electrostatic precipitators - modelling and analytical verification...
TRANSCRIPT
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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
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ElectrostaticPrecipitators
DonatoRubinetti
Introduction
Assumptions
Electrostatics
COMSOLSetup
COMSOLSolution
AnalyticalVerification
Discussion
ExperimentalValidation
Summary
2
Outline
• Introduction
• Assumptions
• Electrostatics
• COMSOL Setup
• COMSOL Solution
• Analytical Verification
• Discussion
• Experimental Validation
• Summary
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ElectrostaticPrecipitators
DonatoRubinetti
Introduction
Assumptions
Electrostatics
COMSOLSetup
COMSOLSolution
AnalyticalVerification
Discussion
ExperimentalValidation
Summary
3
IntroductionCutout of a wire-tube ESP
4000 𝑚𝑚 200 𝑚𝑚
0.3 𝑚𝑚
18 𝑘𝑉
𝑤0
𝑤𝑝
𝑟
𝑧
𝑤0
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ElectrostaticPrecipitators
DonatoRubinetti
Introduction
Assumptions
Electrostatics
COMSOLSetup
COMSOLSolution
AnalyticalVerification
Discussion
ExperimentalValidation
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
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ElectrostaticPrecipitators
DonatoRubinetti
Introduction
Assumptions
Electrostatics
Numerical Model
COMSOLSetup
COMSOLSolution
AnalyticalVerification
Discussion
ExperimentalValidation
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)
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ElectrostaticPrecipitators
DonatoRubinetti
Introduction
Assumptions
Electrostatics
COMSOLSetup
BoundaryConditions
Iteration Scheme
COMSOLSolution
AnalyticalVerification
Discussion
ExperimentalValidation
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
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ElectrostaticPrecipitators
DonatoRubinetti
Introduction
Assumptions
Electrostatics
COMSOLSetup
BoundaryConditions
Iteration Scheme
COMSOLSolution
AnalyticalVerification
Discussion
ExperimentalValidation
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
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ElectrostaticPrecipitators
DonatoRubinetti
Introduction
Assumptions
Electrostatics
COMSOLSetup
COMSOLSolution
Particle results
AnalyticalVerification
Discussion
ExperimentalValidation
Summary
8
COMSOL SolutionParticle results
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ElectrostaticPrecipitators
DonatoRubinetti
Introduction
Assumptions
Electrostatics
COMSOLSetup
COMSOLSolution
AnalyticalVerification
Discussion
ExperimentalValidation
Summary
9
Analytical VerficationElectric Field Strength along the radius
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ElectrostaticPrecipitators
DonatoRubinetti
Introduction
Assumptions
Electrostatics
COMSOLSetup
COMSOLSolution
AnalyticalVerification
Discussion
ExperimentalValidation
Summary
10
Analytical VerficationSpace Charge Density along the radius
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ElectrostaticPrecipitators
DonatoRubinetti
Introduction
Assumptions
Electrostatics
COMSOLSetup
COMSOLSolution
AnalyticalVerification
Discussion
ExperimentalValidation
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
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ElectrostaticPrecipitators
DonatoRubinetti
Introduction
Assumptions
Electrostatics
COMSOLSetup
COMSOLSolution
AnalyticalVerification
Discussion
ExperimentalValidation
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.
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ElectrostaticPrecipitators
DonatoRubinetti
Introduction
Assumptions
Electrostatics
COMSOLSetup
COMSOLSolution
AnalyticalVerification
Discussion
ExperimentalValidation
Summary
13
Experimental Validation
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ElectrostaticPrecipitators
DonatoRubinetti
Introduction
Assumptions
Electrostatics
COMSOLSetup
COMSOLSolution
AnalyticalVerification
Discussion
ExperimentalValidation
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
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ElectrostaticPrecipitators
DonatoRubinetti
Introduction
Assumptions
Electrostatics
COMSOLSetup
COMSOLSolution
AnalyticalVerification
Discussion
ExperimentalValidation
Summary
15
Thank you for your attention.
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ElectrostaticPrecipitators
DonatoRubinetti
Appendix
IndustrialStandard
Coupled Physics
Velocity Profile
AnalyticalVerification
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
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ElectrostaticPrecipitators
DonatoRubinetti
Appendix
IndustrialStandard
Coupled Physics
Velocity Profile
AnalyticalVerification
Exp. Validation I
Exp. ValidationII
MaxwellsEquations
Schiller-Naumann-Drag
CunninghamCoefficient
DepositionEfficiency
Corona OnsetField Strength
ChargingProcesses
Demo
17
AppendixCoupled Physics in ESPs
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ElectrostaticPrecipitators
DonatoRubinetti
Appendix
IndustrialStandard
Coupled Physics
Velocity Profile
AnalyticalVerification
Exp. Validation I
Exp. ValidationII
MaxwellsEquations
Schiller-Naumann-Drag
CunninghamCoefficient
DepositionEfficiency
Corona OnsetField Strength
ChargingProcesses
Demo
18
AppendixVelocity Profile
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ElectrostaticPrecipitators
DonatoRubinetti
Appendix
IndustrialStandard
Coupled Physics
Velocity Profile
AnalyticalVerification
Exp. Validation I
Exp. ValidationII
MaxwellsEquations
Schiller-Naumann-Drag
CunninghamCoefficient
DepositionEfficiency
Corona OnsetField Strength
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)
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ElectrostaticPrecipitators
DonatoRubinetti
Appendix
IndustrialStandard
Coupled Physics
Velocity Profile
AnalyticalVerification
Exp. Validation I
Exp. ValidationII
MaxwellsEquations
Schiller-Naumann-Drag
CunninghamCoefficient
DepositionEfficiency
Corona OnsetField Strength
ChargingProcesses
Demo
20
AppendixExperimental Validation I
Space Charge Density
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ElectrostaticPrecipitators
DonatoRubinetti
Appendix
IndustrialStandard
Coupled Physics
Velocity Profile
AnalyticalVerification
Exp. Validation I
Exp. ValidationII
MaxwellsEquations
Schiller-Naumann-Drag
CunninghamCoefficient
DepositionEfficiency
Corona OnsetField Strength
ChargingProcesses
Demo
21
AppendixExperimental Validation II
Electric Potential
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ElectrostaticPrecipitators
DonatoRubinetti
Appendix
IndustrialStandard
Coupled Physics
Velocity Profile
AnalyticalVerification
Exp. Validation I
Exp. ValidationII
MaxwellsEquations
Schiller-Naumann-Drag
CunninghamCoefficient
DepositionEfficiency
Corona OnsetField Strength
ChargingProcesses
Demo
22
AppendixMaxwells Equations
∇ ·D = ρel (10)
∇×H − ∂D
∂t= J (11)
∇×E +∂B
∂t= 0 (12)
∇ ·B = 0 (13)
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ElectrostaticPrecipitators
DonatoRubinetti
Appendix
IndustrialStandard
Coupled Physics
Velocity Profile
AnalyticalVerification
Exp. Validation I
Exp. ValidationII
MaxwellsEquations
Schiller-Naumann-Drag
CunninghamCoefficient
DepositionEfficiency
Corona OnsetField Strength
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)
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ElectrostaticPrecipitators
DonatoRubinetti
Appendix
IndustrialStandard
Coupled Physics
Velocity Profile
AnalyticalVerification
Exp. Validation I
Exp. ValidationII
MaxwellsEquations
Schiller-Naumann-Drag
CunninghamCoefficient
DepositionEfficiency
Corona OnsetField Strength
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
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ElectrostaticPrecipitators
DonatoRubinetti
Appendix
IndustrialStandard
Coupled Physics
Velocity Profile
AnalyticalVerification
Exp. Validation I
Exp. ValidationII
MaxwellsEquations
Schiller-Naumann-Drag
CunninghamCoefficient
DepositionEfficiency
Corona OnsetField Strength
ChargingProcesses
Demo
25
AppendixDeposition Efficiency
ηESP = 1− Nout
N0= 1− exp
(−wpAc
V
)(19)
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ElectrostaticPrecipitators
DonatoRubinetti
Appendix
IndustrialStandard
Coupled Physics
Velocity Profile
AnalyticalVerification
Exp. Validation I
Exp. ValidationII
MaxwellsEquations
Schiller-Naumann-Drag
CunninghamCoefficient
DepositionEfficiency
Corona OnsetField Strength
ChargingProcesses
Demo
26
AppendixCorona Onset Field Strength
E0 = 3× 106fr
(ms + 0.03
√ms
de2
)(20)
ms =p
pref
TrefT
(21)
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ElectrostaticPrecipitators
DonatoRubinetti
Appendix
IndustrialStandard
Coupled Physics
Velocity Profile
AnalyticalVerification
Exp. Validation I
Exp. ValidationII
MaxwellsEquations
Schiller-Naumann-Drag
CunninghamCoefficient
DepositionEfficiency
Corona OnsetField Strength
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)
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ElectrostaticPrecipitators
DonatoRubinetti
Appendix
IndustrialStandard
Coupled Physics
Velocity Profile
AnalyticalVerification
Exp. Validation I
Exp. ValidationII
MaxwellsEquations
Schiller-Naumann-Drag
CunninghamCoefficient
DepositionEfficiency
Corona OnsetField Strength
ChargingProcesses
Demo
28
AppendixDemo (Source: youtube.com/pentenrieder)
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ElectrostaticPrecipitators
DonatoRubinetti
Appendix
IndustrialStandard
Coupled Physics
Velocity Profile
AnalyticalVerification
Exp. Validation I
Exp. ValidationII
MaxwellsEquations
Schiller-Naumann-Drag
CunninghamCoefficient
DepositionEfficiency
Corona OnsetField Strength
ChargingProcesses
Demo
29
AppendixDemo
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ElectrostaticPrecipitators
DonatoRubinetti
Appendix
IndustrialStandard
Coupled Physics
Velocity Profile
AnalyticalVerification
Exp. Validation I
Exp. ValidationII
MaxwellsEquations
Schiller-Naumann-Drag
CunninghamCoefficient
DepositionEfficiency
Corona OnsetField Strength
ChargingProcesses
Demo
30
AppendixDemo
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ElectrostaticPrecipitators
DonatoRubinetti
Appendix
IndustrialStandard
Coupled Physics
Velocity Profile
AnalyticalVerification
Exp. Validation I
Exp. ValidationII
MaxwellsEquations
Schiller-Naumann-Drag
CunninghamCoefficient
DepositionEfficiency
Corona OnsetField Strength
ChargingProcesses
Demo
31
AppendixDemo
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ElectrostaticPrecipitators
DonatoRubinetti
Appendix
IndustrialStandard
Coupled Physics
Velocity Profile
AnalyticalVerification
Exp. Validation I
Exp. ValidationII
MaxwellsEquations
Schiller-Naumann-Drag
CunninghamCoefficient
DepositionEfficiency
Corona OnsetField Strength
ChargingProcesses
Demo
32
AppendixDemo