A fusion reactor solid state blanket design method based on topology optimization

Abstract

The application discloses a fusion reactor solid-state blanket design method based on topology optimization, and is characterized in that based on the topology structure characteristics of the fusion reactor solid-state blanket arranged in layers along the radial direction, the coupling mechanism of the multi-physical fields of neutronics, thermal-hydraulics and structural mechanics is researched, a coupling model between various parameters of the multi-physical fields is established through theoretical analysis and a multivariate nonlinear regression method; under the constraint conditions of material temperature and structural mechanical properties, a constrained topology optimization model for maximizing the tritium breeding ratio is constructed; the constrained topology optimization model is converted into an unconstrained topology optimization model for maximizing the tritium breeding ratio by using a Lagrange function and a KKT condition, the unconstrained topology optimization model is solved by using a gradient descent algorithm, and a blanket radial topology structure capable of meeting the design criteria is obtained. A blanket three-dimensional model is established, and the performance of neutronics, thermal-hydraulics and structural mechanics in the whole reactor is analyzed, the tritium production, heat removal and structural safety performance of the blanket are evaluated, and it is verified that the topology optimization model can efficiently obtain a blanket design scheme with optimal comprehensive performance of multiple fields.

Description

TECHNICAL FIELD

[0001] The application belongs to the field of fusion reactors, and particularly relates to a fusion reactor solid-state blanket design method based on topology optimization. BACKGROUND

[0002] Nuclear fusion has excellent characteristics such as rich reserves of raw materials, low environmental pollution, and inherent safety of devices, and has always been considered an effective way to completely solve the human energy problem. The blanket is a core component of a fusion reactor, and is operated in a harsh service environment of high temperature and high pressure, high heat load, and strong neutron irradiation, and mainly performs core functions such as tritium self-sustaining, energy conversion, and radiation shielding. According to the form of tritium breeder, the blanket can be divided into a solid-state breeder and a liquid-state breeder, wherein the solid-state blanket does not have a magnetohydrodynamic effect, and is favored by domestic and foreign fusion research institutions. The design of the blanket needs to meet the requirements of tritium breeding ratio (TBR) > 1, material temperature lower than a limit value, and guarantee of structural integrity under normal operation and accident conditions, and the design process involves multidisciplinary cross such as neutronics, thermal-hydraulics, and structural mechanics, so the design of the blanket is a typical multivariable-multiojective iterative optimization process, and has always been considered a key scientific problem in the development of magnetic confinement fusion. However, due to the complexity of the 'neutron-thermal-structure' coupling, the existing research methods are mostly simplified, the core design indicators of the reference tritium breeding ratio and the temperature of the material are used, and only the relatively key 'neutron-thermal' coupling field is solved; according to engineering experience, a'step-by-step method' is used to realize one-way iteration, and a relatively optimal feasible scheme is obtained from the perspective of neutron-thermal optimization, and this process does not consider the coupling effect of the structural force field, and still needs to manually perform structural mechanics analysis, so the efficiency is low, and a global optimal solution cannot be often given. SUMMARY

[0003] To solve the above technical problems, the application provides a fusion reactor solid state blanket design method based on topology optimization. Based on the topology structure characteristics of the fusion reactor solid state blanket arranged in layers along the radial direction, firstly, the multi-physical field coupling mechanism of neutronics, thermal hydraulics and structural mechanics is studied, and the coupling model between the parameters of the multi-physical fields is established through theoretical analysis and multivariate nonlinear regression method; secondly, under the constraint conditions of material temperature and structural mechanical properties, a topology optimization model maximizing tritium breeding ratio is further constructed; finally, the topology optimization model is converted into an unconstrained topology optimization model by using the Lagrange function and the KKT (Karush-Kuhn-Tucker) condition, and the blanket design meeting the design criteria is obtained by using the gradient descent algorithm. On this basis, a three-dimensional model of the blanket is established, and the neutronics, thermal hydraulics and structural mechanical performance analysis of the whole reactor are carried out, the tritium production, heat removal and structural safety performance of the blanket are evaluated, and it is verified that the topology optimization model can efficiently obtain the blanket design scheme with the optimal comprehensive performance of multiple fields. The application can solve the problems of the existing fusion reactor blanket optimization method, such as relying on engineering experience and trial and error, only solving the "neutron-thermal" coupled field, and ignoring the influence of the structural field, low efficiency and inaccurate results.

[0004] In order to achieve the above purpose, the technical scheme adopted by the application is:

[0005] A fusion reactor solid state blanket design method based on topology optimization, comprising the following steps:

[0006] Step (1) based on the topology structure characteristics of the fusion reactor solid state blanket arranged in layers along the radial direction, the coupling mechanism between the neutronics, thermal hydraulics and structural mechanics physical fields is studied, and the coupling model between the parameters of the physical fields is further constructed, comprising the following steps:

[0007] Step (1.1) constructing a neutronics model of the fusion reactor blanket, obtaining the spatial distribution of tritium breeding ratio and nuclear heat deposition in the blanket through Monte Carlo neutron transport analysis, further using single variable control method to quantitatively analyze the spatial distribution characteristics of tritium breeding ratio and nuclear heat deposition, and constructing a "structure-neutron" coupling model integrating "neutron wall load, spherical bed filling structure, tritium breeding ratio, nuclear heat deposition and topology structure" through theoretical analysis and multivariate nonlinear regression;

[0008] Step (1.2) based on Fourier heat conduction law and Robin condition, constructing a multilayer flat wall heat transport equation for the radial topology structure of the blanket, and introducing the spatial distribution of nuclear heat deposition for solving, so as to obtain the temperature distribution of the first wall steel structure, cooling components and breeding area and other blanket structure / function components, and accordingly establishing a "neutron-thermal" coupling model;

[0009] Step (1.3) is based on the temperature field of the first wall steel structure, cooling components and blanket structure / function components such as the breeding zone. First, through the beam theory, a function model of the primary stress of the first wall steel structure, cooling components and other blanket structure components is established as the change of the thermal expansion load of the coolant and the breeding ball bed. Second, through the thermal elastic constitutive law, the relationship between stress and strain is linearized, as shown in formulas (1)-(4). Under the action of thermal gradient, through the integral processing of external force and external moment, the "thermal-structure" coupling model is constructed;

[0010] Thermal elastic constitutive law:

[0011]

[0012] In the formula, ε ij is the strain tensor; G is the shear modulus, Pa; σ ij and σ kk are stress tensors in different coordinate directions; v is the Poisson's ratio; a is the linear expansion coefficient, 1 / K; ΔT is the temperature change, K; δ ij is the Kronecker symbol.

[0013] One-dimensional stress-strain linearization processing:

[0014] σ=E[ε-α(△T)] (2)

[0015] ε=Ax+B (3)

[0016] σ=E[Ax+B-α(△T)] (4)

[0017] In the formula, A and B are constants to be solved; E is the Young's modulus; G is the shear modulus, Pa; σ is the stress, Pa; ε is the strain; v is the Poisson's ratio; δ is the Kronecker symbol; a is the linear expansion coefficient, 1 / K; ΔT is the temperature change, K; x is the coordinate position.

[0018] Step (2) is based on the "structure-neutron", "neutron-thermal" and "thermal-structure" coupling model. The response model of the tritium breeding ratio, material temperature and stress-strain associated with the width w of each layer of the topology structure, the material type β and the ball bed filling structure γ is constructed, and the objective function of maximizing the tritium breeding ratio is further established, as shown in formula (5). The optimization variables include the width w of each layer of the topology structure, the material type β and the ball bed filling structure γ.

[0019] Objective function:

[0020]

[0021] In the formula, TBR is the tritium breeding ratio; is the width of the material of each layer of the topology structure, m; is the material type; is a packed structure of pebbles.

[0022] Step (3) introduces two types of constraint conditions h(x) and g(x) to the objective function, including the maximum temperature of the material being lower than the upper limit t limit , and the maximum stress-strain of the cladding structure components such as the first wall steel structure and the cooling components satisfying the relevant design criteria σ limit , a constrained topological optimization model is constructed for maximizing the tritium breeding ratio, and further, through the Lagrange multiplier method, auxiliary variables λ and μ are introduced to convert it into an unconstrained topological optimization model for maximizing the tritium breeding ratio.

[0023] The constraint conditions are:

[0024]

[0025] Lagrange function:

[0026]

[0027] Step (4) sets the packed structure of pebbles and the topological structure as the initial optimization parameter vector θ j , and through the unconstrained topological optimization model, the gradient of the tritium breeding ratio with respect to the optimization parameters is calculated The parameters are "lowered" along the gradient direction to obtain the latest optimization parameter vector θ j+1 , and the iteration is updated until all initial parameters are completely retrieved and converged, and through the KKT condition criterion, the cladding radial topological structure with the best tritium production performance under the constraint conditions is determined.

[0028]

[0029] In the formula, θ j is the initial optimization parameter vector, including the packed structure of pebbles and the topological structure; and are the gradients of the tritium breeding ratio with respect to the optimization parameters; β1, β2 and β3 are auxiliary variables between 0 and 1; θ j+1 is the optimized parameter vector.

[0030] Step (5) establishes a three-dimensional fusion reactor cladding model based on the cladding radial topological structure obtained from the topological optimization model, and carries out neutron analysis of the full reactor, thermal-hydraulic analysis and structural mechanics analysis of the full cladding module, evaluates the cladding tritium production, heat removal and structural safety performance, and verifies that the topological optimization model used in this project can efficiently obtain a cladding design scheme with the best comprehensive performance in multiple fields.

[0031] Further, a thermal-mechanical coupling model of the breeding pebble bed and the first wall steel structure and the cooling components is constructed through experimental research, which is an important input of the breeding pebble bed thermal expansion load in step (1.3).

[0032] Compared with the existing fusion reactor blanket optimization method, the beneficial effects are:

[0033] 1. The existing method simplifies the multi-physical field analysis of the fusion reactor blanket, refers to the core design index of the tritium breeding ratio and the temperature of the material, and only solves the relatively key 'neutron-thermal' coupling field, while ignoring the influence of the structural force field. The present application can simultaneously consider the 'neutron-thermal-structural' multi-field full coupling analysis, and ensure that the fusion reactor blanket can meet the design criteria of multiple physical fields at the same time.

[0034] 2. The existing method relies on engineering experience and trial and error, and uses the'step method' to realize one-way iteration, and obtains a better feasible scheme from the perspective of neutron-thermal optimization, which has the disadvantages of low efficiency and low accuracy. The present application establishes a topology optimization model of the blanket multi-physical coupling from the mathematical point of view, and further uses the gradient descent algorithm to realize global solution, which improves the efficiency and accuracy of the blanket optimization design. BRIEF DESCRIPTION OF DRAWINGS

[0035] Figure 1 The radial topology structure diagram of the fusion reactor solid-state blanket of the present application.

[0036] Figure 2 The fusion reactor solid-state blanket design flowchart based on topology optimization of the present application.

[0037] 1: first wall steel structure; 2-1: first breeding zone ball bed; 2-2: second breeding zone ball bed; 2-3: third breeding zone ball bed; 2-4: fourth breeding zone ball bed; 3-1: first cooling component; 3-2: second cooling component; 3-3: third cooling component; 3-4: fourth cooling component. DETAILED DESCRIPTION

[0038] In order to make the purpose, technical scheme and advantages of the present application clearer and more apparent, the present application will be further described in detail below in combination with the drawings and examples. It should be understood that the specific examples described herein are only used to explain the present application and do not limit the present application. In addition, the technical features involved in each embodiment of the present application described below can be combined with each other as long as they do not conflict with each other.

[0039] As Figure 1As shown, the fusion reactor solid state blanket design method based on topology optimization of the application is suitable for the topology structure arranged in radial layers, which specifically includes a first wall steel structure 1, a first breeding zone pebble bed 2-1 at different radial positions, a second breeding zone pebble bed 2-2, a third breeding zone pebble bed 2-3, a fourth breeding zone pebble bed 2-4, and a first cooling component 3-1 at different radial positions, a second cooling component 3-2, a third cooling component 3-3, and a fourth cooling component 3-4, and the optimization variables include the width w of each layer material, the material type β, and the pebble bed filling structure γ.

[0040] As shown, Figure 2 The fusion reactor solid state blanket design method based on topology optimization of the application includes the following steps:

[0041] Step (1) Based on the topology structure characteristics of the fusion reactor solid state blanket arranged in radial layers, the coupling mechanism between the neutron, thermal-hydraulic, and structural mechanics physical fields is studied, and a coupling model between the multi-physical field parameters is further constructed, including the following steps:

[0042] Step (1.1) Construct a neutron model of the fusion reactor blanket, obtain the spatial distribution of tritium breeding ratio and nuclear heat deposition in the blanket through Monte Carlo neutron transport analysis, further use the single variable control method to quantitatively analyze the spatial distribution characteristics of tritium breeding ratio and nuclear heat deposition, and through theoretical analysis and multivariate nonlinear regression, construct a "structure-neutron" coupling model integrating "neutron wall load, pebble bed filling structure, tritium breeding ratio, nuclear heat deposition, and topology structure";

[0043] Step (1.2) Based on the Fourier heat conduction law and Robin condition, construct a multi-layer flat wall heat transport equation of the radial topology structure of the blanket, the calculation model includes the breeding zone pebble bed and the cooling components on both sides, and introduces the spatial distribution of nuclear heat deposition for solving, which can obtain the temperature distribution of the first wall steel structure 1, the first cooling component 3-1, the second cooling component 3-2, the third cooling component 3-3, the fourth cooling component 3-4, and the first breeding zone pebble bed 2-1, the second breeding zone pebble bed 2-2, the third breeding zone pebble bed 2-3, and the fourth breeding zone pebble bed 2-4, and accordingly establish a "neutron-thermal" coupling model; On this basis, the optimal width of the tritium release temperature of the breeding zone pebble bed can be determined, and the radial extension is extended, and the position corresponding to the saturation state of the tritium breeding ratio is taken as the truncation point, thereby determining the radial topology structure of the blanket.

[0044] Step (1.3) is based on the temperature field of the first wall steel structure 1, the first cooling component 3-1, the second cooling component 3-2, the third cooling component 3-3, the fourth cooling component 3-4, and the cladding structure / function components such as the first breeding zone pebble bed 2-1, the second breeding zone pebble bed 2-2, the third breeding zone pebble bed 2-3, and the fourth breeding zone pebble bed 2-4. First, by beam theory, a function model of the primary stress of the first wall steel structure 1, the first cooling component 3-1, the second cooling component 3-2, the third cooling component 3-3, the fourth cooling component 3-4, and other cladding structure components with the change of coolant and breeding pebble thermal expansion load is established. Among them, the thermal-mechanical coupling model of the breeding pebble and the first wall steel structure 1, the first cooling component 3-1, the second cooling component 3-2, the third cooling component 3-3, and the fourth cooling component 3-4 is studied through experiments, which is an important input of the first breeding zone pebble bed 2-1, the second breeding zone pebble bed 2-2, the third breeding zone pebble bed 2-3, and the fourth breeding zone pebble bed 2-4 thermal expansion load; secondly, the relationship between stress and strain is linearized by the thermal elastic constitutive law, as shown in formulas (1)-(4). Under the action of thermal gradient, the "thermal-structure" coupling model is constructed by integral processing of external force and external moment.

[0045] Thermal elastic constitutive law:

[0046]

[0047] In the formula, ε ij is the strain tensor; G is the shear modulus, Pa; σ ij and σ kk are stress tensors in different coordinate directions; v is the Poisson's ratio; α is the linear expansion coefficient, 1 / K; ΔT is the temperature change, K; δ ij is the Kronecker symbol.

[0048] One-dimensional stress-strain linearization processing:

[0049] σ=E[ε-α(△T)] (2)

[0050] ε=Ax+B (3)

[0051] σ=E[Ax+B-α(△T)] (4)

[0052] In the formula, A and B are constants to be solved; E is the Young's modulus; G is the shear modulus, Pa; σ is the stress, Pa; ε is the strain; v is the Poisson's ratio; δ is the Kronecker symbol; α is the linear expansion coefficient, 1 / K; ΔT is the temperature change, K; x is the coordinate position.

[0053] Step (2) based on the "structure-neutron", "neutron-thermal" and "thermal-structure" coupling model, respectively, the construction of tritium breeding ratio, material temperature and stress-strain associated with the width of each layer of the topological structure w, material type β, the ball bed filling structure γ response model, further established to maximize the objective function of tritium breeding ratio, as shown in equation (5), the optimization variables include the width of each layer of the topological structure w, material type β, the ball bed filling structure γ;

[0054] Objective function:

[0055]

[0056] In the formula, TBR is the tritium breeding ratio; w is the width of each layer of the topological structure, m; β is the material type; γ is the ball bed filling structure.

[0057] Step (3) to the objective function is introduced two kinds of constraint conditions h(x) and g(x), including the highest temperature of the material is lower than the upper limit t limit , and the maximum stress-strain of the first wall steel structure 1, the first cooling component 3-1, the second cooling component 3-2, the third cooling component 3-3, the fourth cooling component 3-4 and other blanket structure components meet the relevant design criteria σ limit , the construction of tritium breeding ratio maximization constrained topological optimization model, further, through the Lagrange multiplier method and KKT (Karush-Kuhn-Tucker) condition, the introduction of auxiliary variable λ and μ, it is converted into the tritium breeding ratio maximization unconstrained topological optimization model;

[0058] The constraint condition is:

[0059]

[0060] Lagrange function:

[0061]

[0062] Step (4) set the ball bed filling structure and topological structure as the initial optimization parameter vector θ j , through the unconstrained topological optimization model, the gradient of tritium breeding ratio with the change of optimization parameters The parameters along the gradient direction "down", get the latest optimization parameter vector θ j+1 , iterative update until all the initial parameters are completely retrieved convergence, through the KKT condition criterion, determine the best tritium production performance of the blanket radial topological structure under the constraint condition;

[0063]

[0064] In the formula, θj is the initial optimization parameter vector, including the ball bed filling structure and the topological structure; and is the gradient of the tritium breeding ratio with the change of each optimization parameter; β1, β2 and β3 are auxiliary variables, between 0 and 1; θ j+1 is the optimized parameter vector.

[0065] Step (5) obtains the radial topological structure of the blanket based on the topological optimization model, establishes a three-dimensional fusion reactor blanket model, carries out full reactor neutron analysis, full blanket module thermal-hydraulic and structural mechanics analysis, evaluates the tritium production, heat removal and structural safety performance of the blanket, and verifies that the topological optimization model can efficiently obtain a blanket design scheme with optimal multi-field comprehensive performance.

[0066] The parts of the present application not described in detail belong to the commonly known technology in the field. Although the above describes the specific embodiments of the present application in a descriptive manner, so as to facilitate the understanding of the present application by the person skilled in the art. It should be clear that the present application is not limited to the scope of the specific embodiments, and for the person skilled in the art, as long as various changes are within the scope of the appended claims and the spirit and scope of the present application, these changes are obvious, and are within the protection of the present application.

Claims

1. A method for designing a solid state blanket of a fusion reactor based on topology optimization, characterized in that, Comprising the following steps: Step (1) based on the topology characteristics of the radial stratified arrangement of the solid state blanket of fusion reactor, the coupling mechanism between the neutron, thermal-hydraulics and structural mechanics physical fields is studied, and the coupling model between the multi-physical field parameters is constructed, comprising the following steps: Step (1.1) construct a neutron model of the blanket of the fusion reactor, obtain the spatial distribution of tritium breeding ratio and nuclear heat deposition in the blanket through Monte Carlo neutron transport analysis, use single variable control method to quantitatively analyze the spatial distribution characteristics of tritium breeding ratio and nuclear heat deposition, and construct a "structure-neutron" coupling model integrating "neutron wall load, pebble bed filling structure, tritium breeding ratio, nuclear heat deposition and topology structure" through theoretical analysis and multivariate nonlinear regression; Step (1.2) based on Fourier heat conduction law and Robin condition, construct a multi-layer flat wall heat transport equation for the radial topology structure of the blanket, and introduce the spatial distribution of nuclear heat deposition for solving, obtain the temperature distribution of the first wall steel structure, cooling components and blanket structure / function components in the breeding region, and accordingly establish a "neutron-thermal" coupling model; Step (1.3) on the basis of the temperature field of the first wall steel structure, cooling components and blanket structure / function components in the breeding region, firstly, through beam theory, a function model of the primary stress of the first wall steel structure and the cooling components of the blanket structure components is established, which changes with the thermal expansion load of the coolant and the breeding pebble bed; secondly, through the thermal elastic constitutive law, the relationship between stress and strain is linearized, as shown in formulas (1)-(4); Under the action of thermal gradient, through the integral treatment of external force and external moment, a "thermal-structure" coupling model is constructed; Thermal elastic constitutive law: where ε ij is the strain tensor; G is the shear modulus, with units of Pa; σ ij and σ kk are the stress tensors in different coordinate directions; v is the Poisson's ratio; a is the linear expansion coefficient, with units of 1 / K; AT is the temperature change, with units of K; δ ij is the Kronecker delta. One-dimensional stress-strain linearization: σ=E[ε-α(△T)] (2) ε=Ax+B (3) σ=E[Ax+B-α(△T)] (4) In the formula, A and B are constants to be solved; E is Young's modulus; G is shear modulus, Pa; σ is stress, Pa; ε is strain; v is Poisson's ratio; δ is the Kronecker symbol; α is the linear expansion coefficient, 1 / K; △T is the temperature change, K; x is the coordinate position; Step (2) based on the "structure-neutron", "neutron-thermal" and "thermal-structure" coupling models, the response model of tritium breeding ratio, material temperature and stress-strain associated with the width w of each layer of the topology structure, material type β and pebble bed filling structure γ is constructed, and a target function for maximizing the tritium breeding ratio is further established, as shown in formula (5), and the optimization variables include the width w of each layer of the topology structure, material type β and pebble bed filling structure γ; Objective function: where TBR is the tritium breeding ratio; is the width of the material of each layer of the topology, m; is the material type; is the pebble bed fill structure; Step (3) introduces two kinds of constraint conditions h(x) and g(x) to the objective function, including the maximum temperature of the material being lower than the upper limit t limit , and the maximum stress-strain of the clad structure component of the first wall steel structure and the cooling component satisfies the relevant design criterion σ limit , a constrained topology optimization model is constructed to maximize the tritium breeding ratio, and through the Lagrange multiplier method and KKT conditions, auxiliary variables λ and μ are introduced to convert it into an unconstrained topology optimization model for maximizing the tritium breeding ratio. The constraint condition is: The Lagrangian function is: Step (4) set the ball bed filling structure and topology as the initial optimization parameter vector θ j , through the unconstrained topology optimization model, calculate the gradient of tritium breeding ratio with the optimization parameter change " down along the gradient direction, get the latest optimization parameter vector θ j+1 , iterative update until all the initial parameters are completely retrieved convergence, through the KKT condition criterion, determine the best tritium production performance of the blanket radial topology structure under the constraint condition; where θ j is the initial optimized parameter vector, including the sphere bed filling structure and the topological structure; and is the gradient of the tritium breeding ratio with respect to each optimized parameter; β1, β2 and β3 are auxiliary variables, between 0 and 1; θ j+1 is the optimized parameter vector; Step (5) based on the topology optimization model, the radial topology structure of the blanket is obtained, a three-dimensional fusion reactor blanket model is established, the neutron, thermal-hydraulic and structural mechanics analysis of the whole reactor and the whole blanket module is carried out, the tritium production, heat removal and structural safety performance of the blanket are evaluated, and it is verified that the topology optimization model can efficiently obtain the blanket design scheme with the optimal comprehensive performance of multiple fields.

2. The method of claim 1, wherein, The thermal-mechanical coupling model of the first wall steel structure and the cooling components is studied by experiments, which is an important input of the step (1.3) for the thermal expansion load of the blanket pebble bed.

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