AIAA 2011-3787
42nd AIAA Thermophysics Conference
27 - 30 June 2011, Honolulu, Hawaii
The Effects of Finite-Rate Reactions at the Gas/Surface
Interface on Thermal Protection System Design
A.F. Beerman*, M.J. Lewis†
Department of Aerospace Engineering, University of Maryland, College Park, MD 20742
R. P. Starkey‡
Department of Aerospace Engineering Sciences, University of Colorado, Boulder, CO, 80309, USA
B. Z. Cybyk§
Global Engagement Department, Johns Hopkins University Applied Physics Laboratory, Laurel, MD, 20732, USA
The Stardust Return Capsule (SRC), which used Phenolic Impregnated Carbon
Ablator (PICA) as its heatshield material, was recovered in 2006. For heatshield recession at
the Core 1 point, recession predictions from computational models were more than 50%
greater than the measurements. In the models, the surface chemistry was assumed to be
occurring in equilibrium – a conservative approach to the recession prediction. Application
of finite-rate reactions beginning during the first occurrence of sublimation, previously
identified as a key reaction in the SRC trajectory, lessened the overprediction. The recession
predicted using finite-rate reactions fell within the error of the extrapolated measured
recession at the stagnation point. The predicted recession was 0.62 cm while the extrapolated
measured recession at the stagnation point was 0.66 cm. The lessening of recession was
driven by the rate of char, which was seen as the physical response most affected by the
finite-rate reactions on the surface. The heating caused by the char and pyrolysis gas
products being injected into the flow from the ablating material becomes greater when
finite-rate reactions are accounted due to an increase in the wall enthalpy and decrease in
radiation leaving the surface.
Nomenclature
B’
CH
CH1
CM
h
Hr
m&
qc
T
λ
=
=
=
=
=
=
=
=
=
=
& / ρ e ueC M
Dimensionless mass blowing rate, m
Stanton number for heat transfer
Stanton number for heat transfer for a nonablating surface
Stanton number for mass transfer
Enthalpy, J/kg
Recovery enthalpy, J/kg
Mass flux, kg/m2s
Conductive heat flux, W/m2
Temperature, K
Blowing reduction parameter
*
Graduate Research Assistant, Department of Aerospace Engineering, 3181 Glenn L. Martin Hall,
abeerman@umd.edu, Student Member AIAA.
†
Professor, Department of Aerospace Engineering, 3181 Glenn L. Martin Hall, mjlewis@umd.edu, Fellow AIAA.
‡
Assistant Professor, Department of Aerospace Engineering Sciences, 429 UCB, rstarkey@colorado.edu,
Senior Member AIAA.
§
Assistant Group Supervisor, Global Engagement Department, 11100 Johns Hopkins Road,
bohdan.cybyk@jhuapl.edu, Associate Fellow AIAA.
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Copyright © 2011 by the American Institute of Aeronautics and Astronautics, Inc. All rights reserved.
Subscripts
c
g
w
= Char
= Pyrolysis gas
= Wall
I. Introduction
V
EHICLES reentering Earth's atmosphere experience both hypersonic speeds and high temperatures and
potentially experience thermochemical nonequilibrium conditions. Nonequilibrium reactions can occur in the
flow around the craft or in the surface reactions. The reentry conditions that cause high heating facilitate the need for
a thermal protection system (TPS), a heatshield, to take the brunt of the energy encountered during this portion of
the craft's flight. These conditions may result in ablation, the phenomenon of surface recession, or erosion, of a
material due to severe thermal attack by an external heat flux. A TPS is designed around predictions as to how its
ablation will dissipate the heating experienced during reentry. If predictions such as recession are higher, than the
heatshield will need to be thick and massive enough such that it does not completely recede away, exposing the
main spacecraft to the reentry conditions. Thus the understanding of ablation is critical to the development of
heatshields.
One key aspect of any reentry model is the chemical reactions taking place in the flow and at the surface of the
material. At the surface of the ablating material, the flow gas and the surface interact with each other. It is very
difficult to simulate these gas-surface interactions at orbital or entry velocities in the lab;1 this places an increased
importance on the computational models that have been developed. However, models may make simplifying
assumptions that lead to a decrease in accuracy of predictions that are calculated during reentry when compared to
actual flight data. In particular, while most models concentrate on the unique condition of chemical equilibrium
surface reactions during hypersonic flight, in reality, nonequilibrium, or finite-rate, surface reactions may occur.
Previous work2,3,4,5 focused on finite-rate reactions on the gas/surface interface. Park and Tauber2 found that at
the stagnation point of such cases as Apollo 4, Pioneer-Venus probes, and the Galileo probe, the equilibrium
assumption lead to heat flux predictions that overestimated the measured values. When Park and Tauber applied a
nonequilibrium assumption, using kinetic boundary conditions, there was a lessening of the overpredictions. For the
Stardust Return Capsule (SRC), the recession prediction6 using an equilibrium assumption resulted in a value more
than 50% larger at the stagnation point and near stagnation point than the actual measured values. Efforts in Refs. 3
and 5 have sought to apply finite-rate reactions at the stagnation point to better recreate the measured values of
recession and temperature. Ref. 5 used a preliminary design trajectory and sought to identify the key reactions in the
finite-rate model (The Modified Park Model). The work carried out presently builds upon that previous effort with
the final design trajectory of the SRC. A new tool is developed to combine equilibrium and nonequilibrium
calculations together such that a more accurate model can be used to take into account the two possible chemical
cases.
The Fully Implicit Ablation Thermal (FIAT) response program7 is used as the material response model. Though
the FIAT program typically assumes chemical equilibrium at the surface, a nonequilibrium surface model is applied
using the Multicomponent Ablative Thermochemistry (MAT) code.8 The capabilities of MAT were previously
extended to include nonequilibrium effects which were input into FIAT in Ref 5. A new implementation, called
BFIAT, is created in this work that links MAT directly to FIAT such that unique surface conditions are calculated at
each time step. This will allow for equilibrium and nonequilibrium to be applied at different times during a
computational analysis.
II. Background
The Stardust Return Capsule used a Phenolic-Impregnated Carbon Ablator (PICA)9 for its heatshield, a relatively
low-density material also selected for NASA’s Mars Science Laboratory (MSL). The carbon fiber insulation of
PICA has an initial density between 0.152 and 0.176 g/cm3 with the overall density falling in the range of 0.224 to
0.248 g/cm3. This overall density is between four to eight times lower than more conventional carbon-phenolics.
PICA was developed in the mid-1990s and there has recently been an increase in arc-jet testing and associated data
due to its selection as the heatshield material for the CEV. The Stardust heatshield also was constructed with a
sandwich-like structure of aluminum honeycomb and faceplates made of graphite-polycyanate. The Stardust Return
Capsule was recovered on January 16, 2006.
The first 100 seconds of its nominal reentry trajectory, as defined by Olynick et al.,10 are presented in Fig. 1.
Kontinos et al.11 determined that the actual trajectory closely followed the nominal trajectory. While the preliminary
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trajectory used in Ref. 5 extends to 750 seconds, the final design trajectory only lasts 133 seconds. There is enthalpy,
pressure, and heat transfer coefficient predictions at every second of the final design trajectory. In addition, while
the final design trajectory has the same total environmental heat flux on the surface (between 1100 and 1200
W/cm2) as the preliminary design trajectory, the only environmental heat flux acting upon the surface is convective
heat flux, as there is no radiative heat flux into the material in the final design trajectory.
A DC-8 flown at an altitude of 11.9 km was used as an airborne observatory to optically determine average
surface temperature.12 Because the capsule was not fully instrumented to measure reentry conditions, Jenniskens13
used an Echelle spectroscope to observe the flow around the capsule as it returned to Earth. Post-flight analysis
determined surface temperature and recession. The observed data suggested that the previous Stardust models were
inaccurate; recession was over-predicted by 50% at some locations on the capsule.6,13
85
34 s
Stardust Design Trajectory
Calculation Point
80
Altitude (km)
75
42 s
70
48 s
Peak Forebody Heating
54 s
65
60
60 s
55
76 s
50
66 s
80 s
45
40
2
4
6
8
10
Velocity (km/s)
12
14
Figure 1. The nominal Stardust reentry trajectory
III. Computational Setup
A. Park Finite-Rate Model
Park derived a finite-rate gas-surface interaction model that accounts for nonequilibrium surface interactions,
including oxidation (Eqs. 1-2), nitridation (Eq. 3), and sublimation of the carbon (Eq. 4).14-16
m& 1 = ρCO vO β O
MC
MO
O+ C (s ) → CO
m& 2 = 2 ρCO 2 vO 2 β O 2
(1a)
(1b)
MC
M O2
(2a)
O2 + 2C( s ) → 2CO
(2b)
MC
MN
(3a)
m& 3 = ρC N v N β N
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N + C(s) → CN
(3b)
m& 4 = ρ (C C 3, E − C C 3 )vC 3 β C 3
(4a)
3C ( s ) → C 3
(4b)
m& c = m& 1 + m& 2 + m& 3 + m& 4 = ρ s S&
(5)
The mean molecular speed, vi for each species i is defined as kTW 2πmi . Using the ideal gas law, the mean
molecular speed can be defined in terms of the molecular weight (MW): C Ru TW 2πMW . C is an assumed
constant that is related to the number of particles in the system. This eliminates the need to assume volume to get the
molecular mass in the original molecular speed equation, as used in Ref. 5, since only the density is known in the
calculations. In the previous analysis, the volume assumption adds a level of complexity to the molecular velocity
equation, as it needs partial pressures to arrive at the mass and is especially difficult to use when MAT needs the
derivative of the mass loss rate equations with respect to pressure and temperature to use in its error equation. The
assumption of the number of particles in the system is directly involved in the velocity calculation, is not affected by
temperature or pressure in this assumption, and does not change as the analysis changes the conditions. By revising
the molecular velocity equation to include molecular weight and to eliminate molecular mass, the analysis is more
direct and less prone to calculations errors due to less steps needed to find all the parameters in the equations.
As per Eq. 4, sublimation produces primarily C3 in this model.3 In the Park Model, the mass loss due to charring
is the sum of the four reactions’ mass fluxes (Eq. 5). In a Park Finite-Rate Model without inputs from a material
response program, species mass conservation at the surface is written as:3
∧
− ρDi ∇X i + ρvw Ci = N i + m& g Ci , g
(6)
∧
The mass transfer through diffusion and convection are the first and second terms on the left, respectively. N i is
the source term and for CO, CN, C3, N, O, and O2 species they are as follows:3
∧
N CO = m& 1
∧
∧
M
M CO
M
+ m& 2 CO , N CN = m& 3 CN , N C3 = m& 4
MC
MC
MC
∧
N N = −m& 3
MO
MN ∧
M ∧
2
& 1 O , N O2 = −m& 2
, N O = −m
MC
MC
2M C
(7)
For all the other species, the source term is zero. Equation 7 is used to get the mass contribution for each
molecule when calculating the total char mass loss rate in the construction of the thermochemistry table from MAT.
The Park Model does not take into account any reverse reactions and the only way for the forward reaction mass
flux to equal zero is for temperature to equal zero; the model can only account for nonequilibrium reactions. The
total mass flux will never be equal to zero, so the state of equilibrium cannot be reached unless there are additional
assumptions.
B. Fully Implicit Ablation and Thermal (FIAT) Response Program
FIAT computes the transient one-dimensional thermal response of Thermal Protection System (TPS) materials
arranged in a multilayer stackup, subject to aerothermal heating on one surface, and can be coupled to a
Computational Fluid Dynamics (CFD) flow solver. The FIAT program is described in Ref. 7.
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Heating may be predicted using a boundary condition that includes convection, radiation flux across the surface,
heating due to chemistry, and conduction. Typically, the heating due to chemistry is considered to be one term, but
in actuality, it is made up of three components: heating due to char formation (hc), heating due to pyrolysis gas (hg),
and heating due to the injection of char and pyrolysis into the flow (hw). Analyzing these particular heat fluxes helps
understand how the reactions on the surface affect heating, as they are the ones most directly linked to the chemical
process. Equation 8 shows all the heat flux terms being used in this analysis:
C H H R + m& g hg + m& c hc − B' hw + qrad − Fσε wTw4 − qcond = 0
(8)
where CH is the blown heat transfer coefficient and HR is the recovery enthalpy. The terms that use the enthalpy
of the pyrolysis gas and char are heating that comes from the internal decomposition of the material. The B’hw can
be referred to as the heat of ablation and is the heating caused by the pyrolysis and char products being injected into
the flow due to ablation. If the material is ablating, the blown heat transfer coefficient is derived from the corrected
form of the unblown heat transfer coefficient, CH1:
CH
2λB'
ln ( 1 + 2λB' )
=
=
C H1 exp( 2λB' ) − 1
2λB'
(9)
where
.
.
m '
m
B =
,B =
C H1
CH
'
1
In the case of a nonablating material, the unblown heat transfer coefficient is used in calculations. Reference 5
shows that B’ will be affected by nonequilibrium surface interaction through the decrease in the charring and
pyrolysis gas rate. Physically, the decrease in the total ablation rate means there is a decrease in the char and
pyrolysis product being injected into the flow by the ablator. Less material in the flow means less absorption by the
product of the heat from the flow before it reaches surface, so heating on the surface should increase.
Mathematically, the decrease of B’ leads to an increase in the ratio used to find the corrected heat transfer
coefficient. This leads to an increase in the convective heat flux when comparing nonequilibrium and equilibrium
cases if wall enthalpy is not considered in the convective calculations (previous analysis6,10 of the SRC trajectory
does not include wall enthalpy in that calculation).
C. MAT Surface Interactions with Nonequilibrium
As in Ref. 5, in the current effort, the surface chemistry inputs are provided to FIAT by an interface with MAT.
There has been various models integrated within MAT to account for nonequilibrium conditions with varying
degrees of success.8,16,17
The equilibrium element conversion equation used in MAT is:8
m& g Ykg + m& cYkc = j kw + ( ρv) w Ykw
(10)
The equilibrium element flux balance can be found to be:
Ykw =
Yke + Bg′ Ykg + Bc′Ykc
1 + Bg′ + Bc′
(11)
Since the mass fraction, Ykw, must be between zero and one, it sets a bound on both the numerator and
denominator of Eq. 11. B’c and B’g are often specified as independent parameters. B’c is the dimensionless char
ablation rate and B’g is the dimensionless pyrolysis gas rate. These dimensionless terms come from
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nondimensionalizing the char or pyrolysis mass flux by the mass transfer coefficient. Reference 5
nondimensionalizes the mass fluxes with the heat transfer coefficient at the previously determined peak heating
point for the Stardust trajectory (54 s).
Equation 12 is the element flux balance equation that takes into account the nonequilibrium reaction mass flux.8
Ykw =
Yke + B′g Ykg + Bc′Ykc − Bkr′
1 + B′g + Bc′
(12)
The temperature and the enthalpy at the wall are functions of B’c, B’g, and pressure. The finite-rate reactions
must be accounted for when their elemental components are called upon in Eqs. 11 and 12. B’kr is the result of
modeling chemical reactions as a conversion of one “pseudo-element” into another element.8 Park’s model only
affects the species created by the reactions defined in Eqs. 1-4, as those are the only reactions that determine the
value of B’kr. Equation 7 provides the mass contributions of each element under consideration by examining the
molecules they are a part of and their mass effects. All other reactions take place as if they were reaching
equilibrium. Recombination of oxygen and nitrogen are allowed to occur as if in equilibrium and the surface is fully
catalytic.
D. BFIAT
To make the calculations more robust and to allow the unique heat transfer coefficient at each trajectory point to
be used to nondimensionalize the nonequilibrium reaction rate, FIAT and MAT are coupled together in a new
program called BFIAT. Under this setup, FIAT can pass the unique pressure and heat transfer coefficient at each
trajectory point to MAT and MAT can create a smaller B’ table to reduce interpolation. BFIAT can also calculate
the mole fraction of defined species and the mole fraction rate of change throughout a trajectory using the calculated
char and pyrolysis gas rates from FIAT. Because the Park Model only deals with forward reactions and only lists
four reactions, it cannot approximate equilibrium no matter the present conditions; previous use of nonequilibrium
and the Park Model in constructing a B’ table assumed that nonequilibrium occurs at every time point in the
trajectory, which may not be true. To correct this in the coupled BFIAT setup, the user can tell the program when to
apply the Park Model, depending on the conditions where it is thought there may be an occurrence of
nonequilibrium.
IV. Finite-Rate Results on the SRC Final Design Trajectory
A. Nonequilibrium over the Full Trajectory
The PICA heatshield in the final design trajectory is slightly thicker (5.82 cm) than the one used in the
preliminary design trajectory (5.08 cm). The thermocouple depths are 0.64, 1.91, 5.48 cm. The main difference
between the final design trajectory and the trajectory in Ref. 5 is that the final design trajectory does not include
radiation to the surface. At the stagnation point, the total heat flux between the final design trajectory and the
trajectory examined in Ref. 5 remain nearly the same (there is about a 6% difference of the total heat flux at 54
seconds, which was identified as the time of peak heating for the preliminary trajectory before analysis), but the cold
wall convective heat flux for the final design trajectory is higher than that for the preliminary trajectory to
compensate for the lack of radiation. The final design trajectory's enthalpy can be 17% smaller than the preliminary
trajectory's enthalpy, so the increase in cold wall convective heat flux is not due the edge enthalpy. The increase is
due to the increase in the heat transfer coefficient term; for example, at the trajectory point 54 seconds into reentry,
the parameter increases 30% between the two trajectories. Figure 2 is the heat transfer coefficients for the two
trajectories at the stagnation point. While these changes will affect how the material responds in terms of recession
rate, they should not affect the chemical processes and it is assumed that sublimation is still the most important
reaction in the Park Model (as found in Ref. 5) because the surface temperature should still exceed 3000 K for some
nontrivial amount of time. In equilibrium, for the final design trajectory, the recession is 0.99 cm, which is a high
overprediction based on the measured value of recession.6, 11
In the finite-rate analysis of the final trajectory at the stagnation point, the mass loss rate is nondimensionalized
by the heat transfer coefficient at 54 seconds. BFIAT does not nondimensionalize the mass loss rate for each unique
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heat transfer coefficient for each trajectory point because the heat transfer coefficients at the beginning of the
trajectory are so small such that when used to nondimensionalize the mass loss rates become too large for MAT to
find converged solutions. At 54 seconds, the coefficient is 0.20 kg/m2s, which is higher than the coefficient at the
same time in the preliminary trajectory (0.15 kg/m2s). Since the mass loss rate is being divided by a larger number in
the final trajectory, it is expected that the recession should be lower as there is less mass ablating away from the
material. When the finite-rate Park Model is applied throughout the entire final trajectory, with the assumption of
constant heat transfer coefficient for nondimensionalization, the final recession is 0.54 cm, which is a reduction from
the finite-rate recession prediction of 0.72 cm for the preliminary trajectory.5
The finite-rate temperature profile as compared to the equilibrium profile is seen in Fig. 3. TC 3 is omitted
because it remains at the initial temperature throughout the trajectory. TC 2 is omitted because only its steady-state
temperature at significantly changes between the equilibrium and finite-rate states, from 690 K to 510 K. The two
biggest differences in the temperature profile come at the surface and at the first depth. At the surface, the
temperatures in both equilibrium and finite-rate assumptions remain about the same for the first thirty seconds, but
after that they diverge and the finite-rate temperature predictions are less than those found in equilibrium.
Nonequilibrium over the entire trajectory causes a peak temperature of 3140 K, which is decreased from 3370 K
when in equilibrium. In both cases, the peak temperature is reached at roughly peak heating. At the first
thermocouple depth, the finite-rate assumption does not cause a stoppage of predictions at 65 seconds. Because of
the decrease in recession due finite-rate chemistry, the PICA material does not ablate past the thermocouple depth,
allowing FIAT to continue to make predictions at that thermocouple. The equilibrium TC 1 predictions become
much hotter than the nonequilibrium predictions until ablation forces the stoppage of predictions. While the hottest
equilibrium temperature at TC 1 is 2890 K, in nonequilibrium, TC 1 only reaches a temperature of 2000 K, which is
31% lower than the last prediction in equilibrium. The finite-rate assumption decreases the recession and
temperature predictions.
The change is recession is caused by changes in the mass loss blowing rates, specifically the char. Figure 4
compares the pyrolysis rate from equilibrium to nonequilibrium in the final design trajectory, Fig. 5 compares the
char rate and Fig. 6 is a comparison of the total ablation. The pyrolysis gas and char rates each experience a
reduction. The peak pyrolysis gas rate remains about the same whether the Park Model is applied or the reactions are
allowed to occur in equilibrium early in the trajectory, however, later in the trajectory there is a more pronounced
divergence. Between 40 and 60 seconds into the trajectory, the biggest divergence is about 16% from the
equilibrium value, between 60 and 70 seconds, it is about 26%, and for the rest of the trajectory, the biggest
divergence is about 90%, but these pyrolysis values are very small, a magnitude of 10-5. The peak char drops from
0.066 kg/m2s in equilibrium to 0.051 kg/m2s in the application of the Park Model. This is a 23% reduction and is the
biggest driver in the decrease of total ablation. The peak total mass loss with finite-rate chemistry is 0.062 kg/m2s,
which is 23% lower than the equilibrium peak and mirrors the percent decrease of the char rate. The finite-rate
chemistry affects the charring rate the most when applied to the final design trajectory. Since char is mostly likely to
occur on the surface of an ablative material, the surface interactions can directly affect the formation of char. The
small impact on pyrolysis gas is an indicator that the PICA material favors an ablative process through charring and
not through the generation of pyrolysis gas.
The net convective heat flux is higher in the finite-rate case than the equilibrium case (900 W/cm2 to 860 W/cm2)
due to the decrease in the total ablative product leaving the surface causing an increase in the amount of heat that
can reach the surface. If the wall enthalpy is included in the analysis of the convective heat flux, the net convective
heat flux decreases substantially. The peak convective heat flux that includes wall enthalpy is 830 W/cm2 in
equilibrium and 600 W/cm2 in nonequilibrium. The equilibrium peak including wall enthalpy is only 30 W/cm2 less
than the equilibrium convective heat flux without wall enthalpy which may be the reason why wall enthalpy is
ignored in previous SRC trajectory analysis. However, in nonequilibrium, the peak value of the convective heat flux
with wall enthalpy is 33% lower and shows the important role wall enthalpy plays when calculating a more robust
net convective heat flux. The decrease of the net convective heat flux when enthalpy is included indicates that the
wall enthalpy is increasing when considering finite-rate reactions. The mole fractions of high enthalpy species are
increasing in the finite-rate case due to the mole fractions of C3 and CN decreasing in their finite-rate
approximations.
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Preliminary
2
Transfer Coefficient, kg/m s
0.25
0.2
Final
0.15
0.1
0.05
0
0
20
40
60
80
100
120
140
Time, s
Figure 2. The heat transfer coefficient at the stagnation point for the preliminary and final SRC design
trajectories.
4000
Surface (Equilibrium)
Temperature, K
3500
TC1 (Equilibrium)
3000
Surface (Finite-Rate)
2500
TC1 (Finite-Rate)
2000
1500
1000
500
0
0
20
40
60
80
100
120
Time, s
Figure 3. The surface and TC 1 temperature predictions for equilibrium and finite-rate chemistry models for
the final design SRC trajectory.
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2
Blowing Rate, kg/m s
0.02
Pyrolysis (Equilibrium)
0.016
Pyrolysis (Finite-Rate)
0.012
0.008
0.004
0
0
20
40
60
80
100
120
Time, s
Figure 4. The pyrolysis gas rate for the final design SRC trajectory in equilibrium and nonequilibrium.
Char (Equilibrium)
2
Blowing Rate, kg/m s
0.08
Char (Finite-Rate)
0.06
0.04
0.02
0
0
20
40
60
80
100
120
Time, s
Figure 5. The char rate for the final design trajectory in equilibrium and nonequilibrium.
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Blowing Rate, kg/m2s
0.1
Total w/o Failure
(Equilibrium)
Total (Equilibrium)
0.08
Total w/o Failure
(Finite-Rate)
Total (Finite-Rate)
0.06
0.04
0.02
0
0
20
40
60
80
100
120
Time, s
Figure 6. The total ablation rate for the final design trajectory in equilibrium and nonequilibrium.
The wall enthalpy is used to calculate the heat injected into the flow by the char and pyrolysis gas products
leaving the surface. Because of the lower char and pyrolysis gas mass fluxes, the char and pyrolysis heat fluxes are
lower in the finite-rate model. The finite-rate peak values for the chemistry terms are compared to their equilibrium
values in Table 1. The char heat flux decreases by 30%, while the pyrolysis gas heat flux decreases by 40%. The
injected heat flux becomes much larger in a finite-rate analysis, more than doubling its value. Due to the low surface
temperature when compared to the equilibrium case, the radiation out of the surface is also lower than in
equilibrium, with a value of 510 W/cm2 compared to 680 W/cm2 in equilibrium, Also reduced in nonequilibrium is
the conduction into the material, which drives down the ablation process. Conduction is not as high in
nonequilibrium because the increase in wall enthalpy due to surface chemistry drives the injected heat flux up,
causing it to carry more heat away from the surface, and reducing the role conduction plays in maintaining zero total
heating on the surface.
Table 1 The peak values of the surface chemistry heating terms in equilibrium and
finite-rate models for the final SRC trajectory. Fluxes are relative to the surface.
Heating Type
Flux (W/cm2)
Flux (W/cm2)
Equilibrium
Finite-Rate
Char Chemistry
39 (In)
27 (In)
Pyrolysis Gas Chemistry
30 (In)
18 (In)
Injected Chemistry
170 (Out)
390 (Out)
B. Nonequilibrium Applied Post 3000 K
Using BFIAT nonequilibrium is applied after the surface temperature has reached 3000 K (where
sublimation will start). Sublimation was identified as the important reaction in the Park Model when looking at the
preliminary SRC trajectory.5 Like in the preliminary trajectory examined in Ref. 5, for the final trajectory, at the
stagnation point, in equilibrium, the surface will remain at temperatures above 3000 K for roughly 25 seconds.
Before these conditions are met, BFIAT is run only in equilibrium. A similar program to BFIAT, called the Fully
Implicit Ablation, Thermal response, and Chemistry (FIATC) program is currently being developed by Milos and
Chen.18 FIATC does not deal with surface chemistry in the same way as BFIAT as there is no generation of a B’
table and its significant contribution is modeling how the pyrolysis gas travels through the material. Reference 19
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states that a problem with reading from B’ tables in FIAT is how the interpolation between pressures can cause
errors. BFIAT diminishes that problem by creating only one B’ table at the current trajectory point pressure.
In equilibrium, the surface temperature reaches 3000 K at 39 seconds. Once the finite-rate assumption is turned
on after crossing the temperature threshold, the surface temperature actually decreases to below 3000 K to 2940 K.
However, the finite-rate assumption remains, though when the temperature is below 3000 K, the Park Model does
not calculate the mass loss due to sublimation, and the surface temperature is predicted to be over 3000 K again a
few seconds later. The recession rate over the trajectory in the finite-rate sublimation case is as would be expected:
follows the equilibrium rate when it is in equilibrium and the nonequilibrium rate when it is in nonequilibrium (Fig.
7). Since the majority of the trajectory is spent in nonequilibrium, the sublimation-activated finite-rate assumption
leads to a final recession close to what is predicted when finite-rate reactions occur over the entire trajectory (Fig. 8).
The final recession prediction in this case is 0.62 cm, which is 15% more recession than predicted with the full
trajectory finite-rate assumption. It is 38% less than the final recession predicted in equilibrium.
The char, pyrolysis gas, and total ablation rates when the finite-rate assumption is made beginning with
sublimation follow mirror the equilibrium development while in equilibrium and the nonequilibrium development
while in nonequilibrium. As in the case with full trajectory nonequilibrium, char is the ablative process most
affected by a nonequilibrium assumption (Fig. 9). The ablation rates impact the heat entering and leaving the surface
of the PICA material. The char and pyrolysis gas heat fluxes follow the equilibrium and nonequilibrium predictions
in those activated phases (Fig. 10). Because of the lower charring during the nonequilibrium phase, the heat flux
contribution from the char mass loss is lower than in equilibrium. Activation of a finite-rate model at some point in
the trajectory leads to the full trajectory equilibrium predictions being a “ceiling,” which the current predictions
cannot exceed, and the full trajectory nonequilibrium predictions being a “floor,” which the current predictions
cannot decrease past. The assumption of when equilibrium and nonequilibrium will occur over a trajectory or under
what circumstances must be developed outside of BFIAT when using the Park Model, due to the Park Model’s
limitations. Once the assumption is made however, BFIAT can be used to calculation both the nonequilibrium
assumption and its subset of equilibrium.
Recession Rate, cm/s
0.035
Equilibrium
0.03
Finite-Rate (Entire Traj.)
0.025
Finite-Rate (Post 3000 K)
0.02
0.015
0.01
0.005
0
0
20
40
60
80
100
120
Time, s
Figure 7. Recession rate predictions for the equilibrium assumption, finite-rate over the entire final design
SRC trajectory assumption, and finite-rate after 3000 K assumption.
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American Institute of Aeronautics and Astronautics
1.2
Equilibrium
Finite-Rate (Entire Traj.)
Recession, cm
1
Finite-Rate (Post 3000 K)
0.8
0.6
0.4
0.2
0
0
20
40
60
80
100
120
Time, s
Figure 8. Recession predictions for the equilibrium assumption, finite-rate over the entire final design SRC
trajectory assumption, and finite-rate after 3000 K assumption.
0.08
2
Blowing Rate, kg/m s
Char (Equilibrium)
0.06
Char (Finite-Rate,
Entire Traj.)
Char (Finite-Rate,
Post 3000 K)
0.04
0.02
0
0
20
40
60
80
100
120
Time, s
Figure 9. The char rate for the final design trajectory in equilibrium during the entire trajectory assumption,
finite-rate during the entire trajectory assumption, and finite-rate after 3000 K assumption.
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American Institute of Aeronautics and Astronautics
Heat Flux, W/cm
2
90
Char (Equilibrium)
Pyrolysis (Equilibrium)
Char (Finite-Rate, Entire Traj.)
Pyrolysis (Finite-Rate, Entire Traj.)
Char (Finite-Rate, Post 3000 K)
Pyrolysis (Finite-Rate, Post 3000 K)
70
50
30
10
-10
0
20
40
60
80
100
120
Time, s
Figure 10. The char and pyrolysis gas heat fluxes on the surface for the final design trajectory in equilibrium
during the entire trajectory assumption, finite-rate during the entire trajectory assumption, and finite-rate
after the 3000 K assumption.
V. Comparison with Measured SRC Recession
Table 2 is the analysis of the recession of the SRC heatshield concerning the actual measured recession, the
predicted recession from the preliminary trajectory5, and the predicted recession for the final trajectory, with all
predictions either being in equilibrium or nonequilibrium. The recession measurement comes for 3-D mapping of
the Stardust capsule, post-reentry, and a comparison of that mapping to the original manufacture dimensions of the
capsule.20 While the actual stagnation point recession is unknown, the predicted heating profile at the near
stagnation point (Core 1 location) is similar to that predicted at the stagnation point and because the PICA material
is the same thickness throughout the heatshield it is assumed the difference between the predicted recession and the
measured recession at the near stagnation point will be found at the stagnation point. Reference 6 found that the
predicted recession at the near stagnation point is 51% greater than the actual recession measurement with a ± 5%
error in the measured recession. The same percent difference is applied to the stagnation point. Assuming
equilibrium over the entire trajectory results in an overprediction of the recession at the stagnation point, 0.99 cm
compared to a hypothetical measured value of 0.66 cm. So the 0.99 cm recession is 51% greater than the
“measured” recession at the stagnation point.
It is seen that with the final trajectory, the assumption of nonequilibrium over the entire trajectory leads to
an underprediction of recession when compared to what is measured. Though the preliminary and final design
trajectories have similar heating on the surface, they have different environmental enthalpies, heat transfer
coefficients, and different material properties for the PICA material, leading to changes in both the equilibrium and
nonequilibrium predictions. The new underprediction of recession when nonequilibrium is applied over the entire
trajectory may indicate that the capsule experiences some equilibrium during parts of its reentry. The longer the
capsule is in equilibrium, the higher the recession will be due to the conservative nature of the assumption. For the
stagnation point, activating the finite-rate reactions when sublimation first occurs decreases the recession such that
the final value falls within the error margin of the measured recession. It is likely then that over the PICA heatshield,
when experiencing the SRC trajectory conditions, sublimation was occurring in a finite-rate sense. As seen in the
analysis of the preliminary trajectory5, sublimation is a main driver in the Park Model and the Stardust Return
Capsule. The measured recession and the predicted recession using the finite-rate model once sublimation is
activated offer physical evidence of the role sublimation. Using finite-rate sublimation in the design of a PICA
heatshield undergoing SRC-like conditions will lead to more accurate recession predictions and help decrease the
mass of a heatshield.
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American Institute of Aeronautics and Astronautics
Table 2. The measured recession and the predicted recession for the SRC.
Predicted
Location
Stagnation
Point
(Preliminary
trajectory)
Stagnation
Point
(Final trajectory)
Measured
(cm)
Extrapolated:
(0.66 ± 0.04)
Predicted (Ref. 6)
(cm)
0.96
Equilibrium
(cm)
Finite-Rate
(cm)
1.12
0.72
[From
Ref. 5]
0.99
0.54
Post 3000 K
(cm)
0.62
V. Future Work
Two additional points on the SRC heatshield were examined in the post-analysis of its reentry: the near
stagnation and Core 2 – Point 47 location. The near stagnation point experienced heating similar to that found at the
stagnation point and the implementation of finite-rate reactions at that point should follow the stagnation point
trends. The Core 2 – Point 47 location is further down the heatshield, closer to the shoulder, and experiences lower
heating than the stagnation point. Because of its position, it may experience shoulder effects as well. Comparison of
finite-rate predictions at these points to the measured values of recession will expand upon the conclusions reached
when examining the stagnation point. In addition to recession data, there are also recorded temperature and species
information from the SRC reentry, based on wavelengths observed during its descent, which can also be used as a
basis for comparison with flight test data.
There also exist various arc-jet tests21,22 run for the PICA material which can help identify heating regimes where
the Modified Park Model is a robust approximation of finite-rate reactions on the surface. The Modified Park Model
may not be applicable to all heating regimes due to its simplicity and the role of sublimation in its calculations.
Improvements upon the model, with more Arrhenius equations and reactions, can improve the usage of the Park
Model and better estimate the surface interactions on the surface of an ablating material. There are additional
sublimation reactions that may be included in the finite-rate model to capture the complete effect of that reaction
process.
VI. Conclusions
During the design process of the Stardust Return Capsule heatshield, an equilibrium assumption of the surface
interactions on the PICA material led to a recession prediction at the stagnation that was 50% greater than what was
actually measured around the stagnation point.6 The heatshield can be thought of as being overdesigned and more
massive than what actually was needed, based on recession. The application of the Modified Park Model to model
finite-rate surface interactions led to a recession prediction that more closely followed the measured quantity.
However, the finite-rate model needs to be judiciously applied, because its application over the entire SRC trajectory
resulted in the recession being underpredicted by nearly 20% compared to the measured value. Sublimation was
identified as the main driver of finite-rate reactions during the SRC. When the Park Model is applied only after
sublimation is activated, the recession predicted matches the measured recession within its error envelope.
Preliminary trajectory analysis also showed the importance of sublimation. By applying the Modified Park Model
only to conditions defined by the user, the results fall in between the two extreme cases where equilibrium is applied
to the entire analysis or where nonequilibrium is applied to the entire analysis. These floors and ceilings serve as a
way to understand the effects of the two chemical cases have on predictions.
The nonequilibrium surface interactions most affected the char rate of the PICA material, which in turn drove
down the recession. Because char forms at or near the surface, it is directly impacted by how the material is reacting
to the flow at the gas/surface interface. This, coupled with the low rate of formation of pyrolysis gas that is a
property of PICA, means that char is the most important ablative process the PICA material undergoes and should
be analyzed not only in how much of it is formed but what its contributions are to the heating on the surface. It was
seen that the product injected into the flow from the charring and pyrolysis gas formation becomes more important
in finite-rate analysis as radiation out of the surface decreases due to decreases in temperatures and an increase in
wall enthalpy. Further study of the effects of a finite-rate modeling on the recession predictions, using experimental
and flight test data, will show if during certain heating regimes, a finite-rate assumption will capture what is
physically going on at the surface of a material.
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American Institute of Aeronautics and Astronautics
Acknowledgments
The authors wish to thank the support and funding of the Space Vehicle Technology Institute (SVTI), one of the
NASA Constellation University Institute Projects (CUIP), under grant NCC3-989, with joint sponsorship from the
Department of Defense. Thanks go to Claudia Meyer of the NASA Glenn Research Center, program manager of
CUIP, and to Dr. John Schmisseur of the Air Force Office of Scientific Research. Also greatly appreciated, the help
provided by Dr. Frank S. Milos and Dr. Thomas H. Squire of NASA Ames Research Center in the understanding of
the FIAT code, Dr. Ioana Cozmuta in determining what material response parameters to examine, Mr. David G.
Drewry of Johns Hopkins University Applied Physics Lab in material response considerations, and Dr. Bernard
Laub for the preliminary review of the results.
References
1
Caledonia, G. E., “Laboratory Simulations of Energetic Atom Interactions Occuring in Low Earth Orbit,” Rarefied Gas
Dynamics, edited by E.P. Muntz, D.P. Weaver, and D.H. Campbell, Vol. 116, Progress in Astronautics and Aeronautics, AIAA,
New York, 1989, pp. 129 -142.
2
Park, Chul and Tauber, Michael E., “Heatshielding Problems of Planetary Entry, A Review,” AIAA Paper 99-3415, June
1999.
3
Chen, Yih-Kang and Milos, Frank S., “Finite-Rate Ablation Boundary Conditions for a Carbon-Phenolic Heat-shield,”
AIAA Paper 2004-2270, June 2004.
4
Milos, F.S., and Chen, Y.K., “Ablation, Thermal Response, and Chemistry Program for Analysis of Thermal Protection
Systems.” AIAA Paper 2010-4663, June 2010.
5
Beerman, A.F., Lewis, M.J., Starkey, R., and Cybyk, B.Z., “Significance of Nonequilibirum Surface Interactions in Stardust
Return Capsule Ablation Modeling,” AIAA Journal of Thermophysics and Heat Transfer, Vol. 23, No. 3, July-September 2009,
pg. 425-432.
6
Kontinos, Dean, and Stackpoole, Mairead, “Post-Flight Analysis of the Stardust Sample Return Capsule Earth Entry,” AIAA
Paper 2008-1197, January 2008.
7
Chen, Y.K. and Milos, Frank S., “Ablation and Thermal Response Program for Spacecraft Heatshield Analysis,” Journal of
Spacecraft and Rockets, Vol. 36, No. 3, May-June 1999, pp. 475-483.
8
Milos, F.S., and Chen, Y.K., “Comprehensive model for multicomponent ablation thermochemistry,” AIAA Paper 97-0141,
January 1997.
9
Tran, H. K., Johnson, C. E., Rasky, D. J., Hui, Frank C. L., Hsu, M. Y., and Chen, Y. K., “Phenolic Impregnated Carbon
Ablators (PICA) for Discovery class missions,” AIAA Paper 96-1911, June 1996.
10
Olynick, David, Chen, Y.K., and Tauber, Michael E., “Aerothermodynamics of the Stardust Sample Return Capsule,”
Journal of Spacecraft and Rockets, Vol. 36, No. 3, May-June 1999. pp. 442-462.
11
Stackpoole, M., Sepka, S., Cozmuta, I., and Kontinos, D., “Post-Flight Evaluation of Stardust Sample Return Capsule
Forebody Heatshield Material,” AIAA Paper 2008-1202, January 2008.
12
Stardust Hypervelocity Entry Observing Campaign Support, NASA Engineering and Safety Center Report, RP-06-80,
August 31, 2006.
13
Jenniskens, P., “Observations of the STARDUST Sample Return Capsule Entry with a Slit-less Echelle Spectrograph,”
AIAA Paper 2008-1210, January 2008.
14
Park, C., “Calculation of Stagnation-Point Heating Rates Associated with Stardust Vehicle,” Journal of Spacecraft and
Rockets, Vol. 44, No. 1, January – February 2007. pp. 24 – 32.
15
Park, C., “Stagnation-Point Ablation of Carbonaceous Flat Disks – Part I: Theory,” AIAA Journal, Vol. 21, No. 11,
November 1983, pp. 1588 – 1594.
16
Park, Chul, “Effects of Atomic Oxygen on Graphite Ablation,” AIAA Journal, Vol. 14, No. 11, November 1976, pp. 1640 –
1642.
17
Scala, S.M, “The Ablation of Graphite in Dissociated Air, I. Theory,” General Electric, Missile and Space Division,
R62SD72, Sept. 1962.
18
Milos, F.S., and Chen, Y.K., “Ablation, Thermal Response, and Chemistry Program for Analysis of Thermal Protection
Systems.” AIAA Paper 2010-4663, June 2010.
19
Maurer, R.E. Powas, C.A., Hartman, G.J., and Foster, T.F., “Graphite Sublimation Under Low and High Convective Mass
Transfer Environments,” ASME Paper 76-ENAs-68, March, 1976.
20
Lavelle, Joseph P., Schuet, Stefan R., Dobell, Chris, Verson, Jeff, Stackpoole, Mairead, and Kontinos, Dean, “The 3-D
Mapping of Stardust’s Post Flight Heatshield,” AIAA Paper 2008-1200, January 2008.
21
Covington, M.A., Heinemann, J.M., Goldstein, H.E., Chen, Y.K.,Terrazas-Salinas, I., Balboni, J.J., Olejniczak, J., and
Martinez, E.R., “Performance of a Low Density Ablative Heatshield Material,” Journal of Spacecraft and Rockets, Vol. 45, No.
2, March-April 2008, pp. 237-247.
22
Covington, M.A., Heinemann, J.M., Goldstein, H.E., Chen, Y.K.,Terrazas-Salinas, I., Balboni, J.J., Olejniczak, J., and
Martinez, E.R., “Performance of a Low Density Ablative Heatshield Material,” AIAA Paper 2004-2273, June 2004.
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