1、Designation: E457 08 (Reapproved 2015)Standard Test Method forMeasuring Heat-Transfer Rate Using a Thermal Capacitance(Slug) Calorimeter1This standard is issued under the fixed designation E457; the number immediately following the designation indicates the year oforiginal adoption or, in the case o
2、f revision, the 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-ty
3、pe calorimeterwhich assumes one-dimensional heat conduction into a cylin-drical piece of material (slug) with known physical properties.1.2 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
4、285, E422, E458, E459,and E511.1.3 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 regulatory limitatio
5、ns prior to use.2. Referenced Documents2.1 ASTM Standards:2E285 Test Method for Oxyacetylene Ablation Testing ofThermal Insulation MaterialsE422 Test Method for Measuring Heat Flux Using a Water-Cooled CalorimeterE458 Test Method for Heat of AblationE459 Test Method for Measuring Heat Transfer Rate
6、Usinga Thin-Skin CalorimeterE511 Test Method for Measuring Heat Flux Using a Copper-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
7、 and specific 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
8、 determined 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.
9、1. The apparatus 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, t
10、husapproximating 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.3.3.1 For the control volume specified in this test method, athermal energy balance during the period of ini
11、tial lineartemperature response where heat losses are assumed negligiblecan be stated as follows:Energy Received by the Calorimeter front face!5Energy Conducted Axially Into the Slugqc5 Cpl T/! 5 MCp/A!T/! (1)where:qc= calorimeter heat transfer rate, W/m2, = density of slug material, kg/m3,Cp= avera
12、ge specific heat of slug material during thetemperature rise (T), J/kgK,l = length or axial distance from front face of slug to thethermocouple location (back-face), m,T =(Tf Ti) = calorimeter slug temperature rise duringexposure to heat source (linear part of curve), K, =(f i) = time period corresp
13、onding to T tempera-ture rise, s,M = mass of the cylindrical slug, kg,A = cross-sectional area of slug, m2.1This test method is under the jurisdiction of ASTM Committee E21 on SpaceSimulation andApplications of Space Technology and is the direct responsibility ofSubcommittee E21.08 on Thermal Protec
14、tion.Current edition approved May 1, 2015. Published June 2015. Originallyapproved in 1972. Last previous edition approved in 2008 as E457 08. DOI:10.1520/E0457-08R15.2For referenced ASTM standards, visit the ASTM website, www.astm.org, orcontact ASTM Customer Service at serviceastm.org. For Annual
15、Book of ASTMStandards volume information, refer to the standards Document Summary page onthe ASTM website.Copyright ASTM International, 100 Barr Harbor Drive, PO Box C700, West Conshohocken, PA 19428-2959. United States1In order to determine the steady-state heat transfer rate witha thermal capacita
16、nce-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 temperaturetransie
17、nt 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.4This equation is based on theidealization of zero heat losses from slug to its holder.R5l2Cpk2lnS21 2q indicatedq inputD
18、(2)where:k = thermal conductivity of slug material, W/mKqindicated= q that would be measured at the back-face of theslug by Eq 1, W/m2qinput= constant qinputat the front-face of the slug begin-ning at =0,W/m23.3.3 Although the goal of good slug calorimeter design isto minimize heat losses, there can
19、 be heating 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 gr
20、eater 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 surfacecatalycity, can cause the Temperature-Time slope to decreasesignificantly more than can be accounted for
21、by the increasingheat capacity with temperature of the Copper slug alone,making it important that the slope be taken early in the processbefore the losses lower the slope too much, introducing moreerror to the downside on the heat flux calculated (see Fig. 3).The degree of losses affect the exact po
22、sition where the bestslope begins to occur, but typically it should be expected atabout time = Rcalculated by Eq 2 for qindicated/qinput= 0.99,which value of Ris abbreviated as R0.99. Fig. 2 and Fig. 3assume that “heat source on” is a step function. This is anidealization, but the reality can be sig
23、nificantly different. Forexample, in some cases a calorimeter may experience a higherheat flux prior to reaching its final position in the heat source,which can cause the initial maximum slope to be higher thanwhat is wanted for the calculation of the heat flux at the finalposition. Therefore, it is
24、 important to note that “zero” time, towhich R0.99is added to determine where to start looking forthe desired slope, is when the calorimeter has reached its finalposition where it is desired to measure the heat flux. Therefore,choosing the best place to take the slope can be very important.Should mo
25、re accurate results be required, the losses form theslug should be modeled and accounted for by a correction termin the energy balance 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 calorime
26、ter which is insulatedby a gap at the back face.6max,opt.5 0.48 lCpTfrontface/q ! (3)3“Thermophysical Properties of High Temperature Solid Materials,” TPRC,Purdue University, or “Handbook of Thermophysical Properties,” Tolukian andGoldsmith, MacMillan Press, 1961.4Ledford, R. L., Smotherman, W. E.,
27、and Kidd, C. T., “Recent Developments inHeat-Transfer Rate, Pressure, and Force Measurements for Hotshot Tunnels,”AEDC-TR-66-228 (AD645764), January 1967.5Childs, P. R. N., Greenwood, J. R., and Long, C. A., “Heat flux measurementtechniques,” Proceedings of the Institution of Mechanical Engineers, V
28、ol 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.FIG. 1 Schematic of a Thermal Capacitance (Slug) CalorimeterE457 08 (2015)2FIG.
29、2 Typical TemperatureTime Curve for Slug CalorimeterFIG. 3 TemperatureTime Curve when Heat and Other Items are Significant During Heating PhaseE457 08 (2015)3where:Tfront face= the calorimeter final front face temperatureminus the initial front face (ambient)temperature, To.3.3.5 Eq 3 is based on th
30、e optimum length of the slug whichcan be obtained by applying Eq 4 as follows:lopt.5 3 k Tfront 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 insul
31、ating gap that is employed should be small, andrecommended to be no 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 su
32、rface, 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.3.5 Since interpretation of the data obtained by this testmethod is not within the scope of this discuss
33、ion, 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 radiative heat transfer rate or combined convective/radiative heat transfer rate values, the surface reflec
34、tivity 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 measure the rate ofthermal energy per unit area transferred into a known piece ofmaterial (slug) for purposes
35、 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 manner, the measured heattransfer rate to the calorimeter can be related to that experi-enced by the test sp
36、ecimen.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 it is not water-cooled. The primary disadvantages are itsshort lifetime and relatively long cool-down tim
37、e 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 evaluation of high-temperature materials, slugcalorimeters are used to measure the heat transfer rate onvario
38、us 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 to thecalorimeter (radiative, convective, or a combination thereof)the measurement is averaged over the ca
39、lorimeter 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 energy, the heattransfer rate calorimeter would tend to average these varia-tions; therefore, the size of
40、the sensing element (that is, theslug) should be limited to small diameters 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 d
41、istribution across the heated surface can bedetermined. In this manner, 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. A
42、pparatus5.1 GeneralThe apparatus shall consist of a thermalcapacitance (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 condi
43、tions.Wherever possible, it is desirable that several measurements 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
44、 should be adhered to inthe calibration and preparation of the thermocouples. 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 succes
45、sfully used. Theerror in measurement of temperature difference between 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
46、of the slugto provide the accuracy required. During the course of opera-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 throughoutthe
47、 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 source
48、 (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 operating at
49、 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 mayE457 08 (2015)4indicate 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 minim
