Hostname: page-component-848d4c4894-ttngx Total loading time: 0 Render date: 2024-06-02T02:59:35.230Z Has data issue: false hasContentIssue false

Electrically driven toroidal Moffatt vortices: experimental observations

Published online by Cambridge University Press:  05 August 2020

Anthony E. Perri
Affiliation:
Department of Mechanical and Industrial Engineering, University of Illinois at Chicago, Chicago, IL60607, USA Spray Analysis and Research Services, Spraying Systems Co., Wheaton, IL60139, USA
Abhilash Sankaran
Affiliation:
Department of Mechanical and Industrial Engineering, University of Illinois at Chicago, Chicago, IL60607, USA
Babak Kashir
Affiliation:
Department of Mechanical and Industrial Engineering, University of Illinois at Chicago, Chicago, IL60607, USA
Christopher Staszel
Affiliation:
Department of Mechanical and Industrial Engineering, University of Illinois at Chicago, Chicago, IL60607, USA
Rudolf J. Schick
Affiliation:
Spray Analysis and Research Services, Spraying Systems Co., Wheaton, IL60139, USA
Farzad Mashayek
Affiliation:
Department of Mechanical and Industrial Engineering, University of Illinois at Chicago, Chicago, IL60607, USA
Alexander L. Yarin*
Affiliation:
Department of Mechanical and Industrial Engineering, University of Illinois at Chicago, Chicago, IL60607, USA
*
Email address for correspondence: ayarin@uic.edu

Abstract

In this work, we report the first experimental observation of electrically driven Moffatt vortices between conical surfaces. The flow field is captured using a synchronized multi-camera particle image velocimetry experiment. The results reveal a flow bifurcation resembling Moffatt vortices in canola oil with −12 kV applied to an axisymmetric point-to-plane electrode set-up. The formation of such vortices was predicted theoretically; however, to the best of our knowledge, experimental observations were not reported earlier. The experimental results of the present work are shown to be in agreement with the available theoretical predictions. In addition, the observed vortices are slightly transient, suggesting the next bifurcation reminiscent of the Taylor vortices in the Taylor–Couette flow.

Type
JFM Papers
Copyright
© The Author(s), 2020. Published by Cambridge University Press

Access options

Get access to the full version of this content by using one of the access options below. (Log in options will check for institutional or personal access. Content may require purchase if you do not have access.)

References

Adrian, R. J. & Westerweel, J. 2011 Particle Image Velocimetry. Cambridge University Press.Google Scholar
Alj, A., Denat, A., Gosse, J. P., Gosse, B. & Nakamura, I. 1985 Creation of charge carriers in nonpolar liquids. IEEE Trans. Elec. Insul. EI-20, 221231.CrossRefGoogle Scholar
Atten, P., Malraison, B. & Zahn, M. 1997 Electrohydrodynamic plumes in point-plane geometry. IEEE Trans. Dielec. Elec. Insul. 4, 710718.CrossRefGoogle Scholar
Castellanos, A. 1998 Electrohydrodynamics. Springer.CrossRefGoogle Scholar
Gazaryan, A., Sitnikov, A., Chirkov, V. & Stishkov, Y. 2017 A method for estimation of functional dependence of injection charge formation on electric field strength. IEEE Trans. Ind. Applics. 53, 39773981.CrossRefGoogle Scholar
Kashir, B., Perri, A. E., Yarin, A. L. & Mashayek, F. 2019 Numerical investigation of ionic conductor liquid charging at low to high voltages. Phys. Fluids 31, 021201.CrossRefGoogle Scholar
King, G. P., Li, W. L. Y., Swinney, H. L. & Marcus, P. S. 1984 Wave speeds in wavy Taylor-vortex flow. J. Fluid Mech. 141, 365390.CrossRefGoogle Scholar
Liu, C. H. & Joseph, D. D. 1978 Stokes flow in conical trenches. SIAM J. Appl. Maths 34, 286296.CrossRefGoogle Scholar
Malhotra, C., Weidman, P. D. & Davis, A. M. J. 2005 Nested toroidal vortices between concentric cones. J. Fluid Mech. 522, 117139.CrossRefGoogle Scholar
Moffatt, H. K. 1964 Viscous and resistive eddies near a sharp corner. J. Fluid Mech. 18, 118.CrossRefGoogle Scholar
Sankaran, A., Staszel, C., Belknap, D., Yarin, A. L. & Mashayek, F. 2019 Effect of atmospheric humidity on electrical conductivity of oil and implications in electrostatic atomization. Fuel 253, 283292.CrossRefGoogle Scholar
Sankaran, A., Staszel, C., Mashayek, F. & Yarin, A. L. 2018 Faradaic reactions’ mechanisms and parameters in charging of oils. Electrochim. Acta 268, 173186.CrossRefGoogle Scholar
Shankar, P. N. 2005 Moffatt eddies in the cone. J. Fluid Mech. 539, 113135.CrossRefGoogle Scholar
Suh, Y. K. 2012 Modeling and simulation of ion transport in dielectric liquids – fundamentals and review. IEEE Trans. Dielec. Elec. Insul. 19, 831848.Google Scholar
Taneda, S. 1979 Visualization of separating Stokes flows. J. Phys. Soc. Japan 46, 19351942.CrossRefGoogle Scholar
Traoré, P., Daaboul, M. & Louste, C. 2010 Numerical simulation and PIV experimental analysis of electrohydrodynamic plumes induced by a blade electrode. J. Phys. D: Appl. Phys. 43, 225502.CrossRefGoogle Scholar
Traoré, P., Wu, J., Louste, C., Pelletier, Q. & Dascalescu, L. 2015 Electrohydrodynamic plumes due to autonomous and nonautonomous charge injection by a sharp blade electrode in a dielectric liquid. IEEE Trans. Ind. Applics. 51, 25042512.CrossRefGoogle Scholar
Tropea, C. 2007. Tracer particles. In Springer Handbook of Experimental Fluid Mechanics (ed. Tropea, C., Yarin, A. L. & Foss, J.), pp. 287296. Springer.CrossRefGoogle Scholar
Van Dyke, M. 1982 An Album of Fluid Motion. Parabolic.CrossRefGoogle Scholar
Vázquez, P. A., Pérez, A. T., Castellanos, A. & Atten, P. 2000 Dynamics of electrohydrodynamic laminar plumes: scaling analysis and integral model. Phys. Fluids 12, 28092818.CrossRefGoogle Scholar
Wakiya, S. 1976 Axisymmetric flow of a viscous fluid near the vertex of a body. J. Fluid Mech. 78, 737747.CrossRefGoogle Scholar
Weidman, P. D. & Calmidi, V. 1999 Instantaneous Stokes flow in a conical apex aligned with gravity and bounded by a stress-free surface. SIAM J. Appl. Maths 59, 15201531.CrossRefGoogle Scholar
Wu, J., Traore, P., Louste, C., Koulova, D. & Romat, H. 2013 Direct numerical simulation of electrohydrodynamic plumes generated by a hyperbolic blade electrode. J. Electrostat. 71, 326331.CrossRefGoogle Scholar