Turbulence closure models for free electroconvection

Abstract

Electroconvection has been simulated in a number of recent studies, given its application in heat transfer enhancement, electrostatic atomizers and flow control. In practical applications, such as in charge injection atomizers, the electric Reynolds number can be sufficiently high such that the well-described ordered large scale electrohydrodynamic (EHD) instabilities that normally appear in electroconvection can dissipate and form into a wider distribution of length-scales. This purely electrohydrodynamically driven chaotic flow has features that resemble turbulent natural convection, and can dominate the operational regime of practical devices. Despite its practical relevance, Reynolds averaged turbulence model closures for EHD are unavailable, which currently makes direct numerical simulation the main viable option for EHD flows. Closure of EHD turbulence in free electro-convection is examined here through implementation of Reynolds stress model (RSM) closures using EHD specific timescales for the unclosed terms appearing in the turbulent scalar flux and space-charge scalar variance equations. A new closure for the highly non-linear triple correlation (q E u ), a term which is specific to EHD, is also presented. The work demonstrates that Reynolds stress closures are a feasible modeling route for EHD flows, with errors approaching similar values as in thermal Rayleigh-Benard convection at analogous levels of turbulence.

Coulomb-driven electroconvection turbulence in two-dimensional cavity

“…The contribution of fluctuation variables is discussed next. There are also several works that discuss the relevant terms of fluctuation and the turbulent closure using the higher-order moments Kourmatzis & Shrimpton 2018), whereas we show the fluctuating contribution through the original variables. The corresponding results are shown in figure 14.…”

“…First, let us give the Reynolds-averaged Navier–Stokes (RANS) equation of EC (Hopfinger & Gosse 1971; Kourmatzis & Shrimpton 2012, 2018) The MKE balance equation is acquired by taking the scalar product of the RANS equation of EHD with the average velocity and then implementing the ensemble average, i.e. where , , , , , and are the material derivative of MKE, the power injected through the mean pressure, the production of TKE, the power transported by the Reynolds stresses, the viscous diffusion of MKE, the mean flow viscous dissipation and the work done by the mean electric field force, respectively, in (2.18) and (2.19) is Reynolds stress.…”