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/sub t0/, E/sub t/spl epsi//), new variables the Debye number D/sub b/, ion drift number F/sub E/ are defined. The results show that the EHD number based on the space charge density /spl Gt/ Re/sup 2/ 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/sub E//spl Gt/1 and F/sub E//spl Gt/ReSc/sub i/ conditions. We propose that the Debye number D/sub b/, Re and Sc/sub 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.