Performance Analysis of Ceramic Composite Thermal Protection System Tiles: Applications

Abstract

The need for more speed for hypersonic aviation, reentry, and rocket propulsion vehicles increases as the quest for space and planetary exploration increases; improved materials are needed to withstand the conditions encountered by wing leading edges and propulsion system components in hypersonic aerospace vehicles as well as the extreme conditions associated with atmospheric reentry and rocket propulsion. Reports on arc-jet testing as the best ground-based simulation of thermal analysis on vehicle structure materials under reentry conditions are available but limited. Such tests provide mechanical, thermal, and chemical behavior of materials. In the present paper, a report on analysis through transient numerical simulation using COMSOL Multiphysics for heat transfer by conduction, convection, and radiation in porous ceramic and ceramic composite TPS tiles under reentry conditions is presented. Temperature profile for pure silica TPS tile is obtained in the first phase of the thermal analysis with surface conditions of pressure and surface heat flux equivalent to the reentry conditions. 1-D, 2-D, and 3-D analyses has been conducted in the next phase and studied the response of ceramic composite tile model from the family of ultrahigh-temperature ceramics at higher heat loads as experienced by leading edges.

Full text

Performance Analysis of Ceramic Composite
Thermal Protection System Tiles
Arjunan Pradeep, Suryan Abhilash, and Kurian Sunish
1 Introduction
When a space craft enters a planetary atmosphere from space, the surface exposes to
high heat fluxes generated by dissipation of kinetic energy due to aerobraking and
friction with atmospheric gases, which depends on many parameters including
entry velocity, entry angle, ballistic coefficient, vehicle bluntness, enthalpy char-
acteristics, and density and temperature of atmospheric gases. The design of a
successful thermal protection system (TPS) is a significant engineering challenge
as its failure will ultimately breakup the entire craft including its payload, structure,
and crew. Reusable TPSs are primarily developed for extended flight durations with
much better insulating capacity than ablators and to maximize reradiation of the
incident aerothermodynamic heat to atmospheric environment (Shukla et al. 2006).
Reentry vehicles with sharp leading edges imply lower aerodynamic drag,
improved performance, safety, and maneuverability but results higher surface
temperature than blunt vehicles. As the leading edge radius decreases, the surface
temperature increases (Savino et al. 2010). Therefore, in order to achieve maximum
performance, materials are needed, which are both capable of withstanding the
reentry environment at temperatures greater than 2000 K and have a high thermal
conductivity that will direct more energy away from the tip of the leading edge
allowing for even further improvements in vehicle performance. It leads to the
demand of development of high-temperature materials which can find applications
in hypersonic flight vehicles with sharp leading edges. From the family of ceramic
materials known as ultrahigh-temperature ceramics (UHTCs), refractory metal
A. Pradeep (*) • S. Abhilash • K. Sunish
University of Kerala, Department of Mechanical Engineering, College of Engineering
Trivandrum, Thiruvananthapuram 695016, India
e-mail: pradeeparch@gmail.com
©Springer International Publishing AG, part of Springer Nature 2018
F. Aloui, I. Dincer (eds.), Exergy for A Better Environment and Improved
Sustainability 2, Green Energy and Technology,
https://doi.org/10.1007/978-3-319-62575-1_40
557

diborides with some additives such as SiC (e.g.: HfB
2
-SiC) and/or refractory metal
carbides (HfC), can be identified as most promising candidates as an effective
thermal protection system for nose cap and other sharp leading edges. These
materials are characterized by improved mechanical and thermal properties, excel-
lent chemical stability like good oxidation resistance, and high melting point
(>3000 K) (Savino et al. 2008).
Figure.1shows how the surface temperature for the sharp UHTC leading edge is
determined by an energy balance of incident heat flux, reradiated energy, and
energy pulled away from the leading edge tip and reradiated out the sides of the
component in which the incident heat flux is lower (Kontinos et al. 2001).
When a steady state is achieved, global radiative equilibrium is established, in
the sense that the overall convective heat flux is perfectly balanced by the overall
surface radiative flux, and, if the material thermal conductivity is high, a relatively
low equilibrium temperature is achieved. Thus, the need for highly conducting yet
refractory materials is essential in the design of sharp vehicles (Gasch et al. 2005).
Nomenclature
1-D,2-D,3-D One, two, three dimensional
TPS Thermal protection system
UHTC Ultrahigh temperature ceramics
SiC Silicon carbide
HfB
2
Hafnium diboride
ZrB
2
Zirconium diboride
HfC Hafnium carbide
ZrC Zirconium carbide
HfN Hafnium nitride
MoSi
2
Molybdenum disilicide
Si
3
N
4
Silicon nitride
(continued)
Fig. 1 Effect of conductivity for a blunt and sharp leading edge of a reentry vehicle
558 A. Pradeep et al.

qHeat flux
RCC Reinforced carbon/carbon
MFI Multifoil insulation
RSI Reusable surface insulation
HSpecific total enthalpy
PWT Plasma wind tunnel
SHS Sharp hot structures
FEM Finite element method
kConductivity
TTemperature
C
p
Specific heat at constant pressure
C
v
Specific Heat at constant volume
Kn Knudsen number
EExtinction coefficient
Greek letters
τTime in seconds
μDynamic viscosity
γRatio of specific heats
αAccommodation coefficient
σStefan-Boltzmann constant
ρDensity
Subscripts
rad Radiative
cond Conductive
conv Convective
s Solid
g Gas
1.1 Problem Definition
The main objective of this work is to investigate the temperature distribution by
conduction, convection, and radiation through ceramic composite porous tile.
Currently, studies on thermal response of nonablating pure ceramic tiles are avail-
able as a TPS material applying on surface other than leading edges of wings and
nose cone of a space vehicle, and in this study, performance analysis of TPS Tile
made of silica-based ceramic composite is considered instead of a single-
component silica tile.
Performance Analysis of Ceramic Composite Thermal Protection System Tiles 559

2 Review of Literature
Comparison of measured and predicted temperature profiles of selected
multicomponent TPS to an aerodynamic arc-jet environment was studied at surface
heating rates high enough to include radiation heat transfer by Stewart and
Leiser (1985).
Stauffer et al. (1992) developed a model for evaluating the steady-state heat
transfer through multifoil insulation (MFI). The model enables the calculation of an
effective thermal conductivity as a function of temperature and pressure. The heat
transfer through MFI, a composite insulation system consisting of thin metallic foils
held apart by tiny ceramic particles, consists of three components: foil to foil
radiation heat transfer, gas conduction via interstitial gas molecules, and solid
conduction through ceramic spacer particles. The radiation heat transfer and gas-
eous conduction models are validated by comparison with test data reported in the
literature. Empirical correlations are developed to describe the nondimensional
contact conductance, and these show that contact conductance is a function of
configuration and operating conditions. The model can provide important informa-
tion to designer of thermal protection system (TPS) of advanced hypersonic
vehicles.
Chiu (1992) developed a simulation model and illustrates the thermal response
of reusable surface insulation (RSI) tiles and blankets during aeropass. For some
cases, experimental measurements were available from arc-jet testing, and com-
parison between calculated and measured temperature is also carried out. Thermal
analyses of both tiles and blankets have been conducted in this study. Comparison
between the in-depth temperatures of an advanced tile calculated using transient
thermal conductivities and those measured under stagnation heating during arc-jet
test show good agreement, which indicates the accuracy of the transient thermal
conductivities. The analysis in this paper was carried out to predict the temperature
performance of a spectrally reflective coating on a tile, to access the temperature
errors in a tile due to thermo couple lead wires installations, to determine the extent
of thermal distortion in a blanket due to adjacent tiles, and to correlate the
temperature measurements of a thermocouple probe in a blanket.
The need of research and development of UHTC materials for low thrust rocket
propulsion and hypersonic spacecraft applications are emphasized by Upadhya
et al. (1997). They observes that by developing an ultrahigh-temperature material
with temperature capabilities in the range of 2200–3000 C, the fuel-film and
regenerative cooling can be significantly reduced and/or eliminated resulting in
cleaner burning of rocket engine. Thus, fuel utilization can be vastly improved,
more payloads can be sent to space, higher specific impulse can be achieved, and
finally, the cost of the rocket engine could be reduced. Mechanical, thermal, and
oxidation behavior of refractory metals and alloys, refractory carbides, refractory
borides, and carbon–carbon composites are summarized in the paper.
Opeka et al. (1999) reported mechanical, thermal, and oxidation properties of
HfB2, HfC, HfN, ZrB
2
, ZrC, and SiC ceramics. It was found that HfB
2
had a much
560 A. Pradeep et al.

lower ductile-to-brittle transition temperature than HfN or HfC. The effect of
lowering the carbon stoichiometry was also to decrease the transition temperature.
The thermal conductivity of HfB
2
was much greater than the carbides or nitride.
The coefficient of thermal expansion of all materials tested was approximately the
same up to 1500 C, with HfN exhibiting a higher expansion than the others up to
2500 C. The HfB
2
ceramics had the highest modulus of the materials tested,
whereas HfC had the lowest. The oxidation behavior of the ceramics was charac-
terized as a function of phase composition. The SiC-containing ZrB
2
ceramics had
high oxidation resistance up to 1500 C compared with pure ZrB
2
and ZrC
ceramics. The ZrB
2
/SiC ratio of about 2 (25 vol% SiC) is necessary for the best
oxidation protection. The presence of ZrC in ZrB
2
ceramics negatively affects their
oxidation resistance. A hypothesis describing oxidation behavior of the ZrB
2
/ZrC/
SiC ceramics is proposed.
Daryabeigi (2002) investigated the use and optimization of high-temperature
insulation for metallic thermal protection systems. The multilayer insulation con-
sidered consists of ceramic foils with high-reflectance gold coatings. Here, the
author’s main aim was to model the combined radiation/conduction heat transfer
through multilayer insulations with a numerical model validated by experimental
lists and to use the numerical model to design optimum multilayer configurations.
The effective thermal conductivity of a multilayer insulation was measured over an
extended temperature of 373–1273 K and a pressure range of 1.3310
5
–
101.32 kPa. A numerical model was developed for modeling combined radiation/
conduction heat transfer in high-temperature multilayer insulations. The numerical
model was validated by comparison with steady-state effective thermal conductiv-
ity measurements and by transient thermal tests simulating reentry aerodynamic
heating conditions. A design of experimental approach was used to determine the
optimum design for multilayer insulations subjected to reentry aerodynamic
heating condition.
The need for materials development, ground testing, and sophisticated modeling
techniques for the development of new TPS material for future space missions are
emphasized by Laub and Venkatapathy (2003). As a base information, they
describe about two classes namely ablative and reusable TPS materials and a
brief history of ablative TPS so far. They also describes the lessons learned and
TPS challenges for future missions based on the Jupiter, Venus, Titan, Mars,
Neptune, and other sample return missions. The authors pointed out that TPS
innovations are required because above missions were done with materials devel-
oped over many decades ago. The authors emphasize on the establishment of a
cross-cutting TPS Technology program with elements focused on sustaining cur-
rent technologies and elements focused on enabling future higher speed return
missions.
Matthew et al. (2005) summarizes experimental results on HfB
2-
and ZrB
2
-based
compositions. They focused on identifying additives like SiC to improve mechan-
ical and thermal properties and to improve oxidation resistance. These are charac-
terized by high melting points, chemical inertness, and good oxidation resistance in
Performance Analysis of Ceramic Composite Thermal Protection System Tiles 561

extreme environments at temperatures greater than 2000 C as experienced during
reentry. They are providing variation of thermal properties with rise in temperature.
Shukla et al. (2006) studied thermal response of the nonablating ceramic tiles by
finite element method. A continuum model for the porous materials is used for the
determination of thermal conductivity. The temperature distribution for the
one-dimensional model is compared with the available arc-jet result. The 1-D and
2-D temperature contours and the heat flux distributions for the silica tiles are also
presented. The expression for the pressure distribution in a silica tile is derived.
They used pure silica material and developed a methodology to analyze the
performance of ablative thermal protection system and proved that, by using
temperature limits provided from the materials used for the structure of the space-
craft, a TPS can be designed to prevent the structure from overheating. The models
used were validated with experimental arc-jet data. The assumptions used in the
computations were an adiabatic back wall, low surface catalysis, and no convective
cooling during soak out.
Upon reviewing this literature, it was realized that performance analysis of TPS
tile made of silica-based ceramic composite can also be considered by a similar
methodology done by them. The application of these tile materials can be found in
nose cap and wing tips of the reentry vehicle or locations where the vehicle
structure interacts with the heat flux to cause the temperature to rise to its peak
values.
Scatteia et al. (2006) reported results of an experimental investigation into the
efficiency of sintered ZrB
2
-SiC compounds and of plasma-sprayed ZrB
2
-SiC coat-
ing for heat radiation and for the recombination of atomic oxygen. Experiments on
emissivity measurements of ZrB
2
-SiC ceramic composite at 200 Pa and 0.001 Pa
pressure conditions are performed. The results under vacuum conditions are lower
than the ones obtained at high pressure. High emissivity values and low recombi-
nation coefficients were found in agreement with previous experimental studies
performed on similar ceramic compounds but at lower temperatures using a differ-
ent measurement technique. According to the surface analysis, the oxide scale is a
silica or borosilicate glassy layer. This represents a rather promising result, because
the radiative efficiency of silica-based glassy compounds is reportedly higher than
that of pristine UHTCs.
Loehman et al. (2006) reported results of thermal diffusivity, thermal conduc-
tivity, and specific heat measurements of ZrB
2
and HfB
2
. Thermal diffusivities
were measured to 2000 C for ZrB
2
and HfB
2
ceramics with SiC contents from 2 to
20%. Thermal conductivities were calculated from thermal diffusivities and mea-
sured heat capacities. Thermal diffusivities were modeled using different two-phase
composite models. They prove that these materials exhibit excellent high-
temperature properties and are attractive for further development for thermal
protection systems.
Zhang et al. (2008) conducted ablation tests of the flat-face models for ZrB
2
–
20vol%SiC ultrahigh-temperature ceramic (UHTC) which was prepared by hot
pressing. The tests conducted under ground simulated atmospheric reentry condi-
tions using arc-jet testing with heat fluxes of 1.7 and 5.4 MW/m
2
under subsonic
562 A. Pradeep et al.

conditions, respectively. For temperatures in the order of 1600–1700 C, the
material was able to endure the heating conditions; however, for temperatures in
the order of 2300 C, evident oxidation and ablation occurred, and the material was
unable to offer a valuable resistance to the applied aerothermal load. Results
indicate that ZrB
2
–SiC ultrahigh-temperature ceramics are the potential candidates
for leading edges. Results indicated that ZrB
2
–SiC can maintain the high-oxidation
resistance coupled with configurational stability at temperatures lower than that
point which results in significant softening and degradation of the oxide scale, and
that point will be the temperature limit for UHTC.
Savino et al. (2008) investigated the behavior of pressure less sintered two
different ultrahigh-temperature ceramics, HfB
2
+ 5% MoSi
2
and HfC +5%MoSi
2
,
which were exposed to an average specific total enthalpy of the flow around the
body of the order of 5–10 MJ/kg and at atmospheric pressure typical of atmospheric
reentry environment, with an arc-jet facility at temperatures exceeding 2000 C.
The surface temperature and emissivity of the materials were evaluated during the
test. The microstructure modifications were analyzed after exposure. The
HfB
2
+ 5%MoSi
2
model surface reached a peak value of 1950 C for specific
total enthalpy (H) approaching 8 MJ/kg. The cross section after exposure showed
the formation of a compact silica oxide (about 15 μm) which sealed the underlying
HfO
2
scale. The HfC + 5% MoSi
2
model surface reached peak values of 2100 and
2400 C. Cross-sectional analysis showed a layered structure, constituted of an
outer layer of porous HfO
2
and an inner layer mainly constituted of HfO
2
and silica.
Borrellia et al. (2009) tested a nose cap demonstrator in the plasma wind tunnel
(PWT) facility to focus on the assessment of the applicability of UHTCs to the
fabrication of high performance and sharp hot structures (SHS) for reusable launch
vehicles. In this paper, the FEM-based thermo-structural analyses are presented.
Comparisons with experimental data measured in the PWT have been introduced to
validate the FEM model and to help in interpreting the experimental test itself.
Synergies between numerical and experimental activities have been finalized to the
improvement of knowledge on the physical phenomenon under investigation. The
effects on the thermal response due to the assumption of the catalytic condition of
the wall, due to the uncertainties related to heat flux and pressure measurements on
the probe (which influence the heat flux computation), and due to uncertainties in
the determination of some UHTC thermal properties, have been investigated.
Discrepancies between the numerical results and experimental ones in terms of
wall temperature distribution on the massive UHTC nose tip were found, and
possible sources of error have been analyzed. The experimental temperatures
curves fall very close to the numerical envelope (taking in account several sources
of error) for all the test duration and the noncatalytic wall model was found more
reliable in reproducing thermal behavior of the nose cap.
Savino et al. (2010) deal with arc-jet experiments on different UHTC models
which have been carried out in two different facilities, to analyze the aerothermal
environment and to characterize the material behavior in high enthalpy hypersonic
nonequilibrium flow. Typical geometries of interest for nose tip or wing leading
edges of hypersonic vehicles, as rounded wedge, hemisphere, and cone are
Performance Analysis of Ceramic Composite Thermal Protection System Tiles 563

considered. The ZrB
2
-based UHTC material sample tested for several minutes to
temperatures up to 2050 K showing a good oxidation resistance in extreme condi-
tions. The flow conditions and the sharpness of the models are similar in both
facilities, but the larger model (rounded wedge) is characterized by a heat flux
distributions (peaking at the leading edge and strongly decreases downstream)
resulting in a lower average surface heat flux and therefore (also due to the
relatively high thermal conductivity) in a smaller equilibrium temperature in
comparison with the smaller specimens. Numerical-experimental correlations
show a good agreement with proper modeling of the surface catalytic behavior.
As expected, the higher temperature achieved in the small-sized specimens, sub-
mitted to hypersonic arc-jet conditions than in the rounded wedge tests and the
lower pressure in comparison with the subsonic arc-jet tests increase the oxidation
phenomena. The change in surface composition can justify the lower value
(0.6–0.65) of the surface emissivity estimated in their work in comparison with
the subsonic experiments (0.9) where poor oxidation phenomena were observed.
Levinskas et al. (2011) report the experimental investigations of the new com-
posite material based on light silicate frame impregnated by polymer composite
tested in high-temperature air jet and generated by means of plasma torch (temper-
ature – (1320–2420) C, velocity – (40–50) m/s). Data of composite material
ablation rate and temperature of protective sample set surface during experiment
are presented. Recent advances in polymer-layered silicate nanocomposites, espe-
cially with the improved thermal stability, flame retardancy, and enhanced barrier
properties promote the investigation of these materials as potential ablatives.
Introduction of the layered nanosilicates (montmorillonite, tobermorite) into poly-
mer matrix results in the increase of thermal stability of polymer nanocomposites
and ablation resistance, which are not observed in each component. Experimental
investigations of the ablation resistance of the set with protective shell were
provided in two different plasma flows–air plasma jet (for first set of samples in
which ablation resistance is found remarkably high in air gas flow environment) and
combustion gases plasma jet with reduced oxygen content (for second set of
samples in which existence of the reinforcement coating remarkably decreased
the ablation rate initially). The light silicate shell has demonstrated good resistance
to the impact of high-temperature gas flow initiated by plasma jet. The additional
impregnation of light silicate shell with epoxy nanocomposite reinforcement coat-
ing increased the temperature on the shell surface due to exothermic reactions but
decreased the ablation rate accordingly. The experiments in reduced oxygen flow
have shown good thermal stability of the protective shell. The structure imparts
high thermal shock resistance and dimensional stability.
Justin and Jankowiak (2011) present ZrB
2
-SiC and some other composites
developed for leading edges or air intakes of future hypersonic civilian aircrafts
flying up to Mach 6. Addition of 20 vol% of SiC is found optimal for good oxidation
resistance. They observe that these composites possess high hardness, high flexural
stress, good machinability, high emissivity, good thermal conductivity, and thermal
shock resistance.
564 A. Pradeep et al.

Mallik et al. (2012) investigated thermal properties of ZrB
2
–SiC, HfB
2
–SiC,
ZrB
2
–SiC–Si
3
N
4
, and ZrB
2
–ZrC–SiC–Si
3
N
4
composites within temperature range
between 25 and 1300 C. Thermal conductivity increases with addition of SiC,
while it decreases on ZrC addition. Variations of thermal conductivity, specific
heat, and thermal diffusivity with temperature are plotted. Gregory et al. (2012)
reviewed results on thermal conductivity of HfB
2
and ZrB
2
. Pure HfB
2
, pure ZrB
2
,
and composites of HfB
2
and ZrB
2
with various vol% of SiC are reviewed in detail.
Can and Yue (2013) are developing a numerical model combining radiation and
conduction for porous materials based on the finite volume method. The model can
be used to investigate high-temperature thermal insulations that are widely used in
metallic thermal protection systems on reusable launch vehicles and high-
temperature fuel cells. The effective thermal conductivities which are measured
experimentally can hardly be used separately to analyze the heat transfer behaviors
of conduction and radiation for high-temperature insulation. By fitting the effective
thermal conductivities with experimental data, the equivalent radiation transmit-
tance, absorptivity and reflectivity, as well as a linear function to describe the
relationship between temperature and conductivity can be estimated by an inverse
problems method.
Yang et al. (2013) compared and investigated the effect of high-temperature
oxidation on mechanical properties and anti-ablation property of ZrB
2
/SiC as a
protective coating that was obtained on the surface of C/SiC composites. The
following are the observations done by the authors: C/SiC composites are good
thermal shielding for aerospace applications, provided that they are protected from
oxidation by suitable coatings. UHTC, and in particular ZrB
2
, is among the best
oxidation resistant materials as known. Mechanical tests were conducted before and
after oxidation test. Anti-ablation property was tested under oxy-acetylene torch.
Compared with the uncoated composites, the linear and mass ablation rates of the
coated composites decreased by 62.1% and 46.1%, respectively, after ablation for
30s. The formation of zirconia and silicon dioxide from the oxidation of ZrB
2
/SiC
improved the ablation resistance of the composites because of the evaporation at
elevated temperature, which absorbed heat from the flame and reduced the erosive
attack to carbon fibers and SiC matrix. They tried to prove that ZrB
2
/SiC coating for
C/SiC composites could fully fulfill the advantages of refractory compounds.
3 Heat Transfer Through Porous Ceramic/Ceramic
Composite Tile
3.1 Heat Transfer by Gas Conduction in Pores
Conduction is one of the main modes of heat transfer in tiles. The heat is transmitted
along the solid skeleton of the tile and through the gas filling the space in the
insulation. With increasing porosity of the insulator, the second way becomes
Performance Analysis of Ceramic Composite Thermal Protection System Tiles 565

dominant. Accordingly, the thermal conductivity of high-quality insulators comes
close to that of the contained gas, which is usually considered as air/inert gas.
According to the fundamental equation of the theory of heat conduction, the steady-
state (stationary) thermal fluxes across an isothermal surface in a body are
q¼k∇Tð1Þ
In general form, the transient equation of heat conduction is
ρCp
∂T
∂τ¼k∇2Tð2Þ
The kinetic theory of gas usually consider two extreme cases of heat transfer by
gas conduction: L<<δand L>>δwhere Lis the mean free path of the gas
molecules and δis the distance between the heat exchanging surfaces (/character-
istic length). The atmospheric pressure under reentry condition at high altitude is
taken as 0.01 atm. The value of Lat this pressure and altitude is very high as
compared with δ(In this case, δis. pore diameter, which is in the range of
micrometers). So, Kn>>1. According to the kinetic theory of gas, when Knudsen
number, Kn <<1, the conductivity is independent of the gas pressure. If the
pressure is sufficiently low and Kn>>1, the gas molecules bounce from wall to
wall without colliding with each other. The amount of heat transferred is then
proportional to the number of molecules participating in the transfer and thus to the
gas pressure. When the distance between the walls is larger, the path of the
molecule becomes longer, but their number per unit surface also increases. As a
result, the rate of heat transfer is independent of the separation of the walls. For a
monatomic gas, the thermal conductivity of gas can be expressed as
kg¼k0
1þ2acKnðÞ ð3Þ
where k
0
¼thermal conductivity of the gas at atmosphere pressure and can be
obtained by k
0
¼eμC
V
where e¼(9γ5)/4
ac¼2e
1þγ

2α
α

α¼accommodation coefficient that allows for incomplete energy exchange
between the gas molecules and surface and is defined by
α¼T0
2T1
T2T1
566 A. Pradeep et al.

where T
1
is the temperature corresponding to the energy of the molecule colliding
with the wall, the temperature of which is T
2
, and T0
2
is the temperature
corresponding to the energy of the reflected molecules.
3.2 Transient Heat Transfer by Radiation
The mode of heat transfer across TPS materials is by solid conduction, gaseous
conduction through gases trapped in the pores, free and forced convection, as well
as radiation in pores. The convection is generally neglected and will not be
considered here. However, it should be noted that especially when considering
the case of an applied rigid fibrous refractory insulation for a space vehicle during
reentry, forced convection may affect the overall heat transfer. The mechanism of
conduction by residual gas and solid conduction, if not similar physically, is similar
mathematically in the sense that the heat flux is proportional to the thermal
conductivity and local heat gradient. Radiation, on the other hand, is a complex
process and has to be treated separately. The local inhomogenities in the material
affect the transmission of radiant energy. For example, radiation leaving a surface,
on passing through the material may (i) pass through voids in the fibrous material,
(ii) be absorbed by the residual gas and subsequently reemitted, (iii) be absorbed by
the particle and subsequently reemitted, (iv) be scattered by particles, and (v) be
scattered by fibers. The TPS material will be considered as homogeneous and
continuous. These assumptions may be justified if the gas voids and the particles
of the insulation are essentially in the equilibrium with the surrounding gas, and if
the particle spacing is sufficiently small, so that the temperature difference between
the adjacent solid particles is small compared with the total temperature. For a
radiative flux,
qrad ¼
16
3Eσn2T3
rad
∂T
∂x¼krad
∂T
∂xð4Þ
where Eis extinction coefficient, nis refractive index (taken as 1), and σis Stefan-
Boltzmann constant.
T3
rad ¼T2þT2
a

TþTa
ðÞ
4
where Tis temperature of the body, and T
a
is temperature of the atmosphere.
The energy flux vector by combined radiation and conduction at any position in
the medium can be expressed as
Performance Analysis of Ceramic Composite Thermal Protection System Tiles 567

q¼qrad þqg¼ krad þkg

∂T
∂xð5Þ
This can be used as heat conduction equation, to obtain an energy balance on a
differential volume element within an absorbing–emitting medium. The medium
behaves like a conductor with thermal conductivity dependent on temperature.
3.3 Effective Thermal Conductivity
Effective thermal conductivity of the bulk material is as follows:
k¼ηA1θðÞksþ1θðÞkgþβA2θðÞkrad ð6Þ
where η¼1.93θ(ηis called bonding efficiency factor), θ¼volume faction,
β¼8.571(1.0 θ) + 0.84 for porosity >0.84, and β¼1.2 for porosity <0.84 (β
is called density scale factor on the change in emittance of composite insulation).
The two adjustment parameters ηand βwhich relate to solid conduction and
radiation heat transfer are found to be independent of composition and fiber
structure and to depend only on the solid volume fraction and porosity.
One-dimensional transient energy equation without internal heat source can be
now expressed as
ρCp
∂T
∂τ¼k∂2T
∂x2ð7Þ
4 Modeling Details
The tile gets heat flux due to air friction. It emits a part of this heat as reradiated
energy. Remaining part is conducting through porous material. Effective conduc-
tivity value, kis applied in governing equation. The thermal analysis is done across
the cross section of tile, and temperature profile is observed on selected nodes in the
line through the center of tile. Upper and bottom surfaces of the tile are considered
as insulated to examine the maximum heat penetration across the tile. A
one-dimensional thermal analysis is sufficient for design purpose to determine the
transient temperature response near the center of the tiles for stagnation heating.
Aerothermal heat flux of 400,000 W/m
2
is applied at the surface of the tile (x¼a).
Heat is reradiated from the surface (at x¼a) to deep space as well as conducted
through TPS component. The emittance and specific heat are functions of temper-
ature and pressure. The normal density, thermal conductivity, heat capacity, and
emittance of various RSI are listed by Chiu and Pitts (1991) and applied for analysis
of pure ceramic TPS tile in phase I. A numerical model built by COMSOL
568 A. Pradeep et al.

Multiphysics is used in the present study. Added physics is heat transfer in porous
media with time-dependent study. Materials listed in COMSOL material library
and material properties collected from the literature reviews are applied for analysis
of composite ceramic tile in phase II. The details of geometry, governing equation,
and boundary condition are described below.
4.1 Geometry and Meshing
The geometry of the present computational model is based on Shukla et al. (2006).
The silica tile is considered as one-dimensional rod element having length of its
cross section and is divided into 20 nodes of equal size. Figure 2shows the
geometry marked with first seven nodes from which variation of temperature with
respect to time is observed during analysis.
The mesh sequence type is selected as physics-controlled mesh having
extremely fine element size.
4.2 Governing Equation
The main objective of this work is to investigate the temperature distribution
through ceramic composite porous tile. As phase I, the analysis with numerical
model built by COMSOL Multiphysics is validated by predicting the thermal
response of the reusable surface insulations made of porous pure ceramic material
and compared with the results of Shukla et al. (2006). In the phase II, tile with
material selected from UHTCs are analyzed. For both cases, the governing equation
can be written as
ρcp
∂T
∂t¼∇k∇TðÞ ð8Þ
Fig. 2 1-Dimensional Analysis rod element of blunt/sharp leading edge of a reentry vehicle
Performance Analysis of Ceramic Composite Thermal Protection System Tiles 569

4.3 Initial and Boundary Conditions
To obtain the temperature distribution in the medium, Eq. (8) will be solved
subjected to initial and boundary conditions. The boundary conditions would
often be specified temperatures of the enclosure surfaces. However, near a bound-
ary, the diffusion approximation is not valid; consequently, the solution is incorrect
near the wall and cannot be matched directly to the boundary conditions. To
overcome this difficulty, the boundary conditions at the edge of the absorbing–
emitting medium are modified, so the resulting solution to the diffusion equation
with this effective boundary condition will be correct in the region away from the
boundaries where the diffusion approximation is valid. In the pure radiation case, a
temperature slip was introduced to overcome difficulty of matching diffusion
solution in the medium to the wall temperature. For combined conduction–radia-
tion, a similar concept was introduced by Howell and Seigel (1981). With the
diffusion approximation, results for combined radiation and conduction can be
obtained for both energy transfer and temperature profile.
Governing Eq. (8) is subjected to following initial and boundary conditions:
Tx;0ðÞ¼T0ð9Þ
k∂T
∂x

x¼a
¼qεσT4ð10Þ
k∂T
∂x

x¼b
¼0ð11Þ
5 Identification of Ceramic Composites
The temperature at the tip of the leading edge is inversely proportional to the square
root of the leading edge nose radius, and the reduced curvature radius results in
higher surface temperature than that of the actual blunt vehicles that could not be
withstood by the conventional thermal protection system materials (Savino et al.
2010). As per the data collected from review of literature, the family of ceramic
matrix composites named as UHTCs are identified as promising candidates of for
such structure materials, because they posses high melting point, dimensional
stability, high hardness, good chemical inertness, and oxidation resistance at ele-
vated temperatures. However, the good thermal conductivity and high melting point
values of UHTCs bound its application in sharp nose cones and leading edges of
space vehicles than in other structures of vehicle. Other TPS materials having low
thermal conductivity like pure ceramic are having comparatively low melting point
and very high value of heat flux developing due to aerobraking of vehicle with sharp
nose cone can melt them. As an RSI system, such materials are not preferable for
sharp nose cone and leading edges.
570 A. Pradeep et al.

The incident convective heat flux is balanced by reradiated energy and energy
conducted away from the leading edge tip to other surface of tile near to another
layer of low thermal conductivity TPS material/substructure of the vehicle. When a
steady state is achieved, global radiative equilibrium is established, and because the
material thermal conductivity is high, a relatively low equilibrium temperature is
achieved. Thus, the need for highly conducting refractory materials can be met with
UHTCs in the design of sharp vehicles (Gasch et al. 2005).
Paul et al. (2012) report that Carbides and borides of transition metal elements
such as Hf and Zr are widely studied due to their desirable combinations of
mechanical and physical properties, including high melting points (>3000 C),
high thermal and electrical conductivities, and chemical inertness against molten
metals. Even though carbides have higher melting points than borides, the latter
have much higher thermal conductivities and thus good thermal shock resistance
making HfB
2
and ZrB
2
more attractive for ultrahigh-temperature applications.
The following observations contribute to the selection of HfB
2
-20vol%SiC and
ZrB
2
-20vol%SiC as the tile materials. Reviews by Upadhya et al. (1997) explore
that addition of SiC can improve oxidation resistance of both HfB
2
and ZrB
2
. They
pointed out the experimental results in the temperature range of 1300–1500 Cwith
SiC addition to ZrB
2
. Inner layer of Zirconium Oxide and outermost rich glassy
layer of Silicon oxide is forming. The formation of this glass provides oxidation
resistance at high temperature due to good wettability and good surface coverage.
As reported by Scatteia et al. (2006), these layers of oxides which partially cover the
pores are characterized by higher emissivity, and that causes an increase in emis-
sivity as the temperature rises. This behavior will yield to increase in reradiated flux
and hence attains steady state at much lower equilibrium temperature.
Addition of 20 vol% SiC to either ZrB2 or HfB2 matrix composites is an
optimum composition which leads to significant increase in their thermal conduc-
tivities as well as effective densification during its production by sintering
(Loehman et al. 2006).
Hereafter, HfB
2
-20vol%SiC and ZrB
2
-20vol%SiC are given sample names
HB20S and ZB20S.
6 Results and Discussions
6.1 Heat Transfer Analysis on Pure Ceramic Tile
The primary objective of this phase-I analysis is to predict the temperature distri-
bution through TPS tile of pure ceramic porous material and to compare with the
results of Shukla et al. (2006) as part of the validation of analysis with numerical
model built by COMSOL Multiphysics. The material properties used are listed in
Table 1.
Performance Analysis of Ceramic Composite Thermal Protection System Tiles 571

The pressure considered here is 0.01 atm. The heat flux value of 400,000 W/m
2
is taken as a time-dependent value, which means after 400 s the heat flux is assumed
as zero.
The thermal conductivity plays a major role in determining accuracy of calcu-
lated temperature response. The silica tile is considered as one-dimensional rod
element and is divided into 20 nodes. Figure 3shows the in-depth temperature
response of first 7 nodes of the TPS tile. The rod will absorb a part of the heat flux
which is conducted through it, and the remainder is reflected as reradiated heat
energy to the outer space. The rod attains a maximum temperature of 1720 K in the
outer surface. The values of the thermal conductivity, specific heat at constant
pressure, and emissivity were used from listed tables/graphs showing variation of
Table 1 Properties of pure
silica TPS tile Property Value
Material Silica
Density, ρ(kg/m
3
) 352
Volume Fraction, θ0.8
Pore Diameter, δ(μm) 0.8
Extinction Coefficient, E(m-1) 14900
Fig. 3 1-D transient temperature distribution in silica tile
572 A. Pradeep et al.

respective property with temperature as given by Chiu (1992), and Touloukian and
Buyco (1970).
These inputs were used in COMSOL Multiphysics model builder. This analysis
helps to find how a tile responds to a high heat load, from one end to another end.
Due to the low value of effective thermal conductivity, each node shows a finite
amount of decrease in temperature as proceeding from outer surface to inner
surface. The nodes beyond 7th node is showing temperature readings converging
to a constant safe value, which is an important observation for designers to fix the
thickness required for the ceramic tile as a TPS.
Figure 4compares the present temperature profile of nodes 1 and 2 with the
temperature profiles of same nodes reported by Shukla et al. (2006).
The present software gives same values for maximum temperature attained by
these nodes, but current data show the extreme temperature values up to 400 s, and
thereafter, the heat flux is withdrawn suddenly. As per reference data, a gradual
withdrawal of heat flux initiated just before reaching 400 s. Otherwise, the two
graphs hardly show any difference in the temperature distribution. Based on these
satisfactory observations, the phase II of the analysis is done with ceramic com-
posite tiles.
Fig. 4 Comparison of temperature distribution
Performance Analysis of Ceramic Composite Thermal Protection System Tiles 573

6.2 Heat Transfer Analysis on Ceramic Composite Tile
The primary objective of this phase-II analysis is to predict the temperature
distribution through TPS tile of composite ceramic porous material and to identify
its ability as TPS. It is reported by Parthasarathy et al. (2012) that UHTC-based
leading-edge samples proved to withstand the simulated hypersonic conditions up
to Mach 7. At this speed, heat flux in the range of 2 MW/m
2
can be evolved. So, by
following the same procedure of phase-I analysis, this heat flux value is applied,
and after 400 sec, the heat flux is assumed as zero. However, during reentry
conditions, the heat flux will be vanished before 400 s due to the increased flight
velocity and lesser time to descent to an altitude of “cooler” conditions. The
pressure applied is 0.01 atm. Volume fraction of 0.8 is applied for selected
HB20S and ZB20S.
The material used for HB20S is chosen from COMSOL Multiphysics material
library, and HfB
2
-20SiC [solid, 99% dense] is selected. Input parameters such as
thermal conductivity, emissivity, specific heat, and density are obtained from
material library. The density observed from COMSOL material library is ranging
from 9338 to 8962 kg/m
3
with respect to temperature ranging from 300 to 2500 K.
Figure 5shows 1-D transient temperature distribution of all node points in HB20S
tile. The rod attains a maximum temperature of 2408 K in the outer surface. All
Fig. 5 1-D Transient Temperature distribution in HB20S tile
574 A. Pradeep et al.

node points reaches a final temperature of 1816 K. Due to high conductivity, the
equilibrium temperature is reached at a faster rate.
Figure 6shows 2-D transient temperature distribution of all node points in
HB20S tile. A maximum temperature of 2452 K is observed, which reaches to
1862 K after withdrawing heat flux. All input parameters are kept same as that
applied in 1-D analysis. The temperature distribution shows 2–3% increase in
temperature than 1-D analysis, and in a broad sense, both temperature distribution
curves can be considered as same.
The material used for ZB20S is chosen from COMSOL Multiphysics material
library, and ZrB
2
-20SiC (solid, 99% dense) is selected. Input parameters such as
thermal conductivity, emissivity, specific heat at constant pressure, and density are
obtained from COMSOL Multiphysics material library. Figure 7shows 1-D tran-
sient temperature distribution of all node points in ZB20S tile.
The rod attains a maximum temperature of 2446 K in the outer surface. All node
points reach a final temperature of 1886 K. The temperature distribution shows 2%
increase in maximum value of temperature in outer surface than maximum value of
temperature obtained in 1-D analysis of HB20S sample whereas an increase of 4%
is observed for steady-state equilibrium temperature of both cases.
The density observed from COMSOL material library is 5560 kg/m
3
at 300 K,
which is applied.
Fig. 6 2-D Transient Temperature distribution in HB20S tile
Performance Analysis of Ceramic Composite Thermal Protection System Tiles 575

Figure 8shows 2-D transient temperature distribution of all node points in
ZB20S tile. A maximum temperature of 2501 K is observed, which reaches to
1936 K after withdrawing heat flux. The temperature distribution of ZB20S sample
shows 2–3% increase in temperature than 1-D analysis of the same.
When comparing the temperature distributions of both HB20S and ZB20S
samples during 2-D analysis, the rise in maximum temperature of outside surface
is 2%, and the rise in steady-state equilibrium temperature is 4%.
Figure 9shows 3-D transient temperature distribution of all node points in
ZB20S tile. A maximum temperature of 2495 K is observed, which reaches to
1944 K after withdrawing heat flux. The temperature distribution shows 2–3%
increase in temperature than 1-D analysis of ZB20S sample, whereas the percentage
difference with temperature of 2-D analysis is negligible.
7 Conclusions
7.1 Summary
The transient temperature distribution of HB20S and ZB20S samples are almost
same. The density of HB20S sample is 68% greater than that of ZB20S. In other
Fig. 7 1-D Transient Temperature distribution in ZB20S tile
576 A. Pradeep et al.

Fig. 8 2-D Transient Temperature distribution in ZB20S tile
Fig. 9 3-D Transient Temperature distribution in ZB20S tile
Performance Analysis of Ceramic Composite Thermal Protection System Tiles 577

words, weight of ZB20S TPS tile having same dimensions of HB20S TPS tile is
40% less than weight of HB20S tile. This is an important contribution to gain in
weight of the vehicle, if TPS of ZB20S samples are selected. The melting points of
both samples are above 3000 K with a difference less than 4%. The evaluation of
these properties and along with other fantastic observations in terms of chemical
and mechanical properties available from the literature survey, even under limited
research facilities, shows that ceramics based on ZrB
2
, especially ZrB
2
-20vol%SiC,
offer promise for use as structural materials in extreme environments.
The HB20S and ZB20S sample materials can find potential applications in
microelectronics, molten metal containments, nuclear reactors, high-temperature
electrodes, wear-resistant surfaces, heat shield structures under extreme environ-
ments, etc. For aerospace vehicles, the leading edges under elevated temperatures
can find its proper candidate from this sample. In rocket propulsion system and
reentry vehicles, extreme heat flux is experienced in sharp structures like leading
edges, nose cones, and nozzles. The proposed type of materials can improve the
ability of these types of vehicle structures in terms of mechanical, thermal, and
chemical perspectives. Sharp leading edges would imply lower aerodynamic drag,
improved flight performances and crew safety, due to the larger cross range and
maneuverability along with more gentle reentry trajectories.
7.2 Scope for Future Work
In this paper, heat penetration across the cross section of a pure ceramic and two
samples of ceramic composites are evaluated. If the incident heat flux value is again
increased beyond Mach 7, phase changes will occur due to melting, which require
another detailed study. Different combinations of UHTCs with low-conductivity
TPS materials like pure ceramic tiles can be examined. It can be in the form of a
UHTC-coated or UHTC–ceramic multilayer TPS tile keeping an eye on the benefit
of weight reduction when the secondary material is having low density. 2-D or 3-D
thermal analysis of a UHTC nose cone model with maximum heat flux at nose cone
tip, which is gradually decreasing in the downstream surface of cone, can be done.
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