Modal and non-modal stability analysis of electrohydrodynamic flow with and without cross-flow
File(s)
Accepted version
Author(s)
Zhang, M
Martinelli, F
Wu, J
Schmid, PJ
Quadrio, M
Type
Journal Article
Abstract
We report the results of a complete modal and non-modal linear stability analysis of the electrohydrodynamic flow for the problem of electroconvection in the strong-injection region. Convective cells are formed by the Coulomb force in an insulating liquid residing between two plane electrodes subject to unipolar injection. Besides pure electroconvection, we also consider the case where a cross-flow is present, generated by a streamwise pressure gradient, in the form of a laminar Poiseuille flow. The effect of charge diffusion, often neglected in previous linear stability analyses, is included in the present study and a transient growth analysis, rarely considered in electrohydrodynamics, is carried out. In the case without cross-flow, a non-zero charge diffusion leads to a lower linear stability threshold and thus to a more unstable flow. The transient growth, though enhanced by increasing charge diffusion, remains small and hence cannot fully account for the discrepancy of the linear stability threshold between theoretical and experimental results. When a cross-flow is present, increasing the strength of the electric field in the high- Poiseuille flow yields a more unstable flow in both modal and non-modal stability analyses. Even though the energy analysis and the input–output analysis both indicate that the energy growth directly related to the electric field is small, the electric effect enhances the lift-up mechanism. The symmetry of channel flow with respect to the centreline is broken due to the additional electric field acting in the wall-normal direction. As a result, the centres of the streamwise rolls are shifted towards the injector electrode, and the optimal spanwise wavenumber achieving maximum transient energy growth increases with the strength of the electric field.
Date Issued
2015-05-01
Date Acceptance
2015-02-26
Citation
Journal of Fluid Mechanics, 2015, 770, pp.319-349
ISSN
1469-7645
Publisher
Cambridge University Press (CUP)
Start Page
319
End Page
349
Journal / Book Title
Journal of Fluid Mechanics
Volume
770
Copyright Statement
© 2015 Cambridge University Press . The final publication is available via Cambridge Journals Online at https://dx.doi.org/10.1017/jfm.2015.134
Subjects
Science & Technology
Technology
Physical Sciences
Mechanics
Physics, Fluids & Plasmas
Physics
instability
MHD and electrohydrodynamics
TURBULENT-BOUNDARY-LAYERS
UNIPOLAR INJECTION
HYDRODYNAMIC STABILITY
SHEAR-FLOW
OPTIMAL PERTURBATIONS
DIELECTRIC LIQUIDS
HEAT-TRANSFER
WALL FLOWS
CONVECTION
INSTABILITIES
Publication Status
Published