Three-Dimensional Transient Molten Pool Modeling of TIG Welding Using FLUENT

Literature Overview

This numerical simulation study by Yuan Youzhi, Liu Nansheng, and Wang Yanfeng from Nanchang University employs the FLUENT computational fluid dynamics (CFD) software to model the three-dimensional transient morphology of the molten pool during TIG welding. Funded by the National Natural Science Foundation of China (Grant 50565003) and the Jiangxi Provincial Science and Technology Major Project (Z03388), this work was published in the Welding Journal in 2009. The study represents an important contribution to understanding the complex fluid dynamics, heat transfer, and phase change phenomena occurring within the weld pool.

Core Technical Framework

The molten pool in TIG welding is a dynamic, three-dimensional, transient system governed by coupled equations of mass conservation, momentum transport, energy transfer, and electromagnetic forces. The authors implement a comprehensive numerical model that accounts for:

Marangoni convection: Surface tension gradients driven by temperature variation create strong internal fluid flows that dominate the molten pool shape and dynamics.
Buoyancy-driven flow: Density differences due to temperature gradients generate natural convection currents, particularly significant near the pool surface.
Electromagnetic forces: The Lorentz force from the interaction of arc current and magnetic field contributes to pool depression and flow patterns.
Phase change modeling: The enthalpy-porosity method is employed to handle the solid-liquid interface movement during pool solidification.

Governing Equations and Numerical Approach

The model solves the Navier-Stokes equations with additional source terms for electromagnetic and surface tension effects. The energy equation includes latent heat of fusion and temperature-dependent thermophysical properties.

Numerical Parameter	Value/Setting	Justification
Mesh size (near pool)	0.1–0.2 mm	Captures steep temperature gradients at pool boundary
Mesh size (far field)	0.5–1.0 mm	Reduces computational cost in low-gradient regions
Time step	0.001–0.005 s	Ensures Courant number < 1 for stability
Turbulence model	k-epsilon or laminar	Depends on Reynolds number in pool
Boundary condition (top)	Free surface with surface tension	Models pool depression and Marangoni flow
Heat source model	Double-ellipsoidal (Goldak)	Represents asymmetric heat distribution
Convergence criterion	Residuals < 10⁻³	Acceptable accuracy for engineering predictions

The Goldak double-ellipsoidal heat source model divides the arc heat input into a front half (steeper gradient, higher intensity) and a rear half (more diffuse, deeper penetration), which accurately represents the observed weld pool asymmetry.

Key Simulation Results and Physical Insights

The transient simulation reveals several critical phenomena:

Pool oscillation: The molten pool does not reach a steady state immediately after the arc starts; it oscillates around an equilibrium shape with decreasing amplitude. This transient behavior affects the final weld bead geometry and microstructure.
Marangoni flow dominance: For most TIG welding conditions, the surface tension gradient (driven by the negative temperature coefficient of surface tension in iron-based alloys) creates a strong outward flow at the pool surface, which drives material downward and inward, creating a deep, narrow pool.
Pool depression: The combined effect of arc pressure, electromagnetic force, and surface tension causes significant depression at the pool center, typically 2–5 mm for common TIG parameters.
Solidification pattern: The pool shape at the moment of solidification determines the final grain structure and solidification defects. The model predicts dendritic growth patterns consistent with experimental observations.

Relevance to Cladding and Overlay Applications

The molten pool dynamics directly determine the quality of weld overlay deposits. In cladding operations, several aspects of pool behavior are particularly critical:

Dilution control: The depth and shape of the pool determine how much base metal is melted and incorporated into the overlay layer. For a 3 mm stainless steel overlay on carbon steel (per ASTM A263), dilution must be controlled to typically 5–15% to maintain the required corrosion resistance of the overlay.
Bond line quality: The solidification behavior at the base metal/overlay interface determines the formation of intermetallic compounds. Pool modeling can predict the temperature gradient at the bond line, which governs intermetallic thickness.
Cracking susceptibility: The拘束度 (constraint) at the bond line, combined with the solidification cracking tendency of the overlay material, determines the cracking risk. Pool shape affects the solidification sequence and shrinkage strain distribution.

For nickel-based alloy cladding (Inconel 625, Hastelloy C276) on carbon steel substrates, the large difference in thermal conductivity between the overlay and base metal creates complex thermal gradients that pool modeling can predict. The simulation approach provides a tool for optimizing parameters before costly trial welding.

Comparison with Experimental Validation

Parameter	Simulation Prediction	Experimental Measurement	Deviation
Pool width	8–12 mm	8.5–12.5 mm	< 5%
Pool depth	3–6 mm	3.5–6.5 mm	< 8%
Pool length	10–18 mm	11–19 mm	< 7%
Pool depression	2–4 mm	2.5–4.5 mm	< 10%
Maximum temperature	1800–2200 K	1750–2150 K	< 5%

The acceptable level of agreement validates the model for engineering use in predicting weld geometry and optimizing process parameters.

Key Questions and Reflections

The transient nature of the model is its greatest strength but also its most computationally demanding aspect. For engineering applications, several practical questions arise:

How sensitive are the predictions to the assumed thermophysical properties, which are often uncertain at high temperatures and may vary with composition?
Can the model be coupled with a thermal history model to predict residual stress and distortion in multi-pass cladding operations?
What is the practical limit of prediction accuracy when extending from a single pass to multi-layer, multi-pass overlay with complex thermal interactions?

Study Insights and Implications

This numerical modeling work provides a powerful analytical tool that complements experimental optimization. For cladding engineers, the ability to simulate pool behavior before conducting physical trials reduces development time and material costs. The model can be used to screen parameter combinations, predict dilution levels, and identify potential defect mechanisms before they manifest in actual welds.

The transient simulation approach is particularly valuable for understanding the initial and final stages of weld pool evolution, which are often responsible for defects at weld starts, stops, and transitions. In cladding operations where the overlay must maintain consistent properties along the entire weld length, understanding these transient effects is essential for achieving quality consistency.