Numerical Analysis on the Stability Conditions of an Electrohydrodynamic Jet

Abstract

The Taylor cone jet is a well-known electrohydrodynamic flow (EHD), usually produced by applying an external electric field to a capillary liquid. The generation of this kind of flow involves a multi-phase and a multi-physics process and its stability has a specific operation window. This operating window is intrinsically dependent on the flow rate and magnitude of the applied electric voltage. In case high voltages are applied to the jet it can atomize and produce an electrospray. Our work presents a numerical study of the process of atomization of a Taylor cone jet using computational fluid dynamics (CFD). The study intents to assess the limit conditions of operation and the applied voltage needed to stabilize an electrospray. The numerical model was implemented within OpenFOAM, where the multi-phase hydrodynamics equations are solved using a volume-of-fluid (VOF) approach. This method is coupled with the Maxwell equations governing an electrostatic field, in order to incorporate the electric body forces into the incompressible Navier-Stokes equations. The leaky-dielectric model is used and, therefore, the interface between the two phases is subject to the hydrodynamic surface tension and electric stress (Maxwell stress). This allows a leakage of charge though the phase due to ohmic conduction. Thus, the permittivity and conductivity of the phases are taken into consideration. A two-fluid system with relevant electric properties can be categorized as, dielectric-dielectric, dielectric-conducting, and conducting-conducting considering the electrical conductivity and permittivities of the participating phases. Due to the usage of the leaky-dielectric model, it is possible to simulate any of this physical situations. By increasing the applied voltage reaches a value where the cone instability is verified, allowing a discussion on this effect. It is demonstrated that to adequately model the process of atomization a fine grid refinement is needed. The validation of the numerical model is made by comparing against diverse experimental data, for the case of a stable jet. The diameter and velocity of the droplet and the electric current of the jet are the main variables that are compared with previous results. The tests were performed with Heptane. The cone and the jet are strongly affected by the flow rate. The dimensionless diameter, as a function of the dimensionless flow rate, agrees with the scaling laws. The model predicts accurate results over a wide range of flow rates with an accuracy of around 10%. The results are obtained using structured meshes.