K. Adamiak

Trajectories of charged aerosol particles near a spherical collector

Abstract Deposition of charged aerosol particles on a spherical object was investigated experimentally and modeled numerically. The validity of the model was confirmed by a qualitative comparison of both results. Charging both the particle and the collector increases the collection efficiency manyfolds.

Simulation of particle trajectories in tribo-powder coating

The modeling of the tribo-powder coating process requires the solution of the electrostatic field problem and the equation for particle motion. Electric field distribution is a function of the space charge density, which is associated with the particle concentration. The particle movement results from the balance of electrical, inertial, air drag and gravitational forces. Therefore, both problems are mutually coupled. In this paper, an iterative algorithm is presented to simulate this problem; the electric field is determined by means of the finite element method, whereas the time-dependent explicit fourth order Runge-Kutta algorithm is used to predict the particle trajectories. Both problems are solved iteratively until a self-consistent solution is found. The results of simulation show the effects of different parameters which characterize the process such as the powder particle size, charge/mass ratio, distance to a coating object, powder outflow and assisted air velocity on the shape of the powder jet.

Incorporation of the Corona Current into a Numerical 3D Model of the Electrostatic Coating Process

Due to the presence of a high voltage and the specific geometry configuration, corona discharge is an inevitable part of many electrostatic coating processes. A full mathematical model of the corona discharge is practically impossible to implement due to the complexity of the problem. In this article, a new, simplified, and efficient method for incorporation of the corona current into the numerical model of the electrostatic coating process is presented. The objective of this article is to describe the novel procedure and fit it into the existing numerical frameworks. A software package Fluent is used to solve a transport equation for a new, user-defined scalar function. The gradient of this function corresponds to the corona current density. The numerical simulation is performed for the full 3D model of the problem and the sample results of the simulations are presented.

FEM-FCT Based 2D Simulation of Trichel Pulses in Air

In this paper a new two-dimensional model is presented for numerical simulation of Trichel pulses in a point-plane configuration. Both radial and axial components of the electric field are considered and it is assumed that three ionic species exist in the air gap: electrons, and positive and negative oxygen ions. The Poisson equation is solved for electric field calculations and three continuity equations are solved for modeling the transport of charge densities in the air gap. The finite element method (FEM) is used for solving the Poisson equation and a combined Flux Corrected Transport-FEM is used for the charge transport equations. Trichel pulses for different applied voltages are shown and the characteristics of these pulses at different voltages are compared with experimental results reported in the literature. The time variation of the electric field on the corona electrode at different stages of one Trichel pulse is also presented. Moreover, the distributions of electron, positive ion and negative ion densities at different stages of the Trichel pulse are discussed.

Dynamics of EHD flow in pin-plate configuration generated by electric corona discharge in air

Publisher Summary This chapter explains the dynamics of electro-hydrodynamic (EHD) flow in pin-plate configuration generated by electric corona discharge in air. The characteristics of the electro-hydrodynamic flow in air produced by the electric corona discharge in a pin-plate configuration are investigated numerically. The numerical algorithm based on the Boundary Element Methods (BEMs) and Finite Element Methods (FEMs) and the Method of Characteristics (MOC) is employed to simulate the electric field. The electric field is calculated by means of the BEM, FEM and MOC. The FLUENT software is used to calculate the airflow parameters. The electric corona discharge produces the EHD flow with the velocity distribution pattern affected not only by the air gap geometry but also by the applied voltage; the length of time that it takes to reach the steady state axial velocity is greatly affected by the applied voltage. Usually, it takes several milliseconds to reach the steady state, and the higher the applied voltage, the shorter the time it takes to produce the steady EHD airflow. The chapter predicts the EHD flow patterns and the velocity distributions at different instants of time. The simulation results indicate that the applied voltage level greatly affects the transient dynamics of the process.

Deposition efficiency of dust particles on water droplets in electrostatic scrubbers

A numerical algorithm for simulating dust particle deposition on a charged spherical collector is presented in the paper. Trajectories of the charged dust particles are traced in three-dimensional space by solving the Newton equation, taking into account inertial, air drag, gravitational and electrostatic forces. The collector (charged droplet) falls down freely and its trajectory is also determined. A laminar viscous model is assumed for the air flow in the vicinity of the collector and modelled using the finite element method in two-dimensional cylindrical coordinates. The deposition efficiency is defined in terms of the volume of space, from which all particles are deposited. The calculation results for different Stokes, Coulomb and Reynolds numbers are given.

The control of corona current distribution using shaped electrodes

Abstract The mobility model for ionic flow in a corona discharge restricts the trajectories of ions to follow electric field lines. An axisymmetric arrangement of electrodes consisting of a short wire supported by metallic rods inside a grounded cylinder was used to produce ion emission along a localized section of corona wire. By varying the geometry of the support structure of the central corona electrode it was possible to vary the field configuration in the ionic region, and hence the corona current density in the axial direction. The hybrid Finite Element-Method of Characteristics technique used to analyze the configuration confirmed the experimental results and shows that this ionic focusing can be used to concentrate the current onto a localized section of the outer electrode. This may have useful applications in such areas as electrostatic coating and surface treatment.

Estimation of droplet charge forming out of an electrified ligament in the presence of a uniform electric field

The charge on a liquid droplet is a critical parameter that needs to be determined to accurately predict the behaviour of the droplet in many electrostatic applications, for example, electrostatic painting and ink-jet printing. The charge depends on many factors, such as the liquid conductivity, droplet and ligament radii, ligament length, droplet shape, electric field intensity, space charge, the presence of adjacent ligaments and previously formed droplets. In this paper, a 2D axisymmetric model is presented which can be used to predict the electric charge on a conductive spherical droplet ejected from a single ligament directly supplied with high voltage. It was found that the droplet charging levels for the case of isolated electrified ligaments are as much as 60 times higher than that in the case of ligaments connected to a planar high voltage electrode. It is suggested that practical atomization systems lie somewhere between these two extremes and that a better model was achieved by developing a 3D approximation of a linear array of ligaments connected to an electrode having variable width. The effect on droplet charge and its radius was estimated for several cases of different boundary conditions.

Rate of charging of spherical particles in mono-ionised electric fields

The paper presents a numerical algorithm to simulate the charging dynamics of high resistivity spherical particles by the ionic bombardment in an electric field. The algorithm is based on solving the Poisson equation, governing the electric field distribution, and the differential equation expressing the charge conservation law. Results of simulation are also presented and they illustrate the effect of different parameters on the charging dynamics.

The charging level of a ligament-droplet system atomized in a uniform electric field

In this paper, a numerical algorithm has been formulated for calculating the charge magnitude on a spherical droplet created by breakup of a cylindrical ligament in an external electric field. The algorithm is based on the finite-element method and it determines the droplet charge as a function of the droplet radius and ligament length. It has been found that the droplet charge is a function of particle radius to some exponent, which is equal to 2 when the droplet is in direct contact with the atomizer and decreases dramatically to approach 1.1, as the ligament length increases. The effect of the ligament radius on the charging level has been found to be significant and increases with the ligament length. It was determined that the charging level is affected by the presence of adjacent ligaments and previously ejected droplets. To investigate the dynamics of the droplet atomization, the Navier-Stokes equations, describing the fluid motion, as well as the level-set equation for tracking the interfaces between air and liquid have been solved. A comparison between the charging level of the dynamically formed droplets and an assumed spherical one has been presented. It has been found that the predicted charging level of the spherical droplet is lower than the one of the actual shape in the range 15%-26%.