IPPW6, Atlanta, June 2008 PICA-like materials : Surface or Volume ablation ? 1/25
Ablation of PICA-like MaterialsSurface or Volume phenomenon?
Jean Lachaud*, Ioana Cozmutax, and Nagi N. Mansour+
+ NASA Ames Research Center : [email protected] * NASA Postdoctoral Fellow at Ames : [email protected]
xELORET Corporation : [email protected]
Sponsored by NASA’s Fundamental Aerodynamic Hypersonic Program
6th International Planetary Probe Workshop, Atlanta, June 2008
Stardust (PICA TPS)Lunar return : CEV with a PICA TPS
IPPW6, Atlanta, June 2008 PICA-like materials : Surface or Volume ablation ? 2/25
. Introduction and Objective. Introduction and Objective
• Introduction :– The ablation of the char layer in ablative material is usually described in term of
recession velocity. This “surface” description is valid for dense materials. – However, the recession of the average surface in porous materials may not recede
uniformly but matrix and fibers may progressively vanish in depth inside the structure : “volume ablation”.
– PICA-like materials are porous and may undergo volume ablation with two important consequences :
• The material weakens in volume and is possibly subject to mechanical erosion (Spallation)
• The ablation enthalpy distributed in volume modifies the thermal response
• Objectives of this presentation:– Model and understand ablation using a porous medium model– Estimate whether volume ablation is an important phenomenon or not – Decide if an elaborated model taking into account a volume ablation fully coupled
with pyrolysis have to be developed (many years of development). If it is the case, a first model will be presented.
“The time to study and fully understand the limits of PICA is NOW” B. Laub and E. Venkatapathy, IPPW5, 2007.
IPPW6, Atlanta, June 2008 PICA-like materials : Surface or Volume ablation ? 3/25
. OUTLINE. OUTLINE
1. Modeling of the structure of PICA-like materials
2. Modeling of the Ablation of porous materials
- Microscopic model
- Numerical Simulation at microscopic scale
- Homogenization macroscopic behavior
3. Application to Stardust Reentry Conditions
- Macroscopic model including blowing effects
- Volume or Surface Ablation?
4. Possible ablation model for a volumetric coupling with Pyrolysis
5. Conclusion & Next steps
IPPW6, Atlanta, June 2008 PICA-like materials : Surface or Volume ablation ? 4/25
1. Modeling of the structure of PICA-like materials1. Modeling of the structure of PICA-like materials
• Preform :
– Random arrangement of carbon fibers
– High porosity
• Matrix :
– Phenolic resin
– Low mass fraction
• Material type :
– Ablator
– Low density
Structure of “PICA-like” materials
M. Stackpoole et al., AIAA 2008-1202 (Reno 2008)M. Stackpoole et al., AIAA 2008-1202 (Reno 2008)
char transition
IPPW6, Atlanta, June 2008 PICA-like materials : Surface or Volume ablation ? 5/25
1. Modeling of the structure of PICA-like materials1. Modeling of the structure of PICA-like materials
• Random drawing of non-overlapping cylinders (Monte-Carlo algorithm)
• Cylinders more or less parallel to the surface (Bias on azimuthal angle)
• Choice of a Length/Radius ratio (around 50 for PICA-like materials)
Fibrous preform : fiber size / orientation / porosity (statistical)
Totally Random Complementary Azimutal angle : +/- 15°
Interesting result : limit porosity = 0.85 for totally random structures / 0.9 for parallel
IPPW6, Atlanta, June 2008 PICA-like materials : Surface or Volume ablation ? 6/25
• Before pyrolysis : different possibilities
– Thin layer of matrix surrounding the fibers
– “Fluffy” matrix occupying the pores of the fibrous structure
• After pyrolysis : matrix structure is modified
– Due to an important mass loss during pyrolysis
– Resulting structure varies with experimental conditions
• Models :
1. Modeling of the structure of PICA-like materials1. Modeling of the structure of PICA-like materials
Matrix
Thin matrix layer around the fibers Virgin fluffy matrix homogeneous at fiber scale
IPPW6, Atlanta, June 2008 PICA-like materials : Surface or Volume ablation ? 7/25
• Objective :– Estimate whether volume ablation is an important phenomenon or not
using a simple model In order to decide if an elaborated model taking into account a volume
ablation fully coupled with pyrolysis have to be developed
• Main Hypothesis :– If volume ablation occurs, it occurs mainly in the char layer Ablation model loosely coupled with pyrolysis
• Approach :– Multiscale modeling: microscopic scale (fibers) macroscopic scale
(composite)– Numerical models to provide guidelines and accurate results– Simplified analytical models to provide understanding– Application of the models to flight conditions (includes a loosely coupling
with pyrolysis)
2. Ablation model for porous media2. Ablation model for porous media
Objective and assumptions
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2. Ablation model for porous media2. Ablation model for porous media
• Idea : Use a simplified model to try and understand the Ablation of porous media
• Hypotheses :– Simplified structure : carbon fibers randomly oriented
– Simple chemistry (Cs oxidized by 02 or sublimated)
• Starting point : differential recession of a
heterogeneous surface S by gasification
Reaction/Transport & Recession model in a carbon felt
N.B. : oxidation notations BUT sublimation is mathematically equivalent
xz
J
v
CO2(x,y,z=0,t)=CoVertical mass transfer of oxygen
CO2(x,y,z,t)
FIBERS
. 0S
St
v
J v n
fJ k C
( ) 0gC
D C v Ct
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Simulationtool
2. Ablation model for porous media2. Ablation model for porous media
Reaction/Diffusion : Simulation (1/2) : diffusion << reaction (D/L << kf)
Surface
Bottom
Oxygendiffusion
Periodiccell in x,y
Hypotheses:-Isothermal-No pyrolysis gas
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Reaction/Diffusion : Simulation (2/2) : diffusion >> reaction (D/L >> kf)
2. Ablation model for porous media2. Ablation model for porous media
Surface
Bottom
Oxygendiffusion
Periodiccell in x,y
Hypotheses:-Isothermal-No pyrolysis gas
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Volume Ablation (D/L >> kf ) Surface Ablation (D/L << kf )
2. Ablation model for porous media2. Ablation model for porous media
Surface or Volume ? depends on experimental conditions
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Homogenization and Analytical solution (hyp. : no recession)
2. Ablation model for porous media2. Ablation model for porous media
• Volume or surface? Key information : C, oxidant concentration
• 1D model to obtain an analytical solution : C (z) = f (experimental conditions)
Hyp., bulk diffusion between perpendicular fibers:
( ) ( ) ( )z z yq z q z dz q z
( ( ) ( )) ( )p f fD C z C z dz S k C z P dz p fS /P = /ss (m2/m3) : specific surface
Mass balance in steady state :
0
cosh ( / 1)( )
coshsz L
C z C
Thiele number : s
eff
f
L
D
sk
effD D
BUT…
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2. Volume Ablation model2. Volume Ablation model
• Knudsen number : (continuous regime for Kn < 0.02)
• Pore size around 50µm Knudsen regime for mean free path < 1µm
• Air :
Validity domain of the continuous regime hypothesis
/ pKn d
59 10
95 10298
T
P
Reentry conditions :Knudsen regime inside the porous medium
Model still correct inKnudsen regime?
Stardust peak heating (Kn=0.08)
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2. Ablation model for porous media2. Ablation model for porous media
• Knudsen effects : Diffusion coefficient in a capillary (Bosanquet model)
• Fibers randomly oriented : tortuosity effects non negligible in Kn regime
Model still correct in Kn regime but with a modified diffusion coefficient
eff refD D
1 13 3
1 1 1 1 1
ref B K pD D D v vd (harmonic average)
Tortuosity has to be obtained by Monte Carlo simulation inside the porous media (not available yet in the literature fornon-overlapping fibers)
1 1 1
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1) Displacement of 10000 walkers followed during (chosen for convergence)
2) Einstein relation on diffusion process :
2. Ablation model for porous media2. Ablation model for porous media
• Monte Carlo Simulation :– Random Walk rules :
• (T,P) fixed = (λ,D) fixed• λ : Maxwell-Boltzmann distribution• constant velocity norm
(D = 1/3 v λ) with 3D random
direction drawing• Tortuosity as a function of Kn for the fibrous material of this study
Determination of the effective diffusion coefficient Deff
2
2j
e jD
Illustration : path of a walker in a periodic cell
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Parametrical analysis
2. Ablation model for porous media2. Ablation model for porous media
0
cosh ( / 1)( )
coshsz L
C z C
z/Ls
• Concentration gradient (1D model) as a function of Thiele number
Ls: material depth (m)Deff: effective diffusivity (m²/s)kf: fiber reactivity (m/s)s : specific surface (m2/m3)
Consumption / diffusion velocitiesfor porous media
Volume Ablation
Surface Ablation
Thiele number
s
eff
f
L
D
sk
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• Steady state equation including the convective term (continuous regime)
• Solution (of the quadratic ODE with one Dirichlet B.C. : C(z=0)=C0)
3. Application to Stardust Reentry Conditions3. Application to Stardust Reentry Conditions
2
² 1 10
² C R
C CC
z L z L
Model must include blowing effect (pyrolysis gas)
Cg
DL
v eff
Rf
DL
skwith and
2
0( ) exp 1 1/ 4 C
C R
LzC z C
L L
10C RL L Blowing effect negligible (on concentration gradient)
Example : Stardust peak heating
/ 0.145C RL L Blowing effect almost negligible
IPPW6, Atlanta, June 2008 PICA-like materials : Surface or Volume ablation ? 18/25
3. Application to Stardust Reentry Conditions3. Application to Stardust Reentry Conditions
• model including blowing effects + thermal gradients (data from FIAT simulations) : Concentration in the char layer (FE solution: FlexPDE code)
Stardust Peak Heating (stagnation point)
Temperature gradient imposedDiffusion coefficient computed100*exp( / )f Ak E RT
S. Drawin et al., AIAA 92-210
Nor
mal
ized
con
cent
ratio
n
Volume Ablation0.5 mm = 50 fiber diameters
Cha
r la
yer
bott
om
surf
ace
IPPW6, Atlanta, June 2008 PICA-like materials : Surface or Volume ablation ? 19/25
0
0,2
0,4
0,6
0,8
1
0 20 40 60 80 100 120
time (s)
0
0,0005
0,001
0,0015
0,002
0,0025
0,003
0,0035
0,004
0,0045
C(z=Ls)/Cw
Ls
z: C(z)=10%Cw
3. Application to Stardust Reentry Conditions3. Application to Stardust Reentry Conditions
Stardust trajectory (stagnation point)
C/C0
z (m)
Peak Heating
Post flight analysis
> 10 % C> 10 % C00< 10 % C< 10 % C00
Nor
mal
ized
con
cent
ratio
n
Dep
th
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4. Volume coupling of Pyrolysis & Ablation4. Volume coupling of Pyrolysis & Ablation
Integration of ablation in the pyrolysis model : first ideas
( ) f fg m mg g tv
t t
g
Kv p
0m f
( ) ( ) f fm mg g f f f m am m g g g p bl
Tc c c k T c v h
th
t tT
_
, ,1
( ) 1 expi i
n lawsn Ai
m v v i p i i i ii
Ewith A
t RT
.f const ?f
t
Mass balance
Momentum balance
Energy balance
Pyrolysis law
Ablation law (fibers)
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• Ablation : surface phenomenon at microscopic scale, but volumetric at macroscopic scale
4. Volume coupling of Pyrolysis & Ablation4. Volume coupling of Pyrolysis & Ablation
( , )2 ( ) ( , )f
s f
d z tk T C z t
t
rf
Ablation fluxLocal approach
2
0_ 0
( , )( , ) 1 (1 ) f
f
d z tz t
d
0.5f0
f_0
( , ) 4 k (T) C(z,t)( ( , ) ( ( , ))) (1- ( , ))(1- )
deff
C z tdiv D T P grad C z t z t
t
– Homogenization : fiber diameter mean porosity
– Convenient variable for ablation modeling : ε
– Mean fiber diameter evolution
– Density :
(1 )material f
Multiscale modeling of the ablation of the carbon felt
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4. Volume coupling of Pyrolysis & Ablation4. Volume coupling of Pyrolysis & Ablation
Illustration of the proposed Ablation law for Stardust Peak Heating thermal conditions
• Simulation of the “oxidation part” of ablation (loosely coupled with pyrolysis) in the carbon felt
IPPW6, Atlanta, June 2008 PICA-like materials : Surface or Volume ablation ? 23/25
• Simulated in the carbon felt
4. Volume coupling of Pyrolysis & Ablation4. Volume coupling of Pyrolysis & Ablation
Stardust conditions : pure oxidation from 90s (T<Tsublim) to 130s (T>Toxi)
IPPW6, Atlanta, June 2008 PICA-like materials : Surface or Volume ablation ? 24/25
. Material Behavior Analysis (cont.). Material Behavior Analysis (cont.)
• Overall behavior well predicted by current models (FIAT simulation presented below)
• BUT : char zone density overestimated Volume ablation could
be the cause of the lower
density observed The fluffy matrix of
PICA is likely to play an
important role into
volume ablation
prevention
Literature : Stardust Post-flight Analysis
M. Stackpoole et al., AIAA 2008-1202 (Reno 2008)
IPPW6, Atlanta, June 2008 PICA-like materials : Surface or Volume ablation ? 25/25
. Conclusion / Next steps. Conclusion / Next steps
• Porous media model for the ablation of fibrous materials Porous media model for the ablation of fibrous materials – Importance of Importance of Thiele Number Thiele Number (diffusion/reaction competition in porous media)(diffusion/reaction competition in porous media)– Knudsen regimeKnudsen regime inside the porous media inside the porous media– Volume / Surface Volume / Surface phenomenon? phenomenon? depends on experimental conditions depends on experimental conditions– Stardust conditions:Stardust conditions:
• Low effect of blowing on mass transfer Low effect of blowing on mass transfer inside the porous media inside the porous media • ablationablation by oxidation in by oxidation in volume volume for a carbon feltfor a carbon felt
– Idea for volume coupling of pyrolysis and ablation at macroscopic scaleIdea for volume coupling of pyrolysis and ablation at macroscopic scale
• Next steps : Next steps : – ModelingModeling
• Improve material structure descriptionImprove material structure description• SublimationSublimation• In depth equilibrium chemistryIn depth equilibrium chemistry• Spallation model (more basic : density threshold)Spallation model (more basic : density threshold)• Same approach for heat transfer in porous media (conduction, convection, Same approach for heat transfer in porous media (conduction, convection,
radiation)radiation)
– Specific experiments to validate the porous media model and the future pyrolysis-Specific experiments to validate the porous media model and the future pyrolysis-ablation coupled modelablation coupled model
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ANNEXES
IPPW6, Atlanta, June 2008 PICA-like materials : Surface or Volume ablation ? 27/25
. Simulation tool : . Simulation tool : AMAAMA Brownian Motion simulation technique / Marching Cube front tracking
Efficient, Robust, No matrix inversion
h
Original features:- Sensory Brownian Motion : automatic refinement close to the wall (cf. mesh refinement for Eulerian methods)- Sticking probability adapted to Brownian Motion (to simulate first order heterogeneous reactions)
IPPW6, Atlanta, June 2008 PICA-like materials : Surface or Volume ablation ? 28/25
3 kinds of Experiments3 kinds of Experiments
Parametrical study on P, T, v
Global vali-dation
fluid + mater
-test conditions
-data analysis
2-3 years3D micro
2D orthomacro
idemPlasma tests**
Parametrical study on blowing and grad(T)
Ablation/pyrolysis coupling
Spallation
Model validation
-thermocou-ple position
-quantify spallation= f( shear stress)
1-2 years3D micro
2D orthomacro
Thermal gradient
Density profile
Recession
Long steady state
IR tests**
(+ tangential blowing)
Needed ASAP
Useful for radiation analysis
-thermocouple position
-data analysis
6 month3D
macro
Effective conductivity
k=f(T)
Short ramp
IR tests*
0-2500K
- No rush
- Data from 1970
- Useful again for porous TPS
Understanding of heterogeneous and homogeneous chemistry
- data analysis
1+ year1D
micro
Chemistry
Pyrolysis gas analysis Carbon fibers reactivity to these gas
TGA** (Thermo Gravimetric Analysis)
+ mass spectrometer
Key results
-> master or PhD student in Bordeaux?
+10kEuros
Enable an accurate direct numerical simulation
- prepare samples
- image segmentation
1+ year3D
micro
Architecture
(accurate)
resolution :
1µm
TOMO**
(X-ray scanning
micro-tomography)
Relatively low cost for fast preliminary results
Help into architecture modeling at all scales
Image analysis
1 month2D surface
micro to macro
Architecture
(intuitive)
resolution: 100 nm
SEM*
(Scanning Electron Microscopy)
Other comments
InterestDifficultyTime scaleDimension & scale
Measured dataDevice
Parametrical study on P, T, v
Global vali-dation
fluid + mater
-test conditions
-data analysis
2-3 years3D micro
2D orthomacro
idemPlasma tests**
Parametrical study on blowing and grad(T)
Ablation/pyrolysis coupling
Spallation
Model validation
-thermocou-ple position
-quantify spallation= f( shear stress)
1-2 years3D micro
2D orthomacro
Thermal gradient
Density profile
Recession
Long steady state
IR tests**
(+ tangential blowing)
Needed ASAP
Useful for radiation analysis
-thermocouple position
-data analysis
6 month3D
macro
Effective conductivity
k=f(T)
Short ramp
IR tests*
0-2500K
- No rush
- Data from 1970
- Useful again for porous TPS
Understanding of heterogeneous and homogeneous chemistry
- data analysis
1+ year1D
micro
Chemistry
Pyrolysis gas analysis Carbon fibers reactivity to these gas
TGA** (Thermo Gravimetric Analysis)
+ mass spectrometer
Key results
-> master or PhD student in Bordeaux?
+10kEuros
Enable an accurate direct numerical simulation
- prepare samples
- image segmentation
1+ year3D
micro
Architecture
(accurate)
resolution :
1µm
TOMO**
(X-ray scanning
micro-tomography)
Relatively low cost for fast preliminary results
Help into architecture modeling at all scales
Image analysis
1 month2D surface
micro to macro
Architecture
(intuitive)
resolution: 100 nm
SEM*
(Scanning Electron Microscopy)
Other comments
InterestDifficultyTime scaleDimension & scale
Measured dataDeviceM
icro
str
uc
ture
Ph
ysic
o-c
he
mis
try
Val
idat
ion
* : to be done in priority with available funding / ** : to plan now and begin in 1 year
Improvement & Validation of the models
IPPW6, Atlanta, June 2008 PICA-like materials : Surface or Volume ablation ? 29/25
ANNEXE. Ablation model for porous mediaANNEXE. Ablation model for porous media
The effective reactivity of the porous media is not intrinsic
x 3x 3
Surface ablation
Volume ablation
Effective reactivity = reactivity of a flat and homogeneous material (cf graphite) that would lead to the same ablation rate under similar entry conditions
(D~1/P)
T≈
2500
K