On the modelling of the particle dynamics in electro-hydrodynamic flow-fields: I. Comparison of Eulerian and Lagrangian modelling approach

Electro-hydrodynamic two-phase flows are encountered in various applications, e.g. electrically enhanced coating, electrostatic precipitation or toner application. In all cases there is a complex interaction between a turbulent flow field, a strong electric field, a corona discharge and the particle motion. This paper starts with an overview and classification of possible modelling approaches for all major phenomena. Afterwards the manuscript focuses on the modelling of particle dynamics: A Lagrangian, continuous random walk model is compared with an Eulerian approach for a number of test cases. The study is mostly focused on fine particles, i.e. roughly smaller than 100 μm in diameter for the Lagrangian approach and smaller than about 10 μm in the case of Eulerian modelling. It is shown that a local turbulent dispersion coefficient may be derived based on flow field calculations with a constant of proportionality identical to the Lagrangian random walk model. In this case the turbulent dispersion is equally described by both models even for inhomogeneous turbulence. For a superimposed particle drift velocity a model equation introduced by Csanady gives a reasonable agreement. Finally it is shown that modelling of the charging kinetics is a very crucial point in Eulerian modelling. This is demonstrated for the example of electrostatic precipitation where good agreement between Lagrangian and Eulerian modelling is achieved only if local particle charging kinetics is accounted for. Even though Lagrangian particle tracking is still superior in terms of physical modelling of electro-hydrodynamic particulate flows, it is shown that an Eulerian approach may lead to reasonable results with substantially reduced numerical effort.