electrostatic precipitators - modelling and analytical verification...
TRANSCRIPT
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
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
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
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
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)
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
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
ElectrostaticPrecipitators
DonatoRubinetti
Introduction
Assumptions
Electrostatics
COMSOLSetup
COMSOLSolution
Particle results
AnalyticalVerification
Discussion
ExperimentalValidation
Summary
8
COMSOL SolutionParticle results
ElectrostaticPrecipitators
DonatoRubinetti
Introduction
Assumptions
Electrostatics
COMSOLSetup
COMSOLSolution
AnalyticalVerification
Discussion
ExperimentalValidation
Summary
9
Analytical VerficationElectric Field Strength along the radius
ElectrostaticPrecipitators
DonatoRubinetti
Introduction
Assumptions
Electrostatics
COMSOLSetup
COMSOLSolution
AnalyticalVerification
Discussion
ExperimentalValidation
Summary
10
Analytical VerficationSpace Charge Density along the radius
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
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.
ElectrostaticPrecipitators
DonatoRubinetti
Introduction
Assumptions
Electrostatics
COMSOLSetup
COMSOLSolution
AnalyticalVerification
Discussion
ExperimentalValidation
Summary
13
Experimental Validation
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
ElectrostaticPrecipitators
DonatoRubinetti
Introduction
Assumptions
Electrostatics
COMSOLSetup
COMSOLSolution
AnalyticalVerification
Discussion
ExperimentalValidation
Summary
15
Thank you for your attention.
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
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
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
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)
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
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
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)
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)
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
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)
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)
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)
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)
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
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
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
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