Flow electrification induced electrohydrodynamic secondary flow

Theoretical and numerical investigations have been conducted to evaluate the on-set conditions of flow electrification induced electrohydrodynamic secondary flow in smooth pipe and pipe with multiple cylinders in cross flow conditions. The nondimensional parameters control flow electrification and electrohydrodynamic (EHD) flow were derived from the mass conservation, momentum conservation, energy conservation, charged particle transport and Poisson´s equations for liquid flow. For single-phase flow of liquid, in addition to conventional dimensionless numbers for flow heat and mass transfers (Re, Ra, Pr, Sc), and EHD flow (E_t0, E_tε), new variables the Debye number D_b, ion drift number F_E are defined. The results show that the EHD number based on the space charge density ≫ Re² is required for the inducing EHD secondary flow in the downstream of pipe for single phase flow. The results also show that the change in relaxation time should be used only when F_E≫1 and F_E≫ReSc_i conditions. We propose that the Debye number D_b, Re and Sc _i replace the change relaxation time for the transient change relaxation estimation in fluid flow. The effect of flow on the electrification is also expressed in terms of diffusion Reynolds number of ions