Numerical analysis of electrohydrodynamic instability with and without crossflow

The study focuses on the electrohydrodynamic (EHD) instability problem with and without cross-flow. Lattice Boltzmann Method (LBM) with two-relaxation time (TRT) model is used for 3-dimensional numerical simulation. In the absence of cross-flow, the base-state of the problem is hydrostatic and the electric field is one-dimensional. The base-state is an unstable equilibrium under strong charge injection and high electric Rayleigh number. Perturbed by different perturbation patterns (rolling pattern, square pattern and hexagon pattern), the flow would develop according to the most unstable mode. The growth rate and the unstable modes can be obtained by performing dynamic mode decomposition (DMD) on the transient numerical solutions. The steady-state flow patterns depend on the patterns used to perturb the flow. Once the steady-state solution is reached, a Couette-type and/or Poiseuille-type cross-flow is applied to the steady-state solution. The flow patterns will change according to the direction and strength of the cross-flow. When the cross-flow velocity is greater than a threshold value, the instability flow patterns would develop into 2-dimensional rolling patterns with vortices in the direction of the cross-flow.