electrostatic precipitators

ElectrostaticPrecipitators

DonatoRubinetti

Introduction

Assumptions

Electrostatics

COMSOLSetup

COMSOLSolution

AnalyticalVerification

Discussion

ExperimentalValidation

Summary

Electrostatic PrecipitatorsModelling and Analytical Verification Concept

Donato Rubinetti 1 Daniel A. Weiss 1 Walter Egli 2

1Institute of Thermal- and Fluid-EngineeringUniversity of Applied Sciences Northwestern Switzerland

2EGW Software Engineering

DonatoRubinetti

Introduction

Assumptions

Electrostatics

COMSOLSetup

COMSOLSolution

Discussion

Summary

Outline

• Introduction

• Assumptions

• Electrostatics

• COMSOL Setup

• COMSOL Solution

• Analytical Verification

• Discussion

• Experimental Validation

• Summary

DonatoRubinetti

Introduction

Assumptions

Electrostatics

COMSOLSetup

COMSOLSolution

Discussion

Summary

IntroductionCutout of a wire-tube ESP

4000 𝑚𝑚 200 𝑚𝑚

0.3 𝑚𝑚

18 𝑘𝑉

𝑤𝑝

DonatoRubinetti

Introduction

Assumptions

Electrostatics

COMSOLSetup

COMSOLSolution

Discussion

Summary

Assumptions

• spherical particles

• fluid (air) incompressible, ideal gas behavior, turbulentflow

• fully developed velocity profile

• isothermal flow

• buoyancy neglected

• convective and diffusive terms neglected

• free slip electrode

DonatoRubinetti

Introduction

Assumptions

Electrostatics

Numerical Model

COMSOLSetup

COMSOLSolution

Discussion

Summary

ElectrostaticsNumerical Model

∇ ·E =ρelε0

E = −∇φ (2)

∇ · J = 0 (3)

J = ρel(��ZZw + bE)−��XXXXD∇ρel (4)

∇2φ = −ρelε0

E∇ρel = −ρel2

ε0(6)

DonatoRubinetti

Introduction

Assumptions

Electrostatics

COMSOLSetup

BoundaryConditions

Iteration Scheme

COMSOLSolution

Discussion

Summary

COMSOL SetupBoundary Conditions

Turbulent Flow

Electrostatics + PDE

Particle Tracing

No Slip Wall Free Slip Wall

Bounce Stick

𝜙2: Ground 𝜙1 = 18 𝑘𝑉

𝜌𝑒𝑙0=

𝑏 𝐸0

Outlet

computational domain

DonatoRubinetti

Introduction

Assumptions

Electrostatics

COMSOLSetup

BoundaryConditions

Iteration Scheme

COMSOLSolution

Discussion

Summary

COMSOL SetupIteration Scheme

choose 𝑗0 on emitting

electrode

Dirichlet-BC on

emitting electrode

𝜌𝑒𝑙0=

𝑏 𝐸0

Compute Poisson

continuity coupled

PDEs (5) & (6)

𝐸 𝑅1

≅ 𝐸0 ? 𝐸 𝑅1 < 𝐸0 ?

𝑗0 determined BC for 𝜌0 found

increase 𝑗0

decrease 𝑗0

no yes

DonatoRubinetti

Introduction

Assumptions

Electrostatics

COMSOLSetup

COMSOLSolution

Particle results

Discussion

Summary

COMSOL SolutionParticle results

DonatoRubinetti

Introduction

Assumptions

Electrostatics

COMSOLSetup

COMSOLSolution

Discussion

Summary

Analytical VerficationElectric Field Strength along the radius

DonatoRubinetti

Introduction

Assumptions

Electrostatics

COMSOLSetup

COMSOLSolution

Discussion

Summary

Analytical VerficationSpace Charge Density along the radius

DonatoRubinetti

Introduction

Assumptions

Electrostatics

COMSOLSetup

COMSOLSolution

Discussion

Summary

Discussion

Flow Simulation

• no slip - BC on emitting electrode

COMSOL Setup

• iteration scheme - computation time efficient and robust

• automation of the iterative procedure - fully coupledapproach (solver-tuning)

• include diffusion and convection in the physical model

Analytical Verification

• physical model is mathematically correct

• experimental validation is delicate

DonatoRubinetti

Introduction

Assumptions

Electrostatics

COMSOLSetup

COMSOLSolution

Discussion

Summary

Experimental ValidationAdaptation to other geometries

Source: Poppner, Marc et al. (2005): Electric Fields coupled with ion space charge. Part 1 + 2. Journal ofElectrostatics. Volume 63. S.775-787. Amsterdam: Elsevier.

DonatoRubinetti

Introduction

Assumptions

Electrostatics

COMSOLSetup

COMSOLSolution

Discussion

Summary

Experimental Validation

DonatoRubinetti

Introduction

Assumptions

Electrostatics

COMSOLSetup

COMSOLSolution

Discussion

Summary

Completed Points

• Simulation of an entire ESP including• Flow Simulation• Electrostatics + Charge Conservation• Particle Charging Processes• Particle Motion + Deposition Efficiency

Conclusions

• Customizable code needed (user-defined PDEs)

• Concept numerically robust and practical

• Analytical verification appropiate

• Experimental validation quite delicate

DonatoRubinetti

Introduction

Assumptions

Electrostatics

COMSOLSetup

COMSOLSolution

Discussion

Summary

Thank you for your attention.

DonatoRubinetti

Appendix

IndustrialStandard

Coupled Physics

Velocity Profile

Exp. Validation I

Exp. ValidationII

MaxwellsEquations

Schiller-Naumann-Drag

CunninghamCoefficient

DepositionEfficiency

Corona OnsetField Strength

ChargingProcesses

AppendixIndustrial Standard

Source: http://www.neundorfer.com/knowledgebase/electrostaticprecipitators. Accessed on 13/10/2015

DonatoRubinetti

Appendix

IndustrialStandard

Coupled Physics

Velocity Profile

Exp. Validation I

Exp. ValidationII

MaxwellsEquations

ChargingProcesses

AppendixCoupled Physics in ESPs

DonatoRubinetti

Appendix

IndustrialStandard

Coupled Physics

Velocity Profile

Exp. Validation I

Exp. ValidationII

MaxwellsEquations

ChargingProcesses

AppendixVelocity Profile

DonatoRubinetti

Appendix

IndustrialStandard

Coupled Physics

Velocity Profile

Exp. Validation I

Exp. ValidationII

MaxwellsEquations

ChargingProcesses

AppendixDimensionless Equations

E= E =

√1 + A(r2 − 1) (7)

ρelε0ErE

= ρel =A√

1 + A(r2 − 1)(8)

A =jrE

ε0bE2

DonatoRubinetti

Appendix

IndustrialStandard

Coupled Physics

Velocity Profile

Exp. Validation I

Exp. ValidationII

MaxwellsEquations

ChargingProcesses

AppendixExperimental Validation I

Space Charge Density

DonatoRubinetti

Appendix

IndustrialStandard

Coupled Physics

Velocity Profile

Exp. Validation I

Exp. ValidationII

MaxwellsEquations

ChargingProcesses

AppendixExperimental Validation II

Electric Potential

DonatoRubinetti

Appendix

IndustrialStandard

Coupled Physics

Velocity Profile

Exp. Validation I

Exp. ValidationII

MaxwellsEquations

ChargingProcesses

AppendixMaxwells Equations

∇ ·D = ρel (10)

∇×H − ∂D

∂t= J (11)

∇×E +∂B

∂t= 0 (12)

∇ ·B = 0 (13)

DonatoRubinetti

Appendix

IndustrialStandard

Coupled Physics

Velocity Profile

Exp. Validation I

Exp. ValidationII

MaxwellsEquations

ChargingProcesses

AppendixSchiller-Naumann Drag Model

τpmpwp (14)

τp =4ρpdp

3µCDRep(15)

CD =24

Rep(1 + 0.15Rep

0.637) (16)

Rep =ρwpdpµ

DonatoRubinetti

Appendix

IndustrialStandard

Coupled Physics

Velocity Profile

Exp. Validation I

Exp. ValidationII

MaxwellsEquations

ChargingProcesses

AppendixCunningham Coefficient

λ ∼ 10−8m

Cc = 1 +λ

[2.34 + 1.05 exp

(− 0.39

)](18)

0.001 0.01 0.1 1 10 100 1000 10000 100000

ingham

-‐Faktor

DonatoRubinetti

Appendix

IndustrialStandard

Coupled Physics

Velocity Profile

Exp. Validation I

Exp. ValidationII

MaxwellsEquations

ChargingProcesses

AppendixDeposition Efficiency

ηESP = 1− Nout

N0= 1− exp

(−wpAc

DonatoRubinetti

Appendix

IndustrialStandard

Coupled Physics

Velocity Profile

Exp. Validation I

Exp. ValidationII

MaxwellsEquations

ChargingProcesses

AppendixCorona Onset Field Strength

E0 = 3× 106fr

(ms + 0.03

DonatoRubinetti

Appendix

IndustrialStandard

Coupled Physics

Velocity Profile

Exp. Validation I

Exp. ValidationII

MaxwellsEquations

ChargingProcesses

AppendixParticle Charging Processes

Diffusion Charging

qd(t) =2πε0kTdp

Field Charging

qf (t) =

)πε0Edp

t+ τf(23)

DonatoRubinetti

Appendix

IndustrialStandard

Coupled Physics

Velocity Profile

Exp. Validation I

Exp. ValidationII

MaxwellsEquations

ChargingProcesses

AppendixDemo (Source: youtube.com/pentenrieder)

DonatoRubinetti

Appendix

IndustrialStandard

Coupled Physics

Velocity Profile

Exp. Validation I

Exp. ValidationII

MaxwellsEquations

ChargingProcesses

AppendixDemo

DonatoRubinetti

Appendix

IndustrialStandard

Coupled Physics

Velocity Profile

Exp. Validation I

Exp. ValidationII

MaxwellsEquations

ChargingProcesses

AppendixDemo

DonatoRubinetti

Appendix

IndustrialStandard

Coupled Physics

Velocity Profile

Exp. Validation I

Exp. ValidationII

MaxwellsEquations

ChargingProcesses

AppendixDemo

DonatoRubinetti

Appendix

IndustrialStandard

Coupled Physics

Velocity Profile

Exp. Validation I

Exp. ValidationII

MaxwellsEquations

ChargingProcesses

AppendixDemo

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