Numerical Simulation of Internal Flow Field in TIG Arc Brazing Filler Droplet

Literature Overview

This paper by Li Ruifeng, Yu Zhishui, and Qi Kai, published in the Journal of Jiangsu University (Natural Science Edition) (2007, Vol. 21, Issue 1, pp. 85–89), presents a numerical simulation study of the internal flow field within filler metal droplets during TIG arc brazing. Building upon experimental studies of droplet spreading and wetting behavior, the authors developed a mathematical model that accounts for gravity, surface tension, and arc pressure forces acting on the filler droplet, and used the PHOENICS software with the SIMPLEST algorithm to compute the internal flow field behavior. The study also compares the flow field characteristics of the brazing droplet with those of a conventional TIG welding pool, providing deeper understanding of droplet free surface evolution and final shape formation.

Core Technical Content

Physical Model and Governing Equations

The mathematical model developed for this study incorporates the following physical phenomena acting on the filler metal droplet:

• Gravity: Acts on the droplet mass, causing downward displacement and spreading
• Surface tension: Acts at the droplet free surface, driving the droplet toward a minimum energy configuration (spherical shape in absence of other forces)
• Arc pressure: The electromagnetic and aerodynamic forces from the TIG arc act on the droplet surface, creating pressure gradients that drive internal flow
• Viscous forces: Resist the internal flow, determining the velocity field within the droplet

The governing equations were transformed into finite volume equations for numerical solution using the PHOENICS computational fluid dynamics (CFD) software. The SIMPLEST (Semi-Implicit Method for Pressure-Linked Equations, Single Equation) algorithm was employed for pressure-velocity coupling, which is well-suited for incompressible flow problems with free surfaces.

Key Modeling Assumptions

Technical Analysis

Flow Field Behavior in Brazing Droplets

The internal flow field within a brazing droplet differs fundamentally from that in a conventional welding pool. In welding, the base metal is melted and the weld pool is formed by the direct melting of the workpiece, with flow driven primarily by arc forces, buoyancy, and surface tension gradients (Marangoni convection). In brazing, the base metal remains solid, and the filler metal is melted separately and then flows onto the substrate surface. The droplet dynamics are therefore governed by:

1. Initial droplet formation: The filler wire is melted by the arc, and molten droplets form at the wire tip
2. Droplet transfer: Droplets are transferred from the wire to the substrate (in this case, likely by direct contact or arc-induced transfer)
3. Droplet spreading: The droplet spreads on the substrate surface under the influence of gravity, surface tension, and arc pressure
4. Final shape formation: The droplet reaches a quasi-equilibrium shape determined by the balance of competing forces

The numerical simulation reveals that the internal flow patterns within the droplet are complex, with recirculation zones driven by the interaction of arc pressure, surface tension, and gravity. These flow patterns directly affect the droplet spreading rate, final geometry, and wetting characteristics on the substrate surface.

Comparison with Conventional TIG Welding Pool

The comparison between the brazing droplet flow field and the conventional welding pool flow field reveals important differences:

• Flow driving forces: In welding, Marangoni convection (surface tension gradient driven by temperature gradient) is often the dominant flow driver, whereas in brazing, arc pressure and gravity play relatively more significant roles
• Temperature gradients: The welding pool has steep temperature gradients from the center (molten) to the edges (solid), driving strong Marangoni flows; the brazing droplet is more isothermal, reducing Marangoni effects
• Boundary conditions: The welding pool has a fixed boundary defined by the solid-liquid interface; the brazing droplet has a free surface boundary that evolves during spreading
• Flow symmetry: The welding pool typically exhibits axisymmetric flow patterns; the brazing droplet may show asymmetric flow depending on the arc position and droplet placement

Connection with Engineering Practice

Application to Brazing Process Optimization

Understanding the internal flow field within brazing droplets is critical for optimizing brazing process parameters. The flow patterns within the droplet directly affect:

• Wetting behavior: The internal flow determines how quickly and uniformly the filler metal spreads on the substrate surface
• Joint geometry: The final droplet shape determines the fillet geometry of the brazed joint, which affects mechanical strength and fatigue resistance
• Porosity formation: Internal flow patterns can trap or expel gas bubbles, affecting joint quality
• Contamination sensitivity: The flow field determines how quickly contaminants at the substrate surface are expelled or incorporated into the joint

Relevance to Pipe and Fitting Brazing

In the fabrication of copper and copper alloy pipe systems—common in plumbing, HVAC, and refrigeration applications—TIG arc brazing is widely used for joining pipe to fittings. The quality of the brazed joint directly affects leak tightness, mechanical strength, and long-term durability. The numerical simulation approach presented in this study provides a powerful tool for predicting and optimizing brazed joint quality without the need for extensive trial-and-error experimentation.

For brazing of dissimilar materials—such as copper pipe to nickel fittings, or copper to stainless steel—the flow field behavior becomes even more complex due to differences in wetting characteristics and thermal expansion. The simulation approach can be extended to model these dissimilar material joints, providing valuable insights into joint design and process parameter selection.

Process Parameter Optimization

The numerical simulation framework can be extended to systematically evaluate the effects of key brazing parameters on droplet behavior:

Key Questions and Reflections

The numerical simulation approach presented in this study is valuable but has inherent limitations that must be acknowledged. First, the accuracy of the simulation depends on the accuracy of the physical property data (surface tension, viscosity, density) as functions of temperature and composition, which may not be readily available for all filler metal alloys. Second, the model assumes a simplified representation of arc pressure and surface tension forces; the actual arc force distribution on a real droplet is highly complex and may vary with torch position, wire feed rate, and gas flow conditions. Third, the two-dimensional or axisymmetric simplifications commonly used in such simulations may not capture the full three-dimensional complexity of real droplet flow, particularly in cases where the droplet is asymmetrically positioned relative to the arc.

Despite these limitations, the simulation results provide qualitative and semi-quantitative insights into droplet flow behavior that are invaluable for process understanding and optimization. The comparison with experimental results (droplet spreading and wetting tests) validates the approach and builds confidence in its predictive capability.

Study Insights and Implications

This study demonstrates the power of computational fluid dynamics in understanding and optimizing brazing processes. The ability to simulate the internal flow field within a brazing droplet provides insights that are difficult or impossible to obtain through experimental observation alone. For welding and brazing engineers, this research highlights the importance of integrating numerical simulation with experimental validation in process development and optimization.

The findings have direct practical implications for brazing process design: by understanding how arc pressure, surface tension, and gravity interact to drive droplet flow, engineers can select process parameters that promote uniform spreading, minimize porosity, and achieve optimal joint geometry. As computational resources become more accessible and simulation tools more sophisticated, this type of numerical analysis will become an increasingly important component of welding and brazing process development, complementing traditional experimental approaches and accelerating the path from process design to production qualification.

This comprehensive study of five distinct topics in TIG welding technology—from practical spot welding applications and power electronics to filler wire selection, post-weld thermomechanical processing, and numerical simulation—demonstrates the remarkable breadth and depth of modern welding engineering. Each paper addresses a specific technical challenge through a unique combination of experimental investigation, theoretical analysis, and process innovation, collectively illustrating how the welding field continues to advance through the integration of materials science, power electronics, computational methods, and practical engineering judgment. The common thread running through all five studies is the recognition that weld quality is determined not only by the welding parameters themselves but by the entire process chain—from power source design and filler metal selection to post-weld processing and computational analysis. For practitioners in steel pipe, fitting, and welding engineering, these studies collectively reinforce the importance of a holistic, systems-level approach to welding process development and qualification, where each technical decision is informed by a deep understanding of the underlying physics and metallurgy.