Turbulence closure models for free electroconvection

Highlights: • Reynolds stress closures for free electrohydrodynamic (EHD) convection are suggested and tested for the first time. • Timescales specific to EHD such as the drift and space charge relaxation timescales can successfully be implemented in closure models. • Errors in the model when comparing to direct numerical simulation data, approach similar values as in thermal natural convection. • Variable closures between the top and bottom wall can be used to drastically improve accuracy both near to the wall and in the middle of the domain. - 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 ($\overline{q^{\prime }{E}^{\prime }{u}^{\prime }}$), 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.