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98-250498-2504
DESIGN, CALIBRATION AND TESTING OF TRANSIENTTHIN FILM HEAT
TRANSFER GAUGES
Kevin M. Kinnear†, and Frank K. Lu‡
NASA/UTA Center for Hypersonic ResearchThe University of Texas
at Arlington
Arlington, TX 76019
ABSTRACT
A method for the design, construction, calibrationand testing of
thin film platinum resistancetemperature detectors (RTDs) is
described. Thecalibration and testing was performed to determine
ifRTDs can be used for measuring surfacetemperatures and heat
transfer rates under transientconditions. By depositing a thin film
of platinum onthe surface of a highly polished ceramic
substrate,RTDs were obtained which have a temperaturecoefficient of
resistivity of 0.0019 K-1, an adequatelinear behavior, and a
thermal product of 0.2J/cm2/K/s½. Furthermore, the construction
techniquesproduced gauges that were reliable, reproducible,
andrugged. The results from shock tube tests showedthat the RTDs
had a time response on the order ofmicroseconds and were suitable
for making heattransfer measurements in highly transient
conditions.Suggestions for further developments are included.
1.0 INTRODUCTION
Heat transfer is the dominant problem in the designof hypersonic
vehicles. It also plays an importantrole in many other applications
where experimentaldata is needed to support the design effort. Much
ofthe data that is needed to support the design effortand to
validate and calibrate numerical codes isgenerated from impulse
facilities. When the flows ofinterest are generated in shock tubes,
hypersonicshock tunnels or other short-duration facilities,
thetotal flow time may be only a few milliseconds orless. In such
cases the technique used for heat flux ortemperature measurement
must be suited for transientconditions and must have a response
time fast enoughto trace variations caused by rapidly changing
flowconditions.
† Graduate Student, Member AIAA‡ Associate Professor of
Aerospace Engineering, Associate Fellow AIAA
Thin film platinum resistance temperature detectors(RTDs) are
suitable for measuring surfacetemperatures in flows of this nature.
From the timehistory of the surface temperature, the heat flux
maybe obtained. These RTD gauges consist of thinmetallic films
applied to the surface of substrates oflow thermal conductivity.
The extremely smallthickness of the gauges allows
temperaturemeasurements to be made with a time response ofonly a
few microseconds. Furthermore, data from aproperly mounted gauge
can be reduced to obtainheating rates.
2.0 THIN FILM GAUGE PRINCIPLES
Principles of Thin Film Gauge Operation
The RTD operates on the simple principle that theresistance of
metals increases with a rise intemperature. The method for
determining heattransfer rates consists of measuring the
temperaturerise during the test time and calculating the heat
fluxfrom the data. When using RTDs, the surfacetemperature is
determined from the change inresistance of the gauge film. For
practical purposes,the resistance of platinum RTDs varies linearly
withtemperature as 1
R T R T TR( ) [ ( )]= + −0 01 α (2.1)
where R is the film resistance at surface temperatureT, R0 the
film resistance at temperature T0, and αR isthe film temperature
coefficient of resistance whichmust be experimentally determined
for each RTD.
Since there is a very small change in resistance for agiven
change in temperature, a Wheatstone bridge isused to increase the
output sensitivity by using anulling principle. During testing the
bridge issupplied with a constant current. Thus a change
inresistance of the RTD is converted to a change involtage. In
addition, the bridge ensures stability ofthe output by compensating
for lead resistance2.Therefore, by using Ohm’s law, when the film
is
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2
supplied with a constant current the change intemperature is
given by the equation
( )T TV
VR− =0
0
∆α
(2.2)
where ∆V is the change in the film output voltage andV0 is the
initial voltage applied to the RTD. Fromequation (2.2) it is
apparent that the gauge sensitivityis directly proportional to the
voltage applied to theRTD. Therefore, the sensitivity of the gauge
can beincreased by operation at as high a film voltage aspossible.
However, the maximum excitation voltagethat can be applied to the
gauge is limited by internalheat generation. In order to minimize
the errorsintroduced by this heat generation, a
self-heatingcalibration test must be performed to determine
thisthreshold.
Analysis
The basic time dependent problem of thin filmgauges is
conduction into a thin metallic filmmounted on a semi-infinite
extent of anothermaterial. Figure 2.1 shows the situation which
mustbe analyzed. Theoretically, the film is infinitely thinso that
it does not affect the temperature history ofthe substrate
surface.
Figure 2.1. Heat Conduction In Thin Film RTD.
The equations that are used to calibrate RTDs and tocalculate
the heat flux from the temperature historyare based on three main
assumptions. It is assumedthat the heat transfer is
one-dimensional, that thesubstrate is semi-infinite, and that the
measuringsurface film has a negligible effect on the
heatconduction. The first two assumptions are closelyrelated in
that the thickness of the substratedetermines if one-dimensional
theory may be applied.The third assumption is actually an
approximationwhich introduces an error in the deduced heat
flux.
The amount of this error is a function of the thicknessof the
film. Each of these assumptions is discussedbelow.
One-dimensional Theory
If accurate heat flux measurements are going to bemade, the RTD
must follow the one-dimensionaltheory as best as possible. In order
to achieve this,the substrates on which the thin film gauges
aremounted must be thick enough so that the heattransfer into the
substrate is similar to that into asemi-infinite solid.
Furthermore, the films must beplaced away from substrate
discontinuities atdistances equivalent to or greater than those
requiredfor a semi-infinite substrate behavior. The
minimumthickness required can be obtained by considering
thesubstrate base temperature to surface temperatureratio for the
situation shown in figure 2.1. Forconstant heat flux into the
surface, this ratio is 3
T x t
T te
t
xc
x
t
x
t( , )
( , ) ( )0 2 2
2 12
12
4= −
−α π
α α erf (2.3)
where α is the thermal diffusivity of the substrate andx is the
penetration depth.
Ideally, the temperature at the substrate base shouldbe the same
as ambient for all testing times.Therefore, at the end of a test,
the ratio in equation(2.3) should be negligible. Figure 2.2 is a
graph ofthe temperature ratio plotted as a function of thesubstrate
depth for several different testing times.The thermal diffusivity
of MACOR, a ceramicmaterial used in this investigation, was used in
theequation for plotting the temperature ratio.
x (mm)
0.0 0.5 1.0 1.5 2.0 2.5 3.0
T(x
,t)/T
(0,t)
0.001
0.01
0.1
1
t = 5 mst = 25 mst = 100 mst = 1 s
Figure 2.2. Determination of Minimum SubstrateThickness.
From the graph it can be seen that for a substrate
basetemperature to surface temperature ratio of less than1% the
substrate thickness must be about 3.0 mm
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3
even for the relatively long testing time of about 1second.
However, for reasons of mechanicalstrength, insulating substrates
are actually over 3 mmthick 4. From the graph it is obvious that
substrateswhich exceed this value are satisfactory for alldurations
less than about 1 second. Therefore, forshort duration testing, the
semi-infinite assumption iswell satisfied.
Thin Film Thickness
Although the thin films deposited on the surface ofinsulating
substrates are very thin, they have an effecton the surface
temperature history which should beconsidered. If it is assumed
that the films have nothermal capacitance, a large error could
occur in thededuced heat flux if the testing time is
significantlyshorter than the response time of the RTD. Forexample,
approximately 570 µs must elapse beforethe heat flux indicated by a
painted platinum thin filmhaving a thickness of about 1 µm
approaches towithin 5% of its correct value4. Therefore, careshould
be taken in the design and analysis of thinfilm heat flux
experiments in short duration flowfacilities. Since it is very
difficult to measure thethickness of thin films, for the present
investigationthe thickness of the thin film gauges are assumed tobe
about 0.5 µm. This value is based on studiescarried out by other
investigators in which theaverage thickness of hand painted thin
films wasdetermined to be the stated value. In this case, about100
µs is required before the accuracy in the deducedheat flux reaches
5% of its actual value4.
Heat Flux Determination
In order to relate the measured temperature to theactual heat
transfer rate, it is assumed that the thinfilm gauge has negligible
heat capacity and that heatconduction in the substrate is
one-dimensional into asemi-infinite solid of constant physical
properties.Under these assumptions, the governing equationscan be
solved with the boundary conditions for thesituation shown in
figure 2.1 to give the surfacetemperature and heat flux to the
surface as
Tck
q
tds
st
=−∫
1
0π ρ
ττ
τ& ( )
( )(2.4)
& ( )( )
( )q t
ck
tds
dTd
t
=−
∫ρ
π
τ
τττ 1
20
(2.5)
During calibration of the RTD, a rectangular voltagepulse was
applied to the RTD bridge. In effect, aconstant heat flux is
applied to the thin film. If theheat flux to the surface is
constant, the surface heatflux can be determined by carrying out
theintegration in equation (2.4) and converting thesurface
temperature change to a voltage change byusing equation (2.2) to
give
&qckt
VVs R
=
ρ πα
12 12
02∆ (2.6)
where (ρck)½ is the thermal product of the film.From equation
(2.6) it is easily seen that the voltagechange caused by the
imbalanced bridge circuit isdirectly proportional to the
square-root of time.
If the heat flux is not constant, numerical techniquesmust be
used in the calculation of the heat transferrate. In order to
reduce the error introduced by theuncertainty in the integral term,
equation (2.5) can beintegrated using the Cook-Felderman
algorithm5
& ( )( )
( ) ( )
( )
( ) ( )
( )
( ) ( )
( ) ( )
( ) ( )
.
. .
. .
.
q tck
V
V t
t
V t V t
t t
V t V t
t t
V t V t
t t t t
V t V t
t
nR
n
n
n i
n i
n i
n ii
n
i i
n i n i
n i
=
+−
−−
−
−
+−
− + −
+−
−
−=
−
−
−
−
∑
ρ
πα 00 5
0 51
10 5
1
1
10 5
10 5
10 5
2
∆
(2.7)
where n is the number of equal divisions of time ∆tand t ranges
from 0 to n∆t. Since equation (2.7)involves no integration
approximations, the accuracyof the result obtained in using this
expression islimited only by the degree to which the true
voltageresponse is approximated by the piecewise linearexpression.
Furthermore, this algorithm avoidsdiscontinuities at the endpoints
of the temperaturehistory due to start up and shut down
transientsduring a test.
From equations (2.6) and (2.7) it is apparent that inorder to
perform heat flux calculations, it is necessaryto first determine
two thermal properties of the RTD:the thermal product and
temperature coefficient ofresistance. These thermal properties are
determined
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4
from static and dynamic calibration tests on theRTDs.
3.0 THIN FILM GAUGE CONSTRUCTION
The type of ceramic used as substrate material isMACOR, a
machinable glass ceramic available fromCorning Glass Works6. MACOR
is an ideal substratematerial because it has a low thermal
conductivity.Good insulation properties are required to ensure
thevalidity of the semi-infinite slab assumption.MACOR may also be
heated to 1000°C withoutsignificant geometric deformation.
Temperaturesnear this value are required during gauge
preparation.Table 3.1 shows some of the thermal properties ofMACOR
compared with two other commonly usedinsulating substrate materials
4,6.
Table 3.1 Thermal Properties of Electric Insulators
Insulatorρ
(g/cm3)c
(J/g/K)k
(J/cm/s/K)(ρck)½
(J/cm2/K/s½)MACOR 2.52 0.790 0.0146 0.171
PYREX 2.22 0.775 0.0136 0.153
Quartz 2.21 0.755 0.0140 0.153
It should also be noted that this material may bemachined easily
so that gauges may be placed oncomplex geometrical shapes. Although
MACOR isavailable in many different shapes, a smallcylindrical
substrate is suitable and convenient forconstructing rapid response
RTDs to be used intransient facilities. In the present experiment,
solidrods about 10 mm long with a diameter of 1.6 mmwere used.
The procedure used for constructing platinum RTDson ceramic
substrates includes substrate surfacepreparation, gauge material
application and electricallead connection. Each phase must be
strictlyfollowed if successful temperature measurements areto be
obtained.
Substrate Surface Preparation
In order to apply the gauge material, the substratemust be
smooth and highly polished. The resultingfilm should be between 0.1
and 1.0 micron thick andsharp irregularities should be removed to
ensure asmooth film. To obtain a smooth, polished surface,#600
grain wet or dry silicon carbide sandpaper wasfirst used. The
smoothing was then continued using#1000 and #2000 grain sandpapers
mounted on a
rapidly rotating flat disk. This was performed forseveral
minutes until the ceramic surface appearedvisibly polished. Care
was taken to ensure that thecylinder surface remained flat and
level duringpolishing. The edges of the cylinder were thenslightly
chamfered using #2000 grain sandpaper withthe RTD mounted in a
rapidly rotating drill.Rounding of the edges is required to avoid
wrappingthe lead connections around sharp corners, whichwould
result in poor electrical contact. In order tocomplete the
smoothing process, a crocus cloth wasused with the rotating flat
disk. After the surface hadbeen adequately polished, the ceramic
piece waswashed with water and placed under a heating lampto
dry.
The smoothing process is very important since anygeometric
discontinuities in the substrate materialsuch as fine cracks or
cavities may produce faultysensors. Therefore, the surface of the
substrate wasexamined using a UNITRON MR3-24metallographic
microscope before the gauge materialwas applied. Figures 3.1 and
3.2 are micrographsshowing the surface roughness of two
completedRTDs. These photos clearly show that polishinggreatly
improves the surface quality.
1.6 mm 1.6 mm
(a) (b)Figure 3.1. Micrographs of Complete RTD SurfaceTaken at
17x a) #600 Grain Polishing b) Final ClothPolishing.
0.3 mm 0.3 mm (a) (b)
Figure 3.2. Micrographs of a Section of the RTDSurface Taken at
66x a) #600 Grain Polishingb) Final Cloth Polishing.
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5
Gauge Material Application
After the substrate surface had been adequatelypolished, the
platinum film was applied. Platinumfilms are formed on insulating
substrates by usingcommercially available preparations of
metallo-organics such as “Liquid Bright Platinum 05-X”
fromEngelhard Industries. Metallo-organics are solutionsof metal
compounds in organic solvents. The liquidcontains fine metallic
particles in suspension andchemical agents that attack the surface
of thesubstrate to provide a highly adherent film. Table
3.2contains some of the thermal properties of platinumcompared with
two other commonly used gaugematerials4.
Table 3.1 Thermal Properties of Electric Conductors
Insulatorρ
(g/cm3)c
(J/g/K)k
(J/cm/s/K)(ρck)½
(J/cm2/K/s½)Platinum 21.5 0.13 0.70 1.40
Nickel 8.90 0.45 0.84 1.83
Copper 8.90 0.38 3.97 3.66
Before application to the substrate, the Liquid BrightPlatinum
solution was mixed with the thinningessence toluene. Several
factors must be consideredwhen preparing the solution, including
purity,concentration, and film thickness. The materialsshould be
mixed in a clean environment since anyimpurities introduced during
the mixing may result infaulty gauges. Figure 3.3a shows the
effects ofmixture impurities on the completed film surface.The
relative concentration of the platinum andthinner is also important
because the final resistanceof the gauge depends strongly on the
amount ofplatinum deposited on the surface. Furthermore,
pooradhesion may arise from too thick an application ofliquid
(figure 3.3b). Therefore, the liquid should bethin enough for brush
marks to flow out and take on aluster. During the present
investigation it was foundthat a mixture of three parts thinner and
one partliquid bright platinum applied using a small brushwith fine
hairs produces the best films.
The preferred method for applying the platinum filmsto the
substrate surface consisted of painting a strip ofplatinum about
0.8 mm wide on the surface of thesubstrate. In order to ensure
uniform film thickness,a single stroke was used. Although
regulating theamount of platinum applied to the surface is
difficult,this method ensures the validity of the one-dimensional
analysis assumption.
0.3 mm 0.2 mm (a) (b)
Figure 3.3. Micrographs Taken at 66x and 100× Showing a) Effects
of Impurities on Film Surfaceb) Cracking Due to Film Thickness
Surface.
Immediately after application of the platinum, thegauges were
dried by a high power lamp. The totaldrying time under the lamp
ranged between 10 and20 minutes. Drying was performed in a
cleanenvironment to avoid the collection of dust or otherimpurities
on the gauge surface.
In order for the liquid platinum to form on the surfaceof the
substrate, the piece must be baked at very hightemperatures to
remove the carrier. The substrateswere supported on a steel base
which had been pre-baked and inserted into an electric furnace.
Thetemperature was gradually increased to 750°C overabout one hour
and maintained at that temperature fora further thirty minutes.
During firing, it is necessarythat the rate of increase be gradual
so that blisteringor boiling of the film does not occur.
After baking, the RTDs were cooled slowly overnightin the
furnace in order to avoid cracking. Thesecracks may cause the
film’s resistance to increasewith time due to stress relief. For
properlyconstructed gauges, the final film resistance shouldbe
75−150 ohms.
Lead and Electrical Connections
The thin film leads to the platinum film were madeusing the
metallo-organic solution “Liquid BrightGold NW” from Engelhard
Industries. Gold is aconvenient material for thin film platinum
gaugesbecause the same baking temperatures and times maybe used as
for platinum. It should also be noted thatgold forms thin film
connections, in contrast to othermaterials such as silver, which
forms thick filmconnections with possible surface
discontinuities7.
The gold leads were applied to the middle of theceramic rod. It
is not necessary to polish the outersurface of the rod, but it must
be clean and dry. Theliquid gold was painted on the outer surface
of the
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6
ceramic rod in thin strips on opposite sides of thepiece. The
gold leads were made using a singlestroke of a small paint brush
starting about halfwaydown the ceramic piece and ending at the edge
of theplatinum film. The gold ink was applied with theceramic piece
in a horizontal position to ensureadequate material for conduction.
After applicationof the gold strips, the piece was dried and baked
asdescribed above.
When applying the gold leads, very careful attentionmust be
given to the interface where the two metalsmeet. The overlap point
between the metals must bekept to a minimum. If too much gold is
applied tothe film, the resistance of the film will be lowered
byshortening its effective length. Since the diameter ofthe RTD
surface is only 1.6 mm, a small amount ofgold on the surface could
significantly lower theresistance. However, care must be taken to
ensurethat an adequate amount of gold is applied at theinterface
between the two metals. During calibration,it is necessary to
subject the RTD to a voltage pulseof about 6 V. If there is not
enough gold at thecontact point, or if the edge is not
adequatelyrounded, burnout will occur and the gauge will fail.
The final step in gauge construction is makingelectrical
connections to the gold leads. Uninsulatedconstantan thermocouple
wire (Omega SPCI−003)with an outer diameter of 0.3 mm was used
formaking the connections. The wires were attached tothe gold leads
using a silver loaded epoxy adhesiveEpo-Tek H20E available from
Epoxy Technologies.Following application, the epoxy was cured in
anoven at a temperature of 150°C for 30 minutes.Electrical tape was
then used to insulate the goldleads and to increase the structural
stability of thewire leads. Figure 3.5 is a drawing of a
completedthin film RTD.
Figure 3.5. Thin Film RTD.
4.0 THIN FILM GAUGE CALIBRATION
Thin film heat transfer measurements require anaccurate
knowledge of the thermal properties of thegauge material. For
example, the temperatureresistance coefficient of a thin film gage
depends on avariety of factors including the film material, the
sizeof the deposit, and its shape. The useful linear rangealso
depends on a number of factors including theuniformity of the
metallic layer, purity and bondingto the substrate. Furthermore,
the value of thethermal product depends on the history of the
gaugeconstruction and in particular the firing details of
theceramic production process7. Therefore, each RTDwas calibrated
independently since reproduction offilms which are exactly the same
is not feasible.
Self-Heating Threshold
The excitation current to an RTD must be below athreshold value
to prevent appreciable ohmic heating.This threshold is determined
by a self-heating test.The Wheatstone bridge was balanced and the
RTDwas placed in still air. The supply from a Hewlett-Packard Model
E3630A triple power supply wasslowly increased while the output
voltage wasmeasured. If there were no ohmic heating, the
RTDresistance would not change and the output voltagewould be zero
since the bridge was initially balanced.Therefore, when
self-heating occurs, a voltage will bemeasured.
Static Calibration
Once the threshold of self-heating was determined,static
calibration was performed to determine thetemperature coefficient
of resistance. This test wasalso performed to determine the
sensitivity andlinearity of the RTD. The RTD was immersed in a400
mL beaker filled with 99.99% pure glycerin andplaced on a domestic
heating element. Glycerinprovides a stable medium and does not
containdissolved oxygen or other corrosive gases which
maycomplicate interpretation of the results. Furthermore,glycerin
has a very high boiling point compared towater which allows tests
to be performed over awider range of temperatures. A Radio Shack
Model22-174A multimeter was used to calibrate the RTDagainst an
OMEGA Model CAIN-316(E)-12 Type Kthermocouple probe from ambient to
120°C. Thisrange more than adequately covers the temperaturerises
encountered in shock tube experiments.
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7
Through experience it was found that maintaining aconstant bath
temperature during readings is vital.This is easiest when the bath
is being cooled betweenreadings. If constant bath temperatures
aremaintained during readings, the accuracy of thecalibration is
governed by the accuracies of themultimeter and thermocouple.
A least-squares, linear regression was performed onthe data to
determine the temperature coefficient ofresistivity using the
relationship
α R RRT
= 10
∆∆ (4.1)
where Ro is the resistance of the film in ambientconditions.
Accurate determination of both steady-state and transient heat
transfer rates is dependent onthe value of the temperature
coefficient. Although,equation (4.1) is the expression which is
used todetermine this value, it should be noted that Ro is
theresistance of the film at ambient conditions. If theconditions
in which the static calibrations areperformed are different than
those which exist duringactual testing, the value of Ro should be
obtainedfrom the test conditions. If this adjustment is notmade, an
error of about 1% in the measured heat fluxcould result for a
temperature difference of about 5 to10 °C7.
Dynamic Calibration
Due to the interpenetration of platinum and ceramicthat occurs
at the interface between the thin film andthe substrate, the
physical quantities k, ρ, and c arenot the properties of the bulk
material. Therefore it isimpossible to determine the thermal
product by astandard steady-state method with any acceptabledegree
of accuracy and a transient technique must beused. In order to
accurately determine the value ofthe thermal product, it was
necessary to perform adouble electrical discharge calibration. The
doublecalibration technique was used to minimize errorswhich are
introduced by non-uniform film heatingand other affects.
The RTD was incorporated into a Wheatstone bridgeand supplied
with a rectangular voltage pulse of 6 Vfor 5 milliseconds using a
Hewlett-Packard ModelE3630A triple power supply. The pulse
causedohmic heating within the film and produced a changein
resistance which was recorded as a change inoutput voltage. The
resulting output voltage causedby the imbalanced bridge circuit was
monitored with
a Hewlett-Packard 54540A digital recordingoscilloscope. This
voltage response is equivalent tothe temperature-time history of
the gauge.Furthermore, from equation (2.6) it is known that fora
constant heat transfer rate to the surface, thetemperature change
is a square-root function of time.
The test was first conducted in still air, where theheat loss to
the surroundings was negligible incomparison with heat transferred
by conduction tothe substrate. A plot was then generated of
theresponse voltage as a function of the square-root oftime and a
least-squares, linear regression wasperformed to determine the
slope of the data. Thetest was then repeated with the RTD immersed
inglycerin, where a fraction of the heat generateddiffused into the
liquid. A similar plot was obtainedfrom which the slope of the
transformed responsewas determined. The thermal product was
thencalculated from the relationship7
( )( )
( )( )
.
.
ρρ
ckck gly
Vt air
Vt gly
12
12
0 5
0 5
1
=
−∆
∆
(4.2)
where the thermal product of glycerin was obtainedfrom Ref.
4.
Care must be taken in the use of the electrical pulsecalibration
procedure to reduce potential errors. Thebridge circuit must be
carefully balanced before eachtest. An initial imbalance of the
bridge circuit willresult in a step in the response output at the
start ofthe test. This appears as an infinite heat transfer
rate.The bridge circuit must also be as inductance free aspossible
so that oscillatory responses are eitheravoided or rapidly damped.
Furthermore, theduration of the test must be short enough to
ensurethe validity of the one-dimensional assumption.
5.0 EXPERIMENTAL PROGRAM
Test Facility
The experiments were performed in the pilot shocktube at The
University of Texas at Arlington’sAerodynamics Research Center. The
tests wereperformed in order to determine the response time ofthe
RTDs and to confirm that the devices may beused for making heat
flux calculations in short
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8
duration facilities. A brief description of the shocktube and
set up is given below.
Shock Tube
The UT Arlington pilot shock tube is made ofstainless steel,
with a 100 mm ID driver tube and 50mm ID driven tube connected by a
convergentdiaphragm section (figure 5.1). The driver section
isseparated from the driven section by a diaphragm. Inthe present
experiment, Mylar diaphragms, 0.5 mmthick, without scoring were
used. These diaphragmsburst if subjected to a pressure difference
of 2 ± 0.07MPa. The driven section of the tube was subject
toambient conditions for all test runs. Air to the drivertube was
regulated to 2.0 ± 0.07 MPa. The driversection pressure, p4, was
measured by a WikaGlycerin pressure gauge with ±70 kPa
accuracy.Accurate measurements of p4 are actually notnecessary
because the input pressure pulse can beobtained from accurate
measurements of shock speed(Ms), driven-tube pressure (p1) and
temperature (T1).A run was initiated when the Mylar
diaphragmseparating the driven- and driver-tube was burst.
Figure 5.1. Pilot Shock Tube.
Test Section
The test section, located at the downstream end of thedriven
tube, was instrumented with two wall mountedpressure transducers
and an RTD mounted in a probe(figures 5.2 and 5.3). The test probe
consisted of thethree parts shown in figure 5.2. Before mounting
theRTD into the probe it was necessary to electricallyinsulate the
gold and wire leads. Electrical tape wasused to carefully cover any
exposed leads. The RTDwas then inserted into the teflon casing so
that thefilm surface protruded approximately 1/8” out of thecasing.
The teflon casing was made slightly largerthan the hole it was
inserted into in the probe tip.Therefore, when the casing was
pressed into theprobe tip it constricted tightly around the
RTDholding it firmly in place. This was necessitated bythe high
pressures encountered in the shock tubewhich could force the RTD
out of the probe. Carewas taken during the mounting of the RTD into
theprobe tip to ensure that the film was flush with thecontour of
the probe. The copper probe tip was then
mounted onto the probe body which was attached tothe shock tube
end plate.
Figure 5.2. Probe Design.
Figure 5.3. Pressure Transducer and RTD Mounting.
The pressure transducers were used to measure theshock speed and
to determine the precise time theshock passed over the RTD.
Experiments8 indicatethat theoretically computed shock strengths
arehigher than those actually attained. Initially, thediaphragm
burst delays the formation of a one-dimensional shock wave. Then as
the wave movesdown the tube it decelerates due to boundary
layergrowth. Therefore, the shock speed must bemeasured to evaluate
the actual local shock strength.Shock speeds can be determined by
finding thelapsed time of the wave as it passes two points.
In this experimental program, two 13.8 MPa PCBpiezoelectric
pressure transducers were flush-mounted in the tube wall precisely
152.4 mm apart.The shock Mach number was then computed as
( )M
Lt
as= ∆
1
(5.1)
where a1 is the ambient speed of sound of the driventube, ∆t is
the lapsed time of the wave, and L is thedistance between the two
transducers. Once theshock speed and the driven-tube pressure
and
-
9
temperature were known, the input pressure pulsewas obtained
as9
p p Ms2 121
2
11= +
+−
γγ
( ) (5.2)
where γ is the specific-heat ratio. Furthermore,equation (5.3)
was used to calculated the resultingtemperature rise due to shock
passage9
T T
M M
M2 1
12
12
12
11
2
2
11
2
1
1
2
=+
−
−
−
−+
−
γ γγ
γγ
γ (5.3)
Shock-Tube Experiment
A Hewlett-Packard Model 54540A, four-channel,digital recording
oscilloscope with a maximumsampling rate up to 500 MSa/sec per
channel wasused to gather pressure and temperature data. In
thepresent experiment three channels were used tocapture data at a
sampling rate of 1Megasample/second per channel. Channels 1 and
2were used to gather data from the PCB pressuretransducers, while
channel 4 monitored the RTDresponse. The RTD was again used in
conjunctionwith the Wheatstone bridge and supplied with
anexcitation of 2 V from a Hewlett-Packard E3630Atriple power
supply. The pressure transducers werepowered by a Model 482A04
I.C.P. 24 V powersupply. All input channels were
triggeredsimultaneously by an external trigger source. Theexternal
trigger consisted of a soft, thin wire placedflush with the Mylar
diaphragm on the upstream side.The wire was supplied with 5 V from
a Hewlett-Packard 6235A triple power supply. Triggeringoccurred
when the diaphragm ruptured causing thewire to break and resulting
in a sharp decline in thevoltage measured by the external trigger
channel ofthe oscilloscope. After observing the speed of atypical
shock wave, a delay was set on theoscilloscope in order to focus in
on the test section ofthe run.
6.0 RESULTS AND DISCUSSION
The results of the construction techniques, thecalibration
results, and the verification tests arediscussed in this chapter.
Ten samples were chosen
from the RTDs produced and are consideredrepresentative of all
of the hand-made gauges. FiveRTDs were chosen from those produced
using themethod of coating the entire surface of the RTD
withplatinum, and five were chosen produced by paintinga single
strip of platinum on the substrate surface.Only samples that had
final resistance values ofbetween 75-150 ohms were calibrated and
tested.
Construction Techniques
During the initial trial-and-error phase of theconstruction
process, only about 10% of the RTDsproduced had the desired
resistance. Due to the rapidevaporation of the thinning essence and
the inabilityto closely regulate the platinum contained in
thebrush, the final resistance values were consistentlytoo low. Out
of these 10%, nearly all were destroyedwhen subject to excitation
voltages as low as 2 V.This was caused by an inadequate amount of
leadmaterial at the platinum contact point which resultedin
burnout. After gaining a considerable amount ofexperience, the
success rate was increased to about90% for the RTDs produced by
painting the singlestrip of platinum. Although the amount of
platinumapplied could not be easily regulated, this methodproved to
give more consistent and reliable results.
The construction techniques also produced RTDs thatwere reliable
and rugged. Final shock tube testingshowed that reliable heat
transfer rates could beobtained using the thin film gauges.
Furthermore, atest was performed to determine the effects
ofrepeatedly subjecting the sensors to the harsh
testingenvironment. After eight test runs the thin filmshowed no
signs of deterioration and the filmresistance remained
constant.
Self-Heating
Figure 6.1 shows the results of the self-heating test.The test
shows that the output is practically zero upto an excitation of
about 1 V, above which the effectsof ohmic heating on the RTD
become apparent.However, up to an excitation of about 2 V, the
effectsare minimal and can be accounted for in the
finalcalculations. Although the false signal due to theohmic
heating is not negligible for an excitation of 2V, it should be
recognized as an offset that can be setequivalent to the ambient
conditions. Since thesensitivity of the RTD is a function of the
voltagesupplied to the bridge circuit, it is recommended that2 V be
used as the excitation threshold. Input valuesgreater than this
cause the internal heat generation to
-
10
increase rapidly and burnout usually occurs before anexcitation
of 4 V is reached.
Excitation (V)
0 1 2 3
Out
put V
olta
ge (
mV
)
0
5
10
15
20
25
Figure 6.1. Threshold of Self-Heating in Air.
Static Calibration
Figures 6.2 and 6.3 show the static calibration results.The
sensitivities of each of the RTDs weredetermined by a first-order
least-squares curve fit. Ineach case the value of the correlation
coefficient wascalculated and found to be better than 0.99.
Thenearly perfect correlation in every case was achievedby very
carefully measuring the temperature of theglycerin and the
resistance of the RTD as the bathwas cooling. This was a time
consuming process thatwas useful in confirming the expected linear
behaviorover the temperature range tested. The linearbehavior of
the RTDs confirms that they can be usedto make precise measurements
without complicateddata reduction proceduces.
For experimental purposes it is desired that thesensitivity of
the RTD be as high as possible so thataccurate measurements can be
made. When acorrelation of the sensitivity data was performed itwas
found that as the resistance of the RTDincreased, the sensitivity
increased. Figure 6.4 is aplot of the sensitivity as a function of
film resistance.From the graph it is apparent that there is
anincreasing linear trend with the data. An
interestingcharacteristic of thin platinum films is that as
morematerial is applied the resistance decreases.Similarly, as the
amount of material applied to thesurface of the RTD is decreased,
the resistanceincreases. Therefore, this increasing linear trend
canbe accounted for by the decrease in gauge material.
During testing, the sensitivity of the RTD wasincreased by using
a Wheatstone bridge and rapidchanges in temperature were measured
with a high-speed digital oscilloscope. It was therefore
necessary
to know how the sensitivity varied as a function ofthe
excitation supplied to the bridge. Furthermore,the output voltage
as a function of increasingtemperature had to be known. From figure
6.5 it canbe seen that the sensitivity is a linear function of
theexcitation and that the sensitivity is significantlyincreased by
the use of a Wheatstone bridge.
Temperature (°C)
20 40 60 80 100 120 140
Res
ista
nce
(Ω)
80
100
120
140
160
RTD 1RTD 2RTD 3RTD 4RTD 5Linear Fit
Figure 6.2. Static Calibration for RTDs 1−5.
Temperature (°C)
20 40 60 80 100 120 140
Res
ista
nce
(Ω)
100
120
140
160
180
200RTD 6RTD 7RTD 8RTD 9RTD 10Linear Fit
Figure 6.3. Static Calibration for RTDs 6–10.
Resistance (Ω)
60 80 100 120 140 160 180
Sens
itivi
ty (Ω
/°C
)
0.12
0.14
0.16
0.18
0.20
0.22
0.24
0.26
0.28
0.30
0.32
Figure 6.4. Correlation of RTD Sensitivities.
-
11
Temperature (°C)
30 40 50 60 70 80 90 100
Out
put (
mV
)
-10
0
10
20
30
40
502.0 V - Slope = 0.831.5 V - Slope = 0.621.0 V - Slope =
0.41Linear Regression
Figure 6.5. RTD Sensitivity.
Table 6.1 contains the tabulated data shown in figures6.1
through 6.5 along with the temperaturecoefficient of resistance for
each RTD and the erroranalysis results. For each case, the
coefficient ofresistance was calculated using equation (4.1)
withthe resistance of the RTD taken at 25°C. The error
ofapproximately one percent for each RTD shows thatthe calculated
values are very accurate. If preciseheat flux measurements are
needed, the coefficientshould be calculated from the resistance of
the RTDat the initial testing temperature.
Table 6.1. Static Calibration Results
RTDΩ
at 25°CαR
(K-1)%
ErrorSensitivity
(Ω/°C)r
1 85.4 0.00181 1.24 0.155 0.9997
2 104.6 0.00182 1.35 0.188 0.9993
3 129.3 0.00191 0.95 0.247 0.9998
4 119.0 0.00182 1.35 0.217 0.9999
5 76.1 0.00195 1.55 0.148 0.9999
6 123.7 0.00203 1.02 0.251 0.9999
7 135.9 0.00198 0.91 0.267 0.9997
8 112.1 0.00189 1.09 0.212 0.9999
9 109.4 0.00178 1.24 0.194 0.9998
10 161.8 0.00186 1.07 0.301 0.9999
Dynamic Calibration
Electrical discharge calibrations were performed todetermine the
thermal product of each RTD. Themagnitude of the rectangular
voltage pulse was
varied from 3 V to 20 V to determine an acceptableexcitation
value. For excitation values less thanabout 4 V there was very
little bridge response due toRTD ohmic heating. With 5 − 10 V
excitation, theRTD response was adequate for performing
dynamiccalibrations and the thermal product values wereconsistent
throughout this range. Excitation valuesgreater than 10 V also
produced adequate results, butthere was a high rate of failure due
to RTD burnoutwhich increased rapidly with increasing
voltage.Furthermore, as the voltage was increased, smalldeviations
from a perfectly balanced bridge weregreatly magnified. Although
this did not affect thefinal value of the thermal product, in some
cases theoscilloscope scale had to be reset in order to capturethe
increased response values. For the ten RTDs inthis experimental
program, only the data for the 6 Vexcitation are presented.
Figure 6.6 shows the results of the dynamiccalibration. As
discussed in section 4.3, a rectangularvoltage pulse heats the RTD
such that the bridgecircuit response should ideally follow a
square-rootfunction of time. The figure includes a
least-squaressquare-root of time behavior of the data, with
acorrelation coefficient of 0.99.
Time (ms)
-1.0 0.0 1.0 2.0 3.0 4.0 5.0
Vol
tage
(m
V)
-20.0
0.0
20.0
40.0
60.0
80.0
100.0
Glycerin
Air
Figure 6.6. Dynamic Calibration Results.
The square-root of time behavior is further shown infigure 6.7,
which confirms the theory presented insection 4.3. The figure also
contains confidenceintervals that are used to estimate the error in
thedata. From the graph it is apparent that there is verylittle
error introduced by the linear approximation tothe data. Table 6.2
contains the tabulated dynamiccalibration data for each RTD
including the thermalproduct and the calculated correlation
coefficients.
-
12
Time1/2 (ms)1/2
0.0 1.0 2.0 3.0
Vol
tage
(m
V)
0.0
20.0
40.0
60.0
80.0
100.0
Air
Glycerin
Experimental DataLinear Regression95 % Confidence Lines
Figure 6.7. RTD Response After Square-rootTransformation.
Table 6.2. Dynamic Calibration Results.
RTDΩ
at 25°C(ρck)½
(J/cm2/K/s½)Air Correlation
CoefficientGlycerin
Coefficient1 85.4 0.205 0.9961 0.9954
2 104.6 0.191 0.9818 0.9670
3 129.3 0.193 0.9829 0.9672
4 119.0 0.200 0.9963 0.9963
5 76.1 0.193 0.9913 0.9909
6 123.7 0.190 0.9938 0.9938
7 135.9 0.213 0.9948 0.9911
8 112.1 0.207 0.9947 0.9901
9 109.4 0.216 0.9954 0.9963
10 161.8 0.215 0.9960 0.9917
RTD Testing
Two RTDs were employed for determining heattransfer rates in a
known flow, namely, the stagnationpoint heat transfer to a
hemisperical cap. Thisenabled their performance to be evaluated
against atheoretical benchmark. To accomplish this, an RTDwas
carefully mounted in the tip of the probe shownin figure 5.2 and
placed in the shock tube along withtwo PCB pressure transducers as
shown in figure 5.3.Figure 6.8 is a plot of the pressure transducer
outputsduring a test run. The first time lapse shown on thegraph
indicates the passage of the incident shockwave, while the second
indicates the passage of thereflected shock from the downstream end
of the tube.The time elapsed for the oncoming shock to
travelbetween the two transducers was 246 ± 2 µs.Therefore, the
experimental shock Mach number was
determined to be 1.79 ± 1 percent using equation(5.1). The shock
speed was 619.5 m/s ± 1 percent.Using this velocity and knowing the
distance betweenthe RTD and transducer “B” (figure 5.3), the time
ofarrival of the shock was found to be 113 ± 2 µs afterpassing
transducer “B”. Therefore, the time theshock contacted the RTD
surface was calculated as8.975 ± 0.003 ms.
In order to determine the testing time, it wasnecessary to
consider the influence of both thereflected shock and the contact
surface. The passageof either of these surfaces would cause an
appreciablechange in the temperature of the air.
As shown in figure 6.8, the time elapsed for thereflected shock
to travel between the two transducerswas 503 ± 2 µs. This gave a
reflected shock Machnumber of 0.87 ± 1 percent which corresponds to
aspeed of 304.6 m/s ± 1 percent. Using this velocityand the
geometry of the configuration, it wasdetermined that the reflected
shock passed over theRTD surface at 9.464 ± 0.003 ms.
Time (s)
0.008 0.009 0.010 0.011 0.012
Tra
nsdu
cer
Res
pons
e (V
)
0.0
0.2
0.4
0.6
0.8
PCB "A"PCB "B"
246 µsMS = 1.79
503 µsMRS = 0.87
Figure 6.8. Shock Speed and Test TimeDetermination.
The time that the contact surface passed over theRTD surface is
not precisely known. However, anestimation was calculated by first
determining thetheoretical speed of the contact surface using
theequation10
ua p
p p
p
p = −
+
+−+
1
1
2
1
1
1
2
1
1
1
0 5
1
2
11
1γ
γγ
γγ
.
(6.1)
From equation (6.1) the speed of the contact surfacewas
estimated to be 355.2 m/s. The actual speed of
-
13
the contact surface was probably less than this due toboundary
layer growth. Therefore, equation (6.1) isactually the limiting
case and can be used todetermine the test time. Using the velocity
of thecontact surface and knowing the distance between theRTD and
diaphragm section, the arrival of the contactsurface was estimated
to be 16.9 ms. The shocktrajectory and contact surface interaction
are showngraphically in figure 6.9.
Since the reflected shock passed over the RTD muchsooner than
the estimated time of the contact surface,the test time was
determined to be approximately 489± 4 µs by simply taking the
difference between theinitial and reflected shock passage times.
This testingtime was deemed of adequate length for
thisexperiment.
x (m)
0.0 1.0 2.0 3.0 4.0 5.0 6.0 7.0
time
(ms)
0.0
2.0
4.0
6.0
8.0
10.0
12.0
14.0
conta
ct sur
face
inciden
t shock
reflected shock
end
plat
e
Test Time
RT
D L
ocat
ion
Figure 6.9. Shock and Contact Surface Interaction.
Figure 6.10 is a plot of the response of RTD 9showing about 1 ms
of data before passage of theshock wave and the following 3 ms. For
this run,data was taken at a rate of 1 MSa/s. In order toconvert
the RTD response from a voltage reading to ameaningful temperature
measurement, 1 ms of dataprior to shock passage was averaged and
setequivalent to the ambient temperature of 25°C. Thesensitivity of
the RTD when subjected to anexcitation of 2 V was then used to
convert theresponse voltage into a temperature measurement.
Heat Flux Determination
Three techniques were used to compute thestagnation-point heat
transfer rate and compared withone another for accuracy. Two of the
methods usedthe experimental data obtained with the RTDs andthe
third method was based on theory. Each methodis described below and
the results that were obtainedare presented.
Time (s)
0.008 0.009 0.010 0.011 0.012
Tem
pera
ture
(°C
)
20
30
40
50
60
Shock PassageShock Reflection
8.97
5 m
s
9.46
ms
RTD 9Ms = 1.79
Figure 6.10. RTD Response.
Constant Heat Flux Case
The first method used was based on the assumptionthat the heat
transfer rate was constant over the testtime. Using this
assumption, equation (2.6) wasrearranged to give the change in
voltage as
( )∆V
V
ckq tR s=
2 01 2
1 2α
ρ //& (6.2)
As discussed in section 2.3, if the heat flux isconstant the
voltage change caused by theimbalanced bridge circuit should
ideally be directlyproportional to the square-root of time. It
wastherefore necessary to shift the time scale of theexperimental
data so that the shock wave passed overthe RTD at time zero. A plot
of the RTD response asa function of the shifted square-root of time
is shownin figure 6.11.
Time1/2 (ms)1/2
0.0 0.1 0.2 0.3 0.4 0.5 0.6 0.7
Tem
pera
ture
(°C
)
22
24
26
28
30
32
34
36
38
40
42
Experimental DataLinear Regression95 % Confidence Lines
RTD 9
Figure 6.11. Transformed Temperature Response of RTD 9.
After shifting the time scale and plotting the responseas a
function of the square-root of time, a linear
-
14
regression was performed on the data to obtain anequation of the
form
∆V t c= +λ 1 2/ (6.3)
where λ is the slope of the regression line and c is aconstant
due to an initially imbalanced bridge. Bynoting that c is only an
offset from the origin whichcan be set equal to zero without
affecting the slope,equations (6.2) and (6.3) were equated to yield
anequation for the constant heat transfer rate as
( )&
/
qck
Vs R=
ρ πα
λ1 2
02. (6.4)
By using the values of the thermal product ( ρck =0.216
J/cm2/K/s1/2) and the temperature resistancecoefficient (αR =
0.00178 K
-1) obtained during thecalibration of RTD 9, the
stagnation-point heattransfer rate was found to be 23.2 W/cm2 ±
11percent.
Fay-Riddell Correlation
The second method was used as a theoretical checkof the
experimental results. This method is based onthe work of Fay and
Riddell. They determined thatthe theoretical curve-fit for the
stagnation-point heattransfer rate for a laminar boundary layer of
aspherical cap is given by11
( )( ) ( ) ( )
( )
&
.
Pr
,
,.
., ,
.,
..
q
H h
Leh
H
du
dx
t ref
w t
t t w t w t t w t
d
t
e
t
=
−
+ −
0 763
1 1
0 6 2 20 4 0 1
2
0 52
2 2
0 5
ρ µ ρ µ
*
(10)
where ρ is the density, µ is the viscosity, H is thestagnation
enthalpy, h is the static enthalpy, Le is theLewis number, Pr is
the Prandtl number, and due/dxis the stagnation-point velocity
gradient. However,the bracketed term containing the Lewis number
isonly needed when the temperatures and temperaturegradients are
sufficiently high so that appreciabledissociation and concentration
gradients across theboundary layer are present. Furthermore,
thestagnation-point velocity gradient of a hemisphere isgiven
by11
du
dx R
P Pe
t N
t
t
=− ∞
2
2
2
1 2( )
ρ(6.5)
where P is the pressure and RN is the nose radius.Therefore, the
equation for the heat-flux becomes
( )( ) ( )
( )
&.
Pr
( )
,
,.
., ,
.
,
.
q
H hR
P P
t ref
w t
t t w t w t
t w tN
t
t
=
−−
∞
0 763
1 2
0 6 2 20 4 0 1
22
2
0 5
ρ µ ρ µ
ρ *
(6.6)
where t2 denotes the conditions at the stagnationpoint
downstream of a shock wave, w the surfaceconditions, t the
stagnation-point value, and ∞ thefreestream conditions.
When using equation (6.6), the density and enthalpywere computed
using the perfect gas relations, thePrandtl number was assumed to
be 0.7, and thedownstream pressure was calculated using
equation(5.2). Furthermore, the viscosity was calculatedusing
Sutherland’s Law as12
µ µ=
+
+∞
∞
∞
TT T
T
0 51 0 505
1 0 505
..
.
(6.7)
where T was calculated using equation (5.3).
By going through the above analysis, the theoreticalvalue for
the stagnation-point heat transfer rate for alaminar boundary layer
of a spherical cap was foundto be 26.2 W/cm2 ± 3 percent. This is
only 13percent greater than the experimentally calculatedheat
transfer rate which had an error of ± 11 percent.Therefore, the RTD
was considered to give reliableheat transfer rate results.
Cook-Felderman Algorithm
The final method used to calculate the heat-transferrate was the
Cook-Felderman algorithm discussed insection (2.3). It was found
that when using thismethod the raw RTD response data could not be
usedbecause of the noise present within the data. Thesharp
fluctuations in the RTD response caused largeerrors in the
calculated heat transfer rate.Furthermore, the algorithm failed to
converge on anapproximate heat transfer rate value. However,
the
-
15
algorithm proved useful for calculating the heattransfer rate
from data that the random noise has beenremoved from.
Figure 6.12 shows the RTD response with a parabolicfit that was
determined from the least-squares square-root of time regression
line shown in figure 6.11.Using this parabolic fit data along with
Cook-Felderman algorithm given in equation (2.7), the heatflux was
determined numerically.
Figure 6.13 is a plot of the heat flux results that
werecalculated using all three methods. Although thetesting time
was only about 0.5 ms, the graph showsa time of 1 ms. The longer
time was need to showthat the Cook-Felderman algorithm
actuallyconverges to a value which is very close to
thetheoretically calculated value of 26 W/cm2.
Time (ms)
-0.3 -0.2 -0.1 0.0 0.1 0.2 0.3 0.4 0.5
Tem
pera
ture
(°C
)
25
30
35
40 Expermental DataParabolic Fit
RTD 9
Figure 6.12. Temperature Response of RTD 9.
time (ms)
0.0 0.2 0.4 0.6 0.8 1.0
heat
flu
x (W
/cm
2 )
20
30
40
50
60
70
80
90
100
Cook-Felderman AlgorithmFay-Riddell CorrelationConstant Heat
Flux Method
Figure 6.13. Heat Flux Correlation for RTD 9.
Repeatability
The repeatability of the experiments was checked byperforming
the same shock tube tests under similarconditions with a different
RTD. The same methodsas presented above were used to determine the
heat
flux. Figure 6.14 shows the response of the RTD as afunction of
the square-root of time with a least-squares linear regression line
and 95 percentconfidence intervals. The results of the analysis
forthe two RTDs are tabulated in table 6.3.
Time1/2 (ms1/2)
0.0 0.1 0.2 0.3 0.4 0.5 0.6 0.7
Tem
pera
ture
(°C
)
22
24
26
28
30
32
34
36
38
40
42
Experimental DataLinear Regression95 % Confidence Lines
RTD 10
Figure 6.14. Transformed Temperature Response ofRTD 10.
Table 6.3. Calculated Heat Flux Results
RTDConstant Heat
Flux Case (W/cm2)Fay-Riddell
Method (W/cm2)Cook-Felderman
@ t = 1 ms (W/cm2)9 23.22 ± 11 % 26.2 ± 3 % 28.1
10 25.08 ± 10 % 27.0 ± 3 % 29.8
CONCLUSIONS AND RECOMMENDATIONS
Conclusions
The objective of the investigation was to construct,calibrate,
and test hand-made thin film platinumRTDs that are inexpensive,
reliable, rugged, andsuitable for use in transient facilities.
Theconclusions from this investigation, as discussed inchapter 6,
are summarized as follows:
1. The construction techniques produced RTDswith the desired
characteristics. By closelyfollowing the construction techniques as
detailedin chapter 3, an experienced investigator canproduce
reliable, rugged, hand-made RTDs.
2. The self-heating tests showed that ohmic heatingis
practically zero up to an excitation voltage ofabout 1 V and that
the effects can be accountedfor in the final calculations for
values up to 2 V.For excitation values greater than 2 V theinternal
heat generation increases rapidly andburnout usually occurs before
an excitation of 4V is reached.
-
16
3. Static calibration tests confirmed the expectedlinearity of
the platinum film resistance as afunction of temperature and the
averagetemperature coefficient of resistance was foundto be 0.019
K-1. The expected conclusion thatthe sensitivity of the RTD could
be significantlyincreased with a bridge circuit was alsoevidenced.
Furthermore, a correlation of theRTD sensitivities showed an
increasing lineartrend with film resistance.
4. From the dynamic calibration tests it was foundthat
excitation values between 5−10 V wereadequate for obtaining
accurate thermal productvalues. Excitation values greater than 10 V
alsoproduced adequate results, but there was a highrate of failure
due to RTD burnout. The averagevalue of the thermal product was
determined tobe 0.2 J/cm2/K/s1/2.
5. The final shock tube tests proved that hand-madethin film
RTDs can be used to accuratelymeasure heat transfer rates in
transient facilities.
Recommendations
A complete study of transient thin film heat transfergauges will
require more testing. Severalrecommendations for further testing
are:
1. It is recommended that other techniques ofdepositing the thin
platinum film on thesubstrate are investigated and the
resultscompared with the hand-made films. Sputteringtechniques and
vacuum deposition are twomethods that could be used.
2. The shock tube tests should be repeated usingseveral RTDs
under several different flowvelocities to confirm the reliability
of thegauges. The ruggedness of the films should alsobe tested by
subjecting the RTD to flows withmuch higher Mach numbers.
3. The effective thickness of the thin films shouldbe
investigated. A new experimental methodfor determining the film
thickness is given byButtsworth in ref. 18.
4. Methods for reducing the noise in theexperimental data should
also be considered.
REFERENCES
1. Bechwith, T., “Thermoresistive Elements”,Mechanical
Measurements, Addison-Wesley,Reading, 1995, pp. 668-673.
2. Holman, J. P., “Basic Electrical Measurementsand Sensing
Devices”, Experimental Methodsfor Engineers, 5th edition,
McGraw-Hill, 1989,pp. 113-121. Mechanical
Measurements,Addison-Wesley, Reading, 1995, pp. 668-673.
3. Carslaw H. S. and Jaeger J. C., “The Infinite
andSemi-infinite Solid”, Conduction of Heat inSolids, 2nd edition,
Clarendon Press, 1989, pp.75-76.
4. Schultz, D.L. and Jones, T.V., “Heat-TransferMeasurements in
Short-Duration HypersonicFacilities,” AGARDograph No. 163,
February1973, Department of Engineering Science,University of
Oxford, Great Britain.
5. Cook W. J. and Felderman E. J., “Reduction ofData from
Thin-Film Heat-Transfer Gages: AConcise Numerical Technique”, AIAA
Journal,Vol. 4, No. 3, 1966, pg. 561.
6. MACOR: Machinable Glass Ceramic, CorningGlass Works, Corning,
New York.
7. Ligrani, P.M., Camci, C. and Grady, M.S., “ThinFilm Heat
Transfer Gage Construction andMeasurement Details,” TM33, Nov.
1982, vonKarman Institute for Fluid Dynamics, RhodeSaint Genese,
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