1、Designation: E 457 96 (Reapproved 2002)Standard 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
2、 of revision, the year of last revision. 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 describes the measurement of heattransfer rate using a thermal capacitance
3、-type calorimeterwhich 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
4、 establish appro-priate 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 as thestandard.NOTE 1For information see Test Methods E 285, E 422, E 458,E 459, and E 511.2. Referenced Documents2.1 ASTM
5、Standards:E 285 Test Method for Oxyacetylene Ablation Testing ofThermal Insulation Materials2E 422 Test Method for Measuring Heat Flux Using aWater-Cooled Calorimeter2E 458 Test Method for Heat of Ablation2E 459 Test Method for Measuring Heat Transfer Rate Usinga Thin-Skin Calorimeter2E511 Test Meth
6、od for Measuring Heat Flux Using aCopper-Constantan Circular Foil, Heat-Flux Gage23. 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 specific heat of the slug material,3.1.2 Le
7、ngth 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 determined numerically bymultiplying the densit
8、y, 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 apparatus shown is a typical slug calorim
9、eter 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, thusapproximating one-dimensional heat flow. The
10、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 and Applications of Space Technology and is the direct responsibility o
11、fSubcommittee E21.08 on Thermal Protection.Current edition approved May 10, 2002. Published December 1996. Originallypublished as E 457 72. Last previous edition E 457 72 (1990)e1.2Annual Book of ASTM Standards, Vol 15.03.1Copyright ASTM International, 100 Barr Harbor Drive, PO Box C700, West Consho
12、hocken, PA 19428-2959, United States.3.3.1 For the control volume specified in this test method, athermal energy balance during the period of initial lineartemperature response can be stated as follows:Energy Received by the Calorimeter front face! (1)5 Energy Conducted Axially Into the Slugqc5rCpl
13、DT/Dt! 5 MCp/A! DT/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) = cal
14、orimeter slug temperature 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
15、 capacitance-type 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 temperatu
16、retransient effects 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.4tR5l2rCpkp2lnS21 2q indicatedq inputD(2)where:k = thermal conductivity of slug material, W/mK3.3.3 For maximum
17、linear test time (temperaturetimecurve) within an allowed surface temperature limit, the relationshown as Eq 3 may be used for a calorimeter which is insulatedby a gap at the back face.5tmax,opt.5 0.48 rlCpDTfrontface/q! (3)where:DTfront face= the calorimeter final front face tempera-ture minus the
18、initial front face (ambi-ent) temperature, To.3.3.4 Eq 3 is based on the optimum length of the slug whichcan be obtained by applying Eq 4 as 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 a
19、ninsulating gap or a low thermal diffusivity material, or both.The insulating gap that is employed should be small, andrecommended to be no more than 0.05 mm on the radius. Thus,3“Thermophysical Properties of High Temperature Solid Materials,” TPRC,Purdue University, or “Handbook of Thermophysical P
20、roperties,” Tolukian andGoldsmith, MacMillan Press, 1961.4Ledford, R. L., Smotherman, W. E., and Kidd, C. T., “Recent Developments inHeat-Transfer Rate, Pressure, and Force Measurements for Hotshot Tunnels,”AEDC-TR-66-228 (AD645764), January 1967.5Kirchhoff, R. H., “Calorimetric Heating-Rate Probe f
21、or Maximum-Response-Time Interval,” American Institute of Aeronautics and Astronautics Journal,AIAJA,Vol 2, No. 5, May 1964, pp. 96667.FIG. 1 Schematic of a Thermal Capacitance (Slug) CalorimeterE 457 96 (2002)2if severe pressure variations exist across the face of thecalorimeter, side heating cause
22、d 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 the calorimeter; therefore, the measuredheat transfer rate represents an average heat transfer rate overthe surface of the slug
23、.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 boundary layerreactions are not considered in this test method.3.6 If the thermal capacitance calorimeter is used to mea-sure only ra
24、diative heat transfer rate or combined convective/radiative heat transfer rate values, the surface reflectivity of thecalorimeter should be measured over the wavelength region ofinterest (depending on the source of radiant energy).4. Significance and Use4.1 The purpose of this test method is to meas
25、ure 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 are placed for evaluation. Thecalorimeter and holder size and shape should be identical tothat of the test specimen. In this man
26、ner, 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-cepts used to measure heat transfer rate. This type of calorim-eter is simple to fabricate, inexpensive, and readily installedsince
27、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 transferrate to the calorimeter, accurate measurement of the rate of risein back-face temperature is imperative.4.3 In the eval
28、uation of high-temperature materials, slugcalorimeters are used to measure the heat transfer rate onvarious parts of the instrumented models, since heat transferrate is one of the important parameters in evaluating theperformance of ablative materials.4.4 Regardless of the source of thermal energy t
29、o thecalorimeter (radiative, convective, or a combination thereof)the measurement is averaged over the calorimeter surface. If asignificant percentage of the total thermal energy is radiative,consideration should be given to the emissivity of the slugsurface. If non-uniformities exist in the input e
30、nergy, 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 diameters in order to measureFIG. 2 Typical TemperatureTime Curve for Slug CalorimeterE 457 96 (2002)3local heat transfer rate va
31、lues.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 manner, more representative heat transferrate values can b
32、e 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 thermalcapacitance (slug) calorimeter and the necessary instrumenta-ti
33、on 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 bemade of the required parameters.5.2 Back-Face Tempera
34、ture 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 thermocouples. Attach-ment of the thermocouples should be s
35、uch 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 between theinitial and final times should not exceed 62 %.
36、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 opera-tion of the plasma arc or other heat source, care
37、must be takento minimize deposits on the calorimeter surface.5.3 Data AcquisitionThe important parameter, back-facetemperature rise, shall be automatically recorded throughoutthe calibration period. Recording speed will depend on the heattransfer rate level such that the time range shall approach th
38、etemperature 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 source (environ-ment) be at steady-state conditions prior to testing if thethermal capacitance calorimeter is to produce represe
39、ntativeheat transfer rate measurements. Make a millivolt scale cali-bration of the recorder prior to exposure of the calorimeter tothe environment. With the recorder operating at the properspeed (see 4.3), expose the calorimeter to the thermal environ-ment as rapidly as possible. After removal from
40、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 mor
41、e thanone test method for a given thermal environment. To ensurethat energy losses are minimized, the cooling rate slope shouldcompare with the heating rate slope according to the followingequation:DT/Dt! cooling#0.05 DT/Dt! heating (5)7. Heat Transfer Rate Calculation7.1 The quantities as defined b
42、y Eq 1 shall be calculatedbased on the physical properties of the slug material, dimen-sions of the slug, and the slope of the temperaturetime curveof the calorimeter. The choice of units shall be consistent withthe measured quantities. Variance analyses of thermal testconditions shall provide a sou
43、nd basis for estimation of thereproducibility of the plasma arc or heat source environment.An error analysis of the measurements used in the heat transferor energy determination is advisable.8. Report8.1 Report the following information:8.1.1 Physical properties of the slug material,8.1.2 Configurat
44、ion of the calorimeter body,8.1.3 Dimensions of the slug,8.1.4 Slope of the temperaturetime curve (linear portion),both heating and cooling histories, and8.1.5 Calculated (apparent) corrected heat transfer rate (in-cluding losses).9. Keywords9.1 calorimeter; heat transfer rate; slug calorimeter; the
45、rmalcapacitanceE 457 96 (2002)4APPENDIX(Nonmandatory Information)X1. USE OF THE CALORIMETER SELECTION NOMOGRAMX1.1 The calorimeter selection nomogram presented in thisAppendix may be used to assist instrumentation personnel inchoosing the appropriate calorimeter material, exposure time,front-face (s
46、urface) temperature rise for a given heat transferrate, or any other combination of these parameters. Thisgraphical method is intended as a guideline, not as a designcriteria, and therefore should be used with an understanding ofthe basic test method for thermal capacitance (slug) calorim-eters.X1.2
47、 The time from initial heat, t, determined using thenomogram, will indicate the total exposure time, and notnecessarily the optimum value.Average values of specific heat,Cp, thermal conductivity, k, and density, r, have been used inorder to present a simple graphical representation of the basicequat
48、ion below:t5prkCp!SDT2 qcD2(X1.1)X1.3 For the slug to provide accurate results, the slope ofthe temperature-time curve must be obtained within the linearportion of the curve as defined by the following equation:l2/2k/rCp!# # t #100 l2/k/rCp! (X1.2)NOTE X1.1The upper limit of the operating range is r
49、educed by afactor of up to 100, if the calorimeter back face is in contact with a solidinsulating material.X1.4 To use the calorimeter selection nomogram (see Fig.X1.1), the known (or assumed) parameters must be noted onthe appropriate scales (A, B, C, or D). A straight line mustconnect scales A and D, while another straight line connectsscales B and C. The crossover line (without numbers) providesthe pivot point for the two straight lines, as both must becoincident on the crossover line.E 457 96 (2002)5ASTM International takes no position respe
