alpesh vora supervisor - prof. dr.-ing. ulrich riebel ...€¦ · lehrstuhl mechanische...
TRANSCRIPT
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<distance, electric field strength>
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 µm
Expected Force: Ranging in between 1-10 µN
Accuracy of measurement
instruments (Resolution)
Piezoelectric motor: 0.03nm
Position sensor: < 0.2nm
Electrometer: 1 fA
Maxwell’s 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 Δh→0
Apply Gauss’s 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