1、Designation: E459 05 (Reapproved 2016)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 smoothsurfaces, without insulators or plugs and the attendant tempera-ture discontinuities, to provide more realistic flow conditionsfor aerodynamic
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 5 CpdTd
11、(1)where:q = heat transfer rate, W/m2, = metal density, kg/m3, = metal thickness, m,Cp= metal specific heat, J/kgK, anddT/d = 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 for
12、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 corrections
13、;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.1This test method is under the jurisdiction of ASTM Committee E21 on SpaceSimulation and Applicatio
14、ns of Space Technology and is the direct responsibility ofSubcommittee E21.08 on Thermal Protection.Current edition approved April 1, 2016. Published April 2016. Originallyapproved in 1972. Last previous edition approved in 2011 as E459 05 (2011).DOI: 10.1520/E0459-05R16.Copyright ASTM International
15、, 100 Barr Harbor Drive, PO Box C700, West Conshohocken, PA 19428-2959. United States13.2 The thin-skin calorimeter is one of many concepts usedto measure heat transfer rates. It may be used to measureconvective, radiative, or combinations of convective and ra-diative (usually called mixed or total)
16、 heat transfer rates.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 heatconduct
17、ion 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 hea
18、t transfer rateapplications, the principal drawback to the use of thin-skincalorimeters is the short exposure time necessary to ensuresurvival of the calorimeter such that repeat measurements canbe made with the same sensor. When operation to burnout isnecessary to obtain the desired heat flux measu
19、rements, thin-skin calorimeters are often a good choice because they arerelatively inexpensive 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,0.005 i
20、n., 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-couple t
21、hat 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 thethicknes
22、s 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 beh
23、ind 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 transfer i
24、nto the thermocouple wire is ignored,the initial response time is generally defined as:r5 0.5Cp2k(2)where:r= initial response time, s, and2The boldface numbers in parentheses refer to the list of references at the end ofthis standard.FIG. 1 Typical Thin-Skin Calorimeter for Heat Transfer Measurement
25、E459 05 (2016)2k = thermal conductivity, W/mK.As an example, the 0.76 mm (0.030 in.) thick, 300 seriesstainless 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 dimensionles
26、s 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 thermo
27、couple on a0.76 mm (0.030 in.) thick, 300 series stainless steelcalorimeter, the analysis in Ref (4) indicates the measuredtemperature rise rate is within 2 % of the undisturbed tempera-ture rise rate in approximately 500 ms. An estimate of themeasured temperature rise rate error (or slope error) ca
28、n beobtained from Ref (1) for different material combinations:dTCdt2dTTCdt5 C1expSC22tR2 DerfcSC2tR2D (3)where:TC= calorimeter temperature,TTC= measured temperature (that is, thermocouple output),C1= /(8/2+ ) and C2=4(8 + ), = k/Cp(thermal diffusivity of the calorimeter material), =K/=A ,K = k of th
29、ermocouple wire/k of calorimeter,A = of thermocouple wire/ of calorimeter,R = radius of the thermocouple wire, andt = time.Using thermal property values given in Ref (4) for theAlumel (negative) leg of the Type K thermocouple on 300Series stainless steel (K = 1.73, A = 1.56, = 1.39), Eq 3 canbe used
30、 to show that the measured rate of temperature change(that is, the slope) is within 5 % of the actual rate oftemperature change in approximately 150 ms. For this case, thetime for a 1 % error in the measured temperature rise rate isroughly 50 times as long as the initial response time predictedby Eq
31、 2; this ratio depends on the thermophysical properties ofthe calorimeter 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 smaller than the time forsignificant va
32、riations 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 setting amaximum allowable tempera
33、ture for the front surface asfollows:max5Cp2k*FkTmax2 T0!q213G(4)where:max= 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, maxmust be greater thanR, which requiresthat:kTmax2
34、T0!q.56(5)4.4.2 Determine an optimum thickness that maximizes(max R) (7) as follows:opt535kTmax2 T0!q(6)4.4.3 Then calculate the maximum exposure time using theoptimum thickness as follows:maxopt5 0.48CpkFTmax2 T0qG2(7)4.4.4 When it is desirable for a calorimeter to cover a rangeof heat transfer rat
35、es 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 between the measured and undis-turbed temperature r
36、ise 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.Limiting the maximum temperature to 700 K will ke
37、epradiation 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 calorimeter for a 400 K temperature rise is shown
38、 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 over the surface. Refs (9, 10) both consider theeff
39、ects 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 to the surface heating asECL52tR258ktCpD2(8)TABLE
40、 1 Time Required for Different Error Levels in theUnexposed Surface Temperature Rise RateError Level Due to HeatConduction intoThermocouple10%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 (2016)3wh
41、ere:E = relative heat-transfer rate ratio,R = radius of curvature of the body (D/2), andt = exposure time.Note the lateral conduction error described in Eq 8 is not afunction of the calorimeter skin thickness or the heat-transferrate; the magnitude of the error is shown in Fig. 4 for copperand stain
42、less 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 the other constraints, as described in Eq2 and 3.
43、 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 calculat-ing the ratio of the rates of temperature
44、 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 laser experimentswhere only part of the calorimeter
45、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 , the thickness).4.9 A device for recording the thermocouple signal
46、s 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 response time; the 3 db frequency of any low-passf
47、ilters in the data acquisition system should be greater thanf3db.125h2Cp(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. Operate the recording system forseveral seconds before th
48、e exposure to provide data forevaluating any noise in the calorimeter and data acquisitionFIG. 2 Calorimeter Optimum Material Thickness as a Function of Heat Transfer Rate and MaterialE459 05 (2016)4system. Operate it for enough time after the exposure to obtainan estimate of the lateral heat conduc
49、tion effects as indicated in4.7.5.2 Cool the calorimeter to the initial temperature beforerepeating the measurements.FIG. 3 Maximum Exposure Time for an Optimum Thickness Calorimeter as a Function of Heat-Transfer Rate and MaterialFIG. 4 Radial Conduction as a Function of Time and MaterialE459 05 (2016)55.3 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 de
