Transient Fluid Flow and Heat Transfer Modeling in Stationary Pulsed Current TIG Weld Pool

Literature Overview

The paper by Zheng Wei, Wu Chuansong, and Wu Lin, published in China Welding (Vol. 4, No. 2, 1995, pp. 139-149), presents a mathematical model for describing transient behavior of heat transfer and fluid flow in a stationary pulsed current tungsten inert gas (PC-TIG) weld pool. The model considers three driving forces for weld pool convection: buoyancy force, electromagnetic force, and surface tension force. Additionally, the effect of vaporization heat flux at the free surface and the temperature coefficient of surface tension as a function of temperature and composition are incorporated. The authors employ the AST (Additive Source Term) method, ADI (Alternating Direction Implicit) method, and DBC (Double Blocks Correction) technique to solve the coupled finite difference equations.

Core Technical Points

The fundamental contribution of this work lies in its comprehensive treatment of transient phenomena unique to pulsed current TIG welding. Unlike conventional DC-TIG or AC-TIG processes where the weld pool reaches a quasi-steady state, PC-TIG welding involves periodic variation of welding current that drives corresponding periodic oscillations in fluid flow patterns and thermal fields within the weld pool. This transient behavior has profound implications for weld pool geometry, dilution ratio, microstructural evolution, and ultimately weld quality.

Three Driving Forces in Weld Pool Convection

The model explicitly accounts for three distinct convective driving mechanisms, each of which plays a different role depending on the welding parameters and material system:

The surface tension force is particularly significant because its temperature coefficient (dγ/dT) determines whether surface flow moves outward (negative dγ/dT, typical for clean metals) or inward (positive dγ/dT, caused by surface-active impurities such as sulfur or oxygen). In pulsed welding, the periodic switching of current intensity causes rapid cycling between these flow regimes, creating complex oscillatory flow patterns that cannot be captured by steady-state models.

Numerical Methods and Coupling Strategy

The AST method represents a clever numerical innovation for handling the coupling between thermal energy and momentum equations. In traditional approaches, thermal boundary conditions are applied independently, but in PC-TIG welding, the heat flux at the weld pool surface is strongly coupled with fluid motion through evaporation and Marangoni convection. By extending the AST method from thermal boundary conditions to momentum boundary conditions, the authors achieve mutual coupling between the transient momentum equation and energy equation. This is essential because the velocity field influences heat transport, while the temperature field determines both the surface tension gradient and the vaporization heat flux that act as momentum sources.

The ADI method is employed to handle the implicit time-stepping of the three-dimensional finite difference equations, while the DBC technique accelerates convergence by decomposing the solution domain into blocks that are solved alternately. These numerical strategies are critical for achieving convergence within a reasonable computational time, especially for transient simulations where multiple pulse cycles must be resolved.

Process Analysis and Engineering Relevance

The theoretical predictions from this model are shown to agree well with experimental measurements, validating the approach. For engineering practice, this model provides several important insights:

1. Pulse parameter optimization: The transient model reveals how pulse peak current, pulse base current, and pulse frequency interact to control weld pool dynamics. Higher peak currents create deeper penetration during the peak phase, while lower base currents allow partial solidification between pulses, resulting in narrower weld beads with better aspect ratios.
2. Dilution control: The periodic flow reversal patterns influence the mixing between base metal and filler metal. Understanding these patterns allows engineers to predict and control dilution ratios, which is particularly important for dissimilar metal welding and cladding applications.
3. Microstructural prediction: The oscillatory thermal cycles in PC-TIG welding create distinctive solidification patterns. The periodic cooling and reheating can refine grain structures and reduce hot cracking susceptibility compared to steady-state welding processes.

Connection to Pipe Welding Practice

In the context of steel pipe welding, particularly for high-pressure pipeline applications governed by standards such as API 5L, ASME B31.3, and SY/T standards, PC-TIG welding is widely used for root pass welding of girth welds. The transient model developed in this paper has direct relevance to optimizing root pass parameters for:

• Seamless and welded pipe girth welds: Where root penetration and weld geometry are critical for fatigue performance and leak tightness
• Pipe fitting fabrication: Where multi-pass welding sequences require precise control of each layer's geometry and properties
• Stainless steel and alloy pipe welding: Where dilution control and ferrite content management are essential for corrosion resistance

The model's treatment of surface tension effects is particularly relevant for stainless steel pipe welding, where sulfur and oxygen impurities can reverse the Marangoni flow direction and cause undercuts or insufficient penetration.

Study Insights and Reflections

This 1995 paper represents a pioneering effort in computational welding science in China. At a time when computational resources were limited, the authors demonstrated that sophisticated numerical methods could be applied to practical welding problems. The extension of the AST method to momentum boundary conditions is a methodological contribution that has influenced subsequent work in computational welding modeling.

One key insight that resonates with engineering practice is the recognition that pulsed welding is fundamentally a transient process, and steady-state models are inadequate for capturing its physics. This understanding has practical implications: when setting up PC-TIG welding procedures for critical pipe applications, engineers should consider not only the peak and base current values but also the pulse frequency and the thermal inertia of the weld pool. The pulse frequency determines how many thermal cycles occur during a single pass, and this in turn affects solidification rate, grain structure, and residual stress distribution.

The model also highlights the importance of vaporization heat flux at the weld pool surface. In pipe welding applications, where gas shielding quality is critical, the interaction between the shielding gas flow and the weld pool surface can significantly influence vaporization rates and, consequently, the heat input distribution. This has direct implications for porosity formation, particularly in aluminum alloy pipe welding where hydrogen porosity is a persistent challenge.

Reference Value and Outlook

The mathematical framework established in this paper provides a foundation for more advanced computational welding models. Subsequent developments in computational welding science have built upon these concepts, incorporating more sophisticated thermophysical property models, fluid-structure interaction, and multi-physics coupling. For pipe welding engineers, the key takeaway is that PC-TIG welding offers a powerful tool for controlling weld pool geometry and microstructure, but its effectiveness depends on a deep understanding of the underlying transient physics. The model presented here, while developed under the computational constraints of the mid-1990s, captures the essential physics that remain relevant to modern welding practice. Engineers involved in procedure qualification and optimization should appreciate that the pulse parameters are not merely empirical knobs but are intimately connected to the fundamental fluid dynamics and heat transfer phenomena within the weld pool.