The particle image velocimetry of vortical electrohydrodynamic flows of oil near a high-voltage electrode tip

Abstract

A dual-domain particle image velocimetry (PIV) is employed to characterize the electrohydrodynamic flows arising in an oil bath with a grounded bottom near a high-voltage pin electrode with its tip close to the bottom. The applied voltage is varied to explore its effect on the arising flow field. Spatially, PIV observations are conducted using a dual-domain approach by synchronizing two cameras on the sampling plane. One camera is focused on the electrode tip and the second one on the fluid bulk. By capturing these synchronized domains, the velocity field is explored in its entirety, demonstrating a broad scope of morphology spanning the domain with the high velocity within the inter-electrode gap to the slow eddies in the fluid bulk. At high applied voltages, a transitional regime is observed in which the flow field bifurcates into toroidal Moffatt-like eddies. The experimental technique employed has its limitations. For example, at high applied voltages, the peak velocity domain could not be adequately resolved in every trial due to the deposition of fatty acids on the electrodes. Accordingly, the peak velocity has been measured only in the trials where fatty acid build-up did not interfere. Additionally, due to the axisymmetric geometry, reflections interfere with the observations of the near-surface velocity field.

Graphical abstract

Appendix A

The near-wall errors are primarily due to a combination of how the streamlines are calculated and how the masking was performed post-calculation. In the present work, the PIV calculation was performed using the entire field of view (without masking), and then the rest of the analysis was performed in ParaView. Such a post-processing order was required due to the need for cleaning the surfaces of fatty acid build up between trials. Both the electrodes had to be removed, and the plate cleaned between trials; there were slight transitions of the vessel along the laser plane. Such a transition made the creation of complex mask within DaVis time consuming considering the number of trials performed. By performing the masking post-PIV calculation, vectors in erroneous regions, such as the reflections from the electrode, are considered as possible streamline components. These components, however, should be disregarded as the values correspond to a low or practically zero velocity magnitude. This caused the resulting streamlines to appear to stem from the plate joining with the main wall jet. For example, Fig. 

Fig. 15

Streamlines overlaying a raw image sample for − 8 kV at a time step of 2500 µs for the small domain

15 is an overlaid image of the streamlines and a corresponding raw image from the test set. It shows that the most significant streamline errors occur due to the transition region near the electrode/plate boundary as it crosses over a laser reflection off the metal surface.

Inspecting the corresponding velocity profiles (Fig. 

Fig. 16

Velocity magnitude (U) profiles in the flow along the plane counter-electrode at the cross-sections × where spurious streamline sections stem from the wall (see the inset). The colors of the curves depicting the velocity profiles in the main panel correspond to those of the spurious streamline sections at the wall in these cross-sections. The y coordinate is normal to the wall. The green curve reminds to some extent the velocity profile in the wall jet, whereas the other curves corresponding to the further cross-sections do not

16), however, it can be seen that the flow better approximates the flow field in the planar wall jet (Tetervin 1948; Akatnov 1953; Glauert 1956; cf. Loitsyanskii 1966, Yarin 2007) near the stagnation point of the impingement jet at the wall. As velocity profiles are measured farther away, the intensity significantly diminishes as the wall jet expands radially. For example, despite the relatively distant location from the stagnation point of the impingement jet at the wall (x = 5 mm or x = 7 mm), where some odd streamlines at the boundary are observed, the measured velocity profiles appear to be plausible.