Simulation of Hydrodynamic Behavior of a Conductive Drop Under an Electric Field

Document Type : Research Article

Authors

Department of Engineering, Yasouj University, Yasouj, Iran

Abstract

In this research , the effect of an electric field on the deformation and phase change ofa perfect conductive drop suspended in a perfect dielectric fluid is studied . Basic equations are theincompressible flow and energy equations . Electric field effect appears as normal stresses at interfacewhich are taken into account in solving flow equations . The level-set method is used for interfacetracking. Discontinuities at interface are imposed using the ghost fluid method. In the first step , the effectof an electric field on the hydrodynamic of a drop is studied . A good agreement between the simulationand experimental results is observed. Due to electric stresses , drop deforms in the direction of electricfield . The drop deformation increases with the electric capillary number. If the electric capillary numberexceeds the critical value, deformation will be unsteady. Novelty of this research is related to the studyof electric field effect on the drop evaporation. Based on the results, drop evaporation rate is enhancedin the presence of an electric field . If the electric capillary number exceeds a specific value (evaporationcritical electric capillary number) , drop evaporation will increase considerably . This critical value isintroduced in this research, for the first time.

Keywords

Main Subjects


[1] P. Brazier-Smith, Stability and shape of isolated and pairs of water drops in an electric field, The physics of Fluids, 14(1) (1971) 1-6.
[2] A. Mestel, Maximal accelerations for charged drops in an electric field, Physics of Fluids, 14(4) (2002) 1396-1402.
[3] J. Zhang, D.Y. Kwok, A 2D lattice Boltzmann study on electrohydrodynamic drop deformation with the leaky dielectric theory, Journal of Computational Physics, 206(1) (2005) 150-161.
[4] E. Lac, G. Homsy, Axisymmetric deformation and stability of a viscous drop in a steady electric field, Journal of Fluid Mechanics, 590 (2007) 239-264.
[5] N. Dubash, A.J. Mestel, Breakup behavior of a conducting drop suspended in a viscous fluid subject to an electric field, Physics of Fluids, 19(7) (2007) 072101.
[6] J. Hua, L.K. Lim, C.-H. Wang, Numerical simulation of deformation/motion of a drop suspended in viscous liquids under influence of steady electric fields, Physics of Fluids, 20(11) (2008) 113302.
[7] P.F. Salipante, P.M. Vlahovska, Electrohydrodynamics of drops in strong uniform dc electric fields, Physics of Fluids, 22(11) (2010) 112110.
[8] H. Paknemat, A. Pishevar, P. Pournaderi, Numerical simulation of drop deformations and breakup modes caused by direct current electric fields, Physics of Fluids, 24(10) (2012) 102101.
[9] A. Beroual, Parameters influencing the behavior of water droplets immersed in dielectric liquids submitted to electric stress, in: 2013 Annual Report Conference on Electrical Insulation and Dielectric Phenomena, IEEE, 2013, pp. 996-999.
[10] R.B. Karyappa, S.D. Deshmukh, R.M. Thaokar, Breakup of a conducting drop in a uniform electric field, Journal of Fluid Mechanics, 754 (2014) 550-589.
[11] S.W. Welch, G. Biswas, Direct simulation of film boiling including electrohydrodynamic forces, Physics of Fluids, 19(1) (2007) 012106.
[12] G. Tomar, G. Biswas, A. Sharma, S. Welch, Influence of electric field on saturated film boiling, Physics of Fluids, 21(3) (2009) 032107.
[13] V. Pandey, G. Biswas, A. Dalal, Effect of superheat and electric field on saturated film boiling, Physics of Fluids, 28(5) (2016) 052102.
[14] D.J. Griffiths, Introduction to electrodynamics, in, AAPT, 2005.
[15] D. Saville, Electrohydrodynamics: the Taylor-Melcher leaky dielectric model, Annual review of fluid mechanics, 29(1) (1997) 27-64.
[16] F. Gibou, L. Chen, D. Nguyen, S. Banerjee, A level set based sharp interface method for the multiphase incompressible Navier–Stokes equations with phase change, Journal of Computational Physics, 222(2) (2007) 536-555.
[17] S. Tanguy, T. Ménard, A. Berlemont, A level set method for vaporizing two-phase flows, Journal of Computational Physics, 221(2) (2007) 837-853.
[18] E. Bjørklund, The level-set method applied to droplet dynamics in the presence of an electric field, Computers & Fluids, 38(2) (2009) 358-369.
[19] M. Kang, R.P. Fedkiw, X.-D. Liu, A boundary condition capturing method for multiphase incompressible flow, Journal of Scientific Computing, 15(3) (2000) 323-360.
[20] R.P. Fedkiw, T. Aslam, B. Merriman, S. Osher, A non-oscillatory Eulerian approach to interfaces in multimaterial flows (the ghost fluid method), Journal of Computational Physics, 152(2) (1999) 457-492.
[21] X.-D. Liu, R.P. Fedkiw, M. Kang, A boundary condition capturing method for Poisson's equation on irregular domains, Journal of Computational Physics, 160(1) (2000) 151-178.
[22] M. Sussman, P. Smereka, S. Osher, A level set approach for computing solutions to incompressible two-phase flow, Journal of Computational Physics, 114(1) (1994) 146-159.
[23] G. Son, V.K. Dhir, Numerical simulation of nucleate boiling on a horizontal surface at high heat fluxes, International Journal of heat and Mass transfer, 51(9-10) (2008) 2566-2582.
[24] T.D. Aslam, A partial differential equation approach to multidimensional extrapolation, Journal of Computational Physics, 193(1) (2004) 349-355.
[25] P. Pournaderi, A. Pishevar, A numerical investigation of droplet impact on a heated wall in the film boiling regime, Heat and Mass Transfer, 48(9) (2012) 1525-1538.
[26] G.I. Taylor, Studies in electrohydrodynamics. I. The circulation produced in a drop by an electric field, Proceedings of the Royal Society of London. Series A. Mathematical and Physical Sciences, 291(1425) (1966) 159-166.
[27] D. Whitaker, C. Kim, C. Vicente, M. Weilert, H. Maris, G. Seidel, Shape oscillations in levitated He II drops, Journal of low temperature physics, 113(3-4) (1998) 491- 499.
[28] J.Q. Feng, T.C. Scott, A computational analysis of electrohydrodynamics of a leaky dielectric drop in an electric field, Journal of Fluid Mechanics, 311 (1996) 289-326.
[29] J.-W. Ha, S.-M. Yang, Deformation and breakup of Newtonian and non-Newtonian conducting drops in an electric field, Journal of Fluid Mechanics, 405 (2000) 131-156.
[30] I.I. Inculet, J. Floryan, R.J. Haywood, Dynamics of water droplets breakup in electric fields, IEEE transactions on industry applications, 28(5) (1992) 1203-1204.