Entrainment flow of a jet emerging into a half-space with the no-slip boundary condition

Abstract

The current development of micro-scale technologies increases the interest in viscous flows with low and moderate Reynolds numbers. This work theoretically studies the entrainment flow of a viscous jet emerging from a plane wall into a half-space with the objective to understand the conditions where a similarity model can approximate a realistic flow. Two similarity models having analytic solutions are considered: the flow dominated by the momentum flux and the flow dominated by the mass flux. Algorithms are proposed to evaluate the parameters of the similarity models from the mass and momentum balances. Distributions of flow parameters and stresses on the wall are calculated for the similarity models. They are compared with the corresponding distributions obtained by computational fluid dynamics for a more realistic model with a finite size of the jet source and competitive influence of the mass and momentum fluxes. This comparison validates the mass-dominated similarity model at the jet Reynolds number Re ≤ 10 and the momentum-dominated similarity model at Re ≥ 30. The obtained results are applied to the problem of laser evaporation in selective laser melting. It is shown that the theoretically estimated flow velocity corresponds to the experimentally observed one. The theory explains the formation of the experimentally observed denuded zone and its widening by decreasing the ambient gas pressure.