Thermal Transport Regimes and Effects of Prandtl Number in Molten Pool Transport in Laser Surface Melting Processes

Abstract

The effects of Prandtl number of the molten metal in weld pool convection are studied based on a systematic scaling analysis. It is demonstrated that for a very small Prandtl number the weld pool morphology is predominantly determined by heat conduction whereas convection has a marginal effect on the molten pool morphology. By contrast, for relatively greater values of Prandtl number the convection pattern in the molten pool significantly affects the pool shape and size. The criteria, which demarcate these two regimes, are estimated by a detailed scaling argument. It is also shown from scaling analysis that turbulence in the molten pool affects momentum and thermal transport differently. Turbulence may also significantly affect the momentum transport of the pool whereas the thermal transport is marginally affected. A regime diagram is constructed based on scaling arguments where the above flow regimes are clearly indicated. In order to validate the scaling arguments on which the regime diagram is based, two three dimensional simulations are carried out for laser welding of iron (for Fe, Prandtl number in order of 0.1) and copper (for Cu, Prandtl number in the order of 0.01). It is found that in the case of Cu, the weld pool obtained from conduction solution is almost the same as the pool morphology obtained using laminar and turbulent transport models. By contrast, in the case of Fe, the weld pools obtained from laminar and turbulent transport models are significantly different from each other, and are also different from the pool obtained from the heat conduction solution.

Acknowledgments

The author is grateful to Dr. S. Chakraborty and Dr. M. Home for their comments while preparing this article.

Notes

In momentum equations where f _l is the liquid fraction of a given control volume given by: f _l  = ΔH/L in which ΔH is the latent heat content of a given computational cell. The reference temperature T _ref is taken to be the melting point temperature T _m of the concerned metal.