Initiation of air core in a swirl nozzle using time-independent power-law fluids

It is shown analytically that a limiting value exists for the Reynolds number (Re) at the inlet to a nozzle below which an air core will not form. The hydrodynamic study is limited to a purely viscous power-law fluid within the nozzle, where swirl is introduced by injecting the fluid tangentially. Approximate laminar boundary layer equations are defined and a spherical coordinate system is used for obtaining the solution. The air core radius and its initiation are modeled in terms of core potential pressure and the static pressure. Experimental data with a variety of tangentially-fed nozzles and water and an aqueous carboxymethyl cellulose sodium salt powder at various concentrations are reported for comparisons with theory. The presence of a critical Re is confirmed, indicating that the theory is a useful design tool for sizing nozzles for specific applications.