# Three-dimensional Electro-convective Vortices in Cross-flow

## TL;DR

This paper investigates the formation and transition of three-dimensional electro-convective vortices in flow between parallel electrodes with unipolar charge injection, analyzing the effects of cross-flow and perturbations using numerical simulations and dynamic mode decomposition.

## Contribution

It introduces a detailed numerical study of electro-convective vortices in 3D, examining flow pattern transitions under cross-flow and perturbations, and characterizes hysteresis effects.

## Key findings

- Electro-convective vortices form at high electrical Rayleigh numbers.
- Cross-flow suppresses spanwise structures but not streamwise patterns.
- Transition from 3D to 2D enhances convection and increases electric Nusselt number.

## Abstract

The study focuses on the 3D electro-hydrodynamic (EHD) instability for flow between to parallel electrodes with unipolar charge injection with and without cross-flow. Lattice Boltzmann Method (LBM) with two-relaxation time (TRT) model is used to study flow pattern. In the absence of cross-flow, the base-state solution is hydrostatic, and the electric field is one-dimensional. With strong charge injection and high electrical Rayleigh number, the system exhibits electro-convective vortices. Disturbed by different perturbation patterns, such as rolling pattern, square pattern, and hexagon pattern, the flow patterns develop according to the most unstable modes. The growth rate and the unstable modes are examined using dynamic mode decomposition (DMD) of the transient numerical solutions. The interactions between the applied Couette and Poiseuille cross-flows and electroconvective vortices lead to the flow patterns change. When the cross-flow velocity is greater than a threshold value, the spanwise structures are suppressed; however, the cross-flow does not affect the streamwise patterns. The dynamics of the transition is analyzed by DMD. Hysteresis in the 3D to 2D transition is characterized by the non-dimensional parameter Y, a ratio of the coulombic force to viscous term in the momentum equation. The change from 3D to 2D structures enhances the convection marked by a significant increase in the electric Nusselt number.

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Source: https://tomesphere.com/paper/1908.03861