# Simulations of weld pool dynamics in V-groove GTA and GMA welding

## Authors

- First Online:

- Received:
- Accepted:

DOI: 10.1007/s40194-012-0017-z

- Cite this article as:
- Cho, D., Na, S., Cho, M. et al. Weld World (2013) 57: 223. doi:10.1007/s40194-012-0017-z

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## Abstract

### Introduction

Many simulation models use an axisymmetric arc model for heat flux, arc pressure, and electromagnetic force. In V-groove welding, however, an elliptically symmetric arc model is more acceptable than an axisymmetric model. An elliptically symmetric arc model can be established by applying the Abel inversion method to CCD images of welding arc on V-groove.

### Methods

This study uses an elliptically symmetric arc model for CFD based simulations of fluid flow behavior in weld pool of GMA V-groove welding. It recommends a new method of calculating the electromagnetic force distribution in V-groove welding.

### Conclusion

A volume of fluid method is used to describe the molten pool flow in numerical simulations.

### Keywords (IIW Thesaurus)

Arc weldingElectromagnetic fieldsSimulating## 1 Introduction

Many pipe welding experiments and simulations have been conducted in V-groove or fillet joint for the purpose of analyzing and optimizing the welding parameters [1, 2]. However, optimizing the parameters in gas metal arc (GMA) welding is complicated by the force of gravity, which causes a molten pool to flow to the ground. Because of the need to check the molten pool flow, a computational fluid dynamics (CFD) model is consequently more suitable than a normal finite elements method model.

For the more realistic simulation results, this study suggests a new method of applying the coordinate mapping in V-groove welding and assumes the arc model as an elliptically symmetric shape.

## 2 Numerical formulations

### 2.1 Governing equations

Prosperities used in simulation

Symbol | Nomenclature | Symbol | Nomenclature |
---|---|---|---|

| Thermal conductivity |
| Material permeability, 1.26 × 10 |

\( \overrightarrow{n} \) | Normal vector to free surface |
| Heat input from droplet |

| Arc efficiency in GTAW, 0.7 |
| Density, (solid:7.8, liquid:6.9, g/cm |

| Arc efficiency in GMAW, 0.56 |
| Specific heat of solid, 7.26 × 10 |

V | Welding voltage (average) |
| Specific heat of liquid, 7.32 × 10 |

I | Welding current (average) |
| Solidus temperature, 1768 K |

J | Current density (I/mm |
| Liquidus temperature, 1798 K |

| Effective radius of arc in x-direction, 1.5 mm |
| Room temperature, 298 K |

| Effective radius of arc in y-direction, 0.90 mm |
| Latent heat of fusion, 2.77 × 10 |

| Droplet frequency (Hz) |
| Droplet efficiency in GMAW, 0.24 |

WFR | Wire feed rate (m/min) | z | Vertical distance from top surface |

| Wire diameter in GMAW, 1.2 mm |
| Vertical component of the current density |

| Droplet diameter in GMAW, 1.2 mm |
| Radial component of the current density |

| Permeability of vacuum, 1.26 × 10 |
| Angular component of the magnetic field |

γ | Surface tension |

### 2.2 Boundary conditions

*Q*

_{A}), the heat dissipation by convection (

*Q*

_{conv}) and radiation (

*Q*

_{rad}) and heat loss due to evaporation (

*Q*

_{evap}). The energy balance on the top surface is expressed as the following equations:

*σ*

_{x}= 1.50 mm,

*σ*

_{y}= 0.90 mm) of the arc plasma in Eq. (2). This equation contains the average value of voltage (

*V*), current (

*I*) from the welding experiments and the arc efficiency in GMAW and GTAW.

*η*

_{Arc_GTAW}) in GTAW as 0.7 because many previous studies already used the value in GTAW [9, 10]. On the other hand, the efficiency of the arc in GMAW is predetermined as 0.56 because the heat input efficiency of the droplets was found to be 0.24 from Eqs (3), (4), (5), and (6). Normally, the total GMAW efficiency was set at 0.8 [7, 9].

In Eq. (8), the current density (*J*) is assumed to be linearly proportional to the arc pressure (*P*_{A}) [11]. Thus, the distribution of the arc pressure follows the distribution of the current density. The arc plasma pressure can therefore be modeled, as shown in Eq. (9) with an elliptically symmetric model that has the same effective radii of arc heat flux [2].

### 2.3 EMF model

#### 2.3.1 Derivation of an elliptically symmetric EMF model in bead-on-plate welding

*r*

_{e}) in Fig. 4. This model modifies the current density and electromagnetic field and ultimately determines the EMF for the

*x*,

*y*, and

*z*directions (

*F*

_{x},

*F*

_{y},

*F*

_{z}).

#### 2.3.2 Coordinate mapping

### Mapping is used to calculate the EMF in V-groove welding

*r*-direction and

*z*-direction in BOP welding. However, both directions of the EMF must be different from each other on the V-groove slope surface because, as shown in Fig. 5 the welding current starts to flow into the workpiece through the top surface.

#### 2.3.3 Mapping the coordinates for the V-groove welding

- (a)
The V-groove slope surface is assumed to be a top surface.

- (b)
The current density starts to flow perpendicular to the V-groove slope surface.

- (c)
The use of a spline function forms, the coordinates inside the workpiece.

#### 2.3.4 Redefinition of the material thickness from mapping

*r*-direction as shown in Fig. 7. The newly calculated thickness (

*C*

_{y}) is applied to the EMF models in Eqs. (14), (15), and (16).

#### 2.3.5 Calculation of the elliptically symmetric EMF in V-groove joint

#### 2.3.6 Calculation of the horizontal and vertical forces from vectors

### EMF in V-groove GTAW

*P1*,

*P2*, and

*P3*can be automatically determine the two neighboring angles

*θ*

_{1}and

*θ*

_{2}. Figure 10 shows that it is then possible to obtain the EMF from Eqs. (20) and (21) for the vertical and horizontal directions (

*F*

_{y1},

*F*

_{z1}). In Fig. 8, the locations of the maximum absolute EMF value for the radial and vertical components are different from each other; therefore, the horizontal EMF component has two opposite directions in Fig. 10. If no additional deposit metal is deposited on the surface, this method is acceptable for use in simulations of GTAW processes.

*S*

_{ij}) by considering the free surface location of

*z*-direction as shown in Fig. 11. Therefore, the coordinate of EMF from mapping move upward or downward along the

*z*-direction. Finally, the newly defined EMF values are applied in the simulation.

### EMF in V-groove GMAW

### 2.4 Other welding models

## 3 Result and discussion

### 3.1 Simulation results of GTAW in coordinate mapping of the EMF

Welding parameters in GTAW

Current | Voltage | Arc length | Welding speed | Electrode |
---|---|---|---|---|

200A | 12.6 V | 5 mm | stationary | Tungsten, ϕ 2.4 mm |

### 3.2 Simulation results of GMAW from an elliptically symmetric EMF

Welding parameters in GMAW

Current | Voltage | CTWD | Welding speed | Electrode | Shielding gas |
---|---|---|---|---|---|

255A (WFR:7.5 m/min) | 25 V | 20 mm | 10 mm/s | YGW15, ϕ 1.2 mm | Ar80% CO |

## 4 Conclusions

In V-groove welding, the arc is rather elliptically symmetric than axisymmetric. An elliptically symmetric arc model is therefore useful for the arc heat flux, the arc pressure and the EMF distribution. An arc heat flux and an arc pressure model can be used in boundary conditions; however, the EMF model can be used for the body force, which affects the entire molten pool volume. In V-groove GMAW, the top surface of the molten pool is almost flat; thus, coordinate mapping is not strictly required in CFD-based process simulations. In contrast with GMAW, however, the top surface of the molten pool in GTAW is inclined because there is no additional volume to form the bead shape. This paper suggests and validates a new method that can effectively model the EMF in V-groove GTAW; in the new method, coordinate mapping is applied to CFD-based simulations of weld pool fluid dynamics.

## Acknowledgements

The authors gratefully acknowledge the support by Brain Korea 21 Project and POSCO in Republic of Korea.