Investigation of electrohydrodynamic calculations

Abstract

A perfect dielectric model was incorporated into the OpenFOAM? software and used for investigation and, possibly, improvements of electrohydrodynamic calculations. Two different sets of numerical simulations were analyzed, in which two different fluids were present. The first set was one-dimensional, while in the second, a drop of one fluid was surrounded by the other fluid. It is shown that oscillations and possible artificial generation of a curl of the electric field strength can be observed at applying certain expressions or calculation strategies, which can be thus abandoned. Usage of dynamic meshes, at least those present in the used software, and of limiters for the gradient of the electric field strength can lead to large numerical errors. It is also shown that usage of certain cell face values could improve the results. An electric Courant number was derived by dimensional analysis, and it could be suggested for future calculations. Conclusions made in this paper are expected to be transferable to other more complicated models.

Implementation of the electrohydrodynamics’ perfect dielectric model in OpenFOAM

“…Electrostatic extrusion, which is a process in which electric field is used, has already been used and analyzed by our groups (Bugarski et al 1994;Bugarski, Smith, Wu, & Goosen 1993;Manojlovic, Djonlagic, Obradovic, Nedovic, & Bugarski 2006;Poncelet et al 1994;. Usage of Computa-tional Fluid Dynamics (CFD) was also started (Boskovic, Karac, Vrhovac, Belic, & Bugarski 2022), which is expected to allow better predictions of outcomes of the electrostatic extrusion process and also be applicable and usable for other processes. It was stated in Thirumalaisamy, Natarajan, and Dalal (2018) that the number of EHD implementations was limited at that moment.…”

“…Also, since the perfect dielectric model is not the only model in EHD, the number of its implementations is even more limited. Because of these facts and the facts that the perfect dielectric model (Boskovic et al 2022;Munoz 2015;Supeene, Koch, & Bhattacharjee 2008) can be considered simple, can be upgraded to more complex models and can be used for improving EHD calculations, it was decided to start with this model. Fluids in which polarization of molecules happens, while ohmic conduction does not happen, are considered perfect dielectrics (Boskovic et al 2022).…”

“…Because of these facts and the facts that the perfect dielectric model (Boskovic et al 2022;Munoz 2015;Supeene, Koch, & Bhattacharjee 2008) can be considered simple, can be upgraded to more complex models and can be used for improving EHD calculations, it was decided to start with this model. Fluids in which polarization of molecules happens, while ohmic conduction does not happen, are considered perfect dielectrics (Boskovic et al 2022). The perfect dielectric model was implemented in the CFD software called Open-FOAM® (version 8), which utilizes the Finite Volume Method (FVM) (Moukalled, Mangani, & Darwish 2016) and also the Volume of Fluid (VoF) method (Andersson et al 2011).…”

“…A solver for two isothermal, incompressible and immiscible fluids (interFoam) was expanded. If this solver is used, for example, the Interface Compression (IC) or the Piecewise-Linear Interface Calculation (PLIC) corrected scheme can be used for interface reconstruction (Boskovic et al 2022). The quality of the implementation was checked with a set-up with a drop (Supeene et al 2008), which could be by far the most frequently used in EHD and for which it can be said that it is complex because there is fluid flow, and also with a one-dimensional set-up, which was chosen because it was noticed that it is appropriate for demonstration of one problem.…”

“…The quality of the implementation was checked with a set-up with a drop (Supeene et al 2008), which could be by far the most frequently used in EHD and for which it can be said that it is complex because there is fluid flow, and also with a one-dimensional set-up, which was chosen because it was noticed that it is appropriate for demonstration of one problem. Based on the investigated literature, the perfect dielectric model presented here is the first one in which the electrostrictive force (second of the two electric forces) is not overlooked (Boskovic et al 2022), and the implementation presented here is the first two-phase implementation that includes the mentioned force in all combinations of fluid polarities, while possible effects of this force were analyzed in the following way for the first time. This model and its implementation can be used for chemical engineering processes when appropriate fluids are present without any modification, after adjusting the used geometry and fluid properties.…”