Verification and Validation of a Finite Element Re-entry Ablation Model for PICA with ABAQUS

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Verification and Validation of a Finite
Element Re-entry Ablation Model for
PICA with ABAQUS
Yeqing Wang,
UF-REEF
Crystal L. Pasiliao,
AFRL/RW
Aug 1, 2017
5th Annual Meeting of the AFRL MMOI, Shalimar, FL, Aug. 1-3, 2017

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 Re-entry Speed:
for typical low
earth orbit re-
entry: ~17,500
mph (~25 Mach)
 Max.
Temperature:
~3000 °C
 Heat Shield: a
sacrificial
material layer to
protect the inside
structures
Background
DARPA’s Falcon Hypersonic Technology Vehicle 2
Figure Source: DARPA

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 Objective for ablation modeling research:
 To predict thermal and ablative response of heat shield material (ablator)
 To use the model for screening of new ablative materials
 Current codes:
 Our objective:
 To model charring ablation with Commercial, General purpose FEA software
 Pros: enhanced capabilities of usability, pre, and post-processing, mesh
generation, flexibility, and options to couple with fluid codes
Motivation
CMA FIAT CHAR HERO
Developer Aerotherm Corporation NASA NASA ATK orbital
Year 1960s 1999 2011 2012
Dimensions 1D 1D 3D 3D
Restrictions N/A Upon request ITAR ITAR

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Physical Phenomena
Char layer
Pyrolysis zone
Virgin material
Backup material
Boundary layers (thermal,
concentration & momentum)Radiation & convection
heat transfer
Receding surface
x
y
ṡ
External flow
Pyrolysis
gas flow
 In-depth heat conduction: Radiation and convection heating
 Release of pyrolysis gas: Material decomposition
 Surface material removal: vaporization, oxidation, etc.
 Coupling effects:
 Material
decomposition
couples to heat
conduction
 Material
decomposition
couples to surface
energy balance
 Surface material
removal couples to
heat conduction

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Governing Equations
 Heat conduction equation considering material decomposition and progressive
material removal (for 1D):
  ,
g
p g p g
y y
hT T T
C k h h s C m
t y y t y y

 
     
     
      
& &
,
,
,
exp ,
i
i c ii i
i v i
v i
E
t RT

 
 

   
           
0
.
y
gm dy
t

 
&
0
.
y
gm dy
t

 
&
 Recession rate, needs to be determined from thermochemistry analysis. In
practical cases, a B prime table needs to be provided
 Material properties (e.g., specific heat, thermal conductivity, and enthalpy) are all
temperature and pressure-dependent
s&
Rate of density change: Mass flux of pyrolysis gas:

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Surface Energy Balance Yielded Boundary Conditions
 Driving force for the convective heat exchange is the enthalpy difference:
     4 4
,e e H r w e e H c c g g w w
dT
k U C h h U C B h B h B h T T
dy
   
           
Term I Term II Term III
Term I: Convective heat exchange between boundary layer and material surface
Term II: Heat loss due to the release of pyrolysis gas and char consumption
Term III: Surface radiation to ambient boundary condition
.
g
g
e e H
m
B
u C
 
&
( , , )w w w gh h T p B ( , , )c c w gB B T p B  
.c c e e Hm B u C & ,c
w
m
s


&
&
Using the well-
known B prime
table
Recession rate is then obtained
and plugged into the heat
conduction equation

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Numerical Implementation in ABAQUS
 Default heat transfer analysis in ABAQUS CANNOT model charring ablation:
 ABAQUS default heat conduction equation does not account for material
decomposition or surface material removal
 Surface boundary condition in terms of enthalpy difference CANNOT be
defined in the input file
 Additional subroutines have been developed to model charring ablation:
 UMATHT: to re-define heat conduction considering material decomposition
and surface material removal
 DFLUX: to define the surface energy balance in terms of enthalpy difference
 USDFLD: to update material properties, rate of density change, B’g after
each time increment
 UMESHMOTION: to track the moving boundary condition due to material
removal
 Miscellaneous utility subroutines: to perform 3D linear interpolation
 ALE adaptive remesh algorithm is enabled

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Numerical Implementation in ABAQUS
Calculate
convective heat flux
and heat loss due
to charring (9) with
DFLUX subroutine
at inc kCalculate instant
material properties,
mass flux (8), and
B’g (11) with
USDFLD
subroutine at inc k
B’g
Get
temperature
solution at
inc k
ρ, C, k, and ṁg
Get temperature on
surface using FILM
subroutine at inc k
Solve the charring
energy balance
equation (1) with
UMATHT
subroutine at inc k
Re-mesh the
computational domain
with ALE adaptive
remesh algorithm at inc k
ρ, B’g
Calculate instant
recession rate (14) and
move surface nodes with
UMESHMOTION
subroutine at inc k
new inc: k=k+1
HeatconductionShapechange
 Flowchart of the numerical implementation in ABAQUS:

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Model Verification

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 Material system:TACOT (Theoretical Ablative Composite for Open Testing) 3.0
test case
 A material: a material designed for ablation code verification (with B’ table)
 Based on open-literature data regarding PICA
 Pressure: 1 atm
 Recovery enthalpy: 40 MJ/kg
 heat transfer coefficient: 0.1 kg/m2s
Model Verification: Material System
 Code to code verification: ABAQUS and FIAT:
 Compare temperature at surface
 Compare temperature at five other spatial
locations
 Compare ablation history
1 mm
2 mm
4 mm8 mm
16 mm
External flow

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Model Verification: ABAQUS Results
(a) (b) (c) (d) (e) (f)
A
B
C
A
B
C
A
B
C
A: Char layer
B: Pyrolysis zone
C: Virgin material
1 cm
Temperature distribution Density distribution
Before
ablation
After
ablation
During
ablation
Before
ablation
After
ablation
During
ablation

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Model Verification: Temperature Comparison
0
500
1000
1500
2000
2500
3000
0 10 20 30 40 50
Temperature(°C)
Time (s)
ABAQUS, surface FIAT, surface
ABAQUS, 0.001 m FIAT, 0.001 m
1 mm
2 mm
4 mm8 mm
16 mm
External flow

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Model Verification: Ablation Comparison
0
0.01
0.02
0.03
0.04
0.05
0.06
0 100 200 300 400 500 600
Recession(m)
Time (s)
Result from FIAT
ABAQUS with min. mesh size: 2.00E-3 m
ABAQUS with min. mesh size: 6.00E-5 m
 Effects of mesh size:
 Findings: finer mesh leads to better comparison of ablation history

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Model Validation

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Model Validation: Torch Experimental Tests
 Experimental data for model validation:
 Published torch experimental data by Koo Research Group at UT Austin [1, 2]
 Oxy-acetylene torch ablation test for PICA samples:
[1] J.H. Langston, F. Stefani, M. Salita, J.H. Koo, Validation of ablative material response model using charring ablator response program, SAMPE 2017 ISTC, Seattle,
WA, 2017. [2] J.H. Langston, C. Wong, N. Diaz, F. Stefani, J.H. Koo, M. Salita, Validation of ablation model of PICA using fully implicit ablation and thermal response
program, 55th AIAA Aerospace Sciences Meeting, Grapevine, Texas, 2017, pp. 0896.
Fuel mixture: 0.8 SLPM
acetylene gas to 2.7
SLPM oxygen gas)
Figure source: [1, 2]

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Model Validation: Torch Experimental Tests
 Importance of torch tests:
 Ablation test representing the end-use application is highly cost-prohibitive
 Torch test provides measures to screen new materials
 Samples:
 PICA (phenolic-impregnated carbon ablator)
 4 thermocouples were embedded to allow in-situ temperature measurements
Heat flux
from torch
TC1
TC2
TC3
TC4
TC1 TC2
TC3 TC4
1.5 mm
6 mm
4.5 mm
3 mm
Figure
source: [1, 2]
[1] J.H. Langston, F. Stefani, M. Salita, J.H. Koo, Validation of ablative material response model using charring ablator response program, SAMPE 2017 ISTC, Seattle,
WA, 2017. [2] J.H. Langston, C. Wong, N. Diaz, F. Stefani, J.H. Koo, M. Salita, Validation of ablation model of PICA using fully implicit ablation and thermal response
program, 55th AIAA Aerospace Sciences Meeting, Grapevine, Texas, 2017, pp. 0896.

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Model Validation by Koo Research Group with FIAT
 Heat flux from torch is known, but (1) heat transfer coefficient and (2) recovery
enthalpy are unknown
 Estimation using
NASA Chemical
Equilibrium with
Transport
Properties (CET)
program
 Obtained
unrealistically
high recovery
enthalpy and
incredibly low
heat transfer
coefficient
Koo et al.’s prediction is 2000 K
lower than experimental data!
Figure
source: [2]
[2] J.H. Langston, C. Wong, N. Diaz, F. Stefani, J.H. Koo, M. Salita, Validation of ablation model of PICA using fully implicit ablation and thermal response program,
55th AIAA Aerospace Sciences Meeting, Grapevine, Texas, 2017, pp. 0896.

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Model Validation: Estimation of Heat Transfer
Coefficient and Recovery Enthalpy
 Heat transfer coefficient: estimated using the Sibulkin’s equation for boundary
layer analysis
   
0.5 0.1 0.6
0.6
0
2
0.763 Pr 1 Le 1e e e w w chem
e e e w
U h
h
r h h
   
 
      
             
 Recovery enthalpy: estimated from the relationship between heat transfer
coefficient and the heat flux
0
,r w
q
h h
h
 
 Properties: such as the flow velocity, Prandtl number, viscosity, Lewis number,
density are collected from various literature for identical flames
 Obtained reasonable heat transfer coefficient and recovery enthalpy:
44.19 MJ/kgrh 2
0 0.235 kg/m sh 

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Model Validation: Ablation History Comparison
 Predicted ablation history from ABAQUS agrees well with the experiment
data

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Model Validation: Temperature History Comparison
 Predicted average surface
temperature is 1000 K higher
than experimental data
Average
Surface
Temp (K)
Total
Ablation
Depth
(mm)
Experimen
tal data
2400 7.1
ABAQUS 3400 7.462
FIAT [1, 2] 400 0.093

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Model Validation: Effects of Heat Transfer Coefficient
0
1
2
3
4
5
6
7
8
2200
2400
2600
2800
3000
3200
3400
3600
0.05 0.1 0.15 0.2 0.25
Ablationdepth(mm)
Temperature(K)
Heat transfer coefficient (kg/m2 s)
Avg. surface temperature
Ablation depth
 Keep recovery enthalpy unchanged, reduce heat transfer coefficient from
0.235 to 0.008 kg/m2s (decreased by 66%)
 Findings:
 average surface
temperature is
decreased by
21%
 total ablation
depth is
decreased by
81%
0
,r w
q
h
h
h 

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Model Validation: Effects of Recovery Enthalpy
4
4.5
5
5.5
6
6.5
7
7.5
8
2100
2300
2500
2700
2900
3100
3300
3500
0 10 20 30 40 50
Ablationdepth(mm)
Temperature(K)
Recovery enthalpy (MJ/kg)
Ablation depth
 Keep heat transfer coefficient unchanged, reduce recovery enthalpy from
44.19 to 10 MJ/kg (decreased by 77%)
 Findings:
 average surface
temperature is
decreased by
30%
 total ablation
depth is
decreased by
39%
0
,r wh
q
h
h
 

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Model Validation: Effects of Heat Flux
 Keep heat flux 1000 W/m2 unchanged, reduce heat transfer coefficient
from 0.008 to 0.235 kg/m2s (recovery enthalpy also changes
correspondingly)
 Findings:
 average surface
temperature is
decreased by 3.6%
 total ablation depth is
increased by 55%
 average surface
temperature is mostly
dictated by the heat flux
6
8
10
12
14
16
18
3280
3320
3360
3400
3440
3480
0 0.1 0.2 0.3 0.4 0.5 0.6 0.7
Ablationdepth(mm)
Temperature(K)
Heat transfer coefficient (kg/m2 s)
Ablation depth0
,r wh
h
q
h 

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Conclusion
 A 1D finite element charring ablation model has been developed with
ABAQUS
 Multiple ABAQUS subroutines have been developed to accommodate the
charring heat conduction and the surface energy balance formulations
 Model verification has been performed through a code-to-code
verification with FIAT (developed by NASA Ames) using the TACOT 3.0
test material system
 Model validation has been performed by comparing ABAQUS predictions
with published experiment data by the Koo Research Group
 Temperature differences between ABAQUS prediction and experimental
data necessitates needs for further investigation

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Acknowledgements
This work is supported by AFRL under Contract No. FA8651-08-D-0108, Task
Order No. 42. Any opinions, findings, conclusions, or recommendations
expressed in this work are those of the author and do not necessarily reflect
the views of the AFRL
I also thank Timothy K. Risch (NASA Armstrong Flight Research Center) for
many helpful discussions

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