Multiphysics Modeling for Exhaust Gas Treatment - KIT - · PDF fileContents • What is...
Transcript of Multiphysics Modeling for Exhaust Gas Treatment - KIT - · PDF fileContents • What is...
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Multiphysics Modeling for Exhaust Gas Treatment
Henrik von Schenck, COMSOL AB, Sweden
© COPYRIGHT 2008, COMSOL, Inc
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Contents
• What is Multiphysics?• Capabilities and opportunities of COMSOL Multiphysics• Multiphysics modeling for exhaust gas treatment
– Case 1: Selective catalytic reduction of NO– Case 2: Abatement of VOC in a packed bed– Case 2: Abatement of VOC in a packed bed– Case 3: Diesel particulate filter (DPF)
• Concluding Remarks
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COMSOL
• Started in 1986 with agency products, markets only own products now.• Released COMSOL Multiphysics in1998.• 180 employees worldwide.• 16 offices, 12 in Europe, 3 in the US and 1 in India.• Distributors worldwide.
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COMSOL Products
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COMSOL Products
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What is Multiphysics?
• Reliable simulation requires accurate mathematical modelsElectromagnetics:
Maxwell’s equations
Structural Mechanics:Newton’s laws of motion
Thermal Analysis:Heat transfer equation
Fluid Flow:Navier-Stokes’ equations
• “Single physics” approach is limited since no phenomenon is isolated
• Today’s engineering challenges demand that multiphysics be addressed
Newton’s laws of motion Navier-Stokes’ equations
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The Multiphysics Approach
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Mass, Energy and Momentum Transport
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Mass, Energy and Momentum Transport
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Select from
Mass, Energy and Momentum Transport
Select from predefined modeling interfaces
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Select from
Create your multiphysics model
Mass, Energy and Momentum Transport
Select from predefined modeling interfaces
model
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Predefined Modeling Interfaces – Fluid Flow
• Example - Navier-Stokes equations for fluid flow
( ) ( )( )[ ] FuuIuuu +∇+∇+−⋅∇=∇⋅+
∂∂ Tpt
ηρρ
( )∂ρ ( ) 0=⋅∇+∂∂
uρρt
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Predefined Modeling Interfaces – Fluid Flow
• Couplings– Transport properties (ρ, η) dependent
upon• Temperature• Fluid composition
– Flow field affects– Flow field affects• Convective mass and energy
transport• Turbulent mixing
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Predefined Modeling Interfaces – Mass Transport
• Example - Convection, diffusion and reaction
( ) iiiii cRcDt
c ∇⋅−=∇−⋅∇+∂∂
ut∂
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Predefined Modeling Interfaces – Mass Transport
• Couplings– Affected by
• Convective transport (u)• Temperature (reaction rates, Di)
– Affects• Local mixture composition• Chemical reactions generate or
consume energy
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Predefined Modeling Interfaces – Heat Transfer
• Example – Energy transport by convection and conduction
( ) TCQTkt
TC pp ∇⋅−=∇−⋅∇+
∂∂
uρρt∂
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Predefined Modeling Interfaces – Heat Transfer
• Couplings– Affected by
• Convective transport (u)• Chemical composition• Exothermic/endothermic reactions
– Temperature affects– Temperature affects• Reaction rate• Transport properties
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Coupled Transport Processes
Flow
HeatMass
Convectivetransport
Chemical reactions
Exothermic reactions
Reaction rates
Gas expansion
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Equation Based Modeling
• Enter any PDE in general or coefficient form
FΓ =⋅∇+∂∂+
∂∂
tt
φφ2
2
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NO Reduction in a Catalytic Converter
• Competing reactions– NO reduction by NH3
– NH3 oxidation
• Eley-Rideal kinetics3
3
111NH
NHNO ac
acckr
+=
322 NHckr = )//(22
2 TRgEeAk −=
)//(11
1 TRgEeAk −=
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• Honeycomb monolith with V2O5/TiO2 catalyst
• A single monolith channel• Circular cross-section
approximation
NO Reduction in a Catalytic Converter
approximation
catalytic wash-coat
channel inlet
0.36 m
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Model Equations
• Fluid flow– Coupled free and porous media
flow– Navier-Stokes equations– Brinkman equations
Free flow
Porous media flow
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Model Equations
• Mass transport– N2, NO, NH3, O2, and H2O
transport through convection and diffusion in the open channel
– Diffusion and chemical reaction in the catalytic wash-coat
Non-reactive transport
the catalytic wash-coat
• Energy transport– Convection and conduction in the
open channel– Conduction and heat source due to
reaction in the porous structure
Chemical reaction
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Modeling in COMSOL Multiphysics
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VOC Abatement in a Packed Bed Reactor
• Parallel reactions– Hydrocarbon conversion– CO oxidation
OHCOOHC 22263 6692 +→+
22 22 COOCO →+
• Kinetic expressions2
11 )1(
6363
2
HCHCcoco
COCO
cKcK
cckr
++=
2
22 )1(
6363
263
HCHCcoco
COHC
cKcK
cckr
++=
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• Reactor Equations– Mass balance on the macro-scale;
convection, diffusion and reaction
Model Equations
( ) iiii cRcD ∇⋅−=∇−⋅∇ u
reactor pore scale ~mm
– Ri depends on the transport in the pellets, i.e. the flux into at the pellet surface times surface area per unit volume
– A pellet mass balance is required to calculate the flux
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Model Equations
• Pellet Equations– Mass balance on the micro-scale;
diffusion and reaction
( ) iii RcD ′=′∇′−⋅∇
rp
pellet pore scale ~µm
– Boundary conditions
– The concentration distribution in the pellet gives the flux at all r => the reaction term for the catalyst bed is given by the solution of the micro-scale mass balance
0=⋅′∇′− nii cD 0=r
ii cc ε=′prr =
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Model Equations
• 2 geometries– Reactor– Pellet
• Coupling variables connect the mass transport equations on mass transport equations on each geometry
– Reactor bulk concentrations are coupled to pellet surface concentrations.
– Pellet species surface flux is coupled to reactor mass source term
ii cc ε=′ nN ⋅== )( pipi rrAR
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• Reactor mass transport– C3H6, CO, CO2, H2O, and O2
– Convection, diffusion and reaction
Modeling in COMSOL Multiphysics
( ) cRcD ∇⋅−=∇−⋅∇ u( ) iiii cRcD ∇⋅−=∇−⋅∇ u
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Modeling in COMSOL Multiphysics
• Coupling variables– Couple dependent
variables on different geometries
– Pellet =>reactor
nN ⋅== )( pipi rrAR
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Modeling in COMSOL Multiphysics
• Pellet mass transport– C3H6, CO, CO2, H2O, and O2
– Diffusion and reaction
( ) iii RcD ′=′∇′−⋅∇ ( ) iii RcD ′=′∇′−⋅∇
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Modeling in COMSOL Multiphysics
• Coupling variables– Couple dependent
variables on different geometries
– Pellet =>reactor
– Reactor=>pellet
nN ⋅== )( pipi rrAR
ii cc ε=′
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Results – Reactor Species Distribution
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Results – Pellet Species Distribution
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Results
xr
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Capture and Combustion of Soot in a DPF
5.86x4.66x8 inches
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Model Equations
• Fluid flow– 1000’s of channels– Assume fully developed laminar
flow in the channels– Average flow field if proportional
u1
u2w
Hp1
p2
H/2 ∆xvm
to the pressure difference– Overall mass balance gives the
velocity in the channels– The channels are connected by
mass transfer across the porous membrane
( ) mvH
pkt 1111 4 ρρρ −=∇−⋅∇+
∂∂
( ) mvH
pkt 1222 4 ρρρ =∇−⋅∇+
∂∂
( )21 ppvm
m −=ηδ
κ
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Model Equations
• Soot balance– Soot enters channel 1– Deposition at the membrane
results in a sink term
u1
u2w
Hp1
p2
H/2 ∆xvm
( ) smsss cv
HccD
t
c 41 −=+∇−⋅∇+
∂∂
u
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Model Equations
• Species mass balances– O2, CO, and CO2
– O2 sink terms– Soot oxidation– Transfer across membrane
u1
u2w
Hp1
p2
H/2 ∆xvm
– Transfer across membrane
( ) sOmOOoO R
Hcv
HccD
t
c 441,211,21,22
1,2 −−=+∇−⋅∇+∂
∂u
( ) 2,222,22,222,2 4
OmOOOO cv
HccD
t
c=+∇−⋅∇+
∂∂
u
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Model Equations
• Soot layer thickness, δs
– Decreases through oxidation– Increases by deposition of soot
particles in the exhaust gas– Affects vm
u1
u2w
Hp1
p2
H/2 ∆xvm
ms
ss
s
ss vc
RM
t ρρδ +−=∂
∂
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Model Equations
• Energy balances– Channels– Filter walls; this temperature field
is connected for the entire system such that heat flow between channels
u1
u2w
Hp1
p2
H/2 ∆xvm
channels
( ) ( )11111111111
11
444TTh
HQ
HTvC
HTCTk
t
TC msmppp −++−=+∇−⋅∇+
∂∂ ρρρ u
( ) ( )22222222222
22
44TTh
HTvC
HTCTk
t
TC mmppp −+=+∇−⋅∇+
∂∂ ρρρ u
( ) ( ) ( )2111122 2 TTTh
TCTCv
Tkt
TC m
mpmp
m
mmm
mpmm −−+−−=∇−⋅∇+
∂∂
δρρ
δρ
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Predefined Modeling Interfaces
• 9 coupled partial differential equations
• Use predefined modeling interfaces
– Pressure driven flow; Darcy’s – Pressure driven flow; Darcy’s Law interface
– Mass transport; Convection and Diffusion interface
– Energy transport; Convection and Conduction interface
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The General Form PDE
• The general form PDE
• The equation for the soot
FΓ =⋅∇+∂∂+
∂∂
tt
φφ2
2
• The equation for the soot layer thickness
ms
ss
s
ss vc
RM
t ρρδ +−=∂
∂
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Equation System View
• All predefined equations are viewable and editable
– Modify anisotropic transport properties; permeability and thermal conductivities
• PDEs displayed on a general form
FΓ =⋅∇+∂∂+
∂∂
tt
φφ2
2
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Results – Flow Field
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Results – Temperature Distribution
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Results – Oxygen Concentration
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Results – Soot layer in a central channel
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Results – Soot layer in a peripheral channel
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Concluding Remarks
• COMSOL offers a simulation environment for unlimited Multiphysics couplings
• The Chemical Engineering Module provides many of the Module provides many of the equations describing fluid flow, mass, and energy transport in predefined modeling interfaces
• You can also type in your own equations directly into the graphical user intefarce
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• Model library– NO reduction, VOC abatement,
DPF– Model set up and solved + Model
doc
Resources and Contact
– COMSOL Multiphysics + Chemical Engineering Module ~100 models
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• Introduction to Chemical Engineering Simulations CD
• COMSOL Conference CD 2008• Contact, software trial, training and
support
Resources and Contact
support– www.comsol.com– [email protected]
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Thank you for your attention!