Scale analysis of surface roughness impacted by airflow

This study scales the roughness, parallel to the scanning direction, on a solid surface solidified from thermocapillary surfaces under various working conditions as well as the gas inflow introduced from above. This roughness is commonly observed in autogenous and non-autogenous welding processes, additive manufacturing, and polishing techniques, leading to reduced yield, increased fatigue and fracture strength, and heightened stress concentration in the solidified area. The roughness of the solidified surface subjected to gas inflow from above is quantitatively scaled by applying the Young–Laplace equation, accounting for surface deformation due to differences in impact pressure across the free surface and dynamic pressure in the shear layer beneath the free surface. Surface velocity is scaled by balancing viscous stress with thermocapillary force and inertial force with viscous stress in the shear layer, while also considering mass conservation during melting and solidification. Results indicate that concave depth in the central region and bulge height at the edge increase as the impact pressure difference across the free surface, Weber number, Marangoni number, and Prandtl number increase, while the Peclet number decreases. The widths of the central and edge regions, which are independent of inflow velocity from above, increase with dimensionless beam power, solid-to-liquid thermal conductivity ratio, and other factors. COMSOL Multiphysics version 6.0 is used to compute surface deformation roughness influenced by unsteady two-dimensional fluid flow and heat transfer. The predicted roughness amplitude and pitch align well with scaling analysis data.