Numerical Simulation of Electrified Liquid Jets Using a Geometrical VoF Method

Abstract

The stretch of interfacial flows due to the external application of an electric field has considerable importance in several applications. These range from engineering nanofibres to propulsion, the electrified jets bring us an outstanding technique to perform the emission of microdroplets. The present investigation concerns the resolution of interfacial electrohydrodynamic flows from a numerical standpoint using computational fluid dynamics. The reduced form of the Maxwell equations, for an electrostatic field, and a transport equation for the electric charges are coupled to the standard interFoam solvers on OpenFOAM, which resolves an immiscible two-phase flow. A laminar condition is assumed for the flow thus the laminar incompressible Navier-Stokes’s equations are used to compute the hydrodynamic behavior of the flow and, associated with them, electrically induced body forces are incorporated into the hydrodynamic momentum equation. The Maxwell Stress Tensor (MST) describes electrical surface forces acting on the liquid, making it possible to incorporate that effect on the momentum equation. A new efficient geometric Volume-of-Fluid (VoF) method for general meshes, called isoAdvector, was implemented in OpenFOAM, as a substitute for the Multidimensional Universal Limiter for Explicit Solution (MULES). The open literature on the subject presents quantitative benchmarks that demonstrated a significant improvement in the quality with which we can compute sharper interfaces on immiscible two-phase flows (Gamet, L. et al. 2020). Following this approach, we present here an application of that method to the simulation of the breakup of electrified liquids jets. To validate the implementation of the electric field equations, the order of the accuracy of the spatial and time discretization is herein computed. The validation of the discretization of the electric field equations is accomplished with a planar test case that is considered a benchmark test for this class of flows. The test case showed good accuracy on the resolution of the electric potential and electric field having lesser than 0.1% of difference against the theoretical solution. The code is then applied to a Taylor cone jet. This type of jets is at the base of the Electro-hydrodynamic sprays (EHDS) physics. These latter operate by a potential difference between a conductive liquid, usually on the tip of a needle, and an extractor electrode. The numerical model shows a remarkable accuracy on the prediction of the charged droplet size.