Numerical modeling of vibration effects on the surface tension of a liquid drop in additive technologies with SPH

The aim of this work is devoted to the numerical modeling of the vibration effects on the hydrodynamic behavior of drops in additive manufacturing processes. A mathematical model of the liquid flow taking into account the surface tension force in the formalism of the smoothed particle hydrodynamics method (SPH) is proposed, which lets to directly consider the influence of vibrations through the introduction of additional boundary conditions. The verification of this SPH approach is carried out in comparison with experimental results, where the dependence of the value of the surface tension coefficient on the speed amplitude of the vibrations was determined. The SPH model satisfactorily describes the effect of a surface tension coefficient reduction for water under vibrations. Therefore, a series of numerical experiments to determine the effect of vibration influences on the value of the surface tension coefficient for 12 $$\times $$ 18H10T steel in layer-by-layer wire cladding were conducted. It was found that the proposed SPH mathematical model is a promising numerical tool for further studying the effects of vibration influences in additive manufacturing processes.