1、Designation: E511 07 (Reapproved 2015)Standard Test Method forMeasuring Heat Flux Using a Copper-Constantan CircularFoil, Heat-Flux Transducer1This standard is issued under the fixed designation E511; the number immediately following the designation indicates the year oforiginal adoption or, in the
2、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 describes the measurement of radiativeheat flux using a transducer whos
3、e sensing element (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 con
4、cerns, 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. Summary of Test Method2.1 The purpose of this test method is to facilitate mea
5、sure-ment of a 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
6、 in response to 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 secondthermo
7、couple junction 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 t
8、ransferdown the 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, q.
9、 With prescribedfoil diameter, thickness, and materials, the potential E is almostlinearly proportional to the average heat flux q absorbed by thefoil. This relationship is described by the following equation:E 5 Kq (1)where:K = a sensitivity constant determined experimentally.2.3 For nearly linear
10、response, the 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 basica
11、lly offsetting 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 Instru
12、ment3.1 Fig. 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 po
13、inton the heat-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 .3.2 As noted in 2.3, an approximately linear output (versusheat flux) is produced wh
14、en the body 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 t
15、hermocouple, no coldjunction compensation is required with this instrument. Thewire leads used to convey the signal from the transducer to thereadout device are normally made of stranded, tinned copper,1This test method is under the jurisdiction of ASTM Committee E21 on SpaceSimulation and Applicati
16、ons 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 1973. Last previous edition approved in 2007 as E511 07. DOI:10.1520/E0511-07R15.2The boldface numbers in parentheses
17、refer to the list of references at the end ofthis standard.Copyright ASTM International, 100 Barr Harbor Drive, PO Box C700, West Conshohocken, PA 19428-2959. United States1insulated with TFE-fluorocarbon and shielded with a braidover-wrap that is also TFE-fluorocarbon-covered.3.4 Transducers with a
18、 heat-sink thermocouple can be usedto indicate the foil center temperature. Once the edge tempera-ture is known, the temperature difference from the foil edge toits center may be directly read from the copper-constantan(Type T) thermocouple table. This temperature difference thenis added to the body
19、 temperature, indicating the foil centertemperature.3.5 Water-Cooled Transducer:3.5.1 A water-cooled transducer should be used in anyapplication where the copper heat-sink would rise above 235C(450F) without cooling. Examples of cooled transducers areshown in Fig. 2. The coolant flow must be suffici
20、ent to preventlocal boiling of the coolant inside the transducer body, with itscharacteristic pulsations (“chugging”) of the exit flow indicat-ing that boiling is occurring. Water-cooled transducers can usebrass water tubes and sides for better machinability andmechanical strength.3.5.2 The water pr
21、essure required for a given transducerdesign and heat-flux level depends on the flow resistance andthe shape of the internal passages. Rarely will a transducerrequire 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/cm
22、2(3000 Btu/ft2/s)may require transducers with thin internal shells for efficienttransfer of heat from the foil/heat sink into a high-velocitywater channel. 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 b
23、e used for its combi-nation of strength and high thermal conductivity.NOTE 1Changing the heat sink from pure copper to zirconium coppermay change the 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,
24、 the high-absorptance coatingshould provide a nearly diffuse absorbing surface, whereabsorption is independent of the angle of incidence of radiationon 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 nor
25、mal. An ideal coating also wouldhave no dependency of absorption with wavelength, approxi-mating a gray-body. Only a few coatings approach these idealcharacteristics.3.6.2 Most high absorptivity coatings have different absorp-tivities when exposed to hemispherically-incident or narrower-angle, incid
26、ent radiation. For five coatings, measurements byAlpert, et al, showed the near-normal absorptivity was 3 to 5 %higher than the hemispherical absorptivity (5). This work alsoshowed that commercial heat flux gauge coatings generallymaintain Lambertian (Cosine Law) behavior out to incidenceangles 60 t
27、o 70 off-normal.3.6.3 Acetylene soot (total absorptance T= 0.99) and cam-phor soot (T= 0.98) have the disadvantages (4) of lowFIG. 1 Heat DrainEither by Water Cooling the Body with a Surrounding Water Jacket or Conducting the Heat Away with SufficientThermal MassE511 07 (2015)2oxidation resistance a
28、nd poor adhesion to the transducersurface. Colloidal graphite coatings dried from acetone oralcohol solutions (T= 0.83) are commonly used because theyadhere well to the transducer surface over a wide temperaturerange. Spray black lacquer paints (T= 0.94 to 0.98), some ofwhich may require baking, als
29、o 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, may be used to reduce
30、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 temperature than that of con
31、stantan 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.Catalysis can be controlle
32、d 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. For a given heat flux, the
33、transducer 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 temperature at the center of the
34、 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):cR2/4k (2)where the foil properties and dimensions are: = radial coordinate, = density,c = s
35、pecific 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, with most gagesbetween 1.02 an
36、d 6.35 mm. The time constants, , 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 = 0.0094 d2, where d is in mm. The effects of foildimensions on the nominal time constant are shown in Fig. 3.Keltner andWildin provide a de
37、tailed 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 BTUft2/s).Higher sensitivities can be achieved, but the foils of moresensiti
38、ve 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 output. This is thepotential prod
39、uced 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 the life and possiblychange the tra
40、nsducer 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 GagesE511 07 (2015)3use. Care should be taken not to exceed recommended
41、 tem-perature limits to ensure linear response. This is designed for intwo ways: active cooling and 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
42、 the effects ofheat transfer down the center wire.4.4 Water-cooled sensors are recommended for any 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
43、 the surrounding structure if it is also hot.This will improve the effectiveness of cooling and reduce 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.
44、4.6 For measurements of purely radiant heat flux, thetransducer output signal is a direct response 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
45、conduc-tion heat-flux measurements.4.8 The circular foil transducer should be used with greatcare 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 select
46、ion can minimize the increase;and, (c) the uncertainty varies with the free-stream velocityvector (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, co
47、nvective and radiative heat lossesfrom the foil surfaces are negligible, and heat transfer down thecenter wire is neglected, then the foil temperature distributionis parabolic:Tr! 5qr4kR22 r2! (3)where:qr= absorbed radiant heat flux, = foil thickness,R = foil radius, andk = foil conductivity.and the
48、 center to edge temperature difference is:FIG. 3 Chart for Design of Copper-Constantan Circular Foil Heat-Flow Meters (SI Units)E511 07 (2015)4T 5qrR24k(4)4.9.1.1 Net Radiative Heat TransferFor calibrations oftransducers at low heat fluxes, the net radiant heat flux varieswith radial position on the
49、 foil due to reradiation. For anominal full-scale output of 10 mV, the center-to-edge tem-perature difference is approximately 150 K. If this foil tem-perature variation is significant with respect to the sourcetemperature, the uncertainty will increase. For example, if theheat sink temperature is 300 K, reradiation from the center ofthe foil (450 K) will be 2 to 2.5 kW/m2while at the edge of thefoil it is only 20 % of the center level. For incident blackbodyheat fluxes of 50 and 150 kW/m2, the blackbody temperaturesare approximately 1
