Three-dimensional computational fluid dynamics simulation of the hollow-cone spray process: The stability of the conical liquid sheet

The characterization of atomization in small-scale applications, such as those typical of the consumer goods industry, is not widely investigated, despite its enormous interest as in the case of sanitation. In this field, the features of the atomizer are selected to achieve a wide spray pattern. This is the case of the pressure-swirl atomizer, where the swirl flow leads the liquid sheet to exhibit a distinctive hollow-cone shape. The configuration of the atomizer and the properties of the multiphase system (liquid-gas) affect the spray morphology and the droplets/ligaments distribution. The aim of the work is to investigate through computational fluid dynamics the stability of the gas-liquid interface produced by a swirling liquid injection. By implementing the volume-of-fluid method, we show transient simulations, in which the liquid-gas interactions take place within and outside the nozzle simultaneously. Depending on the different liquid properties and geometric features, we examine the hollow-cone spray performance in terms of cone angle and liquid sheet morphology. A stability analysis allows to determine whether spraying or jetting conditions are attained depending on Reynolds and Ohnesorge numbers, as the hollow-cone shape can degenerate into a straight jet under specific operating conditions. Viscosity is known to be a relevant parameter in fluid formulation, which impacts on both relevant dimensionless parameters. Newtonian and non-Newtonian rheologies are here considered for their ubiquitous presence in detergent or sanitation fluids. In both cases, we find a critical condition that marks the switch from the spraying to the jetting regime.