1、Designation: E 457 08Standard Test Method forMeasuring Heat-Transfer Rate Using a Thermal Capacitance(Slug) Calorimeter1This standard is issued under the fixed designation E 457; the number immediately following the designation indicates the year oforiginal adoption or, in the case of revision, the
2、year 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 describes the measurement of heattransfer rate using a thermal capacitance-type calorimeterwh
3、ich assumes one-dimensional heat conduction into a cylin-drical piece of material (slug) with known physical properties.1.2 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-pr
4、iate safety and health practices and determine the applica-bility of regulatory limitations prior to use.1.3 The values stated in SI units are to be regarded asstandard. No other units of measurement are included in thisstandard.NOTE 1For information see Test Methods E 285, E 422, E 458,E 459, and E
5、 511.2. Referenced Documents2.1 ASTM Standards:2E 285 Test Method for Oxyacetylene Ablation Testing ofThermal Insulation MaterialsE 422 Test Method for Measuring Heat Flux Using aWater-Cooled CalorimeterE 458 Test Method for Heat of AblationE 459 Test Method for Measuring Heat Transfer Rate Usinga T
6、hin-Skin CalorimeterE511 Test Method for Measuring Heat Flux Using aCopper-Constantan Circular Foil, Heat-Flux Transducer3. Summary of Test Method3.1 The measurement of heat transfer rate to a slug orthermal capacitance type calorimeter may be determined fromthe following data:3.1.1 Density and spec
7、ific heat of the slug material,3.1.2 Length or axial distance from the front face of thecylindrical slug to the back-face thermocouple,3.1.3 Slope of the temperaturetime curve generated bythe back-face thermocouple, and3.1.4 Calorimeter temperature history.3.2 The heat transfer rate is thus determin
8、ed numerically bymultiplying the density, specific heat, and length of the slug bythe slope of the temperaturetime curve obtained by the dataacquisition system (see Eq 1).3.3 The technique for measuring heat transfer rate by thethermal capacitance method is illustrated schematically in Fig.1. The ap
9、paratus shown is a typical slug calorimeter which, forexample, can be used to determine both stagnation region heattransfer rate and side-wall or afterbody heat transfer ratevalues. The annular insulator serves the purpose of minimizingheat transfer to or from the body of the calorimeter, thusapprox
10、imating one-dimensional heat flow. The body of thecalorimeter is configured to establish flow and should have thesame size and shape as that used for ablation models or testspecimens.1This test method is under the jurisdiction of ASTM Committee E21 on SpaceSimulation andApplications of Space Technol
11、ogy and is the direct responsibility ofSubcommittee E21.08 on Thermal Protection.Current edition approved May 1, 2008. Published June 2008. Originallyapproved in 1972. Last previous edition approved in 2002 as E 457 96 (2002).2For referenced ASTM standards, visit the ASTM website, www.astm.org, orco
12、ntact ASTM Customer Service at serviceastm.org. For Annual Book of ASTMStandards volume information, refer to the standards Document Summary page onthe ASTM website.1Copyright ASTM International, 100 Barr Harbor Drive, PO Box C700, West Conshohocken, PA 19428-2959, United States.3.3.1 For the contro
13、l volume specified in this test method, athermal energy balance during the period of initial lineartemperature response where heat losses are assumed negligiblecan be stated as follows:Energy Received by the Calorimeter front face! (1)5 Energy Conducted Axially Into the Slugqc5rCpl DT/Dt! 5 MCp/A! D
14、T/Dt!where:qc= calorimeter heat transfer rate, W/m2,r = density of slug material, kg/m3,Cp= average specific heat of slug material during thetemperature rise (DT), J/kgK,l = length or axial distance from front face of slug tothe thermocouple location (back-face), m,DT =(Tf Ti) = calorimeter slug tem
15、perature rise dur-ing exposure to heat source (linear part of curve),K,Dt =(tf ti) = time period corresponding to DT tem-perature rise, s,M = mass of the cylindrical slug, kg,A = cross-sectional area of slug, m2.In order to determine the steady-state heat transfer rate witha thermal capacitance-type
16、 calorimeter, Eq 1 must be solved byusing the known properties of the slug material3(for example,density and specific heat)the length of the slug, and the slope(linear portion) of the temperaturetime curve obtained duringthe exposure to a heat source. The initial and final temperaturetransient effec
17、ts must be eliminated by using the initial linearportion of the curve (see Fig. 2).3.3.2 In order to calculate the initial response time for agiven slug, Eq 2 may be used.4This equation is based on theidealization of zero heat losses from slug to its holder.tR5l2rCpkp2lnS21 2q indicatedq inputD(2)wh
18、ere:k = thermal conductivity of slug material, W/mKqindicated= q that would be measured at the back-face ofthe slug by Eq 1, W/m2qinput= constant qinputat the front-face of the slugbeginning at t =0,W/m23.3.3 Although the goal of good slug calorimeter design isto minimize heat losses, there can be h
19、eating environments,such as very high heat fluxes, where even a good slugcalorimeter design cannot meet the recommended 5 % maxi-mum heat loss criterion of 6.1. Also, this criterion only dealswith heat losses measured during the cooling phase, not lossesduring the heating phase, which can be greater
20、 than the coolinglosses. Under these circumstances, significant heat losses fromslug to holder during the heating phase, as well as otherpossible decaying processes such as a drop in surface cataly-city, can cause the Temperature-Time slope to decrease signifi-cantly more than can be accounted for b
21、y the increasing heatcapacity with temperature of the Copper slug alone, making itimportant that the slope be taken early in the process before thelosses lower the slope too much, introducing more error to thedownside on the heat flux calculated (see Fig. 3). The degree oflosses affect the exact pos
22、ition where the best slope begins tooccur, but typically it should be expected at about time t = tR3“Thermophysical Properties of High Temperature Solid Materials,” TPRC,Purdue University, or “Handbook of Thermophysical Properties,” Tolukian andGoldsmith, MacMillan Press, 1961.4Ledford, R. L., Smoth
23、erman, W. E., and Kidd, C. T., “Recent Developments inHeat-Transfer Rate, Pressure, and Force Measurements for Hotshot Tunnels,”AEDC-TR-66-228 (AD645764), January 1967.FIG. 1 Schematic of a Thermal Capacitance (Slug) CalorimeterE457082calculated by Eq 2 for qindicated/qinput= 0.99, which value of tR
24、is abbreviated as tR0.99. Fig. 2 and Fig. 3 assume that “heatsource on” is a step function. This is an idealization, but thereality can be significantly different. For example, in somecases a calorimeter may experience a higher heat flux prior toreaching its final position in the heat source, which
25、can causethe initial maximum slope to be higher than what is wanted forthe calculation of the heat flux at the final position. Therefore,FIG. 2 Typical TemperatureTime Curve for Slug CalorimeterFIG. 3 TemperatureTime Curve when Heat and Other Items are Significant During Heating PhaseE457083it is im
26、portant to note that “zero” time, to which tR0.99is addedto determine where to start looking for the desired slope, iswhen the calorimeter has reached its final position where it isdesired to measure the heat flux. Therefore, choosing the bestplace to take the slope can be very important. Should mor
27、eaccurate results be required, the losses form the slug should bemodeled and accounted for by a correction term in the energybalance equation.53.3.4 For maximum linear test time (temperaturetimecurve) within an allowed surface temperature limit, the relationshown as Eq 3 may be used for a calorimete
28、r which is insulatedby a gap at the back face.6tmax,opt.5 0.48 rlCpDTfrontface/q! (3)where:DTfront face= the calorimeter final front face tempera-ture minus the initial front face (ambi-ent) temperature, To.3.3.5 Eq 3 is based on the optimum length of the slug whichcan be obtained by applying Eq 4 a
29、s follows:lopt.5 3 k DTfront face/5qc(4)3.4 To minimize side heating or side heat losses, the body isseparated physically from the calorimeter slug by means of aninsulating gap or a low thermal diffusivity material, or both.The insulating gap that is employed should be small, andrecommended to be no
30、 more than 0.05 mm on the radius. Thus,if severe pressure variations exist across the face of thecalorimeter, side heating caused by flow into or out of theinsulation gap would be minimized. Depending on the size ofthe calorimeter surface, variations in heat transfer rate mayexist across the face of
31、 the calorimeter; therefore, the measuredheat transfer rate represents an average heat transfer rate overthe surface of the slug.3.5 Since interpretation of the data obtained by this testmethod is not within the scope of this discussion, such effectsas surface recombination and thermo-chemical bound
32、ary layerreactions are not considered in this test method.3.6 If the thermal capacitance calorimeter is used to mea-sure only radiative heat transfer rate or combined convective/radiative heat transfer rate values, the surface reflectivity of thecalorimeter should be measured over the wavelength reg
33、ion ofinterest (depending on the source of radiant energy).4. Significance and Use4.1 The purpose of this test method is to measure the rate ofthermal energy per unit area transferred into a known piece ofmaterial (slug) for purposes of calibrating the thermal environ-ment into which test specimens
34、are placed for evaluation. Thecalorimeter and holder size and shape should be identical tothat of the test specimen. In this manner, the measured heattransfer rate to the calorimeter can be related to that experi-enced by the test specimen.4.2 The slug calorimeter is one of many calorimeter con-cept
35、s used to measure heat transfer rate. This type of calorim-eter is simple to fabricate, inexpensive, and readily installedsince it is not water-cooled. The primary disadvantages are itsshort lifetime and relatively long cool-down time after expo-sure to the thermal environment. In measuring the heat
36、 transferrate to the calorimeter, accurate measurement of the rate of risein back-face temperature is imperative.4.3 In the evaluation of high-temperature materials, slugcalorimeters are used to measure the heat transfer rate onvarious parts of the instrumented models, since heat transferrate is one
37、 of the important parameters in evaluating theperformance of ablative materials.4.4 Regardless of the source of thermal energy to thecalorimeter (radiative, convective, or a combination thereof)the measurement is averaged over the calorimeter surface. If asignificant percentage of the total thermal
38、energy is radiative,consideration should be given to the emissivity of the slugsurface. If non-uniformities exist in the input energy, the heattransfer rate calorimeter would tend to average these varia-tions; therefore, the size of the sensing element (that is, theslug) should be limited to small d
39、iameters in order to measurelocal heat transfer rate values.Where large ablative samples areto be tested, it is recommended that a number of calorimetersbe incorporated in the body of the test specimen such that aheat transfer rate distribution across the heated surface can bedetermined. In this man
40、ner, more representative heat transferrate values can be defined for the test specimen and thus enablemore meaningful interpretation of the test. The slug selectionmay be determined using the nomogram as a guide (seeAppendix X1).5. Apparatus5.1 GeneralThe apparatus shall consist of a thermalcapacita
41、nce (slug) calorimeter and the necessary instrumenta-tion to measure the thermal energy transferred to the calorim-eter. All calculations should use only those data taken after theheat source has achieved steady-state operating conditions.Wherever possible, it is desirable that several measurements
42、bemade of the required parameters.5.2 Back-Face Temperature MeasurementThe method oftemperature measurement must be sufficiently sensitive andreliable to ensure accurate temperature rise data for theback-face thermocouple. Procedures should be adhered to inthe calibration and preparation of the ther
43、mocouples. Attach-ment of the thermocouples should be such that the trueback-side temperatures are obtained.Although no standardizedprocedures are available, methods such as resistance welding(small spot) and peening have been successfully used. Theerror in measurement of temperature difference betw
44、een theinitial and final times should not exceed 62 %. The tempera-ture measurements shall be recorded continuously using acommercially available recorder whose frequency response isat least ten times the expected frequency response of the slugto provide the accuracy required. During the course of o
45、pera-tion of the plasma arc or other heat source, care must be takento minimize deposits on the calorimeter surface.5.3 Data AcquisitionThe important parameter, back-facetemperature rise, shall be automatically recorded throughout5Childs, P. R. N., Greenwood, J. R., and Long, C. A., “Heat flux measu
46、rementtechniques,” Proceedings of the Institution of Mechanical Engineers, Vol 213, PartC, 1999, pp. 664665.6Kirchhoff, R. H., “Calorimetric Heating-Rate Probe for Maximum-Response-Time Interval,” American Institute of Aeronautics and Astronautics Journal,AIAJA,Vol 2, No. 5, May 1964, pp. 96667.E457
47、084the calibration period. Recording speed will depend on the heattransfer rate level such that the time range shall approach thetemperature rise displacement on the recording paper. Timingmarks shall be an integral part of the recorder output.6. Procedure6.1 It is essential that the thermal energy
48、source (environ-ment) be at steady-state conditions prior to testing if thethermal capacitance calorimeter is to produce representativeheat transfer rate measurements. Make a millivolt scale cali-bration of the recorder prior to exposure of the calorimeter tothe environment. With the recorder operat
49、ing at the properspeed (see 4.3), expose the calorimeter to the thermal environ-ment as rapidly as possible. After removal from the thermalenvironment, record the back-face temperature for sufficienttime to determine the heat loss rate from the slug. Significantdifferences between the maximum and post-test values mayindicate heat conduction losses to the calorimeter body. Iffeasible, obtain more than one measurement with more thanone test method for a given thermal environment. To ensurethat energy losses are minimized, the cooling rate slope shouldcompare
