A computer simulation for predicting electrostatic spray coating patterns

Abstract Although electrostatic spray coating (E-spray) is widely used, its complexity requires optimization based on an empirical understanding of the spray dynamics. The project goal is to develop a mathematical model of the electrostatic field, continuum flow-field, and particle trajectories in an E-spray process. By restricting the use of empirically based equations to the atomization phase of the spray process, this model should have the flexibility to tolerate “real-world” system complexities (i.e. multiple applicators, complicated geometries, etc.) and the ability to be used with any type of E-spray gun sharing the same atomization characteristics. This model predicts coupling between three components: the fluid mechanics of the continuum flow field, the electrostatic field, and the particle trajectories. The system is a vertical bell-cup sprayer and a grounded disc centered on the gun axis. An axisymmetric electrostatic model is assumed, while the fluid mechanics and particle trajectories are solved in 3-D. A dilute spray assumption (i.e. no direct particle–particle interactions) allows modeling single-particle trajectories resulting from a balance of electrostatic force, drag and inertia. Varying the particle size generates volume-averaged properties of individual paths to simulate the charge density and fluid drag of a sprayed particle distribution. A turbulence energy–dissipation rate (k–ɛ) model provides the continuum velocity for the particle drag. These individual systems are solved sequentially and that sequence is iterated to convergence. Results include the effect of charged particles on the electrostatic field and identification of the dominant factors affecting coating thickness distribution.