Estimation method of spray diameter and size distribution based on energy conservation law

Abstract

An analytical method was proposed and validated for droplet diameters and size distributions. The method was developed based on the energy conservation law including surface free energy and Laplace pressure. Under several hypotheses, the law derived an equation indicating that atomization resulted from a kinetic energy loss. Thus, once the amount of loss was obtained, the droplet diameter was able to be calculated without any experimental parameters. When the effects of ambient gas were ignorable, injection velocity profiles of liquid jets were the essential factor for the reduction of kinetic energy. The minimum Sauter mean diameter produced by liquid sheet atomization was inversely proportional to the injection Weber number under the conditions of injection velocity profiles with laminar or turbulent. By applying the mean diameter model, a non dimensional distribution function was also derived assuming Nukiyama-Tanasawa's function. The validity of these estimation methods were favorably confirmed by comparisons with corresponding mean diameters and the size distributions, which were experimentally measured under atmospheric pressure.