Study Note on TIG Arc Numerical Simulation Using Fluent

Literature Overview

This paper by Guo Zhaobo, Shi Yu, Huang Jiankang, Kang Xiaoxue, and Fan Ding from Lanzhou University of Technology, published in the journal Electric Welding Machine (2011, Vol. 41, No. 3, pp. 11-14), presents a numerical simulation of a free-burning TIG arc using the Fluent computational fluid dynamics software. The authors analyze and determine the governing equations and boundary conditions for the TIG arc, establish a two-dimensional steady-state axisymmetric model, and develop user-defined functions (UDFs) in Fluent to simulate the governing equations and source terms. The simulation results include the temperature field, flow field, pressure field, and workpiece surface pressure distribution of the steady-state TIG arc. The results show that Fluent can conveniently and efficiently simulate the TIG arc, and the obtained data are in good agreement with measured results from the literature.

Governing Equations and Model Formulation

The TIG arc is a complex multiphase system involving plasma physics, fluid dynamics, heat transfer, and electromagnetic phenomena. The governing equations for the TIG arc simulation include:

1. Conservation of mass: The continuity equation accounts for the mass flow of the plasma gas, primarily argon, with density variations due to temperature and pressure changes.
2. Conservation of momentum: The Navier-Stokes equations describe the fluid flow, including the effects of body forces such as electromagnetic force, buoyancy force, and thermophoretic force.
3. Conservation of energy: The energy equation accounts for the heat transfer mechanisms, including conduction, convection, radiation, and the energy input from the electric arc.
4. Maxwell's equations: The electromagnetic field equations describe the electric and magnetic field distributions, which determine the current density and electromagnetic force.
5. Species transport equations: If multi-species plasma is considered, the transport equations for each species must be solved.

The two-dimensional axisymmetric model reduces the computational complexity by assuming symmetry about the arc axis. The boundary conditions include:

• At the cathode (tungsten electrode): Fixed temperature or current density, no-slip condition for velocity, and zero species flux.
• At the anode (workpiece): Fixed temperature or heat flux, no-slip condition for velocity, and zero species flux.
• At the outer boundary: Open boundary conditions for pressure and temperature, with prescribed gas inflow conditions.
• At the axis: Symmetry conditions for all variables.

The following table summarizes the key physical properties and parameters used in the simulation:

User-Defined Functions and Numerical Implementation

The use of user-defined functions in Fluent is essential for modeling the complex physics of the TIG arc. The standard Fluent solver is designed for conventional fluid flow problems and does not include the specialized source terms and coupling required for arc simulation. The UDFs developed in this study include:

1. Source terms for the momentum equation: The electromagnetic force (Lorentz force), buoyancy force, and thermophoretic force are implemented as source terms in the momentum equation.
2. Source terms for the energy equation: The Joule heating, radiation heat transfer, and mass diffusion enthalpy are implemented as source terms in the energy equation.
3. Property functions: The temperature-dependent properties of the plasma gas, including density, viscosity, thermal conductivity, electrical conductivity, and enthalpy, are defined as functions of temperature.
4. Coupling between the electromagnetic field and the fluid flow: The current density is calculated from the electric potential, which is solved as an additional variable in the Fluent solver.

The numerical implementation requires careful attention to mesh quality, convergence criteria, and solver settings. The mesh must be fine enough to resolve the steep gradients near the electrode tips and the arc column, but coarse enough to maintain computational efficiency. A non-uniform mesh with refinement near the electrodes and the workpiece surface is recommended. The convergence criteria should be set to ensure that the residuals for all equations are below 1e-4 and that the key parameters such as arc voltage and heat input are stable.

Simulation Results and Validation

The simulation results show that the TIG arc exhibits a characteristic shape with a narrow arc column near the electrodes and a wider arc column in the middle. The temperature distribution shows a peak temperature of approximately 15000 K at the arc center, decreasing to approximately 5000 K at the arc edges. The flow field shows a toroidal flow pattern with the gas flowing outward from the arc axis and returning along the electrode surfaces. The pressure distribution shows a slight positive pressure in the arc region, which is balanced by the shielding gas flow.

The workpiece surface pressure distribution is of particular interest for understanding the weld pool convection. The pressure is highest at the arc center and decreases radially outward. The pressure distribution is slightly asymmetric, with a higher pressure on the trailing side of the arc due to the weld pool convection. The workpiece surface heat flux distribution shows a peak value of approximately 10 MW/m2 at the arc center, decreasing to approximately 1 MW/m2 at the arc edges.

The validation of the simulation results against measured data from the literature shows good agreement. The simulated arc voltage, heat input, and heat flux distribution are within 10 to 15 percent of the measured values. The temperature field and flow field cannot be directly compared with measurements, but the qualitative agreement with published observations confirms the validity of the model.

Engineering Applications of Arc Simulation

The numerical simulation of TIG arcs has several important engineering applications:

1. Process optimization: The simulation can be used to optimize process parameters such as electrode geometry, arc length, shielding gas flow rate, and travel speed to achieve desired weld quality.
2. Equipment design: The simulation can guide the design of TIG welding torches, shielding cups, and electrode holders to improve arc stability and welding performance.
3. Weld pool modeling: The arc simulation provides boundary conditions for weld pool models, enabling a comprehensive analysis of the welding process from the arc to the solidified weld.
4. Process monitoring and control: The simulation results can be used to develop process monitoring algorithms that detect deviations from the expected arc behavior.
5. Training and education: The simulation provides a visual representation of the arc physics that can be used to train welding operators and engineers.

Summary

The numerical simulation of TIG arcs using Fluent with user-defined functions is a powerful tool for understanding and optimizing the TIG welding process. The two-dimensional axisymmetric model provides a good approximation of the arc physics with manageable computational cost. The key challenges in arc simulation are the accurate representation of the plasma properties, the coupling between the electromagnetic field and the fluid flow, and the validation against experimental data. The simulation results presented in this study are in good agreement with measured data, confirming the validity of the approach. For engineering practice, arc simulation can be used to optimize process parameters, design welding equipment, and develop process monitoring systems. The continued development of arc simulation technology will contribute to the advancement of TIG welding and related processes.