PICA-like materials : Surface or Volume ablation ? 1/25 IPPW6, Atlanta, June 2008 Ablation of...

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


. 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.


. 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


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



• 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


• 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 :


Matrix

Thin matrix layer around the fibers Virgin fluffy matrix homogeneous at fiber scale


• 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



• 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


Simulationtool


Reaction/Diffusion : Simulation (1/2) : diffusion << reaction (D/L << kf)

Surface

Bottom

Oxygendiffusion

Periodiccell in x,y

Hypotheses:-Isothermal-No pyrolysis gas


Reaction/Diffusion : Simulation (2/2) : diffusion >> reaction (D/L >> kf)


Surface

Bottom

Oxygendiffusion

Periodiccell in x,y

Hypotheses:-Isothermal-No pyrolysis gas


Volume Ablation (D/L >> kf ) Surface Ablation (D/L << kf )


Surface or Volume ? depends on experimental conditions


Homogenization and Analytical solution (hyp. : no recession)


• 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…


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)



• 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


1) Displacement of 10000 walkers followed during (chosen for convergence)

2) Einstein relation on diffusion process :


• 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


Parametrical analysis


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


• 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



• 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


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


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


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)


• Ablation : surface phenomenon at microscopic scale, but volumetric at macroscopic scale


( , )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



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


• Simulated in the carbon felt


Stardust conditions : pure oxidation from 90s (T<Tsublim) to 130s (T>Toxi)


. 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)


. 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


ANNEXES


. 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)


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


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

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