Integrated ellipsoidal lower end socket model for serious accident analysis and modeling method

Abstract

The invention belongs to the field of pressurized water reactor serious accident analysis, and discloses an integrated ellipsoidal lower end socket model for serious accident analysis and a modeling method.According to the method, an approximate assumption that an ellipsoidal lower end socket is a rotary ellipsoidal shell is adopted, node division is conducted on the ellipsoidal lower end socket, and key geometric information of the ellipsoidal lower end socket is calculated; calculating transverse and radial heat exchange areas of an ellipsoidal lower seal head, the volume of a lower seal head section, the volume of a lower cavity unit connected with the lower seal head and the heat transfer area of a molten pool; and finally, an ellipsoidal lower end socket model is constructed. By adopting the method, the ellipsoidal lower end socket can be modeled correctly, and more accurate lower end socket model parameters are provided for integrated serious accident prediction and analysis of deformation failure behaviors of the lower end socket; the problems that an existing lower end socket model is poor in modeling precision of an ellipsoidal lower end socket and cannot model a deformed lower end socket are solved.

Description

Technical Field

[0001] The invention belongs to the technical field of severe accident analysis of pressurized water reactors, and in particular relates to an ellipsoidal lower head model for integrated severe accident analysis and a modeling method. Background Art

[0002] A severe pressurized water reactor accident refers to an accident that goes beyond the design basis event, causing serious damage to the reactor core of a pressurized water reactor nuclear power plant and endangering the integrity of multiple layers or all barriers used to prevent the release of radioactive materials, thereby causing environmental radioactive pollution and huge losses.

[0003] When a serious accident occurs, the core is not effectively cooled, causing the temperature to rise sharply and melt. A large amount of molten material falls into the lower head, and heat and mass transfer occurs with the lower head, causing the lower head to fail under high temperature and pressure. The measures taken to deal with serious accidents will vary depending on the shape of the lower head. The current shapes of the lower heads are mainly divided into spherical lower heads with a semicircular longitudinal section and ellipsoidal lower heads with a semi-elliptical longitudinal section. The spherical lower heads are mostly used in reactors in power plants, while the ellipsoidal lower heads are mostly used in reactors on ships. The currently used circular lower heads, such as the advanced pressurized water reactor Hualong One, CAP1400, AP1000, etc., use the in-vessel retention strategy (In-vessel Retention, IVR), while for the special-shaped lower heads, because their mechanical properties are not as good as the spherical lower heads, it is difficult to use the IVR strategy. In power plants, the VVER reactor with an ellipsoidal lower head applies the Ex-Vesselmelt Retention (EVR) strategy. However, since the EVR strategy requires a large space, it is not suitable for reactors on ships.

[0004] Since ships are in the marine environment, there will be unexpected violent swaying and collisions during navigation, which may cause serious accidents. Nuclear-powered ships are in the ocean most of the time. In the event of a serious accident, their location is uncertain and it is difficult to obtain external technical support. At the same time, due to the limited space on the ship and the small margin of dedicated safety facilities, there will be a lack of effective measures after a serious accident. The reactor core will be severely damaged, and a large amount of melted core materials will fall into the lower head of the pressure vessel. The lower head is likely to fail, and the molten material will fall into the pile pit, endangering the safety of personnel and the hull. Therefore, it is necessary to study the failure behavior of the ellipsoidal lower head under severe accidents; this study can predict the failure time and failure position of the lower head of the marine reactor after a severe accident.

[0005] An integrated severe accident analysis program is usually used to study the failure behavior of the ellipsoidal lower head under severe accidents. However, the existing integrated severe accident analysis program lacks a high-precision modeling method for the lower head model, which makes the analysis program unable to effectively collect the accurate parameters of the lower head model, thereby affecting the accuracy of the analysis results. Summary of the invention

[0006] The present invention provides an ellipsoidal lower head model and a modeling method for integrated severe accident analysis, so as to solve the technical problem that the existing integrated severe accident analysis program lacks a high-precision modeling method for the lower head model, resulting in the inability of the analysis program to effectively collect accurate parameters of the lower head model.

[0007] In order to achieve the above object, the present invention adopts the following technical contents: In a first aspect, the present invention provides a modeling method for an integrated ellipsoidal lower head model for severe accident analysis, comprising: The ellipsoidal lower head is equivalent to the initial model of the rotating ellipsoidal shell; Perform node division on the initial model of the rotating ellipsoid shell to obtain key geometric information of the initial model of the rotating ellipsoid shell; Based on the key geometric information of the initial model of the rotating ellipsoid shell, the radial heat transfer area of ​​the lower head, the lateral heat transfer area of ​​the lower head, the volume of the lower head section, the unit volume of the lower chamber in contact with the lower head, and the heat transfer area of ​​the molten pool are calculated respectively; An ellipsoidal lower head model is constructed based on the radial heat exchange area of ​​the lower head, the lateral heat transfer area of ​​the lower head, the volume of the lower head section, the unit volume of the lower chamber in contact with the lower head, and the heat transfer area of ​​the molten pool.

[0008] Furthermore, the specific steps for node division of the initial model of the rotating ellipsoid shell are as follows: A lower head with a thickness of t is divided into n layers, and the thickness of each layer is t / n. The intersection of the boundary of each layer of the lower head and the boundary of each section of the lower head is taken as the temperature node of the lower head; Among them, if a lower head is divided into m sections and n layers, the number of temperature nodes of this lower head is (m+1)*(n+1). Furthermore, the specific steps of obtaining key geometric information of the initial model of the rotating ellipsoid shell include: According to the initial model of the rotating ellipsoid shell after node division, the boundary geometric information of each layer of the ellipsoidal lower head is calculated; the shape of each layer of the lower head is expressed in a two-dimensional rectangular coordinate system, and the formulas for the boundary height, angle and radius of the lower head section are as follows:

[0009]

[0010]

[0011]

[0012] in, a , c are the horizontal semi-axis and vertical semi-axis of the lower head layer respectively; h is the boundary height of the lower head section; θ is the angle of the lower head section; L is the radius of the lower head section.

[0013] Furthermore, the radial heat exchange area of ​​the lower head is obtained based on the surface area integral of the initial model of the rotating ellipsoid shell, and the specific calculation formula is as follows:

[0014]

[0015] Among them, Scaph, Scaph1, and Scaph2 are the surface areas of the lower head from the bottom of the lower head to the heights h, h1, and h2 respectively; S is the radial heat conduction area of ​​the lower head section.

[0016] Furthermore, the calculation formula of the transverse heat transfer area of ​​the lower head is as follows:

[0017]

[0018] Where m is the thickness of the lower head of the mth section n2 layer, m; L m,n1 , L m,n2 , L m,n3 are the radii of the n1th, n2th and n3th layers of the lower head of the mth section respectively; A is the transverse heat transfer area of ​​the n2th layer of the lower head of the mth section.

[0019] Furthermore, the volume calculation method of the rotating body is used to calculate the volume of the lower head section by integration. The specific formula is as follows:

[0020]

[0021] Among them, E0, E1, and E2 are the elliptical curves of the longitudinal sections of the innermost layer, middle layer, and outermost layer of the lower head respectively; L1 and L2 are the left and right boundary straight lines of the lower head section respectively; , , , are the z coordinates of the four intersection points formed by the intersection of E1, E2 and L1, L2; Vseg is the volume of the lower head section; For and The volume of the solid of revolution formed by rotating the curve E2 around the z-axis; exist and The volume of the rotating body formed by rotating the straight line L2 around the z-axis; exist and The volume of the rotating body formed by rotating the straight line L1 around the z-axis; For and The volume of the solid of revolution formed by rotating the curve E1 around the z-axis.

[0022] Furthermore, the unit volume of the lower chamber in contact with the lower head is corrected based on the shape of the ellipsoidal lower head, and the specific formula is as follows:

[0023] in, is the unit volume of the lower chamber in contact with the lower head section; a and c are the horizontal semi-axis and vertical semi-axis of the inner surface of the lower head, respectively; h1 and h2 are the left boundary height and boundary height of the lower head section, respectively.

[0024] Furthermore, the specific calculation formula of the heat transfer area of ​​the molten pool is as follows:

[0025] Where A is the heat transfer area of ​​the molten pool; h is the height of the molten pool.

[0026] Furthermore, during the modeling process, the deformation of the lower head of the ellipsoidal lower head fed back by the integrated severe accident analysis program is obtained in real time; the lower head is modeled at each time step according to the deformation of the lower head; and finally, the parameters of the ellipsoidal lower head model are fed back to the integrated severe accident analysis program, so that the integrated severe accident analysis program can perform deformation thermal coupling calculations of the lower head according to the parameters of the ellipsoidal lower head model.

[0027] In a second aspect, the present invention provides an ellipsoidal lower head model for integrated severe accident analysis, which is constructed based on the above-mentioned modeling method.

[0028] Compared with the prior art, the present invention has the following beneficial effects: The present invention provides a modeling method for an ellipsoidal lower head model for integrated severe accident analysis. The method makes an approximate assumption that the ellipsoidal lower head is a rotating ellipsoidal shell, divides the ellipsoidal lower head into nodes, calculates key geometric information of the ellipsoidal lower head, and then calculates the transverse and radial heat exchange areas of the ellipsoidal lower head, the volume of the lower head section, the unit volume of the lower chamber connected to the lower head, and the heat transfer area of ​​the molten pool; finally, the ellipsoidal lower head model is constructed according to the radial heat exchange area of ​​the lower head, the transverse heat transfer area of ​​the lower head, the volume of the lower head section, the unit volume of the lower chamber in contact with the lower head, and the heat transfer area of ​​the molten pool; the method can correctly model the ellipsoidal lower head, and provide more accurate lower head model parameters for integrated severe accident prediction and analysis of the deformation failure behavior of the lower head; and makes up for the problem that the existing lower head model has poor modeling accuracy for the ellipsoidal lower head and cannot model the deformed lower head.

[0029] Preferably, in the present invention, by dividing the lower head into multiple layers and multiple sections and determining the temperature nodes, the thermal behavior of the lower head in a severe accident can be simulated and analyzed more accurately, thus improving the accuracy of the model, making the analysis results more reliable, and helping to evaluate the safety and durability of the lower head in an accident.

[0030] Preferably, in the present invention, key geometric information of the initial model of the rotating ellipsoid shell is obtained, including the geometric information of the boundaries of each layer segment, to provide necessary basic data for subsequent modeling and analysis; the accuracy of the above geometric information directly affects the accuracy and reliability of the model, so this step is of great significance for improving the accuracy and practicability of the model.

[0031] Preferably, in the present invention, the radial heat exchange area of ​​the lower head is obtained by constructing the surface area integral of the initial model of the rotating ellipsoid shell, so that the heat exchange amount of the lower head in the heat transfer process can be calculated more accurately; which is of great significance for evaluating the thermal performance of the lower head, optimizing the thermal design and improving the thermal efficiency.

[0032] Preferably, in the present invention, a calculation formula for the lateral heat transfer area of ​​the lower head is provided, so that the heat exchange amount of the lower head during the lateral heat transfer process can be calculated more accurately; this is also of great significance for evaluating the thermal conductivity performance of the lower head, optimizing thermal design and improving thermal efficiency.

[0033] Preferably, in the present invention, the rotating body volume calculation method is adopted to calculate the volume of the lower head section by integration, which can more accurately calculate the volume and capacity of the lower head, which is of great significance for evaluating the structural performance of the lower head, optimizing the structural design and improving the structural safety.

[0034] Preferably, in the present invention, the volume of the lower chamber unit is corrected based on the shape of the ellipsoidal lower head, so that the volume and capacity of the lower chamber unit can be calculated more accurately; it is also of great significance for evaluating the structural performance of the lower chamber unit, optimizing the structural design and improving the structural safety; in addition, accurate volume calculation is also helpful for fluid dynamics simulation and heat transfer analysis.

[0035] Preferably, in the present invention, a specific calculation formula for the heat transfer area of ​​the molten pool is provided, so that the heat exchange area of ​​the molten pool during the heat transfer process can be calculated more accurately; this is of great significance for evaluating the thermal performance of the molten pool, optimizing thermal design, and improving thermal efficiency. In particular, in severe accident analysis, accurate calculation of the heat transfer area of ​​the molten pool helps to evaluate the cooling effect and safety of the molten pool.

[0036] Preferably, in the present invention, in order to consider the deformation of the lower head, the ellipsoidal lower head model is further provided with a feedback function, which can receive the lower head deformation data fed back by the analysis program at each time step and remodel the lower head.

[0037] The present invention also provides an ellipsoidal lower head model for integrated severe accident analysis, which is constructed based on the modeling method of the ellipsoidal lower head model for integrated severe accident analysis. The use of this lower head model can more accurately simulate the geometric characteristics of the ellipsoidal lower head, and provide more accurate parameter input for the integrated severe analysis program to calculate and analyze the deformation failure behavior of the ellipsoidal lower head, thereby ensuring the accuracy of the analysis results. BRIEF DESCRIPTION OF THE DRAWINGS

[0038] FIG1 is a schematic diagram of the basic geometric shape of an ellipsoidal lower head provided in an embodiment of the present invention; FIG2 is a schematic diagram of the division of the lower head section provided in an embodiment of the present invention; FIG3 is a schematic diagram of geometric information of the inner surface of the lower head provided by an embodiment of the present invention; FIG4 is a diagram showing the relationship between the lower head and the debris molten pool provided in an embodiment of the present invention; FIG5 is a schematic diagram of a lower head section provided in an embodiment of the present invention; FIG6 is a schematic diagram of the transverse heat transfer surface of the ellipsoidal lower head provided in an embodiment of the present invention; FIG7 is a schematic diagram of the radial range of the temperature node of the lower head provided in an embodiment of the present invention; FIG8 is a volume schematic diagram of a lower head section provided in an embodiment of the present invention; FIG9 is a schematic diagram of a lower chamber unit in contact with a lower head provided in an embodiment of the present invention; Fig.10 A simplified diagram of the OLHF-1 experimental device provided in an embodiment of the present invention; FIG11 is a simulation result of an OLHF experiment provided by an embodiment of the present invention, wherein (a) is the temperature of the lower head, and (b) is a comparison of the lower head before and after deformation; Fig.12 A flow chart of a modeling method for an ellipsoidal lower head model for integrated severe accident analysis provided in an embodiment of the present invention.

[0039] Reference numerals: 1. Lower head section; 2. Coolant; 3. Metal molten pool; 4. Oxide molten pool; 5. Fragments; 6. Penetration. DETAILED DESCRIPTION

[0040] In order to make the technical problems, technical solutions and beneficial effects solved by the present invention more clearly understood, the present invention is further described in detail in the following specific 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.

[0041] In order to make the purpose, technical solutions and advantages of the embodiments of the present invention clearer, the technical solutions in the embodiments of the present invention will be clearly and completely described below in conjunction with the drawings in the embodiments of the present invention. Obviously, the described embodiments are part of the embodiments of the present invention, not all of the embodiments. Generally, the components of the embodiments of the present invention described and shown in the drawings here can be arranged and designed in various different configurations.

[0042] Therefore, the following detailed description of the embodiments of the present invention provided in the accompanying drawings is not intended to limit the scope of the invention claimed for protection, but merely represents selected embodiments of the present invention. Based on the embodiments of the present invention, all other embodiments obtained by ordinary technicians in this field without creative work are within the scope of protection of the present invention.

[0043] Example As mentioned in the background technology, an integrated severe accident analysis program is usually used to study the failure behavior of the ellipsoidal lower head under severe accidents; however, the existing integrated severe accident analysis program lacks a high-precision modeling method for the lower head model, resulting in the analysis program being unable to effectively collect the accurate parameters of the lower head model, thereby affecting the accuracy of the analysis results.

[0044] In order to solve the above problems, the present invention provides a modeling method for an ellipsoidal lower head model for integrated severe accident analysis. The modeling method can effectively solve the problem of inaccurate failure behavior analysis of pressure vessels using ellipsoidal lower heads in severe accidents due to the lack of modeling function for the ellipsoidal lower head in existing integrated severe accident analysis programs.

[0045] like Fig.12As shown, this embodiment provides a modeling method for an integrated ellipsoidal lower head model for severe accident analysis, and the specific steps include: The ellipsoidal lower head is equivalent to the initial model of the rotating ellipsoidal shell; that is, the ellipsoidal lower head is equivalent to the rotating ellipsoidal shell; Perform node division on the initial model of the rotating ellipsoid shell to obtain key geometric information of the initial model of the rotating ellipsoid shell; Based on the key geometric information of the initial model of the rotating ellipsoid shell, the radial heat transfer area of ​​the lower head, the lateral heat transfer area of ​​the lower head, the volume of the lower head section, the unit volume of the lower chamber in contact with the lower head, and the heat transfer area of ​​the molten pool are calculated respectively; An ellipsoidal lower head model is constructed based on the radial heat exchange area of ​​the lower head, the lateral heat transfer area of ​​the lower head, the volume of the lower head section, the unit volume of the lower chamber in contact with the lower head, and the heat transfer area of ​​the molten pool.

[0046] It can be seen that this method makes an approximate assumption that the ellipsoidal lower head is a rotating ellipsoidal shell, divides the ellipsoidal lower head into nodes, calculates the key geometric information of the ellipsoidal lower head, and then calculates the transverse and radial heat exchange areas of the ellipsoidal lower head, the volume of the lower head section, the unit volume of the lower chamber connected to the lower head, and the heat transfer area of ​​the molten pool; finally, the ellipsoidal lower head model is constructed according to the radial heat exchange area of ​​the lower head, the transverse heat transfer area of ​​the lower head, the volume of the lower head section, the unit volume of the lower chamber in contact with the lower head, and the heat transfer area of ​​the molten pool; this method can correctly model the ellipsoidal lower head and provide more accurate lower head model parameters for the integrated severe accident prediction and analysis of the deformation failure behavior of the lower head; it makes up for the problem that the existing lower head model has poor modeling accuracy for the ellipsoidal lower head and cannot model the deformed lower head.

[0047] In this embodiment, the specific steps of performing node division on the initial model of the rotating ellipsoid shell are as follows: A lower head with a thickness of t is divided into n layers, and the thickness of each layer is t / n. The intersection of the boundary of each layer of the lower head and the boundary of each section of the lower head is taken as the temperature node of the lower head; Among them, if a lower head is divided into m sections and n layers, the number of temperature nodes of this lower head is (m+1)*(n+1). In this embodiment, the specific steps of obtaining key geometric information of the initial model of the rotating ellipsoid shell include: According to the initial model of the rotating ellipsoid shell after node division, the boundary geometric information of each layer of the ellipsoidal lower head is calculated; the shape of each layer of the lower head is expressed in a two-dimensional rectangular coordinate system, and the formulas for the boundary height, angle and radius of the lower head section are as follows:

[0048]

[0049]

[0050]

[0051] in: a, c are the horizontal semi-axis and vertical semi-axis of the lower head layer, m; h is the boundary height of the lower head section, m; θ is the angle of the lower head section, rad; L is the radius of the lower head section, m .

[0052] In this embodiment, the radial heat exchange area of ​​the lower head is obtained based on the surface area integral of the initial model of the rotating ellipsoid shell. The specific calculation formula is as follows:

[0053]

[0054] Where: Scaph, Scaph1, Scaph2 are the surface areas of the lower head from the bottom of the lower head to the height h, h1, h2, respectively, m 2 ; S is the radial heat conduction area of ​​the lower head section, m 2 .

[0055] In this embodiment, the calculation formula of the transverse heat transfer area of ​​the lower head is as follows:

[0056]

[0057] Where: m is the thickness of the lower head of the mth section n2 layer, m; L m,n1 , L m,n2 , L m,n3 are the radii of the n1, n2, and n3 layers of the mth section lower head, respectively; A is the transverse heat transfer area of ​​the n2th layer of the mth section lower head, m 2 .

[0058] In this embodiment, the volume calculation method of the rotating body is adopted to calculate the volume of the lower head section by integration. The specific formula is as follows:

[0059]

[0060] Among them: E0, E1, E2 are the elliptical curves of the longitudinal sections of the innermost layer, middle layer, and outermost layer of the lower head respectively; L1 and L2 are the left and right boundary straight lines of the lower head section respectively; , , , are the z coordinates of the four intersection points formed by the intersection of E1, E2, L1, and L2, m; Vseg is the volume of the lower head section, m 3 ; For and The volume of the solid formed by rotating the curve E2 around the z axis, m 3 ; exist and The volume of the solid formed by rotating the straight line L2 around the z axis, m 3 ; exist and The volume of the solid formed by rotating the straight line L1 around the z axis, m 3 ; For and The volume of the solid formed by rotating the curve E1 around the z axis, m 3 .

[0061] In this embodiment, the unit volume of the lower chamber in contact with the lower head is corrected based on the shape of the ellipsoidal lower head, and the specific formula is as follows:

[0062] in: is the unit volume of the lower chamber in contact with the lower head section, m 3 ; a, c are the horizontal semi-axis and vertical semi-axis of the inner surface of the lower head, respectively, m; h1, h2 are the left boundary height and boundary height of the lower head section, respectively, m.

[0063] In this embodiment, the specific calculation formula of the heat transfer area of ​​the molten pool is as follows:

[0064] in, A is the heat transfer area of ​​the molten pool, m 2 , that is, the heat transfer area at the top of the molten pool; h is the molten pool height, m.

[0065] In this embodiment, during the modeling process, the deformation of the lower head of the ellipsoidal lower head fed back by the integrated severe accident analysis program is obtained in real time; the lower head is modeled at each time step according to the deformation of the lower head; and finally, the parameters of the ellipsoidal lower head model are fed back to the integrated severe accident analysis program, so that the integrated severe accident analysis program can perform deformation thermal coupling calculation of the lower head according to the parameters of the ellipsoidal lower head model.

[0066] In order to further understand the technical solution provided by the present invention, a more detailed embodiment is now provided for illustration: The present invention provides a modeling method for an ellipsoidal lower head model for integrated severe accident analysis, which provides accurate and reasonable input of lower head geometric parameters for program analysis of lower head failure. The structural schematic diagram of the ellipsoidal lower head is shown in FIG. Figure 1 As shown. The ellipsoidal lower head is a rotating semi-ellipsoidal shell, in which the two horizontal semi-axes a and b on the inner surface are equal; the vertical semi-axis c is smaller than the horizontal semi-axis a. When c is equal to a, the semi-ellipsoid is a hemisphere. For ease of calculation, it is assumed that the semi-ellipsoid formed by the inner and outer walls of the lower head is a concentric sphere, and the wall thickness t of the lower head acts as the growth amount of the horizontal semi-axis and the vertical semi-axis on the ellipsoid formed on the outer surface. The lower head modeled by this method has a wall thickness of t only at the horizontal semi-axis and the vertical semi-axis, and the wall thickness is not t at other positions. However, due to the large ratio of the semi-axis length to the thickness of the lower head, the thickness of the lower head obtained by modeling is very different from the actual thickness of the lower head. The specific calculation steps of the present invention are as follows: About the stratification and temperature node division of the lower head; In order to calculate the temperature of the lower head more accurately, the ISAA program divides the lower head with a thickness of t into n layers, and the thickness of each layer is t / n , the intersection of the boundary of each layer of the lower head and the boundary of each section of the lower head is the temperature node of the lower head. If a lower head is divided into m sections and n layers, the number of temperature nodes of this lower head is (m+1)*(n+1).

[0067] When modeling the lower head, a complete lower head is divided into several sections, and each section of the lower head is divided into several sections according to the angle of the inner surface of the lower head. Divide, Figure 2 It is a part of the lower head which is divided into three layers. J is the temperature node layer number of the lower head. , , and L1 , L2 , L3 It is the angle corresponding to the right boundary of the lower head section 1, 2, and 3 and the radius of the right boundary of the section.

[0068] Calculation of boundary geometry information of each layer of the special-shaped lower head; The boundary position of each layer and each section of the lower head is the key to the calculation of the lower head by the ISAA program, so it is necessary to determine the geometric information of each layer and each section of the lower head. Figure 3 shown.

[0069] like Figure 3 As shown, P is the boundary of the lower head section, r It is the horizontal distance from the center of the lower head to the boundary P of the lower head section; h It is the vertical distance from the bottom of the inner surface of the lower head to the boundary P of the lower head section; is the angle of the lower head section boundary P; L is the radius of the lower head section boundary; the following is the derivation of the relevant geometric parameters: The ellipse equation of the two-dimensional contour of the inner surface of the lower head in the rectangular coordinate system is: (1) Then at the boundary P we have: (2) After sorting, we get: (3) Lower head section boundary angle Defined as: (4) The value of L can be found using the Pythagorean theorem: (5) The calculation of the segment boundaries of other layers of the lower head can be based on the calculated values ​​of the innermost layer. Angle calculation: (6) Through the above arrangement, h, , L can be expressed by a, c, and r, so the user only needs to input the horizontal semi-axis a of the lower head, the vertical semi-axis c of the lower head, the thickness t of the lower head, and the horizontal distance r from the boundary of each section of the lower head to the center of the lower head to calculate the geometric parameters of each layer and segment of the boundary of the lower head.

[0070] About the calculation of radial heat conduction area of ​​special-shaped lower head; The surface area of ​​the inner surface of the lower head in the ISAA program is used to calculate the heat exchange area between the coolant 2, the metal molten pool 3, the oxide molten pool 4, the fragments 5, the penetration 6, and the lower head section 1 in the lower chamber unit. The relationship diagram is shown in the figure below. Figure 4 shown.

[0071] The area of ​​the special-shaped lower head section is a part of the total surface area of ​​the ellipsoid. Figure 5 In the figure, a is the horizontal semi-axis length of the lower head; c is the vertical semi-axis length of the lower head; h1 , h2 It is the vertical distance from the left and right boundaries of the lower head section to the bottom of the lower head.

[0072] The calculation process of the inner surface area of ​​the lower head section is as follows: The equation of the rotating ellipsoid formed by the inner surface of the lower head in the rectangular coordinate system is: (7) For the ellipsoid in formula (7), its total surface area is S total for: (8) Height is h The surface area of ​​the ball cap S cap By the integral lower limit -c and the integral upper limit -c+h Sure: (9) Then the inner surface area of ​​the lower head section is S for: (10) About the calculation of the transverse length of the lower head section; When calculating the lateral heat transfer of the lower head (heat transfer between the lower head sections on the same layer), the lateral length of the lower head (the length of the elliptical arc between the left and right boundaries of the lower head section) is used as the characteristic length of the effective heat transfer coefficient. m1 and m2 The heat transfer coefficient expression at the interface is: (11) in: HTC Adjacent section of lower head m1 and m2 Heat transfer coefficient at the interface; S m1 and S m2 Lower head section m1 and m2 Horizontal length; T Cm1 and T Cm2 Lower head section m1 and m2 Thermal conductivity.

[0073] The calculation formula for the transverse length of the lower head section is as follows: The parametric equation of the semi-ellipse of the longitudinal section of the lower head is: (12) in: a , c The ellipse is y Direction and z The semi-axis length of the direction; The line connecting any point on the ellipse and the center point of the ellipse z The angle in the negative direction of the axis.

[0074] The arc length S of the semi-ellipse is calculated using a line integral: (13) Then the transverse length S of the lower head section m is mfor: (14) in: , are the right boundary angle and the left boundary angle of the lower head section respectively; a , c are the lengths of the horizontal semi-axis and vertical semi-axis of the lower head respectively; About the calculation of the transverse heat transfer area of ​​the lower head; The lateral heat transfer of the lower head exists at the boundary with the lower head section. When calculating the lateral heat transfer of the lower head, the lateral area at the boundary of the lower head section is required. Figure 6 As shown, Figure 6 The middle part is a part of the lower head which is divided into three layers. The lower head has four layers of temperature node boundaries, which are represented by j=1 to j=4 from the outside to the inside; L 2,4 is the right boundary radius at the fourth temperature node of the second lower head. The transverse heat transfer area is calculated based on the temperature node, so there are four transverse heat transfer areas for four temperature nodes. The calculation of the transverse heat transfer area belongs to the radial range length of the lower head at temperature node j. m , and then rotate that length around the vertical axis m To generate area.

[0075] The current research perspective is The transverse heat transfer area at the right boundary j=2 of the second lower head is as follows: Figure 7 shown.

[0076] In the calculation of the transverse area m It is half of the difference between the adjacent outer radius length and the adjacent inner radius length. For the right boundary of the second section lower head at j=2, we have: (15) in: L 2,3 and L 2,1 They are the radius lengths at j=3 and j=1 on the right boundary of the second section lower head respectively.

[0077] The lateral heat transfer area A for: (16) in: L 2,2 is the radius length at j=2 on the right boundary of the second section lower head; The angle at the segment boundaries.

[0078] About the volume calculation of the ellipsoidal lower head section; The volume of the lower head section is used to calculate the heat capacity of the lower head. The heat capacity of the lower head section can be calculated according to different lower head materials and temperatures. The heat capacity of the lower head section is the key data for calculating the energy balance of the lower head section.

[0079] The volume calculation of each layer of the lower head section can refer to Figure 8 Calculate, for simplicity, Figure 8 Only two layers of lower heads are shown: Assume that the boundary of each layer of lower heads is a concentric elliptical curve (the difference between the semi-major axes of different ellipses is equal to the difference between the semi-minor axes) E0, E1, E2, etc. In addition, the boundary of each section of the lower head is the straight lines L1 and L2 in the figure, which pass through the center point of the ellipse and the boundary points of the inner surface of the lower head section. The z coordinates of the four intersection points formed by the intersection of E1, E2 and L1, L2 are , , , .

[0080] The following is the calculation derivation of the volume of the lower head section: exist and The volume calculation formula of the rotating body generated by rotating the curve or straight line y=f(z) around the z axis is: (17) For elliptic equations or linear equations, the calculation of this integral is very simple, so the figure enclosed by the curves E1, E2 and the lines L1, L2 ( Figure 8 The volume V of the solid of revolution formed by rotating around the z-axis) seg That is the volume of the lower head section: (18) in: For and The volume of the solid of revolution formed by rotating the curve E2 around the z-axis; exist and The volume of the rotating body formed by rotating the straight line L2 around the z-axis; exist and The volume of the rotating body formed by rotating the straight line L1 around the z-axis; For and The volume of the solid of revolution formed by rotating the curve E1 around the z-axis.

[0081] Calculation of the unit volume of the lower chamber in contact with the lower head; The shape of the lower chamber unit initially divided by the ISAA program is cylindrical, and the contact with the lower head is not taken into account. When modeling the lower head, the volume of the lower chamber unit in contact with the lower head will be corrected to simulate the contact between the lower chamber unit and the lower head.

[0082] The unit volume of the lower chamber in contact with the lower head is Fig. 9 As shown: h1 and h2 are the left and right boundary heights of the lower head section; r1 and r2 are the horizontal distances from the left and right boundaries of the lower head section to the center of the lower head; the red part is the volume that needs to be corrected.

[0083] Rearrange formula (3), the horizontal distance r from the lower head section boundary to the lower head center and the vertical distance from the lower head section boundary to the bottom of the lower head h The relationship is: (19) Height is h The volume V of the ellipsoid cap cap for: (20) Height h 1 and h2 The volume V of the ellipsoid segment between Fig. 9 The shaded and red parts in the middle are h2 The ellipsoid cap with height is h1 The difference in volume of the ellipsoid cap is: (twenty one) The volume to be corrected . is the volume of the ellipsoid segment minus the volume of the shaded area: (twenty two) Calculation of heat transfer area of ​​molten pool.

[0084] As mentioned above, the heat transfer area of ​​the molten pool depends on the depth of the molten pool. In the original ISAA program, the calculation formula for the heat transfer area of ​​the molten pool is selected based on the circular lower head and the flat lower head. Now that it has been modified to a special-shaped lower head, the calculation formula must also be changed accordingly.

[0085] For an ellipsoidal lower head, if the top surface of any molten pool is located within the spherical part of the lower head, the surface area of ​​the top of the molten pool is A for: (twenty three) in: r Corresponding to the molten pool depth h The horizontal radius below.

[0086] Molten pool depth hThe relationship with the horizontal radius is given by formula (19), so the heat transfer area of ​​the molten pool is: (twenty four) In order to make the purpose, technical scheme and advantages of the embodiments of the present invention clearer, the technical scheme in the embodiments of the present invention will be clearly and completely described below in conjunction with the drawings in the embodiments of the present invention. Obviously, the described embodiments are part of the embodiments of the present invention, rather than all of the embodiments. The components of the embodiments of the present invention described and shown in the drawings here can usually be arranged and designed in various different configurations. Therefore, the following detailed description of the embodiments of the present invention provided in the drawings is not intended to limit the scope of the claimed invention, but merely represents selected embodiments of the present invention. Based on the embodiments in the present invention, all other embodiments obtained by ordinary technicians in this field without making creative work are within the scope of protection of the present invention.

[0087] In order to verify the correctness of the ellipsoidal lower head model suitable for severe accidents, the integrated severe accident analysis program ISAA with the ellipsoidal lower head model was used to simulate the lower head failure (OLHF) experiment conducted by the Organization for Economic Co-operation and Development (OECD). The lower head of the OLHF experiment was spherical before deformation and very close to an ellipsoid after deformation. The correctness of the model can be verified by comparing the simulated shape of the lower head before and after failure with the actual shape of the lower head before and after failure.

[0088] The OLHF test vessel is representative of the lower head area of ​​a typical U.S. pressurized water reactor (PWR), with a scaled-down ratio of 4.85 times. The hemispherical lower head is manufactured with a diameter of 0.914 meters (36 inches) and is made of U.S. steel SA533B1. The upper cylindrical portion of the lower head is 460 mm high and has a cross-sectional wall thickness of 74 mm. The experimental vessel simulates the lower cylindrical portion of the reactor pressure vessel (RPV), the weld between the cylinder and the head, and the hemispherical head. The main components are a cover, three long weld neck flanges (as the cylindrical portion of the test vessel) and six hemispherical lower heads. A blank flange forms a closed environment at the top of the experimental device. A simplified diagram of the experimental device is shown below. Fig.10 As shown. When simulating the OLHF experiment, the vertical semi-axis of the lower head was shortened from 0.457 meters to 0.455 meters so that the ellipsoidal lower head model could also be used when initializing the modeling of the lower head. The calculation results obtained after simulating the OLHF experiment were compared with the experimental results. The corresponding results are shown in Fig.11 As shown; specifically as Fig.11From the comparison between simulation and experiment, it can be seen that the ellipsoidal lower head model for integrated severe accident analysis developed by the present invention can correctly model the ellipsoidal or approximately ellipsoidal lower head and can be applied to the integrated severe accident analysis program.

[0089] Table 1 Comparison of calculated and theoretical values ​​of heat exchange area of ​​the lower head

[0090] In summary, the present invention provides an ellipsoidal lower head model and modeling method for integrated severe accident analysis. The method approximates the ellipsoidal lower head into a rotating ellipsoidal shell; then models the ellipsoidal lower head, divides the lower head into nodes, determines the key geometric information of the lower head, and uses the key geometric information to complete the modeling of the lower head radial heat exchange area, lateral heat transfer area, lower head section volume, lower chamber unit volume in contact with the lower head, and molten pool heat transfer area. The lower head information is fed back to the integrated severe accident analysis program to predict the failure behavior of the lower head.

[0091] The above embodiment is only one of the implementation methods that can realize the technical solution of the present invention. The scope of protection claimed by the present invention is not limited only to this embodiment, but also includes changes, replacements and other implementation methods that can be easily thought of by any technician familiar with the technical field within the technical scope disclosed by the present invention.

Claims

1. A modeling method for an integrated ellipsoidal lower head model for severe accident analysis, characterized in that: include: The ellipsoidal lower head is equivalent to the initial model of the rotating ellipsoidal shell; Perform node division on the initial model of the rotating ellipsoid shell to obtain key geometric information of the initial model of the rotating ellipsoid shell; Based on the key geometric information of the initial model of the rotating ellipsoid shell, the radial heat transfer area of ​​the lower head, the lateral heat transfer area of ​​the lower head, the volume of the lower head section, the unit volume of the lower chamber in contact with the lower head, and the heat transfer area of ​​the molten pool are calculated respectively; An ellipsoidal lower head model is constructed based on the radial heat exchange area of ​​the lower head, the lateral heat transfer area of ​​the lower head, the volume of the lower head section, the unit volume of the lower chamber in contact with the lower head, and the heat transfer area of ​​the molten pool.

2. The modeling method of the integrated ellipsoidal lower head model for severe accident analysis according to claim 1 is characterized in that: The specific steps for node division for the initial model of the rotating ellipsoid shell are as follows: A lower head with a thickness of t is divided into n layers, and the thickness of each layer is t / n. The intersection of the boundary of each layer of the lower head and the boundary of each section of the lower head is taken as the temperature node of the lower head; Among them, if a lower head is divided into m sections and n layers, the number of temperature nodes of this lower head is (m+1)*(n+1).

3. The modeling method of the integrated ellipsoidal lower head model for severe accident analysis according to claim 1 is characterized in that: The specific steps to obtain the key geometric information of the initial model of the rotating ellipsoid shell include: According to the initial model of the rotating ellipsoid shell after node division, the boundary geometric information of each layer of the ellipsoidal lower head is calculated; the shape of each layer of the lower head is expressed in a two-dimensional rectangular coordinate system, and the formulas for the boundary height, angle and radius of the lower head section are as follows: in, a , c are the horizontal semi-axis and vertical semi-axis of the lower head layer respectively; h is the boundary height of the lower head section; θ is the angle of the lower head section; L is the radius of the lower head section.

4. The modeling method of the integrated ellipsoidal lower head model for severe accident analysis according to claim 3 is characterized in that: The radial heat exchange area of ​​the lower head is obtained by integrating the surface area of ​​the initial model of the rotating ellipsoid shell. The specific calculation formula is as follows: Among them, Scaph, Scaph1, and Scaph2 are the surface areas of the lower head from the bottom of the lower head to the heights h, h1, and h2 respectively; S is the radial heat conduction area of ​​the lower head section.

5. The modeling method of the integrated ellipsoidal lower head model for severe accident analysis according to claim 3 is characterized in that: The calculation formula of the transverse heat transfer area of ​​the lower head is as follows: Where m is the thickness of the lower head of the mth section n2 layer, m; L m,n1 , L m,n2 , L m,n3 are the radii of the n1th, n2th and n3th layers of the lower head of the mth section respectively; A is the transverse heat transfer area of ​​the n2th layer of the lower head of the mth section.

6. The modeling method of the integrated ellipsoidal lower head model for severe accident analysis according to claim 3 is characterized in that: The volume of the lower head section is calculated by the rotation body volume calculation method using the integral method. The specific formula is as follows: Among them, E0, E1, and E2 are the elliptical curves of the longitudinal sections of the innermost layer, middle layer, and outermost layer of the lower head respectively; L1 and L2 are the left and right boundary straight lines of the lower head section respectively; , , , are the z coordinates of the four intersection points formed by the intersection of E1, E2 and L1, L2; Vseg is the volume of the lower head section; For and The volume of the solid of revolution formed by rotating the curve E2 around the z-axis; exist and The volume of the rotating body formed by rotating the straight line L2 around the z-axis; exist and The volume of the rotating body formed by rotating the straight line L1 around the z-axis; For and The volume of the solid of revolution formed by rotating the curve E1 around the z-axis.

7. The modeling method of the integrated ellipsoidal lower head model for severe accident analysis according to claim 3 is characterized in that: The unit volume of the lower chamber in contact with the lower head is corrected based on the shape of the ellipsoidal lower head, and the specific formula is as follows: in, is the unit volume of the lower chamber in contact with the lower head section; a and c are the horizontal semi-axis and vertical semi-axis of the inner surface of the lower head, respectively; h1 and h2 are the left boundary height and boundary height of the lower head section, respectively.

8. The modeling method of the integrated ellipsoidal lower head model for severe accident analysis according to claim 3 is characterized in that: The specific calculation formula of the heat transfer area of ​​the molten pool is as follows: Where A is the heat transfer area of ​​the molten pool; h is the height of the molten pool.

9. The modeling method of the integrated ellipsoidal lower head model for severe accident analysis according to claim 1 is characterized in that: During the modeling process, the deformation of the lower head of the ellipsoidal lower head fed back by the integrated severe accident analysis program is obtained in real time; the lower head is modeled at each time step according to the deformation of the lower head; finally, the parameters of the ellipsoidal lower head model are fed back to the integrated severe accident analysis program, so that the integrated severe accident analysis program can perform deformation thermal-mechanical coupling calculations of the lower head according to the parameters of the ellipsoidal lower head model.

10. Ellipsoidal lower head model for integrated severe accident analysis, characterized in that: The method is constructed based on any one of the modeling methods described in claims 1-9.

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