Mathematical Modelling of Wall Films Formed by Impinging Sprays

This paper presents a mathematical model for the prediction of the dynamic characteristics of wall films formed by impinging sprays. The model takes into account the impingement pressure due to bombardment of impinging droplets, tangential momentum transfer resulting from oblique droplet impingement on the film surface, and the gas shear force at the film surface. The general transport equations of mass, momentum and energy for wall film flows are established in the boundary-layer framework. It is shown that this set of equations can be substantially simplified if local equilibrium occurs and a dimensional analysis is performed to identify the conditions for the applicability of the local equilibrium model.

Solution of the full film equations is obtained by an efficient hybrid integral/numerical method, which allows numerical calculations to be performed in a two-dimensional framework. An implicit finite volume scheme is employed for this purpose. The methodology is first tested against some simple problems with analytical solutions. Then assessment is performed against several sources of experimental data for films formed by impinging sprays. Satisfactory agreement is obtained.