Numerical Simulation of TIG Weld Pool Morphology Evolution

Literature Overview

This paper by Wu Jianhua (2009, Hot Working Technology, Vol. 38, No. 5) presents a two-dimensional transient numerical simulation of the TIG welding process for AISI 304 stainless steel, using a Gauss heat source model to analyze the temperature field and velocity field distributions. The study specifically examines how varying sulfur content influences the Marangoni convection direction and, consequently, the weld bead morphology.

Core Technical Content

Mathematical Model

The simulation employs a Gauss heat source distribution, which is a widely used approach for modeling the heat flux input in arc welding processes. The model is formulated in two dimensions and solved transiently, capturing the time-dependent evolution of the weld pool as the arc traverses the workpiece.

The key governing equations include:

Energy conservation equation with convective and conductive terms
Momentum conservation equation incorporating buoyancy and Marangoni forces
Continuity equation for incompressible flow
Surface tension gradient boundary condition at the weld pool surface

Role of Sulfur in Marangoni Convection

The central technical insight of this paper is the critical role of sulfur content in determining the direction of thermocapillary (Marangoni) convection at the weld pool surface.

Sulfur Content	Surface Tension Temperature Coefficient	Marangoni Flow Direction	Weld Pool Morphology
Low sulfur	Positive (dγ/dT > 0)	From center toward edges	Wide, shallow pool
High sulfur	Negative (dγ/dT < 0)	From edges toward center	Narrow, deep pool

In clean stainless steels with low sulfur content, the surface tension decreases with increasing temperature, causing surface flow from the hot center of the pool toward the cooler edges. This produces a wide, shallow weld pool. Conversely, when sulfur content is elevated, sulfur accumulates at the cooler pool edges, creating a surface tension gradient that drives flow inward toward the hot center, resulting in a deeper, narrower weld pool.

Simulation Results vs. Experimental Validation

The paper reports that the simulated temperature and velocity field distributions are in good agreement with experimental observations, confirming the validity of the Gauss heat source model and the coupled thermal-fluid approach for TIG welding of austenitic stainless steel.

Engineering Practice Integration

Practical Implications for Welding Process Design

Filler metal selection — The sulfur content of the filler metal (typically ER308L or ER308) directly influences weld pool shape and penetration. Low-sulfur fillers produce wider beads suitable for surface reinforcement, while higher-sulfur fillers produce deeper penetration suitable for root passes.
Welding position effects — In vertical-up or overhead positions, the Marangoni-driven flow interacts with buoyancy-driven convection, further complicating the weld pool shape. Understanding the base Marangoni behavior is essential for predicting these interactions.
Welding speed optimization — The travel speed must be matched to the Marangoni convection pattern to achieve the desired weld geometry. Too fast a speed with inward Marangoni flow can cause incomplete fusion; too slow a speed can cause excessive dilution and distortion.

Process Window Recommendations

Parameter	Low Sulfur (Clean 304)	High Sulfur (Industrial 304)
Typical S content	< 0.015%	0.020–0.030%
Preferred current range	100–180 A	120–200 A
Typical travel speed	4–8 mm/s	5–10 mm/s
Expected penetration	Shallow (1–3 mm)	Deep (3–6 mm)
Bead width	Wide (6–10 mm)	Narrow (4–7 mm)

Key Questions and Reflections

The simulation is limited to two dimensions, which inherently simplifies the three-dimensional nature of real weld pools. In practice, weld pool shape is influenced by electrode angle, shielding gas flow patterns, and gravity effects that are not fully captured in a 2D model. Additionally, the study focuses on a single material (AISI 304) and does not address the more complex behavior of dissimilar joints or thick-section welding where multiple passes interact.

The Gauss heat source model, while widely used, has known limitations in accurately representing the heat flux distribution of a real TIG arc, particularly at higher currents where arc constriction and plasma jet effects become significant. More advanced models using double-ellipsoid or conical heat sources may provide better predictions.

Study Insights and Implications

This paper provides a clear and instructive demonstration of how sulfur content governs weld pool morphology through its effect on Marangoni convection. The practical takeaway for welding engineers is that sulfur control in filler metals and base materials is not merely a metallurgical concern but a process parameter that directly determines weld geometry. This understanding enables more rational selection of consumables and welding parameters for achieving target weld profiles in austenitic stainless steel applications.