1、Designation: E 511 07Standard Test Method forMeasuring Heat Flux Using a Copper-Constantan CircularFoil, Heat-Flux Transducer1This standard is issued under the fixed designation E 511; the number immediately following the designation indicates the year oforiginal adoption or, in the case of revision
2、, 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 describes the measurement of radiativeheat flux using a transducer whose sensing eleme
3、nt (1, 2)2is athin circular metal foil. These sensors are often called GardonGauges.1.2 The values stated in SI units are to be regarded as thestandard. The values stated in parentheses are provided forinformation only.1.3 This standard does not purport to address all of thesafety concerns, if any,
4、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. Summary of Test Method2.1 The purpose of this test method is to facilitate measure-ment of a
5、radiant heat flux. Although the sensor will measureheat fluxes from mixed radiative convective or pure convec-tive sources, the uncertainty will increase as the convectivefraction of the total heat flux increases.2.2 The circular foil heat flux transducer generates a milli-Volt output in response to
6、 the rate of thermal energy absorbed(see Fig. 1). The perimeter of the circular metal foil sensingelement is mounted in a metal heat sink, forming a referencethermocouple junction due to their different thermoelectricpotentials. A differential thermocouple is created by a secondthermocouple junction
7、 formed at the center of the foil using afine wire of the same metal as the heat sink. When the sensingelement is exposed to a heat source, most of the heat energyabsorbed at the surface of the circular foil is conducted radiallyto the heat sink. If the heat flux is uniform and heat transferdown the
8、 center wire is neglected, a parabolic temperatureprofile is established between the center and edge of the foilunder steady-state conditions. The center perimeter tempera-ture difference produces a thermoelectric potential, E, that willvary in proportion to the absorbed heat flux, q8. With pre-scri
9、bed foil diameter, thickness, and materials, the potential Eis almost linearly proportional to the average heat flux q8absorbed by the foil. This relationship is described by thefollowing equation:E 5 Kq8 (1)where:K = a sensitivity constant determined experimentally.2.3 For nearly linear response, t
10、he heat sink and the centerwire of the transducer are made of high purity copper and thefoil of thermocouple grade Constantan. This combination ofmaterials produces a nearly linear output over a gauge tem-perature range from 45 to 232C (50 to 450F). The linearrange results from the basically offsett
11、ing effects oftemperature-dependent changes in the thermal conductivityand the Seebeck coefficient of the Constantan (3). All furtherdiscussion is based on the use of these two metals, sinceengineering practice has demonstrated they are commonly themost useful.3. Description of the Instrument3.1 Fig
12、. 1 is a sectional view of an example circular foilheat-flux transducer. It consists of a circular Constantan foilattached by a metallic bonding process to a heat sink ofoxygen-free high conductivity copper (OFHC), with copperleads attached at the center of the circular foil and at any pointon the h
13、eat-sink body. The transducer impedance is usually lessthan 1 V. To minimize current flow, the data acquisition system(DAS) should be a potentiometric system or have an inputimpedance of at least 100 000 V.3.2 As noted in 2.3, an approximately linear output (versusheat flux) is produced when the bod
14、y and center wire of thetransducer are constructed of copper and the circular foil isconstantan. Other metal combinations may be employed foruse at higher temperatures, but most (4) are nonlinear.3.3 Because the thermocouple junction at the edge of thefoil is the reference for the center thermocoupl
15、e, no coldjunction compensation is required with this instrument. Thewire leads used to convey the signal from the transducer to the1This test method is under the jurisdiction of ASTM Committee E21 on SpaceSimulation and Applications of Space Technology and is the direct responsibility ofSubcommitte
16、e E21.08 on Thermal Protection.Current edition approved Nov. 1, 2007. Published December 2007. Originallyapproved in 1973. Last previous edition approved in 2001 as E 511 01.2The boldface numbers in parentheses refer to the list of references at the end ofthis standard.1Copyright ASTM International,
17、 100 Barr Harbor Drive, PO Box C700, West Conshohocken, PA 19428-2959, United States.Copyright by ASTM Intl (all rights reserved); Wed Jan 9 22:53:16 EST 2008Downloaded/printed byGuo Dehua (CNIS) pursuant to License Agreement. No further reproductions authorized.readout device are normally made of s
18、tranded, tinned copper,insulated with TFE-fluorocarbon and shielded with a braidover-wrap that is also TFE-fluorocarbon-covered.3.4 Transducers with a heat-sink thermocouple can be usedto indicate the foil center temperature. Once the edge tempera-ture is known, the temperature difference from the f
19、oil edge toits center may be directly read from the copper-constantan(Type T) thermocouple table. This temperature difference thenis added to the body temperature, indicating the foil centertemperature.3.5 Water-Cooled Transducer:3.5.1 A water-cooled transducer should be used in anyapplication where
20、 the copper heat-sink would rise above 235C(450F) without cooling. Examples of cooled transducers areshown in Fig. 2. The coolant flow must be sufficient to preventlocal boiling of the coolant inside the transducer body, with itscharacteristic pulsations (“chugging”) of the exit flow indicat-ing tha
21、t boiling is occurring. Water-cooled transducers can usebrass water tubes and sides for better machinability andmechanical strength.3.5.2 The water pressure required for a given transducerdesign and heat-flux level depends on the flow resistance andthe shape of the internal passages. Rarely will a t
22、ransducerrequire more than a few litres of water per minute. Mostrequire only a fraction of litres per minute.3.5.3 Heat fluxes in excess of 3400 W/cm2(3000 Btu/ft2/s)may require transducers with thin internal shells for efficienttransfer of heat from the foil/heat sink into a high-velocitywater cha
23、nnel. Velocities of 15 to 30 m/s (49 to 98 ft/s) areproduced by water at 3.4 to 6.9 MPa (500 to 1000 psi). Forsuch thin shells, zirconium-copper may be used for its combi-nation of strength and high thermal conductivity.NOTE 1Changing the heat sink from pure copper to zirconium coppermay change the
24、sensitivity and the linearity of the response.3.6 Foil Coating:3.6.1 High-absorptance coatings are used when radiantenergy is to be measured. Ideally, the high-absorptance coatingshould provide a nearly diffuse absorbing surface, whereabsorption is independent of the angle of incidence of radiationo
25、n the coating. Such a coating is said to be Lambertian and thesensor output is proportional to the cosine of the angle ofincidence with respect to normal. An ideal coating also wouldhave no dependency of absorption with wavelength, approxi-mating a gray-body. Only a few coatings approach these ideal
26、characteristics.3.6.2 Most high absorptivity coatings have different absorp-tivities when exposed to hemispherically-incident or narrower-angle, incident radiation. For five coatings, measurements byAlpert, et al, showed the near-normal absorptivity was 3 to 5 %higher than the hemispherical absorpti
27、vity (5). This work alsoshowed that commercial heat flux gauge coatings generallymaintain Lambertian (Cosine Law) behavior out to incidenceangles 60 to 70 off-normal.3.6.3 Acetylene soot (total absorptance aT= 0.99) and cam-phor soot (aT= 0.98) have the disadvantages (4) of lowFIG. 1 Heat DrainEithe
28、r by Water Cooling the Body with a Surrounding Water Jacket or Conducting the Heat Away with SufficientThermal MassE511072Copyright by ASTM Intl (all rights reserved); Wed Jan 9 22:53:16 EST 2008Downloaded/printed byGuo Dehua (CNIS) pursuant to License Agreement. No further reproductions authorized.
29、oxidation resistance and poor adhesion to the transducersurface. Colloidal graphite coatings dried from acetone oralcohol solutions (aT= 0.83) are commonly used because theyadhere well to the transducer surface over a wide temperaturerange. Spray black lacquer paints (aT= 0.94 to 0.98), some ofwhich
30、 may require baking, also are used. They are intermediatein oxidation resistance and adhesion between the colloidalgraphites and soots. Colloidal graphite is commonly used as aprimer for other, higher-absorptance coatings.3.6.4 Low-absorptance metallic coatings, such as highlypolished gold or nickel
31、, may be used to reduce a transducersresponse to radiant heat. Because these coatings effectivelyincrease the foil thickness, they reduce the transducer sensitiv-ity. Gold coating also makes the transducer response nonlinearbecause the thermal conductivity of this metal changes morerapidly with temp
32、erature than that of constantan or nickel; thecoating must be thin to avoid changing the Seebeck Coeffi-cient.3.6.5 Exothermic reactions occurring at the foil surface willcause additional heating of the transducer. This effect may behighly dependent on the catalytic properties of the foil surface.Ca
33、talysis can be controlled by surface coatings (3).4. Characteristics and Limitations4.1 The principal response characteristics of a circular foilheat flux transducer are sensitivity, full-scale range, and thenominal time constant, which are established by the foilmaterial, diameter and thickness. Fo
34、r a given heat flux, thetransducer sensitivity is proportional to the temperature differ-ence between the center and edge of the circular foil. Toincrease sensitivity, the foil is made thinner or its diameter isincreased. The full-scale range of a transducer is limited by themaximum allowed temperat
35、ure at the center of the foil. Therange may be increased by making the foil smaller in diameter,or thicker. An approximate transducer time constant is propor-tional to the square of the foil radius, and is characterized by (1,3, 6):trcR2/4k (2)where the foil properties and dimensions are:t = radial
36、coordinate,r = density,c = specific heat,R = radius, andk = conductivity.4.2 Foil diameters and thicknesses are limited by typicalmanufacturing constraints. Maximum optimum foil diameter tothickness ratio is 4 to 1 for sensors less than 2.54 mm diameter.Foil diameters range from 25.4 to 0.254 mm, wi
37、th most gagesbetween 1.02 and 6.35 mm. The time constants, t, for a25.4-mm and 0.254-mm diameter foil are 6 s and 0.0006 s,respectively. For constantan, the time constant is approximatedby t = 0.0094 d2, where d is in mm. The effects of foildimensions on the nominal time constant are shown in Fig. 3
38、.Keltner and Wildin provide a detailed analysis of the sensitivityand dynamic response that includes the effect of heat transferdown the center wire (7).4.3 The radiative sensitivity of commercially availabletransducers is limited to about 2 mV/W/cm2(1.76 BTU/ft2/s).Higher sensitivities can be achie
39、ved, but the foils of moresensitive transducers are extremely fragile. The range ofcommercial transducers may be up to 10 000 W/cm2(8800BTU/ ft2/s), and typically is limited by the capacity of the heatsink for heat removal. The full-scale range is normally speci-fied as that which produces 10 mV of
40、output. This is thepotential produced by a copper-constantan transducer with atemperature difference between the foil center and edge of190C (374F). These transducers may be used to measure heatfluxes exceeding the full-scale (10 mV output) rating; however,more than 50 % over-ranging will shorten th
41、e life and possiblychange the transducer characteristics. If a transducer is usedbeyond 200 % of its full-scale rating, it should be returned tothe manufacturer for inspection and recalibration before furtherFIG. 2 Cross-Sectional View of Water-Cooled Heat-Flux GagesE511073Copyright by ASTM Intl (al
42、l rights reserved); Wed Jan 9 22:53:16 EST 2008Downloaded/printed byGuo Dehua (CNIS) pursuant to License Agreement. No further reproductions authorized.use. Care should be taken not to exceed recommended tem-perature limits to ensure linear response. This is designed for intwo ways: active cooling a
43、nd by providing a heat sink with thecopper body. The effects of foil dimensions on the transducersensitivity are shown in Fig. 4. Refs (7-9) provide moredetailed analysis of the sensitivity that includes the effects ofheat transfer down the center wire.4.4 Water-cooled sensors are recommended for an
44、y appli-cation in which the sensor body would otherwise rise above235C (450F). When applying a liquid-cooled transducer in ahot environment, it may be important to insulate the body ofthe transducer from the surrounding structure if it is also hot.This will improve the effectiveness of cooling and r
45、educe therequired liquid flow rate.4.5 The temperature of the gage body normally is low incomparison to the heat source. The resulting heat flux mea-sured by the gage is known as a “cold wall” heat flux.4.6 For measurements of purely radiant heat flux, thetransducer output signal is a direct respons
46、e to the energyabsorbed by the foil; the absorptivity of the surface of thecoating must be known to correctly calculate the incidentradiation flux (5).4.7 The circular foil transducer cannot be used for conduc-tion heat-flux measurements.4.8 The circular foil transducer should be used with greatcare
47、 for convective heat-flux measurements because (a) thereare no standardized calibration methods; (b) the uncertaintyincreases rapidly for free-stream temperatures below 1000C,although proper range selection can minimize the increase;and, (c) the uncertainty varies with the free-stream velocityvector
48、 (10,11). In shear flows, the sensors can display nonlinearresponse and high uncertainty (12,13).4.9 Error Sources:4.9.1 Radiative Heat TransferIf there is a uniform inci-dent heat flux over the foil, convective and radiative heat lossesfrom the foil surfaces are negligible, and heat transfer down t
49、hecenter wire is neglected, then the foil temperature distributionis parabolic:Tr! 5qr4kdR2 r2! (3)where:qr= absorbed radiant heat flux,d = foil thickness,R = foil radius, andk = foil conductivity.and the center to edge temperature difference is:DT 5qrR24kd(4)FIG. 3 Chart for Design of Copper-Constantan Circular Foil Heat-Flow Meters (SI Units)E511074Copyright by ASTM Intl (all rights reserved); Wed Jan 9 22:53:16 EST 2008Downloaded/printed byGuo Dehua (CNIS) pursuant to License Agreement. No further reproductions authorized.4.9.1.1 Net Radiative Heat Tra
