Computation of steady flow in the molten pool at electric-arc heating

Peculiarities of the formation of melt hydrodynamics in the molten pool of electric arc as a result of a viscous interaction with the arc plasma flow and the effect of electromagnetic forces are considered. It is shown that in a relatively shallow pool, the role of viscous interaction with plasma flow predominates electromagnetic forces. In a deeper pool, the flow in peripheral upper region is formed as before by a viscous interaction between plasma and melt, and the electromagnetic forces dominate in deep regions.     

Behavior of Sustained High-Current Arcs on Molten Alloy Electrodes during Vacuum Consumable Arc Remelting

Vacuum consumable arc remelting is a casting process carried out in a vacuum with the aim of remelting the consumable electrode in such a way that the new ingot has improved chemical and physical homogeneity. The power which causes the melting is supplied by a vacuum arc burning between the electrodes. In order to determine the furnace partitions of electrical power and current, experiments were conducted on molten-faced round electrodes. The quasi-steady melt rate was determined for both horizontally opposed 15-cm-diameter Ni electrodes and for vertically suspended 40-cm-diameter Inconel 718 electrodes. The cathode thermal power is directly proportional to the melt rate which, for the horizontally opposed electrode experiment, agrees to within 10 percent with the Ni breaker switch calorimetry measurements and with predictions from retarded potential analyzer plasma data. However, for the vertically suspended electrode experiments, the measured thermal power at the cathode is 50 percent higher than for nickel. When CO is introduced into the vertical alloy electrode system and electrode gap is increased, the cathode thermal power is reduced by approximately 50 percent. Furthermore, the electrode position measurements and observation of the ingot surface suggest that a concentrated arc is formed under these conditions.     

The Influence of the Self-Magnetic Field on the Steady-State Current Distribution in an Axially Flowing Conducting Medium

The steady-state electric current distribution in a multicathode-spot vacuum arc was determined by a solution of the magnetic transport equation subject to various boundary conditions. The inter-electrode region of the arc is modeled as a uniform plasma flowing from the cathode to the anode. Dimensional analysis shows that three parameters determine the magnetic field, and hence the current density which is derived from it: AR-the ratio of the electrode separation to the electrode radius, Rmm-magnetic Reynolds number of the axial material flow, and Rme-magnetic Reynolds number of the axial electron flow. While the anode side of the conducting medium is described as an equipotential surface, the following three cases of boundary conditions for the cathode side are examined: 1) a known current density distribution is assumed over the entire cathode side of the plasma surface; 2) the cathode side is an equipotential surface; and 3) the current is allowed to cross the cathode surface only through a finite number of ring shaped regions. Numerical solutions of the nonlinear magnetic transport equation show a constriction of the current at the anode side for all boundary conditions mentioned. On the other hand, the current moves to the perimeter of the cathode for boundary condition 2). When AR, Rmm, and Rme equal 0.72,-0.16, and 1.73, respectively, and a uniform current density flows at the cathode side, the on-axis current density at the anode is six times larger than its value at the cathode.     

Anode Phenomena in Vacuum and Atmospheric Pressure Arcs

This paper summarizes recent experimental data related to anode phenomena in both vacuum and atmospheric pressure arcs. Currents in the range 10A to 3OkA are discussed, and particular emphasis is placed on the effect of plasma flow from the cathode. For vacuum arcs this plasma flow is the directed motion of metal ions from the cathode spots. These ions reduce the anode voltage drop, and maintain a diffuse anode termination. At atmospheric pressure the ion flow is impeded by gas-atom collisions. However, a plasma flow towards the anode can result from magnetic pinch forces at the constricted cathode termination. In the absence of plasma flow, the anode termination constricts to a vigorously evaporating anode spot. For a typical non-refractory electrode such as copper, the spot operates at a temperature close to the boiling point irrespective of the gas pressure. The spot temperature is dictated by the balance between electrical input power and evaporative losses. These anode phenomena are discussed in relation to vacuum switchgear, arc welding and arc furnaces.     

A physical model of the low-current-density vacuum arc

A one-dimensional (1-D) physical model of the low-current-density steady-state vacuum arc is proposed. The model is based on the continuity equations for ions and electrons and the energy balance for the discharge system; the electric potential distribution in the discharge gap is assumed to be nonmonotonic. It is supposed that the ion current at the cathode is generated within the cathode potential fall region due to the ionization of the evaporated atoms by the plasma thermal electrons having Boltzmann's energy distribution. The model offers a satisfactory explanation for the principal regularities of a hot-cathode vacuum arc with diffuse attachment of the current. The applicability of the model proposed to the explanation of some processes occurring in a vacuum arc, such as the flow of fast ions toward the anode, the current cutoffs and voltage bursts, and the backward motion of a cathode spot in a transverse magnetic field is discussed     

大面积分散电弧等离子体的ICCD图像分析

用增强型电荷耦合检测器(ICCD)和窄带干涉滤光片相结合的方法拍摄了未饱和氩等离子体的分散电弧的非饱和图像。对不同励磁电流下电弧形态的分析比较,证实了在强电磁力的作用下弧柱趋于扩散。在电弧完全分散条件下,对ICCD拍摄非饱和图像的光强分析,表明分散电弧具有较为均匀的分布。所采集的电弧电压的脉动幅度显著降低,分散电弧稳定运行。实验中观测到了稳定的多阴极弧根和弥散阴极弧根的现象,这表明电弧已扩散。     

Temperature Dependence of Retrograde Velocity of Vacuum Arcs in Magnetic Fields

Retrograde velocity of vacuum arcs in transverse magnetic fields is known to depend on, among other things, the magnetic induction, the arc current, the electrode spacing, the cathode material, and the cathode surface condition, and was also found to depend on the cathode temperature. Using the optical method, the retrograde velocity was measured as a function of the cathode temperature with copper, aluminum, and stainless steel as cathode materials. The optical measurement shows that by increasing the cathode temperature, the arc velocity decreases. It appears that with the increase in the cathode temperature, the decrease of the arc velocity is related to the increase of the cathode crater radius. The experimentally measured temperature dependence of the retrograde velocity of vacuum arcs can be explained by the ion jet model for retrograde motion of vacuum arcs [10]. The relative decrease of retrograde velocity as a function of the cathode temperature calculated according to this model agrees quantitatively with the reported measurements.     

Numerical modelling of unsteady heating and melting of the anode by electric arc. Part 2. Numerical characteristics of the anode weldpool

Numerical computations of the electric-arc heating and anode melting were carried out within the framework of the two-dimensional unsteady mathematical model. The influence of the viscous interaction ??plasma-melt??, surface tension forces, electromagnetic forces, and gravitational convection on the formation of the hydrodynamics of the anode melt was considered.     

Plasma expansion and current flow in a vacuum arc with a smallanode

A low-density plasma flow in a vacuum arc with a small anode, which intercepts only part of the cathodic plasma jet, was studied theoretically using a two-dimensional approximation. The plasma expansion was modeled using the sourceless steady-state hydrodynamic equations, where the free boundary of the plasma was determined by a self-consistent solution of the gasdynamic and electrical current equations. Magnetic forces from the azimuthal self-magnetic field were taken into account. The influence of the ratio of the anode radius to initial plasma jet radius on the plasma density, velocity, current distribution, and anode sheath potential drop is analyzed. It is shown that the mass and current flow in a 500 A arc are compressed near the axis. This leads to an increase in the plasma density by a factor of two and in the axial current density by a factor of 1.5     

Analytical calculation of cathode spot parameters on the electrode surface in arc discharge

The model of a heat transfer in the cathode spot on an electrode in the arc discharge is developed and analytical expressions for the spot radius and temperature as the functions of basic characteristics of the discharge and the electrode material are obtained. The dependence of the spot radius on the voltage drop of the cathodic discharge, which is consistent with results of numerical simulation, is calculated.     

Measurement of the temperature and flow fields of the magnetically stabilized cross-flow N2 arc

A straight, steady-state cross-flow arc is burning in an N₂ wind tunnel. The arc is held in position by the balance of the Lorentz forces produced by an external magnetic field perpendicular to the arc axis and by the viscous forces of the gas flow acting on the arc column. The temperature field in the discharge is determined spectroscopically using the radiation of N I lines. Because of the lack of rotational symmetry an inversion method developed by Maldonado was used to determine the local emission coefficient from the measured integrated spectral intensity distributions across the arc in various directions. For known local temperature the mass flow field inside the arc may be evaluated from the convective term of the energy equation and the continuity equation. This is done by expanding the terms of these two equations around the point of the temperature maximum into Fourier-Taylor series and determining coefficients of the same order and power. The solution of the resulting set of algebraic equations yields the unknown coefficients of the mass flow. The flow field obtained by these calculations shows a relatively strong counterflow through the arc core. In the region for which the series expansion holds a partial structure pertaining to a closed double vortex can be recognized. The terms of the momentum equation are calculated on the basis of these results. In order to obtain a better understanding of the importance attributed to the individual local forces acting on the plasma, a simple model was devised which separates the momentum equation into gradient and curl terms. The discussion shows that the gradient part of the Lorentz force causes mainly the pressure gradient, while the much smaller rotational part of thej×B forces is responsible for propelling the mass flow. The momentum transport inside the arc as well as in its neighbourhood is due to the viscous forces and to the pressure gradient. By contrast, at larger distances from the arc it is essentially the inertial force that determines the momentum transport. It is shown that viscosity as a damping mechanism is necessary for the existence of stationary flow fields as investigated in this work.     

A Model of the Multicathode-Spot Vacuum Arc

A model is proposed for the multicathode-spot (MCS) vacuum arc. A zero-order model is filrst constructed, whereby the interelectrode plasma is produced by the multitude of cathode spots, and flows to the anode upon which it condenses. The electron density is calculated by assuming that the plasma is uniform within a cylinder bounded by the electrodes and using expenmental data for the ionic velocities and ion current fraction obtained in single cathode spot arcs. The electron density thus obtained is proportionate to the current density, and is equal to 5 × 1020 m-3 in the case of a 107-A/m2 Cu arc. The model predictions are a factor of 3-4 lower than measured values. First-order perturbations to the zero-order model are considered taking into account inelastic electron-ion collisions, plasma-macroparticle interactions, the interaction of the self-magnetic field with the plasma and electric current flows, and the interaction with the anode. Inelastic collisions tend to increase the ionicity of the plasma as a function of distance from the cathode, in agreement with spectroscopic observations. Macroparticles are heated by ion impact until they have significant evaporation rates. The vapor thus produced is ultimately ionized, and most probably accounts for the discrepancy between the zero-order prediction of electron densities and the measured values. Constrictions near the anode in both the plasma and electric current flows have been calculated. An overabundant electron current supply forces the anode to assume a negative potential with respect to the adjacent plasma.     

Experimental and theoretical investigation of high-pressure arcs.II. The magnetically deflected arc (three-dimensional modeling)

While Part I deals with cylindrical arcs, Part II studies the influence of transverse magnetic fields on the arc column for ambient pressures of 0.1-5.0 MPa. If exposed to a magnetic induction of several millitesla, the column of an arc is deflected by the Lorentz forces. In this paper, heat transfer and fluid flow with coupled electromagnetic forces are modeled for the magnetically deflected arc. To verify the predictions, the three-dimensional temperature distributions of the arc column are determined by line and continuum radiation measurements using tomographic methods. These temperature maps are compared with the results of the numerical simulations. To gain insight into the physical professes of the discharge and to make the arc properties available which are not readily measured, a self-consistent numerical model of the arc column is applied to the time-dependent and three-dimensional case. The temperature, velocity, pressure, and current densities are predicted by solving the conservation equations for mass, momentum, and energy, and Ohm's and Biot-Savart's law using material functions of the plasma. A control volume approach facilitates a numerically conservative scheme for solving the coupled partial differential equations. The predictions are in fair agreement with experimental results. A time-dependent fully implicit simulation of the arc was used to investigate the arc instabilities for large magnetic inductions     

HL-2M装置5 MW中性束加热束线离子源放电室研制

为了给HL-2M装置建设一条5 MW中性束加热束线,开展了中性束加热用热阴极弧放电离子源放电室的研制。这条中性束束线包含4套80 kV/45 A/5 s离子源,放电室的设计指标为850 A/5 s。首先采用CST软件中的电磁工作室对特定几何结构的放电室会切磁场进行了模拟计算,得到了会切磁场分布,验证了会切磁场布局的合理性。针对放电室加工工艺和实验过程中局部拉弧等问题,对放电室结构进行了不断改进。放电室侧壁由40列会切磁体改为7圈环形磁体,阴极灯丝结构从灯丝板结构最终改为陶瓷可伐结构,并且在放电室和加速器之间增加了陶瓷屏蔽。在阴极板结构放电室和阴极陶瓷可伐结构放电室内都获得了正常的弧放电。最终定型的放电室采用周边7圈环形会切磁体和陶瓷可伐结构。在定型的放电室内达到了5 MW中性束束线离子源弧放电的指标。弧放电时间接近5 s,最大弧放电电流达到1 000 A。     

电磁悬浮条件下液态Fe_(50)Cu_(50)合金的对流和凝固规律研究

基于轴对称电磁悬浮模型,理论计算了二元Fe_(50)Cu_(50)合金熔体内部的磁感应强度和感应电流,分析了其时均洛伦兹力分布特征,进一步耦合Navier-Stokes方程组计算求解了合金熔体内部流场分布规律.计算结果表明,电磁悬浮状态下合金内部流场呈现环形管状分布,并且电流强度、电流频率或合金过冷度的增加,均会导致熔体内部流动速率峰值减小,平均流动速率增大,并使流动速率大于100 mm·s~(-1)区域显著增大.通过与静态凝固实验对比发现,电磁悬浮条件下熔体中强制对流使得合金内部富Fe和富Cu区的相界面呈波浪状起伏形貌,并且富Cu相颗粒在熔体上部分出现的概率增加.     

Ion Flux from the Cathode Region of a Vacuum Arc

This paper reviews the properties of the cathode ion flux generated in the vacuum arc. The structure and distribution of mass erosion from individual cathode spots and the characteristics of current carriers from the cathode region at moderate arc currents are described. An appreciable ion flux (～10% of total arc current) is emitted from the cathode of a vacuum arc. This ion flux is strongly peaked in the direction of the anode, though some ion flux may be seen even at angles below the plane of the cathode surface. The observed spatial distribution of the ion flux is expressed quite well as an exponential function of solid angle. The ion flux is quite energetic, with average ion potentials much larger than the arc voltage, and generally contains a considerable fraction of multiply-charged ions. The average ion potential and ion multiplicity increase significantly for cathode materials with higher arc voltages, but decrease with increasing arc current for a particular material. The main theories concerning ion acceleration in cathode spots are the potential hump theory (PH), which assumes that all ions are created at the same potential, and the gas dynamic theory (GD), which assumes that all ions are created with the same flow velocity. Experimental data on the potentials and energies of individual ions indicates that these theories in their original forms are not quite correct, however extensions or modifications of the PH and GD theories seem very likely to be able to predict correct values for the charge states, potentials, and energies of individual ions.     

纵磁作用下真空电弧单阴极斑点等离子体射流三维混合模拟

真空电弧的特性直接受到从阴极斑点喷射出的等离子体射流的影响,对等离子体射流进行数值仿真有助于我们深入了解真空电弧的内部物理机制.然而,磁流体动力学和粒子云网格仿真方法受限于计算精度和计算效率的原因,无法有效地应用于真空电弧等离子体射流仿真模拟.本文开发了一套三维等离子体混合模拟算法,并在此基础上建立了真空电弧单阴极斑点射流仿真模型,模型中将离子作宏粒子考虑,而电子作无质量流体处理,仿真计算了自生电磁场与外施纵向磁场作用下等离子体的分布运动状态.仿真结果表明,单个阴极斑点情况下真空等离子体射流在离开阴极斑点后扩散至极板间,其整体几何形状为圆锥形,离子密度从阴极到阳极快速下降.外施纵向磁场会压缩等离子体,使得等离子体射流径向的扩散减少并且轴线上的离子密度升高.随着外施纵向磁场的增大,其对等离子体射流的压缩效应增强,表现为等离子体射流的扩散角度逐渐减小.此外,外施纵向磁场对等离子体射流的影响也受到电弧电流大小的影响,压缩效应随电弧电流的增加而逐渐减弱.     

Vacuum arc cathode spot grouping and motion in magnetic fields

Two of the important vacuum arc phenomena observed when the arc runs in a transverse magnetic field are cathode spot grouping and the cathode spot retrograde motion, i.e., in the anti-Amperian direction. This paper summarizes the main experimental observations and proposes a physical model for spot grouping and spot retrograde motion. The proposed spot motion model take in account the previous theoretical model of the cathode thermal regime and the plasma flow near the cathode surface that is based on two conditions: i) the heat loss in the cathode bulk is relatively small to the heat influx, and ii) the plasma flow in the Knudsen layer is impeded. In the present model, the current per group spot is calculated by assuming that the plasma kinetic pressure is comparable to the self-magnetic pressure in the acceleration region of cathode plasma jet. The model includes equations for the current per spot group, spot velocity dependence on the magnetic field and on the arc current in vacuum, as well as in gas filled arc gap. The calculated currents per spot group and spot velocity increase linearly with the magnetic field and arc current, and this dependencies well agree with previous observations. The cathode spot retrograde motion in short electrode gaps and at atmospheric pressure arcs, and the reversal motion in strong magnetic fields (>1 T) observed by Robson and Engel are discussed. The details of the retrograde motion observed in the last decades including the spot velocity dependence on the electrode gap, roughness, temperature, and material could be understood in the frame of the proposed model.     

电弧特性及其对熔池形貌影响的数值模拟

通过电弧模型与熔池模型耦合数值模拟,研究了氩弧和氦弧特性及其对SUS304不锈钢钨极惰性气体保护（TIG）焊熔池形貌的影响.通过比较氩弧和氦弧的温度轮廓线以及阳极表面电流密度和热流密度分布发现,氦弧的径向距离比氩弧收缩明显,导致更多热量传递给阳极.模拟了氩弧和氦弧下浮力、电磁力、表面张力和气体剪切力分别对熔池形貌的影响.结果表明：不论是在氩弧还是在氦弧下熔池中表面张力是影响熔池形貌的最主要驱动力.在氩弧下,影响熔池形貌的另一个重要的驱动力是气体剪切力,而氦弧下则是电磁力.由于电磁力引起的内对流运动增加了熔深,从而导致相同氧含量时氦弧下的熔深和焊缝深宽比要高于氩弧下的熔深和焊缝深宽比.随着氧含量的增加,氩弧和氦弧下的焊缝深宽比均先增加而后保持不变.焊缝深宽比的模拟结果与实验结果符合较好. 关键词： 氩弧 氦弧 电弧特性 熔池形貌