Electrohydrodynamic ionic wind, force field, and ionic mobility in a positive dc wire-to-cylinders corona discharge in air

Ionic wind refers to the acceleration of partially ionized air between two high-voltage electrodes. We study the momentum transfer from ions to air, resulting from ionic wind created by two asymmetric electrodes and producing a net thrust. This electrohydrodynamic (EHD) thrust, has already been measured in previous studies with digital scales. In this study, we provide more insights into the electrohydrodynamic momentum transfer for a wire-to-cylinder(s) positive dc corona discharge. We provide a simple and general theoretical derivation for EHD thrust, which is proportional to the current/mobility ratio and also to an effective distance integrated on the surface of the electrodes. By considering various electrode configurations, our investigation brings out the physical origin of previously obtained optimal configurations, associated with a better tradeoff between Coulomb forcing, friction occurring at the collector, and wake interactions. By measuring two-dimensional velocity fields using particle image velocimetry (PIV), we are able to evaluate the resulting local net force, including the pressure gradient. It is shown that the contribution of velocity fluctuations in the wake of the collecting electrode(s) must be taken into account to recover the net thrust. We confirm the proportionality between the EHD force and the current/mobility ratio experimentally, and evaluate the ion mobility from PIV measurements. A spectral analysis of the velocity fluctuations indicates a dominant frequency corresponding to a Strouhal number of 0.3 based on the ionic wind velocity and the collector size. Finally, the effective mobility of charge carriers is estimated by a PIV based method inside the drift region.

Figure 1

Schematic diagrams of (a) 3D general case, (b) 1D planar case, and (c) 2D wire/cylinder case.

Figure 2

Schematic of the control volume $\mathrm{\Omega }$ and its contour $\partial \mathrm{\Omega }=S_e\cup S_c\cup S_{\mathrm{ext}}$. The blue streamlines represent the ion paths, hence EHD force. The red arrows represent pressure and viscous forces applied to the air by the collector.

Figure 3

Experimental PIV setup.

Figure 4

(a) Typical current-voltage characteristic curves obtained with and without incense smoke; $d=4$ cm, $s=0$ cm. (b) Measured intensity in ambient air versus measured intensity with incense smoke for various cases. (c) Force (digital scale) and current versus time $(d=4$ cm, $s=0$ cm): voltage is set to 15 kV at $t=13$ s, switched off at $t=60$ s, then on again at $t=104$ s with injection of smoke.

Figure 5

(a)–(d) Vertical averaged velocity field ${\overline{U}}_x$ and streamlines for $V=10,15,20,25$ kV. Distance $d=4$ cm, spacing $s=0$ cm. (e) Velocity profiles 1 cm upstream of the collector and (f) maximum velocity 1 cm upstream of the collector $(x=3$ cm).

Figure 6

Eddy length versus Reynolds number, monocollector configuration, $R_c=5$ mm.

Figure 7

(a)–(d) Vertical averaged velocity field ${\overline{U}}_x$ and streamlines for distance of $d=3$, 4, 5, and 6 cm respectively. (e) and (f) Vertical velocity profile 1 cm upstream and downstream, respectively, of the collector surface. Spacing $s=2$ cm, electric field $V/d=5$ kV/cm.

Figure 8

(a)–(c)Vertical averaged velocity field ${\overline{U}}_x$ and streamlines for various collector spacing. (e) and (f) transversal velocity profile 1cm upstream and downstream from the collector surface. Distance $d=4$ cm, voltage $v=20$ kV.

Figure 9

Strouhal number of the velocity fluctuations in the wake of the collector versus the Reynolds number for two different distances.

Figure 10

(a)–(f) Volumetric force reconstructed from PIV measurement (arrows), and vertical component of the force $F_x$ (colors). Voltage $V=20$ kV, distance $d=5$ cm, spacing $s=0,2,4,6,8$ cm.

Figure 11

(a) Integral method compared to the digital scale measurement. Geometry: $s=0$ cm, $d=4$ cm. (b) Comparison scale/PIV for various geometries and voltages, with distinction between monocollector and bicollector cases. Dashed lines represent $\pm 10\%$ error range.

Figure 12

(a) Integrated force $F=F_{\overline{u}}+F_{u^{\prime }}$ versus integration frame length when border $ab$ is in the collector wake. (b) Nondimensional integrated force, with $F_o=I\times \mathrm{\Delta }{x}_{\max }/{\mu }_0$ and ${\mu }_0=1.8{\mathrm{cm}}^2{\mathrm{V}}^{-1}{\mathrm{s}}^{-1}$, vs nondimensional integration frame length; $d=5$ cm, $s=4$ cm. The integration frame starts below the emitter at $x_0=1$ cm to avoid hidden areas.

Figure 13

Kinetic to electric power ratio versus collector spacing angle $tan\theta =s/\left(2d\right)$. Empty symbols combine both stationary and fluctuating contributions while filled symbols are the contribution of fluctuating contributions only.

Figure 14

(a) Effective mobility ${\mu }_{\mathrm{eff}}$ versus reference electric field $V/d$. (b) Measured mobility of positive core ions in air or pure nitrogen at 300 K, 1 bar from Vielhand [45], retrieved from the LXcat data project.