Numerical modelling of finite-amplitude electro-thermo-convection in a dielectric liquid layer subjected to both unipolar injection and temperature gradient

Abstract

In this paper, we solve numerically the entire set of equations associated with the electro-thermo-convective phenomena that take place in a planar layer of dielectric liquid heated from below and subjected to unipolar injection. For the first time the whole set of coupled equations is solved: Navier-Stokes equations, electrohydrodynamic (EHD) equations and the energy equation. We first validate the numerical simulation by comparing the electro-convection stability criteria with ones obtained with a stability approach. The numerical solution of the electrothermo-convection problem is then presented entirely with a detailed analysis of stability parameters. In particular, the relation between fluid velocity, non-dimensional electrical parameter T, Rayleigh number Ra and Prandtl number Pr is given. An analytical model is presented in order to understand the flow behaviour at some critical conditions. The way that the onset of motion passes from purely electrical convection to purely thermal convection is, in particular, investigated and explained in detail. Finally, a result on the heat transfer enhancement due to electro-convection is exhibited and compared with data from experimental works available in this field.

Characteristics of electrohydrodynamic roll structures in laminar planar Couette flow

“…The absence of rolls exist s when t he velocity U W is high enough t o destroy the instabilities, and t his may be seen through gures 3(q) and 3(r ). These morphological feat ures of the rolls are ant icipat ed t o have important implicat ions in problems such as heat t ransfer augment at ion [4,3,31,32,33] and int ernal charge inject ion at omizer ow [21]. In charge inject ion at omizers in part icular, it is possible t hat features of inter-electrode mixing due to an imposed forced ow would a ect t he charge dist ribut ion in t he liquid jet [40] which would subsequent ly impact t he droplet size distributions.…”

“…The eld has numerous indust rial applicat ions t hat range from heat t ransfer enhancement [3,4], elect rost at ic spraying applicat ions [5,6,7,8], and elect rost at ic precipit at ors [9,10,11]. Here, discussion is rest rict ed t o dielect ric liquids, where charged dipoles and monopoles are separat ed by neut ral ent it ies [12], and elect ric charge resides in t he liquid volume.…”

“…Previous st udies in`free-convect ion' elect rohydrodynamics, where no imposed bulk mean ow is present have largely concent rat ed on linear inst ability analysis in order t o de ne inst ability t hresholds [2,13,14] above which roll st ruct ures manifest in a way part ly analogous t o t hermal nat ural convect ion [3,4]. T he precise mechanisms leading t o elect ro-convect ive roll format ion have been described at lengt h in [14] and [13].…”

“…These are crit ical areas in t he cont ext of designing forced charge inject ion syst ems which have applicat ions in elect rost at ic at omizat ion and heat t ransfer enhancement [4,3,31,32,33,34]. In t his cont ribut ion, we examine a fundament al parallel-plat e EHD problem where t he t op grounded elect rode is moving at a wall velocity relat ive t o t he adjacent row of cont rol volumes.…”

The Dependence of the Efficiency of Electrohydrodynamic Heat Exchanger on the Electric Conductivity of Liquid

“…Electrohydrodynamic (EHD) flows are of great interest, since they can be used to intensify heat exchange [1][2][3][4][5][6] and have many advantages. Namely, an EHD heat exchanger (EHDHE) features very low power consumption, practically unlimited operation life, the ability to operate in microgravity, and high efficiency at meso-and micro-scale as opposed to other approaches [7].…”