Application of large eddy simulation models to electroconvection turbulence study with lattice Boltzmann method

Electroconvection (EC) turbulence is an important branch of electrohydrodynamics (EHD). Because the turbulence model for EHD has not been well studied, in this work we apply the large eddy simulation (LES) to electrohydrodynamic turbulence based on the lattice Boltzmann method (LBM). The eddy-viscosity methods (the Smagorinsky and wall-adapting local eddy-viscosity models) are used to model the momentum equation, and the charge transport equation is modeled with the help of the turbulent Schmidt number. Three EC cases are chosen to test the reliability of the LBM-LES models, including two-dimensional (2D) EC turbulence in square and rectangular cells, and three-dimensional (3D) EC turbulence between two parallel plates. For 2D cases, the LES results are compared to the results of different numerical methods, including direct numerical simulation and LES. The long-time statistics of maximum velocity, charge current and its probability distribution, and flow evolution are used to validate the 2D EC turbulence. We also analyze the flow patterns and average characteristics for 3D cases. The LES results could capture the main flow features of EC turbulence for all cases, and demonstrate a good agreement when compared with references. The mentioned LBM-LES models have demonstrated reliability and high computational speed, making them suitable for further simulations of electrohydrodynamic turbulence.