A numerical analysis method for arc characteristics in the design of environmentally friendly circuit breakers

Abstract

A numerical analysis method for arc characteristics in the design of environmentally friendly circuit breakers The present invention provides a numerical analysis method for are characteristics used in the design of environmentally friendly high-voltage circuit breakers, and relates to the technical field of airflow field simulation of a high—voltage circuit breaker. The method specifically includes: calculating a particle composition of a gas are plasma system in a circuit breaker, solving equilibrium—state physical parameters of a gas are plasma system in the circuit breaker, constructing a non-equilibrium-state physical parameter calculation model by using a machine learning method according to the equilibrium-state physical parameters of the gas are plasma system in the circuit breaker, and screening the particle composition by using the model; solving steady-state results of an equilibrium-state airflow field of the gas arc plasma system in the circuit breaker, to obtain temperature, pressure, and particle number density of the gas are plasma system in the current circuit breaker; and iterating the course to obtain a final chemical non—equilibrium-state physical parameter of the gas are plasma system in the circuit breaker. The present invention reduces computational difficulty of a non-equilibrium-state airflow field by particle screening and constructing a mathematical model of physical parameters, providing reliable technical support for the design of environmentally friendly high-voltage circuit breakers.

Description

BACKGROUND OF THE INVENTION 1. Field of the Invention

[0001] The present invention relates to the technical eld of airow eld simulation for a high-voltage circuit breaker, in particular to a numerical analysis method for arc characteristics of a circuit breaker. 2. The Prior Arts

[0002] Simulation of a chemical nonequilibriumstate airow eld is an important numerical simulation method. In the design process of environmentally friendly high-voltage circuit breakers, dynamic behaviors of an arc are a key issue in evaluating, predicting, and optimizing the performance of a circuit breaker. The success or failure of breaking fault current in the highvoltage circuit breaker is closely related to arc characteristics, involving a course of medium state transition from conductivity to insulation, which includes a large number of basic scientic problems. Conducting research on simulation of the chemical nonequilibrium state airow eld ,evaluating the breaking capacity of environmentally friendly high-voltage circuit breakers, can provide reliable technical support for the design of environmentally friendly highvoltage circuit breakers and accelerate the research and development process of environmentally friendly highvoltage circuit breakers.

[0003] However, there are many difculties in establishing a chemical non-equilibrium model for the circuit breaker: (1) it is necessary to establish transportation equations for each particle in an arc area, which leads to a signicant increase in computational complexity; (2) physical quantities involved in a particle transportation equation have a large order of magnitude, for example, the magnitude of chemical reaction constants ranges from 10'25 to 1014, and number density of particles also varies from 0 to 1025 . Therefore, solving the transportation equation poses great risks and is prone to divergence due to the variables being solved not being within its physical range; and (3) a complete and consistent chemical non- equilibrium model needs to consider inuence of a particle composition on arc physical parameters under nonequilibrium conditions, and calculation of the arc physical parameters is a complex course. Not only is the modeling complex, but it is also likely to cause instability in solving multiple equations simultaneously. SUMMARY OF THE INVENTION

[0004] In response to defects in the prior art, the present invention proposes a numerical analysis method for arc characteristics of a circuit breaker by particle screening and establishing a mathematical model of physical parameters, which reduces computational difculty of non-equilibrium-state airow elds.

[0005] The present invention provides a numerical analysis method for arc characteristics of a circuit breaker, including the following steps:

[0006] Step 1: calculating a particle composition of a gas are plasma system in a circuit breaker, solving equilibriumstate physical parameters of the gas arc plasma system in the circuit breaker based on the particle composition, and constructing a non-equilibrium-state physical parameter calculation model by using a machine learning method according to the equilibrium-state physical parameters of the gas are plasma system in the circuit breaker, where the equilibrium-state physical parameters include thermodynamic parameters and arc transportation coefcients;

[0007] Step 2: calculating chemical non-equilibrium-state physical parameters of the gas arc plasma system in the circuit breaker by using the nonequilibriumstate physical parameter calculation model, and performing screening on the particle composition based on the chemical non-equilibriumstate physical parameters;

[0008] Step 3: solving steady-state results of an equilibrium-state airow eld of the gas arc plasma system in the circuit breaker;

[0009] Step 4: using the steadystate results of the equilibrium-state airow eld as initial values of the gas arc plasma system in the circuit breaker at time 0 in a non-equilibrium state, then solving a mass conservation equation, a momentum conservation equation and an energy conservation equation of a magnetic uid in a chemical nonequilibrium state according to screening results of the particle composition to obtain temperature and pressure distribution of the gas arc plasma system in the circuit breaker in the nonequilibrium state, and solving a particle transportation equation to obtain temperature, pressure, and particle number density of the gas arc plasma system in the circuit breaker;

[0010] Step 5: judging whether the temperature, the pressure, and the particle number density of the gas arc plasma system in the circuit breaker are converged, and if not, re- calculating the temperature, the pressure, and the particle number density of the gas arc plasma system in the circuit breaker by using the non-equilibriumstate physical parameter calculation model;

[0011] Step 6: determining whether a current time step reaches a preset time step, if not, using the temperature, the pressure, and the particle number density of the gas arc plasma system in the circuit breaker, calculated in the Step 5 as initial values of the temperature, the pressure, and the particle number density of the gas arc plasma system in the circuit breaker in the next time step, returning to the Step 5 until preset time step is reached, and outputting nal chemical non-equilibrium-state physical parameters of the gas are plasma system in the circuit breaker; and

[0012] Step 7: substituting the nal chemical non-equilibrium-state physical parameters of the gas arc plasma system in the circuit breaker into the Step 3 and the Step 4, to obtain distribution characteristics of temperature and pressure and change laws of arc voltage, conductivity and arc energy in an arc-extinguishing chamber of the circuit breaker;

[0013] in the Step 1, a course of solving the equilibrium-state physical parameters of the gas are plasma system in the circuit breaker according to the particle composition, includes:

[0014] Step Sl: calculating the thermodynamic parameters of the gas are plasma system in the circuit breaker, including: gas density, enthalpy, and specic heat;

[0015] Step SZ: calculating a collision integral of charged particles in the gas arc plasma system in the circuit breaker; and

[0016] Step S3: calculating the arc transportation coefcients, including a diffusion coefcient, a viscosity coefcient, thermal conductivity, and conductivity;

[0017] in the step Sl, the gas density is: N ,0 : Z "fm. / ' j=l

[0018] where p is gas density of the gas arc plasma system; N is the number of particles in the gas are plasma system; j is the jth particle in the gas arc plasma system; n_, is number density of the jth particle; m]- is mass of the jth particle;

[0019] the enthalpy is: N h = ZYjhj .]: 1 Ô ln Z _ hi Z[gktrT-l-ktrTzaTJ-l-AH / j . m .

[0020] where h is the enthalpy of the gas arc plasma system; hf is the enthalpy of the jthparticle; Yi is a distribution function of the jth particle in a six dimensional phase space; m is mass of the gas arc plasma system; k" is translational thermal conductivity; T is temperature; Zi is an internal partition function of the jthparticle; A H]- is a formation enthalpy of the jth particle;

[0021] the specic heat is: äh ôT P cp +)

[0022] where CP is the specic heat; and P is pressure;

[0023] in the step S2, the collision integral is: r k T °° s+ af; = lf ex75»; pggm ij 0 Q?)

[0024] where "1 represents a (I, S) order collision integral of interaction between the ith particle and the jth particle in the gas arc plasma system; ] represents the type of the collision integral; s represents the order of the collision integral; kB represents a Boltzmann constant; u represents reduced mass of interaction between the ith particle and the jthparticle; 77 represents reduced initial velocity of the interaction between the ith partiele and the jthparticle; ! Qf (g) represents a (l) order collision cross-section of the interaction between the ith particle and the jth particle; and g represents that the particle state of the charged particles in the gas arc plasma system is a gas particle.

[0025] in the Step S3, the normal diffusion coefcient is: pnt, 2k T 1,, Di," (98) = _ Bci]0 (!) ZNmj m j

[0026] Where [Di / (ë) is the normal diffusion coefcient; f represents niteterm expansion series of a Sonine polynomial for rstorder perturbations of the distribution function; n, represents the number density of the i particle; 451) is a spreading coefcient of the normal diffusion coefcient;

[0027] an expression for a thermal diffusion coefcient is: _ . 2k T DiT(SZ) : ntm! B ai0(§) 2 \] m T

[0028] where D !' () represents the thermal diffusion coefcient of the im particle; m, is the mass of the i particle; a() represents the spreading coefcient of the thermal diffusion coefcient;

[0029] the thermal conductivity is: k = k,. +k 15 N n- ktr : ÎkBZNj : 2 ] 1 Zt / "Ay .I: N C _ N kim:sz iâ xi / ZXÍAÉD . / '=1 R 2 j:] '!

[0030] where k is thermal conductivity; kim is the internal thermal conductivity; @] is an intermediate coefcient; C! is the specic heat ofthe im particle; R is a gas constant; X AU) A0) " is avolume fraetion of the im particle; both "J' and are intermediate variables; both 902) and 9) are collision integrals;

[0031] the viscosity coefcient7 is: N m.n. 77:2 N . / .l '=1 } ;nlA

[0032] the thermal conductivity is calculated as below: e2 N 0': n.m.Z.D_ pkBT _ / :1;¢e( .l .l . / !)

[0033] where a is conductivity; is amount of charges carried by an electron, and e = l.6><lO_19C; and D- is the diffusion coefcient of the jth particle;

[0034] in the Step 1, a course of constructing the nonequilibriumstate physical parameter calculation model according to the equilibrium-state physical parameter of the gas arc plasma system in the circuit breaker by adopting the machine learning method, includes:

[0035] Step A1 : obtaining and using the particle number density, the temperature, and the pressure in the gas arc plasma system in the circuit breaker as eigenvalues x, and using the equilibriumstate physical parameter in the gas arc plasma system in the circuit breaker as a variable y;

[0036] Step A2: constructing a training dataset by using the eigenvalues x and the variable y; and

[0037] Step A3: training the training dataset by adopting a linear regression model and constructing the nonequilibriumstate physical parameter calculation model in a form of y=f(X);

[0038] the non-equilibrium-state physical parameter calculation model includes: a chemical non-equilibrium-state mathematical model p =f(n,T,P) of the gas density, a chemical non-equilibrium-state mathematieal model h : f(n,T,P) of the enthalpy, a chemical non-equilibrium-state mathematical model CP =f(n,T,P) of constant-pressure specic heat capacity, a chemical non-equilibrium-state mathematical model 77 = f(n,T,P) of the Viseosity eoefcient, a chemical non-equilibrium-state mathematical model k zf ("T P ) of the thermal conductivity, a chemical non-equilibrium-state mathematical model D =f(n,T,P) of the diffusion coefcient, and a chemical non-equilibrium-state mathematical model of the conductivity, where n is partiele number density of the gas arc plasma system, and D is the diffusion coefcient;

[0039] the step 2 further includes:

[0040] Step 2.1: sorting particles according to the number density of the particles in the gas are plasma system in the circuit breaker, and screening out the particle with the smallest number density in the gas arc plasma system in the circuit breaker, to obtain the screened-out gas arc plasma system in the circuit breaker;

[0041] Step 2.2: according to the non-equilibrium-state physical parameter calculation model, calculating the thermodynamic parameter and the arc transportation coefcient of the gas arc plasma system in the circuit breaker, and the thermodynamic parameter and the arc transportation coefcient of the screenedout gas arc plasma system in the circuit breaker, calculating whether an error between the thermodynamic parameter and the arc transportation coefcient of the gas arc plasma system in the circuit breaker, and the thermodynamic parameter and the arc transportation coefcient of the screened-out gas arc plasma system in the circuit breaker meets a given threshold condition, if yes, returning to the step 2.1, and screening out the particle with the smallest number density in the gas arc plasma system in the current circuit breaker; else, retaining the particle and returning to the step 2.1 to screen out the particle with the smallest number density in the gas arc plasma system in the current circuit breaker, except for the particle; and

[0042] Step 2.3 : judging whether the quantity of the particles in the gas arc plasma system in the current circuit breaker is within a given range or whether all the particles have been traversed, if not, returning to the step 2.1, else, outputting the particle number density of the gas arc plasma system in the current circuit breaker;

[0043] the step 3 further includes:

[0044] Step 3.1: according to initial pressure, initial temperature, and initial number density distribution of the gas arc plasma system in the given circuit breaker, solving a mass conservation equation, a momentum conservation equation, and an energy conservation equation regarding density;

[0045] Step 3.2: solving a gas state equation, an electromagnetic eld equation, and a turbulent ow model to obtain temperature and pressure of the gas arc plasma system in the circuit breaker in the current state; and

[0046] Step 3.3: judging whether temperature and pressure of the gas are plasma system in the circuit breaker in the current state are converged, if not, repeating the steps 3.13.2 until converging is achieved, to obtain temperature, pressure, and number density distribution of each particle in the equilibrium state as the steadystate results of an equilibriumstate airow eld of the gas are plasma system in the circuit breaker;

[0047] in the step 4, the energy conservation equation is: ô N 2 ä(p8)+V-(v(p8+P))=V' kVT+(r -v)+ZpDjhjVYj q+0'E . /

[0048] where ï represents time; 3 is internal energy; 7 is axial velocity of an arc plasma; V represents a velocity gradient operator; T represents a pressure tensor; Dj is the diffusion coefcient of the jth particle; q is a net radiation loss of the arc plasma per unit time 2 and per unit volume; 0 E represents a radiation source term;

[0049] the particle transportation equation is: ôpY . J " _ 7+V'(PC)V(PD.;VC)+S; ôpYi

[0050] where at represents a change term of the particle composition along with . . . . . . . v - (LY / DY.) time, 1.e. a non-equrlrbrrumstate term; represents a partrcle velocrty vector; ] represents changes in the particle composition caused by convection, i.e. a convection term; V- DV Y. . . . . . . . (p - - ) represents changes rn the partrcle compos1t10n caused by dlffuSion, 1.e. a diffusion term; Sf represents a source term; and: K . [ K . K " S] :"jílljp _ßjp) kp' HlX / cl _ _kp THX / cl p= p= p=

[0051] where K represents the total number of reactions that occur in the gas arc plasma system in the circuit breaker; ßI'P and ip represent rst and second derivatives of k f . a stochiometric number of the jth particle in the pth reaction; P represents a positive reaction . . th . X . th . k r time constant rn the p reaction; k represents a mole fraetion of the k partrcle; and P represents a reverse reaction time constant in the pth reaction.

[0052] The method adopting the technical solution has the benecial effects:

[0053] the present invention proposes a particle screening method that reduces computational difculty by reducing the number of transportation equations. Reducing computational cost of simulation of the airow eld improves convergence speed.

[0054] The method of the present invention constructs a non-equilibrium-state physical parameter calculation model by a machine learning method. Using the model for calculation of non-equilibrium-state physical parameters can shorten calculation time and quickly predict evolution of the airow eld of the circuit breaker while ensuring certain accuracy. BRIEF DESCRIPTION OF DRAWINGS

[0055] FIG. 1 is a owchart of a numerical analysis method for arc characteristics of a circuit breaker in the embodiment;

[0056] FIG. 2 is a schematic diagram of a numerical analysis method for arc characteristics of a circuit breaker in the embodiment;

[0057] FIG. 3 is a schematic diagram of constructing a non-equilibrium-state physical parameter calculation model in the embodiment; and

[0058] FIG. 4 is a owchart of particle composition screening in the embodiment. DETAILED DESCRIPTION OF THE PREFERRED EMBODIMENT

[0059] For the convenience of understanding the present application, detailed description of the present invention will be explained in detail in conjunction with the accompanying drawings and embodiments. The following embodiments are intended to illustrate but not limit the scope of the present invention. On the contrary, the purpose of providing the embodiments is to provide a more thorough and comprehensive understanding of the disclosed content of the present application.

[0060] A numerical analysis method for arc characteristics of a circuit breaker in the implementation, as shown in FIG. 1 and FIG. 2, includes the following steps:

[0061] Step 1: calculating a particle composition of a gas arc plasma system in a circuit breaker, solving equilibrium-state physical parameters of the gas arc plasma system in the circuit breaker based on the particle composition, and constructing a non-equilibrium-state physical parameter calculation model by using a machine learning method according to the equilibrium-state physical parameters of the gas arc plasma system in the circuit breaker, where

[0062] the equilibrium-state physical parameters include thermodynamic parameters and are transportation coefcients;

[0063] a course of solving the equilibriumstate physical parameters of the gas arc plasma system in the circuit breaker according to the particle composition, includes:

[0064] Step Sl: the thermodynamic parameters of the gas arc plasma system in the circuit breaker, including: gas density, enthalpy, and specic heat, are calculated.

[0065] The gas density is: N p = E mjm]. j:! (1)

[0066] where p is gas density of the gas arc plasma system; N is the number of particles in the gas arc plasma system; j is the jth particle in the gas arc plasma system; n]- is number density of thejth partiele, in m3; mjis mass of the jth particle, in kg;

[0067] the enthalpy is: N h = E Yjhj (2) 1 Ô ln Z _ hi I[gktrT+ktrTZÖTJ+AHIJ . m . (3)

[0068] where h is the enthalpy of the gas arc plasma system; hf is the enthalpy of the jth particle, in j -kg'1; Y] is a distribution function of the jth particle in a six dimensional phase space; m is mass of the gas arc plasma system; k is translational thermal conductivity, in W(m-K)'1; T is temperature; Zj is an internal partition function of the jthparticle; AHj is a formation enthalpy of the jth particle;

[0069] the specic heat is: , =e} ÔT P (4)

[0070] where CP is the specic heat; and P is pressure.

[0071] Step S2: a collision integral of charged particles in the gas are plasma system in the circuit breaker is caleulated.

[0072] In the embodiment, obtaining collision integrals for partiele interactions is basis and prerequisite for solving thermodynamie parameters and transportation coefcients, and the accuracy of the collision integrals has a signicant impact on the credibility of the transportation coefcients. The collision integrals also include interactions between neutral particles, between the neutral particles and ions, between the neutral particles and electrons, and between charged particles. Except for the interactions between the charged particles, other types of collision integrals can be summarized as functions of temperature, and their values do not vary with the composition.

[0073] The collision integral is: S k T OO $+ Qi; ) =1i27î / 2. Iexp(; / ;)} / ; 3Q,î.(g)drÿ ° (5) or»

[0074] where represents a (l, 3) order collision integral of interaction between the ith partiele and the jth particle in the gas arc plasma system; l represents the type of the collision integral; s represents the order of the collision integral; kB represents a Boltzmann constant; # represents reduced mass of interaction between the ith particle and the jth partiele, in kg; % represents reduced initial velocity of the interaction between the ith particle and the jth ! particle, in m-s"; Qf (g) represents a (l) order collision cross-section of the interaction between the ith particle and the jth particle in m2; and g represents that the particle state of the charged particles in the gas arc plasma system is a gas particle.

[0075] Step S3: the arc transportation coefcients, including a diffusion coefcient, a viscosity coefcient, thermal conductivity, and conductivity, are calculated.

[0076] The diffusion coefcients include normal diffusion coefcients and thermal diffusion coefcients.

[0077] In the embodiment, the normal diffusion coefcients and the thermal diffusion coefcients are respectively related to particle migration generated under the inuence of a concentration gradient and a temperature gradient in the gas arc plasma system.

[0078] The normal diffusion coefcient is: ,on, 2k T ., D.,-() =JmBcijû () j j (6)

[0079] where () is the normal diffusron coefcrent, in kg-m'l-K'l; 95 represents nite-term expansion series of a Sonine polynomial for rstorder perturbations of the . . . . _ n. - . . CW?) - distribution functron, represents the number densrty of the 2th particle, and 10 rs a spreading coefcient of the normal diffusion coefcient.

[0080] An expression for a thermal diffusion coefcient is: _ _ 2 T Dir(§)=nl;nl ij ai0(§) " (7) T

[0081] where Di (i) represents the thermal diffusion coefcient of the ith particle, in kg-m K"; mi is the mass of the i particle, in kg; a () represents the spreading coefcient of the thermal diffusion coefcient;

[0082] In the embodiment, the spreading coefcient of the thermal diffusion coefcients is calculated using an existing linear equation system of the collision integrals.

[0083] The thermal conductivity is: k : ktr + kint (8) N n. kn = % kB Z Nj Fl 2 ggf. / "Ay) (9) N C _ N kim = kBZHl ä] x, {Emyn .i=' R 2 j=1 (10) 1 / 2 L_3|:7szT(mi+mj)] 1 (1) _ _ (1,1) A 8 2mim]. fzQ (11) 1 / 2 L _ 5 [mum, ml.)] 1 (2) _ _ (2,2) A 16 2mimj fzQ (12) lm. / m. 0.452.54 . / . áj :1+( 1 [)( 2 ml ml) (1+mi / mj) (13)

[0084] where k is thermal eonductivity; kim is the internal thermal conductivity; is an intermediate coefcient; C! is the specic heat of the ith particle; R is a gas constant; x AU) A I' is a volume fraction ofthe ith particle; both N' and are intermediate variables; both Q&Q) and 9) are collision integrals; and by consulting a phenomenological potential tting parameter table of the collision integrals, tting parameters for calculating QM) and Q) are obtained.

[0085] In the embodiment, the tting parameters are obtained by consulting the phenomenological potential tting parameter table of the collision integrals, QW) and Q) are further calculated, and then the thermal conductivity is calculated based on QM) and QM). For a chemical equilibrium model and a chemical non-equilibrium model, only translational thermal conductivity and internal thermal conductivity need to be calculated when calculating thermal conductivity.

[0086] The viscosity coefcient 77 is: N m .n. 77 22 N j ] :l ] ZniAij i=1 (14)

[0087] In the embodiment, neglecting contribution of heavy particles to conductivity and only considering inuence of electrons to simplify calculation of the conductivity.

[0088] The thermal conductivity is calculated as below: e2 N 0'= Z (njmjZ / Dq) pkBT FI, / ie (15)

[0089] where 5 is conductivity, in S-ml; e is amount of charges carried by an electron, and e :1'6X10719C; and Def is the diffusion coefcient of the jth particle.

[0090] A course of constructing the non-equilibrium-state physical parameter calculation model according to the equilibrium-state physical parameter of the gas arc plasma system in the circuit breaker by adopting the machine learning method, includes:

[0091] in the embodiment, in chemical non-equilibrium-state magnetic uid dynamics simulation, each iteration requires re-calculating equilibriumstate physical parameters, namely thermodynamic parameters and transportation coefcients. An original calculation model requires large computational complexity, and machine learning is used to simplify a calculation model. The prediction of the physical parameters belongs to a regression problem. Therefore, a machine learning method is used to simplify a physical parameter calculation model to construct a nonequilibrium-state physical parameter calculation model, greatly reducing the computational difculty of the chemical non-equilibrium-state physical parameters.

[0092] Step Al: obtaining and using particle number density, temperature, and pressure in the gas arc plasma system in the circuit breaker as eigenvalues x, and using the equilibrium state physical parameter in the gas arc plasma system in the circuit breaker as a variable y;

[0093] Step A2: constructing a training dataset by using the eigenvalues x and the variable y; and

[0094] Step A3: training the training dataset by adopting a linear regression method and constructing the non-equilibrium-state physical parameter calculation model in a form of y=f(x).

[0095] In the implementation, as shown in FIG. 3, the machine learning method is used to train the mathematical model in steps S lS3 to construct the nonequilibrium-state physical parameter calculation model. Firstly, it is necessary to prepare a training dataset, i.e., the particle number density, the temperature, and the pressure in the gas arc plasma system in the circuit breaker are taken as the eigenvalues x, and the equilibrium-state physical parameter of the gas arc plasma system in the circuit breaker calculated earlier is taken as a variable y; secondly, it is necessary to choose appropriate machine learning algorithms and models based on the characteristics of the problem to be solved and data situations. In the implementation, a linear regression model is selected and trained using the training dataset. Usually, optimization algorithms such as gradient descent are used to iteratively update model parameters to minimize a loss function. During the model training course, accuracy is evaluated to determine the performance of the model. After the model is trained, it is necessary to save the trained model and ultimately obtain a simplied physical parameter mathematical model as a non- equilibrium-state physical parameter calculation model.

[0096] The non-equilibrium-state physical parameter calculation model includes: a chemical non-equilibrium-state mathematical model ,0 =f(n,T,P) of the gas density, a chemical non-equilibrium-state mathematical model h = f (n,T P ) of the enthalpy, a chemical non-equilibriumstate mathematical model CP =f(n,T,P) of constant-pressure specic heat capacity, a chemical non-equilibrium-state mathematieal model 77 = f (n,T P ) of the viscosity coefcient, a chemical nonequilibriumstate mathematical model k =f(n,T,P) of the thermal conductivity, a chemical nonequilibriumstate mathematical model D =f(n,T,P) of the diffusion coefcient, and a chemical non-equilibrium-state mathematical model of the conductivity, where n is partiele number density of the gas are plasma system, and D is the diffusion coefcient.

[0097] Step 2: chemical nonequilibrium-state physical parameters of the gas are plasma system in the circuit breaker by using the non-equilibrium-state physical parameter caleulation model are calculated, and the particle composition is screened out based on the chemical non equilibriumstate physical parameters.

[0098] Step 2.1: particles are sorted according to the number density of the particles in the gas arc plasma system in the circuit breaker, and the particle with the smallest number density in the gas are plasma system in the circuit breaker is screened out, to obtain the screened-out gas arc plasma system in the circuit breaker;

[0099] Step 2.2: according to the nonequilibriumstate physical parameter calculation model, the thermodynamic parameter and the arc transportation coefcient of the gas arc plasma system in the circuit breaker, and the thermodynamic parameter and the arc transportation coefcient of the screened-out gas arc plasma system in the circuit breaker are calculated respectively, whether an error between the thermodynamic parameter and the arc transportation coefcient of the gas arc plasma system in the circuit breaker, and the thermodynamic parameter and the arc transportation coefcient of the screened-out gas arc plasma system in the circuit breaker meets a given threshold condition is calculated, if yes, the step 2.1 is performed, and the particle with the smallest number density in the gas arc plasma system in the circuit breaker is screened out; else, the particle is retained and the step 2.1 is performed to screen out the particle with the smallest number density in the gas arc plasma system in the circuit breaker, except for the particle; and

[00100] Step 2.3: whether the quantity of the particles in the gas arc plasma system in the current circuit breaker is within a given range or whether all the particles have been traversed is judged, if not, the step 2.1 is performed, else, the particle number density of the gas arc plasma system in the current circuit breaker is outputted.

[00101] In the implementation, as shown in FIG. 4, chemical nonequilibrium-state physical parameters of the gas are plasma system in the circuit breaker are calculated by using the non-equilibrium-state physical parameter calculation model, and the particle composition is screened based on the chemical non-equilibrium-state physical parameters.

[00102] Step 3: steady-state results of an equilibrium-state airow eld of the gas are plasma system in the circuit breaker are solved according to the screening results of the particle composition.

[00103] Step 3.1: according to initial pressure, initial temperature, and initial number density distribution of the gas arc plasma system in the given circuit breaker, the mass conservation equation, the momentum conservation equation, and the energy conservation equation regarding density are solved.

[00104] The mass conservation equation is: 5p + v . (,0?) = o ôt (16)

[00105] where ï represents time; V represents a velocity gradient operator; and Ï? represents a velocity vector.

[00106] The momentum conservation equation is: 2(p17)+v.(,or717) =vp+v-(E)+jx§ ôt (17)

[00107] where ; represents a pressure tensor;} represents current density; Ë represents magnetic induction intensity; and jXË represents Lorentz force.

[00108] In the embodiment, the Lorentz force is generated by interaction between the arc current and the magnetic eld generated by the arc current.

[00109] The pressure tensor is: %: n[(v17+vr7T)Êv-171] 3 (18)

[00110] where I represents a unit tensor.

[00111] The energy conservation equation is: 2(pg)+v-(I7(pg+10)) =v-(k,VT%.I7)+0E2 q ôt (19)

[00112] where 5 is internal energy; Ê is intensity of an electric eld; GEZ represents a radiation source term; and q is a net radiation loss of arc plasma per unit time and per unit volume.

[00113] In the embodiment, for incompressible uids, in the energy conservation equation, usually pressure work and kinetic energy terms are ignored. In compressible uids, it is generally necessary to consider the pressure work and kinetic energy terms. [00 1 14] The internal energy is: P 2 g = h + V P 2 (20)

[00115] Where V is volume of the gas arc plasma system.

[00116] In the embodiment, the enthalpy h of the gas arc plasma system is determined by temperature T and pressure p.

[00117] Step 3.2: a gas state equation, an electromagnetic eld equation, and a turbulent ow model are solved to obtain temperature and pressure of the gas arc plasma system in the circuit breaker in the current state; and

[00118] the gas state equation is: p = f (P T ) (21)

[00119] where f(PT) represents a change curve of gas density along with pressure and temperature.

[00120] In the embodiment, a gas state equation is given by the change curve of the gas density along with pressure and temperature.

[00121] The electromagnetic eld equation is:

[00122] the value of a magnetic eld can be calculated using an Ampere circuit law. #OJJZ Zéddgd Bg : _° 27zr (22)

[00123] where B is magnetic induction intensity of the magnetic eld, in T; JZ is axial current density; fd is a distance from an arc plasma to a center of the arc, in m; uo represents uniform magnetic permeability of an arc medium, in units of H'lm'l; is a radius of the arc plasma, in m.

[00124] Intensity E of the electric eld and current density J are calculated by simplifying an Ohm's law, assuming that a radial electric eld of the arc can be ignored. I A = E Î 0'27zrdr 0 (23)

[00125] where IA represents are current, in A; and r represents the radius of the arc plasma, in m.

[00126] In the implementation, the arc magnetic uid, like ordinary uids, also includes laminar ow and turbulent ow in ow state. The laminar ow is a layered ow state, where uid particles ow parallel to a pipe axis and there is no exchange of uid clusters perpendicular to the ow direction. The turbulent owis a non-linear ow state that is disordered in space and time, and there is strong irregular lateral motion in the turbulent ow. In uid mechanics, the Reynolds number is commonly used to determine whether a uid is the laminar ow or the turbulent ow, meaning that a ow with small Reynolds number is the laminar ow and a ow with large Reynolds numbers is the turbulent ow. For an annular channel ow, it is generally believed that the ow with Reynolds number greater than 2100 is considered as the turbulent ow. In highvoltage switch arcs, the Reynolds number is generally in the order of 106-109, whereby inuence of the turbulent owmust be considered. The turbulent ow is a common irregular ow phenomenon in a supersonic nozzle arc of the high- voltage circuit breaker, which has signicant impact on the momentum and energy transportation of the arc;

[00127] a turbulent owmodel is:

[00128] in the embodiment, due to closure property of the three conservation equations, a new relationship is needed to calculate the viscosity coefcient and the thermal conductivity of turbulent ow enhancement. A zero-dimensional Prandtl mixing length model is used as the turbulent ow model, in which the turbulent ow viscosity coefcient and the turbulent ow thermal conductivity are related to a length scale and the characteristic velocity of the turbulent ow. #, = pli ? r (25) [m = cô (26)

[00129] where u; represents the turbulent ow Viseosity coefcient; l'" represents a mixing length of a turbulent ow boundary layer; W represents radial velocity of the are plasma; & represents the thermal radius of the arc, in m; c represents the turbulent ow parameter.

[00130] The turbulent ow thermal conductivity kt is associated with the Prandtl number Pr, the turbulent ow viscosity coefcient uf, and the specic heat CP . Pr = L k, / CP (27)

[00131] where Pr represents the Prandtl number.

[00132] Step 3.3: whether temperature and pressure of the gas arc plasma system in the circuit breaker in the current state are converged is judged, if not, the steps 3.1-3.2 are repeated until converging is achieved,and temperature, pressure, and number density distribution of each particle in the equilibrium state are obtain as the steadystate results of the equilibrium state airow eld of the gas are plasma system in the circuit breaker.

[00133] Step 4: the steadystate results of the equilibrium-state airow eldare used as initial values ofthe gas arc plasma system in the circuit breaker at time O in the non-equilibrium state, then a mass conservation equation, a momentum conservation equation and an energy conservation equation of a magnetic uid in a chemical non-equilibrium state are solved according to screening results of the particle composition to obtain temperature and pressure distribution of the gas are plasma system in the circuit breaker in the non-equilibrium state, and a partiele transportation equation is solved to obtain temperature, pressure, and partiele number density of the gas are plasma system in the circuit breaker.

[00134] In the embodiment, the mass conservation equation and the momentum conservation equation of the chemical non-equilibrium-state magnetic uid are consistent with those of a chemical equilibrium-state magnetic uid, as shown in step 3.1.

[00135] The energy conservation equation of the chemical non-equilibrium-state magnetic uid has changed compared to that of the chemical equilibrium-state magnetic uid, specically: a _ _ _ N _, ä(p8)+V-(v(pg+p)) =V- kVT+(z' -v)+ZpD_ / h_ / VY]. q+0'E f (28)

[00136] where 7 is axial velocity of the arc plasma; Djis the diffusion coefcient of the jN'particle.

[00137] After obtaining corresponding temperature and pressure distributions by solving the three conservation equations, the particle transportation equation is solved.

[00138] The transportation equation for the jhparticle in the gas arc plasma system in the circuit breaker is as follows: ôpY . +V« ü Y. =V- DVY, +5. 6, (p)) (p) .) . (29) ôpYj

[00139] where at represents a change term of the particle composition along with . . . . . » . . V ü Y . time, 1.e. a nonequrlrbrrum-state term; u represents a particle velocrty vector; ( p 1 ) represents changes in the particle composition caused by convection, i.e. a convection term; V- DV Y. . . . . . . . (p - - ) represents changes rn the partrcle compos1t10n caused by diffuSion, 1.e. a diffusion term; Sf represents a source term; and: In general, components that do not belong to the rst three terms can be plaeed in the source term, which refer to chemical reaction terms. K _ __ f K B'. K ß" S.) =m_ / Z(ßjp WB. / ;;) kp' HlXkl _ _kp HlXkl p:1 p=] p=l (30)

[00140] where K represents the total number of reactions that occur in the gas arc plasma system in the circuit breaker; Bfp and ip represent rst and second derivatives of k f a stochiometric number of the jth particle in the pth reaction; P represents a positive reaction time constant in the pth reaction, in m3s'1; X represents a mole fraction of the kth particle; and kp represents a reverse reaction time constant in the pth reaction, in m3s.

[00141] Step 5 : whether the temperature, the pressure, and the particle number density of the gas arc plasma system in the current circuit breaker are converged is judged, and if not, the temperature, the pressure, and the particle number density of the gas arc plasma system in the circuit breaker at the current time step are recalculated by using the non-equilibrium-state physical parameter calculation model.

[00142] Step 6: whether the current time step reaches a preset time step is judged, if not, the temperature, the pressure, and the particle number density of the gas are plasma system in the circuit breaker, calculated in the Step 5 are used as initial values of the temperature, the pressure, and the particle number density of the gas arc plasma system in the circuit breaker in the next time step, the Step 5 is performed until preset time step is reached, and nal chemical non-equilibrium-state physical parameters of the gas arc plasma system in the circuit breaker are outputted; and

[00143] Step 7: the nal chemical non-equilibrium-state physical parameters of the gas are plasma system in the circuit breaker are substituted into the Step 3 and the Step 4, to obtain distribution characteristics of temperature and pressure and change laws of arc voltage, conductivity and arc energy in an arc-extinguishing chamber of the circuit breaker.

[00144] Finally, it should be noted that the above embodiments are merely used to illustrate but not limit the technical solution of the present invention. Although the present invention has been described in detail with reference to the embodiments, those skilled in the art should understand that it is still possible to modify the technical solution recorded in the embodiments, or to equivalently replace some or all of the technical features thereof; and these modications or replacements do not make the essence of the corresponding technical solution deviate from the scope limited by the claims of the present invention.

Claims

1. Numerical analysis method for arc characteristics to be used in the design of an environmentally friendly high voltage circuit breaker, containing the next steps: Step 1: Calculate the particle composition of a gas arc plasma system in a circuit breaker, solving equilibrium physical parameters of the gas arc plasma system in the circuit breaker based on the particle composition and building a non-equilibrium physical parameter calculation model by using a machine learning method according to the equilibrium physical state parameters of the gas arc plasma system in the circuit breaker, where the equilibrium state physical parameters thermodynamic parameters and arc transfer contain coefficients; Step 2: Calculate chemical non-equilibrium physical parameters of the gas arc plasma system in the circuit breaker by using non-equilibrium physical parameter calculation model and performing a screening of the particle composition based on the chemical non-equilibrium state physical parameters; Step 3: Solving the steady state results of an equilibrium condition airflow field of the gas arc plasma system in the circuit breaker; Step 4: Using the steady state results from the equilibrium air flow field as initial conditions of the gas arc plasma system in the circuit breaker at time 0 in a non-equilibrium state, then solve for a mass conservation equation, a momentum conservation equation and an energy conservation equation of a magnetic fluid in a chemical non-equilibrium state according to the screening results of the particle composition to determine temperature and pressure distribution of the gas arc plasma system in the circuit breaker in the non- to obtain equilibrium and solve a particle transfer equation to temperature, pressure and particle number density of the gas arc plasma system in the to obtain circuit breaker; Step 5: Assess the temperature, pressure, and particle number density of the gas arc plasma system in the circuit breaker has converged, and if do not recalculate the temperature, pressure and particle number density of the gas arc plasma system in the circuit breaker by using the non- equilibrium state physical parameter calculation model; Step 6: Determine if a current time step reaches a predetermined time step, if do not use the temperature, pressure and particle number density of the gas arc plasma system in the circuit breaker calculated in step 5 as the initial value of the temperature, pressure and particle number density of the gas arc plasma system in the circuit breaker at the next time step, return to step 5 until the pre-set certain time step is reached and delivery of the final chemical non-equilibrium state physical parameters of the gas arc plasma system in the circuit breaker; and Step 7: Substitute the final chemical non-equilibrium physical state parameters of the gas arc plasma system in the circuit breaker in step 3 and step 4 to determine the distribution characteristics of temperature and pressure and the change laws of high voltage, conductivity and arc energy in an arc extinction chamber of the circuit interrupter available.

2. Numerical analysis method for arc characteristics to be used in the design of an environmentally friendly high-voltage circuit breaker according to conclusion l, where in step 1, a sequence for solving the equilibrium physical parameters of the gas arc plasma system of the circuit breaker according to the particle composition contains: Step S1: Calculate the thermodynamic parameters of the gas arc plasma system in the circuit breaker containing: gas density, enthalpy and specific heat; step S2: calculate a collision integral of charged particles in the gas arc plasma system in the circuit breaker; and Step S3: Calculate the arc transfer coefficients including a diffusion coefficient, a viscosity coefficient, thermal conductivity and conduction.

3. Numerical analysis method for arc characteristics to be used in the design of an environmentally friendly high-voltage circuit breaker according to conclusion 2, where in step S1 the gas density: N p = Zn. / mj j=1 is, where p is a gas density of the gas arc plasma system; N is the number of particles in the gas arc plasma system is; j is the jth particle in the gas arc plasma system, nj is the number is the density of the jth particle; mj is the mass of the jth particle; the enthalpy: N h : Z j=1 Y / h / . . 1 5 2 ôlnZ _ h]. = k_T+k T +AH. m 2 ' r ôT ] is, where h is the enthalpy of the gas arc plasma system, hj is the enthalpy of the jÜle particle is; Yj is a distribution function of the jth particle in a six-dimensional phase space; m is the mass of the gas arc plasma system; ku is the transfer thermal conductivity; T is the temperature; Zj is an internal distribution function of the jth particle; A is a enthalpy of formation is of the jth particle; and the specific heat: h ôT ,, , {à} is, where Cp is the specific heat and P is the pressure.

4. Numerical analysis method for arc characteristics to be used in the design of an environmentally friendly high-voltage circuit breaker according to conclusion 3, where in step S2 the collision integral is: k T °° Qi) : B; eXp(_7 / i2' )712'H3Qil' (8)5? J 27Ï / Jl-j ([ ] J ] ] Q?) where ' is an (Ls) order collision integral of the interaction between the ith particle and the jth represents the particle in the gas arc system; 1 represents the type of collision integral; s represents the order of represents the collision integral, kB represents a Boltzmann constant; ij represents the reduced mass of the interaction between the ith particle and the jth particle; Yij represents the reduced initial velocity of the interaction between the iOth particle and the jth particle; Ql ij(g) a (1) represents the order collision cross section of the interaction between the iÜle particle and the jÜle particle; and g that particle state of charged particles in the gas arc plasma system a gas particle is.

5. Numerical analysis method for arc characteristics to be used in the design of an environmentally friendly high-voltage circuit breaker according to conclusion 4, where in step 83 the normal diffusion coefficient: on. 2kBT ., D = lc: / () 2Nmj} m]. 0 () is, where DU" (5) is the normal diffusion coefficient; f final term expansion series of a Sonine polynomial for first order perturbations of the distribution function; Îli de number density of the iOle particle; 6131(6) is a spreading coefficient of the normal diffusion coefficient is; an expression for a thermal diffusion coefficient: nm. f2k T DfT(é:) = # Bafo () 2 m. is, where DU (98) represents the thermal diffusion coefficient of the ith particle; mi is the mass of the iOle particle is; a() the spreading coefficient of the thermal diffusion coefficient proposes; the thermal conductivity: k : ktr + kim 1 N n- ktr = ÎSkE EN / HZ ff / "Aij j=1 NC i 5 N k, : kBEHÎPÎJX" {E&M / DH .le .le is, where k is the thermal conductivity; ki is the internal thermal conductivity; â, is an intermediate coefficient; C! is the specific heat of the ith particle, R is a gas constant is; xi is a volume fraction of the iOle particle is; both A5) and A5) intermediate variables zn; both 90.2) and Q) collision integrals are; the viscosity coefficient 77 is: 77 = Ë Nm. / "j j=1 <2) ;nlA the thermal conductivity as calculated below: e2 N O' = pkBT 1:12:48 (Miz / Def) where 0 is a conductivity; e is an amount of charge carried by an electron and e= l.6xlO9C; and Dej is the diffusion coefficient of the jth particle.

6. Numerical analysis method for arc characteristics to be used in the design of an environmentally friendly high-voltage circuit breaker according to conclusion 5, where step 1 shows a progression of the build-up of the non-equilibrium physical state parameter calculation model according to the equilibrium physical parameter of the gas arc plasma system in the circuit interruption by accepting the machine learning method, containing: Step Al: Obtain and use particle number density, temperature, and pressure in the gas arc plasma system in the circuit breaker as eigenvalues ​​X and use of the equilibrium physical parameter in the gas arc plasma system in the circuit interrupter as a variable y; Step A2: Building a training dataset using the eigenvalues ​​X and the variable y; and Step A3: Training the training dataset by assuming a linear regression model and construction of the non-equilibrium physical parameter calculation model in the form of y=f(x).

7. Numerical analysis method for arc characteristics to be used in the design of an environmentally friendly high-voltage circuit breaker according to conclusion 6, where the non-equilibrium physical parameter calculation model contains: a chemically non-equilibrium state mathematical model 0 = f (n,TP ) of the gas density; a chemically non-equilibrium mathematical model h = f (n TP ) of the enthalpy, a chemically non-equilibrium mathematical model CP : f(n,T,P) of constant pressure specific heat capacity, a chemically non-equilibrium state mathematically model 77 =f(n,T,P) of the viscosity coefficient, a chemically non-equilibrium state mathematical model k : f(n,T,P) of the thermal conductivity, a chemically non- equilibrium state mathematical model D : f(n,T,P) of the diffusion coefficient and a chemically non-equilibrium mathematical model of conductivity, where n is a particle number density of the gas arc plasma system is and D is the diffusion coefficient.

8. Numerical analysis method for arc characteristics to be used in the design of an environmentally friendly high-voltage circuit breaker according to conclusion 7, where step 2 further contains: Step 2.1: Sorting particles according to the number density of the particles in the gas arc plasma system in the circuit breaker and the screening of the particle with the smallest number density in the gas arc plasma system in the circuit breaker to to obtain sieved gas arc plasma system in the circuit breaker; step 2.2: according to the non-equilibrium physical parameter calculation model, calculation of the thermodynamic parameter and the arc transfer coefficient of the gas arc plasma system in the circuit breaker and the thermodynamic parameter and the arc transfer coefficient of the sieved gas arc plasma system in the circuit breaker, calculate whether a fault exists between the thermodynamic parameter and the arc transfer coefficient of the gas arc plasma system in the circuit breaker and the thermodynamic parameter and the arc transfer coefficient of the sieved gas arc plasma system in the circuit breaker reaches a given threshold condition, if so, return to step 2.1, and screening out the particle with the smallest number density in the gas arc plasma system in the current circuit breaker; otherwise, hold back the particle and return to step 2.1 to find the particle with the smallest number density in the gas arc plasma system in the flow to filter out the circuit breaker, except for the particle; and Step 2.3: Assess the amount of particles in the gas arc plasma system in the circuit breaker is within a given range or if all particles transferred, if not, return to step 2.1, otherwise, the particle number density of the gas arc plasma system in the circuit breaker aeveren.

9. Numerical analysis method for arc characteristics to be used in the design of an environmentally friendly high-voltage circuit breaker according to conclusion 8, where step 3 further contains: step 3.1: according to an original pressure, original temperature and original number density distribution of the gas arc plasma system in the given circuit breaker, solving a mass conservation equation, momentum conservation equation and an energy conservation equation involving density; step 3.2: solving a gas state equation, an electromagnetic field equation and a turbulent flow model to determine the temperature and pressure of the gas arc plasma system in the circuit breaker to obtain the current state; and Step 3.3: Assess the temperature and pressure of the gas arc plasma system in the circuit breaker in the current state converge, if not, repeat the steps 3.1 - 3.2 until convergence is reached for temperature, pressure and number density distribution of each particle in an equilibrium state as steady results of a equilibrium state air flow field va, the gas arc plasma system in the circuit is an interrupter.

10. Numerical analysis method for arc characteristics to be used in the design of an environmentally friendly high-voltage circuit breaker according to conclusion 9, where in step 4 the energy conservation equation is: _ N 8 ä(pg)+v_($(pg+iv)) =v.[kvr+(ï.$)+;pDjhjVi / jjq+aE2 where t represents time; 5 is the internal energy; 7 is the axial velocity of a plasma arc is; V represents a velocity gradient operator; does not represent a pressure tensor; Dj represents a diffusion coefficient of the jth particle; q is a net radiation loss of the arc plasma per unit time . . 2 . and per unit volume is; Ü E represents a radiation source term; the particle transfer equation: ôpY. ] _ Î+V'(PÏÔ)V'(PDJVÏÔ)+SJ ôpYj is, where at represents a change term of a particle composition over time, that is to say a non-equilibrium term; Ü represents a particle velocity vector, V-(üpYj) . . . . . shows changes in particle composition caused by convection, it is to say a convection term; V- DVY. . . . . . . (pf ) represents changes in particle composition caused by diffusion, that is to say a diffusion term; Sf represents a source term; and: K , f K ß KB" SJ 2111-1421(31)) _ßjp) kp H[Xk] _kp HiXk] m p=1 p=1 p=1 where K represents the total number of reactions occurring in the gas arc plasma circuit breaker system; ip and 81P first and second derivatives . . . . . kf representing a stoichiometric number of the jÜle particle in the pOle reaction; P a positive reaction time constant in the pÜle reaction; Xk represents a mole fraction of the kth particle and kP represents an inverse reaction time constant in the pth reaction. DRAWINGS Calculate a particle composition of a gas arc plasma system in a circuit breaker, solve equilibrium-state physical parameters of the gas arc plasma system in the circuit breaker based on the particle composition, and construct a non-equilibrium-state physical parameter calculation model by using a machine learning method according to the equilibrium-state physical parameters of the gas arc plasma system in the circuit breaker Calculate chemical non-equilibrium-state physical parameters of the gas arc plasma system in the circuit breaker by using the non-equilibrium-state physical parameter calculation model, and perform screening on the particle composition based on the chemical non-equilibrium-state physical parameters ve steady-state results of an equilibrium-state airflow field of the gas arc plasma system in the circuit breaker Use the steady-state results of the equilibrium-state airflow field as initial values of the gas plasma system in the circuit breaker at time 0 in a non-equilibrium state, then solve three conservation equations and a particle transportation equation in the chemical non-equilibrium state according to screening results of the particle composition, to obtain temperature, pressure, and particle number density of the gas arc plasma system in the circuit breaker dge whether the temperature, the pressure, and the particle number density of the gas arc asma system in the circuit breaker are converged, and if not, re-calculate the temperature, the pressure, and the particle number density of the gas arc plasma system in the circuit breaker by using the non-equilibrium-state physical parameter calculation model Judge whether a current time step reaches a preset time step, if not, use the temperature, the sure, and the particle number density of the gas arc plasma system in the circuit breaker at e current time step as initial values in the next time step, perform iteration until preset time step is reached, and output final chemical non-equilibrium-state physical parameters Through the final chemical non-equilibrium-state physical parameters of the gas arc plasma em in the circuit breaker, calculate distribution characteristics of temperature and pressure and change laws of arc voltage, conductivity and arc energy in an arc-extinguishing chamber of the circuit breaker Fig.1 Start Calculate particle composition Calculate equilibrium-state physical parameters and construct a non- equilibrium-state physical parameter calculation model Screen particle composition Solve steady-state results in an equilibrium state, and output T, P and number density distribution Use simplified models to calculate physical parameters Solve three conservation equations Update T, P, and and a particle transportation number density equation of a magnetic fluid distribution date T, P, and number ity distribution to start the next time step Judge whether T, P, and number de nsity of No each particle are converged or reach the maximum iteration step Yes Output T, P, and the number density distribution of various types of particles No Judge whether the time is ended Yes End Fig.2