A method for calculating the thermal release of fission gases in U3Si2 fuel

Abstract

The present invention belongs to the field of numerical simulation methods for the in-reactor irradiation behavior of fuel rods, and particularly relates to a method for calculating the thermal release of fission gas in U3Si2 fuel, comprising the following steps: calculating the concentration of newly generated fission gas within a time interval Δt between the current moment and the previous moment and the total amount of fission gas generated at the current moment; calculating the total number of intragranular gases and the total number of intergranular gases at the current moment; calculating the concentration of intergranular bubbles, the bubble volume, the bubble radius, and the bubble area after the growth and aggregation of intergranular bubbles at the current moment; calculating the intergranular bubble coverage fraction and determining whether the condition for the start of gas release is met, and when the opening condition is reached, calculating the total number of intergranular gas atoms and the number of gas atom releases at the current moment. The present invention derives and establishes a calculation method for solving the concentrations of intragranular and intergranular gas bubbles and fission gas release in U3Si2 fuel, truly reflecting the mechanism of fission gas release, and can be used to predict the fission gas release of U3Si2 fuel in a reactor.

Description

Technical Field

[0001] The present invention belongs to the field of numerical simulation methods for in-pile irradiation behavior of fuel rods, and particularly relates to a method for calculating the thermal release of fission gas in U3Si2 fuel. Background Technique

[0002] After the Fukushima nuclear accident, the research and development of accident-tolerant fuels has increasingly become a focus in the international nuclear fuel field. U3Si2 fuel is one of the main candidate materials for accident-tolerant fuels due to its high thermal conductivity, high uranium density and other advantages. When U3Si2 fuel undergoes a chain fission reaction in a reactor, a variety of fission products are generated, and a part of them are stable inert gases of Xe and Kr (hereinafter simply referred to as fission gases). Fission gases are generated inside fuel grains, and then diffuse to grain boundaries under the drive of concentration gradient and temperature gradient. Fission gases form bubbles at grain boundaries and continuously grow. When the grain boundary bubbles aggregate with each other to form a channel connected to the open pores, the fission gases begin to be released into the free space. The released fission gases will affect the heat transfer process in the fuel rod, significantly change the temperature field distribution and stress / strain field distribution in the fuel rod, and may cause the internal pressure in the fuel rod to exceed the safety limit in the high burnup range, resulting in fuel rod failure and radioactive substance leakage. Therefore, establishing an accurate method for predicting the release of fission gases in fuel rods is very important for protecting the operation safety of nuclear fuels.

[0003] This method is usually used in a comprehensive fuel rod irradiation behavior analysis program to comprehensively simulate the thermodynamic behavior and fission gas release behavior of fuel rods during irradiation, etc., and their interactions. Since the impact of fission gas release on thermodynamic behavior and fuel rod safety mainly depends on the total amount of fission gas release, calculating how much of the generated fission gas is released into the free space, that is, the fission gas release fraction, is one of the most concerned issues for developers of fuel rod irradiation behavior analysis programs.

[0004] According to the temperature dependence, the physical processes of fission gas release are generally divided into two categories: athermal release and thermal release. Athermal release is the recoil and knock-out of fission gas atoms when the reaction occurs, which is basically not affected by temperature; thermal release mainly involves the diffusion, aggregation into bubbles, and bubble coalescence of fission gas atoms in the fuel lattice, and these processes are greatly affected by temperature. Due to the different physical mechanisms, the calculation methods for these two types of fission gas release are also different. When the fuel rod burnup is low, athermal release dominates the fission gas release, but the release fraction is low; as the burnup increases, the fraction of thermal release in the total fission gas release becomes larger and larger. Since the moment when fission gas release poses a threat to the safety of fuel rods is mainly in the high burnup range, the accurate prediction of thermal release is more important for nuclear fuel safety. Since the late 1950s, the nuclear industry has started research on the calculation method for the thermal release of fission gas in UO2 fuel. With the continuous research and improvement of domestic and foreign nuclear fuel-related research institutions, the predicted value of fission gas release in UO2 fuel has reached a certain accuracy.

[0005] The existing patent (application number CN201710959109.1) regarding the fission gas release of nuclear fuel is a calculation method for the thermal release rate of UO2. The method mainly derives and establishes the relationship between the grain boundary gas concentration and the fission gas thermal release rate, and can accurately calculate the fission gas thermal release rate of UO2 fuel. However, the description of the behavior of fission gas in the fuel in this patent is relatively simple, ignoring behaviors such as the nucleation, capture, and coalescence of gas bubbles. In addition, the crystal structures and material physical properties of U3Si2 and UO2 are different, resulting in differences in the diffusion and other behaviors of fission gas, and ultimately different fission gas releases. Therefore, the existing calculation method for the fission gas thermal release of UO2 fuel in the prior art is not applicable to U3Si2 fuel.

[0006] In view of the above prior art, there is an urgent need to design an improved method for calculating the fission gas thermal release of U3Si2 fuel. Summary of the Invention

[0007] The main object of the present invention is to provide a method for calculating the fission gas thermal release of U3Si2 fuel, establish calculation methods for the concentration and size of intragranular gas bubbles, the concentration and size of intergranular bubbles, and the fission gas thermal release rate, and accurately predict the fission gas thermal release rate of U3Si2 fuel.

[0008] The technical solution adopted by the present invention is as follows:

[0009] A method for calculating the fission gas thermal release of U3Si2 fuel, comprising the following steps:

[0010] Step 1: Calculate the newly generated fission gas concentration ΔG within the time interval Δt between the current moment and the previous moment, and the total fission gas generation amount G(t) at the current moment:

[0011] ΔG = yFΔt (1),

[0012] where y is the fission gas yield and F is the fission rate at the current moment;

[0013] G(t) = G(t - Δt) + ΔG (2),

[0014] G(t - Δt) is the total fission gas generation amount at the previous moment;

[0015] Step 2: Calculate the intragranular gas diffusivity D, nucleation rate ν, capture rate β, and remelting rate α at the current moment, as well as the total number of intragranular gas G1(t) and the total number of intergranular gas G2(t) at the current moment;

[0016] G2(t) = G(t) - G1(t) - f(t - Δt) (3)

[0017] f(t - Δt) is the total number of fission gas releases at the previous moment;

[0018] Step 3: Calculate the total number of intragranular dissolved gas G 1s (t) and the total number of gas in intragranular bubbles G 1b (t);

[0019] Step 4: Determine whether the intragranular bubble concentration C b (t - Δt) at the previous moment is greater than 0. If yes, jump to Step 5; otherwise, assume that the number of atoms per intragranular bubble at the previous moment is equal to 0 and jump to Step 6;

[0020] Step 5: Calculate the number of atoms per intragranular bubble n1(t - Δt) at the previous moment;

[0021] Step 6: Calculate the intragranular bubble concentration C b (t), the number of atoms per intragranular bubble n1(t), and the intragranular bubble radius R b (t);

[0022] Step 7: Calculate the grain surface area - volume ratio S / V and the number of atoms per intergranular bubble n2(t) at the current moment;

[0023] Step 8: Determine whether the number of atoms per intergranular bubble n2(t) at the current moment is greater than 0. If yes, jump to Step 9; otherwise, assume that the number of vacancies per intergranular bubble n v (t) is equal to 0 and jump to Step 10;

[0024] Step 9: Calculate the previous intergranular coverage fraction F c(t - Δt) and the current bubble growth rate v gb and the number of vacancies n per bubble between grains v (t);

[0025] Step Ten: Calculate the volume V of the intergranular bubbles at the current moment gb (t), the bubble radius R gb (t) and the bubble area A gb (t);

[0026] Step Eleven: Calculate the concentration C of the intergranular bubbles after bubble aggregation at the current moment gb (t), the number of atoms n2(t) per bubble, the number of vacancies n v (t), the bubble volume V gb (t), the radius R gb (t) and the projected area A gb (t);

[0027] Step Twelve: Calculate the value F of the intergranular bubble coverage fraction at the current moment c , and judge whether the value F of the intergranular bubble coverage fraction c is greater than the saturation value F of the intergranular bubble coverage fraction c,sat . If so, jump to Step Thirteen; otherwise, it is considered that the number of gas atoms released at the current moment is equal to 0;

[0028] Step Thirteen: Update the projected area A of the intergranular bubbles gb (t), the concentration C of the intergranular bubbles gb (t), the volume V of the intergranular bubbles gb (t), the radius R of the intergranular bubbles gb (t), the number of atoms n2(t) per bubble and the number of vacancies n v (t), and calculate the total number G2(t) of intergranular gas atoms and the number f(t) of gas atoms released at the current moment.

[0029] As a further improvement of the present invention, the following steps are also carried out before Step One in the above method for calculating the thermal release rate of fission gas in U3Si2 fuel:

[0030] Read the local temperature T(t) and local fission rate F(t) at the current moment from the external interface, and obtain the fission gas production G(t - Δt), the total amount G1(t - Δt) of intragranular gas atoms, the total number G 1s (t - Δt) of dissolved gas in the grains, the total number G 1b (t - Δt) of gas in the intragranular bubbles, the concentration C b (t - Δt) of intragranular bubbles, the size R b (t - Δt) of intragranular bubbles, the concentration C gb (t - Δt) of intergranular bubbles, the projected area A gb(t - Δt), the intergranular bubble size R gb (t - Δt), the fission gas release f(t - Δt), and the grain radius r.

[0031] Furthermore, in Step 2, the calculation methods for the intragranular gas diffusivity D, nucleation rate ν, capture rate β, redissolution rate α, and the total number of intragranular gases G1(t) at the current moment are as follows:

[0032] Calculate the intrinsic diffusion coefficient D1:

[0033] Calculate the radiation-enhanced thermal diffusion coefficient D2:

[0034] Calculate the radiation-induced non-thermal diffusion coefficient D3: D3 = AF(6)

[0035] The total lattice diffusion coefficient D of fission gas atoms is: D = D1 + D2 + D3 (7)

[0036] k is the Boltzmann constant, ΔH is the diffusion enthalpy, s is the jump distance, j v is the thermal activation vacancy jump frequency, C v 0 is the supersaturated vacancy concentration, D0 and A are constants, and T is the temperature at the current moment.

[0037] The nucleation rate ν is:

[0038] The capture rate β is: β = 4πD(R b + R g )C b (9)

[0039] The redissolution rate α is:

[0040] f n is the nucleation factor, R g is the radius of the Xe atom, η re is the redissolution efficiency, μ ff , Z, and E max are the moderation distance, atomic number, and initial energy of the fission fragment, respectively, and E min is the minimum recoil energy for permanent redissolution.

[0041] The total number G1(t) of intragranular gases at the current moment is:

[0042]

[0043] In this formula,

[0044]

[0045] r is the grain radius.

[0046] Furthermore, in step three, the total number of dissolved gas G 1s inside the crystal grains and the total number of gas G 1b inside the gas bubbles in the crystal grains are calculated as follows:

[0047]

[0048] G 1b (t) = G1(t) - G 1s (t) (14)

[0049] Furthermore, in step five, the number of atoms n1(t - Δt) in each gas bubble inside the crystal grains at the previous moment is calculated as follows:

[0050] n1(t - Δt) = G 1b (t - Δt) / C b (t - Δt) (15)

[0051] Furthermore, in step six, the concentration C b (t) of gas bubbles inside the crystal grains, the number of atoms n1(t) in each gas bubble inside the crystal grains, and the radius R b (t) of the gas bubbles inside the crystal grains are calculated as:

[0052]

[0053] n1(t) = G 1b (t) / C b (t) (17)

[0054]

[0055] V g is the volume of Xe atoms.

[0056] Furthermore, in step seven, the surface area - volume ratio S / V of the crystal grains and the number of atoms n2(t) in each gas bubble between the crystal grains at the current moment are calculated as:

[0057]

[0058] C gb (t) = C gb (t - Δt) (20)

[0059] The number of atoms n2(t) in each gas bubble between the crystal grains is

[0060]

[0061] Furthermore, in step nine, the coverage fraction F c between the crystal grains at the previous moment and the gas bubble growth rate v at the current momentgb and the number of vacancies n per bubble between grains v (t) The calculation method is as follows:

[0062] F c (t - Δt) = C gb (t - Δt)·A gb (t - Δt) (22)

[0063] The bubble growth rate v gb is

[0064]

[0065] d gb is the grain boundary thickness, D v is the vacancy diffusion coefficient between grains, V c is the vacancy volume.

[0066] The number of vacancies n per bubble between grains v (t) is as follows:

[0067] n v (t) = 0.5[n v (t - Δt) + PΔt + (n v (t - Δt) + PΔt) 2 + 4v gb (t)Δt] (24)

[0068] In the formula, P is

[0069]

[0070] Furthermore, in step ten, the volume V of the intergranular bubble at the current moment gb (t), the bubble radius R gb (t) and the bubble area A gb (t) are calculated as follows:

[0071] V gb (t) = n2(t)V g + n v (t)V c (26)

[0072]

[0073] In the formula is the shape factor:

[0074]

[0075] θ is the bubble semi - dihedral angle.

[0076] A gb (t) = π(Rgb (t)sinθ 2 (29)

[0077] Furthermore, in step eleven, at the current moment, the intergranular bubble concentration C gb (t), the number of atoms n2(t) in each bubble, the number of vacancies n v (t), the bubble volume V gb (t), the radius R gb (t) and the projected area A gb (t) are calculated as follows:

[0078]

[0079] The number of atoms n2(t) and the number of vacancies n v (t) in each intergranular bubble are:

[0080] n2[0] = n2(t) (31)

[0081] n v [0] = n v (t) (32)

[0082]

[0083] The bubble volume V gb (t) is:

[0084] V gb (t) = n2(t)V g +n v (t)V c (35)

[0085] The bubble radius R gb (t) is

[0086]

[0087] The bubble projected area A gb (t) is

[0088] A gb (t) = π(R gb (t)sinθ) 2 (37)

[0089] Furthermore, in step twelve, the value of the intergranular bubble coverage fraction F c at the current moment is calculated as follows:

[0090] F c (t) = C gb (t)·A gb (t) (38)

[0091] The condition for the start of fission gas release is F c >F c,sat 。

[0092] Furthermore, in step thirteen, update the projected area A gb (t), the intergranular bubble concentration C gb (t), the intergranular bubble volume V gb (t), the intergranular bubble radius R gb (t), the number of atoms per bubble n2(t) and the vacancy number n v (t) are calculated as follows:

[0093] Similarity ratio:

[0094]

[0095] A′ gb (t) = A gb (t)R f (40)

[0096] C′ gb (t) = C gb (t)R f (41)

[0097] F′ c (t) = F c (t)R f 2 (42)

[0098] V′ gb (t) = V gb (t)R f 1.5 (43)

[0099] R′ gb (t) = R gb (t)R f 0.5 (44)

[0100] n′2(t) = n2(t)R f 1.5 (45)

[0101] n′ v (t) = n v (t)Rf 1.5 (46)

[0102] The calculation methods for the total number of intergranular gas atoms G′2(t) and the number of gas atoms released f(t) at the current moment are as follows:

[0103] G′2(t) = G2(t)Rf 2.5 (47)

[0104] f(t) = G(t) - G1(t) - G'2(t) (48)

[0105] Furthermore, after step thirteen, there is also step fourteen

[0106] Step fourteen: Return the intragranular bubble concentration C b (t), the number of atoms n1(t) in each intragranular bubble, and the intragranular bubble radius R b (t), as well as the projected area A gb (t) of the intergranular bubbles, the intergranular bubble concentration C gb (t), the intergranular bubble volume V gb (t), the intergranular bubble radius R gb (t), the number of atoms n2(t) per bubble, the number of vacancies n v (t), the total number of gas atoms G2(t) in the intergranular region, and the gas atom release number f(t) to the upper-level program to provide input for calculating the fission gas release at the next moment.

[0107] The present invention has the following advantages:

[0108] 1. The present invention takes accident-tolerant fuel U3Si2 as the object. Based on the crystal structure of U3Si2 fuel, it considers the diffusion of fission gas bubbles in the grains, the nucleation of gas atoms into bubbles, the redissolution and capture of gas atoms, as well as the growth, aggregation, and gas release in the grain boundaries. The intergranular equation considers processes such as bubble growth and bubble aggregation. When the bubble coverage value reaches saturation, fission gas begins to be released. It truly reflects the behavior of fission gas bubbles in U3Si2 fuel and can accurately predict the fission gas thermal release rate of U3Si2 fuel.

[0109] 2. The present invention derives and establishes calculation methods for the intragranular gas bubble concentration and size, the intergranular bubble concentration and size, and the fission gas thermal release rate, truly reflecting the mechanism of fission gas release.

[0110] 3. The present invention couples the intragranular gas diffusion equation with the grain boundary bubble evolution equation, and is applicable to the calculation of fission gas thermal release of accident-tolerant fuel U3Si2.

[0111] 4. Through the present invention, the change in the internal pressure of the fuel rod can be accurately predicted, thereby effectively avoiding the situation where the internal pressure of the fuel rod exceeds the safety limit and improving the operation safety of nuclear fuel. Brief Description of the Drawings

[0112] Figure 1 is the calculation flow chart of the fission gas thermal release rate of U3Si2 fuel of the present invention.

[0113] Figure 2 It is a comparison between the calculation results of U3Si2 fuel and the irradiation experiment results of ATF-1. Specific implementation manner

[0114] The present invention will be described in detail below with reference to the accompanying drawings and specific embodiments.

[0115] The present invention discloses a method for calculating the thermal release of fission gas in U3Si2 fuel. The main steps include: calculating the concentration of newly generated fission gas within the time interval Δt between the current moment and the previous moment and the total amount of fission gas generated at the current moment; calculating the total number of intragranular gases and the total number of intergranular gases at the current moment; calculating the concentration, bubble volume, bubble radius, and bubble area of intergranular bubbles after growth and aggregation at the current moment; calculating the intergranular bubble coverage fraction and determining whether the condition for the start of gas release is met. When the opening condition is reached, calculate the total number of intergranular gas atoms and the number of gas atoms released at the current moment.

[0116] Example 1

[0117] As Figure 1 shown, a method for calculating the thermal release rate of fission gas in U3Si2 fuel includes the following steps:

[0118] S0. Read the local temperature T(t), local fission rate F(t) at the current moment from the external interface, and obtain the fission gas generation amount G(t - Δt), total amount of intragranular gas atoms G1(t - Δt), total number of intragranular dissolved gases G 1s (t - Δt), total number of gases in intragranular bubbles G 1b (t - Δt), intragranular bubble concentration C b (t - Δt), intragranular bubble size R b (t - Δt), intergranular bubble concentration C gb (t - Δt), projected area A of intergranular bubbles gb (t - Δt), intergranular bubble size R gb (t - Δt), fission gas release amount f(t - Δt), and grain radius r. In the fuel performance analysis program, the fuel pellet (cylindrical) is spatially divided into several volume elements, and its spatial position can be represented as the L-th section in the axial direction and the i-th ring in the radial direction (L and i are variables, L is a positive integer not greater than the total number of axial sections, and i is a positive integer not greater than the total number of radial rings, determined according to the position of the fuel pellet). The local temperature refers to the temperature of a certain volume element. The radial average temperature is the volume average temperature of all rings in the j-th section; the fuel average temperature is the volume average temperature of the entire fuel column.

[0119] S1. Calculate the newly generated fission gas concentration ΔG within the time interval Δt between the current moment and the previous moment, and the total fission gas generation amount G(t) at the current moment:

[0120] The fission gas concentration newly generated due to the fission reaction within the time interval Δt is ΔG.

[0121] ΔG = yFΔt (1),

[0122] y is the fission gas yield, and F is the fission rate at the current moment; the total fission gas generation amount at the previous moment is G(t - Δt), and the calculation method for the total fission gas generation amount G(t) at the current moment is as follows:

[0123] G(t) = G(t - Δt) + ΔG (2),

[0124] During the calculation, G(t - Δt) = 0 for the first time step, and afterwards, G(t - Δt) is iterated.

[0125] S2. Calculate the in - grain gas diffusivity D, nucleation rate ν, capture rate β, and redissolution rate α at the current moment, as well as the total number of in - grain gases G1(t) and the total number of inter - grain gases G2(t) at the current moment.

[0126] The diffusion coefficient consists of three terms:

[0127] The intrinsic diffusion coefficient D1:

[0128] The radiation - enhanced thermal diffusion coefficient D2:

[0129] The radiation - induced non - thermal diffusion coefficient D3: D3 = AF (5);

[0130] The total fission gas atomic lattice diffusion coefficient D is: D = D1 + D2 + D3 (6);

[0131] In equations (3) - (6), k is the Boltzmann constant, ΔH is the diffusion enthalpy, s is the jump distance, j v is the thermal - activated vacancy jump frequency, C v 0 is the supersaturated vacancy concentration, D0 and A are constants, and T is the temperature at the current moment.

[0132] The nucleation rate ν is:

[0133] The capture rate β is: β = 4πD(R b +R g )C b (8);

[0134] The redissolution rate α is:

[0135] In formulas (7)-(9), f n is the nucleation factor, R g is the radius of the Xe atom, η re is the redissolution efficiency, μ ff , Z, and E max are respectively the moderation distance, atomic number, and initial energy of the fission fragment, and E min is the minimum recoil energy for permanent redissolution.

[0136] The total number of intragranular gases G1(t) at the current moment is:

[0137]

[0138] In this formula,

[0139]

[0140] r is the grain radius.

[0141] The total number of intergranular gases G2(t) at the current moment;

[0142] G2(t) = G(t) - G1(t) - f(t - Δt) (12);

[0143] f(t - Δt) is the total amount of fission gas released at the previous moment.

[0144] S3. Calculate the total number of dissolved gases G 1s (t) and the total number of gases G 1b in the intragranular bubbles at the current moment:

[0145] G 1b (t) = G1(t) - G 1s (t) (14).

[0146] S4. Determine whether the intragranular bubble concentration C b (t - Δt) at the previous moment is greater than 0. If it is, jump to step five. Otherwise, assume that the number of atoms per intragranular bubble at the previous moment is equal to 0 and jump to step six.

[0147] S5. Calculate the number of atoms n1(t - Δt) per intragranular bubble at the previous moment:

[0148] n1(t - Δt) = G 1b (t - Δt) / C b (t - Δt) (15).

[0149] S6. Calculate the intragranular bubble concentration C b (t), the number of atoms n1(t) per intragranular bubble, and the intragranular bubble radius R b(t):

[0150]

[0151] n1(t) = G 1b (t) / C b (t) (17);

[0152]

[0153] In the above formula, V g is the volume of Xe atoms.

[0154] S7. Calculate the grain surface area - volume ratio S / V and the number of atoms n2(t) in each bubble between grains at the current moment:

[0155]

[0156] C gb (t) = C gb (t - Δt) (20);

[0157] The number of atoms n2(t) in each bubble between grains is

[0158]

[0159] S8. Determine whether the number of atoms n2(t) in each bubble between grains at the current moment is greater than 0. If so, jump to step nine; otherwise, consider the number of vacancies n v (t) equal to 0 and enter step ten.

[0160] S9. Calculate the grain boundary coverage fraction F c (t - Δt) and the bubble growth rate v gb and the number of vacancies n v (t) at the current moment.

[0161] F c (t - Δt) = C gb (t - Δt)·A gb (t - Δt) (22);

[0162] The bubble growth rate v gb is

[0163]

[0164] d gb is the grain boundary thickness, D v is the intergranular vacancy diffusion coefficient, V c is the vacancy volume.

[0165] The number of vacancies n v (t) is:

[0166] n v (t)=0.5[n v (t - Δt)+PΔt+(n v (t - Δt)+PΔt) 2 +4v gb (t)Δt](24);

[0167] In the formula, P is

[0168]

[0169] S10. Calculate the volume V of intergranular bubbles, the bubble radius R gb (t), and the bubble area A gb (t). gb (t).

[0170] V gb (t)=n2(t)V g +n v (t)V c (26);

[0171]

[0172] In the formula is the shape factor:

[0173]

[0174] θ is the half dihedral angle of the bubble.

[0175] A gb (t)=π(R gb (t)sinθ) 2 (29).

[0176] S11. Calculate the concentration C of intergranular bubbles after bubble aggregation, the number of atoms n2(t) per bubble, the number of vacancy sites n gb (t), the bubble volume V v (t), the radius R gb (t), and the projected area A gb (t). gb (t).

[0177]

[0178] The number of atoms n2(t) per intergranular bubble and the number of vacancy sites n v (t) are:[[]]

[0179] n2[0]=n2(t)(31);

[0180] nv [0] = n v (t)(32);

[0181]

[0182] Bubble volume V gb (t) is:

[0183] V gb (t) = n2(t)V g +n v (t)V c (35);

[0184] Bubble radius R gb (t) is

[0185]

[0186] Bubble projected area A gb (t) is

[0187] A gb (t) = π(R gb (t)sinθ) 2 (37).

[0188] S12. Calculate the intergranular bubble coverage fraction value F at the current moment, and judge the coverage fraction F c , and determine whether the coverage fraction F c is greater than the intergranular bubble coverage fraction saturation value F c,sat . If so, jump to step thirteen; otherwise, it is considered that the number of gas atoms released at the current moment is equal to 0.

[0189] Intergranular bubble coverage fraction value F at the current moment c The calculation method is as follows:

[0190] F c (t) = C gb (t)·A gb (t) (38);

[0191] The condition for the start of fission gas release is F c > F c,sat .

[0192] S13. Update the intergranular bubble projected area A gb (t), the intergranular bubble concentration C gb (t), the intergranular bubble volume V gb (t), the intergranular bubble radius R gb (t), the number of atoms per bubble n2(t) and the number of vacancies n v (t), and calculate the total number of intergranular gas atoms G2(t) and the number of gas atoms released f(t) at the current moment.

[0193] Similarity ratio:

[0194]

[0195] A′ gb (t) = A gb (t)R f (40);

[0196] C′ gb (t) = C gb (t)R f (41);

[0197] F′ c (t) = F c (t)R f 2 (42);

[0198] V′ gb (t) = V gb (t)R f 1.5 (43);

[0199] R′ gb (t) = R gb (t)R f 0.5 (44);

[0200] n′2(t) = n2(t)R f 1.5 (45);

[0201] n′ v (t) = n v (t)R f 1.5 (46);

[0202] The calculation methods of the total number G′2(t) of intergranular gas atoms and the gas atom release number f(t) at the current moment are as follows:

[0203] G′2(t) = G2(t)R f 2.5 (47);

[0204] f(t) = G(t) - G1(t) - G′2(t) (48).

[0205] Example 2

[0206] Based on Example 1, this example further includes S14 after step S13:

[0207] S14: Return the intragranular bubble concentration C b (t), the number of atoms n1(t) in each intragranular bubble, and the intragranular bubble radius R b (t), as well as the projected area A gb (t) of the intergranular bubbles, the intergranular bubble concentration C gb (t), the intergranular bubble volume V gb (t), the intergranular bubble radius R gb (t), the number of atoms n2(t) per bubble, the number of vacancies n v (t), the total number of gas atoms G2(t) in the intergranular region, and the number of gas atom releases f(t) to the upper-level program, providing inputs for calculating the fission gas release at the next moment, so that the fission gas thermal release rates at multiple time steps can be obtained iteratively in sequence.

[0208] The external interface in this embodiment refers to the external interface of the calculation program.

[0209] The above is only the preferred embodiment of the present invention. The protection scope of the present invention is not limited to the above embodiments. All technical solutions falling within the concept of the present invention belong to the protection scope of the present invention. It should be noted that for those of ordinary skill in the art, several improvements and refinements made without departing from the principle of the present invention should be regarded as within the protection scope of the present invention.

Claims

1. A method for calculating the thermal release of fission gas in U3Si2 fuel, characterized in that: Including the following steps: Step 1: Calculate the newly generated fission gas concentration ΔG within the time interval Δt between the current moment and the previous moment, and the total fission gas generation amount G(t) at the current moment: ΔG = yFΔt (1), where y is the fission gas yield and F is the fission rate at the current moment; G(t) = G(t - Δt) + ΔG (2), and G(t - Δt) is the total fission gas generation amount at the previous moment; Step 2: Calculate the intragranular gas diffusivity D, nucleation rate ν, capture rate β, and remelting rate α at the current moment, as well as the total number of intragranular gases G1(t) and the total number of intergranular gases G2(t) at the current moment; G2(t) = G(t) - G1(t) - f(t - Δt) (3) where f(t - Δt) is the total number of fission gas releases at the previous moment; Step 3: Calculate the total number of dissolved gases G 1s (t) in the crystal and the total number of gases G 1b (t) in the bubbles within the crystal; Step 4: Determine whether the concentration C of intragranular bubbles at the previous moment b (t - Δt) is greater than 0. If so, jump to Step 5; otherwise, assume that the number of atoms per bubble in the crystal at the previous moment is 0 and jump to Step 6. Step 5: Calculate the number of atoms n1(t - Δt) in each bubble within the crystal at the previous moment; Step Six: Calculate the intragranular bubble concentration C b (t), the number of atoms n1(t) in each intragranular bubble, and the intragranular bubble radius R b (t); Step 7: Calculate the grain surface area - volume ratio S / V and the number of atoms n2(t) in each intergranular bubble at the current moment; Step Eight: Determine whether the number of atoms n2(t) in each intergranular bubble at the current moment is greater than 0. If so, jump to Step Nine; otherwise, assume that the number of vacancies n v (t) is equal to 0 and jump to Step Ten; Step Nine: Calculate the intergranular coverage fraction F c (t - Δt) at the previous moment and the bubble growth rate v gb and the number of vacancies per bubble n v (t) at the current moment; Step 10: Calculate the volume V gb (t) of the intergranular bubbles, the bubble radius R gb (t), and the bubble area A gb (t) at the current moment; Step Eleven: Calculate the intergranular bubble concentration C gb (t), the number of atoms n2(t) in each bubble, the vacancy number n v (t), the bubble volume V gb (t), the radius R gb (t) and the projected area A gb (t); Step Twelve: Calculate the value of the intergranular bubble coverage fraction F at the current moment c , and determine the value of the intergranular bubble coverage fraction F c whether it is greater than the saturation value F of the intergranular bubble coverage fraction c,sat . If so, jump to Step Thirteen; otherwise, it is considered that the number of gas atom releases at the current moment is equal to 0; Step Thirteen: Update the projected area A of the intergranular bubbles gb (t), the intergranular bubble concentration C gb (t), the intergranular bubble volume V gb (t), the intergranular bubble radius R gb (t), the number of atoms per bubble n2(t) and the number of vacancies n v (t), and calculate the total number of intergranular gas atoms G2(t) and the number of released gas atoms f(t) at the current moment.

2. The method for calculating the thermal release of fission gas of U3Si2 fuel according to claim 1, wherein: Before the said Step 1, the following steps are further included: Read the local temperature T(t), local fission rate F(t) at the current moment from the external interface, and obtain the fission gas production G(t-Δt), total amount of intragranular gas atoms G1(t-Δt), total number of intragranular dissolved gases G 1s (t-Δt), total number of gases in intragranular bubbles G 1b (t-Δt), intragranular bubble concentration C b (t-Δt), intragranular bubble size R b (t-Δt), intergranular bubble concentration C gb (t-Δt), projected area of intergranular bubbles A gb (t-Δt), intergranular bubble size R gb (t-Δt), fission gas release f(t-Δt) and grain radius r.

3. The method for calculating the thermal release of fission gas of U3Si2 fuel according to claim 1 or 2, characterized in that: In the said Step 2, the calculation methods of the intragranular gas diffusivity D, nucleation rate ν, capture rate β, remelting rate α, and the total number of intragranular gases G1(t) at the current moment are as follows: Calculate the intrinsic diffusion coefficient D1: Calculate the radiation-induced enhanced thermal diffusivity D2: Calculate the radiation - induced non - thermal diffusion coefficient D3: D3 = AF(6) The total lattice diffusion coefficient D of fission gas atoms is: D = D1 + D2 + D3(7) k is the Boltzmann constant, ΔH is the enthalpy of diffusion, s is the jump distance, j v is the thermally activated vacancy jump frequency, C v 0 is the supersaturated vacancy concentration, D0 and A are constants, and T is the temperature at the current time; The nucleation rate ν is as follows: The capture rate β is: β = 4πD(R b +R g )C b (9) The redissolution rate α is as follows: f n is the nucleation factor, R g is the atomic radius of Xe atom, η re is the remelting efficiency, μ ff , Z and E max are respectively the moderation distance, atomic number and initial energy of the fission fragment, E min is the minimum recoil energy for permanent remelting; The total number of intragranular gases G1(t) at the current moment is: In this formula, r is the grain radius.

4. The method for calculating the thermal release of fission gas of U3Si2 fuel according to claim 3, characterized in that: In the third step, the total number of dissolved gases G within the crystal at the current moment 1s and the total number of gases G in the gas bubbles within the crystal 1b are calculated as follows:

5. The method for calculating the thermal release of fission gases of U3Si2 fuel according to claim 4, characterized in that: In the said Step 5, the calculation method of the number of atoms n1(t - Δt) in each bubble within the crystal at the previous moment is as follows: n1(t - Δt) = G 1b (t - Δt) / C b (t - Δt)(15).

6. The method for calculating the thermal release of fission gas of U3Si2 fuel according to claim 5, characterized in that: In the sixth step, the concentration of intragranular bubbles C b (t), the number of atoms n1(t) in each intragranular bubble, and the intragranular bubble radius R b (t) are calculated as follows: n1(t) = G 1b (t) / C b (t)(17) V g is the volume of Xe atom.

7. The method for calculating the thermal release of fission gas of U3Si2 fuel according to claim 6, wherein: In the said Step 7, the calculation methods of the grain surface area - volume ratio S / V and the number of atoms n2(t) in each intergranular bubble at the current moment are: The number of atoms n2(t) in each intergranular bubble is 8. The method for calculating the thermal release of fission gas of U3Si2 fuel according to claim 7, wherein: In the ninth step, the intergranular coverage fraction F at the previous moment c and the bubble growth rate v at the current moment gb and the number of vacancies n per bubble in the intergranular region v (t) are calculated as follows: Bubble growth rate v gb is d gb is the grain boundary thickness, D v is the intergranular vacancy diffusion coefficient, V c is the vacancy volume; The number of vacancies n per bubble among crystal grains v (t) is as follows: n v (t) = 0.5[n v (t - Δt) + PΔt + (n v (t - Δt) + PΔt) 2 + 4v gb (t)Δt] (24) where P is 9. The method for calculating the fission gas thermal release of U3Si2 fuel according to claim 8, characterized in that: In Step Ten, the volume V of intergranular bubbles, the bubble radius R gb (t), and the bubble area A gb (t) are calculated as follows: gb (t) The calculation methods are as follows: V gb I(t) = n2(t)V g +n v I(t)V c (26) where is the shape factor: θ is the half dihedral angle of the bubble; A gb (t) = π(R gb (t)sinθ) 2 (29).

10. The method for calculating the thermal release of fission gas of U3Si2 fuel according to claim 9, characterized in that: In Step Eleven, the calculation methods for the intergranular bubble concentration C gb (t), the number of atoms n2(t) in each bubble, the vacancy number n v (t), the bubble volume V gb (t), the radius R gb (t), and the projected area A gb (t) are as follows: The number of atoms per bubble n2(t) and the number of vacancies n v (t) are as follows: n2[0] = n2(t) (31) n v [0] = n v (t) (32) Bubble volume V gb (t) is as follows: V gb (t) = n2(t)V g +n v (t)V c (35) Bubble radius R gb (t) is Bubble projected area A gb (t) is A gb (t) = π(R gb (t)sinθ) 2 (37).

11. The method for calculating the thermal release of fission gas of U3Si2 fuel according to claim 10, wherein: The current value F of the intergranular bubble coverage fraction in Step Twelve c The calculation method is as follows: F c f(t) = C gb f(t) · A gb f(t) (38) The condition for the start of fission gas release is F c > F c,sat .

12. The method for calculating the thermal release of fission gas of U3Si2 fuel according to claim 11, characterized in that: In step thirteen, update the projected area A gb (t) of the intergranular bubbles, the concentration C gb (t) of the intergranular bubbles, the volume V gb (t) of the intergranular bubbles, the radius R gb (t) of the intergranular bubbles, the number of atoms per bubble n2(t), and the vacancy number n v (t) are calculated as follows: Similarity ratio: A′ gb A(t) gb R(t) f (40) C′ gb C(t) = gb R(t) f (41) F′ c F(t) = c F(t)R f 2 (42) V′ gb (t) = V gb (t)R f 1.5 (43) R′ gb (t) = R gb (t)R f 0.5 (44) n′2(t) = n2(t)R f 1.5 (45) n′ v (t) = n v (t)R f 1.5 (46) The calculation methods of the total number of intergranular gas atoms G′2(t) and the gas atom release number f(t) at the current moment are as follows: G′2(t) = G2(t)R f 2.5 (47) f(t) = G(t) - G1(t) - G′2(t) (48).

13. The method for calculating the thermal release of fission gas of U3Si2 fuel according to claim 1 or 2, characterized in that: After Step 13, there is further Step 14: Return the intragranular bubble concentration C b (t), the number of atoms n1(t) in each intragranular bubble, and the intragranular bubble radius R b (t), as well as the projected area A gb (t) of the intergranular bubbles, the intergranular bubble concentration C gb (t), the intergranular bubble volume V gb (t), the intergranular bubble radius R gb (t), the number of atoms n2(t) per bubble, the number of vacancies n v (t), the total number of gas atoms G2(t) in the intergranular region, and the number of released gas atoms f(t) to the upper-level program, providing inputs for calculating the fission gas release at the next moment.

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