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Large carbon cluster thin film gauges for measuring aerodynamic heat transfer rates in
hypersonic shock tunnels
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2015 Meas. Sci. Technol. 26 025901
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Measurement Science and Technology
Meas. Sci. Technol. 26 (2015) 025901 (12pp)
doi:10.1088/0957-0233/26/2/025901
Large carbon cluster thin film gauges for
measuring aerodynamic heat transfer rates
in hypersonic shock tunnels
S Srinath and K P J Reddy
Department of Aerospace Engineering, Indian Institute of Science, Bangalore, Karnataka 560012, India
E-mail: [email protected]
Received 14 October 2014, revised 25 November 2014
Accepted for publication 5 December 2014
Published 7 January 2015
Abstract
Different types of Large Carbon Cluster (LCC) layers are synthesized by a single-step
pyrolysis technique at various ratios of precursor mixture. The aim is to develop a fast
responsive and stable thermal gauge based on a LCC layer which has relatively good electrical
conduction in order to use it in the hypersonic flow field. The thermoelectric property of the
LCC layer has been studied. It is found that these carbon clusters are sensitive to temperature
changes. Therefore suitable thermal gauges were developed for blunt cone bodies and were
tested in hypersonic shock tunnels at a flow Mach number of 6.8 to measure aerodynamic
heating. The LCC layer of this thermal gauge encounters high shear forces and a hostile
environment for test duration in the range of a millisecond. The results are favorable to use
large carbon clusters as a better sensor than a conventional platinum thin film gauge in view of
fast responsiveness and stability.
Keywords: hypersonic, heat transfer measurement, thermal gauge, large carbon cluster,
nanotechnology
(Some figures may appear in colour only in the online journal)
1. Introduction
generate experimental data for all the new configurations at
high enthalpy conditions using hypersonic wind tunnels and
shock tunnels.
The design of a hypersonic flight vehicle is predominantly
dominated by the aerodynamic drag and heating characteristics. Blunt nose configurations are commonly used for hypersonic flight vehicles to mitigate the aerodynamic heating
problems such that the existing thermal protection system
technology can be used to protect the flight vehicle. However
this results in enhancing the aerodynamic drag encountered
by the vehicle in flight. These two conflicting demands usually drive the research in the field of hypersonics. Hence current research is centered around developing technologies and
flow control strategies to reduce the aerodynamic drag while
achieving the desired decreased heating for blunt body configurations at hypersonic Mach numbers. These developments
are carried out in ground based test facilities which include
high-enthalpy tunnels such as hypersonic shock tunnels. The
heat transfer rates for a given configuration flying at re-entry
There has been renewed global interest in the field of hypersonic aerodynamics in recent times due to the potential application for the commercialization of space travel. An impetus
to revisit all aspects of hypersonic flows has been given by
the paradigm shift in the hypersonic flight vehicle configuration due to the advancement in material science and allied
fields. This shift has necessitated the generation of design
data for new configurations which can be achieved either by
numerical simulations using CFD codes or experimentally
using high speed test facilities with associated advanced
instrumentation. Although the capabilities of the CFD codes
have increased substantially they are still inadequate to produce the reliable data for high enthalpy flows encompassing
real gas effects and chemical reactions which are encountered
by a typical hypersonic vehicle in flight. In addition, the data
generated by these numerical codes still need to be validated
using the experimental data. Hence there is an urgent need to
0957-0233/15/025901+12$33.00
1
© 2015 IOP Publishing Ltd Printed in the UK
S Srinath and K P J Reddy
Meas. Sci. Technol. 26 (2015) 025901
Figure 1. Schematic of the hypersonic shock tunnel HST2.
Figure 2. Typical Pitot signal at the test section.
velocities are typically measured in high enthalpy shock tunnels such as free piston driven or detonation driven hypersonic
shock tunnels. These tunnels are capable of producing flow
speeds matching re-entry velocities albeit for short durations
of about a millisecond. Once the flow velocities are matched
it is assumed that the accompanying flow phenomena such
as real gas effects are simulated in the tunnel. In general, the
heat transfer rates are measured using platinum or nickel thin
film gauges deposited on an insulating backing material and
flush mounted on the test model surface [1]. These thin films
are deposited on the backing material either by hand painting
using platinum paint or sputtered using a platinum target. The
adherence of the gauge to the thermally insulating surface,
which is usually a machinable ceramic (Macor) is enhanced
by baking at 973 K in an oven. The durability of these thin
films is very good for the specific flow enthalpies of about
2 MJ kg−1 which are usually obtained in a typical pressure
driven hypersonic shock tunnel such as HST2 in the Indian
Institute of Science (IISc) [2, 3]. For the flow enthalpies
beyond 2 MJ kg−1 obtained in a free piston driven hypersonic
shock tunnel such as HST3 in IISc, the durability of these thin
films is very poor due to the high shear forces produced at elevated surface temperatures. Typically the gauges will survive
one or two shots and hence it is essential to replace the gauges
frequently. Since gauge making is a time consuming process,
measuring heat transfer rates at high-enthalpy conditions is
time consuming as well as expensive.
In this paper, we present a solution to this problem by
incorporating the field of nanotechnology into the measurement of the hypersonic flow field. The electrical and thermal
properties of graphitic carbon materials such as graphene,
carbon nanotubes and large carbon clusters (LCC) have
been extensively analyzed in recent times to develop novel
devices and sensors. It was found that the electrical properties of these materials are greatly affected by their chemical
bonding and crystalline structure [4–11]. Efforts have also
been made to identify the thermoelectric properties of carbon
porous materials with the aim of generating heat pumps and
power generators in micro scales [12–15]. Some researchers
have reported that single and multi walled carbon nanotubes
(CNT) are sensitive to temperature changes and can be used
as thermal probes for low temperature regimes [16–21]. Apart
from CNT, other allotropes of carbon are also sensitive to temperature with varying sensitivity factors. But so far no practical thermal measurement device based on nanotechnology
has been developed for heat flux measurements in hypersonic
shock tunnels. Here we report the development of interconnected large carbon cluster (LCC) based thin film gauges for
measuring heat transfer rates in high enthalpy shock tunnels.
These gauges are grown chemically on the backing material
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S Srinath and K P J Reddy
Meas. Sci. Technol. 26 (2015) 025901
Table 1. Typical flow conditions obtained in the HST2 hypersonic
shock tunnel.
Parameters
Details
Driver gas
Driven gas
Primary shock Mach number
Total enthalpy (ho)
Free-stream pressure (P∞)
Free-stream temperature (T∞)
Free-stream density (ρ∞)
Free-stream flow velocity (u∞)
Flow Mach number (M∞)
Free stream Reynolds number (Re∞)
Helium
Air at 0.3 bar
3.7
1.81 MJ kg−1
306.6 N m−2
225.7 K
0.007188 kg m−3
1605 m s−1
6.8
0.78073 × 106 m−1
directly, and successfully used for measuring the heat fluxes
over a large angle blunt cone flying at a freestream Mach
number of 6.8 in the hypersonic shock tunnel HST2. Details
of the LCC thin film gauges and the chemical steps followed
for the deposition of the gauges on the thermally insulating
backing material along with typical heat transfer data obtained
using these films for the large angle blunt cone model are presented in this paper.
2. Experimental facility and test models
All the experimental measurements presented in this paper are
carried out in a conventional pressure driven hypersonic shock
tunnel HST2 [22]. The schematic of HST2 is shown in figure 1.
The shock tunnel consists of a shock tube of 50 mm diameter
with a 2 m long driver tube and a 6 m long driven tube, which
are separated by a metallic diaphragm. The open end of the
driven tube is connected to a Mach 8 convergent-divergent
nozzle connected to the 300 mm × 300 mm × 450 mm size
test section attached to a dump tank. The nozzle-test sectiondump tank assembly is separated from the shock tube by a
thin paper diaphragm and is evacuated to a vacuum of about
1 × 10−6 mbar using a roots pump–diffusion pump combination. The tunnel is capable of producing a Mach 8 hypersonic
flow for about a millisecond duration as seen from the typical
Pitot pressure signal, shown in figure 2. Therefore all the measurement systems employed in this flow field should respond
and acquire data within the test time. The tunnel is capable of
generating flow enthalpies in the range of 0.7 to 3 MJ kg−1 and
the flow conditions achieved in the test section for a typical
test are given in table 1.
Two generic aerodynamic models are chosen to test the LCC
thin film gauges in the hypersonic shock tunnel. Firstly a blunt
cone model with a hemispherical nose cone is used to evaluate
the capability of the LCC thin film gauge for measuring the
heat transfer rates. For this purpose we selected a scaled down
version of the Space-capsule Recovery Experiment (SRE)
module shown in figure 3(a) which has a hemispherical nose
cone of radius 24 mm and a base diameter of 96.2 mm. A single
LCC thin film gauge is mounted at the stagnation point and
heat transfer rates are measured for various flow conditions.
The second model is a 120° apex angle blunt cone body
which is shown in figure 3(b). The nose radius of the model
Figure 3. Aerodynamic models. (a) Space-capsule recovery
experiment (SRE) model. (b) 120° apex angle blunt cone model.
Figure 4. Photo image of single step pyrolysis set-up.
is 25 mm and the base diameter is 100 mm. In this model
one half of the blunt body is mounted with a conventional
platinum thin film gauge and the other half is mounted with
a LCC thin film gauge. The corresponding estimated values
of the stagnation point heat transfer rate for both models are
calculated using the analytical equations proposed by Fay and
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S Srinath and K P J Reddy
Meas. Sci. Technol. 26 (2015) 025901
Figure 5. Raman spectra of active carbon deposition.
Riddell [31]. The performance of the new gauge is compared
with the estimated values.
are formed from ferrocene by the reaction mechanism [25] as
shown in chemical equation (1).
3. Development of large carbon cluster (LCC) thin
films
Fe(C5H5)2 → C5H5 + C5H5 + Fe
(1)
These iron particles act as a catalyst in the formation of the
carbon clusters.
A pyrolysis study performed by Baur and Aten (BA) [26]
to dissociate benzene at a temperature range of 690–1900 K
had brought out the basic reaction sequence as given in the
chemical equation (2).
Generally, Macor material is used as a substrate for depositing thermal thin film sensors because it is both an electrically
and thermally insulating material and also it can be machined
easily to form any shape matching the aerodynamic body configurations used in the shock tunnel tests. In the present study
we have grown the LCC thin film gauges on the Macor substrate inserts. A single-step pyrolysis technique is adopted to
synthesize the carbon nanomaterials. The experimental set-up
as shown in figure 4 consists of a 70 mm diameter quartz tube
which is heated to high temperatures. The Macor pieces are
inserted along with the precursor mixture in the quartz tube
used for manufacturing the carbon nanomaterial. The precursor mixture consists of benzene and ferrocene in a certain
ratio. Benzene is taken as the source of carbon and ferrocene
as the source of the catalyst iron material for the growth of
carbon clusters and nanoparticles [23, 24].
Macor substrates are kept inside the quartz tube at the portion where the temperature of 1023 K is maintained by a single
stage tube heating furnace. The quartz tube is connected to a
rubber bladder to collect reactant gases. When the quartz tube
is heated, the precursor mixture evaporates and expands into
the rubber bladders attached. At higher temperatures benzene
decomposes to generate active carbon particles. In the pyrolysis zone, the newly formed iron catalytic particles react with
the carbon species to form carbon clusters [25].
The formation of carbon clusters is a complex chemical
mechanism still under study. There are two stages in this
pyrolysis process. In the first stage, benzene and ferrocene dissociate. In the second stage carbon clusters are formed from
carbon chains which have formed from benzene. Iron particles
C 6H 6 → C 6H5 + H
(2a)
C 6H 6 + H → C 6H5 + H2
(2b)
C 6H5 → C4H3 + C2H2
(2c)
C4H3 → C4H2 + H
(2d)
The products of the BA reaction mechanism undergo secondary reactions and form large polycyclic aromatic hydrocarbons (PAH). Naphthalene, acenaphthylene, pyracylene and
other isomers are produced from the secondary reactions of
C6H5 + C6H6/C6H5 at different temperatures. The formation of
PAH molecules occurs based on the HACA (hydrogen abstraction and acetylene addition) reaction mechanism as shown in
the chemical equation (3) and the self-reaction between benzene/phenyl [27].
(+C2H2)(−H2)
(+C2H2)(−H2)
(+C2H2)(−H2)
C 6H 6 ⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯→ C8H 6 ⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯→ C10H 6 ⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯→ C11H 6
(+C2H2)(−H2)
⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯→ C12H 6
(3)
In addition to the HACA route, other PAH molecules like
dihydrocyclopenta[a]indene, dihydro-s-indacenes, dihydro-asindacenes, biphenylene and naphthalene were produced from
other reaction mechanisms as well. From large PAH molecules
large carbon clusters are formed by pathways of H-abstraction/
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S Srinath and K P J Reddy
Meas. Sci. Technol. 26 (2015) 025901
Figure 6. Carbon clusters formed at different ratios of benzene and ferrocene. (a) Benzene 11 ml: ferrocene 77 mg; sheet resistance is
around 200 kΩ sq−1. (b) Benzene 11 ml: ferrocene 90 mg; sheet resistance is around 55 kΩ sq−1. (c) Benzene 15 ml: ferrocene 135 mg;
sheet resistance is around 10 kΩ sq−1. (d) Benzene 20 ml: ferrocene 440 mg; sheet resistance is around 800 Ω sq−1. (e) Benzene 22 ml:
ferrocene 374 mg; sheet resistance is around 1.8 kΩ sq−1. (f) Benzene 20 ml: ferrocene 400 mg; sheet resistance is around 4 Ω sq−1.
(g) Benzene 18 ml: ferrocene 270 mg; sheet resistance is around 3 kΩ sq−1.
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S Srinath and K P J Reddy
Meas. Sci. Technol. 26 (2015) 025901
C2H2-addition (HACA) and polyyne [28]. Carbon cluster formation depends on certain parameters which include induction
time, the carbon cluster growth rate and its yield. Based on the
simulation study by Sojka [29], further large carbon clusters
may be produced from individual carbon atoms, molecules
and small clusters by reacting with each other. This reaction
mechanism is given by the chemical equation (4).
Cn + C1 → Cn + 1
(4a)
Cn + C2 → Cn + 2
(4b)
Cn + Cm → Cn + m
(4c)
Figure 7. Carbon thin film over Macor substrate.
The formation of carbon isomers in this synthesis technique
primarily depends on the ratio of the precursor mixture,
pressure, temperature and time taken for complete pyrolysis.
By varying the precursor mixture of benzene and ferrocene
at different ratios, at a temperature of 1023 K and nearly at
atmospheric pressure for 5 h of pyrolysis, the process produces different carbon allotropes formed at the inner surface of the quartz tube and all over the samples kept inside
of it. The laser Raman spectra technique clearly identifies
the bonding structures in order to characterize the carbon
depositions on the samples as shown in figure 5. Two Raman
line peaks, i.e. D-band and G-band, are observed at nearly
1347 cm−1 and 1586 cm−1 respectively. These two peaks
are observed in all polycrystalline graphitic materials. The
ratio between the intensities of these two peaks is around
one, which implies the obtained material is an active carbon
cluster [30].
Scanning electron microscope (SEM) analysis revealed
the formation of a large carbon cluster on the Macor substrate
as shown in figure 6. The different ratios of the benzene and
­ferrocene precursor mixture lead to the formation of different
carbon clusters of varying size and shapes. Correspondingly
the sheet resistance of the carbon deposit is measured for
a LCC layer of 10 mm length and 5 mm width, which also
varies from 800 Ω sq−1 to 50 kΩ sq−1 depending on the density,
shape and size of the carbon clusters formed over the surface.
Figure 6(a) shows that fullerene balls and small carbon clusters are formed in lesser amounts over the Macor substrate.
Figure 6(b) shows the formation of larger carbon clusters at a
few locations on the surface. Figure 6(c) shows the formation
of more carbon clusters than in the previous case and more
carbon fullerenes are also found and correspondingly the
sheet resistance also drops down.
At a precursor ratio of 1 : 11 a joined fullerenes chain has
formed and uniformly dispersed all over the surface as shown
in figure 6(d) and this formation has given a sheet resistance
of 800 Ω sq−1. At a ratio of 1 : 17, carbon nanotube structures
have projected from lumped carbon clusters as shown in
figure 6(e). Since the surface density of this combined carbon
cluster and nanotube formation is less than the previous case,
the resistance has increased to 1.8 kΩ sq−1. Several thermal
gauges have been formed based on this carbon cluster’s thin
layers. These gauges are calibrated and tested in hypersonic
shock tunnels to measure the heat flux rate in a Mach 6.8 flow
condition.
Figure 8. α-calibration set-up.
4. LCC thin layer as a thermal sensing element
A few Macor pieces are machined to the desired size and shape
for a blunt cone aerodynamic model. A small strip of thin LCC
film has to be formed on these Macor surface as a thermal
sensing layer. It is found that after synthesizing in the reactor,
LCC had formed a thin film all over the Macor substrate
pieces. Heat flux gauges are carved out of this continuous thin
film by removing the extra film using an emery sheet. Figure 7
shows a few samples of LCC based thermal gauges formed on
the Macor substrate. It is found that the surface contains amorphous carbon and ferrous particles that got deposited along
with carbon clusters at some locations. As the first stage, no
step has been taken to remove these impurities. Therefore, the
impurities will also play a role in thermal sensing.
The least resistive carbon cluster thin film is selected and
silver coating is done at the ends of each strip of the sensing
area for taking out the electrical connections. These Macor
pieces are flush mounted in aerodynamic test models to be
used in hypersonic flow conditions.
5. Calibration of LCC thin film thermal gauges
To find the thermal coefficient of resistance ‘α’ for a LCC thin
film thermal gauge, the following calibration methodology is
adopted. The gauge is kept in contact with the bulb of a thermometer and kept inside a beaker. This set-up is immersed
6
S Srinath and K P J Reddy
Meas. Sci. Technol. 26 (2015) 025901
Figure 9. Calibration curve for LCC thin film thermal gauge.
Figure 11. SEM image showing the thickness of the LCC thin film
Figure 10. Schematic of the carbon cluster thermal gauge.
layer.
in an oil bath as shown in figure 8. As the oil is heated up,
the temperature is noted down from the thermometer and the
corresponding voltage variations are also monitored from a
digital voltmeter. The voltage variation with respect to the rise
in temperature is plotted in figure 9.
The calibration curve showed a nearly linear variation of
voltage drop corresponding to the rise in temperature. This
trend is similar to the physical model provided by Naeemi et
al [14] for a multi-walled carbon nanotube of diameter greater
than 50 nm. The temperature coefficient of resistance α of the
gauge is calculated from the following expression.
α=
[ΔV ]
roIo [ΔT ]
Preliminary experiments are carried out at Mach 6.8 flow
in a hypersonic shock tunnel to measure aerodynamic heating
over SRE and blunt cone models. At Mach 6.8 flow conditions, the theoretically estimated value of the stagnation point
heat flux rate for the SRE model is 624 kW m−2 and the corresponding value for the blunt cone model is 521 kW m−2 based
on the Fay and Riddell [31] expression.
The thermal gauge essentially consists of two layers of different materials. The top layer is a carbon cluster and the bottom
layer is a Macor substrate. Therefore it is considered to be a nonhomogeneous thermal body. Figure 10 shows a cross sectional
view of the carbon cluster thermal sensing element with the
Macor substrate. Figure 11 shows the SEM image of the LCC
thin film layer’s cross section. The average thickness of the layer
is around 160 nm, but at certain locations the LCC protrudes from
the substrate and in those regions the thickness is around 450 nm
to 1 μm. The second layer’s thickness is 6 mm and is assumed to
have a characteristic thickness of infinity, when compared to the
(5)
where ro is the initial resistance of the carbon cluster thermal
gauge and Io is the initial current supplied. The temperature
coefficient of resistance of the LCC thin film layer is found to
be −2.60 × 10−4 K−1.
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S Srinath and K P J Reddy
Meas. Sci. Technol. 26 (2015) 025901
Figure 12. LCC thermal gauge signal and the corresponding heat transfer history. (a) Time history of the temperature rise on the LCC
thin film gauge at stagnation point of the SRE model in Mach 6.8 flow. (b) Heat transfer rate obtained by numerically integrating the
temperature signal shown in part (a).
test duration. The rise in temperature of the carbon cluster flake
is dictated by the heat transfer to the aerodynamic body whereas
the rise in temperature at the bottom surface of the Macor is zero.
The heat transfer in the lateral direction is negligible due to the
thickness of the LCC layer, which is mostly less than a micron.
Considering the prevailing conditions, a one-dimensional heat
transfer model is assumed for heat transfer phenomena through
layers of the thermal gauge.
With these assumptions, the one-dimensional heat flux rate
is represented by Fourier’s law of heat conduction as given by
equation (6).
q˙ (t ) = −k
dT
dy
The temperature variation across the one dimensional heat
transfer model is governed by the heat conduction equations for two layers which are given as follows:
For the carbon cluster thin flake region 0 ⩽ y ⩽ dcc
∂T1 ⎛ k ⎞ ∂ 2T1
⎟
=⎜
∂t
⎝ ρCp ⎠1 ∂y 2
(7)
with initial and boundary conditions
(6)
8
t ⩽ 0 : T1 (y ) = Twi
⎛ ∂T ⎞
1
= − q˙ (t )
t > 0, y = 0 : ⎜ 1 ⎟
k1
⎝ ∂y ⎠ y = 0
(8)
S Srinath and K P J Reddy
Meas. Sci. Technol. 26 (2015) 025901
Figure 13. LCC thin film gauge signal at the stagnation point for three experiments.
subscript f indicates the initial voltage supplied. The value of
the gauge backing material β is taken as 2200 W1/2 m−2 K−1.
The passive LCC thermal sensor was given with an initial
power supply depending upon the resistance to maintain a
constant current of 20 mA. The resistance of the LCC layer
drops down due to the rise in temperature and the corresponding voltage variation is taken as the output. The change
in voltage across the gauge and the history during the experimental test time is stored as a continuous signal in a PC using
the data acquisition system NI PXI-1031 with a sampling rate
of 10 MHz capable of acquiring 12 channels.
The SRE model, which is shown in figure 3(a), is subjected
to hypersonic flow at a Mach number of 6.8. During the steady
flow of 1 ms, a bow shock wave is formed at the nose of the
body with a shock stand of distance. The thermal energy of
the free stream molecules rises as they enter the shock layer.
At the stagnation point the total kinetic energy is converted
into thermal energy and is transferred to the body surface.
The LCC thermal gauge at the stagnation location senses the
temperature rise due to the heating from this surrounded high
energy fluid medium. The LCC structure temporarily deforms
on this temperature rise and alters the resistance. Figure 12(a)
shows the time history of the voltage variation obtained at the
stagnation point on the SRE model. A parabolic voltage dropping signal is an indication of a constant heat flux condition
during the steady flow. This signal is processed by a Matlab
code written based on equation (11) at n discrete points in
the time interval (0, t) to obtain the heat flux rate. The result
is shown in figure 12(b). The consistency of the LCC thin
film heat transfer gauge is evident from the signals shown
in figure 13 for three different runs. A minor variation from
one test flow to another is obvious in the shock tunnel experiments. But the responses of the gauges are reciprocal to the
prevailing test flow condition. From figure 2 it can be seen
that a useful test time is not more than 800 µs. Thus the variation between the three experiments is acceptable for the first
600–800 µs only where the parabolic rise of the signal is quite
For the Macor substrate region dcc < y ⩽ ∞,
∂T2 ⎛ k ⎞ ∂ 2T2
⎟
=⎜
∂t
⎝ ρCp ⎠2 ∂y 2
(9)
with initial and boundary conditions
t ⩽ 0 : T2 (y ) = Twi
t > 0, y = dcc : T2 (y ) = T1 (y ) ,
⎛ ∂T ⎞
⎛ ∂T ⎞
k1⎜ 1 ⎟
= k2⎜ 2 ⎟
⎝ ∂y ⎠ y = L
⎝ ∂y ⎠ y = L
(10)
lim T2 = 0
y→∞
where subscript 1 denotes the top layer, which is a LCC flake,
subscript 2 is a Macor substrate and subscript ‘wi’ is the initial
wall condition, T is the temperature, t is time, k is the thermal
k
conductivity dcc is the thickness of the LCC layer and
is
ρCp
the thermal diffusivity.
The general solution for the above heat conduction equations is solved and represented in terms of the voltage variation with respect to time. A numerical procedure was given by
Cook et al [32] to find the total heat flux rate from the voltage
profile obtained. Equation (11) gives a numerically adopted
general solution.
q (t ) =
β
π αE f
⎡ E (t )
n
⎢
⎢⎣ tn
n−1 ⎧
E (tn ) − E (ti )
E (tn ) − E (ti − 1)
−
+∑⎨
(tn − ti )
(tn − ti − 1)
i=1 ⎩
⎪
+2
⎫
E (ti ) − E (ti − 1)
E (tn ) − E (tn − 1) ⎤⎥ (11)
⎬+
⎥⎦
Δt
(tn − ti ) + (tn − ti − 1) ⎭
⎪
where β is the property of the Macor substrate, which is equal
to (ρ Cp)1/2, E is the thermal sensor’s output in voltage and the
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S Srinath and K P J Reddy
Meas. Sci. Technol. 26 (2015) 025901
Figure 14. Stagnation point heat flux rate over the SRE model.
Figure 15. Heat flux rate over the blunt cone body.
repeatable. The further part of the signal does not lie in the test
time and thus is not important.
The non-dimensional heat flux rate can be expressed based
on the flow conditions in terms of the Stanton number as follows.
St =
q˙
ρ∞V∞ (ho − h w )
the blunt cone model for six experimental conditions with
slightly varying enthalpy conditions. In this plot, the abscissa
coordinate corresponds to the gauge location (denoted by ‘s’)
from the stagnation point and it is normalized by the base
radius (denoted by Rb) of the blunt cone body. The zero value
of abscissa is corresponding to the stagnation point, the negative values are corresponding to distances of the platinum
thermal gauge locations and the positive values are the distances of the LCC thermal gauge locations. Beyond s/Rb of
0.5, there is a small variation from one experiment to another.
This variation is more predominant in platinum gauges than
in the LCC thermal gauge. This may be due to a local disturbance in the flow. But overall the trend in variation of the heat
flux values is maintained and it is clear that the LCC thermal
gauge’s repeatability is better than the platinum gauge’s
repeatability.
(12)
Figure 14 shows the comparison of the experimental heat
flux rate with theoretical estimations in terms of the Stanton
number. From these results it is seen that the measured heat
flux rates closely match with the theoretical values.
A 120° apex angle blunt cone model which is shown in
figure 3(b) is chosen for comparing the response of the LCC
thermal gauges with conventional platinum thin film gauges.
The model is subjected to a hypersonic flow of Mach 6.8 at
HST-2. Figure 15 shows the results of the heat flux rate over
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S Srinath and K P J Reddy
Meas. Sci. Technol. 26 (2015) 025901
Figure 16. Variation of non-dimensionalised sheet resistance after every experimental flow.
Figure 17. Comparison of the LCC and platinum signals for experiment runs 1 and 11.
From the data presented in figure 15 it is clear that large
carbon clusters perform better as thin film gauges for measuring the heat transfer rates in hypersonic shock tunnels. The
electrical resistance of the thermal gauges increases after each
experimental flow due to erosion by shear forces. After every
experiment, the sheet resistance is measured, normalised with
the initial sheet resistance value and the variation is plotted as
shown in figure 16. The plot clearly shows that the erosion of
the LCC is less than the platinum sensing layer. In particular,
after the seventh experiment the material erosion drastically
increases. Before the first experimental flow the resistances of
the platinum and LCC thin film gauges were 14.5 Ω and 4.54 kΩ
respectively. During the eleventh experiment the resistance
of the platinum and LCC thin film gauges became 118 Ω and
8.55 kΩ respectively. Figure 17 shows the comparitive signals
for the different flows. At the 11th experiment the platinum
gauge signal rise was not significant, whereas the LCC thin
layer was responding properly even after it became 8.5 kΩ. In
other words, the signal to noise ratio becomes much less in the
case of platinum at higher resistances. Therefore the LCC thin
film gauges can be used for a greater number of experiments.
6. Conclusion
Large carbon cluster based thin film gauges have been developed for measuring the heat transfer rates in hypersonic shock
11
S Srinath and K P J Reddy
Meas. Sci. Technol. 26 (2015) 025901
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tunnels. These films are developed on thermally insulating
backing material inserts by the pyrolysis technique. LCC
gauges are used in preliminary experiments to measure the
stagnation point heat flux rate over the SRE model and a 120°
apex angle blunt cone body at a flow Mach number of 6.8. The
measured values are found to match well with the theoretically estimated values. Furthermore the performance of the
LCC thin film gauges is compared with the performance of
traditional platinum thin film gauges by measuring the heat
transfer rates over the 120° apex angle blunt cone model
in hypersonic flow simultaneously using the two types of
gauges. It is found that the performance of the LCC based thin
film gauges is better than the performance of the platinum thin
film gauges. Also since the LCC thin film gauges are grown
over the backing material directly using the pyrolysis technique their endurance in high enthalpy flows is better than the
hand-painted platinum thin film gauges. The results presented
here clearly demonstrate the suitability of LCC based thin film
gauges for the experimental measurement of heat transfer rates
in high enthalpy flows produced in hypersonic shock tunnels.
Acknowledgments
We gratefully acknowledge the financial support from DRDO,
New Delhi. We acknowledge Mr Varadharajaperumal from
the Centre for Nano Science and Engineering, Indian Institute
of Science, Bangalore for helping us to take SEM images of
the LCC samples.
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