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

Abstract

Current development of micro-scale technologies increases the interest to 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. Methods are developed to find physically meaningful similarity solutions of the Navier-Stokes equations with finite values of mass and momentum fluxes and having no characteristic size. Two models are considered: flow dominated by momentum flux and flow dominated by mass flux. A new one-parameter set of momentum-dominated similarity solutions is found. Two linearly independent mass-dominated similarity solutions are found. Algorithms are proposed to evaluate the parameters of the similarity models from the mass and momentum balances. Distributions of flow parameters and stresses at 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 origin and competitive influence of the mass and momentum fluxes. Such 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 evaporation at selective laser melting. It is shown that the theoretically estimated flow velocity corresponds to the experimentally observed one. The theory explains formation of the experimentally observed denuded zone and its widening with decreasing the pressure of the ambient gas.