Numerical simulation of the electro-convective onset and complex flows of dielectric liquid in an annulus

We conducted a numerical study on the onset of electro-convection as well as the complex flow phenomena of dielectric liquid subjected to unipolar autonomous charge injection in the annular gap between two concentric circular cylindrical electrodes. The Nernst-Planck equations governing the charge density transport, the Poisson equation for the electric potential and the Navier-Stokes equations for the fluid flow are solved numerically using the finite volume method. The developed code is validated by comparing the critical sta-bility parameter values for the onset of electro-convection with those obtained from the linear stability analysis. We identify in a parame-ter space the stable hydrostatic state and the electro-convection state. The electro-convection is again divided into three regimes: station-ary, oscillatory and chaotic. For inner cylinder radius r_i ≥ 1. 0, we observed an increase in the number of charged plumes and vortex pairs with stability parameter T before the electro-convection becomes chaotic. For outer injection, although the onset of electro-convection starts at T higher than the inner injection, the onset of chaotic motion occurs at lower T.