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Alpesh Vora Supervisor - Prof. Dr.-Ing. Ulrich Riebel ... · PDF fileLehrstuhl Mechanische Verfahrenstechnik Brandenburg Technical University, Cottbus. ... chtMultiRegionFOAM solver

Aug 27, 2018

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  • 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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