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

Literature Overview

The study by Zheng Wei, Wu Chuansong, and Wu Lin (published in China Welding, 1995) presents a mathematical model for the transient fluid flow and heat transfer phenomena occurring in the weld pool during stationary pulsed current TIG welding. This early computational work represents a foundational contribution to the numerical simulation of welding processes, providing theoretical insight into the complex multiphysics phenomena governing weld pool behavior under pulsed current conditions.

Core Technical Content

The weld pool during TIG welding is governed by coupled phenomena including heat conduction, convective heat transfer, fluid flow driven by multiple forces, phase change (melting and solidification), and electromagnetic effects. The pulsed current mode introduces time-varying forcing functions that create complex transient behavior in the weld pool, including periodic oscillations of pool geometry, fluid flow patterns, and temperature distributions.

Governing Equations and Physical Models

The mathematical model is based on the following fundamental equations:

1. Momentum equation (Navier-Stokes):

• Describes fluid flow in the liquid weld pool
• Accounts for density variations (Boussinesq approximation or full density variation)
• Includes body forces: electromagnetic (Lorentz), surface tension (Marangoni), buoyancy (natural convection), and arc pressure

1. Energy equation:

• Governs temperature distribution in the weld pool
• Includes latent heat of fusion for phase change modeling
• Accounts for convective heat transfer and heat conduction

1. Continuity equation:

• Mass conservation for incompressible fluid flow

1. Electromagnetic equations:

• Current density distribution in the weld pool
• Magnetic field generation and interaction with current density

Key Driving Forces in the Weld Pool

Technical Points and Engineering Relevance

Pulsed Current Effects on Weld Pool Dynamics

Pulsed current TIG welding introduces periodic variations in heat input, creating transient weld pool behavior:

• Peak current phase: Maximum heat input causes rapid pool expansion, intense fluid flow, and deep penetration. The Marangoni effect dominates near the surface, while electromagnetic forces drive deeper penetration.
• Background current phase: Reduced heat input allows partial solidification at pool edges, reduced fluid velocities, and potential resolidification of previously melted material. This phase affects the final microstructure through controlled cooling rates.
• Cycle effects: The periodic nature of pulsed welding creates cyclic stresses in the solidifying material, which can influence microstructure formation and residual stress development.

Surface Tension Gradient (Marangoni Effect)

The Marangoni effect, driven by temperature-dependent surface tension gradients, is one of the most influential forces governing weld pool fluid flow. The surface tension coefficient of liquid metals typically decreases with increasing temperature (positive surface tension gradient coefficient), causing:

• Surface flow from high-temperature center toward cooler edges (outward flow)
• Shallow, wide weld pools with reduced penetration
• Enhanced horizontal spread of the weld bead

However, sulfur content in the base metal or filler material can reverse the surface tension gradient (negative coefficient), causing:

• Inward surface flow from edges toward center
• Deep, narrow penetration
• Enhanced vertical mixing

For weld overlay cladding applications, the Marangoni effect directly influences dilution rates by controlling the mixing between overlay material and base metal.

Electromagnetic Force (Lorentz Force)

The Lorentz force, generated by the interaction of current density and magnetic field within the weld pool, provides a body force that acts throughout the liquid volume. Its primary effects include:

• Radial inward flow: Creates a stagnation point near the pool bottom, driving fluid downward and increasing penetration depth
• Downward flow: Enhances vertical mixing and penetration
• Circulation pattern: Establishes a characteristic flow pattern with surface outward flow (if Marangoni-dominated) and deep inward/downward flow (electromagnetic-driven)

Numerical Solution Methodology

The transient nature of the problem requires time-dependent numerical solutions. Key aspects of the computational approach include:

1. Mesh generation: Adaptive mesh refinement near the solidification front and pool boundaries
2. Time stepping: Implicit or explicit time integration with appropriate time step size for stability
3. Boundary conditions:

• Arc heat flux distribution (Gaussian or double-Gaussian)
• Evaporation heat loss at the pool surface
• Convective and radiative heat loss at exposed surfaces
• No-slip condition at solid boundaries

1. Phase change modeling:

• Enthalpy method or temperature enthalpy method
• mushy zone treatment using Carman-Kozeny equation
• Solidification front tracking

Integration with Engineering Practice

Application to Weld Overlay Cladding Process Optimization

The computational model provides valuable insight for optimizing weld overlay cladding processes:

Residual Stress Prediction

The transient thermal and mechanical coupling in the weld pool directly influences residual stress development. The model can predict:

• Peak temperatures and cooling rates at various locations
• Phase transformation sequences during solidification
• Thermal strain development and relaxation
• Elastic-plastic stress state evolution

For pressure vessel cladding applications, residual stress prediction is critical for:

• Assessing stress corrosion cracking susceptibility
• Evaluating fatigue life under cyclic loading
• Determining the need for post-weld stress relief
• Verifying compliance with code requirements

Microstructure Prediction

The thermal history predicted by the model can be correlated with expected microstructure through:

• Cooling rate calculations (°C/s) at various distances from the weld centerline
• Peak temperature mapping to predict grain growth and phase stability
• Solidification rate and gradient (G) and growth rate (R) for predicting dendrite morphology
• Time above critical temperatures for predicting phase transformations

Key Questions and Reflections

The accuracy of computational weld pool models depends critically on the accuracy of material property data used in the calculations. Properties such as thermal conductivity, electrical conductivity, surface tension coefficient, density, and viscosity are all temperature-dependent and may vary significantly between the liquid and solid phases. For multicomponent alloys used in cladding applications (e.g., Inconel 625, Hastelloy C276), these properties may not be well-characterized in the literature, introducing significant uncertainty into model predictions.

Another important consideration is the validation of computational models against experimental measurements. Direct measurement of fluid flow within the weld pool is extremely challenging due to the small dimensions (mm scale), high temperatures (above 1500°C), and rapid dynamics (ms timescales). Indirect validation through comparison of predicted and measured weld geometry, dilution rates, and hardness profiles provides useful but limited verification.

Study Insights and Implications

This research represents an important early contribution to the computational modeling of welding processes, establishing the theoretical framework for understanding transient weld pool behavior under pulsed current conditions. For engineers in the cladding and pressure vessel fabrication industry, the key insight is that computational modeling provides a powerful tool for process understanding and optimization that complements experimental investigation. The ability to simulate weld pool dynamics enables:

• Prediction of process outcomes before physical trials, reducing development time and cost
• Systematic exploration of parameter interactions through parametric studies
• Identification of critical process windows for achieving desired quality characteristics
• Understanding of fundamental mechanisms governing dilution, microstructure, and residual stress

As computational resources and modeling capabilities continue to advance, these approaches will become increasingly important for developing and qualifying advanced cladding processes for critical pressure vessel applications, where the consequences of process errors are particularly severe. The work demonstrates that fundamental physics-based modeling, combined with appropriate experimental validation, provides a rigorous pathway toward process optimization and quality improvement in welding overlay applications.