This paper presents a fundamental study of electro-thermo-convective flows within a layer of dielectric liquid subjected to both an electric field and a thermal gradient. A low-conductivity liquid enclosed between two horizontal electrodes and subjected to unipolar charge injection is considered. The interplay between electric and thermal fields ignites complex physical interactions within the flows, all governed by a set of coupled electro-thermo-hydrodynamic equations. These equations include Maxwell, Navier–Stokes, and energy equations and are solved numerically using an in-house code based on the finite volume method. Electro-thermo-convective flows are driven by two dimensionless instability criteria: Rayleigh number Ra and the stability parameter T, and also by the dimensionless mobility parameter M and Prandtl number Pr. The electric Nusselt number (Ne) analogue to the Nusselt number (Nu) in pure thermal problems serves as an indicator to monitor the shift from a thermo- to an electro-convective flow and its eventual evolution into unsteady, and, later, chaotic flow. This change in regime is observed by tracking the electric Nusselt number’s behavior as a function of the stability parameter (T), for different values of the non-dimensional parameters (M, Ra, and Pr). The important role of mobility parameter M for the development of the flow is shown. The flow structure during different development stages in terms of the number of convective cells is also discussed.

In this article we analyse the results of a numerical simulation of an electro-thermo-convective flow induced in a dielectric liquid layer by the simultaneous action of an external electric field and a thermal gradient. A low conductivity liquid is placed between two horizontal electrodes and subjected to strong unipolar charge injection which set the fluid in motion under the combined action of Coulomb and buoyancy forces. The motion induced by the charge injection has a vigorous character and strongly increases the electric charge transfer and heat transfer between the electrodes. The full set of governing equations including Navier-Stokes equation, the conservation equations of electric charge and energy and Poisson equation for electric potential is solved by a finite volume method. We define an electric Nusselt number (Ne) as the ratio of the effective current and the current existing without liquid motion, number which can be considered as the analog of Nusselt number (Nu) for a pure thermal problem. The case of heating and strong injection of electric charges from lower electrode is considered. The variation of the electric Nusselt number Ne with electrical parameter T for different values of the non-dimensional parameter mobility number M and Rayleigh number is then analyzed. It is shown that the mobility number M is a parameter which plays an important role in the characterization of electro-thermo-convective flows and also that the physical mechanisms of the different instability regimes can be better understood considering the electric Nusselt number Ne.

In this paper the behaviour of the waves generated on insulating liquid-air interfaces and subjected to an electric field is experimentally studied. The experimental device is mainly composed of a tank filled with diesel oil and two parallel metallic electrodes; one of them immersed in the liquid and brought to a high potential and the other one placed above the liquid. The waves are created by a vibrator the frequency and amplitude of which are controlled. The electric charges present at the liquid/air interface come from injection and/or dissociation and/or conduction phenomena. A high speed camera records the shape of the waves and an associated image analysis system extracts from them all the information needed (frequency, amplitude, wavelength). This information is used to investigate the influence of the electric field and liquid conductivity on the wavelengths at different amplitudes and frequencies and to calculate the surface tension. The propagation of waves on electrically charged liquid/air interfaces is also studied. The measurements are carried out for different frequencies and amplitudes of the vibrator at various applied voltages with different electrical conductivities of the diesel oil. We found that the wavelength and the apparent surface tension decreased with the applied voltage. The amplitude of the vibrator practically has no influence on the wavelength and the surface tension.

This paper is an experimental study on electroconvective flows produced by an asymmetric electric field in a cavity. It is part of a scientific project aiming to develop electrohydrodynamic (EHD) flow actuator in order to enhance heat transfer and mixing efficiency in fluidic and microfluidic systems. In this study, the EHD flow is obtained by applying a de voltage between two electrodes (cylinder/plane) immersed in a working liquid. The produced velocity fields strongly depend on the applied voltage. Whatever may be the applied voltage, the fluid goes from the cylinder toward the plate or the other way round. The velocity fields obtained by particle image velocimetry for different potentials are analyzed in both cases with the usual mechanisms (injection and conduction) at the origin of the motion of the liquid. A discussion on the transition between injection and conduction phenomena is finally presented.

The article deals with the propagation of surface waves in a tank filled with a dielectric liquid. The waves are created by a vibrator, the frequency and amplitude of which are controlled. Two parallel metallic electrodes are placed in the tank and an adjustable potential difference is applied between them. The immerged electrode injects electric charges into the liquid and the top-electrode attracts them. They remain on the liquid-gas interface which therefore becomes electrically charged. A high velocity camera records the shape of the waves and an associated image analysis system extracts from them all the information needed (frequency, amplitude, wavelength) to investigate the influence of the electric charges on the propagation of the waves on the liquid/gas interface as well as the influence of the electrical conductivity of the liquid on the wavelengths. For this purpose we made measurements with different diesel oil electrical conductivities, for various frequencies and amplitudes of waves at different applied voltages.

The presented work is an experimental study on electroconvective cavity flow patterns produced by a cylinder-plane electrode geometry. Flows are recorded by the use of the well-known Particle Image Velocimetry technique. The main objective of this work is to develop flow control methods in order to enhance heat transfer and mixing efficiency in fluidic and microfluidic systems. In this study, the electrohydrodynamic flow motion is obtained by applying a DC voltage to a set of electrodes immersed in a working liquid. It is shown that the produced velocity fields strongly depend on the applied voltage and a reverse flow is obtained when the polarity is inverted. An analysis of the velocity field is then realized in order to highlight the electric force map.

The influence of the electric field on surface waves in diesel oil is studied experimentally. The experimental device is mainly composed of a tank filled with diesel oil and two parallel metallic electrodes: one of them is immersed in the liquid and brought to a high potential, the other one is placed above the liquid. The surface waves are generated by a vibrator for which the frequency and amplitude of the vibrations can be controlled. The differences of potential applied can vary. Particle Image Velocimetry (PIV) is used to measure the velocity of the propagation waves on the diesel oil/air surface. The objective is to determine the influence of the electric field on the wavelengths at different amplitudes and frequencies as well as to calculate the surface tension. In this article we show that the apparent surface tension of the diesel oil decreases when the voltage is applied.

In this article we study the electro-thermal convection in a dielectric liquid layer placed between two electrodes and subjected to the simultaneous action of an electric field and a thermal gradient. The full set of equations describing the electro-thermo-convective phenomena is directly solved using a finite volume method. We first heat the liquid from below at time t = 0, wait for the thermal steady state and then inject the electric charges by applying the electric potential. The development of the electro-convective motion is analysed in detail in two cases: 1) strong injection from the lower electrode, 2) strong injection from the upper one. We also study the heat transfer enhancement due to electro-convection. The evolution in time of the Nusselt number Nu for different combinations of the two usual non-dimensional parameters associated to the electro-thermo-convection phenomena (Rayleigh number Ra and the electrical parameter T) is also given and analysed. (C) 2013 Elsevier B.V. All rights reserved.

In this article the electro-thermo-convective phenomena in a dielectric liquid enclosed in a 2D cavity and subjected to the simultaneous action of an electric field and a thermal gradient is studied. We solved directly the full set of coupled equations of Electro-Hydro-Dynamic (EHD) and energy equation using a finite volume method. In order to characterize the influence of the electric field on heat transfer the liquid is first heated (from a lateral wall) till the thermal steady state is obtained and then the electric potential and injection of electric charge is applied. Two cases of injection are considered: from the lower electrode and from a lateral wall (left or right). The flow pattern and Nusselt number strongly depend on the non-dimensional characteristic parameters: electrical parameter, Rayleigh number, Prandtl number and mobility parameter M. The convective motion passing from a purely thermal convection to a purely electrical convection and the number of electro-thermo-convective rolls patterns are investigated.As a consequence of the analysis of the combined effect of electric and thermal fields on the flow structure and on Nusselt number, we have also evaluated the heat transfer enhancement due to electroconvection. It is shown that the injection of electric charge increases the heat transfer and Nusselt number is independent of Rayleigh number for high enough values of T. (c) 2013 Elsevier B.V. All rights reserved.

An impinging jet in a dielectric liquid is generated by applying a high potential difference to a blade-plane geometry. This kind of jet is both a fluid flow and an electrical phenomenon. In our study, an overview of the flow field is easily obtained by using the classical particle velocity method. Two patterns of electrohydrodynamic velocity profiles of the jet can be observed when the applied high voltage varies. A typical method for a classical impinging jet is used in order to point out the specific characteristics of electrohydrodynamic jets. Electric current measurements and particle-image-velocimetry investigations are conducted synchronously, which contribute to the analysis of this electrohydrodynamic phenomenon. Two electrical current regimes are presented according to the potential difference.

This paper presents a numerical study of two-dimensional EHD flow occurring between a hyperbolic blade and a plate electrode. The whole set of coupled equations is solved: Navier-Stokes equations, Poisson equation and charge conservation equation. A finite volume approach designed for non-orthogonal structured grid is used to discretize all governing equations. An efficient numerical procedure based on total variation diminishing (TVD) scheme is implemented to compute the distribution of charge density. Two different injection laws are considered: a simple autonomous one and a non autonomous which relates the charge injected by the blade and the local electric field. The flow structure which results in an EHD plume analogous to a thermal plume, has also been successfully characterized numerically by the temporal evolution of the charge density distribution. Preliminary results indicate that the flow is characterized by two different regimes according the value of the applied voltage. The critical Reynolds number for which the transition between the steady and unsteady regimes occurs has been determined to be within the range Re = [1000, 1100]. (c) 2012 Elsevier B.V. All rights reserved.

An impinging jet in a dielectric liquid is produced by applying a high potential difference to a blade-plane geometry. This kind of jet is both a fluid flow and an electrical phenomenon. In our study, an overview of flow field is easily obtained by using the classical particle velocity method. Two patterns of electrohydrodynamic velocity profiles of jet can be observed when the applied high voltage varies. A typical method for classical impinging jet is used in order to point out the specific characteristics of electrohydrodynamic jets. Electric current measurements are made at the same time of the particle image velocimetry investigations which contributes to the analysis of this electrohydrodynamical phenomenon. Two electrical current regimes are presented according to the potential difference.

The electro-thermo-convective motion in a plane horizontal dielectric liquid layer subjected to simultaneous action of electric field and thermal gradient is numerically investigated. We consider the case of a strong unipolar charge injection C=10 from above or below. Therefore in this context, we only take into account the Coulomb force, disregarding the dielectric one. The effect of the electric field on the heat transfer is analyzed through the characterization of the time history of the Nusselt number as well as its evolution according to the characteristic dimensionless electric parameter T. It is demonstrated that the electric effects dominate the buoyancy ones resulting in an electrically induced convection which significantly enhance the heat transfer.

For more than three years now, a new electrohydrodynamic (EHD) actuator based on a dielectric barrier injection system has been developed in order to enhance fuel atomization in air blast atomizers. Dielectric barrier injection devices are very interesting because they allow reaching very high electric field while preventing the occurrence of electric sparks. Experiments have been carried out on thin sheets of commercial Diesel oil without active surface agent. The flow rate and the liquid sheet thickness are similar to the ones used in turbo engines. In the contrary of typical air blast atomizers, the atomization is not obtained by the use of a shear air flow or any other form of mechanical disturbance but only with the help of electric forces. As a consequence, the liquid sheet produced by the injector is stable when the EHD actuator is switched off. On the other hand, it could be fully atomized when the actuator is on. Investigations have been made with a high speed camera on the primary breakup modes and on the droplet formation mechanisms. The present study mainly focuses on the influence of the signal shape, amplitude, and frequency.

We study the electro-thermo-convective phenomena in a dielectric liquid layer of depth H placed between two electrodes and subjected to the simultaneous action of an electric field and a thermal gradient. The full set of governing equations is directly solved using a finite volume method. In this paper we first heat from the lower electrode and apply the electric potential when the thermal steady state is obtained. Only the case of strong injection of electric charges is considered. The flow pattern and Nusselt number strongly depend on the following non dimensional characteristic parameters: electrical parameter T, Rayleigh number Ra, Prandtl number Pr and mobility parameter M. The electro-convective flow structure is analysed in a rectangular cavity of length 2H, where the pure thermo-convection gives rise to two rolls whereas the pure electro-convection (with injection) gives a four roll pattern. The combined effect of both electric and thermal field on the flow patterns and on Nusselt number is analyzed for different values of Pr and M.

Atomization of deposited diesel oil droplet is studied in the presence of pulsed high voltage electric field. Experiments are carried out on 10μl droplets by the use of a high speed camera. Three new modes of atomization are described: the stretched ligament mode, the bush-like mode and the splashing mode.

The paper describes an extension of the well‐known Convective Boundedness Criterion (CBC). It is shown that the newly proposed criterion is a combination of the CBC and the extended convective boundedness criterion (ECBC), as shown in Fig.1. A new scheme (NECBC1) based on the new criterion is designed and tested by two problems: (1) convection of a stepwise profile in an oblique uniform velocity field and (2) convection of an elliptical profile in a stagnation point flow. The numerical tests show the effectiveness of the new criterion and reveal the limitation of the CBC and the ECBC. Moreover, some numerical experiments of some specially‐designed schemes and two TVD‐Type schemes: the van Albada scheme and Miroslav Cada & Manuel Torrilhon’s new third‐order scheme, are carried out. Through these numerical experiments, some extra constraints for the new criterion are observed and in the meantime some other possible regions in the normalized diagram (NV) for high‐resolution schemes reveal themselves.

In this paper, we focus on the transient convection problems of which physically bounds are already known. In tradition, the high-resolutions (HR) schemes that use some parameters to measure the local monotonicity in the predicted scalar field, including the well-known TVD-type and NVD-type schemes, ale widely used. Recently, Qin Qian, et al., [1] proposed a new approach which use the upwind approximation as the 'unbounded indicator". During the computation, the actual scheme switches between QUICK scheme and 1st-order upwind (FUD) scheme, according to whether the indicator locates in the range of physical bounds or not. However, the new approach does not apply to unstructured grids as the far-upwind point for QUICK scheme is not easy to determine. Considering the easy implementation of central differencing (CD) scheme on structured and unstructured meshes, we propose a new convective scheme following the idea of [1], but using CD scheme as the high-order base scheme. The new scheme is extremely simple, but with 2nd-order accuracy. And best of all, the scheme can be applied to arbitrary grids. Testing is carried out on the 1D (transport of a top-hat pulse) problem on a uniform grid. Further testing on the problem of advection of a square-shaped scalar field on structured and unstructured grids are also done. Finally, we compare the solution obtained by FUD, Gamma, MUSCL and the proposed scheme and find that the new scheme performs well for all the lest cases considered.