CN116522682A - A Calculation Method of Heat Flux in the First Wall of Tokamak Fusion Reactor - Google Patents

Abstract

The invention discloses a calculation method of heat flux density of a first wall of a Tokamak fusion reactor, which is used for establishing a radiation heat exchange three-dimensional calculation model and a charged particle heat flux density three-dimensional calculation model based on plasma configuration, a magnetic field and spatial distribution of the first wall; the method comprises the steps of carrying out iteration on plasma temperature by referring to a conservative average heat flux density designed by Tokamak of a radiation heat exchange three-dimensional calculation model, and obtaining first wall radiation heat flux density distribution when the average heat flux densities are consistent; the three-dimensional calculation model of the heat flux density of the charged particles establishes the space projection of the charged particles on the first wall according to the plasma configuration and the magnetic field space distribution, and obtains the heat flux density distribution of the charged particles on the first wall by combining the attenuation outside the outermost closed magnetic surface; according to the method, the influence of radiation heat exchange between the first walls, the space coordinates and the magnetic field distribution on the heat flux density is considered, the fine calculation result of the heat flux density of the first walls is obtained, the input errors of the heat exchange of the first walls and the structural calculation are reduced, and the design cost is reduced.

Description

A Calculation Method of Heat Flux in the First Wall of Tokamak Fusion Reactor

technical field

The patent of the present invention relates to the technical field of tokamak fusion reactor, in particular to a method for calculating the heat flux density of the first wall of the tokamak fusion reactor.

Background technique

Tokamak is a device that creates an environment and ultra-high temperature for fusion of deuterium and tritium through electromagnetic field confinement and drive, and realizes controllable nuclear fusion reactions. The first wall is the solid structure that directly faces the plasma during the tokamak fusion reaction. It is used to seal the vacuum chamber and absorb the radiation energy and part of the charged particle energy released by the plasma.

In this context, a large number of tokamak fusion reactor designs have been carried out in recent years. The first wall is an important part of the vacuum chamber and the cladding, and the heat flux on its surface is an important boundary condition in the design process. It is the first The most important safety load of the wall. However, there is no unified method for calculating the heat flux of the first wall. The radiation heat flux is mostly estimated by the core power and loaded on the first wall with a uniform load. This method ignores the spatial inhomogeneity of the radiation heat flux. It is impossible to focus on the area where the load is concentrated; the heat flux of charged particles is mostly simplified by spherical simplification in the calculation process, and because the result is extremely sensitive to the relative position in three-dimensional space, the existing methods lack accurate results for charged particles on the first wall; At the same time, the existing method lacks a coupling calculation method for the heat flux density of the two first walls, and cannot provide complete heat flux calculation results, and the calculation efficiency is low, and it is not economical.

Contents of the invention

In order to solve the above problems and realize the three-dimensional accurate calculation of the first wall radiation heat flux and charged particle heat flux, the object of the present invention is to provide a method for calculating the first wall heat flux of a Tokamak fusion reactor. The present invention provides a complete and effective The calculation method of the heat flux of the first wall of the tokamak fusion reactor considers the influence of the relative angle and distance of the first wall to the plasma in the three-dimensional space on the heat flux, the influence of the magnetic field distribution on the heat flux, and the first The radiation heat exchange between the walls has higher accuracy for the spatial distribution of the heat flux density of the first wall, which reduces the input error of the first wall heat transfer and structural calculation, and reduces the design cost.

In order to achieve the above object, the technical scheme adopted in the present invention is as follows:

A method for calculating the heat flux density of the first wall of a tokamak fusion reactor. The method is based on the plasma configuration, the spatial distribution of the magnetic field, and the spatial distribution of the first wall. 3D calculation model of particle heat flux;

The three-dimensional calculation model of radiation heat transfer refers to the conservative average heat flux of the Tokamak fusion reactor engineering design, iteratively calculates the plasma temperature, and finally obtains the radiation heat flux distribution of the first wall when the average heat flux is consistent;

The three-dimensional calculation model of the charged particle heat flux density establishes the spatial projection of the charged particles on the first wall according to the plasma configuration and the spatial distribution of the magnetic field, and considers the attenuation of the charged particles outside the outermost closed magnetic surface, and finally obtains the charged particle heat flux on the first wall density distribution;

The calculation object of this method includes the first wall 1 and the plasma 2; wherein the first wall 1 is arranged according to the design of the tokamak fusion reactor, and the plasma 2 is the outermost closed magnetic surface of the configuration under the calculation condition;

When calculating, the following parameters need to be known or can be preliminarily obtained: the allowable temperature T ₀ of the first wall material, the radiation degree ε of the first wall material, the space coordinates of the outermost closed magnetic surface of the plasma configuration under the calculation conditions, the first Wall design structure and space coordinates, design conservative average heat flux Q ₀ of the first wall of the fusion reactor, magnetic field spatial distribution B, decay length λ _q under working conditions, and final closed magnetic flux parallel heat flux q ₀ .

Specifically, the inventive method comprises the following steps:

Step 1, establish the 3D calculation model of radiation heat transfer: according to the space coordinates of the outermost closed magnetic surface of the plasma configuration and the space coordinates of the first wall in the tokamak design, establish the complete 3D structure of the 3D calculation model of radiation heat transfer, and according to the complete 3D structure loop Symmetry, select the minimum repeating structure as the three-dimensional structure used in the calculation;

The radiation heat transfer calculation is discrete based on the finite element method, and the radiation heat transfer calculation formula adopts the Stephen-Boltzmann law, and the radiation emission power E expression is:

E=σT ⁴

where σ is the Boltzmann constant;

According to heat balance, the radiation heat flux distribution q _r of the first wall is the total incident radiation heat flux G minus the total diffuse reflection heat flux J=ρ _d G+E(T ₀ ) and the total specular reflection heat flux ρ _s G at the corresponding point, where ρ _d is the diffuse reflection coefficient, ρ _s is the specular reflection coefficient, and ε=1-(ρ _d +ρ _s ), the final expression is:

q _r ＝G-(J+ρ _s G)＝ε(E(T)-E(T ₀ ))

In the formula: E(T) is the radiation emission power of the plasma, E(T ₀ ) is the radiation emission power of the first wall; in the expression, the allowable temperature T ₀ of the first wall material is selected as the temperature of the first wall, and the spatial distance and the surface The normal angle is obtained from the coordinates of the three-dimensional structure, and the plasma temperature T is an unknown quantity. The iterative method is used to iteratively calculate the plasma temperature T until the average value of q _r calculated by all coordinates of the three-dimensional structure is equal to Q ₀ . The radiation heat flux distribution q _r of the first wall at time is taken as the model calculation result;

Step 2, establish a three-dimensional calculation model of charged particle heat flux: the three-dimensional calculation model of charged particle heat flux adopts the same three-dimensional structure as step 1; the calculation of charged particle heat flux adopts the finite element method for discretization, firstly, the spatial distribution B of the magnetic field is known, and the three-dimensional structure is selected The direction of the magnetic field at each calculation point in is taken as the direction of the charged particles at its coordinates. If the magnetic field is a tokamak coordinate, the Cartesian coordinates are substituted for the magnetic field tokamak coordinates, and the expression is:

Since the magnetic field has circumferential uniformity, B(r, phi, z) = B(r, z), B(r, phi, z) is the magnetic field that changes with the coordinates of the tokamak, and B(r, z) is the The axisymmetric magnetic field of the tokamak coordinate change; the parallel heat flux q of the magnetic field adopts the exponential decay model, and the expression is:

Where q is the heat flux parallel to the magnetic field, q ₀ is the heat flux parallel to the last closed magnetic force line, d is the spatial distance between the calculation point and the outermost closed magnetic surface, and λ _q is the attenuation length under working conditions;

Then the heat flux q _b of charged particles on the first wall is:

Where n is the normal vector of the calculation point, n _x , _ny , and _nz are the components of the normal vector of the calculation point in the Cartesian coordinate system, B _phi , B _r , and B _z are the magnetic field spatial distribution B in the tokamak coordinate system The lower component, at this time q _b is the model calculation result.

Compared with the prior art, the present invention has the following advantages:

1. The present invention provides a complete and effective calculation method for the heat flux of the first wall of the Tokamak fusion reactor, which considers the influence of the relative angle and distance from the first wall to the plasma in the three-dimensional space on the heat flux, and considers the influence of the magnetic field distribution on the heat flux The influence of density takes into account the radiation heat transfer between the first walls, and the calculation of the spatial distribution of the heat flux density of the first wall has higher accuracy, which reduces the input error of the first wall heat transfer and structure calculation.

2. The present invention provides a unified calculation method for radiation heat flux density and charged particle heat flux density, which reduces the design cost.

3. The present invention has short design process, high efficiency, and strong operability of calculation modularization, which greatly shortens the time of analysis and design.

Description of drawings

Fig. 1 is a schematic diagram of a method for calculating the heat flux density of the first wall of a tokamak fusion reactor.

Figure 2 is the first wall and plasma model.

Figure 3 shows the calculation results of radiation heat flux.

Figure 4 shows the calculation results of the charged particle heat flux.

Detailed ways

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 It is a part of embodiments of the present invention, but not all embodiments. Based on the embodiments of the present invention, all other embodiments obtained by persons of ordinary skill in the art without creative efforts fall within the protection scope of the present invention.

The invention discloses a method for calculating the heat flux density of the first wall of a tokamak fusion reactor. The method is based on the plasma configuration, the spatial distribution of the magnetic field and the spatial distribution of the first wall, and respectively establishes a three-dimensional calculation model of radiation heat transfer according to the source of the heat flux density of the first wall. and a three-dimensional calculation model of charged particle heat flux;

The three-dimensional calculation model of radiation heat transfer refers to the conservative average heat flux of the Tokamak fusion reactor engineering design, iteratively calculates the plasma temperature, and finally obtains the radiation heat flux distribution of the first wall when the average heat flux is consistent;

The three-dimensional calculation model of the charged particle heat flux density establishes the spatial projection of the charged particles on the first wall according to the plasma configuration and the spatial distribution of the magnetic field, and considers the attenuation of the charged particles outside the outermost closed magnetic surface, and finally obtains the charged particle heat flux on the first wall density distribution;

When performing calculations, the following parameters need to be known or can be preliminarily obtained: allowable temperature T0 of the first wall material, radiance ε of the first wall material, space coordinates of the outermost closed magnetic surface of the plasma configuration under calculation conditions, and the first wall The design structure and space coordinates, the design conservative average heat flux Q ₀ of the first wall of the fusion reactor, the spatial distribution of the magnetic field B, the decay length λ _q under working conditions, and the final closed magnetic flux parallel heat flux q ₀ .

The calculation object of this method is shown in Figure 2, which is established according to the known first wall structure of the tokamak fusion reactor and the coordinates of the outermost closed magnetic surface of the plasma, including the first wall 1 and the plasma 2; where the first wall 1 is The first wall of the Mark fusion reactor vacuum chamber is arranged according to the design of the Tokamak fusion reactor, and the plasma 2 is the outermost closed magnetic surface of the configuration under the calculation condition;

The inventive method step is as shown in Figure 1:

Step 1, establish the 3D calculation model of radiation heat transfer: according to the space coordinates of the outermost closed magnetic surface of the plasma configuration and the space coordinates of the first wall in the tokamak design, establish the complete 3D structure of the 3D calculation model of radiation heat transfer, and according to the complete 3D structure loop Toward symmetry, select the minimum repeating structure as the three-dimensional structure used in the calculation, the structure is shown in Figure 2;

The radiation heat transfer calculation is discrete based on the finite element method, and the radiation heat transfer calculation formula adopts the Stephen-Boltzmann law, and the radiation emission power E expression is:

E=σT ⁴

where σ is the Boltzmann constant;

According to heat balance, the radiation heat flux distribution q _r of the first wall is the total incident radiation heat flux G minus the total diffuse reflection heat flux J=ρ _d G+E(T ₀ ) and the total specular reflection heat flux ρ _s G at the corresponding point, where ρ _d is the diffuse reflection coefficient, ρ _s is the specular reflection coefficient, and ε=1-(ρ _d +ρ _s ), the final expression is:

q _r ＝G-(J+ρ _s G)＝ε(E(T)-E(T ₀ ))

In the formula: E(T) is the radiation emission power of the plasma, E(T ₀ ) is the radiation emission power of the first wall; in the expression, the allowable temperature T ₀ of the first wall material is selected as the temperature of the first wall, and the spatial distance and the surface The normal angle is obtained from the coordinates of the three-dimensional structure, and the plasma temperature T is an unknown quantity. The iterative method is used to iteratively calculate the plasma temperature T until the average value of q _r calculated by all coordinates of the three-dimensional structure is equal to Q ₀ . The first wall radiative heat flux distribution q _r is taken as the calculation result of the model, as shown in Figure 3, the spatial distribution of the first wall radiative heat flux can be obtained from the figure, and its value varies with the coordinate change. Using the average value of radiation heat flux as the thermal boundary, the refined results calculated by the present invention are more accurate and conservative, which reduces calculation errors and improves safety.

Step 2, establish a three-dimensional calculation model of charged particle heat flux: the three-dimensional calculation model of charged particle heat flux adopts the same three-dimensional structure as in step 1; the calculation of charged particle heat flux adopts the finite element method for discretization, firstly, the spatial distribution of the magnetic field B is known, usually recorded as The tokamak coordinates are represented by three sets of data in the radial direction, the circumferential direction, and the polar direction in each coordinate system. The magnetic field direction of each calculation point in the three-dimensional structure is selected as the direction of the charged particles at its coordinates, and the magnetic field tokamak coordinates are calculated. Carr coordinate substitution, the expression is:

Since the magnetic field has circumferential uniformity, B(r, phi, z) = B(r, z), B(r, phi, z) is the magnetic field that changes with the coordinates of the tokamak, and B(r, z) is the The axisymmetric magnetic field of the tokamak coordinate change; the parallel heat flux q of the magnetic field adopts the exponential decay model, and the expression is:

Where q is the heat flux parallel to the magnetic field, q ₀ is the heat flux parallel to the last closed magnetic force line, d is the spatial distance between the calculation point and the outermost closed magnetic surface, and λ _q is the attenuation length under working conditions;

Then the heat flux q _b of charged particles on the first wall is:

Where n is the normal vector of the calculation point, n _x , _ny , and _nz are the components of the normal vector of the calculation point in the Cartesian coordinate system, B _phi , B _r , and B _z are the magnetic field spatial distribution B in the tokamak coordinate system The lower component, at this time q _b is the calculation result of the model, as shown in Figure 4. From the figure, we can get the distribution of the heat flux of charged particles on the first wall considering the direction of the magnetic field and the angle between the first wall and the attenuation. It can be seen that The influence of the included angle and distance on the calculation results, the results are more accurate and efficient, the calculation error is reduced, and the efficiency and safety are improved.

Claims (2)

1. A calculation method for the heat flux density of a first wall of a Tokamak fusion reactor is characterized by comprising the following steps of: the method is based on plasma configuration, magnetic field spatial distribution and first wall spatial distribution, and a radiation heat exchange three-dimensional calculation model and a charged particle heat flux density three-dimensional calculation model are respectively built according to a first wall heat flux density source;

the radiation heat exchange three-dimensional calculation model refers to the conservative average heat flux density of the Tokamak fusion reactor engineering design, iterative calculation is carried out on the plasma temperature, and finally the first wall radiation heat flux density distribution when the average heat flux density is consistent is obtained;

the three-dimensional calculation model of the heat flux density of the charged particles establishes the space projection of the charged particles on the first wall according to the plasma configuration and the magnetic field space distribution, and considers the attenuation of the charged particles outside the outermost closed magnetic surface to finally obtain the heat flux density distribution of the charged particles on the first wall;

the method calculates the object to include the first wall (1), plasma (2); the first wall (1) is arranged according to the design of the tokamak fusion reactor, and the plasma (2) is the outermost closed magnetic surface of the configuration under the working condition;

in performing the calculations, the following parameters need to be known or can be obtained initially: first wall material allowable temperature T ₀ Calculating the radiation epsilon of the first wall material, calculating the spatial coordinate of the outermost closed magnetic surface of the plasma configuration under the working condition, the design structure and the spatial coordinate of the first wall, and the design conservation average heat flow density Q of the first wall of the fusion reactor ₀ The magnetic field space distribution B and the attenuation length lambda under the working condition _q And finally closing the magnetic force line parallel heat flow density q ₀ 。

2. The method for calculating the heat flux density of the first wall of the tokamak fusion reactor according to claim 1, wherein the method comprises the following steps: the method comprises the following steps:

step 1, establishing a radiation heat exchange three-dimensional calculation model: establishing a complete three-dimensional structure of a radiation heat exchange three-dimensional calculation model according to the space coordinates of the outermost closed magnetic surface of the plasma configuration and the space coordinates of the first wall in the Tokamak design, and selecting the minimum repeated structure as a three-dimensional structure for calculation according to the circumferential symmetry of the complete three-dimensional structure;

the radiation heat exchange calculation is based on the finite element method, the radiation heat exchange calculation formula adopts the Stefan-Boltzmann law, and the radiation emission power E expression is as follows:

E＝σT ⁴

wherein σ is the boltzmann constant;

according to the heat balance, the first wall radiates the heat flux density distribution q _r Subtracting the total diffuse reflected heat flux density j=ρ from the total incident radiant heat flux density G for the corresponding point _d G+E(T ₀ ) And total specular heat flux density ρ _s G, where ρ _d Is the diffuse reflection coefficient ρ _s Is a specular reflection coefficient and has epsilon=1- (ρ) _d +ρ _s ) The final expression is:

q _r ＝G-(J+ρ _s G)＝ε(E(T)-E(T ₀ ))

wherein: e (T) is the radiation emission power of plasma, E (T) ₀ ) Radiating an emission power for the first wall; the allowable temperature T of the first wall material is selected in the expression ₀ As the first wall temperature, the space distance and the surface normal angle are obtained by three-dimensional structure coordinates, the plasma temperature T is unknown, and iterative calculation is carried out on the plasma temperature T by using an iterative method until q is obtained by calculating all coordinates of the three-dimensional structure _r Average value of (1) and Q ₀ Equally, the first wall radiation heat flow density distribution q at this time is selected _r As a model calculation result;

step 2, establishing a three-dimensional calculation model of the heat flux density of the charged particles: the three-dimensional calculation model of the heat flux density of the charged particles adopts the same three-dimensional structure as that of the step 1; the method comprises the steps of performing dispersion on the heat flux density of charged particles by adopting a finite element method, firstly knowing the spatial distribution B of a magnetic field, selecting the magnetic field direction of each calculated point in a three-dimensional structure as the charged particle direction at the coordinate position of the calculated point, and performing Cartesian coordinate substitution on the Tokamak coordinate of the magnetic field if the magnetic field is the Tokamak coordinate, wherein the expression is as follows:

since the magnetic field has circumferential uniformity, B (r, phi, z) =b (r, z), B (r, phi, z) is a magnetic field that varies with tokamak coordinates, and B (r, z) is an axisymmetric magnetic field that varies with tokamak coordinates; the parallel heat flux density q of the magnetic field adopts an exponential decay model, and the expression is:

wherein q is the magnetic field parallel heat flux density, q ₀ Parallel heat flux density for closing magnetic force lines finallyDegree, d is the spatial distance between the calculated point and the outermost closed magnetic surface, lambda _q The attenuation length under the working condition;

the heat flux density q of the charged particles on the first wall _b The method comprises the following steps:

where n is the normal vector of the calculated points, n _x 、n _y 、n _z Respectively calculating components of normal vectors of points in a Cartesian coordinate system, B _phi 、B _r 、B _z The spatial distribution B of the magnetic field is respectively the component under the Tokamak coordinate system, q is the moment _b Results are calculated for the model.