Bidirectional coupling numerical simulation method for plasma arc and molten pool

Abstract

The invention discloses a numerical simulation method for bidirectional coupling of a plasma arc and a molten pool. The method comprises the following steps: S1, establishing a numerical model of repeated cross iteration between the molten pool and the plasma arc in a plasma melting furnace; s2, realizing bidirectional coupling solution of the plasma arc and the molten pool through sequential iteration based on the numerical model; and S3, ending. According to the method, a numerical model of repeated cross iteration between a molten pool in a plasma melting furnace and a plasma arc is established, distribution of a flow field and a temperature field of the plasma arc is obtained by adopting an MHD equation, and change of a free liquid level of the molten pool is tracked by utilizing a VOF model. The heat transfer and flowing effects of a plasma arc on a molten pool are simulated based on a numerical model, and pits with specific depth and width are formed in the surface of the molten pool.

Description

Technical Field

[0001] The invention belongs to the technical field of plasma melting, and relates to a bidirectional coupling numerical simulation method of a plasma arc and a molten pool. Background Art

[0002] Plasma melting technology, with its high energy density, high energy utilization, and low flue gas pollution, has become an effective method for treating hazardous waste ash. This technology can completely eliminate dioxin-like organic compounds in hazardous waste ash, achieving harmless treatment and resource utilization. As a key component of plasma melting technology, PMF is widely used for heavy metal extraction and harmless treatment of hazardous waste ash.

[0003] The PMF operation process involves multiphase interactions among gas, liquid, solid, and plasma states, and the coupling of multiple physical fields such as velocity, temperature, concentration, and electromagnetic fields. This creates complexity in the flow and heat transfer within the plasma melting reaction system. To address the complexity of the PMF operation process, some researchers have used CFD to simulate the heat transfer and flow effects of the plasma arc on the molten pool. This has verified the influence of different parameters on the fluid flow and heat transfer behavior, providing a reliable reference for optimizing the operating conditions of the plasma melting furnace. However, this approach has not yet considered the impact of changes in the free surface of the molten pool on the plasma arc. Changes in the free surface of the molten pool can affect the stability and heat transfer of the arc, thereby affecting the efficiency and quality of the operation process. Therefore, it is difficult to meet the requirements for dynamic simulation of the flow and temperature fields under the complex interaction between the plasma arc and the molten pool during the development of PMF in plasma melting technology.

[0004] Therefore, it is urgent to establish a bidirectional coupling numerical simulation method for plasma arc and molten pool, which can not only clarify the dynamic change law of flow field and temperature field under the interaction between plasma arc and molten pool, but also clarify the key characteristics of molten pool pit formation, liquid surface flow characteristics and arc morphology changes, so as to efficiently realize the numerical simulation of plasma arc and molten pool. Summary of the Invention

[0005] In order to overcome at least one of the deficiencies of the prior art, the present invention provides a bidirectional coupling numerical simulation method of a plasma arc and a molten pool.

[0006] To achieve the above object, the present invention adopts the following technical solution: a numerical simulation method for bidirectional coupling between plasma arc and molten pool, comprising the following steps:

[0007] S1. Establish a numerical model of repeated cross-iteration between the molten pool and the plasma arc in the plasma melting furnace;

[0008] S2, based on the numerical model, realize the bidirectional coupling solution between plasma arc and molten pool through sequential iteration;

[0009] S3, end;

[0010] The numerical model includes MHD equation, VOF model and turbulence model. The MHD equation and turbulence model are used for the calculation of plasma arc, and the VOF model and turbulence model are used to realize the coupling calculation of gas-liquid two-phase flow of equivalent replacement jet and molten pool.

[0011] Furthermore, the plasma melting furnace includes a furnace top, a furnace chamber and a furnace bottom, the molten pool is located at the furnace bottom, the graphite cathode penetrates vertically into the molten pool from the center of the furnace top, the space above the free liquid surface is the furnace cavity, and the area between the plane where the bottom of the graphite cathode in the furnace cavity is located and the surface of the molten pool is the plasma arc area. The numerical model simulates the flow field and temperature field in the plasma arc area, and performs coupling calculations on the plasma arc and the molten pool.

[0012] Furthermore, the working equation of the MHD equation is as follows:

[0013] 1) Continuity equation:

[0014]

[0015] 2) Momentum equation:

[0016]

[0017] F L =J×B (3)

[0018] Where, is the Hamiltonian operator; ρ is the density, kg·m -3 ; u is the velocity vector, m·s -1 ; p is pressure, pa; F L is the Lorentz force source term, N·m -3 ; J is the current density vector, A·m -2 ; B is the magnetic induction intensity, T; μ e Indicates the effective viscosity coefficient, kg·m -1 ·s -1 , expressed by formula (4);

[0019] μ e =μ Ar +μ t (4)

[0020] Where μ Ar Indicates the dynamic viscosity of the argon plasma arc, kg·m -1 ·s -1 ;μ t represents the turbulent viscosity, kg·m -1 ·s -1 ;

[0021] 3) Energy equation:

[0022]

[0023] Where h is the plasma enthalpy, j·kg -1 ; T is the temperature of each point in the calculation area, K; S j and S d represent Joule heat and electron migration heat source terms, w·m -3 ;S R is the net radiated power, W·m -3 ;

[0024]

[0025] Where σ is the electrical conductivity, S·m -1 ;j r and j z Represent radial current density and axial current density, A·m -2 ;k B represents the Boltzmann constant, which is 1.38×10 -23 j.k -1 ; e represents the electron charge, which is 1.6×10 -19 C; r is the radial coordinate system; z is the axial coordinate system; λ e is the effective thermal conductivity, w·m -1 ·K -1 , expressed by the following formula:

[0026]

[0027] Where λ Ar Represents the thermal conductivity of the argon plasma arc, w·m -1 ·K -1 ;c p is the specific heat at constant pressure, j·kg -1 ·K -1 ;Pr t It represents the turbulent Prandtl number, which is 0.85;

[0028] The radiation loss source term adopts the net radiation model. When the net radiation model is used for calculation, each control body is regarded as an independent radiation emission source, and the net radiation emission power per unit volume S is obtained. R , expressed by formula (9);

[0029] S R =4πε N (9)

[0030] Where, ε N represents the net radiation coefficient of argon plasma, w·m-3 ·sr -1 When the energy absorbed by the plasma arc itself is not considered, the static radiation coefficient of the plasma medium is taken as the average radius of the plasma R p =The corresponding value when 0mm;

[0031] 4) Current continuity equation:

[0032]

[0033] 5) Magnetic induction intensity:

[0034]

[0035] Where, is the electric potential, V; B is the magnetic induction intensity, T; A is the magnetic vector potential, V·s·m -1 .

[0036] Furthermore, the working equation of the VOF model is as follows:

[0037] 1) For phase i, the continuity equation is:

[0038]

[0039] Where t represents time, s; α i is the volume fraction of the i-th phase; u i is the velocity vector of the ith node; ρ i is the density of phase i, in kg·m -3 ; is the mass source term, in kg·m -3 ·s -1 ; Phase volume fraction α in the formula i Satisfy formula (12); where m = 1 means there is one phase, m = 2 means there are two phases. For the study of gas-liquid two-phase flow, m = 2 is taken;

[0040]

[0041] 2) Momentum equation:

[0042]

[0043] Where g is the acceleration due to gravity, m·s -2 ;

[0044] 3) Energy equation:

[0045]

[0046] Where E is the total energy per unit mass, j·kg -1 ;Ei is the energy based on the specific heat of phase i and the common temperature, in units of j; S h is the source item.

[0047] Furthermore, the turbulence model is a turbulence closed model of the plasma arc, which describes the turbulence by turbulent kinetic energy k and dissipation rate ε.

[0048] The flow transport function is as follows:

[0049]

[0050] Where G k represents the turbulent kinetic energy generated by the mean velocity gradient, Y M is the dissipation rate caused by pulsating expansion in compressible turbulent flow, and are the turbulent Prandtl numbers k and ε, which are 1.0 and 1.3 respectively; C s1 and C s2 are model constants, with values ​​of 1.44 and 1.92, μ t Calculated by the following formula:

[0051]

[0052] Where C μ is the model constant, which is taken as 0.09.

[0053] Furthermore, the S2 includes the following steps:

[0054] S21, setting the molten pool surface to a rigid plane and setting initial parameters of the initial state;

[0055] S22, initialize the numerical model and run it, use the MHD equation to perform steady-state calculations on the plasma arc, and solve it iteratively until the flow field and temperature field distribution converge;

[0056] S23. Identify the section with the highest velocity in the arc column as the jet inlet, extract the total pressure and temperature distribution of this section from the calculation results of the MHD equation, turn off the Lorentz force and Joule heat source terms in the electromagnetic equation, and adjust the numerical model to approximate the plasma arc in the form of a jet;

[0057] S24, open the VOF model, perform transient simulation on the jet and molten pool in step S23 as a whole, calculate and track the temperature field, flow field and dynamic behavior of the free liquid surface in the molten pool;

[0058] S25, determining whether the free liquid surface changes with time, if so, executing step S24, if not, outputting the shape and temperature distribution information of the phase interface;

[0059] S26. Determine whether the free liquid surface at the current time is consistent with that at the previous time. If so, it is considered that the free liquid surface shape of the molten pool remains unchanged in the continuous cycle iteration, and the flow and heat exchange system composed of the plasma and the molten pool is considered to have reached a stable state. The cycle ends, and the calculation parameters are analyzed and sorted out. If not, close the VOF model, re-enable the electromagnetic equation, update the shape and temperature distribution of the free liquid surface to the stable state of the previous time, execute step S22, and repeat steps S22 to S26 based on the new molten pool shape.

[0060] Furthermore, in step S22, the MHD equation performs steady-state calculation on the plasma arc through a two-dimensional axisymmetric model to obtain the boundary of the calculation area.

[0061] Furthermore, the initial parameters include initial pole pitch, initial speed, and initial temperature.

[0062] Furthermore, the initial pole pitch is set to 100 mm.

[0063] In summary, the present invention is beneficial in that:

[0064] The present invention establishes a numerical model of repeated cross-iteration between the molten pool and the plasma arc in the plasma melting furnace, obtains the flow field and temperature field distribution of the plasma arc by adopting the MHD equation, and uses the VOF model to track the changes in the free liquid surface of the molten pool. Based on the numerical model, the heat transfer and flow effects of the plasma arc on the molten pool are simulated, and a pit with a specific depth and width will be formed on the surface of the molten pool. The pit reaches a stable state at t=3s. After the liquid surface of the molten pool is transformed into a concave surface, it will flow counterclockwise, while the speed and temperature decrease, and the arc column morphology also changes. The fluid near the pit of the molten pool circulates clockwise, and the melt speed can reach 0.3m·s -1 The numerical model not only clarifies the dynamic changes in the flow and temperature fields under the interaction between the plasma arc and the molten pool, but also identifies the key characteristics of the molten pool pit formation, liquid surface flow characteristics, and arc morphology changes, thus enabling efficient numerical simulation of the plasma arc and molten pool. BRIEF DESCRIPTION OF THE DRAWINGS

[0065] Figure 1 Graph showing the net radiation coefficient distribution of the argon plasma of the present invention.

[0066] Figure 2 Schematic diagram of the physical model of the plasma melting furnace simulation calculation domain of the present invention.

[0067] Figure 3 It is a schematic diagram of the calculation process of the bidirectional coupling between the plasma arc and the molten pool of the present invention.

[0068] Figure 4This is the pressure and temperature distribution diagram of the jet inlet at t=0s of the present invention.

[0069] Figure 5 This is a graph showing how the physical parameters of the high-temperature melt of the present invention vary with temperature.

[0070] Figure 6 This is a cloud diagram of the temperature field distribution in the plasma arc column area when the free liquid surface of the molten pool remains unchanged.

[0071] Figure 7 This is a distribution curve diagram of the multi-physical field parameters of the arc column axis when the free liquid surface of the molten pool remains unchanged.

[0072] Figure 8 It is a schematic diagram of the structural parameters of the molten pool pit of the present invention.

[0073] Figure 9 The velocity cloud diagram and vector diagram of the plasma arc column area are shown in the embodiment of the present invention when the free liquid surface of the molten pool remains unchanged.

[0074] Figure 10 This is the radial distribution diagram of the plasma arc multi-physical field at 1 mm away from the molten pool surface when the free liquid surface of the molten pool remains unchanged.

[0075] Figure 11 This is a cloud diagram showing the change of the gas phase volume fraction in the molten pool over time.

[0076] Figure 12 This is a distribution diagram of the pit depth and width of the molten pool at different times of the present invention.

[0077] Figure 13 This is a temperature distribution cloud diagram of the plasma arc of the present invention.

[0078] Figure 14 These are the velocity cloud diagram and vector diagram of the plasma arc of the present invention.

[0079] FIG15( a ) is a temperature distribution diagram of the plasma arc along the axis at different times according to the present invention.

[0080] FIG15( b ) is a diagram showing the velocity distribution of the plasma arc along the axis at different times according to the present invention.

[0081] FIG16( a ) is a diagram showing the potential gradient distribution of the plasma arc along the axis at different times according to the present invention.

[0082] FIG16( b ) is a diagram showing the current density distribution of the plasma arc along the axis at different times according to the present invention.

[0083] FIG17( a ) is a velocity distribution cloud diagram in the molten pool at t=3 s according to the present invention.

[0084] FIG17( b ) is a cloud diagram of the temperature distribution in the molten pool at t=3 s according to the present invention.

[0085] Figure 18 This is a current density distribution diagram of the molten pool surface in the plasma arc region at t=3s in the present invention. DETAILED DESCRIPTION

[0086] The following describes the embodiments of the present invention through specific examples. Those skilled in the art can easily understand other advantages and effects of the present invention from the content disclosed in this specification. The present invention can also be implemented or applied through other different specific embodiments. The details in this specification can also be modified or changed based on different viewpoints and applications without departing from the spirit of the present invention. It should be noted that the following embodiments and features in the embodiments can be combined with each other unless they conflict.

[0087] It should be noted that the illustrations provided in the following embodiments are merely schematic illustrations of the basic concept of the present invention. Therefore, the illustrations only show components related to the present invention and are not drawn according to the number, shape, and size of components in actual implementation. In actual implementation, the type, quantity, and proportion of each component may be changed arbitrarily, and the component layout may also be more complex.

[0088] All directional indications in the embodiments of the present invention (such as up, down, left, right, front, back, horizontal, vertical...) are only used to explain the relative position relationship, movement status, etc. between the components in a certain specific posture. If the specific posture changes, the directional indication will also change accordingly.

[0089] Due to installation errors and other reasons, the parallel relationship referred to in the embodiments of the present invention may actually be an approximately parallel relationship, and the perpendicular relationship may actually be an approximately perpendicular relationship.

[0090] Example 1:

[0091] A method for numerically simulating bidirectional coupling of a plasma arc and a molten pool comprises the following steps:

[0092] S1. Establish a numerical model of repeated cross-iteration between the molten pool and the plasma arc in the plasma melting furnace;

[0093] The geometric configuration of the plasma melting furnace is as follows Figure 2As shown, the plasma melting furnace includes a furnace top, a furnace hearth, and a furnace bottom. The molten pool is located in the furnace hearth, and the bottom of the molten pool is the furnace bottom. The graphite cathode penetrates vertically from the center of the furnace top into the furnace hearth molten pool. The surface of the molten pool is the free liquid surface. The space above the free liquid surface is called the furnace chamber. The furnace chamber can be regarded as a cylinder. The furnace chamber is divided into two areas. The plane where the bottom of the graphite cathode is located is the boundary. The area above is the flue gas area, and the area from the bottom of the graphite cathode to the surface of the molten pool is the plasma arc area. The spherical crown area at the bottom of the molten pool, i.e., the furnace bottom, is used to fix the molten steel and connect the needle electrode (anode) at the bottom. r represents the radial coordinate system, z represents the axial coordinate system (the direction of the jet gas), and the calculation area is approximately regarded as an axisymmetric cylindrical area, and a two-dimensional axisymmetric model is established. Preferably, when simulating the flow field and temperature field of the plasma arc area, in the initial state, the model radius of the plasma arc calculation area is 1.25m and the axial distance is 0.1m. In the cross-coupling calculation of the jet and the molten pool, the radius of the molten pool calculation area is 1.331m, the depth is 0.4m, and the initial pole distance is 100mm.

[0094] When the free surface of the molten pool changes, the flow field and temperature field in the plasma arc area are simulated based on the numerical model, and the plasma arc and the molten pool are coupled. This includes the MHD equation, VOF model and turbulence relationship. The MHD equation and turbulence relationship are used to calculate the plasma arc. The VOF model and turbulence relationship realize the equivalent replacement of the jet and the gas-liquid two-phase flow coupling calculation of the molten pool.

[0095] The basic working equation of the MHD equation is as follows:

[0096] 1) Continuity equation:

[0097]

[0098] 2) Momentum equation:

[0099]

[0100] F L =J×B (3)

[0101] Where, is the Hamiltonian operator; ρ is the density, kg·m -3 ; u is the velocity vector, m·s -1 ; p is pressure, pa; F L is the Lorentz force source term, N·m -3 ; J is the current density vector, A·m -2 ; B is the magnetic induction intensity, T; μ e Indicates the effective viscosity coefficient, kg·m -1 ·s -1 , expressed by formula (4).

[0102] μ e =μ Ar +μ t (4)

[0103] Where μ Ar Indicates the dynamic viscosity of the argon plasma arc, kg·m -1 ·s -1 ;μ t represents the turbulent viscosity, kg·m -1 ·s -1 .

[0104] 3) Energy equation:

[0105]

[0106] Where h is the plasma enthalpy, j·kg -1 ; T is the temperature of each point in the calculation area, K; S j and S d represent Joule heat and electron migration heat source terms, w·m -3 ;S R is the net radiated power, W·m -3 ;λ e is the effective thermal conductivity, w·m -1 ·K -1 .

[0107]

[0108] Where σ is the electrical conductivity, S·m -1 ;j r and j z Represent radial current density and axial current density, A·m -2 ;k B represents the Boltzmann constant, which is 1.38×10 -23 j.k -1 ; e represents the electron charge, which is 1.6×10 -19 C; r is the radial coordinate system; z is the axial coordinate system; λ e It is expressed by the following formula:

[0109]

[0110] Where λ Ar Represents the thermal conductivity of the argon plasma arc, w·m -1 ·K -1 ;c p is the specific heat at constant pressure, j·kg -1 ·K -1 ;Pr tIt represents the turbulent Prandtl number, which is 0.85.

[0111] The radiation loss source term adopts the net radiation model. When the net radiation model is used for calculation, each control body is regarded as an independent radiation emission source, and the net radiation emission power per unit volume S can be obtained. R , expressed by formula (9).

[0112] S R =4πε N (9)

[0113] Where, ε N represents the net radiation coefficient of argon plasma, w·m -3 ·sr -1 When the energy absorbed by the plasma arc itself is not considered, the static radiation coefficient of the plasma medium is taken as the average radius of the plasma R p =0mm, see the corresponding value for specific values. Figure 1 .

[0114] 4) Current continuity equation:

[0115]

[0116] 5) Magnetic induction intensity:

[0117]

[0118] Where, is the electric potential, V; B is the magnetic induction intensity, T; A is the magnetic vector potential, V·s·m -1 .

[0119] The specific control equation of the VOF model is as follows:

[0120] 1) For phase i, the continuity equation is:

[0121]

[0122] Where t represents time, s; α i is the volume fraction of the i-th phase; ui is the i-th velocity vector; ρ i is the density of phase i, in kg·m -3 ; is the mass source term, in kg·m -3 ·s -1 The phase volume fraction α in the formula i Satisfies equation (12). Where m = 1 means there is one phase, m = 2 means there are two phases. For the study of gas-liquid two-phase flow, m = 2 is used.

[0123]

[0124] 2) Momentum equation:

[0125]

[0126] Where g is the acceleration due to gravity, m·s -2 .

[0127] 3) Energy equation:

[0128]

[0129] Where E is the total energy per unit mass, j·kg -1 ;E i is the energy based on the specific heat and common temperature of the phase, j; S h is the source item.

[0130] The turbulence model uses the standard k-ε turbulence model, whose equation is suitable for turbulence simulation under high Reynolds numbers. This application uses it as a closed model of plasma arc turbulence. The model describes the turbulent transport effect through turbulent kinetic energy k and dissipation rate ε. The specific equation is as follows:

[0131]

[0132] Where G k represents the turbulent kinetic energy generated by the mean velocity gradient, Y M is the dissipation rate caused by pulsating expansion in compressible turbulent flow, and are the turbulent Prandtl numbers k and ε, which are 1.0 and 1.3 respectively. s1 and C s2 are model constants, with values ​​of 1.44 and 1.92, μ t It can be calculated by the following formula:

[0133]

[0134] Where C μ is the model constant, which is taken as 0.09.

[0135] S2, based on the numerical model, realize the bidirectional coupling solution between plasma arc and molten pool through sequential iteration;

[0136] The S2 comprises the following steps:

[0137] S21, setting the molten pool surface as a rigid plane, and setting initial parameters of the initial state, including initial pole distance, initial speed, initial temperature, etc.;

[0138] S22, initialize the numerical model and run it, use the MHD equation to perform steady-state calculations on the plasma arc, and solve it iteratively until the flow field and temperature field distribution converge;

[0139] S23. Identify the section with the highest velocity in the arc column as the jet inlet, extract the total pressure and temperature distribution of this section from the calculation results of the MHD equation, turn off the Lorentz force and Joule heat source terms in the electromagnetic equation, and adjust the numerical model to approximate the plasma arc in the form of a jet;

[0140] S24, open the VOF model, perform transient simulation on the jet and molten pool in step S23 as a whole, calculate and track the temperature field, flow field and dynamic behavior of the free liquid surface in the molten pool;

[0141] S25, determining whether the free liquid surface changes with time, if so, executing step S24, if not, outputting the shape and temperature distribution information of the phase interface;

[0142] S26. Determine whether the free liquid surface at the current time is consistent with that at the previous time. If so, it is considered that the free liquid surface shape of the molten pool remains unchanged in the continuous cycle iteration, and it is considered that the flow and heat exchange system composed of the plasma and the molten pool has reached a stable state. The cycle ends, and the calculation parameters are analyzed and sorted out. The parameters include the temperature field, flow field, free liquid surface shape and plasma arc of the molten pool. If not, close the VOF model, re-enable the electromagnetic equation, update the shape and temperature distribution of the free liquid surface to the stable state of the previous time, execute step S22, and repeat steps S22 to S26 based on the new molten pool shape.

[0143] In step S22, the MHD equation performs steady-state calculation on the plasma arc through a two-dimensional axisymmetric model. The calculation area is half of the symmetry axis section. The boundary conditions of the entire calculation area are shown in Table 1.

[0144] Table 1 Boundary conditions of plasma arc calculation area

[0145]

[0146] The plasma arc itself has a high temperature and is almost non-conductive when the temperature is below 4000K. In conventional calculations, the arc column area (i.e. Figure 2The initial temperature of the area (the dotted line between the bottom of the graphite cathode and the surface of the molten pool) is set lower than 4000K, which results in a slow calculation of the potential distribution. The potential gradient near the cathode spot will always be at a large value, causing excessive Joule heating in the area near the spot, and ultimately causing the plasma arc temperature to exceed the positive range. In addition, due to the large radial range of the geometric model, the temperature in the gas area outside the arc column is much less than 4000K. Therefore, to improve the above problem, the temperature initialization value of the calculation area is set to a piecewise function of the calculation domain radius R during calculation in this embodiment. This can prevent the temperature calculation value from exceeding the normal range, accelerate gas ionization and plasma arc formation, and improve the convergence speed. The specific temperature values ​​are as follows:

[0147]

[0148] The jet inlet in step S23 refers to the inlet of the jet gas. In the cross-coupling calculation of the jet and the molten pool, the arc column cross section where the maximum velocity is located in the plasma arc calculation result is used as the jet inlet. The plasma arc is a compressible gas with a high airflow velocity. The dynamic pressure converted from kinetic energy is much greater than the static pressure. Therefore, when calculating, the inlet boundary type of the jet gas is set to a pressure inlet, and its pressure and temperature are the total pressure (the sum of dynamic pressure and static pressure) and temperature distribution on the arc column cross section. The jet inlet pressure and temperature distribution under initial conditions are as follows: Figure 4 The temperature and pressure of the remaining boundaries of the jet region remain consistent with those in the plasma arc calculation. The initial conditions for the jet and molten pool calculations are based on the temperature, pressure, velocity, turbulent kinetic energy, and turbulent kinetic energy dissipation rate of the jet region, which are derived from the plasma arc calculation. The initial velocity within the molten pool is 0, and the temperature is 1600 K.

[0149] The thermal conductivity and constant pressure specific heat of the high temperature melt used in the calculation are based on the mass ratio of the high temperature slag composed of Al2O3-SiO2-CaO. The density, dynamic viscosity and electrical conductivity are measured by the high temperature melt physical parameter measuring device model VWR1600. The specific parameters are shown in Figure 5 .

[0150] S3. End.

[0151] When the PMF starts running, hazardous waste ash and SiO2 flux enter the furnace and fall into the molten pool. A high-temperature plasma arc is formed between the graphite cathode and the molten pool anode to heat the molten pool. This embodiment monitors the temperature field and velocity field changes of the plasma arc and the flow field changes of the molten pool during this process, and obtains Figure 6-Figure 12 Schematic diagram, the following results are obtained:

[0152] Figure 6 and Figure 7The figures are respectively the temperature distribution cloud diagram of the plasma arc column area and the multi-physics field parameter distribution curve diagram of the arc column axis when the free liquid surface of the molten pool remains unchanged. In the initial state, that is, when the free liquid surface of the molten pool does not change, the temperature field of the arc column presents a typical bell-shaped shape; Figure 8 It can be seen that in the axial direction, the temperature and velocity of the arc column gradually decrease from the cathode to the anode, and the pressure at the center of the arc column first decreases and then increases. Figure 9 It can be seen that in the radial direction, the temperature and velocity of the arc column show that the center temperature is higher than those on both sides.

[0153] Figure 10 Schematic diagram of the molten pool pit structure parameters. Figure 11 The cloud diagram of the change of gas phase volume fraction in the molten pool over time. As the free liquid surface of the molten pool changes over time, a pit of a certain depth and width is formed on the surface of the molten pool due to the high pressure of the plasma arc. Bubble groups are generated on both sides of the pit due to the flow of plasma. The depth and width are obtained by existing means. Figure 12 It can be seen that at t = 3s, the pit depth is stable at 0.072m and the width is 0.103m.

[0154] In this embodiment, when simulating the flow field changes of the molten pool and the plasma arc in a plasma arc furnace for 3 seconds, the free liquid surface of the molten pool changes from a horizontal surface to a concave surface, and the shape, temperature distribution, and velocity distribution of the arc column undergo significant changes. The results are as follows: Figures 13-18 shown.

[0155] Figure 13 This is a temperature distribution cloud diagram of the plasma arc. The arc column in the figure is no longer bell-shaped, and a secondary high-temperature zone (temperature greater than 7000K) is generated at the bulge of the molten pool. The Joule heat at the bulge of the molten pool is relatively large, and the heat exchange with the surrounding plasma arc is more intense, thus expanding the high-temperature area of ​​the plasma arc.

[0156] Figure 14 These are the velocity contours and vector diagrams of the plasma arc. When pits are present on the molten pool surface, the plasma arc forms a counterclockwise flow near the center. At bulges on the molten pool surface, the radial Lorentz force of the plasma arc points toward the central axis, causing the plasma to flow toward the center. Upon reaching the graphite cathode, it is entrained and then rises along the axis, forming a closed-loop flow path.

[0157] Figure 15(a) shows the temperature distribution of the plasma arc along the axis at different times. When the free surface of the molten pool changes from a flat surface to a concave surface, the plasma arc temperature at the axis decreases. The formation of the pit reduces the current density along the axis, reducing Joule heating and, consequently, the plasma arc temperature. The maximum temperature of the plasma arc drops from 19,991 K to 19,387 K.

[0158] Figure 15(b) shows the velocity distribution of the plasma arc along the axis at different times. As time changes from 0s to 3s, the plasma arc velocity at the axis decreases. Figures 16(a) and 16(b) show the potential gradient and current density distribution of the plasma arc along the axis at different times, respectively. Combining the analysis of Figures 16(a) and 16(b), it can be seen that the change in the shape of the molten pool surface reduces the potential gradient on the axis, and the current density decreases accordingly, thereby reducing the Lorentz force on the plasma, and ultimately causing its velocity to decrease from 2116m·s -1 Down to 1593m·s -1 .

[0159] Figure 17(a) shows the velocity distribution and melt flow trajectory in the molten pool at t = 3s. At this time, the fluid near the molten pool pit circulates clockwise with a maximum velocity of 0.3m·s -1 The plasma arc stops at the deepest part of the pit and then moves to both sides, pushing the melt to flow upward along the surface of the molten pool. The melt at the bottom of the pit continuously fills the central area, forming a clockwise flow pattern.

[0160] Figure 17(b) shows the temperature distribution of the molten pool at t = 3 s. The bubble cluster near the pit plays an important role in heating the molten pool. The high-temperature gas transfers heat to the melt through the bubble cluster, effectively raising the molten pool temperature.

[0161] Figure 18 The current density distribution on the melt pool surface in the plasma arc region at t = 3 s is shown in the figure. As can be seen from the figure, at t = 3 s, a higher current density is generated at the protrusions on the melt pool surface. Therefore, the melt at these protrusions is more affected by Joule heating. Since the influence of Joule heating is not considered when calculating the temperature field within the melt pool, the calculated melt temperature distribution will be lower than the actual value.

[0162] Obviously, the embodiments described are only some of the embodiments of the present invention, not all of them. Based on the embodiments of the present invention, all other embodiments obtained by ordinary technicians in this field without making creative efforts should fall within the scope of protection of the present invention.

Claims

1. A numerical simulation method for bidirectional coupling between plasma arc and molten pool, characterized by: The following steps are involved: S1. Establish a numerical model of repeated cross-iteration between the molten pool and the plasma arc in the plasma melting furnace; S2, based on the numerical model, realize the bidirectional coupling solution between plasma arc and molten pool through sequential iteration; S3, end; The numerical model includes MHD equation, VOF model and turbulence model. MHD equation and turbulence model are used to calculate plasma arc. The VOF model and turbulence model are used to realize the coupled calculation of the gas-liquid two-phase flow of the equivalent replacement jet and the molten pool.

2. The method for numerically simulating bidirectional coupling between a plasma arc and a molten pool according to claim 1, characterized in that: The plasma melting furnace includes a furnace top, a furnace chamber and a furnace bottom. The molten pool is located at the furnace bottom. The graphite cathode vertically penetrates the molten pool from the center of the furnace top. The space above the free liquid surface is the furnace cavity. The area between the plane where the bottom of the graphite cathode is located in the furnace cavity and the surface of the molten pool is the plasma arc area. The numerical model simulates the flow field and temperature field in the plasma arc area and performs coupling calculations on the plasma arc and the molten pool.

3. The method for numerical simulation of bidirectional coupling between plasma arc and molten pool according to claim 1, characterized in that: The working equation of the MHD equation is as follows: 1) Continuity equation: 2) Momentum equation: F L =J×B (3) Where, is the Hamiltonian operator; ρ is the density, kg·m -3 ; u is the velocity vector, m·s -1 ; p is pressure, pa; F L is the Lorentz force source term, N·m -3 ; J is the current density vector, A·m -2 ; B is the magnetic induction intensity, T; μ e Indicates the effective viscosity coefficient, kg·m -1 ·s -1 , expressed by formula (4); m e =μ Ar +m t (4) Where μ Ar Indicates the dynamic viscosity of the argon plasma arc, kg·m -1 ·s -1 ;μ t represents the turbulent viscosity, kg·m -1 ·s -1 ; 3) Energy equation: Where h is the plasma enthalpy, j·kg -1 ; T is the temperature of each point in the calculation area, K; S j and S d represent Joule heat and electron migration heat source terms, w·m -3 ; S R is the net radiated power, W·m -3 ; Where σ is the electrical conductivity, S·m -1 ;j r and j z Represent radial current density and axial current density, A·m -2 ;k B represents the Boltzmann constant, which is 1.38×10 -23 j.k -1 ; e represents the electron charge, which is 1.6×10 -19 C; r is the radial coordinate system; z is the axial coordinate system; λ e is the effective thermal conductivity, w·m -1 ·K -1 , expressed by the following formula: Where λ Ar Represents the thermal conductivity of the argon plasma arc, w·m -1 ·K -1 ;c p is the specific heat at constant pressure, j·kg -1 ·K -1 ; Pr t It represents the turbulent Prandtl number, which is 0.85; The radiation loss source term adopts the net radiation model. When the net radiation model is used for calculation, each control body is regarded as an independent radiation emission source, and the net radiation emission power per unit volume S is obtained. R , expressed by formula (9); S R =4πε N (9) Where, ε N represents the net radiation coefficient of argon plasma, w·m -3 ·sr -1 When the energy absorbed by the plasma arc itself is not considered, the static radiation coefficient of the plasma medium is taken as the average radius of the plasma R p =The corresponding value when 0mm; 4) Current continuity equation: 5) Magnetic induction intensity: Where, is the electric potential, V; B is the magnetic induction intensity, T; A is the magnetic vector potential, V·s·m -1 .

4. The method for numerically simulating bidirectional coupling between a plasma arc and a molten pool according to claim 2, characterized in that: The working equation of the VOF model is as follows: 1) For phase i, the continuity equation is: Where t represents time, s; α i is the volume fraction of the i-th phase; u i is the velocity vector of the ith node; ρ i is the density of phase i, in kg·m -3 ; is the mass source term, in kg·m -3 ·s -1 ; Phase volume fraction α in the formula i Satisfy formula (12); where m = 1 means there is one phase, m = 2 means there are two phases. For the study of gas-liquid two-phase flow, m = 2 is taken; 2) Momentum equation: Where g is the acceleration due to gravity, m·s -2 ; 3) Energy equation: Where E is the total energy per unit mass, j·kg -1 ; E i is the energy based on the specific heat of phase i and the common temperature, in units of j; S h is the source item.

5. The method for numerically simulating bidirectional coupling between a plasma arc and a molten pool according to claim 4, characterized in that: The turbulence model is a turbulence closed model of the plasma arc. The model describes the turbulent transport effect through the turbulent kinetic energy k and the dissipation rate ε. The equation is as follows: Where G k represents the turbulent kinetic energy generated by the mean velocity gradient, Y M is the dissipation rate caused by pulsating expansion in compressible turbulent flow, and are the turbulent Prandtl numbers k and ε, which are 1.0 and 1.3 respectively; C s1 and C s2 are model constants, with values ​​of 1.44 and 1.92, μ t Calculated by the following formula: Where C μ is the model constant, which is taken as 0.

09.

6. The method for numerically simulating bidirectional coupling between a plasma arc and a molten pool according to claim 4, characterized in that: The S2 comprises the following steps: S21, setting the molten pool surface to a rigid plane and setting initial parameters of the initial state; S22, initialize the numerical model and run it, use the MHD equation to perform steady-state calculations on the plasma arc, and solve it iteratively until the flow field and temperature field distribution converge; S23. Identify the section with the highest velocity in the arc column as the jet inlet, extract the total pressure and temperature distribution of this section from the calculation results of the MHD equation, turn off the Lorentz force and Joule heat source terms in the electromagnetic equation, and adjust the numerical model to approximate the plasma arc in the form of a jet; S24, open the VOF model, perform transient simulation on the jet and molten pool in step S23 as a whole, calculate and track the temperature field, flow field and dynamic behavior of the free liquid surface in the molten pool; S25, determining whether the free liquid surface changes with time, if so, executing step S24, if not, outputting the shape and temperature distribution information of the phase interface; S26. Determine whether the free liquid surface at the current time is consistent with that at the previous time. If so, it is considered that the free liquid surface shape of the molten pool remains unchanged in the continuous cycle iteration, and the flow and heat exchange system composed of the plasma and the molten pool is considered to have reached a stable state. The cycle ends, and the calculation parameters are analyzed and sorted out. If not, close the VOF model, re-enable the electromagnetic equation, update the shape and temperature distribution of the free liquid surface to the stable state of the previous time, execute step S22, and repeat steps S22 to S26 based on the new molten pool shape.

7. The method for numerical simulation of bidirectional coupling between plasma arc and molten pool according to claim 4, characterized in that: In step S22, the MHD equation performs steady-state calculation on the plasma arc through a two-dimensional axisymmetric model to obtain the boundary of the calculation area.

8. The method for numerical simulation of bidirectional coupling between plasma arc and molten pool according to claim 5, characterized in that: The initial parameters include initial pole pitch, initial speed, and initial temperature.

9. The method for numerically simulating bidirectional coupling between a plasma arc and a molten pool according to claim 5, characterized in that: The initial pole pitch is set to 100 mm.

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