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Open Journal of Fluid Dynamics, 2013, 3, 100-107
http://dx.doi.org/10.4236/ojfd.2013.32A016 Published Online July 2013 (http://www.scirp.org/journal/ojfd)
A Study of Thermal Response and Flow Field Coupling
Simulation around Hayabusa Capsule Loaded with
Light-W eight Ablator
Hisashi Kihara, Naoya Hirata, Ken-ichi Abe
Department of Aeronautics and Astronautics, Kyushu University, Fukuoka, Japan
Received July 17, 2013; revised August 15, 2013; accepted August 29, 2013
Copyright © 2013 Hisashi Kihara et al. This is an open access article distributed under the Creative Commons Attribution License,
which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.
The numerical simulation of flow field around Hayabusa capsule loaded with light-weight ablator thermal response
coupled with pyrolysis gas flow inside the ablator was carried out. In addition, the radiation from high temperature gas
around the capsule was coupled with flow field. Hayabusa capsule reentered the atmosphere about 12 km/sec in veloc-
ity and Mach number about 30. During such an atmospheric entry, space vehicle is exposed to very savior aerodynamic
heating due to convection and radiation. In this study, Hayabusa capsule was treated as a typical model of the atmos-
pheric entry spacecraft. The light-weight ablator had porous structure, and permeability was an important parameter to
analyze flow inside ablator. In this study, permeability was a variable parameter dependent on density of ablator. It is
found that the effect of permeability of light-weight ablator was important with this analysis.
Keywords: Light-Weight Ablator; Coupling Calculation; Pyrolysis Gas Flow; Hayabusa Capsule
About the space mission in near future, it is expected that
the sample return mission like Stardust and Hayabusa in-
creases. In those missions, the space vehicle reenters to
atmosphere at very high speed. In an atmospheric entry
condition, a strong shock wave and a high enthalpy flow
field are generated around the flight vehicle. For example,
Hayabusa reentry capsule, which returned to Earth in
2010, had the velocity of about 12 km/sec and experi-
enced the heating rate of about 20 MW/m2 . To protect
an entry vehicle from such a severe aerodynamic heating,
thermal protection system (TPS) is one of the key com-
ponents in its design. Especially, an ablator has been
widely used as a TPS material for a vehicle under such a
high-heating condition. In addition, in such high enthalpy
flow, the estimation of heat flux from flow to the vehicle
is very complex and difficult. Although a carbon ablator
is known as an often-used one, its heaviness had been a
critical problem in considering the severe weight limita-
tion of a space vehicle. However, a light-weight ablator
named phenolic impregnated carbon ablator (PICA) was
developed at NASA Ames Research Center in 1990’s
and used for the Stardust sample return capsule fore body
heat shield. Its density is lower than 300 kg/m3 , while
most of the conventional carbon ablators have the density
of over 1000 kg/m3.
In Japan, a light-weight ablator (300 - 400 kg/m3) for
middle range heat flux is being developed in JAXA .
These light-weight ablators will become more and more
important for expanding the capability of future missions
and thus sophisticated numerical models are needed to
predict their thermal response more correctly.
An ablator under severe heating environment involves
several complex physics. When the ablator is heated, the
inside resin pyrolyzes and the pyrolysis gas is generated.
Then, the pyrolysis gas flow through the ablator, which is
porous media, ejects from its surface to the outer flow
field. This flow contributes to reduction of the heat flux
to the ablator surface. Furthermore, the pyrolysis of the
resin that is endothermic reaction contributes to cooling
the ablator itself. From these characteristics, the ablator
can be used as an effective passive thermal protection.
However, the aforesaid complex phenomena are involved
in its analysis and thus there still remain uncertainties in
predicting the thermal response of the ablator. Several
efforts have focused on identifying thermal response of
an ablator. Charring Materials Ablation (CMA) code and
Fully Implicit Ablation and Thermal response (FIAT)
opyright © 2013 SciRes. OJFD
H. KIHARA ET AL. 101
program  simulated the internal heat conduction and
the thermal decomposition in one dimension. More so-
phisticated simulation code named Two-dimensional Im-
plicit Thermal response and Ablation (TITAN)  en-
abled two-dimensional simulation.
On the other hand, Ahn H. et al. developed a computa-
tional code named Super Charring Materials Ablation
(SCMA) . In SCMA code, the motion of the pyrolysis
gas inside an ablator was simulated in one dimension by
solving the mass and momentum equations for the gas
phase. Suzuki T. et al. extended SCMA code for two
dimensional simulation and named the code (SCMA2)
. Moreover, they coupled SCMA2 code with a CFD
code using the Park’s two-temperature model and che-
mical reactions with 21 species for a thermochemical
nonequilibrium flow .
In our research group, numerical and experimental
studies have been conducted for determining the thermal
response of a light-weight ablator exposed to a flow field
generated by an arc-heated wind tunnel, which is often
used for a heating test of an ablator [9-11]. Therefore, in
the present study, the thermal response simulation code is
extended so that it can treat the pyrolysis gas flow as
unsteady phenomena in two-dimensional axisymmetric
coordinate. Besides, the CFD code is also extended so as
to include more chemical species, leading to more de-
tailed evaluation of the ablation-gas injection consisting
of the pyrolysis gas and the carbonaceous gas generated
by the surface reactions. Furthermore, the code is devel-
oped for application to wider range of the flow condi-
tions not only for a nitrogen flow but also for an air flow.
2. Computational Models
To simulate the process of heat shield using ablator, we
have to treat many complex situations like the blowing
flow of pyrolysis gas from ablator, chemical reaction on
the surface recession of ablator, radiation heat conduc-
tion from strong shock heated gas, and interaction be-
tween blowout gas and free stream, etc. To understand
such complex phenomena, the coupling simulation of
outer flow-field and inside of ablator was employed.
Flow-field is assumed continuous and axisymmetric flow.
Navier-Stokes equation extends to thermo-chemical non-
equilibrium flow is adopted as governing equation. The
present simulation treats 11 species (N2, O2, NO, 2
2, NO+, N, O, N+, O+, e−) for free stream and 9 spe-
cies (H2, C2, C3, CN, CO, H, C, H+, C+) are related to
ablation gas. These 20 Species and 153 chemical reac-
tions are considered .
The four temperature model is employed to handle in
detail thermal non-equilibrium. These are translation,
rotation, vibration and electron respectively. The electro
excited temperature treats as equilibrium to electron tem-
perature. The energy transfers between each of the inter-
nal energy modes are considered as follows: translation-
rotation , translation-vibration , translation-elec-
tron [15,16], rotation-vibration , rotation-electron 
and vibration-electron . The energy losses for vibra-
tion and rotation due to the heavy particle-impact disso-
ciation  and the electron energy loss due to the elec-
tron-impact dissociation/ionization reactions are consid-
ered. In addition, radiated heat transfer is not ignored, so
the radiation field of high temperature gas is calculated
coupled with flow field around capsule. For the calcula-
tion of radiation field, the present paper employed 3-band
model  extended to chemical nonequilibrium flow
field, which is very low cost method .
The char layer at the ablator surface is lost due to the
surface reactions and then the ablator surface recedes.
The recession rate r is determined using the carbon mass
The shape change should be accounted in the simula-
tion because the magnitude and distribution of the heat
flux are very sensitive to the surface shape . Thus, in
order to consider the shape change due to the surface
recession, the computational domains for both the ablator
and the flow field are reconstructed according to the sur-
face recession. In this calculation, the grid system was
rebuilt at the each 1 μm recession quantity.
2.2. Thermal Response of Ablator
In this simulation, the ablator is made of carbon foam
material impregnated with phenolic resin. It is easy pre-
dicted that the flow of pyrolysis gas inside the light-
weight ablator was different because it had much vacant
spaces. The permeability of virgin layer of conventional
ablator has quite little compare with the permeability of
light-weight ablator’s one. Therefore, it is considered the
phenomena inside the ablator include the conversion
from the solid to the gas phases (pyrolysis), the heat con-
duction in the solid and the gas phases and the gas phase
flow with convective heat transfer. The governing equa-
tions inside ablator are shown as follows.
Solid mass conservation:
Solid energy conservation:
Copyright © 2013 SciRes. OJFD
H. KIHARA ET AL.
Gas mass conservation
Gas momentum conservation
Gas energy conservation
where subscripts s and g represent the solid and the gas
In Equation (2), R represents the pyrolysis rate. It
shows as follow :
In Equations (3) and (6), represent the effective-
ness of reaction heat for gas phase and
1a is for
solid phases respectively. The third term in Equation (3)
and fourth term in Equation (6) represents the energy ex-
change between the solid and the gas phases. The fourth
term in Equation (3) and fifth term in Equation (6) are
the energy loss and energy gain due to the pyrolysis, re-
spectively. The last term in Equations (3) and (6) are the
source terms due to the reaction heat of the pyrolysis.
The pyrolysis gas made from C, H, O and calculated by
chemical equilibrium code .
The solid phase consists of char and resin and then the
solid density is given by the sum of those densities:
Note that the char density char
is constant, while the
resin density sinre
decreases by the pyrolysis. Similarly,
the internal energy of the solid phase is divided into the
parts of char and resin:
The specific heat is given in the form proposed by
Potts . This form is based on the characteristics that
the specific heat of graphite.
and 1 are determined by curve fitting
based on JANAF’s data sheet of graphite .
The pressure of the gas phase is given by the equation
The internal energy of the gas phase is given by
The thermal conductivity is determined by a curve-fit-
ting method with a manufacturing data sheet on carbon
fiber material. Porosity is given by
represents the porosity in case that the resin
The friction force per unit volume f is given by
where K is the permeability tensor.
is the direction along the capsule surface for light-
weight ablator or the laminated direction for conven-
tional ablator. 1
is the permeability of
is the normal direction of
are measured by experiment in our laboratory.
2.3. Coupling and Conditions
The analysis of Flow field and thermal response of the
ablator coupling is done through the boundary condition
of these two fields. The boundary conditions change time
after time. The reentry trajectory determined by JAXA
 is treated in present study. The calculation condition
shows in Table 1 . Time 0sec was altitude at 200 km. The
calculation was done during 40 sec to 100 sec for ablator.
As the boundary condition of inflow, pseudo steady con-
dition is used. Inflow boundary condition changed every
5 sec. The calculation conditions are shown in Table 1.
Numerical domain is shown in Figure 1. The compu-
tation mesh are 110 × 60 for flow field and 60 × 60 for
3. Result and Discussions
Figure 2 shows temperatures distribution along center
Copyright © 2013 SciRes. OJFD
H. KIHARA ET AL. 103
Table 1. Free stream conditions at calculated point.
Fl eight time Altitude Velocity Density Temperatur
S Km km/s kg/m3 K
55 77.75 11.695 2.408 × 10−5 213.7
60 68.59 11.546 9.065 × 10−5 226.8
65 59.94 11.061 2.897 × 10−4 242.3
70 52.16 9.868 7.785 × 10−4 256.4
75 45.74 7.807 1.785 × 10−3 258.1
80 40.99 5.422 3.516 × 10−3 247.7
-50 050100150 200
Figure 1. Numerical grid system.
Distance from wall,mm
-40 -30 -20 -10 0
Figure 2. On axis temperatures distribution at 52.16 km.
xis in front of vehicle at 52.12 km in altitude and 70 sec
ows temperature profiles for each time
ressure distribution and mass
after reentry as a typical condition. We discuss about
condition 52.12 km which the typical data of present
simulation. The zero point of x-axis shows the initial
position of capsule surface. A precursor is remarkably
seen because gas becomes a very high temperature with
the shock wave. The numerical domain of flow field is
selected that the effect of precursor could not ignore. The
translational temperature becomes about 40,000 K. It can
be seen that it is the strong thermal nonequilibrium up-
stream than 5 mm of initial surface. The temperature of
the plateau part behind shock wave exceeds 10,000 K
and the four temperatures are almost equilibrium.
Figure 3 shows temperatures distribution along
ows the difference in the temperature profiles along the
centerline without ablator or ablator. The zero point of
x-axis shows the surface of capsule. To be easy to look,
only translational temperature and vibrational tempera-
ture are shown here. There seems to be no difference
between two conditions. However, the peak translational
temperature and the temperature gradient of approach to
the surface are different and this difference indicates ab-
Figure 4 sh
ong the center line using heavy ablator. The calculation
started t = 40 sec cause of the heat flux is enough small
to able to ignore. At t = 40 sec to 60 sec, it assumed that
the heat flux and pressure interpolated by quadratic func-
tion. On the other hand, it assumed that the heat flux be-
came 0 at t = 100 and calculation was stopped. The peak
temperature of the surface is about 3100 K at 70 sec.
This value has good agreement with measured value 
when Hayabusa reentered.
Figures 5 and 6 show p
x vectors of pyrolysis gas for heavy ablator and light-
weight ablator at 52.16 km, respectively. The permeabil-
ity of conventional heavy ablator at virgin layer is quite
large so that the pyrolysis gas could not penetrate to the
direction of rear wall. So the pyrolysis gas must flow out
Distance From Wall, mm
-14 -12 -10 -8 -6-4-20
Translation with ablator
Vibration without ablator
Translation without ablator
Figure 3. Difference of temperatures distribution between
with and without ablated flow at 52.16 km.
Copyright © 2013 SciRes. OJFD
H. KIHARA ET AL.
Time fromreentry, sec
40 6080 100
Figure 4. Surface temperature history at stagnation with
050 100 150200
Figure 5. Pressure distribution and mass flux vectors of
front side only. On the other hand, the pyrolysis gas
pyrolysis gas at 52.16 km with heavy ablator.
inside light-weight ablator flows not only front but also
rear and radial direction. The pyrolysis gas in light-
weight ablator is more transmissible than heavy weight
ablator. Therefore, the pressure distribution of pyrolysis-
gas in light-weight type became broad. In addition, cause
of the anisotropy of permeability (distribution of poro-
sity) the flow to the radial direction is occurred strongly.
Particularly, the flow of the shoulder part in the ablator is
influenced strong by the expansion wave from the corner.
The shapes of ablator surface at 100 sec are shown in
gure 7. The black line is the initial line, the green line
and the red line show heavy ablator and light-weight ab-
050100 150 200
Figure 6. Pressure distribution and mass flux vectors of
pyrolysis gas at 52.16 km with light-weight ablator.
050100 150 200
ablator 010 20 30
Figure 7. Shape change of ablator at 100 sec.
around stagnation region is imposed.
more than about 1000 K. The total surface recession at
The zooming up
e quantity of the recession at stagnation point is large
for high heat flux. However, extreme change of shape
does not occur and it keeps similarity shape mainly. The
recessions of surface at stagnation point at 100 sec of
heavy ablator and light-weight ablator are 1.4 mm and
6.6 mm respectively. In addition, the surface temperature
at 100 sec is between 1300 K and 1450 K. The surface
recession does not occur dramatically in such tempera-
ture region. On the other hand, there is little the surface
recession at side wall. The temperature of side wall is not
Copyright © 2013 SciRes. OJFD
H. KIHARA ET AL. 105
stagnation point has predicted with 2 mm from 1 mm by
Suzuki et al. . The present study has good agreement
to heavy ablator. Figure 8 shows the history of convec-
tive heat flux at stagnation point. The Solid lines show
conventional heat flux and the black line shows non ab-
lated wall condition for compared. The radiative equilib-
rium condition is used at the surface condition. Green
and red lines are heavy and light-weight respectively.
The dashed line shows net heat flux with surface chemi-
cal reaction that includes surface reactions (nitrization,
oxization, sublimation). The effusion of pyrolysis gas
works effectively to decrease heat flux. The dashed lines
are higher than 30% of solid lines. We can see that the
surface reaction play important role. In comparison with
Flight time, sec
Convective heat flux, W/m2
55 60 65 70 75 80 85
Figure 8. Time profiles of convective heat flux at stagnation
Radiative heat flux, W/m2
55 60 65 70 7580 85
Figure 9. Time profiles of radiative heat flux at stagnation
is not so much. On the other hand, radiative heat
ulation around Hay-
model and it was clear that
it, the difference between heavy ablator and light-weight
flux (Figure 9) does not decrease using by ablating ma-
terial. It rather increase slightly cause of radiation from
ablating species. It can find a very slight difference be-
tween heavy ablator and light-weight ablator in radia-
tive heat flux.
Temperature distribution along center axis at each time
is shown in Figure 10. The peak temperature is 3100 K
for heavy ablator and 3200 K for light-weight ablator at
70 sec. The rear wall temperature does not rise until 80
sec. Though there is no heating, the rear wall temperature
is increasing at 100 sec. On other hand, the rear wall tem-
perature of heavy ablator keeps initial temperature. The
light-weight ablator does not have enough thickness for
this condition. However, it suggests that it can prevent
heat by slightly increasing the thickness of the light-
weight ablator. Present study calculated until 100 sec,
because the heat flux became quite small estimated in ref.
A trajectory-based flow field sim
abusa capsule loaded light-weight ablator
thermal response was carried out as a test case of near
future mission. To validate this calculation, the conven-
tional heavy ablator condition was carried out, too. The
light-weight ablator in this calculation had been made
and tested in our laboratory. In addition, the radiative
heat flux had computed using 3-band model extended to
To calculate flow field around capsule, present simula-
tion adopted four-temperature
e flow field had strong thermal nonequilibrium behind
shock wave and thermo-chemical equilibrium near the
05 10 15 20 25 30
70 sec100 sec
Figure 10. Temperature profiles along center axis.
Copyright © 2013 SciRes. OJFD
H. KIHARA ET AL.
wall surface. The precursor phenomenon could see using
In thermal response for light-weight ablator, the state
of the pyrolysis gaits movement play important
roles to the flow inside of ablator. The pyrolysis gas
heavy ablator flows towaear boundary surface but
the pyrolysis gas in light-weight ablator flows none one-
dimensionally. The pyrolysis gas flow transports energies
to the direction of rear wall and it makes the apparent
heat conduction higher.
The difference of stagnation hebetween heavy
ablator and light-weight ablator is small. Especially radi-
ated heat fluxes of these are almost the same. On the
other hand, theation heat flux taking account of
surface reaction becomes 30% larger than convectional
heat flux without surface reaction.
The surface recession of light-weight ablator is few
ity. This work was partially
ial,” Journal of Spacecraft and
08, pp. 854-864.
and Thermal Re-
sponse Program for Spacecraft Heatshield Analysis,”
Journal of Spal. 36, No. 3, 1999
n, C. Park and K. Sawada, “Response of Heatshield
zaka, H. Kihara and K. Abe, “Experi-
ber 2010, IAC-10-C2.7.7.
rds a n
Material at Stagnation Point of Pioneer-Venus Probes,”
Journal of Thermophysics and Heat Transfer, Vol. 16, No.
3, 2002, pp. 432-439.
 T. Suzuki, K. Sawada, T. Yamada and Y. Inatani, “Ther-
mal Response of Ablative Test Piece in Arc-
mental and Numerical Studies of Spallation Particles Ejec-
ted from A Light-Weight Ablator,” Proceedings of 61st
International Astronautical Congress, Prague, 27 Sep-
s larger than heavy ablator in addition; the heat [10
transfer is slightly higher than heavy ablator. Therefore,
this study shows light-weight ablator in this paper cannot
use same configuration of heavy ablator and same thick-
ness but it suggests that it can prevent heat by slightly in-
creasing the thickness of the lightweight ablator.
The computation was mainly carried using the computer
facilities at the Research Institute for Information Tech-
nology, Kyushu Univers sup-
rted by Grant-in-Aid for Scientific Research, No.
23460954, sponsored by Ministry of Education, Culture,
Sports, Science and Technology, Japan.
T. Yamada, N. Ishii, Y. Inatani and M. Honda, “Thermal
Protection System of the Reentry Capsule with Superor-
bital Velocity,” Institute of Space and Astronautical Sci-
ence Report Source Publishing No. 17, 2003, pp. 245-
 M. A. Covington, J. M. Heinemann, H. E. Goldstein,
Y.-K. Chen, I. Terrazas-Salinas, J. A. Balboni, J. Olejnic-
zak and E. R. Martinez, “Performance of a Lowensity
Ablative Heatshield Mater
Rockets, Vol. 45, No. 4, 20
 T. Yamada, Y. Ishida, T. Suzuki, K. Takasaki, K. Fujita,
T. Ogasawara and T. Abe, “Development of High and
Low Density Ablators for Dash-II and Future Reentry
Missions,” Proceedings of the 27th International Sympo-
sium on Space Technology and Science, Tsukuba, 5-12
July 2009, p. e-03.
 Y. K. Chen and F. S. Milos, “Ablation
, cecraft and Rockets, Vo
 Y. K. Chen and F. S. Milos, “Two-Dimensional Implicit
Thermal Response and Ablation Program for Charring
Materials,” Journal of Spacecraft and Rockets, Vol. 38,
No. 4, 2001, pp. 473-481.
 H. Ah
nel,” AIAA Paper No. 2004-0341, 2004.
 T. Suzuki, T. Sakai and T. Yamada, “Calculation of
Thermal Response of Ablator under Arcjet Flow Condi-
tion,” Journal of Thermophysics and Heat Transfer, Vol.
21, No. 2, 2007, pp. 257-266.
 S. Nozawa, T. Kana
] Y. Takahashi, H. Kihara and K. Abe, “Effect of Radiative
Heat Transfer in Arc-Heated Nonequilibrium Flow Simu-
lation,” Journal of Physics D: Applied Physics, Vol. 43,
2010, Article ID: 185201.
 N. Hirata, S. Nozawa, Y. Takahashi, H. Kihara and K.
Abe, “Numerical Study of Pyrolysis Gas Flow and Heat
Transfer inside an Ablator,” Computational Thermal Sci-
nal of Ther-
ophysics and Heat Trans-
ences, Vol. 4, No. 3, 2012, pp. 225-242.
 C. Park, R. L. Jaffe and H. Partridge, “Chemical-Kinetic
Parameters of Hyperbolic Earth Entry,” Jour
mophysics and Heat Transfer, Vol. 15, No. 1, 2001, pp.
 C. Park, “Rotational Relaxation of N2 behind a Strong
Shock Wave,” Journal of Therm
fer, Vol. 18, No. 4, 2004, pp. 527-533.
 C. Park, “Problems of Rate Chemistry in the Flight Re-
gimes of Aeroassisted Orbital Transfer Vehicles,” AIAA
Paper 84-1730, 1985.
 J. P. Appleton and K. N. C. Bray, “The Conservation
Equations for a Nonequilibrium Plasma,” Journal of Flu-
id Mechanics, Vol. 20, No. 4, 1964, pp. 659-672.
 P. A. Gnoffo, R. N. Gupta and J. L. Sh
Equations and Physical Models for Hyp
ersonic Air Flows
ctron and Vibra-
ee, “Electron-Impact Vibrational Relaxation in
in Thermal and Chemical Nonequilibrium,” National
Aeronautics and Space Administration, Washington DC,
 S. S. Lazdinis and S. L. Petrie, “Free Ele
tional Temperature Nonequilibrium in High Temperature
Nitrogen,” Physics of Fluids, Vol. 17, No. 8, 1974, pp.
 J.-H. L
High-Temperature Nitrogen,” Journal of Thermophysics
and Heat Transfer, Vol. 7, No. 3, 1993, pp. 399-405.
 T. Sakai, “Computational Simulation of
Arc Heater Flows,” Journal of Thermophysics
Transfer, Vol. 21, No. 1, 2007, pp. 77-85.
 M. Yamada, Y. Matsuda, H. Hirata, Y. Takahashi, H.
Copyright © 2013 SciRes. OJFD
H. KIHARA ET AL.
Copyright © 2013 SciRes. OJFD
umerical Simulation of Flow Field
urnal of Physical and Chemical
Paper 2011-3759, 2011.
Kihara and K. Abe, “N 
and Heat Transfer around HAYABUSA Reentry Cap-
sule,” Proceedings of the 28th International Symposium
on Space Technology and Science, Okinawa, 5-12 June
2011, p. e-38.
 Y. K. Chen and F. S. Milos, “Loosely Coupled Simula-
tion for Two-Dimensional Ablation and Shape Change,”
Journal of Spacecraft and Rockets, Vol. 47, No. 5, 2010,
 T. Kanzaka, S. Nozawa, Y. Takahashi, H. Kihara and K.
Abe, “Numerical Investigation of Thermal Response of
Ablator Exposed to Thermochemical Nonequilibrium
Flow,” Proceediongs of the 6th Asian-Pacific Conference
on Aerospace Technology and Science, Huangshan, 15-19
November 2009, B2-2.
S. Gordon and B. J. McBridge, “Computer Program for
Calculation of Complex Chemical Equilibrium Computa-
tion and Application,” NASA Reference Publication 1311,
 R. L. Potts, “Application of Integral Methods to Ablation
Charring Erosion: A Review,” Journal of Spacecraft and
Rockets, Vol. 32, No. 2, 1995, pp. 200-209.
 M. W. Chase Jr., C. A. Davies Jr., J. R. Downey, D. J. Fru-
rip, R. A. McDonald and A. N. Syverud, “JANAF Ther-
mochemical Tables,” Jo
Reference Data, Vol. 14, 1985, pp. 535.
 T. Suzuki, K. Fujita, T. Yamada, Y. Inatani and N. Ishii,
“Post-Flight TPS Analysis fo Hayabusa Reentry Capsul,”