CRMHT

SFT- Poitiers- February 6th 2009

B. Rousseau*,

H. Gomart, D. De Sousa Meneses, P. Echegut

J.-F. Thovert

*benoit.rousseau@cnrs-orleans.fr

(ex CRMHT) Conditions Extrêmes et Matériaux : Haute Température et Irradiation1D, avenue de la Recherche Scientifique, 45071, Orléans, Cedex 02

Interest of the multi-scale characterization of a heterogeneous

material for the prediction of its thermal radiative behaviour

CRMHT

SFT- Poitiers- February 6th 2009

1500 K1000 K

RADIATIVE HEAT TRANSFER IN COMPLEX INDUSTRIAL DEVICES

2000 K500 K 2500 K

M 88 SNECMAIFP

S. Gauthier, Ph. D, CETHIL, 2008

E. Chalopin, Ph. D, EM2C, 2008

CRMHT

SFT- Poitiers- February 6th 2009

POROUS MEDIUM : RELEVANT LENGTH SCALE?

nmHeat Tranfer

µm

mm

cm

Ex : Metallic Foam Thermal Radiative Properties

Microstructure Chemistry

Material Characterization

CRMHT

SFT- Poitiers- February 6th 2009

DIRECT RADIATIVE PROPERTIES

( )TA ,,θσ

( )TRd ,,θσ

( )TRs ,,θσ

( )TTs ,,θσ( )TTd ,,θσ

Kirchhoff ‘s law:

( )TA ,,θσ( ) =TE ,,θσ

( ) ( ) ( )TTTRTA ,,,,1,, θσθσθσ

−−=

Local Thermodynamic Equilibrium

Energy balance

1000 100000.0

0.2

0.4

0.6

0.8

1.0

FIR MIR NIR UVVIS

500 K 1000 K 2000 K 2500 K 5800 K

Norm

alize

d S

pect

ral I

rradi

ance

Wave number (cm-1)

ds RRR +=

ds TTT +=

1),(

2

310

−=

TC

e

CTL σσσ

∆dΩ

T

)T,,(L θσ

d

( ) ( )( )TL

TLTE,,, ,, 0 σ

θσθσ =

Planck‘s law

CRMHT

SFT- Poitiers- February 6th 2009

EXPERIMENTAL SET UP

DETECTORS

IR SOURCES

INTERFEROMETERS•REFLECTANCE•TRANSMITTANCE

LASER CO2 (500 W)

4 - 1200 K10 - 40 000 cm-1

(1 000 - 0.25 µm)

SAMPLE

CO2 LASER (500 W)

BLACK BODY

DIAPHRAGM

•EMITTANCE500 - 2 500 K10 - 14 500 cm-1

(1 000 - 0.7 µm)

Bruker IFS 113+

Bruker IFS 88

300 K400 à 5 500 cm-1

(25 à 1.8 µm)

CRMHT

SFT- Poitiers- February 6th 2009

500 1000 1500 2000 2500 3000 3500 4000 45000.0

0.2

0.4

0.6

0.8

1.05101520Wavelength (µm)

SiO2

Norm

al S

pect

ral E

mitt

ance

Wave number (cm-1)

T=1300 K

MODEL POROUS MEDIUM : SILICA GLASS WITH BUBBLES

4 35

Thickness = 1 mm

P = 2.7%

100 µm

P = 5.6%

P = 12.9%

P= 0%

CRMHT

SFT- Poitiers- February 6th 2009

1000 2000 3000 4000 50000.0

0.2

0.4

0.6

0.8

1.0

Norm

al s

pect

ral e

miss

ivity

Wave number (cm-1)

Ceramic tile

T=1000 K

Wavelength (µm)510

20 µmRousseau et al., Appl. Phys. Lett., 79 (2001), 3633.

IR heater

IR heaters• Ceramic tile• Praseodymium nickelate (Pr2NiO4+δ) 100 µm

Rough Coating Pr2NiO4+δ

• roughness• nearly black body behavior

BLACK BODY COATING

single crystal Pr2NiO4+δ

A = La3+ ou Pr3+

B = Ni2+

O2-

ABO3

c

b

a

A = La3+ ou Pr3+

B = Ni2+

O2-

ABO3

c

b

a

CRMHT

SFT- Poitiers- February 6th 2009

OBJECTIVE

Thermal Radiative Properties

Texture Chemistry

Material Characterization

Modelling

Experimental

300 - 2500 K10 - 40 000 cm-1

(1 000 - 0.25 µm)

Infared emission spectroscopy

CRMHT

SFT- Poitiers- February 6th 2009

A SEMI TRANSPARENT COMPOUND :

SILICA GLASS WITH BUBBLES

CRMHT

SFT- Poitiers- February 6th 2009

Chemical Analysis-fused silica based on grain quartz grains of high purity (99.99 %)-amount of metallic impurities ∼ 100 ppm

Textural Analysis

CLASSICAL CHARACTERIZATION OF THE GLASS

CRMHT

SFT- Poitiers- February 6th 2009

IMAGE ANALYSING OF 3D DATA (P = 12.9 %)

SiO2_plane_075.jpg

SiO2_plane_150.jpg

ESRF ID15 AM. Di Michiel, Rev. Sci. Instrum. 76, 0432702 (2005)

SiO2_plane_01.jpg

1 px = 14.6 µm

10 mm150 slides

Image analyzing

Threshold

Binarised Image

Coll. J.-F. Thovert LCD Poitiers

CRMHT

SFT- Poitiers- February 6th 2009

“MATERIAL PARAMETERS”→ RAY TRACING?

No interferences

Multiple scattering

Geometrical optics

No diffraction1

2>=

λπ r

x

25 < λ < 2 µm (400 < σ < 5000 cm-1)

gr ≈

21>λ

g

Multiple reflection

1 voxel = 14.6 µm

20 40 60 800.00.10.20.30.40.50.60.70.80.91.0

Norm

alize

d fre

quen

cy

Radii (µm)

B. Rousseau et al., Applied Optics (2007)

Siegel & Howell, 1992

CRMHT

SFT- Poitiers- February 6th 2009

NUMERICAL EXPERIMENT

zyx

Forward

Backward

T

R

( ) ( ) ( )TTTRTE ,,,,1,, θσθσθσ

−−=

Large number of rays : 105-106

Simulation in a realistic reconstructed volume

Large spectral domain [1-25 µm]

Large set of statistic data

path length in the solid phase (transparent, semitransparent, opaque)

path length in the void phase

number of intercepted interfaces

position and incident angle of a photon (at the beginning of its travel)

position and exhaust angle of a photon (at the end of its travel)

CRMHT

SFT- Poitiers- February 6th 2009

ιlim

rinSiO~sinsin~

2 =

i

r

( ) ( )( )

( )

( )( )

( )

( ) ( )( )

( ) ( )( )

+

−+

+

−=

2

21

21

2

21

21

,~,~cos

,~cos,~,~

cos,~cos

,~,~,~cos

cos,~,~

,~coscos

21,

TnTn

iTr

TnTn

iTr

TnTn

Tri

TnTn

Tri

T

σσσ

σσσ

σσ

σ

σσ

σσρ

MCRT procedure (0< ξ <1)

ξ<ρ : reflexionξ>ρ : refraction

ABSORPTION/SCATTERING PROCESSRefraction index gradient : scattering

Snell-Descartes ‘s law

Fresnel’s law

iKili eII −= 0

Chemin optique : absorption

Beer-Lambert ‘s law

lSiO2

MCRT procedure 01.0<∑i

iI

2~

SiOn

2~

SiOn

Key role :

Optical function (n, k , K)

lAir

CRMHT

SFT- Poitiers- February 6th 2009

ε~~ =n

1000 2000 3000 4000 50000.0

0.2

0.4

0.6

0.8

1.01020 Wavelength (µm)

SiO2

162 µm

T = 300 K T = 856 K T = 1305 K T = 1818 K

Norm

al S

pect

ral E

miita

nce

Wave number (cm-1)

0.0

0.5

1.0

1.5

2.0

2.5

3.0

3.5

Refra

ctive

inde

x

T = 300 K T = 856 K T = 1305 K T = 1818 K

1000 2000 3000 4000 50000.01

0.1

1

10

100

1000

10000 K = 45 cm-1

σ = 2130 cm-1

K = 10 cm-1

σ = 2130 cm-1

T=300 K T=856 K T=1305 K T=1818 K

Abso

rptio

n Co

effic

ient

(cm

-1)

Wave number (cm-1)

OPTICAL FUNCTIONS OF SIO2

( ) ( ) ( )TikTnTn ,,,~ σσσ +=( ) ( )TkTK ,4, σπσσ =

( ) ( )∑+= ∞j

jLjGjjVCT γγωωεωε ,,;,~0

( ) ( )( ) ( )( )( ) ( )dTK

dTK

eTeTTE ,

,

,11,1, ω

ω

ωρωρω −

−

−−−

=

De Sousa Meneses et al., JNCS, 351, (2005)

CRMHT

SFT- Poitiers- February 6th 20091000 2000 3000 4000 5000

0.0

0.2

0.4

0.6

0.8

1.01020 2

Wave length (µm)

Norm

al S

pecr

tal E

mitt

ance

Wave number (cm-1)

Experiment MCRT

Thickness = 1 mmT = 1300 K

5

CHEMISTRY+MICROSTUCTURE ?

1000 2000 3000 4000 50000.0

0.2

0.4

0.6

0.8

1.0

R,T

Wave number (cm-1)

R

T

TRE

−−=1

106 photons

(× 10)10 mm1

mm

1000 2000 3000 4000 50001E-71E-61E-51E-41E-30.010.1

110

1001000

10000

Abso

rptio

n Co

effic

ient

(cm

-1)

Wave number (cm-1)

SiO2 without OH SiO2 with OH

B. Rousseau et al. COLSUA, 300, pp. 162-168 (2007)

CRMHT

SFT- Poitiers- February 6th 2009

DESIGN OF POROUS GLASSES

COALESNCE MODEL

p= 5 % p= 10 % p= 15 % p= 20 % p= 25 %

TomoS = 89 cm-1

TomoS25.0 TomoS5.0 TomoS TomoS25.1 TomoS5.1

%10=p

TomoS

CRMHT

SFT- Poitiers- February 6th 2009

1000 2000 3000 4000 50000.00.10.20.30.40.50.60.70.80.91.0

5% 10% 15% 20% 25%

Tran

smitt

ance

Wave number (cm-1)

1000 2000 3000 4000 50000.00.10.20.30.40.50.60.70.80.91.0

Refle

ctan

ce

Wave number (cm-1)

5% 10% 15% 20% 25%

NUMERICAL RESULTS

T = 1 300 K,

L*l*h = 10 * 10 * 1 mm, S = Stomography

1000 2000 3000 4000 50000.00

0.05

0.10

0.15

0.20

0.25

0.30

0.35

0.40 0.5 S1 0.75 S1 1.0 S1 1.25 S1 1.5 S1

Refle

ctan

ce

Wave number (cm-1)

1000 2000 3000 4000 50000.0

0.2

0.4

0.6

0.8

1.0

Tran

smitt

ance

Wave number (cm-1)

p = 10 %

CRMHT

SFT- Poitiers- February 6th 2009

2.0 2.5 3.0 3.5 4.02400

2600

2800

3000

4.0

4.5

5.0

5.5

6.0

6.5

7.0

7.5

d (µ

m)

Wavelength (µm)

n

2.0 2.5 3.0 3.5 4.00

5

10

15

20

25

Méthode semi-inverse (Baillis - CETHIL) Simulation MCLR

Wavelength (µm)

l -1sca (cm-1)

Scat

terin

g co

effic

ient

(cm

-1)

20 40 60 80 100 120 140 160 1805

10

15

20

25

30

35

Simulation MCRT Γ=S/4

Volumic surface (cm-1)

Sca

tterin

g coe

fficien

t (cm

-1)

5 10 15 20 2505

101520253035404550

Porosité

Sca

tterin

g coe

fficien

t (cm

-1)

Simulation MCLR

( )

∫

∫∞

∞

=Γ

0

3

0

2

)(43

drrrf

drrrfp

INFLUENCE OF THE VOLUMETRIC SURFACE

CRMHT

SFT- Poitiers- February 6th 2009

AN OPAQUE MEDIUM

ROUGH COATING OF Pr2NiO4+δ

100 µm

CRMHT

SFT- Poitiers- February 6th 20091000 2000 3000 4000 5000

0

1

2

3

4

5

Com

plex

e re

fract

ive in

dex

Wave number (cm-1)

n(σ,T) k(σ,T)

d > 2 µmOpaque material

( ) ( )( )

( )( )

( )( )

22

0 1,~1,~

1,~1,~

,,

,+−

=+−

==TT

TnTn

TITI

T reflected

σεσε

σσ

σσ

σρ

( ))(

,~

,

,22

,

,22

,

,22

,

To

TplTpl

j TTOjTTOj

TLOjTLOj

ii

iiT

γσσσγσ

σγσ

σγσεσε

−

+−Ω−

+−Ω

+−Ω= ∏

∞

B. Rousseau et al. PRB 2005

0 1000 2000 3000 4000 50000.0

0.2

0.4

0.6

0.8

1.0

Norm

al s

pect

ral r

efle

ctivi

vty

Wave number (cm-1)

OPTICAL FUNCTIONS OF Pr2NiO4+δ

T = 1000 K

CRMHT

SFT- Poitiers- February 6th 2009

HOW CAN WE EXTRACT THE GEOMETRIC SURFACE?

Rough coating Pr2NiO4+δ

Alumino-silicate tile

20°C

HEIGHT CARD ONA REGULAR GRID

[280×250]

20°C20°C

X-RAY µ-TOMOGRAPHY Resolution ∼0.7 µm

CRMHT

SFT- Poitiers- February 6th 2009

ωrm

s/τ

0.01

0.1

1

10

0.01 0.1 1 10

cosθ.ωrms/ λ

Light Matter InteractionTang et Buckius, IJHMT, 1997

2rms )y,x(Z=ω

2Z )y,x(Z))y,ux(Z)y,x(Z(

)u(R+

=

( )1z eR −=τ

300 Kωrms =5. 5 µmτ = 8.4 µm

500 K

ωrms = 5.7 µmτ = 8.7 µm900 Kωrms =5. 6 µmτ = 8.3 µm

STRATEGY OF SIMULATION ?Statistical parameters

Geometrical optics

CRMHT

SFT- Poitiers- February 6th 2009

R

MODELLING : ROUGH SURFACE

LOCAL SCALEReflected Intensity Fresnel ‘s law

( )iT θσρ ,,

θin

θr

3D image of the coating surfaceT = 900 K

To reproduce an experiment where :

Large number (106) of rays issued from an infrared parallel beam are thrown onto the numeric surface

RE

−=1

1000 2000 3000 4000 50000.00.10.20.30.40.50.60.70.80.91.0

Ray Tracing + Tomography Single crystal

Norm

al s

pect

ral e

miss

ivity

Wavenumber (cm-1)

Rough Coating Pr2NiO4+δ

CRMHT

SFT- Poitiers- February 6th 2009

2D-surface with V-groove cavities:An analytic model(Sacadura, IJHMT, 1972 & Maruyama et al., SEMSC, 2004)

3D-random rough surface (gaussian):Literature-ray tracing data (Bergstrom et al., JAP, 2008)

0,0 0,2 0,4 0,6 0,8 1,0 1,2 1,4 1,6 1,8 2,00,0

0,2

0,4

0,6

0,8

1,0

Rh

Cu

Norm

al s

pect

ral e

miss

ivity

ωrms / τ

Ti

30°<θ<45

0 10 20 30 40 50 60 70 80 900,00

0,05

0,10

0,15

0,20

Norm

al s

pect

ral r

efle

ctivi

ty

Angle θ (degrees)

Analytic Analytic Analytic

RAY TRACING VALIDITY : LITERATURE COMPARISON

Ray tracingRay tracingRay tracing

n = 2.5, k = 0

n = 2, k = 0

n = 1.5, k = 0 Bergström et al.This work

This workMaruyama et al.

CRMHT

SFT- Poitiers- February 6th 2009

pore : 50 -200 nm

D.E. Apnes, optical properties of thin films, Thin Solid Films 89 (1982) 249

dpore<< λinfrared (2-20 µm)

EFFECT OF THE INTERNAL MICROSTRUCTURE

( ) ( ) ( )( ) ( ) ( )( )

( ) ( )( ) ( ) ( )( ) 0

,~,~,~,~,~

,~,~,~,~,~

1 =−+

−+

−+

−−

TTyTTT

pTTyT

TTp

effporeporeeff

effpore

effpolypolyeff

effpoly

σεσεσεσεσε

σεσεσεσεσε

1000 2000 3000 4000 50001.0

1.5

2.0

2.5

3.0

3.5

4.0

Ref

ract

ive

inde

x, n

(σ,T

)

Wave number (cm-1)

p = 0.0 p = 0.40 p = 0.60 p = 0.70

Effective Medium Approximation

( )Tnpoly ,~ σ

( ) ( )TTn effeff ,~,~ σεσ =

( ) 1,~ =Tnair σ

d

d 1000 2000 3000 4000 50000

5000

10000

15000

20000

25000

30000

Extin

ctio

n co

effic

ient

k(σ

,T)

Wave number (cm-1)

p=0 p=0.40 p=0.60 p=0.70

p =70% d> 11 µm (opaque)

CRMHT

SFT- Poitiers- February 6th 2009

1000 2000 3000 4000 50000.500.550.600.650.700.750.800.850.900.951.00

Ray Tracing + Tomography Single crystal

Norm

al s

pect

ral e

miss

ivity

Wavenumber (cm-1)p = 0.6

p = 0.4

Rough Coating Pr2NiO4+δ

HYBRID MODEL : RAY TRACING+EMA

p = 0

p = 0

ESTIMATION OF THE POROSITY OF A COLLECTION OF GRAINS?

Thèse Hector Gomart, Université d’Orléans, 2008

CRMHT

SFT- Poitiers- February 6th 2009

Heterogeneous materialmicro & nano porous

Glass-Ceramic-Foam

Thermal Radiative Properties

Equivalent:

Bi-directional Reflectance and TransmittanceExperimental characterization

Infrared emittance spectroscopy300-3000 K, 0.8-1000 µm

MATERIAL

ENERGY

3D image of the porous materialPhoton transport at the local scale

MULTIPHYSIC COMPUTING CODE

( )µP ′,,, µωβ

Numerical experiment

ELABORATION

Validation

STRATEGY OF PREDICTION

Direct : E,R,T

CRMHT

SFT- Poitiers- February 6th 2009

A MORE COMPLEX SAMPLE :MULLITE FOAMWORK PERFORMED WITH EM2C & CETHIL

Mullite foam(porosity 0.85)

for catalytic combustion

p = 0.85

600 µm 40 µm 1 µm pore size classes

•

500 µm 20 µm 10 µm

Hg porosimetry

CRMHT

SFT- Poitiers- February 6th 2009

1 µm

7 µm

La2-xNiO4 δ 2h – 1000°C

YSZ

SOFC CATHODE

MIEC cathode

1000 2000 3000 4000 50000.00.10.20.30.40.50.60.70.80.91.0

3 La2-xNiO4+δ layers 2 La2-xNiO4+δ layers 1 La2-xNiO4+δ layer

Norm

al S

pect

ral E

miss

ivity

Wave number (cm-1)

T = 900 K

CRMHT

SFT- Poitiers- February 6th 2009

HEAT TRANSFER IN SOFC?

Thermo-mechanical failures in the ceramics used in the design of SOFC

Local temperature gradient at the interface of each component

Prediction of the temperature field in the cell(ceramics+interconnects)

Murthy et al., J. Power Sources 2006 K.J. Daum et al. , J. Power Sources (2006) Damm et al., Transaction of the ASME, 2005