A calculation method for the generation, diffusion, and release of fission gases in UO2 fuel pellets

Abstract

The present invention discloses a calculation method, system, medium and device for the generation, diffusion and release of fission gases in UO2 fuel pellets. The method models the diffusion process of fission gases generated in the fuel pellets based on the Booth diffusion equation, adopts a two-dimensional geometric model, and calculates the concentration distribution of fission gases in the pellet grains at each moment through the finite element analysis method. Based on the concentration distribution, the volume release rate of fission gases released from the grains to the grain boundaries is calculated through the concentration gradient on the surface of the pellet grains, and finally the volume release amount of fission gases released from the grains to the grain boundaries and the volume release amount of fission gases accumulated on the grain boundaries are calculated. Based on the traditional Booth diffusion equation of UO2 fuel, the present invention develops a calculation model for the generation, diffusion and release of fission gases in UO2 fuel pellets, and at the same time considers the influence of the geometric shape of the fuel pellets and the fuel temperature transition. Therefore, the concentration distribution of fission gases in the fuel pellets obtained by using the present invention will be more accurate.

Description

Technical Field

[0001] The present invention relates to the technical field of calculating the release amount of fission gas in a nuclear reactor, and particularly relates to a calculation method, system, medium and device for the generation, diffusion and release of fission gas in UO2 fuel pellets during the service period of a reactor. Background Art

[0002] During the service period of a reactor, the process of fission gas generating from irradiated UO2 fuel pellets and diffusing into the fuel gap is very complex. The generation, diffusion and release of fission gas products are adverse to the thermal performance of the fuel. Its diffusion into the fuel gap will reduce the thermal conductivity of the gap, resulting in an increase in the fuel center temperature, further release of fission gas, an increase in the cladding internal pressure, which is likely to cause cladding failure, and a large amount of fission product leakage contaminating the coolant. Therefore, understanding and calculating the process of fission gas diffusing from the pellet to the cladding gap is crucial for optimizing fuel use. In the past few decades, great progress has been made in understanding the key mechanisms of fission gas behavior through research on reactor experiments and simplified analysis models. Considering that UO2 fuel is a key material widely used in nuclear reactors, but there is currently no complete calculation method for the diffusion process of fission gas in UO2 fuel pellets. Therefore, it is necessary to propose a stable, reliable and accurate method for determining the process of fission gas released from UO2 fuel pellets diffusing to the pellet surface. Summary of the Invention

[0003] In order to overcome the defects and deficiencies existing in the prior art, the first object of the present invention is to provide a calculation method for the generation, diffusion and release of fission gas in irradiated UO2 fuel pellets. In the present invention, based on the Booth diffusion equation, a model of fission gas generated in the fuel pellet is established, the diffusion model of fission gas in microscopic grains is coupled with the macroscopic pellet model, and the concentration distribution of fission gas in the pellet grains at each moment is calculated by means of finite element analysis. On this basis, the volume release amount of fission gas released from the grains to the grain boundaries can be further determined.

[0004] The second object of the present invention is to provide a calculation system for the diffusion distribution of fission gas in a fuel pellet.

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

[0006] The fourth object of the present invention is to provide a calculation device.

[0007] To achieve the above first objective, the present invention provides a calculation method for the generation, diffusion, and release of fission gases in UO2 fuel pellets during the service of a reactor. Under the condition of different constant temperature jumps at different time points, the Booth diffusion equation is used to simulate the diffusion distribution of the fission gas concentration in the grain domain of the fuel pellet, and the finite element numerical solution is used to solve the fission gas concentration released to the grain boundary, including the following steps:

[0008] (1) Use the finite element method to construct the Booth diffusion equation for the microscopic grains of fission gases generated in the fuel pellet, and transform the Booth diffusion equation into a dimensionless form;

[0009] (2) Based on the constructed fission gas diffusion equation, couple the two-dimensional geometric model of the microscopic grains of fission gases to the macroscopic fuel pellet model;

[0010] (3) Set the temperature of the UO2 fuel pellet, the initial concentration of fission gases, and the boundary conditions;

[0011] (4) Calculate the volumetric rate of fission gas generation in the pellet, and obtain the radial concentration distribution of fission gases on the microscopic grains in the fuel pellet by solving the Booth diffusion equation;

[0012] (5) Based on the obtained radial concentration distribution of fission gases on the microscopic grains, calculate the volumetric release rate of fission gases released from the grains to the grain boundary through the concentration gradient on the surface of the pellet grains;

[0013] (6) Calculate the saturation value of the volumetric release amount of fission gases on the grain boundary, and calculate the volumetric release rate of fission gases released from the grain boundary to the fuel gas gap based on the saturation value;

[0014] (7) Based on the volumetric release rate of fission gases released from the grains to the grain boundary and the volumetric release rate of fission gases released from the grain boundary to the fuel gas gap, obtain the volumetric release amount of fission gases released from the grains to the grain boundary and the cumulative volumetric release amount of fission gases on the grain boundary.

[0015] The Booth diffusion equation is given by the following formula:

[0016]

[0017] In the formula, C is the concentration of fission gases in the microscopic grains of the fuel pellet, t is the running time of the fission reaction, D is the diffusion coefficient of fission gases in the microscopic grains of the fuel pellet, is the Laplace operator in the spherical coordinate system, P fg is the volumetric rate of fission gas generation. Among them, the volumetric rate of fission gas generation P fg can be obtained by multiplying the fission yield y and the fission rate F rateMultiplication is obtained, and the fission rate can be expressed in terms of the volumetric rate of heat production Q prod and the thermal energy E released per fission f as the ratio:

[0018]

[0019]

[0020] The fission yield per fission is approximately 0.251, and the energy released per fission is approximately 200 MeV. It is assumed that the fission gas consists of approximately 90% xenon and 10% krypton. The exact values of these parameters depend on the isotopes involved in the fission and the initial neutron energy.

[0021] The sum of the initial conditions and the above boundary conditions is given by:

[0022] C(r, t = 0) = 0 (4)

[0023] C(r = g r , t) = 0 (5)

[0024] where r is the radial coordinate of the grain, and g r is the radius of the microscopic grain of the fuel pellet.

[0025] In the case of using a time-independent geometric model, considering the growth of the grains, the Booth diffusion equation is transformed into a dimensionless form by:

[0026]

[0027] where η is the dimensionless ratio of the radial coordinate to the grain radius.

[0028] Thus, the radial concentration distribution of fission gas on the grains is obtained:

[0029]

[0030] Since the grain model is continuously growing and changing, appropriate values for the fission gas grain radius, fission gas diffusion coefficient, and fission gas production are taken, and the equation is solved on the normalized grain geometry. The concentration gradient at the grain surface of the pellet is obtained by:

[0031]

[0032] The atomic flux R of fission gas from the grain to the grain boundary fgfux is in units of atoms m -2 s -1 and is given by:

[0033]

[0034] To apply this equation on a continuous scale, it is necessary to convert the fission gas flux at the fuel grain surface to a volume release rate. The volume release rate R of fission gas released to the grain boundary is obtained by the ratio of the fuel grain surface area to the volume. gb , in units of atoms m -3 s -1 .

[0035]

[0036] And convert it to a dimensionless form:

[0037]

[0038] The saturation value G of the volume release of fission gas on the grain boundary bsat is given by:

[0039]

[0040] where: r f is the radius of curvature of the fission bubble, f(θ fg ) is a function explaining the bubble shape, θ fg is the half angle between the bubble surfaces, f B is the fraction of the grain surface covered by bubbles, k B is the Boltzmann constant, T is the temperature in K, P ext is the externally applied hydrostatic pressure in Pa, γ se is the surface energy of the bubble, g r is the grain radius in m. In this work, for simplicity of calculation, it is assumed that the external hydrostatic pressure is 0.

[0041] The volume release rate of fission gas released from the grain boundary of the microelement volume dV to the fuel gas gap is calculated by:

[0042]

[0043] where τ fg is the time constant of fission gas release (the time required to completely release more than the saturation value if released at the current rate).

[0044] The volume release rate of fission gas on the grain boundary is given by

[0045]

[0046] where G b is the cumulative volume release of fission gas on the grain boundary, R gb is the volume release rate of fission gas released from the grain to the grain boundary, Re is the volume release rate of fission gas released from grain boundaries into the fuel gas gap.

[0047] The volume release amount G of fission gas released from grains to grain boundaries gb is given by the following formula:

[0048]

[0049] To achieve the above second object, the present invention adopts the following technical solutions:

[0050] A calculation system for the generation, diffusion and release distribution of fission gas in fuel pellets during the service of a reactor, including a fission gas concentration diffusion distribution calculation module, a volume rate calculation module for fission gas generation, a volume release rate calculation module for fission gas, and a volume release amount calculation module for fission gas.

[0051] The fission gas concentration diffusion distribution calculation module is used to calculate the change value of the fission gas concentration distribution at different times in the microscopic grains of fuel pellets;

[0052] The volume rate calculation module for fission gas generation is used to calculate the volume rate of fission gas generation;

[0053] The volume release rate calculation module for fission gas is used to calculate the volume release rate of fission gas released from grains to grain boundaries, on grain boundaries, and from grain boundaries to the fuel gas gap;

[0054] The volume release amount calculation module for fission gas is used to calculate the volume release amount of fission gas released from grains to grain boundaries and accumulated on grain boundaries.

[0055] To achieve the above third object, the present invention adopts the following technical solutions:

[0056] A storage medium stores a program, and when the program is executed by a processor, it implements the calculation method of the fission gas concentration diffusion distribution in the fuel pellet as described above.

[0057] To achieve the above fourth object, the present invention adopts the following technical solutions:

[0058] A computing device includes a processor and a memory for storing a program executable by the processor. When the processor executes the program stored in the memory, it implements the calculation method of the fission gas concentration diffusion distribution in the fuel pellet as described above.

[0059] Compared with the prior art, the present invention has at least the following beneficial effects:

[0060] (1) The present invention obtains the radial concentration distribution of fission gas in the fuel pellet over time by numerically solving the Booth diffusion equation using finite elements, and then calculates the corresponding volume release of fission gas. By comparing this result with the volume release of fission gas obtained using the analytical solution in MATLAB, the calculated result of the volume release of fission gas in the fuel pellet is more reliable, thus facilitating the optimization of fuel use more conveniently;

[0061] (2) On the premise of using fixed geometric parameters, in order to adapt to pellet growth, the Booth diffusion equation is converted into a dimensionless form for use in the present invention, making the calculated value of the fission gas concentration distribution in the fuel pellet more accurate;

[0062] (3) The present invention uses an operator to couple the geometry of fission gas in microscopic grains with the macroscopic geometry of the fuel pellet. Compared with previous technologies, this two-dimensional method can easily use a finite element mesh to change the number of gas grains at the pellet radius without modifying the pellet geometry to insert more points or predefining additional coupling operators.

[0063] (4) The finite element numerical solution used in the present invention does not require precise discretization in time, which makes the model solution easier to implement. BRIEF DESCRIPTION OF THE DRAWINGS

[0064] Figure 1 is a schematic flow chart of the steps of the calculation method for the generation, diffusion, and release of fission gas in the UO2 fuel pellet of the present invention;

[0065] Figure 2 is a schematic diagram of the comparison result of the volume release of fission gas released from the fuel pellet grains to the grain boundary obtained numerically by the finite element method and the volume release of fission gas obtained using the analytical solution in MATLAB;

[0066] Figure 3 is a schematic diagram of the comparison between the result of the fission gas release from the fuel pellet grains to the gas gap obtained in the present invention and the result recorded in the existing BISON. DETAILED DESCRIPTION OF THE EMBODIMENTS

[0067] In order to make the objectives, technical solutions, and advantages of the present invention clearer, the present invention will be further described in detail below with reference to 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 used to limit the present invention.

[0068] Embodiment 1

[0069] This embodiment provides a calculation method for the generation, diffusion, and release distribution of fission gases varying with time inside UO2 fuel pellets. The Booth diffusion equation is used to simulate and calculate the concentrations of fission gases at different positions in the fuel pellet domain at different times, and the finite element numerical solution is used to solve the volume release amount of fission gases released from grains to grain boundaries, including the following steps:

[0070] Step S1: Use the finite element method to construct the Booth diffusion equation for the microscopic grains of fission gases generated inside the fuel pellet. As a prerequisite for processing, then transform the Booth diffusion equation into a dimensionless form;

[0071] Among them, the Booth diffusion equation is

[0072]

[0073] In the formula, C is the concentration of fission gases in the microscopic grains of the fuel pellet, t is the reaction operation time, D is the diffusion coefficient of fission gases in the microscopic grains of the fuel pellet, is the Laplace operator in the spherical coordinate system, and P fg is the volume rate of fission gas generation.

[0074] Among them, the volume rate of fission gas generation P fg can be obtained by the following formula:

[0075]

[0076]

[0077] In the formula, y is the fission yield, and F rate is the fission rate, and the fission rate can be obtained from the volume rate of heat generation Q prod and the thermal energy E released per fission f The ratio is obtained. Further preferably, the fission gas yield per fission is about 0.251, and the energy released per fission is about 200 MeV. It is assumed that the fission gas consists of approximately 90% xenon and 10% krypton. The accurate values of these parameters depend on the isotopes in the fission and the initial neutron energy.

[0078] In the case of using a geometry that does not change with time, considering the grain growth situation, the Booth diffusion equation is transformed into a dimensionless form through the following formula:

[0079]

[0080] Thus, the radial concentration distribution equation of fission gases is obtained:

[0081]

[0082] Where η is the dimensionless ratio of the radial coordinate to the grain radius, r is the radial coordinate of the grain, and g r is the radius of the microscopic grains of the fuel pellet. Since the grain model is continuously growing and changing, the values of the grain radius, the fission gas diffusion coefficient, and the fission gas production value of an appropriate continuous model are used to solve this equation on the normalized grain geometry.

[0083] S2: Based on the established fission gas diffusion equation, the two-dimensional Cartesian geometry model of the fission gas microscopic grains is coupled to the macroscopic fuel pellet model using the operator equipped with the COMSOL finite element platform. Among them, the operator can be used to transfer temperature, fission rate density, and the average grain size from the pellet geometry to the fission gas grain geometry.

[0084] S3: Set the temperature of the UO2 fuel pellet, the initial concentration of the fission gas, and the boundary conditions.

[0085] In this embodiment, it is assumed that the initial fission gas concentration is set to zero in the entire grain domain, and the Dirichlet (fixed value) boundary condition is used to set the fission gas concentration to zero on the fuel grain surface.

[0086] Among them, the pellet temperature is described by a piecewise function. Temperature values common in engineering applications are selected within a certain range, and the time period is divided into three equal parts during the running time. For example, three-stage constant temperature changes of 1000K - 1500K - 2000K are achieved at two time points of 5×10 6 s and 10×10 6 s respectively; the initial concentration and boundary conditions are given by the following formula:

[0087] C(r, t = 0) = 0 (4)

[0088] C(r = g r , t) = 0 (5)

[0089] Where r is the radial coordinate of the grain, and g r is the radius of the microscopic grains of the fuel pellet.

[0090] S4: Calculate the volumetric rate of fission gas generation in the pellet, and obtain the radial concentration distribution of fission gas on the microscopic grains in the fuel pellet by solving the Booth diffusion equation.

[0091] S5: According to the fission gas concentration distribution in the pellet grains obtained, the volumetric release rate of fission gas released from the grains to the grain boundaries can be calculated through the concentration gradient on the pellet grain surface.

[0092] Among them, the concentration gradient on the grain surface is obtained by the following formula:

[0093]

[0094] The fission gas atomic flux R from grain to grain boundary fgfux has the unit of atoms m -2 s -1 , and is given by:

[0095]

[0096] To apply this equation on a continuous scale, it is necessary to convert the fission gas flux at the fuel grain surface to a volume release rate R gb , with the unit of atoms m -3 s -1 .

[0097]

[0098] And convert it to a dimensionless form:

[0099]

[0100] where C is the concentration of fission gas in the microscopic grains of the fuel pellet, r is the radial coordinate of the grain, η is the dimensionless ratio of the radial coordinate to the grain radius, g r is the radius of the microscopic grains of the fuel pellet, t is the reaction operation time, and D is the diffusion coefficient of fission gas in the microscopic grains of the fuel pellet.

[0101] S6: Calculate the saturation value G of the volume release of fission gas on the grain boundary bsat , and calculate the volume release rate of fission gas released from the grain boundary to the gas gap based on the saturation value.

[0102] wherein, the saturation value G of the volume release of fission gas on the grain boundary bsat is calculated by the following formula:

[0103]

[0104] where: r f is the curvature radius of the fission bubble, f(θ fg ) is a function explaining the bubble shape, θ fg is the half angle between the bubble surfaces, f B is the fraction of the grain surface covered by bubbles, k B is the Boltzmann constant, T is the temperature in K, P ext is the externally applied hydrostatic pressure in Pa, γ se is the surface energy of the bubble, g r is the grain radius in m.

[0105] Preferably, rf = 5×10 -7 , θ fg = 50°, f B = 0.5, k B = 1.3806×10 -23 J / K, γ se = 0.626J / m 2 , P ext Assume it is 0, substituting the above values into Equation (10) gives:

[0106]

[0107] Among them, the fission gas volume release rate R released from the grain boundary of the infinitesimal volume dV to the fuel gas gap e is calculated by the following formula:

[0108]

[0109] Among them, τ fg is the time constant of fission gas release (the time required to completely release more than the saturation value if continuing to release at the current rate), G b is the volume release amount of the fission gas accumulated on the grain boundary.

[0110] S7: Calculate the volume release amount of the fission gas accumulated on the grain boundary released from the grains to the grain boundary.

[0111] The volume release amount of the fission gas accumulated on the grain boundary is given by the following formula:

[0112]

[0113] Among them, R gb is the fission gas volume release rate released from the grains to the grain boundary.

[0114] The fission gas volume release amount G released from the grains to the grain boundary gb is given by the following formula:

[0115]

[0116] In this embodiment, the finite element method will be used to numerically solve the fission gas volume release rate and compare it with the calculation results of the analytical solution considering factors such as radioactive decay and generation and non-constant fission rate in MATLAB.

[0117] The simplest analytical solution of the volume release rate is presented in the form of an infinite sum of exponential terms as:

[0118]

[0119] Among them, n is the summation index.

[0120] In MATLAB, radioactive decay and production, non-constant fission rates, diffusion coefficients, and grain sizes are considered. By discretizing the time history into k c cycles, each cycle lasting for a t s seconds, the diffusion coefficient, grain size, and the calculated volumetric rate of fission gas production are all constants for each cycle. The cumulative release fraction released to the grain boundaries of the pellet is obtained through the following equation :

[0121]

[0122] where n, s, and q are summation indices, and the superscript represents the cycle number.

[0123] The volumetric release of fission gas F released from the grains to the grain boundaries for the analytical solution can be obtained through the following equation gb .

[0124]

[0125] The solution results obtained using the method described in this embodiment can be used as a reference for the diffusion distribution of fission gas concentration in a detailed UO2 fuel pellet.

[0126] As Figure 2 shown, it can be seen from the figure that the change over time of the volumetric release of fission gas released to the grain boundaries of the fuel pellet obtained by the present invention (numerical solution calculation results) is consistent with the recorded results calculated by the MATLAB analytical value. As time goes by, the volumetric release of fission gas on the outer surface of the pellet grains gradually increases, and at the temperature change point, the fission gas concentration also has a certain mutation, indicating the effectiveness of the method of the present invention.

[0127] Example 2

[0128] It is basically the same as Example 1, except that this embodiment also provides a calculation system for fission gas generation, diffusion, and release in a UO2 fuel pellet, including: a fission gas concentration diffusion distribution calculation module, a volumetric rate calculation module for fission gas generation, a fission gas volumetric release rate calculation module, and a fission gas volumetric release calculation module.

[0129] The fission gas concentration diffusion distribution calculation module is used to calculate the change value of the fission gas concentration distribution at different times in the microscopic grains of the fuel pellet.

[0130] In this embodiment, within the normal reaction temperature operating range, several pellet temperatures that may occur during the fission reaction are selected, and the input parameters conform to the characteristics of a piecewise function. The fuel pellet temperature is described by a piecewise function, and a three-stage constant temperature change of 1000K - 1500K - 2000K is realized at two time points respectively.

[0131] In this embodiment, the fission gas concentration diffusion distribution calculation module is used to calculate the change value of the fission gas concentration distribution in the fuel pellets at different times.

[0132] The concentration calculation distribution value is obtained by the following method:

[0133] Booth diffusion equation

[0134]

[0135] Convert to dimensionless form

[0136]

[0137] Among them, the dimensionless ratio of the radial coordinate to the grain radius is r is the radial coordinate of the grain, g r is the radius of the microscopic grain of the fuel pellet, C is the concentration of fission gas atoms in the fuel pellet grain, D is the diffusion coefficient of the fission gas in the fuel pellet grain, is the Laplace operator in spherical coordinates, P fg is the volume rate of fission gas production, and t is the reaction running time.

[0138] The volume rate calculation module of fission gas production is used to calculate the volume rate of fission gas production.

[0139] The volume rate of fission gas production P fg It can be obtained by the following formula:

[0140]

[0141]

[0142] Where y is the fission yield, F rate is the fission rate, which can be calculated from the volume rate of heat generation Q prod and the heat energy E released by each fission f The ratio is obtained.

[0143] When setting the initial condition C(r,t=0)=0 and the boundary condition C(r=g r , t) = 0, the finite element method is used to numerically solve the fission gas concentration.

[0144] In this embodiment, the fission gas volume release rate calculation module is used to calculate the fission gas volume release rate released from grains to grain boundaries, on grain boundaries, and from grain boundaries to fuel gas gaps.

[0145] Fission gas atom flux from grain to grain boundary in atoms m -2 s -1 .

[0146] To apply this equation on a continuous scale, the flux at the fuel grain surface is converted to a volume release rate R gb in atoms m -3 s -1 .

[0147]

[0148] and transformed into a dimensionless form

[0149] The saturation value G of the volume release of fission gas on the grain boundary bsat is given by:

[0150]

[0151] where: r f = 5×10 -7 is the radius of curvature of the fission bubble, f(θ fg ) is a function that accounts for the bubble shape, θ fg = 50° is the half angle between the bubble surfaces, f B = 0.5 is the fraction of the grain surface covered by bubbles, k B = 1.3806×10 -23 J / K is the Boltzmann constant, T is the temperature in K, P ext is the externally applied hydrostatic pressure in Pa, γ se = 0.626 J / m 2 is the surface energy of the bubble, g r is the grain radius in m. In this work, for simplicity of calculation, the external hydrostatic pressure is assumed to be 0.

[0152] Substituting the above values into the equation gives:

[0153]

[0154] The volume release rate of fission gas released from the grain boundary into the fuel gas gap from an infinitesimal volume dV is calculated by:

[0155]

[0156] where τ fg is the time constant of fission gas release (the time required to completely release beyond the saturation value if continuing to release at the current rate).

[0157] In this embodiment, the fission gas volume release calculation module is used to calculate the fission gas volume release amount that is released from the grains to the grain boundaries and accumulates on the grain boundaries.

[0158] Fission gas volume release rate on the grain boundary is given by the following formula

[0159]

[0160] where G b is the fission gas volume release amount accumulated on the grain boundary, R gb is the fission gas volume release rate from the grains to the grain boundary, and R e is the fission gas volume release rate from the grain boundary to the fuel gas gap.

[0161] The fission gas volume release amount G from the grains to the grain boundary gb is given by the following formula:

[0162]

[0163] The obtained result is compared with the analytical solution calculation result in MATLAB, and the trends of the two results are basically the same, thus indicating the effectiveness of the present invention, as Figure 2 shown.

[0164] The analytical solution of the fission gas volume release rate released to the grain surface is presented in the form of an infinite sum of exponential terms:

[0165]

[0166] where n is the summation index.

[0167] The cumulative release fraction released to the grain boundary is obtained through the following equation:

[0168]

[0169] In the formula, n, s, and q are summation indices, and the superscript represents the number of cycles.

[0170] Through the equation the analytical solution of the fission gas volume release amount from the grains to the grain boundary can be obtained.

[0171] Figure 3 This is a comparison chart of the fission gas release results calculated by the present invention on the COMSOL platform and the existing results calculated on BISON. It can be clearly seen from the figure that the numerical trends of the two fission gas release results are basically the same, further proving the effective accuracy of the present invention.

[0172] In order to obtain more accurate and reliable calculation results of the diffusion distribution of fission gas concentration in the fuel pellets, the foregoing invention embodiments not only use the finite element numerical solution in COMSOL to solve the concentration, but also use a more complete analytical solution considering radioactive decay and generation as well as non-constant fission rate in MATLAB to form a comparison. At the same time, compared with the prior art, the more intuitive visualization operation interface of COMSOL and the more concise and rapid calculation process of the present invention give it greater advantages.

[0173] Embodiment 3

[0174] Basically the same as Embodiment 2, the difference is that: this embodiment also provides a storage medium, which can be a storage medium such as ROM, RAM, disk, optical disc, etc. The storage medium stores one or more programs, and when the programs are executed by a processor, the calculation method of the generation, diffusion and release distribution of fission gas changing with time in the UO2 fuel pellet of the foregoing Embodiment 1 is realized.

[0175] Embodiment 4

[0176] Basically the same as Embodiment 3, the difference is that: 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 devices with a display function. The computing device includes a processor and a memory. The memory stores one or more programs, and when the processor executes the programs stored in the memory, the calculation method of the generation, diffusion and release distribution of fission gas changing with time in the UO2 fuel pellet of the foregoing Embodiment 1 is realized.

[0177] Embodiment 5

[0178] In this embodiment, the MATLAB implementation code used in the calculation process is:

[0179]

[0180]

[0181] In this specification, each embodiment is described in a progressive manner. The key point of each embodiment is the difference from other embodiments. The same or similar parts among the embodiments can be referred to each other. For the calculation system, storage medium and computing device of the generation, diffusion and release of fission gas in the UO2 fuel pellet disclosed in the embodiments, since they correspond to the method disclosed in the embodiments, the description is relatively simple, and the relevant parts can be referred to the description of the method part.

[0182] The above embodiments are preferred embodiments of the present invention, but the embodiments of the present invention are not limited to the above embodiments. Any other changes, modifications, substitutions, combinations, and simplifications made without departing from the spirit and principle of the present invention shall be equivalent replacement methods and are all included in the protection scope of the present invention.

Claims

1. A calculation method for the generation, diffusion, and release of fission gases within UO2 fuel pellets, characterized in that, The finite element modeling calculation of the fission gas generated in the fuel pellet is carried out by using the Booth diffusion equation, including the following steps: Use the finite element method to construct the Booth diffusion equation for the microscopic grains of the fission gas generated in the fuel pellet, and transform the Booth diffusion equation into a dimensionless form; Based on the established fission gas diffusion equation, couple the two-dimensional geometric model of the microscopic grains of the fission gas to the macroscopic fuel pellet model; Set the temperature of the UO2 fuel pellet, the initial concentration of the fission gas and the boundary conditions; Calculate the volume rate of fission gas generation in the pellet, and obtain the radial concentration distribution of the fission gas on the microscopic grains in the fuel pellet by solving the Booth diffusion equation; Based on the obtained radial concentration distribution of the fission gas on the microscopic grains, calculate the volume release rate of the fission gas released from the grains to the grain boundaries through the concentration gradient on the surface of the pellet grains; Calculate the saturation value of the volume release amount of the fission gas on the grain boundary, and calculate the volume release rate of the fission gas released from the grain boundary to the fuel gas gap based on the saturation value; Based on the volume release rate of the fission gas released from the grains to the grain boundary and the volume release rate of the fission gas released from the grain boundary to the fuel gas gap, obtain the volume release amount of the fission gas released from the grains to the grain boundary and the cumulative volume release amount of the fission gas on the grain boundary; The Booth diffusion equation is: (1) Where \(t\) is the running time of the fission reaction, \(C\) is the concentration of fission gas in the microscopic grains of the fuel pellet, \(D\) is the diffusion coefficient of fission gas in the microscopic grains of the fuel pellet, \(\nabla\) 2 is the Laplace operator in the spherical coordinate system, is the volumetric rate of fission gas generation; The Booth diffusion equation is transformed into a dimensionless form by the following formula: (2) Thus, the expression of the radial concentration distribution of the grain fission gas is obtained: (3) In the formula, is the dimensionless ratio of the radial coordinate to the grain radius, r is the radial coordinate of the grain, g r is the radius of the microscopic grains of the fuel pellet, C is the concentration of fission gas in the microscopic grains of the fuel pellet, t is the operation time of the fission reaction, D is the diffusion coefficient of fission gas in the microscopic grains of the fuel pellet, is the volume rate of fission gas generation; The volume rate of the fission gas generation is expressed as: (4) where y is the fission yield, is the fission rate, is the volumetric rate of heat production, is the thermal energy released per fission.

2. The calculation method for the generation, diffusion and release of fission gases in UO2 fuel pellets according to claim 1, characterized in that The concentration gradient on the surface of the pellet grains is (7) where C is the concentration of fission gas in the microscopic grains of the fuel pellet, r is the radial coordinate of the grain, is the dimensionless ratio of the radial coordinate to the grain radius, g r is the radius of the microscopic grains of the fuel pellet.

3. The calculation method for the generation, diffusion, and release of fission gases within UO2 fuel pellets according to claim 1, wherein The expression of the volume release rate of the fission gas released from the grains to the grain boundary is (8) And transform it into a dimensionless form: (9) In the formula, C is the concentration of fission gas in the microscopic grains of the fuel pellet, r is the radial coordinate of the grain, is the dimensionless ratio of the radial coordinate to the grain radius, g r is the radius of the microscopic grains of the fuel pellet, t is the operation time of the fission reaction, and D is the diffusion coefficient of fission gas in the microscopic grains of the fuel pellet.

4. The calculation method for the generation, diffusion and release of fission gas in UO2 fuel pellets according to claim 1, characterized in that, The saturation value of the volume release of fission gas on the grain boundary It is calculated by the following formula: (10) In the formula, is the radius of curvature of the fission bubble, is the function explaining the bubble shape, is the half angle between the bubble surfaces, is the fraction of the grain surface covered by bubbles, is the Boltzmann constant, T is the temperature, is the externally applied hydrostatic pressure, is the surface energy of the bubble, is the radius of the microscopic grains of the fuel pellet; The calculation formula for the volume release rate of the fission gas released from the grain boundary to the fuel gas gap is: (12) wherein, is the volumetric release rate of fission gas released from the grain boundary into the fuel gas gap, represents the volume of the grain microelement, is the time constant of fission gas release, is the cumulative volumetric release amount of fission gas on the grain boundary, is the saturation value of the volumetric release amount of fission gas on the grain boundary.

5. The calculation method for the generation, diffusion, and release of fission gases in UO2 fuel pellets according to any one of claims 1-4, characterized in that, The cumulative volume release amount of the fission gas on the grain boundary is given by the following formula: (13) Among them, is the volume release amount of the fission gas accumulated on the grain boundary, is the volume release rate of the fission gas released from the grain to the grain boundary, is the volume release rate of the fission gas released from the grain boundary to the fuel gas gap, and t is the operation time of the fission reaction; The volume release amount of the fission gas released from the grains to the grain boundary is given by the following formula: (14) Among them, is the volume release amount of fission gas released by the crystal grains into the grain boundary, is the volume release rate of fission gas released by the crystal grains into the grain boundary, and t is the operation time of the fission reaction.

6. A calculation system for the generation, diffusion and release of fission gases in UO2 fuel pellets during the service of a reactor, characterized in that, For implementing the method according to any one of claims 1-5, the system includes: A fission gas concentration diffusion distribution calculation module, configured to calculate the change value of the fission gas concentration distribution at different times in the microscopic grains of the fuel pellet; A volume rate calculation module for fission gas generation, configured to calculate the volume rate of fission gas generation; A fission gas volume release rate calculation module, configured to calculate the volume release rates of the fission gas released from the grains to the grain boundary, on the grain boundary, and from the grain boundary to the fuel gas gap; A fission gas volume release amount calculation module, configured to calculate the volume release amounts of the fission gas released from the grains to the grain boundary and accumulated on the grain boundary.

7. A storage medium stores a program, characterized in that, When the program is executed by the processor, it implements the calculation method for the generation, diffusion and release of fission gas in the UO2 fuel pellet according to any one of claims 1-5.

8. A computing device, comprising a processor and a memory for storing processor-executable programs, characterized in that, When the processor executes the program stored in the memory, it implements the calculation method for the generation, diffusion and release of fission gas in the UO2 fuel pellet according to any one of claims 1-5.

Images