1、Designation: E459 05 (Reapproved 2011)Standard Test Method forMeasuring Heat Transfer Rate Using a Thin-SkinCalorimeter1This standard is issued under the fixed designation E459; the number immediately following the designation indicates the year oforiginal adoption or, in the case of revision, the y
2、ear of last revision. A number in parentheses indicates the year of last reapproval. Asuperscript epsilon () indicates an editorial change since the last revision or reapproval.1. Scope1.1 This test method covers the design and use of a thinmetallic calorimeter for measuring heat transfer rate (also
3、called heat flux). Thermocouples are attached to the unexposedsurface of the calorimeter. A one-dimensional heat flow analy-sis is used for calculating the heat transfer rate from thetemperature measurements. Applications include aerodynamicheating, laser and radiation power measurements, and firesa
4、fety testing.1.2 Advantages:1.2.1 Simplicity of ConstructionThe calorimeter may beconstructed from a number of materials.The size and shape canoften be made to match the actual application. Thermocouplesmay be attached to the metal by spot, electron beam, or laserwelding.1.2.2 Heat transfer rate dis
5、tributions may be obtained ifmetals with low thermal conductivity, such as some stainlesssteels, are used.1.2.3 The calorimeters can be fabricated with smooth sur-faces, without insulators or plugs and the attendant temperaturediscontinuities, to provide more realistic flow conditions foraerodynamic
6、 heating measurements.1.2.4 The calorimeters described in this test method arerelatively inexpensive. If necessary, they may be operated toburn-out to obtain heat transfer information.1.3 Limitations:1.3.1 At higher heat flux levels, short test times are neces-sary to ensure calorimeter survival.1.3
7、.2 For applications in wind tunnels or arc-jet facilities,the calorimeter must be operated at pressures and temperaturessuch that the thin-skin does not distort under pressure loads.Distortion of the surface will introduce measurement errors.1.4 The values stated in SI units are to be regarded assta
8、ndard. No other units of measurement are included in thisstandard.1.4.1 ExceptionThe values given in parentheses are forinformation only.1.5 This standard does not purport to address all of thesafety concerns, if any, associated with its use. It is theresponsibility of the user of this standard to e
9、stablish appro-priate safety and health practices and determine the applica-bility of regulatory limitations prior to use.2. Summary of Test Method2.1 This test method for measuring the heat transfer rate toa metal calorimeter of finite thickness is based on the assump-tion of one-dimensional heat f
10、low, known metal properties(density and specific heat), known metal thickness, and mea-surement of the rate of temperature rise of the back (orunexposed) surface of the calorimeter.2.2 After an initial transient, the response of the calorimeteris approximated by a lumped parameter analysis:q 5rCpddT
11、dt(1)where:q = heat transfer rate, W/m2,r = metal density, kg/m3,d = metal thickness, m,Cp= metal specific heat, J/kgK, anddT/dt = back surface temperature rise rate, K/s.3. Significance and Use3.1 This test method may be used to measure the heattransfer rate to a metallic or coated metallic surface
12、 for avariety of applications, including:3.1.1 Measurements of aerodynamic heating when the calo-rimeter is placed into a flow environment, such as a windtunnel or an arc jet; the calorimeters can be designed to havethe same size and shape as the actual test specimens tominimize heat transfer correc
13、tions;3.1.2 Heat transfer measurements in fires and fire safetytesting;3.1.3 Laser power and laser absorption measurements; aswell as,3.1.4 X-ray and particle beam (electrons or ions) dosimetrymeasurements.3.2 The thin-skin calorimeter is one of many concepts usedto measure heat transfer rates. It m
14、ay be used to measureconvective, radiative, or combinations of convective and ra-diative (usually called mixed or total) heat transfer rates.1This test method is under the jurisdiction of ASTM Committee E21 on SpaceSimulation and Applications of Space Technology and is the direct responsibility ofSu
15、bcommittee E21.08 on Thermal Protection.Current edition approved Oct. 1, 2011. Published April 2012. Originallyapproved in 1972. Last previous edition approved in 2005 as E459 05. DOI:10.1520/E0459-05R11.1Copyright ASTM International, 100 Barr Harbor Drive, PO Box C700, West Conshohocken, PA 19428-2
16、959, United States.However, when the calorimeter is used to measure radiative ormixed heat transfer rates, the absorptivity and reflectivity of thesurface should be measured over the expected radiation wave-length region of the source.3.3 In 4.6 and 4.7, it is demonstrated that lateral heatconductio
17、n effects on a local measurement can be minimizedby using a calorimeter material with a low thermal conductiv-ity.Alternatively, a distribution of the heat transfer rate may beobtained by placing a number of thermocouples along the backsurface of the calorimeter.3.4 In high temperature or high heat
18、transfer rate applica-tions, the principal drawback to the use of thin-skin calorim-eters is the short exposure time necessary to ensure survival ofthe calorimeter such that repeat measurements can be madewith the same sensor. When operation to burnout is necessaryto obtain the desired heat flux mea
19、surements, thin-skin calo-rimeters are often a good choice because they are relativelyinexpensive to fabricate.4. Apparatus4.1 Calorimeter DesignTypical details of a thin-skin calo-rimeter used for measuring aerodynamic heat transfer rates areshown in Fig. 1. The thermocouple wires (0.127 mm OD,0.00
20、5 in., 36 gage) are individually welded to the back surfaceof the calorimeter using spot, electron beam, or laser tech-niques. This type of thermocouple joint (called an intrinsicthermocouple) has been found to provide superior transientresponse as compared to a peened joint or a beaded thermo-coupl
21、e that is soldered to the surface (1, 2).2The wires shouldbe positioned approximately 1.6 mm apart along an expectedisotherm. The use of a small thermocouple wire minimizes heatconduction into the wire but the calorimeter should still berugged enough for repeated measurements. However, when thethick
22、ness of the calorimeter is on the order of the wire diameterto obtain the necessary response characteristics, the recommen-dations of Sobolik, et al. 1989, Burnett 1961, and Kidd1985 (2-4) should be followed.4.2 When heating starts, the response of the back (unheated)surface of the calorimeter lags
23、behind that of the front (heated)surface. For a step change in the heat transfer rate, the initialresponse time of the calorimeter is the time required for thetemperature rise rate of the unheated surface to approach thetemperature rise rate of the front surface within 1 %. Ifconduction heat transfe
24、r into the thermocouple wire is ignored,the initial response time is generally defined as:tr5 0.5rCpd2k(2)where:tr= initial response time, s, andk = thermal conductivity, W/mK.As an example, the 0.76 mm (0.030 in.) thick, 300 series2The boldface numbers in parentheses refer to the list of references
25、 at the end ofthis standard.FIG. 1 Typical Thin-Skin Calorimeter for Heat Transfer MeasurementE459 05 (2011)2stainless steel calorimeter analyzed in Ref (4) has an initialresponse time of 72 ms. Eq 2 can be rearranged to show thatthe initial response time also corresponds to a Fourier Number(a dimen
26、sionless time) of 0.5.4.3 Conduction heat transfer into the thermocouple wiredelays the time predicted by Eq 2 for which the measured backface temperature rise rate accurately follows (that is, within1 %) the undisturbed back face temperature rise rate. For a0.127 mm (0.005 in.) OD, Type K intrinsic
27、 thermocouple on a0.76 mm (0.030 in.) thick, 300 series stainless steel calorim-eter, the analysis in Ref (4) indicates the measured temperaturerise rate is within 2 % of the undisturbed temperature rise ratein approximately 500 ms. An estimate of the measured tem-perature rise rate error (or slope
28、error) can be obtained fromRef (1) for different material combinations:dTCdt2dTTCdt5 C1expSC22atR2 DerfcSC2 atR2 D(3)where:TC= calorimeter temperature,TTC= measured temperature (that is, thermocouple out-put),C1= b/(8/p2+ b) and C2= 4/(8/p + bp),a = k/rCp(thermal diffusivity of the calorimeter mate-
29、rial),b = K/=A ,K = k of thermocouple wire/k of calorimeter,A = a of thermocouple wire/a of calorimeter,R = radius of the thermocouple wire, andt = time.Using thermal property values given in Ref (4) for the Alumel(negative) leg of the Type K thermocouple on 300 Seriesstainless steel (K = 1.73, A =
30、1.56, b = 1.39), Eq 3 can be usedto show that the measured rate of temperature change (that is,the slope) is within 5 % of the actual rate of temperaturechange in approximately 150 ms. For this case, the time for a1 % error in the measured temperature rise rate is roughly 50times as long as the init
31、ial response time predicted by Eq 2; thisratio depends on the thermophysical properties of the calorim-eter and thermocouple materials (see Table 1).4.3.1 When the heat transfer rate varies with time, thethin-skin calorimeter should be designed so the response timesdefined using Eq 2 and 3 are small
32、er than the time forsignificant variations in the heat transfer rate. If this is notpossible, methods for unfolding the dynamic measurementerrors (1,5) should be used to compensate the temperaturemeasurements before calculating the heat flux using Eq 1.4.4 Determine the maximum exposure time (6) by
33、setting amaximum allowable temperature for the front surface asfollows:tmax5rCpd2k*FkTmax2 T0!qd213G(4)where:tmax= maximum exposure time, s,T0= initial temperature, K, andTmax= maximum allowable temperature, K.4.4.1 In order to have time available for the heat transferrate measurement, tmaxmust be g
34、reater thantR, which requiresthat:kTmax2 T0!qd.56(5)4.4.2 Determine an optimum thickness that maximizes(tmax tR) (7) as follows:dopt535kTmax2 T0!q(6)4.4.3 Then calculate the maximum exposure time using theoptimum thickness as follows:tmax opt5 0.48rCpkFTmax2 T0qG2(7)4.4.4 When it is desirable for a
35、calorimeter to cover a rangeof heat transfer rates without being operated to burn-out,design the calorimeter around the largest heat-transfer rate.This gives the thinnest calorimeter with the shortest initialresponse time (Eq 2); however, Refs (2, 3, 8, 9) all show thetime to a given error level bet
36、ween the measured and undis-turbed temperature rise rates (left hand side of Eq 3) increasesas the thickness of the calorimeter decreases relative to thethermocouple wire diameter.4.5 In most applications, the value of Tmaxshould be wellbelow the melting temperature to obtain a satisfactory design.L
37、imiting the maximum temperature to 700 K will keepradiation losses below 15 kW/m2. For a maximum temperaturerise (Tmax T0) of 400 K, Fig. 2 shows the optimum thicknessof copper and stainless steel calorimeters as a function of theheat-transfer rate. The maximum exposure time of an optimumthickness c
38、alorimeter for a 400 K temperature rise is shown asa function of the heat-transfer rate in Fig. 3.4.6 The one-dimensional heat flow assumption used in 2.2and 4.34.4 is valid for a uniform heat-transfer rate; however,in practice the calorimeter will generally have a heat-transferrate distribution ove
39、r the surface. Refs (9, 10) both consider theeffects of lateral heat conduction in a hemispherical calorimeteron heat transfer measurements in a supersonic stream. For acosine shaped heat flux distribution at the stagnation-point ofthe hemisphere, Starner gives the lateral conduction errorrelative t
40、o the surface heating asECL52atR258ktrCpD2(8)where:E = relative heat-transfer rate ratio,R = radius of curvature of the body (D/2), andt = exposure time.TABLE 1 Time Required for Different Error Levels in theUnexposed Surface Temperature Rise RateError Level Due to HeatConduction intoThermocouple10%
41、5%2%1%Negative Leg (Alumel) ofType K on 304 Stainless35 ms 150 ms 945 ms 3.8 sNegative Leg (Constantan)of Type T on Copper1 ms 1 ms 1 ms 4 msE459 05 (2011)3Note the lateral conduction error described in Eq 8 is not afunction of the calorimeter skin thickness or the heat-transferrate; the magnitude o
42、f the error is shown in Fig. 4 for copperand stainless steel. The errors for most other base metalcalorimeters will fall in between these two lines. While thelateral conduction errors can be minimized by using materialswith low thermal diffusivity and short exposure times, thesemay aggravate some of
43、 the other constraints, as described in Eq2 and 3. Ref (9) also describes the lateral conduction errors forcones and cylinders.4.7 An approximation of the lateral conduction error can beobtained experimentally by continuing to record the unexposedsurface temperature after the heating is removed and
44、calculat-ing the ratio of the rates of temperature change.E ;dTdt|cool downdTdt|test(9)4.8 When the average heat transfer rate over the exposedarea is desired, Wedekind and Beck 1989 (11) give anotherapproach for evaluation of the measured rate of temperaturechange. The analysis was developed for la
45、ser experimentswhere only part of the calorimeter surface was exposed toheating and the exposure time was long compared to thethermal penetration time to the edges of the unexposed area(penetration time calculation is similar to Eq 2 with L, thedistance to the edge, substituted for d, the thickness)
46、.4.9 A device for recording the thermocouple signals withtime is required. The response time of an analog recordingsystem should be an order of magnitude smaller than thecalorimeter response time (see Eq 2). The sampling time of adigital recording system should be no more than 40 % of thecalorimeter
47、 response time; the 3 db frequency of any low-passfilters in the data acquisition system should be greater thanf3db.12pt5h2prCpd(10)where:h = estimated heat transfer coefficient for the experiment.5. Procedure5.1 Expose the thin-skin calorimeter to the thermal environ-ment as rapidly as practical. O
48、perate the recording system forseveral seconds before the exposure to provide data forevaluating any noise in the calorimeter and data acquisitionsystem. Operate it for enough time after the exposure to obtainan estimate of the lateral heat conduction effects as indicated in4.7.5.2 Cool the calorime
49、ter to the initial temperature beforerepeating the measurements.FIG. 2 Calorimeter Optimum Material Thickness as a Function of Heat Transfer Rate and MaterialE459 05 (2011)45.3 Take enough measurements with the same calorimeter ata particular test condition to obtain an estimate of the repro-ducibility of the technique. The density and thickness of thecalorimeter material may be determined with good accuracy. Ifthe calorimeter is used over temperature ranges where thespecific heat of the calorimeter material is well established; theFIG. 3 Maximum Exposure Time
