electrostatic precipitators - modelling and analytical ... · pdf fileelectrostatic...

ElectrostaticPrecipitators

DonatoRubinetti

Introduction

Assumptions

Electrostatics

COMSOLSetup

COMSOLSolution

AnalyticalVerification

Discussion

ExperimentalValidation

Summary

1

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

2

Outline

• Introduction

• Assumptions

• Electrostatics

• COMSOL Setup

• COMSOL Solution

• Analytical Verification

• Discussion

• Experimental Validation

• Summary


DonatoRubinetti

Introduction

Assumptions

Electrostatics

COMSOLSetup

COMSOLSolution


Discussion


Summary

3

IntroductionCutout of a wire-tube ESP

4000 𝑚𝑚 200 𝑚𝑚

0.3 𝑚𝑚

18 𝑘𝑉

𝑤0

𝑤𝑝

𝑟

𝑧

𝑤0


DonatoRubinetti

Introduction

Assumptions

Electrostatics

COMSOLSetup

COMSOLSolution


Discussion


Summary

4

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

5

ElectrostaticsNumerical Model

∇ ·E =ρelε0

(1)

E = −∇φ (2)

∇ · J = 0 (3)

J = ρel(��ZZw + bE)−��XXXXD∇ρel (4)

∇2φ = −ρelε0

(5)

E∇ρel = −ρel2

ε0(6)


DonatoRubinetti

Introduction

Assumptions

Electrostatics

COMSOLSetup

BoundaryConditions

Iteration Scheme

COMSOLSolution


Discussion


Summary

6

COMSOL SetupBoundary Conditions

Turbulent Flow

Electrostatics + PDE

Particle Tracing

No Slip Wall Free Slip Wall

Bounce Stick

𝜙2: Ground 𝜙1 = 18 𝑘𝑉

𝜌𝑒𝑙0=

𝑗0

𝑏 𝐸0

Outlet

Inlet

Outlet

Inlet

computational domain

𝑅1

𝑅2

𝑟

𝑧


DonatoRubinetti

Introduction

Assumptions

Electrostatics

COMSOLSetup

BoundaryConditions

Iteration Scheme

COMSOLSolution


Discussion


Summary

7

COMSOL SetupIteration Scheme

choose 𝑗0 on emitting

electrode

Dirichlet-BC on

emitting electrode

𝜌𝑒𝑙0=

𝑗0

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

no yes

yes


DonatoRubinetti

Introduction

Assumptions

Electrostatics

COMSOLSetup

COMSOLSolution

Particle results


Discussion


Summary

8

COMSOL SolutionParticle results


DonatoRubinetti

Introduction

Assumptions

Electrostatics

COMSOLSetup

COMSOLSolution


Discussion


Summary

9

Analytical VerficationElectric Field Strength along the radius


DonatoRubinetti

Introduction

Assumptions

Electrostatics

COMSOLSetup

COMSOLSolution


Discussion


Summary

10

Analytical VerficationSpace Charge Density along the radius


DonatoRubinetti

Introduction

Assumptions

Electrostatics

COMSOLSetup

COMSOLSolution


Discussion


Summary

11

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

12

Experimental ValidationAdaptation to other geometries

Setup

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

13

Experimental Validation


DonatoRubinetti

Introduction

Assumptions

Electrostatics

COMSOLSetup

COMSOLSolution


Discussion


Summary

14

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

15

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

Demo

16

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

Demo

17

AppendixCoupled Physics in ESPs


DonatoRubinetti

Appendix

IndustrialStandard

Coupled Physics

Velocity Profile


Exp. Validation I

Exp. ValidationII

MaxwellsEquations





ChargingProcesses

Demo

18

AppendixVelocity Profile


DonatoRubinetti

Appendix

IndustrialStandard

Coupled Physics

Velocity Profile


Exp. Validation I

Exp. ValidationII

MaxwellsEquations





ChargingProcesses

Demo

19

AppendixDimensionless Equations

E

E= E =

1

r

√1 + A(r2 − 1) (7)

ρelε0ErE

= ρel =A√

1 + A(r2 − 1)(8)

A =jrE

ε0bE2

(9)


DonatoRubinetti

Appendix

IndustrialStandard

Coupled Physics

Velocity Profile


Exp. Validation I

Exp. ValidationII

MaxwellsEquations





ChargingProcesses

Demo

20

AppendixExperimental Validation I

Space Charge Density


DonatoRubinetti

Appendix

IndustrialStandard

Coupled Physics

Velocity Profile


Exp. Validation I

Exp. ValidationII

MaxwellsEquations





ChargingProcesses

Demo

21

AppendixExperimental Validation II

Electric Potential


DonatoRubinetti

Appendix

IndustrialStandard

Coupled Physics

Velocity Profile


Exp. Validation I

Exp. ValidationII

MaxwellsEquations





ChargingProcesses

Demo

22

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

Demo

23

AppendixSchiller-Naumann Drag Model

FD =1

τpmpwp (14)

τp =4ρpdp

2

3µCDRep(15)

CD =24

Rep(1 + 0.15Rep

0.637) (16)

Rep =ρwpdpµ

(17)


DonatoRubinetti

Appendix

IndustrialStandard

Coupled Physics

Velocity Profile


Exp. Validation I

Exp. ValidationII

MaxwellsEquations





ChargingProcesses

Demo

24

AppendixCunningham Coefficient

λ ∼ 10−8m

Cc = 1 +λ

dp

[2.34 + 1.05 exp

(− 0.39

dpλ

)](18)

0.1

1

10

100

1000

10000

0.001 0.01 0.1 1 10 100 1000 10000 100000

Cunn

ingham

-‐Faktor

dp/λ


DonatoRubinetti

Appendix

IndustrialStandard

Coupled Physics

Velocity Profile


Exp. Validation I

Exp. ValidationII

MaxwellsEquations





ChargingProcesses

Demo

25

AppendixDeposition Efficiency

ηESP = 1− Nout

N0= 1− exp

(−wpAc

V

)(19)


DonatoRubinetti

Appendix

IndustrialStandard

Coupled Physics

Velocity Profile


Exp. Validation I

Exp. ValidationII

MaxwellsEquations





ChargingProcesses

Demo

26

AppendixCorona Onset Field Strength

E0 = 3× 106fr

(ms + 0.03

√ms

de2

)(20)

ms =p

pref

TrefT

(21)


DonatoRubinetti

Appendix

IndustrialStandard

Coupled Physics

Velocity Profile


Exp. Validation I

Exp. ValidationII

MaxwellsEquations





ChargingProcesses

Demo

27

AppendixParticle Charging Processes

Diffusion Charging

qd(t) =2πε0kTdp

eln

(1 +

t

τd

)(22)

Field Charging

qf (t) =

(3ε

ε+ 2

)πε0Edp

2 t

t+ τf(23)


DonatoRubinetti

Appendix

IndustrialStandard

Coupled Physics

Velocity Profile


Exp. Validation I

Exp. ValidationII

MaxwellsEquations





ChargingProcesses

Demo

28

AppendixDemo (Source: youtube.com/pentenrieder)


DonatoRubinetti

Appendix

IndustrialStandard

Coupled Physics

Velocity Profile


Exp. Validation I

Exp. ValidationII

MaxwellsEquations





ChargingProcesses

Demo

29

AppendixDemo


DonatoRubinetti

Appendix

IndustrialStandard

Coupled Physics

Velocity Profile


Exp. Validation I

Exp. ValidationII

MaxwellsEquations





ChargingProcesses

Demo

30

AppendixDemo


DonatoRubinetti

Appendix

IndustrialStandard

Coupled Physics

Velocity Profile


Exp. Validation I

Exp. ValidationII

MaxwellsEquations





ChargingProcesses

Demo

31

AppendixDemo


DonatoRubinetti

Appendix

IndustrialStandard

Coupled Physics

Velocity Profile


Exp. Validation I

Exp. ValidationII

MaxwellsEquations





ChargingProcesses

Demo

32

AppendixDemo

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