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Matteo CalonaciFederica Furnari
A COMPUTATIONAL FRAMEWORK FOR THESIMULATION OF GAS-SOLID CATALYTIC REACTORSBASED ON A MULTIREGION APPROACH
Anno accademico 2011-2012
Dipartimento di Energia &Dipartimento CMIC Giulio Natta
Relatori: Dr. Alberto Cuoci & Dr. Matteo Maestri
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Background
Catalytic Reactor Engineering
Catalytic Reactor Design~90% of industrialchemical processes
are catalytic
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Background
Catalytic Reactor Engineering
Catalytic Reactor Design~90% of industrialchemical processes
are catalytic
Need for an accuratedesign to provide
high yields ($)
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Background
Catalytic Reactor Engineering
Catalytic Reactor Design~90% of industrialchemical processes
are catalytic
Need for an accuratedesign to provide
high yields ($)
Need for a deepunderstanding foradvanced design
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Time [s]
Length[m]
MICROSCALE
MESOSCALE
MACROSCALE100
10-6
10-3
10-9
10-15 10-6 100
(*) Microkinetic analysis of complex chemical processes at surfaces
M. Maestriin New strategy for chemical synthesis and catalysis Wiley, 2011
Background
A Multiscale Phenomenon
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Time [s]
Length[m]
MICROSCALE
Making and breakingof chemical bond
MESOSCALE
MACROSCALE100
10-6
10-3
10-9
10-15 10-6 100
(*) Microkinetic analysis of complex chemical processes at surfaces
M. Maestriin New strategy for chemical synthesis and catalysis Wiley, 2011
Background
A Multiscale Phenomenon
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Time [s]
Length[m]
MICROSCALE
Making and breakingof chemical bond
MESOSCALE
Interplay among thechemical events
MACROSCALE100
10-6
10-3
10-9
10-15 10-6 100
(*) Microkinetic analysis of complex chemical processes at surfaces
M. Maestriin New strategy for chemical synthesis and catalysis Wiley, 2011
Background
A Multiscale Phenomenon
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Time [s]
Length[m]
MICROSCALE
Making and breakingof chemical bond
MESOSCALE
Interplay among thechemical events
MACROSCALE
Mass and energytransport phenomena
100
10-6
10-3
10-9
10-15 10-6 100
(*) Microkinetic analysis of complex chemical processes at surfaces
M. Maestriin New strategy for chemical synthesis and catalysis Wiley, 2011
Background
A Multiscale Phenomenon
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Time [s]
Length[m]
MICROSCALE
Making and breakingof chemical bond
MESOSCALE
Interplay among thechemical events
MACROSCALE
Mass and energytransport phenomena
Developmentof a new solver
100
10-6
10-3
10-9
10-15 10-6 100
(*) Microkinetic analysis of complex chemical processes at surfaces
M. Maestriin New strategy for chemical synthesis and catalysis Wiley, 2011
Background
A Multiscale Phenomenon
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Time [s]
Length[m]
MICROSCALE
MACROSCALE100
10-6
10-3
10-9
10-15 10-6 100
(*) Microkinetic analysis of complex chemical processes at surfaces
M. Maestriin New strategy for chemical synthesis and catalysis Wiley, 2011
Background
A Multiscale Phenomenon
MESOSCALE
k d
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Time [s]
Length[m]
MICROSCALE
Detailed kineticmechanism
MACROSCALE100
10-6
10-3
10-9
10-15 10-6 100
(*) Microkinetic analysis of complex chemical processes at surfaces
M. Maestriin New strategy for chemical synthesis and catalysis Wiley, 2011
Background
A Multiscale Phenomenon
MESOSCALE
B k d
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Time [s]
Length[m]
MICROSCALE
Detailed kineticmechanism
MACROSCALE100
10-6
10-3
10-9
10-15 10-6 100
(*) Microkinetic analysis of complex chemical processes at surfaces
M. Maestriin New strategy for chemical synthesis and catalysis Wiley, 2011
Background
A Multiscale Phenomenon
MESOSCALE
Mean fieldapproximation
B k d
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Time [s]
Length[m]
MICROSCALE
Detailed kineticmechanism
MACROSCALE
CFD
100
10-6
10-3
10-9
10-15 10-6 100
(*) Microkinetic analysis of complex chemical processes at surfaces
M. Maestriin New strategy for chemical synthesis and catalysis Wiley, 2011
Background
A Multiscale Phenomenon
MESOSCALE
Mean fieldapproximation
Th Ph i l P bl
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The Physical Problem
Phases of a Catalytic Reaction
Fluid Phase
Th Ph i l P bl
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The Physical Problem
Phases of a Catalytic Reaction
Fluid Phase
The Ph sical Problem
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The Physical Problem
Phases of a Catalytic Reaction
Intra-solid phenomena not detailed
Fluid Phase
The Physical Problem
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The Physical Problem
Phases of a Catalytic Reaction
Intra-solid phenomena not detailed
Unacceptable if transport limitations
in the catalyst play a major role!
Fluid Phase
The Physical Problem
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The Physical Problem
Phases of a Catalytic Reaction
All steps of a catalytic reactive process
need to be described
Fluid Phase
The Physical Problem
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The Physical Problem
Phases of a Catalytic Reaction
All steps of a catalytic reactive process
need to be described
Model intra-phase phenomena in the solid
Fluid Phase
The Physical Problem
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The Physical Problem
Phases of a Catalytic Reaction
multiRegion
All steps of a catalytic reactive process
need to be described
Model intra-phase phenomena in the solid
Fluid Phase
The Physical Problem
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The Physical Problem
Aim of the work
multiRegion
The solid phase needs to becharacterized:
Fluid Phase
The Physical Problem
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The Physical Problem
Aim of the work
multiRegion
The solid phase needs to becharacterized:
Mathematical model to describetransport and reactive phenomena
Fluid Phase
The Physical Problem
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The Physical Problem
Aim of the work
multiRegion
The solid phase needs to becharacterized:
Mathematical model to describetransport and reactive phenomena
()
()
kT ()
0
Fluid Phase
Fluid Phase
The Physical Problem
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The Physical Problem
Aim of the work
multiRegion
The solid phase needs to becharacterized:
Mathematical model to describetransport and reactive phenomena
()
()
kT ()
0
() , ( , )
,()
kT ,
,
Fluid Phase
Solid Phase
Fluid Phase
The Physical Problem
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The Physical Problem
Aim of the work
multiRegion
The solid phase needs to becharacterized:
Mathematical model to describetransport and reactive phenomena
()
()
kT ()
0
Separate pseudo-phase with effectiveproperties
() , ( , )
,()
kT ,
,
Fluid Phase
Solid Phase
Fluid Phase
The Physical Problem
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The Physical Problem
Aim of the work
multiRegion
The solid phase needs to becharacterized:
Mathematical model to describetransport and reactive phenomena
()
()
kT ()
0
Separate pseudo-phase with effectiveproperties
Need to correctly describe twophase coupling at the interface
() , ( , )
,()
kT ,
,
Fluid Phase
Solid Phase
Fluid Phase
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Outline
MultiRegion Structure
Multiple meshes Mixed BCs at the interface Coupling partitioned approach
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Outline
MultiRegion Structure
Multiple meshes Mixed BCs at the interface Coupling partitioned approach
Numerical Tests
Coupling strategy effectiveness Splitting operator testing Test global architecture with cases of increasing complexity
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Outline
MultiRegion Structure
Multiple meshes Mixed BCs at the interface Coupling partitioned approach
Numerical Tests
Coupling strategy effectiveness Splitting operator testing Test global architecture with cases of increasing complexity
Solver Validation Comparison with experimental data
Importance of intra-solid phenomena description
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Outline
MultiRegion Structure
Multiple meshes Mixed BCs at the interface Coupling partitioned approach
Numerical Tests
Coupling strategy effectiveness Splitting operator testing Test global architecture with cases of increasing complexity
Solver Validation Comparison with experimental data
Importance of intra-solid phenomena description
Conclusions
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Outline
MultiRegion Structure
Multiple meshes Mixed BCs at the interface Coupling partitioned approach
Numerical Tests
Coupling strategy effectiveness Splitting operator testing Test global architecture with cases of increasing complexity
Solver Validation Comparison with experimental data
Importance of intra-solid phenomena description
Conclusions
New Structure
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Multiple Meshes for Multiple Regions
MultiRegion nature of the solver
New Structure
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Multiple Meshes for Multiple Regions
Mesh 1: Fluid Region
Mesh 2: Solid Region 1
Multiple meshes
Mesh 3: Solid Region 2
MultiRegion nature of the solver
New Structure
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Multiple Meshes for Multiple Regions
Mesh 1: Fluid Region
Mesh 2: Solid Region 1
Multiple meshes
Different propertiesfor each region
Mesh 3: Solid Region 2
MultiRegion nature of the solver
New Structure
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Multiple Meshes for Multiple Regions
Mesh 1: Fluid Region
Mesh 2: Solid Region 1
Multiple meshes
Different propertiesfor each region
Separate governingequations on each cell
Mesh 3: Solid Region 2
MultiRegion nature of the solver
New Structure
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Multiple Meshes for Multiple Regions
Mesh 1: Fluid Region
Mesh 2: Solid Region 1
Multiple meshes
Different propertiesfor each region
Separate governingequations on each cell
Full support for multiregion post-processing
Mesh 3: Solid Region 2
MultiRegion nature of the solver
Make Separate Regions Interact
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Boundary conditions for coupled interfaces
How to couple at theinterface ?
Make Separate Regions Interact
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Boundary conditions for coupled interfaces
How to couple at theinterface ?
INBR,IOWN,
)(INBR,)(IOWN,
T=T
Tk=TkINBRIOWN
INBR,IOWN,C=C
CD=CDINBRNBRIOWNOWN
Make Separate Regions Interact
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Boundary conditions for coupled interfaces
2 different
approaches
How to couple at theinterface ?
INBR,IOWN,
)(INBR,)(IOWN,
T=T
Tk=TkINBRIOWN
INBR,IOWN,C=C
CD=CDINBRNBRIOWNOWN
Make Separate Regions Interact
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Boundary conditions for coupled interfaces
Monolithicworks on multiple meshesjust for loose inter-equationcoupling
2 different
approaches
How to couple at theinterface ?
INBR,IOWN,
)(INBR,)(IOWN,
T=T
Tk=TkINBRIOWN
INBR,IOWN,C=C
CD=CDINBRNBRIOWNOWN
Make Separate Regions Interact
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Boundary conditions for coupled interfaces
Monolithicworks on multiple meshesjust for loose inter-equationcoupling
PartitionedWorks on multiple mesheseven for stiff inter-equationcoupling
2 different
approaches
How to couple at theinterface ?
INBR,IOWN,
)(INBR,)(IOWN,
T=T
Tk=TkINBRIOWN
INBR,IOWN,C=C
CD=CDINBRNBRIOWNOWN
Make Separate Regions Interact
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How to Couple at the Interface?
Mixed boundary
conditions at theinterface
INBR,IOWN,
)(INBR,)(IOWN,
T=T
Tk=TkINBRIOWN
INBR,IOWN,C=C
CD=CDINBRNBRIOWNOWN
Make Separate Regions Interact
l h f
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How to Couple at the Interface?
NBR
NBR
OWN
OWN
NBR
NBRNBR
OWN
OWNOWN
I.OWN
k+
k
Tk+
Tk
=T
NBR
NBR
OWN
OWN
NBR
NBRNBR
OWN
OWNOWN
I.OWN
D
+
D
CD+
CD
=C
Mixed boundary
conditions at theinterface
INBR,IOWN,
)(INBR,)(IOWN,
T=T
Tk=TkINBRIOWN
INBR,IOWN,C=C
CD=CDINBRNBRIOWNOWN
Make Separate Regions Interact
l h f
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How to Couple at the Interface?
Partitioned Approach
1) Solve in each zone with mixed BCs
NBR
NBR
OWN
OWN
NBR
NBRNBR
OWN
OWNOWN
I.OWN
k+
k
Tk+
Tk
=T
NBR
NBR
OWN
OWN
NBR
NBRNBR
OWN
OWNOWN
I.OWN
D
+
D
CD+
CD
=C
Mixed boundary
conditions at theinterface
INBR,IOWN,
)(INBR,)(IOWN,
T=T
Tk=TkINBRIOWN
INBR,IOWN,C=C
CD=CDINBRNBRIOWNOWN
Make Separate Regions Interact
l h f
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How to Couple at the Interface?
Partitioned Approach
1) Solve in each zone with mixed BCs
2) Update interface values and solve in theneighboring region
NBR
NBR
OWN
OWN
NBR
NBRNBR
OWN
OWNOWN
I.OWN
k+
k
Tk+
Tk
=T
NBR
NBR
OWN
OWN
NBR
NBRNBR
OWN
OWNOWN
I.OWN
D
+
D
CD+
CD
=C
Mixed boundary
conditions at theinterface
INBR,IOWN,
)(INBR,)(IOWN,
T=T
Tk=TkINBRIOWN
INBR,IOWN,C=C
CD=CDINBRNBRIOWNOWN
Make Separate Regions Interact
H C l h I f ?
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How to Couple at the Interface?
Partitioned Approach
1) Solve in each zone with mixed BCs
2) Update interface values and solve in theneighboring region
3) Iterate till convergence is reached
NBR
NBR
OWN
OWN
NBR
NBRNBR
OWN
OWNOWN
I.OWN
k+
k
Tk+
Tk
=T
NBR
NBR
OWN
OWN
NBR
NBRNBR
OWN
OWNOWN
I.OWN
D
+
D
CD+
CD
=C
Mixed boundary
conditions at theinterface
INBR,IOWN,
)(INBR,)(IOWN,
T=T
Tk=TkINBRIOWN
INBR,IOWN,C=C
CD=CDINBRNBRIOWNOWN
Make Separate Regions Interact
H t C l t th I t f ?
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How to Couple at the Interface?
Partitioned Approach
1) Solve in each zone with mixed BCs
2) Update interface values and solve in theneighboring region
3) Iterate till convergence is reached
Embedded in two newly coded libraries
NBR
NBR
OWN
OWN
NBR
NBRNBR
OWN
OWNOWN
I.OWN
k+
k
Tk+
Tk
=T
NBR
NBR
OWN
OWN
NBR
NBRNBR
OWN
OWNOWN
I.OWN
D
+
D
CD+
CD
=C
Mixed boundary
conditions at theinterface
INBR,IOWN,
)(INBR,)(IOWN,
T=T
Tk=TkINBRIOWN
INBR,IOWN,C=C
CD=CDINBRNBRIOWNOWN
The partitioned approach for heat and mass transfer coupling
C li L S
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Coupling Loop Structure
The partitioned approach for heat and mass transfer coupling
C li L St t
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Fluid Region
with the mixed BCs on the interface:
SOL
SOL
FLU
FLU
SOL
SOLSOL
FLU
FLUFLU
k+
k
Tk+
Tk
=T
FLUI,
SOL
SOL
FLU
FLU
SOL
SOLSOL
FLU
FLUFLU
D+
D
CD+
CD
=C
FLUI,
)(
imix,
TCTk=dt
Tcd
YYD=dt
Yd
mix
p
pmat
iimix
imix
Coupling Loop Structure
The partitioned approach for heat and mass transfer coupling
C li L St t
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FLU
FLU
SOL
SOL
FLU
FLUFLU
SOL
SOLSOL
D+
D
CD+
CD
=C
SOLI,
Tk=dt
Tcd
YD=dt
Yd
pmat
imix
imix
imix,
FLU
FLU
SOL
SOL
FLU
FLUFLU
SOL
SOLSOL
k+
k
Tk+
Tk
=T
SOLI,
Solid Region Fluid Region
with the mixed BCs on the interface: with the mixed BCs on the interface:
SOL
SOL
FLU
FLU
SOL
SOLSOL
FLU
FLUFLU
k+
k
Tk+
Tk
=T
FLUI,
SOL
SOL
FLU
FLU
SOL
SOLSOL
FLU
FLUFLU
D+
D
CD+
CD
=C
FLUI,
)(
imix,
TCTk=dt
Tcd
YYD=dt
Yd
mix
p
pmat
iimix
imix
Coupling Loop Structure
The partitioned approach for heat and mass transfer coupling
C li L St t
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Coupling Loop Structure
FLU
FLU
SOL
SOL
FLU
FLUFLU
SOL
SOLSOL
D+
D
CD+
CD
=C
SOLI,
Tk=dt
Tcd
YD=dt
Yd
pmat
imix
imix
imix,
FLU
FLU
SOL
SOL
FLU
FLUFLU
SOL
SOLSOL
k+
k
Tk+
Tk
=T
SOLI,
Solid Region Fluid Region
with the mixed BCs on the interface: with the mixed BCs on the interface:
SOL
SOL
FLU
FLU
SOL
SOLSOL
FLU
FLUFLU
k+
k
Tk+
Tk
=T
FLUI,
SOL
SOL
FLU
FLU
SOL
SOLSOL
FLU
FLUFLU
D+
D
CD+
CD
=C
FLUI,
Coupling Loop
Convergence Criteria
Y
k
i
k
i
T
kk
absTolYY
absTolTT
1
1
Y
k
i
k
i
k
i
T
kkk
relTolYYY
relTolTTT
11
11
CouplingMethod1) Solve alternatively for every cell ofthe 2 coupled regions
2) Check for convergence: if reached,proceed to next time step
)(
imix,
TCTk=dt
Tcd
YYD
=
dt
Yd
mix
p
pmat
iimix
imix
A Comprehensive Solver for Describing Multi-Region Phenomena
M ltiR i S l A hit t
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Solve Solid Solve Fluid
for each time step...
MultiRegion Solver Architecture
A Comprehensive Solver for Describing Multi-Region Phenomena
M ltiR i S l A hit t
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Solve Solid
Navier-stokes Equation
Pressure Corrector
Solve Fluid
for each time step...
P
ISOpredictor-correctorloop
MultiRegion Solver Architecture
Continuity Equation
A Comprehensive Solver for Describing Multi-Region Phenomena
M ltiR i S l A hit t
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Solve Solid
Navier-stokes Equation
Pressure Corrector
Fluid Chemistry
Update Fluid Properties
Solve Fluid
for each time step...
P
ISOpredictor-correctorloop
MultiRegion Solver Architecture
Continuity Equation
Mass Transfer Equation
Heat Transfer Equation
Homogeneous reactions
A Comprehensive Solver for Describing Multi-Region Phenomena
MultiRegion Solver Architecture
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Solve Solid
Solid Chemistry
Update Solid PropertiesNavier-stokes Equation
Pressure Corrector
Fluid Chemistry
Update Fluid Properties
Mass Transfer Equation
Heat Transfer Equation
Solve Fluid
for each time step...
P
ISOpredictor-correctorloop
MultiRegion Solver Architecture
Site species conservation
Homogeneous and heterogeneous reactions
Continuity Equation
Mass Transfer Equation
Heat Transfer Equation
Homogeneous reactions
A Comprehensive Solver for Describing Multi-Region Phenomena
MultiRegion Solver Architecture
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Solve Solid
Solid Chemistry
Update Solid PropertiesNavier-stokes Equation
Pressure Corrector
Fluid Chemistry
Update Fluid Properties
Mass Transfer Equation
Heat Transfer Equation
Solve Fluid
CouplingLoop
CouplingLoop
for each time step...
P
ISOpredictor-correctorloop
Coupling loopconvergence
check
MultiRegion Solver Architecture
Site species conservation
Homogeneous and heterogeneous reactions
Continuity Equation
Mass Transfer Equation
Heat Transfer Equation
Homogeneous reactions
Outline
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Outline
MultiRegion Structure
Multiple meshes Mixed BCs at the interface Coupling partitioned approach
Numerical Tests Coupling strategy effectiveness Splitting operator testing Test global architecture with cases of increasing complexity
Solver Validation Comparison with experimental data
Importance of intra-solid phenomena descriptionConclusions
Coupling Strategy Testing1 D Conjugate Heat Transfer
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1-D Conjugate Heat Transfer
Compare withanalyticalsolution at steady state
Coupling Strategy Testing1 D Conjugate Heat Transfer
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1-D Conjugate Heat Transfer
Compare withfully-coupledMatlab solver
Compare withanalyticalsolution
during transient
at steady state
Coupling Strategy Testing1 D Conjugate Heat Transfer
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Alluminium Steel
Hot side:
Fixed T = 500 [K]
Cold side:
Fixed T = 300 [K]
Initial T =
uniform 400 [K]Interface
Compare withfully-coupledMatlab solver
Compare withanalyticalsolution
during transient
at steady state
1-D Conjugate Heat Transfer
Coupling Strategy Testing1 D Conjugate Heat Transfer
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2
2
2
2
22
1
2
1
1
11
Tk=t
TCp
Tk=
t
TCp
K=x,T
K=T
K=T
=tT=tT
tT=tT
tx
Tk=t
x
Tk
4000
5000,0.1
3000,0
3000.1,5000,
0.05,0.05,
0.05,0.05,
2
1
2
1
21
22
11
Model equationsBoundary Conditions
Initial Conditions
Alluminium Steel
Hot side:
Fixed T = 500 [K]
Cold side:
Fixed T = 300 [K]
Initial T =
uniform 400 [K]Interface
Compare withfully-coupledMatlab solver
Compare withanalyticalsolution
during transient
at steady state
1-D Conjugate Heat Transfer
Coupling Strategy Testing1 D Conjugate Heat Transfer
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TransientSolution
Accurate prediction of T profilesalong the two bars :
Compared to fully-coupled solutionduring transient
Compared with the analytical solutionat steady state
Steady StateSolution
300
320
340
360
380
400
420
440
460
480
500
0 1 2 3 4 5 6 7 8 9 10
Temperature[K]
Bar Length [cm]
CatalyticFOAM
SolutionAnalytical
Solution
1-D Conjugate Heat Transfer
Does our splitting scheme make sense?
Testing MultiRegion Splitting Method
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Testing MultiRegion Splitting Method
How to test for validity of our splitting scheme ?
Does our splitting scheme make sense?
Testing MultiRegion Splitting Method
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Testing MultiRegion Splitting Method
How to test for validity of our splitting scheme ?
CatalyticFOAMMulti-Region
Solver
CatalyticFOAMMulti-Region
Solver
Does our splitting scheme make sense?
Testing MultiRegion Splitting Method
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Testing MultiRegion Splitting Method
How to test for validity of our splitting scheme ?
CatalyticFOAMMulti-Region
Solver
CatalyticFOAMMulti-Region
Solver
Matlab
Fully CoupledSolver
Does our splitting scheme make sense?
Testing MultiRegion Splitting Method
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Testing MultiRegion Splitting Method
How to test for validity of our splitting scheme ?
Effect of timestepCatalyticFOAM
Multi-RegionSolver
Matlab
Fully CoupledSolver
Does our splitting scheme make sense?
Testing MultiRegion Splitting Method
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Testing MultiRegion Splitting Method
How to test for validity of our splitting scheme ?
Effect of timestep
Effect of meshrefinement
CatalyticFOAMMulti-Region
Solver
Matlab
Fully CoupledSolver
Does our splitting scheme make sense?
Testing MultiRegion Splitting Method
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Testing MultiRegion Splitting Method
How to test for validity of our splitting scheme ?
Effect of timestep
Effect of meshrefinement
Test in differentconditions
CatalyticFOAMMulti-Region
Solver
Matlab
Fully CoupledSolver
Does our splitting scheme make sense?
Testing MultiRegion Splitting Method
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Testing MultiRegion Splitting Method
Test Case:
200 Fluid Cells
200 Solid Cells
2 Gas Phase Species
1 Reaction: A->B
Description:
Transport in the fluid region
Diffusion + Reaction in the solid region
Coupling at the interfaceA0.6
A0.4
How to test for validity of our splitting scheme ?
Effect of timestep
Effect of meshrefinement
Test in differentconditions
CatalyticFOAMMulti-Region
Solver
Matlab
Fully CoupledSolver
Does our splitting scheme make sense?
Testing MultiRegion Splitting Method
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Decreasing time step
Testing MultiRegion Splitting Method
0.010
0.012
0.014
0.016
0.018
0.020
0.022
0.024
0.0 0.2 0.4 0.6 0.8 1.0
CA
[mol/m3]
Slab Length [cm]
dt=1e-4
dt=1e-5
dt=1e-6
fully coupled
dt = 110-4 dt = 110-5 dt = 110-6
8.3810-5 2.6510-5 5.2410-6
Euclidean norm of the error
Does our splitting scheme make sense?
Testing MultiRegion Splitting Method
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Decreasing time step
Using a finer mesh
0.010
0.012
0.014
0.016
0.018
0.020
0.022
0.024
0.0 0.2 0.4 0.6 0.8 1.0
CA
[mol/m3]
Slab Length [cm]
dt=1e-4
dt=1e-5
dt=1e-6
fully coupled
0
0.005
0.01
0.015
0.02
0.025
0.03
0 0.5 1
CA
[mol/m3]
Slab Length [cm]
10 Cells
50 Cells
100 Cells
Fully Coupled - 600 Cells
Testing MultiRegion Splitting Method
dt = 110-4 dt = 110-5 dt = 110-6
8.3810-5 2.6510-5 5.2410-6
Euclidean norm of the error
10 cells 50 cells 100 cells
6.4110-4 5.7110-5 1.8610-5
Euclidean norm of the error
Does our splitting scheme make sense?
Testing MultiRegion Splitting Method
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Decreasing time step
Using a finer mesh
0.010
0.012
0.014
0.016
0.018
0.020
0.022
0.024
0.0 0.2 0.4 0.6 0.8 1.0
CA
[mol/m3]
Slab Length [cm]
dt=1e-4
dt=1e-5
dt=1e-6
fully coupled
0
0.005
0.01
0.015
0.02
0.025
0.03
0 0.5 1
CA
[mol/m3]
Slab Length [cm]
10 Cells
50 Cells
100 Cells
Fully Coupled - 600 Cells
Testing MultiRegion Splitting Method
y = 0.0232x0.602
1.0E-06
1.0E-05
1.0E-04
1.0E-03
1.E-07 1.E-05 1.E-03
error
time step [s] dt = 110-4 dt = 110-5 dt = 110-6
8.3810-5 2.6510-5 5.2410-6
Euclidean norm of the error
Convergence Order 0.6 (ideal 1)
10 cells 50 cells 100 cells
6.4110-4 5.7110-5 1.8610-5
Euclidean norm of the error
Does our splitting scheme make sense?
Testing MultiRegion Splitting Method
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Decreasing time step
0.010
0.012
0.014
0.016
0.018
0.020
0.022
0.024
0.0 0.2 0.4 0.6 0.8 1.0
CA
[mol/m3]
Slab Length [cm]
dt=1e-4
dt=1e-5
dt=1e-6
fully coupled
0
0.005
0.01
0.015
0.02
0.025
0.03
0 0.5 1
CA
[mol/m3]
Slab Length [cm]
10 Cells
50 Cells
100 Cells
Fully Coupled - 600 Cells
10 cells 50 cells 100 cells
6.4110-4 5.7110-5 1.8610-5
Euclidean norm of the error
Testing MultiRegion Splitting Method
y = 0.0232x0.602
1.0E-06
1.0E-05
1.0E-04
1.0E-03
1.E-07 1.E-05 1.E-03
error
time step [s]
y = 0.022x1.5312
1.E-05
1.E-04
1.E-03
0.001 0.1
error
step size [cm]
Convergence Order 1.6 (ideal 2)
dt = 110-4 dt = 110-5 dt = 110-6
8.3810-5 2.6510-5 5.2410-6
Euclidean norm of the error
Convergence Order 0.6 (ideal 1)
Using a finer mesh
Does our splitting scheme make sense?
Testing MultiRegion Splitting Method
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Diff/k 0.1 1 10 1000
2 10-6
2 10-5
2 10-4
0
0.005
0.01
0.015
0.02
0.025
0 0.2 0 .4 0 .6 0 .8 1
CatalyticFOAM
Fully Coupled
0
0.005
0.01
0.015
0.02
0.025
0 0.2 0 .4 0 .6 0 .8 1
CatalyticFOAMFully Coupled
0
0.005
0.01
0.015
0.02
0.025
0 0.2 0 .4 0 .6 0 .8 1
CatalyticFOAM
Fully Coupled
0
0.005
0.01
0.015
0.02
0.025
0 0.2 0.4 0.6 0.8 1
CatalyticFFully Coupled
0
0.005
0.01
0.015
0.02
0.025
0 0.2 0.4 0.6 0.8 1
CatalyticFOAMFully Coupled
0
0.005
0.01
0.015
0.02
0.025
0 0.2 0.4 0.6 0.8 1
CatalyticFOAM
Fully Coupled
0
0.005
0.01
0.015
0.02
0.025
0 0.2 0.4 0.6 0.8 1
CatalyticFOAM
Fully Coupled
0
0.005
0.01
0.015
0.02
0.025
0 0.2 0 .4 0 .6 0 .8 1
CatalyticFOAMFully Coupled
0
0.005
0.01
0.015
0.02
0.025
0 0.2 0 .4 0 .6 0 .8 1
CatalyticFOAM
Fully Coupled
0
0.005
0.01
0.015
0.02
0.025
0 0.2 0 .4 0 .6 0 .8 1
CatalyticFOAM
Fully Coupled
0
0.005
0.01
0.015
0.02
0.025
0 0.2 0 .4 0 .6 0 .8 1
CatalyticFOAMFully Coupled
0
0.005
0.01
0.015
0.02
0.025
0 0.2 0 .4 0 .6 0 .8 1
CatalyticFOAM
Fully Coupled
Testing MultiRegion Splitting Method
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Does our splitting scheme work with more complex cases?
Testing Full Solver Architecture
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Testing Full Solver Architecture
2D Case : pipe with
cylindrical obstacle full solver architecture tested
solid catalyst
Does our splitting scheme work with more complex cases?
Testing Full Solver Architecture
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est g ull Sol e c tectu e
2D Case : pipe with
cylindrical obstacle full solver architecture tested
non-elementary geometry
solid catalyst
Does our splitting scheme work with more complex cases?
Testing Full Solver Architecture
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g
2D Case : pipe with
cylindrical obstacle full solver architecture tested
non-elementary geometry
detailed kinetic scheme(H2 on Rh : 18 reactions, 5 adsorbed species)
solid catalyst
Does our splitting scheme work with more complex cases?
Testing Full Solver Architecture
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g
Resolution of Navier-Stokes equationsin fluid domain
2D Case : pipe with
cylindrical obstacle full solver architecture tested
non-elementary geometry
detailed kinetic scheme(H2 on Rh : 18 reactions, 5 adsorbed species)
solid catalyst
Does our splitting scheme work with more complex cases?
Testing Full Solver Architecture
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g
Intra-solid profiles canbe investigated
2D Case : pipe with
cylindrical obstacle full solver architecture tested
non-elementary geometry
detailed kinetic scheme(H2 on Rh : 18 reactions, 5 adsorbed species)
Radial Profile
solid catalyst
Does our splitting scheme work with more complex cases?
Testing Full Solver Architecture
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g
2D Case : pipe with
cylindrical obstacle full solver architecture tested
non-elementary geometry
detailed kinetic scheme(H2 on Rh : 18 reactions, 5 adsorbed species)
Intra-solid profiles canbe investigated
Axial Profile
solid catalyst
Outline
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MultiRegion Structure
Multiple meshes Mixed BCs at the interface Coupling partitioned approach
Numerical Tests Coupling strategy effectiveness
Splitting operator testing Test global architecture with cases of increasing complexity
Solver Validation Comparison with experimental data
Importance of intra-solid phenomena descriptionConclusions
Solver Validation
Case Description
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Combustion of a fuel-rich H2 over Rh catalyst in an annular
reactor(
*)
.
(*) Two-dimensional detailed modeling of fuel-rich H2 combustion over Rh/Al2O3 catalyst.M. Maestri, A. Beretta, T. Faravelli, G. Groppi, E. Tronconi, D.G. VlachosChem. Eng. Sci. 2008
p
Operating conditions
Inner radius 0.235 cm
Outer radius 0.450 cm
Reactor length 1.5 cm
H2 mole fraction 0.04 (-)
O2 mole fraction 0.01 (-)
N2 mole fraction 0.95 (-)
Pressure 1 atm
Catalytic layer width 50 m
Flow rate 0.274 Nl/min
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Solver Validation
Comparison with Experimental Data
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(*) 2D detailed modeling of fuel-rich H2 combustion over Rh/Al2O3 catalyst.M. Maestri, A. Beretta, T. Faravelli, G. Groppi, E. Tronconi, D. VlachosCES 2008
Combustion of a fuel-rich H2 over Rh catalyst in an annular reactor(*)
0
0.2
0.4
0.6
0.8
1
1.2
0 100 200 300 400 500 600
O2Conversion[%]
Temperature [C]
Previous Models(no description of the solid phase)
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Solver Validation
Case Setup
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Identification of the calculation domain
Cylindrical symmetry
(*) 2D detailed modeling of fuel-rich H2 combustion over Rh/Al2O3 catalyst.M. Maestri, A. Beretta, T. Faravelli, G. Groppi, E. Tronconi, D. VlachosCES 2008
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Solver Validation
Case Setup
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Identification of the calculation domain
Cylindrical symmetry
2D domain
Lower computationaleffort
(*) 2D detailed modeling of fuel-rich H2 combustion over Rh/Al2O3 catalyst.M. Maestri, A. Beretta, T. Faravelli, G. Groppi, E. Tronconi, D. VlachosCES 2008
Solver Validation
Comparison with Experimental Data
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(*) Determination of the effective diffusion coefficient in porous media includingKnudsen effects. D. Mu, Z.S. Liu, C. Huang, N. Djilali2008
Combustion of a fuel-rich H2 over Rh catalyst in an annular reactor(*)
0
0.2
0.4
0.6
0.8
1
1.2
0 100 200 300 400 500 600
O2Conversion[%]
Temperature [C]
multiRegion
Better fit due to thedescription of intra-solid
phenomena
1%1% Main catalytic bed
Solver Validation
Comparison with Experimental Data
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(*) Determination of the effective diffusion coefficient in porous media includingKnudsen effects. D. Mu, Z.S. Liu, C. Huang, N. Djilali2008
Combustion of a fuel-rich H2 over Rh catalyst in an annular reactor(*)
0
0.2
0.4
0.6
0.8
1
1.2
0 100 200 300 400 500 600
O2Conversion[%]
Temperature [C]
multiRegion
Better fit due to thedescription of intra-solid
phenomena
1%1% Main catalytic bed
()
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Solver Validation
Comparison with Experimental Data
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(*) 2D detailed modeling of fuel-rich H2 combustion over Rh/Al2O3 catalyst.M. Maestri, A. Beretta, T. Faravelli, G. Groppi, E. Tronconi, D. VlachosCES 2008
Combustion of a fuel-rich H2 over Rh catalyst in an annular reactor(*)
multiRegion0
0.2
0.4
0.6
0.8
1
1.2
0 100 200 300 400 500 600
O2Conversion[
%]
Temperature [C]
1%1% Main catalytic bed
, . /, . /, . /
Solver Validation
Comparison with Experimental Data
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(*) 2D detailed modeling of fuel-rich H2 combustion over Rh/Al2O3 catalyst.M. Maestri, A. Beretta, T. Faravelli, G. Groppi, E. Tronconi, D. VlachosCES 2008
Combustion of a fuel-rich H2 over Rh catalyst in an annular reactor(*)
0
0.2
0.4
0.6
0.8
1
1.2
0 100 200 300 400 500 600
O2Conversion[
%]
Temperature [C]
multiRegion
Same results obtained withrefined mesh
1%1% Main catalytic bed
600 cells 1200 cells
Solver Validation
Comparison with Experimental Data
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Different controllingregimes at different T
multiRegion
Solver Validation
Comparison with Experimental Data
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0.000
0.002
0.004
0.006
0.0080.010
0.012
0.014
0.016
0 10 20 30 40 50
O2massfrac
tion
Catalytic Layer Width [m]
0.0E+00
5.0E-04
1.0E-03
1.5E-03
2.0E-03
2.5E-03
3.0E-03
3.5E-03
4.0E-03
0 10 20 30 40 50
O2massfraction
Catalytic Layer Width [m]
Different controllingregimes at different T
0.E+00
1.E-04
2.E-04
3.E-04
4.E-04
5.E-04
6.E-04
7.E-04
8.E-04
0 10 20 30 40 50
O2massfraction
Catalytic Layer Width [m]
multiRegion
0.E+00
1.E-05
2.E-05
3.E-05
4.E-05
5.E-05
6.E-05
7.E-05
8.E-05
9.E-05
0 10 20 30 40 50
O2massfraction
Catalytic Layer Width [m]
373 K423 K
523 K823 K
0.E+00
2.E-03
4.E-03
6.E-03
8.E-03
1.E-02
1.E-02
0 10 20 30 40 50
O2massfraction
Catalytic Layer Width [m]
373 K
423 K
523 K
823 K
Outline
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MultiRegion Structure
Multiple meshes Mixed BCs at the interface Coupling partitioned approach
Numerical Tests Coupling strategy effectiveness
Splitting operator testing Test global architecture with cases of increasing complexity
Solver Validation Comparison with experimental data Importance of intra-solid phenomena description
Conclusions
Conclusions
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Segregated approach (operator splitting) Multiple meshes for multiple regions Partitioned approach with coupling at the interface for
multiRegions handling
SolverStructure
multiRegion
Conclusions
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multiRegion
Operator splitting strategy for reactive and transport terms Multiple meshes for multiple regions Partitioned approach for coupling at the interface between
two different phases
SolverStructure
Conclusions
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multiRegion
Operator splitting strategy for reactive and transport terms Multiple meshes for multiple regions Partitioned approach for coupling at the interface between
two different phases
SolverStructure
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Conclusions
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Comparison with analytical and numerical solutions incases with increasing complexity
Validation of the solver through comparison withexperimental data
Tests andValidation
multiRegion
Operator splitting strategy for reactive and transport terms Multiple meshes for multiple regions Partitioned approach for coupling at the interface between
two different phases
SolverStructure
Conclusions
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Comparison with analytical and numerical solutions incases with increasing complexity
Validation of the solver through comparison withexperimental data
Tests andValidation
multiRegion
Operator splitting strategy for reactive and transport terms Multiple meshes for multiple regions Partitioned approach for coupling at the interface between
two different phases
SolverStructure
Conclusions
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Comparison with analytical and numerical solutions incases with increasing complexity
Validation of the solver through comparison withexperimental data
Tests andValidation
multiRegion
Operator splitting strategy for reactive and transport terms Multiple meshes for multiple regions Partitioned approach for coupling at the interface between
two different phases
SolverStructure
Conclusions
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Comparison with analytical and numerical solutions incases with increasing complexity
Validation of the solver through comparison withexperimental data
Tests andValidation
multiRegion
Detailed description of intra-solid phenomena Complex kinetic schemes Arbitrary number of regions with different properties Handles geometries of arbitrary complexity
SolverPotential
Operator splitting strategy for reactive and transport terms Multiple meshes for multiple regions Partitioned approach for coupling at the interface between
two different phases
SolverStructure
Conclusions
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Comparison with analytical and numerical solutions incases with increasing complexity
Validation of the solver through comparison withexperimental data
Tests andValidation
multiRegion
Detailed description of intra-solid phenomena Complex kinetic schemes Arbitrary number of regions with different properties Handles geometries of arbitrary complexity
SolverPotential
Operator splitting strategy for reactive and transport terms Multiple meshes for multiple regions Partitioned approach for coupling at the interface between
two different phases
SolverStructure
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Show Case
Case Setup
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Mesh Size: 8700 Cells
Operating conditions
H2 mole fraction 0.04 (-)
O2 mole fraction 0.01 (-)
N2 mole fraction 0.95 (-)
Pressure 1 atm
Show Case
Case Setup
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Mesh Size: 8700 Cells
1 Fluid Region and 4 Solid Regions
Operating conditions
H2 mole fraction 0.04 (-)
O2 mole fraction 0.01 (-)
N2 mole fraction 0.95 (-)
Pressure 1 atm
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Show Case
Velocity Profiles
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1 Fluid Region and 4 Solid Regions Different Properties for each catalytic
solid
Detailed H2 on Rh kinetic scheme
(18 reactions, 7 gas species, 5 adsorbed species)
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Show Case
Oxygen mass fraction profiles
1 2E 02
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0.0E+00
2.0E-03
4.0E-03
6.0E-03
8.0E-03
1.0E-02
1.2E-02
0 0.2 0 .4 0.6 0.8 1 1.2
O2massfraction
Catalytic Layer Width [mm]
0.0E+00
4.0E-03
8.0E-03
1.2E-02
1.6E-02
0 0.2 0.4 0.6 0.8
O2mass
fraction
Catalytic Layer Width [mm]0.0E+00
2.0E-03
4.0E-03
6.0E-03
8.0E-03
1.0E-02
1.2E-02
0 0.2 0.4 0.6 0.8
O2massfraction
Catalytic Layer Width [mm]
Different regimes inside the catalystregions depending on their properties
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Acknowledgements
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Thank you for yourattention!
Acknowledgements
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Any questions?
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BACK-UP SLIDES
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Operator splitting scheme
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Reaction Diffusion,convection...
(
*)
Second-order splitting schemes for a class of reactive systemsZ. Ren, S. B. PopeJournal of Computational Physics - 2008
Strang splitting scheme
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Solution procedure
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Main features:
Solution of the Navier-Stokesequations (laminar and
turbulent regime)
No limit to the number ofspecies and reactions
Isothermal and adiabatic
conditions
Navier-Stokes Eqs.(PISO predictor)
Batch series(Strang predictor)
Propertiesevaluation
Transport Eqs.(Strang corrector)
Pressure Eqn.
Velocity correction(PISO corrector)
+
Interface Coupling Validation1-D Diffusion
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CH4=1 [w/w]
O2=1 [w/w]
- FluidSx: 2e-5 [m^2/s]
- FluidDx: 1e-5 [m^2/s]
Diffusion coefficientsCH4-O2 Diffusion in aN2-full volume(T = 573[K],P=1[atm])
0
0.005
0.01
0.015
0.02
0.025
0.03
0.035
0 2 4 6 8 10
ConcA
[mol/m3]
Slab length [cm]
Steady state
solutionanalytical solution CH4catalyticFOAM solution CH4
analytical solution O2
catalyticFOAM solution O2
Steadystate
Analytical Validation of Solver with Integrated Reaction TermDiffusion and Reaction in a Solid Slab
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Solid slab with constantmassive fraction on the sides
Reaction: A->B
Analytical solution:
LDiff
k
xDiff
k
C=CsAA
cosh
cosh
A= 0.3
A= 0.3
0.00
0.05
0.10
0.15
0.20
0.25
0.30
0.35
0 0.5 1 1.5 2
Awt/wt
Slab length [cm]
Steady statesolution
analytical solution
catalyticFOAM solution
A
A Comprehensive Solve for Describing Multi-Region PhenomenaMultiRegion Solver Architecture
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Solve Solid
0=+dt
dmix
sitesRh
cat
SOL
cell
itoti
mix
i
tot
MW
dVYdmMWR+
R=
dt
dYm igas,
ihom,
mixpc
Q+Q=
dt
dT
mix
hethom
sites
i
R=
dt
d isurf,
Solid Chemistry
Rho Eq.
Update Solid PropertiesU Eq.
*v=
a
P
p
Pressure Eq.
mix
i
R=
dt
dY ihom,
mixpc
Q=
dt
dT
mix
hom
Fluid Chemistry
Update Fluid Properties
iimiximix YYD=
dt
Yd mixi,
TcTk=dt
Tcdpmat
mat
matp
Mass Transfer Eq.
HeatTransfer Eq.
imix
imixYD=
dt
Yd
mixi,
Mass Transfer Eq.
Tk=dt
Tcd
mat
mat
matp
Heat Transfer Eq.
Solve Fluid
PimpleLoop
Pimple
Loop
for each time step...
PISOpredictor-correctorloop
PIMPLEconvergence
check
() ()-
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Solver ValidationComparison with Experimental Data
C b ti f f l i h H Rh t l t i l t (*)
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0
0.2
0.4
0.6
0.8
1
1.2
0 100 200 300 400 500 600
O2Conversion
[%]
Temperature [C]
(*) 2D detailed modeling of fuel-rich H2
combustion over Rh/Al2
O3
catalyst.
M. Maestri, A. Beretta, T. Faravelli, G. Groppi, E. Tronconi, D. VlachosCES 2008
Main catalytic bed
Combustion of a fuel-rich H2 over Rh catalyst in an annular reactor(*)
multiRegion
Solver ValidationComparison with Experimental Data
C b ti f f l i h H Rh t l t i l t (*)
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0
0.2
0.4
0.6
0.8
1
1.2
0 100 200 300 400 500 600
O2Conversion
[%]
Temperature [C]
(*) 2D detailed modeling of fuel-rich H2 combustion over Rh/Al2O3 catalyst.
M. Maestri, A. Beretta, T. Faravelli, G. Groppi, E. Tronconi, D. VlachosCES 2008
Main catalytic bed
Combustion of a fuel-rich H2 over Rh catalyst in an annular reactor(*)
multiRegion
Better fit due to thedescription of intra-solid
phenomena
7/29/2019 Calonaci Furnari Final Presentation
133/136
Solver ValidationComparison with Experimental Data
Combustion of a fuel rich H over Rh catalyst in an annular reactor (*)
7/29/2019 Calonaci Furnari Final Presentation
134/136
0
0.2
0.4
0.6
0.8
1
1.2
0 100 200 300 400 500 600
O2Conversion
[%]
Temperature [C]
(*) 2D detailed modeling of fuel-rich H2 combustion over Rh/Al2O3 catalyst.
M. Maestri, A. Beretta, T. Faravelli, G. Groppi, E. Tronconi, D. VlachosCES 2008
Combustion of a fuel-rich H2 over Rh catalyst in an annular reactor(*)
multiRegion
Better fit due to thedescription of intra-solid
phenomena
1%1% Main catalytic bed
When an extended bed isconsidered.
Solver ValidationComparison with Experimental Data
7/29/2019 Calonaci Furnari Final Presentation
135/136
Adsorbed speciesprofiles
0
0.1
0.2
0.3
0.4
0.5
0.6
0.7
0.8
0 0.3 0.6 0.9 1.2 1.5
SiteFraction[%]
Reactor Length [cm]
H(S)
O(S)
OH(S)
Rh(S)
multiRegion
Solver ValidationComparison with Experimental Data
Combustion of a fuel rich H over Rh catalyst in an annular reactor (*)
7/29/2019 Calonaci Furnari Final Presentation
136/136
Combustion of a fuel-rich H2 over Rh catalyst in an annular reactor(*)
0.2
0.4
0.6
0.8
1
1.2
O2Conversion
[%]
Better fit due to thedescription of intra-solid
phenomena
1%1% Main catalytic bed
()
, . /
. /
23
1.5
210.5
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