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ABSTRACT
This paper is an attempt to study the evolution of temperature profiles and weld pool geometry during plasma arc welding (PAW) by solving the transient Navier–Stokes and Energy equations. The analysis for an AISI 304 stainless steel rectangular plate was carried out using a flexible written program in Fortran. Due to the low accuracy of the Fourier heat transfer equation for short times and large dimensions, a non-Fourier form of heat transfer equation was used. Gaussian heat source is considered as the heat source model. The fluid flow in the molten pool is of interest because it can change the temperature distribution in and around the molten zone. The governing equations for fluid flow were solved by the finite-volume method in which the SIMPLE method was utilized for pressure–velocity coupling. The effects of heat conduction, fluid flow, and force actions at the weld pool were considered. Thermo-physical properties such as thermal conductivity, specific heat, and dynamic viscosity vary as a function of temperature. There are two mechanisms involved which actively cause heat transfer to the surroundings: radiation and convection heat transfer. The numerical results are compared to the experimental data. The results corroborate that the weld pool thickness in the cross section of PAW and the time taken by molten metal to reach the end of thick metal are in good agreement with the experimental measurements. Finally, the results obtained from the assumed Fourier heat transfer are compared for the same study.
Nomenclature
| acr | = | thermal diffusion coefficient (W/m2 K) |
| Cj | = | adjustment factor |
| CP | = | specific heat (J/kg K) |
| Fb | = | body force (Pa) |
| Fbu | = | buoyancy (Pa) |
| Fe | = | electromagnetic force (Pa) |
| Ff | = | surface force (Pa) |
| fL | = | liquid fraction |
| g | = | gravitational acceleration (m/s2) |
| I | = | welding current (A) |
| i | = | vector along x direction |
| k | = | vector along z direction |
| K | = | thermal conductivity (W/m K) |
| l | = | thickness of workpiece (m) |
| L | = | latent heat of fusion (J/kg) |
| P | = | pressure (Pa) |
| q | = | heat flux (W/m2) |
| rh | = | radius of heat source (m) |
| Sh | = | source term according to latent heat content |
| Su | = | components of the force in x direction |
| Sw | = | components of the force in w direction |
| SP, SU | = | source term |
| t | = | time (s) |
| T | = | temperature (K) |
| TL | = | liquidus temperature (K) |
| T0 | = | ambient temperature (K) |
| TS | = | solidus temperature (K) |
| u | = | velocity along x direction (m/s) |
| U | = | arc voltage (V) |
| uls, wls | = | velocity at liquid–solid interface (m/s) |
| w | = | velocity along z direction (m/s) |
| x | = | along x direction |
| z | = | along z direction |
| Greek | = | |
| ρ | = | density (kg/m3) |
| dγ/dT | = | temperature coefficient of surface tension (N/m K) |
| β0 | = | coefficient of thermal expansion (K−1) |
| τ | = | relaxation time (s) |
| σj | = | current density distribution parameter (m) |
| μ | = | dynamic viscosity (kg/m s) |
| μ0 | = | magnetic permeability (H/m) |
| φ | = | general variable |
| η | = | arc efficiency |
Nomenclature
| acr | = | thermal diffusion coefficient (W/m2 K) |
| Cj | = | adjustment factor |
| CP | = | specific heat (J/kg K) |
| Fb | = | body force (Pa) |
| Fbu | = | buoyancy (Pa) |
| Fe | = | electromagnetic force (Pa) |
| Ff | = | surface force (Pa) |
| fL | = | liquid fraction |
| g | = | gravitational acceleration (m/s2) |
| I | = | welding current (A) |
| i | = | vector along x direction |
| k | = | vector along z direction |
| K | = | thermal conductivity (W/m K) |
| l | = | thickness of workpiece (m) |
| L | = | latent heat of fusion (J/kg) |
| P | = | pressure (Pa) |
| q | = | heat flux (W/m2) |
| rh | = | radius of heat source (m) |
| Sh | = | source term according to latent heat content |
| Su | = | components of the force in x direction |
| Sw | = | components of the force in w direction |
| SP, SU | = | source term |
| t | = | time (s) |
| T | = | temperature (K) |
| TL | = | liquidus temperature (K) |
| T0 | = | ambient temperature (K) |
| TS | = | solidus temperature (K) |
| u | = | velocity along x direction (m/s) |
| U | = | arc voltage (V) |
| uls, wls | = | velocity at liquid–solid interface (m/s) |
| w | = | velocity along z direction (m/s) |
| x | = | along x direction |
| z | = | along z direction |
| Greek | = | |
| ρ | = | density (kg/m3) |
| dγ/dT | = | temperature coefficient of surface tension (N/m K) |
| β0 | = | coefficient of thermal expansion (K−1) |
| τ | = | relaxation time (s) |
| σj | = | current density distribution parameter (m) |
| μ | = | dynamic viscosity (kg/m s) |
| μ0 | = | magnetic permeability (H/m) |
| φ | = | general variable |
| η | = | arc efficiency |
Acknowledgements
The authors would like to express their gratitude to Mr. M. Bovand for his loyal support and encouragement.