Mitigation of turbophoresis in particle-laden turbulent channel flows by using incident electric fields

It is known that the dynamics of particles dispersed in turbulent flows can be significantly altered by electric charges and external electric fields. The next step therefore involves the investigation of whether these electric interactions can be exploited in engineering applications to control processes involving the transport of particles in turbulence. In this study, direct numerical simulations of incompressible turbulent channel flows laden with a positively isocharged suspension of monodisperse small inertial particles are employed to investigate the effect of electric charges carried by the particles on their dispersion, and to illustrate the intentional abatement of turbophoretic effects using incident electric fields. An Eulerian-Lagrangian formulation is employed along with a fast multipole method for the electric potential conveniently corrected with wall boundary conditions. Operating conditions are identified in terms of characteristic dimensionless parameters where an AC electric field applied across the channel walls decreases the time-averaged concentration of particles near the walls by up to two orders of magnitude.

Figure 1

Schematics of the model problem: a positively isocharged suspension of monodisperse small inertial particles laden in a biperiodic turbulent channel flow whose walls are connected to an AC voltage source.

Figure 2

Dispersed-phase statistics without an applied electric field: (a) time-averaged number-density profiles in the wall-normal direction for increasing values of ${\text{Re}}_{\tau }{\text{St}}_{\mathrm{el}}^{\mathrm{int}}$, and (b) wall-normal profiles of the absolute value of each term on the right-hand side of the momentum balance equation (5) multiplied by ${\langle n^{★}\rangle }^{-1}$.

Figure 3

Dispersed-phase statistics with an applied electric field, including (a) time-averaged number-density profiles in the wall-normal direction for ${\text{St}}_{\mathrm{el}}^{\mathrm{ext}}=1$ while varying ${\omega }_{\mathrm{el}}^{+}$; (b) time-averaged number-density profiles in the wall-normal direction for ${\text{St}}_{\mathrm{el}}^{\mathrm{ext}}=0.01$ while varying ${\omega }_{\mathrm{el}}^{+}$; (c) time-averaged variance of the wall-normal particle velocity ${\text{St}}_{\mathrm{el}}^{\mathrm{ext}}=1$ while varying ${\omega }_{\mathrm{el}}^{+}$; and (d) time-averaged number-density profiles in the wall-normal direction for ${\omega }_{\mathrm{el}}^{+}=0.02\pi$ while varying ${\text{St}}_{\mathrm{el}}^{\mathrm{ext}}$.

Figure 4

Dispersed-phase statistics with an applied electric field: (a) Phase-averaged number density for ${\text{St}}_{\mathrm{el}}^{\mathrm{ext}}=0$. (b)–(e) Phase averages of the incident electric field (top subpanel: white, upwards field; light blue, downwards field), wall-normal particle velocity (middle subpanel: white, upwards velocity; light blue, downwards velocity), and number density (bottom subpanel: white, high concentration; light blue, low concentration) for (b) ${\text{St}}_{\mathrm{el}}^{\mathrm{ext}}=1$ and ${{\omega }_{\mathrm{el}}}^{+}=0.02\pi$, (c) ${\text{St}}_{\mathrm{el}}^{\mathrm{ext}}=0.1$ and ${{\omega }_{\mathrm{el}}}^{+}=0.02\pi$, (d) ${\text{St}}_{\mathrm{el}}^{\mathrm{ext}}=1$ and ${{\omega }_{\mathrm{el}}}^{+}=0.2\pi$, and (e) ${\text{St}}_{\mathrm{el}}^{\mathrm{ext}}=0.01$ and ${{\omega }_{\mathrm{el}}}^{+}=0.002\pi$.