ASTM E459-05(2016)

NOTICE: This standard has either been superseded and replaced by a new version or withdrawn.
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Designation: E459 − 05 (Reapproved 2016)
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 (´) indicates an editorial change since the last revision or reapproval.
1. Scope 1.4.1 Exception—The values given in parentheses are for
information only.
1.1 This test method covers the design and use of a thin
1.5 This standard does not purport to address all of the
metallic calorimeter for measuring heat transfer rate (also
safety concerns, if any, associated with its use. It is the
calledheatflux).Thermocouplesareattachedtotheunexposed
responsibility of the user of this standard to establish appro-
surface of the calorimeter.Aone-dimensional heat flow analy-
priate safety and health practices and determine the applica-
sis is used for calculating the heat transfer rate from the
bility of regulatory limitations prior to use.
temperature measurements. Applications include aerodynamic
heating, laser and radiation power measurements, and fire
2. Summary of Test Method
safety testing.
2.1 This test method for measuring the heat transfer rate to
1.2 Advantages:
a metal calorimeter of finite thickness is based on the assump-
1.2.1 Simplicity of Construction—The calorimeter may be
tion of one-dimensional heat flow, known metal properties
constructedfromanumberofmaterials.Thesizeandshapecan
(density and specific heat), known metal thickness, and mea-
often be made to match the actual application. Thermocouples
surement of the rate of temperature rise of the back (or
may be attached to the metal by spot, electron beam, or laser
unexposed) surface of the calorimeter.
welding.
1.2.2 Heat transfer rate distributions may be obtained if
2.2 After an initial transient, the response of the calorimeter
metals with low thermal conductivity, such as some stainless
is approximated by a lumped parameter analysis:
steels, are used.
dT
1.2.3 The calorimeters can be fabricated with smooth
q 5 ρC δ (1)
p
dτ
surfaces,withoutinsulatorsorplugsandtheattendanttempera-
ture discontinuities, to provide more realistic flow conditions
where:
for aerodynamic heating measurements.
q = heat transfer rate, W/m ,
1.2.4 The calorimeters described in this test method are
ρ = metal density, kg/m ,
relatively inexpensive. If necessary, they may be operated to
δ = metal thickness, m,
burn-out to obtain heat transfer information. C = metal specific heat, J/kg·K, and
p
dT/dτ = back surface temperature rise rate, K/s.
1.3 Limitations:
1.3.1 At higher heat flux levels, short test times are neces-
3. Significance and Use
sary to ensure calorimeter survival.
3.1 This test method may be used to measure the heat
1.3.2 For applications in wind tunnels or arc-jet facilities,
transfer rate to a metallic or coated metallic surface for a
the calorimeter must be operated at pressures and temperatures
variety of applications, including:
such that the thin-skin does not distort under pressure loads.
3.1.1 Measurements of aerodynamic heating when the calo-
Distortion of the surface will introduce measurement errors.
rimeter is placed into a flow environment, such as a wind
1.4 The values stated in SI units are to be regarded as
tunnel or an arc jet; the calorimeters can be designed to have
standard. No other units of measurement are included in this
the same size and shape as the actual test specimens to
standard.
minimize heat transfer corrections;
3.1.2 Heat transfer measurements in fires and fire safety
testing;
This test method is under the jurisdiction of ASTM Committee E21 on Space
Simulation andApplications of SpaceTechnology and is the direct responsibility of
3.1.3 Laser power and laser absorption measurements; as
Subcommittee E21.08 on Thermal Protection.
well as,
Current edition approved April 1, 2016. Published April 2016. Originally
3.1.4 X-ray and particle beam (electrons or ions) dosimetry
approved in 1972. Last previous edition approved in 2011 as E459–05(2011).
DOI: 10.1520/E0459-05R16. measurements.
Copyright © ASTM International, 100 Barr Harbor Drive, PO Box C700, West Conshohocken, PA 19428-2959. United States
E459 − 05 (2016)
FIG. 1 Typical Thin-Skin Calorimeter for Heat Transfer Measurement
3.2 The thin-skin calorimeter is one of many concepts used niques. This type of thermocouple joint (called an intrinsic
to measure heat transfer rates. It may be used to measure thermocouple) has been found to provide superior transient
convective, radiative, or combinations of convective and ra- response as compared to a peened joint or a beaded thermo-
diative (usually called mixed or total) heat transfer rates. couple that is soldered to the surface (1, 2). The wires should
However, when the calorimeter is used to measure radiative or be positioned approximately 1.6 mm apart along an expected
mixedheattransferrates,theabsorptivityandreflectivityofthe isotherm.Theuseofasmallthermocouplewireminimizesheat
surface should be measured over the expected radiation wave- conduction into the wire but the calorimeter should still be
length region of the source. ruggedenoughforrepeatedmeasurements.However,whenthe
thicknessofthecalorimeterisontheorderofthewirediameter
3.3 In 4.6 and 4.7, it is demonstrated that lateral heat
toobtainthenecessaryresponsecharacteristics,therecommen-
conduction effects on a local measurement can be minimized
dations of Sobolik, et al. [1989], Burnett [1961], and Kidd
by using a calorimeter material with a low thermal conductiv-
[1985] (2-4) should be followed.
ity.Alternatively, a distribution of the heat transfer rate may be
obtainedbyplacinganumberofthermocouplesalongtheback 4.2 Whenheatingstarts,theresponseoftheback(unheated)
surface of the calorimeter. surface of the calorimeter lags behind that of the front (heated)
surface. For a step change in the heat transfer rate, the initial
3.4 In high temperature or high heat transfer rate
response time of the calorimeter is the time required for the
applications, the principal drawback to the use of thin-skin
temperature rise rate of the unheated surface to approach the
calorimeters is the short exposure time necessary to ensure
temperature rise rate of the front surface within 1%. If
survival of the calorimeter such that repeat measurements can
conductionheattransferintothethermocouplewireisignored,
be made with the same sensor. When operation to burnout is
the initial response time is generally defined as:
necessary to obtain the desired heat flux measurements, thin-
ρC δ
skin calorimeters are often a good choice because they are
p
τ 5 0.5 (2)
r
relatively inexpensive to fabricate. k
where:
4. Apparatus
τ = initial response time, s, and
r
4.1 Calorimeter Design—Typicaldetailsofathin-skincalo-
rimeter used for measuring aerodynamic heat transfer rates are
shown in Fig. 1. The thermocouple wires (0.127 mm OD,
0.005 in., 36 gage) are individually welded to the back surface
The boldface numbers in parentheses refer to the list of references at the end of
of the calorimeter using spot, electron beam, or laser tech- this standard.
E459 − 05 (2016)
4.4 Determine the maximum exposure time (6) by setting a
k = thermal conductivity, W/m·K.
maximum allowable temperature for the front surface as
As an example, the 0.76 mm (0.030 in.) thick, 300 series
follows:
stainless steel calorimeter analyzed in Ref (4) has an initial
response time of 72 ms. Eq 2 can be rearranged to show that ρC δ k T 2 T 1
~ !
p max 0
τ 5 * 2 (4)
F G
max
the initial response time also corresponds to a Fourier Number
k qδ 3
(a dimensionless time) of 0.5.
where:
4.3 Conduction heat transfer into the thermocouple wire
τ = maximum exposure time, s,
max
delaysthetimepredictedbyEq2forwhichthemeasuredback
T = initial temperature, K, and
face temperature rise rate accurately follows (that is, within
T = 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
rate measurement, τ must be greater thanτ , which requires
0.76 mm (0.030 in.) thick, 300 series stainless steel
max R
calorimeter, the analysis in Ref (4) indicates the measured that:
temperature rise rate is within 2% of the undisturbed tempera-
k~T 2 T ! 5
max 0
. (5)
ture rise rate in approximately 500 ms. An estimate of the
qδ 6
measured temperature rise rate error (or slope error) can be
obtained from Ref (1) for different material combinations:
4.4.2 Determine an optimum thickness that maximizes
(τ − τ ) (7) as follows:
max R
dT dT αt αt
C TC
2 5 C exp C erfcS C D (3)
S D Œ
1 2 2 2 2
3 k~T 2 T !
dt dt R R
max 0
δ 5 (6)
opt
5 q
where:
4.4.3 Then calculate the maximum exposure time using the
T = calorimeter temperature,
C
T = measured temperature (that is, thermocouple output),
optimum thickness as follows:
TC
C = β/(8/π + β) and C =4⁄(8⁄π + βπ),
1 2
T 2 T
max 0
α = k/ρC (thermaldiffusivityofthecalorimetermaterial),
τ 5 0.48ρC k (7)
p F G
maxopt p
q
β =
=
K/ A ,
4.4.4 When it is desirable for a calorimeter to cover a range
K = k of thermocouple wire/k of calorimeter,
of heat transfer rates without being operated to burn-out,
A = α of thermocouple wire/α of calorimeter,
design the calorimeter around the largest heat-transfer rate.
R = radius of the thermocouple wire, and
This gives the thinnest calorimeter with the shortest initial
t = time.
response time (Eq 2); however, Refs (2, 3, 8, 9) all show the
Using thermal property values given in Ref (4) for the
time to a given error level between the measured and undis-
Alumel (negative) leg of the Type K thermocouple on 300
turbed temperature rise rates (left hand side of Eq 3) increases
Series stainless steel (K=1.73, A=1.56, β=1.39), Eq 3 can
as the thickness of the calorimeter decreases relative to the
be used to show that the measured rate of temperature change
thermocouple wire diameter.
(that is, the slope) is within 5% of the actual rate of
temperaturechangeinapproximately150ms.Forthiscase,the
4.5 In most applications, the value of T should be well
max
time for a 1% error in the measured temperature rise rate is
below the melting temperature to obtain a satisfactory design.
roughly 50 times as long as the initial response time predicted
Limiting the maximum temperature to 700 K will keep
by Eq 2; this ratio depends on the thermophysical properties of
radiation losses below 15 kW/m . For a maximum temperature
the calorimeter and thermocouple materials (see Table 1).
rise (T − T ) of 400 K, Fig. 2 shows the optimum thickness
max 0
4.3.1 When the heat transfer rate varies with time, the
of copper and stainless steel calorimeters as a function of the
thin-skin calorimeter should be designed so the response times
heat-transfer rate.The maximum exposure time of an optimum
defined using Eq 2 and 3 are smaller than the time for
thickness calorimeter for a 400 K temperature rise is shown as
significant variations in the heat transfer rate. If this is not
a function of the heat-transfer rate in Fig. 3.
possible, methods for unfolding the dynamic measurement
errors (1,5) should be used to compensate the temperature
4.6 The one-dimensional heat flow assumption used in 2.2
measurements before calculating the heat flux using Eq 1.
and 4.3–4.4 is valid for a uniform heat-transfer rate; however,
in practice the calorimeter will generally have a heat-transfer
ratedistributionoverthesurface.Refs (9, 10)bothconsiderthe
TABLE 1 Time Required for Different Error Levels in the
effectsoflateralheatconductioninahemisphericalcalorimeter
Unexposed Surface Temperature Rise Rate
on heat transfer measurements in a supersonic stream. For a
Error Level Due to Heat
Conduction into 10% 5%2%1% cosine shaped heat flux distribution at the stagnation-point of
Thermocouple
the hemisphere, Starner gives the lateral conduction error
Negative Leg (Alumel) of 35 ms 150 ms 945 ms 3.8 s
relative to the surface heating as
Type K on 304 Stainless
Negative Leg (Constantan) <1 ms <1 ms 1 ms 4 ms
2αt 8kt
of Type T on Copper
E 5 5 (8)
C 2 2
L
R ρC D
p
E459 − 05 (2016)
FIG. 2 Calorimeter Optimum Material Thickness as a Function of Heat Transfer Rate and Material
where: approach for evaluation of the measured rate of temperature
change. The analysis was developed for laser experiments
E = relative heat-transfer rate ratio,
where only part of the calorimeter surface was exposed to
R = radius of curvature of the body (D/2), and
t = exposure time. heating and the exposure time was long compared to the
thermal penetration time to the edges of the unexposed area
Note the lateral conduction error described in Eq 8 is not a
(penetration time calculation is similar to Eq 2 with L, the
function of the calorimeter skin thickness or the heat-transfer
distance to the edge, substituted for δ, the thickness).
rate; the magnitude of the error is shown in Fig. 4 for copper
and stainless steel. The errors for most other base metal
4.9 A device for recording the thermocouple signals with
calorimeters will fall in between these two lines. While the time is required. The response time of an analog recording
lateral conduction errors can be minimized by using materials system should be an order of magnitude smaller than the
with low thermal diffusivity and short exposure times, these calorimeter response time (see Eq 2). The sampling time of a
mayaggravatesomeoftheotherconstraints,asdescribedinEq digital recording system should be no more than 40% of the
2 and 3. Ref (9) also describes the lateral conduction errors for calorimeter response time; the 3 db frequency of any low-pass
cones and cylinders. filters in the data acquisition system should be greater than
4.7 An approximation of the lateral conduction error can be 1 h
f . 5 (10)
3db
obtainedexperimentallybycontinuingtorecordtheunexposed 2πτ 2πρC δ
p
surface temperature after the heating is removed and calculat-
where:
ing the ratio of the rates of temperature change.
h = estimated heat transfer coefficient for the experiment.
dT
cool down
dt 5. Procedure
?
E; (9)
test
?
dT
5.1 Expose the thin-skin calorimeter to the thermal environ-
dt
ment as rapidly as practical. Operate the recording system for
4.8 When the average heat transfer rate over the exposed several seconds before the exposure to provide data for
area is desired, Wedekind and Beck [1989] (11) give another
evaluating any noise in the calorimeter and data acquisition
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