Abstract
For many applications, Reduced Order Models (ROMs) use linear tools such as Proper Orthogonal Decomposition (POD) as a method for analysing the spatio-temporal coherence of dynamical systems and to construct reduced order models of fluid flows and optimally balanced control laws and identify correlations between different flow quantities. In particular, these techniques are of interest for liquid injection systems due to the inherent complexity of multiphase interactions, and extracting the underlying flow processes is desirable. In this study, we propose to use these techniques to determine a ROM for electrohydrodynamic interfacial flows, more specifically for a Taylor cone jet. From engineering nanofibres to propulsion, the electrohydrodynamic jets bring us an outstanding technique for the emission of microdroplets. This is due to the stretching of interfacial flows due to the external application of an electric field. The present investigation uses an efficient geometric Volume-Of-Fluid (VOF) method, called isoAdvector, to compute the advection equation of the phase fraction. This algorithm computes an immiscible two-phase flow, that is then coupled with the reduced form of the Maxwell equations for an electrostatic field and a transport equation for the electric charges. Electrically induced body forces are incorporated into the hydrodynamic momentum equation with the Maxwell Stress Tensor (MST). A laminar condition is assumed for the flow, thus the laminar incompressible Navier-Stokes’s equations are used to compute the hydrodynamic behaviour of the flow and the associated The modal decomposition POD uses the snapshot technique with a set of high-definition snapshots of the transient behaviour of the jet. The dynamic structures, formed by the velocity field and the electric charge dynamics, determine the fundamental dynamics of the droplet emission. The results show that 2D POD based ROM models can accurately reconstruct the flow field details, properly identifying the flow characteristics. The axial velocity transports the jet almost in a steady regime since a low number of POD modes are needed to preserve 99% of the kinetic energy. The flow fluctuations, principally the breakup of the jet, are represented by the fluctuations of the electric charge density, which is transported by the velocity field and the external electric field.
