1、Designation: E 2684 09Standard Test Method forMeasuring Heat Flux Using Surface-Mounted One-Dimensional Flat Gages1This standard is issued under the fixed designation E 2684; the number immediately following the designation indicates the year oforiginal adoption or, in the case of revision, the year
2、 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 the netheat flux normal to a surface using flat gages mounted onto t
3、hesurface. Conduction heat flux is not the focus of this standard.Conduction applications related to insulation materials arecovered by Test Method C 518 and Practices C 1041 andC 1046. The sensors covered by this test method all use ameasurement of the temperature difference between two par-allel p
4、lanes normal to the surface to determine the heat that isexchanged to or from the surface in keeping with FouriersLaw. The gages operate by the same principles for heat transferin either direction.1.2 This test method is quite broad in its field of application,size and construction. Different sensor
5、 types are described indetail in later sections as examples of the general method formeasuring heat flux from the temperature gradient normal to asurface (1).2Applications include both radiation and convec-tion heat transfer. The gages have broad application fromaerospace to biomedical engineering w
6、ith measurements rang-ing form 0.01 to 50 kW/m2. The gages are usually square orrectangular and vary in size from 1 mm to 10 cm or more ona side. The thicknesses range from 0.05 to 3 mm.1.3 The values stated in SI units are to be regarded as thestandard. The values stated in parentheses are provided
7、 forinformation only.1.4 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 t
8、o use.2. Referenced Documents2.1 ASTM Standards:C 518 Test Method for Steady-State Thermal TransmissionProperties by Means of the Heat Flow Meter ApparatusC 1041 Practice for In-Situ Measurements of Heat Flux inIndustrial Thermal Insulation Using Heat Flux TransducersC 1046 Practice for In-Situ Meas
9、urement of Heat Flux andTemperature on Building Envelope Components3. Terminology3.1 Definitions of Terms Specific to This Standard:3.1.1 heat fluxthe heat transfer per unit area, q, with unitsofW/m2(Btu/ft2-s). Heat transfer (or alternatively heat-transferrate) is the rate of thermal-energy movemen
10、t across a systemboundary with units of watts (Btu/s). This usage is consistentwith most heat-transfer books.3.1.2 heat-transfer coeffcient, (h)an important parameterin convective flows with units of W/m2-K (Btu/ft2-s-F). This isdefined in terms of the heat flux q as:h 5qDT(1)where DT is a prescribe
11、d temperature difference between thesurface and the fluid. The resulting value of h is intended to beonly a function of the fluid flow and geometry, not thetemperature difference. If the surface temperature is non-uniform or if there is more than a single fluid free streamtemperature, the proper def
12、inition of DT may be difficult tospecify (2). It is always important to clearly define DT whencalculating the heat-transfer coefficient.3.1.3 surface emissivity, ()the ratio of the emitted ther-mal radiation from a surface to that of a blackbody at the sametemperature. Surfaces are assumed to be gra
13、y bodies where theemissivity is equal to the absorptivity.4. Summary of Test Method4.1 A schematic of the sensing technique is illustrated inFig. 1. Temperature is measured on either side of a thermalresistance layer of thickness, d. This is the heat-flux sensingmechanism of this test method.The mea
14、sured heat flux is in thesame direction as the temperature difference and is propor-tional to the temperature gradient through the thermal-resistance layer (TRL). The resistance layer is characterized byits thickness, d, thermal conductivity, k, and thermal diffusivity,a. The properties are generall
15、y a weak function of temperature.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 June 15, 2009. Published August 2009.2The b
16、oldface numbers in parentheses refer to the list of references at the end ofthis test method.1Copyright ASTM International, 100 Barr Harbor Drive, PO Box C700, West Conshohocken, PA 19428-2959, United States.q 5kdT12 T2! (2)From this point the different gages may vary substantially inhow the tempera
17、ture difference T1 T2is measured and thethickness of the thermal resistance layer used. These aspects ofeach different type of sensor are discussed along with theimplications for measurements.4.2 Heat-flux gages using this test method generally useeither thermocouple elements or resistance-temperatu
18、re ele-ments to measure the required temperatures.4.2.1 Resistance temperature detectors (RTDs) generallyhave greater sensitivity to temperature than thermocouples, butrequire separate temperature measurements on each side of thethermal-resistance layer. The temperature difference must thenbe calcul
19、ated as the small difference between two relativelylarge values of temperature.4.2.2 Thermocouples can be arranged in series across thethermal-resistance layer as differential thermocouple pairs thatmeasure the temperature difference directly. The pairs can alsobe put in series to form a differentia
20、l thermopile to increase thesensitivity to heat flux.S 5Eq5NsTdk(3)Here N represents the number of thermocouple pairs formingthe differential thermopile and sTis the effective temperaturesensitivity (Seebeck coefficient) of the two thermocouplematerials. Although the voltage output is directly propo
21、rtionalto the heat flux, the sensitivity may be a function of the gagetemperature.5. Significance and Use5.1 This test method will provide guidance for the measure-ment of the net heat flux to or from a surface location. Todetermine the radiant energy component the emissivity orabsorptivity of the g
22、age surface coating is required and shouldbe matched with the surrounding surface. The potential physi-cal and thermal disruptions of the surface due to the presenceof the gage should be minimized and characterized. For thecase of convection and low source temperature radiation to orfrom the surface
23、 it is important to consider how the presence ofthe gage alters the surface heat flux. The desired quantity isusually the heat flux at the surface location without thepresence of the gage.5.1.1 Temperature limitations are determined by the gagematerial properties and the method of application to the
24、surface. The range of heat flux that can be measured and thetime response are limited by the gage design and constructiondetails. Measurements from 10 W/m2to above 100 kW/m2areeasily obtained with current sensors. Time constants as low as10 ms are possible, while thicker sensors may have responsetim
25、es greater than 1 s. It is important to choose the sensor styleand characteristics to match the range and time response of therequired application.5.2 The measured heat flux is based on one-dimensionalanalysis with a uniform heat flux over the surface of the gagesurface. Because of the thermal disru
26、ption caused by theplacement of the gage on the surface, this may not be true.Wesley (3) and Baba et al. (4) have analyzed the effect of thegage on the thermal field and heat transfer within the surfacesubstrate and determined that the one-dimensional assumptionis valid when:dkRks1 (4)where:ks= the
27、thermal conductivity of the substrate material,R = the effective radius of the gage,d = the combined thickness, andk = the effective thermal conductivity of the gage andadhesive layers.5.3 Measurements of convective heat flux are particularlysensitive to disturbances of the temperature of the surfac
28、e.Because the heat transfer coefficient is also affected by anynon-uniformities of the surface temperature, the effect of asmall temperature change with location is further amplified, asexplained by Moffat et al. (2) and Diller (5). Moreover, thesmaller the gage surface area, the larger is the effec
29、t on theheat-transfer coefficient of any surface temperature non-uniformity. Therefore, surface temperature disruptions causedby the gage should be kept much smaller than the surface toenvironment temperature difference causing the heat flux. Thisnecessitates a good thermal path between the gage and
30、 thesurface onto which it is mounted.5.3.1 Fig. 2 shows a heat-flux gage mounted onto a platewith the surface temperature of the gage of Tsand the surfacetemperature of the surrounding plate of Tp. The goal is to keepthe gage surface temperature as close as possbible to the platetemperature to minim
31、ize the thermal disruption of the gage.This requires the thermal resistance of the gage and adhesive tobe minimized along the thermal pathway from Tsand Tp.FIG. 1 Layered Heat-Flux GageE26840925.3.2 Another method to avoid the surface temperaturedisruption problem is to cover the entire surface with
32、 theheat-flux gage material. This effectively ensures that thethermal resistance through the gage is matched with that of thesurrounding plate. It is important to have independent mea-sures of the substrate surface temperature and the surfacetemperature of the gage. The gage surface temperature must
33、 beused for defining the value of the heat-transfer coefficient.When the gage material does not cover the entire surface, thetemperature measurements are needed to ensure that the gagedoes indeed provide a small thermal disruption.5.4 The time response of the heat-flux gage can be estimatedanalytica
34、lly if the thermal properties of the thermal-resistancelayer are well known. The time required for 98 % response toa step input (6) based on a one-dimensional analysis is:t 51.5 d2a(5)where a is the thermal diffusivity of the TRL. Covering orencapsulation layers must also be included in the analysis
35、.Uncertainties in the gage dimensions and properties require adirect experimental verification of the time response. If thegage is designed to absorb radiation, a pulsed laser or opticallyswitched Bragg cell can be used to give rise times of less than1s(7,8). However, a mechanical wheel with slits c
36、an be usedwith a light to give rise times on the order of 1 ms (9), whichis generally sufficient.5.4.1 Because the response of these sensors is close to anexponential rise, a measure of the time constant t for the sensorcan be obtained by matching the experimental response to stepchanges in heat flu
37、x with exponential curves.q 5 qss1 2 e2t/t! (6)The value of the step change in imposed heat flux is repre-sented by qss. The resulting time constant characterizes thefirst-order sensor response.6. Apparatus-Sensor Construction6.1 Temperature sensors are mounted or deposited on eitherside of the ther
38、mal-resistance layer (TRL), which is usually athin material which can be mounted on the test object. Themethod of construction and details of operation varies for eachdifferent type of gage. Although most of the gages place thetemperature sensors directly over top of each other across theTRL, it is
39、not a requirement for proper measurement. Thebottom temperature sensors simply need to be at a uniformtemperature and the top temperature sensors need to be at atemperature dictated by the heat flux perpendicular to thesurface. This can be accomplished on a high-conductivitysubstrate by separate the
40、rmal-resistance pads for the toptemperature measurements. Several examples are given of thethermopile and RTD based types of gages.6.2 Thermopile GagesThermopile gages are based onthermocouples forming multiple junctions on either side of theTRL. If properly mounted and designed for the application,
41、 theoperation of these heat-flux gages is simple. There is noactivation current or energy required for the thermocouplesensor units. The output voltage is continuously generated bythe gage in proportion to the number of thermocouple pairswired in series. The output can be directly connected to anapp
42、ropriate differential amplifier and voltage readout device.6.2.1 An early report of the layered sensor (6) used a singlethermocouple pair across the resistance layer. Ortolano andHines (10) used a number of thermocouple pairs as describedby Eq 3 to give a larger voltage output. The thermocouples are
43、placed as foils around a Kapton thermal-resistance layer andbutt welded on either side, as illustrated in Fig. 3. Kaptonsheets are used around the gage for encasement and protection.The resulting Micro-Foil gage is 75 to 400 m thick andflexible for easy attachment to surfaces, but the low conduc-tiv
44、ity (high thermal resistance) of the materials must beconsidered when used for convection measurements. Thesensors are limited to temperatures below (250C) and heatfluxes less than 100 kW/m2. The time response can be as fastas 20 ms, but transient signals may be attenuated unless thefrequency of the
45、 disturbance is less than a few hertz.6.2.2 Terrell (11) describes a gage design (Episensor) madewith screen printing techniques of conductive inks. A copper/nickel thermocouple pair is used with a dielectric ink for thethermal-resistance layer. The inks are printed onto anodizedaluminum shim stock
46、for the substrate. Although the entirepackage is 350 m thick, the thermal resistance is low becauseof the high thermal conductivity of all of the materials.Because of the large number of thermocouple pairs (up to10,000), sensitivities are sufficient to measure heat fluxes aslow as 0.1W/m2.The therma
47、l time constant is about 1 s and theupper temperature limit is approximately 150C. The alumi-num base allows some limited conformance to a surface.6.2.3 The thermopile connections can also be made throughsmall holes in the TRL. Plating of copper and nickel is used tocreate such a gage (BF Heat Flux
48、Transducer) from 1 cmsquare to 32 cm square with a high density of junctions perarea. The thickness is 200 m which gives a time constant ofapproximately 1 s. It has limited flexibility and has a maximumoperating temperature of 150C.6.2.4 Another design uses welded wire to form the thermo-pile across
49、 a TRL about 1 mm thick. This gives a higherFIG. 2 Diagram of an Installed Surface-Mounted Heat-Flux GageE2684093sensitivity to heat flux, but also a larger thermal resistance.Time constants are greater than 1 s and the upper temperaturelimit is 300C. These are manufactured in a range of sizes.Applications include heat transfer in buildings and physiology.Sensors with higher sensitivity are made with semi-conductorthermocouple materials for geothermal applications. Lowersensitivity sensors are made for operating temperatures up to1250C.6.2.5 Another technique for meas
