1、Designation: E 459 05Standard Test Method forMeasuring Heat Transfer Rate Using a Thin-SkinCalorimeter1This standard is issued under the fixed designation E 459; the number immediately following the designation indicates the year oforiginal adoption or, in the case of revision, the year of last revi
2、sion. A number in parentheses indicates the year of last reapproval. Asuperscript epsilon (e) 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 (alsocalled heat flu
3、x). 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 firesafety testing.1.
4、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 distributions may
5、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 heating measur
6、ements.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.1.3.2 For applicat
7、ions 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 as thestandard. The
8、values given in parentheses are for informationonly.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 establish appro-priate safety and health practices and determine the applica-bility of
9、 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 flow, known metal properties(density and specific heat), known metal thickness, and me
10、a-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 5rCpddTdt(1)where:q = heat transfer rate, W/m2,r = metal density, kg/m3,d = metal thickness,
11、 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 for avariety of applications, including:3.1.1 Measurements of aerodynamic heating wh
12、en 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;3.1.2 Heat transfer measurements in fires and fire safetytesting;3.1.3 Laser po
13、wer 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 may be used to measureconvective, radiative, or combinations of convective and ra-diat
14、ive (usually called mixed or total) heat transfer rates.However, when the calorimeter is used to measure radiative or1This test method is under the jurisdiction of ASTM Committee E21 on SpaceSimulation and Applications of Space Technology and is the direct responsibility ofSubcommittee E21.08 on The
15、rmal Protection.Current edition approved Sept. 15, 2005. Published September 2005. Originallyapproved in 1972. Last previous edition approved in 1997 as E 459 97.1Copyright ASTM International, 100 Barr Harbor Drive, PO Box C700, West Conshohocken, PA 19428-2959, United States.mixed heat transfer rat
16、es, 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 heatconduction effects on a local measurement can be minimizedby using a calorimeter material with a low thermal con
17、ductiv-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 transfer rate applica-tions, the principal drawback to the use of thin-skin calorim-eters is the short
18、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 measurements, thin-skin calo-rimeters are often a good choice because they are relativelyinexpensive to fa
19、bricate.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 in., 36 gage) are individually welded to the back surfaceof the calorimeter using spot, electron beam
20、, 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 that is soldered to the surface (1, 2).2The wires shouldbe positioned approximately 1.6 mm apart alon
21、g 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 thethickness of the calorimeter is on the order of the wire diameterto obtain the necessary response characteri
22、stics, 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 behind that of the front (heated)surface. For a step change in the heat transfer rate, the initialrespo
23、nse 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 into the thermocouple wire is ignored,the initial response time is generally defined as:tr5 0.5rCpd2k
24、(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 at the end ofthis standard.FIG. 1 Typical Thin-Skin Calorimeter for Heat Transfer MeasurementE459052st
25、ainless 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 dimensionless time) of 0.5.4.3 Conduction heat transfer into the thermocouple wiredelays the time predicted by Eq 2
26、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 thermocouple on a0.76 mm (0.030 in.) thick, 300 series stainless steel calorim-eter, the analysis in Ref (4) i
27、ndicates 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 error) can be obtained fromRef (1) for different material combinations:dTCdt2dTTCdt5 C1expSC22atR2 DerfcSC2 atR
28、2 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-rial),b = K/=A ,K = k of thermocouple wire/k of calorimeter,A = a of thermocouple wire/a of calorimeter,R = rad
29、ius 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 = 1.56, b = 1.39), Eq 3 can be usedto show that the measured rate of temperature change (that is,the slope) is wi
30、thin 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 initial response time predicted by Eq 2; thisratio depends on the thermophysical properties of the calorim-eter and
31、 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 variations in the heat transfer rate. If this is notpossible, methods for unfol
32、ding 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 temperature for the front surface asfollows:tmax5rCpd2k*FkTmax2 T0!qd213G(4)where:tm
33、ax= 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 greater thantR, which requiresthat:kTmax2 T0!qd.56(5)4.4.2 Determine an optimum thickness that maximizes(tmax tR
34、) (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 calorimeter to cover a rangeof heat transfer rates without being operated to burn-out,design the calorimeter ar
35、ound 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 rise rates (left hand side of Eq 3) increasesas the thickness of
36、 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 keepradiation losses below 15 kW/m2. For a maximum temperatureris
37、e (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 asa function of the heat-transfer rate in Fig. 3.4.6 The one-d
38、imensional 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 theeffects of lateral heat conduction in a hemispherical calorimetero
39、n 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 asECL52atR258ktrCpD2(8)where:E = relative heat-transfer rate ratio,R = radius of curvatur
40、e 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%5%2%1%Negative Leg (Alumel) ofType K on 304 Stainless35 ms 150 ms 945 ms 3.8 sNegative Leg (Constantan)of Type
41、T on Copper1 ms 1 ms 1 ms 4 msE459053Note 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 stainless steel. The errors for most other base metalcalorimeters will fal
42、l 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. Ref (9) also describes the lateral conduction errors forcones and cy
43、linders.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 change.E ;dTdt|cool downdTdt|test(9)4.8 When the average heat transf
44、er 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 surface was exposed toheating and the exposure time was long compared
45、 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).4.9 A device for recording the thermocouple signals withtime is required. The response time of an analog recordingsyst
46、em 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-passfilters in the data acquisition system should be greater thanf3db.12p
47、t5h2prCpd(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 the exposure to provide data forevaluating any noise in the calor
48、imeter 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 calorimeter to the initial temperature beforerepeating the measurements.FIG. 2 Calorimeter Optimum Material Thickness as a Func
49、tion of Heat Transfer Rate and MaterialE4590545.3 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 for an Optimum Thickness Calorimeter as a Function of Heat-Transfer Rate and MaterialFIG. 4 Radial Conduction as a Function of Time
