Comparison between net emission coefficient and P-1 methods in modelling radiation in a plasma arc welding torch

Radiative processes often represent an important component in energy transport, and the calculation of the radiative flux is necessary in advanced modelling of thermal plasma systems. The method based on net emission coefficients (nec), which represent the difference between the power radiated and absorbed in a volume unit, is commonly used in thermal plasma modelling. These coefficients have been reported in literature for specific plasma mixtures as function of temperature, in the hypothesis of Local Thermodynamic Equilibrium (LTE) plasma composition.The strong simplifications in the nec approach may lead to inaccurate results in plasma modelling (e.g. the plasma radius must be known in advance and it is fixed for all the discharge regions) and radiation transport from plasma to confinement walls can only be estimated globally and not locally. The P-1 radiation model, which is based on the expansion of the radiation intensity function into an orthogonal series of spherical harmonics, can be used to overcome the nec approach simplifications in order to take into account discharge spatial distribution and local absorption. However, this method is computationally expensive and need the knowledge of the absorption coefficients as function of radiation wavelength and of plasma composition and temperature. In this work, the nec approach and the P-1 radiation model have been applied to a plasma arc welding (PAW) torch working with Ar as plasma gas for currents varying from 50A to 200A in order to underline the differences between the two different models in the predicted plasma fields and radiation fluxes on the walls. Ar radiation properties have been calculated by means of a detailed line-by-line method, implemented to compute the net emission coefficient of Ar plasmas at temperatures ranging from 1000 K to 30000 K at different plasma pressures for optically thin and partially auto-absorbed (optically thick) plasmas. The spectral domain was then divided into bands and- the mean absorption coefficients for each band were computed from the nec model and then introduced in the P-1 radiation model. Total radiative fluxes as computed from the two modelling approaches were compared for the PAW torch at varying operating currents in order to identify the range of validity of the nec assumptions, whereas local radiative fluxes to torch walls were calculated using the P-1 model.