# 3D Numerical Simulation of the Var Consumable Electrode Melting Process

Abstract:Ā A 3D numerical model was set up to simulate the formation and dynamics of the liquid metal film under the consumable electrode during VAR process. In the present paper, the implementation of this model is described. It was developed using the open source computational fluid dynamics (CFD) software OpenFOAM. The model solves coupled momentum and energy equations combined with a volume of fluid (VOF) method to track the liquid metal free surface. The melting of the electrode material is modeled with an enthalpy-porosity approach. The electric power supplied by the arc is supposed to be uniformly distributed over the surface of the electrode tip. For a given electric arc power, the model enables to quantitatively predict the dripping rate and hence the overall melt rate. Besides the thermal behavior of the electrode, simulation results illustrate the dynamics of the liquid film and the transfer mechanisms of the liquid metal during VAR melts performed with short and long interelectrode gaps.

## SummaryĀ (4 min read)

### I. Introduction

- Vacuum arc remelting (VAR) is a secondary remelting process used to improve cleanliness as well as chemical and mechanical homogeneity of metal ingots.
- The arc is created between the electrode and the base plate of a water-cooled copper crucible at the beginning of the melt, then between the electrode and the secondary ingot forming in the crucible.
- At any instant, the ingot is composed of three zones: the fully solidified metal, the liquid pool fed by metal drops and an intermediate mushy zone.

### II. Numerical model

- The formation and dynamics of the liquid film under the consumable electrode during the VAR process is simulated with a multiphase CFD approach.
- The developed model is based on the following assumptions.
- (2) As a first step towards a complete description of the liquid film behavior, magnetohydrodynamic effects produced by the arc current (i.e. electromagnetic forces acting on the liquid metal) are not taken into account.
- (4) All thermophysical properties are considered to be independent of temperature and identical in the solid and liquid phases.
- (5) As explained later in section II.A, when computing the flow, a specific procedure was introduced to eliminate non-physical spurious velocities generated near the interface in the gas region.

### A. Governing equations

- Fluid flow and behavior of the free surface.
- This term compresses the interface by minimizing the numerical diffusion of the volume fraction while ensuring its boundedness.
- To the best of the authors knowledge, existing attempts to model melting (e.g. [34,35]) are all based on the assumption of the existence of a mushy region and treats this region using the classical enthalpy-porosity technique originally developed to deal with solidification.
- In the fully liquid cells (Ī³ = 0), the source term is zero and the "classical" Navier-Stokes equation is solved.
- Since the solid phase is kept at rest in their simulations, this velocity reduces here to the fluid velocity.

### Heat transfer with phase change

- The second term on the right hand side of Eq. 10 accounts for the evolution of the latent heat during phase change.
- The liquid-solid interface is not tracked explicitly.
- The third term on the right hand side of Eq. 10 is the thermal power provided by the electric arc to the metal.
- The radiative heat fluxes at the electrode base can be neglected, given the small difference between the electrode and ingot diameters and the similarity of the metal temperatures at the electrode base and on the ingot top.
- The energy flux density radiated by a surface element of the electrode lateral wall may thus simply be expressed as: EQUATION.

### B. Boundary conditions

- Figure 2 shows a vertical cross-section of the 3D computational domain and illustrates the boundary conditions used for the simulation.
- The red lines represent the surface of application of the arc power while the purple lines represent the surface associated to radiative losses.
- In order to get a realistic simulation of the formation of molten metal bridges (i.e. drip-short) between the electrode and the ingot, the domain includes a liquid region under the electrode representing a part of the molten metal pool present at the ingot top.
- Turbulent kinetic energy and its dissipation rate:.
- The normal gradients are set to zero at all boundaries.

### C. Computational details

- The pressure-velocity coupling is handled by the PIMPLE algorithm (combination of the PISO [24] and SIMPLE [25] algorithms).
- The convective terms in the conservation equations are discretized with a second order VanLeer scheme, while the diffusion terms are central differenced.
- The transport equation of the metal volume fraction is solved using the OpenFOAM solver called InterFoam, which is based on the MULES limited interface compression method.
- Temporal integration is done using a first order implicit Euler method.

### III. Application of the model

- The numerical model described above was applied to simulate two different melt 300 configurations.
- The first one is the melt of a small diameter Ti-6Al-4V electrode with a long 301 interelectrode gap performed experimentally by Chapelle et al. [6] , while the second one is [26].
- A. Small diameter electrode with a long gap Fig. 3 shows a vertical cut of the computational domain with the initial metal represented in yellow.
- The electrode diameter is 160 mm, its height is 150 mm and the interelectrode gap is 66 mm.

### Gas

- The electrode and the metal bath at the ingot top are considered to receive respectively 60% and 40 % of this power [11] .
- The liquid bath is at the liquidus temperature of the alloy.
- The computational grid is a uniform structured mesh consisting of around 3.5 million cells.

### Liquid film behavior

- At the initial state, the electrode is isothermal.
- As soon as the temperature of the tip reaches the solidus temperature, the electrode starts to melt and a distorted liquid film is formed.
- The drop remains attached to the liquid film by a filament which gradually becomes thinner.
- The simulated behavior remains close to the experimental visualizations.
- Protuberances tend to form near the center of the electrode and migrate to the periphery of the electrode forming approximately concentric circles.

### Fluid flow inside a protuberance

- The fluid flow is fed by the drainage of the liquid film and is governed by buoyancy forces.
- In the protuberance, the turbulence level is moderate, with a maximum value of the ratio of the turbulent to molecular viscosities of about 180.
- In the liquid film, the viscosity ratio is much lower, which corresponds to a flow regime remaining laminar.

### Heat transfer in the electrode

- Due to the consumption of the electrode, the power supplied by the electric arc affects mainly a small region at the electrode tip, usually referred to as the "heat affected zone".
- Accordingly, figure 7 .b shows a sharp exponential decay in the axial direction of the temperature from the base of the electrode toward the upper part of the electrode.
- Also, the temperature distribution over the surface of the liquid film (excluding the drops) is relatively homogeneous, which is partly related to the uniform arc heat flux distribution considered here.
- On the other hand, a much higher superheat is calculated inside the protuberance, which reaches about 400 Ā°C at the tip of the protuberance.
- The predicted value of the superheat of the metal at the free surface of the liquid film is consistent with values reported in the literature for different materials (namely about 100 Ā°C for IN718 [10] and between 150 Ā°C and 200 Ā°C for a zirconium alloy [12] ).

### B. Large diameter electrode with a short gap

- Simulation results are presented for an industrial VAR melt of a maraging steel electrode.
- In order to reduce further the computational time, an irregular mesh was used.
- The mesh is refined inside the gap and in its vicinity and gets progressively coarser moving further away from this area.

### Predicted melt rate

- The time evolution of the electrode melt rate calculated (with a sampling rate of 10 s) from the evolution of the electrode total mass (including both solid and liquid regions) is plotted in Fig. 12 .
- The electrode begins effectively to melt after a pre-heating stage of about 7 min.
- The variation of the melt rate is characterized by a sharp increase until reaching a quasi-stationary regime.
- In the current model, it should be noted that the process starts at full power, contrary to the real process in which the electric current is gradually increased.
- This value is in good agreement with that monitored during the actual melt which quantitatively validates the present model.

### Conclusion

- This work couples the enthalpy-porosity approach to simulate the melting process and the volume of fluid method to model the deformation of the liquid film formed under the electrode.
- The model was applied to simulate the melt of a small diameter Ti-6Al-4V electrode with a long interelectrode gap and that of a large diameter maraging steel electrode with a short interelectrode gap.
- The model was shown to be able to reproduce two different modes of electrode consumption in accordance with experimental observations.
- The metal temperature is larger inside the protuberance than that in the liquid film, which may be caused by the flow structure of the metal in the protuberance.

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