Direct-current arc plasma torch numerical simulation method based on thermodynamic non-equilibrium state and coupling electrode sheath effect

Abstract

The invention discloses a numerical simulation method for a direct-current arc plasma torch based on a thermodynamic unbalanced state and a coupling electrode sheath effect, and the method comprises the steps: building a two-dimensional axial symmetry or three-dimensional equivalent geometric model of the plasma torch based on an actual physical structure of the direct-current arc plasma torch; performing mesh generation to obtain a discretization analysis model; establishing thermodynamic parameters and transport coefficients of a plasma working medium; constructing a control equation set of the coupling electrode sheath effect based on the thermodynamic non-equilibrium state; setting boundary conditions of the plasma torch according to actual conditions; in the discretization analysis model, carrying out numerical value initialization on each grid unit; performing steady state and transient state simulation calculation; and performing post-processing on the steady-state and transient simulation results. According to the invention, the actual unbalanced effect of an electrode boundary layer is simulated through a thermodynamic unbalanced state; through the coupling electrode sheath effect, the interaction between the plasma and the electrode is simulated, and the error caused by manually applying boundary conditions is avoided; the requirement of current continuity is met through self-adaptive iterative solution of sheath voltage, so that the numerical simulation precision of the plasma torch is improved.

Description

Technical Field

[0001] The present invention relates to the technical field of numerical simulation of arc plasma torches, and specifically to a numerical simulation method for a DC arc plasma torch based on thermodynamic non-equilibrium and coupled electrode sheath effects. Background Art

[0002] Thermal plasma technology exhibits unique advantages in the fields of solid waste treatment, material synthesis and surface modification, and combustion assistance ignition due to its remarkable high temperature, high heat flux density, and high power output characteristics. Compared with radio frequency and microwave plasma torches, DC arc plasma torches have been widely used in industrial-scale waste treatment due to their insensitivity to interference, high efficiency, and flexibility. Existing experimental measurements are usually limited to the ex post analysis of static or dynamic volt-ampere characteristics, torch thermal efficiency, and electrode erosion due to harsh experimental conditions, and it is difficult to provide a reasonable phenomenological explanation. Analyzing the microscopic mechanism process inside the arc through comprehensive modeling is an efficient research method.

[0003] Previous arc plasma torch models usually simplify the arc-electrode boundary as Neumann or Dirichlet boundary conditions of plasma temperature and current density, without considering the characteristics of the electrode. This makes the setting of boundary conditions rely on empirical values in the absence of experimental data. Moreover, during the arc discharge process, the electrode not only serves as a current conduction medium but also bears the high-temperature heat flux from the arc, and this interaction significantly affects its physical and chemical properties. In addition, the presence of the electrode sheath will further affect the characteristics of the arc. Therefore, it is a very urgent topic to perform a global simulation of a DC arc plasma torch including the electrode.

[0004] Electrode coupling models in the prior art often only consider partial physical mechanisms and fail to comprehensively cover the complexity of the sheath. For example, many models rely on empirical values to set the sheath voltage, which limits the self-consistency and accuracy of the model, and the simulation results have poor accuracy. Summary of the Invention

[0005] In order to solve the problems existing in the above prior art, the object of the present invention is to propose a numerical simulation method for a DC arc plasma torch based on thermodynamic non-equilibrium and coupled electrode sheath effects. The present invention fully considers the microscopic mechanism of the sheath, the boundary conditions at the plasma-electrode interface are based on the coupled solutions of adjacent domains, and the sheath voltage is calculated by an adaptive Newton downhill iteration algorithm. It avoids the assumption limitations on the arc attachment size or the cathode surface current path, and realizes the self-consistent coupling of non-equilibrium plasma and the electrode. Based on theoretical research and experiments, the present invention not only helps to improve the accuracy of numerical simulation but also provides guidance for the application of plasma technology in various industrial applications.

[0006] To achieve the above technical object, the present invention adopts the following technical solutions:

[0007] A numerical simulation method for a DC arc plasma torch based on the non-equilibrium state of thermodynamics and the coupled electrode sheath effect, comprising the following steps:

[0008] Step 1: Based on the physical structure of an actual DC arc plasma torch, construct a two-dimensional axisymmetric or three-dimensional equivalent geometric model of the plasma torch including the electrodes;

[0009] Step 2: Perform finite volume grid meshing on the geometric model established in Step 1 to obtain a discretized analysis model suitable for numerical calculation;

[0010] Step 3: Establish the thermodynamic parameters (including density, specific heat at constant pressure, and mole fraction of each component) and transport coefficients (including conductivity, thermal conductivity, viscosity, and net volumetric radiation coefficient) of the working medium of the DC arc plasma torch, where both the thermodynamic parameters and transport coefficients are expressed as non-linear functions of temperature;

[0011] Step 4: Construct control equations based on the non-equilibrium state of thermodynamics and the coupled electrode sheath effect, including control equations for the fluid phase, control equations for the solid phase, and control equations for the cathode-plasma coupling interface and the anode-plasma coupling interface;

[0012] Step 5: Set the boundary conditions for the numerical simulation of the DC arc plasma torch according to the actual working conditions;

[0013] Step 6: Numerically initialize the pressure field, temperature field, velocity field, turbulent kinetic energy, turbulent dissipation rate, electric potential field, and magnetic vector potential field of each grid cell in the discretized analysis model obtained in Step 2;

[0014] Step 7: Perform steady-state simulation calculations on the discretized analysis model obtained in Step 2 to obtain the steady-state distribution solutions of various physical parameters; perform transient simulation calculations on the discretized analysis model obtained in Step 2 to obtain the dynamic solutions of the evolution of various physical parameters over time;

[0015] Step 8: Post-process the steady-state and transient simulation results obtained in Step 7, including distribution contour maps and vector maps of characteristic parameters, as well as curves of the variation of characteristic parameters with spatial position or time, etc.

[0016] Further, in the control equation of the fluid phase in Step 4, source term correction is performed based on the Navier-Stokes equations, the current continuity equation, and the magnetic vector potential conservation equation, specifically including the following equations:

[0017] The Navier-Stokes equations include the mass conservation equation, the momentum conservation equation, the electron energy conservation equation, and the heavy particle energy conservation equation;

[0018] Mass conservation equation:

[0019]

[0020] ρ is the mass density, t is the time, and u is the velocity vector;

[0021] Momentum conservation equation:

[0022]

[0023] p is the pressure, τ is the viscous stress tensor, j is the current density vector, and B is the magnetic induction intensity vector.

[0024] Electron energy conservation equation:

[0025]

[0026] k B is the Boltzmann constant, n e is the electron number density, c p e is the electron specific heat at constant pressure, T e is the electron temperature, is the number density of ions with charge number ζ, represents the formation energy of ions with charge number ζ formed from neutral atoms, λ e is the electron thermal conductivity, λ r is the reaction thermal conductivity, E is the electric field strength vector, e is the elementary charge, ε r is the net volume radiation coefficient of the plasma, δ e is the proportion of electron radiation in the total radiation of the plasma, K ex is the energy exchange coefficient between electrons and heavy particles, T h is the heavy particle temperature.

[0027] Heavy particle energy conservation equation:

[0028]

[0029] n h is the heavy particle number density, Z is the maximum charge carried by the ion, c p h is the heavy particle specific heat at constant pressure, λ h is the heavy particle thermal conductivity.

[0030]

[0031] N is the number of heavy particle species, is the mass of the heavy particle with charge ζ, m e is the electron mass, is the collision frequency of electrons and heavy particles, is the inelastic collision factor.

[0032] Current continuity equation:

[0033]

[0034] σ is the conductivity, is the electric potential.

[0035] Magnetic vector potential conservation equation:

[0036]

[0037] A is the magnetic vector potential, and μ0 is the magnetic permeability of vacuum.

[0038] Furthermore, the control equation of the solid phase in step 4 is corrected for the source term based on the energy conservation equation, the current continuity equation, and the magnetic vector potential conservation equation, including the following equations:

[0039] Energy conservation equation:

[0040]

[0041] T is the temperature, c p is the specific heat at constant pressure, κ is the thermal conductivity, ε is the emissivity, σ sb is the Stefan-Boltzmann constant.

[0042] Current continuity equation:

[0043]

[0044] Magnetic vector potential conservation equation:

[0045]

[0046] Furthermore, the control equation of the cathode-plasma coupling interface in step 4 is corrected for the boundary source term based on the microscopic physical mechanism of the cathode sheath layer. The specific microscopic physical mechanism is described as follows: During the arc discharge process, the electron sources on the cathode surface mainly include three contributions: thermionic emission, secondary electron emission, and electron back-diffusion, while the effects of photoionization and strong field emission in gas discharge can be ignored.

[0047] In the analysis of heat flux balance at the boundary, in addition to considering the heat conduction flux between the plasma and the electrode, specific sheath effects must also be considered: namely, 1) the emission of electrons produces a cooling effect on the cathode. 2) To maintain the surface temperature of the cathode at the threshold of thermionic emission, this cooling effect is compensated by the following mechanisms, including the heat flux generated by the acceleration of ions in the space charge region and the heat flux carried by the electrons diffusing back from the ionization region to the cathode. 3) In addition, the cathode also absorbs the heat from plasma radiation. 4) The present invention also considers the heat released when plasma ions recombine on the cathode surface.

[0048] Based on the above microscopic physical mechanisms, the present invention establishes the following control equations:

[0049] Current balance equation:

[0050]

[0051] σ cath is the cathode conductivity, the cathode potential, n is the normal vector, inter represents the interface, σ pl is the plasma conductivity, is the plasma potential, is the average ion charge number, φ i is the ion flux, φ em is the emitted electron flux, φ ems is the secondary electron emission flux, φ bd is the back-diffusing electron flux.

[0052]

[0053] n i is the ion number density, T cath is the cathode temperature, m i is the ion mass.

[0054]

[0055] γ cath is the material correction factor, h is the Planck constant, W is the work function, ΔW is the Schottky reduction.

[0056]

[0057] φ ems =γφ i (15)

[0058] U c is the cathode sheath voltage drop, γ is the secondary electron emission rate.

[0059] Heat flux balance equation:

[0060]

[0061] κ cath is the cathode thermal conductivity, κ h is the heavy particle thermal conductivity, q i is the ion heat flux, q em is the emitted electron heat flux, q bd is the back-diffused electron heat flux, q ems is the secondary electron emission heat flux, q r is the absorbed radiative heat flux, q re is the ion recombination heat flux at the cathode surface.

[0062]

[0063] U c is the cathode sheath voltage drop, E i is the ionization energy

[0064] q em = φ em (2k B T cath + W - ΔW) (18)

[0065] q bd = φ bd (2k B T e + W - ΔW) (19)

[0066] q ems = φ ems (2k B T cath + W - ΔW) (20)

[0067] q r = 4πε r (21)

[0068]

[0069] Furthermore, the governing equation of the anode-plasma coupling interface in step 4 is corrected for the boundary source term based on the microphysical mechanism of the anode sheath. The specific microphysical mechanism is described as follows: In the anode region, the accumulation of negative space charge due to the ion drift motion forms a negative anode voltage drop. To maintain current continuity, the anode jet compensates for the charge effect by additional ionization of neutral particles in the near-anode region, such as field emission under strong fields and thermal ionization at high temperatures.

[0070] In the above microphysical mechanism, the particle flux flowing towards the anode is mainly dominated by electrons. In the energy balance analysis of the coupling boundary, in addition to considering the heat conduction between the electrode and the plasma, it also includes the heating effect of the electrons collected through the arc channel on the anode and the radiant energy absorbed by the anode.

[0071] Based on the above microphysical mechanism, the present invention establishes the following control equations:

[0072] Current balance equation:

[0073]

[0074] σ an is the anode conductivity, is the anode potential, φ e is the electron flux.

[0075] Heat flux balance equation:

[0076]

[0077] κ an is the thermal conductivity of the anode, T an is the anode temperature, q e is the electron heat flux, q r is the radiant flux of the plasma.

[0078]

[0079] U a is the anode sheath voltage drop.

[0080] q r =4πε r (26)

[0081] Furthermore, the boundary conditions in step 5 are set as follows:

[0082] 1) At the coupling interface between the cathode and the plasma, the boundary condition of the cathode potential is calculated using Equation (11); the boundary condition of the heavy particle temperature is the heat flux boundary condition, calculated using Equation (16); the boundary condition of the electron temperature is zero flux; the boundary condition of the magnetic vector potential is zero flux.

[0083] 2) At the coupling interface between the anode and the plasma, the boundary condition of the anode potential is calculated using Equation (23); the boundary condition of the heavy particle temperature is the heat flux boundary condition, calculated using Equation (24); the boundary condition of the electron temperature is zero flux; the boundary condition of the magnetic vector potential is zero flux.

[0084] 3) The outer surface of the anode, with its temperature boundary condition being a fixed temperature to simulate the effect after forced cooling by cooling water; the electric potential boundary condition being a fixed zero value to simulate the actual grounded state; and the boundary condition of the magnetic vector potential being zero flux.

[0085] 4) The outer surface of the cathode, with its temperature boundary condition being a fixed temperature to simulate the effect after forced cooling by cooling water; its electric potential boundary condition being a fixed electric flux to simulate a constant current input, and the constant electric flux is shown in Equation (27); the boundary condition of the magnetic vector potential being zero flux.

[0086]

[0087] I is the input current, and R is the radius of the cathode tip.

[0088] 5) The inlet boundary, with its velocity boundary condition being a fixed mass flow rate; the boundary conditions of both the electron temperature and the heavy particle temperature being fixed values; the boundary condition of the electric potential being zero flux, and the boundary condition of the magnetic vector potential being a fixed zero value.

[0089] 6) The outlet boundary, which is in direct contact with the atmospheric pressure, and the boundary conditions of all variables are zero flux.

[0090] Furthermore, in the simulation calculation of step 7, the following numerical solution strategies are adopted: ① A Coupled pressure-velocity coupling algorithm is used for steady-state solution; ② A PISO pressure-velocity coupling algorithm is used for transient solution; ③ An adaptive Newton downhill method is used to iteratively solve the cathode sheath voltage drop. This method ensures the accurate calculation of the cathode sheath voltage drop by dynamically adjusting the iteration step size, thereby accurately simulating the microscopic physical mechanism of the cathode sheath and meeting the requirements of current continuity.

[0091] Furthermore, the post-processing of the steady-state simulation results and transient simulation results in step 8 includes analyzing: the spatial distribution contour maps of physical property parameters such as velocity, electron temperature, heavy particle temperature, thermodynamic non-equilibrium degree, current density, and pressure; the vector diagram of the velocity vector; and the current and heat flow streamline trajectories of the sheath interface; as well as the time fluctuations of parameters such as voltage and electron temperature.

[0092] Compared with the prior art, the present invention has the following advantages:

[0093] 1) Since the plasma conductivity is significantly reduced due to the low temperature of the electrode boundary layer, the present invention avoids the limitation of the traditional equilibrium-based simulation that requires artificially applying a high conductivity to allow the current to flow to the anode by simulating the actual non-equilibrium effect of the electrode boundary layer based on the thermodynamic non-equilibrium state, thereby improving the physical authenticity of the simulation.

[0094] 2) By means of the coupled electrode sheath effect, the present invention accurately simulates the actual interaction between the plasma and the electrode, avoiding the errors caused by introducing artificial empirical parameters due to the neglect of the electrode sheath effect in the traditional technology, and significantly improving the simulation accuracy.

[0095] 3) The present invention uses the adaptive Newton downhill method to solve the cathode sheath voltage drop. While ensuring the current continuity, it improves the convergence speed of the numerical simulation and accurately captures the contribution of the sheath voltage drop to the input voltage of the plasma torch. Since the sheath voltage drop cannot be ignored in the input voltage of the plasma torch, this method further improves the overall accuracy of the numerical simulation and provides a more reliable theoretical basis for the design and optimization of the plasma torch. Brief Description of the Drawings

[0096] Figure 1 It is a schematic diagram of the finite volume discrete grid of the plasma torch of the present invention.

[0097] Figure 2 It is a schematic diagram of the non-linear function of the physical property parameters of the working medium (water vapor) of the plasma torch of the present invention with respect to temperature.

[0098] Figure 3 It is a flow chart of the iterative solution of the cathode sheath voltage drop by the adaptive Newton downhill method of the present invention.

[0099] Figure 4 It is a contour map of the temperature and pressure distribution of the steady-state calculation of the present invention.

[0100] Figure 5 It is a streamline diagram of the cathode sheath current density and a radial distribution diagram of the current flux components of the present invention.

[0101] Figure 6 It is a streamline diagram of the cathode sheath heat flux density and a radial distribution diagram of the heat flux components of the present invention.

[0102] Figure 7 It is a comparison diagram of the transient voltage waveform and the experimental measurement results of the present invention. Detailed Embodiment

[0103] The following further describes the present invention in detail in conjunction with the drawings and specific embodiments.

[0104] In the description of the present invention, it should be particularly noted that the expressions of the azimuth or positional relationships such as "center", "axial direction", "radial direction", "circumferential direction", "edge", etc. are all based on the relative positional relationships shown in the drawings. Such expressions are only used to simplify the description of the technical solutions of the present invention and do not limit the specific azimuth and structural forms of the devices or components, and therefore should not be construed as a restrictive interpretation of the present invention.

[0105] Regarding the connection relationships involved in the present invention, unless otherwise clearly defined, the terms "connected" and "coupled" should be understood in a broad sense. Specifically, it may include, but is not limited to, direct connection methods such as mechanical connection and electrical connection, and may also cover indirect connection achieved through an intermediate medium, as well as functional communication within two components. For those skilled in the art, the above terms can be accurately understood according to specific technical solutions.

[0106] As Figure 1 shown, based on the physical structure of the DC arc plasma torch in practical applications, a three-dimensional plasma torch geometric model is constructed, and mesh discretization processing is carried out to obtain a discretized analysis model for numerical calculation. In this embodiment, hexahedral unstructured meshes are used for discretization, and the mesh quality coefficients are all greater than 0.9, ensuring the accuracy and stability of numerical calculations.

[0107] As Figure 2 shown, functional relationships between the thermodynamic parameters and transport coefficients of the plasma torch working medium and temperature are established, specifically including: density, viscosity, conductivity, thermal conductivity of heavy particles, thermal conductivity of electrons, specific heat at constant pressure of heavy particles, and specific heat at constant pressure of electrons in the plasma phase; density, thermal conductivity, specific heat capacity, and conductivity of the cathode material; density, thermal conductivity, specific heat capacity, and conductivity of the anode material. It should be noted that all the above physical property parameters are non-linear functions of temperature, fully considering the influence of the temperature field on material properties. In this embodiment, water vapor plasma is selected as the plasma medium, tungsten is used as the cathode material, and copper is used as the anode material. These material selections are based on their excellent physical and chemical properties and engineering application experience.

[0108] A control equation set based on the theory of thermodynamic non-equilibrium state and coupling electrode sheath effect is established, specifically including: control equations for the fluid phase, control equations for the solid phase, control equations for the cathode-plasma coupling interface, and control equations for the anode-plasma coupling interface. This equation set completely describes the multi-physical field coupling behavior inside the plasma torch.

[0109] Boundary conditions for the numerical simulation of the DC arc plasma torch are set according to actual working conditions. In this example, the specific boundary condition parameters are shown in Table 2, and the setting of these parameters fully considers the physical constraint conditions in actual engineering applications.

[0110] Table 2 Boundary Conditions

[0111]

[0112] As Figure 3As shown in the figure, when calculating the coupling boundary conditions at the interface between the cathode and the plasma, the present invention proposes to use the adaptive Newton downhill method to iteratively solve the cathode sheath voltage drop. The specific solution process is as follows: ① First, obtain the electric potentials at the centers of the first-layer grids on both sides of the interface and the conductivities (σ cath , σ pl ) respectively, and calculate the distances (d cath , d pl ) from the centers of the first-layer grids on both sides of the interface to the interface; ② Based on the obtained parameters, calculate the equivalent conductivity between the first-layer grids on both sides of the interface ③ Calculate the conductive electric flux passing through this interface ④ Subsequently, set the initial value of the cathode sheath voltage drop (U c ), such as U c 0 = 5.0V; ⑤ Based on equations (12) - (15), calculate the ion flux (φ i ), emitted electron flux (φ em ), back-diffused electron flux (φ bd ), and secondary-emitted electron flux (φ ems ) at the interface, and then obtain the total electric flux ⑥ Then, determine whether the absolute error between the total electric flux (φ compute ) calculated in step ⑤ and the conductive electric flux (φ) calculated in step ③ is less than the preset allowable error (R); ⑦ If the two meet the accuracy requirements, calculate the ion heat flux (q i ), emitted electron heat flux (q em ), back-diffused electron heat flux (q bd ), secondary-emitted electron heat flux (q ems ), absorbed radiation heat flux (q r ), and the heat flux of ion recombination on the cathode surface (q re ) based on equations (17) - (22). Otherwise, use the adaptive Newton downhill method to iteratively solve the cathode sheath voltage drop, and the iteration formula is: In this embodiment, the value of the adaptive relaxation factor (α) is Subsequently, repeat the above steps ⑤ - ⑦ until the accuracy requirements are met. By introducing the adaptive relaxation factor, this method effectively improves the stability of iterative convergence and the calculation efficiency, providing reliable technical support for accurately solving the cathode sheath voltage drop.

[0113] During the steady-state calculation of the numerical simulation, the Coupled pressure-velocity coupling algorithm is adopted to synchronously solve the pressure field and the velocity field, and corresponding under-relaxation factors are set for each control equation to ensure the convergence of the calculation. Subsequently, the grid cells of the computational domain are initialized with the boundary conditions at the inlet. During the transient calculation of the numerical simulation, iterative solutions are carried out by setting a reasonable time step. If the time step is too large, it will lead to the inability to capture the finer dynamic evolution process, while if the time step is too small, it will result in huge computational resource consumption. In this embodiment, the initial conditions for the steady-state calculation are set as follows: the electron temperature is 10,000 K, the heavy particle temperature is 8,000 K, and the electrode temperature is 3,000 K. These initial conditions can effectively simulate the thermodynamic non-equilibrium state of the plasma after the arc ignition; the time step for the transient calculation is set to 0.1 μs to ensure the accuracy of the time resolution.

[0114] In the result post-processing stage, the spatial distribution characteristics of the following physical quantities are mainly analyzed: the velocity field, the electron temperature field, the heavy particle temperature field, the degree of thermodynamic non-equilibrium, the current density field, and the pressure field; meanwhile, the time evolution characteristics of parameters such as voltage are investigated; in addition, the current streamline diagram and the heat flux trajectory diagram of the sheath interface are also plotted to reveal the mass and heat transfer mechanisms at the electrode-plasma coupling interface.

[0115] As Figure 4 shown, this embodiment realizes the full-domain numerical steady-state simulation of the DC arc plasma torch of water vapor under the thermodynamic non-equilibrium state and the coupled electrode sheath effect. Specifically, Figure 4 in (a), it shows that the highest temperatures of the cathode and the anode are 3428.2 K and 1472.22 K respectively, where the highest temperature of the cathode is located in the central region of the cathode tip, and the highest temperature of the anode appears at the starting end of the anode. The highest temperature of the heavy particles reaches 11640.8 K. Figure 4 in (b), it shows that the highest electron temperature is 11687.2 K, and its spatial distribution shows the characteristics of higher amplitudes at the center of the arc column and the edges of the electrodes. In Figure 4 in (c), it shows that the maximum value of the plasma non-equilibrium degree is 6.77, which is located in the edge region of the middle electrode, while the minimum value is close to 1 and is distributed on the central axis of the arc column. In Figure 4 in (d), it shows the characteristics of the electric potential distribution: the electric potential of the anode is close to zero, and the electric potential of the plasma decreases along the axis from upstream to downstream. The total output voltage of the plasma torch is 59 V, which is composed of the arc column voltage, the cathode sheath voltage, and the anode sheath voltage.

[0116] As Figure 5As shown, this embodiment deeply reveals the physical mechanism of the cathode sheath. The current flows axially inside the cathode and converges at the tip center, and then is injected into the plasma through the sheath. In the plasma region, the current mainly flows into the anode through the anode arc root attachment point, and a small amount of current is conducted through the inner surface of the anode. It should be noted that there is also a current concentration area at the stepped expansion of the anode, where most of the current flows into the anode through the arc root attachment point, and the leakage current is connected to the inner surface of the anode. Figure 5 The radial distribution characteristics of the electric flux components in the cathode sheath are also shown: the total electron flux decreases with the increase of the radial radius, but there is a local peak at the electrode edge due to the field strength distortion. The electron emission flux of the electrode decreases with the increase of the radial radius when the radius is less than 2.5 mm, and tends to be stable when the radius exceeds 2.5 mm. In the region where the radial radius is less than 1 mm, the emission electron flux is greater than the ion flux; while when the radius exceeds 1 mm, the ion flux dominates. In contrast, the contributions of the secondary emission electron flux and the back-diffusion electron flux can be ignored.

[0117] As Figure 6 shown, this embodiment details the simulation of the heat flux transmission path in the cathode sheath. Inside the cathode, the heat flux diffuses from the tip to the boundary and the surface. The heat flux density in the plasma region is mainly concentrated in the arc column center and radiates towards the electrode boundary. In the near-anode region, the heat flux mainly shows a normal inflow into the anode. Figure 6 The radial distribution characteristics of the heat flux components at the cathode sheath boundary are also shown: the ion heat flux plays a dominant role in the sheath heat balance. Ions are accelerated from the plasma into the sheath and hit the cathode surface, and their kinetic energy is converted into heat energy, significantly increasing the local temperature. The energy released by ion recombination makes an important contribution to the cathode heating, while the cooling effect of the emitted electrons partially offsets the heat brought by the ions. The heat conduction between the electrode and the plasma mainly maintains the local heat redistribution, and its influence is relatively limited. The thermal effects of the secondary emission electron flux and the back-diffusion electron flux can be ignored.

[0118] As Figure 7 shown, this embodiment simulates the transient waveform of the voltage at both ends of the plasma torch electrode and conducts a comparative analysis with the experimental measurement results. The changing trends of the voltage waveforms in the simulation and the experiment are highly consistent, both indicating that the anode arc root is in a stable attachment mode and the arc length remains constant. The average measured voltage is 61.7 V, the numerical simulation result is 59.0 V, and the relative error is 4.4%. This deviation is mainly due to the influence of factors such as measurement system noise, electromagnetic interference in the experimental environment, and the surface state and wear degree of the electrode. Nevertheless, the error is still within an acceptable range, fully verifying the accuracy and reliability of the numerical simulation method of the present invention.

Claims

1. A numerical simulation method of a DC arc plasma torch based on thermodynamic non-equilibrium state and coupled electrode sheath effect, characterized in that: The following steps are involved: Step 1: Based on the physical structure of the actual DC arc plasma torch, a two-dimensional axisymmetric or three-dimensional equivalent geometric model of the plasma torch including the electrode is constructed; Step 2: Perform finite volume meshing on the geometric model established in step 1 to obtain a discretized analysis model suitable for numerical calculation; Step 3: Establishing thermodynamic parameters of the working medium of the DC arc plasma torch, including density, specific heat at constant pressure, mole fraction of each component, and transport coefficients including electrical conductivity, thermal conductivity, viscosity, and net volume radiation coefficient, wherein both thermodynamic parameters and transport coefficients are expressed as nonlinear functions of temperature; Step 4: Construct the control equations of the coupled electrode sheath effect based on the thermodynamic non-equilibrium state, including the control equations of the fluid phase, the control equations of the solid phase, the control equations of the cathode-plasma coupling interface, and the control equations of the anode-plasma coupling interface; Step 5: According to the actual working conditions, the boundary conditions of the DC arc plasma torch numerical simulation are set; Step 6: In the discretized analysis model obtained in step 2, the pressure field, temperature field, velocity field, turbulent kinetic energy, turbulent dissipation rate, electric potential field and magnetic vector potential field of each grid cell are numerically initialized; Step 7: Perform steady-state simulation calculation on the discretized analysis model obtained in step 2 to obtain steady-state distribution solutions of various physical parameters; perform transient simulation calculation on the discretized analysis model obtained in step 2 to obtain dynamic solutions of the evolution of various physical parameters over time; Step 8: Post-process the steady-state and transient simulation results obtained in step 7, including the distribution cloud map and vector map of the characteristic parameters and the curve of the characteristic parameters changing with spatial position or time.

2. The method for numerical simulation of a DC arc plasma torch based on thermodynamic non-equilibrium state and coupled electrode sheath effect according to claim 1, characterized in that: The control equations of the fluid phase in step 4 are corrected for source terms based on the Navier-Stokes equations, the current continuity equation, and the magnetic vector potential conservation equation, and specifically include the following equations: The Navier-Stokes equations include the mass conservation equation, momentum conservation equation, electron energy conservation equation, and heavy particle energy conservation equation; The mass conservation equation: ρ is mass density, t is time, and u is velocity vector; Momentum conservation equation: p is the pressure, τ is the viscous stress tensor, j is the current density vector, and B is the magnetic induction intensity vector; The electron energy conservation equation is: k B is the Boltzmann constant, n e is the electron number density, c p e is the specific heat of electron at constant pressure, T e is the electron temperature, is the number density of ions with charge ζ, represents the formation energy of an ion with charge ζ from a neutral atom, λ e is the electronic thermal conductivity, λ r is the thermal conductivity of the reaction, E is the electric field intensity vector, e is the elementary charge, ε r is the net volume radiative coefficient of the plasma, δ e is the proportion of electron radiation to the total plasma radiation, K ex is the energy exchange coefficient between electrons and heavy particles, T h is the heavy particle temperature; Heavy particle energy conservation equation: n h is the number density of heavy particles, Z is the maximum charge carried by the ion, c p h is the constant-pressure specific heat of heavy particles, λ h is the heavy particle thermal conductivity; N is the number of heavy particle types, is the mass of a heavy particle with charge ζ, m e is the mass of the electron, is the collision frequency of electrons and heavy particles, is the inelastic collision factor; Current continuity equation: σ is the conductivity, It is the electric potential. Magnetic vector potential conservation equation: A is the magnetic vector potential and μ0 is the magnetic permeability of vacuum.

3. The method for numerical simulation of a DC arc plasma torch based on thermodynamic non-equilibrium state and coupled electrode sheath effect according to claim 1, characterized in that: The control equation of the solid phase in step 4 is corrected by source terms based on the energy conservation equation, the current continuity equation and the magnetic vector potential conservation equation, including the following equations: Energy conservation equation: T is temperature, c p is the specific heat at constant pressure, κ is the thermal conductivity, ε is the emissivity, σ sb is the Stefan-Boltzmann constant. Current continuity equation: Magnetic vector potential conservation equation:

4. The method for numerical simulation of a DC arc plasma torch based on thermodynamic non-equilibrium state and coupled electrode sheath effect according to claim 1, characterized in that: The control equation of the cathode-plasma coupling interface in step 4 is modified by boundary source terms based on the microscopic physical mechanism of the cathode sheath. The specific microscopic physical mechanism is described as follows: During the arc discharge process, the electron sources on the cathode surface include three contributions: thermal electron emission, secondary electron emission, and electron back diffusion; In the heat flow balance analysis at the boundary, in addition to considering the heat conduction flux between the plasma and the electrode, the sheath effect must also be considered; Based on the above microscopic physical mechanism, the following control equation is established: Current balance equation: σ cath is the cathode conductivity, cathode potential, n is the normal vector, inter represents the interface, σ pl is the plasma conductivity, is the plasma potential, is the average ionic charge, φ i is the ion flux, φ em is the emitted electron flux, φ ems is the secondary emission electron flux, φ bd is the reverse diffusion electron flux; n i is the ion number density, T cath is the cathode temperature, m i is the mass of the ion; γ cath is the material correction factor, h is Planck's constant, W is the work function, and ΔW is the Schottky reduction; f ems =gf i (15) U c is the cathode sheath voltage drop, γ is the secondary electron emission rate; Heat flow balance equation: κ cath is the cathode thermal conductivity, κ h is the heavy particle thermal conductivity, q i is the ionic heat flux, q em is the emitted electron heat flux, q bd is the back-diffusion electron heat flux, q ems is the secondary emission electron heat flux, q r is the absorbed radiative heat flux, q re is the composite heat flux of ions on the cathode surface; U c is the cathode sheath voltage drop, E i is the ionization energy; q em =φ em (2k B T cath +W-ΔW)(18) q bd =φ bd (2k B T e +W-ΔW)(19) q ems =φ ems (2k B T cath +W-ΔW)(20) q r =4πε r (21) 5. The method for numerical simulation of a DC arc plasma torch based on thermodynamic non-equilibrium state and coupled electrode sheath effect according to claim 1, characterized in that: The control equation of the anode-plasma coupling interface in step 4 is corrected by the boundary source term based on the microscopic physical mechanism of the anode sheath. The specific microscopic physical mechanism is described as follows: in the anode region, the accumulation of negative space charge due to ion drift motion forms a negative anode voltage drop; To maintain current continuity, the anode jet compensates for the charge effect by additional ionization of neutral particles in the near-anode region; In the above microscopic physical mechanism, the particle flux to the anode is mainly dominated by electrons; in the energy balance analysis of the coupled boundary, in addition to considering the heat conduction between the electrode and the plasma, the heating effect of the electrons collected through the arc channel on the anode and the radiation energy absorbed by the anode are also included; Based on the above microscopic physical mechanism, the following control equation is established: Current balance equation: σ an is the anode conductivity, is the anode potential, φ e is the electron flux; Heat flow balance equation: κ an is the thermal conductivity of the anode, T an is the anode temperature, q e is the electron heat flux, q r is the radiative flux of the plasma; U a is the anode sheath voltage drop; q r =4πε r (26)。 6. The method for numerical simulation of a DC arc plasma torch based on thermodynamic non-equilibrium state and coupled electrode sheath effect according to claim 1, characterized in that: The boundary conditions in step 5 are set as follows: 1) At the coupling interface between cathode and plasma, the boundary condition of electric potential is the coupled current flux boundary condition to accurately describe the current continuity; the boundary condition of heavy particle temperature is the coupled heat flux boundary condition to ensure energy conservation; the boundary condition of electron temperature is zero flux, which is consistent with the physical mechanism of electron energy transfer; the boundary condition of magnetic vector potential is zero flux; 2) At the coupling interface between the anode and the plasma, the boundary condition of the electric potential is the coupled current flux boundary condition; the boundary condition of the heavy particle temperature is the heat flux boundary condition; the boundary condition of the electron temperature is zero flux; and the boundary condition of the magnetic vector potential is zero flux; 3) The temperature boundary condition of the anode outer surface is a fixed temperature to simulate the effect of forced cooling by cooling water; the electric potential boundary condition is a fixed zero value to simulate the actual grounding state; the magnetic vector potential boundary condition is zero flux; 4) The temperature boundary condition of the cathode outer surface is a fixed temperature to simulate the effect of forced cooling by cooling water; the electric potential boundary condition is a fixed electric flux to simulate a constant current input, and the constant electric flux is shown in formula (27); the boundary condition of the magnetic vector potential is zero flux; I is the input current, R is the radius of the cathode tip; 5) Inlet boundary, the velocity boundary condition is a fixed mass flow rate; the boundary conditions of electron temperature and heavy particle temperature are fixed values; the boundary condition of electric potential is zero flux, and the boundary condition of magnetic vector potential is a fixed zero value; 6) The outlet boundary is in direct contact with the atmospheric pressure, and the boundary conditions for all variables are zero flux.

7. The method for numerical simulation of a DC arc plasma torch based on thermodynamic non-equilibrium state and coupled electrode sheath effect according to claim 1, characterized in that: In the simulation calculation of step 7, the following numerical solution strategies are adopted: ① using the Coupled pressure-velocity coupling algorithm for steady-state solution; ② using the PISO pressure-velocity coupling algorithm for transient solution; ③ using the adaptive Newton downhill method to iteratively solve the cathode sheath voltage drop.

8. The method for numerical simulation of a DC arc plasma torch based on thermodynamic non-equilibrium state and coupled electrode sheath effect according to claim 1, characterized in that: The step 8 is to post-process the steady-state simulation results and the transient simulation results, including analyzing: the spatial distribution cloud diagram of velocity, electron temperature, heavy particle temperature, thermodynamic non-equilibrium, current density, and pressure physical parameters; the vector diagram of the velocity vector; and the current and heat flow streamline trajectory diagram of the sheath interface; and the time fluctuation of voltage and electron temperature parameters.

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