Direct numerical simulation of electrohydrodynamic plumes generated by a hyperbolic blade electrode

This paper presents a numerical study of two-dimensional EHD flow occurring between a hyperbolic blade and a plate electrode. The whole set of coupled equations is solved: Navier–Stokes equations, Poisson equation and charge conservation equation. A finite volume approach designed for non-orthogonal structured grid is used to discretize all governing equations. An efficient numerical procedure based on total variation diminishing (TVD) scheme is implemented to compute the distribution of charge density. Two different injection laws are considered: a simple autonomous one and a non autonomous which relates the charge injected by the blade and the local electric field. The flow structure which results in an EHD plume analogous to a thermal plume, has also been successfully characterized numerically by the temporal evolution of the charge density distribution. Preliminary results indicate that the flow is characterized by two different regimes according the value of the applied voltage. The critical Reynolds number for which the transition between the steady and unsteady regimes occurs has been determined to be within the range Re = [1000, 1100].