Numerical Methods for Simulating Multiphase Electrohydrodynamic Flows with Application to Liquid Fuel Injection

One approach to small-scale fuel injection is to capitalize upon the benefits of electrohydrodynamics (EHD) and enhance fuel atomization. There are many potential advantages to EHD aided atomization for combustion, such as smaller droplets, wider spray cone, and the ability to control and tune the spray for improved performance. Electrohydrodynamic flows and sprays have drawn increasing interest in recent years, yet key questions regarding the complex interactions among electrostatic charge, electric fields, and the dynamics of atomizing liquids remain unanswered. The complex, multi-physics and multi-scale nature of EHD atomization processes limits both experimental and computational explorations. In this work, novel, numerically sharp methods are developed and subsequently employed in high-fidelity direct numerical simulations of electrically charged liquid hydrocarbon jets. The level set approach is combined with the ghost fluid method (GFM) to accurately simulate primary atomization phenomena for this class of flows. Surface effects at the phase interface as well as bulk dynamics are modeled in an accurate and robust manner. The new methods are implemented within a conservative finite difference scheme of high-order accuracy that employs state-of-the-art interface transport techniques. This approach, validated using several cases with exact analytic solutions, demonstrates significant improvements in accuracy and efficiency compared to previous methods used for EHD simulations. As a final validation, the computational scheme is applied in direct numerical simulation of a charged and uncharged liquid kerosene jet. Then, a detailed numerical study of EHD atomization is conducted for a range of relevant dimensionless parameters to predict the onset of liquid break-up, identify characteristic modes of liquid disintegration, and report elucidating statistics such as drop size and spray dispersion. Because the methodologies developed and validated in this work open new, simulations-based avenues of exploration within a broader category of electrohydrodynamics, some perspectives on extensions or continuations of this work are offered in conclusion

Simulations of a weakly conducting droplet under the influence of an alternating electric field

We investigate the electrohydrodynamics of an initially spherical droplet under the influence of an external alternating electric field by conducting axisymmetric numerical simulations using a charge-conservative volume-of-fluid based finite volume flow solver. The mean amplitude of shape oscillations of a droplet subjected to an alternating electric field for leaky dielectric fluids is the same as the steady-state deformation under an equivalent root mean squared direct electric field for all possible electrical conductivity ratio $(K_r)$ and permittivity ratio $(S)$ of the droplet to the surrounding fluid. In contrast, our simulations for weakly conducting media show that this equivalence between alternating and direct electric fields does not hold for $K_r \ne S$. Moreover, for a range of parameters, the deformation obtained using the alternating and direct electric fields is qualitatively different, i.e. for low $K_r$ and high $S$, the droplet becomes prolate under alternating electric field but deforms to an oblate shape in the case of the equivalent direct electric field. A parametric study is conducted by varying the time period of the applied alternating electric field, the permittivity and the electrical conductivity ratios. It is observed that while increasing $K_r$ has a negligible effect on the deformation dynamics of the droplet for $K_r<S$, it enhances the deformation of the droplet when $K_r>S$ for both alternating and direct electric fields. We believe that our results may be of immense consequence in explaining the morphological evolution of droplets in a plethora of scenarios ranging from nature to biology.Comment: 10 pages, 8 figure

Finite amplitude electroconvection induced by strong unipolar injection between two coaxial cylinders

We perform a theoretical and numerical study of the Coulomb-driven electroconvection flow of a dielectric liquid between two coaxial cylinders. The specific case where the inner to outer diameter ratio is 0.5 is analyzed. A strong unipolar injection of ions either from the inner or outer cylinder is considered to introduce free charger carriers into the system. A finite volume method is used to solve all governing equations including Navier-Stokes equations and a simplified set of Maxwell’s equations. The flow is characterized by a subcritical bifurcation in the finite amplitude regime. A linear stability criterion and a nonlinear one that correspond to the onset and stop of the flow motion, respectively, are linked with a hysteresis loop. In addition, we also explore the behavior of the system for higher values of the stability parameter. For inner injection, we observe a transition between the patterns made of 7 and 8 pairs of cells, before an oscillatory regime is attained. Such a transition leads to a second finite amplitude stability criterion. A simple modal analysis reveals that the competition of different modes is at the origin of this behavior. The charge density as well as velocity field distributions are provided to help understanding the bifurcation behavior.Ministerio de ciencia y tecnología FIS2011-25161Junta de Andalucía P10-FQM-5735Junta de Andalucía P09-FQM-458

Numerical Modeling of Deformation, Oscillation, Spreading and Collision Characteristics of Droplets in an Electric Field

Electric field induced flows, or electrohydrodynamics (EHD), have been promising in many fast-growing technologies, where droplet movement and deformation can be controlled to enhance heat transfer and mass transport. Several complex EHD problems existing in many applications were investigated in this thesis. Firstly, this thesis presents the results of numerical simulations of the deformation, oscillation and breakup of a weakly conducting droplet suspended in an ambient medium with higher conductivity. It is the first time that the deformation of such a droplet was investigated numerically in a 3D configuration. We have determined three types of behavior for the droplets, which are less conducting than ambient fluid: 1) oblate deformation (which can be predicted from the small perturbation theory), 2) oscillatory oblate-prolate deformation and 3) breakup of the droplet. Secondly, a numerical study of droplet oscillation placed on different hydrophobic surfaces under the effect of applied AC voltage including the effect of ambient gas was investigated. The presented algorithm could reproduce droplet oscillations on a surface considering different contact angles. It has been found that the resonance frequency of the water droplet depends on the surface property of the hydrophobic materials and the electrostatic force. Thirdly, a new design of an electrowetting mixer using the rotating electric field was proposed which offers a new method to effectively mix two droplets over a different range of AC frequencies. Two regimes were observed for droplet coalescence: 1) coalescence due to the high droplet deformation, 2) coalescence due to the interaction of electrically induced dipoles. Fourthly, the spreading and retraction control of millimetric water droplets impacting on dry surfaces have been investigated to examine the effect of the surface charge density and electric field intensity. The effect of the surface charge on the spreading of droplets placed gently on surfaces was investigated in the first part. It was found that the maximum spreading diameter increases with an increasing charge. In the second part, the impact of a droplet on a ground electrode was considered. It was also found that in order to keep the maximum diameter after the impact, less charge is needed for surfaces with lower contact angle. Finally, the interaction between two identical charged droplets was investigated numerically. The effects of the impact velocity, drop size ratio and electric charge on the behavior of the combined droplet were investigated. It was shown that two conducting droplets carrying charges of the same polarity under some conditions may be electrically attracted. The formation of charged daughter droplets has been investigated and it was found that the number of the satellite droplets after collision appears to increase with an increase in the droplet charge

Controlling wetting with electrolytic solutions: phase-field simulations of a droplet-conductor system

The wetting properties of immiscible two-phase systems are crucial in a wide range of applications, from lab-on-a-chip devices to field-scale oil recovery. It has long been known that effective wetting properties can be altered by the application of an electric field; a phenomenon coined as electrowetting. Here, we consider theoretically and numerically a single droplet sitting on an (insulated) conductor, i.e., within a capacitor. The droplet consists of a pure phase without solutes, while the surrounding fluid contains a symmetric monovalent electrolyte, and the interface between them is impermeable. Using nonlinear Poisson--Boltzmann theory, we present a theoretical prediction of the dependency of the apparent contact angle on the applied electric potential. We then present well-resolved dynamic simulations of electrowetting using a phase-field model, where the entire two-phase electrokinetic problem, including the electric double layers (EDLs), is resolved. The simulations show that, while the contact angle on scales smaller than the EDL is unaffected by the application of an electric field, an apparent contact angle forms on scales beyond the EDL. This contact angle relaxes in time towards a saturated apparent contact angle. The dependency of the contact angle upon applied electric potential is in good compliance with the theoretical prediction. The only phenomenological parameter in the prediction is shown to only depend on the permeability ratio between the two phases. Based on the resulting unified description, we obtain an effective expression of the contact angle which can be used in more macroscopic numerical simulations, i.e. where the electrokinetic problem is not fully resolved

Estudos numéricos em eletrohidrodinâmica

Orientador: Marcos Akira D'ÁvilaTese (doutorado) - Universidade Estadual de Campinas, Faculdade de Engenharia MecânicaResumo: A eletrohidrodinâmica (EHD) descreve o movimento do fluido induzido por tensões elétricas. Sob o efeito de um campo elétrico, as moléculas de fluido podem polarizar e uma migração de íons carregados ou cargas livres através do fluido é induzida. Estes fenômenos dão origem a forças elétricas que atuam sobre a superfície do fluido colocando-a em movimento até que a tensão superficial e as tensões viscosas proporcionem o equilíbrio necessário. Aplicações como atomização de líquidos, transferência de calor e massa, dispersão de polímeros e tecnologias microfluídicas fizeram com que a eletrohidrodinâmica fosse extensivamente estudada ao longo dos anos no intuito de compreender as respostas de sistemas de fluidos submetidos a campos elétricos e de desenvolver novos processos. No entanto, a natureza complexa dos processos EHD limita as explorações tanto experimentais como de desenvolvimento. Portanto, para obter resultados mais rápidos e com custos menores, são frequentemente utilizados estudos envolvendo modelagem e simulações numéricas. Neste trabalho, utilizando um solver eletrohidrodinâmico baseado no modelo leaky dielectric, analisamos dois problemas diferentes relacionados à EHD. O primeiro consiste em investigar o efeito da viscoelasticidade na deformação e quebra de gotículas inseridas em um campo elétrico uniforme. Este é um dos primeiros e mais fundamentais problemas em EHD, porém nunca foi avaliado através de simulações numéricas utilizando fluidos não-Newtonianos. Assim, com os resultados aqui apresentados, pretendemos elucidar alguns dos principais aspectos da deformação viscoelástica em problemas de EHD. O segundo caso é um problema aplicado tem atraído um crescente interesse nos últimos anos. Consiste na deformação de lentes líquidas pela aplicação de um campo elétrico. Por meio de simulações numéricas, investigamos a influência do formato do eletrodo na deformação da lente e analisamos seu desempenho usando uma plataforma de design óptico. Esta abordagem nunca foi feita antes e sugere uma nova visão sobre os sistemas micro-ópticos adaptáveisAbstract: Electrohydrodynamics (EHD) describes the fluid motion induced by electric stresses. Under the effect of an electric field the fluid molecules may get polarized and a migration of charged ions or free charges through the fluid is induced. These phenomena give rise to electric forces that act on the fluid surface putting it into motion until the surface tension and viscous stresses provide the necessary balance. Applications such as liquid atomization, heat and mass transfer, polymer dispersion and microfluidic technologies have made electrohydrodynamics to be extensively studied over the years in order to understand the responses of fluids systems subjected to electric fields and to develop new processes. However, the complex nature of EHD processes limits both experimental and development explorations. Therefore, in order to obtain faster results and at lower costs, studies involving modeling and numerical simulations are frequently used. In this work, using an EHD solver based on the leaky dielectric model, we analyze two different problems related to electrohydrodynamics. The first one consists on the investigation of the effect of viscoelasticity on the deformation and breakup of droplets inserted in a uniform electric field. This is one of the first and most fundamental problems in EHD. However it has never been evaluated through numerical simulations using non-Newtonian fluids. Thus, with the results presented here we aim to elucidate some of the main aspects of the viscoelastic deformation in EHD problems. The second case is an applied problem that has drawn increasing interest in the past few years. It consists in the deformation of liquid lenses by the application of an electric field. By means of numerical simulations we investigate the influence of the electrode shape on the lens deformation and we analyze its performance using an optical design platform. This approach has never been done before and it suggests a new insight into the adaptive micro-optical systemsDoutoradoMateriais e Processos de FabricaçãoDoutor em Engenharia Mecânica233361/2014-6CNP

EH-DPD: a dissipative particle dynamics approach to electrohydrodynamics

Abstract: Electrohydrodynamics is crucial in many nanofluidic and biotechnological applications. In such small scales, the complexity due to the coupling of fluid dynamics with the dynamics of ions is increased by the relevance of thermal fluctuations. Here, we present a mesoscale method based on the Dissipative Particle Dynamics (DPD) model of the fluid. Two scalar quantities, corresponding to the number of positive and negative ions carried by each DPD particle, are added to the standard DPD formulation. We introduced a general framework that, given the definition of the free-energy of the DPD particle, allows to derive a fluctuation-dissipation relation and the expression for ionic fluxes between the DPD particles. This provides a link between the dynamics of the system and its equilibrium properties. The model is then validated simulating a planar electroosmotic flow for the cases of overlapping and non overlapping electric double layers. It is shown that using a Van der Waals equation of state the effect of ionic finite size can be accounted, leading to significant effects on the concentration and velocity profiles with respect to the ideal solution case. Graphic abstract: [Figure not available: see fulltext.]

Simulation of Electrospray Emission Processes for Highly Conductive Liquids

An electrohydrodynamic numerical model is used to explore the electrospray emission behavior of both moderate and high electrical conductivity liquids under electrospray conditions. The Volume-of-Fluid method, incorporating a leaky-dielectric model with a charge relaxation consideration, is used to conserve charge to accurately model cone-jet formation and droplet breakup. The model is validated against experiments and agrees well with both droplet diameters and charge-to-mass ratio of emitted progeny droplets. The model examines operating conditions such as flow rate and voltage, with fluid properties also considered, such as surface tension, electrical conductivity, and viscosity for both moderate and high conductivity. For high conductivity and surface tension, the results show that high charge concentration along with the meniscus and convex cone shape results in a higher charge-to-mass ratio of the emitted droplets while lower conductivity and surface tension tend towards concave cone shapes and lower charge-to-mass droplets. Recirculation flows inside the bulk liquid are investigated across a range of non-dimensional flow rates, and electric Reynolds numbers. For high conductivity liquid emission at the minimum stable flow rate, additional recirculation cells develop near the cone tip suggesting the onset of the axisymmetric instability.Comment: submitted to Journal of Fluid Mechanic