[Paper Review] Simulation of the liquid pool for VT3-1 titanium alloy during vacuum arc remelting process

E. N. Kondrashov, M. I. Musatov+3 more|arXiv (Cornell University)|Jun 14, 2005

Engineering and Environmental Studies3 references3 citations

TL;DR

This study presents a finite-volume method-based numerical model simulating the liquid pool dynamics during vacuum arc remelting (VAR) of VT3-1 titanium alloy, solving the nonlinear heat conduction equation with temperature-dependent material properties and apparent heat capacity for phase change. The model accurately predicts liquid pool depth and profile with less than 15% deviation from experimental radiographic data across varying ingot diameters (435–750 mm) and current levels (15–37 kA), demonstrating strong predictive capability for industrial VAR process optimization.

ABSTRACT

This article describes a simple heat model of the vacuum arc remelting (VAR) process that includes solution of the nonlinear heat conductivity equation with the nonlinear boundary conditions which are typical for VAR process. The finite-difference analogue of the model equations was obtained through the finite volume method. To check the efficiency of the simplified model that does not include magnetohydrodynamic phenomena in the liquid metal pool, the comparison has been made of the numerical calculation of the metal pool depth when melting the Russian titanium alloy VT3-1 with the results of radiographical tests. It was established that the model adequately describes the test data for various melting modes (ingot diameter and current strength).

Motivation & Objective

• To develop a reliable mathematical model of heat transfer during VAR for titanium alloys, particularly VT3-1, to support automation of the process.
• To address the challenge of real-time monitoring of critical solidification parameters such as liquid pool depth and mushy zone width, which are difficult to measure directly.
• To validate the model against experimental radiographic data to ensure accuracy across different ingot sizes and melting currents.
• To enable predictive simulation of key solidification parameters for optimizing VAR process parameters and improving ingot quality.

Proposed method

• A nonlinear heat conduction equation is solved numerically, incorporating temperature-dependent density, specific heat, thermal conductivity, and heat transfer coefficients.
• The apparent heat capacity method is used to model latent heat release during solidification without explicitly tracking the phase boundary.
• The finite volume method is applied to discretize the governing equation and boundary conditions, ensuring numerical stability and accuracy.
• Boundary conditions are defined based on physical zones: symmetry at the centerline, temperature overheat at the melt pool surface, variable temperature across the ring gap, and heat flux at the contact belt.
• The model uses Marchuk’s method of integral identities for time discretization and handles non-commuting spatial operators in the heat equation.
• The model is validated by comparing simulated liquid pool depth and profile against experimental data obtained via radioactive isotope tracking and radiographic testing.

Experimental results

Research questions

• RQ1 Can a simplified heat transfer model without magnetohydrodynamic effects accurately predict liquid pool depth in VAR melting of VT3-1 titanium alloy?
• RQ2 How well does the model simulate the evolution of the liquid metal pool profile over time across different ingot diameters and current levels?
• RQ3 To what extent does the model’s prediction of pool depth and profile match experimental radiographic measurements?
• RQ4 Does the model maintain accuracy across a range of melting conditions after being calibrated on a single set of parameters?
• RQ5 Can the model reliably predict key solidification parameters such as temperature gradient, isotherm travel rate, and local solidification time?

Key findings

• The model predicts liquid pool depth with a relative error of less than 15% compared to experimental data from radiographic measurements across multiple ingot diameters and current levels.
• For a 750 mm ingot at 37 kA, the model achieves quasi-steady state pool depth, closely matching experimental data.
• For a 570 mm ingot at 25 kA, the model captures the transient behavior but does not reach quasi-steady state, consistent with experimental observations.
• For a 435 mm ingot at 15 kA, the model successfully predicts the achievement of quasi-steady state, with good agreement between simulated and experimental pool surface and bottom positions.
• The model demonstrates robustness and transferability, providing accurate predictions beyond the initial calibration conditions.
• The simulation of liquid metal pool profiles shows consistent agreement with experimental profiles, confirming the model's ability to represent the volume and shape of the melt pool throughout the melting process.