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Characterization of flow regimes and heat/mass

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POLITECNICO
DI MILANO
Characterization of flow regimes
and heat/mass transfer inside
Kelvin cell type foams by means
of OpenFOAM
Augusto Della Torre, Gianluca Montenegro
Department of Energy, Politecnico di Milano, Italy
Federico Brusiani, Gian Marco Bianchi
ALMA MATER STUDIORUM - Università di Bologna, Italy
WCCM XI – ECCM V - ECFD VI Barcelona 2014
Introduction
POLITECNICO
DI MILANO
!   Open cell foams are interesting supports for catalysts in various
application fields (reforming, after-treatment, etc.)
!   Flow resistance, heat and mass transfer properties must be
determined in detail to assess ad-hoc optimization for best
performance (pressure drop, chemical conversion)
!   Micro-structure behaviour can be investigated to extract
information which can be up-scaled for full scale simulations
!   Real foam geometries needs to be reconstructed with
sophisticated technology. Artificial and repeatable structures
may be used as templates.
WCCM XI – ECCM V - ECFD VI Barcelona 2014
POLITECNICO
DI MILANO
Main concept: applied to ICE
Engine scale
Component scale
Quasi-3D
Micro-structure scale
CFD
F. Lucci et al. / Chemical Engineering Science 112 (2014) 143–151
Fig. 3. Sample of the fina
1000
∆xP [Pa/mm]
100
10
1
0.1
0.01
Fig. 2. Sample view of randomized Kelvin cell structure. Grid resolution is plotted
on the foam surface.
WCCM XI – ECCM V - ECFD VI Barcelona 2014
We simulate the transport of methane CH4 in air. A Sutherland
model is applied for the transport air properties and the thermal
properties are extracted from Janaf tables. The methane inflow
mass concentration is X CH4 ¼ 0:001 and is assumed to have Smidth
number equal to 1.
The catalyst operates in a transport limited regime so the
temperature at the inflow is kept constant at 700 K. No conjugate
heat transfer between the solid and the fluid is solved but a
constant temperature of 750 K is imposed at the solid–fluid
Richa
Richa
Dimopoulos Eggensch
Dimopoulos Eggensch
0
2
4
6
Fig. 4. Pressure drop per unit length in Pa/
cases. Lines: literature correlations; Symbol
that are most used in the literature
different characteristic length scale
the definition of pore diameter. E
present work is computed using th
respective author. Then it is resca
characteristic length of the externa
In Fig. 4 the pressure drop is p
Outline
!   Choice of the best idealized representative for open cell
foams
!   Impact of geometrical parameters of flow
!   Detailed modeling (DNS and RANS)
!   Up scaling for full scale simulations
!   Adding the chemistry
!   Examples and conclusions
WCCM XI – ECCM V - ECFD VI Barcelona 2014
POLITECNICO
DI MILANO
POLITECNICO
DI MILANO
Geometry reconstruction
Foam samples
Geometry idealization:
Cubic cell model
Kelvin cell model
Geometry reconstruction:
Micro-CT scanner
WCCM XI – ECCM V - ECFD VI Barcelona 2014
X-ray image
Image segmentation
Analysis of the flow field
Cubic cell
Kelvin cell
Micro-CT
WCCM XI – ECCM V - ECFD VI Barcelona 2014
POLITECNICO
DI MILANO
Analysis of the temperature field
Cubic cell
Kelvin cell
WCCM XI – ECCM V - ECFD VI Barcelona 2014
POLITECNICO
DI MILANO
Comparison of the pressure drop
! 
Same porosity and cell size
measured
real foam
Kelvin cell
cubic cell
WCCM XI – ECCM V - ECFD VI Barcelona 2014
POLITECNICO
DI MILANO
POLITECNICO
DIPOLITECNICO
MILANO
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DI DI
MILANO
MILANO
Correction of
the
KC
model
Correction
of
the
KC
model
Correction of the KC model
X-ray images
X-ray
X-rayimages
images
 ,
 , ,
 ,
Porosity,
Porosity,
Cell
size
Porosity,
Cell
Cellsize
size
A = const
≈ 1.37
≈ 1.37
Si-C
Si-C
Si-CAl
AlAl
Test on 3 samples:
Test
Testonon3 3samples:
samples:
Sample
A
A
A
Correction
procedure:
Correction
Correction procedure:
procedure:
, 
, 


WCCM XI – ECCM V - ECFD VI Barcelona 2014
WCCM XI – ECCM V - ECFD VI Barcelona 2014
WCCM XI – ECCM V - ECFD VI Barcelona 2014

,

,
,  ∗
,  ∗
Cu
Cu
Cu


Correction
of
the
KC
model:
pressure
drop
Correction of the KC model: pressure drop

 ,
=
=
,
measure
d
real foam
KC corr
KC
CUB corr
CUB
WCCM XI – ECCM V - ECFD VI Barcelona 2014
WCCM XI – ECCM V - ECFD VI Barcelona 2014
real foam
KC corr
KC
CUB corr
CUB
POLITECNICO
POLITECNICO
DI MILANO
DI MILANO
POLITECNICO
DI MILANO
Comparison of pressure drop on different foams
!   Reconstruction of real sample by Kelvin cell
type idealized foam
B
Measured sample B
Measured sample C
Measured sample D
Calculated sample B
Calculated sample C
C
D
WCCM XI – ECCM V - ECFD VI Barcelona 2014
Calculated sample D
POLITECNICO
DI MILANO
Further enhancement
! 
A. Della Torre et al. /
Introduction of an additional degree
of freedom
Material clustering
at cell vertexes
(a)
(b)
F. Lucci et al. / Chemical Engineering Science
Fig. 1. Approaches adopted for the foam micro-structure modeli
idealization and (b) micro-CT geometry reconstruction.
Randomization
(edge length)
WCCM XI – ECCM V - ECFD VI Barcelona 2014
pore density, has been considered in this work. Mi
Tomography has been applied for the reconstruction
geometry of the sample. In a micro-CT scanner a X-r
passes through the sample and is collected by a
sample is rotated providing a series of 2D projection
ferent angles. A 3D voxel dataset is then reconstru
stack of 2D images using inverse methods. In the c
Nikon Metrology Benchtop 160 micro-CT system w
is equipped with an electron gun operating at up to
with a metal target to generate a cone of X-rays th
strahlung; both the electron gun voltage and target
altered to provide a range of spectra and penetratio
POLITECNICO
DI MILANO
Detailed simulation: cold flow
Numerical schemes accuracy:
•  Time: second order
•  Space: third order
Pressure
WCCM XI – ECCM V - ECFD VI Barcelona 2014
TKE spectrum
UDeNS: heat
Analysis
of transfer
the temperature field
Velocity
Temperature
mesh: 16 mln cells – runtime: 30 days on 16 processors
WCCM XI – ECCM V - ECFD VI Barcelona 2014
POLITECNICO
DI MILANO
POLITECNICO
DI MILANO
Cold flow RANS simulations
!   Similar results obtained with:
•  Laminar simulation
•  RANS simulation
•  DNS simulation
DNS
!   Investigation of the velocity field at
different Reynolds
Re = 5
Re = 50
WCCM XI – ECCM V - ECFD VI Barcelona 2014
Re = 700
toReturbulence
nFOAMOpenFOAM
vsSensitivity
Fluent: UvsmagFluent:
= 1000
Umag Re =models
1000
Laminare
POLITECNICO
POLITECNICO
DI MILANO
DI MILANO
k-epsilon
OF - k-Epsilon
Lien-Leschziner
OFLaminar
- Laminare
OF - k-Epsilon Lien-Leschziner
Lien Leschziner
OpenFOAM vs Fluent: caduta di pressione
con modello di turbolenza
Le simulazioni OF forniscono
Le simulazioni OF forniscono
campi di velocità simili
neldi velocità simili nel
campi
caso senza e con modello
di e con modello di
caso senza
turbolenza.
turbolenza.
nFOAM: kOmegaSST, Re = OpenFOAM
1000
essione
POLITECNICO
DI MILANO
k-omega
Velocità SST
Fluent
POLITECNICO
DI MILANO
vs Fluent: Umag Re = 1000
k-epsilon
OF
- Laminare
Fluent
OF - k-Epsilon Lien-Leschziner
Residui
Setup
POLITE
Mode
DI MILA
•
•
•
•
OF
kE
kO
Lie
Le simulazioni Fluent
Le simulazioni FluentLe simulazioni OF forniscon
Condi
campi
di
velocità
simili
evidenziano gli effetti
di una gli effetti di una
evidenziano
• nelNo
caso senza e con modello d
elevata viscosità turbolenta
elevata viscosità turbolenta
nel caso si applichi ilnel
modello
caso si applichi ilturbolenza.
modello
k-Epsilon
k-Epsilon
•
Le simulazioni OpenFOAM forniscono gli stessi valori della caduta di pres
laminare sia nel caso venga adottato un modello di turbolenza.
FluentOF ottenuti con modello kEpsilon differiscono sensibilmente da
I risultati WCCM XI – ECCM V - ECFD VI Barcelona• 2014
w.engines.polimi.it
http://www.engines.polimi.it
simulato con Fluent, mentre sono in accordo con altri modelli di turbole
POLITECNICO
DI MILANO
Geometry tranformations
Mathematical transformations of
the geometry of the real foam:
dilation
•  Dilation: pore density modification
•  Opening: porosity modification
Pore density
WCCM XI – ECCM V - ECFD VI Barcelona 2014
Porosity
di ‟slip”
a paretevalida
può essere
considerata
valida a
per
valori di Kn superiori a 1e-3.
L’ipotesi di ‟slip” a pareteL’ipotesi
può essere
considerata
per valori
di Kn superiori
1e-3.
Verifica dei
La schiuma considerata, quindi, ricadente nel regime del continuo.
La schiuma considerata, quindi, ricadente nel regime del continuo.
Ciò nonostante, in previsione di un possibile utilizzo futuro, si è provveduto ad implementare
Ciò nonostante,
in
di un
utilizzo
si è provveduto ad implementare inPOLITECNICO
Fluent 14 il
F attore
scala
Lcprevisione
[m] modello
ddis possibile
[m]
Kn[futuro,
] il quale
Maxwell
attraverso
è possibile gestire condizioni di slip a parete.
M esh
di Maxwell
attraversoin
il quale
è possibile gestirethe
condizioni
di slipsize?
a parete.
Ismodello
there
a
limit
reducing
cell
1
4.3 ⇥ 10
0.66 ⇥ 10
7.52 ⇥ 10
3
Base
0.1
0.01
0.005

=
0.001
Ridotta 1
Ridotta 2
Ridotta 3
3
DI MILANO
5
4
4.3 ⇥ 10 4 0.66 ⇥ 10 4 7.52 ⇥ 10
No-Slip
No-Slip
Slip
4.3 ⇥ 10 5 0.66 ⇥ 10 5 7.52 ⇥ 10 3
 ∙  
5
0.33
⇥ 10 2
 ∙ 2.15
 ⇥ 10 
= ⇥ 10 5 1.50 essere
6
210 6 7.52 ⇥ 10 2 analizzato
4.3
⇥
10
0.66
⇥
2 
Slip
con le classiche equazioni di Na
soluzioni speciali delle equazioni di Boltzmann,
Tabella 5.2: Parametri geometrici e valutazione Kn per le mesh utilizzate
layer le equazioni di Navier-Stokes rimangono an
Per Kn < Equazione
0.1 per`odiilMaxwell
Knudsen layer copre me
4000
Equazione di Maxwell
DP no-slip BC
canale, perci`o 2questo
substrato
pu`
oessere
trascu
−



3

3500
DP Maxwell BC
−
= 3  fuori
λ
+ Knudsen
+
2 −soluzione

 

calcolata
dal
layer fino a

 
4  
Ridotta 4
3000
DP [Pa]
2500
2000

Limit for cordierite pore structure
−
=

λ

+

+
4  
 = tangential momentum accomodation coefficient
 = tangential momentum accomodation coefficient
http://www.engines.polimi.it
http://www.engines.polimi.it
1500
1000
500
0
0.00
0.01 0.02 0.03 0.04 0.05 0.06 0.07 0.08
Kn []
Figura 5.2: Schematizzazione di un metodo
WCCM
XIE↵etto
– ECCM
- ECFD VI
Barcelona
2014
Figura
5.4:
dellaVcondizione
al bordo
di Maxwell
Ci`o da luogo ad una velocit`a di slittamento
From Micro-scale to Macro-scale
WCCM XI – ECCM V - ECFD VI Barcelona 2014
POLITECNICO
DI MILANO
POLITECNICO
DI MILANO
Double-average of continuity and momentum
•  Continuity equation:
No source terms
•  Momentum equation:
Form drag
Viscous drag
WCCM XI – ECCM V - ECFD VI Barcelona 2014
Resistance source
term in macro-scale
equation
Turbulent Reynolds stress,
dispersion, turbulent dispersion
Modelling the
resistance source
term
Extracting
information
for upscaling
POLITECNICO
POLITECNICO
MILANO
DIDI
MILANO
Resistance source term
in macro-scale equation
Non-dimensional
Non-dimensional
relationshipsevaluated
evaluated
relationships
onthe
thebasis
basisofofmicromicroon
scalesimulations
simulations
scale
Variable
Variablepore
poredensity
density
Π 
Π 
http://www.engines.polimi.it
WCCM
XI – ECCM V - ECFD VI Barcelona 2014
Variable
Variableporosity
porosity
POLITECNICO
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Double-average of energy equations
•  Energy equation – fluid phase:
Inter-phase heat
transfer
Effects of time fluctuations, spatial
deviation and combined time-space dev.
•  Energy equation – solid phase:
WCCM XI – ECCM V - ECFD VI Barcelona 2014
Extra-terms
related to
viscosity
Inter-phase heat
transfer
Modelling the heat transfer source term
Non-dimensional
relationship evaluated
on the basis of microscale simulations
Al foam
()
WCCM XI – ECCM V - ECFD VI Barcelona 2014
POLITECNICO
DI MILANO
Inter-phase heat transfer
source term in macroscale energy equation
SiC foam
Micro-scale: conjugate heat-transfer
Al foam
10x10x10 mm
6.0 mln cells
SiC foam
3x3x3 mm
2.1 mln cells
WCCM XI – ECCM V - ECFD VI Barcelona 2014
POLITECNICO
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Cordierite
0.35x0.35x0.35 mm
3.2 mln cells
POLITECNICO
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DI MILANO
DI MILANO
Mass and
heat transfer
Modelling
catalytic
reactions
! 
! 
A library
modelling
of surface
has been implemented
on
Heat for
andthe
mass
transfer
analogyreactions
makes validation
easier
the basis of the OpenFOAM code.
Surface reaction chemistry has been implemented in OpenFOAM
Mass transfer between
gas phase and washcoat
catalytic surface
gas
near wall
gas
washcoat
solid wall
Reaction heat is released and
transferred to fluid and solid
phase
WCCM XI – ECCM V - ECFD VI Barcelona 2014
http://www.engines.polimi.it
773 K
473 K
Diffusion limit
Figure 11: Foam-type reactor, sample E: CO field inside the channel for an inlet CO mass fraction YCO =
3000Ncc/min.
100
100
80
80
60
40
CO conversion [%]
km [m/s]
CO conversion [%]
773 K
573 K
6. Conclusio
100
573 K
473 K
POLITECNICO
DI MILANO
4.6% and a feed flow rate Q =
60
40
Figure 11: Foam-type reactor, sample E: CO field inside the channel for an inlet CO mass fraction YCO = 4.6% and a feed flow rate Q =
CFD (YCO 3 %)
20
3000Ncc/min.
CFD (Y
3 %)
foam A (Y
3 %) - CFD
foam D - CFD
20
measured (YCO 3 %)
CO
CO
foam A (YCO 3 %) - measured
473 K
foam A (YCO 1 %) - CFD
foam A (YCO 1 %) - measured
10−1
foam D - measured
foam E - CFD
foam E - measured
B
N u= A ( R e ) P r
0
1
10!
0
"YCO = 4.6% and a feed flow rate100
Figure 11: Foam-type reactor,
E: CO field inside the channel for an inlet CO mass
Q =
10sample
5fraction
3
Q 10 · m /s
3000Ncc/min.
400
CFD (YCOCFD
5 %)
(YCO 5 %)
measuredmeasured
(YCO 5(Y%)
CO 5 %)
0
400
500
B
S h= A ( R e ) S c (1/3)
500
600700 700 800 800
600
T [K] T [K]
CO conversion [%]
( Rflow
N u= A
e ) rate
P rQ = 6000Ncc/min.
feed
60
foam-type one does not allow an efficient
surface, which are responsible for its mass transfer to- B figuration,
S h= A ( R e ) Sremoval
c (1/3) ofthe
60
the heat from the catalytic surface. Therewards the reaction region.
It can be seen in Figures 12
fore, the temperature of the catalyst is expected to be
and 13 that CFD simulations give a reasonable predic40
higher than the temperature measured in the front of
tion of the light-off curve,40describing the transition from
the foam, where the thermocouple is located. For this
a kinetic-controlled to a diffusion-controlled process.
CFD (Y
3 %)
foam D - CFD
20
CFDis
(YCO
3 %) towards a
foam
A (YCO 3 %) - CFD
foam
D
CFD
reason, the computed light-off curve
shift
20
measured (Y
3 %)
foam D - measured
The CO conversionfoam
atDhigh
temperature is correctly
foam
- CFD
foam
AE(Y
measured (YCO 3 %)
CFD (Y
5 %)
- measured
CO 3 %) - measured
higher temperature, if compared to CFD
the(Ymeasured
one.
foam E - measured
5 %)
(Y
predicted
while an overestimation
of the light-offmeasured
temfoam E - CFD
foam A (Y
1 %) - CFD
5 %)
CO conversion [%]
km [m/s]
80
km [m/s]
(1/3)
Figure 10: Foam-type reactor: mass-transfer coefficients for different
Figure 12: Foam-type reactor, sample E: CO conversion for an inlet
80
100
Figure 13:B Foam-type
reactor,
sample E: CO conversion for an inlet
(1/3)
foam samples.
feed
flow rate
Q = 3000Ncc/min.
100
foam A (YCO 3 %) - CFD
foam A (YCO 3 %) - measured
foam A (YCO 1 %) - CFD
foam A (YCO 1 %) - measured
10−1
measured (YCO 3 %)
101
CO
CO
CO
CO
CO
0
CO 1 %) - measured
"foam A (Y
perature
with
500
600
700
measurements
T [K]can be
CO
measured
CO 5 %)
respect to the
ob-800
Moreover, it can be seen that, at
the (Ylight-off
temQ 105 · m3/s
−1
0
10
served,
for the lower CO concentration.
perature,
the conversion
is700
reaching
400 when500
600
800its maxi10!1in particular
"
3
T
[K]
This Q
can10
be5 explained
considering
the
assumption,
made
mum
value,
the
curve
exhibits
a
smooth
transition
from
Figure 10: Foam-type reactor: mass-transfer coefficients for different · m /s
Figure 12: Foam-type reactor, sample E: CO conversion for an inlet
in the simulations,
temperature distribution
kinetic- to reactor,
diffusion-controlled
conversion.
Figure 14: Foam-type
sample E: COCO
iso-surfaces
for As
an a
foam samples.
feedof
flowuniform
rate Q = 3000Ncc/min.
on the foam catalyst surface. Actually, this assumption
matter
of fact,
model
does
include
inlet CO mass
fraction
YCO the
= present
4.6% and
a feed
flownotrate
Q = a
3000Ncc/min.
WCCM
– ECCM
V mass-transfer
- ECFD
VI
Barcelona
2014condition
Figure 10:XI
Foam-type
reactor:
coefficients
different
Figure 12: Foam-type
reactor,
sample E:
CO conversion
an inlet
does
not
describe accurately
theforexperimental
pore-diffusion
sub-model,
therefore
a sharp for
transition
figuration, thewere
foam-type
one doesAs
notaallow
an efficient
surface, which
aresamples.
responsible for its mass
transfer
to- measurements
foam
feed
rate
Q = be
3000Ncc/min.
under
which
performed.
mat-flow
should
expected in this region. However, in this case
of of
thethe
heatplate-type
from the catalytic
wards the reaction region. It can be seen ter
in Figures
of fact,12on theremoval
contrary
reactor surface.
con- Therethe explanation for the smoothness of the curve can be
!
400
foam E - measured
In this wor
alytic surface
sis of the ope
solver was co
in order to de
account the d
the washcoat
surface. Stead
sumption of
the surface. T
Langmuir-Hi
priori on the b
ture for simila
validated for
plate-type rea
ing a satisfac
experiments.
a foam subst
curve was co
tal data is reg
the simplifica
lar, the slight
curve is consi
perature of th
istic for this
sumption, a m
model is nee
mal balance o
actual temper
Examples of application
POLITECNICO
DI MILANO
!   Macro-scale approach is based on a multi-regions framework, in which fluid and
solid phases are simulated on different (partially or totally) overlapping mesh.
!   Models are introduced for the coupling between the solid and fluid phases.
Micro-scale approach
Macro-scale approach
Check on
consistency between
macro- and microscale approaches
WCCM XI – ECCM V - ECFD VI Barcelona 2014
POLITECNICO
DI MILANO
Examples of application
Heating runs
WCCM XI – ECCM V - ECFD VI Barcelona 2014
Cooling runs
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Examples of application
Simulation of flow trhrough a
couple of DPF channels
EX80-100/17
WCCM XI – ECCM V - ECFD VI Barcelona 2014
EX80-200/14
Examples of application
DPF thermal transient
Multi-layer foam catalyst
thermal transient
WCCM XI – ECCM V - ECFD VI Barcelona 2014
POLITECNICO
DI MILANO
Conclusions
! 
! 
! 
! 
! 
POLITECNICO
DI MILANO
Full set of libraries for volume averaging and surface chemistry
has been implemented in OpenFOAM.
Real open cell foams can be approximated by Kelvin cell type
structures having similar properties and similar behaviour
(pressure drop and heat/mass transfer).
Flow resistance is mainly dependent on inertial effect of the
fluid dodging the foam struts.
Properties can be summarized in look up tables and used for
full scale simulations with coupled multi regions.
Applications have shown that the approach can be used to
perform full scale simulation exploiting the information
extracted with detailed simulation of the micro scale.
WCCM XI – ECCM V - ECFD VI Barcelona 2014
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