CN113158520B - Fuel ice layer interface tracking simulation method for freezing target system - Google Patents

Fuel ice layer interface tracking simulation method for freezing target system Download PDF

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CN113158520B
CN113158520B CN202110384783.8A CN202110384783A CN113158520B CN 113158520 B CN113158520 B CN 113158520B CN 202110384783 A CN202110384783 A CN 202110384783A CN 113158520 B CN113158520 B CN 113158520B
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厉彦忠
郭富城
李翠
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Xian Jiaotong University
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Abstract

A fuel ice layer interface tracking simulation method for a freezing target system is characterized in that an Euler coordinate system and a Lagrange coordinate system are combined, data transfer between the two coordinate systems is completed through Gaussian kernel function estimation, a heat conduction differential equation is reconstructed by combining a Stefan equation, tracking calculation of a fuel ice layer interface is completed, profile distribution of a solid fuel ice layer in fuel target pellets in the freezing target system under different boundary loads is obtained, and requirements of low mode roughness of ice layer uniformity ignition being less than 0.5 mu m, ice layer thickness being +/-3 mu m and gas density are met; the method can more intuitively and comprehensively represent the influence of the temperature field on the morphology of the fuel ice layer in the target pellet and provide theoretical technical guidance for experiments.

Description

Fuel ice layer interface tracking simulation method for freezing target system
Technical Field
The invention belongs to the technical field of design simulation of a freezing target system, and particularly relates to a fuel ice layer interface tracking simulation method for the freezing target system.
Background
The inertial confinement nuclear fusion is to irradiate the surface of the frozen target pellet with laser uniformly so as to achieve the ignition condition of high temperature and high density and realize the fusion reaction. In order to meet the ignition requirement and avoid Rayleigh-Taylor instability, the thickness uniformity of a deuterium-deuterium fuel ice layer in a target pellet needs to be more than 99 percent, and the root-mean-square roughness of the inner surface of the fuel ice layer needs to be less than 1 mu m. The low mode roughness of the fuel ice layer is mainly determined by the temperature field around the target pellet, and therefore the importance of the control of the temperature field of the frozen target is particularly prominent.
At present, the uniformity of the fuel ice layer is mainly characterized by an experimental mode, and specific characterization methods comprise LED backlight characterization and X-ray phase contrast imaging characterization. Since the fuel ice layer profile within the target pellet can only be observed in a specific direction (north-south dipolar direction, equatorial direction), a large amount of information on the fuel ice layer profile is masked. In order to more intuitively and comprehensively characterize the influence of a temperature field on the morphology of a fuel ice layer in a target pellet and provide theoretical technical guidance for experiments, a fuel ice layer interface tracking simulation method for a freezing target system needs to be established urgently.
Disclosure of Invention
In order to overcome the defects of the prior art, the invention aims to provide a fuel ice layer interface tracking simulation method for a freezing target system, which can more intuitively and comprehensively represent the influence of a temperature field on the appearance of a fuel ice layer in a target pellet and provide theoretical technical guidance for experiments.
In order to achieve the purpose, the invention adopts the technical scheme that:
a tracking simulation method for a fuel ice layer interface in a freezing target system is characterized in that an Euler coordinate system and a Lagrange coordinate system are combined, data transfer between the two coordinate systems is completed through Gaussian kernel function estimation, a heat conduction differential equation is reconstructed by combining a Stefan equation, tracking calculation of the fuel ice layer interface is completed, profile distribution of a solid fuel ice layer in fuel target pellets in the freezing target system under different boundary loads is obtained, and requirements of low mode roughness of ice layer uniformity ignition being less than 0.5 mu m, ice layer thickness being +/-3 mu m and gas density are met.
A method for simulating fuel ice layer interface tracking in a freeze target system, comprising the steps of:
(1) Setting the initial morphology of the fuel ice layer, the temperature distribution of the outer surface of the target pellet and the density parameter of the fuel gas;
(2) Calculating t m The actual volume of the fuel ice layer in the grid of the Euler coordinate system at the moment is beta:
assuming that the arrangement of the fuel ice layer contour particles within a single Euler grid is approximately a straight line, β is expressed as:
Figure BDA0003014352420000021
wherein, deltax, delay and Delaz are the grid sizes in the directions of x, y and z respectively, and the central point of the target pill is arranged as
Figure BDA0003014352420000022
The position coordinate of the central point of the Euler grid is
Figure BDA0003014352420000023
The mean position vector of all fuel ice layer profile particles in a single Euler grid;
(3) Obtaining the corresponding saturation state temperature according to the density of the fuel gas, and loading the saturation state temperature to the boundary of the inner surface of the fuel ice layer;
(4) Calculating t m Temperature field distribution under the time Euler coordinate system:
considering the interface temperature of the fuel ice layer to be uniform at each moment, wherein the value of the interface temperature is equal to the phase change saturation temperature corresponding to the density of the fuel gas at the moment; meanwhile, equivalent treatment is carried out on the fuel gas as a solid, under an Euler coordinate, only a temperature field of a solid domain needs to be solved, and the adopted control equation is an unsteady state heat conduction equation:
Figure BDA0003014352420000031
where T is the temperature, T is the time, α eff For the equivalent thermal diffusivity, the expression is as follows:
Figure BDA0003014352420000032
where k is the thermal conductivity, ρ is the density, c p Constant pressure heat capacity;
(5) According to the temperature field distribution and the Stefan equation, calculating t under the Euler coordinate system m The normal displacement speed of the fuel ice layer interface at the moment:
the solution of the normal moving speed of the interface of the fuel ice layer is based on a Stefan equation, and the form of the Stefan equation is as follows:
Figure BDA0003014352420000033
where v is the normal moving velocity, Δ H is the latent heat, subscript ice denotes the fuel solid, gas denotes the fuel gas;
(6) Calculating t under a Lagrange coordinate system through Gaussian kernel function estimation m Normal displacement speed of profile particles of different fuel ice layers at different moments:
according to the distribution condition of each fuel ice layer profile particle in an Euler grid, determining the velocity of each particle by a kernel function estimation method, wherein the kernel function is a Gaussian function and has the form:
Figure BDA0003014352420000041
wherein b is taken as the average size of the grid, i.e. b = (Δ x + Δ y + Δ z)/3, Δ x, Δ y and Δ z are the grid sizes in the x, y and z directions, respectively;
if t m The position coordinate of the contour particle of the s th fuel ice layer at the moment is
Figure BDA0003014352420000042
The position coordinate of the central point of the Euler grid is
Figure BDA0003014352420000043
The normal moving speed of the profile of the fuel ice layer obtained by calculation of the Euler grid is v i,j,k That t m At the time of the normal direction of the profile pointThe moving speed is as follows:
Figure BDA0003014352420000044
(7) Calculating t m+1 Position vector of the fuel ice layer profile particle at time:
fuel ice layer profile particle at t m After the determination of the normal displacement speed at the moment, it is at t m+1 The position vector of the time is:
Figure BDA0003014352420000045
(8) According to t m+1 Calculating t from the position vector of the profile particle of the fuel ice layer at the moment m+1 The mass of the fuel ice layer at the moment of time, thereby obtaining t m+1 The time-of-day fuel gas density; meanwhile, calculating the actual volume ratio beta of the fuel ice layer in the grid of the Euler coordinate system through Gaussian kernel function estimation;
the density of the fuel gas is indirectly obtained by the volume change of the fuel ice layer, the total number of the profile particles of the fuel ice layer is recorded as N, the radius of the inner surface of the target pellet is recorded as R, and the central point of the target pellet is positioned as
Figure BDA0003014352420000047
Then t m The mass of the fuel ice layer at the moment is:
Figure BDA0003014352420000046
the mass of the fuel ice layer and the fuel gas at the initial time is recorded as m ice (0) And m gas (0) Then t is m The fuel gas density at that time is:
Figure BDA0003014352420000051
(9) Returning to the step (2), calculating the next moment until the morphology of the fuel ice layer is basically unchanged or the next moment is calculated to the specified moment, and ending the calculation; the profile distribution of the solid fuel ice layer in the fuel target pellets in the freezing target system under different boundary loads is obtained, and the requirements of low mode roughness of ice layer uniformity ignition being less than 0.5 mu m, ice layer thickness being +/-3 mu m and gas density are met.
In the step (1), the temperature distribution of the outer surface of the target pill is in a distribution trend of high temperature in the north and south and low temperature in the equator.
And (2) the initial appearance of the fuel ice layer in the step (1) is characterized by the profile particles of the fuel ice layer in a Lagrange coordinate system.
In the step (3), because the target pellet has a small size, the time constant of thermal diffusion is compared with the calculated time step length to be a small amount, and the temperature of the fuel gas in the target pellet is considered to be equal everywhere.
In the step (3), the fuel gas in the target pellet is considered to be in a phase-change saturation state all the time.
In the step (8), the temperature of the fuel gas in the saturation state is found by the NIST REFPROP database under the premise that the density of the fuel gas in the saturation state is known.
The invention has the beneficial effects that:
the invention discloses a fuel ice layer interface tracking simulation method for a freezing target system, which can calculate the outline migration condition of an ice layer in a target pellet according to different thermal boundary loads and solve the problem that the appearance of the ice layer cannot be completely observed and the uniformity of the ice layer cannot be evaluated in an experiment. By the method, the uniformity of the ice layer in the target pellet under different thermal boundary loads can be measured, a set of control flow of the freezing target temperature field can be reversely provided, and clear theoretical guidance is provided for experiments.
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Fig. 1 is a schematic view of a target pellet structure according to an embodiment of the present invention.
FIG. 2 is a flow chart of the method of the present invention.
Fig. 3 is a calculation result of the embodiment of the present invention.
Detailed Description
The technical solutions of the present invention are described below clearly and completely with reference to the following embodiments, and it is obvious that the described embodiments are only a part of the embodiments of the present invention, and not all embodiments. All other embodiments, which can be derived by a person skilled in the art from the embodiments given herein without making any creative effort, shall fall within the protection scope of the present invention.
The target pellet of this embodiment has a structure as shown in fig. 1, the outermost CH target shell 1, an outer diameter of 1.1mm and an inner diameter of 0.91mm is attached to the inner side of the CH target shell 1, a solid fuel ice layer 2 with a thickness of 68 μm is attached to the inner side of the CH target shell 1, and a fuel gas cavity 3 is provided in the center of the target pellet.
Referring to fig. 2, a method for fuel ice layer interface tracking simulation in a freezing target system includes the steps of:
(1) Setting the initial morphology of the fuel ice layer, the temperature distribution of the outer surface of the target pellet and the density parameter of the fuel gas;
setting the initial morphology of the fuel ice layer to be uniform distribution, setting the temperature distribution of the outer surface of the target pellet to be 18.05K at the north and south poles and 18.00K at the equator, and performing linear transition, wherein the temperature distribution of the outer surface of the target pellet is the distribution trend that the north and south poles are high and the equator is low; the initial appearance of the fuel ice layer is characterized by the profile particles of the fuel ice layer of a Lagrange coordinate system;
(2) Calculating t m The actual volume ratio beta of the fuel ice layer in the grid of the Euler coordinate system at the moment;
at known t m On the premise of position vector of contour particles of fuel ice layer at moment, t is obtained m The actual volume ratio beta of the fuel ice layer in the Euler grid of the fuel ice layer interface exists at any moment; assuming that the arrangement of the fuel ice layer contour particles within a single Euler grid is approximately a straight line, β is expressed as:
Figure BDA0003014352420000071
wherein, deltax, delay and Delaz are the grid sizes in the directions of x, y and z respectively, and the central point of the target pill is arranged as
Figure BDA0003014352420000072
Euler gridThe position coordinate of the central point is
Figure BDA0003014352420000073
The mean position vector of all fuel ice layer profile particles in a single Euler grid; for a non-interface euler grid, β =1 indicates that all fuel ice layers are in the euler grid, and β =0 indicates that all fuel gas is in the euler grid;
(3) Obtaining the corresponding saturation state temperature according to the density of the fuel gas, and loading the saturation state temperature to the boundary of the inner surface of the fuel ice layer; considering that the fuel gas in the target pellet is always in a phase-change saturation state;
(4) Calculating t m Distributing the temperature field under the Euler coordinate system at the moment;
because the fuel gas has no pressure and temperature gradient, the interface temperature of the fuel ice layer can be considered to be uniform at each moment, and the value of the interface temperature is equal to the phase change saturation temperature corresponding to the density of the fuel gas at the moment; meanwhile, the fuel gas is treated equivalently as a solid, so that the calculation requirement is reduced, therefore, under the Euler coordinate, only the temperature field of the solid domain needs to be solved, and the adopted control equation is an unsteady state heat conduction equation:
Figure BDA0003014352420000074
where T is the temperature, T is the time, α eff For the equivalent thermal diffusivity, the expression is as follows:
Figure BDA0003014352420000081
where k is the thermal conductivity, ρ is the density, c p Constant pressure heat capacity;
(5) According to the temperature field distribution and the Stefan equation, calculating t under the Euler coordinate system m The normal displacement speed of the interface of the fuel ice layer at any moment;
the solution of the normal moving speed of the interface of the fuel ice layer is based on a Stefan equation, and the form of the Stefan equation is as follows:
Figure BDA0003014352420000082
where v is the normal moving velocity, Δ H is the latent heat, subscript ice denotes the fuel solid, gas denotes the fuel gas;
(6) Calculating t under a Lagrange coordinate system through Gaussian kernel function estimation m The normal displacement speeds of profile particles of different fuel ice layers at different moments;
calculating t from Stefan equation m After the normal moving speed of the fuel ice layer interface on the Euler grid node is reached, the speed of each particle is determined by a kernel function estimation method according to the distribution condition of each fuel ice layer profile particle in the Euler grid, wherein the kernel function is a Gaussian function with higher precision and has the form:
Figure BDA0003014352420000083
wherein b is taken as the average size of the grid, i.e. b = (Δ x + Δ y + Δ z)/3, Δ x, Δ y and Δ z are the grid sizes in the x, y and z directions, respectively;
if t m The position coordinate of the contour particle of the s th fuel ice layer at the moment is
Figure BDA0003014352420000084
The position coordinate of the central point of the Euler grid is
Figure BDA0003014352420000085
The normal moving speed of the profile of the fuel ice layer obtained by calculation of the Euler grid is v i,j,k That t m The normal moving speed of the profile particle at the moment is as follows:
Figure BDA0003014352420000091
(7) Calculating t m+1 The position vector of the profile particle of the fuel ice layer at the moment;
fuel ice layer profilePoint is at t m After the normal movement speed at time is determined, it is at t m+1 The position vector of the time is:
Figure BDA0003014352420000092
(8) According to t m+1 Calculating t from the position vector of the profile particle of the fuel ice layer at the moment m+1 The mass of the fuel ice layer at the moment of time, thereby obtaining t m+1 The time-of-day fuel gas density; meanwhile, calculating the actual volume ratio beta of the fuel ice layer in the grid of the Euler coordinate system through Gaussian kernel function estimation;
in the phase change process, the change of the shape of the fuel ice layer inevitably causes the change of the density of the fuel gas at the center of the target pellet, and the density of the fuel gas simultaneously determines the temperature of the inner surface of the fuel ice layer; the density of fuel gas is indirectly obtained by the volume change of the fuel ice layer, and on the premise that the thickness of the local fuel ice layer is far smaller than the inner surface radius of the target pellet, the mass of the fuel ice layer is obtained by approximating the position coordinates of the profile particles of the fuel ice layer, wherein the total number of the profile particles of the fuel ice layer is N, the inner surface radius of the target pellet is R, and the central point of the target pellet is positioned as
Figure BDA0003014352420000095
Then t m The mass of the fuel ice layer at the moment is:
Figure BDA0003014352420000093
the mass of the fuel ice layer and the fuel gas at the initial time is recorded as m ice (0) And m gas (0) Then t is m The fuel gas density at that time is:
Figure BDA0003014352420000094
on the premise of knowing the density of the fuel gas in the saturation state, the temperature of the fuel gas in the saturation state is found through a NIST REFPROP database;
(9) Returning to the step (2), calculating the next moment until 1000s, and finishing the calculation; the profile distribution of the solid fuel ice layer in the fuel target pellets in the freezing target system under different boundary loads is obtained, and the requirements of the ice layer uniformity ignition low-mode roughness less than 0.5 mu m, the ice layer thickness +/-3 mu m and the gas density are met;
the thickness distribution curves of the fuel ice layers at different moments are shown in FIG. 3, wherein 90 degrees represents the south pole, 90 degrees represents the north pole, and 0 degrees represents the equator; because the temperature of the outer surface of the target pellets is in the distribution trend of high temperature in the south and north and low temperature in the equator, the fuel ice layer in the south and north poles is gradually thinned, and the fuel ice layer in the equator is gradually thickened.

Claims (6)

1. A method for simulating fuel ice layer interface tracking in a freezing target system, comprising the steps of:
(1) Setting the initial morphology of the fuel ice layer, the temperature distribution of the outer surface of the target pellet and the density parameter of the fuel gas;
(2) Calculating t m The actual volume of the fuel ice layer in the grid of the Euler coordinate system at the moment accounts for beta:
assuming that the arrangement of the fuel ice layer contour particles within a single Euler grid is approximately a straight line, β is expressed as:
Figure FDA0003806856820000011
wherein, deltax, delay and Delaz are the grid sizes in the directions of x, y and z respectively, and the central point of the target pill is arranged as
Figure FDA0003806856820000012
The position coordinate of the central point of the Euler grid is
Figure FDA0003806856820000013
The mean position vector of all fuel ice layer profile particles in a single Euler grid;
(3) Obtaining the corresponding saturation state temperature according to the density of the fuel gas, and loading the saturation state temperature to the boundary of the inner surface of the fuel ice layer;
(4) Calculating t m Temperature field distribution under the Euler coordinate system at the moment:
considering the interface temperature of the fuel ice layer to be uniform at each moment, wherein the value of the interface temperature is equal to the phase change saturation temperature corresponding to the density of the fuel gas at the moment; meanwhile, equivalent treatment is carried out on the fuel gas as a solid, under an Euler coordinate, only a temperature field of a solid domain needs to be solved, and the adopted control equation is an unsteady state heat conduction equation:
Figure FDA0003806856820000021
where T is the temperature, T is the time, α eff For the equivalent thermal diffusivity, the expression is as follows:
Figure FDA0003806856820000022
where k is the thermal conductivity, ρ is the density, c p Constant pressure heat capacity;
(5) According to the temperature field distribution and the Stefan equation, calculating t under the Euler coordinate system m The normal displacement speed of the interface of the fuel ice layer at the moment:
the solution of the normal moving speed of the interface of the fuel ice layer is based on a Stefan equation, and the form of the Stefan equation is as follows:
Figure FDA0003806856820000023
where v is the normal moving velocity, Δ H is the latent heat, subscript ice denotes the fuel solid, gas denotes the fuel gas;
(6) Calculating t under a Lagrange coordinate system through Gaussian kernel function estimation m Normal displacement velocity of profile particles of different fuel ice layers at different times:
according to the distribution condition of each fuel ice layer profile particle in an Euler grid, determining the velocity of each particle by a kernel function estimation method, wherein the kernel function is a Gaussian function and has the form:
Figure FDA0003806856820000024
wherein b is the average size of the grid, i.e. b = (Δ x + Δ y + Δ z)/3, and Δ x, Δ y and Δ z are the grid sizes in the x, y and z directions, respectively;
if t m The position coordinate of the contour particle of the s th fuel ice layer at the moment is
Figure FDA0003806856820000025
The position coordinate of the central point of the Euler grid is
Figure FDA0003806856820000026
The normal moving speed of the profile of the fuel ice layer obtained by calculation of the Euler grid is v i,j,k That t m The normal moving speed of the profile particle at the moment is as follows:
Figure FDA0003806856820000031
(7) Calculating t m+1 Position vector of the fuel ice layer profile particle at time:
fuel ice layer profile particle at t m After the normal movement speed at time is determined, it is at t m+1 The position vector of the time is:
Figure FDA0003806856820000032
(8) According to t m+1 Calculating t from the position vector of the profile particle of the fuel ice layer at the moment m+1 The mass of the fuel ice layer at the moment of time, thereby obtaining t m+1 The time-of-day fuel gas density; meanwhile, calculating the actual volume ratio beta of the fuel ice layer in the grid of the Euler coordinate system through Gaussian kernel function estimation;
the density of fuel gas is indirectly obtained by the volume change of the fuel ice layer, the total number of contour particles of the fuel ice layer is recorded as N, the radius of the inner surface of the target pellet is recorded as R, and the central point of the target pellet is positioned as
Figure FDA0003806856820000033
Then t m The mass of the fuel ice layer at the moment is:
Figure FDA0003806856820000034
the mass of the fuel ice layer and the fuel gas at the initial time is recorded as m ice (0) And m gas (0) Then t is m The fuel gas density at that time is:
Figure FDA0003806856820000035
(9) Returning to the step (2), calculating the next moment until the morphology of the fuel ice layer is basically unchanged or the next moment is calculated to the specified moment, and ending the calculation; the profile distribution of the solid fuel ice layer in the fuel target pellets in the freezing target system under different boundary loads is obtained, and the requirements of low mode roughness of ice layer uniformity ignition less than 0.5 mu m, ice layer thickness +/-3 mu m and gas density are met.
2. The method for simulating the tracking of the fuel ice layer interface in the freezing target system according to claim 1, wherein: in the step (1), the temperature distribution of the outer surface of the target pill is in a distribution trend of high temperature in the north and south and low temperature in the equator.
3. The method for simulating the tracking of the fuel ice layer interface in the freezing target system according to claim 1, wherein: and (2) in the step (1), the initial appearance of the fuel ice layer is characterized by the profile particles of the fuel ice layer in a Lagrange coordinate system.
4. The method for simulating the tracking of the fuel ice layer interface in the freezing target system according to claim 1, wherein: in the step (3), because the target pellet has a small size, the time constant of thermal diffusion is compared with the calculated time step length to be a small amount, and the temperature of the fuel gas in the target pellet is considered to be equal everywhere.
5. The method for simulating the tracking of the fuel ice layer interface in the freezing target system according to claim 1, wherein: in the step (3), the fuel gas in the target pellet is considered to be in a phase-change saturation state all the time.
6. The method for simulating the tracking of the fuel ice layer interface in the freezing target system according to claim 1, wherein: in the step (8), the temperature of the fuel gas in the saturation state is found by the NIST REFPROP database under the premise that the density of the fuel gas in the saturation state is known.
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