Analytical re-examination of the submerged laminar jet’s velocity evolution

Abstract

Understanding laminar submerged jet flight is important to many transport processes, although existing theory is insufficient within the most relevant near-nozzle region defined by the effective distance x′/(D·Re) < 0.05. A linearized convection diffusion momentum equation is employed to derive an approximate flow description within the jet core, for all archetypal issuing profiles. This is validated in the core region near the nozzle by numerical simulations and experimental measurements, and it provides novel insights and adaptation of the far-field (self-similar) Schlichting jet solution. It is employed here to reveal the detailed contour of each profile’s potential core and allows its differentiation from a new “boundary core” concept—the region unaffected by the change of the jet-edge shear transition from pipe flow to free-jet. This new concept reveals the minimal distance at which self-similarity can begin to exist, thereby analytically determining the virtual origin required to bring the existing far-field solution nearest to the nozzle. Thus, profile evolution and jet width become predictable within the near-nozzle region for all issuing profiles. As an alternative to the lengthy full prediction, current analysis also facilitates analytical rederivation of physically based parameters for two existing correlations describing the full uniform profile evolution and the centerline velocity decay for all other issuing profiles.