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Aug 27, 2018

Alpesh Vora

Supervisor - Prof. Dr.-Ing. Ulrich Riebel

Lehrstuhl Mechanische Verfahrenstechnik

Brandenburg Technical University, Cottbus.

Electrical & Mechanical process are closely linked together in high

impedance particle-particle contact.

High field strength leads to an electric polarization in particles

resulting in a significant increase of adhesive force.

Non-Ohmic behaviour of resistance can lead to gas discharges or

electric spark.

To study Electric Conduction and Electric Forces in dust

layer (Electrostatic Precipitation) on microscopic level by

considering the single Particle-Particle Contact Gap.

Methods

Experiment Measurement of force and current

as a function of distance & Electric

field strength

Measuring the emission of light

and ions from the contact area

Measurement charge density on

the surface

Simulation

Electric Field and distribution of

current flow in particle

Charge transport in the gap

Electric force:

f

E field affects due to dielectric particles

Calculate E(r) field in both region

Charge transport in particle

f( volume & surface conductivity)

Charge transport in gas

f(thermionic emission, discharge)

Thermionic emission is a

f(E, Temp, material(work function))

Particle size: order of 100 m

Expected Force: Ranging in between 1-10 N

Accuracy of measurement

instruments (Resolution)

Piezoelectric motor: 0.03nm

Position sensor: < 0.2nm

Electrometer: 1 fA

Maxwells Equations

1st stage (for E field strength)

2nd stage (Charge conservation law)

J in particle is f(volume & surface current) &

J in gas is f(Thermionic emission, discharge)

0

; & f b bE P

0( ) ; But 0.f fE P

0 0 ; & ; & (1+ )e e RD E P P E

00 0RD E

0J

0

0

charge; charge

f b

e

E Electric Field Strength

B Magnetic Filed

D Electric Displacement Field

permeability of freespace

permittivity of freespace

free bound

P polarization

electric susceptibility

J Current Density

Line integral in closed path

Path is very small with respect to

the variation of E and As h0

Apply Gausss law to the small pillbox

But,

Hence,

Normal E is discontinuous & tangential E is continuous

0E dL

tan1 tan2 0E w E w

tan1 tan 2tan1 tan 2

1 2

D DE E

tan1 tan2E E

1 2N N sD S D S Q S 0s

1 2N ND D 1 1 2 2N NE E

Gmsh used for Meshing, OpenFOAM used as Solver and Paraview for post-processing

Why OpenFOAM?

Open source & C++ Object Oriented Programming

Number of solvers exist & allow to extend or modify

Utilities available for pre & post-processing work

Multi Region Problem (Particle-Particle + Gas)

chtMultiRegionFOAM solver

Solve N-S equation (momentum & thermal) in fluid region

Solve heat conduction equation in solid region

oRemove N-S Equation from fluid region & Heat conduction equation from the solid

oRemove N-S equation related parameters & dynamic link

oImplement the electrostatic Laplace equation in both regions

oSolver solves both region one by one

Interface boundaries are defined as

Coupling boundary condition access field data from the neighbour

patch and manipulate

*.deltaCoeffs() returns the normal vector with magnitude

BlockMesh utility for mesh in OpenFOAM

Gmsh (Open Source) used for mesh

3D Tetrahedral mesh for two solid spheres

(surrounded with gas) inside the cube

Spheres & cube defined as physical volumes

Surfaces defined as physical surfaces

Boundary Condition:

minX & maxX : Fixed Potential

Remaining : Zero Gradient Potential

Initial Electric potential distribution & after 30 steps

Correct the non orthogonal effect by solving each steps three times

3particle

gas

Electric Field strength distribution after 50 steps

Maximum field strength is in particles gap

Two planes: 1) to E or mid-X (through particles gap)

2) to mid-Z or to E (through particles & gap)

3particle

gas

Non-smoothness due to coarser tetrahedral mesh.

Require fine & structured grid.

3particle

gas

Generate the Hexagonal Mesh for spheres by SnappyHexMesh utility

Simulate by using the non-dimensional parameter in order to make

ideal experiment set up

Implement the charge continuity equation with appropriate boundary

condition

Implement charge continuity equation model for solid [f(volume &

surface charge)] & gas [f(thermionic field emission, discharge)]

Validate the model by comparing the results with analytical solution &

experimental results

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