1、Designation: E 637 05Standard 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 E 637; the number immediately following the designation indicates t
2、he 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 (e) indicates an editorial change since the last revision or reapproval.INTRODUCTIONThe enthalpy (energy per unit mass) determinatio
3、n 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 average enthalpy val
4、ues are energy balance (see PracticeE 341), 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 E 470), or the spectrometrictechnique described in Ref (4).1. Scope1.1 This test method covers
5、 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. This valuegive
6、s 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 to an error
7、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 and expansio
8、ns 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 streammay have fr
9、ee 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 Number EffectsT
10、he 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 model shape.1.3.8
11、 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 E 469 andTest Methods E 422, E 457, E 459, and E 511).1.3.10 ContaminationThe electrode material may
12、 be of alarge enough percentage of the mass flow rate to contribute tothe heat transfer rate measurement.1.4 The values stated in SI units are to be regarded as thestandard. The values given in parentheses are for informationonly.1This test method is under the jurisdiction of ASTM Committee E21 on S
13、paceSimulation andApplications of Space Technology, and is the direct responsibility ofSubcommittee E21.08 on Thermal Protection.Current edition approved Sept. 15, 2005. Published November 2005. Originallyapproved in 1978. Last previous edition approved in 1998 as E 637 98.2The boldface numbers in p
14、arentheses refer to the list of references appended tothis method.1Copyright ASTM International, 100 Barr Harbor Drive, PO Box C700, West Conshohocken, PA 19428-2959, United States.1.5 This standard does not purport to address all of thesafety concerns, if any, associated with its use. It is theresp
15、onsibility 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:3E 341 Practice for Measuring Plasma Arc Gas Enthalpy byEnergy BalanceE 422 Test Method for
16、Measuring Heat Flux Using aWater-Cooled CalorimeterE 457 Test Method for Measuring Heat-Transfer Rate Usinga Thermal Capacitance (Slug) CalorimeterE 459 Test Method for Measuring Heat-Transfer Rate Usinga Thin-Skin CalorimeterE 469 Method for Measuring Heat Flux Using a Multiple-Wafer Calorimeter4E
17、470 Method for Measuring Gas Enthalpy Using Calori-metric Probes4E511 Test Method for Measuring Heat Flux Using aCopper-Constantan Circular Foil, Heat-Flux Gage3. Significance and Use3.1 The purpose of this test method is to provide a standardcalculation of the stagnation enthalpy of an aerodynamics
18、imulation 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 stagnationpressure for ablation computations.4. Enthalpy Computations4.1 Th
19、is 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 stagnation-pointheat transfer on a hemispherical body. The equilibrium cata-lyti
20、c 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 atm),R = hemispherical nose radius, m (or ft),He= stagnation enthalpy, J/kg (
21、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). However, Eq 1 is based on a stagnation-point velocity gradient derived using “mod
22、ified” 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 velocity gradi-ent,KM= enthalpy computation constant,(N1/2m1/2 s)/kg or (ft3
23、/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 =0for ahemisphere based on “classical” Newtonian flow theory ispresented i
24、n Ref (7) as follows:3For referenced ASTM standards, visit the ASTM website, www.astm.org, orcontact ASTM Customer Service at serviceastm.org. For Annual Book of ASTMStandards volume information, refer to the standards Document Summary page onthe ASTM website.4Withdrawn.TABLE 1 Heat Transfer and Ent
25、halpy Computation Constantsfor Various GasesGasKi, kg/(N1/2m1/2s)(lb/(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
26、(0.0431) 2740 (23.20)E637052SbDUDx 5 05 H8g21!M2 1 2g11!M2F1 1g212g21!M2 1 22gM2 2 g21!G21g21J0.5(5)A variation of (bD/U)x =0with Mand 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,M54Sg21g
27、D(6)and thus, since g, the ratio of specific heats, is a function ofenthalpy, (bD/U)x =0is also a function of enthalpy. Again, aniteration 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
28、/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 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
29、(a) and Fig. 2(b) arereproduced from Ref (8) for the readers convenience indetermining Mach numbers for supersonic flows.4.3.2 The subsonic Mach number may be determined fromFig. 3 (see also Test Method E511). An iteration is necessaryto determine the Mach number since the ratio of specific heats,g,
30、 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 air 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 dim
31、ensionless stagnation-point velocitygradient may be obtained from an experimentally measuredpressure distribution by using Bernoullis 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.
32、 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 point.4.5 Model ShapeThe nondimensional stagnation-pointvelocity gradient is a function of the model shape and the Machnumber. For supersonic Mach numbers, the heat tra
33、nsferrelationship between a hemisphere and other axisymmetricblunt bodies is shown in Fig. 5 (10).InFig. 5, rcis the cornerradius, rbis 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
34、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-point heat transfer, anyradiant energy absorbed by the calorimeter surface and incor-rectly attributed to the convective mode will directly affect theoverall accurac
35、y of the test method. Generally, the sources ofradiant energy are the hot gas stream itself or the gas heatingdevice, or both. For instance, arc heaters operated at highpressure (10 atm or higher) can produce significant radiantfluxes at the nozzle exit plane.FIG. 1 Dimensionless Velocity Gradient a
36、s a Function of Mach Number and Ratio of Specific HeatsE637053FIG. 2 (a) Variation of Area Ratio with Mach NumbersFIG. 2 (b) Variation of Area Ratio with Mach Numbers (continued)E6370544.6.2 The proper application requires some knowledge ofthe radiant environment in the stream at the desired operati
37、ngconditions. Usually, it is necessary to measure the radiant 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 inc
38、identradiant flux while excluding the convective heat transfer. In itssimplest form, the radiometer is a slug, thin-skin, 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 tr
39、ansferfrom affecting the calorimeter while transmitting the radiantenergy. The window is usually made of quartz or sapphire. 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 12
40、0 or greater.This technique allows for immersion of the radiometer in thetest stream and direct measurement of the radiant heat transferrate. There is a major limitation to this technique, however, inthat even with high-pressure water cooling of the radiometerFIG. 3 Subsonic Pressure Ratio as a Func
41、tion of Mach Number and gFIG. 4 Isentropic Exponent for Air in EquilibriumE637055enclosure, the window is poorly cooled and thus the use ofwindows is limited to relatively low convective heat transferconditions or very short exposure times, or both. Also, streamcontaminants coat the window and reduc
42、e 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. 7). Good resultscan be obtained by using a simple calorimete
43、r in place of theradiometer with a material of known absorptance. When usingthis configuration, the measured radiant heat transfer rate isused in the following equation to determine the stagnation-point radiant heat transfer, assuming diffuse radiation:FIG. 5 Stagnation-Point Heating-Rate Parameters
44、 on Hemispherical Segments of Different Curvatures for Varying Corner-Radius RatiosE637056qr151a2F12qr2(8)where:qr1= radiant transfer at stagnation point,qr2= radiant transfer at bottom of cavity (measured),a2= absorptance of sensor surface, andF12= configuration factor.For a circular cavity geometr
45、y (recommended), F12isConfiguration A-3 of Ref (11) and can be determined from thefollowing equation:F125 1/2 X X24E2D2!1/2# (9)where:E = r2/d,D = d/r1,FIG. 6 Stagnation-Point Heat Transfer Ratio to a Blunt Body and a Hemisphere as a Function of theBody-to-Nose Radius in a Subsonic StreamFIG. 7 Test
46、 ProbeE637057X = 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 contribute to the radiant heat transfer
47、 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 thestagnation area such that the cavity opening is maintained at atemperature less than about 700 K.4.6
48、.2.3 Indirect MeasurementAt the highest convectiveheating rates, the accurate determination of 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 inth
49、e 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 radiant componentcontributed by the hot surface may be subtracted from themeasured flux, yielding the reflected radiant flux. (The basiclimitation to this method of measuring the radiant environmentis the almost c
