Self-consistent scaling of amplitude and pitch of ripples on a solidified surface. (July 2022) - Wei, P.S.; Lu, S.X.; Hung, C.F.; Huang, S.K.
Abstract: Amplitude and pitch of ripples on a solidified surface during arc welding or electron beam welding are self-consistently and realistically scaled. Defects of surface rippling or humping after solidification usually accompany solute segregation, porosity, etc. Surface ripples have also been contemporarily used to excite surface plasmon with wavelength less than that of incident laser and local concentrated energy near the surface to enhance efficiencies of LEDs, solar energy absorption and medical detections, etc. This work modified the previous scaling of the amplitude and pitch of surface ripples induced by Marangoni or thermocapillary flow in the molten pool by further accounting for joule heat and electromagnetic Lorentz force due to electric current from the top electrode. Combining the modified scaling of surface ripples with surface velocity in the pool, the results find that amplitude and pitch of surface ripples depend on modified Marangoni, Peclet, Prandtl numbers, loss coefficient and current frequency parameter. The loss coefficient and current frequency play a role in amplitude and pitch, respectively. Predicted surface amplitudes and pitches affected by electromagnetic, fluid, energy and concentration transport variables using COMSOL code are in good agreement with available experimental data.