# ASTM E458-08 (Reapproved 2015)

Designation: E458 − 08 (Reapproved 2015)Standard Test Method forHeat of Ablation1This standard is issued under the fixed designation E458; 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.This standard has been approved for use by agencies of the U.S. Department of Defense.1. Scope1.1 This test method covers determination of the heat ofablation of materials subjected to thermal environments requir-ing the use of ablation as an energy dissipation process. Threeconcepts of the parameter are described and defined: cold wall,effective, and thermochemical heat of ablation.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-priate safety and health practices and determine the applica-bility of regulatory limitations 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 CalorimeterE457 Test Method for Measuring Heat-Transfer Rate Usinga Thermal Capacitance (Slug) CalorimeterE459 Test Method for Measuring Heat Transfer Rate Usinga Thin-Skin CalorimeterE511 Test Method for Measuring Heat Flux Using a Copper-Constantan Circular Foil, Heat-Flux TransducerE617 Specification for Laboratory Weights and PrecisionMass Standards3. Terminology3.1 Descriptions of Terms Specific to This Standard:3.1.1 heat of ablation—a parameter that indicates the abilityof a material to provide heat protection when used as asacrificial thermal protection device. The parameter is a func-tion of both the material and the environment to which it issubjected. In general, it is defined as the incident heat dissi-pated by the ablative material per unit of mass removed, orQ* 5 q/m (1)where:Q* = heat of ablation, kJ/kg,q = incident heat transfer rate, kW/m2, andm = total mass transfer rate, kg/m2·s.3.1.2 The heat of ablation may be represented in threedifferent ways depending on the investigator’s requirements:3.1.3 cold-wall heat of ablation—The most commonly andeasily determined value is the cold-wall heat of ablation, and isdefined as the incident cold-wall heat dissipated per unit massof material ablated, as follows:Q*cw5 qcw/m (2)where:Q*cw= cold-wall heat of ablation, kJ/kg,qcw= heat transfer rate from the test environment to a coldwall, kW/m2, andm = total mass transfer rate, kg/m2·s.The temperature of the cold-wall reference for the cold-wallheat transfer rate is usually considered to be room temperatureor close enough such that the hot-wall correction given in Eq8 is less than 5 % of the cold-wall heat transfer rate.3.1.4 effective heat of ablation—The effective heat of abla-tion is defined as the incident hot-wall heat dissipated per unitmass ablated, as follows:Q*eff5 qhw/m (3)where:Q*eff= effective heat of ablation, kJ/kg,qhw= heat transfer rate from the test environment to anonablating wall at the surface temperature of thematerial under test, kW/m2, andm = total mass transfer rate, kg/m2·s.3.1.5 thermochemical heat of ablation—The derivation ofthe thermochemical heat of ablation originated with thesimplistic surface energy equation employed in the early 60s todescribe the effects of surface ablation, that is:qhw2 qrr5 qcond1qabl1qblock(4)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 1972. Last previous edition approved in 2008 as E458–08. DOI:10.1520/E0458-08R15.2For 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 States1where:qrr= energy re-radiated from the heated surface, kW/m2,qcond= net energy conducted into the solid during steady-state ablation = mcp(Tw−To), kW/m2,qabl= energy absorbed by surface ablation which, insimple terms, can be represented by m∆ Hv,kW/m2,qblock= energy dissipated (blockage) by transpiration ofablation products into the boundary layer, which, insimple terms, can be represented by mη(hr− hw),kW/m2,Tw= absolute surface temperature of ablating material, K,cp= specific heat at constant pressure of ablatingmaterial, kJ/kg·K,To= initial surface temperature of ablating material, K,∆Hv= an effective heat of vaporization, kJ/kg,η = a transpiration coefficient,hr= gas recovery enthalpy, kJ/kg, andhw= the wall enthalpy, kJ/kg.Using the definitions above, Eq 4 can be rewritten as:qhw2 qrr5 mcp~Tw2 To!1m∆Hv1mη~hr2 hw! (5)where it should be apparent that the definition of the ther-mochemical heat of ablation is obtained by dividing Eq 4 bym, where it is understood that m is a steady-state ablationrate. The result is:Q*tc5 ~qhw2 qrr!/m 5 cp~Tw2 To!1∆Hv1η~hr2 hw! (6)As seen from Eq 6, definition of the thermochemical heatof ablation requires an ability to measure the cold-wall heatflux, an ability to define the recovery enthalpy, an ability tomeasure the surface temperature, knowledge of the totalhemispherical emittance (at the temperature and state of theablating surface), and the ability to determine the steady-state mass loss rate. Assuming these parameters can be mea-sured (or estimated), the right hand side of Eq 6 implies thatthe thermochemical heat of ablation is a linear function ofthe enthalpy difference across the boundary layer, that is,(hr− hw). Consequently, a plot of Q*tc(determined from sev-eral tests at different conditions) versus (hr− hw) shouldallow a linear fit of the data where the slope of the fit is in-terpreted as η, the transpiration coefficient, and they-intercept is interpreted as cp∆ T + ∆Hv. If the specific heatof the material is known, the curve fit allows the effectiveheat of vaporization to be empirically derived.3.2 The three heat of ablation values described in 3.1.2require two basic determinations: the heat transfer rate and themass transfer rate. These two quantities then assume variousforms depending on the particular heat of ablation value beingdetermined.4. Significance and Use4.1 General—The heat of ablation provides a measure of theability of a material to serve as a heat protection element in asevere thermal environment. The parameter is a function ofboth the material and the environment to which it is subjected.It is therefore required that laboratory measurements of heat ofablation simulate the service environment as closely as pos-sible. Some of the parameters affecting the heat of ablation arepressure, gas composition, heat transfer rate, mode of heattransfer, and gas enthalpy. As laboratory duplication of allparameters is usually difficult, the user of the data shouldconsider the differences between the service and the testenvironments. Screening tests of various materials under simu-lated use conditions may be quite valuable even if all theservice environmental parameters are not available. These testsare useful in material selection studies, materials developmentwork, and many other areas.4.2 Steady-State Conditions—The nature of the definition ofheat of ablation requires steady-state conditions. Variancesfrom steady-state may be required in certain circumstances;however, it must be realized that transient phenomena make thevalues obtained functions of the test duration and thereforemake material comparisons difficult.4.2.1 Temperature Requirements—In a steady-statecondition, the temperature propagation into the material willmove at the same velocity as the gas-ablation surface interface.A constant distance is maintained between the ablation surfaceand the isotherm representing the temperature front. Understeady-state ablation the mass loss and length change arelinearly related.mt 5 ρoδL1~ρo2 ρc!δc(7)where:t = test time, s,ρo= virgin material density, kg/m3,δL= change in length or ablation depth, m,ρc= char density, kg/m3, andδc= char depth, m.This relationship may be used to verify the existence ofsteady-state ablation in the tests of charring ablators.4.2.2 Exposure Time Requirements—The exposure time re-quired to achieve steady-state may be determined experimen-tally by the use of multiple models by plotting the total massloss as a function of the exposure time. The point at which thecurve departs significantly from linearity is the minimumexposure time required for steady-state ablation to be estab-lished. Cases exist, however, in the area of very high heatingrates and high shear where this type of test for steady-state maynot be possible.5. Determination of Heat Transfer Rate5.1 Cold-Wall Heat Transfer Rate:5.1.1 Determine the cold-wall heat transfer rate to a speci-men by using a calorimeter. These instruments are availablecommercially in several different types, some of which can bereadily fabricated by the investigator. Selection of a specifictype is based on the test configuration and the methods used,and should take into consideration such parameters as instru-ment response time, test duration, and heat transfer rate (13).5.1.1.1 The calorimeters discussed in 5.1.1 measure a “cold-wall” heat transfer rate because the calorimeter surface tem-perature is much less than the ablation temperature. The valuethus obtained is used directly in computing the cold-wall heatof ablation.3The boldface numbers in parentheses refer to the references listed at the end ofthe standard.E458 − 08 (2015)25.1.2 Install the calorimeter in a calorimeter body thatduplicates the test model in size and configuration. This is donein order to eliminate geometric parameters from the heattransfer rate measurement and to ensure that the quantitymeasured is representative of the heat transfer rate to the testmodel. If the particular test run does not allow an independentheat transfer rate measurement, as in some nozzle liner andpipe flow tests, mount the calorimeter as near as possible to thelocation of the mass-loss measurements. Take care to ensurethat the nonablating calorimeter does not affect the flow overthe area under test. In axisymmetric flow fields, measurementsof mass loss and heat transfer rate in the same plane, yetdiametrically opposed, should be valid.5.2 Computation of Effective and Thermochemical Heats ofAblation:5.2.1 In order to compute the effective and thermochemicalheats of ablation, correct the cold-wall heat transfer rate for theeffect of the temperature difference on the heat transfer. Thiscorrection factor is a function of the ratio of the enthalpypotentials across the boundary layer for the hot and cold wallas follows:qhw/qcw5 @~he2 hhw!/~he2 hcw!# (8)where:he= gas recovery enthalpy at the boundary layer edge,kJ/kg,hhw= gas enthalpy at the surface temperature of the testmodel, kJ/kg, andhcw= gas enthalpy at a cold wall, kJ/kg.5.2.2 This correction is based upon laminar flow in air andsubject to the restrictions imposed in Ref (2). Additionalcorrections may be required regarding the effect of temperatureon the transport properties of the test gas. The form and use ofthese corrections should be determined by the investigator foreach individual situation.5.3 Gas Enthalpy Determination:5.3.1 The enthalpy at the boundary layer edge may bedetermined in several ways: energy balance, enthalpy probe,spectroscopy, etc. Details of the methods may be foundelsewhere (3-6). Take care to evaluate the radial variation ofenthalpy in the nozzle.Also, in low-density flows, consider theeffect of nonequilibrium on the evaluation. Determination ofthe gas enthalpy at the ablator surface and the calorimetersurface requires pressure and surface temperature measure-ments. The hot-wall temperatures are generally measured byoptical methods such as pyrometers, radiometers, etc. Othermethods such as infrared spectrometers and monochromatorshave been used (7,8). Effects of the optical properties of theboundary layer of an ablating surface make accurate determi-nations of surface temperature difficult.5.3.2 Determine the wall enthalpy from the assumed state ofthe gas flow (equilibrium, frozen, or nonequilibrium), if thepressure and the wall temperature are known. It is furtherassumed that the wall enthalpy is the enthalpy of the freestreamgas, without ablation products, at the wall temperature. Makethe wall static pressure measurements with an ordinary pitotarrangement designed for the flow regime of interest and byusing the appropriate transducers.5.4 Reradiation Correction:5.4.1 Calculate the heat transfer rate due to reradiation fromthe surface of the ablating material from the following equa-tion:qrr5 σεTw4(9)where:σ = Stefan-Boltzmann constant, and,ε = thermal emittance of the ablating surface.5.4.2 Eq 9 assumes radiation through a transparent mediumto a blackbody at absolute zero. Consider the validity of thisassumption for each case and if the optical properties of theboundary layer are known and are deemed significant, or theabsolute zero blackbody sink assumption is violated, considerthese effects in the use of Eq 9.5.5 Mechanical Removal Correction:5.5.1 Determine the heat transfer rate due to the mechanicalremoval of material from the ablating surface from the mass-loss rate due to mechanical processes and the enthalpy of thematerial removed as follows:qmech5 mmechhm(10)5.5.2 Approximate the enthalpy of the material removed bythe product of the specific heat of the mechanically removedmaterial, and the surface temperature (9-13).6. Determination of Mass Transfer Rate6.1 The determination of the heat of ablation requires themeasurement of the mass transfer rate of the material undertest. This may be accomplished in several ways depending onthe type of material under test. The heat of ablation value canbe affected by the choice of method.6.1.1 Ablation Depth Method:6.1.1.1 The simplest method of measurement of mass-lossrate is the change in length or ablation depth. Make a pretestand post-test measurement of the length and calculate themass-loss rate from the following relationship:m 5 ρo~δL/t! (11)6.1.1.2 Determine the change in length with the time of amodel under test, by using motion picture techniques. Note thatobservation of the front surface alone does not, however, verifythe existence of steady state ablation. Take care, however, toprovide appropriate reference marks for measuring the lengthchange from the film. Timing marks on the film are alsorequired to accurately determine the time parameter. Avoidusing framing speed as a reference, as it generally does