# ASTM E598-08 (Reapproved 2015)

Designation: E598 − 08 (Reapproved 2015)Standard Test Method forMeasuring Extreme Heat-Transfer Rates from High-EnergyEnvironments Using a Transient, Null-Point Calorimeter1This standard is issued under the fixed designation E598; the number immediately following the designation indicates the year oforiginal adoption or, in the case of 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 covers the measurement of the heat-transfer 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 positionon 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 radiant 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 × 101MJ/kg (5 × 102to greater than 2 × 104Btu/lb.), and body pressures from 105to greater than 1.5 × 107Pa (atmospheric to greater than 1.5 × 102atm). Measuredheat-transfer rates have ranged from 5.68 to 2.84 × 102MW/m2(5×102to 2.5 × 104Btu/ft2-sec).1.3 The most common use of null-point calorimeters 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 angle-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 practices and determine the applica-bility of regulatory limitations prior to use.2. Referenced Documents2.1 ASTM Standards:2E422 Test Method for Measuring Heat Flux Using a Water-Cooled CalorimeterE511 Test Method for Measuring Heat Flux Using a Copper-Constantan Circular Foil, Heat-Flux Transducer3. Terminology3.1 Symbols:a = Radius of null-point cavity, m (in.)b = Distance from front surface of null-point calorimeter tothe null-point cavity, m (in.)Cp= Specific heat capacity, J/kg–K (Btu/lb-°F)d = Diameter of null-point cavity, m (in.)k = Thermal conductivity, W/m–K (Btu/in.-sec-°F)L = Length of null-point 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 analyti-cal model, m (in.)r = Radial distance from axial centerline of null-pointcavity, 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.)α = Thermal diffusivity, m2/sec (in.2/sec)ρ = Density, kg/m3(lb⁄in.3)1This 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 approved May 1, 2015. Published June 2015. Originallyapproved in 1977. Last previous edition approved in 2008 as E598 – 08. DOI:10.1520/E0598-08R15.2For referenced ASTM standards, visit the ASTM website, www.astm.org, orcontact ASTM Customer Service at service@astm.org. For Annual Book of ASTMStandards volume information, refer to the standard’s Document Summary page onthe ASTM website.Copyright © ASTM International, 100 Barr Harbor Drive, PO Box C700, West Conshohocken, PA 19428-2959. United States14. History 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 primarily concerned with thedeviation of the temperature measured in the bottom of thecavity 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 rigorous math-ematical treatment of the deviation of the transienttemperature, Tb, on the bottom centerline of the cavity ofradius, a, and thickness, b, from the surface temperature Ts.The results of Masters and Stein indicated that the error intemperature measurement on the bottom centerline of thecavity would decrease with increasing values of a/b and alsodecrease with increasing values of the dimensionless time,αt/b2, where α is the thermal diffusity of the wall material.They also concluded that the most important factor in the errorin temperature measurement was the ratio a/b and the error wasindependent of the level of heat flux. The conclusions ofMasters and Stein may appear to be somewhat elementarycompared with our knowledge of the null-point concept today.However, the identification and documentation of the measure-ment concept was a major step in leading others to adapt thisconcept to the transient measurement of high heat fluxes inground test facilities.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 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 1.1. 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 DiCristina (3) were the first to perform anactual thermal analysis of this measurement concept. Althoughthe 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 sec 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-clude: (1) “., thermocouple outputs can yield deceivingly fast3The boldface numbers in parentheses refer to the list of references at the end ofthis test method.NOTE 1—1-Ts(0,t) = Surface temperature (x = 0) of a solid, semi-infinite slab at some time, t.NOTE 2—2-Tb(0,b,t) = Temperature at r = 0, x = b of a slab with a cylindrical cavity at some time, t, heat flux, q, the same in both cases.FIG. 1 Semi-infinite Slab with Cylindrical CavityE598 − 08 (2015)2response 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 heating rates for the minimum cavity depth.” (Note:R and Eas 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:~αt!L2#0.34.4 Powars, Kennedy, and Rindal (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 hasthe advantages of (1) measuring the radial distributions acrossthe arc jet, and (2) preserving the probe/sensor structuralintegrity for repeated measurements. This 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-ars et. al. stressed the importance of performing thermalanalyses to “characterize the response of a typical real nullpoint calorimeter to individually assess a variety of potentialerrors, .”. Powars et. al. complain that Howey a/b = 2.4, thecalculated heat flux will be 20 % higher than the actual heatflux. In more recent documentation using more accurate andsophisticated heat conduction computer codes as well as anestablished numerical inverse heat conduction equation (6), theerror in indicated heat flux is shown to be considerably higherthan 20 % and is highly time dependent.4.5 The latest and most comprehensive thermal analysis ofthe null-point 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 points and is shown in block diagramform in Fig. 2. Timewise results of normalized heat flux fordifferent physical dimensional parameters (ratios of ato 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 response 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 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 thisdifference 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 and 4) that the calculated heatflux can be considerably higher than the actual input heatflux—especially as the ratio of a/b is raised consistently 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/(αt)1/2≤ 1.8 in order that the error inindicated heat flux does not exceed one percent (6 and 7). Thisrestriction agrees well with the earlier work of Howey andDiCristina (3).4.6 Asection 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 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 thermoelements. 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 of the thermocouplewith the copper slug are generally considered to be proprietaryby the sensor manufacturers. Kidd in Ref (7) states that theattachment is made by thermal fusion 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 measurements, 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(ρCpk)1/2for OFHC copper varies less than three percent fromroom temperature to the melting point, 1356 K (1981°F); (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 calorimeters.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 theE598 − 08 (2015)3measured null-point cavity temperature, the problem to besolved is the inverse problem of heat conduction. Severalversions of the well known Cook and Felderman numericalintegration equation (9) can be used to obtain the surface heatflux as a function of time. These equations are described inSection 10.FIG. 2 Finite Element Model of Null-Point CalorimeterFIG. 3 Null-Point Calorimeter Analytical Time Response DataE598 − 08 (2015)45. 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 exposures during the mea-surement period. Heat-transfer rates ranging up to 2.84 × 102MW/m2(2.5 × 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 ablation). 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