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ABSTRACT
A three-dimensional numerical model of Gas Tungsten Arc welding has been developed to predict weld a bead shape, fluid flow in the weld pool, as well as thermal field in the workpiece. This model accounts for coupled electromagnetism, heat transfer, and fluid flow with a moving free surface to simulate different welding positions. The solution strategy of the coupled non-linear equations that has been implemented in the CastɜM finite-element code is also discussed. The capabilities of our numerical model are first assessed by comparison to the experimental results. Then, as fluid flows in a weld pool play a prominent role in the weld quality as well as in the final shape of the weld bead seam, the effect of various welding positions on the weld pool shape has been investigated. This constitutes the main novelty of this work. The performed computations point out a strong sensitivity to gravity on the weld pool shape depending on assisting or opposing the weld direction with respect to gravity. This study contributes to assessing the model capabilities that provide a deeper physical insight into a more efficient optimization of welding processes.
Nomenclature
| A | = | magnetic vector potential, T·m |
| B | = | magnetic induction, T |
| E | = | electric field, V·m−1 |
| fArc | = | arc pressure, N·m−2 |
| fBody | = | gravity force, N·m−3 |
| fExt | = | velocity extinction force, N·m−3 |
| fLor | = | Lorentz force, N·m−3 |
| fMar | = | Marangoni force, N·m−2 |
| j | = | electric current density, A·m−2 |
| n | = | normal vector |
| sCvs | = | convective heat loss, W·m−2 |
| sRay | = | radiation loss, W·m−2 |
| sSur | = | surface heat source, W·m−2 |
| t1, t2 | = | tangent vectors |
| u | = | flow velocity, m·s−1 |
| us | = | welding speed, m·s−1 |
| c | = | constant |
| cp | = | specific heat, J·kg−1·K−1 |
| fl | = | liquid metal fraction |
| g | = | gravity, m·s−2 |
| h | = | enthalpy per unit mass, J·kg−1 |
| hc | = | convective heat transfer coefficient, W·m−2·K−1 |
| I | = | total electric current, A |
| L | = | latent heat, J·kg−1 |
| p | = | pressure in the liquid phase, N·m−2 |
| pmax | = | maximum arc pressure, N·m−2 |
| rp | = | radius of the arc pressure, mm |
| rq | = | radius of the heat source, mm |
| rϕ | = | radius of the electric current, mm |
| sJoule | = | Joule effect, W·m−3 |
| T | = | temperature field, K |
| U | = | voltage, V |
| Greek Variables | = | |
| β | = | thermal expansion coefficient, K−1 |
| γ | = | surface tension, N·m−1 |
| ϵ | = | radiation emissivity |
| η | = | process efficiency |
| λ | = | thermal conductivity, W·m−1·K−1 |
| µ | = | dynamic viscosity, kg·m−1·s−1 |
| µ0 | = | magnetic permeability, H·m−1 |
| ρ | = | density, kg·m−3 |
| σ | = | electrical conductivity, S·m−1 |
| σB | = | Stefan–Boltzmann constant, W·m−2·K−4 |
| ϕ | = | electric scalar potential, V |
Nomenclature
| A | = | magnetic vector potential, T·m |
| B | = | magnetic induction, T |
| E | = | electric field, V·m−1 |
| fArc | = | arc pressure, N·m−2 |
| fBody | = | gravity force, N·m−3 |
| fExt | = | velocity extinction force, N·m−3 |
| fLor | = | Lorentz force, N·m−3 |
| fMar | = | Marangoni force, N·m−2 |
| j | = | electric current density, A·m−2 |
| n | = | normal vector |
| sCvs | = | convective heat loss, W·m−2 |
| sRay | = | radiation loss, W·m−2 |
| sSur | = | surface heat source, W·m−2 |
| t1, t2 | = | tangent vectors |
| u | = | flow velocity, m·s−1 |
| us | = | welding speed, m·s−1 |
| c | = | constant |
| cp | = | specific heat, J·kg−1·K−1 |
| fl | = | liquid metal fraction |
| g | = | gravity, m·s−2 |
| h | = | enthalpy per unit mass, J·kg−1 |
| hc | = | convective heat transfer coefficient, W·m−2·K−1 |
| I | = | total electric current, A |
| L | = | latent heat, J·kg−1 |
| p | = | pressure in the liquid phase, N·m−2 |
| pmax | = | maximum arc pressure, N·m−2 |
| rp | = | radius of the arc pressure, mm |
| rq | = | radius of the heat source, mm |
| rϕ | = | radius of the electric current, mm |
| sJoule | = | Joule effect, W·m−3 |
| T | = | temperature field, K |
| U | = | voltage, V |
| Greek Variables | = | |
| β | = | thermal expansion coefficient, K−1 |
| γ | = | surface tension, N·m−1 |
| ϵ | = | radiation emissivity |
| η | = | process efficiency |
| λ | = | thermal conductivity, W·m−1·K−1 |
| µ | = | dynamic viscosity, kg·m−1·s−1 |
| µ0 | = | magnetic permeability, H·m−1 |
| ρ | = | density, kg·m−3 |
| σ | = | electrical conductivity, S·m−1 |
| σB | = | Stefan–Boltzmann constant, W·m−2·K−4 |
| ϕ | = | electric scalar potential, V |
Acknowledgments
This work was carried out at the French Alternative Energies and Atomic Energy Commission (CEA) in partnership with AREVA NP. The authors would like to acknowledge the financial support provided by both entities. This work was also partially supported by the French government throughout its funding of the FUI-AAP14 MUSICAS project (http://www.systematic-paris-region.org/fr/projets/musicas).