1、Designation: E 598 96 (Reapproved 2002)Standard Test Method forMeasuring Extreme Heat-Transfer Rates from High-EnergyEnvironments Using a Transient, Null-Point Calorimeter1This standard is issued under the fixed designation E 598; the number immediately following the designation indicates the year o
2、foriginal adoption or, in the case 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 covers the measurement of the heat-trans
3、fer rate or the heat flux to the surface of a solid body (testsample) using the measured transient temperature rise of athermocouple located at the null point of a calorimeter that isinstalled in the body and is configured to simulate a semi-infinite solid. By definition the null point is a unique p
4、ositionon the axial centerline of a disturbed body which experiencesthe same transient temperature history as that on the surface ofa solid body in the absence of the physical disturbance (hole)for the same heat-flux input.1.2 Null-point calorimeters have been used to measure highconvective or radia
5、nt heat-transfer rates to bodies immersed inboth flowing and static environments of air, nitrogen, carbondioxide, helium, hydrogen, and mixtures of these and othergases. Flow velocities have ranged from zero (static) throughsubsonic to hypersonic, total flow enthalpies from 1.16 togreater than 4.65
6、3 101MJ/kg (5 3 102to greater than2 3 104Btu/lb.), and body pressures from 105to greater than1.5 3 107Pa (atmospheric to greater than 1.5 3 102atm).Measured heat-transfer rates have ranged from 5.68 to2.84 3 102MW/m2(5 3 102to 2.5 3 104Btu/ft2-sec).1.3 The most common use of null-point calorimeters
7、is tomeasure heat-transfer rates at the stagnation point of a solidbody that is immersed in a high pressure, high enthalpy flowinggas stream, with the body axis usually oriented parallel to theflow axis (zero angle-of-attack). Use of null-point calorimetersat off-stagnation point locations and for a
8、ngle-of-attack testingmay pose special problems of calorimeter design and datainterpretation.1.4 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 prac
9、tices and determine the applica-bility of regulatory limitations prior to use.2. Referenced Documents2.1 ASTM Standards:E 422 Test Method for Measuring Heat Flux Using aWater-Cooled Calorimeter2E 511 Test Method for Measuring Heat Flux Using aCopper-Constantan Circular Foil, Heat-Flux Gage23. Termin
10、ology3.1 Symbols:a = Radius of null-point cavity, m (in.)b = Distance from front surface of null-point calorimeterto the null-point cavity, m (in.)Cp= Specific heat capacity, J/kgK (Btu/lb-F)d = Diameter of null-point cavity, m (in.)k = Thermal conductivity, W/mK (Btu/in.-sec-F)L = Length of null-po
11、int calorimeter, m (in.)q = Calculated or measured heat flux or heat-transfer-rate,W/m2(Btu/ft2-sec)q0= Constant heat flux or heat-transfer-rate, W/m2(Btu/ft2-sec)R = Radial distance from axial centerline of TRAX ana-lytical model, m (in.)r = Radial distance from axial centerline of null-pointcavity
12、, m (in.)T = Temperature, K (F)Tb= Temperature on axial centerline of null point, K (F)Ts= Temperature on surface of null-point calorimeter, K(F)t = Time, secZ = Distance in axial direction of TRAX analytical model,m (in.)a = Thermal diffusivity, m2/sec (in.2/sec)r = Density, kg/m3(lb/in.3)4. Histor
13、y of Test Method4.1 From literature reviews it appears that Masters and Stein(1)3were the first to document the results of an analytical studyof the temperature effects of axial cavities drilled from thebackside of a wall which is heated on the front surface (see Fig.1). These investigators were pri
14、marily concerned with thedeviation of the temperature measured in the bottom of the1This 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 Thermal Protection.Current edition ap
15、proved Oct. 10, 1996. Published December 1996. Originallypublished as E 598 77. Last previous edition E 598 77 (1990).e12Annual Book of ASTM Standards, Vol 15.03.3The boldface numbers in parentheses refer to the list of references at the end ofthis test method.1Copyright ASTM International, 100 Barr
16、 Harbor Drive, PO Box C700, West Conshohocken, PA 19428-2959, United States.cavity from the undisturbed temperature on the heated surface.Since they were not in possession of either the computingpower or the numerical heat conduction codes now available tothe analyst, Masters and Stein performed a r
17、igorous math-ematical treatment of the deviation of the transient tempera-ture, Tb, on the bottom centerline of the cavity of radius, a, andthickness, b, from the surface temperature Ts. The results ofMasters and Stein indicated that the error in temperaturemeasurement on the bottom centerline of th
18、e cavity woulddecrease with increasing values of a/b and also decrease withincreasing values of the dimensionless time, at/b2, where a isthe thermal diffusity of the wall material. They also concludedthat the most important factor in the error in temperaturemeasurement was the ratio a/band the error
19、 was independent ofthe level of heat flux. The conclusions of Masters and Steinmay appear to be somewhat elementary compared with ourknowledge of the null-point concept today. However, theidentification and documentation of the measurement conceptwas a major step in leading others to adapt this conc
20、ept to thetransient measurement of high heat fluxes in ground testfacilities.4.2 Beck and Hurwicz (2) expanded the analysis of Mastersand Stein to include steady-state solutions and were the first tolabel the method of measurement “the null-point concept.”They effectively used a digital computer to
21、generate relativelylarge quantities of analytical data from numerical methods.Beck and Hurwicz computed errors due to relatively largethermocouple wires in the axial cavity and were able to suggestthat the optimum placement of the thermocouple in the cavityoccurred when the ratio a/b was equal to 1.
22、1. However, theiranalysis like that of Masters and Stein was only concerned withthe deviation of the temperature in the axial cavity and did notaddress the error in measured heat flux.4.3 Howey and DeCristina (3) were the first to perform anactual thermal analysis of this measurement concept. Althou
23、ghthe explanation of modeling techniques is somewhat ambigu-ous in their paper, it is obvious that they used a finite element,two dimensional axisymmetric model to produce temperatureprofiles in a geometry simulating the null-point calorimeter.Temperature histories at time intervals down to 0.010 se
24、c wereobtained for a high heat-flux level on the surface of theanalytical model. Although the analytical results are notpresented in a format which would help the user/designeroptimize the sensor design, the authors did make significantgeneral conclusions about null point calorimeters. These in-clud
25、e: (1) “., thermocouple outputs can yield deceivingly fastresponse rates and erroneously high heating rates ( + 18 %)when misused in inverse one-dimensional conduction solu-tions.” (2) “The prime reason for holding the thermocoupledepth at R/E = 1.1 is to maximize thermocouple response athigh heatin
26、g rates for the minimum cavity depth.” (Note:R and E as used by Howey and DeChristina are the same termsas a and b which are defined in 4.1 and are used throughout thisdocument.) (3) A finite length null-point calorimeter body maybe considered semi-infinite for:at!L2# 0.34.4 Powers, Kennedy, and Rin
27、dal (4 and 5) were the first todocument using null point calorimeters in the swept mode.This method which is now used in almost all arc facilities hasNOTE 11-Ts(0,t) = Surface temperature (x = 0) of a solid, semi-infinite slab at some time, t.NOTE 22-Tb(0,b,t) = Temperature at r = 0, x = b of a slab
28、 with a cylindrical cavity at some time, t, heat flux, q, the same in both cases.FIG. 1 Semi-infinite Slab with Cylindrical CavityE 5982the advantages of (1) measuring the radial distributions acrossthe arc jet, and (2) preserving the probe/sensor structuralintegrity for repeated measurements. This
29、technique involvessweeping the probe/sensor through the arc-heated flow field ata rate slow enough to allow the sensor to make accuratemeasurements, yet fast enough to prevent model ablation.4.4.1 Following the pattern of Howey and DiCristina, Pow-ers et. al. stressed the importance of performing th
30、ermalanalyses to “characterize the response of a typical real nullpoint calorimeter to individually assess a variety of potentialerrors, .”. Powers et. al. complain that Howey a/b = 2.4, the calculatedheat flux will be 20 % higher than the actual heat flux. In morerecent documentation using more acc
31、urate and sophisticatedheat conduction computer codes as well as an establishednumerical inverse heat conduction equation (6), the error inindicated heat flux is shown to be considerably higher than20 % and is highly time dependent.4.5 The latest and most comprehensive thermal analysis ofthe null-po
32、int calorimeter concept was performed by Kidd anddocumented in Refs (6 and 7). This analytical work wasaccomplished by using a finite element axisymmetric heatconduction code (7). The finite element model simulating thenull-point calorimeter system is comprised of 793 finite ele-ments and 879 nodal
33、points and is shown in block diagramform in Fig. 2. Timewise results of normalized heat flux fordifferent physical dimensional parameters (ratios of a to b) aregraphically illustrated on Figs. 3 and 4. The optimum value ofthe ratio a/b is defined to be that number which yields thefastest time respon
34、se to a step heat-flux input and maintains aconstant value of indicated q/input q after the initial timeresponse period. From Figs. 3 and 4, it can be seen that thisoptimum value is about 1.4 for two families of curves forwhich the cavity radius, a, is held constant while the cavitythickness, b, is
35、varied to span a wide range of the ratio a/b. Thisis a slightly higher value than reported by earlier analysts. It isimportant to note that the analytical results do not necessarilyhave to give a value of indicated q/input q = 1.0 since thisFIG. 2 Finite Element Model of Null-Point CalorimeterE 5983
36、difference can be calibrated in the laboratory. The data graphi-cally illustrated on Figs. 3 and 4 and substantiate conclusionsdrawn by the authors of Refs (3 nd 4) that the calculated heatflux can be considerably higher than the actual input heatfluxespecially as the ratio of a/b is raised consiste
37、ntly above1.5. All of the users of null-point calorimeters assume that thedevice simulates a semi-infinite body in the time period ofinterest. Therefore, the sensor is subject to the finite bodylength, L, defined by L/(at)1/2# 1.8 in order that the error inindicated heat flux does not exceed one per
38、cent (6 and 7). Thisrestriction agrees well with the earlier work of Howey andDiCristina (3).4.6 A section view sketch of a typical null-point calorimetershowing all important components and the physical configu-ration of the sensor is shown in Fig. 5. The outside diameter is2.36 mm (0.093 in.), the
39、 length is 10.2 mm (0.40 in.), and thebody material is oxygen-free high conductivity (OFHC) cop-per. Temperature at the null point is measured by a 0.508 mm(0.020 in.) diam American National Standards Association(ANSI) type K stainless steel-sheathed thermocouple with0.102 mm (0.004 in.) diam thermo
40、elements. Although nothermocouple attachment is shown, it is assumed that theindividual thermocouple wires are in perfect contact with thebackside of the cavity and present no added thermal mass to thesystem. Details of installing thermocouples in the null pointcavity and making a proper attachment
41、of the thermocoupleFIG. 3 Null-Point Calorimeter Analytical Time Response DataFIG. 4 Null-Point Calorimeter Analytical Time Response DataE 5984with the copper slug are generally considered to be proprietaryby the sensor manufacturers. Kidd in Ref (7) states that theattachment is made by thermal fusi
42、on without the addition offoreign materials. Note that the null-point body has a smallflange at the front and back which creates an effective dead airspace along the length of the cylinder to enhance one-dimensional heat conduction and prevent radial conduction.For aerodynamic heat-transfer measurem
43、ents, the null-pointsensors are generally pressed into the stagnation position of asphere cone model of the same material (OFHC copper).4.7 The value of the lumped thermal parameter of copper isnot a strong function of temperature. In fact, the value of(rCpk)1/2for OFHC copper varies less than three
44、 percent fromroom temperature to the melting point, 1356 K (1981F); (seeFig. 6). Thermal properties of OFHC copper are well docu-mented and data from different sources are in good agreement(8). Most experimenters use the room temperature value of theparameter in processing data from null-point calor
45、imeters.4.8 The determination of surface heat flux as a function oftime and temperature requires a digital computer, programmedto calculate the correct values of heat-transfer rate. Having themeasured null-point cavity temperature, the problem to besolved is the inverse problem of heat conduction. S
46、everalversions of the well known Cook and Felderman numericalFIG. 5 Section View Sketch of Null-Point CalorimeterFIG. 6 Variation of (rCpk)1/2with TemperatureE 5985integration equation (9) can be used to obtain the surface heatflux as a function of time. These equations are described inSection 10.5.
47、 Significance and Use5.1 The purpose of this test method is to measure extremelyhigh heat-transfer rates to a body immersed in either a staticenvironment or in a high velocity fluid stream. This is usuallyaccomplished while preserving the structural integrity of themeasurement device for multiple ex
48、posures during the mea-surement period. Heat-transfer rates ranging up to 2.84 3 102MW/m2(2.5 3 104Btu/ft2-sec) (7) have been measured usingnull-point calorimeters. Use of copper null-point calorimetersprovides a measuring system with good response time andmaximum run time to sensor burnout (or abla
49、tion). Null-pointcalorimeters are normally made with sensor body diameters of2.36 mm (0.093 in.) press-fitted into the nose of an axisym-metric model.5.2 Sources of error involving the null-point calorimeter inhigh heat-flux measurement applications are extensively dis-cussed in Refs (3-7). In particular, it has been shown bothanalytically and experimentally that the thickness of the copperabove the null-point cavity is critical. If the thickness is toogreat, the time response of the instrument will not be fastenough to pick up important flow characteristics. On the oth
