Implement the electric conduction equation in OpenFOAM to study

16 Pages·2011·1.72 MB·English

Alpesh Vora
Supervisor - Prof. Dr.-Ing. Ulrich Riebel
Lehrstuhl Mechanische Verfahrenstechnik
Brandenburg Technical University, Cottbus.
Electrical & Mechanical process are closely linked together in high
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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
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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
Simulation

Measurement of force and current

as a function of distance & Electric
Electric Field and distribution of
field strength
current flow in particle

Measuring the emission of light
Charge transport in the gap

and ions from the contact area
Electric force:
Measurement charge density on
f<distance, electric field strength>
the surface
E field affects due to dielectric particles
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Calculate E(r) field in both region
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Charge transport in particle
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 f( volume & surface conductivity)

Charge transport in gas
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 f(thermionic emission, discharge)

Thermionic emission is a
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f(E, Temp, material(work function))
Particle size: order of 100 µm
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Expected Force: Ranging in between 1-10 µN
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Accuracy of measurement
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instruments (Resolution)

Piezoelectric motor: 0.03nm

Position sensor: < 0.2nm
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Electrometer: 1 fA
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Maxwell’s Equations
1st stage (for E field strength)

 E  ;    &    P
f b b

0
( E  P)   ; But   0.
0 f f
D  E  P ; & P  E ; & (1+) 

0 e 0 e R
 D  0   E  0

R 0
2nd stage (Charge conservation law)
E  Electric Field Strength
BMagne tic Filed   J  0
D Electric Displacement Field

  permeability of freespace J in particle is f(volume & surface current) &
0
  permittivity of freespace
0
J in gas is f(Thermionic emission, discharge)
  free charge; bound charge
f b
P polarization
 electric susceptibility
e

J Current Density
Line integral in closed path

 E  dL  0

Path is very small with respect to
the variation of E and As Δh→0
E w E w  0
tan1 tan2

D D
E  E
tan1  E  E  tan2
tan1 tan2 tan1 tan2
 

1 2
Apply Gauss’s law to the small pillbox
D  S  D  S  Q    S But,   0
N1 N2 s s

E  E
Hence, D  D
1 N1 2 N2
N1 N2

Normal E is discontinuous & tangential E is continuous
Gmsh used for Meshing, OpenFOAM used as Solver and Paraview for post-
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processing

Why OpenFOAM?
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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)
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chtMultiRegionFOAM solver
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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
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Coupling boundary condition access field data from the neighbour
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patch and manipulate

*.deltaCoeffs() returns the normal vector with magnitude
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