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

An enriched finite element/level-set model for two-phase electrohydrodynamic simulations

In this work, a numerical model for the simulation of two-phase electrohydrodynamic (EHD) problems is proposed. It is characterized by a physically consistent treatment of surface tension as well as a jump in the electric material properties. The formulation is based on a finite element method enriched with special shape functions, capable of accurate capturing discontinuities both in the fluid pressure and the gradient of the electric potential. Phase interface is, thus, represented as a zero-thickness boundary. The proposed methodology allows modeling the electric force as an interfacial one, strictly abiding with the physics. The approach is tested using the droplet deformation benchmarks. Moreover, application of the method to study a three-dimensional (3D) case, not characterized by symmetry of revolution, is shown. The proposed methodology defines a basis for an enriched finite element method for a wide range of EHD problems.The authors acknowledge the financial support of the Ministerio de Ciencia, Innovaci on e Universidades of Spain via the “Severo Ochoa Programme” for Centres of Excellence in R&D (Referece No. CEX2018-000797-S) given to the International Centre for Numerical Methods in Engineering (CIMNE). The work of C. Narvaez-Mu~noz was supported by the “Severo Ochoa Ph.D. Scholarship” Reference No. PRE2020-096632. Parts of this work were done in the framework of DIDRO project (Toward establishing a Digital twin for manufacturing via drop-on-demand inkjet printing. Proyectos Estrat egicos Orientados a la Transici on Ecol ogica y a la Transici on Digital. Reference No. TED2921-130471B-I00) supported by the Ministerio de Ciencia, Innovaci on e Universidades of Spain. M. Hashemi acknowledges the funding received from European Union’s Horizon 2020 Research and Innovation Programme (European High-Performance Computing Joint Undertaking Grant Agreement No. 955558) as part of EFLOWS4HPC project. P. Ryzhakov and J. Pons-Prats are Serra Hunter fellows.Peer ReviewedPostprint (published version

Dynamics of Falling Droplet Under Effects of Electric Fields

Physical properties and especially the size of drops are important parameters in many industrial and medical applications. High voltage electric field is one of the effective means to control the final size of drops during the fabrication process which could greatly influence the final size of the product. Therefore a detailed study of electric field effect on a liquid drop is very important. In this work deformation and fragmentation of a falling droplet under gravity and electric force have been studied numerically. The electric force is used as an effective external controlling mechanism to influence the deformation of a drop. The three-dimensional deformation of a falling droplet is studied numerically using the open-source volume of-fluid solver, Gerris with dynamic adaptive grid refinement. The numerical results are compared with previous analytical, experimental and numerical data and excellent agreements between the results are obtained. The results are presented for a broad range of Bond numbers (Bo) from low Bond number (drop with small deformation) to large Bond number (drop breakup and fragmentation). The results revealed that the electric field can be used as a powerful controlling tool in delaying and expediting the falling drop breakup process. The results also showed that falling drop deforms severely by increasing Bo number which leads to the breakup and fragmentation compared to the cases of low Bo number in which the drop deforms mildly without breakup. Moreover, analytical solutions of drop’s deformation are presented in detail and then the outcomes were compared with numerical results. The numerical results are presented for various values of density ratios and electrical conductivity and permittivity. The comparison of the results shows a great agreement between the analytical solutions and the direct numerical simulation (DNS) results

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

A time splitting projection scheme for compressible two-phase flows. Application to the interaction of bubbles with ultrasound waves

This paper is focused on the numerical simulation of the interaction of an ultrasound wave with a bubble. Our interest is to develop a fully compressible solver in the two phases and to account for surface tension effects. As the volume oscillation of the bubble occurs in a low Mach number regime, a specific care must be paid to the effectiveness of the numerical method which is chosen to solve the compressible Euler equations. Three different numerical solvers, an explicit HLLC (Harten–Lax–van Leer-Contact) solver [48], a preconditioning explicit HLLC solver [14] and the compressible projection method , and , are described and assessed with a one dimensional spherical benchmark. From this preliminary test, we can conclude that the compressible projection method outclasses the other two, whether the spatial accuracy or the time step stability are considered. Multidimensional numerical simulations are next performed. As a basic implementation of the surface tension leads to strong spurious currents and numerical instabilities, a specific velocity/pressure time splitting is proposed to overcome this issue. Numerical evidences of the efficiency of this new numerical scheme are provided, since both the accuracy and the stability of the overall algorithm are enhanced if this new time splitting is used. Finally, the numerical simulation of the interaction of a moving and deformable bubble with a plane wave is presented in order to bring out the ability of the new method in a more complex situation

Droplet Dynamics Under Extreme Ambient Conditions

This open access book presents the main results of the Collaborative Research Center SFB-TRR 75, which spanned the period from 2010 to 2022. Scientists from a variety of disciplines, ranging from thermodynamics, fluid mechanics, and electrical engineering to chemistry, mathematics, computer science, and visualization, worked together toward the overarching goal of SFB-TRR 75, to gain a deep physical understanding of fundamental droplet processes, especially those that occur under extreme ambient conditions. These are, for example, near critical thermodynamic conditions, processes at very low temperatures, under the influence of strong electric fields, or in situations with extreme gradients of boundary conditions. The fundamental understanding is a prerequisite for the prediction and optimisation of engineering systems with droplets and sprays, as well as for the prediction of droplet-related phenomena in nature. The book includes results from experimental investigations as well as new analytical and numerical descriptions on different spatial and temporal scales. The contents of the book have been organised according to methodological fundamentals, phenomena associated with free single drops, drop clusters and sprays, and drop and spray phenomena involving wall interactions

Droplet Dynamics Under Extreme Ambient Conditions

This open access book presents the main results of the Collaborative Research Center SFB-TRR 75, which spanned the period from 2010 to 2022. Scientists from a variety of disciplines, ranging from thermodynamics, fluid mechanics, and electrical engineering to chemistry, mathematics, computer science, and visualization, worked together toward the overarching goal of SFB-TRR 75, to gain a deep physical understanding of fundamental droplet processes, especially those that occur under extreme ambient conditions. These are, for example, near critical thermodynamic conditions, processes at very low temperatures, under the influence of strong electric fields, or in situations with extreme gradients of boundary conditions. The fundamental understanding is a prerequisite for the prediction and optimisation of engineering systems with droplets and sprays, as well as for the prediction of droplet-related phenomena in nature. The book includes results from experimental investigations as well as new analytical and numerical descriptions on different spatial and temporal scales. The contents of the book have been organised according to methodological fundamentals, phenomena associated with free single drops, drop clusters and sprays, and drop and spray phenomena involving wall interactions