ASTM E459-97
(Test Method)Standard Test Method for Measuring Heat Transfer Rate Using a Thin-Skin Calorimeter
Standard Test Method for Measuring Heat Transfer Rate Using a Thin-Skin Calorimeter
SCOPE
1.1 This test method describes the design and use of a thin metallic calorimeter for the measurement of heat-transfer rate using a steady one-dimensional heat flow analysis.
1.2 Advantages:
1.2.1 Simplicity of Construction -The calorimeter may be constructed identical to the material specimen in size and shape, and thermocouples may be attached to the metal by spot, electron beam, or laser beam welding.
1.2.2 Heat-transfer rate distribution may be obtained if metals of low thermal conductivity are used.
1.2.3 Smooth continuous surface without insulators or plugs for more realistic flow simulation.
1.2.4 This test method is relatively inexpensive and, if necessary, may be operated to burn-out to obtain heat-transfer rate measurement.
1.3 Limitations:
1.3.1 The short test time necessary to ensure calorimeter survival.
1.3.2 The calorimeter must be operated at pressures and temperatures such that the thin skin does not distort under the pressure loads.
1.4 This standard may involve hazardous materials, operations, and equipment. This standard does not purport to address all of the safety problems associated with its use. It is the responsibility of the user of this standard to establish appropriate safety and health practices and determine the applicability of regulatory limitations prior to use.
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Designation:E459–97
Standard Test Method for
Measuring Heat Transfer Rate Using a Thin-Skin
Calorimeter
This standard is issued under the fixed designation E459; the number immediately following the designation indicates the year of
original adoption or, in the case of revision, the year of last revision.Anumber in parentheses indicates the year of last reapproval.A
superscript epsilon (e) indicates an editorial change since the last revision or reapproval.
1. Scope priate safety and health practices and determine the applica-
bility of regulatory limitations prior to use.
1.1 This test method describes the design and use of a thin
metallic calorimeter for measuring heat transfer rate (also
2. Summary of Test Method
calledheatflux).Thermocouplesareattachedtotheunexposed
2.1 This test method for measuring the heat transfer rate to
surface of the calorimeter.Aone-dimensional heat flow analy-
a metal calorimeter of finite thickness is based on the assump-
sis is used for calculating the heat transfer rate from the
tion of one-dimensional heat flow, known metal properties
temperature measurements. Applications include aerodynamic
(density and specific heat), known metal thickness, and mea-
heating, laser and radiation power measurements, and fire
surement of the rate of temperature rise of the back (or
safety testing.
unexposed) surface of the calorimeter.
1.2 Advantages:
2.2 After an initial transient, the response of the calorimeter
1.2.1 Simplicity of Construction—The calorimeter may be
is approximated by a lumped parameter analysis:
constructedfromanumberofmaterials.Thesizeandshapecan
dT
often be made to match the actual application. Thermocouples
q5rC d (1)
p
dt
may be attached to the metal by spot, electron beam, or laser
welding.
where:
1.2.2 Heat transfer rate distributions may be obtained if
q 5 heat transfer rate, W/m ,
metals with low thermal conductivity, such as some stainless 3
r5 metal density, kg/m ,
steels, are used.
d5 metal thickness, m,
1.2.3 The calorimeters can be fabricated with smooth sur-
C 5 metal specific heat, J/kg·K, and
p
faces,withoutinsulatorsorplugsandtheattendanttemperature
dT/dt5 back surface temperature rise rate, K/s.
discontinuities, to provide more realistic flow conditions for
3. Significance and Use
aerodynamic heating measurements.
1.2.4 The calorimeters described in this test method are
3.1 This test method may be used to measure the heat
relatively inexpensive. If necessary, they may be operated to
transfer rate to a metallic or coated metallic surface for a
burn-out to obtain heat transfer information.
variety of applications, including:
1.3 Limitations:
3.1.1 measurements of aerodynamic heating when the calo-
1.3.1 At higher heat flux levels, short test times are neces-
rimeter is placed into a flow environment, such as a wind
sary to ensure calorimeter survival.
tunnel or an arc jet; the calorimeters can be designed to have
1.3.2 For applications in wind tunnels or arc-jet facilities,
the same size and shape as the actual test specimens to
the calorimeter must be operated at pressures and temperatures
minimize heat transfer corrections;
such that the thin-skin does not distort under pressure loads.
3.1.2 heat transfer measurements in fires and fire safety
Distortion of the surface will introduce measurement errors.
testing;
1.4 This standard does not purport to address all of the
3.1.3 laser power and laser absorption measurements; as
safety concerns, if any, associated with its use. It is the
well as,
responsibility of the user of this standard to establish appro-
3.1.4 X-ray and particle beam (electrons or ions) dosimetry
measurements.
3.2 The thin-skin calorimeter is one of many concepts used
This specification is under the jurisdiction ofASTM Committee E-21 on Space
to measure heat transfer rates. It may be used to measure
Simulation andApplications of SpaceTechnology and is the direct responsibility of
convective, radiative, or combinations of convective and ra-
Subcommittee E21.08 on Thermal Protection.
diative (usually called mixed or total) heat transfer rates.
Current edition approved April 10, 1997. Published August 1997. Originally
e1
published as E459–72. Last previous edition E459–72 (1990) . However, when the calorimeter is used to measure radiative or
Copyright © ASTM International, 100 Barr Harbor Drive, PO Box C700, West Conshohocken, PA 19428-2959, United States.
E459
FIG. 1 Typical Thin-Skin Calorimeter for Heat Transfer Measurement
mixedheattransferrates,theabsorptivityandreflectivityofthe couple that is soldered to the surface (1,2). The wires should
surface should be measured over the expected radiation wave- be positioned approximately 1.6 mm apart along an expected
length region of the source. isotherm.Theuseofasmallthermocouplewireminimizesheat
conduction into the wire but the calorimeter should still be
3.3 In 4.6 and 4.7, it is demonstrated that lateral heat
ruggedenoughforrepeatedmeasurements.However,whenthe
conduction effects on a local measurement can be minimized
thicknessofthecalorimeterisontheorderofthewirediameter
by using a calorimeter material with a low thermal conductiv-
toobtainthenecessaryresponsecharacteristics,therecommen-
ity.Alternatively, a distribution of the heat transfer rate may be
dations of Sobolik, et al. [1989], Burnett [1961], and Kidd
obtainedbyplacinganumberofthermocouplesalongtheback
[1985] (2-4) should be followed.
surface of the calorimeter.
4.2 Whenheatingstarts,theresponseoftheback(unheated)
3.4 In high temperature or high heat transfer rate applica-
surface of the calorimeter lags behind that of the front (heated)
tions, the principal drawback to the use of thin-skin calorim-
surface. For a step change in the heat transfer rate, the initial
eters is the short exposure time necessary to ensure survival of
response time of the calorimeter is the time required for the
the calorimeter such that repeat measurements can be made
temperature rise rate of the unheated surface to approach the
with the same sensor. When operation to burnout is necessary
temperature rise rate of the front surface within 1%. If
to obtain the desired heat flux measurements, thin-skin calo- conductionheattransferintothethermocouplewireisignored,
rimeters are often a good choice because they are relatively the initial response time is generally defined as:
inexpensive to fabricate. 2
rC d
p
t 50.5 (2)
r
k
4. Apparatus
where:
4.1 Calorimeter Design—Typicaldetailsofathin-skincalo-
t 5 initial response time, s, and
r
rimeter used for measuring aerodynamic heat transfer rates are
k 5 thermal conductivity, W/m·K.
shown in Fig. 1. The thermocouple wires (0.127 mm OD,
As an example, the 0.76 mm (0.030 in.) thick, 300 series
0.005 in., 36 gage) are individually welded to the back surface
stainless steel calorimeter analyzed in Ref (4) has an initial
of the calorimeter using spot, electron beam, or laser tech-
niques. This type of thermocouple joint (called an intrinsic
thermocouple) has been found to provide superior transient 2
Theboldfacenumbersinparenthesesrefertothelistofreferencesattheendof
response as compared to a peened joint or a beaded thermo- this standard.
E459
response time of 72 ms. Eq 2 can be rearranged to show that
rC d k~T 2 T ! 1
p max 0
t 5 * 2 (4)
F G
max
the initial response time also corresponds to a Fourier Number k qd 3
(a dimensionless time) of 0.5.
where:
4.3 Conduction heat transfer into the thermocouple wire
t 5 maximum exposure time, s,
max
delaysthetimepredictedbyEq2forwhichthemeasuredback
T 5 initial temperature, K, and
face temperature rise rate accurately follows (that is, within
T 5 maximum allowable temperature, K.
max
1%) the undisturbed back face temperature rise rate. For a
4.4.1 In order to have time available for the heat transfer
0.127 mm (0.005 in.) OD, Type K intrinsic thermocouple on a
ratemeasurement, t mustbegreaterthant ,whichrequires
max R
0.76 mm (0.030 in.) thick, 300 series stainless steel calorim-
that:
eter,theanalysisinRef (4)indicatesthemeasuredtemperature
k~T 2 T ! 5
rise rate is within 2% of the undisturbed temperature rise rate
max 0
. (5)
qd 6
in approximately 500 ms. An estimate of the measured tem-
perature rise rate error (or slope error) can be obtained from
4.4.2 Determine an optimum thickness that maximizes
Ref (1) for different material combinations:
(t − t ) (7) as follows:
max R
dT dT at at
C TC
2 3 k~T 2 T !
max 0
2 5 C exp C erfc C (3)
1 S 2 2 D S 2 2D
Πd 5 (6)
dt dt
opt
R R
5 q
4.4.3 Then calculate the maximum exposure time using the
where:
optimum thickness as follows:
T 5 calorimeter temperature,
C
T 5 measured temperature (that is, thermocouple out-
TC
T 2 T
max 0
t 50.48rC k (7)
F G
put), max opt p
q
C 5b/(8/p + b) and C 54/(8/p+ bp),
1 2
4.4.4 When it is desirable for a calorimeter to cover a range
a5 k/rC (thermal diffusivity of the calorimeter mate-
p
of heat transfer rates without being operated to burn-out,
rial),
design the calorimeter around the largest heat-transfer rate.
b5 K/ A ,
=
K 5 k of thermocouple wire/k of calorimeter, This gives the thinnest calorimeter with the shortest initial
A 5a of thermocouple wire/a of calorimeter, responsetime(Eq2);however,Refs (2,3,8,9)allshowthetime
R 5 radius of the thermocouple wire, and
to a given error level between the measured and undisturbed
t 5 time.
temperature rise rates (left hand side of Eq 3) increases as the
Using thermal property values given in Ref (4) for theAlumel
thickness of the calorimeter decreases relative to the thermo-
(negative) leg of the Type K thermocouple on 300 Series
couple wire diameter.
stainless steel (K 51.73, A 51.56, b51.39), Eq 3 can be
4.5 In most applications, the value of T should be well
max
used to show that the measured rate of temperatur
...
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