Modelling dielectric charged drop break up using an energy conservation method

In the light of experimental evidence a previously published model to predict the charge and mass redistribution when charged dielectric drops break up has been updated. In particular we have taken the dielectric nature of the liquid, the existence of an external electric field and used photographic evidence of drop break up as a basis for geometrical assumptions that are physically realistic. We have assessed the sensitivity of the charge redistribution assumption and the improved model compares well with the recent accurate experimental evidence. The results apply to ratio of quantities of mass and charge, making the model extremely simple and economical to apply to multi-dimensional charged spray computer codes in order to predict evaporating charged sprays accurately

Drop-charge correlations for polydisperse electrostatically atomized liquid sprays

In many applications liquid sprays are atomized using electrostatic methods, and typically these spray plumes containing drops that have a range of diameters. To understand and predict the dynamics of polydisperse electrically charged spray plumes, knowledge of how the electrical charge is distributed amongst the drops is required. This has been achieved by post-processing phase Doppler anemometry data for two electrostatically atomized liquid sprays and fitting the drop diameter-charge correlation to an assumed relationship of form q=ADn, Here q and D are drop charge and diameter and n and A are empirical constants that describe the correlation. Values of n and A were calculated to be 2.1 to 2.9 and 5.8 ×10-5 for a spray of specific charge 1.8 C/m3 and 2.1 to 3.2 and its value of A is 2.5×10-4 for a spray of specific charge 1.2 C/m3. It was found that the mean drop charge, for all drop diameters, for both data-sets, was almost always less than the drop Rayleigh limit. This latter fact gives confidence in the procedure used since no restriction was placed on this parameter during the processing. We also estimate the distribution of drop charge about the mean value and as a function of diameter and suggest that small drops possess higher rms charge levels

Dielectric charged drop break-up at sub-Rayleigh limit conditions

The maximum charge a drop may hold, for an electrically isolated, electrically conducting drop, in vacuum, is defined by the Rayleigh Limit. For spray plumes of electrically charged drops this condition is clearly not met due to the space charge field. We would like to simulate such spray plumes and to simulate drop break up within them, using stochastic methods. Since many simulated particles are required a dynamic drop stability analysis is clearly not computationally feasible. Based upon a static analysis, and a thorough review of the previous experimental data on charged drop stability, it is shown that for dielectric drops in the presence of significant electric fields, and particularly those within spray plumes, the maximum charge a drop may hold is less than the Rayleigh Limit. Typical values of stable drop charge of 70-80% of the conducting drop Rayleigh Limit are predicted, and this is supported by a majority of recent experimental work. We present an explanation of the sub-Rayleigh Limit drop fission within charged spray plumes for dielectric drops, based upon a static, rather than a dynamic analysis. This permits sub-Rayleigh Limit drop fission to be incorporated into stochastic particle simulations

Direct numerical simulation of forced flow dielectric EHD within charge injection atomizers

A charge injection atomizer functions by introducing electric charge discharged from a high voltage electrode into a dielectric liquid, which subsequently atomizes the ejected liquid jet. Atomizer evolution thus far has proceeded through trial and error analysis of the experimentally measured electrical characteristics of the atomizer and of the quality of atomization. Within the atomizer, a coupled space charge and electric field exist, which can alter the internal flow pattern, thus creating electrohydrodynamic (EHD) instabilities that affect atomizer operation. Such a system has not been simulated in the past under forced flow conditions. In this work we simulate the internal flow of such a charge injection device in two dimensions; using experimental based boundary conditions. Initial results indicate that in the linear injection regime defined by the experimental data, the flow is only slightly unstable but in the transitional and highly non-linear regimes, the coupled space charge and electric field produce more instability in the liquid that must be investigated furthe

Pulsed charged sprays: application to DISI engines during early injection

Numerical predictions of the temporal evolution of pulsed sprays, typical of those used in gasoline direct injection spark ignition engines are presented, with the novelty that the drops are electrically charged. The rate of spray expansion, in terms of the fraction of maximum possible spray charge for a typical engine timescale, is investigated. The engine timescale chosen is the time available between spray injection and ignition, and for a low-speed engine operation, with injection during the intake stroke. The aim is to quantify the amount of electric charge, required to spread the spray throughout the engine cylinder, without causing excessive piston and wall impingement, prior to hypothetical ignition. It is found that experimentally realizable amounts of electric charge are sufficient to cause spray expansion throughout the engine cylinder within the timescale permitted. Also noted is a segregation of the smaller drops from their larger cousins, by virtue of the known non-linear variation in drop charge with drop mass. Since it is known that pulsed fuel injectors producing charged sprays of insulating liquids are a reality then electric charge seems to be a viable route to control and optimize in-cylinder mixture distribution and hence engine performance, robustness and emissions

A mesoscopic description of polydispersed particle laden turbulent flows

Turbulent polydispersed multiphase flows are encountered in many engineering and environmental applications and particularly in combustion applications, spray polydispersity is the norm rather than the exception. In this review we summarize the current state of Eulerian transport models for turbulent polydispersed particulate flows without size class discretization. The stochastic nature of both carrier and dispersed phase justifies a stochastic approach to describe the behavior of such systems. In this regard Brownian motion of a single microscopic particle is discussed to intuitively introduce the subject and point out the need for a stochastic representation of the phenomena based on stochastic differential equations (SDEs). Understanding the stochastic tools and mathematical framework based on Langevin equation is compulsory for the rest of this review but here we restrict our coverage to definitions and general remarks and give references for further readings. A stochastic foundation based on Langevin equation is defined for fluid and particle and derivation of the transport equation up to third order statistics without binning the particle diameter is discussed based on corresponding Fokker–Planck equation. Terms that appear in the process of contracting a probability density function (PDF) causing closure problems are identified. The Maximum entropy method is discussed as a tool for closure of particle acceleration terms in Eulerian transport equations followed by current closure issues such as realizability and generalit

Fully resolved simulation of particle deposition and heat transfer in a differentially heated cavity

In this paper a fictitious domain method is used to study the motion of particles in a differentially heated cavity. A collision strategy is implemented which is validated using the problem of two freely falling particles with natural convection taking place from the leading hot particle. The motion of the particles in a differentially heated cavity is considered where the vertical walls are subject to a temperature difference ?T?T whereas horizontal walls are assumed to be adiabatic. Depending on the fluid Grashof number different flow regimes and two critical Grashof numbers are identified. Sustained motion of the suspended particles is also studied and different behaviour is observed compared to the limiting case of tracer particles where simulations are usually performed using one-way coupled point-particle assumptions. Finally the effects of the particles on the heat transfer from the hot wall are studied and it is found that addition of large particles can adversely influence the heat transfer rate. However, if hot particles are effectively removed from the wall, e.g. by increasing the Grashof number, wall heat transfer properties can still be enhanced

Turbulent three-dimensional dielectric electrohydrodynamic convection between two plates

The fundamental mechanisms responsible for the creation of electrohydrodynamically driven roll structures in free electroconvection between two plates are analysed with reference to traditional Rayleigh–Bénard convection (RBC). Previously available knowledge limited to two dimensions is extended to three-dimensions, and a wide range of electric Reynolds numbers is analysed, extending into a fully inherently three-dimensional turbulent regime. Results reveal that structures appearing in three-dimensional electrohydrodynamics (EHD) are similar to those observed for RBC, and while two-dimensional EHD results bear some similarities with the three-dimensional results there are distinct differences. Analysis of two-point correlations and integral length scales show that full three-dimensional electroconvection is more chaotic than in two dimensions and this is also noted by qualitatively observing the roll structures that arise for both low (ReE = 1) and high electric Reynolds numbers (up to ReE = 120). Furthermore, calculations of mean profiles and second-order moments along with energy budgets and spectra have examined the validity of neglecting the fluctuating electric field E'i in the Reynolds-averaged EHD equations and provide insight into the generation and transport mechanisms of turbulent EHD. Spectral and spatial data clearly indicate how fluctuating energy is transferred from electrical to hydrodynamic forms, on moving through the domain away from the charging electrode. It is shown that E'i is not negligible close to the walls and terms acting as sources and sinks in the turbulent kinetic energy, turbulent scalar flux and turbulent scalar variance equations are examined. Profiles of hydrodynamic terms in the budgets resemble those in the literature for RBC; however there are terms specific to EHD that are significant, indicating that the transfer of energy in EHD is also attributed to further electrodynamic terms and a strong coupling exists between the charge flux and variance, due to the ionic drift term.35 page(s