1、Designation: E637 05 (Reapproved 2011)Standard Test Method forCalculation of Stagnation Enthalpy from Heat TransferTheory and Experimental Measurements of Stagnation-PointHeat Transfer and Pressure1This standard is issued under the fixed designation E637; the number immediately following the designa
2、tion 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.INTRODUCTIONThe enthalpy (energy per unit mas
3、s) determination in a hot gas aerodynamic simulation device isa difficult measurement. Even at temperatures that can be measured with thermocouples, there aremany corrections to be made at 600 K and above. Methods that are used for temperatures above therange of thermocouples that give bulk or avera
4、ge enthalpy values are energy balance (see PracticeE341), sonic flow (1, 2),2and the pressure rise method (3). Local enthalpy values (thus distribution)may be obtained by using either an energy balance probe (see Method E470), or the spectrometrictechnique described in Ref (4).1. Scope1.1 This test
5、method covers the calculation from heattransfer theory of the stagnation enthalpy from experimentalmeasurements of the stagnation-point heat transfer and stagna-tion pressure.1.2 Advantages:1.2.1 A value of stagnation enthalpy can be obtained at thelocation in the stream where the model is tested. T
6、his valuegives a consistent set of data, along with heat transfer andstagnation pressure, for ablation computations.1.2.2 This computation of stagnation enthalpy does notrequire the measurement of any arc heater parameters.1.3 Limitations and ConsiderationsThere are many fac-tors that may contribute
7、 to an error using this type of approachto calculate stagnation enthalpy, including:1.3.1 TurbulenceThe turbulence generated by adding en-ergy to the stream may cause deviation from the laminarequilibrium heat transfer theory.1.3.2 Equilibrium, Nonequilibrium, or Frozen State ofGasThe reaction rates
8、 and expansions may be such that thegas is far from thermodynamic equilibrium.1.3.3 Noncatalytic EffectsThe surface recombinationrates and the characteristics of the metallic calorimeter maygive a heat transfer deviation from the equilibrium theory.1.3.4 Free Electric CurrentsThe arc-heated gas stre
9、ammay have free electric currents that will contribute to measuredexperimental heat transfer rates.1.3.5 Nonuniform Pressure ProfileAnonuniform pressureprofile in the region of the stream at the point of the heattransfer measurement could distort the stagnation point veloc-ity gradient.1.3.6 Mach Nu
10、mber EffectsThe nondimensionalstagnation-point velocity gradient is a function of the Machnumber. In addition, the Mach number is a function of enthalpyand pressure such that an iterative process is necessary.1.3.7 Model ShapeThe nondimensional stagnation-pointvelocity gradient is a function of mode
11、l shape.1.3.8 Radiation EffectsThe hot gas stream may contributea radiative component to the heat transfer rate.1.3.9 Heat Transfer Rate MeasurementAn error may bemade in the heat transfer measurement (see Method E469 andTest Methods E422, E457, E459, and E511).1.3.10 ContaminationThe electrode mate
12、rial may be of alarge enough percentage of the mass flow rate to contribute tothe heat transfer rate measurement.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
13、 Protection.Current edition approved Oct. 1, 2011. Published April 2012. Originallyapproved in 1978. Last previous edition approved in 2005 as E637 05. DOI:10.1520/E0637-05R11.2The boldface numbers in parentheses refer to the list of references appended tothis method.1Copyright ASTM International, 1
14、00 Barr Harbor Drive, PO Box C700, West Conshohocken, PA 19428-2959, United States.1.4 The values stated in SI units are to be regarded asstandard. No other units of measurement are included in thisstandard.1.4.1 ExceptionThe values given in parentheses are forinformation only.1.5 This standard does
15、 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 Stand
16、ards:3E341 Practice for Measuring Plasma Arc Gas Enthalpy byEnergy BalanceE422 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 T
17、hin-Skin CalorimeterE469 Measuring Heat Flux Using a Multiple-Wafer Calo-rimeter4E470 Measuring Gas Enthalpy Using Calorimeter Probes4E511 Test Method for Measuring Heat Flux Using aCopper-Constantan Circular Foil, Heat-Flux Transducer3. Significance and Use3.1 The purpose of this test method is to
18、provide a standardcalculation of the stagnation enthalpy of an aerodynamicsimulation device using the heat transfer theory and measuredvalues of stagnation point heat transfer and pressure. Astagnation enthalpy obtained by this test method gives aconsistent set of data, along with heat transfer and
19、stagnationpressure for ablation computations.4. Enthalpy Computations4.1 This method of calculating the stagnation enthalpy isbased on experimentally measured values of the stagnation-point heat transfer rate and pressure distribution and theoreticalcalculation of laminar equilibrium catalytic stagn
20、ation-pointheat transfer on a hemispherical body. The equilibrium cata-lytic theoretical laminar stagnation-point heat transfer rate fora hemispherical body is as follows (5):qRPt25 KiHe Hw! (1)where:q = stagnation-point heat transfer rate, W/m2(or Btu/ft2s),Pt2= model stagnation pressure, Pa (or at
21、m),R = hemispherical nose radius, m (or ft),He= stagnation enthalpy, J/kg (or Btu/lb),Hw= wall enthalpy, J/kg (or Btu/lb), andKi= heat transfer computation constant.4.2 Low Mach Number CorrectionEq 1 is simple andconvenient to use since Kican be considered approximatelyconstant (see Table 1). Howeve
22、r, Eq 1 is based on a stagnation-point velocity gradient derived using “modified” Newtonianflow theory which becomes inaccurate for Moo0.1where:b = stagnation-point velocity gradient, s1,D = hemispherical diameter, m (or ft),U= freestream velocity, m/s (or ft/s),(bD/U)x=0= dimensionless stagnation v
23、elocity gradi-ent,KM= enthalpy computation constant,(N1/2m1/2 s)/kg or (ft3/2atm1/2s)/lb, andM = the freestream Mach number.For subsonic Mach numbers, an expression for (bD/U)x=0for a hemisphere is given in Ref (6) as follows:SbDUD x 5 05 3 0.755 M2M, 1! (4)For a Mach number of 1 or greater, (bD/U)x
24、 =0for ahemisphere based on “classical” Newtonian flow theory ispresented in Ref (7) as follows:SbDUDx 5 05 H8g21!M2 1 2g11!M2F1 1g212g21!M2 1 22gM2 2 g21!G21g21J0.5(5)3For referenced ASTM standards, visit the ASTM website, www.astm.org, orcontact ASTM Customer Service at serviceastm.org. For Annual
25、 Book of ASTMStandards volume information, refer to the standards Document Summary page onthe ASTM website.4Withdrawn. The last approved version of this historical standard is referencedon www.astm.org.TABLE 1 Heat Transfer and Enthalpy Computation Constantsfor Various GasesGasKi, kg/(N1/2m1/2s)(lb/
26、(ft3/2satm1/2)KM,(N1/2m1/2s)/kg(ft3/2satm1/2)/lb)Air 3.905 3 104(0.0461) 2561 (21.69)Argon 5.513 3 104(0.0651) 1814 (15.36)Carbon dioxide 4.337 3 104(0.0512) 2306 (19.53)Hydrogen 1.287 3 104(0.0152) 7768 (65.78)Nitrogen 3.650 3 104(0.0431) 2740 (23.20)E637 05 (2011)2A variation of (bD/U)x =0with Man
27、d g is shown in Fig.1. The value of the Newtonian dimensionless velocity gradientapproaches a constant value as the Mach number approachesinfinity:SbDUD x 5 0,M54Sg21gD(6)and thus, since g, the ratio of specific heats, is a function ofenthalpy, (bD/U)x =0is also a function of enthalpy. Again, aniter
28、ation is necessary. From Fig. 1, it can be seen that(bD/U)x =0for a hemisphere is approximately 1 for largeMach numbers and g = 1.2. KMis tabulated in Table 1 using(bD/U)x =0= 1 and Kifrom Ref (5).4.3 Mach Number Determination:4.3.1 The Mach number of a stream is a function of the totalenthalpy, the
29、 ratio of freestream pressure to the total pressure,p/pt1, the total pressure, pt1, and the ratio of the exit nozzle areato the area of the nozzle throat, A/A8. Fig. 2(a) and Fig. 2(b) arereproduced from Ref (8) for the readers convenience indetermining Mach numbers for supersonic flows.4.3.2 The su
30、bsonic Mach number may be determined fromFig. 3 (see also Test Method E511).An iteration is necessary todetermine the Mach number since the ratio of specific heats, g,is also a function of enthalpy and pressure.4.3.3 The ratio of specific heats, g, is shown as a function ofentropy and enthalpy for a
31、ir in Fig. 4 from Ref (9). S/R is thedimensionless entropy, and H/RT is the dimensionless en-thalpy.4.4 Velocity Gradient Calculation from PressureDistributionThe dimensionless stagnation-point velocitygradient may be obtained from an experimentally measuredpressure distribution by using Bernoullis
32、compressible flowequation as follows:SUUD51 2 p/pt2!g21g #0.51 2 p/pt2!g21g #0.5(7)where the velocity ratio may be calculated along the bodyfrom the stagnation point. Thus, the dimensionless stagnation-point velocity gradient, (bD/U)x =0, is the slope of the U/Uand the x/D curve at the stagnation po
33、int.4.5 Model ShapeThe nondimensional stagnation-pointvelocity gradient is a function of the model shape and the Machnumber. For supersonic Mach numbers, the heat transferrelationship between a hemisphere and other axisymmetricblunt bodies is shown in Fig. 5 (10).InFig. 5, rcis the cornerradius, rbi
34、s the body radius, rnis the nose radius, and qs,his thestagnation-point heat transfer rate on a hemisphere. For sub-sonic Mach numbers, the same type of variation is shown inFig. 6 (6).4.6 Radiation Effects:4.6.1 As this test method depends on the accurate determi-nation of the convective stagnation
35、-point heat transfer, anyradiant energy absorbed by the calorimeter surface and incor-rectly attributed to the convective mode will directly affect theoverall accuracy of the test method. Generally, the sources ofradiant energy are the hot gas stream itself or the gas heatingdevice, or both. For ins
36、tance, arc heaters operated at highpressure (10 atm or higher) can produce significant radiantfluxes at the nozzle exit plane.4.6.2 The proper application requires some knowledge ofthe radiant environment in the stream at the desired operatingconditions. Usually, it is necessary to measure the radia
37、nt heattransfer rate either directly or indirectly. The following is a listof suggested methods by which the necessary measurementscan be made.4.6.2.1 Direct Measurement with RadiometerRadiometers are available for the measurement of the incidentFIG. 1 Dimensionless Velocity Gradient as a Function o
38、f Mach Number and Ratio of Specific HeatsE637 05 (2011)3FIG. 2 (a) Variation of Area Ratio with Mach NumbersFIG. 2 (b) Variation of Area Ratio with Mach Numbers (continued)E637 05 (2011)4radiant flux while excluding the convective heat transfer. In itssimplest form, the radiometer is a slug, thin-sk
39、in, or circularfoil calorimeter with a sensing area with a coating of knownabsorptance and covered with some form of window. Thepurpose of the window is to prevent convective heat transferfrom affecting the calorimeter while transmitting the radiantenergy. The window is usually made of quartz or sap
40、phire. Thesensing surface is at the stagnation point of a test probe and islocated in such a manner that the view angle is not restricted.The basic radiometer view angle should be 120 or greater.This technique allows for immersion of the radiometer in thetest stream and direct measurement of the rad
41、iant heat transferrate. There is a major limitation to this technique, however, inthat even with high-pressure water cooling of the radiometerenclosure, the window is poorly cooled and thus the use ofwindows is limited to relatively low convective heat transferconditions or very short exposure times
42、, or both. Also, streamcontaminants coat the window and reduce its transmittance.4.6.2.2 Direct Measurement with Radiometer Mounted inCavityThe two limitations noted in 4.6.2.1 may be overcomeby mounting the radiometer at the bottom of a cavity open tothe stagnation point of the test probe (see Fig.
43、 7). Good resultsFIG. 3 Subsonic Pressure Ratio as a Function of Mach Number and gFIG. 4 Isentropic Exponent for Air in EquilibriumE637 05 (2011)5can be obtained by using a simple calorimeter in place of theradiometer with a material of known absorptance. When usingthis configuration, the measured r
44、adiant heat transfer rate isused in the following equation to determine the stagnation-point radiant heat transfer, assuming diffuse radiation:qr151a2F12qr2(8)where:qr1= radiant transfer at stagnation point,qr2= radiant transfer at bottom of cavity (measured),a2= absorptance of sensor surface, andF1
45、2= configuration factor.For a circular cavity geometry (recommended), F12isConfiguration A-3 of Ref (11) and can be determined from thefollowing equation:FIG. 5 Stagnation-Point Heating-Rate Parameters on Hemispherical Segments of Different Curvatures for Varying Corner-Radius RatiosE637 05 (2011)6F
46、125 1/2 X X24E2D2!1/2# (9)where:E = r2/d,D = d/r1,X = 1+(1+E2)D2, andr1, d, and r2are defined in Fig. 8.The major limitation of this particular technique is due toheating of the cavity opening (at the stagnation point). If thetest probe is inadequately cooled or uncooled, heating at thispoint can co
47、ntribute to the radiant heat transfer measured at thesensor and produce large errors. This method of measuring theradiant heat transfer is then limited to test conditions and probeconfigurations that allow for cooling of the probe in theFIG. 6 Stagnation-Point Heat Transfer Ratio to a Blunt Body and
48、 a Hemisphere as a Function of theBody-to-Nose Radius in a Subsonic StreamFIG. 7 Test ProbeE637 05 (2011)7stagnation area such that the cavity opening is maintained at atemperature less than about 700 K.4.6.2.3 Indirect MeasurementAt the highest convectiveheating rates, the accurate determination of
49、 the radiant fluxlevels is difficult. There are many schemes that could be usedto measure incident radiant flux indirectly. One such would bethe measurement of the radiant flux reflected from a surface inthe test stream. This technique depends primarily on theaccurate determination of surface reflectance under actual testconditions. The surface absorptance and a measurement of thesurface temperature at the point viewed by the radiant fluxmeasuring device are required so that the
