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Numerical analysis of the Rayleigh–Taylor instability in an electric field

Published online by Cambridge University Press:  03 March 2016

Qingzhen Yang ,
Ben Q. Li ,
Zhengtuo Zhao ,
Jinyou Shao  and
Feng Xu
Qingzhen Yang
Affiliation:
The Key Laboratory of Biomedical Information Engineering of Ministry of Education, School of Life Science and Technology, Xi’an Jiaotong University, Xi’an, Shaanxi 710049, PR China Bioinspired Engineering and Biomechanics Center (BEBC), Xi’an Jiaotong University, Xi’an, Shaanxi 710049, PR China
Ben Q. Li*
Affiliation:
Department of Mechanical Engineering, University of Michigan, Dearborn, MI 48128, USA
Zhengtuo Zhao
Affiliation:
Department of Mechanical Engineering, University of Michigan, Dearborn, MI 48128, USA
Jinyou Shao
Affiliation:
State Key Laboratory for Manufacturing Systems Engineering, Xi’an Jiaotong University, Xi’an, Shaanxi 710049, PR China
Feng Xu
Affiliation:
The Key Laboratory of Biomedical Information Engineering of Ministry of Education, School of Life Science and Technology, Xi’an Jiaotong University, Xi’an, Shaanxi 710049, PR China Bioinspired Engineering and Biomechanics Center (BEBC), Xi’an Jiaotong University, Xi’an, Shaanxi 710049, PR China
*
†Email address for correspondence: benqli@umich.edu
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Abstract

A numerical analysis is presented of the Rayleigh–Taylor instability (RTI) in the presence of an external electric field, with an emphasis on nonlinear phenomena associated with the evolution of complex interfacial morphology. The Poisson equation for the electric field and the Navier–Stokes equation for fluid flow field are solved simultaneously along with the Cahn–Hilliard phase field equation for interface deformation and morphology development. Numerical model is validated against the existing data and the results of linear analysis. Extensive numerical simulations are carried out for a wide range of fluid flow and electric field conditions. Computed results show that, in both linear and nonlinear regimes, a horizontal field suppresses the RTI, while a vertical electric field aggravates it. However, the vertical field does not affect the secondary instability; specifically, it does not contribute to the baroclinical generation of vorticity and consequently does not affect the roll-up formation. Linear analysis predicts that the RTI remains the same with the interchange of the dielectric constants of the two fluids, which is also confirmed by the numerical model for small interface deformations. This prediction, however, does not hold true in the nonlinear regimes in that complex interfacial morphology may evolve quite differently if the dielectric constants of two fluids are interchanged.

JFM classification

Flow Control: Instability control MHD and Electrohydrodynamics: MHD and Electrohydrodynamics Multiphase and Particle-laden Flows: Multiphase flow
Type
Papers
Information
Journal of Fluid Mechanics , Volume 792 , 10 April 2016 , pp. 397 - 434
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© 2016 Cambridge University Press 

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