CN110377963B - Simulation analysis method for influence of uniform magnetic field on plasma decompression effect - Google Patents
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Abstract
The invention discloses a simulation analysis method for the influence of a uniform magnetic field on a plasma decompression effect, which belongs to the field of simulation analysis methods and comprises the following steps: s1: establishing a plasma double-fluid equation set; s2: combining a plasma double-fluid equation set with a Maxwell equation set, and adding ohm's law and local thermal equilibrium state conditions to obtain a magnetic fluid equation set of the plasma; s3: establishing a plasma fluid pressure finite element model, and establishing a two-dimensional axisymmetric model in comsol software according to a magnetofluid equation set of plasma; s4: and carrying out simulation result analysis on the plasma fluid pressure finite element model. On the basis of theoretical analysis of the motion state of the plasma in the magnetic field, the invention establishes a plasma fluid pressure finite element model by applying COMSOL software, researches the influence of uniform magnetic fields with different strengths on the pressure of the cylinder wall surface, and can quickly obtain the influence of the uniform magnetic fields on the plasma decompression effect.
Description
Technical Field
The invention relates to the field of simulation analysis methods, in particular to a simulation analysis method for the influence of a uniform magnetic field on a plasma decompression effect.
Background
The characteristic of the plasma in the magnetic field depends on the size of magnetic induction intensity and the shape of magnetic lines of force, the plasma has different motion states in different magnetic field configurations, wherein the uniform magnetic field refers to a magnetic field in which the magnetic induction intensity in the axial direction and the radial direction inside the cylinder is uniform, the motion of the center of gyration of the charged particles perpendicular to the direction of the magnetic lines of force is called drift, the drift phenomenon of the plasma in these non-uniform magnetic fields can also affect the radial stress, therefore, when the charged particles move in the uniform magnetic field region in the cylinder, only the acting force of the charged particles in the external field is considered, the interaction between the charged particles and the external field is ignored, that is, the motion of the charged particles in the plasma under the action of the external magnetic field is studied, and the influence of the uniform magnetic field on the plasma decompression effect is simulated and analyzed by using a single particle motion model of the plasma in which the action of other particles on the charged particles is completely ignored, but the existing simulation analysis method is not scientific and reasonable when the influence of the uniform magnetic field on the plasma decompression effect is studied, the pressure of the uniform magnetic field on the cylinder wall surface can not be obtained from the influence of the uniform magnetic field on the plasma decompression effect.
Disclosure of Invention
The invention aims to provide a simulation analysis method for the influence of a uniform magnetic field on a plasma decompression effect so as to solve the problems in the background technology.
In order to achieve the purpose, the invention provides the following technical scheme: the simulation analysis method for the influence of the uniform magnetic field on the plasma decompression effect comprises the following steps:
s1: the plasma usually contains more than one kind of positive ions, and when the positive ions and the electrons do not reach balance, the positive ions and the electrons are considered as two different particle systems and a plasma double-fluid equation set is established;
s2: according to the mass conservation, momentum conservation and energy conservation equations of the plasma, a plasma double-fluid equation set and a Maxwell equation set are combined, and the ohm's law and the local thermal equilibrium state condition are added to obtain a magnetic fluid equation set of the plasma;
s3: establishing a plasma fluid pressure finite element model, and establishing a two-dimensional axisymmetric model in comsol software according to a magnetofluid equation set of plasma;
s4: and carrying out simulation result analysis on the plasma fluid pressure finite element model.
Preferably, the method for establishing the plasma two-fluid equation set in S1 adopts a simplified two-fluid model.
Preferably, the magnetofluid equation of the plasma in S2 is as follows:
preferably, the specific establishment method of the two-dimensional axisymmetric model in S3 is as follows:
setting the length of a fluid area to be 200mm and the width to be 15mm, enabling the fluid to enter a cylinder from the lower end and flow out from the upper end, neglecting the influence of gravity in a model, representing coils in the model by a cube, calling a magnetic field module which generates a uniform magnetic field in an AC/DC module in COMSOL software, setting a coil conductor model to be uniform and multiple turns, wherein the number of turns of each coil is 100 turns, and the sectional area of a coil lead is 10 - 6 m 2 The coil material is copper with a conductivity of 6 × 10 7 S/m, setting the solution domain as air.
Preferably, the plasma fluid model in S3 is constructed by using a plasma module and a single-phase laminar flow module, the laminar flow module of the single-phase fluid is used to analyze the motion of the plasma as the fluid, the two physical field modules are coupled by the lorentz force applied to the plasma, and the magnetic source is coupled with the plasma and the fluid by the plasma conductance coupling field in the multi-physical field for calculation.
Preferably, the method for analyzing the simulation result of the plasma fluid pressure finite element model in S4 comprises:
s401: according to the fact that the magnetic field is a constant and stable magnetic field, the magnetic field distribution is calculated firstly, the coil excitation mode is set to be current excitation, and current 10A is introduced to obtain the magnetic field distribution in the cylinder;
s402: after the uniform magnetic field is obtained, transient analysis is carried out on the plasma fluid, the fluid is set to be compressible flow with the Mach number smaller than 0.3 in the laminar flow module, and a motion equation of the fluid is obtained.
Preferably, the equation of motion of the fluid in S402 is:
preferably, the step S4 further includes calculating the change of the pressure in the axial direction and the radial direction by using the corrected non-ideal plasma pressure calculation formula in the non-thermodynamic equilibrium stationary state, so as to obtain the change of the fluid pressure in the axial direction and the radial direction of the cylinder.
Compared with the prior art, the invention has the beneficial effects that: on the basis of theoretical analysis of the motion state of the plasma in the magnetic field, the invention establishes a plasma fluid pressure finite element model by applying COMSOL software, studies the influence of uniform magnetic fields with different strengths on the pressure of the cylinder wall surface, and can easily obtain the result that the pressure reduction effect of the plasma in the uniform magnetic field is expressed as the pressure reduction on the cylinder wall and the pressure increase in the central axis area of the cylinder, when the plasma flow is stable, the pressure has smaller amplitude change along the axial direction and larger radial change.
Drawings
FIG. 1 is a flow chart of a simulation analysis method of the present invention;
FIG. 2 illustrates a two-dimensional axisymmetric model geometry in the plasma fluid pressure finite element model of the present invention;
FIG. 3 is a magnetic flux density cloud plot of the magnetic flux density distribution of the domain solved by the simulation model of the present invention;
FIG. 4 is a magnetic force line distribution diagram of the magnetic flux density distribution in the domain solved by the simulation model of the present invention;
FIG. 5 is a graph of magnetic induction variation along an axis and along an axis of a radius variation curve for a simulation model of the present invention;
FIG. 6 is a graph of the magnetic induction along the axis and the variation along the radius of the magnetic induction variation curve for a simulation model of the present invention;
FIG. 7 is an electron density profile of a fluid at various times in accordance with the present invention;
FIG. 8 is a graph of the mass fraction of argon ions for the present invention;
FIG. 9 is a graph showing the axial and radial changes in plasma pressure according to the present invention;
FIG. 11 is a graph of the fluid pressure profile of the present invention with different magnetic induction as the fluid pressure varies axially and radially along the cylinder.
Detailed Description
The technical solutions in the embodiments of the present invention will be clearly and completely described below, 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 obtained by a person skilled in the art without making any creative effort based on the embodiments in the present invention, belong to the protection scope of the present invention.
Example one
Referring to fig. 1, the present invention provides a technical solution: the simulation analysis method for the influence of the uniform magnetic field on the plasma decompression effect comprises the following steps:
s1: the plasma usually contains more than one kind of positive ions, and when the positive ions and the electrons do not reach balance, the positive ions and the electrons are considered as two different particle systems and a plasma double-fluid equation set is established;
in the formula
angle alpha-represents a different positive ion or electron,
q-is the exchange of thermal energy caused by the collision of different types of ions,
because the plasma satisfies quasi-electroneutrality, the ion charge number is considered to be equal to the electron charge number, and in order to reduce the calculation difficulty and simplify the model, the fields generated by the charge and the current of the plasma are not considered, and the following assumptions are made:
ρ＝n i m i +n e m e ≈n(m i +m e )
rho-the reduction density of the alloy,
s2: according to the mass conservation, momentum conservation and energy conservation equations of the plasma, a plasma double-fluid equation set and a Maxwell equation set are combined, ohm's law and local thermal equilibrium state conditions are added to obtain a magnetic fluid equation set of the plasma, and the equation sets can be simplified as follows:
the equation set of the formula comprises mass conservation, momentum conservation and energy conservation equations of the plasma, the formula is combined with a Maxwell equation set, and ohm's law and local thermal equilibrium state conditions are added to finally obtain a magnetofluid equation set of the plasma:
s3: constructing a plasma fluid pressure finite element model, please refer to fig. 2, establishing a two-dimensional axisymmetric model in COMSOL software according to a magnetofluid equation set of plasma, as shown in fig. 2, wherein r =0 is a symmetric axis, a fluid region is 200mm long and 15mm wide, fluid enters a cylinder from a lower end and flows out from an upper end, the influence of gravity is ignored in the model, a coil in the model is represented by a cube, a magnetic field module (mf) which generates a uniform magnetic field in an AC/DC module in COMSOL software is called, a coil conductor model is set to be uniform multi-turn, the number of turns of each coil is 100 turns, and the sectional area of a coil lead is 10 -6 m 2 The coil material is copper with a conductivity of 6 × 10 7 S/m, a solution domain is set as air, a plasma fluid model is constructed by a plasma module (plas) and a single-phase laminar flow (spf) module together, the laminar flow module of the single-phase fluid is used for analyzing the motion of the plasma as fluid, two physical field modules are coupled by Lorentz force applied to the plasma, a magnetic source, the plasma and the fluid are coupled and calculated by a plasma conductive coupling field in a multi-physical field, wherein the ionization mechanism of argon is considered to be simple, only one-time electron excitation is usually carried out, the number of electrons is equal to that of positive ions, and a mature modeling process is provided at present, so that the plasma module adopts the ionization form of argon to generate electrons and positive ions,
s4: as shown in fig. 3 to 11, because the magnetic field is a steady magnetic field, the magnetic field distribution is calculated first, the coil excitation mode is set as current excitation, current 10A is introduced, the magnetic field distribution in the cylinder is shown in fig. 3 to 6, it can be known from the figure that the magnetic flux density change at the position of 0.05m to 0.15m in the middle area of the cylinder is small, the magnetic flux densities at the positions of 0.05m and 0.15m are both 0.0092t, the magnetic flux density at the position of 0.1m is 0.0095T, the change amplitude is 3.1%, the magnetic induction intensities of the central axis of the cylinder and the inner wall of the cylinder close to the coil are the same, which indicates that the magnetic field distribution in the cylinder is uniform distribution, after obtaining a uniform magnetic field, transient analysis is performed on the plasma fluid, a fluid is set in a laminar flow (spf) module as a compressible flow with a mach number smaller than 0.3, and at this time, the equation of motion of the fluid in the formula becomes:
wherein F is Lorentz force of the fluid unit under the action of magnetic field, the magnetic field is generated by the motion of the energized coil and the plasma fluid together, the fluid flow mass flow SCCM is set to be 10mL/min, and the initial electron density of the plasma is 10 20 m -3 The initial electron temperature is 10eV, and the ambient pressure is 1[ Torr ]]Since the steady state magnetic field has been calculated, the transient fluid flow is directly calculated, as shown in fig. 7-9, to obtain the electron density distribution of the fluid at different times, and it can be seen from the figure that as time increases, the electron density of the plasma fluid gradually decreases, the high electron density region of the fluid gradually gathers in the middle of the cylinder, the electron density near the cylinder wall is minimal, and the magnetic field has no effect on the neutral argon atoms, while the Ars ions and Ar ions + The ion distribution rule is similar to that of electrons, the ions are mainly concentrated in the area near the central axis, and then a corrected non-ideal plasma pressure calculation formula of a non-thermodynamic equilibrium stationary state is adopted:
when the temperature of the individual particles is isotropic but not equal:
in the formula m i Is the mass of the ith particle, k is the Boltzmann constant, q i Is the charge amount of the ith particle,
when the respective particles are at equal temperatures, i.e. in thermodynamic equilibrium:
the change of the pressure in the axial direction and the radial direction is calculated by the above formula, the change condition of the fluid pressure along the axial direction and the radial direction of the cylinder is obtained, as can be seen from fig. 10, similar to the electron distribution rule, the change amplitude of the axial pressure at the same distance is smaller, the change amplitude of the radial pressure is larger, the plasma can be contracted by the external magnetic field, like the pressure on the surface of the plasma fluid from outside to inside, according to fig. 11, the magnitude of the coil seed current is changed, the pressure distribution on the center radius of the cylinder when the magnetic induction intensity in the calculation domain is corresponding to 0.01T, 0.05T and 0.1T, the electron density is increased along with the increase of the magnetic induction intensity, and the pressure reduction effect can be improved by the enhancement of the magnetic field.
On the basis of theoretical analysis of the motion state of the plasma in the magnetic field, COMSOL software is used for establishing a plasma fluid pressure finite element model, the influence of uniform magnetic fields with different strengths on the pressure of the wall surface of the cylinder is researched, the pressure reduction effect of the plasma in the uniform magnetic field is expressed as the pressure reduction on the wall of the cylinder and the pressure increase in the central axis area of the cylinder, and when the flow of the plasma is stable, the pressure has small amplitude change along the axial direction and large radial change.
Although embodiments of the present invention have been shown and described, it will be appreciated by those skilled in the art that changes, modifications, substitutions and alterations can be made in these embodiments without departing from the principles and spirit of the invention, the scope of which is defined in the appended claims and their equivalents.
Claims (7)
1. The simulation analysis method for the influence of the uniform magnetic field on the plasma decompression effect is characterized by comprising the following steps of:
s1: the plasma usually contains more than one kind of positive ions, and when the positive ions and the electrons do not reach balance, the positive ions and the electrons are considered as two different particle systems and a plasma double-fluid equation set is established;
s2: according to the mass conservation, momentum conservation and energy conservation equations of the plasma, a plasma double-fluid equation set and a Maxwell equation set are combined, and the ohm's law and the local thermal equilibrium state condition are added to obtain a magnetic fluid equation set of the plasma;
s3: establishing a plasma fluid pressure finite element model, and establishing a two-dimensional axisymmetric model in comsol software according to a magnetofluid equation set of plasma;
s4: carrying out simulation result analysis on the plasma fluid pressure finite element model;
the method for analyzing the simulation result of the plasma fluid pressure finite element model in the S4 comprises the following steps:
s401: according to the fact that the magnetic field is a constant and stable magnetic field, the magnetic field distribution is calculated firstly, the coil excitation mode is set to be current excitation, and current 10A is introduced to obtain the magnetic field distribution in the cylinder;
s402: after the uniform magnetic field is obtained, transient analysis is carried out on the plasma fluid, the fluid is set to be compressible flow with the Mach number smaller than 0.3 in the laminar flow module, and a motion equation of the fluid is obtained.
2. The method for simulation analysis of the influence of the uniform magnetic field on the plasma decompression effect according to claim 1, wherein: and establishing a plasma double-fluid equation set in the S1 by adopting a method of simplifying a double-fluid model.
3. The method for simulation analysis of the influence of the uniform magnetic field on the plasma decompression effect according to claim 1, wherein: the magnetofluid equation set of the plasma in the S2 is as follows:
4. the method for simulation analysis of the influence of the uniform magnetic field on the plasma decompression effect according to claim 1, wherein: the specific establishment method of the two-dimensional axisymmetric model in the S3 comprises the following steps:
setting the length of a fluid area to be 200mm and the width to be 15mm, enabling the fluid to enter a cylinder from the lower end and flow out from the upper end, neglecting the influence of gravity in a model, representing coils in the model by a cube, calling a magnetic field module which generates a uniform magnetic field in an AC/DC module in COMSOL software, setting a coil conductor model to be uniform and multiple turns, wherein the number of turns of each coil is 100 turns, and the sectional area of a coil lead is 10 -6 m 2 The coil material is copper with a conductivity of 6 × 10 7 S/m, setting the solution domain as air.
5. The method for simulation analysis of the influence of the uniform magnetic field on the plasma decompression effect according to claim 1, wherein: the plasma fluid pressure finite element model in the S3 is constructed by adopting a plasma module and a single-phase laminar flow module together, the laminar flow module of the single-phase fluid is used for analyzing the motion of the plasma serving as the fluid, the two physical field modules are coupled through Lorentz force applied to the plasma, and the magnetic source, the plasma and the fluid are coupled and calculated through a plasma conductive coupling field in a multi-physical field.
6. The method for simulation analysis of the influence of the uniform magnetic field on the plasma decompression effect according to claim 1, wherein: the motion equation of the fluid in S402 is:
7. the method for simulation analysis of the influence of the uniform magnetic field on the plasma decompression effect according to claim 1, wherein: and S4, calculating the change of the pressure in the axial direction and the radial direction by adopting a corrected non-ideal plasma pressure calculation formula in a non-thermodynamic equilibrium stationary state to obtain the change of the fluid pressure in the axial direction and the radial direction of the cylinder, wherein the calculation formula is as follows: when the temperature of the individual particles is isotropic but not equal:
in the formula m i Is the mass of the ith particle, k is the Boltzmann constant, q i Is the charge amount of the ith particle,
when the temperatures of the particles are equal, i.e. in thermodynamic equilibrium:
and calculating the change of the pressure in the axial direction and the radial direction by the above formula to obtain the change condition of the fluid pressure in the axial direction and the radial direction of the cylinder.
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