Direct numerical simulation of supercritical annular electroconvection

Tsai, Peichun Amy; Daya, Zahir A.; Deyirmenjian, V. B.; Morris, Stephen W.

doi:10.1103/physreve.76.026305

Cited by 24 publications

(31 citation statements)

References 21 publications

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“…Only a few numerical simulations have been attempted on pure EHD convection problems (Castellanos, Atten & Pérez 1987;Chicón, Castellanos & Martín 1997;Chicón, Castellanos & Pérez 1999;Vázquez, Georghiou & Castellanos 2006, 2008Tsai et al 2007). To our knowledge, a direct and fully coupled numerical simulation of the ETHD problem has never been performed in a satisfactory way.…”

Section: Introductionmentioning

confidence: 98%

Numerical modelling of finite-amplitude electro-thermo-convection in a dielectric liquid layer subjected to both unipolar injection and temperature gradient

Traoré¹,

et al. 2010

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In this paper, we solve numerically the entire set of equations associated with the electro-thermo-convective phenomena that take place in a planar layer of dielectric liquid heated from below and subjected to unipolar injection. For the first time the whole set of coupled equations is solved: Navier-Stokes equations, electrohydrodynamic (EHD) equations and the energy equation. We first validate the numerical simulation by comparing the electro-convection stability criteria with ones obtained with a stability approach. The numerical solution of the electrothermo-convection problem is then presented entirely with a detailed analysis of stability parameters. In particular, the relation between fluid velocity, non-dimensional electrical parameter T, Rayleigh number Ra and Prandtl number Pr is given. An analytical model is presented in order to understand the flow behaviour at some critical conditions. The way that the onset of motion passes from purely electrical convection to purely thermal convection is, in particular, investigated and explained in detail. Finally, a result on the heat transfer enhancement due to electro-convection is exhibited and compared with data from experimental works available in this field.

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Section: Introductionmentioning

confidence: 98%

Numerical modelling of finite-amplitude electro-thermo-convection in a dielectric liquid layer subjected to both unipolar injection and temperature gradient

Traoré¹,

et al. 2010

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“…Another attempt to solve the entire set of coupled equations can be attributed to Tsai et al 12 for their study of electroconvection in an annular film. They used a pseudo-spectral method with Chebyshev polynomials in the radial direction and azimuthal direction to compute the velocity field from the Navier-Stokes equations which are considered in stream-vorticity formulation.…”

Section: Introductionmentioning

confidence: 99%

Two-dimensional numerical analysis of electroconvection in a dielectric liquid subjected to strong unipolar injection

2012

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Two-dimensional numerical simulations are carried out to examine the problem of transient electroconvection stability of dielectric liquids subjected to unipolar injection. The entire set of electrohydrodynamics equations associated with the electroconvective phenomena that occur in a layer of a dielectric liquid between two parallel electrodes subjected to a potential difference are solved numerically. We first validate the numerical simulation by comparing our linear stability electroconvection criteria with those obtained by other authors with a stability approach. In this paper, we restrict the study to the strong injection case, which corresponds to values of the non-dimensional injection parameter C greater than or equal to 10. The numerical solution of the electroconvective problem is then presented for rigid lateral boundary conditions. A detailed analysis of the scenario that occurs for different characteristic values of the stability parameter T is provided. The flow structure and its behaviour highlight the existence of different regimes, from laminar to chaotic. The development of charged plumes has been observed in particular. We compute the electrical Nusselt number for different values of the stability parameter and ion mobility. The electrical Nusselt number saturates with increasing T, a fact that it is in agreement with available experimental data. Finally, a spectral analysis is conducted for different aspect ratios of the computational domain. The spectral analysis gives an insight into the physical origin of the velocity and current oscillations. C 2012 American Institute of Physics. [http://dx

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“…We consider two settings: infinite and slim electrodes. The former corresponds to the simulation reported in Daya et al [13,14], Tsai et al [30] while the later is related to the analysis in Constantin et al [11]. Worth mentioning, vanishing charge densities on ∂Ω are considered in Constantin et al [11] allowing for smoother charge densities and simplifications of the mathematical model.…”

Section: Mathematical Modelsmentioning

confidence: 82%

“…In this work, we follow the experimental setting in Daya et al [13] and Tsai et al [30]. The thin film of liquid crystal is at room temperature and the crystals are arranged in layers with their long axis aligned with the normal of the film plane (semectic-A phase).…”

Section: Introductionmentioning

confidence: 99%

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Electroconvection of thin liquid crystals: Model reduction and numerical simulations

Bonito

Wei

2020

Journal of Computational Physics

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We propose a finite element method for the numerical simulation of electroconvection of thin liquid crystals. The liquid is located in between two concentric circular electrodes which are either assumed to be of infinite height or slim. Each configuration results in a different nonlocal electro-magnetic model defined on a two dimensional bounded domain. The numerical method consists in approximating the surface charge density, the liquid velocity and pressure, and the electric potential in the two dimensional liquid region. Finite elements for the space discretization coupled with standard time stepping methods are put forward. Unlike for the infinite electrodes configuration, our numerical simulations indicate that slim electrodes are favorable for electroconvection to occur and are able to sustain the phenomena over long period of time. Furthermore, we provide a numerical study on the influence of the three main parameters of the system: the Rayleigh number, the Prandtl number and the electrodes aspect ratio.

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Direct numerical simulation of supercritical annular electroconvection

Cited by 24 publications

References 21 publications

Numerical modelling of finite-amplitude electro-thermo-convection in a dielectric liquid layer subjected to both unipolar injection and temperature gradient

Numerical modelling of finite-amplitude electro-thermo-convection in a dielectric liquid layer subjected to both unipolar injection and temperature gradient

Two-dimensional numerical analysis of electroconvection in a dielectric liquid subjected to strong unipolar injection

Electroconvection of thin liquid crystals: Model reduction and numerical simulations

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