Calonaci Furnari Final Presentation

7/29/2019 Calonaci Furnari Final Presentation

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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


3/136

Background



are catalytic

Need for an accuratedesign to provide

high yields ($)


4/136

Background



are catalytic

Need for an accuratedesign to provide

high yields ($)

Need for a deepunderstanding foradvanced design


5/136

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



Background



7/136

Time [s]

Length[m]

MICROSCALE


MESOSCALE

Interplay among thechemical events

MACROSCALE100

10-6

10-3

10-9

10-15 10-6 100



Background



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Time [s]

Length[m]

MICROSCALE


MESOSCALE


MACROSCALE

Mass and energytransport phenomena

100

10-6

10-3

10-9

10-15 10-6 100



Background



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Time [s]

Length[m]

MICROSCALE


MESOSCALE


MACROSCALE

Mass and energytransport phenomena

Developmentof a new solver

100

10-6

10-3

10-9

10-15 10-6 100



Background



10/136

Time [s]

Length[m]

MICROSCALE

MACROSCALE100

10-6

10-3

10-9

10-15 10-6 100



Background


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



Background


MESOSCALE

B k d


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Time [s]

Length[m]

MICROSCALE


MACROSCALE100

10-6

10-3

10-9

10-15 10-6 100



Background


MESOSCALE

Mean fieldapproximation

B k d


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Time [s]

Length[m]

MICROSCALE


MACROSCALE

CFD

100

10-6

10-3

10-9

10-15 10-6 100



Background


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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Fluid Phase

The Ph sical Problem


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Intra-solid phenomena not detailed

Fluid Phase



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Intra-solid phenomena not detailed

Unacceptable if transport limitations

in the catalyst play a major role!

Fluid Phase



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All steps of a catalytic reactive process

need to be described

Fluid Phase



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Model intra-phase phenomena in the solid

Fluid Phase



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multiRegion



Model intra-phase phenomena in the solid

Fluid Phase



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Aim of the work

multiRegion

The solid phase needs to becharacterized:

Fluid Phase



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Aim of the work

multiRegion


Mathematical model to describetransport and reactive phenomena

Fluid Phase



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Aim of the work

multiRegion



()

()

kT ()

0

Fluid Phase

Fluid Phase



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Aim of the work

multiRegion



()

()

kT ()

0

() , ( , )

,()

kT ,

,

Fluid Phase

Solid Phase

Fluid Phase



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Aim of the work

multiRegion



()

()

kT ()

0

Separate pseudo-phase with effectiveproperties

() , ( , )

,()

kT ,

,

Fluid Phase

Solid Phase

Fluid Phase



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Aim of the work

multiRegion



()

()

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


28/136

Outline



Numerical Tests

Coupling strategy effectiveness Splitting operator testing Test global architecture with cases of increasing complexity


29/136

Outline



Numerical Tests


Solver Validation Comparison with experimental data

Importance of intra-solid phenomena description


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Outline



Numerical Tests




Conclusions


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Outline



Numerical Tests




Conclusions

New Structure


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Multiple Meshes for Multiple Regions

MultiRegion nature of the solver

New Structure


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Mesh 1: Fluid Region

Mesh 2: Solid Region 1

Multiple meshes



New Structure


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Multiple meshes

Different propertiesfor each region



New Structure


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Multiple meshes


Separate governingequations on each cell



New Structure


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Multiple meshes


Separate governingequations on each cell

Full support for multiregion post-processing



Make Separate Regions Interact


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Boundary conditions for coupled interfaces

How to couple at theinterface ?



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INBR,IOWN,

)(INBR,)(IOWN,

T=T

Tk=TkINBRIOWN

INBR,IOWN,C=C

CD=CDINBRNBRIOWNOWN



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2 different

approaches


INBR,IOWN,

)(INBR,)(IOWN,

T=T

Tk=TkINBRIOWN

INBR,IOWN,C=C

CD=CDINBRNBRIOWNOWN



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Monolithicworks on multiple meshesjust for loose inter-equationcoupling

2 different

approaches


INBR,IOWN,

)(INBR,)(IOWN,

T=T

Tk=TkINBRIOWN

INBR,IOWN,C=C

CD=CDINBRNBRIOWNOWN



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Monolithicworks on multiple meshesjust for loose inter-equationcoupling

PartitionedWorks on multiple mesheseven for stiff inter-equationcoupling

2 different

approaches


INBR,IOWN,

)(INBR,)(IOWN,

T=T

Tk=TkINBRIOWN

INBR,IOWN,C=C

CD=CDINBRNBRIOWNOWN



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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


l h f


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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


INBR,IOWN,

)(INBR,)(IOWN,

T=T

Tk=TkINBRIOWN

INBR,IOWN,C=C

CD=CDINBRNBRIOWNOWN


l h f


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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


INBR,IOWN,

)(INBR,)(IOWN,

T=T

Tk=TkINBRIOWN

INBR,IOWN,C=C

CD=CDINBRNBRIOWNOWN


l h f


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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


INBR,IOWN,

)(INBR,)(IOWN,

T=T

Tk=TkINBRIOWN

INBR,IOWN,C=C

CD=CDINBRNBRIOWNOWN


H C l h I f ?


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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


INBR,IOWN,

)(INBR,)(IOWN,

T=T

Tk=TkINBRIOWN

INBR,IOWN,C=C

CD=CDINBRNBRIOWNOWN


H t C l t th I t f ?


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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


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


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



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



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,

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




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Solve Solid

Navier-stokes Equation

Pressure Corrector

Solve Fluid


P

ISOpredictor-correctorloop


Continuity Equation




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Solve Solid

Navier-stokes Equation

Pressure Corrector

Fluid Chemistry

Update Fluid Properties

Solve Fluid


P



Continuity Equation

Mass Transfer Equation

Heat Transfer Equation

Homogeneous reactions




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Solve Solid

Solid Chemistry

Update Solid PropertiesNavier-stokes Equation

Pressure Corrector

Fluid Chemistry




Solve Fluid


P



Site species conservation

Homogeneous and heterogeneous reactions

Continuity Equation







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Solve Solid

Solid Chemistry

Update Solid PropertiesNavier-stokes Equation

Pressure Corrector

Fluid Chemistry




Solve Fluid

CouplingLoop

CouplingLoop


P


Coupling loopconvergence

check


Site species conservation

Homogeneous and heterogeneous reactions

Continuity Equation




Outline


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Outline



Numerical Tests Coupling strategy effectiveness Splitting operator testing Test global architecture with cases of increasing complexity


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



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Compare withfully-coupledMatlab solver

Compare withanalyticalsolution

during transient

at steady state



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Alluminium Steel

Hot side:

Fixed T = 500 [K]

Cold side:

Fixed T = 300 [K]

Initial T =

uniform 400 [K]Interface



during transient

at steady state




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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



during transient

at steady state




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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


Does our splitting scheme make sense?

Testing MultiRegion Splitting Method


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How to test for validity of our splitting scheme ?




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CatalyticFOAMMulti-Region

Solver


Solver




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Solver


Solver

Matlab

Fully CoupledSolver




66/136



Effect of timestepCatalyticFOAM

Multi-RegionSolver

Matlab

Fully CoupledSolver




67/136



Effect of timestep

Effect of meshrefinement


Solver

Matlab

Fully CoupledSolver




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Effect of timestep


Test in differentconditions


Solver

Matlab

Fully CoupledSolver




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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


Effect of timestep


Test in differentconditions


Solver

Matlab

Fully CoupledSolver




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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

dt = 110-4 dt = 110-5 dt = 110-6

8.3810-5 2.6510-5 5.2410-6

Euclidean norm of the error




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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


dt = 110-4 dt = 110-5 dt = 110-6

8.3810-5 2.6510-5 5.2410-6


10 cells 50 cells 100 cells

6.4110-4 5.7110-5 1.8610-5





72/136


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



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


Convergence Order 0.6 (ideal 1)


6.4110-4 5.7110-5 1.8610-5





73/136


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



6.4110-4 5.7110-5 1.8610-5



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]


dt = 110-4 dt = 110-5 dt = 110-6

8.3810-5 2.6510-5 5.2410-6



Using a finer mesh




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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


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


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


0

0.005

0.01

0.015

0.02

0.025

0 0.2 0 .4 0 .6 0 .8 1

CatalyticFOAM

Fully Coupled



75/136

Does our splitting scheme work with more complex cases?

Testing Full Solver Architecture


76/136


2D Case : pipe with

cylindrical obstacle full solver architecture tested

solid catalyst




77/136

est g ull Sol e c tectu e

2D Case : pipe with


non-elementary geometry

solid catalyst




78/136

g

2D Case : pipe with



detailed kinetic scheme(H2 on Rh : 18 reactions, 5 adsorbed species)

solid catalyst




79/136

g

Resolution of Navier-Stokes equationsin fluid domain

2D Case : pipe with




solid catalyst




80/136

g

Intra-solid profiles canbe investigated

2D Case : pipe with




Radial Profile

solid catalyst




81/136

g

2D Case : pipe with




Intra-solid profiles canbe investigated

Axial Profile

solid catalyst

Outline


82/136



Numerical Tests Coupling strategy effectiveness

Splitting operator testing Test global architecture with cases of increasing complexity


Importance of intra-solid phenomena descriptionConclusions

Solver Validation

Case Description


83/136

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


84/136

Solver Validation

Comparison with Experimental Data


85/136

(*) 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)


86/136

Solver Validation

Case Setup


87/136

Identification of the calculation domain

Cylindrical symmetry



88/136

Solver Validation

Case Setup


89/136

Identification of the calculation domain

Cylindrical symmetry

2D domain

Lower computationaleffort


Solver Validation



90/136

(*) Determination of the effective diffusion coefficient in porous media includingKnudsen effects. D. Mu, Z.S. Liu, C. Huang, N. Djilali2008


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



91/136

(*) Determination of the effective diffusion coefficient in porous media includingKnudsen effects. D. Mu, Z.S. Liu, C. Huang, N. Djilali2008


0

0.2

0.4

0.6

0.8

1

1.2

0 100 200 300 400 500 600

O2Conversion[%]

Temperature [C]

multiRegion


phenomena


()


92/136

Solver Validation



93/136



multiRegion0

0.2

0.4

0.6

0.8

1

1.2

0 100 200 300 400 500 600

O2Conversion[

%]

Temperature [C]


, . /, . /, . /

Solver Validation



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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]

multiRegion

Same results obtained withrefined mesh


600 cells 1200 cells

Solver Validation



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Different controllingregimes at different T

multiRegion

Solver Validation



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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


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


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


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


373 K

423 K

523 K

823 K

Outline


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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


99/136

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


100/136

multiRegion



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



SolverStructure

Conclusions


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Tests andValidation

multiRegion



SolverStructure

Conclusions


104/136



Tests andValidation

multiRegion



SolverStructure

Conclusions


105/136



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



SolverStructure

Conclusions


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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



SolverStructure


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108/136


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Show Case

Case Setup


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Mesh Size: 8700 Cells





Pressure 1 atm

Show Case

Case Setup


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Mesh Size: 8700 Cells

1 Fluid Region and 4 Solid Regions





Pressure 1 atm


112/136


113/136

Show Case

Velocity Profiles


114/136

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)


115/136

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


117/136

Acknowledgements


118/136

Thank you for yourattention!

Acknowledgements


119/136

Any questions?


120/136

BACK-UP SLIDES


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122/136

Operator splitting scheme


123/136

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


126/136

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


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


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


multiRegion


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.


Main catalytic bed


multiRegion


phenomena


133/136


Combustion of a fuel rich H over Rh catalyst in an annular reactor (*)


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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.



multiRegion


phenomena


When an extended bed isconsidered.



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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


Combustion of a fuel rich H over Rh catalyst in an annular reactor (*)


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0.2

0.4

0.6

0.8

1

1.2

O2Conversion

[%]


phenomena


()

, . /

. /

23

1.5

210.5

Calonaci Furnari Final Presentation

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Transcript of Calonaci Furnari Final Presentation