CN114021380A - A failure evaluation model of silicon carbide composite cladding under reactor accident conditions - Google Patents
A failure evaluation model of silicon carbide composite cladding under reactor accident conditions Download PDFInfo
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Abstract
The invention discloses a silicon carbide composite cladding failure evaluation model under a reactor accident condition, belonging to the technical field of nuclear industrial materials. The model obtains the stress distribution caused by internal and external pressure difference, radial temperature gradient and radiation swelling by analyzing the heat transfer behavior between the cladding of the multilayer silicon carbide composite material and a coolant in the re-submerging stage of the large-break accident LOCA and introducing the cladding oxidation factor when the LOCA occurs, and then calculates the cladding failure probability under the pseudo-plasticity of the silicon carbide composite material by applying the Weibull fracture theory; the invention not only considers the change of the heat transfer coefficient, but also has more comprehensive related variable factors; oxidation reactions between the silicon carbide composite cladding and the coolant at the time of an accident and the effect of silicon carbide composite pseudoplasticity on the probability of failure are also introduced. The invention can evaluate the cladding integrity of the nuclear reactor in the accident stage and ensure the safety of the nuclear reactor. The obtained failure probability data has more reference value for safety evaluation.
Description
Technical Field
The invention belongs to the technical field of nuclear industrial materials, and particularly relates to a silicon carbide composite cladding failure evaluation model under a reactor accident condition.
Background
Accident-resistant fuel (ATF) has become a focus of attention in the nuclear fuel community, and the design and development of accident-resistant fuel cladding is one of the important tasks. The silicon carbide has the characteristics of high melting point, corrosion resistance, good heat conductivity, low neutron absorption cross section and the like, has more advantages in the aspects of high temperature resistance, irradiation resistance, steam oxidation resistance and the like compared with the traditional zirconium alloy material, and the silicon carbide composite material can improve the fracture toughness of the whole cladding, so that the silicon carbide composite material is used as a candidate material for the accident-resistant fuel cladding.
Generally, silicon carbide materials are evaluated internationally by calculating and testing the probability of failure of the silicon carbide cladding under normal operating conditions. However, in practice, since the core is exposed to air in the event of a large breach accident, the cladding temperature rises sharply, and in order to prevent the cladding temperature from being excessively high, the reactor injects cooling water into the core to lower the cladding temperature, which is called a re-flooding phase. When the reactor core is in a re-submerging stage, a complex heat transfer phenomenon can occur between cooling water and cladding, so that the heat exchange coefficient is changed. Therefore, the heat transfer coefficient under normal conditions is usually set to a constant amount, which simplifies the model but causes large errors in the final result. Meanwhile, the cladding environment under the accident condition is worse than that under the normal condition, and the evaluation on the integrity of the cladding under the accident condition has reference value in terms of the safety of the reactor.
Disclosure of Invention
The invention aims to provide a silicon carbide composite cladding failure evaluation model under a reactor accident condition, which is characterized in that the silicon carbide composite cladding failure evaluation model under the reactor accident condition is characterized in that the heat transfer behavior between a multilayer silicon carbide composite cladding and a coolant in an LOCA (large break accident) accident re-submergence stage is analyzed, and a cladding oxidation factor in the LOCA is introduced to obtain the stress distribution caused by internal and external pressure difference, radial temperature gradient and irradiation swelling, so that the cladding failure probability under the pseudo-plasticity of a silicon carbide composite is calculated by applying a Weibull fracture theory; the method comprises the following steps:
step 1: setting the initial time T to be 0, and starting simulation calculation;
step 2: initializing parameters in an initial parameter input plate; the initial parameter input plate parameters comprise the thickness of each layer of the cladding, the thermal conductivity coefficient, the density, the specific heat capacity, the elastic modulus, the characteristic stress, the Weibull modulus, the thermal expansion coefficient and the Poisson ratio;
and step 3: calculating to obtain the heat exchange coefficient value of the surface of the ladle shell by submerging the heat transfer plate; wherein, considering the re-submergence state, the initial parameter input plate parameters comprise the internal and external pressure of the cladding, the temperature of the coolant and the temperature of the cladding measuring point at the T moment;
and 4, step 4: calculating a stress analysis plate to obtain the distribution of stress in the cladding; wherein, considering the characteristics of each layer of the multi-layer silicon carbide composite material cladding,
and 5: calculating a failure probability analysis plate to obtain the total failure probability of the cladding;
step 6: and (5) finishing the calculation of the failure probability analysis plate and the stress analysis plate, and returning to the step 2 to calculate the next time step.
And 7: and (5) iteratively calculating to set termination time, finishing the calculation of the failure evaluation model, and displaying the total failure probability value of the cladding at each time point.
The calculation method of the stress analysis plate in the step 2 comprises the following steps:
step (21): calculating the thickness of the outermost cladding reduced by the oxidation of the cladding, and correcting the thickness of the outermost cladding;
step (22): calculating the distribution of mechanical stress caused by the internal and external pressure difference in the radial direction, the axial direction and the circumferential direction;
step (23): calculating the distribution of thermal stress caused by radial temperature gradient in radial, axial and circumferential directions;
step (24): calculating the distribution of stress caused by irradiation swelling in the radial direction, the axial direction and the circumferential direction;
step (25): fitting the stress caused by the internal and external pressure difference, the radial temperature gradient and the radiation swelling to obtain the distribution of the comprehensive stress in the radial direction, the axial direction and the circumferential direction.
The calculation method of the re-submerging heat transfer plate block in the step 3 comprises the following steps:
step (31): setting an initial heat flow density assumed value.
Step (32): and obtaining a temperature calculated value according to a temperature field control equation.
Step (33): and calculating according to the sensitivity coefficient field control program to obtain a sensitivity coefficient calculated value.
Step (34): obtaining a heat flux density correction value according to the sensitivity coefficient calculation value, the temperature calculation value and the temperature measurement value;
step (35): and (4) judging whether the error between the heat flow density corrected value and the heat flow density assumed value meets the minimum error range, if so, substituting the result into the stress analysis plate, and if not, giving the heat flow density corrected value to the heat flow density assumed value and repeating the step (32).
When the stress analysis plate is calculated in the step 4, introducing a cladding oxidation factor to analyze the thickness of the silicon carbide cladding; the distribution of the stress in the cladding is shown as follows:
where k is 1, 2 denotes an inner layer (silicon carbide composite layer) and an outer layer (silicon carbide single layer). Sigmar，σθ，σzIndicating hoop, radial and axial stresses. EkIs modulus of elasticity, vkIs Poisson's ratio, alphakIn order to be a coefficient of thermal expansion,
and solving the equation set for the undetermined constant according to the boundary condition.
The calculation method of the failure probability analysis plate block in the step 5 comprises the following steps:
step (51): calculating the failure probability of the silicon carbide single layer;
step (52): determining epsilonΔUP，σΔUP，σPThe corresponding parameter value at the peak of the probability density curve; sigmaPProportional ultimate stress; sigmaΔUPIs the stress difference between PLS (proportional ultimate stress) and UTS (ultimate tensile stress); epsilonΔUPIs the strain difference between PLS (proportional ultimate stress) and UTS (ultimate tensile stress).
Step (53): taking the elastic modulus of the middle point of the stress-strain curve of the composite material as the equivalent elastic modulus of the material;
step (54): calculating the failure probability of the silicon carbide composite material layer;
step (55): obtaining the total failure probability of the cladding by using the failure probabilities of the silicon carbide composite material layer and the single layer; and when the failure probability analysis plate is calculated, introducing a pseudo-plastic factor to analyze the failure probability of the silicon carbide composite material layer.
And (55) obtaining the total failure probability of the cladding by using the failure probabilities of the silicon carbide composite material layer and the single-layer, wherein:
the calculation formula of the failure probability of the simple substance layer is as follows:
wherein m is the Weibull modulus, σ0For characteristic stresses, these two parameters can be determined by fitting experimental data; j is 1, 2, 3 to represent radial, circumferential and axial 3 main stress directions;
when the failure probability of the silicon carbide composite material layer is calculated, a pseudo-plasticity factor is introduced when the silicon carbide composite material layer is calculated, the failure probability of the composite material layer is calculated by applying nonlinear elasticity mechanics, and the calculation formula is as follows:
in the formula
σP-PLS proportional ultimate stress;
σΔUP-the difference in PLS and UTS stress;
εΔUP-strain difference of PLS and UTS;
Pf(εΔUP，σΔUP，σP) -probability of failure given a parameter;
pdf(σP) Parameter σPA probability density function of;
pdf(σΔUP) Parameter σU-PA probability density function of;
pdf(εΔUP) Parameter εU-PA probability density function of;
p heref(εΔUP，σΔUP，σP) From the maximum first principal stress σ calculated at each timemax(εΔUP，σΔUP，σP) Determination, i.e. when σmaxUTS is greater than or equal to 1, otherwise it is 0.
The total failure probability of the multilayer silicon carbide composite cladding is as follows:
P＝1-(1-Pf)(1-Pm)。
the invention has the beneficial effects that: the model can evaluate the cladding integrity of the nuclear reactor in an accident stage and ensure the safety of the nuclear reactor. Compared with the silicon carbide cladding failure probability model under the normal working condition, the silicon carbide composite cladding failure probability model in the accident working condition re-submergence stage is more complex in the cladding environment, and the failure probability data obtained under the condition that the temperature difference between the cladding and the coolant is extremely large has reference value for safety evaluation; meanwhile, through expert analysis, the safety of the multilayer silicon carbide composite cladding (the inner layer is a silicon carbide composite material layer, and the outer layer is a silicon carbide single layer) is higher than that of a single-layer pure silicon carbide cladding, so that the safety of the reactor can be further improved. On the other hand, in order to be closer to the actual condition, the variable factors related to the silicon carbide composite cladding failure evaluation model under the accident condition are more comprehensive, the change of the heat transfer coefficient is considered, and the influence of the oxidation reaction between the silicon carbide composite cladding and the coolant and the pseudo plasticity of the silicon carbide composite on the failure probability during the accident is introduced. The invention has the following characteristics:
(1) the model is suitable for a re-submerging stage under a large break accident (LOCA), the heat exchange coefficient of the re-submerging stage is changed greatly, and the cladding is likely to break and fail, so that the instability of the nuclear reactor is aggravated. In the aspect of nuclear reactor safety, compared with a steady-state normal working condition, the re-submerging stage has higher analysis value, and the model is mainly used for researching the state of the cladding re-submerging stage and can be used for safety assessment of the nuclear reactor when an accident occurs.
(2) The model adopts a double-layer cladding structure with an outer layer made of pure silicon carbide and an inner layer made of silicon carbide composite material. The silicon carbide composite material layer can improve the fracture toughness of the cladding, keep the solid fission product from leaking under normal working conditions and in case of accidents, prevent the fission gas from escaping and maintain the basic geometric shape of the cladding. The silicon carbide simple substance layer can increase the density, provide corrosion protection and prevent abrasion, and simultaneously prevent the coolant outside the cladding from penetrating into the silicon carbide cladding.
(3) In the event of loss of water due to a large breach, silicon carbide undergoes an inert oxidation reaction with water vapor to produce a SiO2 film, which reacts with water vapor to produce volatile silicon hydroxide. Therefore, the stress analysis plate provided by the invention considers the influence of oxidation factors on the cladding, and corrects the thickness of the silicon carbide single layer, so that the analysis and calculation of the stress distribution of the cladding are more accurate.
(4) The failure probability analysis plate of the invention considers the influence of the pseudo-plasticity of the silicon carbide composite material on the cladding. From the failure probability alone, it was demonstrated that the multilayer silicon carbide composite cladding has greater resistance to rupture than the single layer silicon carbide cladding under the same conditions by analyzing the "pseudoplasticity" of the silicon carbide composite fibers.
Drawings
FIG. 1 is a flow chart of a silicon carbide composite cladding failure assessment model under reactor accident conditions.
FIG. 2 is a schematic diagram of the heat transfer during the re-flood stage;
FIG. 3 is a table of the program of the modules of the failure assessment model.
Detailed Description
The invention provides a silicon carbide composite cladding failure evaluation model under a reactor accident condition, and the invention is further described in detail by combining the attached drawings and specific embodiments.
Silicon carbide materials are evaluated internationally by calculating and testing the probability of failure of the silicon carbide cladding under normal operating conditions. In practice, however, the heat transfer coefficient is changed due to the complex heat transfer between the cooling water and the cladding when an accident occurs and the core is in the re-flooding phase. Therefore, the heat transfer coefficient is usually set to a constant value, which simplifies the model but causes a large error in the final result;
according to the invention, by analyzing the heat transfer behavior between the multilayer silicon carbide composite cladding and the coolant in the re-submerging stage of the large-break accident LOCA and introducing the cladding oxidation factor in the LOCA, the stress distribution caused by internal and external pressure difference, radial temperature gradient and radiation swelling is obtained, and then the cladding failure probability under the pseudo-plasticity of the silicon carbide composite is calculated by applying the Weibull fracture theory.
The specific embodiment of the invention is as follows:
1. initial parameter input plate construction scheme
The initial parameter input plate is used as a preposed plate of the model, and the function of simulating the heat transfer behavior between the multilayer silicon carbide composite cladding and the coolant in the re-submerging stage is achieved. In the initial parameter input plate, the main input parameters are two parts, namely the thermophysical parameters of each layer of the multilayer silicon carbide composite cladding and the environmental parameters such as the internal pressure and the external pressure of the cladding.
2. Environmental parameter input
During the re-submergence phase of the reactor under accident conditions such as LOCA, a very complex heat transfer phenomenon occurs between the cooling water and the fuel cladding, which has a large impact on the failure of the cladding. Therefore, the environment simulated by the model is the re-submergence stage under the accident condition. The environmental parameters mainly comprise the internal and external pressure of the cladding, the temperature of the coolant and the temperature of the measuring point of the cladding at the time T when a large break accident (LOCA) re-flooding stage occurs.
3. Input of thermal physical property parameter of cladding
The cladding is composed of a silicon carbide composite material layer as an inner layer and a silicon carbide single layer as an outer layer. The silicon carbide composite material layer can improve the fracture toughness of the cladding, keep the solid fission product from leaking under normal working conditions and in case of accidents, prevent the fission gas from escaping and maintain the basic geometric shape of the cladding. The silicon carbide simple substance layer can increase the density, provide corrosion protection and prevent abrasion, and simultaneously prevent the coolant outside the cladding from penetrating into the silicon carbide cladding. The cladding thermophysical parameters include cladding layer thickness, thermal conductivity, density, specific heat capacity, elastic modulus, characteristic stress, weibull modulus, coefficient of thermal expansion, and poisson's ratio. After the data input is finished, all the data are called by the re-submerged heat transfer plate block and used as an initial basis for calculating the heat transfer coefficient.
4. Construction scheme of re-submerged heat transfer plate
After the data input of the initial parameter input plate is finished, all the data are called by the re-submerged heat transfer plate and are used as an initial basis for calculating the heat transfer coefficient. In a re-submerging heat transfer plate block, different from a general heat transfer model, the model mainly relates to a re-submerging stage under a LOCA accident, as a series of complex heat transfer modes (shown in figure 2) such as nucleate boiling, transition boiling, film boiling, dispersed flow boiling and the like can be carried out between a cladding and a coolant in the re-submerging stage, a heat transfer coefficient between the cladding and the coolant cannot be directly calculated by using a formula under a steady state condition, and meanwhile, the heat transfer coefficient is also related to the temperature difference between the cladding and the coolant, and the heat transfer coefficient cannot be regarded as a constant quantity, so that the analysis of the re-submerging heat transfer plate block and the simulation of the heat transfer behavior of the cladding are required to be established.
5. Calculation of heat flux density correction values
And then submerging the heat transfer plate, wherein a heat flow density value is assumed before calculation, a temperature field control equation and a sensitivity coefficient field control equation are used for calculating a heat flow density correction value and repeatedly iterating, iteration is stopped when the difference value of the heat flow density assumed value and the correction value is within an error range, the surface temperature and the heat flow density of the cladding are obtained, and a heat exchange coefficient change curve is obtained. And transmitting the obtained heat exchange coefficient data to a multilayer silicon carbide cladding stress analysis model plate.
6. Stress analysis plate construction scheme
And after the heat transfer plate block is submerged again, the temperature of the wall surface of the cladding and the heat exchange coefficient are calculated, and the data are transmitted to the multilayer silicon carbide cladding stress analysis model plate block. The stress analysis model plate has the main functions of calculating the stress distribution of each point of the cladding, analyzing the stress after correcting the thickness of the outer wall cladding reduced by oxidation reaction, calculating the sum of mechanical stress caused by the pressure difference between the inside and the outside of the cladding, thermal stress caused by radial temperature gradient and thermal stress caused by irradiation swelling in three directions (radial direction, axial direction and circumferential direction), and calculating the failure probability of the cladding after obtaining the stress distribution of the cladding so as to carry out safety evaluation on the cladding.
7. Correcting for reduced cladding thickness due to oxidation
Because of the inert oxidation reaction of silicon carbide and water vapor under the accident of water loss at large break opening, a SiO2 film is produced, and the film can react with water vapor to generate volatile silicon hydroxide. This reaction reduces the thickness of the outermost silicon carbide monolayerThe cladding stress distribution is changed, and the evaluation of the failure probability is influenced. Therefore, before calculating the stress distribution, the stress analysis model needs to analyze the influence of the oxidation factors on the stress distribution of the cladding. Oxidation to form SiO2The calculation formula of the film is shown below
Wherein: delta is SiO2The thickness of the film; ω is the relative molecular mass (M) increment, KUIs a parabolic oxidation rate constant, KlIs a linear volatilization rate constant; corrected cladding thickness is SiO subtracted2The thickness of the envelope after the thickness of the film.
The molecular mass of (a);
-molecular mass of oxygen; mC-carbon molecular mass;
the density of (c).
8. Calculation of cladding stress distribution
And analyzing the stress after obtaining the thickness of the outer wall cladding reduced by the oxidation reaction, and calculating the sum of mechanical stress caused by the pressure difference between the inside and the outside of the cladding, thermal stress caused by radial temperature gradient and thermal stress caused by radiation swelling in three directions (radial direction, axial direction and circumferential direction). The specific formula of the stress distribution is as follows:
where k is 1, 2 denotes an inner layer (silicon carbide composite layer) and an outer layer (silicon carbide single layer). Sigmar，σθ，σzIndicating hoop, radial and axial stresses. EkIs modulus of elasticity, vkIs Poisson's ratio, alphakIn order to be a coefficient of thermal expansion,
and solving the equation set for the undetermined constant according to the boundary condition.
9. Failure probability analysis plate construction scheme
After the stress analysis model obtains the transient stress distribution in the cladding, the data are finally transmitted to a failure probability evaluation plate for failure probability calculation, and the cladding failure probability calculation result of the failure probability evaluation plate can directly reflect the integrity and the anti-fracture capability of the fuel cladding and can be used as an evaluation of the safety of the reactor. The model respectively calculates the failure probability of the single-layer material layer and the composite material layer, and further obtains the failure probability of the whole silicon carbide cladding.
10. Failure probability calculation for silicon carbide single layer
In the calculation of the failure probability of the simple substance layer, the Weibull fracture theory is suitable for describing the material strength of the brittle material, so that after the cladding failure probability evaluation model obtains stress distribution information, the Weibull fracture theory is used for analyzing the failure probability of the silicon carbide simple substance layer, and the calculation formula is as follows:
wherein m is the Weibull modulus, σ0These two parameters can be determined by fitting experimental data to the characteristic stressDetermining; j is 1, 2, 3 denotes the radial, hoop and axial 3 principal stress directions.
11. Failure probability calculation for silicon carbide composite layers
When the failure probability of the silicon carbide composite material layer is calculated, the influence of the factor of pseudo-plasticity on the failure analysis of the composite material cladding is considered by the model. During the re-flooding phase, when the cladding is subjected to excessive pressure, the silicon carbide composite fiber exhibits a rather complex failure mode that exhibits some degree of pseudo-plasticity. The silicon carbide composite fiber improves the fracture toughness through pseudo-plasticity and reduces the failure probability of the cladding. However, the common failure technology model usually does not consider the characteristic, so that a certain error exists in the calculation result, and therefore, a pseudo plasticity factor is introduced in the calculation of the silicon carbide composite material layer.
Some experts typically use nonlinear elasticity mechanics to calculate the probability of failure of a composite layer. The calculation formula is as follows:
in the formula
σP-proportional ultimate stress;
σΔUP-the stress difference of PLS (proportional ultimate stress) and UTS (ultimate tensile stress);
εΔUP-strain difference of PLS and UTS;
Pf(εΔUP，σΔUP，σP) -probability of failure given a parameter;
pdf(σP) Parameter σPA probability density function of;
pdf(σΔUP) Parameter σU-PA probability density function of;
pdf(εΔUP) Parameter εU-PA probability density function of;
p heref(εΔUP，σΔUP，σP) By maximum first of each calculationPrincipal stress sigmamax(εΔUP，σΔUP，σP) Determination, i.e. when σmaxUTS is greater than or equal to 1, otherwise it is 0.
The basic solving process is as follows: first of all using epsilonΔUP，σΔUP，σPRandomly taking values of probability density functions of the three parameters to obtain PLS and UTS values which are currently calculated, comparing the maximum stress obtained by the stress calculation model with the PLS, and if the maximum stress is smaller than the PLS, then P isf(εΔUP，σΔUP，σP) Is 0, otherwise, the maximum stress is solved again by applying nonlinear mechanics according to the current parameter value and then is compared with UTS, thereby obtaining Pf(εΔUP，σΔUP，σP) The value is obtained. Calculating according to the above process, and determining P according to probability density function distributionf(εΔUP，σΔUP，σP) The weight coefficient of (2) is weighted to average to obtain Pf。
As can be seen from the above, the key of the solving process is to calculate the maximum stress by using nonlinear mechanics, but considering the uncertainty of 3 individual performance parameters, a large amount of calculation cost is brought in multiple times of nonlinear mechanics solution. For convenient processing, the model simplifies the processing and respectively calculates epsilonΔUP，σΔUP，σPThe corresponding parameter value at the peak of the probability density curve, then taking the elastic modulus at the midpoint of the stress-strain curve of the composite material as the equivalent elastic modulus of the material, and then calculating the failure probability of the silicon carbide composite material by using a similar silicon carbide simple substance survival probability formula. Both is
Wherein σjfThe cladding stress at equivalent modulus of elasticity.
12. Cladding Total failure probability calculation
And respectively calculating the failure probability of the silicon carbide composite material layer and the silicon carbide single layer, and then calculating the total failure probability of the cladding. The total probability of failure for the multilayer silicon carbide composite cladding is as follows:
P＝1-(1-Pf)(1-Pm)
13. iteration of time steps
And after the total failure probability of the cladding is obtained, returning the model to the initial parameter input plate, taking the temperature distribution of the cladding obtained by the calculation as the initial temperature distribution of the next time point, continuously carrying out iterative calculation until the set end time is obtained by the calculation, and arranging to obtain a curve of the total failure probability of the cladding along with the time.
14. Total flow of silicon carbide composite cladding failure evaluation model under reactor accident condition
The total flow of the silicon carbide composite cladding failure evaluation model under the reactor accident condition is as follows:
a step (101): setting the initial time T to be 0, and starting simulation calculation
A step (102): initializing parameters in an initial parameter entry pad
Step (103): setting an initial heat flow density assumed value.
A step (104): and obtaining a temperature calculated value according to a temperature field control equation.
A step (105): and calculating according to the sensitivity coefficient field control program to obtain a sensitivity coefficient calculated value.
Step (106): and obtaining a heat flow density correction value according to the sensitivity coefficient calculation value, the temperature calculation value and the temperature measurement value.
Step (107): and judging whether the error between the heat flow density corrected value and the heat flow density assumed value meets the minimum error range, if so, substituting the result into the step (108), otherwise, giving the heat flow density corrected value to the heat flow density assumed value, and repeating the step (104).
Step (108): the thickness of the outermost cladding reduced by the oxidation of the cladding is calculated and corrected.
Step (109): calculating the distribution of mechanical stress caused by internal and external pressure difference in radial, axial and circumferential directions
A step (110): calculating the distribution of thermal stress in radial, axial and circumferential directions caused by radial temperature gradient
Step (111): calculating distribution of stress in radial, axial and circumferential directions caused by radiation swelling
Step (112): fitting the stress caused by the internal and external pressure difference, the radial temperature gradient and the radiation swelling to obtain the distribution of the comprehensive stress in the radial direction, the axial direction and the circumferential direction.
Step (113): and calculating the failure probability of the silicon carbide single layer.
Step (114): determining epsilonΔUP，σΔUP，σPThe corresponding parameter value at the vertex of the probability density curve.
Step (115): and taking the elastic modulus at the middle point of the stress-strain curve of the composite material as the equivalent elastic modulus of the material.
Step (116): and calculating the failure probability of the silicon carbide composite material layer.
Step (117): and obtaining the total failure probability of the cladding by using the failure probabilities of the silicon carbide composite material layer and the single layer.
Step (118): and (5) finishing the calculation of the current time step, setting the temperature distribution at the current time point as the initial temperature distribution at the next time point, and returning to the step (102) to repeat the calculation.
Step (119): and stopping the calculation when the set end time is calculated, and finishing the change curve of the total failure probability of the cladding along with the time.
Claims (6)
1. The silicon carbide composite cladding failure evaluation model under the reactor accident condition is characterized in that the silicon carbide composite cladding failure evaluation model under the reactor accident condition is used for obtaining stress distribution caused by internal and external pressure difference, radial temperature gradient and irradiation swelling by analyzing heat transfer behavior between a multilayer silicon carbide composite cladding and a coolant in a re-submerging stage of a large-break-opening accident LOCA and introducing cladding oxidation factors when the LOCA occurs, and further calculating cladding failure probability under the pseudo-plasticity of a silicon carbide composite by applying a Weibull fracture theory; the method comprises the following steps:
step 1: setting the initial time T to be 0, and starting simulation calculation;
step 2: initializing parameters in an initial parameter input plate; the initial parameter input plate parameters comprise the thickness of each layer of the cladding, the thermal conductivity coefficient, the density, the specific heat capacity, the elastic modulus, the characteristic stress, the Weibull modulus, the thermal expansion coefficient and the Poisson ratio;
and step 3: calculating to obtain the heat exchange coefficient value of the surface of the ladle shell by submerging the heat transfer plate; wherein, considering the re-submergence state, the initial parameter input plate parameters comprise the internal and external pressure of the cladding, the temperature of the coolant and the temperature of the cladding measuring point at the T moment;
and 4, step 4: calculating a stress analysis plate to obtain the distribution of stress in the cladding; wherein, considering the characteristics of each layer of the multi-layer silicon carbide composite material cladding,
and 5: calculating a failure probability analysis plate to obtain the total failure probability of the cladding;
step 6: and (5) finishing the calculation of the failure probability analysis plate and the stress analysis plate, and returning to the step 2 to calculate the next time step.
And 7: and (5) iteratively calculating to set termination time, finishing the calculation of the failure evaluation model, and displaying the total failure probability value of the cladding at each time point.
2. The model for evaluating the failure of the silicon carbide composite cladding under the accident condition of the reactor as recited in claim 1, wherein the calculation method of the stress analysis plate block in the step 2 comprises the following steps:
step (21): calculating the thickness of the outermost cladding reduced by the oxidation of the cladding, and correcting the thickness of the outermost cladding;
step (22): calculating the distribution of mechanical stress caused by the internal and external pressure difference in the radial direction, the axial direction and the circumferential direction;
step (23): calculating the distribution of thermal stress caused by radial temperature gradient in radial, axial and circumferential directions;
step (24): calculating the distribution of stress caused by irradiation swelling in the radial direction, the axial direction and the circumferential direction;
step (25): fitting the stress caused by the internal and external pressure difference, the radial temperature gradient and the radiation swelling to obtain the distribution of the comprehensive stress in the radial direction, the axial direction and the circumferential direction.
3. The model for evaluating the failure of the silicon carbide composite clad under the accident condition of the reactor as recited in claim 1, wherein the calculation method of the re-submerging heat transfer plate block in the step 3 comprises the following steps:
step (31): setting an initial heat flow density assumed value.
Step (32): and obtaining a temperature calculated value according to a temperature field control equation.
Step (33): and calculating according to the sensitivity coefficient field control program to obtain a sensitivity coefficient calculated value.
Step (34): obtaining a heat flux density correction value according to the sensitivity coefficient calculation value, the temperature calculation value and the temperature measurement value;
step (35): and (4) judging whether the error between the heat flow density corrected value and the heat flow density assumed value meets the minimum error range, if so, substituting the result into the stress analysis plate, and if not, giving the heat flow density corrected value to the heat flow density assumed value and repeating the step (32).
4. The model for evaluating the failure of the silicon carbide composite cladding under the accident condition of the reactor as recited in claim 1, wherein when the stress analysis plate block is calculated in the step 4, a cladding oxidation factor is introduced to analyze the thickness of the silicon carbide cladding; the distribution of the stress in the cladding is shown as follows:
where k is 1, 2 denotes an inner layer (silicon carbide composite layer) and an outer layer (silicon carbide single layer). Sigmar，σθ，σzIndicating hoop, radial and axial stresses. EkIs modulus of elasticity, vkIs Poisson's ratio, alphakIn order to be a coefficient of thermal expansion,
and solving the equation set for the undetermined constant according to the boundary condition.
5. The silicon carbide composite cladding failure assessment model under reactor accident conditions as claimed in claim 1, wherein the calculation method of the failure probability analysis plate block in the step 5 comprises the following steps:
step (51): calculating the failure probability of the silicon carbide single layer;
step (52): determining epsilonΔUP，σΔUP，σPThe corresponding parameter value at the peak of the probability density curve; sigmaPProportional ultimate stress; sigmaΔUPIs the stress difference between PLS (proportional ultimate stress) and UTS (ultimate tensile stress); epsilonΔUPIs the strain difference of PLS and UTS;
step (53): taking the elastic modulus of the middle point of the stress-strain curve of the composite material as the equivalent elastic modulus of the material;
step (54): calculating the failure probability of the silicon carbide composite material layer;
step (55): obtaining the total failure probability of the cladding by using the failure probabilities of the silicon carbide composite material layer and the single layer; and when the failure probability analysis plate is calculated, introducing a pseudo-plastic factor to analyze the failure probability of the silicon carbide composite material layer.
6. The silicon carbide composite cladding failure assessment model under reactor accident conditions of claim 5, wherein said step (55) uses the failure probabilities of the silicon carbide composite material layer and the single layer to obtain a total cladding failure probability, wherein:
the calculation formula of the failure probability of the simple substance layer is as follows:
wherein m is the Weibull modulus, σ0For characteristic stresses, these two parameters can be determined by fitting experimental data; j is 1, 2, 3 to represent radial, circumferential and axial 3 main stress directions;
when the failure probability of the silicon carbide composite material layer is calculated, a pseudo-plasticity factor is introduced when the silicon carbide composite material layer is calculated, the failure probability of the composite material layer is calculated by applying nonlinear elasticity mechanics, and the calculation formula is as follows:
in the formula
σP-PLS proportional ultimate stress;
σΔUP-the difference in PLS and UTS stress;
σΔUP-strain difference of PLS and UTS;
Pf(σΔUP，σΔUP，σP) -probability of failure given a parameter;
pdf(σP) Parameter σPA probability density function of;
pdf(σΔUP) Parameter σU-PA probability density function of;
pdf(εΔUP) Parameter εU-PA probability density function of;
p heref(σΔUP，σΔUP，σP) From the maximum first principal stress σ calculated at each timemax(σΔUP，σΔUP，σP) Determination, i.e. when σmaxIf UTS is greater than or equal to UTS, the value is 1, otherwise 0;
the total failure probability of the multilayer silicon carbide composite material cladding is P ═ 1- (1-P)f)(1-Pm)。
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