Numerical analysis of electrohydrodynamics in a round pipe

A numerical analysis on electrohydrodynamics (EHD) in a round pipe is presented based on the PISO (pressure-implicit with splitting of operators) scheme under a periodic boundary condition. The numerical results show that a vortex ring is generated between the electrodes due to the nonuniform distribution of velocity and charge density during the starting process. The increase of value of T (the ratio of electric stress to viscous stress) affects the developing process because of the unsteadiness repulsion among the charges will increase with T during this period. When the flow field finally reaches steady state, it becomes a fully developed pipe flow. The steady outlet velocity is in direct proportion to the square of the voltage imposed between electrodes. The spatial distribution of the pressure is similar to that of the electric potential between the electrodes because of the direct analogy between potential and pressure.