure 1 When the state point in is located in the area enclosed by lines 3, 4, 5, and 6, the alloy is in the β+γ phase;

[0080] (6) When the temperature-Zr molar concentration state of the ternary alloy is Figure 1 When the state point is located in the area above the temperature line 6 or in the area to the right of line 5 and above line 3, the alloy is in the γ phase.

[0081] Figure 2 Each line in can be expressed by the temperature-molar concentration analytical equation, as shown in the following table:

[0082]

[0083] Wherein, T is temperature, and the unit of temperature is Kelvin (K).

[0084] According to the above judgment criteria, the alloy phase can be judged. According to the calculated concentration of each element and temperature distribution in the fuel pellet, the conditions of being in a certain phase at each location of the fuel pellet at each moment are determined by comparing with the alloy phase judgment criteria, and the location is set as this phase at that moment.

[0085] S4: According to the calculated alloy phase distribution at each location of the fuel pellet at each time, the diffusion and redistribution process of Zr is calculated by using the Fick's law of Zr metal and the empirical formula of thermal diffusion in different U-Pu-Zr element phase states, the migration rate and migration direction of Zr are determined, and the Zr concentration distribution at each time and each location in the fuel pellet is obtained;

[0086] Among them, Zr is in a non-steady diffusion state in the fuel pellet, and its diffusion equation is:

[0087] (3)

[0088] in, is the concentration of Zr element, is the Fick's law diffusion coefficient of Zr element, is the diffusion coefficient of thermal diffusion of Zr element, is the concentration gradient, is the temperature gradient, is the Hamiltonian operator, representing Since only the heat transfer in the radial direction and the migration of Zr are considered (because there is no temperature difference in the axial direction to drive the heat transfer and the concentration difference and chemical potential difference to drive the migration of Zr), the Hamiltonian operator in the present invention is , only represents .

[0089] Among them, in formula (2) as well as The absolute value of represents the migration rate, and the positive and negative signs of the above two items represent the migration direction, where the positive sign represents the direction away from the fuel centerline and the negative sign represents the direction close to the fuel centerline.

[0090] For the above two diffusion coefficients, a unified calculation method is used:

[0091] For single-phase area:

[0092] (4)

[0093] (5)

[0094] in, represent Fick's law diffusion rate of the phase, Refers to any phase that an alloy may be in. is the diffusion pre-exponential factor, represent The Fick's law diffusion pre-exponential factor of the phase, is the diffusion activation energy, represents the universal gas constant under standard conditions, which is 8.314 J·mol -1 ·K -1 , represent The thermal diffusion rate of the phase, for Fick's law diffusion coefficient of phase Zr element, is the concentration of Pu metal element in the metal fuel pellet, for Thermal diffusion of phases effectively transports heat.

[0095] For the two-phase region:

[0096] (6)

[0097] (7)

[0098] in, for Fick's law diffusion rate in the two-phase region, , They refer to different alloy phases. For the alloy The volume fraction of the phase, , They are phase and The Fick's law diffusion pre-exponential factor of the phase, for The thermal diffusion rate in the two-phase region, is the dissolution enthalpy, for The effective heat transported by the thermal diffusion of the phase, represent Fick's law diffusion rate of the phase, Zr is the element in the ternary alloy. Phase concentration, Zr is the element in the ternary alloy. Phase concentration.

[0099] Among them, formulas (3) and (5) are Fick's laws, and formulas (4) and (6) are empirical formulas for thermal diffusion.

[0100] For different phases, the calculation parameters under different alloy phases are given as follows:

[0101]

[0102] in, is the diffusion pre-exponential factor, is the diffusion activation energy, To transport heat;

[0103] For the two-phase region, the lever law is used to calculate the volume fractions of different phases:

[0104] (8)

[0105] (9)

[0106] in , Zr is Mutually, The Zr concentration at a certain calculated time on the solid solubility curve of the phase and at a calculated temperature at a certain location of the metal fuel pellet, and , is the U-Pu-Zr ternary alloy at a certain point in the calculation time. Mutually, The Zr concentration of the phase.

[0107] In this embodiment, formulas (3)-(9) are calculated using the domain partial differential equation module in COMSOL.

[0108] The method provided in this embodiment is used for calculation. The heat conduction and temperature distribution of the current time step are calculated first, and the migration distribution of Zr is calculated in combination with the alloy phase judgment criteria. Then, it is determined whether the current heat conduction state is met. If it is and it is the last time step, the calculation result is output. If it does not meet the current heat conduction state, the distribution of Zr calculated currently is used as a new fuel parameter input, and the migration distribution of Zr is continued to be calculated until the current heat conduction state is met and it is the last time step. The solution results obtained by the method described in this embodiment can be used as a reference for detailed research on the migration and redistribution of Zr elements in U-Pu-Zr ternary metal fuel.

[0109] like Figure 3 As shown in the figure, from top to bottom are: the Zr element concentration distribution result obtained by experimental data measurement, the Zr element concentration distribution result calculated by Galloway et al. using a fixed temperature distribution curve, the Zr element concentration distribution result obtained by Galloway et al. (Modeling constituent redistribution in U–Pu–Zr metallic fuel using the advanced fuel performance code BISON) by coupling temperature calculation, the Zr element concentration distribution result obtained by Jacob et al. (A CALPHAD-informed approach to modeling constituentredistribution in Zr-based metallic fuels using BISON) by coupling temperature calculation, the Zr element concentration distribution result obtained by Jacob et al. by optimizing the phase transition temperature, the Zr element concentration distribution result obtained by the present invention by coupling temperature calculation, and the Zr element concentration distribution result obtained by the present invention by optimizing the phase transition temperature. According to the comparison of these graphs, after optimizing the phase transition temperature, the Zr element concentration distribution calculated by the present invention is closer to the experimental measurement result, and the calculation accuracy is higher.

[0110] Example 2

[0111] This embodiment provides a calculation system for Zr element migration and redistribution in U-19Pu-10Zr ternary metal fuel, including: a heat conduction module, an alloy phase judgment module, and a Zr migration and redistribution calculation module;

[0112] In this embodiment, the heat conduction module is used to calculate the heat generation of the fuel pellets and the conduction of heat in the fuel pellets, air gaps, and cladding. The calculation formula is as follows:

[0113] (1)

[0114] In the formula is the density of the material, is the heat capacity of the fuel pellet or cladding, is the uncorrected temperature of the fuel pellet or cladding, For time, is the thermal conductivity of the fuel pellet or cladding, is the distance from the centerline of the fuel pellet, is the heat generation rate per unit volume of the fuel pellet. Formula (1) is used to calculate the heat transfer process and temperature distribution in the fuel pellet. As for the heat transfer process and temperature distribution in the cladding and the gap between the fuel pellet and the cladding, since there is no heat source, the heat generation term in Formula (1) is rounding.

[0115] It also includes a correction module for correcting the phase transition temperature of the ternary alloy, increasing the phase transition temperature by 58K, that is, correcting the temperature in formula (1), thereby relatively increasing the phase transition temperature by 58K:

[0116] (2)

[0117] Formula (1) and formula (2) are calculated using the solid heat transfer module in COMSOL.

[0118] In this embodiment, the alloy phase judgment module is based on the pseudo-binary phase diagram of the ternary metal fuel to judge the phase of the alloy at each position of the fuel pellet at each time. The pseudo-binary phase diagram of the ternary metal fuel is shown as follows: Figure 2 .

[0119] Based on this phase diagram, the alloy phase judgment criteria are as follows:

[0120] (1) When the temperature-Zr molar concentration state of the ternary alloy is Figure 1 When the state point in is located in the area to the left of line 1 and below line 3, the alloy is in the α phase;

[0121] (2) When the temperature-Zr molar concentration state of the ternary alloy is Figure 1 When the state point in is located in the area between the right side of line 1, the left side of line 2, and the bottom side of line 3, the alloy is in the α+δ phase;

[0122] (3) When the temperature-Zr molar concentration state of the ternary alloy is Figure 1When the state point in is located to the right of line 2 and below line 3, the alloy is in the δ phase;

[0123] (4) When the temperature-Zr molar concentration state of the ternary alloy is Figure 1 When the state point in is located above line 3, to the left of line 4 and below line 6, the alloy is in the β phase;

[0124] (5) When the temperature-Zr molar concentration state of the ternary alloy is Figure 1 When the state point in is located in the area enclosed by lines 3, 4, 5, and 6, the alloy is in the β+γ phase;

[0125] (6) When the temperature-Zr molar concentration state of the ternary alloy is Figure 1 When the state point is located in the area above the temperature line 6 or in the area to the right of line 5 and above line 3, the alloy is in the γ phase.

[0126] Figure 1 Each line in can be expressed by the temperature-molar concentration analytical equation, as shown in the following table:

[0127]

[0128] The unit of temperature is Kelvin (K).

[0129] According to the above judgment criteria, the calculation system is used to judge the alloy phase.

[0130] In this embodiment, the Zr migration and redistribution calculation module is used to calculate the Zr concentration distribution inside the fuel pellet at each time and the migration rate and direction of the Zr element at each time. The diffusion equation of the Zr element is:

[0131] (3)

[0132] in, is the concentration of Zr element, is the Fick's law diffusion coefficient of Zr element, is the diffusion coefficient of thermal diffusion of Zr element, is the concentration gradient, is the temperature gradient, is the Hamiltonian operator.

[0133] For the above two diffusion coefficients, a unified calculation method is used:

[0134] For single-phase area:

[0135] (4)

[0136] (5)

[0137] In the formula, represent Fick's law diffusion rate of the phase, Refers to any phase that an alloy may be in. is the diffusion pre-exponential factor, subscript represent The Fick's law diffusion pre-exponential factor of the phase, is the diffusion activation energy, represents the universal gas constant under standard conditions, represent The thermal diffusion rate of the phase, for Fick's law diffusion coefficient of phase Zr element, is the concentration of Pu metal element in the metal fuel pellet, for The effective heat transport by thermal diffusion of phases;

[0138] For the two-phase region:

[0139] (6)

[0140] (7)

[0141] In the formula, for Fick's law diffusion rate in the two-phase region, , They refer to different alloy phases. For the alloy The volume fraction of the phase, , They are phase and The Fick's law diffusion pre-exponential factor of the phase, for The thermal diffusion rate in the two-phase region, is the dissolution enthalpy, for The effective heat transported by the thermal diffusion of the phase, represent Fick's law diffusion rate of the phase.

[0142] For different phases, the calculation parameters under different alloy phases are given as follows:

[0143]

[0144] For the two-phase region, the lever law is used to calculate the volume fractions of different phases:

[0145] (8)

[0146] (9)

[0147] in , Zr is Mutually, The Zr concentration at a certain calculated time on the solid solubility curve of the phase and at a temperature calculated at a certain location of the metal fuel pellet. , The calculation time and location of the U-Pu-Zr ternary alloy are Mutually, The concentration of the phase. The diffusion and distribution of the Zr element can be calculated by combining equations (3)-(9). Equations (3)-(9) are calculated using the domain partial differential equation module in COMSOL.

[0148] Example 3

[0149] This embodiment also provides a storage medium, which may be a storage medium such as ROM, RAM, disk, or CD. The storage medium stores one or more programs, and when the program is executed by the processor, the calculation method for the migration and redistribution of the Zr element in the U-Pu-Zr ternary metal fuel of the above-mentioned embodiment 1 is implemented.

[0150] Example 4

[0151] This embodiment provides a computing device, which can be a desktop computer, a laptop computer, a smart phone, a PDA handheld terminal, a tablet computer or other terminal device with a display function. The computing device includes a processor and a memory, and the memory stores one or more programs. When the processor executes the program stored in the memory, the calculation method for the migration and redistribution of the Zr element in the U-Pu-Zr ternary metal fuel of the above-mentioned embodiment 1 is implemented.

[0152] The embodiment of the present invention provides a calculation method for the migration and redistribution of Zr elements in a U-Pu-Zr ternary metal fuel. The metal fuel contains three metal elements, U, Pu and Zr, and the Pu element is considered to have a fixed content and does not diffuse. A U-Zr pseudo-binary phase diagram with a fixed Pu content is used to establish the phase discrimination condition of the metal Zr. The migration rate, direction and concentration distribution of the Zr element inside the ternary metal fuel pellet are calculated by Fick's law, Soret effect (thermal diffusion) and heat conduction coupling, so that the heat transfer calculation and temperature distribution of the metal fuel are more accurate, thereby making the prediction of the thermal performance of the metal fuel more accurate.

[0153] The embodiment of the present invention can achieve the effect of rapid modeling and calculation of various metal fuels by using COMSOL to quickly adjust the initial mass fraction and phase diagram of the metal fuel on the existing metal fuel model.

[0154] The above embodiments are preferred implementation modes of the present invention, but the implementation modes of the present invention are not limited to the above embodiments. Any other changes, modifications, substitutions, combinations, and simplifications that do not deviate from the spirit and principles of the present invention should be equivalent replacement methods and are included in the protection scope of the present invention.

Claims

1. A method for calculating the migration and redistribution of Zr elements in a ternary metal fuel, characterized in that: The metal fuel contains three metal elements: U, Pu and Zr, and the Pu element is considered to have a fixed content and not diffuse. The method specifically includes the following steps: (1) determining the initial concentration percentages of U, Pu and Zr in the metal fuel, and obtaining a U-Zr pseudo-binary phase diagram at the Pu content; (2) calculating the temperature distribution of the fuel pellets and the cladding at each time based on the fuel pellet linear power of the metal fuel and the physical properties of the fuel pellets, the cladding, and the gap between the fuel pellets and the cladding; (3) Based on the temperature distribution in the fuel pellet of the metal fuel and the U-Zr pseudo-binary phase diagram, a criterion for determining the alloy phase at each time and position in the fuel pellet is established to obtain the distribution of the alloy phase; (4) Based on the distribution of alloy phases at various times and locations in the fuel pellets in the metal fuel, the diffusion and redistribution process of Zr is calculated using Fick's law of Zr metal and the empirical formula for thermal diffusion under different U-Pu-Zr elemental phase states, and the Zr concentration distribution at various times and locations in the fuel pellets is obtained.

2. The method for calculating the migration and redistribution of Zr elements in a ternary metal fuel according to claim 1, characterized in that: The heat transfer calculation of the fuel pellets, cladding and the gap between the fuel pellets and the cladding in the metal fuel is specifically calculated as follows: (1) In the formula, is the density of the material, is the heat capacity of the fuel pellet or cladding, is the uncorrected temperature of the fuel pellet or cladding, For time, is the thermal conductivity of the fuel pellet or cladding, is the distance from the centerline of the fuel pellet, is the heat generation rate per unit volume of fuel pellets; Formula (1) is used to calculate the heat transfer process and temperature distribution in the fuel pellets. As for the heat transfer process and temperature distribution in the cladding and the gap between the fuel pellets and the cladding, since there is no heat source, the source term in formula (1) is rounding.

3. The calculation method for Zr element migration and redistribution in a ternary metal fuel according to claim 1, characterized in that: In step (2), the phase transition temperature of the ternary alloy was also corrected, increasing the phase transition temperature by 58 K, that is, (2) In the formula, is the uncorrected temperature of the fuel pellet or cladding, T is the corrected temperature, K is the unit, Kelvin.

4. The method for calculating the migration and redistribution of Zr elements in a ternary metal fuel according to claim 1, characterized in that: In step (4), Zr is in a non-steady-state diffusion state in the fuel pellets, and the diffusion equation of the Zr element is: (3) In the formula, is the concentration of Zr element, is the Fick's law diffusion coefficient of Zr element, is the diffusion coefficient of thermal diffusion of Zr element, is the concentration gradient, is the temperature gradient, is the Hamiltonian operator, T is the corrected temperature, For time.

5. The method for calculating the migration and redistribution of Zr elements in a ternary metal fuel according to claim 4, characterized in that: The diffusion equation is solved using Fick's law and the empirical formula for thermal diffusion: For single-phase area: (4) (5) In the formula, represent Fick's law diffusion rate of the phase, Refers to any phase that an alloy may be in. is the diffusion pre-exponential factor, represent The Fick's law diffusion pre-exponential factor of the phase, is the diffusion activation energy, represents the universal gas constant under standard conditions, represent The thermal diffusion rate of the phase, for Fick's law diffusion coefficient of phase Zr element, is the concentration of Pu metal element in the metal fuel pellet, for The effective heat transport by thermal diffusion of phases; For the two-phase region: (6) (7) In the formula, for Fick's law diffusion rate in the two-phase region, , They refer to different alloy phases. For the alloy The volume fraction of the phase, , They are phase and The Fick's law diffusion pre-exponential factor of the phase, for The thermal diffusion rate in the two-phase region, is the dissolution enthalpy, for The effective heat transported by the thermal diffusion of the phase, represent Fick's law diffusion rate of the phase, Zr is the element in the ternary alloy. Phase concentration, Zr is the element in the ternary alloy. Phase concentration.

6. The method for calculating the migration and redistribution of Zr elements in a ternary metal fuel according to claim 5, characterized in that: For the two-phase region, to calculate the volume fractions of different phases, the lever rule is used: (8) (9) In the formula, , Zr is Mutually, The Zr concentration at a certain calculated time on the solid solubility curve of the phase and at a calculated temperature at a certain location of the metal fuel pellet, and , is the U-Pu-Zr ternary alloy at a certain point in the calculation time. Mutually, The Zr concentration of the phase.

7. A calculation system for Zr element migration and redistribution in ternary metal fuel, characterized in that: Used to implement any of the methods of claims 1-6, comprising a heat conduction module, an alloy phase judgment module, and a Zr migration and redistribution calculation module, The heat conduction module is used to calculate the temperature change and distribution of the fuel pellets, the cladding and the gap between them; The alloy phase judgment module is used to judge the phase of the alloy at each position of the fuel pellet at each moment; The Zr migration and redistribution calculation module is used to calculate the Zr concentration distribution inside the fuel pellet at each time and the migration rate and direction of the Zr element at each time.

8. The calculation system for Zr element migration and redistribution in ternary metal fuel according to claim 7, characterized in that: A correction module is also included for correcting the phase transition temperature of the ternary alloy, and the phase transition temperature is increased by 58K, where K is the unit, Kelvin.

9. A storage medium storing a program, characterized in that: When the program is executed by a processor, the calculation method for migration and redistribution of Zr elements in a ternary metal fuel as described in any one of claims 1 to 6 is implemented.

10. A computing device comprising a processor and a memory for storing a program executable by the processor, characterized in that: When the processor executes the program stored in the memory, the calculation method for the migration and redistribution of the Zr element in the ternary metal fuel according to any one of claims 1 to 6 is implemented.

Images