Annular Liquid Jets: Formulation and Steady State Analysis

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Abstract
The equations governing the fluid dynamics of long annular liquid, jets and long annular liquid membranes are derived by means of an integral formulation which is valid for Newtonian and non‐Newtonian Fluids. Analytical solutions for long, inviscid, steady state, annular liquid membranes are obtained in Eulerian coordinates as a function of the Froude and Weber numbers, nozzle exit angle, and pressure difference across the annular membrane. It is shown that the convergence length of the annular membrane increases as the Froude and Weber numbers, nozzle exit angle and pressure difference across the annular membrane are increased. The range of parameters for which the analytical solutions are valid is determined as a function of the Froude and Weber numbers for the case of zero nozzle exit angle and zero pressure difference. Analytical and numerical solutions for long, inviscid, steady state, annular liquid jets are also obtained and show that the convergence length decreases us the jet thickness‐to‐radius ratio at the nozzle exit is increased and increases at the Froude and Weber numbers, nozzle exit angle and pressure difference across the annular liquid jet are increased.

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